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Numerical investigation of transitional supersonic axisymmetric wakes
No full textTransitional supersonic axisymmetric wakes are investigated by
conducting various numerical experiments. The main objective is to identify hydrodynamic instability mechanisms in the flow at M=2.46 for several Reynolds numbers, and relating these to coherent structures that are found from various visualization techniques. The premise for this approach is the assumption that flow instabilities lead to the formation of coherent structures. Three high-order accurate compressible codes were developed in cylindrical coordinates for this research: a spatial Navier-Stokes (N-S) code to conduct Direct Numerical Simulations (DNS), a linearized N-S code for linear stability investigations using axisymmetric basic states, and a temporal N-S code for performing local stability analyses. The ability of numerical simulations to deliberately exclude physical effects is exploited. This includes intentionally eliminating certain azimuthal/helical modes by employing DNS for various circumferential domain-sizes. With this approach, the impact of structures associated with certain modes on the global wake-behavior can be scrutinized. Complementary spatial and temporal calculations are carried out to investigate whether instabilities are of local or global nature. Circumstantial evidence is presented that absolutely unstable global modes within the recirculation region co-exist with convectively unstable shear-layer modes. The flow is found to be absolutely unstable with respect to modes k>0 for ReD>5,000 and with respect to the axisymmetric mode k=0 for ReD>100,000. It is concluded that azimuthal modes k=2 and k=4 are the dominant modes in the trailing wake, producing a four-lobe wake pattern. Two possible mechanisms responsible for the generation of longitudinal structures within the recirculation region are suggested
Investigation of supersonic wakes using conventional and hybrid turbulence models
No full textTransitional and turbulent supersonic wakes behind axisymmetric bodies with a blunt base are investigated numerically using state-of-the-art RANS models and the Flow Simulation Methodology (FSM). The centerpiece of the FSM is a strategy to provide the proper amount of modelling of the subgrid scales. This is accomplished by a contribution function which locally and instantaneously compares the smallest relevant scales to the local grid size. The underlying compressible Navier-Stokes code in cylindrical coordinates developed for this research employs high-order accurate finite differences and a high-order accurate axis treatment.The turbulence closures chosen are a state-of-the-art wall-distance free explicit Algebraic Stress Model (EASMalpha), or a standard K-epsilon model (STKE) for comparison. Axisymmetric RANS and fully three-dimensional FSM calculations are performed on various computational grids for wakes at M=2.46 for several Reynolds numbers. The data obtained from all simulation strategies are compared to available DNS results for the transitional cases and to experimental results at the highest Reynolds number investigated. Of particular interest is the performance of commonly used compressibility corrections and modifications to closure-coefficients specifically derived for high-Reynolds number flows. The ability of FSM to reproduce flow structures found in DNS is scrutinized and a reason for the failure of RANS calculations to correctly predict the base pressure distribution is given
A methodology for simulation of complex turbulent flows
No full textA flow simulation Methodology (FSM) is presented for computing the time-dependent behavior of complex compressible turbulent flows. The development of FSM was initiated in close collaboration with C. Speziale (then at Boston University). The objective of FSM is to provide the proper amount of turbulence modeling for the unresolved scales while directly computing the largest scales. The strategy is implemented by using state-of-the-art turbulence models (as developed for Reynolds averaged Navier-Stokes (RANS)) and scaling of the model terms with a "contribution function." The contribution function is dependent on the local and instantaneous "physical" resolution in the computation. This physical resolution is determined during the actual simulation by comparing the size of the smallest relevant scales to the local grid size used in the computation. The contribution function is designed such that it provides no modeling if the computation is locally well resolved so that it approaches direct numerical simulations (DNS) in the fine-grid limit and such that it provides modeling of all scales in the coarse-grid limit and thus approaches a RANS calculation. In between these resolution limits, the contribution function adjusts the necessary modeling for the unresolved scales while the larger (resolved) scales are computed as in large eddy simulation (LES). However, FSM is distinctly different from LES in that it allows for a consistent transition between RANS, LES, and DNS within the same simulation depending on the local flow behavior and "physical" resolution. As a consequence, FSM should require considerably fewer grid points for a given calculation than would be necessary for a LES. This conjecture is substantiated by employing FSM to calculate the flow over a backward-facing step and a plane wake behind a bluff body, both at low Mach number, and supersonic axisymmetric wakes. These examples were chosen such that they expose, on the one hand, the inherent difficulties of simulating (physically) complex flows, and, on the other hand, demonstrate the potential of the FSM approach for simulations of turbulent compressible flows for complex geometries
Numerical investigation of transitional supersonic base flows with flow control
No full textDrag reduction by means of flow control is investigated forsupersonic base flows at Mach number M = 2.46 using DirectNumerical Simulations (DNS) and the Flow Simulation Methodology(FSM). The objective of the present work is to understand theevolution of coherent structures in the flow and how flow controltechniques modify these structures. For such investigations,simulation methods that capture the dynamics of the large turbulentstructures are required. DNS are performed for transitional baseflows at Re_D = 30,000. Due to the drastically increasedcomputational cost of DNS at higher Reynolds numbers, a hybridRANS/LES method (FSM) is applied to simulate base flows with flowcontrol at Re_D = 100,000. Active and passive flow controltechniques that alter the near-wake by introducing axisymmetric andlongitudinal perturbations are investigated. A detailed analysis ofthe dynamics of the resulting turbulent (coherent) structures ispresented
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Numerical investigation of transitional and turbulent supersonic axisymmetric wakes
No full textTransitional and turbulent supersonic axisymmetric wakes are investigated by conducting various numerical experiments. The main objective is to identify hydrodynamic instability mechanisms in the flow at M = 2.46 for several Reynolds numbers, and relating these to coherent structures that are found from various visualization techniques. The premise for this approach is the assumption that flow instabilities lead to the formation of coherent structures. The effect of these structures on the mean flow is of particular interest, as they strongly affect the base drag. Three high-order accurate compressible codes were developed in cylindrical coordinates for this research: A spatial Navier-Stokes (N-S) code to conduct Direct Numerical Simulations (DNS), a linearized N-S code for linear stability investigations using two-dimensional basic states, and a temporal N-S code for performing local stability analyses. The ability of numerical simulations to deliberately exclude physical effects is exploited. This includes intentionally eliminating certain azimuthal/helical modes by employing DNS for various circumferential domain-sizes. With this approach, the impact of structures associated with certain modes on the global wake-behavior can be scrutinized. It is concluded that azimuthal modes with low wavenumbers are responsible for a flat mean base-pressure distribution and that k = 2 and k = 4 are the dominant modes in the trailing wake, producing a four-lobe wake pattern. Complementary spatial and temporal calculations are carried out to investigate whether instabilities are of local or global nature. Circumstantial evidence is presented that absolutely unstable global modes within the recirculation region coexist with convectively unstable shear-layer modes. The flow is found to be absolutely unstable with respect to modes k > 0 for ReD > 5,000 and with respect to the axisymmetric mode for ReD > 100,000. Furthermore, it is investigated whether flow control measures designed to weaken the naturally most significant modes can decrease the base drag. Finally, the novel Flow Simulation Methodology (FSM), using state-of-the-art turbulence closures, is shown to reproduce DNS results at a fraction of the computational cost
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A high-order immersed boundary method for unsteady incompressible flow calculations
No full textA high-order immersed boundary method (IBM) for the computation of unsteady, incompressible fluid flows on two-dimensional, complex domains is proposed, analyzed, developed and validated. In the IBM, the equations of interest are discretized on a fixed Cartesian grid. As a result, domain boundaries do not always conform to the (rectangular) computational domain boundaries. This gives rise to 'immersed boundaries', i.e., boundaries immersed inside the computational domain. A new IBM is proposed to remedy problems in an older existing IBM that had originally been selected for use in numerical flow control investigations. In particular, the older method suffered from considerably reduced accuracy near the immersed boundary surface where sharp jumps in the solution, i.e., jump discontinuities in the function and/or its derivatives, were smeared out over several grid points. To avoid this behavior, a sharp interface method, originally developed by LeVeque & Li (1994) and Wiegmann & Bube (2000) in the context of elliptic PDEs, is introduced where the numerical scheme takes such discontinuities into consideration in its design. By comparing computed solutions to jump-singular PDEs having known analytical solutions, the new IBM is shown to maintain the formal fourth-order accuracy, in both time and space, of the underlying finite-difference scheme. Further validation of the new IBM code was accomplished through its application to several two-dimensional flows, including flow past a circular cylinder, and T-S waves in a flat plate boundary layer. Comparison of results from the new IBM with results available in the literature found good agreement in all cases
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Numerical investigation of transitional and turbulent compressible axisymmetric wakes
No full textA numerical method has been developed for solving the complete compressible Navier-Stokes equations. The method is applicable for Direct Numerical Simulations (DNS) and Large-Eddy Simulations (LES) and was used here to study the evolution of three-dimensional disturbances in the laminar and turbulent near wake of axisymmetric bluff bodies with a blunt base in supersonic flows. The main objective of this research is to investigate the time dependent behavior of these disturbances and their influence on and interaction with the global flow field. The equations are solved in a cylindrical coordinate system using finite difference approximations of fourth-order accuracy in axial and radial directions and and a fourth-order accurate explicit Runge-Kutta scheme for the time integration. A pseudo-spectral method is employed in the azimuthal direction. Direct Numerical Simulations (DNS) were performed for a subsonic free stream Mach number of M ͚ = 0.2 and for supersonic free stream Mach numbers of M ͚ = 1.2 and M ͚ = 2.46. Large-Eddy Simulations (LES) were carried out for a subsonic free stream Mach number of M ͚ = 0.2 and a global Reynolds number of ReD = 2,000 and for a supersonic free stream Mach number of M ͚ = 2.46 and global Reynolds numbers of ReD = 30,000 and ReD = 100,000. Comparison of the instantaneous flow field for subsonic calculations with water channel experiments and incompressible simulations show good qualitative agreement. An absolute instability with regard to helical disturbances was found for the subsonic flow at ReD = 1,000 and for the supersonic flows for M ͚ = 1.2 and ReD ≥ 4,000 and for M ͚ = 2.46 and ReD ≥ 30,000. Small disturbances appear in the flow field near the corner of the base. As the disturbances are propagating downstream they grow and form intense vortical structures. These structures have a strong influence on the flow field, which results in a drastic change of the base pressure distribution and thus of the base drag.This item was digitized from a paper original and/or a microfilm copy. If you need higher-resolution images for any content in this item, please contact us at [email protected] file replaced with corrected file October 2023
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Numerical investigation of transitional compressible plane wakes
No full textAir flow in the wake region of a two-dimensional (plane) body with a blunt base has been studied using numerical simulations. The objective of this study is (1) to observe the behavior of large dynamic structures in the plane wake at several Mach numbers from low (almost incompressible) up to M = 2.46 and examine their effect on the base pressure, and (2) to address the nature of the instability in the shear layers bounding the wake flow at M = 2.46 and observe the structures that arise from this instability. A code was developed for this study which solves the compressible Navier-Stokes equations in two or three dimensions. This code may be used for either Direct Numerical Simulations (DNS) or Large Eddy Simulations (LES). A spatial model is used, with the computational domain arranged around the trailing edge of a two-dimensional flat plate with a blunt base. Two-dimensional simulations were carried out at Mach numbers of M = 0.25, M = 1.20, and M = 2.46. At all Mach numbers, the flow was found to be unstable with respect to sinuous (antisymmetric) disturbances, with the critical Reynolds number increasing with increasing Mach number. These disturbances grow to a periodic state, and a Karman vortex street is formed. Examination of the supersonic cases revealed that expansion fans in the flow at the corners are the primary cause of the low base pressure, and that disruptions in the expansions raise the base pressure. At M = 2.46 and Reynolds numbers starting at Re = 100, 000, an intermittent shear layer instability was also found, excited by sinuous disturbances. The two instability 2 modes interact to produce a chaotic behavior. Above Re = 200, 000, the shear layer instability appears close to the base without sinuous disturbances, forming rows of vortices in the shear layers. Preliminary three-dimensional simulations were carried out at M = 2.46, examining the variation in the growth rate of three-dimensional disturbances with spanwise wavelength.This item was digitized from a paper original and/or a microfilm copy. If you need higher-resolution images for any content in this item, please contact us at [email protected] file replaced with corrected file October 2023
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Numerical investigation of forced transitional and turbulent wall jets
No full textThe generation and development of large 2D vortical disturbances (coherent structures) in forced transitional and turbulent wall jets is investigated using several numerical techniques. For the early and late transition stages, 2D Numerical Simulation (2D-NS) and Direct Numerical Simulation (DNS) are employed, while for the forced turbulent flow Unsteady Reynolds-Averaged Navier-Stokes (URANS) calculations are used including a new, simplified approach called "Stability" RANS (SRANS) which substantially reduces the computational effort when compared to URANS. As base flows for the investigations, three prototypical wall jets are considered: Low and high Reynolds number laminar wall jets, represented by the Glauert similarity solution, and a turbulent wall jet (Rej = 10,000), modeled using a nearly self-preserving RANS solution starting at a virtual nozzle. The investigations of 2D vortical disturbances in both the transitional and the turbulent wall jet follow the 2D stages of shear flow transition, beginning with receptivity to harmonic forcing, followed by linear and nonlinear disturbance development, and 2D secondary instability. It is shown that the disturbance development in the turbulent flow parallels the one in the transitional flow in many respects. In particular, a 2D subharmonic resonance is found in both flows leading to a subharmonic resonance cascade with repeated vortex merging. Competing 3D fundamental and subharmonic resonances in the transitional wall jet are studied using a linearized Navier-Stokes code and 3D DNS. These 3D secondary instabilities weaken or diminish the 2D disturbances and lead to turbulent breakdown. Yet, for large amplitude forcing, the 3D resonances are surpassed by the 2D subharmonic resonance which leads to vortex merging upstream of the breakdown. With a 3D DNS of bypass transition, where a high Reynolds number laminar wall jet is tripped with large amplitude 3D forcing, it is demonstrated that 2D vortical structures persist in the presence of 3D turbulent fluctuations. In this simulation, 2D vortical structures emerge during transition and undergo repeated merging in the turbulent flow downstream
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Two-dimensional Navier Stokes simulations of instability waves in a flat plate boundary layer flow at M = 4.5
No full textThis thesis addresses the investigation of mechanisms involved in the transition from laminar to turbulent flow. The flow studied is a compressible flat plate boundary layer at a free stream velocity of M = 4.5. The two-dimensional compressible unsteady Navier Stokes equations are solved numerically in a rectangular region at a distance downstream from the leading edge. Disturbances are introduced by periodical suction and blowing through a slot in the wall. These disturbances propagate downstream in the flow field. At every point in the flow field the response of the flow is analyzed using a Fourier analysis in time. Results obtained are interpreted with reference to linear stability theory. One important result is the existence of multiple undamped waves for one wave frequency. The second important result demonstrates that an amplified wave of a certain frequency can generate disturbances at multiples of its frequency which may then be amplified more strongly
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