Granular pressure

Qingang Xiong · May 7, 2012, 12:37

Dear members,
I am incorporating KTGF for sovling the alphaEqn.H in twoPhaseEulerFoam. In this sovler, is the "ppMagf" to be differentiated alpha to particle granular temperature? If so, I think it is so complex. Looking forward to your reply. Thank you!

alberto · May 8, 2012, 03:24

Quote:

Originally Posted by Qingang Xiong

Dear members,
I am incorporating KTGF for sovling the alphaEqn.H in twoPhaseEulerFoam. In this sovler, is the "ppMagf" to be differentiated alpha to particle granular temperature? If so, I think it is so complex. Looking forward to your reply. Thank you!

The ppMagf term is related to the normal stress modulus of the phase $G(\alpha_s)$ . You should check the definition of this term in the relevant literature, to have some background on the model. If you consider a granular phase, with equation of state:

$p_s = p_s(\alpha_s, \Theta_s)$ ,

the normal stress modulus is

$G(\alpha_s, \Theta_s) = \frac{\partial p_s}{\partial \alpha_s}$

In twoPhaseEulerFoam ppMagf = $G(\alpha_s)/(\alpha_s \rho_s)$ , due to the treatment used in discretizing the phase momentum equation.

Best,

Qingang Xiong · May 8, 2012, 12:49

Quote:

Originally Posted by alberto

The ppMagf term is related to the normal stress modulus of the phase G(alpha). You should check the definition of this term in the relevant literature, to have some background on the model. If you consider a granular phase, with equation of state:

p_s = p_s(alpha_s, Theta_s),

the normal stress modulus is (d indicates partial derivative)

G(alpha_s, Theta_s) = d(p_s)/d(alpha_s)

In twoPhaseEulerFoam ppMagf = G(alpha_s)/(alpha_s*rho_s), due to the treatment used in discretizing the phase momentum equation.

Best,

Dear Alberto,
Thank you very much for your reply. So from your description, Theta_s can be regarded as an independent variable to alpha_s though Theta_s is implicitly obtained from alpha_s. Am I right?

alberto · May 8, 2012, 13:29

Quote:

Originally Posted by Qingang Xiong

Dear Alberto,
Thank you very much for your reply. So from your description, $\Theta_s$ can be regarded as an independent variable to $\alpha_s$ though $\Theta_s$ is implicitly obtained from $\alpha_s$ . Am I right?

You are, in short, treating the particle phase as a compressible fluid. All you need to compute it $1/\psi$ , being $\psi$ the compressibility of the particle phase, which is defined as

$\psi = \frac{\partial \alpha_s}{\partial p_s}$

This is analogous to the case of an ideal gas, where you have

$\rho = \frac{p}{RT}$

so

$\psi = \frac{\partial \rho}{\partial p} = \frac{1}{RT}$

The difference is that, in a granular flow, generally $\rho_s = const$ , and the compressibility is due to changes in the phase fraction $\alpha_s$ .

Best,

Qingang Xiong · May 8, 2012, 13:49

Quote:

Originally Posted by alberto

You are, in short, treating the particle phase as a compressible fluid. All you need to compute it $1/\psi$ , being $\psi$ the compressibility of the particle phase, which is defined as

$\psi = \frac{\partial \alpha_s}{\partial p_s}$

This is analogous to the case of an ideal gas, where you have

$\rho = \frac{p}{RT}$

so

$\psi = \frac{\partial \rho}{\partial p} = \frac{1}{RT}$

The difference is that, in a granular flow, generally $\rho_s = const$ , and the compressibility is due to changes in the phase fraction $\alpha_s$ .

Best,

Dear Alberto,
I understand what you mean. This point is clear to me. Thank you veru much!

Best

May 7, 2012, 12:37	Granular pressure	#1
Qingang Xiong New Member Qingang Xiong Join Date: May 2012 Location: Ames, IA, USA Posts: 20 Rep Power: 14	Dear members, I am incorporating KTGF for sovling the alphaEqn.H in twoPhaseEulerFoam. In this sovler, is the "ppMagf" to be differentiated alpha to particle granular temperature? If so, I think it is so complex. Looking forward to your reply. Thank you!

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