CFD of Air Cavity

8/11/2019 CFD of Air Cavity

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CHAPTER 3

MATHEMATICAL MODELLING AND CFD ANALYSIS

In this chapter air cavity is modeled using Gambit software 2.3.16.The thermal analysis

of same is done in fluent software 12.0.16.

3.1 Thermal aspects of an air cavity

In the present work 2-dimensional air cavity is considered in which top and

bottom wall are maintained at different temperature while other two walls are kept

adiabatic. When temperature of bottom plate exceeds that of the top plate, density

decrease in the direction of gravitational force The geometry of bottom heating is shown

in fig. ( )

Fig 3.1: Geometry of an air cavity

Convection appears when temperature gradient is large enough to cause small

volume of fluid to move towards colder region of higher density. If buoyancy force cause

by difference of density is large enough so that small volume of fluid moves upwards so

that temperature cannot drop and convective flow appears. It is also possible that when

buoyancy force is not enough, then temperature of small volume is able to drop before it

can move up too much; as a result fluid remains stable.


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Fig 3.2: Formation of convection cells for bottom heating

The condition of bottom heating is known as RayleighBenard problem.The small

circulating cells are known as RayleighBenard cells shown as in fig. (3.2)

In case of top heating the temperature of top plate exceeds the temperature of

bottom plate.The density no longer decreases in the direction of gravitational force.

Hence there is no fluid motion and this condition is thermally stable. The heat transfer in

bottom heating is due to conduction.

3.2 Mathematical modeling

The fig.(3.3) shows geometric representation an air cavity of length L and width

W is considered as mentioned in reference [ ].The geometry consists of two adiabatic

side walls and two isothermal walls where upper wall is at lower temperature Tcand

bottom wall at higher temperature THfor bottom heating and vice-versa for top heating.

The air cavity is tilted at various inclinations from 0

0

to 90

0

.The gravity vector is directedin negative y coordinate direction.

Fig 3.3: Geometric representation of an air cavity with tilt angle


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3.3 Governing equation

The governing equations are Navier-Stokes equation for fluid flow and thermal energy

diffusion equation. As a result of assumed 2-D geometry only vertical and horizontal

velocity components are considered. The form of Navier-Stokes equations for present

case is as follows:

(3.1)

(3.2)

The thermal diffusion equation for the present case is as follows:

(3.3)

If the fluid remain stable (heat transfer is due to conduction) the temperature changes

linearly in accordance with the height (from the bottom to top)

()

(3.4)

More important is how the temperature changes when convection appears so

that relation is not linear anymore. The function which describes temperature deviation

from linear is (x, y, t):

() ()

(3.5)

This function satisfies the equation:


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(3.6)

Fluid convection is the result of fluid density variation which depends directly on the

temperature. The higher the temperature, the density decreases so a buoyant force appearscausing the convection phenomena. The fluid density variation can be described by

Taylors series expansion:

()

( ) (3.7)

where 0 is density at TH.It can be presented in another form by introducing thermal expansion coefficient.

(3.8)

The expression (TTw) in eq. (3.5) is used, thus the equation of density is as follows:

() () (3.9)

According to Boussinesq approximation the density variation is neglected in all terms

except in body force in Navier-Stokes equation. The vy in eq. (3.1) may now written by

applying this approximation in the following form:

()

(3.10)


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3.3 Modeling in Gambit

In the present work preprocessing is done using Gambit Software 2.3.16.In this 2-D air

cavity is modeled at various inclinations. As same procedure is adopted for differentinclinations hence it is convenient to show figure for any particular inclination

Modeling of flow topology is done in Gambit software which is based on hierarchical

order. This means first all the vertices of flow region are generated then curves are drawn

through those points and finally face is created within those curves. The air cavity of

dimension 1 m 0.035 m is considered as mentioned in reference[ ] is modeled using

gambit software to create the flow region is shown in fig.(3.4 ).The same methodology is

adoptd for aspect ratios 14 and 7.

Fig 3.4: 2-D representation of an air cavity with tilt angle 600in Gambit


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After creating the topology it is required to discrete the flow region. This is called

Meshing of the flow region. To create the mesh, hierarchical logic is also followed.

First, all the curves defining the flow area have been discretized and then finally the flow

region has been meshed. There are two types of grid either structured or unstructured

grid. Generally structured grid is preferred over unstructured grid as less no of cells are

generated using structured grid which reduces the computational time and results are

more accurate. The uniform grid size of dimension 20016 is use to mesh the geometry

using logic as MAP and element type as QUAD. The meshing is shown in fig.

(3.5).The same meshing strategy is adopted for aspect ratios 14 and 7

Fig 3.5: Meshing of an air cavity with tilt angle 600in Gambit


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After completing the meshing process Face Zone and Cell Zone definition have been

completed. In this problem following Face Zones is selected as Wall Cell-Zone is

selected as Fluid. Theboundary condition is shown in fig.(3.6).

Fig 3.6: Boundary types in Gambit with tilt angle 600

After completion of meshing and zone definition in Gambit, the work has been

saved and exported as a mesh file with .msh extension to use in Fluent software.

3.4 CFD analysis in Fluent.

In Fluent *.msh file is read and shown in fig.(3.7)


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Fig 3.7: Mesh in Fluent for tilt angle 600

Now checking is perform to see whether there is any negative cell volume. If

there is negative cell volume then mesh is incorrect. The fig. of grid check is shown in

fig. (3.8).


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Fig 3.8: Grid check in Fluent for tilt angle 600

The fluid in cavity is air and properties of air are evaluated at mean temperature

of (350c) and (30

0c) which is found to be 32.5

0c.The analysis is carried out using

boussinesq approximation which assumes that density is constant in all governing

equation except for buoyancy term in momentum equation.

Table 3.1: Properties of an air cavity at 305.5 K

Property Units Method Values

Temperature K Constant 305.5

Density Kg/m Boussinesq 1.15575

Specific heat J/kg-k Constant 1005

Thermal

conductivity

W/m-k Constant 0.02634

Viscosity Kg/m-s Constant 1.87e-05

Thermal

expansion

1/K Constant 0.003273


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The energy is On. The dimensionless number known as Rayleigh number which

is based on dimension of domain and assuming constant properties. The Rayleigh number

is use to distinguish laminar and turbulent flow.

The Rayleigh number for an air cavity is 1.87 104 .Therefore flow is considered as

laminar flow.

Table 3.2: Boundary condition

Boundary Type Bottom heating Top heating

Top wall Isothermal Temperature=303K Temperature=308K

Bottom wall Isothermal Temperature=308K Temperature=303K

Right wall Adiabatic Heat flux=0 W/m Heat flux=0 W/m

Left wall Adiabatic Heat flux=0 W/m Heat flux=0 W/m

Relaxation factor are taken as default values

Table 3.3: Relaxation factors

Pressure Density Body force Momentum Energy

0.3 1 1 0.7 1


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The pressure based solver is used and the pressure velocity coupling is taken as Semi

Implicit Method for Pressure Linked Equation SIMPLE algorithmis used. Standard is

used for pressure discretization and second order upwind is used for momentum and

energy discretization.The solution initialization is shown in fig.(3.9)

Fig 3.9: Solution initialization in fluent for tilt angle 600

Convergence criterion is set as 10-4

for continuity equation, x-momentum and y-

momentum equation and 10-6

for energy equation.The convergence is shown in fig.(3.10)


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Fig 3.10: Convergence of an air cavity in Fluent with tilt angle 600

After calculations flow variable such as temperature, velocity, pressure etc are calculated

throughout the computational domain. The dimensionless number i.e. nusselt number is

plotted at various inclinations.

CFD of Air Cavity

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