两相流中的 massTransfer

General
,
1

Frössling 模型

\frac{dm}{dt}=4\pi\Delta\frac{ \mathcal{M}p}{\mathscr{R}T}\times r \left(1+k \sqrt{Re}\right)

where, m is the mass, t is the time, \mathcal{M} is the molecular weight, \mathscr{R} is the gas constant, p is the pressure, T is the abosolute temperature, r is the diameter of the drop, Re is the Reynolds number, and

k=\dfrac{0.276}{\sqrt[3]{\sigma}}

在 OpenFOAM (v1812) 中， k 是这样计算的 applications/solvers/multiphase/reactingEulerFoam/interfacialCompositionModels/massTransferModels/Frossling/Frossling.C

Foam::tmp<Foam::volScalarField>
Foam::massTransferModels::Frossling::K() const
{
    volScalarField Sh(scalar(2) + 0.552*sqrt(pair_.Re())*cbrt(Le_*pair_.Pr()));

    return 6.0*pair_.dispersed()*Sh/sqr(pair_.dispersed().d());
}

pair_dispersed(): 计算分散相的体积分数
pair_dispersed().d(): 分散相的 Sauter 直径

在 OpenFOAM 中，Sherwood 数，对于 Frossling 模型来说，

Sh = 2 + 0.552 \sqrt{Re} \sqrt[3]{Sc}

where, Sc=Le\times Pr is the Schmidt 数， Le is Lewis number read from the phase properties and Pr is calculated from phase pair properties as in phasePair.C

组分传输模型

RMT: rate of mass transfer 传质速率
MTC: mass transfer coefficient 传质系数
AI: interfacial area 界面面积
DY: concentration gradient 浓度梯度
\alpha_g: volume fraction of gas 气体体积分数
D_s: sauter diameter 索特直径，将立方体拍片成等体积球体后对应的直径
D_f: diffusivity 扩散

RMT=MTC\times AI\times DY\tag{1}

对于多相流中某网格中气相界面面积

AI=6\alpha_g/Ds\tag{2}

联合(1)和(2)，有

RMT=MTC\times\dfrac{6\alpha_g DY}{D_s}\tag{3}

而 MTC 可由 Sh 数计算：

MTC=Sh\times D_f/D_s\tag{4}

联合(3)和(4)，有

RMT=Sh\times D_f \times\dfrac{6\alpha_g DY}{D_s^2}\tag{5}

式(5)中， D_f 和 DY 都由求解可得，则所有其他项共同组合成一个参数 K

K=6Sh\times \alpha_g/D_s^2

Spherical 模型

Spherical 模型基于层流假设， Sh=10, OpenFOAM 直接代到 K() 的计算当中。

applications/solvers/multiphase/reactingEulerFoam/interfacialCompositionModels/massTransferModels/sphericalMassTransfer/sphericalMassTransfer.C

Foam::tmp<Foam::volScalarField>
Foam::massTransferModels::sphericalMassTransfer::K() const
{
    return 60.0*pair_.dispersed()/sqr(pair_.dispersed().d());
}