[Jochen]

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

[Jochen]

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_c-dot 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.