Maybe you can calculate the averaged properties such as, for the density, rho_mixture=VF_liq*rho_liq+(1-VF_liq)*rho_gas where VF is the volume fraction and then calculate the Re number of the mixture.

Franco

Thank you Thomasz, I will definitely go through the journal.Thank you Franco for your suggestion.

Hi Chinmoy, I don't know which software you are using for your simulation. But if you are ANSYS-CFX, then it can compute the Reynolds number for each phase. If not, based on Franco's suggestion on the computation of mixture density, similar approach can be used for computing mixture viscosity as: Visc_mix = visc_liq*VF_liq + (1 - VF_liq)*visc_gas

There are a variety of possibilities.

If it is for each phase:

Re_g=rho_g*U_g*D/mu_g

Re_l=rho_l*U_l*D/mu_l

where U_g=Q_g/A and U_l=Q_l/A are the superficial velocity

(velocity seen as every phase fill all the area).

For mixture:

Re=rho*U*D/mu

rho=(1-theta)*rho_g+theta*rho_l    (arithmetic mixture rule)

mu=mu_g^(1-theta)*mu_l^theta     (geometric mixture rule)

U=U_g+U_l=Q/A       theta=Q_l/Q       Q=Q_g+Q_l

There are other mixture rules for viscosity (may be arithmetic).

The charasteristic diameter D is for smaller area. May be hydraulic or full

diameter. Hydraulic diameter when the flow pattern is stratified. Full diameter

when the flow pattern is disperse. For intermittent pattern any of them.

Hydraulic Diameter=4Ap/Sp

Ap=wet area of flow (liquid ideal startified flow)

Sp=wet perimeter (wet in contact with solid wall)

Chinmoy, why do you need to calculate the mixture Reynolds?

Chinmoy, why do you need to calculate the mixture Reynolds?

Chinmoy, why do you need to calculate the mixture Reynolds?

Chinmoy, why do you need to calculate the mixture Reynolds?

Chinmoy, why do you need to calculate the mixture Reynolds?

IN multi-phase flow one phase continuous and the other one will be discontinuous flow will implement to always turbulent flow..,   

You describe your geometry very well, but not the fluid system!

There isn't a single multiphase Re definition.The various definitions  should correspond to among other things, ratio between fluids, their intefacial tension, density and viscosity difference, and flow type (mist, slug, segregated, etc). 

A complete dimensional analysis includes all the variables:

rho_l, mu_l, U_l,

rho_g, mu_g, U_g,

T, To, P, Po, D, Epsilon, sigma.

13 variables.

U_l, U_g = superficial velocities (see definition above)

rho_l, rho_g = densities

mu_l, mu_g = viscosities

T, To, P, Po = temperature, pression (actual and reference)

Epsilon = roughness

Sigma = surface tension

According to PI theorem there are produced 13-4 = 9 adimensional parameters:

Reynolds = rho U D / mu

Euler =delta P / (rho U^2)

Weber = sigma / (rho U^2 D)

theta = U_l / U = Q_l / Q

epsilon / D

T / To

rho_g / rho_l

mu_g / mu_l

There is a lack of one parameter. Then Reynolds must be proposed

for two different conditions (e.g. mixture-one phase, liquid-gas, etc.).

U = U_l, U = U_g, U = U_l+U_g.

See for example:

https://www.academia.edu/11945927/An%C3%A1lisis_Dimensional 

Traditionally flow pattern for two-phase flow has been established on superficial velocities coordinates (see Taitel, Shoham, etc.). This velocity is fundamental for the description of the flow. Reynolds for gas is important because consider the turbulence character of this flow for some patterns (liquid disperse in gas). Mixture-Gas or Liquid-Gas are good decisions for two Reynolds numbers, based on superficial velocity.

(See also the reference of the above mentioned paper, if you don't understand spanish)

Both correlation are equal for internal flows. For the internal flows, the velocity used in the Re=Ro*V*D/mu must be the average velocity, and therefore it is preferred to use mass flow rate instead. If you have an internal flow, use the first correlation which is based on the mass flow rate and average viscosity.

The calculation of mixture Reynolds number is a tricky issue because in same cases the result is not real (not represent any physical phenomenon). For example, depending the (virtual) viscosity chosen, one can give "opposite" result. So, I come back, @Chinmoy, why do you need to calculate this parameter?

If you see well. \rho U = \rho_l U_l + \rho_g U_g  = rho U = rho Q / A = m / A

(is the same mass flow rate).      U_l = Q_l / A         U_g = Q_g / A   (Superficial Vel.)

rho = theta U_l + (1-theta) U_g     theta = Q_l / Q = U_l / U     Q = Q_l + Q_g

For gas is a custom to express the quantities at standard conditions.

Thus rho_g U_g A = rho_g Q_g is the real gas mass flow rate,

although the quantities involved are at standard conditions.

For average viscosity it is another affair. The arthmetical average doesn't work well.

I prefer the geometrical average. Mass average is another option.

I am going to answer your question luis Enrique.

Did you see the dimensional analysis I made above ?

It is a saving of variables the use of such parameters  9  vs. 13.

Then it is a saving of time in experimentation, results reporting, and analysis.

Mixture Reynolds number is based on "real mass flow rate". But we need another parameter to complete the dimensional analysis: Gas or liquid Reynolds number ?

Hi Chinmoy,

To calculate Re for multiphase flow, you need to go separately for each phase. For continuous phase Re is (rho_fluid*V_fluid*D/viscosity_ fluid) and Re for disperse phase is calculated as ( rho_fluid*V_fluid*Dia_disperse_phase/viscosity_ fluid).

Dear Chinmoy,

Using Re as such is NOT wise as we fundamentally have a different physical domain for single and multi-phase fluid flows. In case of a single phase fluid flow, we have a solid-fluid boundary, where the concept of "NO-SLIP" boundary condition can be applied comfortably,

whereas,

in case of multi-phase fluid flow,

what we have is a fluid-fluid (i.e., an immiscible liquid-liquid boundary) interface at the fluid boundary. Here, we cannot apply the conventional "No-Slip" boundary condition and hence, we may need to apply a "free-slip" boundary condition as the fluid interface is NOT rigid and it is deformable and this deformability depends on the intensity of the interfacial tension. And it requires a knowledge of Laplace number, which is the ratio between the fluid pressure and the Laplace pressure (Sigma/L). Determining the value of L (the capillary length) remains a real challenge.

Good Luck.

Let me supplement what Suresh already stated: Good luck!

See attachment.

For calculating two-phase density and viscosity:

Density_mixture=(x/density_gas+(1-x)density_liquid)^-1

Viscosity_mixture=Viscosity_liquid(Density_mixture/Density_liquid)

Where, x is quality

Source: "Two-phase flow" M.M.Awad page 300 and 302

So,

Re=Density_mixture*Velocity*diameter/Viscosity_mixture