NUMERICAL ANALYSIS OF THE AIRFLOW INSIDE A SOLAR CHIMNEY Toufik CHERGUI.pdf · Technical solar...

CFD & Tech 2016 02- 03 Mai 2016, CRND-Draria, Alger

NUMERICAL ANALYSIS OF THE AIRFLOW INSIDE A

SOLAR CHIMNEY

T. Chergui1, M. Lebbi

1, A.H. Boualit, L. Boutina and A. Bouabdallah

2

1Unité de Recherche Appliquée en Energies Renouvelables, URAER, Centre de

Développement des Energies Renouvelables, CDER, CDER, 47133, Ghardaïa, Algeria. 2LSTE Université des Sciences et de la technologie (USTHB), Alger, Algeria

[email protected]

Abstract: The purpose of this paper is to analysis the airflow thermo-hydrodynamic behavior

in solar chimney device according to Rayleigh number variation. We attempt to improve the

quality of the flow field by controlling the appearance of Rayleigh-Benard-Poiseuille vortices

in the airflow initially stratified and uniform. These vortices represent dissipative phenomena

by the fact that they represent fictitious obstacles and reducing significantly the massflow by

reduces the air flow cross-section. The mathematical model (Naviers-Stokes and Energy

Equations) was analyzed by the Finite volume Method for a series of Rayleigh numbers (Ra)

reaching values up to 108. Structured grid has been employed with increasing density to

guarantee accurate solutions; especially near the walls for high Ra-values. This methodology

allows a detailed visualization of the effects of optimal geometric and operational

characteristics for such devices. Excellent agreement is obtained with previous numerical

solutions

Keywords : solar Chimney; finites volume method; free convection; Rayleigh number;

Rayleigh-Benard; Poiseuille

I. INTRODUCTION

Technical solar chimneys use solar radiation for heating air under the transparent roof of the collector. Once heated, the air flows, by density gradient through the tower-chimney placed in the center of the collector. The solar energy captured by the collector is transformed into kinetic energy. The kinetic energy of the flowing air can be converted into electrical energy using wind turbines. We are talking about the Solar Chimney Power Plant (SCPP) (see Figure 1). Technical Solar Chimneys (SC) may serve in several disciplines us an air flow generators, such as in air conditioning and drying. Starting with Cabanyes (1903) and Günter (1931), several projects on CCS have been communicated across the world until the completion of the first prototype in the Spanish province Manzanares (Haaf, 1983; Haaf et al. 1984). The design of this prototype was done by the consulting firm of Schlaich and Partner (Schlaich, 1994).

Since then, several studies on the evaluation of overall performance (efficiency and power output) CCS plants have been undertaken (Schlaich, 1994; Gannon and Backström, 2000; Bernardes 2003). For CFD studies who are interested in local characteristics of flow through these systems we quote the work of Pastohr et al. (2004) who used the FLUENT software (commercial code of C.F.D.) to model a SCPP power plant geometrically similar to that of Mansaranes with an aim of carrying out an analysis with more detail in the description of the operating mode and the system efficiency. Ming et al. (2008) analyzed by a numerical simulation the impact of several sizes of three different chimney configurations upon the chimney outlet air temperature and velocity, system output power and efficiency. The effect of the height-to-diameter ratio (H/D) of the cylindrical chimney on system performance was


studied as well. The authors proved that the cylindrical chimney would be the best choice among the three basic configurations, whose optimum H/D value ranges from 6 to 8.

Figure 1. Solar chimney power plant.

Tingzhen et al. (2008) presented a numerical simulation method of a CSS considering a wind turbine. Based on the results obtained for the Manzanares prototype with a three-bladed wind they have proved that the increase of the rotational speed of the turbine drops the average speed at the exit of the tower and the mass flow rate, then the average temperature at the exit of the tower and the pressure drop in the turbine is increased as the maximum power available, the power output and performance of each reach a maximum value. Zhou et al. (2009) performed a simulation of the solar chimney power equipment with a self-constructed code and compared the simulated results with experimental measurements. They concluded that the airflow temperature basically increases from the opening to the collector centre since that airflow is gradually heated when forcedly driven by the thermal engine, i.e. solar chimney. However, the maximum of the mean temperatures along a collector radius is usually at a distance of 0.5 to 3-5 m away from the collector centre. As analyzed from the flow field, fluid beside the ground keeps flowing vertically to the roof and turns to the centre. Also, the circumfluence exists next the collector roof. Maia et al. (2009) performed an analytical and numerical study of the unsteady airflow inside a solar chimney. The developed model was used for airflow simulation in solar chimneys with operational and geometric configurations different from those found in the experimental prototype. Based on simple mathematical models, Larbi et al. (2010) presented an analysis of the energy performance of a SCPP designed to deliver electrical energy to isolated villages in the Algerian southwestern.

Chergui et al. (2010) developed a finite volume method code to simulate a thermo-hydrodynamic behavior of the airflow through an axisymmetric system, such as solar chimneys, with defined boundary conditions. They show for different Rayleigh numbers the dimensionless isothermal and velocity lines for two rapport of the height collector at entrance and tower height (e/H = 0.01 and e/H = 0.1). They notice that the velocity magnitude increases with Rayleigh numbers and its maximum is located approximately at the inlet of the chimney. Chergui et al. (2011) determined the temperature distribution and the velocity field in the system 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. Chergui et al. (2012)


predicted numerically 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. Cao et al. (2013) developed a program based on TRNSYS to evaluate the performance of CCS. They checked the influence of meteorological parameters on the performance of CCS and therefore they could perform a technical and economic analysis on the same commercial CCS for sites that are not included in the TRNSYS database. Lebbi et al. (2014) analyzed numerically the influence of a some geometric parameters on the thermal hydrodynamic behavior of the airflow in the solar chimneys. The results obtained shows that the solar tower dimensions allow a direct control of the hydrodynamic field via the flow velocity. Lebbi et al. (2015) analyzed the effects of the tower outlet / inlet radii ratio on the flow performances in a solar chimney. They investigate the optimal point which presents the mass flow rate. They conclude that the radii ratio variation has an optimum value that should not be exceeded. Recently Chergui et al. (2015) were particularly interested in the effect of the shape of some parts of solar chimney devise like the shape of the cover-tower junction, or the convergent-divergent tronconical tower. For this purpose the flow transport equations were modeled and solved numerically for different geometrical shapes using the Finite Volume Method in Generalized Coordinates. We find that a few geometric configurations generated flow perturbations, which reflected on the thermo-hydrodynamic behaviors. Geometrical shape modifications can eliminate this dissipative perturbation. As it has been shown that the most important solar chimney dimensions in the hydrodynamic field control was the tower size, we gave special importance to the tower shape. We tested the influence of the tronconic convergent and divergent tower respecting the flow cross section. The divergence shape increase the mass flow rate but for a certain divergence angle the mass flow drop. The convergent tower shape gives inverse results by decreasing mass flow but the velocity at the outlet is greater due to the contract flow cross section.

II. MATHEMATICAL MODEL

II.1 Physical Problem and Boundary Conditions

The physical problem and its boundary conditions are prescribed in Figure 2 Since the

flow is produced by buoyancy forces then air enters in the collector with zero axial velocity,

and an unknown radial velocity to calculate using a mass balance at each iteration until

convergence of results. At the outlet of the tower, it is assumed that the flow is fully

developed. Since an axisymmetric flow is assumed.

Figure 2. Study domain and boundary conditions.


At the walls, the no-slip and impermeable walls were considered. These conditions

were applied to the cover at the junction, to the walls of the tower and to the ground surface.

However, the air enters the collector at the ambient temperature. The walls of the tower and

junction are assumed adiabatic. The transparent collector roof temperature and the soil

temperature, considered as the system hot temperature, were calculated by heat balance based

on the based on the incident radiation.

II.2 Gouvernng Equations

The airflow governing equations in a solar chimney are: the continuity equation, the equations of momentum, the energy equation in addition to two other transport equations necessary to calculate the turbulent quantities as the eddy viscosity contained in the equations of the mean flow. For the turbulent calculations, the standard model of Launder and Spalding (1974) with wall functions was selected. In this model, the turbulent viscosity is evaluated from the turbulent kinetic energy κ and its dissipation ε:

μt = ρcμ fμκ2

ε (1)

The low governing equations are then (Pasthor et al. 2003)

- The continuity equation

∂

∂xi

ρui = 0 (2)

- The momentum equations

∂

∂xj ρuiuj = −

∂p

∂xi+∂τij

∂xj+ ρgi (3)

- The Energy Equation

∂

∂xj ρcp ujT =

∂

∂xj k

∂T

∂xj + τij

∂ui

∂xj+ βT uj

∂p

∂xj (4)

- Turbulent Kinetic Energy Equation (κ):

∂

∂xj ρujκ =

∂

∂xi μ +

μt

σκ ∂κ

∂xi + Gκ + βgi

μt

Prt− ρε (5)

- Dissipation of Kinetic Energy Equation (ε):

∂

∂xj ρujε =

∂

∂xi μ +

μt

σε

∂ε

∂xi + C1ε

ε

κ Gκ + C3εβgi

μt

Prt

∂T

∂xi − C2ερ

ε2

κ (6)

III. NUMERICAL APPROCH

The governing equations are discretized in general two-dimensional curvilinear

coordinate system by the finite volume procedure. Non-uniform grid sizes with more

significant concentration on the inlet-outlet and junction regions were used. A 35 X 380 =

13300 cells (see figure 3) was adopted for grid-free solution throughout the calculations in the


present study since it has shown a negligible deviation in the respective solutions. In order to

validated our numerical methodology we presented on figure 4 two temperature profiles in a

cross-section of the collector, for the non-dimensional radius of r/Rc = 0.15. Those

temperature profiles are related to the present and the Maia et al. (2009) studies.

Figure 3. Mesh of the cavity (35 x 380 cells)

Figure 4. Temperature profiles in a cross-section of the collector (*) this study (+) study

Reported by Maia et al. (2009).

IV. RESULTS AND DISCUSSION

In order to study the main thermal and hydrodynamic characteristics of the airflow and

to evaluate the quality of our numerical methodology, the basic values of geometric

parameters adopted in the simulation were given by the following values: collector radius (Rc

= 12.5 m); height of the cover at the entrance (HC2 = 0.05 m); height of the cover (HC1 = 0.5

m); chimney radius (Rt = 5 m); height of the chimney (Ht = 12.3 m). In this part of the study,

y/Ht


the numerical simulation of the solar chimney is presented. For a preliminary qualitative

analysis we illustrate in figure 7 (a-c) the stream function distributions in the solar chimney

for different thermal Rayleigh number which take value from 104 to 10

8. We can observe the

appearance of the vortices of Rayleigh-Benard-Poiseuille instability for an Rac. , before they

disappear. By varying some important flow parameters listed in the Rayleigh number, we can

delay or advance the appearance of the Rayleigh-Benard-Poiseuille vortices.

Figure 7. Stream function lines vs. Rayleigh number

Figures 8 shows, the evolution of the temperature along the collector at y = 0.025 m

for different Rayleigh number. We note that from Rayleigh Ra = 107 the velocity increases

rapidly at the outlet of the collector. It is observed that the average temperature of the flow

increases with the increase of Rayleigh number, reflecting the increase of the temperature

gradient and therefore the increase in temperature of the heat source.

a) Ra=4.5*104, Ψ c) Ra=10

7, Ψ

a) Ra=4.5*10

4, Ψ c) Ra=10

7, Ψ


Figure 8. Influence of the Rayleigh number on the temperature evolution along the collector,

y=0.025m.

Figure 9. Effects of the Rayleigh number on the mass flow rate.

.

0.2 0.4 0.6 0.8 1.0

300

305

310

315

320

325

T[k

]

r*

Ra=1.88E+03

Ra=1.41E+03

(A)

Ra=1.01E+03

Ra=7.05E+02

Ra=4.70E+02 Ra=2.35E+02

0.2 0.4 0.6 0.8 1.0

300

305

310

315

320

325

(B)

T[k

]

r*

Ra=2.00E+04

Ra=1.50E+04

Ra=1.00E+04

Ra=7.51E+03

Ra=5.01E+03

Ra=2.50E+03

0.2 0.4 0.6 0.8 1.0

300

305

310

315

320

325

(C)

Ra=2.00E+05

T[k

]

r*

Ra=1.50E+05

Ra=1.00E+05

Ra=7.51E+04 Ra=5.01E+04 Ra=2.50E+04

0.2 0.4 0.6 0.8 1.0

300

305

310

315

320

325

(D)

Ra=2.00E+06

T[k

]

r*

Ra=1.50E+06 Ra=1.00E+06

Ra=7.50E+05 Ra=5.00E+05

Ra=2.50E+05


For each Rayleigh number, we observe that a relatively elevated velocity at the

entrance of the collector decreases going towards the center of the system until it has

stabilized before starting to grow to reach his second maximum. This is due to the variation of

the collector flow passage section towards the center. As may be seen that the velocity in the

collector increases with the increase of Rayleigh reflecting an increase in driving force which

is the temperature gradient. The progressive increasing of the Rayleigh number is

accompanied by the appearance of Rayleigh-Benard-Poiseuille instability of beyond a certain

thresholds critical value with Rac = 5.8x104. These vortices created by the temperature

gradient between the ground and collector continued to appear until its complete

disappearance from Ra = 105.

The evolution of the mass flow rate as function of Rayleigh number is plotted in

Figure 9. Before taking an asymptotic form as a result of hydrodynamic equilibrium between

the driving buoyancy forces resistive viscous forces, the produced mass flow rate increases

proportionally with the Rayleigh number values until Ra = 105. Which is a result of the

superiority of the buoyant forces on the viscous forces. This superiority is sensed in the

Rayleigh number increasing

V. CONCLUSION

In this work, a two-dimensional numerical study has been investigated using 𝜅 −

ε turbulence model. The laminar and turbulent flows of free convection via Rayleigh number

are analyzed. The progressive increasing of the Rayleigh number is accompanied by the

appearance of Rayleigh-Bénard-Poiseuille instability in the collector beyond a certain critical

value of the Rayleigh number. both transversal and longitudinal convection rolls are identified

in the collector, indicating the presence of a Rayleigh-Bénard-Poiseuille instability.

Thereby we can delay or advance the appearance of the Rayleigh-Benard-Poiseuille

vortices by varying some important flow parameters listed in the Rayleigh number. As a

result, the quality of the flow field can be improved by controlling the manifestation of these

dissipative flow field instabilities what is very important for some solar device working in a

specific interval of velocities.

VI. REFERENCES

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NUMERICAL ANALYSIS OF THE AIRFLOW INSIDE A SOLAR CHIMNEY Toufik CHERGUI.pdf · Technical solar...

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