How to add a body force to a momentum equation

hiuluom · May 10, 2021, 05:19

Hi foamer,

I see in the reactingPacelFoam OF4 solver usning momentumSource1 in fvOption file with vectorSemiImplicitSource. I do not know that the unit of U is m/s or what else?
I want to add 4.12m/s to fvOption.

Tobermory · May 10, 2021, 09:41

The units of the source term for any transport equation can be deduced from the equation itself. Consider a general transport equation:

$\frac{\partial \phi}{\partial t} + ... = ... + S_\phi$

then the units of the source, $S_\phi$ , are the rate of change of quantity $\phi$ . The only complication is that the source terms can be quoted as specific terms (as above) or absolute, in which case the term is multiplied by the cell volume (i.e. the result from finite volume discretisation of the above transport equation).

So, returning to your example, I am guessing that you want to add a source of momentum and not velocity (a source of velocity doesn't make physical sense). In which case, $\phi = \rho U$ and the units of the source are therefore

(specific) or

(absolute), i.e. units of mass flow rate times velocity. Of course, if the solver is a kinematic solver like simpleFoam then remember that the solver assumes that $\rho=1$ .

hiuluom · May 10, 2021, 09:48

Thank Tobermory,

You right. I want to add momentum for water in interFoam solver. If I multiply rho.water*U, do I get momentum in fvOptions?
and unit of the absolute source kg.m/s2, how to get it? I see kg/m3*m/s=>kg/m2.s

Tobermory · May 10, 2021, 10:03

Okay. Say you want to add a momentum source of 2kg/s * 2.5m/s = 5kg.m/s2 into your simulation, using a block of cells that has a total volume of 0.5m3. The specific momentum source value is then 5kg.m/s2 / 0.5m3 = 10kg/m2.s2. That's the (specific) value that should be injected in each of the source cells in fvOptions.

hiuluom · May 10, 2021, 23:08

Thank Tobermory. I only have the velocity 2.5m/s, but I do not got flow rate of soure. Does it covert density and volume to mass flow rate?

Tobermory · May 11, 2021, 16:39

No - you need to know the mass flow rate in order to be able to calculate the momentum source ...

May 10, 2021, 05:19	Unit of momentum source	#21
hiuluom Senior Member Huynh Phong Thanh Join Date: Aug 2013 Location: Ho Chi Minh City Posts: 105 Rep Power: 13	Hi foamer, I see in the reactingPacelFoam OF4 solver usning momentumSource1 in fvOption file with vectorSemiImplicitSource. I do not know that the unit of U is m/s or what else? I want to add 4.12m/s to fvOption.

May 10, 2021, 09:41		#22
Tobermory Senior Member Join Date: Apr 2020 Location: UK Posts: 748 Rep Power: 14	The units of the source term for any transport equation can be deduced from the equation itself. Consider a general transport equation: $\frac{\partial \phi}{\partial t} + ... = ... + S_\phi$ then the units of the source, $S_\phi$ , are the rate of change of quantity $\phi$ . The only complication is that the source terms can be quoted as specific terms (as above) or absolute, in which case the term is multiplied by the cell volume (i.e. the result from finite volume discretisation of the above transport equation). So, returning to your example, I am guessing that you want to add a source of momentum and not velocity (a source of velocity doesn't make physical sense). In which case, $\phi = \rho U$ and the units of the source are therefore (specific) or (absolute), i.e. units of mass flow rate times velocity. Of course, if the solver is a kinematic solver like simpleFoam then remember that the solver assumes that $\rho=1$ . hiuluom likes this.

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May 10, 2021, 09:48		#23
hiuluom Senior Member Huynh Phong Thanh Join Date: Aug 2013 Location: Ho Chi Minh City Posts: 105 Rep Power: 13	Thank Tobermory, You right. I want to add momentum for water in interFoam solver. If I multiply rho.waterU, do I get momentum in fvOptions? and unit of the absolute source kg.m/s2, how to get it? I see kg/m3m/s=>kg/m2.s

May 10, 2021, 10:03		#24
Tobermory Senior Member Join Date: Apr 2020 Location: UK Posts: 748 Rep Power: 14	Okay. Say you want to add a momentum source of 2kg/s * 2.5m/s = 5kg.m/s2 into your simulation, using a block of cells that has a total volume of 0.5m3. The specific momentum source value is then 5kg.m/s2 / 0.5m3 = 10kg/m2.s2. That's the (specific) value that should be injected in each of the source cells in fvOptions.

May 10, 2021, 23:08		#25
hiuluom Senior Member Huynh Phong Thanh Join Date: Aug 2013 Location: Ho Chi Minh City Posts: 105 Rep Power: 13	Thank Tobermory. I only have the velocity 2.5m/s, but I do not got flow rate of soure. Does it covert density and volume to mass flow rate?

May 11, 2021, 16:39		#26
Tobermory Senior Member Join Date: Apr 2020 Location: UK Posts: 748 Rep Power: 14	No - you need to know the mass flow rate in order to be able to calculate the momentum source ...