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The structure of a separating turbulent boundary layer. Part 3. Transverse velocity measurements
- K. Shiloh, B. G. Shivaprasad, R. L. Simpson
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- Journal:
- Journal of Fluid Mechanics / Volume 113 / December 1981
- Published online by Cambridge University Press:
- 20 April 2006, pp. 75-90
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Simpson, Chew & Shivaprasad (1981a, b) describe many experimentally determined features of a separating turbulent boundary layer. For the same flow, experimental results for the transverse velocity component are presented here. A specially designed directionally sensitive laser anemometer was constructed and used to make measurements in the separated region. Cross-wire hot-wire anemometer measurements were obtained upstream of separation and in the outer region of the separated flow and are in good agreement with the laser anemometer results.
It was found that w’2 = v’2 in the outer 90% of the shear layer both upstream and downstream of separation. Features of w’2 profiles in the backflow are related to features of the streamwise velocity component. This behaviour is consistent with the large-scale-structures flow model of a separating boundary layer presented by Simpson et al. (1981a, b).
Large-scale structures supply the mean streamwise backflow. These large-scale structures also transport the turbulence energy to the backflow from the outer flow by turbulent diffusion since advection and production of turbulence kinetic energy are negligible there compared with the dissipation rate. Because of continuity requirements fluid motions toward the wall must be deflected and contribute to streamwise and transverse motions near the wall.
The structure of a separating turbulent boundary layer. Part 4. Effects of periodic free-stream unsteadiness
- Roger L. Simpson, B. G. Shivaprasad, Y.-T. Chew
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- Journal:
- Journal of Fluid Mechanics / Volume 127 / February 1983
- Published online by Cambridge University Press:
- 20 April 2006, pp. 219-261
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Unsteady separating turbulent boundary layers are of practical interest because of unsteady aerodynamic phenomena associated with blades in compressors and with helicopter rotors in translating motion during high-loading conditions. Extensive measurements of a steady free-stream, nominally two-dimensional, separating turbulent boundary layer have been reported by Simpson, Chew & Shivaprasad (1981a, b) and Shiloh, Shivaprasad & Simpson (1981). Here measurements are reported that show the effects of sinusoidal unsteadiness of the free-stream velocity on this separating turbulent boundary layer at a practical reduced frequency of 0·61. The ratio of oscillation amplitude to mean velocity is about 0·3.
Upstream of flow detachment, single- and cross-wire, hot-wire anemometer measurements were obtained. A surface hot-wire anemometer was used to measure the phase-averaged skin friction. Measurements in the detached-flow zone of phase-averaged velocities and turbulence quantities were obtained with a directionally sensitive laser anemometer. The fraction of time that the flow moves downstream was measured by the LDV and by a thermal flow-direction probe.
Upstream of any flow reversal or backflow, the flow behaves in a quasisteady manner, i.e. the phase-averaged flow is described by the steady free-stream flow structure. The semilogarithmic law-of-the-wall velocity profile applies at each phase of the cycle. The Perry & Schofield (1973) velocity-profile correlations fit the mean and ensemble-averaged velocity profiles near detachment.
After the beginning of detachment, large amplitude and phase variations develop through the flow. Unsteady effects produce hysteresis in relationships between flow parameters. As the free-stream velocity during a cycle begins to increase, the Reynolds shearing stresses increase, the detached shear layer decreases in thickness, and the fraction of time $\hat{\gamma}_{{\rm p}u}$ that the flow moves downstream increases as backflow fluid is washed downstream. As the free-stream velocity nears the maximum value in a cycle, the increasingly adverse pressure gradient causes progressively greater near-wall backflow at downstream locations, while $\hat{\gamma}_{{\rm p}u}$ remains high at the upstream part of the detached flow. After the free-stream velocity begins to decelerate, the detached shear layer grows in thickness and the location where flow reversal begins moves upstream. This cycle is repeated as the free-stream velocity again increases.
The structure of a separating turbulent boundary layer. Part 5. Frequency effects on periodic unsteady free-stream flows
- Roger L. Simpson, B. G. Shivaprasad
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- Journal:
- Journal of Fluid Mechanics / Volume 131 / June 1983
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- 20 April 2006, pp. 319-339
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Measurements of a steady free-stream, nominally two-dimensional, separating turbulent boundary layer have been reported in earlier parts of this work. Here measurements are reported that show the effects of frequency on sinusoidal unsteadiness of the free-stream velocity on this separating turbulent boundary layer at reduced frequencies of 0.61 and 0.90. The ratio of oscillation amplitude to mean velocity is about 1/3 for each flow.
Upstream of flow detachment, hot-wire anemometer measurements were obtained. A surface hot-wire anemometer was used to measure the phase-averaged skin friction. Measurements in the detached-flow zone of phase-averaged velocities and turbulence quantities were obtained with a directionally sensitive laser anemometer. The fraction of time that the flow moves downstream was measured by the LDV and by a thermal flow-direction probe.
Upstream of any flow reversal or backflow, each flow behaves in a quasisteady manner, i.e. the phase-averaged flow is described by the steady free-stream flow structure. The semilogarithmic law-of-the-wall velocity profiles applies at each phase of the cycle. The Perry & Schofield (1973) velocity-profile correlations fit the mean and ensemble-averaged velocity profiles near detachment.
After the beginning of detachment, large amplitude and phase variations develop through each flow. Unsteady effects produce hysteresis in relationships between flow parameters. As the free-stream velocity during a cycle begins to increase, the detached shear layer decreases in thickness, and the fraction of time $\hat{\gamma}_{{\rm p}u} $ that the flow moves downstream increases as backflow fluid is washed downstream. As the free-stream velocity nears the maximum value in a cycle, the increasingly adverse pressure gradient causes progressively greater near-wall backflow at downstream locations while $\hat{\gamma}_{{\rm p}u}$ remains high at the upstream part of the detached flow. After the free-stream velocity begins to decelerate, the detached shear layer grows in thickness, and the location where flow reversal begins moves upstream. This cycle is repeated as the free-stream velocity again increases.
In both unsteady flows, the ensemble-averaged detached-flow velocity profiles agree with steady free-stream profiles for the same $\hat{\gamma}_{{\rm p}u\min} $ value near the wall when $\partial\hat{\gamma}_{{\rm p}u\min}/\partial\hat{t} < 0 $. However, the reduced-frequency k = 0.90 flow has much larger hysteresis in ensemble-averaged velocity profile shapes when $\partial\hat{\gamma}_{{\rm p}u\min}/\partial{t} \geqslant 0 $. Larger and negative values of the profile shape factor $\hat{H}$ occur for this flow during phases when the non-dimensional backflow is greater and $\hat{\gamma}_{{\rm p}u\min}\rightarrow 0.01$.
The instantaneous structure of mildly curved turbulent boundary layers
- B. R. Ramaprian, B. G. Shivaprasad
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- Journal:
- Journal of Fluid Mechanics / Volume 115 / February 1982
- Published online by Cambridge University Press:
- 20 April 2006, pp. 39-58
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Even mild longitudinal wall curvature is known to produce significant effects on the time-averaged turbulent transport in a boundary layer. The present study was undertaken to study the manner in which the instantaneous structure of turbulence in the boundary layer responds to mild streamline curvature. Both convex and concave boundary layers with a boundary-layer thickness to wall radius ratio of about 0·01 were studied. Attention was directed mainly to two events characterizing the instantaneous turbulence structure. These were the so-called ‘bursting’ and ‘zero-crossing’. Quantitative data on the statistics of these events were obtained using a combination of analog instrumentation and visual counting (from continuous film records). These data were compared with data from flat-wall boundary layers obtained from similar signal-processing techniques. The results indicate that neither the individual nor the joint statistics of these events are significantly affected by curvature in the vicinity of the wall. On the other hand, curvature seems to affect appreciably at least some properties of these events at large distances from the wall. Careful examination of these results shows, however, that neither the process of turbulent production near the wall nor the turbulent dissipative process anywhere in the boundary layer is significantly affected by mild curvature. Apparent curvature effects on the instantaneous structure in the outer part of the boundary layer can be explained as being due to the strong effect of streamline curvature on the turbulent diffusion process. This explanation is consistent with previous observations of the time-averaged structure of the flow. The results of the present study indicate the need to re-examine some of the recent turbulence models for curved flows that involve modification of the production and dissipation terms rather than the diffusion term in the transport equations.
The structure of a separating turbulent boundary layer. Part 2. Higher-order turbulence results
- Roger L. Simpson, Y.-T. Chew, B. G. Shivaprasad
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- Journal:
- Journal of Fluid Mechanics / Volume 113 / December 1981
- Published online by Cambridge University Press:
- 20 April 2006, pp. 53-73
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The velocity-probability-distribution flatness and skewness factors for u and v are reported for the separating turbulent boundary layer described by Simpson, Chew & Shivaprasad (1981). Downstream of separation the skewness factor for u is negative near the wall, whereas it is positive upstream of separation. The flatness factor for u downstream of separation differs from the upstream behaviour in that it has a local maximum of about 4 at the minimum mean velocity location in the backflow. Both upstream and downstream of separation the skewness factor for v has a profile shape and magnitudes that are approximately the mirror image or negative of the skewness factor for u. The flatness factor for v seems to be affected little by separation.
Examination of the momentum and turbulence-energy equations reveals that the effects of normal stresses are important in a separating boundary layer. Negligible turbulence-energy production occurs in the backflow. Turbulence-energy diffusion is increasingly significant as separation is approached and is the mechanism for supplying turbulence energy to the backflow.
The backflow appears to be controlled by the large-scale eddies in the outer region flow, which provides the mechanism for turbulence-energy diffusion. The backflow behaviour does not appear to be significantly dependent on the far downstream near-wall conditions when the thickness of the backflow region is small compared with the turbulent shear layer thickness.
The structure of a separating turbulent boundary layer. Part 1. Mean flow and Reynolds stresses
- Roger L. Simpson, Y.-T. Chew, B. G. Shivaprasad
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- Journal:
- Journal of Fluid Mechanics / Volume 113 / December 1981
- Published online by Cambridge University Press:
- 20 April 2006, pp. 23-51
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The problem of turbulent-boundary-layer separation due to an adverse pressure gradient is an old but still important problem in many fluid flow devices. Until recent years little quantitative experimental information was available on the flow structure downstream of separation because of the lack of proper instrumentation. The directionally sensitive laser anemometer provides the ability to measure the instantaneous flow direction and magnitude accurately.
The experimental results described here are concerned with a nominally two-dimensional, separating turbulent boundary layer for an airfoil-type flow in which the flow was accelerated and then decelerated until separation. Upstream of separation single and cross-wire hot-wire anemometer measurements are also presented. Measurements in the separated zone with a directionally sensitive laser-anemometer system were obtained for U, V, $\overline{u^2}, \overline{v^2}, - \overline{uv}$, the fraction of time that the flow moves downstream, and the fraction of time that the flow moves away from the wall.
In addition to confirming the earlier conclusions of Simpson, Strickland & Barr (1977) regarding a separating airfoil-type turbulent boundary layer, much new information about the separated region has been gathered. (1) The backflow mean velocity profile scales on the maximum negative mean velocity UN and its distance from the wall N. A U+vs. y+ law-of-the-wall velocity profile is not consistent with this result. (2) The turbulent velocities are comparable with the mean velocity in the backflow, although low turbulent shearing stresses are present. (3) Mixing length and eddy viscosity models are physically meaningless in the backflow and have reduced values in the outer region of the separated flow.
Downstream of fully developed separation, the mean backflow appears to be divided into three layers: a viscous layer nearest the wall that is dominated by the turbulent flow unsteadiness but with little Reynolds shearing stress effects; a rather flat intermediate layer that seems to act as an overlap region between the viscous wall and outer regions; and the outer backflow region that is really part of the large-scaled outer region flow. The Reynolds shearing stress must be modelled by relating it to the turbulence structure and not to local mean velocity gradients. The mean velocities in the backflow are the results of time averaging the large turbulent fluctuations and are not related to the source of the turbulence.
The structure of turbulent boundary layers along mildly curved surfaces
- B. R. Ramaprian, B. G. Shivaprasad
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- Journal:
- Journal of Fluid Mechanics / Volume 85 / Issue 2 / 21 March 1978
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- 12 April 2006, pp. 273-303
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This paper describes a detailed study of the structure of turbulence in boundary layers along mildly curved convex and concave surfaces. The surface curvature studied corresponds to δ/Rw = ± 0·01, δ being the boundary-layer thickness and Rw the radius of curvature of the wall, taken as positive for convex and negative for concave curvature. Measurements of turbulent energy balance, autocorrelations, auto- and cross-power spectra, amplitude probability distributions and conditional correlations are reported. It is observed that even mild curvature has very strong effects on the various aspects of the turbulent structure. For example, convex curvature suppresses the diffusion of turbulent energy away from the wall, reduces drastically the integral time scales and shifts the spectral distributions of turbulent energy and Reynolds shear stress towards high wavenumbers. Exactly opposite effects, though generally of a smaller magnitude, are produced by concave wall curvature. It is also found that curvature of either sign affects the v fluctuations more strongly than the u fluctuations and that curvature effects are more significant in the outer region of the boundary layer than in the region close to the wall. The data on the conditional correlations are used to study, in detail, the mechanism of turbulent transport in curved boundary layers.