CFD simulation using OpenFoam software for the case of Flow Over Flat plate and generating Velocity and Temperature Profiles in comparison with Blasiu...
Case: The flow over a flat plate case consists of a fluid moving past a flat wall with a sharp edge. An illustration of the flow geometry and its boundary conditions is shown in Figure 1. The no-slip condition on the wall forces the flow velocity to drop to zero from the initial, freestream velocity U. The boundary layer will develop as the flow proceeds further down the flat plate. Due to the relative simplicity of the flow case, the velocity of the case can be solved even without CFD. The Reynolds number characterising the flow is
More details on the flat plate flow can be found from the textbook byWhite [1]. Use kinematic viscosity of 1.5e-5 and make sure that you present results from the laminar regime (Re < 1000000). A. Prepare a mesh and set the boundary conditions for the flow of air past a flat plate. Your mesh should be dense enough to resolve the boundary layer (say 30 cells for the 10 mm next to the wall) and the computational domain should be large enough for the boundaries not the influence the solution. Also, in order to save precious computational time, you need to apply variable cells sizes so that larger cells are used in regions that are of no interest to your solution. Extend the flow case to include heat transfer with a constant wall temperature using Prandtl number P r = 0:7. This can be easily done by adding a passive scalar which represents the temperature field. The required boundary conditions are given in Figure 1. In your report, include few representative figures of the mesh you and the amount of cells and mesh dimensions in all spatial directions. B. Run the simulation for as long as a steady state is reached. In your report, present the following figures: Streamwise velocity profiles as a function of y from three different sections all of which should be compared to the corresponding Blasius velocity profiles. (single figure) Temperature profiles as a function of y from three different sections all of which should be compared to the corresponding Pohlhausen temperature profiles. (single figure) The friction factor Cf of x compared to the corresponding Blasius solution for the friction factor. (single figure) Illustrative figures of the viscous and thermal boundary layers. (two figures from paraview)
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Part A: Task: Case Setup (Pre-processing) to simulate Flow Over Flat Plate Data:
Initial & Boundary Condition: - Start Time = 0s - Prandtl Number = 0.7 - Kinematic Viscosity = 1.5e-5 m 2/s - Addition of Passive Scalar Field to simulate the Temperature Field - And conditions from Figure below:
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0.3m
1m
Figure 1: Mesh generation of Flat Plate Cells in Mesh = 15000
Part B: Task: Simulation Results while Steady State:
Simulation Time: T= 01 second (steady reaches near 60 milliseconds)
Time Step = 0.0005 2
Transport Model: Newtonian Fluid
Time Discretization Scheme: Backward
Results outcome and comparison Graphs:a) Stream-wise velocity profiles as a function of y from three different sections all of which should be compared to the corresponding Blasius velocity profiles.
Figure 2: Velocity profiles as Function of Y – Compared with Blasius Data
b) Temperature profiles as a function of y from three different sections all of which should be compared to the corresponding Pohlhausen temperature profiles.
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Figure 3: Temperature profiles as Function of Y – Compared with Pohlhausen Data c) The friction factor Cf of x compared to the corresponding Blasius solution for the friction factor.
Figure 4: Friction Factor in X profiles – Compared with Blasius Data
d) Illustrative figures of the viscous and thermal boundary layers.
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Figure 5: Thermal Boundary Layer
Figure 6: Viscous Boundary Layer
Explanation:
1) You were solving N-S equations with OpenFOAM, what equations is the Blasius solution based on?
The Blasius solution is for a flow that is steady state, incompressible and laminar with constant fluid properties. And it is basically based on Continuity Equation & Momentum equation along the wall. The solution is derived from Prandtl's Boundary Layer Equation for Two-Dimensional incompressible low, considering Velocity distributions at different x-distances are similar.
These equations are then simplified into Blasius equation, by applying boundary conditions on u & v.
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2) Why was there a small distance in the mesh before the no-slip plate? 5
The reason there is an inviscid wall (gap) and refi ned mesh, before No-sip wall condition, is where the fluid enters, and to prevent unsteadiness and non-uniformity in the flow due to skin friction when flow enters from defined inlet, and also to study laminar boundary layer formation and get better gradients near wall.
3) Why can the use of passive scalar for the temperature be justified in this assignment?
The Passive Scalar does not affect the fluid flow, as in our case to study the boundary layer development over the wall, and also used to study & simulate the transport of Scalar Quantity i.e Temperature in our case study, with in an incompressible flow.
4) The outlet pressure was fixed to zero. Why is this and how would the situation change if the temperature difference between the inlet and the plate would be larger (say five times)?
As in this case pressure gradient is zero in Y-direction and it is a steady state and no flow across the surface around Boundary Layer that's why pressure is fixed to zero and also different pressure would would probably cause shearing stress in the boundary layer. The increase in temperature difference between plate and inlet would increase convection of heat, resulting increase in thermal boundary layer.
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References: 1) http://auworkshop.autodesk.com/library/convection-heat-lemaster/blasiussimilarity-solution 2) Fluid Mechanics Frank M White 3) http://www.sfu.ca/~mbahrami/ENSC%20388/Notes/Forced%20Convection.pdf
