Cfd Workshop Final Assignment Submission Venkateswareddy M

7/31/2019 Cfd Workshop Final Assignment Submission Venkateswareddy M

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TWO WEEK ISTE WORKSHOP ON

COMPUTATIONAL FLUID DYNAMICS

REPORT OF FINAL ASSIGNMENT

INTRODUCTION

In recent years, numerical modelling of the convective heat transfer problem has been an

area of great interest due to its broad applications in engineering. Compared to the

experimental method, numerical analysis provides a more direct way to enhance/reduce heat

transfer effectively so as to improve the performance or to optimize the structure of a thermal

device.

Natural convection in enclosures has been studied both experimentally and numerically,due to the considerable interest in its many engineering applications, such as building

insulation, solar energy collection, cooling of heat-generating components in the electrical

and nuclear industries, and flows in rooms due to thermal energy sources.

LITERATURE SURVEY

Numerical studies of natural convection heat transfer and flow in closed enclosures

without a local heat source are reported in the literature; we can cite the work of Davis

(1983), Hartmann et aI. (1990), Le Que..e (1991), Mohamad (1998), Carcione (2003), and

Ben-Nakhi and Chamkha (2006).

Other authors have studied the natural convection caused by a heat-generating conducting

body located inside an enclosure: Chu and Churchill, 1976; Khalilollahi and Sarnmakia,

1986; Keyhani et aI., 1988; Farouk, 1988; Ho and Chang, 1994; Ha et aI., 1999; Deng and

Tang, 2002; Oztop et aI., 2004; Bazylak et aI., 2006.

OBJECTIVE OF THE PRESENT STUDY

The present work is a numerical study of natural convection due to the temperature

difference between top and bottom walls and the left and right walls are being insulated. The

study was conducted for two different enclosure with aspect ratio of H/W=1 and H/W=2. For

both the cases the non dimensional numbers i.e.prandtl number and Raleigh number were



taken as benchmark and also for other values of non dimensional parameters.

The study is conducted numerically under the assumption of steady laminar flow for two

different values of both the height-to-width aspect ratio of the enclosure of 1 and 2 the Ray

leigh number based on enclosure height in the range between 103

and 106. The Ra/Ra. ratio

in the range between 0 and 2500.

DESCRIPTION OF THE PROBLEM

For the present study two types of 2D enclosures are considered as shown in the fig(1) &

fig(2). In figure 1 the aspect ratio is considered to be equal to 1 i.e H/W=1 where as in the the

figure 2 the aspect ratio is considered to be 2 , i.e H/W=2.

The boundary conditions are taken as top and bottom are considered to be isothermal

with bottom plate hotter and top plate cold. The left and right boundaries are considered to be

insulated. The non dimensionless numbers like Prandtl number and the Raleigh number are

considered to be benchmark values for the I case of study (Prandtl no.=0.71 and Raleigh

no.=1E4) and for the II case they are consdiered to be other than bench mark values(Prandtl

no.=1 and Raleigh No.=1E2). The results in both the cases are compared with respect to the

dimensions of the enclosures and with respect to values of the non dimension parametes.

2H

H

W W

Fig.1 Fig.2

MATHEMATICAL FORMULATION

To model the flow under study, we use the conservation equations for mass,

momentum, and energy for the two-dimensional, steady, and laminar flow. For the moderate

temperature .difference considered in this work, all the physical properties of the fluid, fl, k,

and cp, are considered constant except density, in the buoyancy term, which obeys the



Boussinesq approximation. In the energy conservation equation, we neglect the effects of

compressibility and viscous dissipation. Thus, the dimensionless equations that govern the

flow are Continuity , X-Momentum, Y-Momentum and Energy.

In this study the fluid is enclosed between left and right walls which are insulated and top

and bottom walls in which bottom wall is taken to be hotter while the right wall is cold.

The code for the above study is the given in the lab_5 III condition i.e., natural convectioncode of open source scilab. In this code a small change has been done by taking left and right

boundaries as adiabatic without any heat transfer and bottom & top boundaries are assumed

to be isothermal with hotter bottom and cold top.

The Grid size for the two types of domain In the first case is considered to be 7 in both X

and Y directions.

The grid size in the second case for both the domains is considered to be 12 in both X and

Y directions.

The time step, steady state mass divergence criteria are as follows:

steady_state_criteria = 1e-3;

mass_div_criteria = 1e-8;

time_step = 0;

total_time = 0;



CASE-I RESULTS(DOMAIN X=1 AND Y=1)

Fig.I-1 Fig.I-2

Fig.I-3 FigI-4

Fig I-5 FigI-6

Discussion:

1. In fig.I-1 the u-velocity contours are seen . There are four different types of contours

observed due to the variation in the temperatures of the boundary.

2. In fig.I-2 the V-velocity contours are seen. Here we can see three types of contours over the

domain

3. In Fig.I-3 the stream function contours are seen which are of two types

4. The FigI-4 shows the temperature contours over the domain which shows that since the

bottom plate is hot the temperature is more near the bottom boundary.

5. Fig.I-5 and Fig.I-6 shows the variation of temperature and U-velocity along the centreline

respectively.



CASE-I RESULTS (DOMAIN X=1 AND Y=2.)

Fig.I-1 Fig.I-2

Fig,I-3 Fig.I-4 Fig.I-5

Fig.I-6

DISCUSSION

1. In fig.I-1 the u-velocity contours are seen . There are two different types of contours observed

due to the variation in the temperatures of the boundary.2. In fig.I-2 the V-velocity contours are seen. Here we can see two types of contours over the

domain

3. In Fig.I-3 the stream function contour is seen.

4. The FigI-4 shows the temperature contours over the domain which shows that since the


5. Fig.I-6 and Fig.I-5 shows the variation of temperature and U-velocity along the centreline

respectively.



CASE-II (RESULTS FOR THE DOMAIN X=1 AND Y=1)

Fig.II-1 Fig.II-2

FigII-3 Fig.II-4

Fig.II-5 Fig.II-6

DISCUSSION

1. In fig.II-1 the u-velocity contours are seen . There are four different types of contours


2. In fig.II-2 the V-velocity contours are seen. Here we can see three types of contours over the

domain

3. In Fig.II-3 the stream function contour is seen.

4. The FigII-4 shows the temperature contours over the domain which shows that since the


5. Fig.II-6 and Fig.II-5 shows the variation of temperature and U-velocity along the centreline

respectively.



CASE II: RESULTS(DOMAIN X=1 AND Y=2)

Fig.II-1 Fig.II-2

Fig.II-3 Fig,II-4

Fig.II-5 Fig.II-6

DISCUSSION

1. In fig.II-1 the u-velocity contours are seen . There are four different types of contours


2. In fig.II-2 the V-velocity contours are seen.

3. In Fig.II-3 the stream function contour is seen.

4. The FigII-4 shows the temperature contours over the domain which shows that since the


5. Fig.II-6 and Fig.II-5 shows the variation of temperature and U-velocity along the centreline

respectively.



CONCLUSION:

1. In case I the U-velocity contours are irregular in shape and the velocity is more near

the right boundary for the domain x=1 and y=1. For the domain x=1 and y=2 the

velocity contours are seen in two colours with greater velocity at the bottom

boundary.

2. In case II the U-velocity are in four colours for domain I and also in four colours for

domain II. The velocity is higher near the left and bottom boundary. The result shows

that in case I and two the contours are in the opposite directions.

3. The stream function contours in case I for the first domain shows greater value at the

right boundary. For the domain II the stream function shows higher value at the

centre. In case II the stream function shows same contours for both the domains.

4. The temperature contours are seen the same for all the cases and all the domains with

high temperature at the bottom boundary.

REFERENCES

1. Chan,Y.L. and Tien, C.L., A Numerical study of two dimensional laminar natural

convection in shallow open cavities, International journal of heat and mass transfer.

2. Numerical heat transfer and fluid flow Suhas V.Patankar.

3. Computational fluid dynamics with basics and applications J.D.Anderson

4. Fundamentals of Computational Fluid dynamics by David W.Zingg.

5. Corcione, M., Effects of the thermal boundary conditions at the side walls upon

natural convection in rectangular enclosures heated from below and cooled fromabove, International Journal of Thermal Sciences.

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Cfd Workshop Final Assignment Submission Venkateswareddy M