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An interferometric study of organized structures in compressible turbulent flowsZhong, Shan January 1993 (has links)
No description available.
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Low-Reynolds-number turbulent boundary layersErm, Lincoln Paul Unknown Date (has links) (PDF)
This thesis documents an extensive experimental investigation into low-Reynolds-number turbulent boundary layers flowing over a smooth flat surface in nominally zero pressure gradients. The way in which these layers are affected by variations in R(theta), i.e. the Reynolds number based on the boundary-layer momentum thickness, type of tripping device used and variations in freestream velocity, each considered independently, are investigated.
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The Resolution and Structure of High Reynolds Number Turbulent Boundary Layers Over Rough and Smooth Walls in Pressure GradientVishwanathan, Vidya 19 January 2023 (has links)
The velocity fields of high Reynolds number, turbulent, wall boundary layers in non-equilibrium pressure gradients are experimentally investigated. Experiments in two wall configurations were performed; one with a hydrodynamically smooth test wall composed of flat aluminum panels, and the other with a rough surface consisting of 2 mm tall, staggered, circular cylindrical elements. A representative set of pressure gradient distributions were generated on the research wall by a systematically rotated NACA 0012 airfoil placed in a wind tunnel section to determine the functional dependence of the boundary layer formation on pressure gradient. Particle image velocimetry (PIV) was the primary measurement technique used to determine time-resolved features of the velocity flow field. newline{}newline{} It is shown that regardless of wall condition and Reynolds number, the non-equilibrium turbulent boundary layers exhibit increasingly non-local behavior with streamwise development. This is apparent as a lag to the pressure gradient distribution observed in the streamwise developing integrated boundary layer parameters. These ``history effects" are also prevalent in mean velocity profiles which are exhibited as a cross-over of the favorable and adverse pressure gradient profiles in the logarithmic layer. Similar cross-over points are observed in the Reynolds shear and normal stresses, particularly at the streamwise station downstream of the pressure gradient switch. The primary effect of the rough wall is to increase the magnitude of flow scales, and, while they exhibit the same qualitative history effects as the smooth wall, the rough wall flows show an earlier relaxation to equilibrium. Despite inherent uncertainties of indirect skin friction methods for the rough wall, the effective sandgrain roughness parameter k_s does not show a functional dependency to pressure gradient history. An evaluation of the wall-similarity hypothesis solely based on boundary layer thickness to roughness parameter ratios delta/k_s is insufficient and additional parameters such as pressure gradient histories, local roughness Reynolds numbers, and bias uncertainties due to instrument spatial resolution must be considered. / Doctor of Philosophy / In the interface between a surface and a moving fluid is the boundary layer where high shear and viscous stresses cause the bulk velocity to decrease to zero. When turbulent, this region of fluid is characterized by random, chaotic, and fluctuating motions of varying sizes. Parameters such as pressure gradients and geometric irregularities of the surface, referred to as roughness, can increase fluctuating pressures and velocities within the boundary layer and cause unwanted noise, vibration, and increased drag. Although many studies have evaluated boundary layers with either roughness or pressure gradient independently, most surfaces in practical application are susceptible to the compounding influences of both of these parameters. Thus, it is necessary to expand the current knowledge database to include complex flow fields necessary to improve data driven modeling and vehicle design.newline{}newline{} This study focuses on experimental observations of the turbulent velocity field developing in both a rough and smooth wall boundary layer that is induced to a family of bi-directional pressure gradients generated by the pressure field of a rotating airfoil inside in a wind tunnel. Through statistical observations of the velocity field it was found that the varying pressure gradients caused the flow to develop non-local dependencies such that the response of the downstream boundary layer was dependent on the upstream flow history. The principal effect of roughness was to increase the magnitude of turbulent scales, but to show the same qualitative response to the pressure gradient history as seen in a smooth wall flow. However, direct comparison of rough and smooth wall turbulence statistics by means of the ``wall-similarity hypothesis" requires careful consideration of multiple parameters including these flow histories, scales prescribed by roughness parameters, and bias errors from experiment under-resolution of the velocity field.
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The Effects of Pressure Gradient and Roughness on Pressure Fluctuations Beneath High Reynolds Number Boundary LayersFritsch, Daniel James 16 September 2022 (has links)
High Reynolds number turbulent boundary layers over both smooth and rough surfaces subjected to a systematically defined family of continually varying, bi-directional pressure gradient distributions are investigated in both wind tunnel experiments and steady 2D and 3D Reynolds Averaged-Navier-Stokes (RANS) computations. The effects of pressure gradient, pressure gradient history, roughness, combined roughness and pressure gradient, and combined roughness and pressure gradient history on boundary growth and the behavior of the underlying surface pressure spectrum are examined. Special attention is paid to how said pressure spectra may be effectively modeled and predicted by assessing existing empirical and analytical modeling formulations, proposing updates to those formulations, and assessing RANS flow modeling as it pertains to successful generation of spectral model inputs.
It is found that the effect of pressure gradient on smooth wall boundary layers is strongly non-local. The boundary layer velocity profile, turbulence profiles, and associated parameters and local skin friction at a point that has seen non-constant upstream pressure gradient history will be dependent both on the local Reynolds number and pressure gradient as well as the Reynolds number and pressure gradient history. This shows itself most readily in observable downstream lagging in key observed behaviors. Steady RANS solutions are capable of predicting this out-of-equilibrium behavior if the pressure gradient distribution is captured correctly, however, capturing the correct pressure gradient is not as straightforward as may have previously been thought. Wind tunnel flows are three-dimensional, internal problems dominated by blockage effects that are in a state of non-equilibrium due to the presence of corner and juncture flows. Modeling a 3D tunnel flow is difficult with the standard eddy viscosity models, and requires the Quadratic Constitutive Relation for all practical simulations. Modeling in 2D is similarly complex, for, although 3D effects can be ignored, the absence of two walls worth of boundary layer and other interaction flows causes the pressure gradient to be captured incorrectly. These effects can be accounted for through careful setup of meshed geometry.
Pressure gradient and history effects on the pressure spectra beneath smooth wall boundary layers show similar non-locality, in addition to exhibiting varying effects across different spectral regions. In general, adverse pressure gradient steepens the slope of the mid-frequency region while favorable shallows it, while the high frequency region shows self-similarity under viscous normalization independent of pressure gradient. The outer region is dominated by history effects. Modeling of such spectra is not straightforward; empirical models fail to incorporate the subtle changes in spectral shape as coherent functions of flow variables without becoming overly-defined and producing non-physical spectral shapes. Adopting an analytical formulation based on the pressure Poisson equation solves this issue, but brings into play model inputs that are difficult to predict from RANS. New modeling protocols are proposed that marry the assumptions and limitations of RANS results to the analytical spectral modeling.
Rough surfaces subjected to pressure gradients show simplifications over their smooth wall relatives, including the validity of Townsend's outer-layer-Reynolds-number-similarity Hypothesis and shortened history effects. The underlying pressure spectra are also significantly simplified, scaling fully on a single outer variable scaling and showing no mid-frequency slope pressure gradient dependence. This enables the development of a robust and accurate empirical model for the pressure spectra beneath rough wall flows. Despite simplifications in the flow physics, modeling rough wall flows in a steady RANS environment is a challenge, due to a lack of understanding of the relationship between the rough wall physics and the RANS model turbulence parameters; there is no true physical basis for a steady RANS roughness boundary condition. Improvements can been made, however, by tuning a shifted wall distance, which also factors heavily into the mathematical character of the pressure spectrum and enables adaptations to the analytical model formulations that accurately predict rough wall pressure spectra.
This work was sponsored by the Office of Naval Research, in particular Drs. Peter Chang and Julie Young under grants N00014-18-1-2455, N00014-19-1-2109, and N00014-20-2821. This work was also sponsored by the Department of Defense Science, Mathematics, and Research for Transformation (SMART) Fellowship Program and the Naval Air Warfare Center Aircraft Division (NAWCAD), in particular Mr. Frank Taverna and Dr. Phil Knowles. / Doctor of Philosophy / Very near to a solid surface, air or water flow tends to be highly turbulent: chaotic and random in nature. This is called a boundary layer, which is present on almost every system that involves a fluid and a solid with motion between them. When the boundary layer is turbulent, the surface of the solid body experiences pressures that fluctuate very rapidly, and this can fatigue the structure and create noise that radiates both into the structure to passengers and out from the structure to observers far away. These pressure fluctuations can be described in a statistical nature, but these statistics are not well understood, particularly when the surface is rough or the average pressure on the surface is changing. Improving the ability to predict the statistics of the pressure fluctuations will aid in the design of vehicles and engineering systems where those fluctuations can be damaging to the structure or the associated noise is detrimental to the role of the system. Wind turbine farm noise, airport community noise, and air/ship-frame longevity are all issues that stand to benefit from improved modeling of surface pressure fluctuations beneath turbulent boundary layers.
This study aims to improve said modeling through the study of the effects of changing average surface pressure and surface roughness on the statistics of surface pressure fluctuations. This goal is accomplished through a combination of wind tunnel testing and computer simulation. It was found that the effect of gradients in the surface pressure is not local, meaning the effects are felt by the boundary layer at a different point than where the gradient was actually applied. This disconnect between cause and effect makes understanding and modeling the flow challenging, but adjustments to established modeling ideas are proposed that prove more effective than what exists in the literature for capturing those effects. Roughness on the surface causes the flow to become even more turbulent and the surface pressure fluctuations to become louder and more damaging. Fortunately, it is found that the combination of roughness with a gradient in surface pressure is actually simpler than equivalent smooth surfaces. These simplifications offer significant insight into the underlying physics at play and enable the development of the first analytically based model for rough wall pressure fluctuations.
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Understanding the Impact of a Serrated Trailing Edge on the Unsteady Hydrodynamic FieldLetica, Stefan Josip 15 September 2020 (has links)
Trailing edge noise is a common noise source in aerodynamic applications, such as wind turbines, duct fan blades, and propellers. As sound is a nuisance for people near this machinery, methods of reducing trailing edge noise are being investigated. A proven method of trailing edge noise reduction is using a serrated trailing edge. Many prior experiments have shown that a trailing edge with sawtooth serrations can reduce trailing edge noise compared to a straight trailing edge, but the mechanism by which sawtooth serrations reduce noise is not fully understood. Previous theoretical models have assumed that the turbulence field convecting past a serrated trailing edge is unchanged by the presence of the serrations, but experiments have shown that this is not the case in reality. This work attempts to further explore the mechanisms behind why trailing edge serrations reduce trailing edge noise. Additionally, it evaluates the usefulness of a wall jet wind tunnel for use in the study of serrated trailing edges. Experiments were conducted in an anechoic wall jet wind tunnel using a straight trailing edge configuration and a serrated trailing edge configuration. It was found that there may be differences in the unsteady surface pressure over serrated edges in one-sided flows as compared to two-sided flows, like on that of an airfoil, most notably in relation to the magnitude of the unsteady pressure on the serrations. In the wall jet and in agreement with other studies, it was found that the unsteady pressure fluctuations increase towards the tip of the serration in one-sided flows. This is counter to what is found in some studies of two-sided flows. Good agreement was found between some models of the wavenumber-frequency wall pressure spectrum of a turbulent boundary layer and the measured wall pressure spectrum on the straight trailing edge, and these models also produced good predictions of the noise produced by this trailing edge using Amiet's equation. A surface pressure microphone array was used to estimate the zero spanwise wavenumber surface pressure spectrum. This spectrum was used in Amiet's method to predict the measured trailing edge noise. Predictions using the wavenumber-filtered measurement tended to overpredict the measured far field noise most likely due to the inclusion of broader wavenumber content through the array's side lobe response and the breadth of the main lobe. The serrated trailing edge was found to increase coherence between two points on the same serration while reducing coherence between two points on different serrations. It was concluded that the presence of the serrations decorrelates small-scale turbulent eddies. Additionally, it was found that while the serrated trailing edge did reduce the noise produced, its destructive effect on the geometry-based resonance of the straight trailing edge configuration may have amplified the magnitude of the reduction. Finally, it was concluded that the serrations do indeed affect the hydrodynamic field near the trailing edge, and the theoretical models which make the assumption otherwise must be refined. / Master of Science / Trailing edge noise is a common noise source in aerodynamic applications, such as wind turbines, duct fan blades, and propellers. As sound is a nuisance for people near this machinery, methods of reducing trailing edge noise are being investigated. A proven method of trailing edge noise reduction is using a serrated trailing edge. Many prior experiments have shown that a trailing edge with sawtooth serrations can reduce trailing edge noise compared to a straight trailing edge, but the mechanism by which sawtooth serrations reduce noise is not fully understood. This work attempts to further explore the mechanisms behind why trailing edge serrations reduce noise. Experiments were conducted in an anechoic wind tunnel facility. It was found that a one-sided flow over a serrated trailing edge may be significantly different from that over a two-sided flow. Good agreement was found between prediction models and measurements of trailing edge noise. The serrated trailing edge was effective at reducing the coherence of turbulent eddies across the roots of the sawtooth serrations. It was concluded that the serrated trailing edge is effective at reducing noise, and that one means of doing so is decreasing the correlation of small-scale turbulent eddies, and that current models of the flow over serrations may need to be refined.
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Structure of 2-D and 3-D Turbulent Boundary Layers with Sparsely Distributed Roughness ElementsGeorge, Jacob 15 July 2005 (has links)
The present study deals with the effects of sparsely distributed three-dimensional elements on two-dimensional (2-D) and three-dimensional (3-D) turbulent boundary layers (TBL) such as those that occur on submarines, ship hulls, etc. This study was achieved in three parts: Part 1 dealt with the cylinders when placed individually in the turbulent boundary layers, thereby considering the effect of a single perturbation on the TBL; Part 2 considered the effects when the same individual elements were placed in a sparse and regular distribution, thus studying the response of the flow to a sequence of perturbations; and in Part 3, the distributions were subjected to 3-D turbulent boundary layers, thus examining the effects of streamwise and spanwise pressure gradients on the same perturbed flows as considered in Part 2. The 3-D turbulent boundary layers were generated by an idealized wing-body junction flow. Detailed 3-velocity-component Laser-Doppler Velocimetry (LDV) and other measurements were carried out to understand and describe the rough-wall flow structure. The measurements include mean velocities, turbulence quantities (Reynolds stresses and triple products), skin friction, surface pressure and oil flow visualizations in 2-D and 3-D rough-wall flows for Reynolds numbers, based on momentum thickness, greater than 7000. Very uniform circular cylindrical roughness elements of 0.38mm, 0.76mm and 1.52mm height (k) were used in square and diagonal patterns, yielding six different roughness geometries of rough-wall surface. For the 2-D rough-wall flows, the roughness Reynolds numbers, based on the element height (k) and the friction velocity, range from 26 to 131. Results for the 2-D rough-wall flows reveal that the velocity-defect law is similar for both smooth and rough surfaces, and the semi-logarithmic velocity-distribution curve is shifted by an amount depending on the height of the roughness element, showing that this amount is a function of roughness Reynolds number and the wall geometry. For the 3-D flows, the data show that the surface pressure gradient is not strongly influenced by the roughness elements. In general, for both 2-D and 3-D rough-wall TBL, the differences between the two roughness patterns (straight and diagonal), as regards the mean velocities and the Reynolds stresses, are limited to about 3 roughness element heights from the wall.
The study on single elements revealed that the separated shear layers emanating from the top of the elements form a pair of counter rotating vortices that dominate the downstream flow structure. These vortices, termed as the roughness top vortex structure (RTVS), in conjunction with mean flow, forced over and around the elements, are responsible for the production of large Reynolds stresses in the neighborhood of the element height aft of the elements. When these elements are placed in a distribution, the effects of RTVS are not apparent. The roughness elements create a large region of back flow behind them which is continuously replenished by faster moving fluid flowing through the gaps in the rough-wall. The fluid in the back flow region moves upward as low speed ejections where it collides with the inrushing high speed flow, thus, leading to a strong mixing of shear layers. This is responsible for the generation of large levels of turbulent kinetic energy (TKE) in the vicinity of the element height which is transported, primarily, by turbulent diffusion. As regards the 3-D rough-wall TBL, the effect of flow three-dimensionality is seen in the large skewing of the distributions of mean velocities, Reynolds stresses and TKE, aft of the elements. In general, the regions of large TKE production-rates seem to propagate in the direction of the local velocity vector at the element height. The data-sets also enable the extraction of the turbulent flow structure to better describe the flow physics of these rough-wall turbulent boundary layers. / Ph. D.
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Experimental study of particle-induced turbulence modification in the presence of a rough wallTay, Godwin Fabiola Kwaku 01 June 2015 (has links)
This thesis reports an experimental investigation of low Reynolds number particle-laden turbulent flows in a horizontal plane channel. Experiments were conducted over a smooth wall and over two rough surfaces made from sand grain and gravel of relative roughness k/h ≈ 0.08 and 0.25, respectively, where k is the roughness height and h is the channel half-height. The flow was loaded with small solid particles with diameters less than 1/10 of the length scale of the energy-containing eddies, and whose concentrations decreased with time due to sedimentation. A novel particle image velocimetry (PIV) method that employed colour filtering for phase discrimination was used to measure the velocities of the fluid and solid particles.
Over the smooth wall, the particles mean velocity, turbulence intensities and Reynolds shear stress matched those of the unladen flow very well. There were substantial differences between particle and fluid profiles over the rough wall, which include more rapid reduction in the particle mean velocity and significantly larger turbulence intensities and Reynolds shear stress compared to the unladen flow values.
Stratification of the particle concentration led to attenuation of the fluid wall-normal turbulence intensity. This effect was nullified by the roughness perturbation leading to collapse of the wall-normal turbulence intensities over the rough wall. The streamwise turbulence intensity also collapsed over the rough wall but it was found that particles augmented the fluid Reynolds shear stress due to enhanced correlation between the rough wall streamwise and wall-normal velocity fluctuations. A quadrant decomposition of the fluid Reynolds shear stress also revealed corresponding enhancements in ejections and sweeps, the dominant contributors to the Reynolds shear stress, over the rough wall.
Based on two-point correlations between the velocity fluctuations and between the velocity fluctuations and swirling strength, it was concluded that both wall roughness and particles modified the turbulence structure by increasing the size of the larger-scale structures. The idea of eddies growing from the wall, thereby enhancing communication between the inner layer and outer parts of the flow, has implications for wall-layer models that assume that the outer layer is detached from the turbulence in the inner region.
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Large-Eddy Simulations of Accelerating Boundary Layer Flows Over Rough SurfacesYUAN, JUNLIN 17 October 2011 (has links)
Large-eddy simulations are carried out to study the combined
effects of roughness and favourable pressure gradient in boundary layer flows,
where the high acceleration (on smooth walls) may cause flow reversion to the
quasi-laminar state. A sand-grain roughness model is used, with the
no-slip boundary condition modeled by an immersed boundary method.
The properties and accuracies of the scheme are studied,
the roughness model is validated, and the spatial-resolution requirements are
determined.
The roughness model is applied to boundary layers subject to mild or strong
acceleration, with simulations carried out underlining the effects of
three parameters: the acceleration parameter, the roughness height,
and the inlet Reynolds number.
The roughness effects are limited to the roughness sublayer; the outer layer is
affected indirectly only, through the changes that roughness causes in the
relaminarization and retransition processes.
The roughness significantly affects the inner-layer
quantities like the friction velocity and the friction coefficient, while
the local Reynolds number, the outer-layer mean velocity, as well as the Reynolds
stresses beyond the roughness sublayer, are not sensitive to the roughness.
The acceleration decreases the Reynolds stresses in the
overlap region and promotes a laminar-like velocity profile.
The acceleration leads to stabilization of near-wall structures and causes
one-dimensional turbulence. The roughness generates small-scale structures
at the bottom wall, which disturb the larger structures originally
stabilized by the pressure gradient, leading to a decrease in the Reynolds-stress
anisotropy. Roughness increases the Reynolds stresses in the roughness sublayer
and tends to restore the fully turbulence flow early. The inlet Reynolds number
affects the flow stability by determining the viscous length scale
compared to the roughness length scales, and by determining how far
the roughness effect extents into the boundary layer. / Thesis (Master, Mechanical and Materials Engineering) -- Queen's University, 2011-10-17 11:19:08.063
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Study of Far Wake of a Surface-Mounted Obstacle Subjected to Turbulent Boundary Layer FlowsChaware, Shreyas Satish 23 August 2023 (has links)
Experimental investigations were conducted with and without the presence of the surface-mounted obstacle to quantify its effects on the far wake. The obstacle chosen for this study was a 3:2 elliptical nose NACA 0020 tail wing-body (Rood body), approximately of height equal to the boundary layer thickness at one of the measurement locations of the flow. The experiments were performed by varying the Reynolds number of the flow and manipulating the pressure gradient distributions using a NACA 0012 airfoil placed within the wind tunnel test section. The measurements were acquired utilizing a spanwise traversing boundary layer rake and a point pressure sensing microphone array.
The findings reveal that the presence of the obstacle introduces disruptions in the flow, such as vortex and jet regions in the wake. However, the overall flow behavior remains consistent with that of an undisturbed turbulent boundary layer, for varying Reynolds numbers and pressure gradients. Notably, an adverse pressure gradient and lower Reynolds number both accentuate the prominence of the jet and vortex region within the wake, with the trend reversing towards the other end of the spectrum. This behavior is akin to the larger turbulent boundary layer under adverse pressure gradients and lower Reynolds numbers. Furthermore, the presence of obstacles induces an increase in the overall level of the wall pressure spectrum by approximately 2 dB, regardless of the flow condition. Additionally, it leads to a deviation in the slope of the mid-frequency range of the autospectra compared to the smooth wall case. Specifically, the mid-slope frequency of an undisturbed turbulent boundary layer is steeper than that observed in the disturbed wake flow caused by the obstacle. / Master of Science / The interaction between turbulence and aerodynamic surfaces gives rise to wall-pressure fluctuations, which in turn induce structural vibrations and acoustic noise. On surfaces turbulent flows meet, antennae, flaps, and other frequently mounted measuring devices. The flow in their wake is impacted by the coherence of a turbulent boundary layer being disrupted by these impediments mounted on aerodynamic surfaces. They also alter the nature of the pressure fluctuations that are generated on the surface of interest. The far wake of a Rood Body obstacle was studied using a point pressure sensing microphone array and a spanwise traversing boundary layer rake. Experimental measurements were taken for a range of Reynolds numbers and pressure gradient environments at the Virginia Tech Stability Wind Tunnel.
Results show that the boundary layer rake measurements resolve the presence of the obstacle wake successfully, by characterizing the wake structures and confirming the presence of jet and vortex regions in the wake of the obstacle. Surface pressure measurements reveal that the presence of the obstacle causes the low-frequency content of the wall pressure to be less dominant than the no obstacle case, while the high-frequency content becomes more dominant in the presence of the obstacle. The presence of obstacles also increases the overall levels of the wall pressure spectrum by approximately 2 dB.
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Structure Of Sink Flow Boundary LayersAjit, Dixit Shivsai 10 1900 (has links)
The work reported in this thesis is an experimental and theoretical investigation of the so-called sink flow boundary layers. These are two-dimensional (in the mean), favourable-pressure-gradient (FPG) boundary layer flows where the boundary layers experience stream-wise acceleration inside a two-dimensional convergent channel with smooth and plane walls. The boundary layers studied are mainly turbulent with few cases that may be identified as reverse-transitional. The sink flow turbulent boundary layers (TBLs) are the only smooth-walled layers that are in ‘perfect equilibrium’ or ‘exact self-preservation’ in the sense of Townsend (1976) and Rotta (1962).
The present boundary layer experiments were conducted in an open-return low-speed wind tunnel. The sink flow conditions were established on the test-plate by using a contoured test-section ceiling for creating a convergent channel with smooth and plane walls. The strength of the streamwise FPG was varied by changing the freestream speed in the test-section. Few zero-pressure-gradient (ZPG) turbulent boundary layers were also measured in the same tunnel for which the contoured ceiling was replaced by a straight one. The velocity measurement techniques used include conventional Pitot-tubes for mean flow measurements and hotwire/crosswire probes for turbulence measurements. For measurement of skin friction in ZPG flows, Preston-tube was used while for the sink flows the so-called surface hotwire method was employed. Static pressures were measured on the test-surface using an alcohol-based projection manometer. Boundary layers were tripped at the beginning of the test-plate to ensure quick transition to turbulence.
The mean velocity scaling in sink flow TBLs in the presence of strong FPG has been studied systematically, especially in view of the apparent pressure-gradient-dependence of the logarithmic laws reported in the literature (Spalart & Leonard, 1986; Nickels, 2004; Chauhan et al., 2007). The experimental study of sink flow TBLs carried out over a wide range of streamwise FPGs has shown that the mean velocity profiles (in inner coordinates) exhibit systematic departures from the universal logarithmic law as the pressure gradient parameter ∆p is varied. Even so, each of these profiles exhibits a logarithmic region, albeit non-universal, whose constants are functions of the pressure gradient. Systematic dependence of these constants on the pressure gradient parameter ∆p is observed. Moreover, the wake region is uniformly absent in all these profiles. In other words, each profile looks like a ‘pure wall-flow’, in the sense of Coles (1957), only if it is viewed in relation to its own non-universal logarithmic law.
To support the experimental observation of the pressure-gradient-dependence of logarithmic laws in sink flow TBLs, a theory based on the method of matched asymptotic expansions has been applied to sink flow TBLs and this theory reveals a systematic dependence of inner and outer logarithmic laws on the pressure gradient parameter ∆p. This dependence is essentially a higher-order effect and therefore becomes significant only in the presence of relatively strong pressure gradients. Comparison of the theory with the experimental data demonstrates that the disappearance of the universal logarithmic law in strong FPG situations does not necessarily imply the absence of classical inner-outer overlap region. The overlap may still manifest itself as a logarithmic functional form with constants that are strongly influenced by the magnitude of the FPG.
An immediate use of the non-universal log laws is towards the estimation skin friction in strong-pressure-gradient equilibrium and near-equilibrium TBL flows and this issue has been studied in some detail. It is shown that the conventional Clauser-chart method for estimation of skin friction (which gives fairly accurate results for ZPG or mild-pressure-gradient flows), originally proposed by Clauser (1954), can be modified to deal with the situations involving strong streamwise pressure gradients, provided that the equilibrium or near-equilibrium TBL under consideration is not very close to relaminarization or separation. In such cases, the overlap layer manifests itself in the form of non-universal logarithmic laws that are dependent on the local strength of the pressure gradient. Using these non-universal log laws in conjunction with the measured pressure distribution (necessary for obtaining the acceleration parameter K) and a measured mean velocity profile, it is possible to obtain the local skin friction coefficient to an accuracy which is typical of skin friction measurements. This modified Clauser-chart method (MCCM) employs a two-fold iterative procedure (one iteration on Cf and the other on ∆p) in contrast to the conventional method that involves only one iteration (on Cf alone). As a by-product of this MCCM, one obtains the local pressure gradient parameter ∆p and the slope 1/κ and intercept C of the non-universal log law for that profile. It is also demonstrated that the arm´MCCM is quite robust to the changes in the universal values of K´arman constant κ0 and intercept C0 for the ZPG turbulent boundary layer.
Various aspects of the large-scale structure in turbulent and reverse-transitional sink flow boundary layers subjected to streamwise FPGs have also been investigated. The use of sink flow configuration allows systematic characterization of the large-scale structure with the strength of the FPG as a parameter where the characterization is not contaminated by the upstream history effects. The large-scale structure is identified by cross-correlating the wall-shear stress fluctuation with the streamwise velocity fluctuation. The structure orientation is found to be linear over a large wall-normal extent typically extending from y/δ of 0.1 to 0.6. Beyond y/δ =0.6, the correlation under consideration becomes very weak to allow any conclusive results. The average structure inclination angle αavg is found to decrease systematically with increase in the streamwise FPG. This result is important and has implications towards modeling of the near-wall region. Further it is found that the structure gets elongated considerably as the FPG is increased, i.e. the streamwise spatial extent of the structure increases. Taken together, it is observed that the structure becomes flatter and longer with the increase in FPG. Structural models are proposed for sink flow TBLs in the form of either the shape of individual hairpin vortices or the possible structural self-organization. These models are then discussed in the light of present experimental results. It is also shown that the process of relaminarization of a TBL by strong FPG may be better appreciated by appealing to these structural models.
The validity of Taylor’s hypothesis for structure angle measurements in the present study has been established experimentally. This exercise is important since the flows under consideration are highly accelerated and sometimes even reverse-transitional. In most of the previous work on the validity of Taylor’s hypothesis, at least for the measurements similar to the present work, the emphasis has been on ZPG turbulent boundary layers. The present exercise is therefore crucial for accelerating flows. Possible reasons for the observed validity of Taylor’s hypothesis have also been identified − specifically it is seen that the condition ∆xp/L << 1 needs to be met for Taylor’s hypothesis to be valid in pressure gradient flows.
Investigation of the structure convection velocity from the space-time correlations has revealed that the convection velocity of a typical structure in the present sink flow boundary layers is almost equal to the local mean velocity (more than 90%). This implies that the structure gets convected downstream almost along with the mean flow.
Near-wall ‘active’ and ‘inactive’ motions in sink flow TBLs have been studied, discussed and compared with the corresponding results for ZPG turbulent boundary layers from five different aspects: (i) turbulent diffusion of TKE, (ii) quadrant statistics, (iii) profiles of the streamwise turbulence intensity, (iv) event correlation length scales obtained from conditional sampling on the instantaneous flux signal and (v) profiles of the Townsend parameter Tp =(−uv) /u2.
Near-wall inactive motion is seen to be related to the strength of the large-eddy structure in the outer region of TBL flow. For APG flows the near-wall inactive motion is known to be more intense (Bradshaw, 1967b) than the ZPG flows, say at the same K´arman number δ+. This observation is consistent with a stronger large-eddy structure that may be perceived from the stronger wake component in the mean velocity variation and the larger mean entrainment in an APG turbulent boundary layer as compared to the ZPG flow at same δ+. In sink flow TBLs, the large-eddy structure is much weaker in comparison to the ZPG flow at same δ+ which is consistent with the absence of wake component in the mean velocity profile as well as the zero mean entrainment into the layer. A sink flow TBL represents, a state of weakest large-eddy structure and hence minimum intensity of inactive motion compared to any other equilibrium or near-equilibrium TBL flow having the same K´arman number δ+. All the analysis of the relevant experimental data seems to support this.
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