the number of particles per volume in Two-phase Flow
 

I am interested in simulating a two-phase jet mixing particles and air. I have as data the mass flow of particles (kg/s) but the parameter that I can modify in the code is the inlet number of particles per volume(N/m3). So, I need a formula that relates the number of particles per unit volume to the volume flow of particles.

You will have to make assumptions on the size(s) of the particles.

do u mean the distribution function of the diameter of particle? i make an assumption that i have a monodiameter particles i take it 800 Kg/m3. Now how can I deduce the number of particle per volume unity at the inlet (Number of particle/m3)?

Since you are trying to simulate the jet, you must be knowing the area of the inlet ( where the jet is coming from) and the velocity at the inlet.

Lets say:
inlet area = 0.01 m^2
velocity at inlet = 100 m/s

So the volume occupied by the jet in one second, if it was moving at constant velocity of 100 m/s and without any diffusion, will be 1 m^3.

If the mass flow rate of particles is 10 kg/s (say) then the mass of particles in the volume occupied by the jet in one second will be 10 kg.

Assuming that the diameter of the mono-diameter particles is 2 microns then the volume of each particle = 4.19E-18 m^3.

Since the density of particles is 800 kg/m^3, the number of particles flowing per second can be calculated as follows.
number of particles flowing per second = mass flow rate of particles / volume of individual particles / density of particles.

So the number of particles per unit volume at the inlet of the jet will be equal to the number of particles flowing per second divided by the hypothetical volume occupied by the jet in one second.

The volume occupied by the jet if it was flowing at a constant velocity is hypothetical and is used for calculation purpose only. In reality, as the jet comes out, it spreads and its diameter increases. So the number of particles per unit volume changes. This will be calculated by your simulation, you only need to specify this value at the inlet of the jet.

Thank u for the detailed explication. I have one more question if u don't mind.
if i have the mass fraction of particle in the air jet (say 0.17) and the volumetric flow of the particle loaded air jet (say .9E-4m3/s) what would be the the mass flow of particles(Kg/s)?

Mention not.

You can calculate the mass flow rate of particles if you know the density of air and the number of particles per unit volume.

in fact i need the mass flow rate of particle to calculate the number of particle per volume unit. So i expressed the mass flow of particles as the mass fraction of particle in the air jet x the volumetric flow of the air jet loaded with particle x density of air. i just want to verify if it's the right expression.

Mass flow rate = volume flow rate * density

Mass flow rate of mixture = (mass flow rate of air + mass flow rate of particles)

= (volume flow rate of air * density of air + number of particles flowing per second * volume of a particle * density of particle)