An inclined wall jet: Mean flow characteristics and effects of acoustic excitation

 The mean velocity field of a 30° inclined wall jet has been investigated using both hot-wire and laser Doppler anemometry (LDA). Provided that the nozzle aspect ratio is greater than 30 and the inclined wall angle (β) is less than 50°, LDA measurements for various β show that the reattachment length is independent of the nozzle aspect ratio and the nozzle exit Reynolds number (in the range 6670–13,340). There is general agreement between the reattachment lengths determined by LDA and those determined using wall surface oil film visualisation technique. The role of coherent structures arising from initial instabilities of a 30° wall jet has been explored by hot-wire spectra measurements. Results indicate that the fundamental vortex roll-up frequency in both the inner and outer shear layer corresponds to a Strouhal number (based on nozzle exit momentum thickness and velocity) of 0.012. The spatial development of instabilities in the jet has been studied by introducing acoustic excitation at a frequency corresponding to the shear layer mode. The formation of the fundamental and its first subharmonic has been identified in the outer shear layer. However, the development of the first subharmonic in the inner shear layer has been severely suppressed. Distributions of mean velocities, turbulence intensities and Reynolds shear stress indicate that controlled acoustic excitation enhances the development of instabilities and promotes jet reattachment to the wall, resulting in a substantially reduced recirculation flow region. Received: 24 November 1998/Accepted: 24 August 1999     

Solitary waves on the surface of a viscoelastic fluid running down an inclined plane

In this paper, we study the existence and the role of solitary waves in the finite amplitude instability of a layer of a second-order fluid flowing down an inclined plane. The layer becomes unstable for disturbances of large wavelength for a critical value of Reynolds number which decreases with increase in the viscoelastic parameter M. The long-term evolution of a disturbance with an initial cosinusoidal profile as a result of this instability reveals the existence of a train of solitary waves propagating on the free surface. A novel result of this study is that the number of solitary waves decreases with in crease in M. When surface tension is large, we use dynamical system theory to describe solitary waves in a moving frame by homoclinic trajectories of an associated ordinary differential equation.     

Solitary waves in stratified fluids and their interaction

A systematic procedure is proposed for obtaining solutions for solitary waves in stratified fluids. The stratification of the fluid is assumed to be exponential or linear. Its comparison with existing results for an exponentially stratified fluid shows agreement, and it is found that for the odd series of solutions the direction of displacement of the streamlines from their asymptotic levels is reversed when the stratification is changed from exponential to linear. Finally the interaction of solitary waves is considered, and the Korteweg-de Vries equation and the Boussinesq equation are derived. Thus the known solutions of these equations can be relied upon to provide the answers to the interaction problem.     

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     

Effects of the separating shear layer on the reattachment flow structure part 2: Reattachment length and wall shear stress

Measurements of reattachment length of a separated flow behind a backward-facing step for a range of Reynolds numbers (8000 < Re _H < 40,000) and initial boundary-layer thickness (0 < /H < 2) were performed with the purpose of explaining the scatter in existing (high quality) data sets and to understand the effect of the initial shear-layer structure on the reattachment zone. The reattachment length for the case of laminar boundary layers upstream of the step were 30% smaller than when the boundary layer upstream of the step was turbulent. Measured values of the mean wall shear stress in the reattachment zone were also measurably affected by the upstream boundary-layer state. The (rms) levels of fluctuating wall stress were not sensitive to boundary-layer state, but rather to /H, as was the case for the pressure profiles in part 1 (Adams and Johnston 1988).List of symbols C _* ^p normalized pressure, (C _p – C _{p, min})/(1 – C _{p, min}) - C _f skin friction coefficient, /0.5 U _ref ² - C _f level (rms) of fluctuation part of skin-friction coefficient - ER duct expansion ratio; outlet to inlet width - H step height - Re _d Reynolds number based on diameter - Re Reynolds number based on inlet boundary-layer momentum thickness, and U _ref - Re _H Reynolds number based on H and U _ref - x _r distance to reattachment - X ^* normalized distance, (x – x _r)/x _r (note: different from x/x _r in part 1) - /H ratio of inlet boundary-layer thickness to step height - gq ₀ momentum thickness upstream of step     

Optimization of multiplane μPIV for wall shear stress and wall topography characterization

Multiplane μPIV can be utilized to determine the wall shear stress and wall topology from the measured flow over a structured surface. A theoretical model was developed to predict the measurement error for the surface topography and shear stress, based on a theoretical analysis of the precision in PIV measurements. The main parameters that affect the accuracy of the measurement are identified. The effect of different parameter settings is studied by means of Monte Carlo simulations, and the results are compared with an experimental test case. The results are used to determine the recommended parameter settings for this measurement approach.     

Nonlinear effects on transverse shear waves in an elastic medium

The effect of second- and third-order nonlinearities on transverse shear waves in an elastic medium is examined. It is found that waveform distortion and shock development occur on a length scale which is an order of magnitude greater than for longitudinal waves. Explicit solutions for modulated traveling waves are obtained.     

Improvement in the frequency response of the electrochemical wall shear stress meter

One of the very few disadvantages of the mass-transfer transducer when compared with the hot-film sensor, is a slightly diminished frequency-response due to the higher Prandtl number encountered. Mass or thermal balance and transfer equations were solved first by Fortuna and Hanratty (1971) for small fluctuations of the wall shear. The solutions allow to make accurate corrections on the frequency spectra and the power of the fluctuations, but in different time. In this paper, the author deduces the frequency response of split rectangular electrodes and shows how a combination of signals improves the response at higher frequencies and makes it comparable to the thermal transducer with the same size, in the same fluid. Two experimental devices are described and compared. With these devices, the measurement of the wall shear fluctuations is improved in real time. Accurate determinations of turbulent power fluctuations and probability density spectra are feasible and illustrate the subject.List of symbols A total area of the electrode - A _j area of the part j of the electrode - a coefficient - C concentration - C bulk concentration - c fluctuation of concentration - D diffusion coefficient - F Faraday's constant - f(n ⁺) transfer function - g gain of the differential electrode - I _j electrolysis current on the part j of the electrode - K transfert coefficient - k fluctuation of K - l electrode length - n frequency - P _r Prandtl number - S wall shear - s fluctuation of the wall-shear - t time - x direction of the flow - y direction normal to the wall - phase delay - v kinematic viscosity A version of this paper was presented at the 11th Symposium on Turbulence, University of Missouri-Rolla, 17–19 October 1988     

In vivo blood flow and wall shear stress measurements in the vitelline network

The wall shear stress plays a key role in the interaction between blood flow and the surrounding tissue. To obtain quantitative information about this parameter, velocity measurements are required with sufficient spatial (and temporal) resolution. We present a methodology for the determination of the wall shear stress in vivo in the vitelline network of a chick embryo. Velocity data is obtained by microscopic particle image velocimetry using correlation ensemble averaging; the latter is used to increase the signal-to-noise ratio of the measurements. The temporal evolution of the pulsatile flow is reconstructed by sorting the image pairs based on a phase estimate. From these flow measurements, the wall shear stress can be derived either directly from the magnitude of the gradients or from fits to velocity profiles. Both methods give results that are in good agreement with each other, while the former method is significantly easier to implement. For more accurate studies, the full three-dimensional velocity field may be required. It is demonstrated how this velocity field can be obtained by scanning the measurement volume.

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Measurements of mean and fluctuating wall shear stress beneath spanwise-invariant separation bubbles

 Pulsed-wire measurements of wall shear stress have been made beneath two separation bubbles. In one a cross flow was generated by means of a (25°) swept separation line. Fluctuating stresses in orthogonal “streamwise” and cross-flow directions are very nearly equal and independent of at least moderate cross flow velocity. These fluctuations are largely determined by large-scale motions in the outer flow, whereas the mean shear stresses are not. The pdf of the “streamwise” fluctuations is unchanged by the cross flow. When a cross flow is present the pdf of the cross-flow stresses is similar to the “streamwise” pdf. Dependence on Reynolds number is the same in both flows. Received: 10 April 1998/Accepted: 17 July 1998     

Flow visualization and wall shear stress of a flapping model hummingbird wing

The unsteady low Reynolds number aerodynamics of flapping flight was investigated experimentally through flow visualization by suspended particle imagery and wall shear stress measurement from micro-array hot-film anemometry. In conjunction, a mechanism was developed to create a flapping motion with three degrees of freedom and adjustable flapping frequency. The flapping kinematics and wing shape were selected for dynamic similarity to a hummingbird during hovering flight. Flow visualization was used to validate the anemometry observations of leading edge vortex (LEV) characteristics and to investigate the necessity of spanwise flow in LEV stability. The shear sensors determined LEV characteristics throughout the translation section of the stroke period for various wing speeds. It was observed that a minimum frequency between 2 and 3.5 Hz is required for the formation and stabilization of a LEV. The vortex strength peaked around 30% of the flapping cycle (corresponding to just past the translation midpoint), which agrees with results from previous studies conducted by others. The shear sensors also indicated a mild growth in LEV size during translation sections of the wing’s motion. This growth magnitude was nearly constant through a range of operating frequencies.     

Experimental study of a wall shear stress sensor based on a porous element

The paper presents a new type of local wall shear stress sensor made of a high-porosity material with filter grade 40 n. The pressure variation caused by the shear stress acting on the surface can be transferred in this porous material, while the effect of the momentum change of the fluid is eliminated. Having neither protrusions nor cavities on the wall surface, the sensor presents little disturbance of the measured boundary layer. A pressure difference reading of the sensor is directly proportional to the local wall shear stress and the wall shear stress can be written as = C P. The present investigation also deals with problems of sensor design and its influence on the performance of the sensor.List of symbols angle - density of fluid - kinematic viscosity of fluid - local wall shear stress - ₀ shear stress for the smooth surface - _P shear stress for the porous element - _po shear stress on the surface of the porous element - _p y ₀/2 _p at a certain depthy ₀/2 - pore-surface area ratio of the porous surface - dynamic viscosity - a length of the porous element surface - A height of the duct with rectangular cross-section - b width of the porous surface - B width of the duct with rectangular cross-section - c thickness of the porous element - C, C ₁ constants - D _h hydraulic diameter of the duct - L, l length or distance - P pressure, see Fig. 3 - P ₀ static pressure at wall - P differential pressure, P-P ₀ - P _l differential pressure over length l - F force - u velocity component parallel to surface at distance y - v _p velocity in the porous element - v _po velocity on the surface of the porous element - x, x ₀ distance - y ₀ height of the rectangular passage     

Effect of tube diameter on Preston tube calibration curves for the measurement of wall shear stress

The effect of tube diameter (d) on Preston tube calibration curves for the measurement of wall shear stress (τ_w) in a zero pressure gradient turbulent boundary layer has been investigated. Five different outside diameter tubes of 1.46, 1.82, 3.23, 4.76 and 5.54 mm, corresponding to (d/δ) of 0.022, 0.027, 0.048, 0.071 and 0.082 were used to measure τ_w at Reynolds numbers based on momentum thickness (R_θ) of 2800–4100. The calibration curves of Patel (V.C. Patel, J. Fluid Mech. 23 (part I) (1965) 185–208) and Bechert (D.W. Bechert, AIAA J. 34 (1) (1995) 205–206) are both dependent on the tube diameter. The maximum difference in the τ_w measurements from the different tubes using Patel's calibration is about 8%, while Bechert's calibration gives a maximum difference of approximately 18%.     

Experimental investigation of the wall shear stress and the vortex dynamics in a circular impinging jet

The wall shear stress and the vortex dynamics in a circular impinging jet are investigated experimentally for Re = 1,260 and 2,450. The wall shear stress is obtained at different radial locations from the stagnation point using the polarographic method. The velocity field is given from the time resolved particle image velocimetry (TR‐PIV) technique in both the free jet region and near the wall in the impinging region. The distribution of the momentum thickness is also inspected from the jet exit toward the impinged wall. It is found that the wall shear stress is correlated with the large-scale vortex passing. Both the primary vortices and the secondary structures strongly affect the variation of the wall shear stress. The maximum mean wall shear stress is obtained just upstream from the secondary vortex generation where the primary structures impinge the wall. Spectral analysis and cross-correlations between the wall shear stress fluctuations show that the vortex passing influences the wall shear stress at different locations simultaneously. Analysis of cross-correlations between temporal fluctuations of the wall shear stress and the transverse vorticity brings out the role of different vortical structures on the wall shear stress distribution for the two Reynolds numbers.     

Cycle-to-cycle variation effects on turbulent shear stress measurements in pulsatile flows

Accurate evaluation of turbulent velocity statistics in pulsatile flows is important in estimating potential damage to blood constituents from prosthetic heart valves. Variations in the mean flow from one cycle to the next can result in artificially high estimates. Here we demonstrate a procedure using a digital, low-pass filter to remove the cycle-to-cycle variation from turbulence statistics. The results show that cycle-to-cycle variations can significantly affect estimates of turbulent Reynolds stress and should be either eliminated or demonstrated to be small when reporting pulsatile flow results.List of symbols D inside diameter of aortic valve - R radius of model aorta - t time window - t time - T period of cycle - T duration of outflow pulse from ventricle - U instantaneous axial velocity - U _L low-pass axial velocity - U _p mean periodic axial velocity - U ensemble averaged axial velocity - uv ensemble-average turbulent velocity product - u root-mean-square of turbulent axial velocity - U _max maximum, ensemble-averaged axial velocity - V instantaneous radial velocity - y vertical distance from aorta centerline - z axial distance downstream of prosthetic heart valve This paper was presented at the Tenth Symposium on Turbulence, University of Missouri-Rolla, Sept. 22–24, 1986     

Rheology of shear thickening suspensions and the effects of wall slip in torsional flow

The rheological characterisation of concentrated shear thickening materials suspensions is challenging, as complicated and occasionally discontinuous rheograms are produced. Wall slip is often apparent and when combined with a shear thickening fluid the usual means of calculating rim shear stress in torsional flow is inaccurate due to a more complex flow field. As the flow is no longer “controlled”, a rheological model must be assumed and the wall boundary conditions are redefined to allow for slip. A technique is described where, by examining the angular velocity response in very low torque experiments, it is possible to indirectly measure the wall slip velocity. The suspension is then tested at higher applied torques and different rheometer gaps. The results are integrated numerically to produce shear stress and shear rate values. This enables the measurement of true suspension bulk flow properties and wall slip velocity, with simple rheological models describing the observed complex rheograms.     

一种确定均匀动脉壁面切应力的非线性方法

从Ling和Atabek提出的``局部流'理论出发，提出一种利用测量血液黏度、管轴上 的血流速度、压力和管径波形计算均匀动脉管壁切应力的非线性方法. 将这种方法与柳兆荣 等提出的利用测量血液黏度、管轴上的血流速度和平均管径计算切应力的线性方法比较，结 果表明，当管壁脉动幅度较小时，两种方法计算的压力梯度、流速剖面和管壁切应力差别较 小；而当管壁脉动幅度增大时，两种方法计算的压力梯度、流速剖面和管壁切应力差别增大. 对于小幅脉动均匀动脉，用线性方法计算管壁切应力有较高的精度；而对于大变形 均匀动脉，则需要考虑非线性因素对管壁切应力的影响. 由于作为输入量的血液黏度、轴心 血流速度、压力波形和管径波形可在活体上通过无损伤或微损伤的检测方法得到， 所提出的计算切应力的方法为在体或离体研究切应力与动脉重建的关系提供了方法学基础.     

Weakly nonlinear long waves in a prestretched Blatz-Ko cylinder: Solitary, kink and periodic waves

This paper studies nonlinear waves in a prestretched cylinder composed of a Blatz-Ko material. Starting from the three-dimensional field equations, two coupled PDEs for modeling weakly nonlinear long waves are derived by using the method of coupled series and asymptotic expansions. Comparing with some other existing models in literature, an important feature of these equations is that they are consistent with traction-free surface conditions asymptotically. Also, the material nonlinearity is kept to the third order. As these two PDEs are quite complicated, the attention is focused on traveling waves, for which a first-order system of ODEs are obtained. We use the technique of dynamical systems to carry out the analysis. It turns out that the system is three parameters (the prestretch, the propagating speed and an integration constant) dependent and there are totally seven types of phase planes which contain trajectories representing bounded traveling waves. The parametric conditions for each phase plane are established. A variety of solitary and periodic waves are found. An important finding is that kink waves can propagate in a Blatz-Ko cylinder. We also find that one type of periodic waves has an interesting feature in the profile slope. Analytical expressions for all bounded traveling waves are obtained.     

Reverse shear on inclined planes at the tip of a sharp crack

Plane strain plastic yielding at a crack tip has been represented by edge dislocations with Burgers vectors parallel to symmetrical planes inclined at 70° and 45° to the plane of the crack. The plastic displacement and the stresses near the crack tip were calculated by a numerical method and the effect of a reduction in applied stress was determined. Removal of the whole or a part of the initial load produces reverse shear in regions of the slip band nearest the crack tip. The amount of reverse shear depends only on the reduction in the load and not on its initial value. The reverse shear is associated with the presence of negative dislocations and the stresses near the crack tip may become compressive even though the applied (remote) stress is still tensile. The degree and extent of compression depends on the reduction in applied stress and on its original value. It is argued that the residual compressive stresses produced under fluctuating loads may produce crack closure and crack arrest. The effect of residual plasticity in a slip band left behind a growing crack has been estimated. It is shown that after an overload the excess residual plasticity opposing crack opening rises to a maximum value when the crack tip has advanced some distance from the point where the overload was applied.