Engineering

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Geometry solid bodyNatural Convection is a heat transfer mode in which fluid motion is not generated by any external source ( like a pump or fan ) but only because of density difference caused by temperature gradient. The fluid surrounding the heating source receives heats, becomes less dense and thus rises. The surrounding cooler fluid then moves to replace it and the process continues to create a convection current. The driving force for natural convection is buoyancy, a result of fluid density difference.

The entire process can be explained by THERMOSIPHONING EFFECT of fluid. When water is heated, it gains Kinetic energy from the heating source and becomes excited. As a result, it expands and thus becomes less dense, and rises upward. On the other hand, when water is cooled, energy is removed from the molecules, it becomes less active and more dense and thus sink. In this process, the difference in natural density of hot and cold water is used for the movement of fluid.

Geometry and Details:

The Geometry is shown in Fig.1, it is created in Ansys Design Modeler. It consist of 2 solid bodies:

  • The outer body is a hollow cylinder of 200mm length, 50mm inner dia. and 52mm outer dia.
  • The inner body is solid cylinder of 20 mm dia. and 50mm length.

Geometry

Fig.1: Geometry

Named Selection:

In ICEM , the first step is to provide material point to volumes so that volumetric meshing can be done. For this purpose, the following  named selection is done for volume regions as shown in Fig.2

  • Water for fluid region.
  • Aluminum for the outer body &
  • Copper for inner body 

Name creation

 

Fig.2: Name Creation

Mesh Details:

Mesh Method: Robust (Octree)

Element Type:Tetrahedral elements

Number Of Nodes: 77847

Number Of Elements: 386944

Meshed Model

Fig.3:Meshed Model 

Solver Setup:

Pressure Based, Transient Solver is used to check the change in temperature and fluid flow for 100 sec.

Gravity is added in negative Y Direction.

TIME STEP SIZE: 0.1  Sec

NUMBER OF TIME STEPS: 1000

TOTAL TIME: 100 Sec

MAX. ITERATONS PER TIMESTEP: 3

 
 

BOUSSINESQ MODEL

This model assumes density to be constant in all terms of momentum equation except in body force term.

This helps to simplify the equation and makes the convergence of solution easier as compared to temperature dependent density.

 

 

Material Properties:

In material section, copper, aluminum and liquid water are selected from fluent database.

In properties of water, BOUSSINESQ Model is used in place of constant density. This makes the water density a linear function of temperature.

Also the thermal expansion coefficient is given the value as 0.000214.

Cell Zone Condition:

The heating element is assigned copper as material and the outer body as aluminum.

The fluid inside is taken as liquid water. 

Boundary Condition:

As it is case of natural convection so there will be no inlet and outlet.

The heat flux of 12500 W/m2 is given to heating element walls and its material is set to copper.

Results:

From the figures given below for velocity vector and temperature contour, the effect of natural convection due to buoyant forces as a result of temperature gradient can be seen easily.

Velocity Vector 5 secs

Fig.4: Velocity Vector after 5 sec.

Velocity Vector 15 secs

Fig.5: Velocity Vector after 15 sec.

Velocity Vector 30 secsFig.6: Velocity Vector after 30 sec.

Velocity Vector 55 secsFig.7: Velocity Vector after 55 sec.

The images shown above are for velocity vector at time 5 sec, 15 sec, 30 sec and 55 sec.

From the images it can be easily seen that the heated water rises upward and its position is replaced by cold water.

With the help of velocity vector the circulation of water in the chamber can be seen due to buoyant forces acting on the water due to temperature gradient.

The heated water moves upward being less dense compared to cold water. The cold water being more dense at top is displaced downward by heated water.

The velocity vector is normal to the heated element surface initially and then it becomes horizontal as the water rises upward.

 

Temperature Contours:

Temperature contour 5secs

 Fig.8: Temperature Contour after 5 sec.

Temperature contour 15 secsFig.9: Temperature Contour after 15 sec.

Temperature contour 30 secs

Fig.10: Temperature Contour after 30 sec.

Temperature contour 55 secsFig.11: Temperature Contour after 55 sec.

The images shown above shows temperature contour at time 5 sec, 15sec, 30 sec & 55 sec.

The maximum temperature is near the heating elements and minimum is above the heating element. The heated water rises upward and the cold water fills that displaced region.

In second image it can be seen that the temperature moving towards left and right above the heating element at the top position. 

Conclusion:
After performing the transient analysis for water heated in a chamber by a heating element, it can be concluded that the water on heating gets lighter and rises upward. The vacant place is replaced by cold water and the process continues until the equilibrium temperature is achieved.

Due to temperature gradient a convection current is created which circulates the water in the chamber.