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September 12, 2013, 07:03 
blowing boundary condition

#1 
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Hi guys,
i am currently working on a problem and am kind off stuck at the boundary condition. i am computing a super sonic Ma=2.6 2d flow over a flat plate with a slot from which a subsonic cooling film is emmitted using a WENO scheme and a flow solver not written by me. the problem is the boundary condition at the slot: a constant massflow rate should be blown into the boundary layer. the mass flow is defined as follows: massflow rate dot m=rho_c*v_c*A (1) therein rho_c*v_c=F_c (2) is a given as the blowing rate F_c. the blowing rates used are small F_c=0.065 also the temperature of the coolant gas is give T_c the area of the slot A is also known. the pressure is taken from the flowfield above the slot p_c and is used to compute the density rho_c as such: rho_c=p_c/T_c (3) for the implementation of the boundary condition i need the pressure p_c which is taken from the flowfield an is not a constant the density rho_c which is also not a constant see (3) the velocity v_c=F_c/rho_c=F_c/p_c my questions/problems are: (a) when i compute the solution using these boundary conditions do i get a constant massflow rate? (b) also by using the pressure from the flow field the density rho_c and the velocity v_c change and cause oscillation how can this be avoided? (c) how would you guys implement a constant massflow rate? (d) does it make sense from a physics standpoint to prescribe the pressure p_c instead of getting it from the flowfield? thanks a lot for your help Last edited by Jochen; September 12, 2013 at 09:14. 

September 13, 2013, 06:15 
further explanation

#2 
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so a day has gone by and nobody was able to help me
anyway to further elaborate on my problem: the boundary conditions in the solver i am using are prescribed for the slot from which the coolant is emmitted as follows: the wall is situated between to cells 4 and 5 the wall normal vector points in y direction (north); to get the pressure from the flowfield the following is used: p[0]=p[9] p[1]=p[8] p[2]=p[7] p[3]=p[6] p[4]=p[5] this essentially says dp/dy=0 the density is defined as the pressure from the flowfield divided by the given coolant temperature T_c: rho[0]=p[9]/T_c . . . rho[4]=p[5]/T_c so now the density is a function of the flowfieldpressure. finally the velocity is set using the given blowing rate F_c: v[0]=F_c/rho[0] . . . v[4]=F_c/rho[4] all variables are double precision. if i then compute the massflux: dot m/A[0]= v[0]*rho[0]=(F_c/rho[0]) *rho[0] it should equal F_c. running this code the computed dot m/A shows a difference from F_c in the order of F_cdot m/A=10^13 after ~ 20,000 iteration steps the computed d m/A equals F_c. is the formula for the massflux correct? is it physically correct that the rho[0] cancels out for the analytical solution? thanks again and any comment is welcome. Last edited by Jochen; September 13, 2013 at 07:19. 

Tags 
boundary, condition, filmcooling, massflow 
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