Colloquium BTP Report Turbulent Jet Impingement Cooling of Cylindrical Surfaces

Project Done by: Anupam Garg (2009ME10563)

under the supervision of

Prof. B. Premachandran

Colloquium Presentation by: Deepak Singla 2012ME10659

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Colloquium BTP Report Turbulent Jet Impingement Cooling of Cylindrical Surfaces

Abstract In the project, computational methods have been used to simulate the flow and investigate the heat transfer in slot jet confined impinging jet configurations. CFD code for simulating the 2D geometries were developed in C++. QUICK discretization scheme was used for convective terms in structured grids. Pressure and velocity are stored at cell centers, momentum interpolation is used to prevent pressure checker boarding and SIMPLE algorithm is used for pressure velocity coupling.

Codes were validated by comparing the results with experimental data sets for e.g.; Navier stokes equations solver was validated using benchmark case of lid driven square cavity. Further two turbulent models namely k-e and v2-f were integrated to solve for turbulent flow and validated against DNS results of fully turbulent channel flow.

Resulting system matrices were first preconditioned using LU decomposition and then solved by Biconjugate Gradient Stabilized method. Marix operations were handled using PETSc. Further to work with any geometry, mesh reader has been developed to read mesh filed generated by GAMBIT.

Governing Equations First equation: Navier Stokes equations for incompressible flows with const. velocity:

Continuity Equation Momentum Equation

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Numerical Proceedure

Finite volume based scheme was used for solving equations governing constant density, incompressible, viscous, Newtonian fluid flows.

• Finite Volume Discretization Method 1. Discretization of convective fluxes 2. Discretization of diffusive forces

After discretization Navier Stokes equations were solved using SIMPLE algorithm

• Gradient Computation Gradient was calculated using least squares gradient reconstruction

Boundary Conditions: Codes were used to specify ‘Boundary conditions’ at locations- • Inlet • Outlet • Wall • Symmetry

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Turbulence Modelling

Navier stokes are general equations for fluid flows and are valid for any value of Reynolds number. To calculate turbulent flows we use time averaged equations such as Reynolds-averaged Navier-Stokes equations.

Turbulence closure problem can be solved by using Eddy Viscosity concept according to Boussinesq.

Chien k-E Model:

2 equation model in which 2 partial differential equations are used to describe development of turbulence kinetic energy and of qty. related turbulent length scale. Here wall treatment is carried out by use of wall functions since exact boundary conditions can’t be used when Reynolds number is not high. It is a low Reynolds number turbulence model which is valid down to solid wall

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v2-f Model:

It has been developed, calibrated and validated using flows parallel to wall. The ‘v2-f ’ model is similar to the Standard k-epsilon model Additionally, it incorporates also some near-wall turbulence anisotropy as well as non-local pressure-strain effects. It is a general turbulence model for low Reynolds-numbers, that does not need to make use of wall functions because it is valid upto solid walls. Instead of turbulent kinetic energy ‘k’, the ‘v2-f ’ model uses a velocity scale ‘v2’ (hence the name v2-f model) for the evaluation of the eddy viscosity.

Problem Description

Fig1. and Fig2. show the computational domain used for studying the jet impingement on flat plate and cylindrical surfaces respectively.

Fig1.

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Fig2.

Results and Discussions:

1.1 Validation for Navier Stokes Equations

Code is validated against flows for which benchmark solutions are present.

l.1.1 Poiseuille Flow

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Fully developed pressure driven flow with no slip boundary conditions at top and bottom walls. Code developed gives solution exactly equal to analytical solution given by the equation: u(y) = -1/2u * dp/dx * [1-(2y/d)2]

l.1.2 Lid Driven Cavity Flow Code is validated using benchmark problem of Lid driven cavity flow.

Lid Driven Cavity Flow

Comparison of V velocity at horizontal mid plane of cavity

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Comparison of U velocity at horizontal mid plane of cavity

Benchmark and Present Case

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Since obtained results are closed to benchmark solutions thus solution for NS equations is validated

1.2 Validation for Temperature Equations

l.2.1 Nature Convection in Square cavity

Code is validated for different values of Rayleigh numbers i.e. 10^3, 10^4, 10^5, 10^6, comparing it with benchmark results

Parameters calculated for different mesh sizes are close to benchmark values given by de Vahl Davis for Rayleigh Numbers 104 and 106

1.3 Validation for Turbulence Models

l.3.1 Chien k-e model

Model is validated for fully developed turbulent channel flow at reynolds number 180 based on friction velocity.

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Parameter Present DNS

Rec 3300 3300

Ret 172 180

Uc/Ut 19.1 18.2

Results are a good match with DNS results l.3.1 k-e-v2 model

Model is validated for fully developed turbulent channel flow at reynolds number

590 based on friction velocity. Results are a good match with Davidson’s results

1.4 Validation for Unstructured Solver

Simulation is done for laminar channel flow with unstructured grid to check accuracy of unstructured solver. Obtained results are close to analytical results, therefore it’s validated.

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Y Computed Analytical Error0.005 0.2391 0.2375 0.680.01 0.4434 0.4500 -1.470.015 0.6344 0.6375 -0.480.02 0.8001 0.8000 0.010.025 0.9368 0.9375 -0.080.03 1.0430 1.0500 -0.670.035 1,1367 1.1375 -0.070.04 1.2034 1.2000 0.280.045 1.2366 1.2375 -0.080.50 1.2529 1.2500 0.23

1.5 Jet Impingement

Simulations are performed for confined jet impingement on flat and cylindrical

surfaces.

Local Nusselt number is compared to experimental values of Colucci.

Conclusions:

CFD simulations were carried out by developing codes in C++ (no reliance on commercial CFD packages) successfully to determine the heat transfer due to turbulent jet impinging on flat and cylindrical surfaces. While code validation problems like Lid driven cavity flow, natural convection in square cavity, turbulent channel flow etc. were studied.

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Features of Code:

• 2D unstructured grid solver • Ability to simulate complex geometries by reading meshes generated by

GAMBIT • Visualize mesh in Para View • Imposing distribution profile of a variable at the boundary • State of simulation can be saved at any iteration. Particular state can be later

loaded to continue simulation at iteration left

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