# Lagrangian equation in parcel.C

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 October 7, 2014, 05:37 Lagrangian equation in parcel.C #1 New Member   Join Date: Sep 2014 Posts: 11 Rep Power: 11 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.

 February 19, 2015, 11:43 Lagrangian particle velocity integration #2 Member   Emeline Noel Join Date: Dec 2013 Location: Paris Posts: 31 Rep Power: 11 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 amolrajan, JuanRodriguez and panachristos like this.

 Tags dieselspray, lagrangian, parcel, particle