Mechanical Engineering - Research Publications
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ItemA wall-wake model for the turbulence structure of boundary layers. Part 2. Further experimental support(Cambridge University Press, 1995)In Part 1 an extension of the attached eddy hypothesis was developed and applied to equilibrium pressure gradient turbulent boundary layers. In this paper the formulation is applied to data measured by the authors from non-equilibrium layers and agreement with the extended theory is encouraging. Also power spectra of the Reynolds stresses as developed from the extended theory compare favourably with experiment. The experimental data include a check of cone-angle effects by using a flying hot wire.
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ItemThe effect of aspect ratio and divergence on the turbulence structure of boundary layers( 2007)The effect of the aspect ratio of a turbulent boundary layer on the mean flow, broadband turbulence intensities and Reynolds shear stress has been studied. The aspect ratio (AR) is defined as the boundary layer thickness divided by the boundary layer width, i.e. the effective wind tunnel width. Measurements have been taken in a nominally zero pressure gradient layer at a single station for three different aspect ratio settings, AR=1/4, AR=1/7, and AR=1/13. The measurements show that the turbulent quantities were unaffected when the aspect ratio was increased from AR=1/13 to AR=1/7. However at AR=1/4 there appears to be a slight increase in the broadband turbulence intensities and Reynolds shear stress.
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ItemA wall-wake model for the turbulence structure of boundary layers. Part 1. Extension of the attached eddy hypothesis(Cambridge University Press, 1995)The attached eddy hypothesis developed for zero pressure gradient boundary layers and for pipe flow is extended here to boundary layers with arbitary streamwise pressure gradients, both favourable and adverse. It is found that in order to obtain the correct quantitative results for all components of the Reynolds stresses, two basiv types of eddy structure geometries are required. The first type, called type-A, is interpreted to give a 'wall structure' and the second, referred to as type-B, gives a 'wake structure'. This is an analogy with the conventional mean velocity formulation of Coles where the velocity is decomposed into a law of the wall and a law of the wake.If the above mean velocity formulation is accepted, then in principle, once the eddy geometries are fixed for the two eddy types, all Reynolds stresses and associated spectra contributed from the attached eddies can be computed without any further empirical constants. This is done by using the momentum equation and certain convolution integrals developed here based on the attached eddy hypothesis. The theory is developed using data from equilibrium and quasi-equilibrium flows. In Part 2 the authors' non-equilibrium data are used.
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ItemWall turbulence closure based on classical similarity laws and the attached eddy hypothesis( 1994)A new look at the closure problem of turbulent boundary layers is taken here using recently derived analytical expressions for the shear stress distributions. These expressions are based on logarithmic law of the wall and law of the wake formulation of Coles [J. Fluid Mech. 1, 191 (1956)] with the mean continuity and the mean momentum differential and integral equations. The concept of equilibrium layers of Clauser [Adv. Mech. 4, 1 (1956)] is extended and using similar ideas as Rotta [Prog. Aeronaut. Sci. 2, 1(1962)] for self-similarity, a closure scheme is proposed for layers developing in arbitrary pressure gradients for the case where the streamwise derivative of the Coles wake factor is not too large. For a given flow case, this Coles wake condition can be tested with internal consistency checks. The mathematical framework is most suitable for incorporating Townsend’s attached eddy hypothesis as recently developed by Perry, Li, and Marusic [Phils. Trans. R. Soc. London. Ser. A 336, 67 (1991)] for closure. This gives an opportunity to incorporate coherent structure concepts into closure schemes. Possible ways of handling the difficult case where the streamwise derivative of the Coles wake factor is significant are discussed.
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ItemOn the streamwise evolution of turbulent boundary layers in arbitrary pressure gradients(Cambridge University Press, 2002)A new approach to the classic closure problem for turbulent boundary layers is presented. This involves, first, using the well-known mean-flow scaling laws such asthe log law of the wall and the law of the wake of Coles (1956) together with the mean continuity and the mean momentum differential and integral equations. The important parameters governing the flow in the general non-equilibrium case are identified and are used for establishing a framework for closure. Initially closure is achieved here empirically and the potential for achieving closure in the future using the wall-wake attached eddy model of Perry & Marusic (1995) is outlined. Comparisons are made with experiments covering adverse-pressure-gradient flows in relaxing and developing states and flows approaching equilibrium sink flow. Mean velocity profiles, total shear stress and Reynolds stress profiles can be computed for different streamwise stations, given an initial upstream mean velocity profile and the streamwise variation of free-stream velocity. The attached eddy model of Perry & Marusic (1995) can then be utilized, with some refinement, to compute the remaining unknown quantities such as Reynolds normal stresses and associated spectra and cross-power spectra in the fully turbulent part of the flow.
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ItemTowards a closure scheme for turbulent boundary layers using the attached eddy hypothesis(Royal Society Publishing, 1991)In this paper, an attempt is made to formulate a closure hypothesis for adverse pressure gradient turbulent layers using the attached eddy hypothesis of Townsend and Perry & Chong, which was developed originally for zero pressure gradient layers and parallel duct flows.To the authors’ knowledge, this work represents one of the few attempts to use coherent structure ideas in the formulation of a closure scheme. At present this closure scheme is primitive and many of the assumptions are of an arbituary nature but the analysis at least points out where the difficulties are and which areas need more work.
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ItemSimilarity law for the streamwise turbulence intensity in zero-pressure-gradient turbulent boundary layers( 1997)A similarity relationship is proposed to describe the streamwise broadband-turbulence intensity in a zero-pressure-gradient boundary layer. The formulation is applicable to the entire region of the flow beyond the viscous buffer zone and is based on the attached eddy hypothesis, the Reynolds-number-similarity hypothesis and the assumed existence of Kolmogorov eddies with a universal inertial subrange. Experimental data of the authors and those from various published works covering a large Reynolds number range are investigated in light of this formulation.
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ItemEvolution and structure of sink-flow turbulent boundary layers( 2001)An experimental and theoretical investigation of turbulent boundary layers developing in a sink-flow pressure gradient was undertaken. Three flow cases were studied, corresponding to different acceleration strengths. Mean-flow measurements were taken for all three cases, while Reynolds stresses and spectra measurements were made for two of the flow cases. In this study attention was focused on the evolution of the layers to an equilibrium turbulent state. All the layers were found to attain a state very close to precise equilibrium. This gave equilibrium sink flow data at higher Reynolds numbers than in previous experiments. The mean velocity profiles were found to collapse onto the conventional logarithmic law of the wall. However, for profiles measured with the Pitot tube, a slight ‘kick-up’ from the logarithmic law was observed near the buffer region, whereas the mean velocity profiles measured with a normal hot wire did not exhibit this deviation from the logarithmic law. As the layers approached equilibrium, the mean velocity profiles were found to approach the pure wall profile and for the highest level of acceleration Π was very close to zero, where Π is the Coles wake factor. This supports the proposition of Coles (1957), that the equilibrium sink flow corresponds to pure wall flow. Particular interest was also given to the evolutionary stages of the boundary layers, in order to test and further develop the closure hypothesis of Perry, Marusic & Li (1994). Improved quantitative agreement with the experimental results was found after slight modification of their original closure equation.
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ItemA study of the Reynolds-shear-stress spectra in zero- pressure-gradient boundary layers( 1989)Measurements of Reynolds-shear-stress spectra in smooth-wall zero-pressure-gradient turbulent boundary layers are presented for four different Karman numbers. The results are plotted using various scaling variables and found to collapse with 'inner-flow' scaling for a modest range of mid-range wavenumbers, the extent of collapse increasing for higher Karman numbers. The results are discussed in light of the attached eddy hypothesis of Townsend (1976)as extended by Perry and Chong (1982). A computation of the cross-power spectra, based upon the same theory, is also presented.
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ItemAn experimental and computational study on the orientation of attached eddies in turbulent boundary layers( 1992)The flow visualisation results of various researchers suggest that the attached eddies align themselves with the direction of the principal rate of mean strain. The principal rate of mean strain is influenced by pressure gradient. With the knowledge of this dependence and using the wall turbulence model proposed by Perry & Chong (1982) and later modified by Perry et al. (1986, 1991) it may be possible to predict the characteristics of a turbulent boundary layer flow subjected to any arbitrary pressure gradient.This work investigates quantitatively the orientation of attached eddies in a turbulent boundary layer. This is achieved by maximising the two point correlation coefficient between the signals obtained from two normal hot-wires having a streamwise offset and a predetermined normal to the wall spacing between them. The experimental results will also be compared with some computational results based on the attached eddy hypothesis.