
[Sponsors] 
July 7, 2004, 14:23 
Dimensionless formulation of Euler equations

#1 
Guest
Posts: n/a

I am having some difficulty in determining a consistent dimensionless form of the Euler equations. In the form I'm presently using, the ICs are set by:
rho_inf = 1.0 u_inf = M_inf * cos(alpha) v_inf = M_inf * sin(alpha) p_inf = 1/(gamma*M_inf^2) Et_inf = (p_inf/(gamma1)) + 0.5*rho_inf*(u^2 + v^2) The problem is, I get the proper wave angle but ratios of quantities across the shock are incorrect. Any suggestions? Thanks, jvn 

July 7, 2004, 23:57 
Re: Dimensionless formulation of Euler equations

#2 
Guest
Posts: n/a

Given Mach number M and angle of attach α
Let unprimed denote dimensional quantities and primed denote nondimensional. q = freestream speed = sqrt(u<sup>2</sup> + v<sup>2</sup>) u' = u/q v' = v/q ρ' = ρ/ρ<sub>∞</sub> The pressure and temperature is determined from M. So at freestream q' = 1 u' = cos(&alpha v' = sin(&alpha ρ' = 1 p' = 1/(γ M<sup>2</sup>), using definition of Mach number Energy/volume E' = p'/(γ 1) + ρ' q'<sup>2</sup>/2 

July 8, 2004, 03:18 
Re: Dimensionless formulation of Euler equations

#3 
Guest
Posts: n/a

I think your anomaly arises from the inconsistent nondimensionalization that you appear to be using. You use the speed of sound as a reference speed when nondimensionalizing the velocities, but you use the freestream speed as a reference speed when nondimensionalizing the pressure and energy. Praveen listed the initial / freestream dimensionless quantities where he consistently uses the freestream speed as a reference speed. Similarly you can write down the corresponding quantities if you consistently used the speed of sound as the reference speed. Just work it out both ways yourself to gain confidence in your understanding of nondimensionalization. Keep in mind the dimensionless form of the Euler equations used in the code. One usually chooses reference quantities so that the freestream Mach number does not explicitly enter the dimensionless form of the Euler equations in the code.


July 8, 2004, 13:29 
Re: Dimensionless formulation of Euler equations

#4 
Guest
Posts: n/a

Thank you, Praveen and Ananda. I decided to use the dimensionless formulation because the "dimensional" one, using units that is, kept on crashing due to sqrt or power functions going out of range. I assumed that these problems were due to dealing with numbers with several orders of magnitude difference between them. Thanks again! jvn


Thread Tools  
Display Modes  


Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Euler equations & expansion shocks  technophobe  Main CFD Forum  5  April 28, 2009 15:11 
Actual drag force from dimensionless equations  slaxmi  CFX  10  September 14, 2007 19:20 
Quasi1D Euler Equations  Lost in CFD  Main CFD Forum  0  March 20, 2007 21:24 
Euler equations with heat conduction!  salem  Main CFD Forum  10  August 2, 2004 03:16 
Euler equations?  Jan Ramboer  Main CFD Forum  2  August 19, 1999 01:58 