Jayahar Sivasubramanian

Direct Numerical Simulation of a Turbulent Spot in a Cone Boundary-Layer at Mach 6

Highly resolved spatial Direct Numerical Simulations (DNS) were performed to investigate the growth and breakdown of a localized disturbance into a turbulent spot in a sharp cone boundary{layer at Mach 6. The ∞ow parameters used in the simulations are based on the experimental conditions of the Boeing/AFOSR Mach 6 quiet{∞ow Ludwieg Tube at Purdue University. 1 In order to model a natural transition scenario, the boundary{layer was pulsed through a hole on the cone surface. The pulse disturbance developed into a three{dimensional wave packet which consisted of a wide range of disturbance frequencies and wave numbers. The dominant waves within the resulting wave packet were identifled as two{dimensional second mode disturbance waves. In addition, weaker oblique waves were observed on the lateral sides of the wave packet. The developing wave packet grows linearly at flrst before reaching the nonlinear regime and eventually leads to localized patches of turbulent ∞ow (turbulent spot). The wall{pressure disturbance spectrum showed strong secondary peaks at the fundamental frequency for larger azimuthal wave numbers. This development indicates that fundamental resonance might be the dominant nonlinear mechanism for a cone boundary{layer at Mach 6. The ∞ow structures within the turbulent spot were studied in detail and general features of the spot were analyzed.

Transition Initiated by a Localized Disturbance in a Hypersonic Flat-Plate Boundary Layer

Direct Numerical Simulations (DNS) were performed to investigate transition initiated by a localized disturbance in a hypersonic ∞at{plate boundary layer. In order to model a natural transition scenario, the boundary{layer was forced by a short duration (localized) pulse through a hole on the ∞at{plate. The pulse disturbance developed into a threedimensional wave packet which consisted of a wide range of disturbance frequencies and wave numbers. First, the linear development of the wave packet was studied by pulsing the ∞ow with a low amplitude (0:001% of the freestream velocity). The dominant waves within the resulting wave packet were identifled as two-dimensional second mode disturbance waves. Hence the wall{pressure disturbance spectrum exhibited a maximum at the spanwise mode number k = 0. The spectrum broadened in downstream direction and the lower frequency flrst mode oblique waves were also identifled in the spectrum. However, the peak amplitude remained at k = 0 which shifted to lower frequencies in the downstream direction. In order to investigate the nonlinear transition regime, the ∞ow was pulsed with a higher amplitude disturbance (5% of the freestream velocity). The developing wave packet grows linearly at flrst before reaching the nonlinear regime. The wall pressure disturbance spectrum conflrmed that the wave packet developed linearly at flrst. The response of the ∞ow to the high amplitude pulse disturbance indicated the presence of a fundamental resonance mechanism. Lower amplitude secondary peaks were also identifled in the disturbance wave spectrum at approximately half the frequency of the high amplitude frequency band, which would be an indication of a subharmonic resonance mechanism. The disturbance spectrum indicates however, that fundamental resonance is much stronger than subharmonic resonance.

Growth and Breakdown of a Wave Packet into a Turbulent Spot in a Cone Boundary Layer at Mach 6

Direct Numerical Simulations are performed to investigate the growth and breakdown of a wave packet into a turbulent spot in a sharp cone boundary layer at Mach 6. In order to understand the natural transition process in hypersonic cone boundary layers, the flow was forced by a short–duration (localized) pulse. The pulse disturbance developed into a three–dimensional wave packet which consisted of a wide range of disturbance frequencies and wave numbers. The flow parameters for the simulations are based on the experimental conditions of the Boeing/AFOSR Mach 6 quiet–flow Ludwieg Tube at Purdue University. First, the linear development of the wave packet was studied by forcing the flow with a low–amplitude pulse (0.001% of the free–stream velocity). The dominant waves within the resulting wave packet were identified as the second–mode two–dimensional disturbance waves. In addition, weaker first–mode oblique waves were also observed on the lateral sides of the wave packet. In order to investigate the weakly nonlinear transition regime, medium–amplitude pulse disturbances (0.5% of the free–stream velocity) were introduced. The response of the flow to the medium–amplitude pulse disturbances indicated the presence of a fundamental resonance mechanism. Lower secondary peaks in the disturbance wave spectrum were identified at approximately half the frequency of the high–amplitude frequency band, which would be an indication of a subharmonic resonance mechanism. Strong peaks were also observed for low–wave–number second–mode oblique waves, which indicate a possible presence of an oblique breakdown mechanism. Finally, in order to identify more clearly which of these mechanisms ultimately leads to turbulent breakdown, a simulation with a higher forcing amplitude (5% of the free–stream velocity) was performed. The resulting strongly nonlinear wave packet eventually leads to localized patches of turbulent flow (turbulent spots). The disturbance wave spectrum indicates that both second–mode fundamental resonance and oblique breakdown mechanisms may be the dominant mechanisms for the investigated flow. Both mechanisms may play a role in the natural transition process for a cone boundary layer at Mach 6.

Numerical Investigation of Transitional Supersonic Base Flows with Flow Control

Drag reduction by means of flow control is investigated for supersonic base flows at Mach number M = 2.46 using Direct Numerical Simulations (DNS) and the Flow Simulation Methodology (FSM). The objective of the present work is to understand the evolution of coherent structures in the flow and how flow control techniques modify these structures. For such investigations, simulation methods that capture the dynamics of the large turbulent structures are required. DNS are performed for transitional base flows at Re_D = 30,000. Due to the drastically increased computational cost of DNS at higher Reynolds numbers, a hybrid RANS/LES method (FSM) is applied to simulate base flows with flow control at Re_D = 100,000. Active and passive flow control techniques that alter the near-wake by introducing axisymmetric and longitudinal perturbations are investigated. A detailed analysis of the dynamics of the resulting turbulent (coherent) structures is presented.

Numerical investigation of boundary-layer transition initiated by a wave packet for a cone at Mach 6

Direct Numerical Simulations are performed to investigate transition initiated by a wave packet in a sharp cone boundary layer at Mach 6. In order to understand the natural transition process in hypersonic cone boundary layers, the ∞ow was pulsed through a hole on the cone surface to generate a wave packet which consisted of a wide range of disturbance frequencies and wave numbers. The ∞ow parameters for the simulations are based on the experimental conditions of the Boeing/AFOSR Mach 6 quiet{∞ow Ludwieg Tube at Purdue University. 1 First, the linear development of the wave packet was studied by forcing the ∞ow with a low amplitude pulse (0:001% of the freestream velocity). The dominant waves within the resulting wave packet were identifled as the second mode two{dimensional disturbance waves. In addition, weaker flrst mode oblique waves were also observed on the lateral sides of the wave packet. In order to investigate the weakly nonlinear transition regime, medium amplitude pulse disturbances (0:5% of the freestream velocity) were introduced. The response of the ∞ow to the medium amplitude pulse disturbances indicated the presence of a fundamental resonance mechanism. Lower secondary peaks in the disturbance wave spectrum were identifled at approximately half the frequency of the high amplitude frequency band for azimuthal mode numbers kc§55, which would be an indication of a subharmonic resonance mechanism. Finally, in order to identify more clearly which of these mechanisms ultimately leads to turbulent breakdown, a simulation with a higher forcing amplitude (5% of the freestream velocity) was performed. The developing strongly nonlinear wave packet eventually leads to localized patches of turbulent ∞ow (turbulent spots). In these nascent turbulent spots various known properties of mature turbulent spots could be identifled.

Numerical Investigation of Shock-Induced Laminar Separation Bubble in a Mach 2 Boundary Layer

A numerical study of the interaction between an impinging oblique shock and a laminar boundary–layer on a flat plate is carried out. The two–dimensional separation bubble resulting from the shock/boundary–layer interaction (SBLI) at freestream Mach number of 2.0 for the approach flow is investigated in detail. The flow parameters used for the present investigation match the laboratory conditions in the experiments by Hakkinen et al. 1 The skin friction and pressure distribution from the simulations are compared to the experimental measurements and numerical results available in the literature. Our results confirm the asymmetric nature of the separation bubble as reported in the literature. In addition to the steady flow field calculations, the response to low–amplitude disturbances is investigated in order to study the linear stability behavior of the separation bubble. For comparison, both the development of two–dimensional and three–dimensional (oblique) disturbances are studied with and without the impinging oblique shock. Furthermore, the effects of the shock incidence angle and Reynolds number are also investigated. Finally, three–dimensional direct numerical simulations were performed in order to explore the laminar-turbulent transition process in the presence of a laminar separation bubble generated by an impinging shock.

High Accuracy DNS and LES of High Reynolds Number, Supersonic Base Flows and Passive Control of the Near Wake

Supersonic axisymmetric base flows are prototypical for flows behind projectiles and missiles. For these flows, drag reduction can be achieved by means of passive control of the near wake. Thereby, large (turbulent) coherent structures play a dominant role. The objective of the present investigation is to elucidate if and how successful passive flow control techniques modify these structures. To this end, first Direct Numerical Simulations (DNS) for a Reynolds number of ReD = 100,000 and Mach number of Ma =2.46 were performed using a high-order accurate and highly parallelized research code which was developed at the University of Arizona. Thereby, roughly 52 million grid points were employed. The DNS data serve to visualize typical structures of the unsteady flow field and to verify that the use of less computational costly RANS/LES methods is applicable for this flow. Two of these methods, the Flow Simulation Methodology (FSM) and Detached Eddy Simulations (DES), were then employed to investigate the supersonic base flow at ReD =3.3 × 106 and Ma = 2.46 using between 460,000 and seven million grid points. For the DES, the commercial CFD-code Cobalt was employed. This unstructured grid solver allowed then to perform simulations with boat-tailing. The obtained mean flow data are compared to available experimental results.

Numerical investigation of supersonic axisymmetric wakes with active and passive flow control

The base drag of axisymmetric bodies at supersonic speeds make a substantial contribution to the total drag. We employed computational ∞uid dynamics for investigating transitional supersonic axisymmetric wakes at a freestream Mach number of M = 2:46. The objective of this research is to study how various active and passive ∞ow control techniques afiect the base drag and to understand how the mean ∞ow properties are altered by these techniques. Simulations were carried out for a Reynolds number based on diameter of ReD = 100; 000. To lower the grid resolution requirements and save computer time we employed a hybrid turbulence model, the ∞ow simulation methodology. We investigated ∞ow control mechanisms that alter the near wake by introducing axisymmetric and longitudinal perturbations in the approach boundary layer. We also investigated passive control using steady bleed jets.

Numerical Investigation of Shockwave Boundary Layer Interactions in Supersonic Flows

The interaction between an impinging oblique shock–wave and a laminar boundary layer on a flat plate is investigated using direct numerical simulations. The two–dimensional separation bubble resulting from the shock boundary layer interaction (SBLI) at freestream Mach number of 2.3 for the approach flow is investigated in detail. The flow parameters used for the present investigation match the laboratory conditions in the experiments conducted at the University of Arizona (UA). In addition to the steady flow field calculations, in order to study the linear stability behavior of the separation bubble, the response to low– amplitude disturbances is investigated using linearized Navier Stokes calculations. For comparison, both the development of two–dimensional and three–dimensional (oblique) disturbances are studied with and without the impinging oblique shock. Furthermore, the effects of the shock incidence angle and Reynolds number are also investigated. Finally, three–dimensional direct numerical simulations were performed in order to investigate the laminar-turbulent transition process in the presence of a laminar separation bubble generated by an impinging shock–wave.

LES and DES of High Reynolds Number, Supersonic Base Flows with Control of the Near Wake

The drag associated with supersonic base flows is of critical importance for the design of aerodynamic bodies, such as missiles and projectiles. The base drag which accounts for a significant part of the total drag may be reduced by means of active and passive control of the near wake. There is evidence that large (turbulent) coherent structures evolve in these flows and strongly influence the mean flow. Therefore, in order to understand the dynamics of coherent structures in the wake and how flow control mechanisms modify these structures, numerical simulations were conducted. We performed large-eddy simulations (LES) based on the flow simulation methodology (FSM) for a Reynolds number of ReD = 100,000 and Mach number M = 2.46 using a high-order accurate research code, which was developed at the University of Arizona. Flow control mechanisms that alter the near wake by introducing axisymmetric and three-dimensional perturbations, thus emulating active and passive flow control were investigated. We also studied supersonic base flows at Reynolds number ReD = 3,300,000 and Mach number M = 2.46 using detached-eddy simulations (DES). These investigations were performed using the commercial CFD-code Cobalt. In addition, for the same Reynolds number, we investigated passive flow control using afterbody boat-tailing. Our results are compared to available experimental data