Mechanical Engineering - Research Publications
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ItemRevisiting the law of the wake in wall turbulence(CAMBRIDGE UNIV PRESS, 2017-01-25)The streamwise mean velocity profile in a turbulent boundary layer is classically described as the sum of a log law extending all the way to the edge of the boundary layer and a wake function. While there is theoretical support for the log law, the wake function, defined as the deviation of the measured velocity profile from the log law, is essentially an empirical fit and has no real physical underpinning. Here, we present a new physically motivated formulation of the velocity profile in the outer region, and hence for the wake function. In our approach, the entire flow is represented by a two-state model consisting of an inertial self-similar region designated as ‘pure wall flow state’ (featuring a log-law velocity distribution) and a free stream state, which results in a jump in velocity at the interface separating the two. We show that the model provides excellent agreement with the available high Reynolds number mean velocity profiles if this interface is assumed to fluctuate randomly about a mean position with a Gaussian distribution. The new concept can also be extended to internal geometries in the same form, again confirmed by the data. Furthermore, adopting the same interface distribution in a two-state model for the streamwise turbulent intensities, with unchanged parameters, also yields a reliable and consistent prediction for the decline in the outer region of these profiles in all geometries considered. Finally, we discuss differences between our model interface and the turbulent/non-turbulent interface (TNTI) in turbulent boundary layers. We physically interpret the two-state model as lumping the effects of internal shear layers and the TNTI into a single discontinuity at the interface.
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ItemGlobal and local aspects of entrainment in temporal plumes(CAMBRIDGE UNIV PRESS, 2017-02-10)To date, the understanding of the role buoyancy plays in the entrainment process in unstable configurations such as turbulent plumes remains incomplete. Towards addressing this question, we set up a flow in which a plume evolves in time instead of space. We demonstrate that the temporal problem is equivalent to a spatial plume in a strong coflow and address in detail how the temporal plume can be realized via direct numerical simulation. Using numerical data of plume simulations up to $Re_{\unicode[STIX]{x1D706}}\approx 100$, we show that the entrainment coefficient can be determined consistently using a global entrainment analysis in an integral framework as well as via a local approach. The latter is based on a study of the local propagation of the turbulent/non-turbulent interface relative to the fluid. Locally, this process is dominated by small-scale diffusion which is amplified by interface convolutions such that the total entrained flux is independent of viscosity. Further, we identify a direct buoyancy contribution to entrainment by baroclinic torque, which accounts for 8 %–12 % of the entrained flux locally, comparable to the 15 % buoyancy contribution at the integral level. It appears that the baroclinic torque is a mechanism that might explain higher values of the entrainment coefficient in spatial plumes compared with jets.
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ItemInterfaces of uniform momentum zones in turbulent boundary layers(CAMBRIDGE UNIV PRESS, 2017-06-10)In this paper we examine the characteristics of the interfaces that demarcate regions of relatively uniform streamwise momentum in turbulent boundary layers. The analysis utilises particle image velocimetry databases that span more than an order of magnitude of friction Reynolds number ($Re_{\unicode[STIX]{x1D70F}}=10^{3}$–$10^{4}$), enabling us to provide a detailed description of the interfacial layers as a function of Reynolds number. As reported by Adrianet al.(J. Fluid Mech., vol. 422, 2000, pp. 1–54), these interfaces appear as persistent regions of strong shear with distinct patches of vorticity consistent with a packet-like structure. Here, however, we treat these interfaces as continuous lines, thus averaging the properties of the vortical patches, and find that their geometry is highly contorted and exhibits self-similarity across a wide range of scales. Specifically, the lengths of the edges of uniform momentum zones exhibit a power-law behaviour with a fractal scaling that has a constant exponent across the boundary layer, while the topmost edge or the turbulent/non-turbulent interface shows a sudden increase in the exponent. The accompanying sharp changes in velocity that occur at these edges are found to change in magnitude as a function of wall-normal height, being larger closer to the wall. Further, a Reynolds number invariance is exhibited when the magnitude of the step-like changes in velocity is scaled by the skin-friction velocity, meanwhile, the width across which it occurs is shown to be of the order of the Taylor microscale. Based on these quantitative measures, the Reynolds number scaling observed and the persistent presence of sharp changes in momentum in turbulent boundary layers, a simple model is used to reconstruct the mean velocity profile. Insight gained from the model enhances our understanding of how instantaneous phenomena (such as a zonal-like structural arrangement) manifests in the averaged flow statistics and confirms that the instantaneous momentum in a turbulent boundary layer appears to mainly consist of a step-like profile as a function of wall-normal distance.
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ItemThe effects of laser-sheet misalignment on Stereo-PIV measurements in wall-bounded turbulence(Australasian Fluid Mechanics Society, 2016)
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ItemCharacteristics of the entrainment velocity in a developing wake(International Symposium on Turbulence and Shear Flow Phenomena, 2015)
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ItemDistance-from-the-wall scaling of turbulent motions in wall-bounded flows(AIP Publishing, 2017-02)An assessment of self-similarity in the inertial sublayer is presented by considering the wall-normal velocity, in addition to the streamwise velocity component. The novelty of the current work lies in the inclusion of the second velocity component, made possible by carefully conducted subminiature ×-probe experiments to minimise the errors in measuring the wall-normal velocity. We show that not all turbulent stress quantities approach the self-similar asymptotic state at an equal rate as the Reynolds number is increased, with the Reynolds shear stress approaching faster than the streamwise normal stress. These trends are explained by the contributions from attached eddies. Furthermore, the Reynolds shear stress cospectra, through its scaling with the distance from the wall, are used to assess the wall-normal limits where self-similarity applies within the wall-bounded flow. The results are found to be consistent with the recent prediction from the work of Wei et al. [“Properties of the mean momentum balance in turbulent boundary layer, pipe and channel flows,” J. Fluid Mech. 522, 303–327 (2005)], Klewicki [“Reynolds number dependence, scaling, and dynamics of turbulent boundary layers,” J. Fluids Eng. 132, 094001 (2010)], and others that the self-similar region starts and ends at z+∼O(δ+) and O(δ+), respectively. Below the self-similar region, empirical evidence suggests that eddies responsible for turbulent stresses begin to exhibit distance-from-the-wall scaling at a fixed z+ location; however, they are distorted by viscous forces, which remain a leading order contribution in the mean momentum balance in the region z+≲O(δ+), and thus result in a departure from self-similarity.
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ItemEntrainment at multi-scales across the turbulent/non-turbulent interface in an axisymmetric jet(CAMBRIDGE UNIV PRESS, 2016-09)We consider the scaling of the mass flux and entrainment velocity across the turbulent/non-turbulent interface (TNTI) in the far field of an axisymmetric jet at high Reynolds number. Time-resolved, simultaneous multi-scale particle image velocimetry (PIV) and planar laser-induced fluorescence (PLIF) are used to identify and track the TNTI, and directly measure the local entrainment velocity along it. Application of box-counting and spatial-filtering methods, with filter sizes $\unicode[STIX]{x1D6E5}$ spanning over two decades in length, show that the mean length of the TNTI exhibits a power-law behaviour with a fractal dimension $D\approx 0.31{-}0.33$. More importantly, we invoke a multi-scale methodology to confirm that the mean mass flux, which is equal to the product of the entrainment velocity and the surface area, remains constant across the range of filter sizes. The results, within experimental uncertainty, also show that the entrainment velocity along the TNTI exhibits a power-law behaviour with $\unicode[STIX]{x1D6E5}$, such that the entrainment velocity increases with increasing $\unicode[STIX]{x1D6E5}$. In fact, the mean entrainment velocity scales at a rate that balances the scaling of the TNTI length such that the mass flux remains independent of the coarse-grain filter size, as first suggested by Meneveau & Sreenivasan (Phys. Rev. A, vol. 41, no. 4, 1990, pp. 2246–2248). Hence, at the smallest scales the entrainment velocity is small but is balanced by the presence of a very large surface area, whilst at the largest scales the entrainment velocity is large but is balanced by a smaller (smoother) surface area.