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Accuracy of the velocity field in a low speed wind tunnel?

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Old   April 24, 2016, 14:01
Red face Accuracy of the velocity field in a low speed wind tunnel?
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hob
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Hi all,

Apologies it is not a direct CFD question but rather an experimental measurement one. As far as I'm aware the velocity field around the object is obtained via the measurement of the static pressure obtained via flush surface static tappings.

From Bernoulli's principle we have:

\frac{1}{2}\rho v^{2} + P + \rho gz = constant,

i.e (assuming a negligible change in height) the dynamic pressure and static pressure are constant. Dynamic pressure is therefore measurable at each static tapping location provided the total pressure is measured (usually instead of a pitot static tube (due to blockage and wake effects) the ratio between two upstream static rings one before and after the contraction ratio gives a k-factor related to the total pressure, which varies (the k factor) for each tunnel).

This gives the following relationship:

C_{P} = 1 - \left(\frac{V}{V_{\infty}}\right)^{2},

where V_{\infty} is the freestream velocity and V is the velocity at the measured static port.


My question is, given that the approximations in using Bernoulli's principle for this relationship is that the flow is steady, irrotational and invicid; does this affect the accuracy of the implied velocity field?

The actual static tapings are within the viscous boundary layer and it is very unlikely for complicated shapes (such as an F1 car) that the flow is irrotational, the flow can be made 'steady' via sufficient sampling but again is it a valid assumption?

The drag force (C_{D}) and downforce measurements I can see as being accurate (without the assumptions above) as they are a physical force that is measured directly.

Is this one of the motivations behing using LDA/LDV in a wind tunnel and if so are there any papers comparing the LDA/LDV measured velocity field to the Bernoulli implied field?


Thanks for any input
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Old   April 24, 2016, 14:35
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Quote:
Originally Posted by hob View Post
Hi all,

Apologies it is not a direct CFD question but rather an experimental measurement one. As far as I'm aware the velocity field around the object is obtained via the measurement of the static pressure obtained via flush surface static tappings.

From Bernoulli's principle we have:

\frac{1}{2}\rho v^{2} + P + \rho gz = constant,

i.e (assuming a negligible change in height) the dynamic pressure and static pressure are constant. Dynamic pressure is therefore measurable at each static tapping location provided the total pressure is measured (usually instead of a pitot static tube (due to blockage and wake effects) the ratio between two upstream static rings one before and after the contraction ratio gives a k-factor related to the total pressure, which varies (the k factor) for each tunnel).

This gives the following relationship:

C_{P} = 1 - \left(\frac{V}{V_{\infty}}\right)^{2},

where V_{\infty} is the freestream velocity and V is the velocity at the measured static port.


My question is, given that the approximations in using Bernoulli's principle for this relationship is that the flow is steady, irrotational and invicid; does this affect the accuracy of the implied velocity field?

The actual static tapings are within the viscous boundary layer and it is very unlikely for complicated shapes (such as an F1 car) that the flow is irrotational, the flow can be made 'steady' via sufficient sampling but again is it a valid assumption?

The drag force (C_{D}) and downforce measurements I can see as being accurate (without the assumptions above) as they are a physical force that is measured directly.

Is this one of the motivations behing using LDA/LDV in a wind tunnel and if so are there any papers comparing the LDA/LDV measured velocity field to the Bernoulli implied field?


Thanks for any input

Bernoulli has also the counterpart in the unsteady formulation, however the flow is always supposed to be without any dissipative effect.
In practical measurement, the double Pitot tube measures directly the pressure difference but the velocity is not computed from the original Bernoulli integral but it is corrected suitably according to a previous calibration.

LDA/LDV measure directly the velocity and has many advantage in the accuracy for complex flows
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