Skin-friction Measurements in Turbulent Boundary Layers

In the context of measurements in the boundary layer, the problem of estimating the skinfriction velocity is relevant because this velocity is proportional to the drag force and therefore is related to the energy wasted by friction in vehicles such as planes, cars, ships, etc. The existing literature is scarce when presenting an overview of the methods appropriate for the estimation in the scenario: (a) flat plate flow, (b) air incompressible regime, (c) outdoor conditions, (d) turbulent flow. As a response to such shortcomings, this manuscript presents an overview of the methods: (1) hot-wire anemometry, (2) hotfilm anemometry and (3) particle image velocimetry (PIV), in the aforementioned scenario. This manuscript reviews the diverse components that these methods require and contrasts the skin-friction velocity measurements stemming from them. Our results show a consistent estimation of the skin-friction velocity with the three methods. Future work is required in assessing the influence of wall proximity on hot-wire measurements and the influence of different Reynolds regimes on the skin-friction velocity estimations. Future work is required in the aspects of comparing the direct measurement of the skinfriction velocity with the hot-wire probe very close to the wall and the assessment of the accuracy of the techniques at different Reynolds numbers. Keyword-Skin-friction, Boundary Layer, Hot-wire, Hot-fil, Turbulent Flow GLOSSARY Free-stream velocity m/s Boundary layer thickness m Kinematic viscosity m/s l Viscous length scale non-dimensional + Viscous scaled parameters non-dimensional Friction velocity m/s Friction coefficient non-dimensional Stream-wise coordinate m Span-wise coordinate m Wall-normal coordinate m Streamwise component ( ) of the velocity m/s Wall-normal component ( ) of the velocity m/s Matrix with average statistics of the stream-wise component m/s Matrix with the average statistics of the wall-normal component m/s Average statistics of the stream-wise component m/s Average statistics of the wall-normal component m/s Sampling time s Δ Sampling frequency Hz Frictional Reynolds number non-dimensional ISSN (Print) : 2319-8613 ISSN (Online) : 0975-4024 Cristian Rendon-Cardona et al. / International Journal of Engineering and Technology (IJET) DOI: 10.21817/ijet/2020/v12i1/201201002 Vol 12 No 1 Jan-Feb 2020 1 Pre-calibration curve for hot-wire Post-calibration curve for hot-wire Measurement curve for hot-wire PIV Particle Image Velocimetry FOV Field of View Number of points in the stream-wise direction Number of points in the wall-normal direction Number of snapshots CTA Constant Temperature Anemometer MUCTA Melbourne University Constant Temperature Anemometer HRNBLWT High Reynolds Number Boundary Layer Wind Tunnel

Turbulence is a chaotic and unpredictable phenomenon which presents challenges when it's necessary to make measurements. In this work, we assess skin-friction measurements inside the boundary layer in: (a) flat plate flow, (b) air incompressible regime, (c) outdoor conditions, (d) turbulent flow. The skin-friction velocity is a form to express the shear stress in velocity units, directly relating velocities in the flow with the shear stress and, therefore, drag. Measuring the skin-friction is crucial in many aspects, ranging from the detection of the influence of roughness in the drag of a ship and the evaluation of active flow control techniques that intend to reduce drag.
The measurement of the skin-friction is executed in two ways. Indirectly calculation from measurements of the boundary layer velocity profile and direct measurements in the wall or very close to the wall. This manuscript presents an overview of methods (a) hot-wire anemometry, (b) hot-film anemometry and (c) Particle Image Velocimetry (PIV). Measurements are conducted within the boundary layer, where viscosity has influence in the flow and skinfriction velocity can be directly measured or estimated from the velocity profile.
The wall-normal position and the stream-wise velocity , are scaled by the skin-friction velocity as follows: By scaling the stream-wise velocity and the wall-normal position by the skin-friction velocity, any nonperturbed boundary layer will collapse into the same profile. Fig. 1 illustrates the profile and Eq. (1) the relation between the profile and the skin-friction. Other important quantity to introduce is the friction Reynolds number, which is a Reynolds number expressed in terms of the friction velocity , the boundary layer thickness and the viscosity . The describes the type of flow occurring in the boundary layer.

=
(2) II. LITERATURE REVIEW The measurement of the skin-friction velocity can be carried on in two ways, (1) directly measuring the skinfriction with floating elements or flush-mounted constant temperature anemometer techniques, and (2) indirectly computing the skin-friction from boundary layer velocity measurements.

A. Direct Methods
Ref. [1] utilizes flush-mounted hot-wire anemometers to directly measure the skin-friction velocity in laminar-turbulent transition flow (low Reynolds numbers). The wire was capable of measuring the fluctuations in the skin-friction with high quality signal but presents a higher application effort.
Ref. [2] presents an alternative for the floating element technique with a custom build force transducer and data acquisition system. The authors directly measure the skin-friction friction coefficient ( ) trying to reduce the signal-noise ratio.
Ref. [3] implements active flow control to reduce skin-friction velocity over a flat plate. The authors perturb the boundary with jets injecting air in cross flow with the boundary layer. The skin-friction measurement is executed with flush-mounted hot-film anemometers since it is not possible to be estimated from the perturbed boundary layer profile.

B. Indirect Methods
Ref. [4] evaluates the viability of different techniques of measuring flow velocity for application on pedestrian level wind conditions. Their work focuses on techniques for measuring flow velocity the accuracy and cost of the techniques.
Ref. [5] compares different indirect methods to estimate the skin-friction velocity. the author introduces a methodology to estimate the skin-friction from velocity measurements.
Ref. [6] Evaluates a technique for high spatial range PIV measurements in the boundary layer and compares the results with previous hot-wire data. The high magnification cameras allow to measure close to the wall and directly compute the skin-friction velocity.
Ref. [7] assesses the accuracy of hot-wire anemometry. Conducting measurements very close to the wall inside the viscous sublayer. This approach also works for perturbed boundary layers but presents difficulties to measure near the wall at high Reynolds numbers.

Approach
Refs. Advantages Disadvantages Directly measurement of the skin-friction velocity.
(2) Accuracy is affected at very low or very high Indirect calculations of the skin-friction.
(1) The boundary layer cannot be perturbed.

C. Conclusions of the Literature Review
Indirect methods for measuring the skin-friction are advantageous in their capability of measuring at different Reynolds numbers but depend on the non-perturbed boundary layer.
Direct methods are viable to measure in perturbed boundary layer but lose accuracy at very high or very low Reynolds numbers.
This manuscript presents an overview of two indirect techniques and one direct method in the response of the lack of literature contrasting different methods the equipment used in the experiments and the measurement of the skin-friction velocity. The Clauser chart method ( [12]) is used to estimate the skin friction from the indirect measurements.
III. METHODOLOGY All the experiments were conducted in the High Reynolds Number Turbulent Boundary Layer Wind Tunnel (HRNBLWT) of Melbourne University, 21 m from the test section start. Fig. 2 presents a scheme of the facility.
Each measurement is carried on at a different free-stream velocity (i.e. different skin-friction Reynolds number ). Table III exhibits the chosen and the approximated for each measurement technique.   Boundary layers present an internal structure which depends on the wall-normal position . In the inner layer, viscosity has a significant effect on the flow over inertial forces. Meanwhile, in the outer layer, viscosity loses its influence, and the flow becomes inviscid. Fig. 3 represents the subdivisions of the boundary layer their governing equations. The measurements were conducted in the inner region of the boundary layer (viscous sublayer and logarithmic region). The logarithmic region is the overlapping zone between the inner and the outer region. In the inner region, the viscosity influences the flow and skin-friction can be directly measured with flush-mounted hot-film or estimated with the Clauser chart method. Eq. (3) shows the relation between the stream-wise velocity and the wall-normal position ( [13]).
Where = 0.384 is the Von Karman constant and = 4.17 is considered as a universal constant.

A. Clauser Chart Method for the Estimation of the Skin-friction Velocity
The Clauser method [12] is useful for indirect estimation of the skin-friction velocity using the velocity profile data of the boundary layer. The method takes advantage of the relation between the stream-wise velocity and the wall-normal position in the logarithmic region of the boundary layer (Eq. (3)). Eq. (4) shows the definition of the skin-friction velocity as a form to re-write the wall-shear stress in velocity units.
Using the definition of the friction coefficient ( [14]) shown in Eq. (5), and replacing it in Eq. (3), the skinfriction velocity can be expressed in terms of and (Eq. (6)).
According to [15], by replacing (6) in (3): The left-hand side of Eq. (7) is the measured velocity profile of the boundary layer , normalized w.r.t. the free-stream velocity. For the right-hand side, all the variables are known except for the friction coefficient. The process consists of finding the value for , which satisfies Eq. (7). Fig. 4 presents a diagram of the method.   Fig. 5, An array of eight cameras (2x4) is employed. At an instant of time, the cameras take a photo, the eight images are collated into a single instantaneous snapshot Fig, 9 presents how the FOV is conformed. The snapshots are processed in an in-house (U. Melbourne) PIV package which returns a set of instantaneous vector fields of the velocity. Field discontinuities exhibited in Fig.10 appear due to the overlapping of the cameras photos and proximity to the wall. 2) Post-processing package: Because of the aim of this manuscript, the PIV post-processing package will be treated as a black box. This section presents a general notion of the inputs and outputs of the post-processing.

INPUT:
• Snapshots taken by the cameras.
• Associated coordinate system for all snapshots.

OUTPUT:
• : ( × ) Matrix with x coordinates of the velocity field.
• : ( × ) Matrix with z coordinates of the velocity field. To obtain the velocity profile of the boundary layer, it is necessary to compute two averages: (1) a temporal mean for and over the number of frames ( ).
(2) A spatial mean over coordinate in the resulting matrices of (1). Eqs. (8) and (9) illustrate the calculation of the mean vector field and the mean velocity profile, respectively.

C. Hot-film Anemometry
Hot-film and hot-wire anemometry work based on the same principle. For both techniques, the wire and the film are resistances of a circuit controlled by a Constant Temperature Anemometer (CTA) or a Constant Current Anemometer (CCA). The CTA variates the voltage, so the hot-wire or the hot-film do not change their temperature when they interact with the flow. A basic polynomial fit can describe the velocity as a function of the voltage. Section III-C-1) describes the calibration to compute the polynomial function.
For the hot-film anemometry measurement, an array of nine flush-mounted Dantec skin-friction sensors (model 55R47) are placed 21 meters downstream from the test section start. Fig. 6 shows the details of the experiment set-up and Table VI presents the variables and conditions for the experiment. Table IV presents the dimensions and material of the hot-film.  The method consists of adding tracing particles into the flow. A selected area is illuminated with a laser sheet, and one or several cameras take images of the area. The images are post-processed in a PIV package generating the displacement vector by auto-and cross-correlation methods.
1) Calibration: The hot-films are calibrated against the free-stream velocity measured with a Pitot tube at = 0.525 m (outside the boundary layer). The kinematic viscosity is calculated from atmospheric conditions measured in the experiment. A transfer function based on previous skin-friction data via floating element ( [16], [8]) transforms the measured to . Hot-film sensors are calibrated in-situ (i.e. the measurement data works as calibration data). The voltage and temperature of the sensors are recorded ten times for each . Five free-stream velocities were chosen (seeTable VII). A total of 50 points were used for the calibration of the hot-films. Using the fit function from Matlab, the polynomial surfaces depend on the temperature of the flow and voltage of the sensor = ( , ).  The error of the calibration is calculated as a relative error between the measured skin-friction and the value in the polynomial surface at the same temperature and voltage. A mean relative error is executed for the 50 points in each sensor and the results are shown in Fig. 14.
Where is the measured skin-friction velocity and is the friction velocity from the surface fitting. Each sensor can measure the skin-friction independently. The sensor with the lower relative error will be used to measure the skin-friction.

D. Hot-wire Anemometry
Two hot-wire measurements were executed at two different free stream velocities. Fig. 7 presents the experimental set-up for the measurements. Since the probe can be moved in z direction, it is possible to obtain the velocity profile within the boundary layer. The probe acquires data during a determined sampling time t and moves to the next established measurement point. After obtaining the velocity profile, the Clauser chart method is applied to determine the skin-friction velocity. Fig. 17 presents the results for the estimation.  1) Calibration: Hot-wire anemometry requires pre-and post-calibration, forces, temperature, and other perturbations during the measurement could alter the hot-wire accuracy. Pre-and post-calibration were conducted at = 0.525 m against 16 free-stream velocities from 0 to 24 m/s. A third-order polynomial was fitted for both sets of calibration data (Eq. (11)).
Using both calibration curves is possible to interpolate a "measurement curve" ( ) as a mid-point of both curves coefficients (Eq. (12)). The resultant curve and the data acquired during the measurement (voltage) are used to determine the stream-wise velocity.

A. Particle Image Velocimetry
After obtaining the velocity fields from the PIV post-processing package, 733 instantaneous snapshots were obtained. Fig 9 illustrates an approximated division of the FOV. Each camera takes a portion of the FOV. Then, the images are collated together to produce a snapshot. Fig. 10 presents one of the instantaneous snapshots for stream-wise and wall-normal velocity. The fields and resulting from appliying Eq. (8), with = 733 are shown in Fig. 11. The stream-wise velocity presents a clear and sooth increasing as it is farther from the wall. Mean wall-normal velocity has insignificant magnitude compared to . For the velocity profile, the spatial mean was calculated with Eq. (9) for the stream-wise component. Obtaining the profile in Fig. 12. 1) Clauser Chart and Skin-friction: Fig 12b presents the estimation of the skin-friction velocity by using the Clauser method. Different values of were tested. With a = 2.076× 10 , the value of the skin-friction is = 0.671 m/s. In Fig. 12b, the blue data is the spatial mean scaled by the free stream velocity. Black lines are curves for different skin friction coefficient values. After obtaining the skin friction velocity, is possible to scale the mean stream-wise velocity and the wall-normal position to obtain the boundary layer mean profile in adimensional quantities (Fig. 12c). The data complies with the logarithmic rule of the boundary layer.    The error in Fig. 14 decreases significantly after increasing the degree for the voltage. After 'poly13' fitting type, there is no considerable change in the error. Sensor presents the lower value for relative error in all the fitting surfaces, this sensor is chosen to calculate the skin-friction.
Using the polynomial fitting with 1-degree and 3-degree for and , respectively, the skin-friction velocity at = 15 m/s can be calculated with (13) Where and are the averaged temperature and voltage at = 15 m/s. The sub-index indicates the sensor used. C. Hot-wire Anemometry Fig. 15 shows the calibration curves for the hot-wire anemometry. The curves present a notable offset after a velocity of 5 m/s.   Therefore, the calibration curve is: Eq. (14) is used in the measurement data to find the mean profile of the boundary layer. Fig. 16 presents the scaled profile and compared with the PIV measurement. Due to spatial resolution and logarithmically spaced points, hot-wire anemometry can measure closer to the wall.    V. CONCLUSIONS AND FUTURE WORK Three different measurement techniques were presented, PIV, hot-wire and hot-film anemometry. The methods present consistent results in the estimation of the skin-friction velocity since the values of the calculated skin-friction velocity had low relative errors (≈ 1.29 %). The Clauser chart mainly depends on the reliable measurement of the velocity profile of the boundary layer.
PIV presents the highest computational cost due to the amount of data to be processed. Since the points in were not logarithmically spaced, there was a low resolution closer to the wall. However, the technique is accurate and could be improved by using high resolution and high magnification cameras. PIV provides a larger field of view than the constant temperature anemometers. Flush mounted hot-film anemometry cannot measure the boundary layer profile but directly measures the instantaneous skin-friction velocity and therefore, its fluctuations. Moreover, they do not depend on the velocity profile.
Future work is required in the assessment of directly measuring skin-friction very close to the wall (viscous sublayer) with hot-wire and PIV. Also, evaluate the accuracy of each technique at different Reynolds numbers.