Week 3: Flow over a backward facing step

Backward-facing:

The backward-facing step is widely used for its application of turbulence in internal flows. The flow separation is caused due

to the sudden changes in the geometry and the inlet and outlet pressure values. The flow separation causes a point of

reattachment and a point of recirculation.

The backward-facing step represents separation flows, which can be widely seen in aerodynamic flows, heat

transfer, engine flows, condensers, vehicles, and flow around the building.

Case setup

The bfs. STL file is loaded into the Converge-CFD set-up.

The "Normal Toggle" is selected from the ribbon, upon selecting the normal toggle it was observed that the normal is pointing

outside the volume, technically the normal should point inside the volume where the fluid is flowing. Therefore in the

geometry dock, the "Transform" option is clicked. The "Normal" tab is selected from the geometry dock and one of the

triangles containing the normal pointing outward is selected. The -Apply option is selected for removing the normals.

The diagnosis dock is selected from the "View" option and the "Find" option is selected. It is found that there is no problem

observed in the geometry ("Intersections(0)","Non manifold Problems(0)","Open Edges(0)-, "Overlapping

Tric(0)-"Normal orientation(0)", "isolated tris (0)"

The "Time. based "Application" type is selected. The "Material" is selected and the predefined mixture is selected as air. The

'Reactant mechanism" is checked off because it is not a combustion problem. The species is selected and the "Apply is

clicked. Under "Gas simulation" the Equation at state is selected as "Redlich Kwong", the critical temperature is 133K and the

critical pressure is 3770000Pa. The Turbulent Prandtl number is 0.9 and the Turbulent

Schmidt number is 0.70 under Global Transport parameters.  Under "Run parameters" the "Steady-state salver is selected.

The "Temporal type" is locked for the steady-state. The "simulation mode" is selected as "Full Hydrodynamic" because the

geometry is simple so while creating the mesh inside the geometry solves the NS equation as well, the geometry is complex

"Na hydrodynamic solver" is selected as such if there is an error it will point out immediately while creating the mesh,

otherwise if the hydrodynamic solver a selected then it will be very tedious to identify the error in the simulation case set up.

Boundary conditions:

Determination of flow velocity:

First of all, let us assume that the flow is incompressible, the Bernoulli Equation for the incompressible flow states that the

sum of the mechanical, potential, and kinetic energy remains constant, so any increase in one form may result in a decrease

in another form. Therefore for the above surface, the equation can be written as

Ps + 1/2 ρ v^2 + ρgh = Ptotal            

Ps + 1/2 ρ v^2 = Ptotal     equation 1

Ps1 = total - 1/2 ρ v^2 = equation 2

Ps2 + 1/2 ρ v2^2 = Ptotal 

Ps2 + 1/2 ρ v2^2 = Ptotal - 1/2 ρ v1^2 +1/2 ρ v1^2

Apply continuity equation:

a1v1 = a2v2

A1,  is the inlet area =H * W

Height of the inlet = 0.008548m

Width of the inlet = 0.025m

Therefore A1 =0.0002137m^2

A2, is the outlet area = H * W

Height of the outlet=0.0199m

Width of the outlet= 0.025m 

Therefore A2 =0.0004975m^2

: v1/v2 =A1/A2

v1/v2 = 2.328

eq 5 is 

ps2 = 101325pa

ptotal = 111325pa

eq 5 beomes

v2^2 = 2000/1.177

v1 = 303.465 m sec^-1

v2 = 130.3547m sec ^-1

Calculating Mach number for the flow

Mach number is defined as the ratio velocity of the object to the velocity of the sound

M = V/A (or) V/C

Minlet = 303.465/346.3 = 0.87

Moutlet = 130.354/346.3 = 0.376

calculating the density of air inlet using the Redlich Kwong equation of state

A cubic equation of state implies an equation that, when expanded, would contain the volume terms raised to the power first

second, and third respective! Mon of the common two barometers cubic e notions can be expressed by the equation

Equation 8  is 

p= RT/(V-b)  - a /T^0.5V(V + b)

 a =  0.42748 * R^2 Tc^2.5/Pc

b = 0.08664 * RTc /Pc

R = 287.05 J/kg k

Critical temp Tc = 132.63k

Critical temp Pc = 3.7858pa

 
Calculating amity at the inlet using the allowing relations. compressible flows

In an isentropic process for the compressible flow, the relationship between static pressure and the total pressure is

pstatic = Ptotal{1+   gamma -1 /2  * M^2)^-$\gamma -\frac{1}{g}ama$