ENTROPY GENERATION ANALYSIS OF THE SOLAR CHIMNEY POWER PLANT

Transcription

1 ENTROPY GENERATION ANALYSIS OF THE SOLAR CHIMNEY POWER PLANT Tewfik Chergui Unité de Recherche Energies Renouvelables Ghardaïa-Algérie Boualit H. Unité de Recherche Energies Renouvelables Ghardaïa-Algérie Corresponding author Amor Bouhdjar Centre de Development des Energies Renouvelables CDER-Bouzréah-Alger Algérie bouhdjar@cder.dz Salah Larbi. Ecole Nationale Polytechnique Alger Algeria larbisalah@yahoo.fr ABSTRACT The objective of this paper is to determine the optimal geometrical configuration of a solar chimneys power plant (SCPP). An analysis corresponding to the effect of some geometrical forms and physical parameters is performed. Air flow modeling through the chimney is performed considering natural convective heat transfer phenomenon that takes place in the SCPP where the thermo hydrodynamic aspects of the air stream are examined. The temperature distribution and the velocity field in the system are determined by solving the energy and momentum equations using the finite element method. The concept of entropy generation minimization was investigated for an optimization purpose in order to look for the optimal geometrical configuration. Numerical predictions of local and global entropy generation rates in natural air convection through solar chimney heated at uniform heat flux are reported. Results of entropy generation analysis are obtained by solving the entropy generation equation based on the velocity and temperature data. Results in terms of fields and profiles of local entropy generation, for various Rayleigh number, Ra, are given. Keywords: solar chimney, heat transfer, numerical simulation, finite element method, entropy generation minimization. 1. INTRODUCTION Consisting basically of three main components (fig. 1) i.e. the collector (Greenhouse), the tower and the wind turbine, a Solar Chimney Power Plant (SCPP) is a power plant generation based on creation and stabilization of the thermosyphon effect. Heated by greenhouse effect, the air inside the collector moves up through the SCPP tower due to density gradient. The kinetic energy of the air is then converted into electric power by suitable turbine. Several theoretical and experimental studies related to the SCPP power plant performances were undertaken in past years. Most of the experimental studies are practically based on the Mansanares experimental set up. The fundamental studies of this Spanish system were carried out by Haaf & al. [1] who presented a short discussion on energy balance, design criteria and cost of the system, and energy production analysis. In a posterior study, Haaf [] presented also results of preliminary tests on the Spanish systems. Since then, much effort was made to dimension and to consider the SCPP energy performances in order to prove their feasibility as well as their profitability. In their article, Schlaich & al. [3] presented the theoretical, experimental and economic aspects of the SCPP. Initially a simplified theoretical SCPP study was described. Then design results, realization and operation of the Mansanares prototype were presented. Technical considerations and basic economic data for future commercial SCPP configurations as the one of Australia were discussed. It should be noted that literature on dynamic analysis i.e. transport equations solved by C.F.D is scarce, because research work concentrates mostly on the total energy performance evaluation of the system. However solving the transport equations shows the effectiveness for the local characteristics study of the flow, such as the detection of the spades and the zones of recirculation as well as the weak temperature variations. Bernardes & al. [4] presented a theoretical SCPP analysis with laminar natural convection in the permanent flow case. In order to consider the thermohydrodynamic behaviour of the air, thermal boundary conditions were forced in order to guarantee a regular laminar flow along the device. The mathematical model was solved by finite volume method in generalized coordinate system. Gannon & Von Backström [5] were interested in a one dimensional compressible flow for thermodynamic variable calculation with respect to the tower height, the wall friction, the additional losses, the internal trail and the bypass section variation. Pastohr & al. [6] used the FLUENT software to model a SCPP power plant geometrically similar to that of Mansaranes, aiming at carrying out a detailed analysis in the description of the operating mode and the system efficiency. They confirmed that the pressure drop in the turbine and the 1

2 mass flow, decisive elements on the system effectiveness, cannot be given only by the coupling of all parts of a SCPP power plant. The numerical results given by FLUENT compete well with the results given by a simple model proposed by the authors and which can be used for parametric studies. Chergui et al. [7,8] simulated a thermo-hydrodynamic behavior analysis of the airflow through an axisymmetric system, such as chimneys, with defined boundary conditions. Emphasis was given to a laminar natural convective heat transfer problem occurring in a solar chimney power plant. This work focused mainly on global analyses which were developed on this type of systems including calculations of output energy, system efficiency, parametric analyses and analytical models. Fig.1: Study domain and boundary conditions The control of the technico-economic analysis tools of SCPP such as those of the dynamic simulation of these systems is essential. The purpose of this paper is to present a preliminary natural convection phenomenon analysis in geometry similar to that drawn in figure 1. Steady-state laminar natural convection with prescribed boundary condition is considered. This analysis considers mainly the phenomena of solar radiation and the wind generator. The optimal design criteria for thermal systems by minimizing their entropy generation have been recently a topic of great interest in the fields related to thermal power plants, heat exchangers, energy-storage systems, and electronic cooling devices [9,10]. In these criteria, the total entropy generation in the designed systems can be minimized under some physical and geometric arrangements, and an optimal configuration with minimum loss of available energy may be obtained [10]. Analytical procedures for evaluating local entropy generation and thermal optimization were summarized in [10,11] and many applications have been carried out to fluid flows with analytical solutions for the velocity and temperature fields [1-14]. Inclusion of entropy generation calculations in computational fluid dynamics codes would allow the evaluation of local entropy generation in more complicated thermal phenomena as remarked in [15]. One theoretically correct measure of thermodynamic performance is the magnitude of thermodynamic irreversibilities associated with a component or process. It can be shown that the minimization of entropy generation results also in the maximum reduction of irreversibility. The development of improved thermal designs is enhanced by the ability to identify clearly the source and the location of entropy generation.. MATHEMATICAL MODELING.1 Flow and governing equations The -D laminar natural convection flow in cylindrical coordinates with Boussinesq approximations, negligible compressibility effects and viscous dissipation can be expressed with the following generic conservation equation. 1 ( ρφ) + ( ρruφ) + ( ρvφ) = t r r 1 φ φ rγ + Γ + S φ φ φ r r r The solution to the generated set of equations must satisfy some boundary conditions. Figure 1 shows the physical model. T cov is the cover temperature. The tower wall is assumed adiabatic (δt/δr=0 at wall). The non-slip condition is imposed on the walls. Constant heat flux (q soil ) is assumed at the ground surface and this is a more realistic assumption than a constant temperature. Since an axisymmetric flow is assumed in the chimney, thus at r =0 we get u = 0, (δv/δr=0), (δt/δr=0). The top of the chimney tower, a fully developed flow region is assumed on the velocity and on the temperature. At the inflow boundary, the entrance temperature T 0 is assumed constant. TABLE 1: EXPRESSIONS FOR PARAMETERS OF EQUATION 1 Equation Ø + Ø+ S Ø+ Mass balance Momentum balance Versus -r Momentum balance versus y Energy u + v + T + Pr Ra p - r u - r Pr p + + Ra + T 1 Ra Pr + (1) Pr Ra As it is specified by [16], in natural convection problems, the mass flow rate at the entrance caused by buoyancy forces is unknown in the beginning. The u-component is built up through iterative calculation in a finite element code.. Entropy Generation The existence of a thermal gradient between the ground of the collector and the moving air makes the fluid in a non- 0

3 equilibrium state which causes entropy generation in the system. According to local thermodynamic equilibrium with linear transport theory, and in a two dimensional cylindrical coordinate system, the local entropy generation is given by [17]: k T S gen T r T y u u v T r r y u v T r y The dimensionless form of the entropy generation equation is: 1 T S ( T ) r With, Pr Ec u T r S k S gen / Lref T y u r Pr Ec u T r v y v y () (4) elements), although the computer program was validated using mesh sizes identical to those used in the reference work. 4. RESULTATS In order to study the main thermal and hydrodynamic characteristics of the laminar flow and to evaluate the quality of our numerical methodology, the magnitudes adopted in the simulation are given by the following values: height of the cover at the entrance (H C = 0.01 m); chimney radius at the outlet (R t = 0.05 m); height of the chimney (H t = 1 m); cover radius (R c = 1 m); uniformly distributed at the domain boundaries with the geometry given by Fig.1. It should be noted that these magnitudes do not constitute real conditions of the system, being established only to insure a laminar flow. The temperature and the mass flow rate (or speed in an incompressible flow) represent the two important parameters in the analysis of a solar chimney regardless of the nature of its use whether ventilation, drying or energy production. In our study and since the flow is regarded as incompressible, the interest is in the determination of the maximum velocity, any configuration can generate. Considering the collector height and the driving force of the flow i.e. the temperature difference through the Rayleigh number, the velocity field through the system is evaluated. Starting from standard geometries (Fig. ), various geometries are introduced in the form of four basic configurations (table ). T ql kt ref T T ql ref 1 The Eckert Number Ec is ; ( / L Ec C T p ref k ) 3. NUMERICAL METHOD A finite element method [18,19] is used to discretize the governing equations. A nine quadratic elements is used. A primitive variable formulation is used to solve the equations. The worked out computer program is validated with respect to the de Vahl Davis benchmark solution [11] and others [1]. Of course, the generated program was validated over a flow in a cylindrical cavity for different flow regimes [7,8,1]. The grid dependence has been investigated using different mesh sizes before settling to a mesh size of (10 X 0 Fig. : Basic configurations 3

4 Curved junctions generate well-distributed temperature fields, recirculation-free flow (Fig. 3b), as well a higher mass flow rate (table ). Straight junction configurations show corner point which cuts a stream function at the base of the chimney (Fig. 3a). Curved junctions with a diffuser show no recirculations (Fig. 3d). Inclined covers may facilitate the appearance of recirculation patterns similar to Bernard cells. The conic chimney (Fig. 4) generates higher mass flow rates (table ), confirming the results of Yan et al. [4]. Global and maximal local entropy generation values with its geometrical position (Ycent and Xcent are the coordinates of centre node of an element) for the different analyzed cases are reported in Table3. We note from table 3 that the slanted configuration gives a large local/global entropy generation then we find, in second position, the conic configuration and this might be due to the large bypass section and the given flowvelocities values. The straight junction presents the lowest value of both local and global entropy generation. The classification of the entropy generation rate follows the same classification as the maximum velocity i.e. the highest value of the entropy generation rate is allotted to the highest velocity configuration and so on. For a curved junction configuration, we report respectively in figures 5 and 6, the evolution of the dimensionless maximum local and global entropy generation versus Rayleigh number Ra. a. Straight Junction b. Curved junction c. Slanted canopy with curved junction d. Slanted canopy, curved junction with diffuser Fig.3: Dimensionless isovelocity lines for different configuration, Ra=10 5 4

5 Y TABLE : GEOMETRICAL PARAMETERS AND MAXIMUM VELOCITY FOR SIMULATED CASES (RA=10 5 ) Case H c1 R in R ex V max Straith junction Curved junction Slanted /curved Slanted / diffuser It is to be noticed that the global entropy generation increases with the Rayleigh number increase. Global entropy generation changes significantly with respect to the Rayleigh number V The evaluation of the entropy production rates for the air natural convection phenomena through a solar chimney system was carried out numerically by means of a computational procedure. The analysis has shown that a need for a more detailed investigation of such systems is essential for an ample definition of basic design directions. The literature available is scarce on this type of analyses, as research mostly concentrates on the evaluation of the global performance of such systems For the design of real systems, more detailed studies of the geometrical and operational aspects are needed, involving meteorological conditions and turbulent flow. Other configurations like conic tower seem important too. Few geometric configurations generated perturbations of the flow (recirculations), which affected the thermohydrodynamic behavior X Fig.4 : Dimensionless isovelocity lines for a conic configuration, Ra=10 5. TABLE 3: LOCAL AND GLOBAL ENTROPY GENERATION RATE (RA=10 8 ) Fig. 5: Evolution of maximum of the dimensionless local entropy generation versus Rayleigh number Curved Junction Case Ycent Xcent S max,local S Global Straith junction Curved junction Slanted /curved Curved/diffuser Conic CONCLUSION Many encouraging studies were reported about the use of solar chimney for air conditioning, drying and to produce electrical power. This study considers the heat transfer process and the fluid flow in the collector and the chimney tower and performance studies were related to geometrical and operating parameters. A validated computer program was adapted to the solar chimney configuration to solve the primitive governing equations (continuity, momentum and energy equations). Fig. 6: Evolution of the dimensionless global entropy generation versus Rayleigh number Curved Junction A straight form for the cover chimney junction gave smaller flow rates, which might due to the occurrence of junction flow recirculations. The use of a curved junction allowed higher flow rates. The introduction of a deflector 5

6 did not bring major thermal or hydrodynamic improvements. Local and global entropy generation rates in terms of Rayleigh number, Ra, were given. The distribution of local values showed different behaviours for different Ra numbers. Global entropy generation rates increased as the Rayleigh number increased. A comparison between table and table 3 enables us to conclude that the classification of the entropy generation rate follows the same classification as the maximum velocity, in other words the highest value of the entropy generation rate is allotted to the highest velocity configuration and so on. 6. NOMENCLATURE: A Surface, m Cp Specific heat, J/kgK D Diameter, m e Mean cover height, m Ec Eckert Number h Heat transfer coefficient, W/m K k Thermal conductivity, W/mK P Pressure, Pa Pr Prandtl Number Heat flux, W/m Ra Rayleigh number, t Time, s T Temperature, K S Source terms Volumetric rate of entropy generation, W/(m 3.K) S Dimensionless volumetric entropy generationrate r,y Space coordinate, m u,v Velocities, m/s Greek letters Thermal diffusivity, m/s ρ Mass density, Kg/m3 γ kinematic viscosity, m/s Φ Generic property Γ Diffusivity β Volumetric thermal expansion coefficient, 1/K θ Dimensionless temperature Subscripts / Superscripts C Cold h Hydraulic H High r Reference value +, Dimensionless 0 Ambient conditions 7. REFERENCES [1] W. Haaf, K. Friedrich, G. Mayr, J. Schlaich. Solar chimneys, part I: principle and construction of the pilot plant in Manzanares. Solar Energy 1983;:3 0. [] W. Haaf. Solar towers: part II: preliminary test results from the Manzanares pilot plant. Solar Energy 1984;: [3] J. Schlaich, R. Bergermann, W. Schiel, Weinrebe G. Design of commercial solar tower systems utilization of solar induced convective flows for power generation. In: Proceedings of the international solar energy conference; 003. [4] [4] MA. Bernardes, RM. Dos S. Valle, MFB. Cortez. Numerical analysis of natural laminar convection in a radial solar heater. International Journal of Thermal Science 1999;38:4 50. [5] T.W. Backström, A.T. Gannon. Compressible flow through solar power plant chimneys. Journal of Solar Energy Engineering 000;1: [6] H. Pastohr, O. Kornadt, K. Gϋrlebeck. Numerical and analytical calculations of the temperature and flow field in the upwind power plant. International Journal of Energy Research 004;8: [7] T. Chergui, S. Larbi, A. Bouhdjar, M. Gahgah. Heat transfer modelling analysis of flows in solar chimneys. In: Proceedings of the fourth international conference on computational heat and mass transfer; 009. [8] T. Chergui T, S. Larbi & A. Bouhdjar. Thermohydrodynamic aspect analysis of flows in solar chimney power plants A case study. Renew Sustain Energy Rev (010) [9] H. Boualit & N. Zeraibi. Numerical Investigation of a Laminar Forced Convection Flow of Nanofluids in a Uniformly Heated Tube. International Conference on Micro and Nano Technologies,006. [10] C.Taylor & T.G. Hughes. Finite Element Programming of the Navier Stokes Equations. Pineridge Press Ltd Swansea, U.K,1981. [11] G. de Vahl Davis. Natural convection of air in a square cavity: A Benchmark numerical solution. International Journal of Numerical Methods in Fluids 1983;3: [1] N. K. Markatos, KA. Pericleous. Laminar and turbulent natural convection in an enclosed cavity. International Journal of Heat and Mass Transfer 1984;7: [13] S. Z. Shuja, B. S. Yilbas and M. O. Budair. Entropy generation due to jet impingement on a surface: effect of annular nozzle outer angle. International Journal of Numerical Methods for Heat & Fluid Flow Vol. 17 No. 7, 007 pp [14] A. Andreozzi, A. Auletta and O. Manca. Entropy generation in natural convection in a symmetrically and uniformly heated vertical channel. International Journal of Heat and Mass Transfer 49 (006) [15] T. Chergui, S. Larbi, A. Bouhdjar, M. Gahgah. Heat transfer modelling analysis of flows in solar chimneys. In: Proceedings of the fourth international conference on computational heat and mass transfer; 009. [16] M.Q. Yan, S.A. Sheri, G.T. Kridli, S.S. Lee, M.M. Padki, Thermo-fluid analysis of solar chimneys, industrial applications of fluid mechanics, ASME FED 13 (1991) [17] C.Taylor & T.G. Hughes. Finite Element Programming of the Navier Stokes Equations. Pineridge Press Ltd Swansea, U.K,1981. [18] A. Bejan. Convection Heat Transfer John Wiley & Sons. 6