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Lagrangian equation in parcel.C

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Old   October 7, 2014, 04:37
Default Lagrangian equation in parcel.C
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Hi everybody,

I'm using OpenFOAM 1.7 with dieselSpray, in order to model gasoline droplets in a turbulent air flow with an Euler approach for the carrier phase and a lagrangian appproach for the droplets.

When I look at the lagrangian equation in parcel.C, I see :

U() = (U() + (timeRatio*Ucorr)+ gcorr*dt)/(1.0 + timeRatio); (Eq 1)

where U() is the droplet velocity, Ucoor the velocity of the gas seen by the droplet and timeRatio=dt/tauMomentum whith tauMomentum the droplet relaxation time.

But this looks very different from any classical lagrangian equation which should be something like :

dUp/dt = (Ug - Up)/Tp + g (Eq 2)

where Up is the velocity of the droplet, Ug the velocity of the gas seen by the droplet ant Tp the droplet relaxation time.

Discretized it should be something like :

U() = (1 - timeRatio)*U() + (timeRatio*Ucorr) + gcorr*dt (Eq 3)


So why does OpenFoam use Eq 1 instead of Eq 3 ?

Any help would be very appreciated.

Thank you.
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Old   February 19, 2015, 11:43
Default Lagrangian particle velocity integration
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Emeline Noel
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Hi Cluap,

Perhaps, you find the answer but I was asking my self the same question and found the solution so I would like to share with other and also to keep memories of the solution. Perhaps, it is obvious for personn who work in the lagrangian world.

First, I should say I was not aware of the tauMomentum so the Euler integration for parcel of openfoam was very strange for me. But I find that the drag force is can be express thanks to the tauMomentum :

tauMomentum = mp*|Uc-Up|/|Fd|

* Uc : carrier phase velocity
* Fd : Drag Force
* Up : particle velocity
* mp : mass of the particle

So,

dUp/dt = Fd/mp + Fg/mp (1)

Using tauMomentum : Tp

dUp/dt = (Ug - Up)/Tp + g (2)

From there, I think the key is to know that in (2) OpenFOAM use the particle velocity at t+dt

Briefly, taking 1/Tp = A

Up(t+dt) = Up(t) + A*dt*(Ug-Up(t+dt)) + Fg*dt

So,

Up(t+dt) = Up(t) + (A*dt*Ug+Fg*dt)/(1+A*dt)

A*dt = timeRatio

So you find the equation in OpenFOAM :

U() = (U() + (timeRatio*Ucorr)+ gcorr*dt)/(1.0 + timeRatio); (Eq 1)

May it can help someone!


Tchuss
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