Approximation of mean mixture fraction in compartment fire

[lganeshs]

Hi,

I have simulated a box with 2 inlets (a fuel and air) and an exhaust. The fuel is wood. The fuel flow rates and air flow rates are simulated as supplies with fixed mass flux values. I monitor the mass flow rates of fuel and air as the simulation progresses using _hrr.csv file , which reach values 0.002kg/s and 0.009kg/s respectively as expected. The exhaust flow rate is 0.011kg/s. I have calculated the density weighted average (favre mean) of Mixture fraction from the quantities in plot_3d data which comes out to be 0.2115 but the expected value is 0.182 (=0.002/(0.002+0.009)). Kindly explain if this deviation is expected. Thank you in advance.

[rmcdermo]

I cannot tell from the information you've provided where the discrepancy may be. It could be many things. I generally to not use plot_3d data, so I would not start there. You should put a DEVC in the compartment and do a volume integral of the concentrations.

[lganeshs]

@drjfloyd

I have monitored the total outflow rate and not the individual species at the outlet(.fds file attached) since the species exiting are different as a result of chemical reactions.

I could repeat the study with the reaction set to inactive to monitor individual species. At this point, fds would not calculate the mixture fraction value (as I understand from the manual). I have calculated the mixture fraction offline and the mean mixture fractions are quite different for the two cases (reaction on and off). This suggests that the behavior is altered by reaction.

[drjfloyd]

Your exhaust ouptut is fuel + air. This does not mean that at 100 s it is 0.009 air and 0.002 fuel. You should look at the mass flow of fuel, air, and products at the exhaust and make sure they have reached steady state. In the example I gave it took about 60 s for the the fuel and air at the exhaust to reach steady state.

I think as developers we are about at the limit of what we can suggest without an input file.

[lganeshs]

Hi @drjfloyd ,
I forgot to attach input file. Please find it attached with this message
share.zip

[drjfloyd]

you have zero thickness OBST for your box. With the default pressure solver these are subject to some velocity error at the wall. A small velocity error over the room surface could account for some of your issue. Making the walls at least one cell thick should help if that is an issue for you.

[lganeshs]

Hi @drjfloyd,

I did two things following your suggestions:

1. Check the flow rate of fuel, air and products at the exhaust to ensure it has reached steady state. The results are as follows and seem to be statistically stationary (kindly correct me if I am wrong):
   
   
2. I changed the thickness of the obstructions such that it spans one cell and the results are as follows:
   
   

The mean mixture fraction in both cases still stays around 0.21.

[drjfloyd]

I simplified your case down to make the compartment walls the domain boundary and have a 1 cell thick roof. Used the UGLMAT pressure solver which strictly enforces the no flux condition at solid walls. I still saw a slight error in Z. I had devices using TOTAL MASS FLUX to get the mass flow in and out for all species as well as the HRR in the box and the mass of all species in the box. If I computed the mass of species using the flows and the HRR (i.e., fuel mass in box is fuel flow into box - fuel flow out of box - HRR in box /heat of combustion). The two slowly diverged and the divergence agreed with the error in Z. It then dawned on me this might be related to #13764. I set FLUX_LIMITER_MW_CORRECTION=T on MISC and the case worked.

[lganeshs]

Hi @drjfloyd ,

I tried setting FLUX_LIMITER_MW_CORRECTION=T on MISC but it throws an error. I use FDS v6.9.1 and run the simulations using pyrosim. From my discussion with Pyrosim tech support, I understand that v6.9.1 does not support FLUX_LIMITER. Should I use an older FDS version, kindly advise.

[drjfloyd]

You need a newer version of FDS.

[lganeshs]

Please find attached the 4 cases.
cases.zip

[lganeshs]

Kindly let me know if you need any additional information.

[rmcdermo]

There was some kind of issue with your .zip file for me, I could not see any cases. Please just send the input files with a .txt extension. Thanks

[lganeshs]

Please find attached the input file with .txt extension
case1_Baseline.txt
case2_fluxOff_thickObs.txt
case3_fluxOn_ZerothickObs.txt
case4_fluxOn_thickObs.txt

[drjfloyd]

I think what you are seeing in case 4 now is just imperfect mixing in the box.

I ran case 4 and added outputs to get the mixture fraction at the top opening. The mixture fraction of the gas flowing out is 0.182 as expected. The mixture fraction inside is not; however, this just means the gas inside is not well mixed. Eventually the gas flowing out the top must equal the gas flowing in; however, the gas inside may not have the same average mixture value over the entire box.

Consider a very large box with an opening at the top with an upward pointing fuel vent just below the opening and an air vent at the bottom. In this case fuel will burn and exit the top of the box almost no mixing downward. Below the fuel vent would be almost all air. The mass exiting the vent will be net of the fuel and air and have the expected mixture fraction, but the box itself being almost all air would have a mixture fraction near zero.

[rmcdermo]

@drjfloyd I don't think we quite have this fully understood. Over the weekend I ran three different cases, one with METHANE fuel (test no oxygen in fuel definition), one with no reaction (set AIT huge), and one with equal diffusivities. Based on the no reac case, I'd say the volume is sufficiently mixed. The usual mixture fraction transport equation we are used to seeing is derived assuming equal diffusivities. But now this is somehow lower, not higher, than the expected. So I am still scratching my head over that. Note that in the plots below the time is run out to 300 s and the expected value comes from the MLR in the _hrr.csv file.

Methane

No REAC

Equal diffusivities

[drjfloyd]

These plots show a steady state is reached. This doesn't demonstrate good mixing. In my simple example of a fuel vent directly below the exit vent plots like these would look the same. You would quickly reach a quasi steady value in the box, but that would be highly stratified with fuel only existing at the top.

When I look at the outflow, that gives the expected value. If the issue was some kind of mass conservation problem, then it seems unlikely to me that the outflow would be correct in all cases I ran.

[lganeshs]

This makes a lot of sense. I was making an assumption that the expected value at the outflow should be equal to the mean value in the box, which is only true for a well-mixed contents inside the box. But, when the contents are not well-mixed inside the box at quasi-steady, the assumption would not work. I am running a few cases to check this as well. Thanks a lot @drjfloyd and @rmcdermo!

[rmcdermo]

I am coming around to agree with Jason. Here are results for METHANE with the outlet vent put on the bottom and burner and air at the top, so the mixing is better in the compartment before the outlet. This looks reasonable to me.

[rmcdermo]

Here you go.

wood_test.fds.txt

[drjfloyd]

I think you need to use MASS MEAN and not MEAN. The fuel, air, and products won't have the same density so volume mean won't capture the actual mass of Z in the box.

[rmcdermo]

OK, I'm rerunning with MASS MEAN

[drjfloyd]

Added outputs to calculate the Z for the outflow and changed to MASS MEAN. Plot shows box mass mean, outflow, target, and box mass mean as 10 slabs over the height.

&DEVC ID='MFOut',QUANTITY='TOTAL MASS FLUX Z',SPATIAL_STATISTIC='AREA INTEGRAL',SPEC_ID='SFPE WOOD_OAK_fuel',XB=0.21872,0.34928,0.27375,0.40375,-0.01,-0.01/
&DEVC ID='MAOut',QUANTITY='TOTAL MASS FLUX Z',SPATIAL_STATISTIC='AREA INTEGRAL',SPEC_ID='AIR',XB=0.21872,0.34928,0.27375,0.40375,-0.01,-0.01/
&DEVC ID='MPOut',QUANTITY='TOTAL MASS FLUX Z',SPATIAL_STATISTIC='AREA INTEGRAL',SPEC_ID='PRODUCTS',XB=0.21872,0.34928,0.27375,0.40375,-0.01,-0.01/

&DEVC ID='ZOut',QUANTITY='CONTROL VALUE',CTRL_ID='ZOutC'/

&CTRL ID='MPFuel',FUNCTION_TYPE='DIVIDE',INPUT_ID='MPOut','CONSTANT',CONSTANT=6.326518/
&CTRL ID='ZOutNum',FUNCTION_TYPE='SUM',INPUT_ID='MFOut','MPFuel'/
&CTRL ID='ZOutDen',FUNCTION_TYPE='SUM',INPUT_ID='MFOut','MAOut','MPOut','CONSTANT',CONSTANT=1E-20/
&CTRL ID='ZOutC',FUNCTION_TYPE='DIVIDE',INPUT_ID='ZOutNum','ZOutDen'/

[rmcdermo]

OK, in the downward configuration, this is the compartment mass mean. Looks close to what you have.

[lganeshs]

@rmcdermo
To quote your earlier message: "I generally to not use plot_3d data, so I would not start there. You should put a DEVC in the compartment and do a volume integral of the concentrations." I have so far used the plot_3d data to calculate the variance/standard deviation of scalar in the box. Is there a way to calculate the same using the Spatial Stats device similar how mass mean is calculated?

[lganeshs]

Hi,

I was able to find averages, weighted means and intergrals in the Spatially-Integrated Outputs in the user guide (Mar,2020). Is there a more recent version I should be looking at?

[mcgratta]

Download the latest version of FDS and consult the user's guide.

[lganeshs]

Hi,

I apologize for the delayed response.
I intend to calculate the std/variance of a scalar (temperature) value over a select volume at every instant of time.
I have gone through the latest manual and it only specifies that MASS MEAN under spatially integrated output. Although, the temporal statistics mentions Favre Root Mean Square value gives an option to calculate this value over a time period between start and end, it uses the running average.

[rmcdermo]

I am not sure FDS does what you are asking. Why don't you write down exactly the math of what you want to do, specify the time integral, spatial integral, definition of the "mean" value you plan to use in the variance, etc. You may be better off to just output a 3D slice of TEMPERATURE and DENSITY and then use pyfdsools to post process.

[lganeshs]

Hi @rmcdermo ,

I am interested in calculating the favre variance defined by the following expression at every instant of time in FDS simulation.

** N is the number of points in the volume.I have used the 3D volume data to calculate the variance value so far.

I have recently come to realize that there is a mismatch in the value reported by the stats device (area integral/ mass mass) defined in FDS vs the value calculated using the 3D volume data. For example, I have computed the mass mean of mixture fraction at the outlet of the box using the stats device and 3D volume data:

The solid line is computed using 3D volume data, by extracting a bounded plane at the outlet and calculating the favre mean of mixture fraction. The dotted line is computed using the spatial statistics device for mass mean of mixture fraction in the same bounded plane. I can share the FDS file and the output file if needed.

In addition, i computed the mass mean for a select volume inside the box once again using stats device and 3D volume data, the match is closer as shown below. Once again, the solid line if using 3D volume data and dotted is from stats device

[rmcdermo]

In the verification suite, it looks like we only have tests for single point Favre average, so you might have found a problem. It will take time for me to dig into this. In the meantime, as I said, if you have the 3D slice data, you can use your own post processing.