Yes it can create supersonic flow velocity it dependent on the pressure ratio up stream down stream flow.If your down stream is atmospheric then you need to increase the inlet pressure and flow rate.

Subsonic  and supersonic are only conditions which depend on the flow rate and the pressure ratio.

Nozzle can create any flow whether subsonic or supersonic.

Refer to High speed flow in convergent divergent nozzles by Hill 1976.

If it is just a convergent nozzle as indicated (i.e., no divegent section) then the max possible velocity will by just sonic at the exit. Of course, provided the pressure ratio is high enough. This is based on gas dynamics (no particles). 

Dear Ahilan,

I agree with Arvin Shmilovich, and in an indirect way with Vitalkumaryadav Pillala, in that regardless of the shape of the cross-section, the flow in a convergent nozzle can at best reach Ma=1, and if it is a convergent-divergent nozzle, then the flow can reach Ma>1. It is a function of pressure ratio and geometry.

Dear Ahilan,

I am not an expert with regard to trying to reach a uniform distribution of solid particles, but I am guessing that you should be able to find something in the literature. With regard to the flow, you are correct, that you should be able to calculate everything you need for the average velocity using your basic Bernoulli and Continuity equations. On the other hand, you will most likely need a simulation to arrive at any further details, since you need to take into account the particle size and mass, as well as the boundary layer, when investigating the distribution of the solids. I am sorry if my previous comment was slightly off topic, but i did not want you to be mislead to think that you can reach supersonic flow using a convergent nozzle.

You can mix the particles of that size but you need to check for the flow distribution at the nozzle exit if you are about to take reading at the exit  check for for uniformity of the flow and the solid particles need to be mixed at some distance upstream from the measuring point so that u can ensure uniformity (around 1.2 m will be ideal).And regarding the calculation of velocity you need to consider the compressible effect after ones you cross 0.3(ideal case) but till 0.45 mach number the compressible effect is very less.But after that effect will seen so better consider compressible equations after Mach 0.45 or 0.5 at Mach 0.7 you need to consider the effect.

I forgot to add something to my last post, but see that someone else luckily caught it. You need to take compressibilty into account. Also, add the energy eq. to your list of equations. Either way, your basic nozzle literature should give you the right amount of info. The equations are derived already, and you should just have to apply them.

One has to distinguish the flow within the nozzle from the flow downstream of the nozzle (outside). The flow in the nozzle will be reasonably well described by a quasi-one- dimensional model. In such a case one can easily demonstrate (when assuming thermodynamic equilibrium) that the largest Mach number (=ratio of velocity to speed of sound) will be M=1 at the nozzle exit. When the pressure ratio between the reservoir upstream of the nozzle and the exit (atmospheric) pressure is increased, the velocity of the flow at the nozzle exit increases and the pressure in the flow remains equal to atmospheric pressure. This is valid until M=1 is reached. At higher reservoir pressures the outlet Mach number remains M=1. One says that the nozzle is chocked. For larger reservoir pressures, the velocity remains constant, but the pressure at the outlet is not anymore atmospheric it is proportional to the reservoir pressure. Furthermore the jet flow downstream of the nozzle becomes a complex non-uniform flow, which does include supersonic regions alternated by subsonic. At very high pressures a very strong shock will separate the supersonic region just outside the nozzle and the subsonic flow further downstream. 

All this does not account for possible effects due to the dust particles. These particles can have a velocity and temperature different from that of the flow. The relaxation of particle velocity and the relaxation of temperature have characteristic time scales, which should be compared to the time scale of convection of dust particles through the nozzle. A general discussion of relaxation in dusty gasses can be found in the literature. In case of mist (liquid droplets)  a nice discussion is provided by Huib Smolders in chapter 4 of his thesis (http://alexandria.tue.nl/repository/books/375903.pdf). There you will find references to literature on dusty gas flows. There is a huge literature on this subject. You may find the book of Vincenti and Kruger most useful when studying the flow of relaxing gasses: http://www.amazon.com/Introduction-Physical-Gas-Dynamics-Vincenti/dp/0882753096

A rectangular nozzle will not be essentially different from a circular nozzle, however the jet flow downstream of a rectangular nozzle is quite different from that of a circular nozzle. This is already the case for subsonic flows, but becomes even more significant for chocked nozzle flows. You will find on Youtube experimental work of Poldervaard and Wijnands on oscillations of supersonic jets from rectangular nozzles (https://www.youtube.com/channel/UC70woPMo8FyR1D7Hj_dux4g). This indicates how complex such flows can be. The dynamic/acoustic behaviour of slot jets has recently been studied by Ziada (Journal of Fluids and Structures

Volume 34, October 2012, Pages 236–25

Self-excited oscillations of a high-speed impinging planar jet

David Arthurs, , Samir Ziada)

Regards, Mico Hirschberg

You will also find some information on dusty gasses in the very nice textbook of;

Compressible Fluid Dynamics (Advanced engineering series) Hardcover use pre formatted date that complies with legal requirement from media matrix – February, 1972

by Philip A. Thompson.

Sir Avraham in lot of literature there are neglect the slip between the particles and the flow.When we can neglect  and when we need to considered (In what conditions).But considering the slip it will be pretty complicated.

Can you please explain some what about nozzles exit conditions in subsonic and at Mach nearly 0.8.

Dear Vitalkumaryadav Pillala,

The book of Thompson and the thesis of Smolders provide a discussion of the conditions when velocity slip is negligible or not. This is a ratio of time scale for viscous relaxation of particle velocity compared to the convection time through the nozzle.

So please read carefully section 4.2 of the thesis and calculate the relevant time scales.

There is no significant difference between low Mach number jet (M

Sir Avraham Hirschberg Thank you very much.

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