# MASS FLOW RATE CALCULATION

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### carlop...@gmail.com

Jan 31, 2023, 5:04:17 AMJan 31
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Good morning to all,

I am estimating the volume mass flow rate of poll fire (mineral oil) using the equations reported in the literature "Enclosure Fire Dynamics" by Karlsson and Quintiere.
Equivalent diameter of 2.54 sq. m. and a total power of 640 kW (thermal power is not fully developed because after 120 seconds the CO2 extinguishing system intervenes) I find a mass flow rate of 13 kg/s.

Modeling the fire with FDS size of 2.20 m x 2.30 m and applying at 5 m height a flow measuring device calculates a peak value of 3 kg/s.

"&DEVC ID='FLOW_FIRE', QUANTITY='MASS FLUX Z', SPATIAL_STATISTIC='AREA INTEGRAL', QUANTITY_RANGE=0.0,1.0E+50, XB=11.3,13.6,22.1,24.3,5.0,5.0/"

How come this difference?

thanks

### dr_jfloyd

Jan 31, 2023, 5:57:09 AMJan 31
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I suspect the equations you are using are a correlation for the burning rate for a fully-developed pool fire.

Correlations are models, and all models have error.
If you are suppressing the fire before it is fully developed then the correlation will overpredict the burning rate
Your burning rates seem extremely high for the pool fire size you gave. Unclear if your pool is 2.54 m2 or a diameter of 2.54 m (~5 m2); however, the maximum burning rate of mineral oil is going to be on the order of 0.1 kg/m2/s which would mean a maximum burning rate on the order of 0.5 kg/m2/s

### carlop...@gmail.com

Jan 31, 2023, 6:19:55 AMJan 31
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yes correct, the equations refer to the fully developed fire, which I considered at the time of activation of the CO2 system, then at after 120 s with a thermal output of 640 kW.  The value of 13 kg/s represents the mass flow rate of the plume.

For my study, i should consider the diameter equivalent to that of the plan projection of an oil transformer. The transformer has a size of 2.20 m x 2.30 m = 5.06 sq m. Equivalent diameter result 2.54 m.

An example, in the cited book, reports that a 1.69 MW fire with an equivalent diameter of 1.60 m has an estimated mass flow rate at 6 meters equal to 17 kg/s of smoke.

The value would seem to be in line with what I calculated.

In FDS I modeled a fire with dimensions of 2.20 m x 2.30 m with HRRpua equal to 126.48 kW/m2 (640kw / 5.06 m2).
Inserting the measuring device at 5 m, I find about 3 kg/s.

Shouldn't it come out 13 kg/s as calculated?

### dr_jfloyd

Jan 31, 2023, 6:47:45 AMJan 31
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My  error, I understand what you are trying to calculate now.

Is your DEVC large enough in area?  Plumes grow in radius as the entrain air. Rule of thumb is about 10 % per m of height. So a 2.2 x 2.3 m fire at 0 m would have a plume with ~0.5 more radius at 5 m or be ~3.2 m in diameter.
Do you have enough grid resolution to resolve the plume flow?
Is your fire definition correct in FDS?
All models have error. FDS has a predictive error. The correlation you are using has predictive error. Neither the value predicted by FDS or the value predicted by correlation are 100 % correct. You should not expect an exact match; however, 13 vs 3 is more discrepancy than one would expect to see.

### carlop...@gmail.com

Jan 31, 2023, 11:18:58 AMJan 31
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I had explained myself wrongly, sorry.

I increased the surface area of the device, extending it 1 meter on each side from the burner, just in case. I think it doesn't change for the result.

I created a mesh with 0.10m x 0.10m x 0.10m cells.

With these arrangements, FDS returns me a mass flow rate of about 16 kg/s, which is very close to the calculated value (13 kg/s).

I also tried to calculate the average visible flame height. The analytically calculated value is about 0.53m, FDS returns me a height of 0.60m.

I think I could consider my model to be sufficiently correct.

Now, I need to provide a smoke disposal system, which will evacuate 13 kg/s of smoke. Considering hot gas temperature 360 K and hot gas density 0.98 kg/m^3 I derive a flow rate of 48233 m^3/h.

HRR_.png
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