 ## Fluids

#### How could I calculate Reynolds No. of A Truncated CD Nozzle with Only limited known quantities?

• KSD
Subscriber

I only know about Nozzle inlet stagnation conditions (Chamber pressure and Chamber temperature).

Ambient condition (Pressure), and properties of fluid passing through nozzle (Gamma, Gas Constant).

Now depending on ambient pressure the flow can either supersonic or subsonic, and viscosity of air is not constant it varies with temperature across the nozzle.

So, how can I calculate Reynold number using the standard relation given by (Rho*U*L)/(Mu),

Where I don't know the values of U, Rho (As Ideal gas and compressible flow) and Mu (Which varies depending on Temperature).

And without knowing Reynold number how could I decide whether my flow is going to be turbulent or laminar, and which turbulence model I should use.

Below image shows the BCs I know beforehand : (1) At Pressure Inlet = (Pc & Tc) (2) At Pressure Outlet = Ambient (P & T)

• Rob
Ansys Employee
Given this looks like an interview or test question I'll make a few suggestions rather than answering. These work for more general projects too.
Go to the courses at the top, there are a couple on flow and turbulence: do those. Write onto the paper what you know and what you need. This includes any equations you think you should be using. Show me this and explain what the next steps are.
• KSD
Subscriber
Sir, good to see you again, I will follow your suggestions first.
• KSD
Subscriber
Sir, could you confirm it whether I have done it right or not.
Reynold Number Calculation For Nozzle
Assuming my nozzle is choked means at throat M = 1 in order to get constant mass flow rate.
So using this relation and as \dot(m) = rho*A*v, so A will get cancel out from both LHS and RHS.
Thus I will get the value of rho*v using above relation as I know the values of Nozzle stagnation condition and air properties.
And for Dynamic viscosity (mu) I will use Isentropic relation of temperature where by substituting M = 1, in above relation I will get static temp at Nozzle throat.
Next, Using this Nozzle throat static temperature I will find out dynamic viscosity (mu) of air at that temp.
So now I will get Re No. as = (rho*v/mu)*(Nozzle Throat Diameter)
And assuming CD nozzle as pipe or duct flow I can conclude whether my flow is turbulent or not.

• Rob
Ansys Employee
That should work. I'd probably just use the gas properties in the up & down stream regions and see what Reynolds Number came out at as we're more interested in the order of magnitude than the actual value.
• KSD
Subscriber
Sir, Yes sir I didn't think in that way. By this way I think, it could help me to predict flow regime even without assumption of choked nozzle.
Thank you for the help.
You are really great sir. Every time you help me out. Thanks a lot. 