NUMERICAL INVESTIGATION OF MIXED CONVECTION FROM A HEAT GENERATING PV CELLS IN VENTILATED HYBRID PHOTOVOLTAIC/THERMAL COLLECTOR Текст научной статьи по специальности «Физика»

СОЛНЕЧНАЯ ЭНЕРГЕТИКА

SOLAR ENERGY

Статья поступила в редакцию 26.12.10. Ред. рег. № 920 The article has entered in publishing office 26.12.10. Ed. reg. No. 920

УДК 662.287:643.334:330.130

ЧИСЛЕННЫЕ ИССЛЕДОВАНИЯ СМЕШАННОЙ КОНВЕКЦИИ ТЕПЛОВЫДЕЛЯЮЩИХ ФОТОГАЛЬВАНИЧЕСКИХ ЯЧЕЕК В ВЕНТИЛИРУЕМОМ ГИБРИДНОМ ФОТОГАЛЬВАНИЧЕСКОМ/ТЕПЛОВОМ КОЛЛЕКТОРЕ

1 112 Я. Нугблега , Х.А. Самах , М. Банна , К. Напо

Лаборатория солнечной энергии/Группа явлений переноса энергии - Университет Ломе BP 1515 Ломе-Того, Тел +228 225 50 94, факс: + 228 221 85 95, e-mail: magbanna@yahoo.fr 2Кафедра ЮНЕСКО возобновляемых источников энергии (CUER) BP 1515 Ломе-Того, Тел +228 2255094, факс: + 228 221 85 95

Заключение совета рецензентов: 16.01.11 Заключение совета экспертов: 20.01.11 Принято к публикации: 25.01.11

Гибридные фотогальванические/тепловые (PV/T) коллекторы являются новым типом устройств, используюшдх солнечную энергию для обеспечения электричеством и необходимой вентиляцией энергосберегающего концептуального проекта здания. В этой работе описываются результаты численного моделирования смешанной конвекции в вертикальном вентилируемом гибридном PV/T - стеновом солнечном коллекторе. Численное моделирование проводилось для оценки переноса тепла, структуры потока и эффективности и охлаждения фотогальванических ячеек. В дополнение к числам Рейнольдса и Ричардсона ключевыми геометрическими параметрами для расчетов являются относительная высота отверстий для входа и выхода потока (e/H), фотогальваническая клеточная пластина (h0/H) и соотношение геометрических размеров (d/H). Результаты исследования показывают зависимость основных параметров от скорости потока, изменения давления и местного критерия Нуссельта.

Ключевые слова: смешанная конвекция, вентилируемый канал, гибридный фотогальванический-тепловой, моделирование, расчеты.

NUMERICAL INVESTIGATION OF MIXED CONVECTION FROM A HEAT GENERATING PV CELLS IN VENTILATED HYBRID PHOTOVOLTAIC/THERMAL COLLECTOR

Ya. Nougblega1, H.A. Samah1, M. Banna1 K. Napo2

'Laboratoire Sur l'Energie Solaire /Groupe Phénomène de Transfert et Energétique - Université de Lomé BP 1515 Lome-Togo, Tel +228 225 50 94, fax: + 228 221 85 95, e-mail: magbanna@yahoo.fr 2Chaire Unesco sur les Energies Renouvelables (CUER) BP 1515 Lome-Togo, Tel +228 2255094, fax: + 228 221 85 95

Referred: 16.01.11 Expertise: 20.01.11 Accepted: 25.01.11

In low energy building design concept, Hybrid Photovoltaic/Thermal (PV/T) collectors are new type of solar energy devices that can provide electricity and necessary ventilation cheaply. The present work reports numerical results of mixed convection within a vertical ventilated Hybrid PV/T-Wall Solar collector. Numerical simulations have been conducted to determine the heat transfer, the flow pattern and the PV cells cooling efficiency. In addition of Reynolds and Richardson numbers, relative height of inflow and outflow openings (e/H), of PV cells plate (h0/H) and aspect ratio (d/H) are the keys geometrical parameters. The results document the dependence of the governing parameters on the flow rate, the pression drops and the local Nusselt number. Keywords: mixed convection, ventilated channel, hybrid photovoltaic-thermal, modelling, simulation.

Organization: University of Lome Togo, Faculty of Science, Department of Physic, Solar Energy Laboratory.

Education: I received my Bachelor of Science degree in physic in 2002 and my master's degree in Material science in 2006 at the University of Lome. I am preparing my Doctorate Thesis at University of Lome.

Experience: Scientific research project, member of Laboratory of Solar Energy of University of Lome, ATER (Attaché Temporaire d'Enseignement et de la Recherche) of University of Lome since January 2007.

Main range scientific interest: Modeling, Heat transfer, Passive cooling.

Yawovi Nougblega

Magolmèèna Banna

Kossi Napo

Organization: University of Lome Togo, Faculty of Science, Department of Physics, Solar Energy Laboratory.

Education: I received my Bachelor of Science degree in physics in 2004 and my master's degree in material science in 2007 at the University of Lome. I am preparing my Doctorate Thesis at University of Lome.

Experience: Scientific research project, member of Laboratory of Solar Energy of University of Lome. Assistant monitor at Physics Department since 2008. Teacher of physics to Agoe college Lome-Togo. Main range of scientific interest: Modeling, Heat transfer, Passive cooling. Publications: One article and one communication.

Organization: University of Lome Togo, Faculty of Science, Department of Physics, Solar Energy Laboratory.

Education: At University of Perpignan (France), I received successively my Bachelor of Science degree of physics in 1985, my master's degree in Thermodynamics/Energetic system in 1987 and Unique Doctorate Thesis in 1990.

Experience: Lecturer at University of Lome since 1993, Assistant Professor since 2003 and Head of Phenomena Transfer and Energetic Group at Solar Energy Laboratory. I am Head of Division in charge of academics inscriptions in master and doctorate programs at University of Lome since 2007.

Main range scientific interest: Modeling, Heat and Mass transfer in porous materials (crops and vegetation). Measure and identification of mechanics and thermal property of material. Solar radiation and systems. Low energy buildings designing and passive cooling. Waste combustion.

Publications: 12 Papers in international and national scientific journal and five oral communications.

Organization: University of Lome Togo, Faculty of Sciences, Department of Physics, Solar Energy Laboratory.

Education: master degree in physic in 1982 at the University of Abidjan (Côte d'Ivoire), DEA in material sciences in 1983 at University of Nantes, First Doctorate Thesis in 1986 at University of Nantes, Second Doctorate Thesis in 1998 at University of Nantes and University of Lome.

Experience: Lecturer at University of Lome since 1988, person in charge of Doctorate training in material science at Faculty of Sciences, National coordinator of UNITWIN of UNESCO, Senior associate of ICTP(Italy), member of scientific committee of University of Lome.

Main range of scientific interest: Renewable Energy, solar energy, thin film research, optoelectric and electronic thin films applications.

Publications: 20 papers in international and national scientific journal, 10 oral communications and 5 posters.

d:

g:

h: H: ReH: ReB: t: T: T :

1 a•

Num:

Nu(Y):

Gr:

P: P: Pr:

Q:

Ri:

u, v: U, V:

U>:

x, y: X, Y :

Nomenclature Letters

channel width (m)

gravitational acceleration (m-s"2)

local convective heat transfer coefficient (W-m"2-K4)

total height of the enclosure (m)

Reynolds number (ReH = pU0H/^)

Reynolds number ReD = (e/H)ReH

time (s)

temperature (K) ambient air temperature (K) mean Nusselt number (NuD = HH/X) Local Nusselt number (NuL = HH/X) Grashof number\dimensionless

(Gr = p2gP(7p - 7a)HV)

Air total pression of the air (Pas) dimensionless air total pression; P = p / pU02

Prandlt number (Pr = (^.CP)/X)

mass flow rate (Kg-s"1)

thermal Richardson number (Ri = Gr/(ReH)2)

velocity component in x and y directions (m-s"1)

dimensionless velocity component in X and Y

directions; U = u/U0, V = v/U0

air inlet velocity (m-s"1)

Coordinates defined in Fig. 1 (m)

dimensionless spatial coordinates; X = x/H, Y = y/H

Greek symbols

p: Density of the air (kg-m"3)

P: Thermal expansion coefficient (K"1)

X: Thermal diffusivity of the air (W-m"1-K"1)

Dynamic viscosity of the air (kg-m"1-s"1) t: Dimensionless time, (t = U0t/H)

8: Dimensionless temperature, 6 = (T - Ta)/(TPV - Ta)

1. Introduction

In hot climate regions, the thermal gains into building exceed the thermal comfort level of the habitants and cooling is desirable. Solar radiation is the main heat gains source into the building which plays an important role as far as thermal comfort in a dwelling is concerned. In low energy building design, the Photovoltaic (PV) modules are integrated in building's fabric as: shading to reduce heat conduction to the interior of the building and as Hybrid Photovoltaic/Thermal systems (Wall Solar Collector or Trombe walls) to provide natural ventilation and generate better more the electricity energy. The Hybrid Photovoltaic/Thermal (PV/T) collectors are new type of solar energy devices that provide electricity and necessary ventilation cheaply. The PV/T collector is a thermal unit, employing low temperature circulating

International Scientific Journal for Alternative Energy and Ecology № 12 (92) 2010

© Scientific Technical Centre «TATA», 2010

fluid, used to extract, by natural ventilation, the absorbed sunlight that is not converted into electricity and that being harmful to the PV cells. The ventilation process on PV panel is used to find an outlet for one's energy.

In fact, the increase of PV cells temperature decreases the electrical efficiency because of the unabsorbed solar radiation that is not converted into electricity. For monocrystalline and polycrystalline silicon solar cells, the efficiency decreases by about 0.45% for every degree rise in temperature. For amorphous silicon cells, the effect is less, with a decrease of about 0.25% per degree rise in temperature depending on the module design [1].

So, natural ventilation used for PV cells and buildings indoor air cooling is a simple, cheap and energy saving method of achieving acceptable thermal comfort and indoor air quality for the occupants especially in developing countries. Natural ventilation is caused by the pressure difference between the inlets and outlets of the building envelope. Night ventilation, wind towers, Trombe walls and solar chimneys are the main natural ventilation techniques. In particularly, the Wall Solar Collector has attracted a lot of attention in the recent past especially in the natural ventilation applications in buildings [2-3]. In this case, the PV cells are integrated into building wall and constitute hybrid PV/T wall solar collectors that operate on stack effect to induce natural air circulation from inside to the outside of the building. During a sunny day, the air flow into the channel will be dominated by thermal buoyancy along the hybrid photovoltaic/thermal collector.

The literature review shows that PV/T models used are most based an electrical analogy where temperatures, flows, flow sources and imposed temperatures are respectively assimilated to potentials, currents, current generators and voltage generators [4-6]. In order to deepen the understanding heat transfer mechanisms by natural convection in such processes and to visualise the flow in the system, some studies have been undertaken to examine natural convection heat transfer in a cavity and classic collectors due to its wide application areas [7-9]. These studies on heat and fluid flow in the cavities and classic collector have proved the effect of wall boundary conditions, inclination, aspect ratio, and cavity and collector geometry.

Otherwise, extensive studies on water and air cooled PV/T collectors have been presented [10-12] and gave a lot of experimental results of their studies and detailed references. Tripanagnostopoulos et al [11] also did experimental and theoretical study of a modified PV/T air system employing a low cost Thin Flat Metallic Sheet (TFMS) for heat extraction improvement from the PV panel.

In this paper, some results of a systematic study of a Hybrid PV/T-Wall Solar Collector with isothermal and/or adiabatic walls are presented. The flow pattern is always an important feature in such problems. Navier-Stokes and energy equations for unsteady laminar mixed convection flow, resulting from thermal buoyancy effect

and laminar vertical jet from below, are used for the airflow visualization. Particularly, numerical simulations have been conducted to determine the heat transfer and the flow rate characteristics of PV cells cooling. The streamlines and the isotherms are drawn to exhibit the mechanism of heat and fluid flow in the cavity. In addition of Reynolds and Richardson numbers, relative height of the inflow and outflow openings and of the PV cells plate as well as their localization on the channel are the keys geometrical parameters of the study.

2. Mathematical formulation and numerical method Consider mixed convection in a vertical wall chimney, composed of two parallel walls heated from one side by the solar cells. Details of the geometry are shown in Fig. 1.

Five Hybrid PV/T-Wall Solar Collector configurations have been studied to compare the flow and the heat transfer characteristics. In each case, the channel is submitted to an imposed flow of ambient air through an opening placed on the lower part of the channel. The forced flow leaves the channel through an outflow opening placed at the top of the channel. More particularly, out of the case 1 of the figure 1, the air generally enters at the bottom on one sidewall at the ambient temperature, Ta, and leaves the cavity through an opening provide at the top of the other sidewall: in the case 1, the air enters directly inside channel; in the he case 2, the air enters at floor height on right wall and leaves at ceiling height on left side of the chimney;

in the case 3, the air enters at floor height on left side and leaves at ceiling height on right wall of the chimney.

As shown in Fig. 1, PV cells, of length ho, are placed on the front wall and are the heat sources in the channel. The localization of these heat sources plays an important role on the flow generation and is investigated in this study. To analyse the effect of this parameter, three Hybrid Photovoltaic/Thermal Chimney design are considered (Cases, 2, 4 and 5): in the case 2, PV cells plate is placed at the top on the front wall and in the case 4, PV cells plate is placed at the bottom on the front wall, when; in the case 5, PV cells plate is placed in the middle of the front wall. The photovoltaic cells are heated by a high solar radiation and are considered to overtake their maximal operating temperature. Indeed, regarding the performance during hot season, many theoretically and experimentally studies observe that the junction temperature of a stand alone PV module can not overtake 52 °C as maximum temperature under 680 W-m-2 solar radiation and at 28 °C of ambient temperature [13]. The height of the entire channel is H with the plates separation d, the heated part of the channel is h0 corresponding to solar cells panel length. Inlet and outlet openings size are e.

The following assumptions are used for mathematical formulation of transfer equations:

■ The upward natural convection airflow is assumed to be incompressible and laminar.

h0 6 =1

_эе эх

- = о

о

Case

ü ^ dY

3

i" T

1а

I"

i I! H

:

6 =1

■

I ! * дх

i

Case 2

эе

dY

= 0

эе

dY

Case 4

_эе

dY

Case 5

_эе

dY

Рис. 1. Схема отверстий для входящего и выходящего потоков и местоположения фотогальванических ячеек Fig. 1. Schematic view of inflow and outflow openings and PV cells localization scenarios

International Scientific Journal for Alternative Energy and Ecology № 12 (92) 2010

© Scientific Technical Centre «TATA», 2010

e

d

1

0

y

y

о

0

■ The air physical properties are considered constant.

■ The part of solar radiation which is not converted into electrical energy is absorbed by the PV cells as thermal energy.

■ The multiple reflections and transmissions between the components (particularly between the photovoltaic cells and the front glass) and the radiation exchange of the PV cells to the glass are considered as negligible.

Taking into account these effects introduces numerous terms difficult to determine and to measure [14]. A very good study of these various effects was performed by Krauter and Hanitsch [15].

■ Owing that the physical system is wide along the coordinate, a 2D approximation is feasible.

■ Out of the PV cells plate, the others walls of the cavity are all considered thermally insulated. The non-dimensional set of the governing equations for a two-dimensional, incompressible laminar airflow are:

Continuity equation

dU dV n

-+-= 0.

dX dY

(1)

Momentum equations

du TTdu au dp 1 (d2u d2u) _

-+ u-+ V-=--+-1 —- +—- ; (2)

дт dX dY dX ReH [dX2 dY2 J

dV+u dV+v dV=

Эт ЭХ dY

ЭР 1 f d2u d2u Ï n n

=--+-1—7 + —7 + Ri.0 . (3)

dY ReH [ dX2 dY2 J W

Energy equation

d9 + u v de

d2 9+Sl. (4)

Эт ' ~ dX " dY ReH Pr IdX2 dY2

These equations have been non-dimensionalized by using the height H as the length scale and defining the variable as:

x y

X = —, Y = H H

T - Ta

, т = Tpv - Ta H

u о1 u =.u

u

v p

V = — and P = ■ F

u о pu о2

(5)

The remaining appropriate boundary conditions respects to the case 4 are:

U = 0, V = 0 9 = 1 at X = 0 and 0 < Y < h0 / H ; (6) U = 0, V = 0 9 = 1 at X = 0 and h0 / H < Y < 1; (7)

du = о, dV = о, о at x = 0 dX dX dX

and 1 - e / H < Y < 1;

(8)

U = - 1, V = 0 9 = 0 at X = d / H

and 0 < Y < e / H ; (9)

d9

U = 0, V = 0, -= 0 at X = d / H and e / H < Y < 1;

dX

(10)

d9

U = 0, V = 0, — = 0 at Y = 0 and 0 < X < d / H ; (11) dY

U = 0, V = 0, — = 0, — = 0 at Y = 1 dY dY

and 0 < X < d / H (12)

From the engineering viewpoint, the most important concern is the heat transfer through the PV cells. This is best represented by Nusselt number, which is a measure of the ratio of the heat transfer by conduction to the flux convected by fluid flow. The local Nusselt number on the front sidewall is given by:

Nu(Y ) =

h(Y ).d

Э9 "dX

(13)

The mass flow rate in the collector is expressed as:

fd / H

Q = pU0H \ V(X,Y0)dX at Y0 = 1 -e/H . (14)

J 0

The numerical results are carried out through the numerical code elaborated by using FreeFem++cs 9.11 programming solvers [16]. Equations are solved in a domain Q = (0,d/H)x(0,1) in a time interval (0,T0). The solution of the governing equations along with the initial and boundary conditions are solved through the Galerkin finite element formulation, and using time discretization which preserve positivity.

An improvement over Chorin's algorithm, given by Rannacher [15], is used to compute a correction to the pressure. Fluid flows require good algorithms and fine triangulation and in this work adapted meshing to the flow is used during calculation. Extensive numerical experimentations are performed to eliminate mesh sensitivity for the considered field variables. The convergence of solutions is assumed when the relative error for each variable between consecutive iterations is recorded below the convergence criterion s such that

)|/X|C|<e where n is the Newton

iteration index and ^ = U, V, 0. The convergence criterion was set to 10-4.

3. Results and discussion

Numerical results are presented in terms of dimensionless local Nusselt numbers and dimensionless pression profiles at mid-plane along the channel as functions of the aspect ratio d/H, relative heights h0/H and e/H, Reynolds and Richardson numbers. Within the framework of a "proof-of-concept", results are reported

for ReH and Ri constant values. Typical values of the aspect ratio, d/H, are assigned in the interval [0.05, 0.20]. The standard relative height of the solar cells plate h0/H is set equal to 0.5. The optimal geometrical configurations are evaluated numerically for the aforementioned data values. The effects of inflow and outflow openings and PV cells localizations on the heat transfer and the flow generation are evaluated and analysed to find the optimal design of the Hybrid Photovoltaic/Thermal Chimney.

The flow rate is function of the pression drop along the channel; the high pression drop recorded for this configuration induces consequently a high flow rate suitable for PV cells cooling. In fact, considering ventilation into the buildings, the case 2 corresponds to the heat removal from the building (cooling) when; the case 3 represents building's indoor air heating commonly used in temperate climatic zones. These results showed that the case 2 appears the best configuration for the heat removal from the chimney.

3.1 Effect of inflow and outflow openings localization The effect analysis of inflow and outflow openings' localization on heat transfer in the channel is carried out and shows the role of chimney openings on PV cells cooling. Standard scenarios were considered, air inlet and outlet have been localized at different zones of the channel as shown in figure 1. When comparing the cases 2 and 3, the results of Fig. 2 and 3 showed that the heat transfer and the pression drops are more performed for the configuration 2.

Ь

1 1 1 1 1 1 1 ' 1 ' 1

—□— Case 1 —o— Case 2 —Д— Case 3

0 ReH=1000 ' Ri=0.5 ■ h0/H=0.5 • e/H=0.1 _ d/H=0.15

-

y/H

Рис. 2. Влияние местоположения отверстий для входа и выхода воздуха на изменение местного критерия Нуссельта вдоль фотогальванической клеточной пластины Fig. 2. Effect of air inlet and outlet localization on local Nusselt number variation along the PV cells plate

3.2 Effect of the PV cells localization The localization of the PV cells heat sources in the channel plays an important role on the flow generation. In the present work, is considered three cases of PV cells insertion in the channel.

1 1 1 1 1 1 1 —□— Case 4 1 1 1 1 1 1

Case 2

Case 5

Ri=0.5 '

h0/H=0.5 -

e/H =0.1

/ d/H =0.15 '

rf

1500

Re,,

Рис. 4. Влияние местоположения ячеек на средний критерий Нуссельта для различной скорости входящих потоков Fig. 4. Effect of PV cells localization on mean Nusselt number for different inflow velocity

—□— Case 1 Re =1000 - 24- □ ReH=1000

Case 2 H 0 \ h0/H=0.5

Case 3 Ri=0.5 J 22- \ \ e/H =0.1

h0/H=0.5 . \ □

□ —□— Case 4

26- \ —o— Case 2

Л —Д— Case 5

e/H=0.1 d/H=0.15

eeeeee

1,61,41,21,0-S 0,8-

CL

0,6 0,4 0,2 0,0-

-i-1-1-1-1-1-1-1-r

0,00 0,13 0,25 0,38 0,50 0,63 0,75 0,88 1,00

y/H

Рис. 3. Влияние местоположения отверстий для входа и выхода воздуха на местное изменение давления вдоль канала Fig. 3. Effect of air inlet and outlet localization on local pression variation along the channel

-i-

10

"Г

15

-I-

20

Ri

Рис. 5. Влияние местоположения фотогальванических ячеек на средний критерий Нуссельта для различных степеней нагрева

Fig. 5. Effect of PV cells localization on mean Nusselt number for different heating levels

International Scientific Journal for Alternative Energy and Ecology № 12 (92) 2010

© Scientific Technical Centre «TATA», 2010

50-

40-

30-

80-

20-

60

10-

40-

0

0

500

1000

2000

20

0-

0,0

0,1

0,2

0,3

0,4

0,5

28

1,8

20

18

16

14

1 1 1 1 1 1 Ш —□— Case 4 i 1 i 1 i

Y Case 2 at X=0.5 _

8 ж Case 5

4 ReH=1000

\ Ri=0.5

L h0/H=0.5

1 e/H=0.1

\ d/H=0.15

y/H

Рис. 6. Влияние местоположения фотогальванических ячеек

на изменения местного давления вдоль канала Fig. 6. Effect of PV cells localization on local pression variation along the channel

"T"

Case 4 Case 2 Case 5

ь

0,0

-i-

0,2

"Г

0,4

"Г

0,8

y/H

movement, when it's required for PV cells (to improve the electricity energy) and building's indoor air cooling. These results are observed in the Fig. 7 and 8, where are showing the local Nusselt number variation along the channel.

Ь

-r~

v

"T"

~r

- Case 2 - e/H=0,2 Case 2 - e/H=0,1

- Case 2 - e/H=0,05 Direct case

ReH=1000 Ri=0.5 d/H=0.15 h0/H=0.5

Рис. 7: Влияние местоположения фотогальванических ячеек на изменение местного критерия Нуссельта вдоль канала Fig. 7. Effect of PV cells localization on local Nusselt number Variation along the channel

Fig. 4-7 show the effect of the PV heat sources localization on heat transfer in the enclosure. Particularly, in Fig. 4, it is clearly showed that mean Nusselt number (Num) increases with Reynolds number, ReH (i.e. inflow velocity) contrarily to Richardson number, Ri (i.e., different heating levels) for which, at a given value, mean Nusselt number, after a decreasing period, increases for the high values of Ri. Considering different value of the Reynolds and Richardson numbers, the results showed that for the case 4, heat removal is better for high Reynolds numbers (Fig. 4) and Richardson numbers less than 11,25 (Fig. 5). Above this value, the case 4 appears to be the best design of the Hybrid Photovoltaic/Thermal Chimney.

The pression drops along the channel are far from different for the configurations under considered (Fig. 6). The heat removal from the chimney, more performed in configuration 4, produces a good pattern of air

-0,1 0,0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1,0

y/H

Рис. 8. Влияние относительного размера отверстий на изменение местного критерия Нуссельта вдоль канала Fig. 8. Effect of openings relative size on local Nusselt number variation along the channel

The airflow injection has an effect on the local heat transfer. Local Nusselt numbers increase and reach a maximum value in the entrance region and then decrease progressively along the channel as shown on the Fig. 8. One could observed that the Nusselt numbers maximum value increase with the relative opening size, e/H. Intensive heat exchanges occur at the air injection region.

In conclusion, the results show that the configuration 4 appears as the best chimney design. This configuration is used for remain work to analyse heat transfer and flow generation inside the channel. To optimise the chimney sizes, a parametric study respect to the aspect ratio d/H, the relative height of PV cells, h0/H and the relative openings size e/H is carried out.

The flow visualization and the heat transfer are illustrated in Fig. 9 as streamlines and isotherms pattern in the channel. The analysis of the streamlines in Fig. 9, obtained for ReH = 1000, Ri = 0.5, d/H = 0.15 and e/H = 0.1, reveals the existence of open lines delimited on its sides by trigonometric cells (recirculation flow structure) whose formation are rather due to the shearing effect and clockwise natural convection cells (their direction of rotation are imposed by the forced flow). The corresponding isotherms are tightened at the level of the heating PV cells wall indicating a good convective heat exchange between this wall and the open lines.

The >>-component of airflow velocity increases and overtakes a maximal value near the hot wall as shown in the Fig. 13. In the present work, we have taken care to preserve the airflow laminar by choosing for the study a typical Reynolds number (ReH) less equal to 1000. The

80 -

60 -

0,2

0,6

1,0

40

20 -

0

80-

60

40-

20-

0

0,6

1,0

Reynolds number, ReH expressed as ReH = (e/H)ReD is related to standard Reynolds, ReD commonly defined for flows between two parallel plates. For a Newtonian laminar flow, ReD must be less than 1000. From the present study, the flows at those ranges (i.e., Re = 100, Ri < 10 and Re = 1000, Ri < 1) are stable and become unstable when the Ri number increases further. As observed by the previous work [17, 18], the continuous increase of the heat transfer with increasing Reynolds for each Ri value is also observed.

T

0.9-

0.8-

0.7-

0.6-

0.5-

0.4-

0.3-

0.2-

0.1-

00 0.05 0.1 0.15 x/H

Streamlines ReH = 1000 - Ri=0.5 -d/H = 0.15 - e/H = 0.1

0.9

0.7

0.6

0.4-

0.3

0.2

0.1-

0 0.05 0.1 0.15 x/H

Isotherms ReH = 1000 - Ri = 0.5 -d/H = 0.15 - e/H = 0.1

Рис. 9. Температурные контуры и линии воздушного потока в полости

Fig. 9. View of temperature contours and streamlines in the cavity

3.3 Effect of the geometrical configuration ratio d/H The variation of the Nusselt number on the PV cells zone and the pression in function of the axial coordinate Y are shown in Fig. 10 and 11 respectively. For different aspect ratio, d/H, Nusselt number and the pressure drops increase significantly at lower d/H; this trend is due to the greatest mass flow rate that brings along a better heat transfer activity (Table). In fact, for a given length H of channel, the d/H enlargement means either the increase in the channel gap d and the decrease of the heat exchange in the channel. It has a bearing on the Nu(Y) amplification at least equal to the ratio between d values.

90807060S 501 40302010-

d/H=0,05 d/H=0,15 d/H=0,20

-r

0,1

"Г

0,2

"I-

0,3

"Г

0,5

y/H

Рис. 10. Влияние геометрических параметров на изменение местного критерия Нуссельта фотогальванической клеточной пластины Fig. 10. Effect aspect ratio on local Nusselt number variation on the PV cells plate

Ь

CL

1 1 1

14-

12- □ V

10-

8- \

6-

4-

2- OOo

0-

-□- d/H=0.05 -о- d/H=0.15 -ж- d/H=0.2

Ri=0.5

h0/H=0.5

e/H=0.1

09

-г-

0,0

-I-

0,2

0,4 0,6

y/H

-I-

0,8

"I-

1,0

Рис. 11. Влияние геометрических параметров на изменение местного давления вдоль канала Fig. 11. Effect of aspect ratio on the local pression variation along the channel

Влияние геометрических параметров на массовую скорость потока Effect of the geometric parameters on the mass flow rate

Parameter (%) Q (Kg-s-1)

5 0.22723

d/H 15 0.07541

20 0.05636

20 0.07539

ho/H 50 0.07541

80 0.07543

5 0.03743

e/H 10 0.07541

20 0.15123

0,0

ReH=1000

International Scientific Journal for Alternative Energy and Ecology № 12 (92) 2010

© Scientific Technical Centre «TATA», 2010

The air gap is a natural draft chimney and the flow in 4. Conclusions

the air gap is driven by buoyancy-(heat) and the wind-

induced pressure difference between the top and the bottom A numerical analysis of a partial heated vertical of the chimney. The force opposing the flow is friction and parallel-plate channel as a framework to study ventilated the end losses at the top and the bottom of the chimney. Hybrid Photovoltaic/Thermal collector has been carried

out. The numerical approach established the existence of 3.4 Effect of PV cells plate relative height h0/H optimal geometrical configurations. Within the

and relative openings size, e/H investigated parameter ranges, the following conclusions

To analyse the effect of the ratio ho/H, Nusselt can be drawn: number are calculated along the entire height of the • The mass flow rate was found to vary with the channel. In the Fig. 12, it's shown that the local Nusselt heated plate (PV cells) height and channel aspect ratio. numbers Nu(Y) increase and overtake a maximum value • The mixed convection Nusselt number is a in the entrance region inside the channel, then decrease decreasing function of the aspect ratio. progressively to the minimum value on unheated part of • The distribution of the heat flux by mixed the walf As shown in Table 1 the mass fl°w rate convection is affected by the surface of the PV cells and increases in function of the pv cells plate height. The y- the heat flux is an increasing function of the PV cells component of the velocity (Fig. 13) and the mass flow height.

rate (Table) increases naturally with the relative • The work also gave qualitative results for the openings size E^ performing the heat removal from streamlines in the channel and gives an idea of

recirculating and ascending flow structure.

For perspectives, future works must being undertaking to study the unsteady behaviour for both high Re and Ri numbers.

References

1. Kalogirou S.A. and Tripanagnostopoulos Y. Hybrid PV/T solar Systems for domestic hot water and electricity production // Energy Conversion and Management 47 (2006). P. 3368-3382.

2. Zrikem Z. and Bilgen E. Theoretical study of a composite Trombe-Michel wall Solar collector system // Solar Egergy. 1987. Vol. 39. P. 409-419.

3. Ben Yedde R. and Bilgen E. Natural convection and conduction in Trombe wall Systems // Int. J. Heat Mass Transfer. 1991. Vol. 34. P. 1237-1248.

4. Bergene T., Lovik O. Model calculations on flat-plate solar heat collector with integrated solar cells // Solar Energy 55(6) (1995) 453-462.

5. Notton G., Cristofari C., Mattei M., Poggi P. Modelling of a double-glass photovoltaic module using finite differences // Applied-Thermal Engineering 25 (2005) 2854-2877.

6. Jones A.D., Underwood C.P. A thermal model for photovoltaic systems // Solar Energy 70(4) (2001) 349-359.

7. Kalabin E.V., Kanashina M.V., Zubkov P.T. Natural convection in a square cavity with time-varying side-wall temperature // Numer. Heat Transf., A Appl. 47 (6) (2005) 621-631.

8. Kalabin E.V., Kanashina M.V., Zubkov P.T. Heat transfer from the cold wall of a square cavity to the hot one by oscillatory natural convection // Numer. Heat Transf., A Appl. 47 (6) (2005) 609-619.

9. Saeid N.H., Yaacob Y. Natural convection in a square cavity with spatial side-wall temperature variation // Numer. Heat Transf., A Appl. 49 (7) (2006) 683-697.

10. Tripanagnostopoulos Y., Nousia Th. and Souliotis M. Low cost improvements to building integrated air hybrid PV-Thermal systems // Proceding.

the cavity (Fig. 8).

0,0 0,2 0,4 0,6 0,8 1,0

y/H

Рис. 12. Влияние относительной высоты фотогальванической

клеточной пластины на местный критерий Нуссельта Fig. 12. Effect of the PV cells plate relative height on the local Nusselt number

x/H

Рис. 13. Влияние относительной высоты фотогальванической клеточной пластины на /-компонент скорости внутри полости Fig. 13. Effect of the PV cells plate relative height on the /-component velocity inside the cavity

16th Europ. PV // Solar energy conf. Glasgow, UK 1-5 May 2000, Vol. II, pp. 1874-1899.

11. Tripanagnostopoulos Y., Nousia Th. and Souliotis M. Test results for air cooled modified PV modules // Proc. 17th Europ. PV solar energy conf. Munich, Germany 22-26 Oct. 2001, pp. 2519-2522.

12. Tripanagnostopoulos Y., Nousia Th., Souliotis M. and Yianoulis P. Hybrid photovoltaic/thermal solar system // Solar energy (2002) 72(3) 217-234.

13. Guiavarch Alain. Etude de l'Amélioration de la qualité environementale du bâtiment par intégration de composants solaires, Novembre 2007, France. PhD Thesis University of Cergy Pontoise, 2007 (in French).

14. Bergene T., Lovik O. Model calculations on flat-plate solar heat collector with integrated solar cells // Solar Energy 55(6) 1995 453-462.

15. Krauter S., Hanitshch R. Actual optical and thermal performance of PV-modules // Solar Energy materials and Solar Cells 41-42, (1996). 557-574.

16. Hecht F. et al. FreeFem++ , Second Edition, Version 2.23-2, Laboratory Jacques-Louis Lions // University of Pierre et Marie Curie, Paris. http://www.freefem.org/ff++.

17. Papanicolaou E., Jaluria Y. Mixed convection from an isolated heat source in a rectangular enclosure // Numerical Heat Transfer, Part A: Applications 18 (4) (1990) 427-461.

18. Papanicolaou E., Jaluria Y. Transition to a periodic regime in mixed convection in square cavity // Journal of Fluid Mechanics 239 (1992) 489-509.

International Scientific Journal for Alternative Energy and Ecology № 12 (92) 2010

© Scientific Technical Centre «TATA», 2010