# Nice Challenge

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 August 25, 2006, 16:05 Nice Challenge #1 Bilir Guest   Posts: n/a Hi everyone, This challenge is about the following: I am performing a simulation of a chamber (e.g. living room, including furniture), with one small inlet and one outlet. The incoming flow is CONSTANT and after a while a STEADY-STATE conditions is found. After this I give a (very) short pulse of inert material(e.g. CO2)at the inlet, and monitor at several points, inside the chamber, the CO2-concentration vs time. The area of this curve found (the integral), is also known as the DOSE (=INTEGRAL(C(t)*dt)) from 0 to infinite, unit: kg.s/m3). The interesting thing is that for EVERY spot inside this chamber, the same DOSE is observed. I checked this with my simulation and this is indeed the case. It is not easy to imagine this, as you would think that e.g. at the corner of this chamber low concentrations levels are measured, however the intergral with time results in the same dose as measured in the outlet for example. Can anyone of you prove this observation, based on the underlying transport equation? This means show that the DOSE is independent of POSITION. Thank you, and looking forward to the outcome. Regards Bilir

 August 25, 2006, 16:44 Re: Nice Challenge #2 Steve_NTUA Guest   Posts: n/a if you get the dose at steady state its logical to have that DOSE is independent of POSITION! Else what time step did you use; and is it right with cfl critirion;;

 August 26, 2006, 06:57 Re: Nice Challenge #3 Bilir Guest   Posts: n/a Hi My time step = 0.005sec Convergece criterion: 5e-4 cfl? where does it stand for? Regards

 August 26, 2006, 08:29 Re: Nice Challenge #4 Jim_Park Guest   Posts: n/a It's not clear from your post. Do you have data as well as results of a simulation? A thorough mixing of the CO2 might result from a really diffusive model for the convection terms in the NS equations. That could occur because of a diffusive (low order) difference approximation or because the space is not well resolved by your grid. Just some possiblitlites to consider.

 August 26, 2006, 09:30 Re: Nice Challenge #5 Steve_NTUA Guest   Posts: n/a if you are using un explicit finite difference there is a criterion namely 'clf' that gives you a minimum time step for a given Dx and Dy ... but i suspect that 0.005 sec is ok. could you send same results maybe i can help if i see them.

 August 26, 2006, 14:00 Response #6 Bilir Guest   Posts: n/a Hi there, Thanks for the replies. So when I monitor the concentration profiles at several points, I observe that near the inlet, I have high peak and more far from the inlet a low peak but wider. And all of them have the same area i.e. same DOSE. This is independent on the degree of mixing and/or diffusion, on provision that I have Steady-state velocity field and homogeneous injection across the inlet-pipe. Even in my experiments I observe this constant DOSE at all spots. The obervation of same DOSE everywhere should also be refelected by the transport equation. If someone could derive this, that would be nice. Thank you.

 September 8, 2006, 12:30 Re: Nice Challenge #7 Jack Guest   Posts: n/a Hi, I doubt that you may have misunderstood the means of 'dose'. The dose should be an integral from inlet to the monitoring point(e.g. on streamlines or particle trajectories). So, dose close to the outlet should be highr that dose at the inlet. The way you performed is a tracer simulation process. So if your chamber is close to a plug flow, you definitely can get the same integral value of cdt at each monitoring point, which actaully shows the recovery of the tracer is close to 100%. To calculate the 'dose', you may need to solve a transport equation for dose with an appropriate source term. Regards, Jack

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