Flow through the Backward Step Flow using Converge CFD
ABSTRACT
Backward step flow (BSF) is arguably the most used and benchmarked geometry for numerical CFD and experimental flow analysis which involves laminar flow, recirculating turbulent flow and turbulence model verification in 2-D and 3-D. As the flow phenomena occurring at one BSF geometry may not happen with another BSF geometry, having a standardized value for these non-dimensional parameters of a BSF geometry will make it easier for comparison and replicability for the specific flow. Some dimensional parameters like the step height (h), upstream height (H), expansion ratio and total length (L) of the 2-D BSF plays an important role. The phenomenon of ‘flow separation’ can be very clearly observed which is formed due to the adverse pressure gradient in the direction of flow.
INTRODUCTION
Recirculating and reattachment flow over a backward-facing step (BSF) has been a benchmark geometry for numerical and experimental turbulent flow study. Despite of the simple geometry, much remain to be explored is when the flow becomes turbulent. In many engineering applications complex turbulent flow involves heat transfer, sudden expansion causing recirculating, flow separation, adverse pressure gradient, mixing and recirculating flow. BSF geometry has become one of the benchmark geometry and often used in numerical analysis and CFD development to benchmarking the turbulence model performance.
Different geometry will have different non-dimensional parameter, and this could rise from the difference in the recirculation and reattachment point. There are several geometrical aspects of BSF, most of them are step height (h), upstream height (H), expansion ratio and total length (L) which need to be standardized. Apart from the geometrical specifications some boundary conditions like the inlet Reynolds number should be specified and the type of working fluid being used.
CFD
There are 3 stages involved in CFD modeling. The first is the preprocessing stage, which involves defining the problem through creating the geometry and setting up the grid or mesh and defining the physics of the problem (including the boundary conditions and the turbulence model).
The second stage is the application of the solver whereby the software uses the information provided in the pre-processing stage to generate the numerical results. Finally, post-processing of results takes place where the numerical results are interpreted, visualized and analyzed.
This report is primarily concerned with observing the flow separation and recirculation through the backward flow step and performing the grid independence test and comparing the results in each case.
The work detailed in this report was conducted using CONVERGE Studios, which generated the input files for the given problem statement. The post-processing is done using the Paraview software.
Flow-through the Backward Step
The backward-facing step is a simple geometry where the flow experiences several conditions which include the upstream velocity at the inlet side, the downstream velocity at the outlet side. The fluid may flow through the expansion zone when the height of the channel is increased. Recirculation vortex occurs at the inner side and gets smaller up to the reattachment point. Reattachment is basically caused by the unbalanced forces and seen by the formation of rotational vortexes or forced vortexes.
On BSF, the recirculation vortexes is highly dependent upon the edge step and height. At the end of the recirculation, the reattachment of the wake occurs. This reattachment point is basically the single point and affected by the expansion ratio.
Generally, the recirculation and reattachment point are frequently used as the representative parameters of the flow on the BSF geometry. Both the recirculation and the reattachment point are generally influenced by the BSF geometry comprising of the step height (h), upstream height (H), expansion ratio, and the total length. Larger length affects the infrastructure or the computational resources.
Wake region:
A region of recirculating flow immediately behind a moving or a stationary blunt body, caused by viscosity which may be accompanied by flow separation and turbulence. Typically, a reversed flow region is created, where the flow is moving towards the body.
The fluid flow becomes detached from the surface resulting in the form of eddies and vortices.
Geometry
During the work it was decided to adopt a consistent frame of reference for the coordinate axis such that the X-direction corresponded to the stream-wise direction, the y-axis was aligned with the lateral direction and the z-axis represented the vertical direction. Furthermore, the origin was placed at the upstream boundary and coincided with the base of the centerline of the channel, and the fluid flowed along the positive direction of X-Axis.
In converge, all the surface information is stored in triangles. So, here we have 3 entities to look at: 1. Vertices; 2. Edges; 3. Triangles.
Vertices form the ‘edges’ and the ‘edges’ forms the ‘triangles’. The channel is made up of triangles and that’s basically the fundamental entity in converge where every part of the geometry is assumed to be a triangle.
The geometry is created in the converge studios itself having dimension along
Step Height (h) = 0.01143 mm
Upstream Height (H) = 0.00855 mm
Expansion ratio (H+h)/H = 2.3368 mm
Total Length (L) = 0.27201 mm
Upstream Length (X) = 0.12384 mm
Now, in order for us to run a CFD Simulation, the normal should be pointed towards the fluid.
Now we need to group these triangles together to create something called boundaries. This is a fundamental step in converge. Defining the boundary conditions is one of the most important step in CFD as we are working on some fundamental mathematical equation i.e. the Navier Stokes Equation, it is the partial differential equation and in order to solve the PDE’s we need a starting point and boundary values.
Here we have 5 distinct surfaces,
- Inlet
- Outlet
- Front 2D
- Rear 2D
- Top and Bottom
A diagnostic test is conducted which is used to check the 3D geometry for errors.
The errors may include 1. Intersection Errors; 2. Open Edges; 3. Non-manifold; 4. Non-manifold Edges; 5. Isolated triangles.
This test was conducted, which pointed out no errors in the geometry.
Defining the problem:
Having built the geometry, the next stage is to define the physics of the problem. This involves things such as specifying the initial and boundary conditions, defining body forces acting on the flow, the type of fluid concerned and its properties. There is also the issue of specifying the type of model to be used and necessary associated data.
The first consideration is whether the simulation will be steady or transient. In our case we will be using a pressure-based steady solver, which means we consider an incompressible flow i.e. the density remains constant. The fluid flow is considered to be air having two species oxygen and nitrogen in chemical composition of 23% and 77% respectively. Since our geometry is simple we set our simulation mode to ‘full hydrodynamic’.
As earlier, we grouped our triangles into the set of boundaries and now we group our boundaries into the set of volumetric flow region. We need volumetric regions to set up the initial conditions, as we are solving the bunch of PDE’s we need a set of boundary conditions and initial conditions.
Initial conditions are given at the volume and the boundary conditions are given at the boundary.
To capture the effects of turbulence and flow separation at the sharp edge of the backward step flow, we make use of Reynolds Averaged Navier Stokes Equation (RANS) in particular ‘k- epsilon model’, where k is the turbulent kinetic energy and epison is the dissipation rate of the kinetic energy.
Boundary Conditions:
- At the inlet, we define a total pressure of 110325 Pa and a temperature of 300K using the Dirichlet boundary conditions.
- At the outlet, we define the pressure of 101325 Pa, so that the flow takes place in the positive X-direction and backflow doesn’t take place.
- No-slip boundary condition is being defined at the top and bottom surface of the channel which means that the velocity at the surface will be zero, ignoring any form of turbulence parameter.
Creating a Mesh:
Another issue closely associated with constructing the geometry is set up the grid. This involves subdividing the geometry into cells or elements in order to allow for a discrete representation of the domain using points at which variable will be computed numerically. Throughout the work, a structured 2D mesh has been utilized and this has permitted the exact specification of the mesh. This has been relatively easy to implement due to the given nature of the geometry.
We perform our analysis with base grid size of 2mm, 1.5mm, and 1mm respectively. We also provide ‘Fixed Embedding’ at the top and bottom boundary of the domain, having a scale of 1, which means that for example, if we have the base mesh of 2mm, we will be having a mesh size of 1 mm at the boundary.
This is generally done to capture more accurate results near the boundary i.e. the influence of the boundary on the velocity or the pressure contour.
- Base Mesh: 2 mm
2. Base Mesh: 1.5 mm
3. Base Mesh: 1 mm
Application of the Solver:
In the end, we are generating the 3D output file after every 100th cycle thus producing 150 3D output files for 15000 cycles. These output files will be then converted into the readable format for Paraview which will generate a visual representation for the flow through the channel.
The input files generated in the Converge Studios, are saved in the particular folder and Cygwin (a command-line interface) is used to read all the input files and then generate output files.
These output files are then post-converted into 3D output files basically in the readable file format for Paraview.
Application of the Solver:
The input files generated in the Converge Studios, are saved in the particular folder and Cygwin (a command-line interface) is used to read all the input files and then generate output files.
These output files are then post-converted into 3D output files basically in the readable file format for Paraview.
Results:
- Velocity Contour:
Pressure Contour:
Plots:
Velocity Plot:
Pressure Plot:
Mass Flow Rate:
Total Cell Count:
- Velocity Contour:
Pressure Contour:
Plots:
Velocity Plots:
Pressure Plots:
Mass Flow Rate:
Total Cell Count:
- Velocity Contour:
Pressure Contour:
Plots:
Velocity Plot:
Pressure Plot:
Mass Flow Rate:
Total Cell Count:
Flow Separation:
Flow separation takes place at the sharp discontinuity in the geometry.
Flow separation occurs when:
- The velocity at the wall is zero or negative and an inflection point exists in the velocity profile.
- A positive or adverse pressure gradient occurs in the direction of flow.
The loss in pressure in the separated flow region behind solid bodies causes an imbalance between the upstream and downstream forces, contributing greatly to an increased net drag force.
This regular pattern of vortices in the wake is called a Karman vortex. It creates an oscillating flow at a discrete frequency that is correlated to the Reynolds number of the flow. The periodic nature of the vortex shedding phenomenon can sometimes lead to unwanted structural vibrations, leading to a loss in energy.
it is the detachment of the boundary layer from the surface into the broader wake. It occurs when the boundary layer closest to the wall reverses in the flow direction. The separation point is defined as the point between the forward flow and reverses flow, where the shear stress is zero. This flow reversal is caused by the adverse pressure gradient imposed by the boundary layer by the outer potential flow.
So, when the boundary layer separates, the ‘displacement thickness’ increases sharply which modifies the outside potential flow and pressure fields.
A separated flow creates a region of low pressure in the wake. Drag acts to directly oppose motion, whereas lift acts in a direction perpendicular to motion. Separation of the boundary layer results in increased drag force, which ultimately leads to loss of energy.
Conclusion:
- The geometrical parameters like the expansion ratio, step height (h), upstream height (H) and total length (L) plays a very important role.
- At sharp edges, the low-pressure region is created, which leads to the formation of eddies or vortices.
- These vortices created increases the drag force and thus enhances the loss of energy.
- At the end of the recirculation, the reattachment of the wake occurs. This reattachment point is basically the single point and affected by the expansion ratio.
- Recirculation vortex occurs at the inner side and gets smaller up to the reattachment point.
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