Solving Backstep Flow model using Excel

sjwon1991 · December 9, 2012, 22:35

Hi, I'm college student in Yonsei Univ, South Korea
My Professor gave us project to solving backstep flow model using Excel.
But I don't know how to make boundary conditions about this time...
Exactly about du/dx=0 using streamline and vorticity
I hope there is someone who can help me

mettler · December 10, 2012, 08:51

first you need to transform the equations into streamfunction/vorticity equations. Using Excel and finite difference

Guess a value for Streamfunction and vorticity (=0).
Using the entrance velocity get your new vorticity values.
Get the new streamfunction values from the new vorticity values.
Get the new velocities from the new stream functions

use the new velocities to get the new vorticity..etc etc

The hardest part is setting up the BCs for the vorticities at the corners.

sjwon1991 · December 10, 2012, 13:44

Yeah.. Actually, I want to know about BCs,
Exactly about Right side, known as du/dx = 0
I set up the equation as Central Difference Method to get 2nd order Truncation Error...

And there is another problem about this problem..
u and v is defined as function of psi, so I setted u as 2, 1.875, etc...
but most of student setted it as 1, 0.875 etc...
I want to know about this reason..

mettler · December 10, 2012, 13:52

what I think your case of du/dx means is that at the exit the velocity is no longer changing in the X-direction. that lets you set a BC at the exit, since U@x = U@x+1. Your grid should be able to get the U@x, but the U@x+1 can't be found, so you assume that the flow is fully developed in order to get that value.

you want U=1 to be freestream velocity, since everything should be dimensionless. You can also assume a uniform flow field coming in, so U=1 at the entire left (flow from left to right), but then your BC to get from the no-slip to the free stream can get a little tricky, but it is not impossible to figure out

December 10, 2012, 13:44	Yeah..	#3
sjwon1991 New Member Sungjin Won Join Date: Dec 2012 Location: Seoul/Republic of Korea Posts: 15 Rep Power: 13	Yeah.. Actually, I want to know about BCs, Exactly about Right side, known as du/dx = 0 I set up the equation as Central Difference Method to get 2nd order Truncation Error... And there is another problem about this problem.. u and v is defined as function of psi, so I setted u as 2, 1.875, etc... but most of student setted it as 1, 0.875 etc... I want to know about this reason..

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December 10, 2012, 08:51		#2
mettler Senior Member Andrew Join Date: Mar 2009 Location: Washington, DC Posts: 209 Rep Power: 18	first you need to transform the equations into streamfunction/vorticity equations. Using Excel and finite difference Guess a value for Streamfunction and vorticity (=0). Using the entrance velocity get your new vorticity values. Get the new streamfunction values from the new vorticity values. Get the new velocities from the new stream functions use the new velocities to get the new vorticity..etc etc The hardest part is setting up the BCs for the vorticities at the corners.

December 10, 2012, 13:52		#4
mettler Senior Member Andrew Join Date: Mar 2009 Location: Washington, DC Posts: 209 Rep Power: 18	what I think your case of du/dx means is that at the exit the velocity is no longer changing in the X-direction. that lets you set a BC at the exit, since U@x = U@x+1. Your grid should be able to get the U@x, but the U@x+1 can't be found, so you assume that the flow is fully developed in order to get that value. you want U=1 to be freestream velocity, since everything should be dimensionless. You can also assume a uniform flow field coming in, so U=1 at the entire left (flow from left to right), but then your BC to get from the no-slip to the free stream can get a little tricky, but it is not impossible to figure out