Instantaneous Reversals Research Articles

Non-periodic phase-space trajectories of roughness-driven secondary flows in high- boundary layers and channels

Turbulent flows respond to bounding walls with a predominant spanwise heterogeneity – that is, a heterogeneity parallel to the prevailing transport direction – with formation of Reynolds-averaged turbulent secondary flows. Prior experimental and numerical work has determined that these secondary rolls occur in a variety of arrangements, contingent only upon the existence of a spanwise heterogeneity (i.e. from complex, multiscale roughness with a predominant spanwise heterogeneity, to canonical step changes, to different roughness elements). These secondary rolls are known to be a manifestation of Prandtl’s secondary flow of the second kind: driven and sustained by the existence of spatial heterogeneities in the Reynolds (turbulent) stresses, all of which vanish in the absence of spanwise heterogeneity. Herein, we show results from a suite of large-eddy simulations and complementary experimental measurements of flow over spanwise-heterogeneous surfaces. Although the resultant secondary cell location is clearly correlated with the surface characteristics, which ultimately dictates the Reynolds-averaged flow patterns, we show the potential for instantaneous sign reversals in the rotational sense of the secondary cells. This is accomplished with probability density functions and conditional sampling. In order to address this further, a base flow representing the streamwise rolls is introduced. The base flow intensity – based on a leading-order Galerkin projection – is allowed to vary in time through the introduction of time-dependent parameters. Upon substitution of the base flow into the streamwise momentum and streamwise vorticity transport equations, and via use of a vortex forcing model, we are able to assess the phase-space evolution (orbit) of the resulting system of ordinary differential equations. The system resembles the Lorenz system, but the forcing conditions differ intrinsically. Nevertheless, the system reveals that chaotic, non-periodic trajectories are possible for sufficient inertial conditions. Poincaré projection is used to assess the conditions needed for chaos, and to estimate the fractal dimension of the attractor. Its simplicity notwithstanding, the propensity for chaotic, non-periodic trajectories in the base flow model suggests similar dynamics is responsible for the large-scale reversals observed in the numerical and experimental datasets.

Turbulent flow downstream of a large solidity perforated plate: near-field characteristics of interacting jets

Measurements of streamwise velocity characteristics in a flow downstream of a perforated plate with 96% solidity were obtained using a single-component laser Doppler system. The channel bulk velocity was 1 m s−1, the diameter D of the holes was 5 mm and the Reynolds number of the flow through the holes was around 10 000. The results are presented in terms of profiles of the mean and rms of streamwise velocity, their decay behaviour on the jet centre line, probability density functions (PDFs) of velocity fluctuations, velocity autocorrelation functions and integral time scales. In comparison with the literature data, the mean velocity decay on the centre line was much larger than that for a free jet but smaller than that for a confined jet. There was a mean reverse flow between the jets, and instantaneous reverse flow events were found also on the centre line of the jets. These were quantified based on the PDF of velocities, and at streamwise position x/D = 12 around 5% of the flow events on the centre line of the jet had negative streamwise velocities. Flow visualizations and laser Doppler anemometer measurements showed that this reverse flow is highly turbulent, and suggest that the penetration of a turbulent fluid is larger than that of a laminar or low-turbulence fluid. Finally, the consequences of the instantaneous flow reversals for droplet injection downstream of the perforated plate were analysed, and it was estimated that a small fraction of 10 μm water droplets injected at x/D = 12 could reverse their direction of flight and deposit on the plate.

Turbulent flow in the near field of a round impinging jet

This paper reports on detailed measurements of the turbulent flow in the stagnation region of a single impinging jet issuing from a round pipe with diameter D and a length of 76 D. The distance between the pipe exit and the flat impingement plate is 2 D, and the Reynolds number (based on the bulk velocity and pipe diameter) is 2.3 × 10 4. Mean velocity components and Reynolds stresses were determined by using a two-component LDA. A modified one-component LDA was used to perform near-wall measurements with minimum wall distances of approximately 40 μm. PIV measurements were taken in a small field of view (approximately 4 × 5 mm 2) to study instantaneous reversals in the near wall region.

Factors influencing the ability to detect motion reversals in rotation simulations.

Five experiments probed the conditions under which observers fail to report instantaneous reversals in the direction of motion of pixels that define the rotation of a transparent sphere or plane. Our results showed that the extent to which rotation reversals were not reported depended upon whether observers used strict or lax criteria to make their judgments, the degree of perspective present in the rotation simulations, and the percentage of pixels that actually reversed direction. Furthermore, we found failures to report rotation reversals both with stimuli whose pixels were confined to smooth surfaces and scattered within volumes. Reversal detection with planar stimuli, unlike sphere stimuli, depended upon the orientation of the stimulus at the moment of reversal. Treue et al. (1995) postulated a surface-interpolation process as the explanation for the apparent insensitivity of observers to such reversals. However, we suggest that other stages of processing (e.g. a structure-from-motion process) are required to account for these results.

Coulomb Friction Limit Cycles in Elastic Positioning Systems

The state space control of a positioning system affected by torsional elasticity at the gearbox is considered, using a motor position transducer only. An output feedback, pole placement controller is used, with an additional integral action on the tracking error to cancel it at steady state. Both experiments and simulations point out that large oscillations may appear for some sets of closed-loop poles which yields, in contrast to stick-slip cycles, instantaneous motor velocity reversals. It is shown that such oscillations are induced by “pure” Coulomb friction. The period of the oscillations is predicted precisely following the Tsypkin’s relay control theory and also by the approximate describing function method. The latter also allows understanding of how oscillations depend on observer and feedback control design and on plant parameters; thus we are able to derive guidelines for the design of an oscillation free closed-loop system.

Turbulent flow in a conical diffuser: A review

This is a review of experimental studies of turbulent flow in a conical diffuser by eight Ph.D. students, eleven M.Sc. students, one M.Eng. student, and myself in the past 29 years. During this time, two conical diffusers were constructed: the first was of cast aluminum construction, and the second was of plastic fabrication. These two diffusers were basically the same in geometry except that the pipe section was constructed as an integral part of the plastic diffuser to avoid the lip at the junction of the inlet pipe and the diffuser. The conical diffuser had a total divergence angle of 8°, an area ratio of 4:1, and an inlet diameter of 0.1016 m (4 in.). The flow at the inlet of the diffuser was usually fully developed pipe flow, but sometimes it was boundary layer grown on the pipe wall. Hot-wire and pulse-wire anemometry together with computer facilities were used to obtain the results of complex flow present in the conical diffuser. Mean velocity profiles were obtained throughout the diffuser, which in turn were used to obtain strain rates and their principal direction. Turbulence moments up to fourth order were measured. The results were used to assess momentum, turbulent kinetic energy, and shear stress equations. Other features such as instantaneous flow reversals in the wall region, relative strength of large eddies, extra strain rate, and the production of kinetic energy also were investigated to find the dynamical picture in the diffuser flow.

Structure of Turbulence in an Incipient-Separating Axisymmetric Flow

The relative intensity, skewness, and flatness of fluctuating streamwise velocity along the centerline of an 8 deg included angle conical diffuser show dramatic rapid growth in the final stages of the flow under the increasing influence of growing instantaneous reversals in the wall-layer. Pulsed-wire anemometry was effectively used for the measurement of quantitative instantaneous reversals and the turbulent flow field. In the severe adverse pressure gradient of the diffuser flow, the maxima of the streamwise and transverse fluctuating velocities, Reynolds shear stress, and turbulent energy production coincide and move away from their near-wall position in the pipe, also the velocity triple products show completely opposite nature as compared to the pipe flow. These measurements reveal the strong influence of instantaneous backflow on the structure of turbulence. The present results further corroborate the ability of the “structural” turbulence model of Nagano and Tagawa (1990) to predict velocity triple products in an axisymmetric diffuser flow.

Behavior of mean and fluctuating skin friction in a conical diffuser with instantaneous flow reversals

Measurements were made of the mean and fluctuating skin friction in an 8° total divergence angle conical diffuser using modern pulsed-wire anemometry. The development of streamwise and spanwise fluctuating skin friction, skewness and flatness factors of streamwise skin friction, and probability density distribution of the wall shear stress show the rapidly changing nature and complexity of the wall layer turbulence structure in an axisymmetric severe adverse pressure gradient flow. The relative intensities of skin friction increase consistently and achieve very high values in the final stages of diffuser flow. The quantitative instantaneous backflow and the mean and fluctuating skin friction distributions were examined to determine their interrelationship. The initiation of instantaneous reversals was found to strongly influence the near-wall flow field and to coincide with the precipitous drop in skewness factor of the streamwise fluctuating wall shear stress, to approximately 10% of its initial value near the diffuser inlet. The flatness factor of the streamwise fluctuating wall shear stress also decreases in the latter stages, indicating a lesser inrush of high-velocity fluid from the central region. Comparison with conventional Preston tube data indicated the appropriateness of pulsed-wire skin friction measurements in severe adverse pressure gradient flows. In this diffuser the minimum streamwise wall shear stress near the diffuser exit is close to 3% of its inlet value, indicating that the flow approaches mean-flow separation. The present results of mean and fluctuating skin friction also differ substantially from those reported by other investigators using hot-film anemometry, both in level and shape of profiles. The differences are attributed to the rectification errors in hot-film anemometry at high turbulence intensities (near-wall turbulence level over 80%) and the appreciable instantaneous backflow (instantaneous reversals up to 30% of the time) present in the final stages of conical diffuser flow.

Measurement of instantaneous flow reversals and velocity field in a conical diffuser

An 8° total divergence angle conical diffuser fed with a fully developed turbulent pipe flow at its inlet was experimentally investigated. Through effective use of pulsed-wire anemometry, some quantitative information about instantaneous reversals was obtained in conical diffuser flow. Profiles of streamwise mean and fluctuating velocities, skewness factor, and flatness factor are presented for the stations in the final stages of the diffuser flow, where appreciable instantaneous reversals were detected in the wall region. Results are also presented for the stations in the earlier stages of the diffuser, where smaller instantaneous backflow was present. Comparative results of conventional pressure measurements and hot-wire anemometer measurements were obtained to determine quantitatively the effects of instantaneous flow reversals on these techniques. In the regions of instantaneous backflow, the pulsed-wire technique was found most accurate for measuring the mean and fluctuating velocities. The hot-wire and pulsed-wire anemometer results were also used to obtain guidelines for hot-wire use in highly turbulent instantaneously reversing flows. The integral constraint of continuity was used at the diffuser stations to evaluate measurement techniques for obtaining mean velocity in a conical diffuser flow. The distributions of streamwise mean and fluctuating wall shear stress were measured with a pulsed-wire skin friction probe. Pulsed-wire wall shear stress probe results indicated serious errors in the values of the mean wall shear stress obtained by the conventional Preston tube in the region of appreciable instantaneous backflow. Some of the separation prediction criteria reported in the literature were evaluated for their validity using the present results of quantitative instantaneous backflow. These measurements illustrate important characteristics of instantaneous flow reversals and the velocity field in the highly turbulent axisymmetric flow developing under a severe adverse pressure gradient.

The structure of instantaneous reversals in highly turbulent flows

Structure of instantaneous flow reversals has been measured in a highly turbulent axisymmetric diffuser flow using pulsed-wire anemometry. In this 8° nominal included angle conical diffuser, the adverse pressure gradient (APG) is strong enough to cause appreciable instantaneous flow reversals (instantaneous backflow up to 30% of the time), but the time-averaged flow is non-separated. The results are compared with the other severe APG separating flows reported in literature. An increase in entry Reynolds number indicated a decrease in the size of near-wall instantaneous reversals region as well as a decrease in the magnitude of instantaneous backflow. Also, the region of instantaneous reversals moves slightly downstream at appreciably higher Reynolds numbers. The initiation and growth of instantaneous reversals in a conical diffuser was found to strongly influence the wall-layer and the central region. Present results also suggest that the instantaneous backflow should be considered for modelling of instantaneously-separating diffuser flows. In the final stages of a conical diffuser, the magnitudes of cross-stream pressure gradient were found to be appreciably larger than that of the longitudinal pressure gradient, indicating that accurate representation of a conical diffuser flow can not be achieved without considering V-momentum equation. A comparison of various separating flows revealed remarkable similarity of instantaneous reversals regions and distributions even in different flow configurations.

Structure of large-scale vortices and unsteady reverse flow in the reattaching zone of a turbulent separation bubble

This paper describes experiments concerning the structure of large-scale vortices and the unsteady reverse-flow properties in the reattaching zone of a nominally two-dimensional separation bubble formed at the leading edge of a blunt flat plate with right-angled corners. The experiment was performed in a wind tunnel with a constant Reynolds number 2.6 × 104 (based on the main-flow velocity and the thickness of the plate). Split-film probes, being sensitive to instantaneous reversals of flow direction, were extensively employed. An important feature of this study is a judicious use of surface-pressure fluctuations as a conditioning signal to educe the structure of the large-scale vortices.Distributions of fluctuating-velocity vectors and contour lines of high-frequency turbulent energy in a few space–time domains are presented and discussed. The most economical interpretation of these space-time distributions is that the large-scale vortices in the reattaching zone are hairpin vortices whose configuration is sketched in the text. The unsteady flow in the reattaching zone is mainly governed by two agents; the motion of the large-scale vortices and the low-frequency unsteadiness. The unsteady flow is clarified in terms of the motion (in a space–time domain) of zeros of the longitudinal velocity close to the surface of the plate; the effects of the two agents on this motion are presented separately. On the basis of these results, a mathematical model of the unsteady flow in the reattaching zone is suggested and found to yield good comparison with measured reverse-flow intermittency and frequency of local-flow reversals. It appears that the separation bubble experiences shrinkage and enlargement in connection with the low-frequency unsteadiness and that the speed of shrinkage is much greater than that of enlargement. The strength of the large-scale vortices in the reattaching zone seems to be dependent on the phase of the low-frequency unsteadiness.

A New Probe for Measurement of Velocity and Wall Shear Stress in Unsteady, Reversing Flow

Separated turbulent flows exhibit instantaneous reversals of flow direction which make measurement of the velocity field extremely difficult. A three-wire heat-tracer technique has been employed to measure streamwise velocity of a low-speed air flow very near a smooth, solid wall; the wall shear stress is calculated using a similarity hypothesis. Initial results presented show the evolution of average wall shear stress and rms fluctuation intensity of wall shear stress in a reattaching 2-D flow downstream of a backward-facing step.

Paper 8: Torsional Oscillations in Distributor Fuel Injection Pump Drives

Torsional oscillations generally occur in the drive to a fuel injection pump and, depending on the drive arrangement and the conditions of operation, the maximum dynamic torque in the drive can be considerably in excess of the pumping torque. It is necessary to allow for this effect in the design of the engine, drive, and pump components. In this paper the methods of measuring the dynamic torque in the drive shaft and the instantaneous acceleration of the rotor of a distributor pump are described. Results of tests on two typical drive arrrangements, both on an engine and on a test machine, are then shown. A theoretical study is made of the drive system with backlash, and the results are compared with experimental values. It is shown that backlash in the drive can lead to high instantaneous torques and large torque reversals. A design of drive which eliminates backlash is described, and tests carried out on it confirm that the expected improvement is obtained.