Revue des Energies Renouvelables CER’07 Oujda (2007) 197 – 200
197
Numerical simulation of vertical solar collector under turbulent natural convection
R. Bennacer 1*, E.H. Kadri 1 and M. El Ganaoui 2
1 LEEVAM/GC, Université Cergy, 5 Mail Gay Lussac, Neuville sur Oise 95031, France 2 Université de Limoges, SPCTS UMR 6638 CNRS, France
Abstract - This concept of PV-T hybrid collector is developed to find the best integration strategy; to make the most efficient use of solar energy collecting surface in terms of both electrical conversion and air heating. This new concept takes into account the fact that thermal effects help maintaining the PV module operating temperature at an optimal level for photovoltaic electric-conversion. The considered turbulent natural convection (chimney effect) flow in a moderately heated vertical solar collector (finite length channel) was simulated using low Reynolds number k−ε model. The numerical results validation was compared to the existing experimental results and to the chimney effect Benchmark exercise. The collector is supposed to receive solar radiation only on part of his height. The heated size and its location on the obtained flow intensity and the position of the transition from laminar to turbulent flow are analyzed. The partially heated collector and heating level affects such transition point location on the vertical hot wall.
1. INTRODUCTION
In industrialized countries, buildings are great energy consumers (before transport and industrial sectors). The integration of renewable energy systems will become one of the solutions to the key issues of economizing fossil resources, whose world reserves are limited, and reducing the earth global warming effects. Solar energy represents the best renewable, environmentally- friendly source of energy that can be used for the heating and cooling of houses. Facing international engagement, the new targeted challenge is that the buildings become energy producer and not any more a simple consumer of energy, thus taking part in their autonomy. In previous work we study the turbulent flow of natural convection in a vertical two-dimensional channel (slot) formed by two parallel plates differentially heated. We focused on the radiative transfer on such coupled system and the humidity effect on the flow was also studied. In the present work we have investigated the performance of hybrid collector included in double skin wall and the effect of its position on the inducing air flow.
2. PROBLEM DEFINITION
In the present work we have investigated the performance of a hybrid collector included in a double skin wall and the effect of its position on the air flow. The last two decade witnessed some major works concerning the turbulent natural convection the most of which concerned the flow of boundary layers or closed cavities but not many studied opened channel. One the pioneer experiment with measurement of turbulent values is Miyamoto et al. [1] who investigated air flow in a channel with one adiabatic plate and the other submitted to an uniform flux for a range of Grashof number from 7×108 to 1.2×1010. Daffa’Alla and Betts [2] conducted measures in tall air filled cavities (Ra = 8.3×105) in turbulent regime with one side kept at a constant heat flux and the other at a constant temperature. The Direct Numerical Simulation (DNS) is a reference numerical experience and provides viable validation data. We cite some simulations of
* rachid.bennacer@u-cergy.fr
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Veersteegh and Nieuwstadt [3] (Ra = 5.4×105) and Boujemadi [4]. A third alternative in modelling is the use a model of k−ε with eddy viscosity assumption and the use of a two layer model for the near wall region Xu et al. [5] and Bennacer et al. [6]. Consider the two dimensional channel sketched in Fig. 1, where we imposes constant flux on a part of the left plate. The other plate is taken adiabatic and the fluid is considered as a perfect gas. The buoyancy forces are thus expressed without any approximation. Radiation and heat viscous dissipation are neglected. The equations to be solved in the two dimensional problem using conservation of mass (continuity), x, z-momentum, energy and the turbulent transport quantities.
( )
0x U
t i
i =
∂ ρ + ∂
∂ρ
∂ (1)
x k 3 2 y µ u y x µ u y x P y
v u x
u u t
u
ef
ef ∂
ρ ∂ +
∂
∂
∂ + ∂
∂
∂
∂ + ∂
∂
−∂
∂ = ρ + ∂
∂ ρ + ∂
∂ ρ
∂ (2)
( )
gx k 3 2 y µ u y x µ v x y P y
v v x
v u t
v
ef 0
ef ρ−ρρ
∂ ρ∂
−
∂ ν
∂
∂ + ∂
∂
∂
∂ + ∂
∂
−∂
∂ = ρ + ∂
∂ ρ + ∂
∂ ρ
∂ (3)
( ) ( )
∂ + ∂
∂ + ∂
∂ + ∂
∂
= ∂
∂ ρ + ∂
∂ ρ + ∂
∂ ρ
∂
y Pr T µ C y k x Pr T µ C x k y
T v x
T u t
T
t t p t
t
p (4)
y G Pr g y
µ k y x µ k x y
k v x
k u t
k
t 1 t
ef 1
ef +
∂ ρ
∂
µ +υ ε ρ
−
∂
∂
∂ + ∂
∂
∂
∂ + ∂
∂ = ρ +∂
∂ ρ + ∂
∂ ρ
∂ (5)
( )
Pr k yC g k / f C G k f y C y µ µ x
x y v x
u
t t
t 3 3 2 2 1
1 1 ef 1
ef ∂
ρ
∂
µ ε + ρ
ε ρ
− ε
+
∂ ε
∂
∂ + ∂
∂ ε
∂
∂ + ∂
∂ = ε ρ +∂
∂ ε ρ +∂
∂ ε ρ
∂ (6)
A constant profile for the velocity calculated from an over all mass balance is used as inlet. A no slip boundary condition is imposed on the velocity components at walls. A constant heat flux is imposed on proportion of the left wall. The right wall is adiabatic. The ambient temperature is specified at inlet. The finite volumes technique is used to discretise the equations. The resolution was done by the SIMPLER algorithm and by using the block correction for solving algebraic systems, Patankar [7].
Table 1
C1=1.5 ; C2=1.9 ; C3=1.4 ; Cµ=0.09 Pr1=0.9 ; σk=1; σε=1.3
0 . 1 1
f = ; f2=1.0−0.3exp
(
−Re2t)
( )
[
3.4/ 1 Ret/50 2]
exp
fµ = − −
t ef =µ+µ µ
k t 1
ef =µ+µ /σ µ =C ρf
( )
k /εµt µ µ 2
ρ
ρ
= µ ε
w 2 / 3 µ 0
0 µx
k k C
2 0 0
0 32 Tu v
k = ×
Fig. 1: Investigated configuration (height = 4 m ; width = 0.1 m
CER’2007: Numerical simulation of vertical solar collector under turbulent… 199 3. NUMERICAL RESULTS
The validation was done in previous work, [6, 8-10]. A typical mixed laminar-transitionnal- turbulent flow is illustrated by the evolution of wall temperature on Fig. 2. The curve shows a laminar evolution of the temperature in the entrance domain, and exhibits a sudden drop which is explained by the amplified transfer between fluid in the boundary layer and that outside, due to the transition to turbulent regime. The transition region is more extended and is situated, nearby the wall, (between approximately 1.8 to 4 m depending on the applied flux). The volumetric air flow increases with the applied heat flux as represented on Fig. 3, and is given by
35 . 0 v 0.015q
Q = .
Fig. 2: Temperature evolution on hot surface for different applied heat flux
Fig. 3: Volumetric air flow versus applied heat flux
It is well known that the chimney effect is increased if all the heating is concentrated in the lower part. The remaining question is the evolution of flow regime. Only a half of the wall (2 m) is radiation exposed and such heated domain is translated from the entrance (y = 0) until the exit (y=2m). The obtained results illustrates clearly that the obtained flow passes from turbulent regime (in case of heating the first half) to laminar (in case of heating on the second half), Fig. 4.
Such reserved effect will modify drastically the mass flow rate (air renewable) and also the efficiency of such collector because we reach more overheats in the laminar case (Fig. 5). Such overheat will increase the radiative and energy loses, it will also induce an uncomforting due to the obtained air temperature distribution on the solar collector out flow.
Fig. 4: Flow shape on the outlet section for different heat flux location
Fig. 5: Temperature evolution on the outlet section for different heat flux location
4. CONCLUSION
The numerical simulation, of the natural convection in a vertical and asymmetrically heated channel of finite length shows the ability of the model to predict such a flow:
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The wall temperature evolution and the transition point position are well predicted for the experience afore cited. It is seen also that the increase in applied heat flux increase the air flow rate and the area where the turbulent exchange occurs. The location (height) where solar collector is incorporated in the double skin is very important. Results illustrate clearly that the air flow rate, efficiency, flow regime and temperature homogeneity are significantly modified. In order to be more accurate, the radiative contribution on such coupled problem is under consideration.
NOMENCLATURE
C p Specific heat, [J(kg K)-1] Greek symbols
f ,1 f ,2 f µ Functions in the k−ε model α Thermal diffusivity, [m2 s-1]
( )
Cp / ρ λg Gravitational acceleration, [m s-2] ε Dissipation rate of turbulent kinetic energy
Gr Thermal Grashof number, 2 T TW3/
gβ ∆ ν T
β Volumetric thermal expansion, [K-1]
H , W Height, width of the channel µ Dynamic viscosity of the fluid, [kg m-1 s-1]
k Kinetic energy of turbulence ν Kinematics viscosity, [m2 s-1]
Pr Prandtl number, ν α ρ Fluid density [kg m-3]
Pr t Turbulent Prandtl number, νt αt σk, , , , σε Turbulent Prandtl number for k et ε
qw Heat flux Subscript
Ra Thermal Rayleigh number, GrPr c Cold wall
T Dimensional temperature, [K] h Hot wall
v , u
y , x
Horizontal and vertical components of the velocity, [m/s] and Coordinate system, [m]
o Reference state (inlet)
REFERENCES
[1] M. Miyamoto, Y. Kaoth, J. Kurima and H. Saki, ‘Turbulent Free Convection Heat Transfer from Vertical Parallel Plates’, Int. Heat Transfer eds C.L. Tien, V.P. Carey and J.K. Ferell, Vol. 4, pp. 1593 – 1598, Hemisphere, Washington, DC, 1986.
[2] A.A. Daffa’Alla and P.L. Betts, ‘Turbulent Natural Convection in a Tall Cavity’, Exp. Heat Transfer, Vol.
9, pp. 94 - 165. 1996.
[3] TAM. Versteegh and FTM. Nieuwstadt, ‘Scaling of Free Convection Between two Differentially Heated Infinite Vertical Plates’, Turbulent Shear Flow, Vol. 11, 1996.
[4] R. Boujemadi, ‘Simulation Numérique Direct et Modélisation de la Convection Naturelle Turbulente dans un Canal Vertical Différentiellement Chauffé’, Thesis University, Paris 6, 1996.
[5] W. Xu, Q. Chen and F.T.M. Nieuwstadt, ‘A New Turbulence Model for Near-Wall Natural Convection’, Int. J. of Heat and Mass Transfer, Vol. 41, pp. 3161 – 3176, 1998.
[6] R. Bennacer, A.A. Mohamad, T. Hammami and H. Beji, ‘Generalisation of Two-Layer Turbulent Model for Passive Cooling in a Channel’, 11th Int. Conf. Nuclear Engineer, Tokyo, Japan, pp. 20-23, April 2003.
[7] S.V. Patankar, ‘Numerical Heat Transfer and fluid Flow’, Hemisphere, Washington, DC, 1980.
[8] G. Desrayaud, R. Bennacer. J.P. Caltagirone, E. Chenier, A. Joulin, N. Laaroussi et K. Mojtabi, ‘Etude Numérique Comparative des Ecoulements Thermoconvectifs dans un Canal Vertical Chauffé Asymmétriquement’, VIIIème Colloque Interuniv. Franco-Québécois, Montréal, 28 - 30 Mai 2007.
[9] C. Muresan, R. Bennacer, C. Ménézo, J. Vareilles and S. Julien, ‘Effect of the Humidity on the Natural Convection in a Vertical Channel’, Progress In Computational Fluid Dynamics (PCFD).
[10] C. Muresan, C. Ménézo, R. Bennacer and J. Vaillon, ‘Numerical Simulation of a Vertical Solar Collector Integrated in Building Frame: Radiation and Turbulent Natural Convection Coupling’, International Journal Heat Transfer Engineering, (accepted in 2005).
