Design of an innovative internal structure for surface solar air heater s

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1 1 Design of an innovative internal structure for surface solar air heater s Arnaud Colleoni TOTAL, Energies Nouvelles 2 place Jean Miller, La Défense Paris, FRANCE arnaud.colleoni@total.com Adrien Toutant Laboratoire PROMES, UPR CNRS rue du four solaire Odeillo, FRANCE Gabriel Olalde Laboratoire PROMES, UPR CNRS rue du four solaire Odeillo, FRANCE ABSTRACT The development of efficient heat exchangers implies the development of compact and high-performance thermal systems. In the concentrated solar industry heating is often asymmetric since the sun heats only one face of the receiver. To optimize such an asymmetric heating, we study an innovative internal design combining two heat transfer enhancement methods: an association of deltawinglet vortex generators (DWVG) with longitudinal riblets. The DWVGs modify the flow field to increase local convection while the riblets canalize the vortices and enhance the transfer surface. Reynolds Averaged Numerical Simulations are carried out to investigate the thermal performance of such a geometry. Comparisons of this geometry with an empty channel and with a classical channel with fins are carried out to demonstrate the potential of this new geometry. 1. INTRODUCTION The Concentrating Solar Power (CSP) technologies offer a great potential to produce electricity using solar resources. However, the efficiency of current solar plants does not exceed 20 % (1) over course of one year. One way to increase this efficiency is to use a gas thermodynamic cycle such as the Brayton cycle. The key to using such a cycle is to heat pressurized air as hot as possible: the higher the temperature at the outlet of the solar receiver, the greater the efficiency of the power plant. Thus, the receiver, which absorbs concentrated solar energy and transmits it to a fluid, is the key part of the power plant. There are two main kinds of receivers: open receivers and pressurized receivers. Open receivers use air at ambient pressure, which is in most of the cases pumped into the receiver through a porous structure (2) from the outside. However, the compression of a gas at high temperature is quite difficult. In regard to pressurized receivers (fluid pressure between 10 and 20 bar), volumetric receivers can be distinguished from surface receivers. Volumetric receivers are simply open receivers located behind a window shield to maintain the fluid under pressure. The main drawback is that the window shield is very expensive and fragile and hence a scale-up difficult to imagine (3). That s why the development of surface solar receivers without window shield is very interesting. The development of efficient surface solar heat exchangers requires the development of compact and high-performance thermal systems. In such kind of receiver, the radiative heating is asymmetrical since the sun heats only one face of the receiver. Various methods have been developed to improve heat transfer for such configurations. These methods can be divided into two categories: the first one encompasses the transfer surface extensions and the second one the modifications of the flow field using passive mechanism to increase local convection. Most studies focus on optimizing either one or the other method. The increase of the transfer surface is generally based on fins. The heat transfer enhancement achieved is very interesting thanks to the increase of the wetted surface but the rise of friction is very high (4). In order to reduce it, investigations on ribbed channels have been carried out. For instance, Hans & al. (5) carried out a study on a multiple V-shaped riblets plate and found that for a Reynolds number of 20,000 the best roughened geometry reached a Nusselt number about 6 times the one of a smooth wall for a friction coefficient 3 times bigger. Regarding to the modification of the flow field, the vortex flow generators are mainly used to increase heat transfer in many engineering domains. They are designed to create vortices which increase turbulence levels resulting in an enhancement of heat transfer with a low pressure drop

2 2 penalty. For instance, Depaiwa & al (6) investigated the thermal enhancement of using rectangular winglet vortex generators in a solar air heater channel. They found a maximum enhancement of the Nusselt number of 200% for a Reynolds number of 20,000 and a friction factor enhancement of 25 % compared to a smooth channel. To further optimize the asymmetric heating of the surface receiver, we study an innovative internal design combining the two heat transfer enhancement methods: an association of delta-winglet vortex generators (DWVG) with longitudinal riblets. The vortices generated by the DWVGs enhance the turbulence level as well as the convective transfers between the fluid and the wall. The riblets canalize the vortices generated by the DWVGs while enhancing the transfer surface at the same time. Reynolds Averaged Numerical Simulations are carried out to investigate the thermal performance of such geometry. Comparisons with an empty channel and a classical channel with fins are carried out. 2. COMPUTATIONNAL DOMAIN The internal geometry of a solar receiver with asymmetric heating is modeled. The exchanger geometry is illustrated in Figure 1. Fig. 1: Sketch of a surface solar air heater Several internal geometries are modeled: an empty channel, a classical channel with fins and two channels with the innovative internal structure. The classical channel with fins was optimized using correlations (4). Regarding the innovative internal structures, the lower wall is smooth whereas the upper wall irradiated on its outer face is covered with DWVGs associated with riblets, as shown in Figure 2. The differences between the two textured channels is that the second one has lower riblets with a larger pitch that the first one. Fig. 2: Sketch of the innovative internal structure The computational domain for each internal geometry is reduced to a minimal box representative of the fluid domain using symmetric boundary conditions for velocity, pressure and temperature in the direction perpendicular to the flow. The minimal box s width depends on the internal geometry. Its length is ten times the height of the channel (2δ). The fluid enters the minimal box at 693K and under a pressure of 10 bars. The Reynolds number at the minimal box inlet is 25,000 and is defined as: = (1) At the end of the minimal box, a pressure outlet boundary condition allows a free outlet of the flow. The discretization of the computational domain implemented is tetrahedral with a refinement near the wall (y + =4,6). The commercial computer code Fluent is used and the calculations are parallelized on a distant server. The fluid is heated by convection with the internal geometry. The temperature of the walls of this internal geometry is calculated by carrying out a heat balance on the overall receiver using Comsol software as well as the results from Fluent for the convection coefficients. The top temperature of the receiver is considered to be constant at 1273K. The material used for the receiver is silicon carbide, with an absorbance of 0,85 on solar wavelengths and a conductivity coefficient of 40 W/m/K. 3. MATHEMATICAL FORMULATION It is assumed that the mean flow is described by threedimensional steady Reynolds Averaged Navier-Stokes and energy equations. Gravity effect is assumed negligible since the Richardson number is equal to 7E-3 (7). Moreover, as the Mach number characteristics of the flow amounts to 0,02 we can use the low Mach number approximation. As we resolve the Reynolds Averaged Navier-Stokes equations, each flow parameter is decomposed as the sum of a mean value and a fluctuating value. For instance, the velocity is expressed as: = + (2) As the density varies strongly, the filtering based on the Favre mean (8) is: = (3) where is the statistic average. Eventually, the governing equations for mass, momentum and energy with a low Mach number approximation are (8): = 0 (4) = = + ( + ) ( ) (5) (6) The thermodynamic properties of the fluid are determined thanks to ideal gas laws. The discretization schemes chosen for solving the equations are of the second order.

3 Turbulence model To carry out the simulations, we use a turbulence Reynolds Averaged Navier Stokes (RANS) model. The Reynlods Stress Model (RSM) is preferred to the k-ɛ model for the main reason that the Boussinesq hypothesis for the k-ɛ model considers the turbulent viscosity to be isotropic which is not adapted to swirling flows as generated by the vortex generators. The RSM model introduces six equations (9) (in a 3D problem) for solving Reynolds stress components of equation (7):. = + ( + ) (7) 3.2. Performance evaluation The heat transfer rate for the smooth and the roughened walls is evaluated through the Nusselt number: = (8) where hc is the convection coefficient of the roughened wall projected on a surface equal to the smooth wall. The Fanning friction factor is evaluated using the formula: = (9) ² In order to evaluate the heat transfer effectiveness of the various simulated combinations, we use the thermal enhancement factor based on the study of Webb and Eckert (10). It is defined as the ratio of the heat transfer coefficient of an augmented surface (hc) to that of a smooth surface (hc 0 ) at the same pumping power: = In literature, the surface ratio (S/S 0 ) is simplified but in this particular case the longitudinal riblets modify the flow passage surface all along the minimal box. The reference values for an empty channel are obtained by simulations. (10) Another criterion is used to compare the various geometries: the dimensionless turbulent kinetic energy (K + ), defined as the ratio of the kinetic energy (K) on the square shear velocity (u τ ) : = (11) This isothermal criterion is based on the hypothesis that the turbulent kinetic energy measuring the intensity of the mixing in the fluid volume is representative of the heat exchanges. Thus, as we want to improve heat transfer while minimizing pressure loss (taken into account by mean of the shear velocity), the dimensionless averaged turbulent kinetic energy seems pertinent. In our study, the turbulent kinetic energy is averaged on the outlet surface. 4. RESULTS The simulations were carried out for the various geometries Hydraulic comparison The results of the evolution of the pressure loss are presented on Figure 3. It shows that Texturation 1 causes more pressure loss all along the computational domain than the fins geometry. The evolution of the pressure loss of Texturation 2 is even more interesting: at first pressure loss is exceedingly high due to the presence of the DWVG and the origin of the vortex at x=0,01m. Then at x=0,02m where the riblets appear on the geometry, the pressure loss increase is proportionally lower than the one of the fins geometry. Thus, after x=0,08 Texturation 2 causes less pressure loss than the fins geometry. Pressure loss (Pa) x(m) Fig. 3: Evolution of pressure loss all along the The comparison of the Fanning friction factor, as shown in Table 1, shows that Texturation 1 and 2 generate more friction than the others geometries. As a matter of fact, the vortices generated by the DWVGs rub against the wall, increasing the friction. The high Fanning friction factor of Texturation 1 combined with the high increase of surface causes more pressure loss than the fins geometry. On the contrary, the increase of surface is lower for Texturation 2, since it has a lower riblets with a larger pitch, and combined with its fanning friction factor it causes less pressure loss than the fins geometry. TABLE 1: FANNING FRICTION COEFFICIENT Internal design Fanning friction factor 0,0227 0,0523 Texturation 1 0,1005

4 4 Texturation 2 0, Thermal comparison Temperature (K) Fig. 4: Evolution of temperature all along the The results of the evolution of the temperature are presented on Figure 4. The Texturation 1 presents the best outlet temperature. The fins geometry shows a similar behavior. The Texturation 2 does not show as much thermal exchanges as Texturation 1, due to its smaller exchange surface. Nu x (m) x(m) Fig. 5: Evolution of Nusselt number all along the The results of the evolution of the Nusselt number are presented on Figure 5. For the fins and the empty geometries, the Nusselt number decreases along with the position in the exchanger, this is due to the augmentation of the fluid temperature. Regarding to Texturation 1 and 2, one can notice an initial increase of the Nusselt number until x=0,04m. This is due to the vortices created by the DWVGs whose enhance the local convection coefficient. After x=0,04m, the Nusselt number decreases. However, it shows the potential of the innovative geometry: if we choose to put another DWVG at the end of the computational domain, it will create another vortex, generating a peak of thermal exchange (or Nusselt number) whereas the Nusselt number of the fins geometry will continue to decrease. TABLE 2: TURBULENT KINETIC ENERGY Internal design Dimensionless turbulent kinetic energy (K + ) 2,08 2,6 Texturation 1 2,32 Texturation 2 2,38 The study of the dimensionless turbulent kinetic energy, as shown in Table 2, shows that the highest K + is obtained with the fins geometry. Although it is not the most efficient geometry for heat exchanges, thanks to the fins the velocity inside the channels is the highest, leading to a rise of turbulent kinetic energy. Texturation 2 has a higher K + than Texturation 1 since the vortices generated are less dissipated at the outlet of the computational domain due to the large pitch of the riblets Performance evaluation The thermal enhancement factor was calculated according to equation 10. TABLE 3: PERFORMANCE EVALUTION Internal design Thermal enhancement factor 1 1,722 Texturation 1 1,412 Texturation 2 1,338 The results of Table 3 show that the fins geometry remains the most efficient internal geometry. As shown previously, Texturation 1 design causes too much pressure loss in comparison with fins geometry and Texturation 2 design does not generate enough thermal transfer. However, by carrying out simulations of the internal design whose parameters are bounded by those of Texturation 1 and Texturation 2, it may be possible to find a geometry that performs at least as well as the fins geometry in future studies. 5. CONCLUSION For the specific case studied, the innovative internal geometries as currently defined do not compete fully with an optimized fins geometry. However, the first investigations show that they are not far behind. Hence, an optimization of pertinent parameters of the geometry, such as the riblet height and pitch, should lead to a more efficient geometry. It should be noted that the investigation was carried out considering only a short length of solar exchanger. A higher length should favor the innovative internal geometry since the DWVGs allow mixing the fluid, heating the center of the fluid volume easily, while the

5 5 fins geometry has troubles heating the center of the fluid volume. Moreover, the comparisons do not take into account the pressure loss due to the air supply, which also favors the innovative internal geometry. Because the innovative internal geometry does not partition the air in the same way as fins geometry, it should not require the same complex air supply, where the flow rate has to be divided up equally between the channels. To be able to efficiently compare the various internal design of the solar heater, a simulation of the whole receiver, from the air supply to the air gathering, should be carried out. 6. NOMENCLATURE C p : specific heat capacity (J/kg/K) f: dimensionless Fanning friction coefficient hc: convection coefficient (W/m²/K) K : turbulent kinetic energy (m²/s²) Nu: dimensionless Nusselt number Re: dimensionless Reynolds number based on the channel s height T: temperature (K) U: mean flow velocity (m/s) u τ : shear velocity (m/s) y + : dimensionless distance from the wall normalized by the viscous length scale δ: half-height of the channel (m) λ: conductivity (W/m/K) ρ: density (kg/m 3 ) ΔP: pressure loss (Pa) υ: kinematic viscosity (m²/s) µ: dynamic viscosity (Pa.s) DWVG : Delta Winglet Vortex Generator RANS : Reynolds Averaged Navier Stokes RSM : Reynolds Stress Model 7. ACKNOWLEDGMENTS We thank the CINES (Centre Informatique National de l Enseignement Supérieur) for granting us the calculation hours necessary to carry out the simulations on their parallel servers. (2) C. Agrafiotis, I. Mavroidis, A. Konstandopoulos, B. Hoffschmidt, P. Stobbe, M. Romero, V. Fernendez- Quero. Evaluation of porous silicon carbide monolithic honeycombs as volumetric receiver/collector of concentrated solar radiation, Solar energy materials and solar cells, October 2006 (3) J. Karni, A. Kribu, R. Rubin, P. Doron. The Porcupine : a novel high-flux absorber for volumetric solar receiver, Journal of solar energy engineering, 1998 (4) X. Daguenet-Frick, A. Toutant, R. Fall, F. Bataille & G. Olalde. Numerical analysis of high temperature pressurized-air solar receiver, Proc. SolarPACES 2009, Int. Symposium on Concentrated Solar Power and Chemical Energy Technologies, September 15-18, 2009, Berlin, Germany (5) Hans V.S., Saini R.P., Saini J.S. (2010), Heat transfer and friction factor correlations for solar air heater duct roughened artificially with multiple v-ribs, Solar energy 84 (2010) , 2010 (6) Depaiwa N., Chompookham T. & Promvonge P. (2010), Thermal enhancement in a solar air heater channel using rectangular winglet vortex generators, PEA-AIT International Conference of Energy and Sustainable Development: Issues and Strategies (ESD 2010), June 2010 (7) Turner, J. S. (1973), Buoyancy Effects in Fluids, Cambridge University Press (8) Pope S. (2000), Turbulent flows, Cornell University, Cambridge (9) Launder B. E., Reece G. J. & Rodi W. (1975), Progress in the development of a reynolds-stress turbulence closure, Journal of Fluid Mechanics 63 (10) Webb R. L. & Eckert E. R. G. (1972), Application of rough surfaces to heat exchanger design, International Journal of Heat and Mass Transfer, Volume 15 (1972), p REFERENCES (1) P. Schwarzbozl, M Schmitz M, R. Pitz-Paal, R. Buck. Analysis of Solar Gas Turbine Systems with Pressurized Air Receivers (REFOS), Proc. 11 th SolarPACES Int. Symposium on Concentrated Solar Power and Chemical Energy Technologies, September 4-6, 2002, Zürich, Switzerland