Thank you. Yes, this can be found from the indefinite integral of the equation I listed a few posts ago (where I took the definite integral):
$$\frac {dT} {T} = \frac {R} {C_V} \frac {dm} m $$
Does this relationship have a name? It resembles the polytropic relationships.
I found the error in my numerical solution above. I messed up my algebra and accidentally left out a term. Rather than: ##u_2 = \Delta t \dot m\left( h_1-u_1\right) + u_1 ## (for volume A), it should be ##u_2 = \Delta t \frac {\dot m}{m}\left( h_1-u_1\right) + u_1 ##
This causes the numerical...
Total internal energy being ##U_A + U_B## in this case, right?
I re-ran the simulation with a variety of time steps. (The 0.5s stair step series is because I sample the data set at .1 seconds but the simulation only ran at .5 seconds.) The pressure values all quite agree (they essentially...
Hey folks, sorry for the delay. Since I was last working on this, my wife and I had a baby. As you can imagine, things have been busy. I have finally had a chance to return to this problem and have made some progress but have also run into a roadblock that indicates I've made a mistake somewhere...
Thank you for your quick response. I wish for such a simple solution, but in my case, the gas in one control volume is expanding into other gas, not a vacuum; work is done on or by another gas and temperature will not be constant between initial and end states. This is truly the root of the...
TL;DR Summary: Struggling to structure the problem and derive an analytical solution for gas expanding into other gas in a rigid tank. Preferred formulation is fixed control volumes. This is not a homework problem.
The problem:
Two control volumes (A and B) are in a rigid tank filled with air...