Flow over a backward facing step
JORGE LOZANO
Advanced Turbomachinery Simulations
Flow over a backward facing step
Objective
Simulate a backward facing step 2D simulation, by selecting a pressure difference and obtaining the velocity, pressure mass flow rate, and total cells for each element mesh size, making a conclusion about how the results converge and how it affects the meshing size. Simulations will be compared as by velocity, pressure, general visible mesh, mass flow rate and total cell count, explaining details about each case.
Geometry
The geometry will be a rectangle as in Fig.1, with the dimensions of 0.6909 x 0.0507 x 0.0635 meters, but in the boundary conditions there’ll be a 2D boundary selection, omitting the z axis.
Fig.1 2-D backward facing step flow geometry
Mesh
Simulation will be mesh with different element sizes, shown as follow:
- dx = 2e-3m dy = 2e-3m dz = 2e-3m
- dx = 1.5e-3m dy = 1.5e-3m dz = 1.5e-3m
- dx = 1.0e-3m dy = 1.0e-3m dz = 1.0e-3m
Set-up
The next most important selections will condition the simulation to a certain kind of flow, main material as mixture with oxygen and nitrogen, simulation parameters as what kind of simulation is, how many iterations are necessary to run according to the geometry and methods applied, algorithm used, initial conditions with the boundaries, grid control, physical models and the post processing variables obtained from the simulation.
The pre-processing was realized in Converge Simple, while the processing of the simulation will be using the software Cygwin which allows systems to be recompiled and run natively on Windows that by using several processors the simulation will be run using the Converge Studio initial conditions.
The Set-up conditions will be mentioned next:
- Applications
-General flow
- Materials
-Predefined mixture will be Air
-Turbulent Prandtl number: 0.9
-Turbulent Schmidt number: 0.78
- Available elements: N (Nitrogen), O (Oxygen)
- Simulation Parameters
-New run
-Pressure-based steady solver
-Full hydrodynamic as simulation mode
-Compressible gas flow solver
-Start time: 0 cycles
-End time: 30000 cycles
-PISO Parameters
-PISO convergence criterion multiplier: 20.0
-PISO tolerance: 1e-04
- Boundary Conditions
- INLET
-INFLOW boundary type
-Total Pressure specified value: 110325.0
-Specified boundary condition: AIR
O2: 0.23
N2: 0.77
- OUTLET
-OUTFLOW boundary type
-Total Pressure specified value: 101325.0
-Specified boundary condition: AIR
O2: 0.23
N2: 0.77
- TOP-BTM-WALL
-WALL boundary type
--Velocity boundary condition: Stationary- Stationary
- FRONT-2D
-Two-D boundary type.
- BACK-2D
-Two-D boundary type.
- Initial Conditions & Events
-Regions and initialization: volumetric-region-ud
-Species: Air
-O2: 0.23
-N2: 0.77
- Physical Models
-Turbulence model as: RNG K-ε
- Grid Control
-Base grid- depends for each case, see mesh conditions
-Fixed embedding: Boundary-TOP-BTM-WALL- Scale:2 -Layers:2
- Output / Post Processing
-Post variable selection
-Density
-Pressure
-Temperature
-Velocity
-Mass fraction
-O2:0.23
-N2:0.77
Post process: contours and graphs
As follow, it will be presented the data obtained for the three meshes containing the main variables and the time for the simulations, obtaining velocity and pressure results directly where in the geometry the step begins (or where the transverse area grows).
As the following contours obtained from the simulation, the next figures will be explained for each mesh size (first mesh, second mesh and third mesh):
Velocity contours
- 2 for the first mesh
- 6 for the second mesh
- 10 for the third mesh.
Pressure contours
- 3 for the first mesh
- 7 for the second mesh
- 11 for the third mesh.
Surface mesh
- 4 Fig.5 for the first mesh
- 8 Fig.9 for the second mesh
- 12 Fig.13 for the third mesh.
- Contents to be shown for the first mesh:
- Velocity and pressure contours for all the 3 base mesh sizes
Fig.2 Velocity Magnitude contour first mesh
Fig.3 Pressure contour first mesh.
- Show mesh (i.e surface with edges) for the 3 base mesh sizes
Fig.4 Surface mesh with edges first mesh.
Fig.5 Detailed Surface mesh with edges first mesh.
- Contents to be shown for the second mesh:
- Velocity and pressure contours for all the 3 base mesh sizes
Fig.6 Velocity Magnitude contour second mesh.
Fig.7 Pressure contour second mesh.
- Show mesh (i.e surface with edges) for the 3 base mesh sizes
Fig.8 Surface mesh with edges second mesh.
Fig.9 Detailed Surface mesh with edges second mesh.
- Contents to be shown for the third mesh:
- Velocity and pressure contours for all the 3 base mesh sizes
Fig.10 Velocity Magnitude contour third mesh.
Fig.11 Pressure contour third mesh.
- Show mesh (i.e surface with edges) for the 3 base mesh sizes
Fig.12 Surface mesh with edges third mesh.
Fig.13 Detailed Surface mesh with edges third mesh.
3.- Plots for velocity, pressure, mass flow rate and total cell count for all 3 base mesh sizes and explain the plots.
Fig. 14 Cycles vs. Average velocity inlet, three meshes graph.
Fig. 15 Cycles vs. Average velocity inlet, three meshes table.
By having graph and table in Fig.14 and Fig.15 respectively it is shown that once the third mesh converges the results are (positive due to the correct flow direction):
First mesh velocity inlet: 138.59 m/s
Second mesh velocity inlet: 138.9025 m/s
Third mesh velocity inlet: 139.4039 m/s
Fig. 16 Cycles vs. Average velocity outlet, three meshes graph.
Fig. 17 Cycles vs. Average velocity inlet, three meshes table.
By having graph and table in Fig.16 and Fig.17 respectively it is shown that once the third mesh converges the results are (positive due to the correct flow direction):
First mesh velocity outlet: 67.15479 m/s
Second mesh velocity outlet: 67.15859 m/s
Third mesh velocity outlet: 66.44583 m/s
Fig. 18 Cycles vs. Total and Static Pressure inlet, three meshes graph.
Fig. 19 Cycles vs. Total and Static Pressure inlet, three meshes table.
By having graph and table in Fig.18 and Fig.19 respectively it is shown that once the third mesh converges the results are (positive due to the correct flow direction):
First mesh Total pressure inlet: 110325 Pa
Second mesh Total pressure inlet: 110325 Pa
Third mesh Total pressure inlet: 110325 Pa
First mesh Static pressure inlet: 98553.11 Pa
Second mesh Static pressure inlet: 98502.24 Pa
Third mesh Static pressure inlet: 98419.92 Pa
Fig. 20 Cycles vs. Total and Static Pressure outlet, three meshes graph.
Fig. 21 Cycles vs. Total and Static Pressure outlet, three meshes table
By having graph and table in Fig.20 and Fig.21 respectively it is shown that once the third mesh converges the results are (positive due to the correct flow direction):
First mesh Total pressure outlet: 104283.5 Pa
Second mesh Total pressure outlet: 104280.2 Pa
Third mesh Total pressure outlet: 104196.3 Pa
First mesh Static pressure outlet: 101325 Pa
Second mesh Static pressure outlet: 101325 Pa
Third mesh Static pressure outlet: 101325 Pa
Fig. 22 Cycles vs. Mass flow rate inlet, three meshes graph.
Fig. 23 Cycles vs. Mass flow rate inlet, three meshes table.
By having graph and table in Fig.22 and Fig.23 respectively it is shown that once the third mesh converges the results are (positive due to the correct flow direction):
First mesh mass flow rate inlet: 3.541071 kg/s
Second mesh mass flow rate inlet: 3.547746 kg/s
Third mesh mass flow rate inlet: 3.558431 kg/s
Fig. 24 Cycles vs. Mass flow rate outlet, three meshes graph.
Fig. 25 Cycles vs. Mass flow rate outlet, three meshes table.
By having graph and table in Fig.24 and Fig.25 respectively it is shown that once the third mesh converges the results are (positive due to the correct flow direction):
First mesh mass flow rate outlet: 3.541406 kg/s
Second mesh mass flow rate outlet: 3.547924 kg/s
Third mesh mass flow rate outlet: 3.558427 kg/s
Fig. 26 Cycles vs. Total cells, three meshes graph.
Fig. 27 Cycles vs. Total cells, three meshes table.
By having graph and table in Fig.26 and Fig.27 respectively it is shown that once the third mesh converges the results are (positive due to the correct flow direction):
First mesh total cells: 16,386 cells
Second mesh total cells: 27,734 cells
Third mesh total cells: 49,473 cells
Results
A good convergence for the three meshes was obtained, in different times but close enough to be an indifferent error, the cycles in the simulations appeared to be more than enough, with around 15,000 cycles the simulation would be good to obtain a considerable convergence in terms of error percentage, although it was obtained a better and more precise result for velocity, total and static pressure, mass flow rate, and cell count.
Mass average results were obtained besides area average due to the materials property of compressibility even though it doesn’t show much of a considerable temperature difference to affect the density and the results at last, but they will be assured to be precise.
Results for velocity magnitude, pressure and mass flow rate is coherent due to the initial conditions by analyzing the mass and momentum governing equations.
Also explain where and why separation is taking place in detail:
Fig. 28 Flow features of Back Facing Step Flow
This recirculation of the flow domain occurs when the transversal area has a major difference according to Fig.28 is when the step occurs, the cause of it is the expansion where pressure gradient exists, generating a turbulent layer causing therefore a backward flow under that region, in the animations for the second mesh is more visible this effect.
Separation and reattachment of turbulent flows occur in many practical engineering applications. It is seen both in internal flow systems such as diffusers, combustors and channels with sudden expansions, and in external flows like flow around airfoil and building [1].
Video 1 Cycles vs. Pressure First mesh [2e-3 element size]
Video 2 Cycles vs. Velocity First mesh [2e-3 element size]
Video 3 Cycles vs. Pressure Second mesh [1.5e-3 element size]
Video 4 Cycles vs. Velocity Second mesh [1.5e-3 element size]
Video 5 Cycles vs. Velocity Third mesh [1e-3 element size]
Video 6 Cycles vs. Pressure Third mesh [1e-3 element size]
Conclusions
According to the simulations performed there isn’t much difference for this kind of geometry due to the variable’s convergence they’ll appeared to have relatively a lo percentage of error by cycle 15,000, for an engineering application the first mesh has a faster processing time and good results as shown in the contours for a better resolution in the backward step region there will be needed a finer mesh in that region, a k-omega turbulence model, and saving the 3D post processing files more often, which could be taken for a later simulation.
References