Mechanical Engineering - Theses
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ItemSensor and actuator selection for feedback control of fluid flows( 2019)The present thesis regards linear estimation and control for two fluid flows, with a particular focus on the placement of sensors and actuators. In the first part of the thesis, we study the complex Ginzburg-Landau equation, a simple model for spatially developing flows such as jets, wakes and cavities. (This equation can be seen as a low-dimensional substitute for the Navier-Stokes equations.) The specific focus is on the extent to which estimation and control are (i) fundamentally difficult and (ii) limited by having only a single sensor and a single actuator. To answer these questions, we study three problems. First, we consider the optimal estimation problem in which a single sensor is used to estimate the entire flow field (without any control). Second, we consider the full information control problem in which the whole flow field is known, but only a single actuator is available for control. Third, we consider the overall input-output control problem in which only a single sensor is available for measurements; and only a single actuator is available for control. By considering the optimal sensor placement, optimal actuator placement or both while varying the stability of the system, fundamental placement trade-offs are made clear. We discuss implications for effective feedback control with a single sensor and a single actuator and compare the results to previous placement studies. In the second part of this thesis, we look at an incompressible turbulent channel flow at a friction Reynolds number of Re$_\tau = 2000$. A linear Navier-Stokes operator is formed about the turbulent mean and augmented with an eddy viscosity. Velocity perturbations are then generated by stochastically forcing the linear Navier- Stokes operator. The objective is to estimate and control these perturbations. The estimation and control problems perform best for the largest scales that (i) are high in energy when stochastically forced, (ii) exhibit large transient growth and (iii) are coherent over large wall-normal distances. We determine the locations of sensors and actuators for which estimation and control are most effective by looking at two arrangements: (i) placing them at the wall; and (ii) placing them some distance off the wall. Finally, it is shown that a control arrangement with a well-placed sensor and actuator performs comparably to either measuring the flow everywhere (while actuating it at a single wall height) or actuating it everywhere (while measuring it at a single wall height). In this way, we gain insight (at low computational cost) into how specific scales of turbulence are most effectively estimated and controlled.
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ItemCharacteristics of energetic motions in turbulent boundary layers( 2019)In this dissertation, we present the first measurements of two-dimensional (2-D) energy spectra of the streamwise velocity component (u) in high Reynolds number turbulent boundary layers. The measurements in the logarithmic region of turbulent boundary layers give new evidence supporting the self-similarity arguments that are based on Townsend’s (1976) attached eddy hypothesis. The 2-D spectrum is found to be able to isolate the range of self-similar scales from the broadband turbulence, which is not possible with the measurement of a 1-D energy spectrum alone. High Reynolds number flows are characterized by large separation of scales. Therefore, to obtain converged 2-D statistics while resolving the broad spectrum of length and time scales, a novel experimental technique is required. To this end, we devise a technique employing multiple hot-wire probes to measure the 2-D energy spectra of u. Taylor’s frozen turbulence hypothesis is used to convert temporal-spanwise information into a 2-D spatial spectrum which shows the contribution of streamwise (λx) and spanwise (λy) length scales to the streamwise variance at a given wall height (z). The validation of the measurement technique is performed at low Reynolds number by comparing against the direct numerical simulation (DNS) data of Sillero et al. (2014). Based on these comparisons, a correction is introduced to account for the spatial resolution associated with the initial separation of the hot-wires. The proposed measurement technique is used to measure the 2-D spectra in the logarithmic region for friction Reynolds numbers ranging from 2400 to 26000. At low Reynolds numbers, the shape of the 2-D spectra at a constant energy level shows λy/z ∼ (λx/z)1/2 behaviour at large scales, which is in agreement with the existing literature. However, at high Reynolds numbers, it is observed that the square-root relationship tends towards a linear relationship (λy ∼ λx) as required for self-similarity and predicted by the attached eddy hypothesis. Finally, we present a model for the logarithmic region of turbulent boundary layers, which is based on the attached eddy framework and driven by the scaling of experimental 2-D spectra of u. The conventional attached eddy model (AEM), which comprises self-similar wall-attached eddies (Type A) alone, represent the large scale motions at high Reynolds numbers reasonably well. However, the scales that are not represented by the conventional AEM are observed to carry a significant proportion of the total kinetic energy. Therefore, in the present study we propose an extended AEM, where in addition to Type A eddies, we also incorporate Type CA and Type SS eddies. These represent the self-similar but wall-detached low-Reynolds number features and the non-self-similar wall-attached superstructures, respectively. The extended AEM is observed to predict a greater range of energetic length scales and capture the low- and high-Reynolds number scaling trends in the 2-D spectra of all three velocity components.
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ItemExperimental investigation of velocity and vorticity in turbulent wall flows( 2019)This thesis details the results of a research effort both to acquire sufficiently-resolved velocity and vorticity vector time-series in turbulent wall-bounded flows, as well as to use the acquired data to juxtapose two canonical wall-bounded flows: the zero-pressure-gradient boundary layer and the fully-developed pipe. Towards these ends, a novel configuration of measurement sensors has been designed, evaluated, and deployed in three of the largest canonical wall-flow facilities in existence: the Flow Physics Facility (FPF) at the University of New Hampshire, the High Reynolds Number Boundary Layer Wind Tunnel (HRNBLWT) at the University of Melbourne, and the Centre for International Cooperation in Long Pipe Experiments (CICLoPE) at the University of Bologna. The datasets presented herein are the first to contain simultaneously-acquired velocity and vorticity statistics in both pipe and boundary layer flows under matched conditions. The capacity of the measurement probe to resolve the velocity and vorticity vectors under idealised conditions is evaluated via `synthetic experiments', whereby the response of the probe to a simulated turbulent flow is modeled, and the resulting aggregate statistics compared to those of the known input. The synthetic experimental results are then compared to statistics obtained from physical experiments, and show close agreement for most quantities despite differences in Reynolds number. Disagreement between the physical and synthetic experimental results in several quantities is used to diagnose a limitation of the present sensor system. An awareness of the measurement capabilities (and limitations) afforded by the comparison between the synthetic and physical experiments pervades the ensuing analysis and discussion of additional physical experimental results. Normalised statistical moments (up to the kurtosis) of velocity and vorticity are presented for both pipe and boundary layer cases. The two flows are shown to exhibit virtually no differences from one another wallward of the wake region aside from the transverse velocity component variances. The boundary layer wake is characterised by higher turbulence enstrophy and turbulence kinetic energy (TKE) than the pipe, despite containing both turbulent and non-turbulent states. Although there is no `free-stream' in the fully-developed pipe, a significant time-fraction of the flow can be described as `quasi-irrotational' near the centreline. This results in a departure of the velocity and vorticity kurtosis (and, when not identically zero, skewness) from Gaussian behaviour in the outer region of the pipe, as is known to occur in the boundary layer (owing to turbulent/non-turbulent intermittency). Spectral properties of the velocity and vorticity signals acquired in both flows are examined, both for their own content as well as to compare the two flows. Despite very little difference in the observed streamwise turbulence kinetic energy, the contributions to the total differ considerably by scale between the two flows. The pipe is observed to contain more streamwise TKE than the boundary layer in scales longer than 10 times the outer length scale $\delta$, while the opposite is true for scales shorter than $10\delta$. This `crossover' scale also applies to the spectra of the transverse velocity components and Reynolds shear stress. The measured enstrophy spectrum is shown to be approximately invariant under Kolmogorov normalisation for wall-distances greater than about 200 viscous-lengths. Finally, local isotropy and axisymmetry in the velocity components are evaluated. Local isotropy is observed to be satisfied over a range of scales for which the characteristic timescale of inertial energy transfer is expected to be small relative to the timescale of the mean strain rate. The relationship between the transverse velocities and the streamwise velocity, however, does not appear to approach isotropy along the pipe centreline, suggesting that the bounding wall also plays a role in imposing a sense of direction on the turbulence. Indeed, the aforementioned timescale criterion is shown to identify a cutoff scale that increases proportionally with wall-distance, confounding a conclusive statement regarding the primary source of anisotropy away from the centreline.
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ItemAnalysis of resolvent method for turbulence inflow generation( 2018)High-fidelity simulations of turbulent flows aim to accurately reproduce the statistical and structural properties of real-life turbulence. Such simulations rely on accurate inflow boundary conditions. A novel turbulent inflow generation method for high-fidelity DNS/LES has been developed which utilizes reduced order modelling (ROM) and evolutionary algorithms. The core idea behind this method is the classical view of turbulence which represents it as a collection of coherent structures. A low-rank approximation approach known as the resolvent analysis, developed by McKeon and Sharma [Journal of Fluid Mechanics, Vol. 658, 336-382 (2010)], is used to represent the governing equations as a linear input-output system. The non-linearities in the governing Navier-Stokes equations are the driving force behind the ow. This forcing of the linear system produces a response which represent the velocity perturbations. The resolvent analysis is performed at different wavenumber-frequency combinations which are selected in a manner to represent a variety of energetic coherent structures like the near-wall longitudinal streaks, hairpin vortices, Large Scale Motions (LSMs) and Very Large Scale Motions (VLSMs). A Singular Value Decomposition (SVD) of the linear operator in the input-output system is performed to generate a set of orthonormal basis functions for the forcing and response fields. A major advantage of the resolvent analysis is its reduced dependence on external data. It requires only the mean statistical quantities as an input which are readily available for various ow problems or can be easily obtained from cost-effective RANS simulations. The amplitudes of the selected modes were linearly scaled such that the turbulence kinetic energy (TKE) of the resolvent modes is equal to the target TKE. This technique successfully resulted in a fully developed turbulent field, although with a large development length. A further improvement of this method is obtained by optimizing the amplitude of each resolvent mode, which represents the energy content of the associated coherent structure. A genetic algorithm approach has been used to optimize the resolvent modes to represent the target Reynolds stress profiles. This modified process results in a significantly improved development length.
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ItemStructure of mean dynamics and spanwise vorticity in turbulent boundary layers( 2016)The overall aim of this research is to develop a refined scaling analysis for the two-dimensional mean momentum balance (MMB) for the zero-pressure gradient turbulent boundary layer (TBL), and to describe the mean and fluctuating spanwise vorticity structure in a context consistent with the mean dynamical scaling. Towards this aim, a custom multi-element hot-wire sensing array was used to measure spanwise vorticity fluctuations and Reynolds shear stress time series in turbulent boundary layers. Smooth wall boundary layer profiles, with very good spatial and temporal resolution, were acquired over a K\'arm\'an number range of $2,400-16,400$ at the Melbourne Wind Tunnel at the University of Melbourne, and in the University of New Hampshire's Flow Physics Facility (FPF). These data represent the most highly resolved measurements over this Reynolds number range available to date. For canonical boundary layers the mean inertia, which is a function of the wall-normal distance, appears instead of the constant mean pressure gradient force in the MMB for pipes and channels. The constancy of the pressure gradient has led to theoretical treatments for pipes/channels, that are more precise than for the TBL. Elements of these analyses include the logarithmic behaviour of the mean velocity, specification of the Reynolds shear stress peak location, the square-root Reynolds number scaling for the log layer onset, and a well-defined layer structure based on the balance of terms in the MMB. The present analyses evidence that similarly well-founded results also hold for turbulent boundary layers. This follows from transforming the mean inertia term in the MMB into a form that resembles that in pipes/channels, and is constant across the outer inertial region of the TBL. The present measurements support these analytical developments. Congruent with the self-similar structure admitted by the transformed mean governing equations, a description of the mean and fluctuating vorticity structure in turbulent boundary layers is presented. Due to the decreasing mean value of vorticity with increasing wall distance and Reynolds number, the fluctuating enstrophy approaches that of the instantaneous enstrophy on the inertial outer domain. Furthermore, this underlies an emerging self-similarity between the mean and standard deviation of vorticity over the same subdomain where the mean velocity profile is logarithmic. The accompanying data analysis includes a detailed description of the spanwise vorticity statistical structure. For flat plate boundary layers the spanwise vorticity is the only component that fluctuates about a non-zero mean, and hence was selected for this study. Empirical support for the proposed similarity structure is also provided.
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ItemThe quiescent core of turbulent channel and pipe flows( 2016)A new conceptual view of turbulent channel and pipe flows is presented via the proposition of the `quiescent core', which is analogous to the free-stream in turbulent boundary layers. The quiescent core is detected as a zone of roughly uniform streamwise momentum, which happens to be relatively quiescent compared to the rest of flow, residing in the central region of channel and pipe flows. It occupies a large proportion of the flow and oscillates with the large-scale wavelengths in a predominantly anti-symmetric manner. Within the intermittent region of wall-turbulence, it is observed that the oscillation of the turbulent/non-turbulent interface or quiescent core can contaminate the fluctuating velocity components under the traditional Reynolds decomposition. A new method of decomposing the total velocity is proposed to remove this contamination. The use of this new decomposition method, along with the zone-averaging technique, enables the examination of `true' turbulent structure and scale purely inside the `turbulent shear flow' region (below the free-stream or outside the quiescent core) of both internal (channel and pipe) and external (boundary layer) flows. The results are compared in internal and external flows to reveal that the structure and scale of turbulence in those flows are indeed much more similar than previous studies have concluded. It is shown that the geometry of the pipe core can be well-represented by a few dominant azimuthal Fourier modes. The dominant azimuthal modes of the pipe core are associated with streamwise streaks and roll-modes in axisymmetric arrangements and they often maintain a high degree of spatial coherence along the streamwise direction (for over a pipe radius). The investigation of temporal progression of the pipe core reveals that it simply convects downstream without azimuthal rotation and rapid evolution. The most energetic modes of channel flow are extracted and investigated by means of proper orthogonal decomposition. It is observed that the large-scale wall-normal eigenfunctions appear in pairs which carry comparable amounts of turbulent kinetic energy and Reynolds shear stress. The turbulent kinetic energy and Reynolds shear stress are mostly concentrated in the large-scale modes (with the first 20 modes carrying about a half of these quantities). The most energetic modes represent the large-scale inclined flow structures with symmetric or anti-symmetric arrangements between the top and bottom channel walls, which can efficiently replicate the associated large-scale geometry of the channel core.
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ItemNumerical methods and turbulence modelling for large-eddy simulations( 2015)Turbulence is of interest in many engineering applications, ranging from aerospace design to naval architecture. The inherent complexities of turbulence make it difficult to measure experimentally, and, to simulate numerically. The focus of this dissertation is the simulation of turbulent flow with the computational methodology known as large-eddy simulation (LES). LES uses a filter to partition a flow-field into large- (or resolved) and small- (or subgrid) scales and solves only for the large-scales. This method provides more accuracy when compared to other computational methods, such as those based on the Reynolds-averaged Navier--Stokes equations. The increased accuracy, however, comes with an associated increase in computational cost. Indeed, the computational cost of LES can often be prohibitive, especially for cases involving wall-bounded flow over complex geometries at high Reynolds numbers. This high computational expense is one of the primary limitations of LES. Methods to reduce the cost of LES form the focus of this dissertation. The high cost of LES is in great part due to the near-wall resolution requirement. To accurately represent a flow-field with LES, it is necessary to sufficiently resolve all of the dynamically important scales of motion. This is relatively inexpensive in free-shear flows, where the large-scales are the most energetic, but it is more difficult in wall-bounded flows, where the energy-containing scales get increasingly small near a wall. These near-wall small-scales make it impractical to resolve all of the energy containing scales. Therefore, models that mimic the effect of the near-wall turbulent structures on the wall and on the core of the flow are often used. These models are known as wall-models, and, if accurate, they are able to significantly reduce the computational cost of a large-eddy simulation. At present there is no wall-modelling approach that has been shown to be apposite in a broad range of applications. In particular, current wall-models are often inaccurate when applied to separating wall-bounded flow and are limited by their inability to predict fluctuations of wall-shear-stress and the near-wall velocity. Because of this, a key focus of this dissertation is the proposal and investigation of a new wall-model that aims to overcome these two limitations. In addition, the new model aims to reduce the computational cost of LES by significantly reducing the near-wall resolution requirement. Before introducing this new wall-model, flow over a circular cylinder is investigated in order to gain familiarity with the large-eddy simulation methodology and to assess the effect of some key computational parameters in LES. In this investigation, the effects of mesh resolution, discretisation schemes, SGS-models, and wall-models on prediction of the flow-field are assessed. One of the primary outcomes of this study is the finding that `standard' wall-models are inadequate for turbulent separating flows. This motivated the investigation of the new wall-model. The new wall-model is able to predict the fluctuating wall-shear-stress from a large-scale velocity input. The model is based on the spectral structure of the turbulent boundary layer and the interaction between large-scale events in the logarithmic layer and small-scale events near the wall. Importantly, the model includes many important parameters that are able to preserve the structure of the boundary layer while remaining relatively straightforward to implement in a solver. Further, the model does not increase the computational cost of a simulation compared to current wall-modelling approaches. The model is implemented in large-eddy simulations of channel flow to assess its efficacy compared to a standard wall-model. The influence of two subgrid-scale models on the large-scale velocity input is also investigated. Results show that the new wall-model is able to resolve more of the wall-shear-stress variance when compared to a standard wall-model, and it has a small effect in the outer-regions of the boundary layer.
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ItemDirect numerical simulation of turbulent natural convection bounded by differentially heated vertical walls( 2013)Using new, high-resolution direct numerical simulation (DNS) data, this study appraises the different scaling laws found in literature for turbulent natural convection of air in a differentially heated vertical channel. The present data is validated using past DNS studies, and covers the Rayleigh number (Ra) range between 5.4 × 10^5 to 1.0 × 10^8. This is followed by an appraisal of various scaling laws proposed by four studies: Versteegh and Nieuwstadt (77), Holling and Herwig (34), Shiri and George (63) and George and Capp (23). These scaling laws are appraised with the profiles of the mean temperature defect, mean streamwise velocity, normal velocity fluctuations, temperature fluctuations and Reynolds shear stress. Based on the arguments of an inner (near-wall) and outer (channel-centre) region, the DNS data is found to support a −1/3 power law for the mean temperature in an overlap region. Using the inner and outer temperature profiles, an implicit heat transfer equation is obtained and a correction term in the equation is shown to be not negligible for the present Ra range when compared with explicit equations found in literature. In addition, I determined that the mean streamwise velocity and normal velocity fluctuations collapse in the inner region when using the outer velocity scale. A similar collapse is noted in the profiles of temperature fluctuations with increasing Ra when normalised with inner temperature and length scale. Lastly, I show evidence of an incipient proportional relationship between friction velocity and the outer velocity scale with increasing Ra. The study is extended to the spectrum of turbulent kinetic energy and temperature fluctuations of the flow. The one-dimensional streamwise spectra collapse onto the −5/3 slope, coinciding with the standard Kolmogorov form of the power spectra reported in literature. This collapse is found to occur in the outer region of the flow in the bounds between the peaks of the mean streamwise velocity. In spectrogram form, I find evidence that the spectral peaks correspond to energetic velocity structures in the channel — the structures of streamwise velocity fluctuations appear to stretch half of the streamwise domain and occur at a quarter intervals in the spanwise direction. From 2-dimensional autocorrelations, the structures of spanwise velocity fluctuations are found to be organised in a hatched pattern in an inner location (z^× i ≈ 7) and at the channel-centre. The respective pattern angles are \theta_ i ≈ 54◦ and \theta_ o ≈ 48◦, both measured from the horizontal. For the temperature spectrum, the −5/3 collapse is also observed in the same bounds as the velocity spectrum. In pre-multiplied form, the spectral peak is found to occur at the wall-normal location which coincides with the peak temperature fluctuations in the channel. With increasing Ra, the wall-parallel isocontours of temperature are found to show standard features of turbulent pressure driven boundary layers — streaks with spanwise length of 100+ units.
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ItemConvective methods of pumping and drag reduction( 2013)It is the convection of the velocity field by itself that renders many fluid mechanics problems mathematically challenging, and produces complicated, and often non-intuitive flow phenomena. Pumping and drag reduction are effectively related concepts, in that they both involve increasing the volume flux of the fluid. In this work, we consider three different methods of pumping and drag reduction, all of which result, partially or entirely, from the effect of convection. The first of these methods is the drag reduction obtained by the addition of elastic polymers to a turbulently flowing liquid. This effect is not well understood, and a complete physical explanation of the phenomenon remains to be made. However, it is clear that the polymer has the capacity to transport energy and momentum within the fluid, and energy may also dissipate within the polymer itself. In this work, it is proved that the addition of elastic polymers to a turbulent flow cannot reduce the drag to a level below that of the equivalent laminar flow. This proof can also be applied to similar methods of drag reduction, such as the presence of surfactant micelles within a turbulently flowing liquid and the presence of sand particles within high winds and water droplets within cyclones. The second method is known as "transpiration", and consists of a dynamic regime of blowing and suction at the wall of the pipe or channel which imparts no net volume flux upon the flow. Using a perturbation analysis, the pumping effect of transpiration has been quantified in this work. It is shown that this pumping results from convection, and relies on the presence of large velocity gradients within the flow. The third method consists of oscillating waves in the wall of the pipe or channel. This has particular relevance to the valveless impedance pump, which consists of a thin tube, one section of which is elastic and is subjected to rhythmic pinching at some point offset from its centre. This pinching induces oscillating waves within the wall of the tube, which in turn induce a flow. The flow induced by small-amplitude oscillations, in the wall, has been derived through a perturbation analysis. In this way, we are able to separate the effect of convection from the more readily intuitive dragging effect that the wave has upon the fluid, and thereby quantify the importance of convection in such systems. It is found that even within small tubes, the effect of convection remains generally of the same order of magnitude as the dragging effect, and that no effective model of the valveless impedance pump could safely neglect the effect of convection.
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ItemEvolution of zero pressure gradient turbulent boundary layers from different initial conditions( 2012)Turbulent boundary layers developing under zero pressure gradient (ZPG) condition are investigated experimentally with the overall aim of learning more about the streamwise evolution of these wall-bounded flows close to the quasi-equilibrium state (The definition of a quasi-equilibrium boundary layer is from Perry et al. [1994] where the wake parameter II is allowed to vary with streamwise distance but it is assumed that the wake gradient is sufficiently small so as to have negligible effect on the shear stress profiles). Scaling of the streamwise broadband turbulence intensity is also investigated. A key aspect of this study is obtaining high fidelity measurements at high Reynolds numbers over a large range of streamwise locations. This has required a novel hot-wire calibration technique. The research work also represents an effort to acquire very high quality ZPG turbulent boundary layer data ranging from Reт = δ Uт/ v ≈2740—22884 (here δ is boundary layer thickness, Uт is friction velocity and v is kinematic viscosity). The inner-normalized wire length l+ ≈ 23 ± 2 is maintained for Reynolds numbers Reт = 2740 —13320. This length increases to 29 and 38 for Reт = 17777 and 22884 respectively. To minimize the effect of changes in boundary conditions for different freestream velocities, the entire set of experiments were performed at three freestream velocities of 20m/s, 30m/s and 40m/s to maintain constant unit Reynolds number U∞/v ≈ 1.295 x 106, 1.91 x 106 and 2/50 x 106 m-1 respectively. Different Reynolds numbers were achieved at 10 different streamwise stations over a 27m long tunnel floor. Mean flow and higher order statistics such as broadband turbulence intensity, skewness, flatness as well as spectral measurements were made for all the Reynolds numbers. The logarithmic law of the wall provides a universal behaviour for the mean velocity profile in the inner region. Universal behaviour in the outer region is provided by the law of the wake. A new scaling is proposed for the streamwise Reynolds stress and energy spectra covering the inner, logarithmic and outer region. Comparisons are made with results from other experiments and numerical simulations. The research work also represents an effort to acquire very high quality ZPG turbulent boundary layer data ranging from Reт = δ Uт/ ѵ ≈2740—22884 (here δ is boundary layer thickness, Uт is friction velocity and ѵ is kinematic viscosity). The inner-normalized wire length l+ ≈ 23 ± 2 is maintained for Reynolds numbers Reт = 2740 —13320. This length increases to 29 and 38 for Reт = 17777 and 22884 respectively. To minimize the effect of changes in boundary conditions for different freestream velocities, the entire set of experiments were performed at three freestream velocities of 20m/s, 30m/s and 40m/s to maintain constant unit Reynolds number U∞/ѵ ≈ 1.295 x 106, 1.91 x 106 and 2/50 x 106 m-1 respectively. Different Reynolds numbers were achieved at 10 different streamwise stations over a 27m long tunnel floor. Mean flow and higher order statistics such as broadband turbulence intensity, skewness, flatness as well as spectral measurements were made for all the Reynolds numbers. The logarithmic law of the wall provides a universal behaviour for the mean velocity profile in the inner region. Universal behaviour in the outer region is provided by the law of the wake. A new scaling is proposed for the streamwise Reynolds stress and energy spectra covering the inner, logarithmic and outer region. Comparisons are made with results from other experiments and numerical simulations.