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M. R. JAHANNAMA September 14, 1999 14:04

Hello Mates,

I am working on a spray code simulating a two phase flow, i.e. liquid and air. Parcels of liquid droplets are injected from an orifice into atmosphere. The gas governing equations are solved using the Euler implicit scheme and the Lagrangian approach is employed for liquid droplets analysis.

The calculation procedure after performing succesful operations over initial time steps suddenly shows negative air densities and after few iterations leads to a run time error due to gas velocity overflow.

Could you please give me help in this respect.Thanks, M. R. Jahannama

Md. Ziaul Islam September 14, 1999 16:52

Liquid droplets are injected from the orifice into the atmosphere. As the liquid droplets flight time increases, more and more liquid is supposed to vaporize. That means in two phase flow mixture, concentration of air increases with decreasing of fuel concentration as the time increases. I don't exactly know why you are getting negative density with the increase of time. Density does not have direction like velocity, displacement etc. If the concentration of air in the two phase flow mixture is equal to zero or approaches very close to zero then we can assume that it is only one phase flow i.e. only liquid is present in the flow. I think there is a love bug (big problem) in your algorithm. The arbitrary-Lagrangian-Eulerian numerical method with finite volume application can be obtained from the following journal.

" Computational and Experimental Study of Liquid Sheet Emanating from Simplex Fuel Nozzle." AIAA Journal, Vol. 36, N0.2, February 1998.

You can also find all other references to do this kind of simulations when you go through the journal.


Md. Ziaul Islam September 14, 1999 19:21

Switching topics to Hurricane Floyd
For simplicity, Tornadoes and Hurricanes are small and very big vortex respectively created by mother nature. These turbulence phenomena seems to be rotating around a center core. The center core is smaller in size and seems to be controlling the direction of the flow. I have heard of creating artificial tornadoes in the laboratories which are controllable by human. My ideas may seem to be idiosyncratic to most people but as a novice in CFD, I would like the liberty of expressing myself. If we place an artificial tornado in the middle core of an Hurricane like Floyd to shift it to the middle of the Atlantic Ocean instead of striking the land, then would it not be very nice thing to accomplish? Then billions of dollars can be saved by preventing devastation. My question is to all CFD gurus that is it possible to do this?

Jin Wook LEE September 14, 1999 22:24

Density is, as you know, calculated by the following equation.

Rho = Pop / [RT sigma(mi/Mi)]

Every variable is physically positive. Pop, R and Mi are positive input. T(temp) and mi are dependent variables, but both shoud be greater than (or sometimes equal to) zero. So, check that calculated T and mi are negative and why negative.

If you use 'Pop + Prel' instead of 'Pop', temporary pressure fluctuation may cause negative density. If so, neglect Prel in equation of state, then you might have very good convergence. Actually, in most cases, Prel is very small compared to Pop, so that it can be neglected.

Sincerely, Jinwook

Rho : density, Pop : operating pressure, Prel : relative pressure, R : universal gas const., T : temp., mi : mass fraction of each species, Mi : molecular weight, sigma : summation.

X. Ye September 15, 1999 04:17

I have had also the experience that the density was negative at very high temperature. The reason may be that the density has a very low value (temperature was very high) you had a oscillation during the solution. What you can do is that you 1) limit the density artificially over zero for updating value during the iteration; 2) raise the damping coefficients to reduce the oscillation.

X. Ye

X. Ye September 15, 1999 04:44

Re: Switching topics to Hurricane Floyd
A very nice idea. But you have to consider following facts:

1) It is normally very difficult to determin the position of a hurrican exactly;

2) A hurrican as Floyd has a very large diameter (1000 km?), that means that it carries a very large energy and you have then almost no chance to influence it.

What the nature must be, let it be.

X. Ye

Shigunov September 19, 1999 10:35


there are a lot of articles on this subject in Journal of Computational Physics for recent years, for instance, of Abgrall, Karni, etc. You can see references there. All the authors connect the density and pressure oscillations with conservative discretization of governing equations. Take a look for details.

With best regards


Md. syed Ali Molla September 29, 1999 21:59


Negative density may arrise for many causes. Please try to reduce slope of flow field or avoid sharp turning or check you data sheet where there may be mistake. I also face some sort of this problem from error in data composition and sharp turning area. Thanks Syed Ali

John C. Chien September 29, 1999 23:59

(1). I really don't want to make any comment on this "negative Density" issue. (2). I can only share my experience of "negative density" with you. (3). When I started checking out this 3-D code for turbomachinery written by a wellknown professor, the negative density has been with me all the way. This was a commercial code. And the author also has published several papers on technical journal. (4). All I can say is he really didn't know what he was doing. (5). The code still has the same problem, the negative density normally occur at the place where there is no corners or something like that. Basically, it is related to the formulation, including the boundary conditions. (6). In another code I am checking out, the starting time steps has to be extremely small, otherwise it will diverge in less than one step. The time steps can only be increased slowly. This is also a so-called above average commercial CFD code. (7). I am trying every possibile ways to use the usable part of the results. But I think, such suicide approach should be stopped eventually. (8). If these codes developers performed careful benchmark test (not in terms of speed, but in terms of the accuracy of the results over a reasonable range of conditions, and mesh arrangement. and the convergence characteristics) ahead of time, and carefully state the range of applications, then this types of problems can be avoided. (9). As for the researchers writing his own code, the guideline is the same. No one knows why the solution gives negative density, and it is the method developer or researchers job to come up with the answer. (10). If no one is doing research in this field, there is no answer to the problem. I would say it is as difficult as the cancer research. Don't be so naive to think that the answer exists somewhere in the code. Anyway,I don't think, CFD is the place where the negative density is discussed. If the method is not here, it is not here. It is not fair to say that the Mach number is too low, the grid is not smooth enough, the time step is too large, the geometry has corners, or .... A responsible code developer, whether as commercial applications or private research, must define the range of application in which the solutions exist. (11). The fact is a slight change in conditions and meshes can upset the convergence of the solution for no apparent reasons. It could be avoided, if you know what you are doing. (12).I am not sure whether CAD users are talking about the negative volumes from their CAD programs all the time.

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