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**Computer Aided Thermal Fluid Analysis Lecture 10**

Dr. Ming-Jyh Chern ME NTUST

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**Road Map for Today What is turbulence?**

Reynolds Averaged Navier-Stokes (RANS) equations Turbulence models Boundary conditions for turbulence models

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**What is turbulence? Part I**

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**What is turbulence? Part II**

Let us see a movie regarding a turbulent flow in a valve.

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**What is turbulence? Part III – Its nature**

Random Effective Mixing High Reynolds number 3-D Energy Dissipation Eddy Motions

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**What is turbulence? Energy Cascade**

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**Reynolds Decomposition**

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**Reynolds Averaged Navier-Stokes (RANS) equations**

is the so-called Reynolds stress.

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**Boussinesq’s Assumption**

How to determine eddy viscosity nt?

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Zero equation model nt is assumed to be a constant and depends on various flow fields.

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One equation model

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Two equations model

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K-e turbulence model

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K-e turbulence model

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Boundary conditions Inlet Conditions

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**Boundary conditions for a solid wall**

1. Wall function

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**Boundary conditions for a solid wall**

1. Wall function

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**Boundary conditions for a solid wall**

2. Two Layer Method

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**Boundary conditions for a solid wall**

2. Two Layer Method

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**Example – Sudden Expansion Flow**

ui 0.1 m 0.13 m 1 m 2.5 m

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**Example – Sudden Expansion Flow – establish mesh**

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**Example – Sudden Expansion Flow – Laminar Flow Case**

Working fluids – air Density = m3/s Dynamics viscosity = 1.81e-5 kg/ms Characteristic length = 0.1 m If we consider a laminar channel flow at Re = 100, then the magnitude of inlet velocity must be m/s.

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**Example – Sudden Expansion Flow – Boundary setup**

Outlet or constant pressure boundary Symmetry boundary Symmetry boundary Inlet boundary

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**Example – Sudden Expansion Flow – Results of laminar Flow**

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**Example – Sudden Expansion Flow – Turbulent Flow Case**

Working fluids – air Density = m3/s Dynamics viscosity = 1.81e-5 kg/ms Characteristic length = 0.1 m If we consider a turbulent channel flow at Re = 30,000, then the magnitude of inlet velocity must be 4.5 m/s. k and e at the inlet boundary (k = , e = 7.859).

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**Example – Sudden Expansion Flow – Results of Turbulent Flow**

Contours of k

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**Simulation of Heat Transfer**

Forced convection or natural convection? Boundary conditions, a. isothermal boundary, b. constant heat flux. Conjugate heat transfer? Heat sources should be imposed inside solids.

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**Example – Forced convection with isothermal boundary**

ui 0.1 m 0.13 m 1 m 2.5 m T = 313 K The constant wall temperature is 293 K, except for the orange region at which the temperature is 313 K.

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**Example – Forced convection with isothermal boundary**

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**Example – Forced convection with isothermal boundary**

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**Example – Forced convection with isothermal boundary**

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**Example – Forced convection with isothermal boundary**

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**Example – Forced convection with isothermal boundary**

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**Example – Forced convection with isothermal boundary**

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**Example – Forced convection with isothermal boundary**

Isothermal contours

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**Example – Natural convection with isothermal boundary**

T = 293 K g 0.01 m Adiabatic boundary Adiabatic boundary 0.01 m T = 294 K

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**Example – Natural convection with isothermal boundary**

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**Example – Natural convection with isothermal boundary**

Boussinesq’s approximation: assume the buoyant force f in N-S equations is

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**Example – Natural convection with isothermal boundary**

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**Example – Natural convection with isothermal boundary**

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**Example – Natural convection with isothermal boundary**

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**Example – Natural convection with isothermal boundary**

Isothermal contours

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**Example – Conjugate Heat Transfer**

Heat conduction in a solid and convection in a fluid are considered in conjugate heat transfer. At least, two materials shall be defined as a fluid and a solid in the model, respectively.

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**Example – Conjugate Heat Transfer**

.

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**Example – Conjugate Heat Transfer**

T = 293 K air g 0.01 m Adiabatic boundary Adiabatic boundary 0.01 m Al T = 294 K

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**Example – Conjugate Heat Transfer**

1 3 2

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**Example – Conjugate Heat Transfer**

4. Choose a solid material from the table or creat a new one. Do not forget to click apply.

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**Example – Conjugate Heat Transfer**

5. Use C> /NEW / Zone to select cells into cset.

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**Example – Conjugate Heat Transfer**

6. Click Tools/Cell Tools to set Type 2 Solid to Material 2

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**Example – Conjugate Heat Transfer**

7. Use cell list to change cells in cset to the type 2 solid

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**Example – Conjugate Heat Transfer**

8. Check if there are two different kinds of cells. Red one is fluid 1. Green one is solid 2.

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**Example – Conjugate Heat Transfer**

Go back to STAR Guide. Click Thermal Options. Click Heat Transfer ON. The rest procedures for simulation of natural convection are as same as the previous example.

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**Example – Conjugate Heat Transfer**

Iosthermal contours + Velocity vectors

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