Taylor Thomas s3331739
MIET2394
– Computational Fluid Dynamics Assignment A Taylor Thomas, s3331739 Thursday, August 15, 2013
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INTRODUCTION
A backward-facing step is commonly used as a benchmark for validation of numerous flow characteristics, including physical models, multiphase flows and fundamental numerical methods. This model also has a broad range of applications in industry, such as HVAC and combustion. The aims of simulating this model are: 1. To learn the process of creating and exporting a mesh for quality CFD modelling. 2. To learn how to set boundary conditions and process a numerical model. 3. To explore the post-processing abilities of the CFD code to analyse numerical results. 4. To practice writing concise and well developed professional reports. 1.1 Problem description In this report/simulation laminar flow is sent through a two dimensional backward-facing step of known dimensions, as shown below in figure 1.
Figure 1: Illustration of the 2D geometry of a backwards-facing step
While the geometry shown above is dimensionless (normalised for the characteristic length), this simulation will be conducted using dimensioned units; specified in the next section. The backwards-facing step is designed so that the fluid can enter through the inlet and exit the channel through the outlet. The outlet will be defined as an outflow, while the other boundaries will be left as no-slip walls. As this simulation neglects turbulent flows; considering only laminar flows. No heat transfer will occur within the specified system and dimensions will be altered throughout the report to ensure fully developed flow at the outlet for the more aggressive simulations.
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1.2 Brief report outline In order to conduct a comprehensive analysis of the problem illustrated above; the backward-facing step must be tested under several different flow, material and boundary scenarios. In this report the backwardfacing step will run through four different mesh simulations; gradually refining the mesh with each successful attempt. Four different flow characteristics will be included; simulating Reynolds numbers of 50, 100, 150 and 200. To close, this report will analyse the effects of a change in boundary conditions; such as a change from no-slip to zero shear.
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MODEL DESCRIPTION, MODEL CREATION AND MESH QUALITY
2.1 Model Geometry The geometric model illustrated in figure 1 will be created using Ansys Design Modeler, and as specified, will span ten units wide and a total of two units high. The simulations in this report will be conducted using dimensioned units “Metric (kg, m, s, ºC, A, N, V)” no other units will be used in this report. 2.2 Material Information The normalised inlet velocity and fluid properties that are also normalised for the characteristic length are provided as: Fluid properties: density, ρ = 1 Dynamic viscosity, μ = 1/Re, where Re is the Reynolds number 2.3 Boundary Conditions Seven named sections boundaries will be created for this simulation. All six are based on the backwardfacing step geometry and include the inlet, outlet, top wall, bottom wall, step wall, and the symmetry planes (geometrical 2D faces, one for each face) Inlet velocity: ux = 1 and uy = 0 Outlet: Outflow All other boundaries: No slip 2.4 Initial Mesh Details ANSYS Mesh will be used to generate the required mesh properties for this report. Initial mesh will be generated automatically based on the created geometry with a “fine relevance centre” resulting in an initial max face size and max size of 0.022092 m and 0.044183 m respectively.
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RESULTS AND DISCUSSIONS
This section of the report will present and briefly discuss all import and relevant findings based on the results generated by the ANSYS CFX simulations of the backward-facing step problem illustrated in section one. 3.1
Flow phenomenon for Re = 100 case
In this simulation ANSYS CFX was used to generate a basic laminar fluid flow through a backward facing step at a Reynolds number of 100. The primary objective of this simulation is to determine whether or not the flow is fully developed at the outlet or at least partially developed behind the step. The secondary objective; if the primary is proven successful; is to determine the location of the flow reattachment point behind the step.
Figure 2: Pressure Contour (Re = 100)
Figure 2 illustrates a pressure contour of the fluid flow through the backwards facing step. In order to determine if the flow is at least partially developed before the step expansion, one must analyse the shape and spacing of the contours before the step. In this case, the pressure contour contains roughly vertical and equally spaced contour segments before the step expansion. This is enough evidence to make the claim that the flow is indeed at least partially developed behind the step.
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Figure 3: Velocity Contour (Re = 100)
Figure 4: Vector 1(Re = 100)
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Figure 5: Vector 1 and 2 (Re = 100)
Figure 6: Streamline and Vector 1 (Re = 100)
In order to determine if the flow is fully developed at the outlet, one needs to analyse the vector/velocity distribution just prior and just after the outlet. Figures 3, 5 and 6 illustrate constant/uniform velocity and fluid flow before the outlet, while figure 4 in particular illustrates uniform and fully developed flow just outside the outlet. This is demonstrated by the curved and uniform velocity profile and even distribution of fluid velocity.
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Reattachment Point (u = 0)
Figure 7: Velocity vs. X and Reattachment Point
Table 1: Reattachment Point Data x (m)
Velocity u (ms-1)
4.694
-0.0233
4.898
-0.0094
5.102
0.0013
5.306
0.0090
5.510
0.0139
The reattachment point is the point where the dividing streamline attaches to the wall again after initial boundary layer separation. The velocity vs. X graph illustrated in figure 7 demonstrates the reattachment point occurring at velocity u = 0. This appears logical as the flow will gradually reverse until it reattaches to the wall and achieves an equilibrium state further downstream. Table 1 illustrates a partial set of data from the main data set in figure 7. The approximate reattachment point is highlighted.
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3.2 Mesh independence test (Re = 100) In this simulation ANSYS CFX is used to generate a mesh comparison of four different tiers of mesh refinement. The objective of this simulation is to determine the sensitivity of the mesh fineness to the location of the reattachment point. In order to achieve this objective, the mesh fineness was increased three times over (halved three times consecutively) to generate a one half, one fourth and one eighth mesh. The results are graphed and tabulated below.
Figure 8: Mesh 1
Figure 9: Mesh 2 (1/2)
Figure 10: Mesh 3 (1/4)
Figure 11: Mesh 4 (1/8)
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Table 2: Mesh Comparison Mesh
Max Face Size (m)
Max Size (m)
1 2 3 4
0.22092 0.11046 0.00552 0.00276
0.44183 0.22092 0.11046 0.00552
X - Velocity Along Step Bottom wall 0.04 0.02 0
-0.04
Mesh 1
-0.06
Mesh 2 (1/2)
-0.08
Mesh 3 (1/4)
-0.1
Mesh 4 (1/8)
-0.12 -0.14 -0.16 0
2
4
6
8
10
X [m]
Figure 12: Mesh Reattachment Comparison (velocity)
Pressure Gradient_X Along Inside Wall vs. X 0.09 0.08
Pressure Gradient X [kg m-2 s-2]
Velocity u [ms-1]
-0.02
0.07 0.06 0.05 0.04
Mesh 1
0.03
Mesh 2 (1/2)
0.02
Mesh 3 (1/4)
0.01
Mesh 4 (1/8)
0 -0.01 -0.02 0
2
4
6
8
10
12
X [m]
Figure 13: Mesh Reattachment Comparison (pressure) 8
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Table 3: Mesh Comparison Data Mesh 1 2 3 4
Velocity Reattachment [m] 5.10204 5.91837 6.12245 6.12245
Pressure Reattachment [m] 5.10204 5.91837 6.12245 6.12245
Table 4: Mesh Solution Runtime Mesh 1 2 3 4
Run time (sec) 9 41 133 466
Figures 8, 9, 10, 11 and Table 2 illustrate the mesh refinement process and the degree to which each mesh is refined. Figures 12, 13 and Table 3 illustrate the sensitivity of the mesh fineness to the location of the reattachment point. Under close observation it appears that the fineness of the mesh has little to no impact on the location of the reattachment point. In this case the solution converges quite quickly resulting in an accurate enough mesh after two refinement procedures; any further refinement does not increase solution accuracy and results in a large increase in solution runtime, as demonstrated in Table 4. Therefore; based on the above results; it is logical to use Mesh 3 (1/4) [Figure 10] as it provides acceptable accuracy with a short runtime, consuming only a small amount of computational resources in the process. However, the importance of mesh refinement should not be overlooked. Having a refined an accurate mesh with uniform mesh geometry (preferably rectangular) is essential to obtain an accurate result. Mesh refinement is crucial when trying to minimise truncation error; based on the below equation. 𝑑𝜙 𝜙𝑖+1 − 𝜙𝑖 𝑖= + 𝑑(𝑥)2 𝑑𝑥 Δ𝑥 (J.Y. Tu)
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3.3
Reattachment point and Reynolds number
In This Simulation, ANSYS CFX is used to compare different variations in fluid flow by altering the Reynolds number. Similar to the mesh independence test; the objective of this simulation is to determine the sensitivity of the reattachment point location to changes in Reynolds number. In order to conduct a comprehensive analysis, four Reynolds number increments will be used: 50, 100, 150 and 200. As mentioned in the mesh independence section; it is logical to use Mesh 3 (1/4) as any further refinement is a waste of computing time. Therefore, for the sake of this simulation, Mesh 3 (1/4) will be used.
Reattachment Point vs. Different Reynolds Numbers (Velocity)
0.005
Velocity u [ms-1]
0
-0.005
Re = 50 Re = 100
-0.01
Re = 150 -0.015
Re = 200
-0.02 0
2
4
6
8
10
12
X [m] Figure 14: Reynolds Reattachment Comparison (velocity)
Pressure Gradient X [kg m-2 s-2]
Reattachment Point vs. Different Reynolds Number (Pressure) 0.14 0.12 0.1 0.08 0.06
Re = 50
0.04
Re = 100
0.02
Re = 150
0
Re = 200
-0.02 -0.04 0
2
4
6
8
10
12
X[m]
Figure 15: Reynolds Reattachment Comparison (pressure) 10
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Table 5: Reynolds Comparison Data Re 50 100 150 200
Velocity Reattachment [m] 3.67347 6.12245 7.95918 8.97959
Pressure Reattachment [m] 3.67347 6.12245 7.95918 8.97959
According to the results published in figures 14, 15 and Table 5; it appears that the location of the reattachment point has a moderate degree of sensitivity to the change in Reynolds number; definitely more so than the effect of mesh refinement. However, the data does appear to have some convergence. Based on the slight convergence identified above, one could make the conclusion that the data would reach a point where an increase in Reynolds number no longer has an effect on the location of the reattachment point. Further testing would be beneficial. 3.4
Changed Top Wall Boundary Conditions
In this simulation, ANSYS CFX is used to alter the boundary conditions of the backward-facing step analysis. The objective is to change the “Top” boundary condition from “Non-slip” wall to “specified shear” (maintaining Shear stresses of X & Y components at ZERO Pascal) for the case where Reynolds number equals 50 (Re = 50) and determine the difference when using two different boundary conditions.
Figure 16: Pressure Contour (Top wall Boundary)
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Figure 17: Velocity Contour (Top Wall Boundary)
Figure 18: Vector 1 (Top Wall Boundary)
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Figure 19: Vector 1 and 2 (Top Wall Boundary)
Figure 20: Streamline and Vector 1 (Top Wall Boundary)
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Figure 22: Velocity Reattachment
Figure 21: Pressure Reattachment
It is quite clear from figures 16, 17, 18, 19, and 20 that the flow in this simulations is not fully developed. The velocity and vector profiles do not express the uniform and constant velocity distribution required for fully developed flow. Figures 21 and 22 demonstrates the inability of the dividing streamline to reattach to the wall. Without successfully reattaching to the wall, the flow cannot fully develop. From these observations; it is clear that the use of two different boundary conditions results in irregular flow that cannot fully develop.
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CONCLUSIONS
A backward-facing step is commonly used as a benchmark for validation of numerous flow characteristics, including physical models, multiphase flows and fundamental numerical methods. After successful completion of this problem it is clear that the above statement is correct. A backwardfacing step is a great way to demonstrate fundamental CFD procedures and generate a practical understanding of simple fluid flow. After careful analysis of the results from these fundamental CFD simulations, several observations can be made. - The separated streamline must reattach to the wall in order to achieve a fully developed flow at the outlet. - Mesh refinement does not appear to have a significant impact on reattachment point location. - Change in Reynolds number does have an effect on the location of the reattachment point; at least to a greater extent than mesh refinement. - Having multiple different boundary conditions may result in an incomplete flow development. -
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REFERENCES
J.Y. Tu, G. Y. (n.d.). Computational Fluid Dynamics - A Practical Approach. UK: Elsevier Science Limited.
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