Numerical calculation of Cl, Cd, Cm from Cf and Cp

mmisu · October 12, 2013, 10:39

Hello,

I have a boundary layer code coupled with an inviscid solver that gives me the pressure coefficient and the skin friction coefficient in "s" (a coordinate along the airfoil that starts from the stagnation point).

My question is how can I correctly integrate Cp and Cf in oder to get Cd, Cl and Cm. I've found some formulas in "Fundamentals of Aerodynamics" by Anderson. However, these formulas are in terms of Cartesian coordinates and suggest the integration from the leading edge to the trailing edge.

1. Is it correct to assume that these formulas must be applied on the two parts of the airfoil obtained after we find the stagnation point and split the airfoil in two parts ?

2. Or should I transfer Cp and Cf back to Cartesian coordinates and integrate on the geometrical lower and upper side ?

Thanks for your understanding and answers for what could be a basic question.

mmisu · October 13, 2013, 23:34

You could use the formulas from Anderson to integrate Cp and Cf on the airfoil in a simpler way:

1. Walk the airfoil from the TE, lower side, LE, upper side, TE. This is the way classical panel method store the airfoil geometry.

2. Keep only the terms with "u" indices from the Anderson formulas. This simplification will avoid the need to split the data in upper/lower side.

aalisha · March 31, 2014, 22:56

Hey can you please help me how to calculate Cp if I have cl, cd and cm. Please I am kind of new in the field.

lovecraft22 · April 1, 2014, 15:45

Quote:

Originally Posted by aalisha

Hey can you please help me how to calculate Cp if I have cl, cd and cm. Please I am kind of new in the field.

If you have the Cp then you have the pressure. If you have the pressure you can integrate on the surface and multiply it by the surface local normal. This will provide you a vector for the two/three components of your simulation.

aalisha · April 4, 2014, 02:22

Quote:

Originally Posted by lovecraft22

If you have the Cp then you have the pressure. If you have the pressure you can integrate on the surface and multiply it by the surface local normal. This will provide you a vector for the two/three components of your simulation.

Thanks for your kind reply. However, I think there is a small confusion, I was to calculate Cp (power co-efficient) as I am trying to study the performance of a turbine.

How to use Cl, Cm, Cd to finally get the power co-efficient

cfdivan · April 6, 2014, 15:26

Hi aalisha,

There are some empirical formulas for the power coefficient of lift based machines:

where

and lambda as TSR.

You may be able to find values lower than 0.6 (Betz limit, I guess)

Regards,

aalisha · April 7, 2014, 01:18

Thank you so much for your help.

! Just for knowledge does coefficient of moment also have some relation with power coefficient.

October 12, 2013, 10:39	Numerical calculation of Cl, Cd, Cm from Cf and Cp	#1
mmisu New Member Join Date: Oct 2013 Posts: 2 Rep Power: 0	Hello, I have a boundary layer code coupled with an inviscid solver that gives me the pressure coefficient and the skin friction coefficient in "s" (a coordinate along the airfoil that starts from the stagnation point). My question is how can I correctly integrate Cp and Cf in oder to get Cd, Cl and Cm. I've found some formulas in "Fundamentals of Aerodynamics" by Anderson. However, these formulas are in terms of Cartesian coordinates and suggest the integration from the leading edge to the trailing edge. 1. Is it correct to assume that these formulas must be applied on the two parts of the airfoil obtained after we find the stagnation point and split the airfoil in two parts ? 2. Or should I transfer Cp and Cf back to Cartesian coordinates and integrate on the geometrical lower and upper side ? Thanks for your understanding and answers for what could be a basic question.

October 13, 2013, 23:34	Solved	#2
mmisu New Member Join Date: Oct 2013 Posts: 2 Rep Power: 0	You could use the formulas from Anderson to integrate Cp and Cf on the airfoil in a simpler way: 1. Walk the airfoil from the TE, lower side, LE, upper side, TE. This is the way classical panel method store the airfoil geometry. 2. Keep only the terms with "u" indices from the Anderson formulas. This simplification will avoid the need to split the data in upper/lower side.

March 31, 2014, 22:56		#3
aalisha New Member Aalisha Join Date: Jan 2014 Posts: 18 Rep Power: 12	Hey can you please help me how to calculate Cp if I have cl, cd and cm. Please I am kind of new in the field.

April 6, 2014, 15:26		#6
cfdivan Member Join Date: Jun 2011 Posts: 51 Rep Power: 14	Hi aalisha, There are some empirical formulas for the power coefficient of lift based machines: where and lambda as TSR. You may be able to find values lower than 0.6 (Betz limit, I guess) Regards,

April 7, 2014, 01:18		#7
aalisha New Member Aalisha Join Date: Jan 2014 Posts: 18 Rep Power: 12	Thank you so much for your help. ! Just for knowledge does coefficient of moment also have some relation with power coefficient.