Flow over Backward Facing Step

• Objective: To perform flow simulation over a backward facing step using Converge Studio software, make a comparative study of various parameters for 3 different base mesh sizes and find where flow separation takes place.

• Procedure:

1. Designing the backward step with the tools available in Converge Studio software for given dimensions.
2. Setting up the input parameters for simulation and generating the input files.
3. Running the converge executable file to generate the output files.
4. Post-processing by running the post-convert executable file.
5. Viewing the simulations of various parameters such as velocity, pressur, etc., using Paraview software.
6. In Converge Studio, the plots of parameters like pressure, velocity, mass flow rate, etc. are made.

• Observations:

#Case 1: For basic mesh size: dx = 2e-3m, dy = 2e-3m, dz = 2e-3m

*Pressure Contour:

=> Inference:

• The above plot is on static pressure, it shows that the static pressure increases through the length of the pipe.
• Also, the pressure at the region of the step is very much lower due to turbulence prevailing at that location.
• So the contour shows higher pressure at outlet(indicated red) and lower pressure at the step and the inlet part.
• The pressure plot is not so smooth as the meshing is done with cells of bigger size and clarity in data is lesser.

*Velocity Contour:

=> Inference:

• The velocity is higher in the inlet, lower in the outlet, and even lower in the region of the step.
• This is similar to that of divergent nozzle as the velocity decreases through the length.
• The plots are not so smooth as the size of the cells are bigger.

*Plots:

• Mass Flow rate at inlet:

• Mass Flow rate at outlet:

=> Observation:

*The mass flow rate is -ve in the inlet and +ve in the outlet(more or less the same modulus value:1.424 kg/s).

*There is a fluctuation of values till a few thousand cycles, then it converges to a constant value.

=> Inference:

*The mass flow rate is optimal as there is sufficient difference between the pressure inlet and outlet.

• Velocity at inlet:

• Velocity at outlet:

=> Observation:

*The velocity is -ve in the inlet and +ve in the outlet.

*Velocity Inlet: 142.07 m/s

*Velocity Outlet: 66.69 m/s

*There is again a fluctuation of values till a few thousand cycles, then it converges to a constant value.

=> Inference:

*The velocity in the inlet is higher and that of the outlet is lower. This is because of the increase in area of cross-section of the outlet w.r.t. inlet.

*This is also because of the low pressure belt formed in the step portion.

• Total Pressure at inlet:

• Total Pressure at outlet:

• Static Pressure at inlet:

• Static Pressure at outlet:

=> Observation:

*There is fluctuation in the pressure value in the starting and converges to a constant value then.

*The pressure converges to the set-up value of total pressure in the inlet and static pressure in the outlet.

*Total Pressure Inlet: 110325 Pa

*Total Pressure Outlet: 104207 Pa

*Static Pressure Inlet: 97979 Pa

*Static Pressure Outlet: 101325 Pa

=> Inference:

*This clearly shows the variation of static pressure, i.e. it increases along the length, having the total pressure decreasing to keep the flow between the inlet and outlet.

*The pressure converges faster than the other variables.

• Total number of cells:

=> Observation:

*The total number of cells is: 1973

=> Inference:

*As the number of cells is very less, the accuracy of the contour and plots is not so good.

#Case 2: For basic mesh size: dx = 1.5e-3m, dy = 1.5e-3m, dz = 1.5e-3m

*Pressure Contour:

=> Inference:('Surface with edges' option is enabled)

• It shows that the static pressure increases through the length of the pipe.
• Also, the pressure at the region of the step is very much lower due to turbulence prevailing at that location(indicated in dark blue colour).
• So the contour shows higher pressure at outlet(indicated red) and lower pressure at the step and the inlet part.
• This is similar to that of a divergent nozzle as the static pressure increases.
• The pressure plot is smoother as the meshing is done with cells of comparatively smaller size and clarity in data is better.

*Velocity Contour:

=> Inference:('Surface with edges' option is enabled)

• The velocity is higher in the inlet, lower in the outlet, and even lower in the region of the step(in the order of .12m/s - dark blue) .
• This is similar to that of divergent nozzle as the velocity decreases through the length.
• The plots are smoother as the size of the cells are smaller.

*Plots:

• Mass Flow rate at inlet:

• Mass Flow rate at outlet:

=> Observation:

*The mass flow rate is -ve in the inlet and +ve in the outlet(more or less the same modulus value:1.375 kg/s).

*There is a fluctuation of values till a few hundred cycles, then there is slight variation in values, further it converges to a constant value.

=> Inference:

*The mass flow rate is optimal as there is sufficient difference between the pressure inlet and outlet.

*The mass flow rate is a little lower than the previous case, as the cell dimensions are lower and accuracy is more comparatively.

• Velocity at inlet:

• Velocity at outlet:

=> Observation:

*The velocity is -ve in the inlet and +ve in the outlet.

*Velocity Inlet: 136.28m/s

*Velocity Outlet: 65.90 m/s

*There is again a fluctuation of values till a few thousand cycles, then it converges to a constant value.

=> Inference:

*The velocity in the inlet is higher and that of the outlet is lower. This is because of the increase in area of cross-section of the outlet w.r.t. inlet.

*This is also because of the low pressure belt formed in the step portion.

*It is slightly lower than the previous case(both inlet and outlet), this is accorded to the less accuracy in previous case due to higher dimension of cells.

• Total Pressure at inlet:

• Total Pressure at outlet:

• Static Pressure at inlet:

• Static Pressure at outlet:

=> Observation:

*There is fluctuation in the pressure value in the starting and converges to a constant value then.

*The pressure converges to the set-up value of total pressure in the inlet and static pressure in the outlet.

*Total Pressure Inlet: 110325 Pa

*Total Pressure Outlet: 104172Pa

*Static Pressure Inlet: 98927 Pa

*Static Pressure Outlet: 101325 Pa

=> Inference:

*It shows the variation of static pressure, i.e. it increases along the length, having the total pressure decreasing to keep the flow between the inlet and outlet. But the values are quite smaller compared to the previous one as the cell dimension is lesser and accuracy is more.

*The pressure converges faster than the other variables.

• Total number of cells:

=> Observation:

*The total number of cells is: 3178

=> Inference:

*As the number of cells is higher comparatively, the accuracy of the contour and plots is good.

#Case 3: For basic mesh size: dx = 1e-3m, dy = 1e-3m, dz = 1e-3m

*Pressure Contour:

=> Inference:('Surface with edges' option is not enabled as the mesh covered the contour)

• It shows that the static pressure increases through the length of the pipe.
• Also, the pressure at the region of the step is very much lower due to turbulence prevailing at that location(indicated in dark blue colour).
• So the contour shows higher pressure at outlet(indicated red) and lower pressure at the step and the inlet part.
• This is similar to that of a divergent nozzle as the static pressure increases.
• The pressure plot is far smoother as the meshing is done with cells of comparatively smaller size and clarity in data is good.

*Velocity Contour:

=> Inference:('Surface with edges' option is not enabled as the mesh covered the contour)

• The velocity is higher in the inlet, lower in the outlet, and even lower in the region of the step(in the order of .17m/s - dark blue) .
• This is similar to that of divergent nozzle as the velocity decreases through the length.
• The plots are far smoother as the size of the cells are smaller comparatively.
• It gives a clear picture on the simulation with greater detail.

*Pressure Contour:('Surface with edges' enabled to show the mesh)

*Mesh size and refinement(Zoomed in):

=> Inference:

• The dimensions of the cells are very small and the refinement is very good, which gives greater detail on the simulation.

*Plots:

• Mass Flow rate at inlet:

• Mass Flow rate at outlet:

=> Observation:

*The mass flow rate is -ve in the inlet and +ve in the outlet(more or less the same modulus value:1.39 kg/s).

*There is a fluctuation of values till a few hundred cycles, then there is slight variation in values, further it converges to a constant value.

=> Inference:

*The mass flow rate is optimal as there is sufficient difference between the pressure inlet and outlet.

*The mass flow rate is a little higher than the previous case, as the cell dimensions are lower and accuracy is more comparatively.

• Velocity at inlet:

• Velocity at outlet:

=> Observation:

*The velocity is -ve in the inlet and +ve in the outlet.

*Velocity Inlet: 138.04 m/s

*Velocity Outlet: 65.91 m/s

*There is again a fluctuation of values till a few thousand cycles, then it converges to a constant value.

=> Inference:

*The velocity in the inlet is higher and that of the outlet is lower. This is because of the increase in area of cross-section of the outlet w.r.t. inlet.

*This is also because of the low pressure belt formed in the step portion.

*It is slightly higher than the previous case(both inlet and outlet), this is accorded to the less accuracy in previous cases due to higher dimension of cells.

• Total Pressure at inlet:

• Total Pressure at outlet:

• Static Pressure at inlet:

• Static Pressure at outlet:

=> Observation:

*There is fluctuation in the pressure value in the starting and converges to a constant value then.

*The pressure converges to the set-up value of total pressure in the inlet and static pressure in the outlet.

*Total Pressure Inlet: 110325 Pa

*Total Pressure Outlet: 104149 Pa

*Static Pressure Inlet: 98641 Pa

*Static Pressure Outlet: 101325 Pa

=> Inference:

*It shows the variation of static pressure, i.e. it increases along the length, having the total pressure decreasing to keep the flow between the inlet and outlet. But the values are quite smaller compared to the previous one as the cell dimension is lesser and accuracy is more.

*The pressure converges faster than the other variables.

• Total number of cells:

=> Observation:

*The total number of cells is: 5796

=> Inference:

*As the number of cells is far higher comparatively, the accuracy of the contour and plots is good.

=>Flow Separation:

*The flow separation takes place in the region of step. This can be clearly viewed in the above velocity stream tracer. *This is the main concern on the simulation.

*This is because of the presence of the step that the separation takes place. From the above, we can infer that a partial vacuum is created in the step region. This adds upon to the notion.

*Moreover, it is because of the formation of the low pressure area in the portion of the step, that the separation in the flow of air takes place in the backward step.

• Result:

Thus the comparative study of the flow parameters for 3 different base mesh sizes has been done and the inferences derived.