AE 342 Aerodynamics II Laboratory Sheet 5 BOUNDARY LAYER MEASUREMENTS

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1 AE 342 Aerodynamics II Laboratory Sheet 5 BOUNDARY LAYER MEASUREMENTS 1. Introduction These set of experiments are designed to get familiar with boundary layer measurements. In this experiment: Velocity profiles will be obtained at various streamwise locations on a smooth flat plate and various integral boundary layer parameters such as δ *, θ, H (shape factor) and C f will be calculated for these profiles. Obtained velocity profiles and parameters will be compared with analytical profiles (1/7 power-law) and parameters found using this profile. 2. Theory The no-slip boundary condition imposed at the solid surface causes the fluid particles in immediate contact with the surface to have the same velocity (and temperature) as the surface. The relative velocity increases from zero at the surface to the velocity in the free stream. The thin layer next to the surface is called BOUNDARY LAYER. If we consider the flow over a flat plate where the inviscid flow velocity U e is constant over its length, it will be apparent that the boundary layer thickness will grow along it. The laminar flow in the beginning will eventually become transitional and then turbulent if the plate is sufficiently long. The transition process starts by small perturbations which amplify to produce turbulent flow. The non-dimensional parameter which characterizes this transition process is the Reynolds number, based on x distance from the leading edge of the plate. The point where transition takes place, x tr is prone to various factors, such as free stream turbulence level, surface roughness, and temperature effects. Therefore, it is not possible to give a single value of transitional Reynolds number but in general it is found in the range of 10 5 to 5x10 5. Boundary Layer Integral Parameters The boundary layer thickness δ where the velocity reaches the free stream value is a vague concept since the velocity reaches the free stream value asymptotically hence this definition depends on the accuracy with which this approach to free stream value is defined. Instead a much more convenient thickness parameter would be the so called displacement thickness δ * which is defined as the thickness by which the fluid at the edge of the boundary layer is displaced away from the boundary layer. This is related to the deficiency in mass flow rate for a viscous flow compared to an inviscid flow across the same cross section. For an incompressible flow with a constant free stream velocity, this parameter can be expressed as, δ * h u U = 0 dy (1) Another important parameter is the momentum thickness θ, which accounts for the deficiencies in momentum flux within the boundary layer. For an incompressible flow with a constant free stream velocity, this parameter can be expressed as, 1

2 θ u U h u = U 0 dy (2) This parameter can also be used in defining the skin friction coefficient C f such that; C f dθ = 2. (3) dx The ratio of the displacement thickness δ * to the momentum thickness θ is defined as the shape factor H. That s, H δ * = θ (4) Power Law For a turbulent flow, the flow is not similar and there is no simple, unique velocity profile that represents of all other velocity profiles in the boundary layer. However, the turbulent velocity distribution in the boundary layer is usually expressed in terms of a power law as; u U y = δ 1 n.. (5) and the value is usually taken as 7. If one performs the calculations; it will be observed that, δ * = x x θ = C f = with the shape factor H=1.29 and. (6). (7) (8) Re = x / ν. 3. Set-Up The figure below shows the experimental arrangement of the test section attached to the outlet of the airflow bench. A flat plate is inserted at mid height of the test section, with a sharpened edge facing the oncoming flow. One side of this plate is smooth and the other side is rough made so by covering this surface with sand paper. Hence, measurements can be realized on both surfaces by turning the plat over. In this experiment, only the smooth surface will be used. A fine pitot tube with its end flattened so that it represents a fine narrow slit opening to the flow, can be traversed through the boundary layer at a section near the downstream edge of the plate. The traversing mechanism is a micrometer attached to the pitot tube with spring loads to prevent the backlash. The pitot tube and micrometer traversing system are delicate equipments and care must be given for their proper use not to damage them. Liners can be placed on the walls of the working section so that flows with positive or negative pressure gradients (i.e. decelerating or accelerating flows) can be achieved 2

3 along the length of the plate. Without the liners, the flow over the plate is uniform without any pressure gradient ( P/ x=0). In order to obtain a velocity profile inside the boundary layer, the pitot tube is set at a distance ( 8 mm) away from the plate in the free stream and a proper wind speed is established in the tunnel. The total pressure P values measured by the pitot tube are then recorded as the micrometer is traversed towards the plate. At first the readings must be fairly constant, indicating that the measurements have been started in the free stream. If this is not the case then the experiment must be restarted at an initial setting further away from the plate. As the pitot tube readings start to decrease, the step length of the traverse should be reduced so that at least the 10 readings are obtained over the range of decreasing velocity. The reading does not fall to zero as the tube touches the wall because of its finite thickness, so that the traversing is stopped as soon as contact is indicated by the readings becoming constant as the micrometer is advanced towards the surface. Figure 1. Arrangement of Test Section 4. Experimental procedure Turbulent boundary layers on smooth surface; i. Input parameters a. Record the air temperature and the atmospheric pressure. b. Calculate air density. c. Calculate air dynamic and kinematic viscosity. d. Measure the length of the plate from the leading edge to the first x location of measurement. 3

4 e. The thickness of the pitot-tube tip is 2t = 0.4 mm. The displacement of the centerline from plate surface when in contact is 0.2 mm. f. Measure the stagnation pressure in air box and the static pressure at the entrance of the test section. g. Using these readings calculate the freestream velocity. ii. Recordings a. Record the pitot-tube readings and the distance y from micrometer readings. b. Traverse the pitot-tube towards the plate in the following manner: 1 st x-location: Between 11-9 mm in steps of 0.5 mm, 9-8 mm in steps of 0.25 mm, 8-7 mm in steps of 0.1 mm. 2 nd x-location: Between mm in steps of 0.5 mm, mm in steps of 0.25 mm, mm in steps of 0.1 mm. 3 rd and 4 th x-locations: Between mm in steps of 0.5 mm, mm in steps of 0.25 mm, mm in steps of 0.1 mm. iii. Calculate the corresponding velocities, u(y) from pitot-tube pressure readings. iv. Make a table with the following format: Micrometer reading (mm) Distance from plate (mm) P pitot -P (mbar) u(y) (m/s) v. Calculate the local Reynolds number at x=l based on the freestream velocity. vi. Repeat the same measurements for the other three x locations. vii. Calculate the velocity defect, viii. Calculate u(y) 1 for all y values at each velocity profile. U e u(y) u(y) for all values at each velocity profile. ix. Make a new table with the following format: Distance from plate (mm) P pitot -P (mbar) u(y) (m/s) u(y) 1 U e u(y) u(y) x. Plot y (mm) vs. u(y)/u e. xi. Plot on the same graph the power-law variation for turbulent boundary layers: 1/ 7 u y =. δ 4

5 xii. Calculate displacement thickness, momentum thickness, shape factor and skin friction coefficient for the measured profiles and compare these with those calculated from equations 6, 7 and 8. xiii. Calculate dθ/dx from the data found above. Check whether the boundary layer parameters found satisfy integral boundary layer equation. xiv. Compare these with the theoretical results. Comment. xv. Show all your results for the displacement thickness, momentum thickness, shape factor, skin friction coefficient and dθ/dx in tabular form. xvi. Comment on the results. 5