Calculating frictional losses in cd nozzle

DA6righthand · June 7, 2017, 12:31

Hi all,

I'm analyzing rectangular, single expansion ramp, converging-diverging nozzles and I'd like to determine what the frictional losses are. I'm using ANSYS software (DesignModeler, Meshing, Fluent, and CFD-Post). So far I've searched this forum, as well as Google, and have come up dry. Maybe I'm not searching the correct terms...anyways...

I have 4 nozzles that I ran at 3 nozzle pressure ratios (NPRs) and I'm wanting to compare them to determine the best performing nozzle. Thus far to compare nozzles I've computed:

1) entropy rise between inlet and outlet
2) discharge coefficient (ratio of actual mass flow rate to ideal mass flow at the nozzle throat)
3) exit velocity coefficient (ratio of actual exit flow velocity to ideal/isentropic exit flow velocity)
4) and gross thrust coefficient (ratio of actual thrust to ideal/isentropic thrust)

To better determine why one nozzle performs better than the others, I'd like to compute the frictional losses. I'm not quite sure how to do this using CFD-Post, let alone what equation(s) I can use to determine frictional losses. If someone could throw me a bone on where to look for more information on this topic, it would be greatly appreciated! Note that I've been mass flow averaging all quantities.

Thanks,
Justin

LuckyTran · June 7, 2017, 21:57

Wall shear stress and total pressure drop.

Quote:

Originally Posted by DA6righthand

1) entropy rise between inlet and outlet
2) discharge coefficient (ratio of actual mass flow rate to ideal mass flow at the nozzle throat)
3) exit velocity coefficient (ratio of actual exit flow velocity to ideal/isentropic exit flow velocity)
4) and gross thrust coefficient (ratio of actual thrust to ideal/isentropic thrust)

1) is ok. Minimizing entropy is one way to determine which thermodynamically better. But the problem with minimizing entropy is that it doesn't capture the performance (thrust). You can have no entropy production, but also no thrust produced. If you can have two nozzles produce the same thrust and compare the entropy produced, then you could make a comparison. But otherwise it's difficult.
2), 3), and 4) look nice on paper, but "ideal" and "isentropic" conditions are very subjective. Usually these ideal conditions are determined with another dozen assumptions, like constant properties, or one-dimensional flow, or even incompressible flow.

Regarding 4) there is a variable called the stream thrust which gives you the potential thrust of a stream. The stream thrust combines the roles of momentum and pressure and plays a similar role to enthalpy in combining internal energy and pressure.

DA6righthand · June 8, 2017, 11:31

Thanks for the reply. Regarding gross thrust coefficient, I determined that by actual and ideal thrust:

$F_{actual}=C_A\dot{m}_{outlet}V_{outlet}+\left(P_{outlet}-P_{\infty}\right)A_{outlet}$

$F_{ideal}=\dot{m}_{ideal}\sqrt{2h_{T}\left(1-NPR^{\frac{1-\gamma}{\gamma}}\right)}$

where

is the coefficient of velocity in the axial direction,

is the total enthalpy, and

is the nozzle pressure ratio. Doesn't the above account for the quantities you're referring to? I tried Googling "stream thrust" and everything I've found so far refers to general thrust. Could you point me in the right direction?

LuckyTran · June 8, 2017, 19:23

You more or less have it. Stream thrust is given by:
$S_{T}=\dot{m}V+P_{s}A$

Notice you don't subtract the ambient pressure. The reaction force is the difference in the stream thrust between the inlet and outlet.

$R_{f}=S_{T_{1}} - S_{T_{2}}$

The reason this is important, is that there is thrust at the inlet stream into the nozzle. This thrust comes from the inlet stream and not the acceleration due to the C-D itself. So if you optimize based on thrust at the outlet instead of the thrust generated by the nozzle, you will get slightly different (non-optimal) C-D nozzle design.

The problem with isentropic thrust is, the formula used to calculate the isentropic thrust normally assumes all the things I mentioned before, which is unrealistic for a real nozzle. For example:

$NPR^{\frac{1-\gamma}{\gamma}}$
assumes you have a ideal gas with all constant properties.

Same thing with ideal flow rate.

But 90-99% of people you work with are not aware of these shortcomings and they think the ideal flowrate is what you'll actually get if your nozzle is isentropic. Sometimes it's more important to speak the same language than to use the correct words (i.e. political correctness).

June 7, 2017, 12:31	Calculating frictional losses in cd nozzle	#1
DA6righthand New Member Justin Join Date: Jan 2015 Posts: 28 Rep Power: 11	Hi all, I'm analyzing rectangular, single expansion ramp, converging-diverging nozzles and I'd like to determine what the frictional losses are. I'm using ANSYS software (DesignModeler, Meshing, Fluent, and CFD-Post). So far I've searched this forum, as well as Google, and have come up dry. Maybe I'm not searching the correct terms...anyways... I have 4 nozzles that I ran at 3 nozzle pressure ratios (NPRs) and I'm wanting to compare them to determine the best performing nozzle. Thus far to compare nozzles I've computed: 1) entropy rise between inlet and outlet 2) discharge coefficient (ratio of actual mass flow rate to ideal mass flow at the nozzle throat) 3) exit velocity coefficient (ratio of actual exit flow velocity to ideal/isentropic exit flow velocity) 4) and gross thrust coefficient (ratio of actual thrust to ideal/isentropic thrust) To better determine why one nozzle performs better than the others, I'd like to compute the frictional losses. I'm not quite sure how to do this using CFD-Post, let alone what equation(s) I can use to determine frictional losses. If someone could throw me a bone on where to look for more information on this topic, it would be greatly appreciated! Note that I've been mass flow averaging all quantities. Thanks, Justin

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June 8, 2017, 11:31		#3
DA6righthand New Member Justin Join Date: Jan 2015 Posts: 28 Rep Power: 11	Thanks for the reply. Regarding gross thrust coefficient, I determined that by actual and ideal thrust: $F_{actual}=C_A\dot{m}_{outlet}V_{outlet}+\left(P_{outlet}-P_{\infty}\right)A_{outlet}$ $F_{ideal}=\dot{m}_{ideal}\sqrt{2h_{T}\left(1-NPR^{\frac{1-\gamma}{\gamma}}\right)}$ where is the coefficient of velocity in the axial direction, is the total enthalpy, and is the nozzle pressure ratio. Doesn't the above account for the quantities you're referring to? I tried Googling "stream thrust" and everything I've found so far refers to general thrust. Could you point me in the right direction?

June 8, 2017, 19:23		#4
LuckyTran Senior Member Lucky Join Date: Apr 2011 Location: Orlando, FL USA Posts: 5,673 Rep Power: 65	You more or less have it. Stream thrust is given by: $S_{T}=\dot{m}V+P_{s}A$ Notice you don't subtract the ambient pressure. The reaction force is the difference in the stream thrust between the inlet and outlet. $R_{f}=S_{T_{1}} - S_{T_{2}}$ The reason this is important, is that there is thrust at the inlet stream into the nozzle. This thrust comes from the inlet stream and not the acceleration due to the C-D itself. So if you optimize based on thrust at the outlet instead of the thrust generated by the nozzle, you will get slightly different (non-optimal) C-D nozzle design. The problem with isentropic thrust is, the formula used to calculate the isentropic thrust normally assumes all the things I mentioned before, which is unrealistic for a real nozzle. For example: $NPR^{\frac{1-\gamma}{\gamma}}$ assumes you have a ideal gas with all constant properties. Same thing with ideal flow rate. But 90-99% of people you work with are not aware of these shortcomings and they think the ideal flowrate is what you'll actually get if your nozzle is isentropic. Sometimes it's more important to speak the same language than to use the correct words (i.e. political correctness).