Accurate measurements of local skin friction coefficient using hot-wire anemometry

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Abstract

The practicality and accuracy of many existing methods of local skin friction measurement suffer when the boundary layer flow under consideration is non-canonical. Such shortcomings are exacerbated in three-dimensional flows, by the necessity to map local cf over a wider area in order to characterise fully the contribution to global skin friction. These problems have led the authors to seek novel experimental methods of cf measurement. The technique proposed herein utilises velocity measurements made using hot-wire anemometry combined with accurate positioning of the sensor element in respect to the test surface. In essence it is proposed that the local skin friction can be evaluated via a single velocity measurement made at a known wall-normal distance within the linear region of the viscous sublayer. This technique relies on accurate probe positioning, and two methods of achieving this are outlined. A study of the hot-wire characteristics in near-wall proximity has revealed a previously unnoticed feature corresponding to probe–wall contact. It is shown that this anomaly can be used as a positional flag to accurately locate the aerodynamic origin of the hot-wire sensor. A second technique using a laser triangulation displacement sensor is also outlined. Both positional techniques are shown to offer positioning to a sufficient level of accuracy for the proposed cf measurement technique. Single-point local cf measurement is tested experimentally, demonstrating the improved repeatability and standard error as predicted by initial error analysis. In this way it is shown that a single 90s velocity sample coupled with accurate wall positioning can define local cf to a standard error of σcf≈1.0%. Analysis of error contributions reveals that longer sampling periods can realise even greater accuracy. The proposed technique is also used to measure local cf in a three-dimensional boundary layer where micro-vortex generators have introduced large-scale spanwise distortions. This is an example of an application in a non-canonical boundary layer, and initial results show that the method is capable of providing repeatable comparative spanwise-averaged skin friction results to within approximately ±1%. The technique is immediately applicable to researchers using hot-wire anemometry in low Reynolds number flow over electrically non-conductive test surfaces.

Introduction

Wherever a fluid is flowing over a wall surface, performance considerations will invariably necessitate the characterisation of skin friction drag. Whether it is aircraft or ship design, or more fundamental laboratory-based research, it is clear that the accurate measurement of the local skin friction coefficient cf is of paramount importance to many aspects of fluid mechanics. Despite the considerable effort devoted to skin friction measurement in the past and the wide variety of techniques currently available, all seem to suffer problems related to accuracy, repeatability and practicality.

The authors’ motivation for the present body of work comes from a concurrent turbulent management and drag reduction study. Previous studies have included work on riblets, large eddy break-up devices (LEBU), spanwise oscillations, compliant coatings, electro-magnetic Lorentz force flows, micro-electro-mechanical systems (MEMS) and polymer injection to list but a few. The need for accurate cf measurement in these cases is obvious, with overall net drag reductions being defined by the often fine margins between device drag and skin friction reductions. In many cases the modifications imposed on the boundary layer by such studies introduce a three-dimensional flow and the boundary layer can no longer be considered as being in equilibrium. The departure from two-dimensional equilibrium boundary layer flow, not only increases the number of cf measurements necessary to calculate the overall net balance (to define drag reduction), but also disqualifies many of the existing techniques available for cf measurement. Inadequate cf measurements and a reluctance to consider true local cf have traditionally caused large disparities between results. For example, in reviewing work on riblets, and attempting an analysis of the available data, Walsh [1] notes that the small drag reduction produced by such devices (of the order of 6–8%) requires extreme accuracy in drag measurements. Such considerations become even more pertinent when attempting to optimise riblet geometry, where geometric changes to riblet design typically cause changes in drag that are within the scatter of skin friction measurements. Walsh [1] also expresses caution when considering skin friction measurements made using the momentum integral equation, where incorrectly assumed zero pressure gradient and zero cross flow can introduce significant errors. This point is reinforced by Anders [2], who attributes much of the disparity between different LEBU experiments to the accuracy of this notoriously difficult measurement, feeling strong enough to devote a whole section of the review paper to cf measurement. Again reference is made to a neglect of three-dimensional effects and it is shown that early efforts at momentum balance calculations tended to overestimate the skin friction reductions downstream of the manipulators. This is hardly surprising since the momentum balance equation is based implicitly on the assumption of a two-dimensional boundary layer. Takagi [3] found that LEBU devices can exaggerate any existing non-uniformity or three dimensionality in the turbulent boundary layer. Two important points are raised here. Clearly when a three-dimensional aspect is introduced to the flow, certain skin friction techniques are no longer viable. In addition to this there is the implication that a more detailed and full mapping of the true local cf will be necessary to accurately assess drag reductions in these cases (local cf will need to be mapped over a surface area, rather than being restricted to centre line measurement coupled with assumed two-dimensional behaviour). Defining local cf over a surface area will greatly increase the number of measurements required, approximately squaring the amount of data and experimental duration. In the past such considerations and the lack of an existing technique that lends itself to such a solution, have perhaps persuaded researchers to accept the two-dimensional approximation. Clearly there is a need for a viable measurement solution that can overcome this problem.

A full description of the available techniques for measuring skin friction is beyond the scope of this paper. For more information the reader is referred to [4], [5], [6]. The aim of the following analysis is to highlight the problems encountered with some of the popular techniques. It is difficult to talk in terms of absolute accuracy, since the reliability of each method is very much dependant on the local flow conditions. The accuracy of skin friction sensors reliant on pressure difference, such as Preston tubes or surface fence type devices (see [5]), will always deteriorate as the local flow velocity reduces. The diminishing difference between static and Pitot pressure (or pressure drop across an obstacle for surface fence) will call for ever more sensitive methods of pressure measurement, and ultimately accuracy will suffer. The same is also true for direct skin friction measurement with floating element devices, where the shear force measured by the device is directly proportional to velocity squared and the surface area of the element. There is always a minimum resolvable force or deflection that can be measured by the device. This leads Winter [4] to talk in terms of the compromise between the requirement to measure local properties and the necessity of having an element of sufficient size that the force acting on it can be measured accurately. If we apply this to boundary layer flows, an increase in freestream velocity will produce a resultant increase in force per unit area, but the boundary layer thickness (and hence spanwise and streamwise scaling) is inversely proportional to velocity. Hence, the possibilities of a truly local cf measurement are unlikely. It will also be shown that the previously discussed three-dimensional effects, non-zero pressure gradients and non-equilibrium conditions can introduce additional errors into cf measurement (the severity of which will depend on the individual technique employed). Finally there is the issue of exactly how the device accuracy is defined. Whilst most papers attempt to quote an accuracy, the device in question is often calibrated against other (imperfect) devices. Such issues become especially pertinent when assessing sensor performance in three-dimensional flow. Vagt and Fernholz [7] allude to this point, choosing in these cases to believe only those calibrations made against a direct force measuring device (which they consider to be relatively insensitive to three-dimensional effects).

Vagt and Fernholz [7] and Fernholz et al. [8] attempt to classify the available techniques according to whether they depend on the logarithmic law of the wall. Such techniques implicitly assume the flow to be fully developed, two dimensional and in equilibrium, hence the credibility becomes increasingly tenuous as each of these conditions is violated (from the authors’ viewpoint all of these conditions are to some extent violated once large-scale distortions are introduced into the turbulent boundary layer). The Preston tube is a widely used method of skin friction measurement, and is also log-law dependent. The most commonly used calibration relationships were proposed by Patel [9], who investigated a wide range of flow conditions and probe geometry, quoting an accuracy ranging from ±3%, up to ±6% for increasing pressure gradients. For the canonical boundary layer the accuracy of the Preston tube seems generally to be accepted as ±3% [8], although such accuracy will begin to deteriorate with the increase in three-dimensional effects. Vagt and Fernholz [7] refer to work by Pierce and Krommenhoek [10], making comparisons with their own results to show that the repeatability of the Preston tube falls to approximately ±5% for the three-dimensional boundary layer. Obviously, the final accuracy depends very much on the extent of the deviation from the two-dimensional case. Hanratty and Campbell [5] conclude that the calibration accuracy of the Preston tube is uncertain unless it is operated within the canonical boundary layer.

Skin friction can also be calculated from a wider velocity profile of the turbulent boundary layer (whether measured by Pitot tube, LDV or hot-wire anemometry). Use of the logarithmic portion of the velocity profile (Clauser-type methods, see [4]) is obviously log-law dependent, and as such will suffer the same fate as the Preston tube once non-equilibrium, three-dimensional boundary layers are considered. The momentum balance method, whilst not strictly log-law dependant, has the same tacit assumption, based as it is on the steady and two-dimensional momentum integral equation with zero pressure gradient. In considering the three-dimensional effects introduced by LEBU studies, Anders [2] estimates that the accuracy of local cf values measured in this way is no better than ±10–15%.

The surface fence, Stanton tube and pulsed hot-wire methods of cf measurement are not log-law dependant. They do, however have a scaling requirement that is based on the viscous sublayer. The sublayer fence measures the pressure difference across an obstruction of height less than the linear velocity region of the viscous sublayer. Fernholz et al. [8] state that the fence height H should not exceed the non-dimensional value H+=Huτ/ν≈5 (which appears to be the standard accepted limit for the linear region of the turbulent boundary layer; see Section 3.1). A similar scaling requirement exists for the Stanton tube and for the pulsed hot wire (where the height of the wire must not extend beyond the viscous sublayer). This scaling requirement effectively limits the range of cf such devices can measure. Hanratty and Campbell [5] point out that because of the larger pressure readings with the sublayer fence, the height of the fence can in theory be somewhat smaller than that of the Stanton tube (hence theoretically a larger cf range is possible). However, they go on to refer to work by Brown [11] and Good and Joubert [12] which indicate that the region of disturbed flow (and hence the region of measurement) is much greater than the obstacle height and hence ‘the advantage of the sublayer fence may not be as great as originally anticipated’. In addition to these problems the surface fence, wall pulsed wire and Stanton tube (unless strict design parameters are observed) all require separate calibration. This can introduce additional error sources if the calibration flow conditions vary widely from the test conditions (see [6] on pulsed wall probes). Fernholz et al. [8] quote an accuracy of ±4% for the Surface fence and wall pulsed wire. This accuracy would suffer from three-dimensional effects, since like the Preston tube, the devices are sensitive to flow alignment. Basically these three devices can be separately grouped as techniques that all require geometry, calibrations and alignment based on a prior knowledge of local flow conditions. As such any application becomes complex and flow specific, with the accuracy remaining undefined.

More recently shear stress measurements have been attempted using liquid crystal and oil-film interferometry. Careful analysis of the flow-induced behaviour of these surface preparations can reveal the underlying local skin friction distribution. Such techniques are attractive in that, like moving wall elements, it is a direct technique relying on force measurement rather than relating some other measured parameter to skin friction (via an assumed property of the boundary layer). As such these two techniques appear immune to three-dimensional effects, pressure gradients and can even cope with flow reversal. In addition, both can give good spatial resolution (local cf) and, aside from early problems of flow modifications caused by coating accumulations [4], such techniques are non-intrusive. Fernholz et al. [8], Naughton and Sheplak [13] and Naughton and Brown [14] give a good introduction to modern oil-film interferometry, where the timed rate of change of oil film thickness is related to skin friction, claiming accuracies for the method of (not less than) ±4%. A further method utilises the unique response of liquid crystals to applied shear stresses, whereby a molecular reorientation can lead to a change in the polarisation of the transmitted or reflected light. Earlier attempts at skin friction measurement with this method were qualitative, using the colour change of liquid crystal, caused by the shear-induced shift in the wavelength of reflected light [15]. Later Rada et al. [16] developed a technique that could give quantitative measurements, although experimentally the method was complicated requiring colour images from at least four different viewing angles. A technique described by Buttsworth et al. [17] utilises a different liquid crystal technique of skin friction measurement. In this case the change in intensity (rather than wavelength) of transmitted light is measured and shown to be proportional to shear stress. By comparing variance in calibration data they argue that skin friction measurements to within ±4% should be possible. This method can also be expanded to give an indication of the skin friction direction vector [18]. For both oil-film and liquid crystal techniques the magnitude of the shear stress (and hence the freestream velocity) determines accuracy. The calibration data of Buttsworth et al. [17] clearly demonstrate this. For surface shear stress measurements of less than 1Pa, the uncertainty seems to rise to ±15%. For measurements in air, a shear stress of 1Pa would require a freestream velocity an order of magnitude greater than that of a standard low-speed boundary layer investigation. Hence both may prove more useful to high-speed tunnel [16] or aeronautical flight test applications [19]. Oil-film interferometry has an added advantage of requiring no calibration. However, since the technique relies on the timed rate of change of the oil film thickness it is not well suited to continuous on-line measurements.

In concluding their reviews of existing skin friction measurement techniques, both Winter [4] and Hanratty and Campbell [5] state that for situations other than two-dimensional, fully developed flows (with zero pressure gradient), heat transfer probes will continue to have the widest applicability. Flush mounted hot-film or hot-wire sensors have been used to measure skin friction. Bruun [6] gives a good referenced introduction to such devices and the problems that arise when the thermal conductivity of the wall becomes significant. This is always the case when the fluid to be used is air. In this instance, the heat loss to the substrate due to conduction will be comparable to or greater than the convective heat loss due to local flow velocity. Hence only a small proportion of the measured signal is convective flow dependent. This causes problems with the flow sensitivity (underestimation of the root-mean-square value of shear stress, see [20]) and also calibration. The calibration displays complex sensitivity to temperature of the tunnel flow and its wall. A change in the temperature distribution of the wall will lead to drift in the calibration data. Further calibration drift can occur when the probe is relocated during the course of an experiment. Reichert and Azad [21] suggest that this phenomenon is probably due to a small change in the quality of thermal contact between the plug body (onto the surface of which the film is deposited) and the test plate, which can significantly alter the thermal conduction through the substrate. Further to this, slight misalignments or protrusion of the plug can also change the calibration (up to 30–40% according to Hanratty and Campbell [5]). Hence, Bruun [6] concludes that it is preferable to calibrate surface mounted hot-film sensors in situ, which pretty much limits their use to measurements in a single fixed location. One attempt at increasing the flow sensitivity is to employ a thermal insulation between the flush mounted sensor and the surrounding wall (see [6] for full references). Recently, miniaturised arrays of surface sensors, employing an air gap, have been used to show the time-varying shear stress occurring at the wall of a turbulent boundary layer [22]. Such advances mean that surface mounted wires and films can provide useful qualitative characterisation of skin friction fluctuations and distributions at the wall. However, calibration difficulties mean that the quantitative accuracy will remain questionable. Before proceeding, it should be re-emphasised that for all the techniques summarised above the accuracy of cf measurement is at best ±3% (with results indicating in many cases that such accuracy will reduce for either low-speed flows or flows exhibiting signs of three dimensionality and pressure gradients).

For determining the local skin friction coefficient from velocity measurements taken in a non-canonical turbulent boundary layer, the only reliable way seems to be to make use of the linear region in the viscous sublayer where u+=y+. A proviso should be added that the existence of linearity in the viscous sublayer is not assured per se (although researchers commonly assume so). Fernholz et al. [8] indicate that the surface fence, wall hot wire and wall pulsed wire can all be used in three-dimensional flows and flows with favourable pressure gradients. Since these techniques all relate velocity measurements made in the sublayer to skin friction, there is a tacit assumption in this statement that linearity is preserved. Azad and Burhanuddin [23] rely on limited experimental results to show that ‘the sublayer next to the wall exists in all flows (i.e., with different types of pressure gradient) and the velocity in this region is linear’. In the limiting cases there is a danger that such assumptions will break down. For nearly parallel, large Reynolds number flows with negligible Reynolds stress up to y+=5, it can be shown [24, p. 160] that the viscous sublayer has a linear velocity region. However, the assumption of near-parallel flows will be violated by strong adverse pressure gradients and ultimately by separating flows. For very rough surfaces, the shear stress close to the wall will be due partly to Reynolds stresses and hence in this instance the assumption of linearity will be compromised. It is safest to assume that linearity is preserved only for flows of moderate three dimensionality, pressure gradient and surface roughness. Ultimately, the existence of linearity should be ascertained experimentally prior to attempting cf measurements with any technique that assumes u+=y+ (as well as the proposed technique described in this paper, this would include surface fence, wall pulsed wire and wall hot-wire measurements).

The hot-wire sensor is the obvious candidate for obtaining the velocity measurements necessary to define the velocity gradient at the wall. We could also use LDA or Pitot tubes, but both have large measurement volumes and consequently suffer reductions in spatial resolution. Since by definition such measurements will be carried out in the near-wall region, other problems arise. Accuracy of LDA measurements can suffer due to deflection of light beams near the wall. Further to this, the influence of electronic noise can become significant for near-wall LDA measurements. At the low velocities that exist in this region, the blockage effect due to Pitot tubes will be detrimental, and measurement difficulties will arise due to the corresponding low-pressure differential (low dynamic head). Further to this Pitot tubes have a poor temporal resolution. In contrast the hot-wire sensor is excellently suited to this application. It has a small measurement volume, high frequency response (good spatial and temporal resolution), and displays insensitivity to three dimensionality near the wall (to the first-order approximation) and pressure gradients. Unlike the hot-film probe the calibration procedure is simple and reliable (conducted in freestream conditions), and other than reversing flows, such calibration will hold regardless of experimental flow conditions. A recent study of computer-controlled hot-wire anemometry by Jørgensen [26] concluded that with careful calibration, signal conditioning and digitising considerations, computer-based anemometry may be considered to be accurate to within 1% error for the single-wire case. It should be stated that this is the ideal case for the velocity measurement accuracy, and further errors will be introduced when attempts are made to relate measured velocities to skin friction. Section 3 will give a brief outline of skin friction measurements made using this velocity gradient method. Included in this are discussions on the wall effect and probe wall positioning. These factors are relevant for all hot-wire measurements in the near-wall region, and both are instrumental in our proposed method being discussed here.

Section snippets

Experimental set-up

The present experiments were performed in an open return low-speed wind tunnel with a 300×534mm working section of length 3.0m. The boundary layer was tripped near the inlet of the working section ensuring a fully developed turbulent boundary layer over the test surface. The test surface is made of a Perspex plate of 12mm overall thickness. Unless otherwise stated, the freestream velocity of the present investigation was U=2.5ms−1, with a turbulence intensity of approximately 0.3%.

Near-wall velocity gradient technique

Measuring skin friction in the boundary layer using the mean velocity gradient at the wall is basically just a matter of accurately measuring the velocity profile in the viscous sublayer. A line is fitted to the linear portion of these data, the gradient of which is then used to calculate the wall shear stress from the following expression:μdudyw,where u is the measured mean velocity, y is the wall-normal distance, μ is the viscosity and τw is the wall shear stress. There are at least three

Wall-effect positioning technique

Janke [29] attributes the wide scatter between data from different wall-effect experiments, to the broad range of parameters, such as probe configuration, wall material and overheat ratio. An earlier experimental investigation by Polyakov and Shindin [40], in which wall thermal conductivity and probe geometry were altered, clearly illustrates this complex parameter dependence. Both Janke [29] and Bruun [6] were moved to conclude that such behaviour makes the possibility of a truly universal

Single velocity cf measurement experimental data

An experimental study has been conducted to judge the repeatability and standard error expected from the proposed single-point velocity method of cf measurement. In principle the experiment is similar to those used to gauge the wall detection accuracy as detailed above. The automated wall detection routine locates the discontinuities in du/dy in the wall-effect curve, from which the aerodynamic origin (y=0) is calculated. From this datum, position the probe is then traversed 480 steps or 0.6mm

Concluding remarks

A thorough analysis of existing skin friction measurement techniques has revealed shortcomings in both accuracy and practicality when dealing with non-canonical boundary layer flows. These shortcomings, coupled with a need to map local cf over a wider area for three-dimensional turbulent boundary layers have led to the development of a novel cf measuring technique. It is shown that the use of hot-wire anemometry to characterise the velocity gradient in the linear portion of the viscous sublayer

Acknowledgements

The authors acknowledge the support from the Royal Society through Research Grant no. 22141. The work was conducted as a part of research funded by EPSRC (Research Studentship to N.H. award no. 99306664). Comments and suggestions made by Professor Mike Gaster are greatly appreciated.

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