Experiments in Fluids

, Volume 51, Issue 1, pp 137–147

A film-based wall shear stress sensor for wall-bounded turbulent flows

Authors

    • Laboratory for Turbulence Research in Aerospace and Combustion, Department of Mechanical and Aerospace EngineeringMonash University
  • Julio Soria
    • Laboratory for Turbulence Research in Aerospace and Combustion, Department of Mechanical and Aerospace EngineeringMonash University
Research Article

DOI: 10.1007/s00348-010-1035-5

Cite this article as:
Amili, O. & Soria, J. Exp Fluids (2011) 51: 137. doi:10.1007/s00348-010-1035-5

Abstract

In wall-bounded turbulent flows, determination of wall shear stress is an important task. The main objective of the present work is to develop a sensor which is capable of measuring surface shear stress over an extended region applicable to wall-bounded turbulent flows. This sensor, as a direct method for measuring wall shear stress, consists of mounting a thin flexible film on the solid surface. The sensor is made of a homogeneous, isotropic, and incompressible material. The geometry and mechanical properties of the film are measured, and particles with the nominal size of 11 μm in diameter are embedded on the film’s surface to act as markers. An optical technique is used to measure the film deformation caused by the flow. The film has typically deflection of less than 2% of the material thickness under maximum loading. The sensor sensitivity can be adjusted by changing the thickness of the layer or the shear modulus of the film’s material. The paper reports the sensor fabrication, static and dynamic calibration procedure, and its application to a fully developed turbulent channel flow at Reynolds numbers in the range of 90,000–130,000 based on the bulk velocity and channel full height. The results are compared to alternative wall shear stress measurement methods.

1 Introduction

Knowledge of two-dimensional wall shear stress is crucial for understanding of all wall-bounded flows and also for many technical applications. The time-averaged wall shear stress can be used to determine averaged properties like skin friction coefficient, and the instantaneous surface stress can be used for active flow control purposes. The mean and fluctuating wall shear stresses are needed to study different phenomena such as flow separation, cavitation, the mechanics governing heat transfer in wall-bounded flows or mass transfer in the vicinity of permeable walls. In turbulence research, to understand the dynamics of the near wall momentum transfer, measurements of dynamic wall shear stress distribution with high spatial resolution is needed. In addition, the field of view should be extensive enough to detect the largest turbulent structures. It is also important that measurements can detect a wide range of scales of the shear stress fluctuations. Furthermore, it is desired that the shear stress-measuring techniques possess an adequate dynamic bandwidth to detect all frequency contents usually in the range of a few kHz depending on the fluid and flow properties. Moreover, measurements should be performed in a non-intrusive way that does not affect the flow field itself. As a result, designing and developing a shear stress sensor that fulfills these characteristics is a critical and challenging task.

In the past decades, owing to the high demand on the ability to measure the magnitude, direction, and distribution of wall shear stress, a large number of studies have been performed. The shear stress measurement techniques are usually divided into direct and indirect methods (Naughton and Sheplak 2002; Haritonidis 1989; Fernholz et al. 1996). The large group of indirect shear stress-measuring techniques includes the obstacle-in-flow methods, velocity profile measurement, and application of heat or mass transfer analogies. A recent thermal sensor in wall shear stress measurement is laser-induced thermal tuft as a relatively non-intrusive technique. It is based on the downstream convection of the thermal energy from a heated spot. A laser is used as the heat source, and a temperature-sensitive coating is implemented to detect the temperature pattern. The orientation and shape of the temperature profile are correlated to the direction and velocity of the flow respectively (Gregory and Peterson 2005). This flow visualization technique, which was first proposed by Baughn et al. (1995), is able to show flow separation regions and laminar–turbulent transition. However, a new application in a laminar boundary layer demonstrates the correlation between the tuft length and the wall shear stress (Gregory et al. 2008). To the best of our knowledge, no shear stress measurement using this technique has been performed in turbulent flows. The technique possesses a better sensitivity at low wall shear stresses.

On the other hand, the small group of direct skin friction-measuring techniques currently available is mostly based on a floating element that responds to the force applied by the fluid on the element. Direct measuring methods are preferable as they directly measure the applied force by the fluid with no assumption of the flow field. However, they are accompanied with different problems mainly associated with measuring very small forces, existence of pressure gradients, misalignment of floating element, a necessary gap around the floating element, temperature change, heat transfer, boundary layer injection or suction, leaks, gravity or acceleration, and transient normal forces (Winter 1977).

Furthermore, insufficient frequency response arising from their typically large size makes them inappropriate to measure shear stress fluctuations. Difficulties in installing owing to the delicate nature of the device is another disadvantage (Haritonidis 1989). Micro-electro-mechanical systems (MEMS) technology has removed many of the limitations existing in conventional mechanical fabrications such as reducing errors associated with thermal expansion, pressure gradient, and sensor misalignment (Schmidt et al. 1988; Löfdahl and Gad-el Hak 1999; Sheplak et al. 2004). However, the nature of the sensors is not suitable for unclean environments, and they also need further development to become standard measuring tools (Naughton and Sheplak 2002).

In addition to floating element sensors, the thin-oil-film and liquid-crystal-coating are other skin friction-measuring techniques that are quasi-direct means of shear stress measurement. Thin-oil-film techniques that have been widely used for the last two decades are based on the behavior of the oil film under shear loading (Naughton and Brown 1999). It is claimed that the oil thinning rate responds to changes in shear stress with a bandwidth in the 10 kHz range (Murphy and Westphal 1986). However, the technique has been used for mean wall shear stress measurements. The major uncertainty arising from the difficulty of precisely measuring the oil viscosity was reported within 4% by Fernholz et al. (1996) and was evaluated less than 2.4% in the range of investigated shear stress by Zanoun et al. (2003). In addition to oil-film methods, the liquid-crystal coating is a tool that is capable of measuring the two-dimensional wall shear stress distribution with high spatial resolution. The temporal resolution is in the range of a few kHz. Although it was introduced more than three decades ago, the following problems have made the technique unsuitable for many turbulent flow applications: difficulties associated with the liquid coating, optical access, complicated calibration, crystal roughness, and more importantly high measurement uncertainty (Naughton and Sheplak 2002). Measurement uncertainties up to 6% in the shear stress magnitude was reported (Fujisawa et al. 2003).

In recent years, by means of application a flexible material, a novel type of sensors has been proposed to measure mean and fluctuating wall shear stress distribution. Micro-pillar shear stress sensor (MPS3), able to measure dynamic wall shear stress in turbulent flows, is based on the flexible micro-pillars immersing in the viscous sublayer. The feasibility of using elastic micro-pillars as a wall shear stress-measuring tool with known frequency response has been first studied by Brücker et al. (2005, 2007). Depending on the pillar dimensions and mechanical properties, length scales better than 50 μm, and time scales in the range of a few kHz can be resolved (Grosse and Schröder 2008a, b). The sensor length to diameter ratio is between 15 and 25, and the Young’s modulus is in the order of a few MPa. The optical detection and array of micro-pillars allow the high spatial resolution determination of two-dimensional shear stress (Grosse 2008).

The surface shear sensitive film (S3F) is another sensor which takes advantage of using a linear elastic material. This technique was first introduced by Tarasov and Orlov in the early 1990s as a direct method for measuring wall shear stress (cited in Tarasov et al. (1997)). A thin elastomer layer is mounted on the solid surface subjected to a flow field, and its resulting viscous shear stress is determined using Hooke’s law from the film deformation. The experimental setup similar to the pressure-sensitive paint (PSP) technique includes a surface- or volume-distributed transducer, a light source, and an image and data acquisition system (Fonov et al. 2006a, b; Crafton et al. 2010). However, unlike PSP which can only be used in air, this technique can be used in most fluids since it does not depend on oxygen quenching. McQuilling et al. (2008) and Crafton et al. (2008) claimed sensor fabrication with frequency response up to 1 kHz with the shear modulus ranging from 25 Pa to a few hundred kPa. In these studies, the film response estimation is based on finite element modeling of the film under unit normal and tangential applied loads. McQuilling et al. (2008) verified the technique using an oil film shear stress measurement in the range of 0.25–1.5 Pa and observed a difference of 0.25–0.33 Pa. Crafton et al. (2008) estimated the accuracy in the tangential displacement detection of 0.05 px (equivalent to 0.3 μm) corresponding to an error of 25 Pa in the shear stress measurements in the range of 50–500 Pa.

The present paper reports on further progress of an in-house developed film-based shear stress sensor at the Laboratory for Turbulence Research in Aerospace and Combustion (LTRAC) at Monash University, and its application to a turbulent channel flow. The paper is structured to give information of the sensor concept, governing equations, film application, sensor static calibration, and a precise dynamic response evaluation followed by the description of the flow facility, the wall shear stress measurements, and finally conclusions.

2 Film-based shear stress sensor

2.1 Sensor general description

The shear stress sensor technique is based on mounting a thin layer film made of a elastic material on the solid surface of the model or the test section of the flow facility. The elastic layer is created by forming the material into a flat rectangular cavity with a smooth surface made of glass as fabricated in the study by Amili et al. (2009). The film is formed from a material that satisfies the linear elastic solid characteristics within the desired range of operation. Depending on the experimental condition, the thickness of the film can be adjusted between 0.5 and 3 mm by varying the cavity depth. The geometry and mechanical properties of the flexible material are accurately measured, and dynamic response of the film to shear stress is estimated in the calibration procedure. Detailed information regarding the manufacturing steps is given in the following subsection. An optical technique is used to measure the film deformation caused by the flow field. The shear stress distribution over the film is determined by implementing the shear stress–strain relationship which is described in Sect. 2.3. The film deformation is a function of the applied load, film’s shear modulus, and thickness. The sensor geometry and mechanical properties are carefully selected so that the deformation does not exceed more than 2% of the film’s thickness under maximum predicted flow loading. In addition, the sensor sensitivity can be adjusted by changing these parameters based on the estimated shear stress range to be measured. An important advantage of the film-based technique is that depending on the employed material, it is applicable to air, water, or any environment where the film is not chemically or physically modified by the working fluid.

2.2 Sensor manufacture

To manufacture, two components of the RTV silicone are mixed well, and immediately after, an appropriate diluent is added to the mixture to reach the desired viscosity. Based on the experimental condition, diluent up to 100% of the mixture volume can be added. This process is manually performed at room temperature and pressure. Final homogeneous mixture is poured into the cavity to be cured. Then, 11 μm Potters spherical particles acting as markers are gently applied to the film’s surface shortly after filling the cavity. For this purpose, an in-house device was used to provide a uniform seeded air stream over the film. The curing time of the film is slightly dependent on the environment temperature, but more on the fraction of used diluent. It can take up to 48 h after pouring the material into the cavity.

The amount of used particles as markers is chosen to achieve approximately 10 particles per interrogation window. Based on the selected imaging resolution and window size, given in Sect. 4, the volume fraction of the particles is less than 0.04% for the thinnest film (h = 1 mm). This fraction has been estimated based on the mass of the film and the mass of particles used on the film. The resolution of mass measurement is 0.001 g. According to the manufacturers, the density of particles and silicone components/diluent is 1.1 g/cm3 and 1.08 g/cm3 respectively. In addition, this fraction has been estimated by counting the number of particles appeared in an image of the sensor using an edge detection algorithm. For the thicker films, this fraction is smaller since the same amount of particles is used.

In this work, the film was formed into a cavity with dimensions of 100 × 70 mm2 and depth of 1 mm made in a perspex plate. The cavity which is machined into a flat plate was designed to fit into the floor of the wind tunnel test section. The bottom surface of the cavity is made of glass, and the cured material is firmly attached to the bottom and side surfaces of the cavity when cured. The no-slip boundary condition has been verified by performing the following experiment; a sensor with particles attached to the bottom surface of the film was used for this purpose; using the static calibration stage shown in the Fig. 2a, the film has been exposed to a uniform shear force even larger than that of used in the calibration procedure. No displacement over 0.01 pixel has been observed which confirms the non-slipping at the bottom surface within the accuracy of the cross-correlation algorithm.

The cavity dimensions as mentioned above were chosen to be ultimately used in conjunction with the largest currently available imaging sensor at LTRAC. However, to avoid edge effects, there is a need for considering appropriate margins between the cavity edges and the imaging area sides. In case of using this CCD sensor and an imaging resolution as used in this work, the cavity width and length will be more than four times the corresponding dimensions of the imaging area. In general, it is preferred to fabricate sensors with dimensions greater than the field of view although making sensors with smaller area is simpler and less material-consuming.

2.3 Sensor governing equations

The governing equations, which are based on linear continuum mechanics (Lai et al. 1993), to determine the shear stress are developed in this section. It is assumed that the film is a linear elastic solid which satisfies the following conditions: the deformations are very small; the relationship between applied loads and deformations is linear; upon removal of applied loading, deformations are completely removed; the loading rate has no effect on deformations. In addition, the isotropic, homogeneous, and incompressible assumption for the material has been made. A schematic of a shear stress film in a cavity of a rigid surface is shown in Fig. 1. By considering the displacement vector and the displacement gradient of a typical point P under loading and its neighboring point Q, changes in lengths undergoing small deformations, known as the strain tensor, can be calculated. The normal strain Enn along an arbitrary unit vector n, and shear strain 2Enm between arbitrary n and m unit vectors are given as the following:
$$ E_{nn}={\bf n}.{\bf En} ,\quad\quad 2E_{nm}=2{\bf n}.{\bf Em} $$
(1)
https://static-content.springer.com/image/art%3A10.1007%2Fs00348-010-1035-5/MediaObjects/348_2010_1035_Fig1_HTML.gif
Fig. 1

The schematic of a film-based shear stress sensor under loading

Assuming an isotropic material in which the film mechanical properties are the same in any orthogonal basis, the elasticity tensor has only two independent components and the constitutive relationship between the stress tensor T and the strain tensor E is given by:
$$ {\bf T}=\lambda e {\bf I}+2\,\mu {\bf E} $$
(2)
where I is the unit matrix, e is dilatation (first invariant of the strain tensor, Ekk), and the dimensionless constants λ and μ are known as the Lame’s coefficients which are determined by the film’s mechanical properties as:
$$ \lambda=\frac{\nu E_y}{(1+\nu)(1-2\nu)},\quad\quad \mu=G=\frac{E_y} {2(1+\nu)} $$
(3)

In the Eq. 3, Ey, G, and ν are the Young’s modulus, Shear modulus, and Poisson’s ratio of the film respectively. The shear components of the stress tensor are stated as \(T_{ij}=2GE_{ij}.\) This relation clearly highlights the point that an arbitrary shear stress component at a point is just a function of its corresponding local strain component. In other words, a normal strain does not create a shear stress or a shear strain does not generate a normal stress. To find the stress components on the film’s surface, it is sufficient to calculate the stress vector which is the product of the stress tensor and the normal unit vector to the surface N, t = TN. The normal component of the stress vector \((\hbox{p}=\mid t_n\mid={\bf t.N})\) represents the local wall pressure, and the tangential component \((\hbox{wss}=\mid t_s \mid = \sqrt{{\mid t \mid}^2-{\mid t_n \mid}^2})\) represents the local wall shear stress. Hence, the wall shear stress distribution is determined by measuring the film deformation while loaded with respect to its initial unloaded condition. Under assumption of a homogeneous material, the shear modulus is unique at all points of the film. For normal stress calculation, Poisson’s ratio based on the assumption of negligible compressibility can be used.

In this study, we are only concerned with measuring the tangential shear stress and not the surface pressure, hence only the in-plane strain deformation of the film is required. The 2D in-plane film deformation is measured by means of a 2C-2D cross-correlation PIV algorithm (Soria 1998). Although in general it is possible to measure the film three-dimensional deformation to include wall pressure, wall shear stress can be derived independently from the normal strain measurement as mentioned above. At this point, it is worth noting that the measurement of the 3D surface deformation of the flexible film can be obtained by a straight forward performance of either digital holographic recording and reconstruction followed by the 3C-3D cross-correlation analysis (Palero et al. 2007; Soria and Atkinson 2008; Soria et al. 2008; Amili and Soria 2008) or stereo-PIV (SPIV) analysis to determine 3C-2D displacements (Parker et al. 2005).

2.4 Sensor static calibration

The static calibration of the sensor involves placing a known mass on the film’s surface and measuring the film deformation under different loading conditions. The calibration stage for this procedure is equipped with a micrometer in a way that the whole setup including the CCD camera can be set at a number of accurately measured angles. A 55-mm Nikon Micro-Nikkor f/2.8 lens fitted to a 12-bit 1,280 × 1,024 px2 PCO Pixelfly camera is used to record the displacement of the tracer particles on the film’s top surface. The tangential component of the weight results in a uniform shear force across the elastic film. The set angle is measured by means of a digital angle-meter with the resolution of 0.1°. The mass, which is made of glass, has a cross-section area larger than 10 times the field of view to ensure that the loading is constant across the imaging area. The mass of the load is measured with the resolution of 0.001 g. The loading area is optically determined as well as measured using a micrometer.

A schematic of the static calibration setup is shown in Fig. 2a, and an example of the measurement of the shear modulus curve for a film-based sensor is illustrated in Fig. 3. All associated errors in the calibration step including specifying the loading angle, mass of the load, load contact area, and the cross-correlation resolvable displacement have been considered, and the overall uncertainty of measuring shear modulus based on the 95% level of confidence is estimated to be better than 2% of the measured modulus for G < 3,000 Pa. Figure 3 shows excellent linear behavior with a negligible hysteresis effect for one of the films developed at our laboratory. The non-zero intercept, which pre-loading, hysteresis, or any other bias error in the measurement system may contribute to, falls within the overall measurement uncertainty.
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Fig. 2

The schematic setup for the sensor static calibration (a) and dynamic calibration (b)

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Fig. 3

An example of the shear stress-strain curve in a static calibration for a film-based shear stress sensor with the thickness of 1 mm. The measurement accuracy is estimated to be better than 0.02 Pa for the applied shear stress and 1 × 10−4 Rad for the shear strain

The shear modulus is determined from the linear least squares fit to the measured shear stress–strain relationship. The measurements of the shear modulus in three arbitrary directions yield similar values within the measurement uncertainty confirming the isotropic assumption. In a similar way, performance of the static calibration at different arbitrary locations of the film proves that the homogeneous assumption is true. To date, at LTRAC, sensors with the shear modulus ranging from 50 Pa to 3,000 Pa and the thickness between 1 mm and 5 mm have been successfully developed. These sensors possess similar static behavior to the sensor shown in Fig. 3.

Owing to the fact that the sensor is planned to be applied to turbulent shear flows, it is important to conduct the calibration in the range of expected wall shear stress values. For the current study, based on the investigated Reynolds numbers, the expected mean wall shear stress is in the order of 1 Pa. In addition, from the probability density function of the fluctuating wall shear stress in turbulent flows reported in the literature (such as Colella and Keith (2003); Grosse (2008)), fluctuations reaching up to twice the mean value can be expected. In this work, the sensor calibrations were carried out by applying the loading up to 4 Pa. However, a typical static calibration curve as shown in Fig. 3 with a larger range of the applied loading shows in fact that the material behaves linearly over a larger range of deformations. The shear modulus obtained from static calibration can be assumed constant at low loading rates. The effect of the loading rate on the sensor behavior has been investigated via dynamic transfer functions described in the following subsection.

2.5 Sensor dynamic calibration

In order to investigate the film frequency response and its first possible eigenfrequency of tangential oscillations, a dynamic calibration apparatus and procedure have been developed. The setup consists of an electro-magnetic vibration exciter (B&K type 4809) capable of producing vibrations in the range of 10 Hz to 20 kHz driven by a B&K power amplifier. A HP 33120A function generator is used as a high fidelity signal input source, and loading is applied via a known mass placed on the top surface of the film. A force transducer, and an accelerometer both from B&K with the sensitivity of 110 mV/N and 10 mV/ms−2 respectively are used for measuring the applied force and corresponding acceleration of the mass. These signals are amplified and then recorded by means of a computer using an A/D device. In case of forcing with white noise, a low-pass filter (at 2 kHz) is used to create the desired frequency bandwidth. A sample length of 600,000 for the signals is recorded at 16 kHz rate to ensure a high enough temporal resolution.

A schematic of the dynamic calibration setup is illustrated in Fig. 2b. There is a transfer function between each component of the setup relating the corresponding variables. Finding the transfer function to indicate the relation between the input force and the output film displacement consists of decomposing the film response into its frequency contents and determining the oscillation amplitudes using Fourier analysis. The process involves dividing the sample recordings into segments and then performing FFT on each sequence. As a result, the amplitude of the film oscillation, normalized by a reference amplitude, is determined in terms of frequency. It is worth noting that the effective mass (me) applied to the film has been accurately measured by a no-film experiment first. The frequency response of the sensor is expected to be a function of the film’s shear modulus, thickness, and density.

The dynamic calibration has been conducted for sensors made of different materials and different thicknesses. Table 1 gives the properties of eight different sensors developed in our laboratory including the one used for this investigation. The bandwidth calculation is based on the frequency which the sensor gain falls to −3 dB. Figure 4 shows the transfer function for three sensors with the same thickness but different shear modulus. The transfer functions show low-pass filter behavior with the cut-off frequency greater than 160 Hz. The arrow in Fig. 4 shows the direction of the increase in shear modulus. In the dynamic calibration, the point should be highlighted that all measurements have been performed in air, and for sensor application in different flow facilities, there is a need for a calibration in the same working fluid. It is expected that sensors show more damped behavior in water because of the damping nature of the fluid.
Table 1

A summary of the characteristics of different fabricated film-based shear stress sensors

Sensor

Shear modulus (Pa)

Thickness (mm)

Bandwidth (Hz)

1

84

1

166

2

112

1

185

3

245

1

187

4

460

1.5

171

5

460

2.5

130

6

460

5

89

7

1,590

1

242

8

845

1

204

https://static-content.springer.com/image/art%3A10.1007%2Fs00348-010-1035-5/MediaObjects/348_2010_1035_Fig4_HTML.gif
Fig. 4

The dynamic transfer function for sensors 1–3 with similar thickness but different shear modulus. The arrow indicates the order of increasing in shear modulus

To investigate the effect of the sensor geometry, the transfer function of three sensors with different thicknesses made of a similar material are shown in Fig. 5. By increasing the film’s thickness, the cut-off frequency becomes shorter. In addition, for the thickest film (sensor 6), underdamped second-order behavior with a maximum gain of 1.32 is observed. A shadowgraph experiment shows the existence of the oscillatory modes on the surface of this sensor when exciting with the dynamic calibration apparatus. For an accurate measurement of the instantaneous wall shear stress, it is important that the sensor does not show a gain greater than 1 in the expected range of frequencies that may exist in the wall shear stress signal. Therefore, a careful selection of the suitable sensor with proper shear modulus and thickness should be made based on the working fluid and flow properties. For all the sensors shown here (except for sensor 6), low-pass filter behavior with the cut-off frequency up to 240 Hz is observed. In this work, sensor 1 was used for wall shear stress measurements in the wind tunnel.
https://static-content.springer.com/image/art%3A10.1007%2Fs00348-010-1035-5/MediaObjects/348_2010_1035_Fig5_HTML.gif
Fig. 5

The dynamic transfer function for sensors 4–6 with different thickness but similar shear modulus. The arrow indicates the order of increasing in thickness

The measurements by Grosse (2008) in a turbulent duct and pipe flow show that frequencies up to 250 Hz for wall shear stress fluctuations in the streamwise direction are expected. In these measurements, investigated Reynolds numbers are less than that of in this study. This indicates that the sensors developed until now in our laboratory are not able to dynamically detect all significant frequencies contained in the instantaneous wall shear stress signal. While a sensor with low-pass filter behavior has been developed and implemented, further development of a sensor with a larger bandwidth is in progress.

2.6 Aging behavior of the film

Figure 6 shows the aging effect on the shear modulus for three different films over a period of time after curing. While sensor 1 showed a strong increase in shear modulus over a week, sensor 7 showed less sensitivity to aging effect and sensor 8 possessed a nearly constant shear modulus during 2-week period. Sensor 1 has been used for the experiments in this work. In general, sensors made of a very low shear modulus material are more sensitive to aging effect. It is worth mentioning that to avoid any possible errors caused by changes in the film’s mechanical properties or thickness, calibration tests were performed before and after each wall shear stress measurement.
https://static-content.springer.com/image/art%3A10.1007%2Fs00348-010-1035-5/MediaObjects/348_2010_1035_Fig6_HTML.gif
Fig. 6

The effect of aging on the shear modulus for three different films in a period of time after curing (over a week for sensor 1, (a) and 2 weeks for sensors 7 and 8, (b))

3 Experimental setup

Wall shear stress measurements were performed in the open-circuit wind tunnel facility located in the Laboratory for Turbulence Research in Aerospace and Combustion (LTRAC) at Monash University. The flow in the facility is generated by a three-phase 5.5 kW electrical motor coupled with an in-line centrifugal blower. The flow rate is accurately controlled by adjusting the motor rotational speed by means of a motor controller. The blower is connected to a very well-designed settling chamber consisting of honeycombs and screens. This ensures that the air flow uniformly enters to the test section. The working section is 4.6 m long, 1 m wide, with the aspect ratio of 9.75:1. The large enough aspect ratio ensures that secondary flows in the channel corners do not affect the mean streamwise velocity profile and the turbulent fluctuations. The sensor is mounted on the lower wall of the test section at a position approximately 41 channel height downstream of the test section entrance. The film was formed into a cavity with dimensions of 100 × 70 mm2 and depth of 1 mm using a perspex plate with dimensions of 320 × 320 mm2. The plate was mounted flush with the tunnel wall to prevent any disturbance to the local flow field. The experiments were conducted at Reynolds numbers ranging from 90,000 to 130,000 based on the bulk flow velocity and the channel full height, \(Re_m=\overline{U}H/\nu.\) The Reynolds number based on the friction velocity is between 2,100 and 2,900, \(Re_\tau=u_{\tau}(H/2)/\nu.\) Deformation of the film-based sensor was imaged at 12.7 fps using a 12-bit 1,280 × 1,024 px2 PCO Pixelfly camera in combination with a 55-mm Nikon Micro-Nikkor lens. An array of LEDs was used as the light source that provided excellent uniform contrast and low signal to noise ratio. A lens F-stop of 2.8 was selected to reduce the depth of field.

In order to remove any possible rigid-body motion of the sensor, a second imaging system was used. These motions, which may contain large scale fluctuations, are mostly caused by the electro-motor and fan vibrations and induced to the whole wind tunnel. They may also include translation, flexure, and any other possible movement of the experimental rig. These movements were measured using a second camera via imaging a reference pattern attached to the bottom surface of the sensor plate. The imaging resolution for the second system was chosen similar to the first one. First, the particle positions and the reference pattern at no-flow condition were recorded as the initial state. Then, images of the film and the reference pattern at flow-on condition were simultaneously taken. In each experimental case, 180 images were acquired. By subtracting the rigid-body movements of the sensor from the particle displacements, net deformation of the film and consequently its strain under flow loading has been obtained.

In addition, planar 2C-2D PIV experiments along the streamwise, wall-normal direction in the same flow region were conducted to compare with direct wall shear stress measurements. A twin Nd:YAG pulsed laser at the wavelength of 532 nm with the maximum energy of 200 mJ per pulse was used for the flow illumination. A 200-mm Nikon Micro-Nikkor AF lens using the F-stop of 5.6 was fitted to a 14-bit PCO.4000 camera with the CCD size of 4,008 × 2,672 px2. An appropriate combination of cylindrical and spherical lenses inside an articulated laser arm produced a collimated light sheet with the thickness of less than 1 mm. The flow was seeded using smoke particles with the nominal diameter of 1−2 μm generated by a Safex F2010 fog machine. At each Reynolds number, 2,000 PIV image pairs were acquired at the sampling rate of 2 Hz.

4 Wall shear stress measurements

The multi-grid cross-correlation digital particle image velocimetry (MCCDPIV) algorithm developed by Soria (1996, 1998) was used to measure the instantaneous wall shear stress distribution. Multi-passing with the final interrogation window size of 32 × 32 px2 with 50% overlap at a high sub-pixel accuracy using 2D Gaussian peak-fitting function enables measurements with a high dynamic range. This leads to a vector spacing of 93 μm corresponding to 3.85–5.10 wall units using the imaging resolution of 5.82 μm/px. The field of view is 5.95 × 7.45 mm2 which is equal to 245–325 by 310–410 wall units based on the Reynolds numbers that have been investigated.

Table 2 shows the mean film deformation, wall shear stress, friction velocity, and skin friction coefficient measured at different flow conditions using sensor 1 (h = 1 mm & G = 84 Pa). Following the film deformation measurement, the local wall shear stress was retrieved using the equations given in Sect. 2.3. The mean wall shear stress calculation is based on the time-average and also the spatial-average of the stress over the film located in the entire field of view. High spatial resolution and a large number of displacement vectors (more than 820,000 vectors) provide reasonable number of samples for statistical estimates.
Table 2

The mean wall shear stress and skin friction coefficient measured by the film-based shear stress sensor (h = 1 mm & G = 84 Pa)

Rem

Reτ

\(\overline{U}\) (m/s)

d+

d/h (%)

τw (Pa)

uτ (m/s)

Cf

9.141 × 104

2,120

13.40

0.23

0.57

0.466

0.622

4.31 × 10−3

9.856 × 104

2,270

14.45

0.29

0.65

0.535

0.667

4.26 × 10−3

1.054 × 105

2,420

15.45

0.35

0.74

0.604

0.708

4.20 × 10−3

1.122 × 105

2,550

16.45

0.41

0.82

0.672

0.747

4.12 × 10−3

1.197 × 105

2,690

17.54

0.48

0.91

0.749

0.789

4.04 × 10−3

1.265 × 105

2,830

18.55

0.55

1.01

0.827

0.829

3.99 × 10−3

The mean skin friction coefficient measured at different experimental conditions is shown in Fig. 7 and compared with the experimental data for different turbulent channel flows. For Cf comparison, it is worth mentioning that several parameters may be associated with data inconsistency in the literature. For example, channel aspect ratio, flow development length, wall roughness, and determination of the mean velocity significantly contribute to the skin friction coefficient value. As a result, measurements in this work are mostly compared with the studies found in the literature which have been performed in the region of fully developed turbulent flows in channels with high aspect ratios and smooth walls. The measured skin friction compares favorably with the measurements by Zanoun et al. (2009), Christensen (2001), Monty (2005), and also the logarithmic skin friction relation by Zanoun et al. (2003, 2007). The oil film interferometry (OFI) and streamwise pressure gradient (PG) results shown in Fig. 7 have an uncertainty less than ±2.5% of the measured shear stress for \(\hbox{Re}_m<2.46\times10^5\) (Zanoun et al. 2009).
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Fig. 7

The mean skin friction coefficient, Cf measured by the film-based shear stress sensor (shear modulus = 84 Pa & thickness = 1 mm) in the channel flow with the aspect ratio of 9.75:1 compared with the experimental data extracted from the literature

At lower Reynolds numbers, the mean film deflection is approximately 1 pixel, while at the highest Reynolds number it is 2 pixel corresponding to 1% of the film thickness. The accuracy of the shear stress measurements is determined by the sub-pixel accuracy of the cross-correlation algorithm and the accuracy of the shear modulus determination which has been assessed in Sect. 2.4. The accuracy of the PIV software in evaluating film’s deformation has been experimentally assessed in a similar condition to the shear stress measurements; this evaluation shows the RMS error is less than 0.02 pixel. The uncertainty of measuring mean wall shear stress based on the 95% level of confidence is estimated to be better than 2.5% of the measured stress for \(\tau<1\,\hbox{Pa}.\) It is worth noting that the potential source of a significant bias error has already been evaluated as mentioned in Sect. 3; the relative movement of the sensor respect to the camera can cause a DC error. As a result, it is loosely dependent on the applied loading during the experiments and consequently has a greater effect on small displacements. By simultaneous measurements of the film displacement and the rigid-body motion of the sensor, this bias error has been removed.

In addition to direct wall shear stress measurements, the mean streamwise velocity profile has been used for the friction velocity estimation. The instantaneous two-component, two-dimensional (2C-2D) velocity field has been evaluated with the same correlation routine. Multi-passing with the final interrogation window size of 32 × 32 px2 with 50% overlap has been used. The dynamic range is 0–8 pixel, imaging resolution is 22.19 μm/px, and the vector spacing is 355 μm. The field of view is 78.6 × 59.3 mm2 which is equal to 3,260–4,340 by 2,460–3,280 wall units based on the investigated Reynolds numbers.

The mean velocity profiles for different investigated Reynolds numbers are shown in wall units in Fig. 8. Each profile is the average of the ensemble-averaged velocity over 217 homogeneous profiles in the streamwise direction. These measurements show a close correspondence with the logarithmic velocity profile between 100 < y+ < 500. In this region, the mean streamwise velocity profile is given by the Eq. 4. In this relation, κ is the von Kármán constant and A is an additional constant. As shown in Fig. 8, taking constants κ = 0.41 and A = 5.0 enables the collapse of the profiles and an excellent agreement with the log law is observed. The friction velocity was estimated using the Clauser method (Clauser 1956) using the mean streamwise velocity profile obtained from the PIV experiments.
$$ \frac{u}{u_\tau}=\frac{1}{\kappa}ln\left(\frac{yu_\tau}{\nu}\right)+A $$
(4)
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Fig. 8

The mean streamwise velocity profiles for the investigated Reynolds numbers

Figure 9 shows the comparison between the mean skin friction coefficient determined using the mean velocity profile measurement and the Clauser method with direct wall shear stress measurements using the film-based sensor. This clearly shows that both measurements are consistent and compare favorably.
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Fig. 9

The mean skin friction coefficient, Cf directly measured by means of the film-based shear stress sensor (G = 84 Pa & h = 1 mm), and indirectly measured using a logarithmic fit to the mean streamwise velocity profile and applying the Clauser method

5 Implementation and limitations

Film-based shear stress sensor provides a good opportunity for directly measuring wall shear stress in turbulent flows. It has the capability of detecting instantaneous wall shear stress in a two-dimensional pattern. However, there are limitations associated with this technique. The mean film displacement at the current flow facility, based on the mentioned film shear modulus and imaging resolution, is in the order of 1–2 pixel. For accurate measuring of turbulent fluctuations, it is preferred to achieve a greater dynamic range. Due to the limitations for manufacturing films with a very low shear modulus, a high magnification has been chosen, and consequently this range of displacement has been achieved to date. There are three important limitations in this regard; the first issue is related to arrive at a very low shear modulus; the second problem is associated with the stability of the mechanical properties of such films; the last limitation is related to the frequency response of the films with a very low shear modulus or thick thickness. It is worth noting that, as shown in Sect. 2.5, sensors developed until now possess a limited bandwidth. As a result, it is not possible to dynamically detect all significant frequencies contained in the wall shear stress fluctuations. Furthermore, since the intention is to arrive to a larger dynamic range, increasing the film thickness or decreasing the shear modulus may result in the sensor gain amplification. In brief, manufacturing sensors which fulfill the mentioned conditions is a very challenging task.

Further work to manufacture films with lower shear modulus with reasonably constant mechanical properties is in progress. However, to overcome the small imaging area due to implementation of a high magnification, larger image sensors in conjunction with current developed film-based sensors can be used. For experiments in current work, a sensor with the lowest feasible shear modulus (G = 84 Pa) and known aging behavior has been used.

6 Conclusions

A shear stress sensor with the working principle based on the deformation of a thin elastic film has been developed and investigated. The static and dynamic calibration of the sensor, and also its application to a fully developed turbulent channel flow to measure the mean wall shear stress have been successfully performed. The technique is applicable to air or water, and its sensitivity can be tuned for different flow conditions by using an available wide range of thickness and shear modulus. The technique allows high spatial resolution measurements of wall shear stress with an uncertainty better than 2.5% of the measured stress for \(\tau<1\,\hbox{Pa}.\)

In addition, the wall shear stress has been indirectly measured by means of a logarithmic fit to the mean streamwise velocity profile obtained from PIV experiments and application of the Clauser method. Good agreement is observed between the measured skin friction coefficients and the measurements by other techniques. The concept of the film-based shear stress sensor has the capability of measuring surface forces over an extended area of a solid surface. The advantage of this non-intrusive technique is the ability to measure dynamic shear stress distribution based on the evaluated dynamic response measured and demonstrated here. A sensor with low-pass filter behavior has been used in this work. Further development of a sensor to increase the constant-gain bandwidth is in progress.

Acknowledgments

The financial support to conduct this research by the Australian Research Council is gratefully acknowledged. In addition, O. Amili has been supported by the scholarships provided by the Monash Research Graduate School while undertaking this research.

Copyright information

© Springer-Verlag 2011