Statistical properties of wall shear stress fluctuations in turbulent channel flows

Instantaneous velocity and wall shear stress measurements are conducted in a turbulent channel flow in the Kármán number range of Re_τ = 74–400. A one-dimensional LDA system is used to measure the streamwise velocity fluctuations, and an electrochemical technique is utilized to measure the instantaneous wall shear stress. For the latter, frequency response and nonuniform correction methods are used to provide an accurate, well-resolved wall statistics database. The Reynolds number dependency of the statistical wall quantities is carefully investigated. The corrected relative wall shear stress fluctuations fit well with the best DNS data available and meet the need for clarification of the small discrepancy observed in the literature between the experimental and numerical results of such quantities. Higher-order statistics of the wall shear stress, spectra, and the turbulence kinetic energy budget at the wall are also investigated. The present paper shows that the electrochemical technique is a powerful experimental method for hydrodynamic studies involving highly unsteady flows. The study brings with it important consequences, especially in the context of the current debate regarding the appropriate scaling as well as the validation of new predictive models of near-wall turbulence.     

Characteristics of wall pressure fluctuations in separated flows over a backward-facing step: Part II. Unsteady wavelet analysis

 Time-dependent characteristics of wall pressure fluctuations in separated and reattaching flows over a backward-facing step were investigated by means of the continuous wavelet transform. Emphasis was placed on the combination of time-localized analyses of the wavelet transform and multi-point measurements of pressure fluctuations. Synchronized wavelet maps revealed the evolutionary behavior of pressure fluctuations and gave further insight into the modulated nature of large-scale vortical structures. It was found that there exist two modes of shed vortices: one is the global oscillation and the other is the vortex convection. The two alternating modes are synchronized with the flapping frequency component of pressure fluctuations. The flapping motion gives rise to the difference in pressure spectra, indicating more intensive pressure activity during the shrinking period of the recirculation region.     

Measurement of wall shear rate in large amplitude unsteady reversing flows

Wall shear rates in large amplitude unsteady flows that cause flow reversal can be measured by using two rectangular electrodes in a sandwich arrangement. The frequency response of this sandwich probe is studied numerically. An inverse mass transfer method is applied to recover the instantaneous shear rate from the measured difference in the mass transfer rate to the two segments. Experimental results for a turbulent pipe flow with imposed large amplitude sinusoidal oscillations are used to test the method.     

Measurements and scaling of wall shear stress fluctuations

Measurements of velocity and wall shear stress fluctuations were made in an external turbulent boundary layer developed over a towed surface-piercing flat plate. An array of eight flush-mounted wall shear stress sensors was used to compute the space-time correlation function. A methodology for in situ calibration of the sensors for ship hydrodynamic applications is presented. The intensity of the wall shear stress fluctuations, τ _rms/τ _avg was measured as 0.25 and 0.36 for R _θ =3,150 and 2,160 respectively. The probability density is shown to exhibit positive skewness, and lack of flow reversals at the wall. Correlations between velocity and wall shear stress fluctuations are shown to collapse with outer boundary layer length and velocity scales, verifying the existence of large-scale coherent structures which convect and decay along the wall at an angle of inclination varying from 10 to 13° over the range of Reynolds numbers investigated. The wall shear stress convection velocity determined from narrow band correlation measurements is shown to scale with outer variables. The space-time correlation of the wall shear is shown to exhibit a well-defined convective ridge, and to decay 80% over approximately 3δ for R _θ =3,150. Published online: 7 November 2002     

Prediction of turbulent wall shear flows directly from wall

The fully elliptic Reynolds-averaged Navier–Stokes equations have been used together with Lam and Bremhorst's low-Reynolds-number model, Chen and Patel's two-layer model and a two-point wall function method incorporated into the standard k-? model to predict channel flows and a backward-facig step flow. These flows enable the evaluation of the performance of different near-wall treatments in flows involving streamwise and normal pressure gradients, flows with separation and flows with non-equilibrium turbulence characteristics. Direct numerical simulation (DNS) of a channel flow with Re =3200 further provides the detailed budgets of each modelling term of the k and ?-transport equations. Comparison of model results with DNS data to evaluate the performance of each modelling term is also made in the present study. It is concluded that the low-Reynolds-number model has wider applicability and performs better than the two-layer model and wall function approaches. Comparison with DNS data further shows that large discrepancies exist between the DNS budgets and the modelled production and destruction terms of the ? equation. However, for simple channel flow the discrepancies are similar in magnitude but opposite in sign, so they are cancelled by each other. This may explain why, even when employing such an inaccurately modelled ?-equation, one can still predict satisfactorily some simple turbulent flows.     

Disturbance growth rate in turbulent wall flows

Disturbance development in turbulent wall flows is numerically investigated. The flows in a circular tube and in a plane channel are considered. The Navier-Stokes equations subjected to the condition of periodicity along the main flow are integrated in time until a statistically stationary “turbulent” flow regime is attained. Then the solution is disturbed and the further evolution of the disturbance is determined by comparing the two solutions, i.e., with and without the disturbance, which are calculated in parallel. It is shown that in the linear stage on average the solutions diverge exponentially. The main result of the study is that the small disturbance growth rate normalized by the wall time scale turns out to be constant, that is, dependent on neither the Reynolds number on the range considered nor the type of the flow: λ⁺ ≈ 0.021. The estimate of the disturbance growth rate is consistent with the previously obtained results concerning downstream disturbance growth and the estimate for the highest Lyapunov exponent calculated for turbulent flow in a plane channel.     

Inner-outer decomposition of wall shear stress fluctuations in turbulent channels

Fluctuating wall shear stress in turbulent channel flows is decomposed into small-scale and large-scale components. The large-scale fluctuating wall shear stress is computed as the footprints of the outer turbulent motions, and the small-scale one is obtained by subtracting the large-scale one from the total, which fully remove the outer influences. We show that the statistics of the small-scale fluctuating wall shear stress is Reynolds number independent at the friction Reynolds number larger than 1000, while which is Reynolds number dependent or the low-Reynolds-number effect exists at the friction Reynolds number smaller than 1000. Therefore, a critical Reynolds number that defines the emergence of universal small-scale fluctuating wall shear stress is proposed to be 1000. The total and large-scale fluctuating wall shear stress intensities approximately follow logarithmic-linear relationships with Reynolds number, and empirical fitting expressions are given in this work.     

Components of wall shear rate in wavy Taylor-Couette flow

The time-resolved axial and azimuthal components of the wall shear rate were measured as function of Reynolds number by a three-segment electrodiffusion probe flush mounted in the inner wall of the outer fixed cylinder. The geometry was characterized by a radius ratio of 0.8 and an aspect ratio of 44. The axial distribution of the wall shear rate components was obtained by sweeping the vortices along the probe using a slow axial flow. The wavelength and phase celerity of azimuthal waves, axial wavelength of vortices and their drifting velocity were calculated from the limiting diffusion currents measured by three simple electrodiffusion probes.     

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

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.     

Unsteady flows in elastico-viscous liquids

Summary Consideration is given to two problems involving the unsteady motion of a sphere in aMaxwell liquid. In both problems the full solutions are obtained and compared in each case to the solution obtained using an approximation procedure. Good agreement is obtained for large values of the elastic parameter. The approximation reduces the mathematics considerably and thus allows experimentalists to determine the elastic parameter involved.With 2 figures     

Relationship between wall shear stresses and streamwise vortices in turbulent flows over wavy boundaries

The relationship between wall shear stresses and near-wall streamwise vortices is investigated via a direct numerical simulation(DNS) of turbulent flows over a wavy boundary with traveling-wave motion. The results indicate that the wall shear stresses are still closely related to the near-wall streamwise vortices in the presence of a wave. The wave age and wave phase significantly affect the distribution of a two-point correlation coefficient between the wall shear stresses and streamwise vorticity. For the slow wave case of c/Um = 0.14, the correlation is attenuated above the leeward side while the distribution of correlation function is more elongated and also exhibits a larger vertical extent above the crest. With respect to the fast wave case of c/U_m=1.4, the distribution of the correlation function is recovered in a manner similar to that in the flat-wall case. In this case, the maximum correlation coefficient exhibits only slight differences at different wave phases while the vertical distribution of the correlation function depends on the wave phase.     

Unsteady flows of inhomogeneous incompressible fluids

In this paper, we study the unsteady motion of inhomogeneous incompressible viscous fluids. We present the results corresponding to Stokes' second problem and for the flow between two parallel plates where one is oscillating.     

Unsteady interaction of uniformly vortex flows

The problem of the decay of an arbitrary discontinuity (the Riemann problem) for the system of equations describing vortex plane-parallel flows of an ideal incompressible liquid with a free boundary is studied in a long-wave approximation. A class of particular solutions that correspond to flows with piecewise-constant vorticity is considered. Under certain restrictions on the initial data of the problem, it is proved that this class contains self-similar solutions that describe the propagation of strong and weak discontinuities and the simple waves resulting from the nonlinear interaction of the specified vortex flows. An algorithm for determining the type of resulting wave configurations from initial data is proposed. It extends the known approaches of the theory of one-dimensional gas flows to the case of substantially two-dimensional flows. Lavrent'ev Institute of Hydrodynamics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 39, No. 5, pp. 55–66, September–October, 1998.     

非加劲钢板剪力墙的高阶弹性剪切屈曲分析

非加劲钢板剪力墙(SPSW)结构在水平荷载作用下易屈曲,形成主拉压应力场,并以拉力带方式提供水平承载力及抗侧刚度。传统拉杆模型(SM模型)用于非加劲SPSW结构分析或设计时忽略压力场的贡献,一般会低估高厚比较小的非加劲SPSW结构的抗侧能力。非加劲SPSW结构在水平力作用下会形成多波面外变形,与剪力墙板的高阶屈曲相似,可通过在修正的SM模型中引入对应于高阶屈曲的主压应力来反映压力场贡献,提高模型分析精度。考虑剪力墙板高厚比、高宽比及边缘构件刚度的影响,共设计66个单层、单跨和梁柱铰接的非加劲SPSW算例,并进行弹性屈曲分析。分析结果表明,高厚比及边缘构件刚度对非加劲SPSW结构的剪切屈曲系数影响不大;随着剪力墙板高宽比的增加,非加劲SPSW结构的剪切屈曲系数呈增大趋势。采用Matlab程序对66个非加劲SPSW算例的2～5阶剪切屈曲系数结果进行统计分析,并提出了简化公式。     

Calibration and use of a MEMS surface fence for wall shear stress measurements in turbulent flows

Microelectromechanical systems (MEMS) sensors are increasingly used for measurements in fluid dynamics since, because of their inherently compact size, they allow access to the information that was previously unavailable. In this paper we describe further testing of a MEMS sensor used to measure surface shear stress. It is a wall-mounted fence that bends under the influence of the pressure difference resulting from the velocity shear at the wall. The fences have been successfully calibrated in a wind tunnel and, as an example of their application, used to determine mean and fluctuating shear stress (along with spectra) in a cylindrical cavity flow.     

Unsteady flows of a viscoplastic medium in channels

We numerically study the nonstationary Poiseuille problem for a Bingham-Il’yushin viscoplastic medium in ducts of various cross-sections. The medium acceleration and deceleration problems are solved by using the Duvaut-Lions variational setting and the finite-difference scheme proposed by the authors. The dependence of the stopping time on internal parameters such as density, viscosity, yield stress, and the cross-section geometry is studied. The obtained results are in good agreement with the well-known theoretical estimates of the stopping time. The numerical solution revealed a peculiar characteristic of the stagnant zone location, which is specific to unsteady flows. In the annulus, disk, and square, the stagnant zones arising shortly before the flow cessation surround the entire boundary contour; but for other domains, the stagnant zones go outside the critical curves surrounding the stagnant zones in the steady flow. The steady and unsteady flows are studied in some domains of complicated shape.     

Electrical fluctuations in turbulent electrogasdynamic flows

Processes in turbulent flows containing charged particles are examined. It is shown that fluctuations of the electrical charge, which can be recorded by special apparatus, occur in the jets of aircraft engines in the presence of charged particles of unburned fuel in them and in turbulent jets created under laboratory conditions by blowing corona sources with air. The problem of determining the characteristics of turbulence in jets from measurements of electrical fluctuations sensed by an electrostatic probe is formulated. The electrical fluctuations generated by a submerged electrogasdynamic jet were measured under laboratory conditions and the results were compared with the data of acoustic measurements. A good correlation of the relative electrical and acoustic characteristics was found. The spectra of electrical fluctuations of a jet during its neutralization were studied by means of a special compensator and the mixing zone of opposite electrical charges was determined. The electrical fluctuations generated by the jets of aircraft were measured under airfield conditions.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 148–159, March–April, 1977.The authors thank A. N. Sekundov for a valuable discussion and help in the work and also A. P. Strekalov and V. F. Kudryashov for participating in the experimental investigations.