Prolate Spheroid

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Helge I. Andersson - One of the best experts on this subject based on the ideXlab platform.

  • forces and torques on a Prolate Spheroid low reynolds number and attack angle effects
    Acta Mechanica, 2019
    Co-Authors: Helge I. Andersson, Fengjian Jiang
    Abstract:

    The three-dimensional flow field around a Prolate Spheroid has been obtained by integration of the full Navier–Stokes equations at Reynolds numbers 0.1, 1.0, and 10. The 6:1 Spheroid was embedded in a Cartesian mesh by means of an immersed boundary method. In the low-Re range, due to the dominance of viscous stresses, an exceptionally wide computational domain was required, together with a substantial grid refinement in the vicinity of the surface of the immersed Spheroid. Flow fields in equatorial and meridional planes were visualized by means of streamlines to illustrate Reynolds number and attack angle effects. Drag and lift forces and torques were computed and compared with the most recent correlation formulas. The largest discrepancies were observed for the moment coefficient, whereas the drag coefficient compared reasonably well.

  • Low-frequency oscillations in flow past an inclined Prolate Spheroid
    International Journal of Heat and Fluid Flow, 2019
    Co-Authors: Håkon Strandenes, Fengjian Jiang, Bjørnar Pettersen, Helge I. Andersson
    Abstract:

    Abstract We analyse the forces on a 45∘ inclined 6:1 Prolate Spheroid at Reynolds number R e D = 8000 . In contrast to flow at lower Reynolds numbers previously investigated, we now find a strong oscillatory behaviour in the global forces. The Strouhal number associated with the forces is 0.05 and the peak-to-peak value of the oscillations in the sideforce is more than 25% of the average. A Fourier transformation of the entire flow field reveals that the cause of the force fluctuations is spatial oscillations in one of the two primary vortices generated behind the Spheroid. This phenomena is attributed to a three-dimensional vortex instability.

  • instabilities in the wake of an inclined Prolate Spheroid
    arXiv: Fluid Dynamics, 2019
    Co-Authors: Helge I. Andersson, Fengjian Jiang, Valery Okulov
    Abstract:

    We investigate the instabilities, bifurcations and transition in the wake behind a 45-degree inclined 6:1 Prolate Spheroid, through a series of direct numerical simulations (DNS) over a wide range of Reynolds numbers (Re) from 10 to 3000. We provide a detailed picture of how the originally symmetric and steady laminar wake at low Re gradually looses its symmetry and turns unsteady as Re is gradually increased. Several fascinating flow features have first been revealed and subsequently analysed, e.g. an asymmetric time-averaged flow field, a surprisingly strong side force etc. As the wake partially becomes turbulent, we investigate a dominating coherent wake structure, namely a helical vortex tube, inside of which a helical symmetry alteration scenario was recovered in the intermediate wake, together with self-similarity in the far wake.

  • the transitional wake behind an inclined Prolate Spheroid
    Physics of Fluids, 2015
    Co-Authors: Fengjian Jiang, Helge I. Andersson, Jose P Gallardo, Zhiguo Zhang
    Abstract:

    The wake behind a 6:1 Prolate Spheroid at 45° incidence has been studied by means of direct numerical simulations (DNSs). The Reynolds number based on the minor axis of the Spheroid was 3000 as compared to 1000 in our preceding study [Jiang et al., “The laminar wake behind a 6:1 Prolate Spheroid at 45° incidence angle,” Phys. Fluids 26, 113602 (2014)]. The resulting wake is no longer laminar and the transitional wake is fundamentally unsteady and highly asymmetric from the very beginning. A substantial side force resulted from the asymmetric pressure field. No signs of vortex shedding could be observed. The forces and the flow field around the Spheroid exhibited a dominant periodicity with a surprisingly low Strouhal number of 0.0733. One part of the counter-rotating vortex pair which dominated the near-wake broke down into small-scale vortices as soon as the vortex left the shadow behind the Spheroid. The other part appeared as a helical vortex inside which the mechanical energy was conserved over a substantial length. The axial flow within this vortex tube experienced a sudden change from having maximum to minimum at the vortex center while maintaining the sign of the circulation. The severe asymmetry of the wake is ascribed to a global instability and may impact on submarine maneuverability.

  • the laminar wake behind a 6 1 Prolate Spheroid at 45 incidence angle
    Physics of Fluids, 2014
    Co-Authors: Fengjian Jiang, Jose P Gallardo, Helge I. Andersson
    Abstract:

    The wake behind a 6:1 Prolate Spheroid at 45° angle of attack has been studied. The three-dimensional unsteady Navier-Stokes equations have been solved numerically for Reynolds numbers Re = 50, 200, and 1000, where Re is based on the inflow velocity U0 and the minor axis D of the Spheroid. The wake at the two lowest Reynolds numbers is steady and symmetric about the meridional plane. Even at Re = 1000 the near-wake, which is dominated by vortex sheets separated from the Spheroid, is still steady and symmetric except in a very limited region of size 0.2D near the tip of the Spheroid. However, the intermediate wake, which extends from 4D downstream of the Spheroid, is distinctly asymmetric and exhibits local oscillations with an amplitude below 1% of U0. The intermediate part of the wake consists of a pair of counter-rotating vortices and the wake is deflected to the side of the strongest vortex, whereas the other vortex is partially wrapped around. It is conjectured that the wake at this particular Reynolds number is on the verge of becoming unsteady. Nevertheless, the forces and torques on the Prolate Spheroid show no sign whatsoever of asymmetry or unsteadiness. The resulting drag coefficients compare to within 30% with the Holzer-Sommerfeld correlation.

Fengjian Jiang - One of the best experts on this subject based on the ideXlab platform.

  • forces and torques on a Prolate Spheroid low reynolds number and attack angle effects
    Acta Mechanica, 2019
    Co-Authors: Helge I. Andersson, Fengjian Jiang
    Abstract:

    The three-dimensional flow field around a Prolate Spheroid has been obtained by integration of the full Navier–Stokes equations at Reynolds numbers 0.1, 1.0, and 10. The 6:1 Spheroid was embedded in a Cartesian mesh by means of an immersed boundary method. In the low-Re range, due to the dominance of viscous stresses, an exceptionally wide computational domain was required, together with a substantial grid refinement in the vicinity of the surface of the immersed Spheroid. Flow fields in equatorial and meridional planes were visualized by means of streamlines to illustrate Reynolds number and attack angle effects. Drag and lift forces and torques were computed and compared with the most recent correlation formulas. The largest discrepancies were observed for the moment coefficient, whereas the drag coefficient compared reasonably well.

  • Low-frequency oscillations in flow past an inclined Prolate Spheroid
    International Journal of Heat and Fluid Flow, 2019
    Co-Authors: Håkon Strandenes, Fengjian Jiang, Bjørnar Pettersen, Helge I. Andersson
    Abstract:

    Abstract We analyse the forces on a 45∘ inclined 6:1 Prolate Spheroid at Reynolds number R e D = 8000 . In contrast to flow at lower Reynolds numbers previously investigated, we now find a strong oscillatory behaviour in the global forces. The Strouhal number associated with the forces is 0.05 and the peak-to-peak value of the oscillations in the sideforce is more than 25% of the average. A Fourier transformation of the entire flow field reveals that the cause of the force fluctuations is spatial oscillations in one of the two primary vortices generated behind the Spheroid. This phenomena is attributed to a three-dimensional vortex instability.

  • instabilities in the wake of an inclined Prolate Spheroid
    arXiv: Fluid Dynamics, 2019
    Co-Authors: Helge I. Andersson, Fengjian Jiang, Valery Okulov
    Abstract:

    We investigate the instabilities, bifurcations and transition in the wake behind a 45-degree inclined 6:1 Prolate Spheroid, through a series of direct numerical simulations (DNS) over a wide range of Reynolds numbers (Re) from 10 to 3000. We provide a detailed picture of how the originally symmetric and steady laminar wake at low Re gradually looses its symmetry and turns unsteady as Re is gradually increased. Several fascinating flow features have first been revealed and subsequently analysed, e.g. an asymmetric time-averaged flow field, a surprisingly strong side force etc. As the wake partially becomes turbulent, we investigate a dominating coherent wake structure, namely a helical vortex tube, inside of which a helical symmetry alteration scenario was recovered in the intermediate wake, together with self-similarity in the far wake.

  • the transitional wake behind an inclined Prolate Spheroid
    Physics of Fluids, 2015
    Co-Authors: Fengjian Jiang, Helge I. Andersson, Jose P Gallardo, Zhiguo Zhang
    Abstract:

    The wake behind a 6:1 Prolate Spheroid at 45° incidence has been studied by means of direct numerical simulations (DNSs). The Reynolds number based on the minor axis of the Spheroid was 3000 as compared to 1000 in our preceding study [Jiang et al., “The laminar wake behind a 6:1 Prolate Spheroid at 45° incidence angle,” Phys. Fluids 26, 113602 (2014)]. The resulting wake is no longer laminar and the transitional wake is fundamentally unsteady and highly asymmetric from the very beginning. A substantial side force resulted from the asymmetric pressure field. No signs of vortex shedding could be observed. The forces and the flow field around the Spheroid exhibited a dominant periodicity with a surprisingly low Strouhal number of 0.0733. One part of the counter-rotating vortex pair which dominated the near-wake broke down into small-scale vortices as soon as the vortex left the shadow behind the Spheroid. The other part appeared as a helical vortex inside which the mechanical energy was conserved over a substantial length. The axial flow within this vortex tube experienced a sudden change from having maximum to minimum at the vortex center while maintaining the sign of the circulation. The severe asymmetry of the wake is ascribed to a global instability and may impact on submarine maneuverability.

  • the laminar wake behind a 6 1 Prolate Spheroid at 45 incidence angle
    Physics of Fluids, 2014
    Co-Authors: Fengjian Jiang, Jose P Gallardo, Helge I. Andersson
    Abstract:

    The wake behind a 6:1 Prolate Spheroid at 45° angle of attack has been studied. The three-dimensional unsteady Navier-Stokes equations have been solved numerically for Reynolds numbers Re = 50, 200, and 1000, where Re is based on the inflow velocity U0 and the minor axis D of the Spheroid. The wake at the two lowest Reynolds numbers is steady and symmetric about the meridional plane. Even at Re = 1000 the near-wake, which is dominated by vortex sheets separated from the Spheroid, is still steady and symmetric except in a very limited region of size 0.2D near the tip of the Spheroid. However, the intermediate wake, which extends from 4D downstream of the Spheroid, is distinctly asymmetric and exhibits local oscillations with an amplitude below 1% of U0. The intermediate part of the wake consists of a pair of counter-rotating vortices and the wake is deflected to the side of the strongest vortex, whereas the other vortex is partially wrapped around. It is conjectured that the wake at this particular Reynolds number is on the verge of becoming unsteady. Nevertheless, the forces and torques on the Prolate Spheroid show no sign whatsoever of asymmetry or unsteadiness. The resulting drag coefficients compare to within 30% with the Holzer-Sommerfeld correlation.

Bjørnar Pettersen - One of the best experts on this subject based on the ideXlab platform.

  • Low-frequency oscillations in flow past an inclined Prolate Spheroid
    International Journal of Heat and Fluid Flow, 2019
    Co-Authors: Håkon Strandenes, Fengjian Jiang, Bjørnar Pettersen, Helge I. Andersson
    Abstract:

    Abstract We analyse the forces on a 45∘ inclined 6:1 Prolate Spheroid at Reynolds number R e D = 8000 . In contrast to flow at lower Reynolds numbers previously investigated, we now find a strong oscillatory behaviour in the global forces. The Strouhal number associated with the forces is 0.05 and the peak-to-peak value of the oscillations in the sideforce is more than 25% of the average. A Fourier transformation of the entire flow field reveals that the cause of the force fluctuations is spatial oscillations in one of the two primary vortices generated behind the Spheroid. This phenomena is attributed to a three-dimensional vortex instability.

  • wakes behind a Prolate Spheroid in crossflow
    Journal of Fluid Mechanics, 2012
    Co-Authors: George El K Khoury, Helge I. Andersson, Bjørnar Pettersen
    Abstract:

    It is well known that most fluid flows observed in nature or encountered in engineering applications are turbulent and involve separation. Fluid flows in turbines, diffusers and channels with sudden expansions are among the widely observed areas where separation substantially alters the flow field and gives rise to complex flow dynamics. Such types of flows are referred to as internal flows since they are confined within solid surfaces and predominantly involve the generation or utilization of mechanical power. However, there is also a vast variety of engineering applications where the fluid flows past solid structures, such as the flow of air around an airplane or that of water around a submarine. These are called external flows and as in the former case the downstream evolution of the flow field is crucially influenced by separation. The present doctoral thesis addresses both internal and external separated flows by means of direct numerical simulations of the incompressible Navier-Stokes equations. For internal flows, the wall-driven flow in a onesided expansion channel and the pressure-driven flow in a plane channel with a single thin-plate obstruction have been studied in the fully developed turbulent state. Since such geometrical configurations involve spatially developing turbulent flows, proper inflow conditions are to be employed in order to provide a realistic fully turbulent flow at the input. For this purpose, a newly developed technique has been used in order to mimic an infinitely long channel section upstream of the expansion and the obstruction, respectively. With this approach, we are able to gather accurate mean flow and turbulence statistics throughout each flow domain and to explore in detail the instantaneous flow topology in the separated shear layers, recirculation regions as well as the recovery zones. For external flows, on the other hand, the flow past a Prolate Spheroid has been studied. Here, a wide range of Reynolds numbers is taken into consideration. Based on the characteristics of the vortical structures in the wake, the flow past a Prolate Spheroid is classified as laminar (steady or unsteady), transitional or turbulent. In each flow regime, the characteristic features of the flow are investigated by means of detailed frequency analysis, instantaneous vortex topology and three-dimensional flow visualizations.

  • crossflow past a Prolate Spheroid at reynolds number of 10000
    Journal of Fluid Mechanics, 2010
    Co-Authors: George El K Khoury, Helge I. Andersson, Bjørnar Pettersen
    Abstract:

    It is well known that most fluid flows observed in nature or encountered in engineering applications are turbulent and involve separation. Fluid flows in turbines, diffusers and channels with sudden expansions are among the widely observed areas where separation substantially alters the flow field and gives rise to complex flow dynamics. Such types of flows are referred to as internal flows since they are confined within solid surfaces and predominantly involve the generation or utilization of mechanical power. However, there is also a vast variety of engineering applications where the fluid flows past solid structures, such as the flow of air around an airplane or that of water around a submarine. These are called external flows and as in the former case the downstream evolution of the flow field is crucially influenced by separation. The present doctoral thesis addresses both internal and external separated flows by means of direct numerical simulations of the incompressible Navier-Stokes equations. For internal flows, the wall-driven flow in a onesided expansion channel and the pressure-driven flow in a plane channel with a single thin-plate obstruction have been studied in the fully developed turbulent state. Since such geometrical configurations involve spatially developing turbulent flows, proper inflow conditions are to be employed in order to provide a realistic fully turbulent flow at the input. For this purpose, a newly developed technique has been used in order to mimic an infinitely long channel section upstream of the expansion and the obstruction, respectively. With this approach, we are able to gather accurate mean flow and turbulence statistics throughout each flow domain and to explore in detail the instantaneous flow topology in the separated shear layers, recirculation regions as well as the recovery zones. For external flows, on the other hand, the flow past a Prolate Spheroid has been studied. Here, a wide range of Reynolds numbers is taken into consideration. Based on the characteristics of the vortical structures in the wake, the flow past a Prolate Spheroid is classified as laminar (steady or unsteady), transitional or turbulent. In each flow regime, the characteristic features of the flow are investigated by means of detailed frequency analysis, instantaneous vortex topology and three-dimensional flow visualizations.

B V Ivanov - One of the best experts on this subject based on the ideXlab platform.

  • Gravitational effects in a rotating Prolate Spheroid
    Classical and Quantum Gravity, 1997
    Co-Authors: B V Ivanov
    Abstract:

    The weak-field approximation to the Ernst equations is formulated in terms of two harmonic functions. The gravitational field of a rotating Prolate Spheroid is found. Formulae are given for the total mass and angular momentum, tension in the shell, gravitational force and dragging of inertial frames. A comparison is made with the case of an infinite rotating hollow cylinder.

George El K Khoury - One of the best experts on this subject based on the ideXlab platform.

  • wakes behind a Prolate Spheroid in crossflow
    Journal of Fluid Mechanics, 2012
    Co-Authors: George El K Khoury, Helge I. Andersson, Bjørnar Pettersen
    Abstract:

    It is well known that most fluid flows observed in nature or encountered in engineering applications are turbulent and involve separation. Fluid flows in turbines, diffusers and channels with sudden expansions are among the widely observed areas where separation substantially alters the flow field and gives rise to complex flow dynamics. Such types of flows are referred to as internal flows since they are confined within solid surfaces and predominantly involve the generation or utilization of mechanical power. However, there is also a vast variety of engineering applications where the fluid flows past solid structures, such as the flow of air around an airplane or that of water around a submarine. These are called external flows and as in the former case the downstream evolution of the flow field is crucially influenced by separation. The present doctoral thesis addresses both internal and external separated flows by means of direct numerical simulations of the incompressible Navier-Stokes equations. For internal flows, the wall-driven flow in a onesided expansion channel and the pressure-driven flow in a plane channel with a single thin-plate obstruction have been studied in the fully developed turbulent state. Since such geometrical configurations involve spatially developing turbulent flows, proper inflow conditions are to be employed in order to provide a realistic fully turbulent flow at the input. For this purpose, a newly developed technique has been used in order to mimic an infinitely long channel section upstream of the expansion and the obstruction, respectively. With this approach, we are able to gather accurate mean flow and turbulence statistics throughout each flow domain and to explore in detail the instantaneous flow topology in the separated shear layers, recirculation regions as well as the recovery zones. For external flows, on the other hand, the flow past a Prolate Spheroid has been studied. Here, a wide range of Reynolds numbers is taken into consideration. Based on the characteristics of the vortical structures in the wake, the flow past a Prolate Spheroid is classified as laminar (steady or unsteady), transitional or turbulent. In each flow regime, the characteristic features of the flow are investigated by means of detailed frequency analysis, instantaneous vortex topology and three-dimensional flow visualizations.

  • crossflow past a Prolate Spheroid at reynolds number of 10000
    Journal of Fluid Mechanics, 2010
    Co-Authors: George El K Khoury, Helge I. Andersson, Bjørnar Pettersen
    Abstract:

    It is well known that most fluid flows observed in nature or encountered in engineering applications are turbulent and involve separation. Fluid flows in turbines, diffusers and channels with sudden expansions are among the widely observed areas where separation substantially alters the flow field and gives rise to complex flow dynamics. Such types of flows are referred to as internal flows since they are confined within solid surfaces and predominantly involve the generation or utilization of mechanical power. However, there is also a vast variety of engineering applications where the fluid flows past solid structures, such as the flow of air around an airplane or that of water around a submarine. These are called external flows and as in the former case the downstream evolution of the flow field is crucially influenced by separation. The present doctoral thesis addresses both internal and external separated flows by means of direct numerical simulations of the incompressible Navier-Stokes equations. For internal flows, the wall-driven flow in a onesided expansion channel and the pressure-driven flow in a plane channel with a single thin-plate obstruction have been studied in the fully developed turbulent state. Since such geometrical configurations involve spatially developing turbulent flows, proper inflow conditions are to be employed in order to provide a realistic fully turbulent flow at the input. For this purpose, a newly developed technique has been used in order to mimic an infinitely long channel section upstream of the expansion and the obstruction, respectively. With this approach, we are able to gather accurate mean flow and turbulence statistics throughout each flow domain and to explore in detail the instantaneous flow topology in the separated shear layers, recirculation regions as well as the recovery zones. For external flows, on the other hand, the flow past a Prolate Spheroid has been studied. Here, a wide range of Reynolds numbers is taken into consideration. Based on the characteristics of the vortical structures in the wake, the flow past a Prolate Spheroid is classified as laminar (steady or unsteady), transitional or turbulent. In each flow regime, the characteristic features of the flow are investigated by means of detailed frequency analysis, instantaneous vortex topology and three-dimensional flow visualizations.