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Wind speed effect on the ﬂow ﬁeld and heat transfer around a parabolic trough solar collector A.A. Hachicha, I. Rodríguez, A. Oliva ⇑ Heat and Mass Transfer Technological Centre (CTTC), Universitat Politècnica de Catalunya-BarcelonaTech (UPC), ETSEIAT, Colom 11, 08222 Terrassa, Barcelona, Spain

h i g h l i g h t s Large Eddy Simulations to study ﬂuid ﬂow and heat transfer on a PTC are performed. Drag and lift forces were shown to be independent on the Reynolds number. Nusselt number is highly dependent on the pitch angle. Heat losses from the HCE are overestimated compared to literature’s correlations. Main frequencies affecting the stability of the PTC structure are determined.

a r t i c l e

i n f o

Article history: Received 30 October 2013 Received in revised form 29 March 2014 Accepted 7 May 2014

Keywords: Parabolic trough solar collector Wind speed effect Large Eddy Simulations Heat transfer coefﬁcient PTC stability

a b s t r a c t Parabolic trough solar collectors are currently one of the most mature and prominent solar technology for the production of electricity. These systems are usually located in an open terrain where strong winds may be found, and could affect their stability and optical performance, as well as the heat exchange between the solar receiver and the ambient air. In this context, a wind ﬂow analysis around a parabolic trough solar collector under real working conditions is performed. A numerical aerodynamic and heat transfer study based on Large Eddy Simulations is carried out to characterise the wind loads and heat transfer coefﬁcients. After the study carried out by the authors in an earlier work (Hachicha et al. 2013) at ReW1 ¼ 3:9 105 , computations are performed at a higher Reynolds number of ReW2 ¼ 1 106 , and for various pitch angles. The effects of wind speed and pitch angle on the averaged and instantaneous ﬂow are assessed. The aerodynamic coefﬁcients are calculated around the solar collector and validated with measurements performed in wind tunnel tests. The variation of the heat transfer coefﬁcient around the heat collector element with the Reynolds number is presented and compared to the circular cylinder in cross-ﬂow. The unsteady ﬂow is studied for three pitch angles: h ¼ 0 ; h ¼ 45 and h ¼ 90 and different structures and recirculation regions are identiﬁed. A spectral analysis around the parabola and its receiver is also carried out in order to detect the most relevant frequencies related to the vortex shedding mechanism which affects the stability of the collector. Ó 2014 Elsevier Ltd. All rights reserved.

1. Introduction Parabolic trough solar collectors (PTCs) are considered to be one of the most mature, successful, and proven solar technology for electricity generation. PTCs are typically operated at 400 °C, and a synthetic oil is commonly used as heat transfer ﬂuid (HTF). A PTC consists of a parabolic trough-shaped mirror that focus sunrays onto a heat collector element (HCE), which is mounted in the focal line of the parabola. The HTF circulates through the solar ⇑ Corresponding author. Tel.: +34 93 739 8192; fax: +34 93 739 8101. E-mail address: [email protected] (A. Oliva). URL: http://www.cttc.upc.edu (A. Oliva). http://dx.doi.org/10.1016/j.apenergy.2014.05.037 0306-2619/Ó 2014 Elsevier Ltd. All rights reserved.

ﬁeld to transport the absorbed heat. The solar ﬁeld is made up of a series of several solar reﬂectors which concentrate the direct solar radiation by means of a Sun-tracking system. The HCE is typically composed of a metal receiver tube and a glass envelope covering with vacuum between the two to reduce the convective heat losses. The thermal and optical performances of PTCs are related to the wind action on the structure and the tracking system. During real working conditions, the array ﬁeld of solar collectors require good precision in terms of both mechanical strength and optical characteristics. Such requirements are sensitive to turbulent wind conditions, and should be considered in the design of these systems. Hence, a wind ﬂow analysis plays a major role for designing the

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Nomenclature Greek letters m kinematic viscosity ðm2 =sÞ h pitch angle Roman letters D diameter (m) f frequency ð1=sÞ h convective heat transfer coefﬁcient ðW=m2 KÞ k thermal conductivity ðW=mKÞ Lr recirculation length (m) T temperature (K) U velocity (m/s) W aperture (m) Abbreviations CFD computational ﬂuid dynamics CV control volume HCE heat collector element solar collectors and can lead to a better understanding of the aerodynamic loading around the parabolic reﬂector, as well as the convection heat transfer from the HCE. Since the 1970s, numerous numerical and experimental studies have been proposed to study the heat transfer characteristics of PTCs [1–3]. However, wind ﬂow studies around the PTC are scarce. Sandia National Laboratories published in the early 1980s some wind tunnel tests [4,5] to investigate characteristics of mean wind loads produced by airﬂow around a PTC. These reports were conducted for different conﬁgurations of the PTC and ﬂow ﬁeld environments. The inﬂuence of various geometric design parameters for isolated PTC and for a collector within an array ﬁeld were assessed. More recently, a series of wind tunnel experiments were conducted by Hosoya et al. [6] from March 2001 to August 2003. The wind-tunnel study included the distribution of local pressure across the face of the solar collector using a 1:45 model. Two versions of instrumented collector models were used to measure the loads and pressure distribution across the face of the collector. One was a light-weight model for measuring wind loads using a high-frequency force balance, and the other was a pressure-tapped model designed to obtain the pressure distribution across the face of the collector. The effect of the PTC position in an array of solar collectors was also examined. The majority of the numerical studies of the wind ﬂow around solar collectors are based on the Reynolds-Averaged Navier Stokes equations (RANS) (see for instance [7,8]), which suffer from inaccuracies in the prediction of ﬂow with massive separations [9]. In this kind of ﬂows, turbulent ﬂuctuations tend to be under-predicted when using RANS models. This is mainly due to the inability of 2D RANS in capturing the three-dimensional effects (e.g. vortex stretching) and the unsteady motion of the vortex shedding mechanism. On the other hand, as in LES all temporal scales of the ﬂow are computed, intermittent ﬂow ﬂuctuations and unsteady ﬂow features can be well captured [9–11] A recent study by the authors [12] based on Large-Eddy Simulations (LES) allowed to analyse the ﬂuid ﬂow and heat transfer around a PTC for various pitch angles and a ﬁxed wind speed 1 m/s. The study showed that this kind of detailed numerical simulations are feasible, but the effects of a higher wind speed was not explored. In the present work, and following the previous experiences, the impact of wind speed close to real working conditions is considered. The hypothesis made in the experimental measurements of down-scaled prototypes about the independence of the drag and lift forces with the Reynolds number [6] is here submitted to

HTF LES MCV Nu PTC RANS Re St

heat transfer ﬂuid Large Eddy Simulations million of control volumes Nusselt number ðhD=kÞ parabolic trough solar collector Reynolds-Averaged Navier Stokes equations Reynolds number ðUD=mÞ Strouhal number

Subscripts amb ambient avg average fsp front stagnation point g glass envelope max maximum min minimum ref reference

investigation. To do this, the wind ﬂow around the PTC at a wind speed of 3 m/s is studied and compared to the results obtained at 1 m/s. These cases correspond with Reynolds numbers of ReW1 ¼ 3:6 105 and ReW2 ¼ 1 106 (the Reynolds number is deﬁned in terms of the free-stream velocity and the aperture, ReW ¼ U ref W=m). These Reynolds numbers are, by far, larger than those used in the experimental wind tunnel tests where prototypes were tested up to Re ¼ 5 104 . The natural frequencies around the PTC structure and the HCE, which may affect the tracking mechanism and the PTC stability are also studied by means of the analysis of the power spectra of several probes located close to or downstream the PTC and the HCE. Furthermore, the wind speed effects on the heat transfer around the HCE at different pitch angles are also analysed. 2. PTC numerical model 2.1. Mathematical and numerical model The same methodology presented in the previous work [12] for solving the ﬂuid ﬂow and heat transfer around the PTC is adopted. The computational ﬂuid dynamics and heat transfer (CFD&HT) code Termoﬂuids [13] is used to simulate the complex ﬂuid dynamics around the solar collector and its receiver by means of Large-Eddy Simulations (LES). In Termoﬂuids, the Navier–Stokes and energy equations are discretised on a collocated unstructured grid arrangement by means of second-order spectra-consistent schemes, i.e. they preserve the symmetry properties of the continuous operators assuring stability even on coarse grids and high Reynolds numbers [14]. As was pointed out by Verstappen and Veldman [14], these symmetry-preserving schemes are a suitable base formulation when LES are carried out. In the present work, the Wall Adapting Local Eddy diffusivity model within a Variational Multiscale framework [15,16] is used for modelling the subgrid-scale stresses. This model has been proven to give accurate results in ﬂows with massive separations such as those here presented [12,17]. 2.2. Deﬁnition of the case. Geometry and boundary conditions Large-Eddy Simulations of the wind ﬂow around a PTC at ReW ¼ 106 and different pitch angles of (h ¼ 0 ; 45 ; 90 ; 135 and 270 ) have been performed. The Reynolds number is here

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deﬁned in terms of the free-stream velocity U ref , and the parabola aperture W (ReW ¼ U ref W=m). This Reynolds number corresponds to a wind speed of U ref ¼ 3 m=s, which is a typical value encountered in solar plants. In addition, the ﬂow around the parabola has been compared to that obtained by the authors at a lower Reynolds numbers of Re ¼ 3:6 105 (U ref ¼ 1 m=s) [12]. All computed ﬂows are around a full-scale Eurotrough solar collector [18] and its typical HCE with a stainless steel absorber (inner/outer diameter of 6:6=7:0 cm) and glass cover (10:9=11:5 cm of inner/outer diameter). As in the previous work [12], the same domain size of 25 W 9 W p W in the stream-, cross-stream and span-wise directions have been used. The parabola of aperture W ¼ 5:8 m is located at 5 W in the stream-wise direction (see Fig. 1). To solve the computational domain, no-slip conditions at the parabola and HCE have been imposed. Although the actual inlet conditions are turbulent, in the present computations a constant inlet velocity proﬁle with zero turbulence level has been prescribed. However, a sufﬁcient distance from the inlet has been set so as the ﬂow entering the PTC could develop. Even if perturbations at the inlet boundary would be added, these ﬂuctuations would be damped by a grid stretched out towards the boundaries, as shown by Breuer [20]. Furthermore, as it is shown hereafter, the impact of such inlet boundary condition in the computations is not important as the results obtained are capable of reproducing with good accuracy, when compared with experiments, the forces acting on the PTC. For the top and bottom boundaries, slip conditions have been set, whereas in the span-wise direction, the ﬂow has been considered to be spatially periodic, thus periodic boundary conditions have been imposed. To solve the energy equation, temperatures of the glass cover and ambient air are ﬁxed at T g ¼ 350 K and T amb ¼ 300 K, respectively. A Neumann boundary condition (@T ¼ 0) is prescribed in the top, bottom @n and outlet boundaries for temperature. For more details about boundary conditions, the reader is referred to [12]. The three-dimensional meshes used to solve the computational domain have been obtained by the constant-step extrusion in the span-wise direction of a two-dimensional unstructured grid. Although not shown here, extensive grid reﬁnements for each pitch angle have been conducted. Details of the ﬁnal computational meshes for each pitch angle are shown in Table 1.

3. Heat transfer from a circular cylinder in cross-ﬂow and wind speed effects In order to analyse the inﬂuence of the wind speed in the heat transfer of the HCE, the numerical model has ﬁrst been used on a circular cylinder in cross-ﬂow. In this work, simulations have been performed for a Reynolds number of ReD ¼ 21; 600 (here the Reynolds number is deﬁned in terms of the free-stream velocity and

Table 1 Details of adopted meshes for each pitch angle. NCV plane , number of control volumes (CV) in the plane, N planes , number of planes in the span-wise direction, NCV total , total number of CVs NCV total ¼ NCV plane N planes . Pitch angle NCV plane N planes NCV total (MCVs)

0 112,322 96 10.78

45 104,477 96 10.02

90 102,914 96 9.87

135 99,281 96 9.53

180 106,223 96 10.19

270 104,188 96 10.0

the cylinder diameter, ReD ¼ U ref D=m) which corresponds to a wind speed of 3 m/s. Heat transfer characteristics around the cylinder have been calculated and compared to experimental measurements by Scholten and Murray [19]. In addition, results have also been compared to the lower Reynolds number of Re ¼ 7200 [12] (which corresponds to a wind speed of 1 m/s). The boundary conditions and mesh distribution have been considered in a similar way as in the previous Section 2.2. The computational domain is extended to ½15D; 25D; ½10D; 10D; ½0; pD in the stream-, cross-stream and span-wise directions, respectively. The cylinder with a diameter D is placed at (0, 0, 0). The results shown herein are computed for a ﬁner grid of 147; 000 64 planes (i.e. 147,000 CVs in the 2D plane extruded in 64 planes yielding approx 9.4 MCVs). In Fig. 2, the predicted local Nusselt number around the circular cylinder is plotted. For comparison, the results by Scholten and Murray [19] are also shown. As can be observed, a fair agreement between both numerical and experimental results has been obtained. In general, numerical results follow the same trend as the experimental ones. The minimum local values of the heat transfer coefﬁcient occur at approx 85 from the stagnation point, whereas the maximum values are reached at the stagnation point and at the rear end of the cylinder. As pointed out in Hachicha et al. [12], at ReD ¼ 7200, the largest differences are found in the back side of the cylinder as the ﬂow ﬂuctuations are the largest, being more difﬁcult to perform the experimental measurements [19]. When comparing both Reynolds numbers (see Fig. 3), i.e. ReD ¼ 7200 and ReD ¼ 21; 600, the increasing of inertial effects due to the increasing of Reynolds number led to the earlier separation of the boundary layer. Indeed, there is a displacement of the location of the minimum Nusselt number at ReD ¼ 21; 600 towards the stagnation point. The variation of the Nusselt number in the rear zone of the cylinder is smoother at ReD ¼ 7200, and a secondary peak is observed for ReD ¼ 21; 600 (at about 118 ). By increasing the Reynolds number from ReD ¼ 7200 to ReD ¼ 21; 600, the overall magnitude of the Nusselt number increases by a factor of 2 from 52:2 to 101:1. The value reported in the experiments was 103:4 for ReD ¼ 21; 600, being the average difference between both numerical and experimental results of approx 2:2%.

Fig. 1. Computational domain of the wind ﬂow study around an Eurotrough solar collector.

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2.5 Present Exp(Scholten and Murray)

(a)

Present(LS-2) Present(ET,ReW1) Present(ET,ReW2) Exp

160 2

140 120

1.5

Nu

CP

100 80

1

60 40

0.5

20 0 0

0 50

100

150

200

250

300

0

350

50

100

150

200

250

300

350

Pitch angle (degree)

angle (degree) Fig. 2. Variation of the Nusselt number around a cross-ﬂow horizontal cylinder, and comparison with experimental measurements [19] at ReD ¼ 21; 600. 2

160

ReD=7200 ReD=21600

(b)

Present(LS-2) Present(ET,ReW1) Present(ET,ReW2) Exp

1

Cf

140 120

0

100

Nu

-1 80 60

-2

40

0

100

150

200

250

300

350

Pitch angle (degree)

20 0

50

0

50

100

150

200

250

300

350

α (degree) Fig. 3. Comparison of Nusselt number around a circular cylinder in cross-ﬂow for two Reynolds numbers: ReD ¼ 7200 and ReD ¼ 21; 600.

4. Results and discussion As aforementioned, simulations have been conducted to study the wind effects around the PTC for two Reynolds numbers based on the aperture ReW1 ¼ 3:6 105 and ReW2 ¼ 1 106 , and different pitch angles of h ¼ 0 ; h ¼ 45 , h ¼ 90 ; h ¼ 135 ; h ¼ 180 , h ¼ 270 . Thereafter, these effects are analysed in terms of the average forces on the parabola, the ﬂow conﬁgurations and the instantaneous ﬂow. 4.1. Wind speed effects on the averaged forces The averaged forces on the parabola have been validated against the experimental data [6] in the previous work [12]. To that end, the wind ﬂow was studied around a typical LS-2 parabolic trough solar collector (without a solar receiver) as proposed in the experimental study [6], and simulations were performed for a full-scale case with a Reynolds number of 2 106 . In the present work, drag and lift coefﬁcients have been computed for the Eurotrough PTC at different pitch angles and for both Reynolds numbers. The comparison with experimental measurements [6] and those obtained for the LS-2 PTC are depicted in Fig. 4. As can be seen in Fig. 4, numerical results obtained are almost within the error-bars of experimental measurements from the wind-tunnel data [6]. Discrepancies between computed and measured aerodynamic coefﬁcients are mainly due to the unsteady ﬂow behaviour and

Fig. 4. Predicted and measured aerodynamic parameters for Eurotrough PTC. Wind speed effect and comparison with wind-tunnel data [6], and numerical results for LS-2 [12]. (a) Drag and (b) lift coefﬁcients.

ground effects, which may affect the ﬂow structures and separations behind the PTC and require long measurement duration. It is worth noting that the averaged aerodynamic coefﬁcients at both Reynolds numbers exhibit an almost identical proﬁle, which proves the stability of the aerodynamic coefﬁcients at this range of Reynolds numbers. The predicted results are also in agreement with the experimental observations of Hosoya et al. [6]. In their scaled-down experimental tests carried out at Reynolds numbers Re < 5 104 , they concluded that beyond Re ¼ 5 104 load coefﬁcients were independent of the Reynolds numbers, thus being directly extrapolated to a full-scale PTC. In the light of the results for the load coefﬁcients here presented, the aforementioned hypothesis of Hosoya et al. [6] can be conﬁrmed. It should be mentioned that in the experimental measurements of Randall et al. [5], they also commented on the independence of averaged aerodynamic coefﬁcients with Reynolds numbers. However, it was mentioned that it could be affected when the leading edge is close to the alignment with the stream causing some errors to the lift coefﬁcient. There are also some differences between numerical results of the LS-2 PTC and Eurotrough PTC, which are due to the geometry of both solar collectors. It should be pointed out that from a numerical point of view the results presented for the LS-2 are statistically more converged in time than those for the Eurotrough. This is due to the complex grid used in the simulation of the Eurotrough PTC, which also included the receiver tube (it was not included in the LS-2 simulations). This fact, imposes large differences in both spatial and temporal scales between the parab-

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ola and the receiver. Thus, in the numerical simulations the explicit algorithm requires smaller time-steps (of about 5 105 ) for solving all the relevant temporal scales of the ﬂow, dominated by the ﬂow around the receiver. This decrease in the time-step, together with the more complex ﬂow around the receiver, imposed a larger simulation time in order to reach a statistical averaged ﬂow. 4.2. Wind speed effects on the averaged ﬂow The time-averaged ﬂow is also studied for different pitch angles and compared for both Reynolds numbers. Different structures and recirculation regions are encountered around the collector and the HCE. These ﬂow structures are strongly related to the collector orientation and the pitch angle. The effect of the wind speed on the structures and recirculation regions observed around the PTC has also been assessed. By increasing the Reynolds number, the ﬂow pattern does not change and the recirculation regions are similar to those found at ReW ¼ 3:6 105 with a small variation of the recirculation length behind the parabola, as shown in Fig. 5. The recirculation length for different pitch angles and for both Reynolds numbers is determined and presented in Table 2. It can be seen in this Table that the recirculation length is almost in the same range for both Reynolds numbers. This similarity has also been depicted in the comparison of averaged streamlines for both Reynolds numbers (see Fig. 5). However, in general terms it is observed that the recirculation length enlarges with the Reynolds number when the concave surface of the parabola is exposed to the wind direction, i.e. h < 90 , and shrinks for the convex surface conﬁguration (h > 90 ). At vertical position of h ¼ 0 , a large recirculation region is observed behind the PTC with maximum drag and minimum lift forces. This region increases with the Reynolds number and extends up to 8:32 W at ReW2 ¼ 1 106 . By moving the PTC to a pitch angle of 45 , the recirculation decreases compared to the vertical position, and the shear layer is reduced. However, its length at ReW2 is almost 30% larger than for ReW1 extending up to 3:06 W. The drag coefﬁcient decreases, whereas the absolute value of the lift coefﬁcient increases. The minimum of recirculation length occurs at the horizontal position of 90 , where only small eddies are encountered in the leeward side of the PTC. This value is about 0:1 W for both Reynolds numbers. The drag forces also reach their minima at this position. At a pitch angle of 135 , the recirculation region enlarges again, and a pair of medium-sized eddies are formed behind the PTC where negative pressure is observed. However, due to the aerodynamic proﬁle of the collector, the recirculation length shrinks with Reynolds number and extends up to 1:47 W at ReW2 . By moving the PTC to the vertical position at 180 , the recirculation length reaches a new maximum and, similar to h ¼ 0 , two large eddies are formed behind the PTC. The shear layer is again elevated and drag forces are also increased. The recirculation zone for the higher Reynolds number is about 7% smaller due to the convex surface conﬁguration. When the PTC is placed at the stow position, i.e. h ¼ 270 , the recirculation region is sharply reduced similarly to the working position h ¼ 90 . Therefore, the drag forces also decrease. At this position, the recirculation length remain almost unchanged with the Reynolds number around 0:2 W. 4.3. Wind speed effects on the heat transfer around the HCE As it was discussed in the previous work [12], for pitch angles of h ¼ 0 ; 45 ; 90 and 270 , convection heat transfer around the HCE can be considered as forced convection, whereas for angles of 135 and 180 mixed convection occurs. In Fig. 6, the distribution of the local Nusselt number for different pitch angles, together with the comparison between both Reynolds numbers, are shown.

According to this Figure, the proﬁle of the Nusselt number around the HCE is affected with the pitch angle and the displacement of the ﬂuid around the HCE due to the tilt of the parabola. At the higher wind speed, i.e. the higher Reynolds number, the proﬁle of the Nusselt number follows a similar trend to that observed at the lower speed, ReW1 . However, the higher the Reynolds number, the higher the magnitude of the Nusselt number and local peaks become more pronounced. Moreover, the effect of the parabola and the ground is more signiﬁcant when increasing the Reynolds number. While at the lower Reynolds number, the local distribution of the Nusselt number was observed to follow the same trend to that of a circular cylinder in cross-ﬂow [12], this is not the case for ReW2 . This can be clearly observed in Fig. 7, where the distribution at pitch angles of h ¼ 90 and h ¼ 270 (working and stow modes), together with the circular cylinder in cross-ﬂow are depicted. Large differences in the behaviour are obtained in the rear zone. At these positions, the combined effect of the parabola and the ground tend to reduce the large ﬂuctuations of the near wake leading to a smoother distribution of the Nusselt number in the rear zone, especially when it comes to the minimum and maximum magnitudes. Table 3 summarises the average, front stagnation, maximum and minimum Nusselt numbers (Nuav g ; Nufsp ; Numax ; Numin , respectively), together with the location where the extrema occurs for both Reynolds number (ReW1 and ReW2 ). These results are also compared with available experimental data [19] and the correlation of Zukauskas [21] for a circular cylinder. In addition to the increase in magnitude of the Nusselt number with the Reynolds number, compared to the circular cylinder in cross-ﬂow at the same Reynolds number, the average Nusselt number decreases. This is due to the effect of the parabola which is desirable as it reduces the heat losses from the HCE, thus improving the performance of the PTC. When the parabola is placed at the vertical position of h ¼ 0 , the averaged Nusselt number is increased by 70% compared to the lower wind speed case and reduced to 59% compared to the circular cylinder in cross-ﬂow case. At a pitch angle of h ¼ 45 , the averaged Nusselt number is 68% higher than the obtained for ReW1 , and a 40% lower compared to the circular cylinder in cross-ﬂow case. Although the effect of the parabola is less important than for the vertical position h ¼ 0 , the peaks at 45 increase considerably at high wind speed (see also Fig. 6b). The proﬁle of the Nusselt number still follows the tilt of the parabola and remains unchanged when increasing the Reynolds number. The distribution of the Nusselt number at the working position h ¼ 90 is symmetric (see Fig. 6c), and its averaged magnitude a 85% higher when compared to the lower wind speed case. At a pitch angle of h ¼ 135 , the averaged Nusselt number increases a 72% relative to the lower wind speed case and decreases a 55% compared to the circular cylinder in cross-ﬂow case. At this position mixed convection occurs, and the proﬁle of Nusselt number is quite different to that of the circular cylinder in cross-ﬂow. The effect of the wind speed is signiﬁcant, and the peaks increase sharply compared to the lower wind speed which exhibits a ﬂatter proﬁle (see Fig. 6d). A similar behaviour also takes place at h ¼ 180 where mixed convection occurs. The averaged Nusselt number at ReW2 is 61% higher than at ReW1 , and about 64% lower compared to the circular cylinder. By moving the PTC to the stow position h ¼ 270 , the Nusselt number proﬁle is also symmetric (see Fig. 6f) and similar to the working position h ¼ 90 . The averaged Nusselt number is 62% higher at ReW2 compared to the lower wind speed case, and 30:5% compared to the circular cylinder. In general, it should be pointed out that the averaged magnitude of the Nusselt number is overestimated when correlations for the circular cylinder in cross-ﬂow are used. Thus, when computing the heat losses around the HCE of a PTC, these

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205

Fig. 5. Streamlines for the time-averaged ﬂow around the parabolic collector for different pitch angles: (a) h ¼ 0 , (b) h ¼ 45 , (c) h ¼ 90 , (d) h ¼ 135 , (e) h ¼ 180 , (f) h ¼ 270 . Comparison between both Reynolds numbers: ReW1 (left) and ReW2 (right).

correlations should be used with due respect as they may over-predict heat losses in more than a 64% depending on the pitch angle. 4.4. Wind speed effects on the unsteady ﬂow In order to be able to control undesirable ﬂuctuating forces, the study of the unsteady ﬂow ﬁeld around the PTC and its behaviour at different pitch angles may be useful. It should be borne in mind

that the collector structure should sustain wind loads as well as keep accurate sun tracking. Vortex shedding in the wake of the PTC induces alternating forces perpendicular to the wind direction which might affect its structure. These vortices, depending on the pitch angle, are shed at a determined frequency, and may produce undesirable effects such as deﬂections, vibrations, torsional moments, resonance with the structure and, at the end, stresses leading to the structure failure. Thus, in order to study the

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Table 2 Variation of the ratio of the non-dimensional recirculation length (Lr =W) to the collector aperture with the pitch angle. Comparison between both Reynolds numbers. ReW

Pitch angle

3:6 10

5

1 106

h ¼ 0

h ¼ 45

h ¼ 90

h ¼ 135

h ¼ 180

h ¼ 270

7.65

2.21

0.09

1.6

9

0.2

8.32

3.06

0.1

1.47

8.3

0.17

unsteady ﬂow behaviour, instantaneous structures and frequencies have been examined at three pitch angles of h ¼ 0 ; h ¼ 45 and

h ¼ 90 . These angles describe the three possible positions occupied by the parabola, i.e. vertical, inclined and horizontal positions. Single-point measurements have also been carried out by positioning probes at different locations around the parabola. The frequencies of the ﬂuctuations of the cross-stream velocity component have been computed by using the Lomb periodogram technique [22], and the resulting spectra have been averaged in the periodic direction. For the sake of brevity, only 3 probes for each pitch angle are shown and compared for both Reynolds numbers. Only the most relevant results are presented. The location of these probes are given in Fig. 8.

80 D

100

ReD=7200

60

Re =21600

(b)

Re =21600

(a)

70

D

ReD=7200

80

Nu

Nu

50 40 30

60

40

20 20 10 0

0

50

100

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200

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300

0

350

0

50

100

α (degree)

250

300

90 Re =21600

(c)

160

ReD=7200

80

140

70

120

60

100

50

80

40

60

30

40

20

20

10

0

50

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0

350

Re=21600 Re=7200

(d)

D

Nu

Nu

200

α (degree)

180

0

150

0

50

100

150

α (degree)

200

250

300

350

α (degree)

60

(e)

Re =21600

50

D

ReD=7200

120 100

Nu

40

Nu

Re =21600

(f)

140

D

ReD=7200

30

80 60

20 40 10

0

20

0

50

100

150

200

α (degree)

250

300

350

0

0

50

100

150

200

250

300

350

α (degree)

Fig. 6. Variation of the local Nusselt number around the HCE for different wind speeds at (a) h ¼ 0 , (b) h ¼ 45 , (c) h ¼ 90 , (d) h ¼ 135 , (e) h ¼ 180 , (f) h ¼ 270 . Data for ReW1 taken from authors previous work [12].

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θ=90 o θ=270 Cylinder

160 140

Nu

120 100 80 60 40 20 0

0

50

100

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300

350

α (degree) Fig. 7. Comparison of the proﬁle of Nusselt number for horizontal positions (h ¼ 90 and h ¼ 270 ) with the Nusselt number for the circular cylinder in crossﬂow case (without parabola) at ReD ¼ 21; 600.

For all pitch angles, and due to the sharp edges of the parabola, the ﬂuid undergoes a rapid transition to turbulence. Depending on the pitch angle, the sharp edges produce ﬂow separation, which prevents the pressure from recovering (large recirculation region behind the parabola), and thus, a high pressure drag is observed. The separated ﬂow at the sharp edges forms a shear-layer which resembles to be much like that formed behind a square cylinder or a normal plate [23]. These shear-layers are characterised by the formation of instabilities, which cause the ﬂuid to become unstable in the presence of sharp corners. These instabilities

increase in amplitude and accumulate into large vortical structures which are shed into the wake. As it will be further explained, the level of coherence of these structures may form a turbulent wake similar to a von Kármán vortex street depending on the pitch angle. In Fig. 9 the velocity ﬂow ﬁeld of the three pitch angles and both Reynolds numbers (ReW1 and ReW2 ) are depicted. Qualitatively, the instantaneous ﬂow ﬁeld is quite similar for both Reynolds numbers. A large separated zone is observed at h ¼ 0 . The turbulent ﬂow in the detached region produces a large depression region in the back of the PTC being responsible for the large value of the drag coefﬁcient obtained. The shear layer is more elevated at this position, and the ﬂow follows the curvature of the PTC. However, the height of the recirculation zone decreases as the Reynolds number increases and the ﬂow becomes more turbulent. Similar to previous observations [12], the height of the detached ﬂow tends to decrease as the pitch angle moves from h ¼ 0 to h ¼ 90 . The latter is the most favourable position for the PTC to work in terms of both unsteady forces and magnitude of averaged aerodynamic coefﬁcients. The structures formed at the different pitch angles are also observed by means of the instantaneous pressure map (see Fig. 10). A striking fact is that the wake structure is completely different depending on the pitch angle. Starting from h ¼ 0 , shear-layer instabilities at both sides of the parabola are observed (see Fig. 10a). The size of these structures grow forming vortex packets, but as a consequence of the interaction of the bottom shear-layer with the ground, the transverse motion of the separated shear layers is suppressed. Thus, vortices formed ﬂow downstream in a parallel manner. As a result, the level of coherence of the ﬂow is low, and only a small peak in the spectrum of the cross-stream velocity ﬂuctuations is observed. This

Table 3 Numerical data of averaged, front stagnation, maximum and minimum Nusselt numbers for each pitch angle and comparison with experiments [19] and the correlation by Zukauskas [21]. Position

0 45 90 135 180 270 Cylinder Exp [19] Corr [21]

Nuav g

Nufsp

Numax =Position

Numin =Position

ReW1

ReW2

ReW1

ReW2

ReW1

ReW2

ReW1

ReW2

24.5 36.4 47.4 25.1 22.5 43.4 52.2 49.5 47.3

41.6 61.0 87.8 54.6 36.3 70.3 101.1 103.4 91.3

33.1 58.0 86.0 25.2 23.7 78.2 86.0 88.0 –

52.3 99.8 161.3 55.0 39.3 138.0 146.7 148.0 –

41.4/289.5 61.2/350.9 86.0/0.0 32.4/269.6 29.1/269.5 78.9/355.8 86.6/357.4 90.3/9.9 –

69.3/265.0 104.2/347.8 161.5/1.89 71.7/182.4 47.9/269.5 139.8/350.5 147.7/359.5 150.1/15.7 –

9.5/196.8 15.9/67.5 27.3/222.0 15.1/64.6 7.4/85.9 21.1/273.4 17.4/272.2 5.5/95.7 –

21.8/203.2 31.1/56.1 46.4/222.0 37.1/48.3 19.5/80.4 39.9/281.7 8.7/78.5 20.9/85.2 –

Fig. 8. Location of the computational probes. (a) h ¼ 0 , (b) h ¼ 45 and (c) h ¼ 90 .

208

A.A. Hachicha et al. / Applied Energy 130 (2014) 200–211

Fig. 9. Instantaneous velocity ﬁeld around the PTC for different pitch angles: (a) h ¼ 0 , (b) h ¼ 45 , (c) h ¼ 90 , and Reynolds numbers: ReW1 (top) and ReW2 (bottom).

and the free-stream velocity). The peak is more pronounced at the higher Reynolds number than for the lower one, but it can still be seen at St W ¼ 0:28 as a small footprint in the energy for ReW1 . At h ¼ 45 , as the bottom corner moves off the ground both shear-layers are allowed to interact, and vortices shed into the wake form a von Kármán-like vortex street (see Fig. 10b). By analysing the energy spectrum for cross-stream velocity ﬂuctuations of probe P1 (see Fig. 12), one can observe that for the higher Reynolds number the peak in the energy is more distinguishable indicating a high coherence in the signal. In fact, the signal captures what can be identiﬁed as a double-peak mechanism. This double-peak mechanism has also been observed in the vortex shedding occurring behind an inclined ﬂat plate [24] and a NACA0012 airfoil at high angles-of-attack [25]. As the process of vortex shedding is asymmetric, vortices formed at the top corner have a slight different period than those formed at the bottom corner leading to the double-peak observed in the energy spectrum. The same double-peak is also captured at the lower Reynolds number, but at a lower frequency. At the lower Reynolds number, the ﬂow is not so coherent and turbulent ﬂuctuations are less energetic.

500 Re =3.6x10

5

W

StW=0.34

Re W=1x10

6

400

300

200

StW=0.28

100

Fig. 10. Instantaneous pressure contours for pitch angle: (a) h ¼ 0 , (b) h ¼ 45 and (c) h ¼ 90 at ReW2 .

peak is captured at probe P2 (see Fig. 11) for ReW2 at St W ¼ f W=U ref ¼ 0:34 (here, the non-dimensional frequency or Strouhal number is evaluated in terms of the parabola aperture

0

0

0.2

0.4

0.6

0.8

1

StW Fig. 11. Energy spectrum of the cross-stream velocity ﬂuctuations at P2 probe close to the PTC (see Fig. 8 for details) for pitch angle h ¼ 0 , and comparison between both Reynolds numbers.

209

A.A. Hachicha et al. / Applied Energy 130 (2014) 200–211 Re =3.6x105

StW2=0.25

25000

W

ReW=1x106

20000 StW1=0.22

15000

10000 StW1=0.05 StW2=0.19

5000

0

0

0.2

0.4

0.6

0.8

1

StW Fig. 12. Energy spectrum of the cross-stream velocity ﬂuctuations at P1 probe close to the PTC (see Fig. 8 for details) for pitch angle h ¼ 45 , and comparison between both Reynolds numbers.

Finally, when the parabola is at h ¼ 90 , leading-edge corner shear-layer instabilities move downstream and interact with those structures formed in the wake of the receiver, breaking down into more complicated and disorganised structures near the trailingedge corner (see Fig. 10c). As a result, the energy spectrum around

3000

2000

ReW =3.6x105

(a)

the PTC at this position cannot capture a distinguishable peak corresponding to the vortex shedding phenomenon (see Fig. 13). For all pitch angles, the observed frequencies are better captured for the high Reynolds number being the energy peak more pronounced. From the stability point of view of the PTC, even though the magnitude of the drag forces at vertical positions is higher, turbulence ﬂuctuations are more important at intermediate positions (0 < h < 90 ). At these positions, the interaction between the shear-layers formed at both corners of the parabola produces an unsteady ﬂow with a highly coherent vortex shedding, which may lead to vibrations. The horizontal position is also demonstrated to be the most favourable position as it presents the minimum drag forces and turbulence ﬂuctuations. In addition, the spectral analysis is also carried out around the HCE to detect the relevant frequencies related to the receiver tube. Depending on the pitch angle, vortex shedding behind the HCE is also detected (see Fig. 14). Similar to the parabola, it is better captured at the higher Reynolds number, but less coherent than the signal captured in the ﬂow past a circular cylinder (for example see [26]). This is due to the interaction of the ﬂow with the parabola, and to the turbulent ﬂuctuations produced as a result of this interaction. This may be seen as broaden peaks in the spectra (for example see Fig. 14b and c), where the energy is distributed along a large range of frequencies. In spite of this, vortex shedding is captured and the results show that as the pitch angle increases from 0 to 90 , the vortex shedding frequency increases and comes close to the typical value

ReW =3.6x105

(b)

6

ReW=1x10

ReW=1x106

2500 1500 2000

1500

1000

1000 500 500

0

0 0

1

2

3

4

5

0

1

2

StW

3

4

5

StW

3000

(c)

ReW =3.6x105

ReW =3.6x105

(d)

1400

ReW=1x106

ReW=1x106

2500

1200

2000

1000 800

1500

600 1000 400 500

200

0

0 0

1

2

3

StW

4

5

0

1

2

3

4

5

StW

Fig. 13. Energy spectrum at two probes around the PTC (P1 for the top, P2 for the bottom) for pitch angle h ¼ 90 , and comparison between both Reynolds numbers. (a and c) stream-wise and (b and d) cross-stream velocity ﬂuctuations.

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A.A. Hachicha et al. / Applied Energy 130 (2014) 200–211 400

500 Re =7200

(a)

350

ReD=7200

(b)

D

ReD=21600 StD=0.05

ReD=21600

400

300 StD=0.11

250

300

200 StD=0.06

200

150

StD=0.12

100 100 50 0

0 0

0.05

0.1

0.15

0.2

0

0.05

0.1

StD

0.15

0.2

StD

600 ReD=7200

(c)

ReD=21600

500 StD=0.19

400

300 StD=0.18

200

100

0 0

0.05

0.1

0.15

0.2

0.25

0.3

StD Fig. 14. Energy spectrum around the HCE (at probe P3) for pitch angle: h ¼ 0 ; h ¼ 45 and h ¼ 90 , and comparison between both Reynolds numbers.

encountered in a circular cylinder St D ¼ f D=U ref ¼ 0:2 [27,28]. Indeed, the value of the Strouhal number changes from St D ¼ 0:05 at pitch angle h ¼ 0 , to St D ¼ 0:19 at pitch angle h ¼ 90 . This can be explained by the effect of the parabola on the HCE which decreases by moving to the horizontal position. It should be pointed out that the unsteady ﬂow and spectral analysis presented in this work for three pitch angles, i.e. 0 , 45 and 90 , can be extrapolated to the other positions because of the similarity of the ﬂow conﬁguration.

5. Conclusions In the present work, a numerical study based on LES of the ﬂuid ﬂow and heat transfer around a parabolic trough solar collector and its receiver tube has been performed. The effects of wind speed and pitch angle on the aerodynamic behaviour, and heat transfer characteristics around the PTC at Reynolds numbers similar to that encountered in working conditions have been addressed. The conclusion is that the averaged aerodynamic coefﬁcients determined in full-scale prototypes are stable with the Reynolds numbers, which conﬁrms the results extrapolated from the experimental measurements in wind tunnels using scaled-down PTC prototypes. Furthermore, the structures and recirculation regions observed in the time-averaged ﬂow around the PTC and the HCE are quite similar for the Reynolds numbers studied. However, a small variation of the recirculation length behind the parabola has been identiﬁed due to the aerodynamic proﬁle, and depending on the

collector orientation. Heat transfer coefﬁcients around the HCE have also been calculated and compared for different pitch angles and wind speeds. The distribution of the Nusselt number for the higher wind speed shows a similar trend to the lower wind speed with higher magnitude and signiﬁcant peaks. Results showed that when computing heat losses from the HCE using correlations for the circular cylinder, results may be overestimated up to a 64% depending on the pitch angle. By studying the unsteady ﬂow around the PTC, undesirable effects on the stability of the collector have been addressed for different pitch angles. Indeed, instantaneous ﬂow structures and frequencies have been studied and compared for different orientations and Reynolds numbers. The turbulence is incoherent in the vertical position and becomes much more coherent by moving to intermediate positions allowing interaction between upper and lower shear layers. This interaction is the consequence of the formation of a von Kármán-like vortex street, and has been clearly detected in different stations. In general, the observed frequencies around the PTC are better captured at high Reynolds numbers, and turbulence ﬂuctuations are more important at inclined position. As a result, care must be taken when operating the collector at these positions, specially under high wind loads, as these turbulent ﬂuctuations may be responsible for vibrations and stresses which lead to structure failure. Similar to the parabola, vortex shedding frequency has also been detected behind the HCE. This frequency varies with the pitch angle and comes close to the typical value encountered in circular cylinder when the parabola is placed at a horizontal position.

A.A. Hachicha et al. / Applied Energy 130 (2014) 200–211

Acknowledgements This work has been partially ﬁnancially supported by the Spanish ‘‘Ministerio de Economia y Competitividad, Secretaria de Estado de Investigación, Desarrollo e Innovación’’, via project ENE201017801 and by the collaboration project between Universitat Politècnica de CatalunyaBarcelonaTech and Termo Fluids S.L. A.A. Hachicha also wishes to thank the ‘‘Agencia Española de Cooperación Internacional para el Desarrollo (AECID)’’ for its support in the form of a doctoral scholarship. References [1] Hachicha A, Rodríguez I, Capdevila R, Oliva A. Heat transfer analysis and numerical simulation of a parabolic trough solar collector. Appl Energy 2013;111:581–92. [2] You C, Zhang W, Yin Z. Modelling of ﬂuid ﬂow and heat transfer in a trough solar collector. Appl Therm Eng 2013;54(1):247–54. [3] Silva R, Pérez M, Fernández-Garcia A. Modelling and co-simulation of a parabolic trough solar plant for industrial process heat. Appl Energy 2013;106:287–300. [4] Peterka J, Derickson R. Wind load design methods for ground-based heliostats and parabolic dish collectors. Tech rep. SAND 92-7009. Sandia National Laboratories; 1992. [5] Randall D, McBride D, Tate R. Parabolic trough solar collector wind loading. In: American society of mechanical engineers, energy technology conference and exhibition, vol. 1; 1980. p. 18–20. [6] Hosoya N, Peterka JA, Gee R, Kearney D. Wind tunnel tests of parabolic trough solar collectors. Tech rep NREL/SR-550-32282. National Renewable Energy Laboratory; 2008. [7] Naeeni N, Yaghoubi M. Analysis of wind ﬂow around a parabolic collector (1) ﬂuid ﬂow. Renew Energy 2007;32(11):1898–916. [8] Zemler M, Bohl G, Rios O, Boetcher S. Numerical study of wind forces on parabolic solar collectors. Renew Energy 2013;60:498–505. [9] Spalart P. Strategies for turbulence modelling and simulations. Int J Heat Fluid Flow 2000;21(3):252–63. http://dx.doi.org/10.1016/S0142-727X(00)00007-2. [10] Rodi W. Comparison of LES and RANS calculations of the ﬂow around bluff bodies. J Wind Eng Ind Aerodyn 1997:55–75. [11] Xie Z, Castro I. LES and RANS for turbulent ﬂow over arrays of wall-mounted cubes. Flow Turbul Combust 2006;76(3):291–312. [12] Hachicha A, Rodríguez I, Castro J, Oliva A. Numerical simulation of wind ﬂow around a parabolic trough solar collector. Appl Energy 2013;107:426–37.

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