LOCAL MEASUREMENTS OF INSTANTANEOUS SKIN FRICTION IN FLOW BEHIND BACKWARD-FACING STEP: LIMITATIONS AND PERSPECTIVES

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1 UDC LOCAL MEASUREMENTS OF INSTANTANEOUS SKIN FRICTION IN FLOW BEHIND BACKWARD-FACING STEP: LIMITATIONS AND PERSPECTIVES N.I. Mikheev, V.M. Molochnikov, P.S. Zanko Research Center for Power Engineering Problems of the Russian Academy of Sciences Keywords: skin friction, separated flow, backward-facing step, hot-wire, turbulent structure Abstract A set of problems connected with skin friction measurements in a flow behind a backward-facing step is considered. Using the example of instantaneous skin friction vector probe developed and applied in some investigations by the authors fundamental and technical difficulties of local skin friction measurements in complex turbulent separated flows are analyzed. A brief review of the main experimental results on skin friction in a flow behind backward-facing step connected with the real space-time flow pattern is presented. On the basis of the accumulated experience some recommendations for future local skin friction measurements in separated flows are proposed. Introduction Turbulent separation behind a backward-facing step is a classic problem of hydrodynamics of complex separated flows. Here, simplicity of the task formulation is in drastic contrast with the baffling complexity of the internal processes. But even after several decades of research of the structure of the flow using experimental and numerical approaches [1, 2] some aspects of the behavior of the flow are still not clear. The wall region is of the crucial significance for scientific description of a turbulent separation especially such an important hydrodynamic characteristic as skin friction. It is common knowledge that even in a two-dimensional separated flow behind a backward-facing step an instantaneous flow pattern is three-dimensional. So a timeresolved vector field of the skin friction is an ideal case for a researcher. It is possible to obtain such fields with the aid of modern numerical methods (direct numerical simulation [3], large eddy simulation [4]). At the same time mean values of flow parameters can be predicted correctly unlike methods which use turbulence models. But how can we estimate reliability of numerical instantaneous flow patterns? It is an extremely hard science problem even if the corresponding experimental data set exists. With regard to instantaneous vector fields of skin friction we have no such experimental data at all. Even a local measurement of a longitudinal skin friction vector component in a separated N.I. Mikheev, V.M. Molochnikov, P.S. Zanko 23

2 turbulent flow is not a simple task for a laboratory to apply uncommon probes and subtle measuring techniques in this case. A remarkable review of various methods of a longitudinal skin friction vector component measurement was presented in the paper [5]. It should be pointed out that among all four techniques considered in the review only the hot wall pulsed wire method can be used for measurements of unsteady skin friction in reversal flows. Moreover, due to limited frequency response (maximal sampling frequency is about 40 Hz) the probe is not well suited to obtain skin friction spectra. This article concentrates on the instantaneous skin friction vector probe and the corresponding experimental data. The probe was developed in the Laboratory on Hydrodynamics and Heat Exchange (Russian Academy of Sciences, Kazan) and has been applied for several years. Some other methods and experimental results will be addressed briefly if they are used for comparison or have more potential for the future. Working Principle and Design of Skin Friction Vector Probe The working principle of hot-wire for measurements of instantaneous skin friction vector is based on effect of heat exchange variation of a wire due to change of an angle of incidence between a flow and the sensor. The effect is used, for instance, in well-known X- or V-shaped velocity probes. However, such probes are not applicable for measurements in reversal flows, because the corresponding output signals are almost identical for opposite directions of a flow. But, one may try to retain the essential dependence of heat exchange on the angle of incidence only in one semicircle of flow directions and to weaken the dependence in the another semicircle. Effect of this sort is possible, if a sensor is located near an obstacle. Sensors can be installed in a shallow cavity or near a low lug. The variant with a cavity was used in a 2-wire V-shaped probe presented in [6]. The probe gave a capability to estimate both the sign and the absolute value of the skin friction. Unfortunately, it showed high noise levels in the output signal. Probably, the problem was caused by the V-shape, because different fluid particles had to have various flight times while going from one wire to another and the signal at one moment was produced by time-asyncronous information. So it was not possible to measure low values of the skin friction in separated and reattaching flows with the aid of this probe. Later the defect was eliminated in a similar probe where sensors were parallel to each other [7]. Using a lug is preferable to cavity. In the case of a lug the effects of the heat exchange and the heat trace variations mutually enlarge each other. Besides, a probe with a lug is better from the technological point of view. We suppose that the lug is entirely located in the viscous sublayer of a turbulent boundary layer. Recirculation zones appear at the windward and the leeward sides of the lug. It is common knowledge that the length of the recirculation zones depends on the Reynolds number Reh (h is the height of the lug) and the angle between direction of the near-wall velocity and the side face of the lug. Anyhow, the recirculation region at the leeward side of a lug is longer than the opposite one. Then one may choose the position of the sensor, so that it is located in a recirculation zone only if the direction of the flow is direct (or reversal). At the same time in the case of the opposite direction of the flow the sensor should be out of a recirculation region. 24

3 Due to the physics of separated flows the heat exchange of the sensor with the medium in the recirculation zone should be worse. The difference between the values of heat exchange at the windward and the leeward sides of the lug is caused mainly by different values of the local velocities near the sensor. The heat trace strengthens the difference as well, but the last effect is noticeable at relatively small velocities only. In contrast to probes based on registering of the heat trace the probe with a lug should have a faster response to direction change of the near-wall velocity. In fact, the role of the heat trace is not so important, and reorganization of the recirculation zones occurs practically simultaneously along the whole perimeter of the lug. A sketch of a skin friction vector probe [8] is presented in Fig. 1. The construction includes a low lug 3 of 0,2 mm height and a heated thin metallic wire 1 located near the lug. The lug is installed on a basis 4. During measurements the basis may be flush mounted on a surface of a wind tunnel. Support needles 2 made from stainless steel are moulded or glued into the basis. A tungsten wire of 5 µm diameter is welded to the support needles of 0,2 mm diameter. The needles are used for electrical supply of the wire. Simultaneously, the needles work as output terminals for the probe signals measurement. The basis and the lug are made from ebonite. The basis is glued into a body 5 made of a metallic bushing of 6 mm diameter (external). The wire sensor is mounted at a height of 0,1 mm from the basis and separated by 0,08...0,15 mm from a side face of the lug, which looks like a hexagon in the plan view. The circum radius of the hexagon is not greater than 2,5 mm. Fig.1. Sketch of skin friction vector probe: 1 - wire, 2 - support needle, 3 - lug, 4 - basis, 5 - body Block diagram of the system for measurements of the skin friction vector is shown in Fig.2. The sensing element of the probe includes 6 hot wires. There are three pairs of the wires connected with each other. These hot-wire pairs form three electrically isolated circuits. Each circuit is connected to an autonomous hot-wire anemometer unit DISA 55M (R=const). A similar scheme of hot-wire sensors connection was used in a 3-film probe for measurements in reversal flows [9]. In fact, the probe of interest is sensible to a near-wall velocity. But one may calibrate it for measurements of a direction and absolute value of the skin friction vector. However, three important conditions must be fulfilled. First of all, the fluid medium must be a Newtonian fluid. Then, the height of a lug must be small in comparison with a boundary layer thickness. In that case a lug and sensors located nearby are completely 25

4 contained in the viscous sublayer, where the dependence of longitudinal and transverse velocity components on y coordinate (normal to the wall) looks like a linear function of distance from the wall. Fig.2. Block diagram of system for skin friction vector measurements Under this condition the probe is practically not sensible to the normal velocity, because this velocity component and the corresponding turbulent fluctuations are negligible in comparison with the other velocity components. And last but not least, a near-wall velocity variation (coordinates x and z) in a surface region of the immediate vicinity of a probe must be negligibly small. If all the three conditions are fulfilled, one may determine instantaneous components of a skin friction vector using u and w velocity components in the following way: τx=µ(du/dy)y=0 µu(hw)/hw, τz=µ(dw/dy)y=0 µw(hw)/hw, where hw is the distance from the wires to the wall. However, near-wall velocity components are not estimated in practice. Direct calibration of probes in a flow with known absolute value and direction of the skin friction is provided instead. Calibration Undoubtedly, it is best to calibrate a probe in a laminar boundary layer with known characteristics of skin friction. Unfortunately, it is not possible to provide a laminar flow with high absolute value of the skin friction vector in most cases. Also, there is a possibility to calibrate a probe in a turbulent boundary layer with known mean characteristics of the skin friction. But it is a common knowledge that strong turbulent skin friction fluctuations take place in such flows. The output signals of a probe are non- 26

5 linear with respect to the fluctuations. This may lead to an additional error of the calibration curve. The error can be practically excluded, if the calibration includes a conditional sampling of output signals. The conditional sampling technique implies that only signal values close to the mean skin friction in the flow are used. It should be noted that it is necessary to provide simultaneous sampling of all three signals of a probe during calibration and measurement. Using a serial sampling analog-todigital converter may cause an essential additional error in instantaneous skin friction vector measurements. Obviously, the error should grow with the decrease of a sampling frequency and increase of the amplitude and frequency of skin friction vector pulsations. Static and Dynamical Characteristics of Skin Friction Vector Probe The reduced error of mean skin friction vector components measurements 2 2 ( 1,96 x z ) with a confidence probability of 0,95 was no greater than 0,8%. max The error of the mean skin friction can be explained, most likely, by a non-linearity of the calibration curve or, more precisely, by an error of the interpolation. Direct estimation of an error of instantaneous skin friction vector components measurements in a turbulent flow is hardly possible, unfortunately. The problem is connected with strong fluctuations of an absolute value and angular direction of the skin friction vector in a turbulent boundary layer where the calibration takes place. One cannot divide fluctuations in a flow and a measurement error even if to compare dispersions about the mean of the absolute value and angular direction with the corresponding estimations obtained with the help of a reference measuring instrument. In fact, increase of a dispersion due to an error of instantaneous skin friction components measuring may be compensated for by a decrease due to a dynamical error which is caused by persistence of a probe and depends on the fluctuations frequency. An indirect estimation of the error of instantaneous skin friction vector components 2 2 measurements ( 1,96 x z ) was no greater than 2% with a confidence max probability of 0,95. Data obtained using the Clauser method played the role of a reference measuring instrument for measurements of the mean skin friction. A relative error of such a reference instrument is about 5%. It should be noted for comparison that an electrodiffusion probe measures the skin friction vector components with the following uncertainties: ±6% for the wall shear rate and ±10 for the flow direction angle [10]. Experimental estimation of dynamical characteristics of a skin friction vector probe hardly seems possible. The problem is connected with the fact that one is not able to provide a flow with the instantaneous skin friction vector changing in time in a predetermined way. In such a situation numeric estimation of dynamical characteristics of instantaneous skin friction vector probes is preferable. The probe's response on a step and a harmonic change of the absolute value and angular direction of the skin friction vector was calculated. Also, a preliminary computational 'calibration' of the probe was provided. In this case output signals of the probe at different combinations of absolute values and angular directions of the skin friction vector were determined with the aid of a mathematical model of the probe. The calculations showed that the probe instantly 27

6 follows a step change of the absolute value of the skin friction from 1 to 2 N/m2 ( =0 ) and the angular direction from 0 to 90 ( 1 N/m2). At the same time, a dynamical error of an estimation of the corresponding skin friction vector component was no greater than 5% of the step value and converged to zero over time. The probe gives an opportunity to obtain reliable experimental information about the skin friction vector over a wide range of its frequencies (more than 1 khz). The frequency response of a DISA 55M hot-wire anemometer has no influence on the frequency range of measurements obtained by the probe as well. The only limitation is the spatial resolution of the probe. The highest frequency of a frequency range of a skin friction measurement corresponds to the turbulence scale length in a boundary layer equal to the size of the probe in the plan view (2,5 mm). It should be noted that an electrodiffusion probe has a very limited frequency response. In fact, the upper boundary of its frequency range is no greater than 10 Hz [11]. On the other hand, experiments proved that a probe of longitudinal component of the skin friction vector with a cavity can measure signals with frequencies at least 2 khz in a reliable way [7]. One-Point Measurements Though one-point measurements are canonical, they give only superficial information on complex processes in a turbulent flow. Let us consider some conclusions which one can make using the results of one-point measurements of skin friction in a flow behind a backward-facing step only. The results of measurements of the mean skin friction and the root mean square skin friction fluctuations along the separation region (Reh=6,2 104) using the skin friction vector probe [12] are comparable with the analogous data obtained with the help of a wall pulsed wire [2] (Reh=4,1 104). There is a hypothesis based on some older experimental data that the absolute value of the instantaneous skin friction vector in a turbulent separated flow never equals to zero, even at the mean reattachment point, where x 0 [13]. Recent measurements using the skin friction vector probe [12] and an electrodiffusion probe [10] confirm the hypothesis in general. However, in the first case it is not easy to estimate the error caused by the probe's size (2,5 mm) when measuring a small absolute value of the skin friction vector in a flow changing the direction. Anyhow, the proposal seems natural: one can hardly imagine that all the energy of turbulent pulsations of a reorganizing separated boundary layer suddenly disappears even at the point where fluid does not move on average. To our knowledge, the first spectral data for the longitudinal component of the skin friction vector in backward-facing step flows were published in [7] and later in a more detailed way in [14]. In those works special attention was paid to the corner eddy's area and the main recirculation zone. Spectra of the both components of the skin friction vector in a flow of this kind were presented in the article [15]. Unfortunately, it is hard to analyze the low-frequency range of the spectra (less than 100 Hz) in the last case due to an imperfection of the experimental equipment. The high-frequency range of the spectra ( Hz) seemed to be similar at all measuring points located under the reattached shear layer (x/h=1...13). But under the recirculation region the role of the high-frequency components of the spectra becomes more significant with moving downstream away from 28

7 the step. Such a tendency had been noticed in the case of wall pressure fluctuations [16] and in the measurements of the longitudinal skin friction component mentioned above [14]. Probably, the phenomenon is connected with the separated shear layer which is gradually approaching the wall. Combined Measurements Simultaneous measurements at least in two positions give a capability to use the correlation analysis and the conditional sampling technique. Both methods have been successfully applied in the study of a conventional turbulent boundary layer. Estimation of a correlation between flow parameters at two or more points of a flow domain as well as a conditional sampling with the correct criterion makes it possible to analyze the turbulence structure including large-scale vortices. Nevertheless, one must have information about the instantaneous flow field a priori in order to choose the right criterion for the conditional sampling technique or to interpret correlation functions adequately. So, the scientific value of two-points measurements depends on the prior information about a flow, and their role, in fact, may be reduced to obtaining of quantitative estimations of a present qualitative description of a phenomenon. Therefore, a combination of local skin friction measurements with modern methods of measuring flow parameters fields in the whole domain of interest (LDV, PIV etc.) seems to be the most productive approach nowadays. The article [17] is a remarkable illustration of the approach. In this study hot-wire probes that were sensitive to flow direction near the wall were used together with a Laser Doppler anemometer (LDA). The probes were located in the reattachment region and used as triggers for the conditional sampling technique. Proper criteria that characterized location of instantaneous reattachment points (early reattachment - xr/h<5,3; intermediate reattachment - 5,3<xR/h<6,8; late reattachment - xr/h>6,8; x R 6,2h ) helped to describe the so called flapping motion of the free shear layer in the vertical plane using conditionally averaged streamlines of the whole flow domain. Amplitude of the oscillation was about 20% of the shear layer width [17]. Similar criteria for the conditional sampling technique were used later in the work [18] in order to study influence of the instantaneous reattachment point oscillations on behaviour of the reattaching shear layer. A hot-wire probe sensitive to flow direction near the wall was installed at the points of the early (reversal flow probability γ=0,9; instantaneous flow direction - direct) and the late (γ=0,1; instantaneous flow direction - reversal) reattachment. Simultaneously conventional 1-wire velocity hot-wire probe measured conditionally sampled velocity profile in the reattached shear layer (x=9,6h). It was shown that the conditionally averaged velocity profile also ''oscillated'' about its mean value. The ''oscillations'' seemed to be connected with the instantaneous reattachment point location in the following way: conditionally averaged velocity was greater than it's mean value during the late reattachment and vice versa during the early reattachment (for instance, the amplitude of the ''oscillation'' was 5-6% from the mean value if the velocity was measured at a distance of 1 mm from the wall; h=23 mm). It is shown [15] that such pulsations of a conditionally averaged velocity profile of the reattached shear layer appear mostly due to transport of large-scale fragments of the 29

8 recirculation zone through the reattachment region. Continual fluctuations of the point where new reattached boundary layer starts play an insignificant role. Another noteworthy investigation [14] was concentrated on the region upstream and downstream of the mean location of the secondary separation, where the lowfrequency flapping motion is dominant according to Fourier power spectra of the skin friction. To tell the truth, there were no simultaneous measurements of the skin friction and space time velocity fields in this study. But the authors used a whole set of methods in order to analyze the low-frequency non-stationarity in the flow behind a backwardfacing step: local measurements of the longitudinal component of the skin friction, simultaneous two-point measurements of the skin friction and the velocity using 1-wire hot-wire probe, DPIV and a qualitative visualization. The experimental data were processed using the correlation, spectral and wavelet analyses. It is important that a combination of such different approaches allowed to connect quantitative data of local skin friction measurements with the real space-time pattern of the flow as well as to describe the low-frequency cycle of the corner eddy. Conclusions The skin friction is one of the most important parameters for study of turbulent flows. It is generally accepted that the lion's share of turbulent kinetic energy is produced near the wall in a conventional turbulent boundary layer. The instantaneous skin friction vector "follows'' and "generalizes'' a very complex turbulent movement of fluid at separation and reattachment of the shear layer. Modern experimental methods allow only local measurements of one or two components of the instantaneous skin friction vector. Obviously, such an approach has a lot of limitations. Some of them were considered above. Nevertheless, using both "oldfashioned'' hot-wire or electrodiffusion probes and other experimental methods which allow to measure the whole flow domain, one can obtain critically important quantitative information about the complex and wonderful phenomenon of turbulent separation. In our opinion, it is the main perspective of local measurements of the skin friction in separated flows. As regards methods of processing and presentation media for the experimental data it seemed that the last word is not said by the well-known conditional sampling technique. This simple and clear technique is not only a convenient method for measurements, but a powerful instrument for analysis which can help to describe and present data obtained from space-time flow fields. Correct criteria for conditional sampling may help to evolve distinct forms from very changeable, elusive instantaneous flow patterns. It is righteous from the physical point of view and convenient for a researcher to set criteria for the conditional sampling technique with the help of local skin friction probes. Nomenclature R - electrical resistance; Re h - Reynolds number based on h and U0, Re h =U 0 h/ν; U 0 - mean velocity in upstream channel section; 30

9 h - step height; u, w - instantaneous velocity components in x and z directions; x, y, z - streamwise, wall-normal and spanwise coordinates; x R - instantaneous reattachment length; - flow direction angle ( =180 for reverse flow); µ - dynamic viscosity; ν - kinematic viscosity; σ τ, σ τx, σ τz - standard deviation of absolute value and components in x and z directions of instantaneous skin friction vector; τ, τ x, τ z - absolute value and components in x and z directions of instantaneous skin friction vector; ˉ - overbar denotes time average. Acknowledgments The authors are grateful to Dr. A.K. Saykin for his invaluable contribution to the development of the skin friction vector probe. This research was supported by the Russian Foundation for Basic Research (grants No a, a, a). References 1. Bradshaw, P. The Reattachment and Relaxation of a Turbulent Shear Layer / P. Bradshaw, F.Y.F. Wong // J. Fluid Mech Vol.52.- No.1.- P Eaton, J.K. A Review of Research on Subsonic Turbulent Flow Reattachment / J.K. Eaton, J.P. Johnston // AIAA J Vol.19.- P Le, H. Direct Numerical Simulation of Turbulent Flow over a Backward-Facing Step / H. Le, P. Moin, J. Kim // J. Fluid Mech Vol P Arnal, M. Large-Eddy Simulation of a Turbulent Flow with Separation // 8th Int. Symp. "Turbulent Shear Flows 8" (F. Durst et al., eds.) / M. Arnal, R. Friedrich.- Springer-Verlag, P Fernholz, H.H. New Developments and Applications of Skin-Friction Measuring Techniques / H.H. Fernholz, G. Janke, M. Schober, P.M. Wagner, D. Warnack // Meas. Sci. Technol Vol.7.- P De Ponte, S. Experiments on a Turbulent Unsteady Boundary Layer with Separation / S. De Ponte, A. Baron // AGARD-CP Spazzini, P.G. Design, Test and Validation of a Probe for Time-Resolved Measurement of Skin Friction / P.G. Spazzini, G. Iuso, M. Onorato, N. Zurlo // Meas. Sci. Technol Vol.10.- P Kozlov, A.P. Characteristics of Skin Friction in Turbulent Separated Flows / A.P. Kozlov, N.I. Miheev, V.M. Molochnikov, A.K. Saykin // Izvestiya Akademii Nauk. Ehnergetika Vol.4.- P.3-31 (in Russian). 9. Jorgensen, F.E. Characteristics and Calibration of a Triple-Split Probe for Reversing Flows / F.E. Jorgensen // DISA Information Vol.27.- P Tihon, J. Near-Wall Investigation of Backward-Facing Step Flows / J. Tihon, J. Legrand, P. Legentilhomme // Experiments in Fluids Vol.31.- P

10 11. Bewersdorff, H.-W. Simultaneous Wall Shear Rate Measurements by a Three Segmented Electrodiffusion Probe and Laser-Doppler-Anemometry / H.-W. Bewersdorff, A. Gyr, K. Hoyer, V. Sobolik // Experiments in Fluids Vol.22.- P Miheev, N.I. Space-Time Structure of Turbulent Separated Flows: Ph.D. thesis / N.I. Miheev.- Kazan: Kazan State Technical University, 1998 (in Russian). 13. Kozlov, A.P. Appearance of 3D-Features in 2D Separated Flows / A.P. Kozlov // Doklady Akademii Nauk Vol No.3.- P (in Russian). 14. Spazzini, P.G. Unsteady Behavior of Back-Facing Step Flow / P.G. Spazzini, G. Iuso, M. Onorato, N. Zurlo, G.M. Di Cicca // Experiments in Fluids Vol.30.- P Zanko, P.S. Transport of Skin Friction Pulsations in a Turbulent Separated Flow Behind a Backward-Facing Step / P.S. Zanko, N.I. Miheev // Proceedings of the Fourth International Symposium on Turbulence, Heat and Mass Transfer "Turbulence, Heat and Mass Transfer 4" (K. Hanjalic, Y. Nagano and M. Tummers, eds.).- Begell House, P Farabee, T.M. Measurements of Fluctuating Wall Pressure for Separated/Reattached Boundary Layer Flows / T.M. Farabee, M.J. Casarella // Journal of Vibration, Acoustics, Stress, and Reliability in Design Vol P Driver, D.M. Time-Dependent Behavior of a Reattaching Shear Layer / D.M. Driver, H.L. Seegmiller, J. Marvin // AIAA J Vol.7.- P Zanko, P.S. Reattached Shear Layer and Oscillating Separation Region in Turbulent Flow Behind Backward-Facing Step / P.S. Zanko, A.P. Kozlov, N.I. Miheev // Izvestiya Akademii Nauk. Ehnergetika Vol.4.- P (in Russian). 32