Static pressure, mean velocity, indirect wall shear from Preston tubes, direct wall shear using a two-dimensional (single line of action) floating element device, and direct wall shear measurements from an omnidirectional floating element capable of simultaneously determining magnitude and direction of a wall shear vector were completed over a modest range of two-dimensional, (near-zero) pressure gradient flows. Static pressure, mean velocity, and direct wall shear measurements using the omnidirectional meter were completed in a pressure driven, and two different shear driven three-dimensional flows. These data were combined to evaluate ten of eleven three-dimensional similarity models found in the literature. Uncertainty estimates on all the data are presented. Two-dimensional experimental results show that the constants in the two-dimensional law of the wall formula appear to be slightly dependent on Reynolds number, and the Patel calibration formulas for Preston tubes to be better than any other available formulas. Three-dimensional results show (1) the Perry and Joubert and the White, Lessmann, and Christoph three-dimensional similarity models to give limited but overall better agreement with experimental data, (2) none of the proposed models adequately model experimental results for y⁺ < 50, (3) near-wall collateral flow does not exist, and (4) pressure gradient effects on the omnidirectional meter appear to be negligible. / Ph. D.

This thesis explores the effects of favourable pressure gradient on the structure of turbulent boundary layers (TBL). In this context, the structure of three types of boundary layers namely a zero-pressure-gradient boundary layer, equilibrium boundary layers under favourable pressure gradient and relaminarising boundary layers is investigated mostly from the point of view of large-scale dynamics. This covers a whole range of flows on the so-called Reynolds number - pressure gradient diagram - from turbulent zero pressure gradient flows to relaminarising flows at relatively low Reynolds numbers. The study of turbulent and relaminarising boundary layers is carried out primarily using direct numerical analyses and some limited experiments in this thesis. The direct numerical simulations (DNS) of a zero-pressure-gradient turbulent boundary layer (ZPG TBL) is validated against the experimental and DNS data available in the literature. Furthermore, the important question of time-averaged signature of a large scale vortex structure and its relation with the two-point correlations in the context of ZPG TBL is addressed. In this context, a synthetic flow consisting of hairpin vortex structures is generated. The two-point correlations in the synthetic TBL and a real TBL are found to be qualitatively similar. This shows that the vortex structure leaves a time-averaged footprint in the form of correlations of velocity and vorticity. A study of two-point correlations in a real TBL shows that the structure angle deduced from two-point correlations varies with wall-normal location. The structure angle is small near the wall and increases away from the wall in agreement with the previous studies. The small angle close to the wall signifies the presence of streamwise structure. Away from the wall, this streamwise coherence is lost and the correlation contours become more isotropic. The presence of the wall and the mean shear affects smaller scales making them anisotropic close to the wall. Towards the edge of the boundary layer, smaller scales tend to become isotropic leading to -5/3 law in the energy spectrum. Further, a relation between a passive scalar in a flow and vorticity is explored. It is found that the scalar product of vorticity and scalar gradient is conserved in a non-diffusive situation. This assertion is demonstrated under various flow conditions. Despite the differences in Schmidt numbers, the structures observed in the outer layer are similar in both numerical and experimental flow visualisations. Further, the equilibrium turbulent boundary layers under favourable pressure gradient are studied. The numerical simulations of equilibrium sink flow TBL are validated against the experimental results of Dixit (2010). A study of two-point correlations reveals that the near-wall structure angle decreases with a favourable pressure gradient in sink flow TBLs. In the outer region, the loss of streamwise coherence occurs at a wall-normal location closer to the wall than in an ZPG TBL. Edge intermittency study reveals that the flow is non-turbulent beyond y/δ = 0.8 inside the mean boundary layer edge. The variation of the ratio of pressure gradient to Reynolds shear stress gradient shows that this ratio is very large (> 50) beyond y/δ = 0.8. The dominance of pressure gradient makes this part of sink flow TBL to behave like a Euler-region. Small scales in sink flow TBL tend to be isotropic near the edge of the boundary layer and spectra shows -5/3 law akin to ZPG TBL, albeit at lower Reynolds numbers. The concept of equilibrium is extended to flows with wall transpiration. The sink flow TBL is a special case of more generalised equilibrium TBLs with wall transpiration. Conditions required for the flow with wall transpiration are derived. It is observed that there is a systematic variation of various statistical properties with wall velocity. Further, it is observed that the motion in these equilibrium flows is purely active like in sink flow TBL. In equilibrium TBL, the Reynolds shear stress is directly related to mean velocity. So we have at our disposal an exact relation between the Reynolds shear stress and the mean velocity gradient without the need to do any ad-hoc modelling for the sink flow. This is an interesting observation from the point of view of modelling TBLs using eddy-viscosity. Eddy-viscosity model derived from sink flow TBL data is found to predict the mean velocity profiles in flows with wall transpiration with a sufficient accuracy. Similarly, it is plausible that any general non-equilibrium flow may be treated as a departure from equilibrium. With suitable modifications, eddy viscosity obtained from equilibrium TBL may be used to model them without invoking ad-hoc assumptions. Finally, the effect of initial Reynolds number on the process of relaminarisation is studied numerically and experimentally. ZPG TBLs with two different initial Reynolds number are subjected to different degrees of acceleration. However, the pressure gradient history is same in both the cases. It is observed that the flow with a higher initial Reynolds number relaminarises at a lower pressure gradient value than the flow with a lower initial Reynolds number. Assessment of different parameter criteria reveals that the criterion proposed by Narasimha & Sreenivasan (1973) is appropriate for the prediction of the onset of relaminarisation. Further, the structures in relaminarising flows are studied. The near-wall structure angle is found to decrease with the increasing FPG and the streamwise length of the structure also increases. The low and high speed streaks in the near-wall region are found to become longer and less undulating with an increase in the spanwise spacing. A stabilisation mechanism of near-wall streaks is also presented which suggests that the kinematic effect of mean vertical velocity directed towards the wall is responsible for the stabilisation of streaks.

A study of the fluctuating wall pressure and unsteady velocity field in a flat plate turbulent boundary layer flow was conducted over a moderate range of Reynolds numbers to better understand the mechanisms by which the two fields are coupled. Individual and coincident measurements of the fluctuating pressure and velocity fields were acquired using a 20 element hydrophone array and a two-component Laser Doppler Anemometer, respectively. Estimates of the velocity power spectral density (PSD) revealed two primary trends predicted by turbulence theory, k⁻¹ in the region of (ky) = 10⁰ due to anisotropy of the large scales, and k⁻⁵/³ for larger values of (ky) where structures appear more isotropic. The mean velocity profiles, having been collapsed using outer scaling variables, exhibited the presence of a slightly adverse pressure gradient with a n = 6 power law shape. As for the fluctuating wall pressure, increased Reynolds numbers produced increases in the amplitude and frequency of the characteristic signatures from which the pressure spectral densities were also found to collapse reasonably well using outer scaling variables. The results suggest the location in the flow where the mechanisms responsible for driving the fluctuating wall pressure signatures reside. Space-time correlations and frequency-wavenumber analysis reveal a convective ridge in the fluctuating wall pressure corresponding to the passage of several organized structures at 75% of the free stream velocity for all Reynolds numbers tested. / text

Unsteady two-dimensional laminar flow of an incompressible viscous fluid over a periodically grooved wall is investigated by numerical simulation using two independent finite-difference methods. One is the vorticity-stream function method, and the other involves the vorticity-velocity induction law formulation. The fluid motion is initiated impulsively from rest and is assumed to be spatially periodic in the streamwise direction. The flow field, which includes the time development of the shear layer and the recirculating flow in the zone of separation, is examined in detail during the transient phase to the steady-state condition. The analytical and numerical formulations, which include the implementation of the boundary conditions, are derived in detail. The generation of vorticity at the solid surfaces is modelled differently in the two approaches. This vorticity production plays an important role in determining the surface-pressure distribution and the drag coefficient. Characteristics of the transient solution for a moderate Reynolds number in the laminar range are presented. Included with the graphical results are the temporal development of the constant stream function contours, including the dividing contour between the zone of separation and the main flow, and the constant vorticity contours. These latter contours show the interactions of separated vortices. The flow is found to approach a steady-state condition comprising an undisturbed uniform flow, a nonuniform irrotational flow, a shear layer adjacent to the grooved wall, and a recirculating vortex flow in the groove. Results also include the time development of the surface shear stress, surface pressure, drag coefficient and several typical velocity profiles, which characterize the flow in the recirculating region. Comparisons of the results obtained by the two numerical methods are made during the major development of the flow. The results showing the general features of the flow development including the time development of the shear layer, free shear layer and recirculating vortex flow are in good agreement. However, a significant deviation does exist at early times for the distribution of surface pressure, which accordingly has noticeable effect on the drag coefficient. Nevertheless, the gap between the distributions of surface pressure and drag coefficients dies out gradually as time progresses. The form of the stream function and vorticity contours at the steady state agrees well with those obtained from a recent numerical investigation of the steady flow in grooved channels.

A numerical model has been developed for investigating boundary layer transition control for a three-dimensional flat plate boundary layer. Control of a periodically forced boundary layer in an incompressible fluid is studied using surface heating techniques. The spatially evolving boundary layer is simulated. The Navier-Stokes and energy equations are integrated using a fully implicit finite difference/spectral method. The Navier-Stokes equations are in vorticity-velocity form and are coupled with the energy equation through the viscosity dependence on temperature. Both passive and active methods of control by surface heating are investigated. In passive methods of control, wall heating is employed to alter the stability characteristics of the mean flow. Both uniform and nonuniform surface temperature distributions are studied. In the active control investigations, temperature perturbations are introduced locally along finite heater strips to directly attenuate the instability waves in the flow. A feedback control loop is employed in which a downstream sensor is used to monitor wall shear stress fluctuations. Passive control of small amplitude two-dimensional Tollmien-Schlichting waves and three-dimensional oblique waves are numerically simulated with both uniform and nonuniform passive heating applied. Strong reductions in both amplitude levels and amplification rates are achieved. Active control of small amplitude two-dimensional and three-dimensional disturbances is also numerically simulated. With proper phase control, in phase reinforcement and out of phase attenuation is demonstrated. A receptivity study is performed to study how localized temperature perturbations are generated into Tollmien-Schlichting waves. It is shown that narrow heater strips are more receptive in that they maximize the amplitude level of the disturbances in the flow. It is also found that the local temperature fluctuations cause mainly a strong normal gradient in spanwise vorticity. Control of the early stages of the nonlinear breakdown process is also investigated. Uniform passive control is applied to both the fundamental and sub-harmonic routes to turbulence. A strong reduction in amplitude levels and growth rates results. In particular, the three-dimensional growth rates are significantly reduced below the uncontrolled levels. Active control of the fundamental breakdown process is also numerically simulated. Control is achieved using either a two-dimensional or three-dimensional control input.

The velocity and temperature fields of several air cavities have been surveyed. The cavities operated in the transitional boundary layer regime with vertical, opposing, isothermal heated and cooled walls. The cavity height, width, temperature difference and wall insulation were all changed during the study, with the aspect ratio varying from 4 to 10, and RaH varying from 2,263x10 to 4.486x101e. The local velocity and temperature were measured simultaneously using a laser Doppler anemometer and a 25jim chromel-alumel thermocouple. This allowed the turbulence quantity tT to be measured directly, as well as the mean and root mean square of the fluctuations of velocity and temperature. Several other quantities, which have not previously been available, were derived from the measured data, these were the wall shear stress, the mean lateral velocity, u'v', and v'T'. The effect of a decrease of the level of insulation on the vertical walls was to decrease the non-dimensional temperature of the fluid at the vertical centre-line. Different thermal boundary conditions on the horizontal walls resulted in significant differences between the heated and cooled wall, thermal and velocity, boundary layers. A decrease in the cavity width was seen to alter the characteristics of the mean velocity and temperature profiles when the width was less than twice the lateral extent of either boundary layer in a cavity with a larger width. Near wall distributions of u'v' have shown that the viscous sub-layer was approximately 4mm thick. Calculations of power spectral density, together with inspection of time histories, have confirmed that a laminar flow was present at the bottom of the heated wall. P.S.D. calculations showed that the dominant frequencies of transition were multiples of a base frequency and dependent on the local temperature drop between the wall and the "environment". The power relationship between frequency and power spectral density has been shown to depend on the local vertical temperature gradient. Three sub-ranges were identified in the velocity spectra, whereas four were identified in the temperature spectra. The equivalent ranges in the velocity and temperature spectra exhibited different powers on the frequency, with those of the temperature field being larger.

<div>The dynamic performance of the momentum and thermal boundary layer linked to the acoustic response dictate the efficiency of heat exchangers and the operational limits of fluid machinery. The specific time required by the boundary layer to establish or adapt to the free stream variations is vital to optimize flow control strategies as well as the thermal management of fluid systems. The proper understanding of the wall fluxes, separated flow regions and free stream response to transient conditions becomes the fulcrum of the further improvement of fluid machinery performance and endurance. Throughout this dissertation the establishment sequence and the main parameters dictating the acoustic response and the boundary layer settlement are quantified together with their implication on the wall fluxes and boundary layer detachment. </div><div><br></div><div>Unsteady Reynolds Average Navier Stokes evaluations, Large Eddy Simulations, Direct Numerical Simulations and wind tunnel experiments are exploited to analyze the transient behavior of attached and detached flow aerodynamics. The core of the research is built upon URANS simulations allowing the realization of multiple detailed parametric analyses. Thanks to its reduced computational cost, hundreds of transient flow evaluations are carried out, enabling the determination of the establishment sequence, the main flow features and relevant non-dimensional numbers. The URANS methodology is verified against experimental and analytic results on the flow conditions of the study. The Large Eddy Simulations and Direct Numerical Simulations allow further characterization of the near wall flow region behavior with much higher resolution while providing an additional source of verification for the coarser numerical tools. An experimental campaign on a novel full visual access linear wind tunnel explores the impact of mean flow sudden accelerations on the boundary layer detachment and reattachment phenomena over an ad-hoc wall mounted hump. The wind tunnel is designed based on the premises of: full visual access, spatial and temporal stability of total and static pressure together with the total temperature and fast flow settlement, minimizing the start-up phase duration of the wind tunnel. A wall mounted hump that mimics the behavior of the aft portion of a low pressure turbine is inserted in the wind tunnel guaranteeing a 2D flow separation phenomena. After steady state test article characterization series of sudden flow discharge experiments reveal the impact of mean flow transients on the boundary layer detachment inception. Finally, taking advantage of the knowledge on transient flow performance, optimum flow control mechanisms to abate boundary layer detachment are proposed. The recommended control approach effectively prevents the boundary layer separation while minimizing the energy requirement.</div>

Cheung Yin Har = 瑞利-柏納德湍流對流中Nusselt與縱橫比的關係以及邊界層性質的研究 / 張燕霞. / Thesis submitted in: October 2004. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2005. / Includes bibliographical references (leaves 115-119). / Text in English; abstracts in English and Chinese. / Cheung Yin Har = Ruili-Bonade tuan liu dui liu zhong Nusselt yu zong heng bi de guan xi yi ji bian jie ceng xing zhi de yan jiu / Zhang Yanxia. / Abstract --- p.i / 摘要 --- p.iii / Acknowledgments --- p.iv / Contents --- p.v / List of Figures --- p.vii / List of Tables --- p.x / Chapter Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Background of turbulence --- p.1 / Chapter 1.2 --- Rayleigh-Benard convection --- p.3 / Chapter 1.3 --- Theoretical background --- p.4 / Chapter 1.3.1 --- The convection equations --- p.4 / Chapter 1.3.2 --- Characteristic parameters --- p.6 / Chapter 1.3.3 --- Reynolds equations --- p.8 / Chapter 1.4 --- Recent developments --- p.10 / Chapter 1.4.1 --- Heat transport --- p.10 / Chapter 1.4.2 --- Large scale flow and thermal plumes --- p.11 / Chapter 1.4.3 --- Boundary layers --- p.12 / Chapter 1.5 --- Motivation --- p.14 / Chapter 1.5.1 --- Nusselt measurements --- p.14 / Chapter 1.5.2 --- Boundary layer properties measurements --- p.14 / Chapter 1.6 --- Synopsis of this thesis --- p.15 / Chapter Chapter 2 --- Experimental setup and measurement techniques --- p.17 / Chapter 2.1 --- The turbulent convection system --- p.17 / Chapter 2.1.1 --- The convection cells --- p.18 / Chapter 2.1.2 --- The temperature probe --- p.21 / Chapter 2.1.3 --- The thermistors --- p.23 / Chapter 2.2 --- Particle Image Velocimetry (PIV) --- p.25 / Chapter 2.2.1 --- Image capture system --- p.27 / Chapter 2.2.2 --- Image analysis system --- p.36 / Chapter Chapter 3 --- Aspect ratio dependence of heat transport and the flow field --- p.39 / Chapter 3.1 --- Motivation for this experiment --- p.39 / Chapter 3.2 --- Heat transfer efficiency measurements --- p.40 / Chapter 3.3 --- Heat correction --- p.44 / Chapter 3.3.1 --- Temperature correction --- p.44 / Chapter 3.3.2 --- Heat current density J correction --- p.45 / Chapter 3.3.3 --- Finite conductivity of plate --- p.50 / Chapter 3.4 --- Aspect ratio dependence --- p.51 / Chapter 3.4.1 --- Without correction of finite conductivity --- p.51 / Chapter 3.4.2 --- With correction of finite conductivity --- p.59 / Chapter 3.5 --- Time-averaged velocity field --- p.65 / Chapter 3.6 --- Summary --- p.70 / Chapter Chapter 4 --- Local temperature and velocity measurements near the boundary layers --- p.71 / Chapter 4.1 --- Motivation for this experiment --- p.71 / Chapter 4.2 --- Temperature profile measurement --- p.72 / Chapter 4.2.1 --- Temperature and fluctuation profiles --- p.73 / Chapter 4.2.2 --- Thermal boundary thickness --- p.77 / Chapter 4.2.3 --- Temperature time series --- p.79 / Chapter 4.2.4 --- PDF --- p.83 / Chapter 4.3 --- Velocity profile measurement --- p.86 / Chapter 4.3.1 --- 2D velocity and fluctuation profiles --- p.86 / Chapter 4.3.2 --- Scaling properties --- p.93 / Chapter 4.4 --- Shear stress --- p.98 / Chapter 4.4.1 --- Viscous and Reynolds stresses --- p.99 / Chapter 4.4.2 --- Laminar or Turbulent? --- p.101 / Chapter 4.5 --- Summary --- p.104 / Chapter Chapter 5 --- Conclusion --- p.106 / Chapter 5.1 --- Heat flux measurement --- p.106 / Chapter 5.2 --- Boundary layers --- p.107 / Chapter 5.3 --- Perspective for further investigation --- p.108 / Appendix A Heat flux measurement for high Prandtl number --- p.109 / Chapter I. --- Experimental conditions --- p.110 / Chapter II. --- Result and discussion --- p.112 / Chapter III. --- Summary and perspective for further investigation --- p.114 / Bibliography --- p.115

Thesis (M.S.)--Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, 1981. / MICROFICHE COPY AVAILABLE IN ARCHIVES AND AERO. / Includes bibliographical references. / by Peter Frederick Lorber. / M.S.

Thesis (Sc. D.)--Massachusetts Institute of Technology and Woods Hole Oceanographic Institution, 1983. / Cover title: Flow and skin friction over natural rough beds. Includes bibliographical references (p. 325-333).