Thermal performance enhancement in a parabolic trough receiver tube with internal toroidal rings: A numerical investigation

Applied Thermal Engineering 162 (2019) 114224

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Research Paper

Thermal performance enhancement in a parabolic trough receiver tube with internal toroidal rings: A numerical investigation

T

⁎

K. Arshad Ahmed , E. Natarajan Institute for Energy Studies, Department of Mechanical Engineering, Anna University, Chennai 600 025, India

H I GH L IG H T S

G R A P H I C A L A B S T R A C T

novel parabolic trough receiver with • Atoroidal rings is examined numerically.

efficient absorber exhibits a • Thermally higher thermal efficiency of 69.32%. for the optimal absorber cases is • Nu 2.33 and 1.49 times higher than SAT. loss for the thermally efficient • Heat case is lower among all the examined cases.

thermal enhancement index of • Higher 1.20 is seen with the energy efficient case.

A R T I C LE I N FO

A B S T R A C T

Keywords: Toroidal rings Solar parabolic trough collector Nu ratio Thermal enhancement index Thermal efficiency

The present work investigates the incorporation of internal toroidal rings in an absorber tube of a solar parabolic trough collector (SPTC) with an objective to enhance the thermal performance. To produce substantial effect on the heat transfer rate, nine different cases of absorbers have been considered. The fully developed turbulent heat transfer characteristics of the absorber tube have been numerically studied and validated under varying inlet temperatures and flow rate of the heat transfer fluid (HTF). Realizable k-ε two-equation turbulence model with enhanced wall treatment has been used with ANSYS FLUENT 15 commercial codes. The influence of toroidal rings on heat transfer and fluid flow are evaluated and presented. The absorber with toroidal ring having a diameter ratio (H) of 0.88 and pitch size (p) of 2d is the thermally efficient optimal case. While the absorber with H = 0.92 and p = 2d is the energy efficient optimal case, with H being the ratio of inner to outer diameter of the toroidal ring and 2d being the distance between the adjacent rings, which is equal to two times the inner diameter of the absorber tube. When the inlet temperature of HTF is 600 K, the increase in efficiency for the thermally efficient and energy efficient optimal case are found to be 3.74% and 1.88%, while the increase in Nusselt number is found to be 2.33 and 1.49 times higher than the smooth absorber tube (SAT), respectively.

⁎

Corresponding author. E-mail addresses: [email protected], [email protected] (K. Arshad Ahmed).

https://doi.org/10.1016/j.applthermaleng.2019.114224 Received 4 April 2019; Received in revised form 25 July 2019; Accepted 7 August 2019 Available online 08 August 2019 1359-4311/ © 2019 Elsevier Ltd. All rights reserved.

Applied Thermal Engineering 162 (2019) 114224

K. Arshad Ahmed and E. Natarajan

Nomenclature A cp d D F f H I k CR T L p V W m q Q h Re Nu Pr u, v, w x, y, z ΔP

ro co ci pro i m o r top bottom th opt

area (m2) specific heat capacity (J/kg. K) inner diameter of absorber tube (m) diameter (m) focal length (m) friction factor diameter ratio solar radiation (W/m2) thermal conductivity (W/m K) concentration Ratio temperature (K) length of the absorber tube (m) pitch size (mm) volumetric flow rate (m3/min) width of the parabola (m) mass flow rate (kg/s) heat flux (W/m2) heat transfer rate (W) heat transfer coefficient (W/m2 K) Reynolds number Nusselt number Prandtl number x, y, z component of velocity (m/s) cartesian coordinates (m) pressure drop (Pa)

Greek letters ρ τ α ε δ θ η μ k ν

reflectivity transmissivity absorptivity emissivity wall thickness (m) angle of incidence (°) efficiency dynamic viscosity (N/m2 s) turbulent kinetic energy (m2/s2) kinematic viscosity (m2/s)

Abbreviations SPTC PTR TEI FVM HTF SAT CFD DISS

Subscripts 0 a ap av b c cal

receiver outer surface outer glass cover inner glass cover produced energy inlet mean outlet receiver top periphery of absorber bottom periphery of absorber thermal optical

reference smooth case ambient aperture available beam glass cover calculated

1. Introduction

solar parabolic trough collector parabolic trough receiver thermal enhancement index finite volume method heat transfer fluid smooth absorber tube computational fluid dynamics direct solar steam systems

effect of internal helically-finned absorbers in SPTC power plants reduced the operation and maintenance costs with 3% improvement in collector efficiency [8,9]. The circumferential temperature difference reduces below 35 K for all the examined values of mass flow rates in a sinusoidal PTR [10]. The numerical analysis of unilateral longitudinal vortex generators in a PTR reduces the thermal loss by 2.23–13.62% in comparison with the smooth tube [11]. Numerical simulation on the inner tube of a SPTC with shallow dimples increased the Nu to about 1–18% more than the smooth tube under the values of Grashoff number ranging from 109 to 3.2 × 1010 [12]. The effect of the converging-diverging absorber and internal longitudinal fins in the receiver section of a SPTC with various HTFs was analyzed by Bellos et al. [13,14]. The effect of asymmetric outward convex corrugated tube in a SPTC was studied with improvement in heat transfer coefficient up to 8.4% and a decrease in thermal strain to about 13.1% [15]. The finite volume method with the pin fin arrays inserting in an absorber tube of a SPTC at DISS (direct solar steam systems) test facility in Spain enhanced the average Nusselt number by 9% with an increase in thermal performance factor to about 12% [16]. The use of inclined ribs in the absorber tube reduces the maximum temperature and heat loss to about 177 °C and 80.1% in comparison to a smooth tube [17]. Kurṣun et al. [18] has studied the effect of longitudinal internal fins having flat surface with a thermal performance factor of about 1.43. The use of inserts in the flow path of HTF in the receiver section of a SPTC is a passive method, which will assist in the heat transfer enhancement [19]. The insertion of metal foams in the receiver of a SPTC

A solar parabolic trough collector (SPTC) is a line focusing imaging solar collector, which has its commercial availability right from the late 1980s [1]. Several simulation programmes, mathematical procedures and experimental techniques [2] are available to study and enhance the thermal performance of a solar parabolic trough receiver (PTR) [3]. With SPTC technology, the supply of thermal energy to the end user at a temperature of 400 °C is possible by making the heat transfer fluid (HTF) to flow in a closed loop [4]. Air, thermal oils, water/steam, molten salts, and liquid metals can be used as HTF in concentrated solar thermal systems [5]. In a SPTC system, the PTR plays a crucial role in extracting the incoming solar radiation and transforming it into useful thermal energy by means of circulating the HTF. Solar flux distribution in an absorber tube plays a crucial role in weakening the mismatch in the SPTC [6]. To intensify the thermal performance of a SPTC, it is necessary to enhance the process of heat transfer in the heat collecting element. Comprehensive heat transfer methodology for augmenting the rate of heat transfer in the absorber section has been analyzed by various researchers with the integration of inserts and internal fins. At this juncture, the studies with respect to absorber with internal fins have been conferred. Reddy et al. evaluated the performance of the SPTC with porous finned receiver of square, triangular, trapezoidal and circular cross-section numerically and found a significant improvement in the heat transfer coefficient with trapezoidal cross-section fins [7]. The 2

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and dirt on the receiver [30]. For zero incidence angle, the optical analysis leads to optical efficiency of about 75.50%. In the present study, the use of circular toroidal rings inside the absorber has been investigated. The toroidal ring resembles a donut and this is the main innovation in this study as shown in Fig. 2. This investigation fills the scientific gap especially for the operation of a SPTC with the liquid working fluid. Nine cases of modified absorbers with circular toroidal rings mounted along the inner surface of the absorber tube have been analyzed with an ‘H’ value of 0.88, 0.92 and 0.94 having pitch size ‘p’ of 2d, 3d and 4d, respectively. ‘H’ is a nondimensional parameter defined as the ratio between the inner diameter to the outer diameter of the toroidal ring. The outer radius of the toroidal ring has a value of 33.50 mm. In an absorber tube, circular toroidal rings have been attached along the circumference of the inner wall with a pitch size of 2d, 3d and 4d. Pitch size is the distance between the two adjacent toroidal rings. The nine cases of the absorber with toroidal rings is designated as H = 0.88, p = 2d; H = 0.88, p = 3d; H = 0.88, p = 4d; H = 0.90, p = 2d; H = 0.90, p = 3d; H = 0.90, p = 4d; H = 0.92, p = 2d; H = 0.92, p = 3d and H = 0.92, p = 4d. The flow of HTF is assumed to be turbulent and fully developed with the system operating under steady state condition. The primary objective of the study is to investigate the impact of the circular toroidal rings in the thermal enhancement of the collector with reference to the SAT case and identify the optimal case. To present the suitable comparisons of the absorber tube with toroidal rings, the reference case of the smooth tube is examined first. At the same time, the major factors influencing heat transfer and fluid flow is also investigated and presented in this study.

increased the Nu and f by 10–12 times and 400–700 times, respectively, with 45% reduction in the circumferential temperature difference [20]. The use of internal hinged blades in the absorber tube improved the thermal efficiency to about 69.33% [21]. Testing of a SPTC as per ASHRAE 93 standard with the insertion of copper metal foam improved the collector efficiency with enhancement in thermal conductivity [22]. To homogenize the absorber tube temperature and to increase the thermal efficiency, helical screw tape inserts were used in a PTR [23]. To generate turbulence in the direction of fluid flow, louvered twisted tape inserts were used in the absorber of a SPTC with an increase in Nu and f to about 150% and 210%, respectively, in comparison with the smooth tube [24]. Numerical analysis of a PTR with porous discs and Therminol – VP1 as HTF enhanced the Nu by 64.2% compared to a tubular receiver [25]. A new optimization method with genetic algorithm and CFD in a PTR improved the solar to thermal conversion efficiency to about 68% with porous inserts [26]. The effect of perforated plate inserts in a SPTC with Syltherm 800 HTF showed 1.2–8% increase in modified thermal efficiency [27]. A swirl flow generator in the form of a wavy tape insert was introduced in the SPTC to enhance its thermal performance with an increase in friction factor to about 382–405% [28]. The thermo hydraulic performance in a PTR was numerically analyzed with conical strip inserts by Liu et al. [29]. The discussion so far indicates the potential available to augment the heat transfer phenomena in the absorber of a SPTC. The heat transfer enhancement techniques seen so far has made use of internal longitudinal fins and inserts, which results in a higher amount of pressure drop. However, the use of toroidal rings in a PTR has not been adopted in any of the previous studies to the best of our knowledge. The bottom periphery of the absorber receives concentrated heat flux, while the top periphery receives non concentrated heat flux resulting in higher temperature difference in PTR. It is found that the presence of toroidal rings will improve the thermal performance of the PTR with reduction in absorber tube temperature and significant increase in pressure drop. In view of all these observations, we are interested in examining the numerical model, which is different from the models discussed in the literature with the use of internal circular toroidal rings attached along the inner circumference of the absorber tube. Nine different cases of the absorber with internal toroidal rings are numerically investigated under varying operating conditions. The investigation has been performed in an LS-2 SPTC operating with Syltherm 800 as the HTF. As Nusselt number and thermal efficiency enhancement are the key merits of the modified absorbers, the main objective of the present numerical study lies in determining the optimal case of the toroidal ring absorber for an effective and efficient operation along with other parameters like heat transfer coefficient, thermal efficiency and thermal enhancement index to evaluate the thermal performance of the SPTC. The numerical simulation has been carried out with ANSYS FLUENT 15 computer codes and the developed numerical model has been validated with the published literature.

2.2. Mathematical formulation The parametric definitions and other mathematical equations used in the present study are described below: The thermal efficiency of the SPTC is defined as the ratio of thermal energy produced to the available solar energy;

ηth =

Qpro (1)

Qav

The produced useful thermal energy is determined as,

Qpro = m × cp × (To − Ti )

(2)

The available solar energy is the product of aperture area and incident solar beam radiation as SPTC accepts only Ib.

Qav = A ap × Ib

(3)

The Nusselt number is represented as,

Nu =

2. Methodology

h×d k

(4)

The heat transfer coefficient (h) between the absorber tube and the HTF is given as,

2.1. The investigated SPTC A concentrating solar collector is the one, which forms the image of the sun over the absorber. The parabolic trough collector is an imaging solar collector, which consists of a reflector made of glass or polished metal sheet bent in the shape of a parabola. Along the focal point, an evacuated absorber tube made of steel enclosed in a glass cover has been mounted for the heat transfer fluid to flow and carry away the heat generated as shown in Fig. 1. The geometrical and optical data of the examined absorber tube in a SPTC is given in Table 1. It is necessary to state that the collector has a concentration ratio of 22.74 with an aperture area of 39 m2. Also, the optical efficiency along with the intercept factor has been calculated by considering various losses like manufacturing errors, mirror clearness

Fig. 1. The examined SPTC designed in solid works. 3

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Table 1 Geometric data of the examined SPTC [31].

f=

Symbol

Dimensions

L W F Dro d Dco Dci ρ α τ CR εc ηopt

7.8 m 5m 1.84 m 0.070 m 0.066 m 0.115 m 0.109 m 0.94 0.96 0.96 22.74 0.86 0.7550

(ΔP /L) × d ρ × win2 /2

(7)

It is important to state that for all the examined cases of the absorber with toroidal rings, the overall comprehensive performance is given by means of a term called thermal enhancement index (TEI). It has been evaluated in terms of having identical pumping work with respect to Nusselt number enhancement ratio and friction factor ratio. For example, if the TEI for the modified absorber case is 1.35, then the modified absorber is said to have 35% higher thermal performance than the reference smooth case. The TEI at identical pump work is given [14,32] as;

TEI =

(Nu/ Nu 0 ) (f / f0 )1/3

(8)

2.3. Simulation procedure The governing equations are discretized using the finite volume method (FVM) and the mathematical equations of the geometric model have been solved by using the commercial computational fluid dynamics codes of ANSYS FLUENT 15 package. Realizable k-ε two-equation turbulence model with enhanced wall treatment has been employed. The convective terms in momentum and turbulent kinetic energy equations are discretized with the QUICK scheme, while the pressure is discretized with PRESTO scheme. The energy equation is discretized with the second-order upwind scheme. SIMPLEC scheme has been used for pressure-velocity coupling [12]. The interface between the solid and fluid is set to the coupled wall prior to the initialization. The convergent criteria for the numerical solutions obtained with k, ε, continuity and momentum equations has the value of residuals less than 10−06 , whereas for energy equation the residual is found to be less than 10−09 . Also, the convergence was achieved within the above-said values of the residuals and it ensures that a constant value has been maintained for the outlet area averaged pressure and temperature.

Fig. 2. Circular toroidal rings.

h=

Qpro (π × d × L) × (Tr − Tm )

(5)

In the above equation, the useful thermal energy produced (Qpro), the mean temperature of the receiver at its inner surface (Tr) and the mean HTF temperature (Tm) are established by the computational tool. The Reynolds number is given by,

Re =

ρ × win × d μ

2.3.1. Governing equations The governing equations for incompressible, steady and forced convection turbulent flow of the HTF in the absorber tube is given as follows [33]:

(6)

where ρ , win and μ are the HTF density, inlet velocity and dynamic viscosity, respectively, of the HTF. If the drop in pressure along the absorber tube is known, the friction factor can be calculated by the following equation as [12],

∂ (ρuj ) = 0 ∂x j Momentum equation;

Fig. 3. Absorber tube with toroidal rings. 4

(9)

Applied Thermal Engineering 162 (2019) 114224

K. Arshad Ahmed and E. Natarajan

∂ (ρui uj ) ∂x j ∂uj ⎞ ∂p ∂ ⎡ 2 ∂u ⎤ ∂u + (μ + μ) ⎛⎜ i + (μt + μ) l δij⎥ − ρβ ⎟ − ∂x i ∂x j ⎢ t ∂ 3 ∂ x x ∂xl j i ⎝ ⎠ ⎣ ⎦ (T − T0 ) g

(iv) The convective heat transfer coefficient between the outer glass cover and atmosphere is selected to be 10 W/m2 K. This value is calculated by choosing the typical value of wind speed as 1 m/s from Eq. (15) as [36],

=−

0.58 hout = 4 × V wind × D−co0.42

(10)

Energy equation;

μ ∂T ⎤ ∂ ∂ ⎡⎛ μ (ρuj T ) = + t⎞ Pr σt ⎠ ∂x j ⎥ ∂x j ∂x j ⎢ ⎝ ⎦ ⎣ ⎜

2.3.3. Material and radiative properties The selected heat transfer fluid for the present study is Syltherm 800. The correlations corresponding to the physical properties of the HTF is shown in Table 2. This is the usual thermic oil used in a SPTC, which can work safely from −40 to 400 °C. As this HTF is not included in the fluent material library, the properties are manually inserted in the CFD program for the temperature levels considered. The absorber tube and the toroidal rings are made up of stainless steel and the material properties of the absorber tube are shown in Table 3. The absorber tube has an absorbance (α) value of 0.96 with a selective coating. The emittance of the absorber tube is a function of temperature and it is given according to Eq. (16) as [37],

⎟

(11)

k equation;

μ ∂k ⎤ ∂ ∂ ⎡⎛ (ρuj k ) = μ + t⎞ + Gk + Gb − ρε ⎥ ∂x j ∂x j ⎢ σ k ⎠ ∂x j ⎦ ⎝ ⎣ ⎜

⎟

(12)

ε equation,

μ ∂ε ⎤ ∂ ∂ ⎡⎛ ε2 ε (ρuj ε ) = μ + t⎞ − ρC2 + C1ε C3ε Gb ⎥ ∂x j ∂x j ⎢ σ ∂ x k υε k + ε j ⎠ ⎣⎝ ⎦ ⎜

⎟

(13)

εr = 0.05599 + 1.039 × 10−04 × Tr + 2.249 × 10−07 × Tr2

where T is the static temperature, p is the static pressure, ui and uj are the velocity components, μt is the turbulent viscosity, k and ε are turbulent kinetic energy and dissipation rate, respectively, σT, σk nd σε represent the turbulent Prandtl numbers, Gk and Gb represents the turbulent kinetic energy due to velocity gradient and buoyancy, respectively.

The solar beam radiation (Ib) is selected to be 1000 W/m for all the examined cases of the absorber. Table 4 shows the parameters, which are kept constant. 2.4. Grid independency The grids of all the examined cases have been generated using ICEM 15 commercial codes. It is mainly performed to compute the numerical solutions with finer grids. To obtain the numerical outcomes with a high level of accuracy and computational efficiency, a hexahedral mesh has been introduced as shown in Fig. 5, with Fig. 5a indicating the mesh structure of the receiver tube with glass cover in a cross sectional view and Fig. 5b illustrating the meshing of the inner absorber tube with toroidal rings. In order to capture the shape of the internal toroidal rings sharply, a denser grid has been generated as shown in Fig. 5b. Table 5 indicates the grid independency test conducted for the SAT and the modified absorber tube of the case H = 0.88 and p = 2d. The friction factor and Nusselt number are the two parameters inspected for the grid independency with four different grid systems. The numerical error obtained with the friction factor and Nusselt number is found to be lower for the grid system with 5,53,161 cells for SAT and 21,30,804 cells for the absorber case H = 0.88 and p = 2d, respectively. Also, it is necessary to state that a grid system with approximately 0.55 million

(i) Inlet boundary condition: The volumetric flow rate (V) is ranged from 0.50 m3/min to 0.250 m3/min in a step of 0.50 m3/min. The mass flow rate (m) using the volumetric flow rate is calculated as,

ρ×V (kg/s) 60 × 1000

(16) 2

2.3.2. Boundary conditions The absorber tube with toroidal rings is shown in Fig. 3. The figure clearly depicts the arrangement of toroidal rings inside the absorber. Here, the absorber tube is divided into two sections by bisecting a plane parallel to the z-axis. The following boundary conditions are introduced for modeling the absorber:

m=

(15)

(14)

The inlet temperature (Ti) is ranged from 350 to 650 K in a step of 50 K. The ambient temperature is fixed as 300 K in all the examined cases. (ii) Wall boundary condition: No slip condition exists inside the pipe wall. Around the outer surface of the walls, the absorber is subjected to an heat flux as follows [15], (a) The top periphery receives a uniform heat flux of qtop = Ib × τ × α (b) The bottom periphery receives a heat flux of qbottom = qcal, which has been calculated by means of MCRT (Monte Carlo Ray Tracing) method. The heat flux distribution with variation in circumferential angle around the absorber tube is given in Fig. 4. This profile has been created with the simulation results using MCRT method by using Tonatiuh ray tracer tool [34], and the similar profile can be found in the other studies related to SPTCs [28,35]. (iii) Outlet boundary condition: The outlet section of the absorber is maintained at zero pressure gradient condition.

Fig. 4. Heat flux distribution by MCRT method. 5

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Table 2 Correlations of Syltherm 800 HTF [23]. a + bT (K ) + cT2 (K ) + dT3 (K ) + eT 4 (K )

Thermal conductivity (W/m K) Heat capacity (J/kg K) Density (kg/m3) Viscosity (Pa s)

a

b

C

d

e

Temperature range (K)

1.9002E−1 1.1077E3 1.36E3 8.4866E−2

−1.8752E−4 1.708 −1.0263157 −5.5412E−4

−5.7534E−4 – – 1.3882E−6

– – – −1.5660E−9

– – – 6.672E−13

283.15–673.15 373.15–673.15 293.15–673.15 283.15–673.15

behavior in the smooth absorber tube. In the second phase of the validation, the present numerical model is compared with the experimental outcomes obtained by Forristall [40] in an LS-2 SPTC under same operating conditions. Table 6 shows the temperature increase and thermal efficiency comparison with the present numerical model. It is seen that the mean deviation in temperature rise at the outlet (To) and thermal efficiency is found to be 0.04% and 1.26%, which indicates a minimal value ensuring the high accuracy of the present numerical model. The deviation encountered here is acceptable and it is within 5% of the experimental values [31]. Obviously, the model presented here can predict the flow behavior and thermal performance enhancement in the absorber tube with toroidal rings correctly. Thus, it is believed that the developed model is found to be reliable and it guarantees the prediction of the thermal performance in the LS-2 solar parabolic trough collector. In addition to this, the parabolic trough receiver has also been validated with the concentrated sunlight distribution along the bottom periphery of the absorber tube. From Fig. 7, it is clear that the distribution of heat flux along the bottom periphery of the absorber is in good agreement with the results obtained by Gong et al. [16], under the same angle of incidence and solar irradiation of 0° and 933.7 W/m2, respectively, with the other geometrical parameters remaining the same as shown in Table 1, while similar validation process can be seen from other studies in the literature [41,42].

Table 3 Absorber tube material properties [30]. Properties

Values

Density Specific heat Thermal conductivity

8027.17 kg/m3 502.40 J/kg K 16 W/m K

Table 4 Constant parameters. Parameters

Value

Ib θ Tsky Ta Vwind

1000 W/m2 0° 287 K 300 K 1 m/s

cells is sufficient for SAT and 2 million cells is sufficient for all the absorber cases involving toroidal rings with the selected number of grids being highlighted in the Table 5. 2.5. Model validation The numerical substantiation for the present study is performed in two phases; in the first phase, to establish the accuracy of the present numerical model with the SAT, the computational outcomes are compared to the classical expressions of Gnielinski and Filonenko correlation for Nusselt number and friction factor for the fluid flow [38,39]. The wall temperature of the tube [23] is fixed to 353 K with Syltherm 800 as heat transfer fluid at room temperature in the present study. In the second phase, for the thermal performance of LS-2 SPTC, the present model is validated with the experimental results obtained by Forristall [40]. Realizable k-ε two-equation turbulence model with enhanced wall treatment is applied to simulate the fluid flow, heat transfer and thermal performance in both the phases. For the first phase of validation, the flow behavior and the heat transfer in the smooth absorber tube is considered. The Gnielinski relation for Nu is given as,

Nu =

f /8 × (Re − 1000) × Pr 1 + 12.7 × (f /8)1/2 × (Pr 2/3 − 1)

3. Results and discussion 3.1. Performance comparison of absorbers for 0.15 m3/min flow rate The following subdivision is connected with the thermal performance results of the examined cases of the absorber. The investigation has been carried out under varying inlet temperatures of the HTF ranging from 350 to 650 K, as most of the SPTCs operate in this range [11,35,43,44]. Fig. 8 shows the performance of the SPTC with SAT with varying flow rates operating under three distinct characteristic inlet temperatures of 400, 500 and 600 K. As seen from the figure, the thermal efficiency of the collector increases with an increase in flow rate of the HTF. However, beyond the flow rate of 0.15 m3/min, the improvement in thermal efficiency is very minimal. This investigation indicates the selection of 0.15 m3/min as the most suitable value of flow rate for the SPTC to operate. To conduct performance comparison in the modified absorber, a reasonable value of flow rate correlating with the real-time operating conditions is essential. And also, it is necessary to summon that the comparative analysis needs to be carried out with an feasible value of HTF flow rate for the outcomes to get correspond to the real time working conditions. Fig. 9 depicts the thermal efficiency for the various examined cases of the absorber under different inlet temperatures of the HTF when the flow rate is equal to 0.15 m3/min. The inlet HTF temperature is expressed with the parameter (Ti − Ta/Ib), as this method is most widely used for the expression of thermal efficiency and other parameters in solar parabolic trough collectors [22,44]. It is seen that the thermal efficiency reduces with the rise in inlet fluid temperature. The larger size of the toroidal ring corresponding to the diameter ratio of H = 0.88

(17)

where, the friction factor ‘f ́ is given by,

f = (0.79lnRe − 1.61)−2

(18)

The Filonenko relation for friction factor is given by,

f = (1.82logRe − 1.64)−2

(19)

In Fig. 6, the numerical results for the smooth tube were found to be in good agreement with the classical expressions with a relative deviation of the simulated Nu and f being 7.5 and 9.7%, respectively. The deviation of Nusselt number and friction factor between the empirical correlations and the numerical outcomes are under the range for most of the industrial applications [11]. Hence, the present numerical analysis is found to be valid for determining the heat transfer and fluid flow 6

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K. Arshad Ahmed and E. Natarajan

Fig. 5. Hexahedral mesh generation: cross section of evacuated tube with glass cover (a) and absorber tube with toroidal rings (b).

means of radiation from the absorber outer surface to the glass cover inner surface. It is clear from the figure that the smooth absorber tube accounts for the higher amount of heat loss, whereas the absorber with the toroidal rings for the case H = 0.88 and p = 2d experiences lower magnitude of heat loss. This condition makes the SAT to undergo higher thermal deformation than the modified absorber tube with toroidal rings [46]. The heat loss for the SAT and the case H = 0.88 and p = 2d varies from 85.66 to 2047.92 W and 61.51 to 1944.01 W, respectively. It is evident from Fig. 11 that the higher operating temperatures of the SPTC results in higher average absorber tube temperature, which in turn increase the heat loss as found in Fig. 10 as the emissivity of the absorber increase at higher temperature levels. The absorber with H = 0.88 and p = 2d exhibits lower average absorber tube temperature than the SAT. Figs. 9 and 10 reveals that the modified absorber with toroidal rings exhibits better thermal performance than the SAT. This is because of the higher heat transfer rate in between the absorber tube and the HTF. Fig. 12 shows the heat transfer coefficient for all the examined cases of the absorber, which clearly shows the higher value of heat transfer coefficient with the toroidal ring absorber having H = 0.88 and p = 2d. At lower pitch size, the distance between the adjacent toroidal rings reduces resulting in higher heat transfer surface area between the absorber and the HTF. Also, the number of toroidal rings, which can accompany inside the absorber tube, are also getting increased at lower pitch size. This condition leads to the formation of a thinner boundary layer thereby making the HTF to undergo better mixing with the stronger intensity of turbulence. The Nusselt number corresponding to

Table 5 Grid independence study. Absorber type

No. of cells

f

ferror

Nu

Nuerror

SAT

1,98,006 2,56,900 5,53,161 8,53,051 13,97,320 14,87,928 21,30,804 22,64,852

0.0207 0.0215 0.0277 0.0291 0.3844 0.3852 0.3952 0.3971

28.86% 26.11% 4.81% Base 3.19% 2.99% 0.47% Base

169.2887 171.5895 177.8521 180.5982 383.4579 386.6510 393.8321 394.4152

6.26% 4.98% 1.52% Base 2.77% 1.96% 0.14% Base

H = 0.88 & p = 2d

and pitch size of 2d gives higher thermal efficiency. The thermal efficiency for the case of H = 0.88 and p = 2d varies from 75.25% to 66.68%, whereas the least performance is seen for the SAT with the thermal efficiency ranging from 73.71% to 65.65%. The overall enhancement in thermal efficiency for the case H = 0.88 and p = 2d is about 2.42% higher in comparison with the SAT. The heat loss from the absorber tube is connected to the fourth power of the temperature according to the Eq. (20) as [45],

Q loss =

Ar × σ × (Tr4 − Tc4 ) 1 εr

+

1 − εc εc

( ) Dro Dci

(20)

Fig. 10 indicates the heat loss for the examined cases of absorber under various operating temperatures when the flow rate is equal to 0.15 m3/min. Heat loss here indicates the wastage of thermal energy by 7

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K. Arshad Ahmed and E. Natarajan

Fig. 7. Heat flux validation on the bottom periphery of the PTR.

Fig. 6. Validation of smooth circular tube: Nu – SAT (a) and f – SAT (b). Fig. 8. Performance of the SAT under varying flow rates.

the heat transfer coefficient in Fig. 12 is shown in Fig. 13. It is seen that the higher value of Nusselt number lies with the case H = 0.88 and p = 2d ranging from 297.87 to 1079.02 with 1.29 times increase in comparison with SAT, whereas for the pitch size of 3d and 4d the increase in Nu is 0.82 and 0.8 times, respectively. It is imperative to point out the consequences of thermal efficiency enhancement in the examined cases of the absorber tube. From the above explanation, it is clear that the least efficient case is with the SAT, while the cases with H = 0.88 follows up. Among them, the case with the pitch size of 2d is highly dynamic, with the cases of 3d and 4d being less efficient to follow further. Subsequently, with these curves, the

cases with H = 0.90 and 0.92 are succeeding. To finish with the comparison, the absorber with the larger size of the toroidal ring and lesser pitch size gives higher thermal performance than the other examined cases of the absorber and it corresponds to H = 0.88 and p = 2d. This investigation substantiates that the size and pitch distance between the adjacent toroidal rings act as an influential parameter in determining the thermal performance of the solar collector. This outcome can be accomplished as a key ground rule in the design of absorbers with internal modifications.

Table 6 Temperature rise and thermal efficiency validation with literature results [40]. S. No

1. 2. 3. 4. 5. 6. 7. 8. Mean

Ib (W/m2)

933.7 968.2 982.3 909.5 937.9 880.6 920.9 903.2

V (LPM)

47.7 47.8 49.1 54.7 55.5 55.6 56.8 56.3

m (kg/s)

0.6869 0.6533 0.6363 0.6600 0.6253 0.6209 0.5434 0.5682

Cp (j/kg K)

1745 1830 1908 2001 2078 2086 2223 2181

ρ (kg/m3)

864 820 777 724 676 670 574 605

Ti (K)

375 424 470 523 570 572 652 628

ηth

To (K) Ref. [40]

Present model

Deviation (%)

Ref. [40]

Present model

Deviation (%)

397 446 492 542 589 590 671 647

397.31 446.49 492.35 542.06 589.43 590.44 671.25 646.18

0.08 0.11 0.07 0.01 0.07 0.07 0.04 −0.13 0.04

0.7251 0.7090 0.7017 0.7025 0.6798 0.6892 0.6234 0.6383

0.7344 0.7120 0.7081 0.7097 0.6901 0.6954 0.6474 0.6394

1.28 0.43 0.90 1.03 1.51 0.90 3.86 0.17 1.26

8

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Fig. 9. Thermal efficiency for the examined cases of the absorber.

Fig. 12. Heat transfer coefficient for the examined cases of the absorber.

Figs. 9–13 exhibit the enhancement in thermal performance of the collector with the use of internal toroidal rings. The presence of toroidal rings inside the absorber increases the rate of turbulence resulting in higher values of friction factor and pressure drop. Fig. 14 indicates the friction factor for the examined cases of the absorber. Obviously, the friction factor remarkably increases with the reduction in pitch size, which is in same line with the Nusselt number from Fig. 13. For the pitch size of 2d, 3d and 4d, the friction factor rises to about 14, 7 and 5 times, respectively, higher than the SAT. The main reason behind this friction factor increase can be realized from Fig. 15, which shows the variation of pressure drop for all the examined cases of the absorber. The curves in Figs. 14 and 15 are in an order of sequence except the cases H = 0.92, p = 2d and H = 0.92, p = 3d with minimal deviation. The higher value of pressure drop is seen with the most thermally efficient case (H = 0.88 and p = 2d), whereas the least pressure drop is seen with the SAT. Thermal performance enhancement is connected with higher friction factor and pressure drop. The smaller pitch size of the toroidal ring results in higher dissipation of HTF pressure causing larger friction. This outcome indicates that the enhancement in thermal performance can only be obtained with the penalty of pressure drop. This pressure drop penalty further increases the pumping power causing higher consumption of electricity for the operation of the solar collector. Fig. 16 shows the Nusselt number ratio for the nine modified cases of the absorber. This parameter presents the Nusselt number in the absorber tube with toroidal rings to the Nusselt number in the SAT under same operating conditions. It is a direct indication of thermal performance enhancement in the modified cases of the absorber. The figure indicates that the absorber with H = 0.88 and p = 2d is the most efficient case for all the values of inlet temperatures followed by H = 0.90 and H = 0.92. This improvement occurs due to the existence of greater flow interruption producing stronger vortex currents thereby promoting high-level mixing of HTF in the flow regime. The pressure drop penalty in the absorber tube with toroidal rings is related to the friction factor ratio as shown in Fig. 17. The friction factor ratio for the smaller size of the toroidal rings corresponding to H = 0.92 with the pitch size of 2d, 3d, and 4d is relatively constant for the examined levels of temperature. Contrary to it, the use of toroidal rings of a larger size corresponding to H = 0.88 give rise to extremely higher values of friction factor ratio close to 15.61 for the pitch size of 2d, followed by the pitch size 3d and 4d having the values of 9.3 and 5.95, respectively. The deeper analysis of this parameter reveals that the increase in friction factor ratio causes severe turbulence, which makes the HTF feed pump to consume a higher magnitude of mechanical work

Fig. 10. Heat loss for the examined cases of the absorber.

Fig. 11. Average absorber tube outer surface temperature for the examined cases.

9

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K. Arshad Ahmed and E. Natarajan

Fig. 13. Nusselt number for the examined cases of absorber.

Fig. 16. Nusselt number ratio for the modified cases of the absorber.

Fig. 14. Friction factor for the examined cases of the absorber.

Fig. 17. Friction factor ratio for the modified cases of absorber.

for its operation. 3.2. Overall performance comparison Fig. 18 presents the overall heat transfer performance for the modified cases of absorber under various operating temperatures by considering both increase in heat transfer and flow resistance by means of a term called thermal enhancement index (TEI). This index combines the Nusselt number ratio and friction factor ratio under the identical level of pumping work with respect to Eq. (8). It compares the absorber with and without toroidal ring characterized by the same amount of pump work for operation. It is seen from the figure that the case with H = 0.92 and p = 2d exhibits a higher value of TEI of about 1.21 making it as an energy-efficient case, whereas the thermally efficient case of H = 0.88 and p = 2d has a lower value of TEI as 1.10. For the HTF inlet temperatures from 400 to 600 K, the optimum energy efficient absorber case is H = 0.92 and p = 2d. When the collector operates at this temperature range, the optimum energy efficient case of the absorber has a smaller size of the toroidal rings. It is noticeable that the toroidal ring absorber with H = 0.88 has a lower value of TEI ranging

Fig. 15. Pressure drop for the examined cases of the absorber.

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enhancement is seen in this temperature level as shown in Table 7. Fig. 20 shows the velocity contour and the corresponding streamlines for the thermally enhanced case of H = 0.88 and p = 2d at z/L = 0.5 at a flow rate of 0.15 m3/min. The presence of toroidal rings disrupts the boundary layer and enables the mixing of HTF from the bottom periphery of the absorber tube to the top periphery of the absorber and vice versa. This boundary layer disruption activates the formation of vortices along the core region of fluid flow. Also, the presence of toroidal rings induces the swirl flow in the absorber tube resulting in fluid agitation for better heat transfer performance. From the velocity field discussed, the presence of toroidal rings improves the mixing of HTF and has a greater impact on the temperature distribution in the absorber tube. Fig. 21 shows the temperature distribution in the absorber tube for the thermally enhanced case and SAT. It can be seen that under the same operating conditions, the tube temperature for the thermally efficient optimal case of H = 0.88 and p = 2d is probably lower than that of SAT. For this case, the absorber tube peak temperature decreases from 636.68 to 629.88 K, whereas the average temperature decreases from 617.65 to 611.39 K. The decrease in tube temperature will attribute to the heat transfer enhancement between the absorber and the HTF for a given condition of solar insolation and fluid inlet temperature. This phenomenon is induced as a result of the significant value of fluid flow rate being used thereby resulting in lower absorber tube temperature with stronger mixing of HTF.

Fig. 18. Overall performance of heat transfer for the modified cases of the absorber.

from 1.10 to 0.92, 1.13 to 0.93, 1.12 to 0.92 for the pitch size of 2d, 3d and 4d, respectively. This condition leads not to a higher TEI for the case H = 0.88, as the friction factor ratio increases tremendously compared to the Nusselt number ratio as seen before.

3.5. Final assessment of outcomes 3.3. Performance analysis of optimal cases of absorbers

The final subsection is dedicated for summarising the outcomes obtained and comparing the results with the other studies of internally modified absorbers. Figs. 22–24 indicates the thermal efficiency, pressure drop and TEI for the examined absorber cases at Ti = 600 K and 0.15 m3/min flow rate. These figures are helpful in determining the thermally enhanced optimal case and energy efficient optimal case of the absorber tube. Fig. 22 proves that the higher value of thermal efficiency is seen for the case H = 0.88 and p = 2d succeeded by H = 0.88 and p = 3d while the case H = 0.88 and p = 4d follows up with the efficiency of 69.32, 69.19 and 68.99%, respectively. It is seen that, the thermal performance enhancement is coupled with the penalty of pressure loss. From Fig. 23, the pressure drop for the respective cases of the absorber is found to be 3544.55, 1419.58 and 1366.87 Pa, respectively. From the above justification, the case H = 0.88 and p = 2d is the thermally efficient optimal case, while the other cases of absorber have been penalized with a lower value of Nusselt number ratio. From

Fig. 19 depicts the overall performance analysis of the energy efficient and thermally efficient optimal cases of the modified absorbers. The energy efficient optimal case of H = 0.92 and p = 2d experiences lower value of pressure drop as seen from Fig. 15, which will lead to a lower value of friction factor ratio as shown in Fig. 17. Hence, this case leads to a higher value of thermal enhancement index, as seen from Fig. 19, which will consequently lead to higher heat transfer performance. On the other hand, the thermally efficient absorber case of H = 0.88 and p = 2d experiences higher value of pressure drop leading to higher friction factor ratio resulting in lower value of thermal enhancement. Hence, the thermally efficient absorber has lower heat transfer performance than the energy efficient absorber. Table 7 outlines the data required for the comparison of the examined cases of absorber tube in the usual operating temperature levels of SPTC from 400 to 600 K. The data with reference to the inlet temperatures of 400, 500 and 600 K is given in the table. It is seen from the table that the higher thermal performance enhancement is seen at higher temperature levels. The thermal efficiency for the SAT at 600 K is 66.82%, while the thermally efficient optimum case with H = 0.88 and p = 2d has a thermal efficiency of 69.32%, which is 3.74% higher than the SAT. The energy efficient optimum case with H = 0.92 and p = 2d exhibiting a higher value of TEI has an efficiency of 68.08%, which is 1.88% higher than the SAT. Moreover, it is vital to state that the Nusselt number ratio reaches to a maximum of 2.33 and 1.49, while the friction factor ratio holds the value of 14.62 and 1.99 for the thermally efficient optimum case and the energy efficient optimum case, respectively. Further, from the TEI point of view, the higher friction factor ratio case is characterized as an unsuitable case, while from thermal performance point of view; higher thermal efficiency case is a suitable case. 3.4. Analysis of velocity and temperature fields at Ti = 600 K Temperature and velocity fields play a vital role in the functioning of a solar thermal system. This subsection depicts the results with respect to the HTF inlet temperature of about 600 K. The highest thermal

Fig. 19. Overall performance analysis of optimal absorber cases. 11

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Table 7 Results at temperature of 400, 500 and 600 K when the flow rate is equal to 0.15 m3/min. HTF inlet temperature (Ti)

Absorber tube

ΔP (Pa)

Nu/Nu0

f/f0

TEI

ηth

H

p (mm)

400 K

0 0.88 0.88 0.88 0.9 0.9 0.9 0.92 0.92 0.92

0 2d 3d 4d 2d 3d 4d 2d 3d 4d

354.50 5251.35 2315.67 2048.94 1739.74 1293.24 972.99 789.50 680.41 602.30

1.000 2.19 1.83 1.72 1.71 1.59 1.44 1.39 1.26 1.23

1.00 14.82 7.52 5.78 4.91 3.65 2.45 2.06 1.92 1.73

1.00 0.89 0.93 0.95 1.00 1.03 1.07 1.17 1.14 1.10

0.7351 0.7485 0.7477 0.7469 0.7460 0.7448 0.7434 0.7411 0.7401 0.7386

500 K

0 0.88 0.88 0.88 0.9 0.9 0.9 0.92 0.92 0.92

0 2d 3d 4d 2d 3d 4d 2d 3d 4d

260.06 4237.46 1827.15 1655.66 1313.58 924.84 738.89 542.04 469.65 425.00

1.00 2.31 1.89 1.81 1.76 1.63 1.52 1.46 1.20 1.16

1.00 15.01 7.55 6.37 5.05 3.56 2.38 1.89 1.65 1.46

1.000 0.94 0.96 0.97 1.03 1.07 1.14 1.20 1.14 1.09

0.7252 0.7404 0.7401 0.7391 0.7382 0.7371 0.7358 0.7335 0.7321 0.7310

600 K

0 0.88 0.88 0.88 0.9 0.9 0.9 0.92 0.92 0.92

0 2d 3d 4d 2d 3d 4d 2d 3d 4d

197.22 3544.55 1419.58 1366.87 1068.83 753.11 584.19 462.79 380.21 348.00

1.00 2.33 1.88 1.82 1.76 1.66 1.58 1.49 1.25 1.07

1.00 14.62 7.62 6.93 5.42 3.82 2.61 1.99 1.83 1.65

1.000 0.95 0.94 0.96 1.01 1.06 1.15 1.19 1.11 1.09

0.6682 0.6932 0.6919 0.6899 0.6873 0.6856 0.6840 0.6808 0.6791 0.6772

Fig. 21. Temperature contours; SAT (a) and H = 0.88 and p = 2d (b).

Fig. 24, the case H = 0.92 and p = 2d has a higher value of TEI equal to 1.19, and hence it is the energy efficient optimal case. The cases with lower TEI have been punished due to higher pressure losses. The final selection of the optimal absorber tube becomes complex as it requires several parameters like thermal efficiency, pressure drop, friction factor, etc to be taken into consideration. The final outcomes indicate that for operating the SPTC at a higher temperature range, the absorber tube with toroidal ring having diameter ratio 0.88 and pitch size of 2d is the best choice. On the other hand, from effective energy utilization point of view, the absorber tube with toroidal ring having a

diameter ratio of H = 0.92 and pitch size p = 2d is the best choice. Also at this point, it is necessary to compare the results of the present study with other internally modified absorbers. Gong et al. [16] examined the incorporation of pin fin arrays on the lower periphery of the absorber tube and obtained a thermal enhancement index value of 1.05. The use of longitudinal vortex generators inside the parabolic trough receiver was numerically studied by Cheng et al. [11] with an thermal enhancement index value of 1.12 for the majority of the analyzed cases. In the present study, the thermal enhancement index is enhanced to

Fig. 20. Velocity and streamline contour for the case H = 0.88 and p = 2d. 12

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Fig. 22. Thermal efficiency for the examined cases of the absorber at Ti = 600 K and flow rate equal to 0.15 m3/min.

been carried out with the inlet temperature of the HTF ranging from 350 to 650 K with the flow ranging from 0.50 m3/min to 0.250 m3/min. Much wider attention has been given to the case with 600 K of HTF temperature as most of the parabolic trough collectors operate in this range for efficient working. From the final outcomes obtained for Ti = 600 K and 0.50 m3/min of HTF flow rate, the toroidal ring having a diameter ratio of 0.88 and pitch size of 2d exhibits a higher thermal efficiency of 69.32% while the SAT leads to a thermal efficiency of 66.82%. The case with H = 0.88 and p = 2d is the thermally efficient optimal case as it has higher thermal efficiency. But, due to the significant increase in friction factor and pressure losses, the TEI for this case is sufficiently lower. The heat loss for the thermally efficient optimal case is lower among all the modified cases and it varies from 61.51 to 1944.01 W, while for SAT it varies from 85.66 to 2047.92 W. The case with H = 0.92 and p = 2d is

a value close to 1.20. This investigation validates the outcome of the present work with the above-said literature and recommends the use of internal toroidal rings in the absorber tube of a SPTC for satisfying thermal performance enhancement. It is also important to state that during the fabrication of internally modified absorbers, care must be taken to minimize the geometrical errors and further a thorough fatigue analysis has to be carried out to study the behavior of thermal stress.

4. Conclusion The present numerical study examines the use of toroidal rings for heat transfer enhancement in an LS-2 parabolic trough collector with Syltherm 800 as HTF. Nine different cases of the absorber with toroidal rings having a diameter ratio of 0.88, 0.90 and 0.92 and pitch size of 2d, 3d and 4d have been investigated with CFD tools. The investigation has

Fig. 23. Pressure drop for the examined cases of the absorber at Ti = 600 K and flow rate equal to 0.15 m3/min. 13

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