The Experts below are selected from a list of 195741 Experts worldwide ranked by ideXlab platform
Lijun Xuan - One of the best experts on this subject based on the ideXlab platform.
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on the karman momentum integral approach and the pohlhausen paradox
Physics of Fluids, 2020Co-Authors: Joseph Majdalani, Lijun XuanAbstract:This work explores simple relations that follow from the Momentum-Integral Equation absent a pressure gradient. The resulting expressions enable us to relate the boundary-layer characteristics of a velocity profile, u(y), to an assumed flow function and its wall derivative relative to the wall-normal coordinate, y. Consequently, disturbance, displacement, and momentum thicknesses, as well as skin friction and drag coefficients, which are typically evaluated and tabulated in classical monographs, can be readily determined for a given profile, F(ξ) = u/U. Here, ξ = y/δ denotes the boundary-layer coordinate. These expressions are then employed to provide a rational explanation for the 1921 Pohlhausen polynomial paradox, namely, the reason why a quartic representation of the velocity leads to less accurate predictions of the disturbance, displacement, and momentum thicknesses than using cubic or quadratic polynomials. Not only do we identify the factors underlying this behavior but also we proceed to outline a procedure to overcome its manifestation at any order. This enables us to derive optimal piecewise approximations that do not suffer from the particular limitations affecting Pohlhausen’s F = 2ξ − 2ξ3 + ξ4. For example, our alternative profile, F = (5ξ − 3ξ3 + ξ4)/3, leads to an order-of-magnitude improvement in precision when incorporated into the Karman–Pohlhausen approach in both viscous and thermal analyses. Then, noting the significance of the Blasius constant, s¯≈1.630 398, this approach is extended to construct a set of uniformly valid solutions, including F=1−exp[−s¯ξ(1+12s¯ξ+ξ2)], which continues to hold beyond the boundary-layer edge as y → ∞. Given its substantially reduced error, the latter is shown, through comparisons to other models, to be practically equivalent to the Blasius solution.
Joseph Majdalani - One of the best experts on this subject based on the ideXlab platform.
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on the karman momentum integral approach and the pohlhausen paradox
Physics of Fluids, 2020Co-Authors: Joseph Majdalani, Lijun XuanAbstract:This work explores simple relations that follow from the Momentum-Integral Equation absent a pressure gradient. The resulting expressions enable us to relate the boundary-layer characteristics of a velocity profile, u(y), to an assumed flow function and its wall derivative relative to the wall-normal coordinate, y. Consequently, disturbance, displacement, and momentum thicknesses, as well as skin friction and drag coefficients, which are typically evaluated and tabulated in classical monographs, can be readily determined for a given profile, F(ξ) = u/U. Here, ξ = y/δ denotes the boundary-layer coordinate. These expressions are then employed to provide a rational explanation for the 1921 Pohlhausen polynomial paradox, namely, the reason why a quartic representation of the velocity leads to less accurate predictions of the disturbance, displacement, and momentum thicknesses than using cubic or quadratic polynomials. Not only do we identify the factors underlying this behavior but also we proceed to outline a procedure to overcome its manifestation at any order. This enables us to derive optimal piecewise approximations that do not suffer from the particular limitations affecting Pohlhausen’s F = 2ξ − 2ξ3 + ξ4. For example, our alternative profile, F = (5ξ − 3ξ3 + ξ4)/3, leads to an order-of-magnitude improvement in precision when incorporated into the Karman–Pohlhausen approach in both viscous and thermal analyses. Then, noting the significance of the Blasius constant, s¯≈1.630 398, this approach is extended to construct a set of uniformly valid solutions, including F=1−exp[−s¯ξ(1+12s¯ξ+ξ2)], which continues to hold beyond the boundary-layer edge as y → ∞. Given its substantially reduced error, the latter is shown, through comparisons to other models, to be practically equivalent to the Blasius solution.
Emile Touber - One of the best experts on this subject based on the ideXlab platform.
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low order stochastic modelling of low frequency motions in reflected shock wave boundary layer interactions
Journal of Fluid Mechanics, 2011Co-Authors: Emile Touber, Neil D SandhamAbstract:A combined numerical and analytical approach is used to study the low-frequency shock motions observed in shock/turbulent-boundary-layer interactions in the particular case of a shock-reflection configuration. Starting from an exact form of the momentum integral Equation and guided by data from large-eddy simulations, a stochastic ordinary differential Equation for the reflected-shock-foot low-frequency motions is derived. During the derivation a similarity hypothesis is verified for the streamwise evolution of boundary-layer thickness measures in the interaction zone. In its simplest form, the derived governing Equation is mathematically equivalent to that postulated without proof by Plotkin (AIAA J., vol. 13, 1975, p. 1036). In the present contribution, all the terms in the Equation are modelled, leading to a closed form of the system, which is then applied to a wide range of input parameters. The resulting map of the most energetic low-frequency motions is presented. It is found that while the mean boundary-layer properties are important in controlling the interaction size, they do not contribute significantly to the dynamics. Moreover, the frequency of the most energetic fluctuations is shown to be a robust feature, in agreement with earlier experimental observations. The model is proved capable of reproducing available lowfrequency experimental and numerical wall-pressure spectra. The coupling between the shock and the boundary layer is found to be mathematically equivalent to a first-order low-pass filter. It is argued that the observed low-frequency unsteadiness in such interactions is not necessarily a property of the forcing, either from upstream or downstream of the shock, but an intrinsic property of the coupled system, whose response to white-noise forcing is in excellent agreement with actual spectra.
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unsteadiness in shock wave boundary layer interactions
2010Co-Authors: Emile TouberAbstract:The need for better understanding of the low-frequency unsteadiness observed in shock wave/turbulent boundary layer interactions has been driving research in this area for several decades. This work investigates the interaction between an impinging oblique shock and a supersonic turbulent boundary layer via large-eddy simulations. Special care is taken at the inlet in order to avoid introducing artificial low-frequency modes that could affect the interaction. All simulations cover extensive integration times to allow for a spectral analysis at the low frequencies of interest. The simulations bring clear evidence of the existence of broadband and energetically-significant low-frequency oscillations in the vicinity of the reflected shock, thus confirming earlier experimental findings. Furthermore, these oscillations are found to persist even if the upstream boundary layer is deprived of long coherent structures. Starting from an exact form of the momentum integral Equation and guided by data from large-eddy simulations, a stochastic ordinary differential Equation for the reflectedshock foot low-frequency motions is derived. This model is applied to a wide range of input parameters. It is found that while the mean boundary-layer properties are important in controlling the interaction size, they do not contribute significantly to the dynamics. Moreover, the frequency of the most energetic fluctuations is shown to be a robust feature, in agreement with earlier experimental observations. Under some assumptions, the coupling between the shock and the boundary layer is mathematically equivalent to a first-order low-pass filter. Therefore, it is argued that the observed lowfrequency unsteadiness is not necessarily a property of the forcing, either from upstream or downstream of the shock, but simply an intrinsic property of the coupled dynamical system.
Thara Prabhakaran - One of the best experts on this subject based on the ideXlab platform.
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asymptotic scaling of drag in flat plate turbulent boundary layers
Physics of Fluids, 2020Co-Authors: Shivsai Ajit Dixit, Abhishek Kumar Gupta, Harish Choudhary, A K Singh, Thara PrabhakaranAbstract:A new asymptotic −1/2 power-law scaling is derived from the momentum integral Equation for the drag in flat-plate turbulent boundary layers. In the limit of infinite Reynolds number, the appropriate velocity scale for drag is found to be M/ν, where M is the boundary layer kinematic momentum rate and ν is the fluid kinematic viscosity. Data covering a wide range of Reynolds numbers remarkably collapse to a universal drag curve in the new variables. Two models, discrete and continuous, are proposed for this universal drag curve, and a robust drag estimation method, based on these models, is also presented.
Abhishek Kumar Gupta - One of the best experts on this subject based on the ideXlab platform.
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asymptotic scaling of drag in flat plate turbulent boundary layers
Physics of Fluids, 2020Co-Authors: Shivsai Ajit Dixit, Abhishek Kumar Gupta, Harish Choudhary, A K Singh, Thara PrabhakaranAbstract:A new asymptotic −1/2 power-law scaling is derived from the momentum integral Equation for the drag in flat-plate turbulent boundary layers. In the limit of infinite Reynolds number, the appropriate velocity scale for drag is found to be M/ν, where M is the boundary layer kinematic momentum rate and ν is the fluid kinematic viscosity. Data covering a wide range of Reynolds numbers remarkably collapse to a universal drag curve in the new variables. Two models, discrete and continuous, are proposed for this universal drag curve, and a robust drag estimation method, based on these models, is also presented.