Homogeneous and Inhomogeneous Model for Flow and Heat Transfer in Porous Materials as High Temperature Solar Air Receivers

Transcription

1 Excert from the roceedings of the COMSOL Conference 1 aris Homogeneous and Inhomogeneous Model for Flow and Heat ransfer in orous Materials as High emerature Solar Air Receivers Olena Smirnova 1 *, homas Fend 1, Schwarzbözl eter 1, Daniel Schöllgen 1 1 German Aerosace Center, Institute of echnical hermodynamics, DLR, Koeln, Germany *Linder Höhe, Köln; mailto: olena.smirnova.@dlr.de; elehone Abstracts: Results of calculations on flow and heat transfer in a orous Silicon Carbide honeycomb structure alied as a solar air receiver are resented. In this alication orous materials are ut in concentrated solar radiation. Flux densities of u to 1 MW/m² are reached. Simultaneously, ambient air flows through the material to be heated u to temeratures of a. 8 C. his hot air is then used to feed the steam generator of a steam turbine to generate solar electricity (solar tower technology). he results are describing the resulting temerature field in the receiver. he main roblem of the solar receiver is connected with the overheating and destruction of arts of the working surface. For the simulation material roerties such as ermeability, thermal conductivity and volumetric convective heat transfer are needed. hese have been determined exerimentally. he study has been carried out in hases: 1. Simulation of the velocity distributions and temerature fields in a single channel of the honeycomb structure. Combined model with the honeycomb structure as a homogenized structure and the suort structure taken with its real geometry. he obtained results of the numerical calculation for the mentioned cases are resented and discussed. he working temeratures, velocities and heat flux distributions which corresond to the used inlet arameters were found from the simulations. he results can be used as a base for the rediction of the working regimes. his aroach can hel to erform a safe oeration and avoid overheating and damage of the receiver material. Keywords: olumetric receiver; Solar ower technology; Coefficient of the erm Secific Heat ransfer Introduction During the last years a lot of theoretical and exerimental research has been connected with the roerties of the oen solar volumetric receiver, because of the increasing imortance of solar ower technology [1-]. A solar volumetric receiver is the central element of the so-called solar tower technology which converts concentrated solar radiation into high temerature heat. In case of a volumetric absorber a cellular material is emloyed to absorb concentrated solar radiation and to transfer the energy to a fluid flowing through its oen cells. he numerical calculation of this rocess is of increasing interest, since ractical roblems like the overheating of the receiver can be assessed and ossible solutions can be found. A general view of the receiver can be seen in Fig. 1. Figure 1: a) hotograh of a single absorber module, which has been cut for a better view, b) hotograh of the SOLAIR 3 MW receiver from the front during installation showing many installed absorber modules (see a) next to each other. In the uer art of the icture there are still some oenings waiting for modules. c) he exerimental solar tower ower station in Juelich (Germany) he task of the numerical calculation of the flow and the heat transfer in the volumetric solar receiver was divided in two indeendent subtasks: 1. Single channel model. his gives the ossibility to select the otimum geometry of the receiver by comarison of the efficiency of the receiver with a different relation between channel size and wall thickness.. Homogeneous model. his considers the receiver as a solid orous continuum with effective ermeability, heat conductivity and heat transfer roerties. For these subtasks the flow and heat transfer rocesses have been considered as stationary and the following COMSOL alication modes have been used: 1. Weakly comressible Navier Stockes;. Convection and heat conduction in air; 3. Heat conduction in the solid body. he use of two heat transfer modes made it ossible to find the temerature distribution both of the solid body and the air indeendent from each other.

2 he geometry of both the single channel model and the homogeneous model are comletely symmetric. herefore - for simlicity only one quarter of the total volume of interest has been defined. he 3D-geometry of the single channel model was done in COMSOL. For the drawing of the 3D-geometry of the homogenous model Autodesk Inventor was used. he volumetric receiver was considered as a orous continuum with determined macro roerties such as orosity and ermeability. he model includes the heat transfer from the hot surface of the solid body to the air flow by taking into account the volumetric heat transfer coefficient, a quantity to be determined exerimentally. he absorbed concentrated solar radiation was considered in this model as a volumetric heat source. Here, is the viscosity [kg/m s], K the ermeability [m²], the density [kg/m³] and the orosity.. he mode Convection and Heat Conduction allows simulating the heat transfer in the air, according to the next equation: k c u Q (3) Here, k [W/m K], c [J/kg K] and Q [W/m³] denote the coefficient of the thermal conductivity, the secific isobaric heat and the heat source term (heating ower er unit volume) resectively. he heating ower er unit volume for the orous structure was determined through the so called volumetric heat transfer coefficient A [W/m³ K] according the equation: Q A (4) Here, and denote the solid body and the air temerature resectively. he volumetric heat transfer coefficient A was calculated according to the following equation: Nu m A c ht Re (5) Figure: 3D-geometry for the calculation of the homogenous model As an examle, the homogeneous model of the receiver is described in detail in the following section. heoretical model and use of COMSOL Multihysics Area Conditions 1. For the numerical calculation of the velocity and ressure fields the Weakly Comressible Navier Stockes alication mode was used in this model. his alication mode describes the connection of the fluid velocity u and the ressure according to the equation: u u u u (1) Since it should be treated as a orous medium, the area of the receiver was described by a slight modification of equation 1, the Brinkman equation, which simlifies the consequence of the boundary conditions between orous structure and air: Here c ht and m are constants which have been determined in a former study [3]. A is the secific surface [m²/m³]. he volumetric heat transfer coefficient was then calculated from the Nusselt-numbers with the equation: A Nu A k (6) Here denotes the characteristic length of the ore structure, which is in this case the channel diameter. 3. he mode Heat Conduction simulates the heat transfer in the solid body, according to the equation: k or q (7) Here, q is the heating ower er unit volume (heat source term), which takes into account the absortion of the solar radiation of the receiver as well as the heat transfer to the fluid. k or [W/m K] is the heat conductivity in the orous structure, which was determined exerimentally as a function of temerature: u 1 () k or 1 8,7 ex,1 u u K (8)

3 he comlete equation for the heat source term is: q A I ex( z) (9) Here, I [W/m²], [1/m] and [m] denote the intensity of the radiation, the measured value of the extinction coefficient, and the coordinate in flow direction. Boundary Conditions For the simulation the hydrodynamic rocess, the following boundary conditions were set: z boundaries of the receiver were set to thermal isolation: n k c u For the model, adative meshing with different meshing stes for each area was used. Results and discussion he results of the temerature distribution and velocity fields for the both models are resented here to comare the two numerical aroaches. he lot in Figure 3 shows the distribution of the fluid s temerature in the single channel model. Inlet: velocity u=u. Outlet: ressure without viscous stress: = u u 1 Other boundaries: wall no - sli u=. For the simulation of the temerature in the air: Inlet: entrance temerature =. Outlet: convective flow: k n. On the boundary Cu Air: =. Other boundaries: thermal isolation n k c u 1. For the simulation of the temerature in the solid body: Figure 3: emerature distribution of the air in the receiver calculated with the single channel model Inlet into the receiver: radiation heat flow: 4 4 k q C n. Here q amb I cos 1 1 F describes the absorbed radiation on the front boundary receiver air and also the losses due to thermal radiation from the receiver to the ambient (C= [W/m² K4] is the emissive constant with denotes the emissivity of the receiver material and amb is the environment temerature). F is the convective heat transfer coefficient describing the convective losses at the front of the receiver. At the outlet of the receiver the temerature was set to =. he boundary conditions at the lateral Figure 4: Comarison of the temeratures of the air ( in the middle of the channel ) and the wall (at the middle of the wall) in flow direction (air inlet is at the right end of the diagram) Figure 4 shows the develoment of the air temerature in the middle of the single channel. his diagram shows that at a deth of 5mm from the channel entrance the temerature of the solid body and air achieve equal values.

4 Figure 5 dislays the velocity field for the homogenous model. he lot shows a nearly arabolic distribution of the velocity field in the cu with the areas of the higher velocities along the cu wall in the outlet area. his effect takes lace because of the reduction of the entrance cross section of the cu. It causes an increase of the convective heat flow and of the thermal tension in this area. he diagram in Figure 5 (b) shows the air velocity in the centre of the cu. hree zones can be observed. he receiver area is of secial interest because in this zone the velocity firstly increases from the inlet value (1. [m/s]) to a maximum value of 1.45 [m/s]. hen, it decreases again to 1. [m/s]. After that it increases to 9.5 [m/s] due to the decreasing cross-sectional area of the cu. Figure 6: he temerature field in the solid body of the homogenous model (a) (b) Figure 5: lot and diagram of the develoment the velocity field in homogenous model he lot in Figure 6 dislays the temerature field in the solid body. It is interesting to study the temerature distribution in the solid body on the inlet surface of the receiver. he lot shows a symmetrical distribution with a decrease of the temerature from 16 [K] in the middle of the receiver to 113 [K] at the edge. Similar results were shown in exeriments []. Figure 7: Comarison of the temerature distribution in the central axis of the receiver both of the wall and of the air (air inlet is at the right end of the diagram) Figure 7 shows the temerature distribution in the central axis of the receiver both of the wall and of the air. Both temeratures become equal from a deth of 45mm. he comarison of two simulation aroaches shows that the outlet temeratures are aroximately equal. However, the oint, from which solid and fluid temeratures become equal, is slightly different. his may be due to the lack of recision in determining the volumetric heat transfer coefficient exerimentally. Conclusions Both simulation aroaches show good stability of the results with a good corresondence of the outlet temerature. he results of the homogenous model show ossible locations of overheating in the center of the inlet surface of the receiver and at the cylindrical surface of the cu in the outlet area. hese results corresond to the exerimental results. A further work-out of the homogeneous model will give the ossibility for a detailed comarison of the numerical and the exerimental results.

5 Nomenclature: u velocity [m/s] ressure [a] dynamical viscosity [kg/m s] density [kg/m³] orosity [-] K ermeability [m²] k thermal conductivity [W/m K] c secific isobaric heat [J/kg K] Q heating ower er unit volume for the convection heat transfer [W/m³] convective heat transfer coefficient [W/m K] air temerature [K] solid temerature [K] A secific surface [m²/m³] Re Reynolds number [-] N u Nusselt number [-] q heating ower er unit volume for the conductivity heat transfer [W/m³] k or effective heat conductivity of the orous material [W/m K] I entrance heat radiation er unit surface [W/m²] extinction coefficient of the radiation [1/m] coordinate along the main flow direction [m] z References: [1] M. Becker, h. Fend at al.: heoretical and numerical investigation of flow stability in orous materials alied as volumetric solar receivers, 1 Solar Energy 8 (6) [] h. Fend, B. Hoffschmidt at al.: orous materials as oen volumetric solar receivers exerimental determination of thermohysical and heat transfer roerties, Energy 9 (4), (5-6), [3] 3B. Hoffschmidt : Comarison and evaluation of different concets of volumetric radiation receivers, Doctoral hesis RWH Aachen, DLR Forschungsbericht 97-35, (1997),.38-41