2D Inviscid Flow Problem

Sma4t · January 11, 2019, 18:06

Hi,

I'm trying to solve the following problem in fluent:

The flow is assumed to be 2D, inviscid and incompressible. The flow domain has an inlet at the bottom and an outlet on the right face.

Boundary conditions are given in terms of Psi (stream function) where:

The governing equation is:

It is required to plot the streamlines (Psi = constant lines) of the flow.

The first Idea that came into my mind was to assume Psi=Temperature and the governing equation will become the Laplace equation. Therefore the Psi-constant B.Cs will turn into Temperature constant and the inlet and outlet velocities can be simulated as the heat flux in the vertical and horizontal direction.

I wanted to know if it's possible to simulate the actual flow in Fluent regardless of the trick above. I don't have any ideas how to set Psi=constant B.Cs in Fluent.

Any help is appreciated.

Kind Regards,
Mohammad

P.S: This is a project for "An Introduction to CFD" undergraduate course which required comparing the FDM and FVM method for this problem. The FVM was said to be solved using Fluent.

LuckyTran · January 11, 2019, 18:17

Fluent has an inviscid flow model, but it solves the Euler equation and not the potential equation.

You would need to use the trick to solve it in Fluent using Psi = temperature. You just set the wall temperatures to specify Psi.

Sma4t · January 11, 2019, 18:23

LuckyTran,

Yes, I know. But how is it possible to give stream function BC's?

The answer the PDE of the problem looks like this (Psi is defined as Temperature):

But using Fluent's inviscid model with only wall BC's and an inlet and outlet velocities gives this:

LuckyTran · January 14, 2019, 12:47

There isn't really an equivalent of specifying the value of the stream function into the Euler equations.

Psi = constant on any boundary just means that there is no velocity normal to the wall and any velocity is in the wall parallel direction. The wall boundary condition does this. And any value of psi satisfies this condition.

I'm not sure why you have values of 0 and 100 for Psi in this particular case, but in airfoils for example, you need to specify psi to satisfy the kutta condition.

January 11, 2019, 18:06	2D Inviscid Flow Problem	#1
Sma4t New Member S.M.A Taleghani Join Date: Jan 2019 Posts: 2 Rep Power: 0	Hi, I'm trying to solve the following problem in fluent: The flow is assumed to be 2D, inviscid and incompressible. The flow domain has an inlet at the bottom and an outlet on the right face. Boundary conditions are given in terms of Psi (stream function) where: The governing equation is: It is required to plot the streamlines (Psi = constant lines) of the flow. The first Idea that came into my mind was to assume Psi=Temperature and the governing equation will become the Laplace equation. Therefore the Psi-constant B.Cs will turn into Temperature constant and the inlet and outlet velocities can be simulated as the heat flux in the vertical and horizontal direction. I wanted to know if it's possible to simulate the actual flow in Fluent regardless of the trick above. I don't have any ideas how to set Psi=constant B.Cs in Fluent. Any help is appreciated. Kind Regards, Mohammad P.S: This is a project for "An Introduction to CFD" undergraduate course which required comparing the FDM and FVM method for this problem. The FVM was said to be solved using Fluent.

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January 11, 2019, 18:17		#2
LuckyTran Senior Member Lucky Join Date: Apr 2011 Location: Orlando, FL USA Posts: 5,754 Rep Power: 66	Fluent has an inviscid flow model, but it solves the Euler equation and not the potential equation. You would need to use the trick to solve it in Fluent using Psi = temperature. You just set the wall temperatures to specify Psi.

January 11, 2019, 18:23		#3
Sma4t New Member S.M.A Taleghani Join Date: Jan 2019 Posts: 2 Rep Power: 0	LuckyTran, Yes, I know. But how is it possible to give stream function BC's? The answer the PDE of the problem looks like this (Psi is defined as Temperature): But using Fluent's inviscid model with only wall BC's and an inlet and outlet velocities gives this:

January 14, 2019, 12:47		#4
LuckyTran Senior Member Lucky Join Date: Apr 2011 Location: Orlando, FL USA Posts: 5,754 Rep Power: 66	There isn't really an equivalent of specifying the value of the stream function into the Euler equations. Psi = constant on any boundary just means that there is no velocity normal to the wall and any velocity is in the wall parallel direction. The wall boundary condition does this. And any value of psi satisfies this condition. I'm not sure why you have values of 0 and 100 for Psi in this particular case, but in airfoils for example, you need to specify psi to satisfy the kutta condition.