 Mechanical Engineering  Research Publications
Mechanical Engineering  Research Publications
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ItemCharacteristics of Reynolds Shear Stress in Adverse Pressure Gradient Turbulent Boundary LayersRomero, S ; Zimmerman, S ; Philip, J ; Klewicki, J (Springer, 2021)The focus of the present work is to characterize the features of the turbulent inertia term (the wallnormal gradient of Reynolds shear stress) through the mean momentum balance and the Reynolds shear stress correlation coefficient (ρuv ). Effects of the Reynolds number and Clauser pressuregradient parameter, β, are discussed. Large eddy simulations of low Reynolds number adverse pressure gradient turbulent boundary layers from Bobke et al. [1], low Reynolds number experimental data from Vila et al. [2] and Volino [3], and newly acquired experimental data at higher Reynolds number from the Flow Physics Facility at The University of New Hampshire are utilized for this analysis. Observations are compared to zero pressure gradient turbulent boundary layer direct numerical simulations of Schlatter and Örlu [4] and Sillero et al. [5], and experimental data from Zimmerman et al. [6] and Zimmerman [7]. These cases show that the correlation coefficient (ρuv ) decreases in magnitude with increasing Reynolds number and β. However, from these initial observations we find that ρuv is more sensitive to changes in the Reynolds number in comparison to the examined range of β. We also find that the location of zerocrossing of the turbulent inertia term seems to scale with δ+ while the minimum of ρuv scales with δ.

ItemStress equation based scaling framework for adverse pressure gradient turbulent boundary layersRomero, SK ; Zimmerman, SJ ; Philip, J ; Klewicki, JC (Elsevier, 20220201)This paper provides a framework for estimating appropriate turbulent velocity scales in adverse pressure gradient turbulent boundary layers (APG TBLs) via a study of the mean stress balance. We examine the velocity scales of APG TBLs using the relationship between the Reynolds shear stress and pressure stress. It is reasoned that as distance from the wall increases the velocity scaling transitions from one dominated by the wallshearstress velocity scale, uτ, to a scaling dominated by the pressure stress. A velocity scale, uhyb, is proposed that varies with distance from the wall and combines the wallshearstress velocity with a pressurestressbased velocity. This investigation uses new high Reynolds number (7000≲Reτ≲7800) experimental measurements, existing lower Reynolds number experimental (600≲Reτ≲2000) and computational (Reτ<700) data sets. The proposed velocity scale realizes similarity in the turbulent stress profiles to a degree that is superior to that achievable via any walldistanceindependent velocity scale when considering the full extent of the flow domain.

ItemReproducing AS/NZS terraintype wind profiles in a shortfetch windtunnelKevin, K ; Philip, J ; Monty, J ; Klewicki, J (AWES, 2018)

ItemDownstream Recovery of Turbulence Kinetic Energy in the Wake of a Turbulent Boundary Layer WingBody Junction FlowZimmerman, S ; Philip, J ; Marino, N ; Klewicki, J (Australasian Fluid Mechanics Society, 2018)A multisensor hotwire probe capable of simultaneously measuring all three components of the velocity vector [Zimmerman et al. 2017] has been deployed in the wake of a turbulent boundary layer wingbody junction flow. The wing shape—a 3:2 semielliptic nose joined to a NACA 0020 airfoil tail—matches that used in a number of existing studies of wingbody junction wake flow (e.g. see the review of Simpson [2001]). Data have been collected in four spanwise/wallnormal measurement planes ranging from 1 to 33 chord lengths behind the trailing edge of the junction. The measurement planes span a domain over which the unperturbed boundary layer would develop from friction Reynolds number Reτ ≈ 8000 –11000. The downstream extent (per chord length) of the present data is the furthest of any experimental effort to date. Despite having a recovery length many times longer than the typical streamwise wavelength of boundary layer ‘superstructure’ motions [Hutchins and Marusic 2007], the turbulence kinetic energy (TKE) profiles at the furthest downstream station still exhibit spanwise inhomogeneity. Data from the measurement planes closer to the junction offer insight into the momentum and turbulence transporting effects of the trailing ‘horseshoe’ vortex, as well as how these effects propagate downstream.

ItemVortex Rings in a Stratified FluidElsnab, J ; Zhen, M ; Philip, J ; Klewicki, J (Australian fluid mechanics society, 2018)

ItemAn invariant representation of mean inertia: theoretical basis for a log law in turbulent boundary layersMorrillWinter, C ; Philip, J ; Klewicki, J (CAMBRIDGE UNIV PRESS, 20170225)A refined scaling analysis of the twodimensional mean momentum balance (MMB) for the zeropressuregradient turbulent boundary layer (TBL) is presented and experimentally investigated up to high friction Reynolds numbers, $\unicode[STIX]{x1D6FF}^{+}$. For canonical boundary layers, the mean inertia, which is a function of the wallnormal 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 squareroot Reynolds number scaling for the log layer onset and a welldefined layer structure based on the balance of terms in the MMB. The present analyses evidence that similarly wellfounded 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 physical reasoning is that the mean inertia is primarily a largescale outer layer contribution, the ‘shape’ of which becomes invariant of $\unicode[STIX]{x1D6FF}^{+}$ with increasing $\unicode[STIX]{x1D6FF}^{+}$, and with a ‘magnitude’ that is inversely proportional to $\unicode[STIX]{x1D6FF}^{+}$. The present analyses are enabled and corroborated using recent high resolution, large Reynolds number hotwire measurements of all the terms in the TBL MMB.

ItemReynoldsnumberdependent turbulent inertia and onset of log region in pipe flowsChin, C ; Philip, J ; Klewicki, J ; Ooi, A ; Marusic, I (CAMBRIDGE UNIV PRESS, 20141001)Abstract A detailed analysis of the ‘turbulent inertia’ (TI) term (the wallnormal gradient of the Reynolds shear stress,$\mathrm{d} \langle uv\rangle /\mathrm{d} y $), in the axial mean momentum equation is presented for turbulent pipe flows at friction Reynolds numbers$\delta ^{+} \approx 500$, 1000 and 2000 using direct numerical simulation. Two different decompositions for TI are employed to further understand the mean structure of wall turbulence. In the first, the TI term is decomposed into the sum of two velocity–vorticity correlations ($\langle v \omega _z \rangle + \langle  w \omega _y \rangle $) and their cospectra, which we interpret as an advective transport (vorticity dispersion) contribution and a changeofscale effect (associated with the mechanism of vorticity stretching and reorientation). In the second decomposition, TI is equivalently represented as the wallnormal gradient of the Reynolds shear stress cospectra, which serves to clarify the accelerative or decelerative effects associated with turbulent motions at different scales. The results show that the innernormalised position,$y_m^{+}$, where the TI profile crosses zero, as well as the beginning of the logarithmic region of the wall turbulent flows (where the viscous force is leading order) move outwards in unison with increasing Reynolds number as$y_m^{+} \sim \sqrt{\delta ^{+}}$because the eddies located close to$y_m^{+}$are influenced by largescale accelerating motions of the type$\langle  w \omega _y \rangle $related to the changeofscale effect (due to vorticity stretching). These largescale motions of$O(\delta ^{+})$gain a spectrum of larger length scales with increasing$\delta ^{+}$and are related to the emergence of a secondary peak in the$uv$cospectra. With increasing Reynolds number, the influence of the$O(\delta ^{+})$motions promotes viscosity to act over increasingly longer times, thereby increasing the$y^{+}$extent over which the mean viscous force retains leading order. Furthermore, the TI decompositions show that the$\langle v \omega _z \rangle $motions (advective transport and/or dispersion of vorticity) are the dominant mechanism in and above the log region, whereas$\langle  w \omega _y \rangle $motions (vorticity stretching and/or reorientation) are most significant below the log region. The motions associated with$\langle  w \omega _y \rangle $predominantly underlie accelerations, whereas$\langle v \omega _z \rangle $primarily contribute to decelerations. Finally, a description of the structure of wall turbulence deduced from the present analysis and our physical interpretation is presented, and is shown to be consistent with previous flow visualisation studies.

ItemSelfsimilarity in the inertial region of wall turbulenceKlewicki, J ; Philip, J ; Marusic, I ; Chauhan, K ; MorrillWinter, C (AMER PHYSICAL SOC, 20141224)The inverse of the von Kármán constant κ is the leading coefficient in the equation describing the logarithmic mean velocity profile in wall bounded turbulent flows. Klewicki [J. Fluid Mech. 718, 596 (2013)] connects the asymptotic value of κ with an emerging condition of dynamic selfsimilarity on an interior inertial domain that contains a geometrically selfsimilar hierarchy of scaling layers. A number of properties associated with the asymptotic value of κ are revealed. This is accomplished using a framework that retains connection to invariance properties admitted by the mean statement of dynamics. The development leads toward, but terminates short of, analytically determining a value for κ. It is shown that if adjacent layers on the hierarchy (or their adjacent positions) adhere to the same selfsimilarity that is analytically shown to exist between any given layer and its position, then κ≡Φ(2)=0.381966..., where Φ=(1+√5)/2 is the golden ratio. A number of measures, derived specifically from an analysis of the mean momentum equation, are subsequently used to empirically explore the veracity and implications of κ=Φ(2). Consistent with the differential transformations underlying an invariant form admitted by the governing mean equation, it is demonstrated that the value of κ arises from two geometric features associated with the inertial turbulent motions responsible for momentum transport. One nominally pertains to the shape of the relevant motions as quantified by their area coverage in any given wallparallel plane, and the other pertains to the changing size of these motions in the wallnormal direction. In accord with selfsimilar mean dynamics, these two features remain invariant across the inertial domain. Data from direct numerical simulations and higher Reynolds number experiments are presented and discussed relative to the selfsimilar geometric structure indicated by the analysis, and in particular the special form of selfsimilarity shown to correspond to κ=Φ(2).

ItemStatistical evidence of an asymptotic geometric structure to the momentum transporting motions in turbulent boundary layersMorrillWinter, C ; Philip, J ; Klewicki, J (ROYAL SOC, 20170313)The turbulence contribution to the mean flow is reflected by the motions producing the Reynolds shear stress (〈uv〉) and its gradient. Recent analyses of the mean dynamical equation, along with data, evidence that these motions asymptotically exhibit selfsimilar geometric properties. This study discerns additional properties associated with the uv signal, with an emphasis on the magnitudes and length scales of its negative contributions. The signals analysed derive from highresolution multiwire hotwire sensor data acquired in flatplate turbulent boundary layers. Spacefilling properties of the present signals are shown to reinforce previous observations, while the skewness of uv suggests a connection between the size and magnitude of the negative excursions on the inertial domain. Here, the size and length scales of the negative uv motions are shown to increase with distance from the wall, whereas their occurrences decrease. A joint analysis of the signal magnitudes and their corresponding lengths reveals that the length scales that contribute most to 〈uv〉 are distinctly larger than the average geometric size of the negative uv motions. Cospectra of the streamwise and wallnormal velocities, however, are shown to exhibit invariance across the inertial region when their wavelengths are normalized by the width distribution, W(y), of the scaling layer hierarchy, which renders the mean momentum equation invariant on the inertial domain.This article is part of the themed issue 'Toward the development of highfidelity models of wall turbulence at large Reynolds number'.