Modeling, simulation and performance analysis of parabolic trough solar collectors: A comprehensive review

Applied Energy 225 (2018) 135–174

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Applied Energy journal homepage: www.elsevier.com/locate/apenergy

Modeling, simulation and performance analysis of parabolic trough solar collectors: A comprehensive review İbrahim Halil Yılmaza, a b

⁎,1

, Aggrey Mwesigyeb,

T

⁎,1

Department of Automotive Engineering, Adana Science and Technology University, Adana, Turkey Department of Mechanical and Industrial Engineering, Ryerson University, Toronto, Canada

H I GH L IG H T S

and past studies on modeling of parabolic trough collector are presented. • Current and thermal models and the modeling approaches are discussed in detail. • Optical and ray-tracing approaches are investigated for optical modeling. • Analytic and transient heat transfer conditions are examined for thermal modeling. • Steady • Novel, passive and nanofluid techniques are outlined in performance enhancement.

A R T I C LE I N FO

A B S T R A C T

Keywords: Parabolic trough collector Optical modeling Thermal modeling Performance enhancement Computational fluid dynamics

Solar thermal systems are advantageous since it is easier to store heat than electricity on a large scale. As such, concentrated solar power is receiving considerable interest among researchers, developers and governments. Several concentrated solar power technologies have been developed including the solar tower, the parabolic trough technology, solar dish and linear Fresnel systems. Among them, the parabolic trough solar collector is a proven technology used dominantly for both industrial process heat and power generation. This technology has matured over the years, and its advancement has become the topic of numerous research studies which were the counter driving force of the field. Particularly in recent years, a significant amount of theoretical and numerical studies have been conducted to assess and improve the performance of parabolic trough solar collectors. This review methodologically holds colossal knowledge of current and past studies to assess the optical and thermal performances of parabolic trough solar collectors, modeling approaches and the potential improvements proposed on behalf of the parabolic trough solar collector design. The optical modeling approaches are identified to be analytical and ray-tracing. The review of thermal modeling approaches presents the steady and transient heat transfer analyses of single and two-phase (with direct steam generation) flows. Also, the computational fluid dynamics models used to analyze the physics of parabolic trough solar collectors with a better insight are reviewed and presented. Finally, the studies conducted on the performance improvement of parabolic trough solar collectors are separately examined and presented, these include novel designs, passive heat transfer enhancement, and nanoparticle laden flows.

1. Introduction Solar energy is the world’s most abundant source of energy, it has been shown to have significant potential to meet a considerable portion of the world’s energy demand [1,2]. With 1.7 × 1014 kW of the sun’s energy received by the earth surface, only 84 min of solar radiation was estimated to give 900 EJ which was equivalent to the world’s energy demand for 2009 [1]. However, significant research and development

⁎

1

efforts are still needed to overcome challenges associated with harnessing this resource [3]. These include developing efficient technologies for harvesting, cost effective and efficient energy storage options, optimization of hybrid energy systems working with solar energy and another renewable energy resource. Concentrating solar power (CSP) is an emerging technology and offers significant advantages such as built-in storage capability, high economic returns and reduced greenhouse gas emissions. The life-cycle

Corresponding authors. E-mail addresses: [email protected] (İ.H. Yılmaz), [email protected] (A. Mwesigye). Both authors contributed equally.

https://doi.org/10.1016/j.apenergy.2018.05.014 Received 5 February 2018; Received in revised form 7 April 2018; Accepted 3 May 2018 0306-2619/ © 2018 Elsevier Ltd. All rights reserved.

Applied Energy 225 (2018) 135–174

İ.H. Yılmaz, A. Mwesigye

Nomenclature

A c , cp C D E f h Ib k keff Kn l Nu Pr Q q″ Ra Re r rr t T UL wa x, y

Subscripts

area, m2 specific heat, J/kg °C concentration ratio diameter, m; absorber’s outer diameter, m total energy per unit mass, J focal length, m convection heat transfer coefficient, W/m2 °C beam radiation, W/m2 thermal conductivity, W/m °C effective thermal conductivity, W/m °C Knudsen number collector length, m Nusselt number Prandtl number heat transfer, W heat flux, W/m2 Rayleigh number Reynolds number local mirror radius, m rim radius, m time, s temperature, °C thermal loss coefficient, W/m2 °C aperture width, m cartesian coordinates

a ae conv e f Gauss htf ia ie nf oa oe p rad s sky tot

Abbreviations 1-D 2-D 3-D CFD CSP DARS DSG FDM FEM FVM HCE HTF IPH LCR MCRT NCPTSC PEC PSA PTSC PV SEGS SNL

Greek symbols

α Γ γ δ ε ηo θ μ ρ σ τ → υ φ ϕr φ ω

ambient air; absorber absorber envelope convection envelope fluid Gaussian distribution heat transfer fluid inside of absorber inside of envelope nanofluid outside of absorber outside of envelope particle radiation support sky total

absorptivity end-loss factor intercept factor; surface azimuth angle, ° declination angle, ° emissivity optical efficiency incidence angle, ° dynamic viscosity, kg/m s reflectivity; density, kg/m3 optical error, mrad transmissivity velocity vector local rim angle, ° rim angle, ° particle concentration, % hour angle, °

one-dimensional two-dimensional three-dimensional computational fluid dynamics concentrating solar power direct absorption receiver system direct steam generation finite difference method finite element method finite volume method heat collector element heat transfer fluid industrial process heat local concentration ratio Monte Carlo ray tracing nanofluid-based concentrating PTSC performance evaluation criterion Plataforma Solar de Almería parabolic trough solar collector photovoltaic solar energy generating systems Sandia National Laboratories

research and development efforts have been put into action to improve the technology and make it competitive with counterpart energy systems [6,7]. The PTSC technology has just maintained a substantial progress in mirror and receiver development, use of alternative heat

CO2 emissions of solar-only CSP plants are estimated to be 17 g/kWh while they are on the level of 776 g/kWh and 396 g/kWh for coal and natural gas combined plants, respectively [4]. Although the investment costs of CSP plants are relatively higher compared to the conventional technologies, new plants are guaranteeing commercial maturity, increased plant efficiency, and reduced levelized costs. With increasing installed CSP capacity, investment and energy costs are estimated to fall. The levelized costs of electricity will come to the level of US $97–130/MWh by 2015–2020 [4] from US$194/MWh [5]. The parabolic trough solar collector (PTSC) is a dominant technology available today in both commercial and industrial scale among the medium-temperature solar collectors. In comparison to other systems, Fig. 1 shows the temperature ranges of commonly used solar thermal systems [1]. Numerous manufacturing companies have focused on this technology, Fresnel and parabolic dish technologies have become largely overshadowed. Feed-in tariffs and grant programs have driven the successful deployment of the technology, as well. Significant

Heliostat field

high-temp.

Parabolic dish Parabolic trough Cylindrical trough medium-temp.

Linear Fresnel Compound parabolic

Evacuated tube Flate plate

low-temp.

Solar pond 0

500 1000 1500 Operating temperature (°C)

2000

Fig. 1. Temperature ranges attainable with different solar technologies. 136

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transfer fluids (HTFs), identification of thermal storage options, and development of process design concepts [8]. Recent developments in the parabolic trough CSP systems [9,10] will raise the plant efficiency by reducing the optical and thermal losses and also by reducing the operation and maintenance costs. The reduced costs will establish a new era as a counter attack to the market that certain solar systems cannot touch, particularly for industrial process heat (IPH) [11,12] and desalination applications. The current status indicates that the research and development efforts, and the operational experience gained over in time will provide significant benefits to the increased deployment of the technology. As introduced above, the operational experience gained with the PTSCs, and continued research and development efforts have made this technology the most commercially and technically mature of all the available CSP technologies. Meanwhile, a moderate number of studies on the analysis of PTSCs have contributed to the significant growth of this technology. The aim of this extended review is to examine various modeling studies and the approaches used for the simulation of PTSCs. A significantly detailed review of the theoretical studies carried out on both the optical and thermal performance, and the studies on the performance improvement techniques which deal with the modification of the PTSC design, heat transfer augmentation by inserting turbulators and the use of nanofluids are consolidated and presented.

was almost zero from 1999 to 2006 due to numerous barriers against the diffusion of the technology. By 2006, the construction of the CSP plants emerged again with an 11 MW plant in Spain, and a 64 MW plant in Nevada. In 2007, about 90 systems for industrial process heat applications were reported in 21 countries with a total installed capacity of 25 MWth. By the end of 2014, the number of installed industrial process heat plants reached 124 all over the world with a cumulative capacity over 93 MWth [14]. There are currently hundreds of megawatts under construction and thousands of megawatts under development worldwide. Algeria, Egypt and Morocco have built integrated solar combined cycle plants, while Australia, China, India, Iran, Israel, Italy, Jordan, Mexico, South Africa and the United Arab Emirates are completing or planning projects [4,15]. Today, there are more than 97 plants at different levels of development based on the parabolic trough technology according to the database by NREL [15].

2.2. Fundamentals of PTSCs A PTSC is a line-focus concentrator which converts concentrated solar energy into high-temperature heat. Depending on the application, temperature up to 550 °C is achievable in these systems [16]. As demonstrated in Fig. 2, the PTSC assembly necessarily has several subsystems to be functionally operated. The PTSC has a mirror or reflector curved in the shape of a parabola which thus allows concentrating the sun’s rays onto the focal line. The mirror is produced from different raw materials such as aluminum or low iron glass to lessen the absorption losses. Not only solar-weighted reflectivity of the mirror but also its cost, durability and abradable properties are important factors during the production of the collector mirrors. After bending the mirror, a set of manufacturing processes such as silvering, protective coating and gluing [18] are followed to improve the solar-weighted reflectivity of the mirror. PTSCs have a characteristic that all rays parallel to the collector’s focal plane are reflected onto the focal axis of the collector. The heat collection element (HCE) also called the receiver is positioned at the focal axis of the mirror. It is basically composed of an absorber and an envelope made of borosilicate glass surrounding the absorber. The absorber, usually a stainless steel tube coated with a selective surface for better solar absorptance, transfers solar heat to a working fluid, i.e., HTF circulating through the absorber. The envelope is coated by anti-reflective layer to reduce heat losses by infrared radiation. The HCE has glass-to-metal seals and metal bellows to accommodate the differential thermal expansion between

2. Parabolic trough solar collector systems 2.1. Background Regarding the PTSC collector technology, the production of these systems dates back to the last quarter of nineteenth century. The first systems were used in small-scale facilities, with outputs lower than 100 kW, like steam generation and water irrigation. The PTSC technology was commercialized in the late 1970s and was deployed into the market in the 1980s [13]. In the early years, several companies manufactured and marketed a number of PTSCs which were developed for industrial process heat applications. During the period of 1984–1990, nine solar energy generating systems (SEGS), 14–80 MWe in size and with a total installed capacity of 354 MWe, were developed in Mojave Desert [8]. These systems have been in operation ever since. Their operational experiences have contributed to the commercial and technical maturity of the PTSCs. However, the average annual growth rate of the PTSC installations

Fig. 2. PTSC structure and components. Adapted from [17]. 137

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theoretical analyses in most cases. Modeling offers significant advantages over experimentation from these aspects while deepening the physics of the study. Yet, developed models need to be verified by experimentation to be considered admissible; hence the role of experimentation cannot be underestimated. In the early stages of the PTSC technology, mathematical models at hand were insufficient for design analysis and performance prediction. This shortcoming led to difficulty in the computation of the optical efficiency and the evaluation of collector performance [20]. Generalized analytical studies in obtaining the collector optical efficiency under off-normal incident conditions, considering various geometrical effects such as end-loss, shadowing, were unavailable but further endeavors contributed to the derivation of functional relationships for the development of PTSCs. After that, synthesizing the optical and thermal characteristics of the collector components was considered, since inefficient and unreliable HCEs played an unfavorable role in the overall performance of the SEGS plants [8]. At first, researchers paid attention to the improvement of current or new HCEs. For this purpose, a heat transfer software model was developed in the early 90s, and upgraded several years later [21]. This model served as a useful tool during improvement of HCE and accordingly the SEGS plants’ performance. Lately, a great number of modeling studies have been performed. All these efforts have offered great benefits to researchers for the advancement of the PTSC technology and its futuristic road-map. Modeling and simulation of a PTSC involves both optical and thermal analyses. These analyses can be decoupled and dealt with separately as the optical material properties are regarded to be temperature independent [22]. This assumption, which is completely reasonable for a PTSC, provides considerable convenience in making both analyses. As the existing studies in the literature are comprehensively reviewed, the scope of the PTSC modeling and simulation can be embraced as depicted in Fig. 4. This review reveals all these works methodologically throughout the paper.

the steel tubing and the glass envelope. Moreover, the annulus between the absorber and glass tubes can be vacuumed to minimize the convective heat loss between them. For a fully evacuated HCE, the vacuum pressure is about 0.013 Pa [8]. To ensure that no hydrogen replaces the vacuum in the HCE, getters are used to absorb gas molecules that permeate into the vacuum annulus over time. The PTSC is supported by a constructional frame with pylons which keep the mirror stable. Supports are used to hold the HCE in the focal alignment. Pipe installations are made at the ends of the collector for connecting the HCE to the header piping. The collector assembly is driven by a driving configuration (gear, jackscrew or hydraulic actuator) to position the collector during its tracking via a control unit. The geometry of the collector can be obtained using geometrical relations defining the parabolic shape that makes up the collector system [19]. The profile of the collector is defined using the coordinate system in Fig. 3 as

x 2 = 4yf

(1)

In Eq. (1), f represents the focal length which determines the location of the heat collection element. The focal length is given by

f = wa/4tan(φr /2)

(2)

where wa is the collector’s aperture width and φr is the rim angle. The rim angle is given by

8(f / wa) ⎤ w = sin−1 ⎛ a ⎞ φr = tan−1 ⎡ 2−1 ⎥ ⎢ 16( / ) 2 f w rr ⎠ a ⎝ ⎣ ⎦ ⎜

⎟

(3)

where rr is the rim radius. At any point of the collector, the local mirror radius can be obtained by

r=

2f 1 + cosφ

(4)

which gives the rim radius rr when the angle φ = φr as

rr =

2f 1 + cosφr

3. Performance analysis of PTSCs (5)

3.1. Optical analysis

When the collector is of perfect shape and alignment, the diameter of a cylindrical HCE needed to intercept all the solar image is determined to be

D = 2rr sin0.267 =

wasin0.267 sinφr

The optical efficiency, ηo is related to the process of the photothermal conversion and can be defined as the ratio of the energy absorbed by the HCE to the energy incident on the collector’s aperture. It is basically the function of the reflectivity of the mirror (ρ ), the transmittance of the glass envelope (τ ), the absorptivity of the coating on the absorber surface (α ) and the intercept factor of the mirror and HCE interaction (γ ) according to:

(6)

The value 0.267° is the half angle of the cone representing the incident beam of solar radiation. The geometrical relations presented by Eqs. (1)–(6) are useful in the design and construction of PTSC systems that are accurate and with less profile errors. For the modeling and analysis of PTSC systems, especially the optical analysis using ray tracing techniques, correct specification of the system geometry is also paramount.

ηo (θ = 0) = ρταγ

(7)

Although efficiency curves of solar collectors are usually measured

2.3. Modeling and simulation of PTSCs With advances in computing and computing power, there has been seen tremendous growth in modeling and simulation of engineering systems. The use of computing tools in the modeling and simulation of PTSC systems has also been utilized extensively and has made analysis and performance optimization of these systems possible. Moreover, unlike experimental studies, modeling does not include uncertainty but necessarily has simplifications/assumptions - and provides wealth of information for the task considered. By this way, the influence of several variables on system performance can easily be investigated with minimum effort and less cost. On the other hand, experimental studies are expensive and time-consuming especially when large test facilities and several variables are involved. Furthermore, they need prior

Fig. 3. Cross-section of a linear PTSC. 138

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İ.H. Yılmaz, A. Mwesigye

Analytic Optical Ray tracing

1-D

Spatial

2-D

3-D

Numerical

Mathematical Time-dependent Modeling & simulation of PTSC

Software

Thermal

FDM CFD FVM

Software MCRT

FEM Optical design

Performance enhancement

Nanofluid

Thermal design

Insertion

Novel design Fig. 4. Methodology pursued for modeling and simulation of PTSCs.

Table 1 Incidence factors for the various tracking alternatives [22]. Type

Incidence angle, cosθ

Remarks

1

No hourly or seasonal variations in output due fully tracking

(1−cos2 δ sin2 ω)1/2

No appreciable variation in seasonal output but considerable variation in hourly output

[(sinγ sinδ + cosγ cosδ cosω)2 + cos2 δ sin2 ω]1/2

No appreciable variation in hourly output but considerable variation in seasonal output

cosδ

No appreciable variation in hourly output but some variation in seasonal output depending on the latitude of the location

139

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visualized the effects of the PTSC’s components on the optical efficiency as shown in Fig. 5. Noting that identifying the partial effects of these factors will clarify the determination of the optical efficiency. During the optical analysis of PTSC systems, a number of parameters can be determined, and their influences on the overall system performance are investigated. These include the determination of the intercept factor, optical efficiency, and the heat flux variation on the HCE as a function of the concentrator configuration (rim angle, HCE size, optical errors, sun shape, etc.). For these tasks, analytical and ray-tracing methods have been used by numerous researchers. The next two sections present how the analytical and ray-tracing methods are considered and used in the analysis of PTSCs.

at normal incidence, the incidence angle of a single-axis tracking collector varies during operation. In such a case, the effect of the incidence angle should be taken into account since the variation of all the optical properties depend on it and can be correlated by a modifier called the incidence-angle modifier [23],

K (θ) =

ηo (θ) ηo (θ = 0)

(8)

The incidence angle changes in accordance with the tracking mode applied. It is worth noting that the incidence angle can be described by the relations shown in Table 1. These relations help the user in the selection of the appropriate equation for any given tracking mode. The theoretical calculation of the incidence angle modifier requires the functional dependence of the reflectivity, transmissivity and absorptivity on incidence angle and the knowledge of optical errors of the collector, as well. The optical efficiency includes the effect of incidence angle and the end-loss factor which accounts for the spilling of radiation out at the end of line-focus collectors. The optical efficiency, taking into account the incidence effects, is expressed as

ηo (θ) = ρταγ Γcosθ

3.1.1. Analytical approach Determining the optical performance of a PTSC has been considered by a number of researchers using the analytical approach to obtain a closed-form solution for the intercept factor. Bendt et al. [28] presented an approach in a closed form that yields all the parameters needed for the optical design. In their study, the evaluation of the intercept factor is given by a mathematical expression, and the sun shape is approximated by a Gaussian distribution instead of the real sun. γGauss is evaluated by solving Eq. (12) numerically.

(9)

The end-loss factor, Γ is estimated using the relation in Eq. (10) [23]

wa2 f Γ = 1− (1 + )tanθ l 48f 2

γGauss = (10)

wa2 r f − (1 + )tanθ l l 48f 2

The end-loss effect for a horizontally oriented north–south axis system is determined in detail by Xu et al. [24]. A method to compensate for the end-loss for short trough collectors was also proposed by Xu et al. [24]. A different approach to account for the end-loss in cylindrical troughs is given by [25]. In practice, the optical design of the trough collector is affected by several factors [26] including: apparent changes in the sun's width and incidence angle effects, physical properties of the materials used in HCE and mirror construction, imperfections (or errors) resulting from manufacture and/or assembly, imperfect tracking of the sun, and poor operating procedures. On the other hand, Mokheimer et al. [27]

2 σmirror

σtot =

θ2 ) 2 2σtot

2 4σslope

2 σtracking

2 2 2 2 σsun + σmirror + 4σslope + σtracking

O l ro

e

t

D

ee

riv

sh

a Pl

ce

M

g Material

Size

in

Control

al

nt

et

Co

s

or

l M

at

Optical efficiency at

Envelope

er ia Si

l

Deformation

ia

irr

er

M

at

rie

M

nt

at

io

n

Reflector

Co

Surface profile

(12) 2 σdisplacement .

(13)

Güven and Bannerot [30] used a modified code, EDEP, which uses a ray-tracing technique to project the effective sun shape, for analyzing the effects of potential optical errors on the intercept factor. This code was used to validate the existence of the universal error parameters whose details are given in [26]. Güven and Bannerot [31] analyzed the

s ce nes rfa th Su moo s

Support structure

σtot 2π

exp(

+ + + + where σtot = This approach gives the total optical error, σtot , i.e., bringing together the various errors in a single-term. Yet, it should be noted that the normal distribution (Gaussian) assumption for all errors is not valid in practical applications. Treadwell and Grandjean [29] have proposed a relation for the total optical error as given in Eq. (12). They separated the effects of tracking and displacement errors from the rest. Besides they introduced error parameters being universal to all geometries but this intuition was the basic deficiency of the approach which portrays the systematic relationships between the errors.

(11)

Tracking system

1

dθf (Cθ) 2 σsun

Eq. (10) is applicable for equal lengths of the HCE and the collector in case the HCE is placed symmetrically. If the HCE length extends beyond the collector length l by an amount r on one side, the end-loss factor is modified to

Γ=1+

+∞

∫−∞

Ti

m

e

D

ay

ze Co at in

Incidence angle

g

Fig. 5. Parameters affecting the optical efficiency. Adapted from [27]. 140

Absorber

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parameters (some of them were evaluated and revised with a ray-tracing software developed by National Renewable Energy Laboratory) depending completely on the PTSC’s specifications. ε4′ and ε5′ are the terms recommended by [19].

optical errors within two groups: random and nonrandom as shown in Fig. 6. Then, they presented universal design curves to display the effects of these errors and geometric parameters (concentration ratio, C and rim angle) on the optical efficiency (see Eq. (7)). The random errors - small-scale slope errors, mirror specularity, apparent changes in sun's width, and small occasional tracking errors are modeled statistically at normal-incidence:

σtot =

2 σsun

2 σmirror

+

+

2 4σslope

ηo = ηabs α = ε1′ ε2′ ε3′ ε4′ ε5′ ε6′ ρταK (θ)

where ε1′: HCE shadowing (bellows, shielding, supports); ε2′: tracking error; ε3′: geometry error (mirror alignment); ε4′: dirt on mirror (reflectivity/clear mirror reflectance); ε5′: dirt on HCE ((1 + ε4′)/2 ; ε6′: unaccounted losses. Jacobson et al. [35] conducted an optical analysis using Eq. (7). In this equation, the optical parameters were evaluated accounting the effect of the incidence angle. The angular variations of the absorptivity and transmissivity were defined with a polynomial equation and Fresnel’s derivation [19], respectively. The intercept factor was estimated using the relations in Duffie and Beckman [19] given by Eqs. (19)–(21). For a perfect linear imaging concentrator, the diameter of a cylindrical receiver to intercept the entire sun’s image is described by

(14)

The nonrandom errors are classified as mirror profile errors, misalignment of the HCE with the effective focus of the mirror, and misalignment of the trough with the sun. In their later work, Güven and Bannerot [26] presented a mathematical derivation, holding the universal error parameters, for predicting the intercept factor as follows:

γ =

1 + cosϕr 2sinϕr

∫0

ϕr

Dγ = 1 = wa

∗ ∗ ⎡⎡ ⎡ sinϕr (1 + cosϕ)(1−2d sinϕ)−πβ (1 + cosϕr ) ⎤ ⎢ ⎢Erf ⎢ ∗ (1 + cosϕ ) ⎥ 2 πσ r ⎣ ⎦ ⎣⎣

2d∗sinϕ)

πβ ∗ (1

sinϕr (1 + cosϕ)(1 + + −Erf ⎡− ∗ (1 + cosϕ ) ⎢ 2 πσ r ⎣ dϕ (1 + cosϕ)

+ cosϕr ) ⎤ ⎤ ⎥⎥ ⎦⎦

Dγ = 1 = wa

(

8f / wa 16(f / wa)2 − 1

(20)

) and δ

d

is the dispersion angle.

The intercept factor can be obtained depending on the values of Eqs. (19) and (20):

1 if D ⩾ Dγ = 1 γ=⎧ D / Dγ = 1 if D < Dγ = 1 ⎨ ⎩

(16)

cos2 θsinϕr , σ 2

and β is the angular position on the HCE. σ where CR = is the circular scattering function to be accepted as realistic from the data of [33]. The overall optical efficiency of the collector was obtained by modifying Eq. (7) and employing Eq. (17). The equation incorporates the physical models of realistic nonuniform solar, incidence angle dependent transmittance and absorptance, and imperfect reflection, as well.

∫ CR γ (θc ) α (θo) Ddβ wa

(21)

Öztürk et al. [36] proposed an optical model based on the vectorial method to calculate the energy collected by the HCE. The equation derived can be applied to any PTSC in cases where the mirror and the HCE dimensions are known. Huang et al. [37] proposed a new analytical method, based on the effective light distribution from a reflected point on a mirror, to calculate the optical efficiency of a PTSC. The derived analytical equation

ρ

ηo =

(19)

sin(0.267 + δd/2) sinϕr

where ϕr = tan−1

(15)

∫ CR Ddβ wa

sin(0.267) sinϕr

For a nonperfect imaging concentrator (defects in the mirror surface)

where C : area concentration ratio, C = wa/ πD ; d∗: universal nonrandom error parameter due to HCE mislocation and mirror profile errors, d∗ = dr / D ; β ∗: universal nonrandom error parameter due to angular errors, β ∗ = βC ; σ ∗: universal random error parameter, σ ∗ = σC . Jeter [32] presented a semi-finite analytical formulation to analyze the concentrated radiant flux on the HCE surface. The obtained concentrated flux density was integrated, subsequently the intercept factor and optical efficiency of the collector were computed.

γ=

(18)

(17)

where θc is the angle computed using the mean envelope radius, θo is the angle with the normal to the HCE at the point of interest. The effects of optical errors over the heat flux distribution on the absorber were investigated by Thomas and Guven [34] to analyze how the intercept factor and optical efficiency vary. The flux distribution on the HCE was examined for the total optical error ranging from 0.01 to 24 mrad. The results of the study showed that the total optical error has a profound effect on the intercept factor and optical efficiency when its value exceeds 8 mrad. Forristall [21] presented a relation given by Eq. (18) to estimate the effective optical efficiency of a PTSC with correction parameters instead of using the intercept factor. This relation has been widely used by researchers to simply calculate the optical efficiency of the LS-2 collector rather than analyzing it for different designs since it simply includes the multiplication of various optical parameters. In the relation, the first three terms and the last term (ε1′,ε2′,ε3′,ε6′) are the estimated

Fig. 6. Description of potential optical errors in PTSCs. Adapted from [31]. 141

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derivation of the optical characteristics of a PTSC. As the computer technology is advanced, time spent for tedious analyses has been shortened, and this provided many advantages to researchers. Even though the ray-tracing approach is time consuming, it is more accurate and commonly used in commercial and scientific works. There are available software tools in the literature using the technique of raytracing including, SolTrace, ASAP, Opticad, SimulTrough and TracePro. In the optical analysis of a PTSC, researchers have extensively utilized the MCRT method either writing their own codes or using the mentioned ray-tracing software tools. Saltiel and Sokolov [43] derived the relations analyzing the energy absorbed by two types of HCEs and investigated the absorber size that gives the maximum absorption using ray-tracing. Prapas et al. [44] performed a detailed optical analysis for a PTSC with small concentration ratios. The analyses indicated that a PTSC with high concentration ratio (C > 10 ) is not able to collect diffuse radiation, and the optical efficiency degrades remarkably as the concentration ratio is equal to or less than 10. Schiricke et al. [45] presented the optical analysis of a PTSC system and determined the influence of certain parameters and their combinations using the commercial software, Opticad [46]. Solar heat flux distribution was simulated for different incidence angles. The intercept factor was studied for varying values of tracking offset and transversal displacement of the absorber. Grena [47] presented the optical simulation of a PTSC with and without a glass envelope. The simulations were realized with wavelength-dependent optical properties under realistic solar irradiation. The 3-D ray-tracing technique was applied, and the effects of various error parameters on the optical efficiency and the distribution of the absorbed radiation over the HCE were examined. Additionally, many optical properties that were not taken into account in other studies were modeled realistically. The applied ray-tracing approach also considered multiple reflections and refractions that occur at the mirror and the HCE. On the other hand, the study considered a realistic sunshape - an average profile of the solar disc with limb-darkening and halo - compared to the previous theoretical studies which used different sunshape models such as Gaussian distribution [28–30,48] or a uniform disc [49]. Yang et al. [50] established their own MCRT code and compared the numerical results with Jeter’s analytical studies [32,49]. The influences of the rim angle and tracking error over the distribution of local concentration ratio (LCR) were investigated for point source and uniform sunshapes. The resulting curves for the LCR were shown to follow the same trend. Cheng et al. [51] introduced an in-house MCRT code together with a design/simulation tool of concentrating solar collectors. The reliability of the numerical results was compared to Jeter’s result [49] and good agreement was obtained. Hachicha et al. [52] developed

was solved using a numerical integration algorithm. The presented model is advantageous in terms of reducing the computational time relative to ray-tracing techniques. The variation of the intercept factor for different incidence angles was also computed and compared with the experimental test data. Although the results agree well with the test data up to an incident angle of 0.6 rad, the deviation after this value becomes larger. Zhu and Lewandowski [38] presented a new analytical method called FirstOPTIC, which is fast and gives accurate results, for optical evaluation of trough collectors in two-dimensional (2-D) analysis. The comparison of the results for the intercept factor showed good agreement with the studies of Bendt et al. [28] and Wendelin et al. [39]. Binotti et al. [40] extended the study of Zhu and Lewandowski [38] to evaluate the geometrical impact of considering three-dimensional (3-D) effects on the optical performance. Thus, the evaluation of the intercept factor for nonzero incidence conditions is made plausible by this method. Zou et al. [41] developed a theoretical method for obtaining the critical tube diameter and the intercept factor in case of tube alignment errors. The proposed method which yields very accurate results as compared to those of Monte Carlo Ray Tracing (MCRT) reduces the computational time from hours to seconds. In contrast to the literature, it is revealed that the offset direction from the focus line is the reason for having the largest optical loss and causing mostly the sun’s rays to escape. From the preceding review, it is worth noting that the 3-D optical analysis is advantageous over the 2-D analysis in examining the effects of optical properties. These effects can be summarized according to Binotti et al. [40] as cosine effect, widened image of the sun, end loss, reduced acceptance angle due to the elongated optical path of reflected rays, and decay of material optical performance with increasing incidence angle. In this section, the analytical studies on the optical analysis of PTSCs have been presented. The analytical approaches proposed in the literature include mostly the determination of intercept factor which changes as a function of the PTSC design. The other optical parameters are the functions of the angle of incidence, wavelength of the solar spectrum, and material properties. Most studies have considered the collector analyses at direct normal irradiance rather than varying incidence angles. In this case, the most decisive parameter becomes the intercept factor. On the other hand, the effects of wavelength on the optical properties are not the matter of consideration due to its insignificant contribution to the optical performance of the system [42]. The analytical determination of the intercept factor has been performed chiefly for design purposes and to increase the optical performance of a PTSC. In the analytical approach, a mathematical relation with a closed-form solution which requires less computational time can be obtained. However, this approach is mainly limited to simple systems. For this reason, ray-tracing becomes attractive since it can be applied to complex systems and is physically more realistic. The next section reviews the studies on the use of ray-tracing in determining the optical performance of PTSCs. 3.1.2. Ray-tracing Ray-tracing is the most widely used technique for analyzing the optical performance and the optical design/optimization of solar concentrating collectors. The technique is more beneficial in the systems with many surfaces where Gaussian and Newtonian imaging equations are unsuitable. It is essentially based on the act of tracing a ray of light through the optical elements and allows the modeling of the propagation of light in different mediums in accordance with the properties assigned to the optical elements (see Fig. 7). Ray-tracing provides an enormous amount of detailed information about the optical characteristics of the system, but obscures functional relationships [28]. Furthermore, ray-tracing is employed using computer-based tools and requires substantial computation time for the

Fig. 7. Visualization of the ray-tracing method. 142

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an optical model for calculating the nonuniform solar flux distribution on the HCE. The finite volume method (FVM) and ray-tracing techniques were used on the spatially and angularly discretized PTSC. The results obtained for LCR were compared to those of Jeter [49], and yielded a maximum deviation lower than 8%. Cheng et al. [53] carried out comparative and sensitivity analyses for different PTSCs/different geometric parameters under different possible operating conditions by a detailed optical model proposed previously by Cheng et al. [51]. In addition, an optimization model was proposed by Cheng et al. [54] for optical performance of PTSCs based on the particle swarm optimization. Zhao et al. [55] developed a simulation code based on the MCRT method to analyze the optical performance of a PTSC. The sunshape was fitted to an optics cone, and the numerical results which were compared with that of Jeter’s study [49] yielded good accordance. Zhao et al. [56] used the same simulation to analyze the influence of installation and tracking rooted errors caused by the absorber and the mirror, respectively. It was clearly shown that the larger the incidence angle is, the larger the errors obtained, but the errors can be reduced by increasing the concentration ratio. Liang et al. [57] developed three different optical models based on ray-tracing. The model estimations for the LCR were compared to Jeter’s study [49], and the average relative errors of the models obtained were very close to each other. Two of the proposed models were superior in terms of runtime and computation effort (enhanced approximately 40% and 60%, respectively) over the model based on MCRT. Besides, the effects of the offset in the absorber tube, variations in the rim angle and aperture width at different tracking errors on the optical efficiency were computed by the models proposed. Liang et al. [58] extended their previous study’s scope by additionally presenting a novel method called CPEM (Change Photon Energy Method). This method which is more efficient than MCRT saves running time and computing cost. This section presented the studies concerned with the application of ray tracing techniques through the optical analysis of PTSCs rather than coupling of ray-tracing with thermal analysis. The studies involving coupled ray tracing and thermal analysis will be addressed in Sections 4.3, 5.1 and 5.2.

50

Local concetration ratio

40

20

0 0

30

60

90

120

150

180

Angle from axis, degrees Fig. 8. The LCR for an ideal PTSC with round receiver, 20× geometrical concentration. And 90° rim angle for a uniform sun of 0.0075 mrad angular radius. Adapted from [49].

LCR varies with the geometrical parameters, i.e., rim angle, concentration ratio, optical errors, and incidence angle. The incident beam radiation, under the case of the uniform sunshape model, affects strongly the LCR as shown in Fig. 8 [49]. The LCR dips near the bottom side of the absorber due to the HCE shadow, and then it shows a steady increase and reaches a peak value where the angle of reflection is lower than the rim angle. It is followed by a drop and diminishes its effect since only a small fraction of the reflected radiation strikes to the upper region of the absorber tube. As the incident angle increases, the LCR falls gradually but its effect is more significant at the higher values. The above evaluation considers the analytical derivation of the LCR, and the effects of imperfect reflection, transmission and absorption of radiation are disregarded. All these effects and nonuniform sunshape were considered in the approach presented in Ref. [32]. This approach offers a more realistic description for estimating the LCR. The obtained LCR profile for different incidence angles exhibits similar characteristics with Ref. [49] but at increased incidence angles, particularly greater than 45°, the degradation is higher. The effect of the optical errors has a significant impact on the distribution of the heat flux on the absorber [34]. The distribution of the heat flux is affected by the intensity of the total optical errors, σtot which acts to decrease the quantity of energy collected at increasing values. At lower total optical error values, the shadow effect due to the HCE is quite salient. The parabola contour and sun tracking errors have negative effects on the LCR [59] as well as the other flaws being statistically effective [26]. The LCR decreases with the increasing tracking error which also changes the regularity of the LCR profile. The contour error can change the LCR profile significantly in case the contour deviates from the ideal. On the other hand, the heat flux distribution on the absorber is nonuniform even if the sun is tracked properly. The nonuniform distribution of solar heat flux will have an effect on the thermal stress distribution and service life of the HCE. With higher values of the incidence angle, the heat flux intensity will vary along the length of the absorber [60]. Khanna et al. [61,62] showed that the absorber tube will bend along its central axis due to thermal stresses. This deflection leads to increasing optical errors [60]. As shown in these studies, both the deflection and the resulting optical errors have

The aim of the thermal analysis in PTSCs is, in general, related to the calculation of the surface temperature profile, the fluid temperature, the conversion efficiency of the absorbed solar radiation, and the determination of the HCE thermal loss. As Fig. 4 shows, different topics have been considered under the option of thermal modeling. In this part, all the thermal modeling issues will be taken into account, and the related works will be discussed elaborately. 3.2.1. Determination of heat flux and temperature profiles Determination of the heat flux distribution on the absorber of the HCE is crucial in assembling a precise thermal model of a PTSC. In practice, the heat flux (q″) and temperature distributions around the absorber tube are not constant or uniform. It has been shown in several studies that the heat flux distribution on the HCE is nonuniform around the circumference of the absorber tube [32,49–53,55,57]. The determination of the realistic heat flux profile is crucial to the accurate determination of the HCE thermal performance. From the obtained heat flux profile, the temperature profile around the HCE can be derived. The local heat flux distribution on the circumference of the HCE is given in terms of the LCR as

q″ Ib,n

30

10

3.2. Thermal analysis

LCR =

75 deg 60 deg 45 deg 30 deg 15 deg 0 deg

(22)

Using the LCR brings more flexibility when it is multiplied with normal incident beam radiation (Ib,n ). The circumferential distribution of the 143

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negative effects on the circumferential heat flux and temperature profiles. Furthermore, Khanna et al. [62] indicated that the differential rise in HTF temperature increases the maximum deflection in the absorber. The rim angle is also an effective parameter on the heat flux distribution and total absorbed heat flux. Determining an appropriate value for the rim angle can reduce the nonuniformity of the heat flux distribution and bending deflections [63]. Larger rim angles produce smaller deflections [62]. When the aperture width is increased, the circumferential nonuniformity in heat flux intensifies. Mwesigye et al. [64] illustrated the variation of the heat flux profile with the rim angle and the concentration ratio as depicted in Figs. 9 and 10, respectively. A rim angle of 110° can be considered as the optimum value for maximizing the total absorbed flux as the width of the aperture is fixed, but it may not correspond to minimum mirror cost [60,63]. However, rim angle above 90° have some mechanical and economic drawbacks [65]. Enlarging the rim angle requires both increased envelope dimension and mirror surface which in turn cause the collector structure to be subjected to growing wind loads and lowered optical efficiency as a result of this condition. For the sake of increasing the maximum heat flux on the absorber, an optimum value should be determined with respect to the assigned aperture width and rim angle combination. The temperature distribution around the absorber tube of the HCE follows the same trend with the heat flux distribution as was shown by Mwesigye et al. [64]. The nonuniformity in the temperature distribution causes temperature gradients that should be kept within safe limits to guarantee longer operation life of the HCE. This can be achieved by ensuring appropriate flow rates through the HCE as well as heat transfer enhancement as will be discussed.

where Aa : aperture area, THCE : HCE temperature, and Ta : ambient temperature. The thermal characterization of the HCE is fundamental to accurately determine the heat loss. Even if different types of HCEs are available in the literature, their physical structures resemble each other. The heat transfer model applied to any HCE involves different governing equations though; they can be utilized in different thermal modeling studies. Several studies in the literature have characterized the HCE thermal performance and determined the thermal loss coefficient. Gee et al. [70] developed a thermal model that shows how the HCE type affects the thermal loss coefficient as a function of the absorber temperature. The results for five different types of HCEs - the reference trough, evacuated, xenon back-filled, heat mirror coated envelope, and reduced emittance selective coating - were obtained for a fixed absorber tube diameter. Antireflection and selective coatings (heat mirror coated envelope and reduced emittance selective coating) were shown to be effective in the reduction of heat losses especially at higher absorber temperatures. A back-filled HCE was more effective than the other types since the use of a less-conductive gas reduces the heat transfer across the annulus. While larger the absorber diameter leads to slight variation in the thermal loss coefficient, increasing the absorber-to-glass gap size influences the thermal loss coefficient favorably. However, it should be noted that a larger gap results in excessive convection heat loss after a certain limit. Contrarily, this argument is not thermally significant for the evacuated HCE. Gong et al. [71] presented a one-dimensional (1-D) theoretical model for a vacuum type HCE and compared it with off-sun experimental tests. The model agrees well with the tests, but when the HCE’s ends are exposed to ambient conditions, the model underestimates the heat loss. This indicates that end losses can be influential depending on the HCE structure. Moreover, the coating’s emittance and vacuum conditions were shown to have significant effects on the heat loss. The coating’s emittance is affected by oxidation since air-leakage is a problem in vacuumed HCEs [72]. Nitrogen can be chosen instead of air to avoid oxidation. Also, the gas properties and vacuum level have significant effects on the heat transfer mode. For example, hydrogen and helium lead to rapid increase of heat loss even at low pressures. The hydrogen, which is absorbed by the HCE made of stainless steel, naturally permeates from the HTF (decomposition of thermal oil at higher temperature) [21], and thus the presence of hydrogen increases the annulus pressure and reduces the HCE performance [73] even if the

3.2.2. Thermal loss coefficient In the evaluation of the overall heat loss from the HCE, the concept of the thermal loss coefficient (UL ) is used to simplify the analysis. The prediction of the thermal loss coefficient requires numerical iterations but several studies have handled it analytically [66–69]. The analytical approach is more convenient with respect to the numerical one, which is tedious and time-consuming, if they are generalized. Obtaining the thermal loss coefficient value provides to evaluate the thermal performance in a simpler form [19]:

ηt =

∫ Aa [ηo (θ) Ib−UL (THCE−Ta)] dt Aa ∫ Ib dt

(23)

4

x10 15

4

x10 12

r

r

100 120

6 4

60

2

Heat flux (W/m )

8

(degrees) 40

40 60 80 90

2

Heat flux (W/m )

10

(degrees)

80

10

90 100 120 5

C= 86

C= 143

2 0

0

40

80

120 (degrees)

160

0

200

0

40

(a)

80 120 (degrees)

(b)

Fig. 9. Variation of heat flux around the absorber tube wall at various rim angles (a) C = 86 (b) C = 143. Adapted from Mwesigye et al. [64]. 144

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4

x10

x10

16

10 C

C

14

10 8 6 4

ϕ

2

o

r

6 4

0 40

80 120 θ (degrees)

160

ϕ

2

= 40

0 0

57 71 86 100 114 129 143

2

Heat flux (W/m )

2

Heat flux (W/m )

8

57 71 86 100 114 129 143

12

200

0

40

80

120

o

r

160

= 100

200

θ (degrees)

(a)

(b)

Fig. 10. Variation of heat flux around the absorber tube wall at various concentration ratios (a) φr = 40° (b) φr = 100°. Adapted from Mwesigye et al. [64].

assumptions are needed to predict the system behavior. Each model has its own characteristic assumptions, but the mutual ones include:

annulus pressure is sufficiently low (< 100 Pa). Injecting inert gases such as argon and xenon have been shown to reduce the heat loss caused by the penalty associated with hydrogen permeation. Prediction of the heat transfer characteristics of HCEs using gas mixtures (hydrogen/argon, hydrogen/xenon) was modeled and tested experimentally by Burkholder [73]. A distinct 1-D heat transfer model was evaluated for different nonvacuum conditions in a study of Wang et al. [72]. Another modeling study to investigate the heat losses from a vacuumed HCE was presented by Pigozzo et al. [74]. A new computational model for heat loss from an absorber tube can be found in a study of Vinuesa et al. [75] over a wide range of pressures and gas compositions. The model gives accurate results as compared with the experimental data even at pressure values between 10−4 and 130 mbar. Additionally, the study holds the knowledge of different correlations for modeling the rarefied gas dynamics [76–79] that are applicable to vacuumed concentric tubes.

• fully-developed flow is present, • the concentrator surface is specularly reflecting, • no variation occurs in the collector dimensions such as constant diameters, • no free surface comes into existence inside the absorber, • the fluid is assumed to be incompressible, • the sky is assumed as a blackbody at an equivalent temperature for long-wave radiation.

The heat transfer analysis involves energy balance, which is employed on each component of the HCE. This balance can be written as [81]

Q−W =

∫CV

∂ ρΘdV + ∂t

∫CS ρE→υn dA

(24)

3.3. Heat transfer analysis Here, Q is the net heat transfer rate, W is the net power interaction. The first term on the right-hand side of the equation represents the time rate of change of the energy content of the control volume (CV),

The HCE of a PTSC is the central component, which is simply composed of the nested absorber tube in an envelope as shown in Fig. 11, for the performance of the entire system. The heat transfer analysis of PTSCs mainly focuses on the prediction of the thermal performance of the HCE. Inside the absorber tube, a HTF such as water, thermal oil, molten salt, gaseous, nanoparticle laden fluid or new alternatives is used for heat carrier [80]. The absorber tube is enclosed by a glass envelope, and the space between them is inherently filled with air but can be vacuumed to significantly reduce the heat losses. The outer surface of the HCE is subjected to ambient conditions. Fig. 12 shows the modes of losses on the cross-sectional view of the PTSC. The heat transfer modeling of a HCE requires some assumptions even if they can limit the accuracy of modeling outputs, but these

υ2

Θ = h + 2 + gz which is the total energy of the flowing fluid per unit mass. The second term gives the net amount of the energy flowing across the control surface (CS) per unit time. And → υn is the normal υ2

component of the velocity vector, E = u + 2 + gz which is the total energy per unit mass. The flow inside the absorber tube involves forced convection whose flow pattern can be in single-phase or two-phase. Unlike two-phase flow, single-phase flow is considered in most of PTSC systems since the phase of the HTF does not change during operation. However, direct steam generation (DSG) collector systems involve two-phase flow which results from boiling of water in the absorber tube. The flow Fig. 11. Schematic of a typical HCE. Adapted from [21].

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Fig. 12. Typical losses from a PTSC.

analyses for predicting the fluid behavior is quite mature for this type of flow. The 1-D heat transfer model is the most often used approach in the literature. In this modeling approach, the temperature gradient is considered to be significant only across the radial direction of the HCE rather than the axial and circumferential directions. The energy balance equations can be defined by conserving energy at each surface of the HCE.

regime is much complicated in these systems as compared to the former since both the liquid and the vapor are forced to flow together. Fig. 12 shows the heat loss interactions among the HCE components. The thermal physics of the HCE involves the combined modes of heat transfer. Table 2 shows the governing equations which are mostly used in modeling the HCE’s heat transfer performance. In the next sections, the physical structure of the single-phase flow will be first examined in detail, and then the modeling of DSG systems will be considered separately. 3.3.1. Single-phase steady flow The single-phase flow provides reliability in operation and controllability of the exit temperature of PTSC systems. Dealing with single-phase steady flow is relatively easy in most cases, and the

Qabsorbed solar = Qresidual + Qradiation,abs + Qsupport ,bellow

(25)

Qbeam radiation = Qoptical + Qconvection + Qradiation,env

(26)

Qheat

(27)

loss

= Qconvection + Qradiation,env + Qsupport ,bellow

where the optical loss is represented in terms of its equivalent heat loss.

Table 2 Equations and heat transfer coefficients for HCE heat transfer modeling [82]. Term

Equation

Heat transfer coefficient and parameters

Absorbed radiation

Qabs = Ib wa ηo

−

Convection inside the absorber tube

Qconv = πDia hhtf (Tia−Thtf )

hhtf = Nuhtf

khtf Dia

Laminar: Nuhtf = 4.36 Turbulence: Nu =

f / 8(Rehtf − 1000)Prhtf Prhtf ⎛ ⎞ Pria ⎠ 1 + 12.7 f / 8 (Pr 2/3 htf − 1) ⎝

0.11

f = (0.79InRehtf −1.64)−2 Convection in the annulus

Qconv =

2πk eff (T −T ) In(Die / Doa) oa ie

k eff k

Fc = Free molecular convection in the annulus

Qconv =

2πk eff (T −T ) In(Die / Doa) oa ie

k eff k

1/4 Pr (Fc Ra)1/4 0.861 + Pr [In(Die / Doa)]4 −3/5 + D −3/5)5 ((Die − Doa) / 2)3 (Die oa

(

= 0.386

= ⎡1 + ⎣

λ = 2.331 × Radiation in the annulus

Qrad =

4 − T 4) σπDoa (Toa ie 1 (1 − εc ) Doa + εa εc Die

Conduction through supports

Qconv =

Convection over the glass envelope

Qconv = πDoe ha (Toe−Ta)

hs ps ks As (Tb−Ta)/ L

)

(2 − a)(9γ − 5) λ a (γ + 1)In(Die / Doa )

146

+

1 Doa

−1

) ⎤⎦

[77]

σ = 5.67 × 10−8 W/m2K4

−

ha = Nu

ka Doe 2 0.387Ra1/6 ⎤ Doe ⎥ 9/16 8/27 [1 + (0.559 / Pr) ]

n Forced: Nu = C Rem Doe Pr a

4 4 Qrad = σπDoe εe (Toe −Tsky )

1 Die

T 10−20 ae2 Pa δ

⎡ Natural: Nu = ⎢0.60 + ⎣

Radiation from the glass envelope

(

Tsky = 0.0553Ta1.5 [83]

⎦

Pra 1/4 Proe

( )

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heat conduction along the HCE wall, mixed convection in the absorber tube, and thermal interaction between the neighboring surfaces (absorber–envelope and envelope–envelope), Behar et al. [18] presented a model with the thermal resistance network method, Liang et al. [106] summarized the 1-D mathematical models under different assumptions and heat interaction cases. All these models were applied to single PTSC modules having short HCE length, thus it is unnecessary to consider the heat conduction cross the absorber and envelope walls, as well as the neighboring nodes along the HCE length. However, the effects of these variables should be considered in long HCEs so that dividing control volume along the length is significant to see the axial influence. The influence of radiation heat transfer between the adjacent discretized volumes [106], and the heat loss through HCE supports improves the model precision once considered [18,21,42,103,106]. The existing models mentioned above assume that the solar energy flux, wall temperature or physical properties are uniform for the whole circumference of the HCE. However, all those are not physically happening in the real case owing to the fact that the fluid inside the tube is heated asymmetrically, and thus the temperature distribution and temperature-dependent properties become nonuniform [107]. Also, the bellows and glass-to-metal joints at either end of the HCE, i.e., the inactive ends, should be taken into account in the thermal analysis. The model results obtained for the heat loss and efficiency terms indicate that the uniform and nonuniform approaches differ slightly [106,108] consequently the uniform model is a reasonable approach to simplify the analysis and to estimate the performance parameters, as well. Up to here, the 1-D models were reviewed. The 1-D modeling is

As the 1-D heat transfer models are reviewed, it is seen that the oldest model is the one presented by Edenburn [25] for a cylindrical PTSC. It includes heat transfer and energy equations which are solved using finite difference method (FDM) to predict the collector performance. This model involves the heat transfer between the mirror and envelope, and the view factors determined for the surfaces. Many other modeling approaches are available in the literature [27,30,84–97] based simply on energy balances. The energy balance approach, as usual, is used to analyze the heat loss from the HCE. Additionally, some models have been developed and used in the analysis of thermodynamic cycles in which PTSC systems are used for heat generation [98–101]. Forristall [21], in his extensive study, used also the 1-D approach to investigate how design conditions and operating parameters affect the PTSC performance. These efforts were significant to identify the design parameters which affect the performance the most and to show which design conditions influence the performance significantly and should be the focus of any performance improvement. The summary of the results is given in Table 3. More comprehensive models were developed in several other studies; García-Valladares and Velázquez [102] considered spatially discretized flow patterns, Padilla et al. [103] proposed more accurate heat transfer correlations and a detailed radiative heat transfer analysis with the discretization approach, Kalogirou [104] presented a detailed thermal analysis, Yılmaz and Söylemez [42] performed a discretized modeling with a radiative heat transfer analysis between the mirror and envelope, Ghoneim and Mohammedein [105] involved the effects of Table 3 Summary of the parametric studies [21]. Design option or parameter

Evaluation range

Absorber base material

304/316L, 321H, B42 copper, and carbon steel

Selective coating

Annulus gas type

HCE condition/wind speed

Annulus pressure

Mirror reflectance

cost considerations.

improvements in coatings have improved HCE performance. • The performance would be sensitive to any variance in selective coating optical • HCE properties. gives the best result. • Vacuum the annulus with an inert gas is better than air. • Filling • Hydrogen permeation can degrade HCE performance. broken glass envelope gives unfavorable performance results, especially with • Awindy conditions. has little influence on HCE performance when the annulus vacuum is intact, but • Wind does when the vacuum is lost. levels less than < 0.1 torr show negligible improvements from the • Vacuum 0.0001 torr level. performance declines appreciably with pressures of 100 torr or greater in the • HCE annulus. • If hydrogen in present, HCE performance is even more sensitive to annulus pressure. The trough performance drops appreciably with solar weighted reflectivity less than • 0.9. • Keeping mirrors clean is very important to solar collector assembly performance. • Trough performance is very sensitive to solar incident angle. performance very sensitive to beam radiation. • Trough such as atmospheric pollutants and particulates should be considered when • Factors choosing a solar site. • HCE performance has weak dependency to HTF flow rate. performance has weak dependency to HTF type. • Trough of the HCE at higher temperatures decreases the HCE performance yet • Operation increases the power cycle efficiency. optimal diameter leads to minimize the heat losses. • An of diameter on heat loss is more sensitive under lost vacuum. • Influence • Clearance for absorber pipe bowing needs to be included. along the length of the HCE increase in a slightly nonlinear. • Temperatures heat transfer fluxes increase nonlinearly. • Radiation • Optical losses per unit HCE length remain constant.

Vacuum, air, argon, and hydrogen

loss vacuum, and broken envelope • Vacuum, • 0–20 mph and hydrogen • Air • 0.0001–760 torr

0.8–0.935

0–60°

Beam radiation

300–1100 W/m2

HTF flow rate

100–160 gpm

HTF type

Therminol VP-1, Xceltherm 600, Syltherm 800, 60–40 Salt, and Hitec XL Salt

Temperature and heat flux variation along HCE

effect on the HCE performance, yet material selection is also driven by • Negligible material strength, corrosion properties, installation ease, coating application, and

black chrome and cermet • Luz • Solel cermets

Incident angle

Envelope diameter

Results and comments

and lost vacuum • Vacuum • 0.08–0.165 m 39.0–740.5 m

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semitransparent, nongray surfaces. These spectral optic properties have not been used in any of the models during the computation of the radiative exchange. Various modeling studies for single-phase steady flow have been proposed by numerous researchers. In these studies, comprehensive numerical analyses have been presented, and their validation compared with the test results of Sandia National Laboratories (SNL) [87]. Since these test results offer functional dataset for a variety of operating conditions of the LS-2 collector. Most of the models in the literature have been examined under the consideration of 1-D approach. The 1-D model is superior compared to the multi-dimensional models, especially since it involves less solution time and complexity. The 1-D energy balance gives reasonable results for short HCEs (< 100 m) [21], but longer HCEs require at least 2-D modeling. The 1-D model becomes insufficient with increasing HCE length, and thus the discretization through the axial direction is needed to reduce the deviation. Liang et al. [106] proposed that the heat conduction across the radial direction (in the absorber and envelope) and the adjacent nodes along the axial direction can be neglected. On the other hand, the conductive resistance through the selective coatings can be disregarded since anti-reflective treatment is a chemical etching process and introduces no thermal resistance [21]. Fig. 13 shows the results of the modeling studies and their comparison with experimental measurements for the collector thermal efficiency. As the model results are examined, it is seen in Fig. 13a that the model developed by Garcia-Valladares and Velásquez [102] deviates significantly from experimental results, particularly at low temperatures, due to the assumptions of constant absorber emissivity and radiation heat loss from the envelope realizing only between the glass and the sky. Liang et al.’s model [106] also results in higher deviations, and some part of the data estimated is outside the experimental error bars due to the similar assumptions proposed in [102]. Contrarily, Liang et al. [106] considered the heat transfer through the support brackets and the radiation heat transfer between the subsequent nodal segments in the annulus region. In Dudley et al.’s report [87], field emittance measurements of the absorbers at 100 °C and 300 °C are mentioned, yet there is no exact information in the report about the coating emittances varying as a function of the absorber temperature. Forristall [21] described the functional relationships using linear curve fitting between the coating emittances and operating temperature. Wirz et al. [112] indicated that the functions proposed by Forristall [21] may underestimate the radiative emission since they were derived from only

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commonplace and is often applied by the introduction of thermal resistance network method. It is simpler and requires less time to perform the analysis relative to the 2-D and 3-D approaches. Although higher degree analysis provides more accurate results, it is more difficult to model, yet it is necessary to account for the axial effect in long HCEs, and/or angular effect around the HCE circumference. As the overall length of the HCE reaches hundreds or thousands of meters, the change in flow rate (caused by the density change) and pressure drop can have an appreciable effect on the heat transfer performance [21]. Thus, the 2-D model is required to take into account these effects. The Forristall’s model revealed that the axial effect become significant after the HCE length reaches ∼80 m. Once the 1-D and the 2-D models of Forristall are compared, the 1-D model is not able to capture the nonlinearity change of the HTF temperature along the HCE and underestimates the heat losses thereof. Tao and He [109] developed a unified 2-D numerical model with uniform heat flux on the absorber tube and isothermal surface inside the envelope. The results show that tube diameter ratio is the effective parameter to change the convection coefficients inside the absorber and annuli. The thermal conductivity of the absorber tube influences the convection regimes at both sides, but after a certain value (200 W/m K), it has little effect over the convection coefficients. Contrast to the studies of Forristall [21], and Tao and He [109], Hachicha et al. [52] and Wang et al. [110] considered nonuniform solar heat flux in their models. This approach is more accurate to determine both the circumferential temperature distribution and the local heat transfer. The effects of the incident angle and eccentric configuration were also investigated by Wang et al. [110]. It is shown that the change in incident angle significantly affects the heat transfer characteristic for the “air in annulus” case. The upward and downward eccentricities have significant effects on local heat transfer coefficients for both “air in annulus” and “vacuum in annulus” cases. These conditions not only influence the heat transfer characteristic but are also effective for the optical errors generated due to deflection of the absorber as mentioned previously. Huang et al. [111] proposed a 2-D thermal model including extraordinarily the radiation loss to the side plates of a PTSC and the direct transmission of the absorber radiation to ambient air as compared to the previous models. Wirz et al. [112] presented the 3-D optical and heat transfer models using a MCRT tool coupled with a FVM solver. Different from the preceding studies, this model takes into account the nonuniform solar flux distribution on a HCE comprising specularly reflecting and

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(b)

Fig. 13. Comparison of the model outputs with experimental data [87] for collector efficiency. (a) Cermet. (b) Black chrome. 148

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controller tracking errors - could lead to negative effects on the simulation results as clearly indicated by Yılmaz et al. [115]. On the other hand, all the used empirical correlations in the models would be the source of deviations since the error involved might reach bigger values in the convection calculations. In the 1-D heat transfer model, the circumferential heat flux is treated as uniform although the actual heat flux distribution is asymmetric. In fact, the distribution depends on random and nonrandom errors as mentioned before. However, the heat flux with uniform profile simplifies the model and allows the use of heat transfer correlations (internal, annulus and external flows in the HCE) derived under the uniform temperature assumption. The studies presented by Cheng et al. [107] and Lu et al. [108] have indicated that the uniform and nonuniform models yield close simulation results so that the uniform model can be used to quickly estimate the performance parameters of a PTSC. Fig. 13b illustrates the efficiency results obtained for the collector with black chrome coating [87]. The efficiencies are slightly lower at high temperatures as compared to the cermet due to the higher emissivity of black chrome at those temperatures and its tendency to become a less specular surface. It is clear from Fig. 13b that an enormous part of the predictions are inside the experimental uncertainty limits except the Behar et al.’s model [18]. It underestimates both the thermal losses (see Figs. 14b and 15b) and collector efficiency. This is mainly due to the unaccounted optical losses and unspecified sky temperature in their model. There are generally two approaches for the prediction of sky temperature in the modeling of PTSCs. In the first one, the sky is assumed as a blackbody at an equivalent temperature and can be expressed with a simple relationship using local air temperature [83]. The second one is the effective sky temperature assumed to be 8 °C below the ambient temperature [21,112]. The former approach can be treated more feasible to find the sky temperature. Contrarily, Wang et al. [110] evaluated the radiation between the envelope and ambient instead of sky temperature. If the experimental dataset for black chrome is reviewed [87], it is observed that the tests had been performed in winter conditions, thus the ambient temperatures are comparatively lower than that of the cermet case. The latter approach may not give satisfactory results under this condition. On the other hand, it is worth noting that all the models neglect the radiation heat transfer to the ground and surrounding objects. This should be also handled as a source of error. Huang et al. [111] exhibited in their study that coupling both 2-D thermal and 3-D optical models yields good simulation results. Here,

two data points. Moreover, there were differences between the temperature measurements determined by the laboratory and the operation of the system under actual field conditions, so this would be the possible source of error in the prediction of emittance. Even if the predictions match the field tests by Dudley et al. [87], the relation between the emittance and temperature would not necessarily be linear. Therefore, better optical and thermal component data are expected to yield improved model predictions as the spectral properties are used [112]. Nonetheless, the spectral, directional and temperature dependence of the absorption, transmittance and emittance of the mirror and the envelope are the weak function of temperature, their effects can be treated as negligible [42]. In fact, the solar absorption of the envelope is also to be considered in the analyses since the solar absorptance coefficient for glass is about 0.02 [113]. Forristall’ [21] and Padilla et al.’ models [103] have growing deviations accompanied by forced convection at elevated operating temperatures. The external flow over the HCE is commonly analyzed in the PTSC models under two cases: natural and forced convection. The empirical correlations derived for isothermal cylinders are constantly used in modeling approaches for the estimation of Nusselt number on the HCE even if the actual temperature distribution is nonuniform. Additionally, the forced convection around the HCE is taken to be crossflow whereas the local Nusselt number distribution is different from this flow pattern in real cases. This approach leads poor simulation results especially for the case of the annulus with filled-air where the thermal losses are significant. Forristall [21] recommended a fitting analysis in his model in order to reduce the error by convection. Likewise, Padilla et al. [103] have altered the fitting parameter and obtained better simulation results. Barbero et al. [114] described a new approach which derives the external heat transfer coefficients as a polynomial function instead of constant or linear dependence. These new functions allow the explicit calculation of the efficiency as a function of some characteristic parameters of the HCE. On the contrary, Yılmaz and Söylemez [42] proposed a more reasonable approach which needs not to have a fitting function since both the combined effects of natural and forced convections over the HCE were inserted into the model and gave better results. Hachicha et al. [52] interrelated the reason of increasing deviations at higher temperatures with the quantification of optical properties at lower temperatures. Furthermore, it was argued that some unaccounted optical parameters - such as HCE and mirror misalignment, aberration in the mirrors, deflections in the collector structure during tracking, and 200

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the 2-D thermal model has improved the simulation results by including the radiation loss to the side plates and the direct transmission of the absorber radiation to the ambient air. Figs. 14 and 15 present the results of the heat loss for the pre-stated cases. It is seen that the agreement between the field tests and the model data in black chrome is basically better than those of the cermet case over the entire temperature range. This could be strongly related to the proper characterization of the emission measurements for black chrome [87]. Besides, the cases specified by no-sun give better agreements for both coatings with the model data which are largely confined within the bounds of the experimental uncertainty. The presence of fullsun increases the deviations in the model predictions accompanied by convection heat transfer from the absorber tube. The temperature difference between the HTF and the absorber tube in full-sun is much higher relative to no-sun conditions. It is at the level of a few degrees in no-sun case which reduces the effect of convection heat transfer and its relative contribution to the heat loss. Meanwhile, the circumferential temperature profile becomes more uniform under the no-sun case [87]; the model predictions would yield better results as a consequence. For this reason the simplest case for comparing heat loss predictions with the model data can be said to be the vacuumed HCE under no-sun conditions since the heat loss from the absorber is almost completely by radiation. Additionally, the no-sun case does not involve any optical influence in contrast to the full-sun case.

(ρcA)htf Δx

∂Thtf (x ,t ) ∂t

= Qu (x ,t )Δx + Qhtf (x ,t )−Qhtf (x + Δx ,t )

(28)

For the absorber tube:

(ρcA)a

∂Ta (x ,t ) = Q0 (x ,t )−Q1 (x ,t )−Qu (x ,t ) ∂t

(29)

For the glass envelope:

(ρcA)e

∂Te (x ,t ) = Q1 (x ,t )−Q2 (x ,t ) ∂t

(30)

A number of studies have considered the transient nature of operation in PTSCs. Unlike 3-D model conducted in [123], a number of researchers have developed 1-D energy models for experimental validation, and for the subsequent implementation of these models into parametric analyses. The variation in the HCE temperature [124,125], HTF temperature [14,124–131], HTF mass flow rate [125,127], HTF type [128,129], solar radiation [129], energy collected [122,130,131] energetic efficiency [125,127,129,130], and exergetic efficiency [125] were considered in these studies to analyze their influence over the dynamics of a specified PTSC. The governing equations describing the 1-D transient behavior of the PTSC can be expressed on the control volume given in Fig. 16. For HTF:

3.3.2. Single-phase transient flow So far, only the cases of single-phase steady flow operation have been reviewed. However, most PTSC systems operate under transient conditions due to the heating of collectors from start-up to shut-down of a daily operation. Moreover, the intermittent nature of the driving environmental conditions will not allow the PTSC to operate steadily for prolonged periods. Several studies have considered the lumped-capacitance analysis [116–122] for analyzing the transient characteristics of PTSCs. The lumped-capacitance analysis involves the transient energy balance equations defined for the various parts of the collector at uniform temperatures. The control volume “A × Δx” for the analysis of the HCE under transient conditions is shown in Fig. 16. The governing equations used for this analysis can be expressed as: For HTF: Fig. 16. Lumped capacitance analysis on the HCE. 150

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(ρcA)htf

∂Thtf ∂t

= −ṁ htf

∂ (cT )htf + Qhtf (Δx ) ∂x

and predicts the transition between the flow regimes. On the other hand, a general operation strategy for considering both the performance and safety aspects in a DSG loop was proposed by Sun et al. [139], and the analyses made were presented on a flow regime map shown in the right-hand side of Fig. 18. Based on the findings, it is essential to operate the DSG loop with high quality (in the range of 0.7–0.8) in case of high direct beam radiation (400–1000 W/m2) for enhanced system performance. At low qualities (between 0.2 and 0.4) and low direct beam radiation (200–400 W/m2) cases, the loop should be operated cautiously to avoid the stratified flow pattern. It was shown that the flow pattern affects the peripheral temperature gradient around the absorber tube, thus lowering in temperature gradients decreases the thermal stresses in the HCE. For this reason, it is better to operate the PTSC in the annular region since the gradient is about 3 K but it could reach up to 50 K in stratified flow [148]. Heidemann et al. [138] concluded that high temperature peaks are obtained in the stratified flow at higher void fractions (volumetric ratio of vapor to water) as a result of their 2-D FDM numerical analyses. It was proposed that these peaks could be reduced using an absorber tube material with high thermal conductivity. By this way, asymmetric thermal expansion of the absorber tube can be then minimized. For low flow rates (< 12 L/min) and low pressures (< 3 bar), Martínez and Almanza [149] presented a theoretical model validated with the experimental results for annular flow and showed that the highest average temperature difference can reach up to 31 K at low flow traits. SerranoAguilera et al. [150] proposed a 3-D thermal and optical model for DSG under the dryout condition and verified it with the experimental results. The 3-D temperature field on the solid bodies of the HCE (bended absorber tube, and glass envelope) was presented, as well. Water evaporation in the absorber tube involves the modeling of two-phase flow that requires more complex processes than the conventional single-phase flow. The DSG evaluations in PTSCs under steady-flow conditions are presented in [93,134,137]. In study by Odeh et al. [93], the variation of the heat transfer coefficients with bulk temperature, efficiencies of different phase sections versus radiation level, thermal loss of collector, variation of collector efficiency with radiation level and inlet temperature, temperature distribution along the absorber tube, variation of collector efficiency with radiation level and water saturation temperature, efficiency of the collector for varying absorber diameters were investigated. Zaversky et al. [151] developed a detailed model using the thermodynamic simulation software IPSEpro, and analyzed the heat loss and pressure drop depending on the collector length. Elsafi [137] introduced a new approach encompassing the thermal and pressure drop modeling of all the flow regimes. The model is meaningful as a consequence of showing the flow patterns along the HCE in DSG loops. The effects of direct beam radiation, inlet

(31)

For the absorber tube:

(ρcA)a

∂Ta ∂ ∂T = Aa ⎛ka a ⎞ + Q0−Q1−Qu ∂t ∂x ⎝ ∂x ⎠

(32)

For the glass envelope:

(ρcA)e

∂Te ∂ ∂T = Ae ⎛ke e ⎞ + Q1−Q2 ∂t ∂x ⎝ ∂x ⎠

(33)

On the other hand, different modeling tools have been widely used for the dynamic simulation. TRNSYS (TRaNsient SYstem Simulation) [132], SAM (Solar Advisor Model) physical model [133], multi-purpose physical system modeling language, Modelica [134,135] are widely accepted and validated programs. A good example for modeling and cosimulation of a PTSC plant is available in [136] where SolTrace (for MCRT modeling), TRNSYS and Modelica tools are coupled, and the dynamic performance of the plant was investigated elaborately. For the single-phase flow transient analysis of the PTSC, two different models have been used. In the lumped-capacitance model, the temperatures of the collector parts vary with time but remain uniform throughout the time. It is less complicated than the 1-D model which considers the variation of temperature with time as well as with the axial position. The lumped-capacitance model provides reasonable simulation results in a shorter computational time. It can be used for energetic calculations to predict the HTF outlet temperature, heat gain/ loss, and thermal performance but is not suitable for obtaining an accurate temperature profile of the HCE relative to the 1-D model. 3.3.3. Two-phase steady flow One of the obstacles in using thermal oil is its maximum temperature limit, called film temperature, which limits the operating temperature up to about 400 °C due to chemical degradation. Although the operation of the PTSC technology is well understood and highly developed, further improvements and reducing its cost are limited due to temperature range, necessary components for the oil loop, and parasitic loads during operation. The pros and cons of using thermal oils as HTFs in PTSC systems can be found in the literature [93,137–140] with detail. On the contrary, DSG and the use of molten salts are possible solutions that offer higher temperature operation and maintain better thermal efficiency. There are possible operation concepts as schematically shown in Fig. 17. These concepts have been commonly discussed in the literature for DSG with PTSCs. The operational details of all these concepts can be found in a study by Lippke [141], and their assessments under the various criteria are presented by Murphy et al. [142]. The two-phase flow in a DSG collector exhibits different flow patterns, including stratified, wavy, slug, intermittent, annular and a possible dryout [137]. The prediction of the distribution of liquid and gas flowing is significant since the distribution affects heat transfer rates, temperature variations, mass velocities and the system stability [144]. Stephan and Green [145] have indicated that for a wide range of mass flux conditions, the maximum heat transfer coefficient in the twophase flow takes place at the quality of 0.8. Hence the inlet and exit states of the collector close to the saturated conditions are desirable for the performance enhancement. The presence of a stratified (vapor + water) or a partially filled flow pattern (water + air) can cause large temperature differences, and these patterns give rise to bending of the absorber and possible breakage of the glass envelope [146]. There are many two-phase flow maps developed for predicting the flow patterns in horizontal tubes, but they do not produce reliable results, or they are complex to handle. Elsafi [137] proposed a generalized map (see the left-hand side of Fig. 18) which was adapted from the study of Wojtan et al. [147]. This map provides more convenient coordinates (mass flux versus quality)

Fig. 17. DSG operational concepts [143] (License number: 4323031148693). 151

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Fig. 18. Flow pattern map [137] (License number: 4320341294556) and [139] (License number: 4325820841046) (from left to right).

pressure, and inlet temperature on the flow patterns were shown in that study. Separately, Nolte et al. [152] analyzed a HCE for DSG from the perspective of the second law of thermodynamics. Mass flow rate, operating pressure, tube diameter, and concentration ratio were optimized for the minimization of entropy generation. Despite the previous literature, Hachicha et al. [153] developed a thermo-hydraulic model coupled with ray tracing optics for the performance prediction of DSG under nonuniform heat flux distribution. This study is significant to understand both the operation characteristics of DSG and the level of thermal stresses induced in more realistically simulated operating conditions.

due to the variation of the heat transfer coefficient in the absorber tube, and high temperature peaks were obtained especially in stratified flow with higher void fractions. The response time of the absorber tube was also studied for the case of stepwise varying solar radiation levels, and it was shown that very high temperature gradients were induced within a short time. Another study which was presented by Steinmann and Goebel [155] enables the detailed calculations of the wall temperature. The 1-D transient homogeneous flow model (the liquid and vapor phases of two-phase flow in thermal equilibrium) was applied in a number of studies [141,156,161,162]. Unlike the homogeneous model, You et al. [157] established a two-phase flow modeling via the subphase approach for a once-through DSG system. The process used in the DSG solar plants is not at the same level of complexity relative to the oil-based PTSC plants. In the SEGS plants, the outlet temperature of the thermal oil flowing through the solar field is controlled by mass flow manipulation at the inlet side however in the DSG solar plants both the fluid temperature and the operating pressure must be controlled to maintain the desired steam conditions at the outlet [143]. As mentioned in the previous section, the thermal-hydraulic behavior of DSG plants is examined under three operational concepts. In the once-through concept, less system complexity is available thus requires lower investment cost, but process control is the main technical problem in this concept. The injection concept seems to be controlled easily but it is more complex and costs more. Besides, the final proof of this concept is still pending [163]. The recirculation concept is the most conservative and can be controlled well relative to the others. Its loop configuration guarantees to prevent stratified flow, but the recirculation increases the parasitic loads and the system cost. Particularly, the dynamic reaction and the concerned controllability of a DSG process are the two major challenges as explicitly shown in [164]. In this context, the numerical simulation can provide wealth of information to answer these important subjects of a practical application, and its control strategy to be defined. Lippke [141] presented the transient response of a once-through process and its control. For these subjects, a numerical solution was performed, and the results were verified with a test facility. First, the reaction of the steam flow under simultaneous changes in the solar radiation was discussed. Second, the reaction of the steam flow and temperature to different sizes of passing cloud fields, and how cloud field velocity affects the flow controllability at varying weather condition were investigated. As a conclusion, the once-through process seems to be controllable even in bad weather conditions according to the simulation results. Eck and Steinmann [165] compared the experimental results with the simulation results of the recirculation concept and obtained good agreement. The experimental results were presented for both once-through and recirculation

3.3.4. Two-phase transient flow In DSG systems, the flow characteristics are more complex compared to the single-phase flow owing to the flow instabilities that happen in case of disturbances in the solar radiation or local shading by clouds passing over the solar field for a limited time. At this point, the transient modeling becomes more valuable for predicting the response of the solar field since the lengths of the single-phase, two-phase, and dry steam regions are significantly affected by the dynamic conditions. This issue causes thermal stability problems in the field, and large fluctuations in the outlet temperature and steam flow rate, as well. In other words, the system may not operate in the desired flow regime. Thus, developing a suitable control strategy for the anticipated system reaction becomes more important. In this context, the use of time-dependent modeling tools is preferred. As the complexity of the system becomes higher, modeling and simulation of such systems provides significant information. Estimating the system behavior by experimental methods when the facilities involved are large is always not feasible. Moreover, the experimental approach is expensive, time-consuming, and might have significant uncertainties. An accurate model can be developed to predict the system’s dynamic reaction, and to assess the subsequent control strategies as presented by Alguacil et al. [154]. Numerous studies have been performed to describe the transient behavior of the DSG PTSC systems. These studies can be categorized in terms of characterizing start-up or shut-down of daily operation of DSG systems, prediction of the thermal instabilities, and control strategies of DSG facilities. A number of these numerical models were principally developed based on energy balance [138,155] or mass, momentum and energy balances [141,156–158]. Lumped-capacitance model [159], quasi-steady dynamic models [160] were developed in the remaining studies. A transient 2-D energy equation was used by Heidemann et al. [138]. It was shown that the temperature field is extremely asymmetric 152

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4. CFD analysis

concepts. It was inferred that the revised simulation program (models for the dynamic and steady behavior of DSG were developed and implemented in [155]) can be used for the controller design and the assessment of different operation modes. More details can be found in the study of Eck et al. [142]. Hirsch et al. [162] developed a two-phase model of a recirculation DSG loop in Modelica combined with the Dymola simulation tool which enabled the numerical integration of the compiled DSG plant. The effects of simultaneous solar disturbance on the overall collector field and the local disturbances like small cloud shading were simulated, and the impact of the recirculation flow rate on the system dynamics was analyzed. Hirsch and Eck [166] also simulated the start-up procedure of the DSG solar field using Modelica. Using the simulation model, estimation of the time consumption during the start-up procedure was performed, and a control layer was built for improving the start-up strategy. In the later work of Eck and Hirsch [161], the dynamic behavior of the recirculation DSG loop was investigated using the previous simulation tool [162]. To understand the control mechanism of the loop, different feed water control systems, liquid level control of the buffer tank, and steam temperature control by an injection cooler were evaluated, and the reaction of the controlled loop was simulated under the variety of conditions. The feed-forward control was shown to have high potential in reducing the necessary buffer size. On the other hand, different modeling tools like Modelica [161,162,166], RELAP [167], ATHLET [168], and TRNSYS [169] have been considered for the dynamic simulation of the DSG systems. The Modelica library “DissDyn” was developed by Hirsch [170] and combined with Dymola [171]. Dymola is a physical modeling and simulation tool which uses the Modelica models as basis. The detail of the physical models considered in DissDyn is given in [168]. RELAP [172] is a commercial software package which is mainly used for the modeling of nuclear reactors. It allows for more accurate modeling and multi-dimensional flow behavior. Moya et al. [167] carried out a numerical study for the thermal-hydraulic behavior of a DSG absorber using RELAP and examined the program suitability. RELAP was subsequently evaluated to be appropriate for DSG studies in concentrating solar systems and can help to deepen understanding of the thermalhydraulic behavior of the two-phase flow in the absorber. The thermalhydraulic system code, ATHLET [173] is actually applicable for nuclear reactor designs, but capable of handling different physical operations, as well. The comparison of the physical models between DissDyn and ATHLET codes is clearly demonstrated in [168]. Although there are no specific models for solar thermal power plants in the ATHLET code, it provides interactions between the thermal-hydraulics and the control components. The obtained simulation results approve that ATHLET is applicable for thermodynamic simulations of DSG processes. The TRNSYS environment has been already used in modeling of SEGSs with different working fluids, however a multi-phase flow modeling requires a more complex treatment relative to the single-phase flow. TRNSYS has a modular structure, thus component routines, not included in the standard TRNSYS library [174], can be implemented into the program. As an example, a new quasi-dynamic approach which replies to the transient conditions of DSG evaluation, such as start-up, shutdown and cloudy transients, has been integrated in the TRNSYS environment [169]. As shown above, DSG is emerging as one of the research focus areas for PTSCs. This is probably because of the cost reduction potential the technology possesses, since it eliminates the risks associated with thermal oils such as their degradation at high temperatures and also reduces the number of heat exchangers required for the system. This technology has not been widely adopted and still some hurdles need to be overcome for commercial deployment of the technology. The dynamic reaction and controllability of the system appear to be the main challenges that are hindering the widespread use of the technology. Further modeling of the DSG phenomena, experimentation and field tests will be vital to move this technology forward.

4.1. Overview With the advances in computing technology and the increase in computing power, the use of computational fluid dynamics in modeling thermal fluid systems has grown tremendously. Computational fluid dynamics has grown to find use in a number of applications such as power generation, food processing, agro-environmental applications, concentrating power systems, heat and mass transfer applications and many others. Computational fluid dynamics (CFD) provides a means of solving the fluid problems which do not have analytical solutions. It also provided a means for simulating, analyzing and optimizing engineering designs. The advancement in the computer technology has had a great impact on the solution of fluid mechanics and heat transfer design problems. With these advances, solution to sophisticated problems with arbitrary geometries and complex physics can be obtained with ease and in a moderate period of time. Improvements in numerical algorithms have also contributed to reducing the cost of computations over the years. On the other hand, the CFD techniques provide many advantages such as obtaining details about the flow field, reproducing data during the design cycle and offer the possibility to examine practical limits of application. CFD is perceived to be fulfilling those aspects better compared with the analytical and experimental methods. Nonetheless, analysts often do experiments to complement the CFD analyses in the validation process. 4.2. Governing equations In the numerical modeling of PTSCs using computational fluid dynamics, the flow can be laminar or turbulent, and other related physics, such as radiation heat transfer, need to be considered. For PTSCs, CFD is used to investigate the thermal-hydraulic performance of the HCE or to investigate the wind flow around the entire system. In general, the CFD modeling process involves numerical solutions of the continuity and momentum, and energy balance equations. Depending on whether the flow is laminar or turbulent, additional equations need to be considered and solved. For turbulent flow, the closure problem originating from the averaging of the Navier-Stokes equations is solved using turbulence models [175]. For turbulent flow as is expected in most actual PTSCs, the general equations required are [175] Continuity equation:

∂ρ υ)=0 + ∇ ·(ρ→ ∂t

(34)

Momentum equation:

∂ → → (ρ υ ) + ∇ ·(ρ→→ υ υ ) = −∇P + ∇ ·(τ ) + ρg ∂t

(35)

→ where P is the pressure, τ is the stress tensor and ρg is the gravitational body force. The stress tensor is given by

2 T τ = μ [(∇→ υ + ∇→ υ )− ∇ ·→ υ I] 3

(36)

Energy equation:

→ ∂ (ρE ) + ∇ ·(→ υ (ρE + p)) = ∇ ·(keff ∇T − ∑ hj Jj + (τeff → υ )) + Sh ∂t j

(37)

where keff represents the effective thermal conductivity (k + kt, with kt the turbulent thermal conductivity which depends on the turbulence → model), and Jj is the diffusion flux of species J. The first three terms on the right-hand side of Eq. (37) are for energy transfer due to conduction, species diffusion, and viscous dissipation, respectively, and Sh contains all the volumetric heat sources. The sensible enthalpy in Eq. (37) is given as 153

FVM

FVM

DSMC/FDM

MCRT/FVM

FVM

MCRT/FVM

Patil et al. [187]

Patil et al. [197]

Tang et al. [198]

Internal flow Cheng et al. [199]

Sahoo et al. [200]

He et al. [180]

FEM

Eck et al. [194]

DSMC/FDM

FDM

Heat loss, and annulus flow Kassem [193]

Roesle et al. [196]

FVM

Tripathy et al. [192]

MCRT/FEM

MCRT/FVM & FEM

Akbarimoosavi and Yaghoubi [191]

Roesle et al. [195]

FEM

MCRT/FEM

Method of solution

Yaghoubi and Akbarimoosavi [190]

Structural analysis Shuai et al. [189]

Reference

Table 4 Summary of CFD analyses for conventional PTSC.

154 3-D steady-state, standard k–ε turbulence model

3-D steady-state, laminar model

3-D steady-state, standard k–ε turbulence model

3-D steady-state

2-D steady-state laminar model, S2S radiation model

2-D steady-state laminar model

2-D and 3-D steady-state

2-D steady-state

3-D steady-state

2-D steady-state, laminar model

3-D steady-state, standard k–ε turbulence model, DO radiation model

3-D steady-state

3-D steady-state

3-D steady-state

Model properties

MCRT-code/Fluent

Fluent

MCRT-code/Fluent

In-house code

Fluent

Fluent

DS2V, DS3V/In-house code

MCRT-code/Ansys CFX

Ansys

In-house code

Ansys Fluent

SolTrace/Ansys Workbench

Ansys

MCRT-code/Ansys

Tool

(continued on next page)

At higher mass flow rates, increasing heat transfer results in high thermal energy potential at the absorber outlet. The outlet temperature decreases as more convection losses occur at high wind speeds. The circumferential temperature gradient is almost uniform for a copper absorber relative to a steel one.

Larger Reynolds number (Re) represents larger heat absorption capability and lower heat loss when other parameters remain the same. The smaller the emissivity of the absorber surface is, the higher the collector efficiency can be obtained.

The gas pressure in annulus less than 0.1 Pa has any contribution on the heat loss. Reducing coating emissivity and envelope diameter have positive effect on heat loss reduction.

The critical RR is lower for bigger absorber diameters. The critical RR for a particular HCE is independent of the HCE temperature and external wind velocity. In a non-evacuated HCE, the comparison of the heat losses in nonuniform and uniform temperature cases differs only by 1.5%. In an evacuated HCE, wind velocity and RR have insignificant effects on the heat losses.

As the nonuniformity in the temperature distribution of the HCE increases, the heat loss decreases. As the hour angle increases, heat loss increases as well. The rate of heat loss progressively decreases as the radius ratio, RR (ratio of the inner radius of the envelope to the outer radius of the absorber) decreases, and it reaches a minimum for RR = 1.375 where the heat transfer only by conduction and convection just begins after this critical value.

At pressures below 5 Pa, the DSMC (direct simulation Monte Carlo) simulations yield higher conduction heat loss predictions than the continuum simulations. The DSMC simulations are more accurate, since the slip flow model is generally accurate for Knudsen (Kn) < 0.1 (pressure higher than 3 Pa). For the very low pressures investigated, the slip flow model is somewhat outside its expected range of validity.

Although the conduction heat loss is small compared to the incident solar heat gain, the heat loss generated can be significant when the entire collector field is considered.

The profile distinction of the heat flux has a significant influence on the determination of the maximum circumferential HCE temperature.

The influence of the eccentricity upon the local Nusselt number is directly indicated by the decrease of the maximum values of the local Nusselt number as the magnitude of eccentricity is increased. The heat flow from the absorber to the envelope is reduced by increasing the eccentricity.

Absorber material type has negligible effect on the heat transfer to the HTF. Bimetallic (Cu-Fe) and tetralayered laminate (Cu-Al-SiC-Fe) materials result in a reduction in the maximum deflection by 7–15% and 45–49%, respectively as compared to steel.

Lowering the HTF velocity increases the deflection. While increasing the Concentration ratio (C) increases the temperature gradient on the peripheral surface, increasing the thermal conductivity of the absorber reduces it.

Lowering the convection coefficient of the HTF increases the elongation of the absorber, and the risk of envelope failure. To minimize the deformation risk in the focal point, the convection coefficient must be increased.

The temperature gradients for the stainless steel and SiC absorbers are much higher than those of the aluminum and copper absorbers. The steel absorber has the highest maximum effective stress whereas the copper absorber has the lowest. The temperature gradient for the concentric HCE, which is higher than that of the eccentric HCE, can lead to higher thermal stresses.

Remarks

İ.H. Yılmaz, A. Mwesigye

Applied Energy 225 (2018) 135–174

FVM

MCRT/FVM

FVM

MCRT/FEM

MCRT/FEM

MCRT/FVM

Cheng et al. [206]

Tijani and Roslan [207]

Wang et al. [208]

Wang et al. [209]

Ghomrassi et al. [210]

FVM

Yaghoubi et al. [203]

Lobón et al. [205]

MCRT/FVM

Mwesigye et al. [186]

FVM

MCRT/FVM

Mwesigye et al. [64]

Lobón et al. [204]

FVM

Mwesigye et al. [202]

MCRT/FVM

FVM

Roldán et al. [201]

Wu et al. [177]

Method of solution

Reference

Table 4 (continued)

155 3-D steady-state, RNG k–ε turbulence model, DO radiation model

3-D steady-state, k–ω turbulence model, S2S radiation model

3-D steady-state, k–ω turbulence model

3-D steady-state, RNG k–ε turbulence model, S2S radiation model

3-D steady-state, standard k–ε turbulence

3-D transient, homogeneous two-phase model

3-D steady-state, homogeneous two-phase model

3-D transient, standard k–ε turbulence model, S2S radiation model

3-D steady-state, standard k–ε turbulence model

3-D steady-state, realizable k–ε turbulence model, DO radiation model

3-D steady-state, realizable k–ε turbulence model

3-D steady-state, realizable k–ε turbulence model

3-D steady-state, standard k–ε turbulence model

Model properties

SolTrace/Fluent

SolTrace/In-house code

SolTrace/In-house code

Ansys Fluent

MCRT-code/Fluent

STAR-CCM+

STAR-CCM+

MCRT-code/Fluent

Fluent

SolTrace/Ansys Fluent

SolTrace/Ansys Fluent

Ansys Fluent

Fluent

Tool

(continued on next page)

The cross-sectional temperature difference of the HTF decreases with increasing inlet velocity of the HTF but increases with rising direct beam radiation, and almost remains the same with increasing HTF inlet temperature. The displacement in the absorber is larger than that of the envelope, especially in the axial direction.

The circumferential temperature gradients on the absorber increases with increasing direct solar radiation and decreases with increasing HTF inlet temperature and velocity. The nonuniform distribution in the solar energy flux affects the circumferential temperature gradient of the HCE while having a little influence on the heat loss and thermal efficiency as compared to the uniform distribution assumption.

As the flow rate reduces, the temperature of the absorber and the outlet temperature of the HTF increase considerably. The convection heat loss across the envelope increases with induced wind speed rise. Convection heat loss constitutes the highest portion of the total heat loss.

Increasing the aperture width always increases the thermal efficiency monotonically, it increases the optical efficiency up to a certain value and then decreases greatly. There are minimum and maximum values for focal lengths beyond which both the thermal and optical efficiencies drop significantly due to the effect of the defocusing of beam radiation. Increasing the rim angle intensifies the degree of nonuniformity in the circumferential thermal properties of the absorber more and more.

An efficient multiphase model is capable of simulating the dynamics of the multiphase fluid in PTSCs under the variation of solar radiation, inlet mass water flow and outlet steam pressure.

The adopted boiling model demonstrates excellent performance without tuning with experimental data. The presented approach is valuable for the design and optimization of DSG collector.

The temperatures of the metal tube-to-bellow joint and bellows are very high and very close to the maximum temperature of the absorber. Heat loss through the bellows accounts for ∼7% of the total heat loss. The stagnation temperature of the HCE increases linearly with time.

While the heat loss from the lost vacuum HCE leads to 3–5% reduction in the collector thermal performance, it is on the level of 12–16% for bare HCE.

The presence of slope errors significantly influences the heat flux distribution on the absorber as well as the thermal and the thermodynamic performance of the HCE. The influence of the specularity error on the thermal efficiency is insignificant as it is lower than 4 mrad. While increasing the slope error reduces both the entropy generation of the HCE, its exergetic performance significantly.

As the rim angle increases, the circumferential temperature gradient reduces on the absorber surface. The reduction in the absorber's peak temperature is small as the rim angle becomes greater than 80°. The Bejan number, which is a measure of which irreversibility between heat transfer and fluid friction irreversibility is dominant, increases with reducing the rim angle and HTF temperature and increasing the concentration ratio.

The entropy generation rate reduces with increasing inlet temperature and increases as the concentration ratio increases. There is an optimal flow rate where the entropy generation is the lowest for every combination of concentration ratio and inlet temperature.

For similar process conditions, the thermal stress produced in the absorber is higher when the HTF is steam. Higher effective direct solar radiation and steam temperature cause higher thermal gradients for similar steam mass flow rates.

With increasing concentration ratio, the heat flux distribution becomes gentler, the angle span of reducing area becomes larger and the shadow effect of absorber becomes weaker. The HTF temperature rise can be also enhanced by increasing the concentration ratio. Increasing the rim angle lowers the maximum possible heat flux. If the rim angle is small, lots of rays are reflected by the glass envelope, and the temperature rise becomes much lower.

Remarks

İ.H. Yılmaz, A. Mwesigye

Applied Energy 225 (2018) 135–174

Method of solution

FVM

FEM

FVM

FVM

MCRT/FVM

MCRT/FVM

FVM

FVM

CFD & HT code

CFD & HT code

FEM

FEM

Reference

Habib et al. [211]

Tzivanidis et al. [94]

Zheng et al. [212]

Li et al. [213]

Qiu et al. [214]

Agagna et al. [215]

External flow over HCE Naeeni and Yaghoubi [216]

Naeeni and Yaghoubi [217]

Hachicha et al. [218]

Hachicha et al. [219,220]

Paetzold et al. [221]

Paetzold et al. [222]

Table 4 (continued)

156 3-D steady-state, SST turbulence model

3-D steady-state, SST turbulence model

3-D time-averaged steady-state, WALE model

3-D time-averaged steady-state, WALE model

2-D steady-state, RNG k–ε turbulence model

2-D steady-state, RNG k–ε turbulence model

3-D steady-state, standard k–ε turbulence model

3-D steady-state, standard k–ε turbulence model, S2S radiation model

3-D steady-state, laminar model

3-D steady-state, standard k–ε turbulence model

3-D steady-state, laminar, transitional and turbulence scheme

2-D and 3-D steady-state, standard k–ε model, DO radiation model

Model properties

Ansys CFX

Ansys CFX

Termofluids

Termofluids

Fluent

Fluent

MCRT-code/Ansys Fluent

MCRT-code/Ansys Fluent

Ansys Fluent

Fluent

Solidworks

Ansys Fluent

Tool

At the positive pitch angles, increasing the yaw angle slightly reduces the Nusselt number at the HCE surface. However, in a few cases at the negative pitch angles, the maximum Nusselt number for a given pitch is observed at high yaw angles. Increasing the yaw angle reduces the aerodynamic forces significantly.

Increasing the depth of the trough increases the maximum aerodynamic forces and pitching moment on the trough. However, a deeper trough which has a sheltering effect on the HCE conduces to reduce the thermal losses accompanied by the forced convection.

The distribution of the Nusselt number for higher wind speeds shows a similar trend to that of the lower wind speeds with higher magnitude and significant peak.

The convection around the HCE might be forced or mixed based on the pitch angle. The magnitude of the averaged Nusselt number is reduced as the pitch angle reduces. The PTSC structure stability is more affected by the wind forces for the pitch angle < 90°.

The wind flow structure around the HCE is completely different than the cross-flow around a horizontal cylinder. The flow field does not strongly depend on the wind speed and is asymmetrical with respect to the horizontal axis. When the wind velocity is high (Reynolds number > 4.5 × 105), the collector effect on the circumferential variation of the Nusselt number over the envelope is considerable.

The wind force on the collector structure and mirror increases sharply when the wind speed increases, especially for large collector angles. The pressure field on the leeward side of the collector is very low far from the region about 15–20 times of the collector aperture.

Increased tracking errors drastically lower the thermal efficiency. E.g. increasing of the tracking error from 0 to 20 mrad reduces the thermal efficiency from 70.64% to 9.41%.

The circumferential temperature gradient of the absorber is found to be within 18–60 K under typical conditions. Enlarging of the secondary flow velocity in the pseudo-critical region causes strong heat transfer enhancement relative to the high temperature region.

The variation of the Nusselt number under uniform heat flux is less than that of the nonuniform heat flux. The flow resistance increases with solar elevation angle. As Grashof number (Gr) increases, Nusselt number increases sharply with solar elevation angle but it starts to decrease slowly at higher Grashof number and lower solar elevation angles.

Under the nonuniform solar flux condition, the solar parabolic trough receiver–reactor (SPTRR) partially filled with a catalyst has better performance than that fully filled with catalyst. Catalyst filling ratio of 0.4 is recommended to improve the chemical energy conversion per unit pumping power relative to that of the fully catalyst-filled SPTRR. The conversion efficiency increases stably with increasing flow rate.

The convection heat transfer coefficient of the HTF is fully dependent on its inlet temperature. Greater incident angles produce higher end losses which affect the efficiency unfavorably.

The 3-D model is more accurate than the 2-D model. Use of a short domain of fixed length would undoubtedly reduce the required meshing time for long HCEs.

Increasing the metallic thickness improves the thermal performance up to a critical level beyond which the heat losses become higher. Increasing the absorber thickness allows to dispose of concentrated heat flux in the lower part of the HCE.

Remarks

İ.H. Yılmaz, A. Mwesigye

Applied Energy 225 (2018) 135–174

FDM

Iteration

Thermal resistance network FVM

Porous HCE with a partially insulated envelope

Absorber with two externally attached longitudinal fins

Double wall vacuum shell

Half-insulated filled-air HCE

Grald and Kuehn [225]

Hegazy [226]

Daniel et al. [227]

Al-Ansary and Zeitoun [188]

157 FVM MCRT/FVM

Cylindrical air-based cavity-HCE

Air-based tubular cavity-HCE: smooth or V-corrugated tube wall, and single or double glazed aperture window

Air-based HCE with an array of helically coiled absorbers contained side-by-side within an insulated groove having a rectangular windowed opening

Absorber with a linear array of water tubes attached to an absorber plate

V-cavity absorber with rectangular fins

Bader et al. [229]

Bader et al. [230]

Good et al. [231]

Kajavali et al. [232]

Xiao et al. [233]

3-D steady-state energy model

MCRT/FVM

3-D steady-state, laminar model

3-D steady-state, laminar model

2-D steady-state energy model

2-D steady-state energy model

2-D steady-state energy model

MCRT-code/Fluent

Ansys Fluent

In-house code

In-house code

In-house code

In-house code

In-house code

In-house code

1-D steady-state

2-D steady-state, laminar model

In-house code

In-house code

In-house code

Tool

1-D steady-state approach

1-D steady-state and transient approach

1-D steady-state approach

Model properties

MCRT/FVM

MCRT/FVM

Cylindrical air-based cavity-HCE

Bader et al. [228]

MCRT/FDM

FDM

V-shape cavity and insulated envelope and rows of copper pipes placed in the space between the cavity and the envelope

Barra and Franceschi [224]

Method of solution

Enhancement technique

Reference

Table 5 Summary of the novel design studies.

(continued on next page)

The daily average thermal efficiency of the proposed absorber system is higher than the conventional single tube about by 58%.

The major heat losses occur at the primary mirror by absorption and spillage of sunlight, at the window by solar reflection, thermal reradiation, and natural convection, and by other loss mechanisms, including conduction trough the insulation and chimney effect.

The optical efficiency of the single-glazed configuration is higher than that of the double-glazed at normal solar radiation. Both increasing the flow rate and using a corrugated absorber lead to increased collector thermal efficiency. The benefit of the corrugations is significant at low HTF mass flow rates, but diminishes after 5 kg/s. While the single-glazed HCE configuration leads to higher collector efficiencies below about 300 °C, it is above about 400 °C for the double-glazed configuration.

One third of the incident solar radiation on the HCE is lost by spillage, and one sixth due to reflection. The HCE thermal efficiency ranges from 45% to 29% at summer solstice solar noon for the corresponding outlet temperatures of the HTF ranging from 250 to 450 °C.

The main energy losses from the incoming solar radiation are spilled and reflected at the HCE aperture but the convection outside the cavity and reradiation losses become predominant with decreasing mass flow rates.

The combined conduction and convection heat loss from the proposed HCE can be smaller than a filled-air HCE as much as 25% once the fiberglass insulation is used. However, the profit reduces with the temperature rise of the HTF due to the increasing thermal conductivity of the insulating material. As the tilt angle becomes smaller, the heat loss reduces.

The performance of the evacuated tube is superior relative to the vacuum shell and non-evacuated tubes. However, the non-evacuated tube is more sensitive to the external wind conditions compared to the vacuum shell.

The intercept factor of the PTSC is strongly dependent on the fin height/absorber diameter ratio. It increases sharply with increasing height/absorber diameter ratio up to a certain value where the curve becomes flat. The collector thermal efficiency increases with the fin height/absorber diameter ratio and falls after the optimal ratio.

Increasing the envelope diameter causes less solar radiation to strike the mirror, thus lowers the thermal efficiency. The insulation conductivity was shown to strongly influence the thermal performance. Heat loss decreased about 40% with the optimized design of the envelope.

The optimum collector efficiency shifts toward the higher flow rate values at higher inlet temperatures for the same number of rows.

Remarks

İ.H. Yılmaz, A. Mwesigye

Applied Energy 225 (2018) 135–174

Enhancement technique

HCE with configurations of RGS, RAI, aplanat and seagull

S-curved/sinusoidal absorber

Triangular cavity absorber

PTSC consisting of a symmetrical absorber with a circular secondary and a concentrator built by a primary discontinuous mirror with two symmetrical portions

PTSC with four ranked HCEs

Upper half insulated HCE

Twin glass tube

S-curved/sinusoidal absorber

Reference

Wirz et al. [65]

Demagh et al. [234]

Chen et al. [235]

Bootello et al. [236]

Ghodbane and Boumeddane [237]

Chandra et al. [238]

Fan et al. [239]

Bitam et al. [240]

Table 5 (continued)

158 MCRT/FVM

Thermal resistance network

FVM

3-D steady-state, SST k–ω turbulence model

In-house code/ Fluent

In-house code

1-D steady-state

The maximum circumferential temperature difference on the absorber tube is almost below 35 K for all the range of the mass flow rates. A maximum performance evaluation criterion (PEC) is obtained to be 135%.

The proposed HCE is suitable for low HTF inlet temperatures due to efficiency sacrifice. The efficiency loss is within the range of 4% as the inlet temperature is about 150 °C.

A maximum of 20% reduction in the overall heat transfer was obtained under the given conditions.

Ansys Fluent

3-D steady-state, standard k–ε turbulence model, S2S radiation model

The proposed optics yield increased concentration ratio at the level of 65% as compared to its counterpart conventional PTSC for the same rim angle. It delivers much more energy onto the same absorber perimeter for the higher acceptance angle.

The absorber’s optical efficiency increases as the aperture width decreases and as the depth-to-width ratio increases. The optical efficiency first increases, reaches a maximum and then decreases with increasing offset distances. The optical efficiency of the optimized absorber obtained was 89.23%.

The concentrated heat flux distribution on the S-curved absorber was found to be almost homogeneous. As the absorber tube deflection reduces, a better heat flux distribution is consequently achieved. The intercept factor of the S-curved absorber should be comparatively better than that of the plain one.

The optical efficiency was increased between 0.8% and 1.6% compared to the benchmark design using different configurations (RGS, RAI, aplanat and seagull).

The V-cavity absorber has a high optical efficiency due to repeated reflection of the sunrays thanks to triangular shape. The rectangular fins in the absorber enhance the heat transfer performance by decreasing the heat loss relative to the absorber without fins.

Remarks

The optical and thermal performances of the collector reach 83.6% and 82.8%, respectively.

Commercial software

TracePro

In-house code

In-house code

Tool

SolTrace/In-house code

1-D transient energy model

2-D model

MCRT

MCRT/FDM

2-D model

3-D model

3-D model

Model properties

MCRT

MCRT

MCRT/FVM

Method of solution

İ.H. Yılmaz, A. Mwesigye

Applied Energy 225 (2018) 135–174

Applied Energy 225 (2018) 135–174

İ.H. Yılmaz, A. Mwesigye

hj =

∫T

T

ref

cp,j dT

modeled using the surface to surface (S2S) radiation model [175] or using the discrete ordinates (DO) radiation model with the vacuum taken to be air, and the air considered as a non-participating medium [175,186]. When the annulus space is not evacuated, both radiation heat transfer and natural convection heat transfer should be considered [187,188]. The natural convection heat transfer inside the annulus space is mostly laminar where the Navier-Stokes equations and the energy equations as presented in [187,188] are used in the modeling. The radiation heat transfer is treated similarly as in the evacuated HCE.

(38)

In Eq. (38), the value of Tref is 298.15 K. The above equations can be modified according to the physics under consideration and several variances in the presentation of these equations can be noted in the literature as shown in [64,176,177]. It can also be noted that solving Eqs. (34)–(38) is not possible due to the closure problem that results from the time averaging process used to derive these equations. To address the resulting closure problem, turbulence modeling becomes inevitable. This can be accomplished using common turbulence models available in the literature. As noted in most studies, the k-ε models are the most widely used for CFD analysis of PTSCs. These models are also widely used for most flow applications. However, the model to be used should be carefully chosen depending on the physics at hand as there is no ‘one size fits all’ for turbulence modeling. In the k-ε models, two additional equations, for turbulent kinetic energy and turbulent dissipation rate are solved together with Eqs. (34)–(38). The equations depend on the type of k-ε model used, i.e. standard k-ε or realizable k-ε model or the RNG k-ε model. The realizable k-ε and the RNG k-ε models, which are the improved form of the standard k-ε, enhance the modeling of specific flow phenomena. A comprehensive presentation of these models is presented the Ansys Fluent® theory guide [175]. To accurately predict the performance of the PTSC during a CFD analysis, actual boundary conditions ought to be used. The crucial one among these boundary conditions is the heat flux on the HCE’s absorber tube which is usually the main thermal boundary condition in the analysis. A number of studies have assumed uniform heat flux profiles on the absorber tube, concentrated heat flux on the lower half, and direct solar flux on the upper half such as [176,178,179]. Precise results of a HCE thermal analysis are obtained when the actual heat flux profile i.e., nonuniform heat flux profile around the absorber tube circumference is used. As such, many studies recommend the coupling of CFD analysis with a MCRT procedure [50,180–184]. Other studies on the determination of heat flux distribution were presented in Section 3.2.1, while studies on ray tracing in PTSCs were presented in Section 3.1.2. The heat transfer mechanisms in the annulus space are modeled depending on the annulus condition. When evacuated, as is the case in commercial HCEs [8,185], only radiation heat transfer between the absorber tube and the glass envelope is considered. This can be

Wall detached twisted tape

Wavy tape

4.3. Related studies The use of CFD in the analysis of PTSC systems is mainly to investigate the thermal-hydraulic performance for the HCE or to determine the flow field and wind loads around the collector itself. This section summarizes the studies where using CFD presents a better insight in the analysis of the PTSCs’ physics. The details of the studies performed with CFD are summarized in Table 4. First, the studies that investigated the structural analysis are reviewed. Second, the studies involving the heat loss and the annulus flow characteristics of HCEs are presented. Third, the internal flow analyses found in the literature are shown. Fourth, the external flow analyses revealed in the literature were considered. The other significant application of CFD in PTSCs is the investigation of different heat transfer enhancement techniques which will be presented in detail in Section 5.

5. Performance enhancement techniques Improving the performance of PTSC systems is one way of ensuring reduced system cost, improved overall system efficiency, minimized HCE temperature gradient, and subsequently improved system reliability. Because of these benefits, many researchers have considered a number of heat transfer enhancement techniques to improve the thermal performance of PTSCs. The performance of a PTSC can be enhanced by either changing its optical design or HCE properties, including augmentation techniques [223]. In recent years, thermal enhancement in the HCE properties has been widely considered by many researchers rather than the optical design. In this section, all the efforts found in literature, including both the optical and the thermal improvements are presented.

Unilateral longitudinal vortexes

Dimpled absorber

Helical screw-tape

Outward corrugated absorber

Fig. 19. Schematic representation of typical inserts. 159

FVM

FVM

FVM

Porous fins

Porous square, triangular, trapezoidal and circular inserts

Porous disc

Porous disc

Helical fin

Reddy et al. [179]

Reddy and Satyanarayana [241]

Kumar and Reddy [176]

Kumar and Reddy [242]

Muñoz and Abánades [178]

160 FVM

FVM

Unilateral longitudinal vortexes

Closed-end solid plug

Closed-end solid plug

Longitudinal externally fin

Wall detached twisted tape

Cheng et al. [243]

Islam et al. [244]

Islam et al. [245]

Mwesigye et al. [246]

Mwesigye et al. [247]

FVM

FVM

MCRT/FVM

Closed-end solid plug

Cheng et al. [184]

MCRT/FVM

FVM

FVM

Iteration

Absorber with two externally attached longitudinal fins

Hegazy [226]

Method of solution

Enhancement technique

Reference

Table 6 Summary of the passive heat transfer enhancement studies.

3-D steady-state, realizable k–ε turbulence model

3-D steady-state, realizable k–ε turbulence model, DO radiation model

3-D steady-state, RNG k–ε turbulence model

3-D steady-state, RNG k–ε turbulence model

3-D steady-state, realizable k–ε turbulence model, DO radiation model

3-D steady-state, standard k–ε turbulence model, S2S radiation model

3-D steady-state, RNG k–ε turbulence model

3-D steady-state, RNG k–ε turbulence model

3-D steady-state, RNG k–ε turbulence model

3-D steady-state, RNG k–ε turbulence model

3-D steady-state, RNG k–ε turbulence model

1-D steady-state approach

Model properties

Ansys Fluent

Ansys Fluent

Ansys Fluent

(continued on next page)

The heat transfer performance increases with reducing twist ratio and increasing Reynolds number and width ratio. The thermal enhancement factor is higher at both the smallest twist ratio and the largest width ratio for the range of Reynolds number considered.

Inserting external fins on the absorber improves the thermal efficiency by 8%. The longer the fin, the more is the heat gain, and the higher is the thermal efficiency but also the higher heat losses due to increased glass temperatures and the absorber tube’s peak temperature.

Even if the absorber tube thickness is reasonably thin (2-mm thick), the thermal conductivity of the absorber may have no significant effect on the temperature uniformity of the absorber tube.

Little or almost no HTF circulation with high velocity is attributed for little temperature change at the upper part of the absorber, which might be improved by applying swirl generation. Uniformity of the heat flux will improve the overall thermal performance of the PTSC.

The thermal loss of the proposed HCEs reduces by 1.35–12.10%, 2.23–13.62%, and 0.11–13.39% compared to that of the plain HCE along with the increase of the Reynolds number, HTF inlet temperature, and incident solar radiation, respectively within the range studied. Both the Nusselt number and the friction coefficient increase as each geometric parameter increases.

MCRT-code/Fluent

Ansys Fluent

Therminol VP-1 and Syltherm 800 have better heat transfer performance and lower pressure drop than that of Nitrate Salt and Hitec XL. Among four typical residual gas conditions, the vacuum results in the best HCE performance, followed by argon, air, and hydrogen, respectively.

A helically finned absorber tube has lower temperature gradients compared to the plain tube and involves less mechanical stress as a consequence. It results in 40% increase of parasitic losses corresponding to 3% improvement in the collector efficiency.

As the porosity and inclination decrease, the Nusselt number and the pressure drop increase for both water and thermal oil. While increasing the pitch reduces the Nusselt number and pressure drop, increasing the height and thickness increase both the former.

While lowering the disc angle and the space between the discs both increase the Nusselt number, lowering the height of the disc has a negative impact on the Nusselt number.

The heat loss from the HCE was found to be approximately the same in all porous configurations.

The porous fins improve the HCE overall performance compared to the solid longitudinal fin. Increasing the aspect ratio and fin thickness enhances the heat transfer coefficient in the absorber, but the rise of pressure drop is a penalty for both cases.

The intercept factor of the PTSC is strongly dependent on the fin height/absorber diameter ratio. It increases sharply with increasing height/absorber diameter ratio up to a certain value where the curve becomes flat. The collector efficiency increases with the fin height/absorber diameter ratio and falls after the optimal ratio.

Remarks

MCRT-code/Fluent

Fluent

Fluent

Fluent

Fluent

Fluent

In-house code

Tool

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161

Porous two segmental rings

Porous three segmental rings

Closed-end solid plug

Perforated louvered twisted-tape

Ghasemi et al. [256]

Raj et al. [257]

Ghadirijafarbeigloo et al. [258]

Metal foam

Wang et al. [252]

Ghasemi et al. [255]

Wall detached twisted tape

Mwesigye et al. [251]

Closed-end solid plug

Perforated conical

Mwesigye et al. [250]

Sadaghiyani et al. [254]

Perforated conical

Mwesigye et al. [249]

Closed-end solid plug

Perforated plate

Mwesigye et al. [248]

Sadaghiyani et al. [253]

Enhancement technique

Reference

Table 6 (continued)

MCRT/FVM

FEM

FVM

FVM

MCRT/FVM

MCRT/FVM

MCRT/FVM

MCRT/FVM

MCRT/FVM

MCRT/FVM

MCRT/FVM

Method of solution

3-D steady-state, RNG k–ε turbulence model

3-D steady-state, standard k–ε turbulence model

3-D steady-state, RNG k–ε turbulence model

3-D steady-state, RNG k–ε turbulence model

3-D steady-state, standard k–ε turbulence model

3-D steady-state, standard k–ε turbulence model

3-D steady-state, standard k–ε turbulence model

3-D steady-state, realizable k–ε turbulence model

3-D steady-state, realizable k–ε turbulence model, DO radiation model

3-D steady-state, realizable k–ε turbulence model

3-D steady-state, realizable k–ε turbulence model, DO radiation model

Model properties

SolTrace/Ansys Fluent

Ansys CFX

Fluent

Fluent

In-house code

In-house code

MCRT-code/Fluent

(continued on next page)

For a typical twisted-tape, the maximum increase in the Nusselt number and friction coefficient are obtained as 150% and 210%, respectively. The thermal performance of the perforated louvered twisted-tape is 26% higher than the typical twisted-tape.

The presence of the cylindrical insertion in the HCE provides higher outlet temperature and lower thermal stresses compared to the no-insertion condition.

Decreasing the inner diameter of the porous three segmental rings enhances the Nusselt number along with increasing pressure loss and lowering of the thermal performance.

While reducing the distance between two segmental rings enhances the Nusselt number, increasing the inner diameter of the segments degrades the Nusselt number.

Increasing the plug diameter impresses the natural convection to be predominated by the mixed convection. Increasing the tube thermal conductivity raises the nondimensional outflow temperature but it becomes nearly constant at higher conductivities. The Nusselt number becomes minimum where the ratio of plug diameter to absorber inner diameter is equal to 0.6.

The outlet temperature for the central plugs is minimum at 40 mm plug diameter but it increases afterward. The maximum outlet temperature and efficiency are obtained where the non-dimensional displacement from the tube center equals to +0.5. Dowtherm-j yields better performance characteristics than Syltherm 800 and Dowtherm-rd as the plug diameter passes over 45 mm.

While the optimum thermo-hydraulic performance is obtained at the dimensionless height = 0.25 (bottom layout), the optimum thermal performance is obtained at the height = 0.75 (top layout). The maximum circumferential temperature gradient decreases by about 45% at the optimum thermal performance. The influence of the height on the thermal performance is greater than the porosity.

Both the heat transfer and fluid friction performances increase as the twist ratio reduces and the width ratio increases. Considerable reduction in the entropy generation is obtained at low Reynolds numbers. The optimal Reynolds number increases with increasing twist ratio and reduced width ratios. The heat transfer performance and thermal efficiency can be increased up to 169% and 10%, respectively and the circumferential temperature gradient can be reduced 68% relative to the plain absorber.

Using the perforated conical inserts, the heat transfer performance increases in the range of 5–124% at the expense of increasing the fluid friction 1.36–69.0 times as compared to the plain absorber tube. The thermal enhancement factor increases in the range of 0.53–1.14. The entropy generation rate can be reduced by up to 45% compared to the plain absorber as the flow rate is lower than 0.0121 m3/s.

SolTrace/Ansys Fluent

SolTrace/Ansys Fluent

Increasing the insert size, cone angle, and reducing the insert spacing improved the heat transfer performance at the expense of increasing the fluid friction. Using the perforated conical inserts increases the thermal efficiency in the range of 3–8% within the provided range.

The Nusselt and friction factor are strongly dependent on the spacing and the size of the insert as well as the Reynolds number. The modified thermal efficiency of the HCE increases 1.2–8% in case of using the perforated plate inserts within the provided range. Increasing the plate diameter or reducing spacing gave higher entropy generation rates.

SolTrace/Ansys Fluent

SolTrace/Ansys Fluent

Remarks

Tool

İ.H. Yılmaz, A. Mwesigye

Applied Energy 225 (2018) 135–174

FVM

MCRT/FVM

FEM

Triangle, inverted triangle and semi-circular inserts

Dimples, protrusions and helical fins

Elliptical absorber tube

Wire-coils

Symmetric outward convex corrugated geometry

Asymmetric outward convex corrugated geometry

Converging-diverging internal surface (in sinusoidal shape)

Porous insert

Dimple

Porous ring

Lower-half pin fin

Internal longitudinal fin

Natarajan et al. [260]

Huang et al. [261]

Jebasingh and Herbert [262]

Diwan and Soni [263]

Fuqiang et al. [264]

Fuqiang et al. [265]

162

Bellos et al. [266]

Zheng et al. [267]

Huang et al. [268]

Ghasemi and Ranjbar [269]

Gong et al. [183]

Bellos et al. [270]

FVM

FVM

FEM

MCRT/FEM & FVM

MCRT/FEM & FVM

FEM

FEM

FVM

FEM

MCRT/FVM

Helical screw-tape

Song et al. [259]

Method of solution

Enhancement technique

Reference

Table 6 (continued)

3-D steady-state, turbulence scheme

3-D steady-state, standard k–ε turbulence model

3-D steady-state, RNG k–ε turbulence model

3-D steady-state, realizable k–ε turbulence model

3-D steady-state, standard k–ε turbulence model

3-D steady-state, turbulence scheme

3-D steady-state, standard k–ε turbulence model, S2S radiation model

3-D steady-state, standard k–ε turbulence model, S2S radiation model

3-D steady-state, k–ε turbulence model

3-D steady-state and transient, k–ε turbulence model

3-D steady-state, realizable k–ε turbulence model

3-D steady-state, SST k–ω turbulence model

3-D steady-state, SST k–ω turbulence model, DO radiation model

Model properties

Solidworks

MCRT-code/Ansys Fluent

Fluent

Ansys Fluent

Fluent

Solidworks

(continued on next page)

Fins with 10 mm length lead to higher exergetic efficiency. Helium is the most efficient working fluid exergetically relative to air and carbon dioxide.

The effect of the increasing number of pin fins on the Nusselt number and pressure drop was shown to be nearly insignificant. The overall heat transfer performance factor can be increased up to 12%.

Decreasing the distance between porous rings increases the heat transfer performance. Increasing the inner diameter of the porous rings decreases the Nusselt number. The heat transfer enhancement with porous rings is much higher compared to that of solid and porous fins, and segmental ring structures.

The average friction factor and Nusselt number in the dimpled HCE under nonuniform heat flux is lower than those under uniform heat flux. As the dimple depth increases, the heat transfer performance is improved up to a dimple depth of 7 mm after that it begins to decrease. The performance can be increased by 21% relative to the plain HCE.

The thermal performance of the porous configuration obtained by genetic algorithm is much higher than those of fully and partially filled porous inserts.

The absorber tube with the wavy insert gives a 4.55% mean efficiency improvement compared to the plain geometry. Enhancing the energetic and exergetic efficiencies is greater for the higher fluid temperature levels.

The use of asymmetric outward convex corrugated design was shown to enhance the heat transfer performance, consequently lowering the thermal deformations better than the symmetric design [264].

Introduction of the symmetric outward convex corrugated design can effectively enhance the heat transfer performance up to 8.4% with the sacrifice of pressure drop and also decrease the thermal deformations up to 13.1% in the HCE.

MCRT-code/Ansys Fluent MCRT-code/Ansys Fluent

Inserting the wire-coils can intensify the Nusselt number as much as 330% at the expense of increasing the pressure drop.

The use of an elliptical absorber tube increases the efficiency and the pressure loss of the HCE by about 9.7% and 24.9% compared to the circular absorber. Its service life is longer due to reduced thermal stresses on the elliptical absorber.

The HCE with dimples has superior heat transfer performance compared with the HCEs with protrusions or helical fins. The dimples with deeper depth, narrower pitch and at increasing numbers in the circumferential direction are useful for enhancing the heat transfer performance while the dimple arrangements have no obvious influence.

No appreciable changes in the outlet temperature are obtained between the plain and the triangle, inverted triangle and semi-circular insertions. The triangular insertion involves lower thermal stresses compared with the other types. The pressure drop is the highest in the semi-circular insertion.

The transverse angle of the incident radiation affects the heat flux distribution more greatly than the longitudinal angle. The helical screw-tape inserts greatly reduce the maximum temperature and the temperature gradient on the HCE. It loses much less heat than the plain HCE, especially at lower flow rates. As the flow rate increases 6-fold, the pressure loss increases 4 and 23 folds in the plain and the helical screw-tape absorbers, respectively.

Remarks

COMSOL Multiphysics

MSC Nastran

Ansys Fluent

Ansys CFX

MCRT-code/Ansys Fluent

Tool

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163

The global-average Nusselt number is enhanced by 261–310%, and the heat loss can be reduced by 17.5–33.1% depending on the operating condition. The insert results in a PEC greater than 2.11. Ansys Fluent

FEM Internal longitudinal fin

Wavy tape

Bellos et al. [272]

Zhu et al. [273]

FVM

FEM Internal longitudinal fin Bellos et al. [271]

3-D steady-state, realizable k–ε turbulence model

The absorber with 10 mm fin length and 2 mm fin thickness is the optimum case based on the criteria of thermal efficiency enhancement at the expense of increasing friction factor. Solidworks

Method of solution

Another way to improve the thermal performance of PTSCs is modifying and improving the thermophysical properties of the HTF used. Enhancing the heat transfer efficiency of the HCE is a primary

Enhancement technique

5.3. Nanoparticle laden fluid flow

Reference

Table 6 (continued)

Model properties

Tool

Convective heat transfer enhancement in the HCE’s absorber tube has received considerable attention due to the associated benefits. It has been shown in a number of studies that heat transfer enhancement on the HCE improves overall performance, reduces the absorber tube temperatures and temperature gradients. Despite these benefits, there are a number of drawbacks such as increasing parasitic loads associated with the increased pressure loss, vibration, and adding extra manufacturing cost. This section deals with the improvement in the performance indicators of the absorber tube by modifying its design, or its configuration by placing insertion or fin. Fig. 19 exhibits some examples of the inserts used in PTSCs in the literature. A great number of studies by different researchers are presented under this section as shown in Table 6. As shown in the summary above, several researchers have investigated the use of passive heat transfer enhancement techniques in the absorber of a PTSC. As shown, some studies focused on the variation of the absorber tube design while the others considered the use of inserts in a plain absorber tube. It can be easily seen that most studies available in the literature were performed numerically and their application to actual PTSC systems still needs to be demonstrated experimentally or using field tests. Some of the studies have used the experimental results of the inserts for heat transfer enhancement in ordinary horizontal tubes available in the literature for validation purposes, such as the use of wall detached twisted tape inserts, porous ring inserts, and helical screw tape inserts [274–279]. Although the passive techniques improve the thermal performance of the PTSCs, there is need to prove the applicability of these techniques in the field, even if a few studies are available [262,280–282]. Besides, these techniques have pressure loss penalty which should be optimized based on the insert configuration in order to achieve significant improvements in the performance of the PTSC as in [283]. Nonetheless, these studies have demonstrated that there is potential for improving the performance of PTSCs with heat transfer enhancement using passive techniques. The potential improvement in the thermal efficiencies, the reduction in the absorber tube temperature gradients and improvements in the thermodynamic performance are demonstrated to be significant for some of the considered enhancement techniques.

3-D steady-state, turbulence scheme

5.2. Passive heat transfer improvement

Solidworks

Remarks

In order to increase the performance of PTSCs, different novel designs have been implemented as summarized in Table 5. The novel design studies have been especially focused on either increasing the optical efficiency to capture most of the absorbed radiation (reducing the spillage) or decreasing the heat loss from the HCE by partially insulating the HCE. Although most studies are theoretical, there are several experimentally validated studies on the subject [224,228–233]. In order to increase the absorbed radiation, different cavities with different shapes, including V-shaped, cylindrical, triangular were proposed. These cavities have positive effects on the optical efficiency, but the thermal efficiencies of these new HCEs need to be enhanced. On the other hand, the overall heat loss for filled-air HCEs was reduced by at least 20% [188,225,238] using partial insulation. If this idea is realized on evacuated HCEs, the results will seem to be satisfactory, but the technical feasibility should be considered in detail. The novel design concept needs to be matured, and its contribution to the performance requires to be proven with further studies and probably field testing.

3-D steady-state, turbulence scheme

5.1. Novel designs

The effect of the fin length on the thermal enhancement index is more intense than the fin thickness. The optimum case is found to be for the fin properties with 20 mm in length and 4 mm in thickness.

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correlations proposed to calculate the thermophysical properties density, specific heat capacity, viscosity, and thermal conductivity - for any nanoparticle and fluid pair. These correlations are general ones that can be used for the estimation of the thermophysical properties of any nanofluid since they have few parameters, such as particle volume concentration, being easily determined. In nanofluid related studies of PTSCs, some of these correlations have been used extensively for the estimation of specific heat [286,287], the viscosity [288,293], and thermal conductivity [297–299,302,303]. There is however need for the experimental determination of thermal physical properties with nanoparticles dispersed in commonly used HTFs, especially at higher temperatures and

restriction with conventional HTFs (such as water, oil, molten salt) due to their inherently low thermal conductivities. The thermal conductivities of metallic particles, metallic oxides and carbon nanotubes are extraordinarily higher than those of the conventional fluids available and dispersing a very small amount of guest colloidal particles i.e., nanoparticle (with average sizes < 100 nm) in the conventional HTFs can have significant impacts on the optical [284] and thermophysical properties of the host fluid [285]. Precise prediction of the thermophysical properties of the synthesized nanofluids is essential to ensure acceptable results in modeling and simulation studies. There are various theoretical models in the literature that can be used for this purpose. Table 7 illustrates the Table 7 Theoretical prediction of thermophysical properties of nanofluids. Correlation

Properties

Density ρnf = ρf (1−φ) + ρp φ

Homogenous, thermodynamically stable-state

Specific heat Pak and Cho model [286]: cp,nf = cp,f (1−φ) + cp,p φ Xuan and Roetzel model [287]: cp,nf =

Effective specific heat approach Based on the heat capacity concept

ρf cp,f (1 − φ) + ρp cp,p φ ρnf

Dynamic viscosity Einstein [288]: μnf = μf (1 + ηφ) Brinkman [289]: μnf = μf (1−φ)−η −ηφm

φ Krieger and Dougherty [290]: μnf = μf ⎡1− ⎤ where φm is the maximum particle packing factor which ⎣ φm ⎦ varies 0.495–0.54 under quiescent conditions and is approximately 0.605 at high shear rates.

For highly concentrated suspensions with uniform solid spheres

1

Frankel and Acrivos [291]: μnf =

9 μ 8 f

⎡ ⎛ φ ⎞3 ⎤ ⎢ ⎜φ ⎟ ⎥ ⎢ ⎝ m⎠ ⎥ 1⎥ ⎢ 3 ⎢ 1 − ⎛⎜ φ ⎞⎟ ⎥ φm ⎠ ⎝ ⎣ ⎦

Taylor series expansion of φ for suspension of spheres

25

Lundgren [292]: μnf = μf ⎡1 + 2.5φ + φ2 + f (φ3)⎤ 4 ⎦ ⎣ Batchelor [293]: μnf = μf (1 + 2.5φ + 6.2φ2)

Including the effect of the Brownian motion, applicable to the isotropic suspension of rigid and spherical particles A generalized form of the Frankel and Acrivos model [291] including the particle radius and inter-particle spacing

⎡ ⎞⎤ ⎛ ⎢ ⎟⎥ ⎜ 1 ⎥ Graham [294]: μnf = μf ⎢1 + 2.5φ + 4.5 2⎟ ⎜ h ⎢ ⎛ ⎞ ⎛2 + h ⎞ ⎛1 + h ⎞ ⎥ ⎜ ⎜ d ⎟⎜ d ⎟⎜ d ⎟ ⎟ ⎥ ⎢ p ⎠⎝ p⎠ ⎠ ⎝ ⎝ p ⎠⎝ ⎣ ⎦ Kitano et al. [295]: μnf =

μf 2 φ ⎞⎤ ⎡ ⎛ ⎢1 − ⎜ φ ⎟ ⎥ ⎝ m ⎠⎦ ⎣

Calculating the viscosity of a two-phase mixture

Based on the intermolecular and intramolecular interactions between particles

Avsec and Oblac [296]: Ward model: μnf = μf [1 + (ηφ) + (ηφ)2 + (ηφ)3 + (ηφ) 4⋯] Renewed Ward model: μnf = μf [1 + (ηφe ) + (ηφe )2 + (ηφe )3 + (ηφe ) 4⋯] where φe = φ (1 +

Applicable to φ ⩽ 2% linearly viscous fluid having dilute, suspended, and spherical particles Modified Einstein’s model [288], applicable to high particle concentrations up to φ ⩽ 4% Randomly monodispersed spherical particles

h 3 ) r

Thermal conductivity Maxwell [297]: knf = kf

For spherical particles and φ < 1%

kp + 2kf + 2φ (kp − kf ) kp + 2kf − φ (kp − kf )

Bruggeman [298]: knf = (3φ−1) kp + [3(1−φ)−1] kf +

For a binary mixture of homogeneous spherical inclusions. No limitation on the concentration of inclusions

Δ

where Δ = (3φ−1)2kp2 + [3(1−φ)−1]2 k f2 + 2[2 + 9φ (1−φ)] kp kf Hamilton and Crosser [299]: knf = kf Jeffrey [300]: knf = kf [1 +

3(α − 1) φ α+2

kp + (n − 1) kf − (n − 1) φ (kf − kp) kp + (n + 1) kf + φ (kf − kp)

where n =

Introducing an empirical shape factor to account for different particles shapes Modified Maxwell’s model [297] and applied to spherical inclusions

3 ψ

+ O (φ2)]

where α = kf / kp Davis [301]: knf = kf ⎡1 + ⎣ Xuan et al. [302]: knf = kf

3(α − 1) [φ [α + 2 − (α − 1) φ]

kp + 2kf + 2φ (kp − kf ) kp + 2kf − φ (kp − kf )

Renovated Maxell [303]: knf = kf

Updated Jeffery’s model [300] by adding the ensembleaveraged dipole strength of a single fixed sphere and a decaying temperature field Considering the Brownian motion and the aggregation process of the nanoparticles

+ f (α ) φ2 + O (φ3)]⎤ ⎦ +

ρp φcp 2

kB T 3πrc μf

Including the effect of solid-like nanolayer between the nanoparticle and the fluid when the particle diameter < 10 nm

kp + 2kf + 2(kp − kf )(1 + β )3φ kp + 2kf − (kp − kf )(1 + β )3φ

where β = h/ r

φ is the particle volume fraction; η is the intrinsic viscosity (equals to 2.5); ψ is the sphericity, the ratio of the surface area of a sphere, with a volume equal to that of the particle, to the surface area of the particle; β is the ratio of the liquid layer thickness to the particle diameter (considered to be 0.1 [304]). 164

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dispersants or surfactants can result in Newtonian fluid behavior. These justifications should be considered in modeling the nanofluid whether it behaves as Newtonian fluid in practice. When the effects of insertions and nanofluids on the heat transfer improvement are compared, it is clearly seen from the analyses that insertions are much effective than nanofluids at the expense of increasing pressure loss and manufacturing cost. The above studies have demonstrated the applicability of nanofluids in PTSCs, significant improvements in performance have been shown in most studies since the thermal conductivity of the HTF increases with the suspension of nanoparticles. However, there are still limited experimental studies [325–331] on PTSCs under actual working conditions such as high temperatures and pressures using nanofluids. The economic viability of using nanofluids would be established with such studies. Moreover, most studies rely on correlations derived for other base fluids which may or may not be applicable to thermal oils operating at high temperatures in terms of PTSCs. Therefore, there still exist opportunities for research on the use of nanofluids in PTSCs. The most pressing ones include the investigation of thermophysical properties of thermal oil-based nanofluids at high temperatures and pressures, and the use of nanofluids in actual systems working under field operating conditions.

pressures, since these studies are not widespread. Then, a comparison with the above models can provide some insight on the accuracy of such models as applied to PTSC HTFs. Some studies on thermophysical properties directly related to PTSCs are available in literature [305,306]. 5.3.1. Nanofluid in conventional PTSC As the popularity of nanofluids increases, its applications in different areas such as solar energy, heat exchanger, fuel cell, nuclear reactors, medical field have widened. The application of nanofluids in solar thermal systems is becoming prevalent. A recent review by Verma et al. [284] presents the studies on the use of nanofluids in solar thermal collectors. Recently, the nanofluid researches have also been extended to PTSCs since one of the barriers to the development of the technology is its high cost. Hence, improving performance and consequently reducing the cost of these systems will increase their deployment. The nanofluids work to capture the solar radiant energy more effectively and also lead to improved heat transfer performance in the HCE. Therefore, using nanofluids instead of conventional HTFs could be seen one of the possible ways to improve performance. Table 8 reviews the studies performed on the nanofluid usage in conventional PTSCs presents the enhancement of heat transfer and thermal efficiency by this technique. In summary, the nanofluids enhance the heat transfer performance of the HCE due to increasing extinction capability of the base fluid. Moreover, increasing the volume fraction of hosted nano particles has a positive effect on the improvement of the convection heat transfer coefficient of the HTF and reducing thermal stresses on the HCE however this will affect the stability of nanofluid leading to agglomeration and also will result in increased pumping power requirement accompanied by reducing the total collector efficiency. For this reason, the volume fraction of the nanoparticle should be optimized for effective heat transfer enhancement for the PTSC. Notably, the pressure loss can be disregarded as the particle volume fraction is lower than 2% [311]. It should also be noted that inclusion of nanoparticles may alter the rheological behavior of the resulting nanofluid. The debate on whether inclusion of nanoparticles in conventional fluids will result in Newtonian or Non-Newtonian behavior is still ongoing and discrepancies still exist in the literature [321]. Agglomeration is a major factor that leads to non-Newtonian behavior of nanofluids at low values of shear rates. Also, the method of preparing the nanofluid and use of

5.3.2. Nanofluid in DARS In contrast to the conventional PTSC, Khullar et al. [332] introduced an idea of harvesting the solar radiant energy through the use of a nanofluid-based concentrating PTSC (NCPTSC). This concept is directly similar to the conventional PTSC only the exception of the HCE in which the absorber tube being made of metallic material is replaced with a glass tube as shown in Fig. 20. Therefore, both absorber and its envelope consist of transparent glass material which makes the HCE directly interact with incident radiation, for this reason it is named as a direct absorption receiver system (DARS). Energy reaching the flowing medium in DARS can be estimated using the procedure presented in Toppin et al. [333] and Tyagi et al. [334]: In cases where the atmospheric absorption is not considered, the spectral power distribution of the sun as a radiant heat source can be approximated by Planck’s law as:

Table 8 Enhancement techniques by nanofluids. Reference

Kasaeian et al. [307] Sokhansefat et al. [308] Zadeh et al. [304] Basbous et al. [309] Mwesigye and Huan [310] Bellos et al. [266] Mwesigye et al. [311] Wang et al. [312] Kaloudis et al. [313] Ghasemi and Ranjbar [314] Mwesigye and Meyer [182] Coccia et al. [315] Ferraro et al. [316] Khakrah et al. [317] Bellos and Tzivanidis [318] Bellos et al. [319] Bellos and Tzivanidis [320] Mwesigye et al. [321] Allouhi et al. [322] Ghasemi and Ranjbar [323] Kasaiean et al. [324]

Nanofluid (nanoparticle/base fluid)

Al2O3/Synthetic oil Al2O3/Sylterm 800 Al2O3/Synthetic oil Al2O3/Syltherm 800 Al2O3/Syltherm 800 Al2O3/Synthetic oil Cu/Therminol VP-1 Al2O3/Dowtherm A Al2O3/Syltherm 800 Al2O3, CuO/Water Cu, Ag, Al2O3/Therminol VP-1 Fe2O3, SiO2, TiO2, ZnO, Al2O3, Au/Water Al2O3/Synthetic oil Al2O3/Synthetic oil Al2O3, CuO/Syltherm 800 CuO/Syltherm 800, CuO/Molten salt Al2O3, TiO2, Al2O3+ TiO2/Syltherm 800 SWCNTs/Therminol VP-1 Al2O3, CuO, TiO2/Syltherm 800 Al2O3/Therminol 66 MWCNT/Mineral oil

165

Enhancement (%) Heat transfer

Efficiency

15 14 11.1 18 76 11 32 − − 28, 35 6.4, 7.9, 3.9 − ∼24 − 35, 41 35, 12 25.7, 26.0, 116.8 234 − − 15

− − − − 8 4.25 12.5 1.2 9.6 − 13.9, 12.5, 7.2 ∼0 ∼0.1 14.3 1.13, 1.26 0.76, 0.26 0.52, 0.52, 1.31 4.4 1.46, 1.25, 1.40 ∼0.5 −

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Fig. 20. (a) Conventional HCE. (b) Nanofluid-based HCE.

Iλ (λ,T ) =

2hc02 λ5 ⎡exp ⎣

( ) hc0 λkB T

qr = −1⎤ ⎦

(39)

(40)

where K aλ is the spectral absorption coefficient and Ksλ the spectral scattering coefficient. The details of calculating the spectral coefficients can be found in [334]. The heat transfer analysis of the DARS shown in Fig. 21 can be represented under 2-D steady conditions by the energy balance equation as follows

1 ∂ ∂T ∂ (rqr ) ∂T (k r )− = ρcp U r ∂r ∂r r ∂r ∂x

(42)

Addition of nanoparticles to the host fluid significantly increases the extinction capability of the fluid resulting in an enhanced solarweighted absorption relative to that of the host fluid alone [333]. Thus, the combination of any nanoparticle and host fluid can exhibit different solar absorption capabilities by virtue of solar intensity attenuation rate within the medium. DARS with larger diameters lead to increased optical thickness and thus the distance traversed by the incident radiation through the medium. As a result, there is a large temperature nonhomogeneity within the medium (the layers near to the absorber surface will have higher temperatures than the center) since the radiation flux is not able to reach the center particularly at low solar intensity. In case the volume concentration is low, the optical efficiency suffers not able to capture the whole reflected radiation. In order to get maximum solar absorption yielded from the DARS, the volume fraction and the diameter of the DARS should be tailored properly. Table 9 reviews the studies made on the DARS and its performance indicators. The DARS differs from the conventional one as declared. Although its optical efficiency is better than the conventional one, it has much higher heat loss particularly at elevated temperatures. Thus, its usage for high temperature applications (e.g. > 250 °C) may not be feasible for efficient energy harvesting. Rather, it can be suitable for medium temperature IPH applications. Up to now, there have been only two

In this expression, λ is the wavelength in m, and T is the temperature in K, h = 6.626 × 10−34 J s is Planck’s constant, c0 = 2.9979 × 108 ms−1 is the speed of light in a vacuum, kB = 1.38 × 10−23 J K−1 is Boltzmann’s constant. The attenuation of radiation corresponds to the energy gained by the medium and can be mathematically expressed using Lambert–Beer’s law:

δ (Iλ r ) = −K eλ Iλ r = −(K aλ + Ksλ ) Iλ r δr

∫λ ∫θ Iλ dθdλ

(41)

The radiative heat flux is defined as

Fig. 21. Section view of the DARS. 166

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Table 9 Summary of studies with DARS. Reference

Nanofluid

Result

Khullar et al. [332]

Al/Therminol VP-1

Adding only 0.05% nanoparticle into the base fluid improves the thermal efficiency of the DARS between 5% and 10% relative to the conventional PTSC.

Toppin-Hector and Singh [333]

Graphene/Therminol VP-1, Al/ Therminol VP-1

Graphene has better solar absorption capability than aluminum. The DARS is able to deliver heat at 265 °C.

Ghasemi and Ahangar [335]

Cu/Water

The optical and thermal efficiencies almost level off beyond the volume concentration of 0.015%.

De Risi et al. [336]

CuO + Ni/Gas

A maximum thermal efficiency reaches 62.5% which gradually lowers beyond the mass flow rate of 2.5 kg/s.

Kasaeian et al. [337]

MWCNT, nanoslica/Ethylene glycol

MWCNT/ethylene glycol achieves about 10% higher thermal efficiency than the nanoslica/ethylene glycol nanofluid at optimum conditions. The optimum volume fraction for MWCNT and nanosilica is found to be 0.5% and 0.4%, respectively.

ceramics, i.e. metal oxide constituents of nanoparticles, are cheaper than those of pure metals and nanotubes. Practically, it is essential to lower the preparation costs of nanofluids needed to achieve high performance. Even though, increasing the particle volume concentration enhances the thermal efficiency positively at somewhat lower volume fractions, the increase in pressure drop intensifies and leads to reduction in the thermal efficiency. There are also concerns of agglomeration as the volume fractions increase. This instability can be suppressed by using surfactants and also by adding inserts in the absorber. In the latter case, the combined effect of enhancing the thermal properties and increased turbulence in the absorber gives significant improvements in performance. An insertion method which causes swirl generation and more intense turbulence can be used against this handicap to enhance the thermal efficiency further. At this stage, vibration must be tolerated against the pressure shocks due to the use of inserts. This is one of the main challenges of using inserts which may result in glass breakage. Noting that nanofluids are rather functional in single phase flows. For this reason, only passive heat transfer improvement can be applicable in DSG systems where the relative effect of flow scheme should be considered rigorously. Pumping devices for nanofluids may need special properties since their mechanical efficiency degrades with increasing of particle volume concentration. Another challenge related to the use of nanofluids is their effect on the lifespan of the system. Various nanofluids are candidates for applications where the degradation of performance should be considered well. Nanoparticles may lead to corrosion and erosion of absorber under a long-term operation. Even if nanoparticles such as Al2O3, TiO2, SiC, ZrO2 nanoparticles with water have no effect on the stainless steel, it erodes aluminum and copper based materials [341]. SiC particles lead to lowest erosion among the others. Particularly, high temperature applications with oil-based nanofluids need to be considered experimentally by researchers. It is too difficult to find well-established thermophysical models of nanofluids at temperatures higher than 100 °C. There is strictly need for experimental studies to complement the already established numerical and theoretical studies. Further experimental studies must be directed in this field since extraordinary disagreements are available in test results performed by different research groups. This may have originated from dissimilarities between structural characterization of dispersed particles and test conditions used by different researchers. The systematic approach is needed at this stage to standardize the results for better comparison. In addition, the effect of various challenges in preparation of nanofluids such as Brownian motion of particles, particle migration, additives, hybrid nanofluid synthesis are required to be clarified. Moreover, there are still limited studies on the use of nanofluids in the temperature and pressure ranges under which PTSCs operate. Thus, demonstration of actual performance of these systems with nanofluids would be a step in the right direction. The literature reveals that passive heat transfer techniques enhance the thermal efficiency up to 10% while the use of nanofluids improves it up to 9% for similar PTSCs. Increasing the concentration ratio from 88

practical applications of this collector operated at very low [338] and medium temperatures [339]. It is essential to say that the structure of this collector may have some problems in practice due to operational reliability. Most failures of HCEs are especially the breakage of the glass envelope due to the circumferential temperature gradients in the absorber tube and mechanical stresses on the HCE. For example, the limited maximum temperature difference on the LS-3 HCE is 50 K to make sure the safety in operation [252]. Recently, improved glass to metal seal designs have put into practice to reduce breakage problems. In DARS, this case should be attentively considered to maintain the reliable life span of the HCEs. Any novel findings going beyond the common knowledge in this field should be studied, and the designs, if needed, are to be innovated. 6. Discussion To increase the performance of PTSC systems, numerous techniques have been studied as presented in the preceding literature review. These techniques can be classified into two main categories: those related with the optical and those related with the thermal performance properties of these systems. The studies on improving the optical performance are relatively limited as compared to the ones on improving the thermal performance since the versatility and the availability of tools to study the thermal characteristics are extensive. There are many choices for thermal enhancement as investigated by numerous researchers; most of them have not been experimentally proven yet. The commercial availability of the proposed enhancement techniques is still in infancy stages due to the existing challenges in front of the technology. One may need to know that the overall installation cost (including manufacturing, assembly, installation equipment, and construction activities) of a commercial PTSC (the SkyTrough) is estimated to be US$170/m2 of which 13% goes to the HCE cost [340]. Mirror panel cost is twice that of the HCE. About 32% of the overall installation cost is for the support structure of mirror, and the rest is used for site equipment, transport, HCE supports, electrical cabling, pylons and foundations, torque plates, and drive system. These data give an idea about what components have highest costs. The use of inserts, modification of the absorber tube and nanofluid usage in the HCE have been shown as the main methods for improving the thermal performance of the PTSC. Unlike nanofluids, the use of inserts appears to cost effective and easier to implement in the HCE. Besides, manufacturing costs associated with the use of inserts are much less than the costs associated with preparation of nanofluids, which include both the costs of materials and the sophisticated devices required for their blending, sonication and stabilization. Presently, the production cost of nanoparticles is composed of size reduction of solid phase particles, and the subsequent synthesis of these particles into the fluidic medium. Not only are the production costs still high, also production quality (size, introduction of contaminants) is still problematic. Inexpensive production steps still need time to clear the limitations for low-cost, high-performance nanoparticles. It should be noted that 167

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a substitute for experimentation as preliminary experimentation studies are essential to validate comprehensively the developed numerical models. As such, most studies on the numerical modeling and the simulation of PTSC systems presented require extensive validations to be considered accurate enough. In some studies where different physics are considered a number of steps are undertaken in the validation of the developed models which may include the validation of the optical performance, the thermal performance, thermodynamic performance and others. From the reviewed studies, it is clear that the optical performance of the PTSC system also requires significant attention relative to the thermal performance. Ray-tracing has been shown to be a powerful tool in the optical characterization of PTSCs or in analysis of new PTSC concepts where the analytical solution is not plausible. Yet, coupling the optical and thermal analyses offers a better insight into the co-optimized design of a PTSC and its performance improvement. It is also shown that heat transfer modeling is not only useful for the enhancement of the thermal performance but also for the thermal stress analysis of the HCE. It is also clear from the literature that obtaining precise heat flux and temperature distribution profiles on the HCE’s absorber tube is paramount for both single and two-phase flows to keep track of the temperature gradients and maintain the operational safety. However, it should be noted that the flow pattern of two-phase systems is much more complex compared to the single-phase one, thus its control is difficult. These flows can be analyzed under steady-state to view the operational limits or under transient analysis to provide knowledge on the long-term performance of a PTSC. It can be said that the steadystate analysis helps mainly in the design stage whilst the transient analysis is useful especially in the simulation of the actual field conditions. The recent advances computing technology and increasing computer power has seen the adoption and widespread use of CFD tools in the analysis of PTSCs and especially HCE with complicated geometries. It seems that CFD analysis will continue to take on an ever-increasing role in analysis and design of PTSCs. CFD analysis ensures comprehension of the physical nature of the PTSC while bringing useful results about the flows with heat transfer characteristics. In the literature, CFD analysis of PTSCs is applicable in the determination of flow fields around the entire system, characterization of HCE performance, investigation of heat transfer enhancement using different absorber tube configurations and modifications and in heat transfer enhancement with nanofluids. To increase the overall performance of the PTSC, different design considerations have been proposed in the literature. The performance of the PTSC is improved by either manipulating its optical design or the thermal properties. It should not be forgotten that even a minor improvement in the performance can induce significant returns for largescale plants. All the research efforts undertaken so far are clearly presented in this paper. There are still significant research opportunities to improve the current state-of-the-art PTSC technologies that support the development of innovative concepts in the collector, HCE, and HTFs. The optical performance of new concepts could possibly be analyzed in detail for improved optical efficiency. Evacuated HCEs have relatively much air-leakage and breakage problems especially with higher temperature gradients. Improved air-filled HCEs have lower costs and higher reliability in operation hence the research studies on this subject have gained priority nowadays. The challenge of achieving uniform temperature profile on the HCE is another open research field requiring attention. New concentrator structures require reduced costs, improved optical accuracy and improved reliability. There are several studies in the literature on the structural analyses of PTSC systems, but there exist potential gaps that could be fulfilled. On the other hand, dynamic simulations of DSG solar plants could be developed for better system controllability strategies in DSG operational concepts. Heat transfer augmentation techniques such as inserting turbulators, modification of

to 113 boosts the thermal efficiency to 13.9% with heat transfer enhancement [182]. Noting that reduction in the overall thermal efficiency due to pumping work has been accounted in these results. The maximum enhancement in the thermal efficiency has been obtained using wall detached twisted tape inserts. This result can be increased additionally by 26% by changing the shape of the twisted-tape as louvered [258]. Their potential to generate swirl motion of the heat transfer fluid and cause effective mixing of the heat transfer fluid inside the absorber is the reason they give higher enhancements. In the recent past, twisted tape and wire coil inserts have been applied widely in various industries due to their cheap in manufacturing cost, easy implementation and high effectiveness. Finned surfaces are relatively high cost among other methods and porous inserts suffers from a high pressure drop and fouling problems [342]. As for nanofluids, thermal efficiency enhancement can be doubled in case of using hybrid nanofluids instead of mono types [320]. The improvement of heat transfer with the use of inserts been proven by experimental results whereas it is still theoretical and numerical for nanofluids at high temperatures. Also, there is need for experimental studies on concentrating collectors using oil as the base fluid rather than compressed fluids. All these methods with potentially high enhancement still need to be implemented in demonstration or actual systems to obtain actual improvements and the associated costs. Although there are experimental results for single and two-phase flows in the literature, there is a need for experimental studies with nanofluids in parabolic trough systems to compare the theoretical and numerical studies. Not only the variation in the heat transfer coefficient, but also the pressure drop should be tested and verified for future studies. Thereafter, models for nanofluids at high temperatures and pressures for PTSCs can be derived and presented. Due to lack of experimental studies for nanofluid in PTSCs, installation and operation costs are not clear and still require further investigations. 7. Conclusion Parabolic trough solar collector systems have emerged as technically and commercially developed CSP systems. Modeling and simulation of these systems provide a means of determining their performance and the possible improvements that can be made. In this paper, research studies aimed at modeling and simulating the performance of PTSCs to characterize their optical and thermal performance have been reviewed and presented. Moreover, the latest status of the research in the field is extensively presented. It is clear from this review that modeling is a powerful tool at the level of improving the PTSC technology. It provides a convenient means of characterizing the performance of PTSC systems and enables parametric analyses of the influence of a number of parameters with minimum effort and less expense compared to experimentation. This review clearly reveals that there is still much room for improvement of the PTSC technology using the powerful tool of modeling. All the current research and development efforts are essential and are mainly aimed at further improving the performance of PTSC systems to reduce their costs and make them competitive with other conventional energy systems. Realistic modeling studies can indicate the poor side of the design or the possible improvements and where these improvements can be executed in the existing design by simulating it parametrically. The studies presented use distinct modeling approaches in the modeling of PTSCs, thus this review provides enormous knowledge to researchers for examining these studies in detail and intending to study the performance of PTSCs through numerical modeling and simulation. Modeling-and-simulation offers significant advantages; generally it is low cost and provides an opportunity for examining numerous parameters when compared to experimentation. Moreover, it is capable of identifying the inefficiencies provoked by which system parameter or parameters and the order of their effects on the resulting system performance. Nonetheless, modeling and simulation cannot be considered 168

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the absorber tube and using nanofluids are increasingly being considered, however, the extensive demonstration of most considered techniques has not been done experimentally. There is therefore room for research studies on the investigation of several heat transfer enhancement techniques experimentally and under actual operating conditions in order to fully justify any commercial implementation to PTSCs.

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