Lecture #17 Boundary Layer Measurements Boundary layer Thickness * Displacement Thickness Momentum Thickness.

Lecture #17Boundary LayerMeasurements

Boundary layer Thickness* Displacement ThicknessMomentum Thickness

Objectives of this Lab

• To obtain a better understanding of the characteristics of a boundary layer over an airfoil.

• To gain an understanding of the value of using a constant temperature hot wire anemometry (CTA) to acquire boundary layer measurements.

• Analyze both a laminar and turbulent boundary layer.

• Compare data with boundary layer data for a flat plate.

Instantaneous and Averaged Boundary Layer Profiles

Recall NSF Film

Boundary Layer Thickness

Boundary layer Thickness

Boundary layer thickness is generally defined as the height above the surface where the velocity reaches 99% of the freestream velocity.

Displacement ThicknessLaminar B.L.

Momentum Thickness

The rate of mass flow across an element of the boundary layer is ( u dy) and the mass has a momentum ( u2 dy ) The same mass outside the boundary layer has the momentum ( u ue dy)

is a measure of the reduction in momentum transport in the Boundary Layer

Empirical Equations of Laminar Boundary Layer Parameters

• Boundary Layer Thickness

• Momentum Thickness

• Displacement Thickness

• Skin Friction Coefficient

Empirical Equations of Turbulent Boundary Layer Parameters

• Boundary Layer Thickness

• Momentum Thickness

• Displacement Thickness

• Skin Friction Coefficient

Skin Friction Coefficient

Mean and Fluctuating Streamwise Velocity Components

• Velocity in streamwise direction

• Instantaneous, mean and RMS velocities

From Bertin and Smith Reference 1

Hot Wire Calibration

• Determine relationship between Hot Wire Output Voltage, E and the Actual Mean Flow Velocity

• King’s Law

Hot Wire Anemometer

Thermal Anemometry

• Frequency Response: > 200 Kilohertz• Size: 5mm in diameter by 2mm long• Velocity range• Component Resolution: Hot wires can be used to resolve

one , two and three components of flow field velocity.• Accuracy: Hot wires are very repeatable. Accuracy is

really a function of how closely the calibration conditions are reproduced. Velocities can be measured to within < 2% of the actual velocity.

• Resolution: One part in 10,000 can be accomplished with a hot wire system.

Influence of Adverse Pressure Gradient

Adverse Pressure Gradient dp/dx>0 can cause flow separation

Turbulent Boundary Layer Measurements over a Flat Plate

From White Reference 2

References

• 1. White, F. M., Viscous Fluid Flow, McGraw-Hill, New York, 1991.

• 2. Bertin , J. J., and Smith, M. L., Aerodynamics for Engineers, Prentice Hall, Englewood Cliffs, New Jersey, 1989

• Schlichting, H., Boundary Layer Theory, 7th edition, McGraw-Hill, New York, 1979.