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.     

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.     

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 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.     

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 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.     

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.     

Vortex structures in shear flows

Large-scale vortex structures in shear flows are investigated. An effective method of describing these objects, which makes it possible to go beyond the framework of weak nonlinearity, is proposed. This is especially important in investigating spatially isolated structures. Evolution-type equations describing the shape of the vortex structures are obtained and their steady-state solutions are examined. A detailed classification of the structures in two-dimensional and cylindrical channels is given. Attention is drawn to the qualitative similarity of some of these structures to the well-known structures in real turbulent flows (wall eddies, turbulent slugs). It is established that isolated vortex structures in a pipe whose radius is fairly large as compared with their transverse dimension have kinematic characteristics similar to those of Hill vortices. The prospects of the method are discussed.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 65–75, March–April, 1989.The author wishes to thank G. S. Golitsyn for his interest and G. I. Barenblatt and V. M. Gryanik for discussing the results and offering useful advice.     

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.     

Unsteady quasi-one-dimensional flows of relaxing nitrogen tetroxide

The decay of an arbitrary discontinuity and the reflection of a fan of rarefaction waves from a fixed wall in dissociating nitrogen tetroxide are considered. The system of the equations of gas dynamics and the equation of the conservation of the mass of component i have been integrated numerically by MacCormack's method. It is shown that the kinetics has a significant influence on the characteristics of a shock wave and a contact discontinuity.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 159–164, July–August, 1981.     

Unsteady flows of a third-order viscoelastic fluid

Summary Unsteady third-order viscoelastic flow is examined for the purpose of determining a method by which certain material constants in theRivlin-Ericksen theory can be measured. The concept of an intrinsic pressure hole error is used, and an expression for this error is derived for third-order flow. It is also shown that the velocity field for unsteady creeping motion of a third-order fluid is identical at any time to a corresponding steady third-order flow. The pressure field, however, depends upon the rate of change of the flow with time.

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Zusammenfassung Es wird die instationäre Strömung dritter Ordnung einer viskoelastischen Flüssigkeit untersucht zu dem Zweck, eine Methode anzugeben, mit deren Hilfe gewisse Stoffkonstanten in der Theorie vonRivlin undEricksen gemessen werden können. Dazu wird das Konzept des intrinsic pressure hole error verwendet, und es wird für diesen Fehler im Rahmen der Theorie dritter Ordnung ein Ausdruck abgeleitet. Weiter wird gezeigt, daß das Geschwindigkeitsfeld für die instationäre schleichende Strömung einer Flüssigkeit dritter Ordnung zu jeder Zeit mit der zugeordneten stationären Strömung dritter Ordnung identisch ist. Im Gegensatz dazu hängt das Druckfeld jedoch von der zeitlichen Änderung der Strömungsgeschwindigkeit ab.

     

Numerical analysis of wall pressure and heat flux fluctuations in shock-turbulent-boundary-layer interaction

The unsteady, compressible, Reynolds-averaged Navier-Stokes equations are solved numerically for an oblique shock-wave-induced turbulent boundary layer sepration. For the freestream Mach number 6 and the freestream Reynolds number 66·1 × 10⁶ m^?1, a time-dependent computation is performed, using MacCormack's explicit-implicit finite difference method with 82 × 42 grid points. A two-layer eddy viscosity turbulence model is employed in conjunction with a relaxation modification. Comparisons of the mean wall pressure and the mean heat transfer coefficient with the available experimental results are made and the evaluation of unsteady data for surface pressure and heat flux fluctuations is presented. It is found that the fluctuations in heat flux have qualitatively the same features as those of wall pressure but are different quantitatively.     

Unsteady effects in weakly perturbed pulsatile channel flows

Pulsatile incompressible laminar flow in a plane channel with slight asymmetric deformation of the walls is considered on the basis of an asymptotic approach to the solution of the Navier-Stokes equations at large Reynolds numbers. It is shown that for extended deformations the change in the direction of the undisturbed flow in the wall regions is accompanied by a sharp increase in the amplitude of the perturbations; this is an essentially unsteady process. For flows with a small positive friction stress two classes of eigensolutions are obtained in the quasisteady approximation.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 96–104, March–April, 1987.The author is grateful to V. V. Sychev and A. I. Ruban for a number of useful consultations in the course of the work.