The high-Reynolds-number axisymmetric wake of a slender body with a turbulent boundary layer is i... more The high-Reynolds-number axisymmetric wake of a slender body with a turbulent boundary layer is investigated using a hybrid simulation. The wake generator is a 6 : 1 prolate spheroid and the Reynolds number based on the diameter D is Re = 10 5. The transition of the wake to a state of complete self-similarity is investigated by looking for the first time into the far field of a slender-body wake. Unlike bluff-body wakes, here the flow is not dominated by vortex shedding in the near wake. Instead, the recirculation region is very small, the near wake is quasi-parallel and is characterised by the presence of broadband turbulence. Until x/D ≈ 20, the wake decay of a slender body with turbulent boundary layer is very similar to the classic high-Re behaviour, U d ∼ x −2/3. Extrapolation of this observation to larger x/D has led to the belief that these wakes decay following the asymptotic −2/3 decay law. Our results show, however, that this is not the case and the wake transitions to a faster decay rate once complete self-similarity is achieved. In this later region (20 < x/D < 80), mean and turbulence profiles are self-similar. Furthermore, despite the high global and local Reynolds numbers, the classic hypotheses that lead to the well-known decay exponents are not fulfilled. Instead, turbulent dissipation follows a non-equilibrium scaling and a new decay rate U d ∼ x −6/5 is observed. The transition from U d ∼ x −2/3 to U d ∼ x −6/5 is preceded by the dominance of the azimuthal |m| = 1 mode and the emergence of a large-scale helical structure.
Proceedings of the Institution of Mechanical Engineers, Part E: Journal of Process Mechanical Engineering
In this paper, a new iso-parametric tool path generation technique has been presented for machini... more In this paper, a new iso-parametric tool path generation technique has been presented for machining truncated free-form surfaces by means of re-parameterisation. Three methods of re-parameterisation have been discussed, namely, the Coons method, partial differential equation method and the newly developed ‘Boundary Interpolation method.’ Tool paths have been generated based on the iso-parametric curves produced by re-parameterisation. The complete mathematical formulations have been given and subsequently their applications have been studied through some typical cases. Case studies show that the Coons and Laplace partial differential equation have some drawbacks in generating tool paths when the surface boundaries are irregular but the new Boundary Interpolation algorithm gives smooth and efficient iso-parametric tool paths by eliminating the problems like overcrossing (in case of Coons method) and uneven distribution of iso-parametrics (in case of Laplace partial differential equat...
ABSTRACT Direct numerical simulation is used to simulate spatially-evolving flow past a sphere in... more ABSTRACT Direct numerical simulation is used to simulate spatially-evolving flow past a sphere in a stratified fluid. The immersed boundary method is used to treat the sphere inside the domain. The main objective of this study is to characterize the near wake region. Statistics of interest include the drag coefficient, separation angle, Strouhal number, and the spatial evolution of the velocity fluctuations and the defect velocity. In addition to quantitative statistics, visualizations of the vortex structures in the wake will also be provided and discussed. Results are compared and contrasted with previous experimental and numerical data for unstratified and stratified flow past a sphere.
ABSTRACT Direct numerical simulations of turbulent stratified shear flow have been performed. Two... more ABSTRACT Direct numerical simulations of turbulent stratified shear flow have been performed. Two cases were considered. In the first case, the mean streamwise velocity varies linearly in the vertical direction. In the second case, the mean streamwise velocity varies linearly in the horizontal direction. Both cases are vertically stably stratified. The gradient Richardson number was varied from Ri=0 to Ri=10. It is known that the turbulent kinetic energy is distributed unequally over the three velocity components. However, the simulations show that the energy partitions are consistently ordered as streamwise &gt; spanwise &gt; transverse. Here, transverse refers to the component in the direction of shear and spanwise refers to the component normal to the plane of shear. Therefore, the anisotropy due to the mean shear, not the mean stratification, already establishes the ordering of the energy partitions in the range of Richardson numbers considered here. In addition, the components of the dissipation rate are compared. It was found that the vertical gradient of the streamwise velocity contributes most to the total value of the dissipation rate. The authors would like to acknowledge the discussions with Charles W. Van Atta. Supercomputer time was provided by the San Diego Supercomputer Center.
In the Eagle Has Returned Proceedings of the Dedication Conference of the International Space Hall of Fame Alamogordo N Mex October 5 9 1976 San Diego Calif American Astronautical Society Univelt Inc 1976 P 87 101, 1976
An investigation of unsteady hydromagnetic natural convection heat and mass transfer flow of an e... more An investigation of unsteady hydromagnetic natural convection heat and mass transfer flow of an electrically conducting, viscous, incompressible and optically thick radiating fluid past an impulsively moving infinite vertical plate embedded in a uniform porous medium in a rotating system with Hall effects in the presence of homogeneous first order chemical reaction is carried out when temperature of the plate has a temporarily ramped profile. Exact solution of the governing equations is obtained in closed form by Laplace transform technique. Expressions for skin friction due to primary and secondary flows and Nusselt number are derived for both ramped temperature and isothermal plates. Expression for Sherwood number is also derived. The numerical values of primary and secondary fluid velocities, fluid temperature and species concentration are displayed graphically whereas those of skin friction are presented in tabular form for various values of pertinent flow parameters. In order t...
Direct numerical simulations are performed to study the evolution of a towed stratified wake subj... more Direct numerical simulations are performed to study the evolution of a towed stratified wake subject to external turbulence in the background. A field of isotropic turbulence is combined with an initial turbulent wake field and the combined wake is simulated in a temporally evolving framework similar to that of Rind & Castro (J. Fluid Mech., vol. 710, 2012a, p. 482). Simulations are performed for external turbulence whose initial level varies between zero and a moderate intensity of up to 7 % relative to the free stream and whose initial integral length scale is of the same order as that of the wake turbulence. A series of simulations are carried out at a Reynolds number of 10 000 and Froude number of 3. Background turbulence, especially at a level of 3 % or above, is found to have substantial quantitative effects in the stratified simulations. Turbulence inside the wake increases due to the entrainment of external turbulence, and the energy transfer through turbulent production fro...
2011 IEEE Seventh International Conference on eScience, 2011
In many respects, numerical simulations involving solutions to partial differential equations hav... more In many respects, numerical simulations involving solutions to partial differential equations have replaced physical experimentation. However, few tools are available to sift through the deluge of data. We present Saaz, a query framework to analyze the simulation results of multi-scale physical phenomena which admit mathematical rules for characterizing features of interest. Saaz provides high-level primitives that free the domainscientist to concentrate more on scientific discovery and less on code implementation and maintenance. It supports user-defined domain-specific query operations which may be subsequently composed into more complex queries. While Saaz supports offline processing of queries, we explore here the online capabilities by attaching Saaz to a running simulation, improving the simulation's effective temporal resolution. We discuss analysis for a computational fluid dynamics simulation of turbulent flow running on a cluster.
Theoretical and Computational Fluid Dynamics, 1991
The purpose of this study is to investigate compressibility effects on the turbulence in homogene... more The purpose of this study is to investigate compressibility effects on the turbulence in homogeneous shear flow. We find that the growth of the turbulent kinetic energy decreases with increasing Mach numbera phenomenon which is similar to the reduction of turbulent velocity intensities observed in experiments on supersonic free shear layers. An examination of the turbulent energy budget shows that both the compressible dissipation and the pressuredilatation contribute to the decrease in the growth of kinetic energy. The pressure-dilatation is predominantly negative in homogeneous shear flow, in contrast to its predominantly positive behavior in isotropic turbulence. The different signs of the pressure-dilatation are explained by theoretical consideration of the equations for the pressure variance and density variance. We obtained previously the following results for isotropic turbulence; first, the normalized compressible dissipation is of O(M'), and second, there is approximate equipartition between the kinetic and potential energies associated with the fluctuating compressible mode. Both these results have now been substantiated in the case of homogeneous shear. The dilatation field is significantly more skewed and intermittent than the vorticity field. Strong compressions seem to be more likely than strong expansions.
eScholarship provides open access, scholarly publishing services to the University of California ... more eScholarship provides open access, scholarly publishing services to the University of California and delivers a dynamic research platform to scholars worldwide.
The present study sheds light on the subgrid modeling problem encountered in the large eddy simul... more The present study sheds light on the subgrid modeling problem encountered in the large eddy simulation ͑LES͒ of practical flows, where the turbulence is both inhomogeneous and anisotropic due to mean flow gradients. The subgrid scale stress ͑SGS͒ tensor, the quantity that is key to the success of LES, is studied here in such flows using both analysis and direct numerical simulation ͑DNS͒. It is shown that the SGS tensor, for the case of inhomogeneous flow, where the filtering operation is necessarily performed in physical space, contains two components: a rapid part that depends explicitly on the mean velocity gradient and a slow part that does not. The characterization, rapid and slow, is adopted by analogy to that used in the modeling of the pressure-strain in the Reynolds-averaged Navier-Stokes equations. In the absence of mean flow gradients, the slow part is the only nonzero component and has been the subject of much theoretical study. However, the rapid part can be important in the inhomogeneous flows that are often encountered in practice. An analytical estimate of the relative magnitude of the rapid and slow components is derived and the distinct role of each component in the energy transfer between the resolved grid scales and the unresolved subgrid scales is identified. Results that quantify this new decomposition are obtained from DNS data of a turbulent mixing layer. The rapid part is shown to play an important role when the turbulence is in a nonequilibrium state with turbulence production much larger than dissipation or when the filter size is not very small compared to the characteristic integral scale of the turbulence, as in the case of practical LES applications. More importantly, the SGS is observed to be highly anisotropic due to the close connection of the rapid part with the mean shear. The Smagorinsky eddy viscosity and the scale-similarity models are tested by performing a priori tests with data from DNS of the mixing layer. It is found that the scale-similarity model correctly represents the anisotropic energy transfer between grid and subgrid scales that is associated with the rapid part, while the eddy viscosity model captures the dissipation associated with the slow part. This may be a physical reason for the recent successes of the mixed model ͑Smagorinsky plus scale similarity͒ reported in the literature.
Predicting sound radiated by turbulence is of interest in aeroacoustics, hydroacoustics, and comb... more Predicting sound radiated by turbulence is of interest in aeroacoustics, hydroacoustics, and combustion noise. Significant improvements in computer technology have renewed interest in applying numerical techniques to predict sound from turbulent flows. One such technique is a hybrid approach in which the turbulence is computed using a method such as direct numerical simulation ͑DNS͒ or large eddy simulation ͑LES͒, and the sound is calculated using an acoustic analogy. In this study, sound from a turbulent flow is computed using DNS, and the DNS results are compared with acoustic-analogy predictions for mutual validation. The source considered is a three-dimensional region of forced turbulence which has limited extent in one coordinate direction and is periodic in the other two directions. Sound propagates statistically as a plane wave from the turbulence to the far field. The cases considered here have a small turbulent Mach number so that the source is spatially compact; that is, the turbulence integral scale is much smaller than the acoustic wavelength. The scaling of the amplitude and frequency of the far-field sound for the problem considered are derived in an analysis based on Lighthill's acoustic analogy. The analytical results predict that the far-field sound should exhibit ''dipole-type'' behavior; the root-mean-square pressure in the acoustic far field should increase as the cube of the turbulent Mach number. The acoustic power normalized by the turbulent dissipation rate is also predicted to scale as turbulent Mach number cubed. Agreement between the DNS results and the acoustic-analogy predictions is good. This study verifies the ability of the Lighthill acoustic analogy to predict sound generated by a three-dimensional, turbulent source containing many length and time scales.
The high-Reynolds-number axisymmetric wake of a slender body with a turbulent boundary layer is i... more The high-Reynolds-number axisymmetric wake of a slender body with a turbulent boundary layer is investigated using a hybrid simulation. The wake generator is a 6 : 1 prolate spheroid and the Reynolds number based on the diameter D is Re = 10 5. The transition of the wake to a state of complete self-similarity is investigated by looking for the first time into the far field of a slender-body wake. Unlike bluff-body wakes, here the flow is not dominated by vortex shedding in the near wake. Instead, the recirculation region is very small, the near wake is quasi-parallel and is characterised by the presence of broadband turbulence. Until x/D ≈ 20, the wake decay of a slender body with turbulent boundary layer is very similar to the classic high-Re behaviour, U d ∼ x −2/3. Extrapolation of this observation to larger x/D has led to the belief that these wakes decay following the asymptotic −2/3 decay law. Our results show, however, that this is not the case and the wake transitions to a faster decay rate once complete self-similarity is achieved. In this later region (20 < x/D < 80), mean and turbulence profiles are self-similar. Furthermore, despite the high global and local Reynolds numbers, the classic hypotheses that lead to the well-known decay exponents are not fulfilled. Instead, turbulent dissipation follows a non-equilibrium scaling and a new decay rate U d ∼ x −6/5 is observed. The transition from U d ∼ x −2/3 to U d ∼ x −6/5 is preceded by the dominance of the azimuthal |m| = 1 mode and the emergence of a large-scale helical structure.
Proceedings of the Institution of Mechanical Engineers, Part E: Journal of Process Mechanical Engineering
In this paper, a new iso-parametric tool path generation technique has been presented for machini... more In this paper, a new iso-parametric tool path generation technique has been presented for machining truncated free-form surfaces by means of re-parameterisation. Three methods of re-parameterisation have been discussed, namely, the Coons method, partial differential equation method and the newly developed ‘Boundary Interpolation method.’ Tool paths have been generated based on the iso-parametric curves produced by re-parameterisation. The complete mathematical formulations have been given and subsequently their applications have been studied through some typical cases. Case studies show that the Coons and Laplace partial differential equation have some drawbacks in generating tool paths when the surface boundaries are irregular but the new Boundary Interpolation algorithm gives smooth and efficient iso-parametric tool paths by eliminating the problems like overcrossing (in case of Coons method) and uneven distribution of iso-parametrics (in case of Laplace partial differential equat...
ABSTRACT Direct numerical simulation is used to simulate spatially-evolving flow past a sphere in... more ABSTRACT Direct numerical simulation is used to simulate spatially-evolving flow past a sphere in a stratified fluid. The immersed boundary method is used to treat the sphere inside the domain. The main objective of this study is to characterize the near wake region. Statistics of interest include the drag coefficient, separation angle, Strouhal number, and the spatial evolution of the velocity fluctuations and the defect velocity. In addition to quantitative statistics, visualizations of the vortex structures in the wake will also be provided and discussed. Results are compared and contrasted with previous experimental and numerical data for unstratified and stratified flow past a sphere.
ABSTRACT Direct numerical simulations of turbulent stratified shear flow have been performed. Two... more ABSTRACT Direct numerical simulations of turbulent stratified shear flow have been performed. Two cases were considered. In the first case, the mean streamwise velocity varies linearly in the vertical direction. In the second case, the mean streamwise velocity varies linearly in the horizontal direction. Both cases are vertically stably stratified. The gradient Richardson number was varied from Ri=0 to Ri=10. It is known that the turbulent kinetic energy is distributed unequally over the three velocity components. However, the simulations show that the energy partitions are consistently ordered as streamwise &gt; spanwise &gt; transverse. Here, transverse refers to the component in the direction of shear and spanwise refers to the component normal to the plane of shear. Therefore, the anisotropy due to the mean shear, not the mean stratification, already establishes the ordering of the energy partitions in the range of Richardson numbers considered here. In addition, the components of the dissipation rate are compared. It was found that the vertical gradient of the streamwise velocity contributes most to the total value of the dissipation rate. The authors would like to acknowledge the discussions with Charles W. Van Atta. Supercomputer time was provided by the San Diego Supercomputer Center.
In the Eagle Has Returned Proceedings of the Dedication Conference of the International Space Hall of Fame Alamogordo N Mex October 5 9 1976 San Diego Calif American Astronautical Society Univelt Inc 1976 P 87 101, 1976
An investigation of unsteady hydromagnetic natural convection heat and mass transfer flow of an e... more An investigation of unsteady hydromagnetic natural convection heat and mass transfer flow of an electrically conducting, viscous, incompressible and optically thick radiating fluid past an impulsively moving infinite vertical plate embedded in a uniform porous medium in a rotating system with Hall effects in the presence of homogeneous first order chemical reaction is carried out when temperature of the plate has a temporarily ramped profile. Exact solution of the governing equations is obtained in closed form by Laplace transform technique. Expressions for skin friction due to primary and secondary flows and Nusselt number are derived for both ramped temperature and isothermal plates. Expression for Sherwood number is also derived. The numerical values of primary and secondary fluid velocities, fluid temperature and species concentration are displayed graphically whereas those of skin friction are presented in tabular form for various values of pertinent flow parameters. In order t...
Direct numerical simulations are performed to study the evolution of a towed stratified wake subj... more Direct numerical simulations are performed to study the evolution of a towed stratified wake subject to external turbulence in the background. A field of isotropic turbulence is combined with an initial turbulent wake field and the combined wake is simulated in a temporally evolving framework similar to that of Rind & Castro (J. Fluid Mech., vol. 710, 2012a, p. 482). Simulations are performed for external turbulence whose initial level varies between zero and a moderate intensity of up to 7 % relative to the free stream and whose initial integral length scale is of the same order as that of the wake turbulence. A series of simulations are carried out at a Reynolds number of 10 000 and Froude number of 3. Background turbulence, especially at a level of 3 % or above, is found to have substantial quantitative effects in the stratified simulations. Turbulence inside the wake increases due to the entrainment of external turbulence, and the energy transfer through turbulent production fro...
2011 IEEE Seventh International Conference on eScience, 2011
In many respects, numerical simulations involving solutions to partial differential equations hav... more In many respects, numerical simulations involving solutions to partial differential equations have replaced physical experimentation. However, few tools are available to sift through the deluge of data. We present Saaz, a query framework to analyze the simulation results of multi-scale physical phenomena which admit mathematical rules for characterizing features of interest. Saaz provides high-level primitives that free the domainscientist to concentrate more on scientific discovery and less on code implementation and maintenance. It supports user-defined domain-specific query operations which may be subsequently composed into more complex queries. While Saaz supports offline processing of queries, we explore here the online capabilities by attaching Saaz to a running simulation, improving the simulation's effective temporal resolution. We discuss analysis for a computational fluid dynamics simulation of turbulent flow running on a cluster.
Theoretical and Computational Fluid Dynamics, 1991
The purpose of this study is to investigate compressibility effects on the turbulence in homogene... more The purpose of this study is to investigate compressibility effects on the turbulence in homogeneous shear flow. We find that the growth of the turbulent kinetic energy decreases with increasing Mach numbera phenomenon which is similar to the reduction of turbulent velocity intensities observed in experiments on supersonic free shear layers. An examination of the turbulent energy budget shows that both the compressible dissipation and the pressuredilatation contribute to the decrease in the growth of kinetic energy. The pressure-dilatation is predominantly negative in homogeneous shear flow, in contrast to its predominantly positive behavior in isotropic turbulence. The different signs of the pressure-dilatation are explained by theoretical consideration of the equations for the pressure variance and density variance. We obtained previously the following results for isotropic turbulence; first, the normalized compressible dissipation is of O(M'), and second, there is approximate equipartition between the kinetic and potential energies associated with the fluctuating compressible mode. Both these results have now been substantiated in the case of homogeneous shear. The dilatation field is significantly more skewed and intermittent than the vorticity field. Strong compressions seem to be more likely than strong expansions.
eScholarship provides open access, scholarly publishing services to the University of California ... more eScholarship provides open access, scholarly publishing services to the University of California and delivers a dynamic research platform to scholars worldwide.
The present study sheds light on the subgrid modeling problem encountered in the large eddy simul... more The present study sheds light on the subgrid modeling problem encountered in the large eddy simulation ͑LES͒ of practical flows, where the turbulence is both inhomogeneous and anisotropic due to mean flow gradients. The subgrid scale stress ͑SGS͒ tensor, the quantity that is key to the success of LES, is studied here in such flows using both analysis and direct numerical simulation ͑DNS͒. It is shown that the SGS tensor, for the case of inhomogeneous flow, where the filtering operation is necessarily performed in physical space, contains two components: a rapid part that depends explicitly on the mean velocity gradient and a slow part that does not. The characterization, rapid and slow, is adopted by analogy to that used in the modeling of the pressure-strain in the Reynolds-averaged Navier-Stokes equations. In the absence of mean flow gradients, the slow part is the only nonzero component and has been the subject of much theoretical study. However, the rapid part can be important in the inhomogeneous flows that are often encountered in practice. An analytical estimate of the relative magnitude of the rapid and slow components is derived and the distinct role of each component in the energy transfer between the resolved grid scales and the unresolved subgrid scales is identified. Results that quantify this new decomposition are obtained from DNS data of a turbulent mixing layer. The rapid part is shown to play an important role when the turbulence is in a nonequilibrium state with turbulence production much larger than dissipation or when the filter size is not very small compared to the characteristic integral scale of the turbulence, as in the case of practical LES applications. More importantly, the SGS is observed to be highly anisotropic due to the close connection of the rapid part with the mean shear. The Smagorinsky eddy viscosity and the scale-similarity models are tested by performing a priori tests with data from DNS of the mixing layer. It is found that the scale-similarity model correctly represents the anisotropic energy transfer between grid and subgrid scales that is associated with the rapid part, while the eddy viscosity model captures the dissipation associated with the slow part. This may be a physical reason for the recent successes of the mixed model ͑Smagorinsky plus scale similarity͒ reported in the literature.
Predicting sound radiated by turbulence is of interest in aeroacoustics, hydroacoustics, and comb... more Predicting sound radiated by turbulence is of interest in aeroacoustics, hydroacoustics, and combustion noise. Significant improvements in computer technology have renewed interest in applying numerical techniques to predict sound from turbulent flows. One such technique is a hybrid approach in which the turbulence is computed using a method such as direct numerical simulation ͑DNS͒ or large eddy simulation ͑LES͒, and the sound is calculated using an acoustic analogy. In this study, sound from a turbulent flow is computed using DNS, and the DNS results are compared with acoustic-analogy predictions for mutual validation. The source considered is a three-dimensional region of forced turbulence which has limited extent in one coordinate direction and is periodic in the other two directions. Sound propagates statistically as a plane wave from the turbulence to the far field. The cases considered here have a small turbulent Mach number so that the source is spatially compact; that is, the turbulence integral scale is much smaller than the acoustic wavelength. The scaling of the amplitude and frequency of the far-field sound for the problem considered are derived in an analysis based on Lighthill's acoustic analogy. The analytical results predict that the far-field sound should exhibit ''dipole-type'' behavior; the root-mean-square pressure in the acoustic far field should increase as the cube of the turbulent Mach number. The acoustic power normalized by the turbulent dissipation rate is also predicted to scale as turbulent Mach number cubed. Agreement between the DNS results and the acoustic-analogy predictions is good. This study verifies the ability of the Lighthill acoustic analogy to predict sound generated by a three-dimensional, turbulent source containing many length and time scales.
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Papers by Sutanu Sarkar