steam solar tower receiver

Applied Thermal Engineering 163 (2019) 114241

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Heat losses and thermal stresses of an external cylindrical water/steam solar tower receiver

T

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Mumtaz A. Qaisrania, Jinjia Weia,b, , Jiabin Fangb, Yabin Jina, Zhenjie Wana, Muhammad Khalidb,c a

State Key Laboratory of Multiphase Flow in Power Engineering, Xi’an Jiaotong University, Xi’an 710049, China School of Chemical Engineering and Technology, Xi’an Jiaotong University, Xi’an 710049, China c Department of Physics, Baluchistan University of Information Technology, Engineering and Management Sciences, Quetta 87300, Pakistan b

H I GH L IG H T S

flux distribution is evaluated around receiver via Monte-Carlo ray tracing tool. • Solar losses are evaluated at different wind directions and wind velocities. • Heat heat transfer coefficient is evaluated and validated against published data. • Combined • Computed receiver thermal efficiency (71–77%) is validated against experimental data.

A R T I C LE I N FO

A B S T R A C T

Keywords: CSP receiver Cylindrical external receiver Heat losses analysis

A receiver serves as a pivotal component in the solar power system as it is responsible for the light-heat conversion. Extensive research has been carried out on cavity receivers while external receivers have been neglected hitherto. Considering this imperative research gap, this work endeavours to narrow the gap by numerically analyzing the thermal performance of an external cylindrical receiver. A methodology is proposed to determine the efficiency of a cylindrical shaped receiver. A heliostat field is simulated using Monte-Carlo Ray Tracing tool to obtain heat flux distribution on the receiver. The peak heat flux obtained, i.e., 425 kW/m2 lies at the centre of the receiver’s front. By designing a tube layout and using boiling heat transfer correlations, temperature at the receiver’s surface and water are obtained. Numerical analysis and simulations are then carried out to evaluate receiver’s thermal efficiency in six different wind directions and four different wind velocities between 3 m/s and 12 m/s. Natural convection and radiation losses were also considered. Combined heat transfer coefficients obtained through numerical simulations are compared with the previous experimental data. The effect of wind in a single direction is precisely evaluated by dividing the cylinder into panels and evaluating heat losses on each panel individually. The thermal efficiency evaluated oscillates between 71% and 77% based on wind velocity, and the results are validated against the real power plants and experimental data for cylindrical solar receivers. A tube at receiver’s centre having the highest temperature gradient is then selected to evaluate thermal stresses. The equivalent stress obtained is less than the yield strength with safety factor > 2.5.

1. Introduction Growing energy demand is forcing the world to adopt renewable energy resources. Solar energy is the most abundant as well as globally exploited source of power generation among the renewable resources. CSP is gaining rapid attention for electricity generation worldwide. Amongst its types, due to its better thermal storage abilities and ability to work under extremely high temperature, the solar tower type is

⁎

gaining increasing attention. A typical solar tower power facility consists of a heliostat field, focusing sunrays towards a receiver mounted on a high tower. The light rays are converted to useful thermal energy inside the receiver to drive turbines for power generation, making it a key component for a power plant. Its efficiency is directly linked to the overall performance of the power plant. The efficiency of the receiver relies on different factors. As the receiver is typically mounted on a height of 100–200 m, it is

Corresponding author at: School of Chemical Engineering and Technology, Xi'an Jiaotong University, Xi'an 710049, China. E-mail address: [email protected] (J. Wei).

https://doi.org/10.1016/j.applthermaleng.2019.114241 Received 1 March 2019; Received in revised form 26 July 2019; Accepted 10 August 2019 Available online 06 September 2019 1359-4311/ © 2019 Elsevier Ltd. All rights reserved.

Applied Thermal Engineering 163 (2019) 114241

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κ θ ν ρ σs σr, σθ, σz

Nomenclature Cp E H v Q Qc ΔTsat ΔTsub Tw Twall.ini Two ṁ V g h hfor hmix hnat r rin rout W x y z

specific heat J/kg K elastic modulus (Pa) enthalpy wind velocity, m/s heat rate, W convective heat losses, W wall superheat = Tw − Tsat, K liquid subcooling = Tsat − Tl, K temperature of wall temperature of inner wall temperature of outer wall mass flow rate [t/h] volume unit, m3 gravitational acceleration, m/s2 convective heat transfer coefficient, W/(m2 K) forced convective heat transfer coefficient, W/(m2 K) mixed convective heat transfer coefficient, W/(m2 K) natural convective heat transfer coefficient, W/(m2 K) radius of the tube, m inner radius of the tube, m outer radius of the tube, m watt x coordinate, m y coordinate, m z coordinate, m

σeq η

absorption coefficient wind direction, radians Poisson’s ratio density (kg m−3) yield strength (MPa) normal stress along radial, tangential and axial direction (MPa) equivalent stress (MPa) efficiency

Subscripts F for I Lg max min mix nat sat sub eq r w z θ

fluid forced convection inlet latent maximum value minimum value mixed convection natural convection saturated (water) subcooling state equivalent value radial direction wall of tube axial direction circumferential direction references

Greek symbols

Abbreviations

α ε λ

CSP NREL UDF

linear thermal expansion coefficient (K − 1) strain thermal conductivity, W/(m K)

Concentrating Solar Power National Renewable Energy Laboratory, USA. User Defined Function

[18] simulated irregular shapes for cavity receivers and successfully achieved better thermal performance. Apart from thermal losses calculation, numerous researchers have investigated thermal stresses on different components of the CSP power plant. Due to the high working temperature of CSP plants, high thermal stresses can cause severe damage. Steam leakage occurred in Solar One external receiver and halted the operation process just after eighteen months of its operation. Similarly, cracks initiated in CESA-1 receiver within a few months of its operation, Baker et al. [19]. Wang et al. [20,21] carried out research on a tube of a PT system, while, Irfan and Chapman [22] characterized stresses due to high temperature in a pipe. However, the study wasn’t particularly aimed for a pipe of a solar receiver. Montoya et al. [23], investigated thermal stresses produced in a molten salt receiver tube, taking into consideration the external constraints. Logie et al. [24] compared stress produced in a tube containing molten salt and liquid sodium and found latter to have 35% lower stresses than the former due to temperature difference caused by the difference in conductivity of the two materials. On a similar note, recent research compared heat transfer characteristics of Liu et al. [25] of liquid sodium with two other mediums, i.e., solar salt, Hitec. They found liquid sodium to have uniform temperature distribution and 4 °C lower local hotspot temperature. The above-mentioned literature mainly included molten salt as the HTF for stress analysis. And thermal performance evaluation is mostly carried out for cavity receivers. Scholars have drawn upon rich insights on different aspects of cavity receivers, whereas the research on cylindrical receivers is limited. Considering the fact, the current research numerically analyzes the thermal performance of an external cylindrical receiver. Earlier experiments were carried out by Stoddard [26] on cylindrical external receivers at the solar-one power plant using water

prone to high heat losses. Cavity receivers have been widely used and researched due to their low radiative heat losses. Clausing [1] presented a numerical modelled to evaluate natural convection for a cubical shaped cavity receiver and proposed heat transfer correlations. Later, Clausing [2] followed by Quere et al. [3] experimented large open cubical shaped cavity receivers for estimation of convective heat losses. Prakash et al. [4] simulated the thermal performance of a cavity receiver at low wind velocities in two wind directions. Jilte et al. [5] simulated different geometries for cavity receivers and observed lowest heat losses for the conical shaped cavity receiver. Flesch et al. [6] numerically and experimentally, Flesch et al. [7], analyzed the effect of wind inclination at different wind velocities on the thermal performance of the receiver. The results suggested that wind-induced losses can be reduced by designing the cavity in such a way that wind flow remains parallel to the plane of the cavity aperture. Gobereit et al. [8] performed CFD-simulations on the thermal performance of particle entrapped cylindrical cavity receiver and observed that side-on wind causes highest losses. Shen et al. [9] numerically studied the wind effect of combined convective heat losses from an up-ward facing cylindrical cavity receiver under different wind velocities and cavity inclinations. They also put forward correlations to predict combined convective losses. Ma [10], Prakash et al. [4], Flesch et al. [7] and Wu et al. [11] experimented cylindrical cavity receivers under varying conditions to evaluate thermal performance. Reynolds et al. [12] and Chaudhari et al. [13] experimented trapezoidal cavity receiver, while the latter also simulated the same shape to evaluate the thermal performance of the receiver. Wan et al. [14] performed an experiment to evaluate thermal losses of a cavity receiver using a small scale solar simulator. Si-quan et al. [15] studied the thermodynamic characteristics of a spherical shaped cavity receiver. Fang et al. [16], Tu et al. [17] and Kim et al. 2

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as heat transfer fluid (HTF), and the results were compared with the correlations proposed by Siebers and Kraabel [27] for cylindrical receivers. An average absolute deviation of around 30% was found between the experiment and correlations. In a recent study, Cagnoli et al. [28] simulated a billboard type external receiver under different wind directions. Previously, Rodríguez-Sánchez et al. [29] presented a detailed model with in-depth insights regarding guidelines for the thermal design of the cylindrical external receiver. Pacheco et al. [30] evaluated efficiencies of subsystems of Solar Two molten-salt power plant by the power-on method in the report “Final Test and Evaluation Results from the Solar Two Project.” Later, Rodriguez-sanchez et al. [31], re-evaluated and provided a simpler method to better evaluate the receiver performance of Solar Two power plant based on heat absorbed by pipes against total energy absorbed by the receiver coming from heliostat field. However, the heat transfer model, including wind effects and radiation losses were not simulated in these studies. Therefore this was also included as a part of the current study. Moreover, most of the researcher discussed above usually considered a uniform heat flux or a temperature to perform thermal analysis. In the current study, heat flux on the surface of the cylindrical external is obtained through the SolarPILOT software by simulating the power plant using the parameters of an existing power plant. An appropriate tube layout is designed, and suitable correlations from the literature and our previous studies are then employed to calculate the heat transferred to boiling tubes surface and water/steam flowing through the tubes. Temperature evaluated on the surface of tubes is then traced on the receiver’s surface through code, and CFD simulations are performed to evaluate the thermal losses. An iterative scheme is used to couple the above-mentioned scheme. Upon convergence, the receiver’s thermal efficiency is mathematically evaluated under different windy conditions. Effects of wind velocities and wind directions are evaluated. For the thermal stresses evaluation, the flux distribution is applied on the outer surface of the pipes through a user-defined function (UDF). The equivalent stress was evaluated using the Von Mises theory of equivalent strength. Du et al. [32] used a similar approach to evaluate stresses for a 3 m long solar receiver tube of a molten salt receiver. A non-uniform heat flux distribution was adopted in both studies. While, Wan et al. [33] investigated thermal stresses for a tube along with the weld quality for a cavity receiver using the same phenomena. The thermal stress analysis, as performed in this study, ensures the operational safety for the conditions as simulated in the current study for an external cylindrical receiver.

Table 1 Receiver Design parameters. Design parameter

Details

Latitude (°) Ground Inclination (°) Tower Height (m) Receiver Height (m) Receiver Diameter (m) Number of receiver panels Number of tubes on each panel Tube thickness (mm) Tube diameter (mm) Receiver panel width (m) Internal Tube Diameter (m)

38.24 N 0 200 20 17.6 16 76 1.65 42 3.5 0.042

2. Receiver geometry and design parameters A cylindrical external receiver is the object of the current study. The geometric parameters (i.e., receiver dimensions, tubes layout design, number of panels and tubes) in the crescent dunes power plant, located at Tonopah, Nevada, USA are adopted in the current study. The receiver shape, along with the wind directions studied, is shown in Fig. 1. There is a total of 16 panels with each panel having 76 tubes parallel to each other, forming a ring manifold at the top and bottom of the panels. It feeds water to all 16 panels simultaneously at a flow rate of 140 t/h at 277 °C temperature and 7 MPa pressure. Crescent Dunes is a large-scale power plant that started operation in 2015. The heat transfer fluid for the current study is water/steam. Details of the geometric parameters are given in Table 1.

3. Numerical modelling description 3.1. Heat flux calculation In the earlier studies, mostly a constant wall temperature or heat flux has been pre-assumed over the receiver’s surface. Fang et al. [16] put forward a comprehensive computational method using Monte-Carlo Ray Tracing method to evaluate heat flux on the cavity receivers. Using a similar approach, Qiu et al. [34] and Jin et al. [35] simulated heat flux in a cavity receiver for the DAHAN power plant, the former validated the results with those computed by DELSOL 3 for PS10, whereas, latter introduced carbon particles into the receiver to uniform the heat

Parallel Fluid Flow

Fluid outlet through pipes

Fluid inlet into the pipes (a)

(b)

(c)

Fig. 1. (a) Cylindrical receiver geometry (b) magnified sectional view of a panel segment with fluid flow directions (c) wind direction Sketch-up from the top view of the receiver. 3

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flux distribution and achieved positive results. While Sánchez-González and Santana [36], developed an optical model to project heat flux using the analytical function on a cylindrical receiver’s surface. However, various optical simulating tools are available in the market now. Specific ray-tracing methods pre-date other commercially available optical codes for solar systems. National Renewable Energy Laboratory (NREL) has developed several tools for this purpose. Their recent product SolarPILOT is one such open-source software to calculate heat flux impinging on the receiver’s surface. The Monte-Carlo Ray-Tracing modus operandi is incorporated in the SOLtrace integrated SolarPILOT. SOLtrace operates on the working principle of the Monte-Carlo ray-tracing method that allows optical characterization of a wide range of possible systems and geometries. The basics concept of MCRT includes the optical receiving object is divided into many units (i.e., surface units and volume units). Afterwards, each unit emits a certain number of light rays. Each of the emitted rays is tracked and then probabilistically determined whether it will be absorbed by the medium or the receiving interface or if it will escape from the system under consideration. Lastly, the number of the light rays that every unit finally gains is calculated, and then the radiation flux map on every unit of the receiving surface is evaluated. The details about radiative heat transfer using the MCRT working principle can be found in the textbook by Modest [37]. With better resolution and graphical displays, Yellowhair et al. [38] the SOLtrace software is chosen for heat flux evaluation in the current study. As a reference, the crescent dunes power facility location, with a heliostat field of same heliostat dimensions (11.28 m × 10.36 m) to produce 110 MW of electricity, as in the actual power plant was simulated to obtain heat flux. An equatorial aiming approach, i.e., all the heliostat focusing the light at the centre of the receiver was employed. A circular Gaussian-alike flux distribution is obtained, as shown in Fig. 2, resulting from the simulation at 12:00 noon, spring equinox. The flux distribution is symmetrical in the northsouth direction. As the receiver lies in the northern hemisphere, the peak heat flux is obtained at the northern face of the receiver, and as expected the lowest lies at the southern side. The similar distribution trend was obtained by Rodríguez et al. [29] for an external cylindrical receiver. The peak heat flux obtained is 425 kw/m2 at the centre of the front of the receiver, gradually declining circumferentially towards the back and the edges of the receiver.

Table 2. The temperature profile on the surface of the receiver is shown in Fig. 3. The overall temperature distribution resembles the flux distribution; however, it is more uniform due to fluid flow across the tubes. The maximum temperature at the given 7 MPa pressure obtained lies at the centre of the receiver, reaching a value of 858 k. 3.3. Governing equations The general governing equations to predict the heat losses and fluid flow can be determined by simultaneously solving the momentum, energy and continuity equations. The conventional equations are extensively represented in literature and therefore not reproduced here, for in-depth insights and theory of the equations, please refer to the work of [41,42]. 3.4. Computational modelling for heat losses evaluation 3.4.1. Grid independence test Upon obtaining the temperature at the surface of the receiver, the thermal losses through the receiver can be obtained through computational modelling. ICEM and ANSYS fluent were used for the modelling, meshing and simulation works. The fluid volume domain to describe the airflow field was 100 m × 100 m × 100 m in size, i.e., multiple times bigger than the receiver, which was setup right in the centre of the domain. The mesh around the vicinity of the receiver was much denser near the receiver’s surface than that at the ends of the fluid domain. The y+ values were handled within < 10, with a few mesh layers very close to airflow field. The boundary layer was especially taken care of with walls functions method, and enhanced wall functions were used in the specified range to take care of the near-wall treatment. A mesh-independence study was also performed based on the residual error of convective heat losses. The results are listed in Table 3. It can be seen that a total of 2.0 × 106 cells was adequate to carry out the simulations. 3.4.2. Boundary conditions and simulations The simulations were carried out using the FLUENT module of ANSYS. Apart from natural convection, a total of 9 wind directions were simulated with 4 different varying wind velocities flowing horizontally against the receivers. The wind speed can be supposed as a function of height using the Suttons law. In actual power plants, the wind speeds vary from 1.2 m/s up to 40 m/s which are from 1.2 m/s to 27.7 m/s at the characteristic height of 10 m Hu et al. [43]. However, these are upper and lowermost limits. Usually, the mean wind velocity varies between 1 and 10 m/s in the power plants. For the same reason, most of the researchers numerically and experimentally investigated convective

3.2. Heat transfer correlations for temperature calculations One of the key advantages of solar tower power plants is its ability to operate at high temperatures. The receiver surface receives high, varying incident flux and thus subcooled water being pumped into the receiver tubes gets heated. The phase transition occurs as water flows through the receiver tubes, and subcooled flow boiling should be considered due to high heat flux on the receiver’s surface. The subcooled water converts into the saturated state as it heats up, and phase transition occurs. Further transition will occur as the water flows up through the superheated region, converting the saturated steam into superheated steam. These phase transitions can be divided into three different regions as the fluid flows through the receiver tubes and exits from the top. The three-phase regions include the single-phase flow region and subcooled flow boiling region and the saturated boiling flow region. The subcooled region is further subdivided into three more regions based on the regional heat transfer mechanism. Namely, the partial boiling region, the fully developed boiling region and the significant void region. A coded program is employed to evaluate the tube’s surface temperature and water/steam temperature throughout the flow. As the conditions at the inlet and heat flux transmitted to the water are known, the temperature at the boiling surfaces can be calculated using the correlations mainly recommended by Kandliker [39], Kandlikar [40]. Apposite correlations for each above-mentioned flow region along with respective selection criteria for every region based on the temperature difference between bulk fluid and wall are listed in

Fig. 2. Heat flux map on the receiver’s surface (Unfolded view). 4

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Table 2 Boiling heat transfer correlations. Flow region

Identification criteria

Boiling heat transfer correlation

Single-phase Region

–

Gnielinski [57]

Nulo = hlo D Partial Boiling Region

Hsu [58]

⎡1 + 1 + λj ilg ΔTsub ⎤ ΔTsat . ONB = ⎢ λl ilg 2δTSat νlg hl ⎥ ⎣ ⎦ qONB = [λj ilg 8δTsat v lg](ΔTsat . ONB )2 Thom et al. [60] and Bowing [61] qFDB = 1.4qD

Significant Void Region

Saha and Zuber [62]

⎧ xNVG = −0.0022 ⎨ ⎩ x⩾0

Saturated Boiling Region

qD ρl ilg λl

(Relo −1000) Prl (f 8)

f = [1.82 lg(Re) − 1.64]−2

1 + 12.7 f 8 ⎜⎛Pr l2 3 −1⎟⎞ ⎝ ⎠

Kandlikar [59] q = a + b (ΔTsat )m

4δTsat v lg hl

Fully Developed Boiling Region

λl =

b=

qFDB − qONB (ΔTSat . FDB )m − (ΔTSat . ONB )m qONB − b (ΔTSat . ONB )m

a= Thom et al. [60]

ΔTSat = 22.65(q 106)0.5e p Kandlikar [40]

= −0.0022BoReto PrReto Pr < 70000l

hTP = hNVG −

8.4 × 106

(hx = 0 − hNVG )(x − xNVG ) xNVG

xNVG = −153.8BoReto Pr > 70000 Gunger and Winterton [63] hTP = Ehlo + ShB

hb = 55pr0.12 (−0.4343 ln Pr )−0.55M−0.5q0.67

E = 1 + 24000Bo1.16 + 1.37Xn−0.86

S = (1 + 1.15 × 10−6E2Rel0.17)−1

heat losses at wind velocities ranging between 1 m/s and 10 m/s. In the current study, heat losses are evaluated at natural convection and at wind velocities up to 12 m/s for forced convection. The airflow field around the receiver was considered as turbulent based on receiver’s cylindrical geometry mounted at a significant height from the ground and having high Gr and Re numbers, evaluated at the film temperature (0.5(Twall − Tair)) Raithby and Hollands [44]. Hence, the commonly employed realizable k-ε turbulence model is used. For natural convection, Boussinesq approximation has been widely adopted by researchers. However, it is employed to define air properties at lower temperatures Prakash et al. [4], and it stands invalids for higher temperature differences Gray and Giorgini [45]. At lower temperatures, the Boussinesq approximation takes into account the difference in density to be very small and buoyant forces drive the motion Fluent [46]. Hence, it neglects the density variation except for the buoyancy term. Also, the Boussinesq approximation doesn’t present accurate results for non-linear temperature variation along the surface Martineau et al. [47]. For the same reasons, natural convection in high-temperature cases, such as in the present study, a Non-Boussinesq variable density approach is employed to incorporate temperature-dependent density variation, as mentioned in Holman [48]. The same approach in hightemperature scenarios for solar parabolic cavity dish receiver, rectangular cavity receiver and cuboid cavity has also been employed by previous researchers Xiao et al. [49], Zhang et al. [50], Kumar and Eswaran [51]. The varying temperature distribution obtained from Section 2 at the receiver’s surface was applied in the fluid setup using a User-Defined Function (UDF). Further details modelling including conditions and convergence criteria are enlisted in Table 4.

Fig. 3. Temperature profile at the surface of the receiver. Table 3 Grid independence test. (wind velocity = 9 m/s in headon wind direction). Grid number/106

Qlosses [kW]

0.8 1.1 2.0 2.4 2.7

70,425 99,221 11,490 11,491 11,491

Table 4 Boundary conditions and settings for numerical modeling. Parameter/Condition

Settings

Solver

Pressure-based solver with steady-state settings for time

Formulation Gradient Algorithm Spatial Discretization settings

Implicit Least Square Cell-based methodology SIMPLE (semi-implicit method for the pressure linked equation) Second order-upwind scheme for the momentum and energy equations, while for turbulent dissipation rate and turbulent kinetic equation a firstorder scheme was chosen 10−3 for Velocity, κ and ε, and 10−6 for Energy

Criteria for Convergence

5

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3.4.3. Thermal efficiency of the receiver Evaluating the heat losses from receivers is complex. The parameters involved to evaluate the efficiency are interrelated. To evaluate the thermal performance through heat losses evaluation (Section 3.4) the surface temperature of the boiling tubes (Section 3.2) and the incident heat flux (Section 3.1) are required. However, to find temperature using the apostle boiling flow heat transfer correlations (Section 3.2) inlet parameters of the tubes as well as the incident heat flux (Section 3.1) are needed. At iterative looping scheme is the workable solution to tackle the issue. The process flow-chart is shown in Fig. 4.

3.4.4. Results and discussion As stated above, 1216 tubes are arranged parallel in 76 panels, where water flows up the receiver tubes from the bottom and exits through the top. The airflow field around the receiver is simulated with varying wind velocities and wind directions. The wind velocity profiles at different wind velocities are shown in Fig. 5. The forced convection results and radiations losses obtained through the simulations are listed in Table 5 For cylindrical receivers, the convective losses are a result of both forced and natural convection losses. To manifest the intensity ratio of free to forced convection, the dimensionless Richardson number Ri can be used. It is characterized by the ratio of Grashof number Gr to the square of Reynold number Re.

Ri =

gβH (Tw − Ta ) Gr = v2 Re 2

Fig. 5. Velocity contours in head-on wind directions at four different wind velocities. (a) 12 m/s (b) 9 m/s (c) 6 m/s (d) 3 m/s.

Re =

vρH μ

(2)

where Ri ⩾ 10 corresponds to natural convection dominating the flow i.e., a buoyancy driven flow while Ri ⩽ 0.1 indicates negligible buoyant forces with forced convection dominating the flow. For the current cylindrical receiver, Tw, avg = 562 °C and velocity range is 1 ⩽ v ⩽ 12 , the mixed flow occurs with 1 < Ri < 10 . However, the radiation losses dominate the total losses, more prominently at lower velocities. Also, the radiation losses do not vary with wind direction. Even though the

(1)

where

Fig. 4. Process flow-chart of the applied iterative methodology. 6

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smooth without rough panel edges, hence, for comparison of local heat losses trends, it is also divided into 24 panels with front panels (1–3 and 22–24) already have the highest temperature. The evaluated convective coefficient is presented in terms of the ratio of Nusselt number to the square root of the Reynolds number, as proposed by Achenbach [53]. A value equal to unity signifies stagnation for the laminar flow boundary layer, i.e., zero wind incidence angle at the point where it strikes the receiver’s surface. The angle can be inferred from the panels located 15° apart from one another. The results obtained are shown in Fig. 9. The results are reported for the side-on wind direction case, the, i.e. incident angle between ambient wind direction and the panel normal at panels 18–19 is zero, this is also the stagnation point as the flow is close to laminar as suggested by the values near unity (marked by a black circle in the figure). The value is not precisely unity partially due to the presence of buoyant forces (natural convection) and also partially because the flow is not purely laminar at this point. The heat transfer reaches the maximum at about 115° from the stagnation panels (panels 1–2 and 10–11 marked by blue circles), this is the wind separation point, and the velocity is at its peak. The heat transfer tends to decrease from this point and falls to a minimum at the opposite end of the cylinder (i.e., panels 6–7, marked with a red circle), i.e., 180° from the stagnation panels followed with small wake flow vortices as shown by velocity vectors in Fig. 10. Similar trends were observed in the experiment by Stoddard [26] in different wind directions and particularly at higher wind velocities. The magnitude differs due to different temperature distribution between the current study and the above-mentioned experiment.

Table 5 Heat losses in different wind directions and wind velocities [kW]. Velocity

3 m/s 6 m/s 9 m/s 12 m/s Radiation

Direction 0°

45°

90°

135°

180°

270°

4028 7910 11,364 14,064 30,476

4049 7811 11,326 14,202 30,476

4177 8040 11,490 14,491 30,476

4045 7952 11,082 13,881 30,476

4109 7920 11,355 14,058 30,476

3991 6961 9984 13,762 30,476

front panels have a higher temperature than the rest of the panels, the overall temperature gradient is not so high, for the same reasons, there are small changes in forced convective heat losses at different wind directions. However, even though the difference is not high, the lowest losses are observed in backward (i.e., 270°) wind direction where the temperature gradient is the least as shown in the comparison of forced convective losses in Fig. 6. It can also be observed that the difference becomes prominent with the increase in velocity. 3.4.4.1. Convective heat transfer coefficient. As discussed above the heat transfer mode in cylindrical receiver relies on mixed convection, the results are divided into two categories(i) receiver’s overall heat transfer coefficient for the entire cylinder(ii) detailed local heat losses analysis (by dividing the cylinder into panels) as a function of wind speed. The data obtained are than verified through data reported in the literature by Siebers and Kraabel [27] and the experiment by Stoddard [26]. 3.4.4.1.1. Mixed convective coefficient. As both natural and forced convection influence the convective heat transfer process, both are evaluated through the simulations individually and mixed convection hmix is calculated through the following correlations from literature Cengel [52], Siebers and Kraabel [27]. 1

a a a hmix = (hnat + hfor )

3.4.4.2. Calculation of receiver thermal efficiency. The thermal efficiency of a receiver is defined as the ratio of power absorbed by the HTF in the receiver to total incident power provided by the heliostat field, i.e., the incident energy and the energy absorbed by the HTF differ by the amount of thermal losses from the receiver. It can be mathematically expressed as

(3)

where hnat and hfor refer to natural and forced heat transfer coefficients respectively. Where, a lie in the range 3–4, with values close to 3 correspond to vertical surfaces and close to 4 are well suited for horizontal surface [52]. Siebers and Kraabel [27] proposed a value of a = 3.2 for cylindrical external receivers, and the same is used in the current study for evaluation of hmix . At lower wind velocities, i.e., < 2 m/s, the heat transfer coefficient is independent of the wind velocity and pure natural convection dominates the heat transfer coefficient. Higher wind velocities elevated the forced heat convection coefficient rapidly that in turn tends to dominate the mixed heat convection at higher wind velocities, as shown in Fig. 7. The trend observed is similar to the results presented by Siebers and Kraabel [27] on Bairstow receiver, California. Their study was carried out at a range of three different receiver surface temperatures. The results are incorporated with the results from the current study, as shown in Fig. 8. As discussed above, forced convection dominates the convection losses at higher velocities, however higher wall temperature intensifies the buoyancy, increasing the free convection losses. The variable air properties effect causes a decrease in forced convection losses, and the net effect is a decrease in the mixed convection coefficient with the increase in temperature, as shown in Fig. 8. It can also be noted that the values for the heat transfer coefficient for the current study lie well within the range of reported literature validating the results as obtained in this study. The effect of wind in a single direction is analyzed with the help of evaluating heat losses at each panel individually. The methodology is adopted from the experiment carried out by Stoddard [26], on a 10 MW Solar One receiver having 24 panels with front panels (1–3 and 22–24) having the highest temperature. As the receiver in the current study is

η=

Pinc − Ploss Pinc

(4)

where Pinc represents incident power and Ploss indicates the energy losses. The same approach has been widely used to evaluate the receiver’s performance and to infer thermal losses by different researchers. For Solar Two receiver, the revised efficiency calculated by Rodriguezsanchez et al. [31] is around 76%, which is in agreement with the global plant efficiency. The currently operating power plants having cylindrical-shaped external receivers such Gemasolar in Spain, and Crescent Dunes power facility in the USA have also shown receiver efficiencies of 76% and 77.2%, respectively, Rodriguez-Sanchez et al. [54]. For the Solar One receiver, Radosevich et al. [55] reported

Fig. 6. Forced losses comparison against different wind directions and wind velocities. 7

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V m/s

Fig. 10. Velocity profile for the side-on wind direction at 9 m/s wind velocity. Fig. 7. Heat transfer coefficient in head-on wind direction.

Heat Transfer Coefficient W /m2 C

40

availability of data in literature published by Stoddard [26] and Baker and Atwood [56], results from the current work are validated against their results in Fig. 11. The receiver efficiency falls by around 5.5% with increasing wind velocity from 3 m/s to 12 m/s. As depicted in Fig. 11, the numerical data are well within the data range reported in the literature.

Tw=150°C Tw=400°C Sieber and Krabeel Tw=650°C Tw=562°C, Current study

35 30 25 20

3.5. Computational modelling for thermal stresses evaluation

15

The receiver, particularly external receiver, faces harsh climatic conditions. Changing weather conditions, the passage of clouds and rains, with daily night-shutdowns and daily receiver operation at high temperatures causes high thermal stress, which in turn increases wear and tear on the receiver surface. The central region of the receiver has the highest heat flux, as shown in Fig. 2, and the same region faces the highest thermal stresses due to a high outer/inner tube temperature gradient. A tube from the centre of the receiver is selected to analyze the thermal stresses. ANSYS Workbench is used to evaluate the temperature. The boundary conditions, i.e., heat flux, surface temperature and fluid temperature, were input, and convergence criterion is the same as for thermal losses evaluation modelling. The grid independence test is performed again, based on the criterion as for thermal losses modelling and 4.64 × 105 hexahedral cells produced converged results. The 20 m long pipe with 42 mm diameter and 1.65 mm thickness exhibits a non-form heat flux profile with peak flux at the centre. The flux distribution is applied on the outer surface of the pipes through a userdefined function (UDF). The flux profile is shown in Fig. 12. The heat flux obtained an axisymmetric temperature distribution i.e., non-uniform along the axial and the radial direction. Thus, heat transfer through conduction also occurs from the outer most surface of

10 5 0 0

2

4

6

8

10

12

14

Wind Velocity m/s Fig. 8. The effect of wind velocity and temperature on combined convective heat transfer coefficient. (Dashed lines represent experimental results from literature Siebers and Kraabel [27]. (Black) Solid line represents results from the current study. 3

Wind Velocity 9 m/s

Nu/Re0.5

2

1

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

0

Panel Number Fig. 9. Convective heat transfer against the wind direction. Stagnation at panel 18–19 at 9 m/s wind velocity.

receiver efficiency oscillating between 70.9% and 76.5% dependent upon wind velocity up to 12 m/s for measured values of absorbed power and calculated values for the incident power. While, Baker and Atwood [56], reported the value for receiver efficiency between 70% and 80% at different wind velocities, although, it included a considerable scatter in the data. They collected 120 data points gleaned from the actual operational data. Stoddard [26] performed large sets of experiments at Solar One receiver to calculate the receiver efficiency at different ambient wind velocities ranging from 2 m/s to 12 m/s. Due to the

Fig. 11. Comparison of current receiver efficiency as a function of different ambient wind velocities against data from Baker and Atwood [56] and Stoddard [26]. 8

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Fluid outlet

20

15

Pipe height (m)

10

5

0

Fluid inlet

0

100

200

300

400

500

Fig. 14. Cross-sectional view of the pipe.

Heat Flux (Kw/m 2 )

Fig. 12. Heat flux profile on the front outer surface of the pipe.

maximum temperature gradient between the inner/outer wall responsible for conduction is in the region of maximum heat flux. The non-receiving solar flux end has almost no temperature difference i.e.180° < ϕ < 360°. Whereas, the maximum temperature difference ΔTmax between the outer/inner surface of the solar flux receiving end of the pipe is 15 K as shown in the cross-sectional view of the pipe at the receiver height of 10 m, in Fig. 14. The highest thermal stresses of equal magnitude, along the axial and the radial direction, exist in this region, i.e., z = 10 m, also observed by Du et al. [32]. For the same reason, the only the stresses in the axial direction are calculated. The temperature difference along the axial direction is similar to flux distribution on the receiver pipe, diminishing towards the ends of the receiver as the heat flux decreases. Also, the solar radiation absorbing side has a higher temperature than the other, as expected. The temperature distribution along the pipe’s axial direction is shown in Fig. 15 The equivalent stress is evaluated using the Von Mises theory of equivalent strength, which can be expressed using the equation

the front part of the pipe towards the inner side of the pipe. While convection heat transfer takes place on both sides of the pipe with inner surface transferring heat to the HTF and outer surface responsible for convection heat losses to the surrounding air. Radiation heat transfer takes places only on the outer surface boundary that receives the concentrated solar rays from the sun and also reflects a fraction of it to the surroundings. With the above conditions, thermal elasticity equationsbased equilibrium differential equations in cylindrical coordinates are expressed in Eq. (5) [41]. A free thermal boundary condition at the top and bottom of tubes is adopted without limiting any force and displacement to investigate the non-uniform temperature effect on the tubes. ∂σ

⎧ ∂rr + ⎨ ∂τrz ⎩ ∂r

+

∂τrz ∂z ∂σz ∂z

+

σr − σθ r

+

τrz r

=0

=0

(5)

The cylindrical coordinate system with a schematic sketch of heat transfer modes, as mentioned above, is shown in Fig. 13.

σeq =

σr2 + σθ2 + σz2 − σr σθ − σθ σz − σz σr

(6)

where 3.5.1. Thermal stresses evaluation The temperature is highest at the centre of the receiver, i.e., at the height of 10 m. The highest observed is around 864 °C whereas the lowest is observed at the inner side of the opposite end of the pipe. The

Fig. 13. Schematic sketch-up of heat through the pipe (a) cross-section of the tube from the top view, (b) conduction heat transfer sketch in cylindrical coordinates. 9

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Fig. 15. Temperature distribution along the pipe’s axial direction (Diameter magnified for clarity).

2 2 αE ΔI ⎧ σ = ⎡−ln r0 − 2 ri 2 ⎛1 − ri2 ⎞ ln r0 ⎤ r ri r0 − r i r ⎪ r 2(1 − ν) ln ( r 0 ) ⎣ ⎝ ⎠ ⎦ r ⎪ 2 2 ⎪ r r αE ΔT ⎪σ = ⎡1 − ln r0 − 2 i 2 ⎛1 + i2 ⎞ ln ro ⎤ θ r ri r0 − r i r r ⎝ ⎠ 2(1 − ν ) ln ⎛ 0 ⎞ ⎣ ⎦ ⎨ r ⎝ i⎠ ⎪ 2 2 r αE ΔT ⎪ ⎡1 − 2 ln r0 − 2 1 2 ln r0 ⎤ σz = r ri r0 − ri r ⎪ ⎦ 2(1 − ν ) ln ⎛ 0 ⎞ ⎣ ⎪ r ⎝ i⎠ ⎩

()

( )

⎜

However, heat losses through radiation are still too high even at higher wind velocities up to 12 m/s. Convection losses only represent a portion of the total heat losses, i.e., < 30% of total losses at 12 m/s wind velocity. (3) Wind direction effect in a single direction is analyzed by investigating the heat losses on individual panels. Nusselt number normalized by the square root of Reynold’s number is employed to determine the convective coefficient on every individual panel. The highest heat losses correspond to wind separation point at around 115° from the angle normal to the wind direction (stagnation point), and the lowest losses occur at the opposite end of stagnation point at 180°. (4) The evaluated thermal efficiency of the receiver oscillates between 71% − 77% based on the wind velocity. The results were validated by comparing them with the results obtained through experiments and studies from the literature. (5) Thermal stresses were evaluated along the axial direction for the centermost pipe, having the highest temperature. It was found that the equivalent stress is lower than the yield strength of the pipe’s material with a safety factor > 2.5.

( )

( )

⎟

( )

( )

(7)

It can be seen from the equations above that the thermal stress in the form of cylindrical coordinates can be obtained when ri and ro are known. The curves for the stresses obtained are similar to temperature distribution along the axial direction of the pipe. The stresses produced are lower than the yield strength of the pipe. The results for the stresses in the pipe along with r, z, and θ with respect to temperature distribution and yield strength with a safety factor of 2.5 are shown in Fig. 16. The stress analysis shows that under the heat flux and temperature as obtained in the current study, it is pertinent to conclude that the tube thickness and material are safe to use. 4. Conclusions

8×10 7 6×10 7

(Pa)

4×10 7

20 20

z

T

r

s eq

15 15

2×10 7

T (k)

A method to evaluate heat losses and thermal efficiency of an external cylindrical receiver was proposed in the current study. Effects of wind direction and wind velocity were also studied. Heat flux was first obtained using Monte-Carlo ray tracing-based software, a suitable tube layout was designed, and surface temperature was evaluated using boiling heat transfer correlations. ANSYS Workbench simulations were carried out to evaluate the heat losses. The results attained are summarized as follows:

10 10

0 55

-2×10 7

(1) The heat flux distribution and the temperature distribution exhibit a non-uniform characteristic along the receiver’s length and circumferential direction. Although the temperature distribution is similar to heat flux distribution, comparatively, it's slightly more uniform than the heat flux distribution due to fluid flow. (2) Heat losses are dominated by radiation. Although increasing the wind velocity significantly increases forced convection heat losses.

-4×10 7 0.0

2.5

5.0

7.5

10.0

12.5

15.0

17.5

0 20.0

Pipe Length (m) Fig. 16. Thermal stresses distribution along the pipe’s axial direction. 10

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Acknowledgements

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12