Ponnampalam Balakumar

Stability of Hypersonic Boundary Layers over a Compression Corner

The stability of hypersonic boundary layers over a compression corner is investigated numerically. To compute the shock and the interaction of the shock with the instability waves, the simulation solves the three-dimensional Navier-Stokes equations using a high-order, weighted, essentially nonoscillatory shock-capturing scheme. After computing the mean flowfield, the procedure then superimposes two-dimensional unsteady disturbances at the inflow and computes the evolution of these disturbances in downstream direction. Because of the interaction of the shock with the boundary layer, a separation bubble forms at the corner, and two compression waves form near the separation and reattachment points. These compression waves merge farther away from the boundary layer to form a shock

Receptivity of Hypersonic Boundary Layers over Straight and Flared Cones

The effects of adverse pressure gradients on the receptivity and stability of hypersonic boundary layers were numerically investigated. Simulations were performed for boundary-layer flows over a straight cone and two flared cones. The steady and the unsteady flowfields were obtained by solving the two-dimensional Navier–Stokes equations in axisymmetric coordinates using the fifth-order-accurate weighted essentially nonoscillatory scheme for space discretization and using a third-order total-variation-diminishing Runge–Kutta scheme for time integration. The mean boundary-layer profiles were analyzed using local stability and nonlocal parabolized stability equations methods. After the most amplified disturbances were identified, two-dimensional plane acoustic waves were introduced at the outer boundary of the computational domain and time-accurate simulations were performed. The adverse pressure gradient was found to affect the boundary-layer stability in two important ways. First, the frequency of the most...

Effects of Nose Bluntness on Hypersonic Boundary-Layer Receptivity and Stability over Cones

The receptivity to freestream acoustic disturbances and the stability properties of hypersonic boundary layers are numerically investigated for boundary-layer flows over a 5 straight cone at a freestream Mach number of 6.0. To compute the shock and the interaction of the shock with the instability waves, the Navier-Stokes equations in axisymmetric coordinates were solved. In the governing equations, inviscid and viscous flux vectors are discretized using a fifth-order accurate weighted-essentially-non-oscillatory scheme. A third-order accurate total-variation-diminishing Runge-Kutta scheme is employed for time integration. After the mean flow field is computed, disturbances are introduced at the upstream end of the computational domain. The appearance of instability waves near the nose region and the receptivity of the boundary layer with respect to slow mode acoustic waves are investigated. Computations confirm the stabilizing effect of nose bluntness and the role of the entropy layer in the delay of boundary-layer transition. The current solutions, compared with experimental observations and other computational results, exhibit good agreement.

Receptivity of Hypersonic Boundary Layers Due to Acoustic Disturbances Over Blunt Cone

The transition process induced by the interaction of acoustic disturbances in the freestream with boundary layers over a 5-degree straight cone and a wedge with blunt tips is numerically investigated at a free-stream Mach number of 6.0. To compute the shock and the interaction of shock with the instability waves the Navier-Stokes equations are solved in axisymmetric coordinates. The governing equations are solved using the 5 –order accurate weighted essentially non-oscillatory (WENO) scheme for space discretization and using third-order total-variation-diminishing (TVD) Runge-Kutta scheme for time integration. After the mean flow field is computed, acoustic disturbances are introduced at the outer boundary of the computational domain and unsteady simulations are performed. Generation and evolution of instability waves and the receptivity of boundary layer to slow and fast acoustic waves are investigated. The mean flow data are compared with the experimental results. The results show that the instability waves are generated near the leading edge and the non-parallel effects are stronger near the nose region for the flow over the cone than that over a wedge. It is also found that the boundary layer is much more receptive to slow acoustic wave (by almost a factor of 67) as compared to the fast wave.

Effects of Nose Bluntness on Stability of Hypersonic Boundary Layers over a Blunt Cone

Receptivity and stability of hypersonic boundary layers are numerically investigated for boundary layer flows over a 5-degree straight cone at a free-stream Mach number of 6.0. To compute the shock and the interaction of shock with the instability waves, we solve the Navier- Stokes equations in axisymmetric coordinates. The governing equations are solved using the 5 th - order accurate weighted essentially non-oscillatory (WENO) scheme for space discretization and using third-order total-variation-diminishing (TVD) Runge-Kutta scheme for time integration. After the mean flow field is computed, disturbances are introduced at the upstream end of the computational domain. Generation of instability waves from leading edge region and receptivity of boundary layer to slow acoustic waves are investigated. Computations are performed for a cone with nose radii of 0.001, 0.05 and 0.10 inches that give Reynolds numbers based on the nose radii ranging from 650 to 130,000. The linear stability results showed that the bluntness has a strong stabilizing effect on the stability of axisymmetric boundary layers. The transition Reynolds number for a cone with the nose Reynolds number of 65,000 is increased by a factor of 1.82 compared to that for a sharp cone. The receptivity coefficient for a sharp cone is about 4.23 and they are very small, ~10 -3 , for large bluntness.

Transition in a Supersonic Boundary Layer Due to Acoustic Disturbances

The boundary layer receptivity process due to the interaction of three-dimensional slow and fast acoustic disturbances with a blunted flat plate is numerically investigated at a free stream Mach number of 3.5 and at a high Reynolds number of 10(exp 6)/inch. The computations are performed with and without two-dimensional isolated roughness element located near the leading edge. Both the steady and unsteady solutions are obtained by solving the full Navier-Stokes equations using the fifth-order accurate weighted essentially non-oscillatory (WENO) scheme for space discretization and using third-order total-variation-diminishing (TVD) Runge-Kutta scheme for time integration. The simulations showed that the linear instability waves are generated very close to the leading edge. The wavelength of the disturbances inside the boundary layer first increases gradually and becomes longer than the wavelength for the instability waves within a short distance from the leading edge. The wavelength then decreases gradually and merges with the wavelength for the Tollmien-Schlichting wave. The initial amplitudes of the instability waves near the neutral points, the receptivity coefficients, are about 1.20 and 0.07 times the amplitude of the free-stream disturbances for the slow and the fast waves respectively. It was also revealed that small isolated roughness element does not enhance the receptivity process for the given nose bluntness.

Roughness Induced Transition in a Supersonic Boundary Layer

Direct numerical simulation is used to investigate the transition induced by threedimensional isolated roughness elements in a supersonic boundary layer at a free stream Mach number of 3.5. Simulations are performed for two different configurations: one is a square planform roughness and the other is a diamond planform roughness. The mean-flow calculations show that the roughness induces counter rotating streamwise vortices downstream of the roughness. These vortices persist for a long distance downstream and lift the low momentum fluid from the near wall region and place it near the outer part of the boundary layer. This forms highly inflectional boundary layer profiles. These observations agree with recent experimental observations. The receptivity calculations showed that the amplitudes of the mass-flux fluctuations near the neutral point for the diamond shape roughness are the same as the amplitude of the acoustic disturbances. They are three times smaller for the square shape roughness.

Receptivity and Transition of Supersonic Boundary Layers Over Swept Wings

The steady flow fields with and without roughness elements are obtained by solving the full Navier-Stokes equations. The N-factors computed in this study at the transition onset locations reported in Ref. 1 for flow over the swept cylinder are approximately 16.5 for traveling crossflow disturbances and 9 for stationary disturbances. The N-factors for the traveling crossflow are high based on our past experiences. However, they are comparatively smaller than those reported by Archambaud et al., who found N-factor values in the range of 20 to 25 for traveling disturbances and 13 to 20 for stationary disturbances. Similarly, the N-factors computed in this study for the traveling and stationary disturbances for the flow over the sharp wing are approximately 7 and 2.5, respectively, and for the flow over the blunt wing are 6.5 and 4.8, respectively. Using the envelope method, Archambaud et al. obtained values of approximately 8.0 and 4.0 for the sharp wing case and 16.0 and 12.0 for the blunt wing case.

Effects of Wall Cooling on Hypersonic Boundary Layer Receptivity Over a Cone

Effects of wall cooling on the receptivity process induced by the interaction of slow acoustic disturbances in the free-stream are numerically investigated for a boundary layer flow over a 5-degrees straight cone. The free-stream Mach number is 6.0 and the Reynolds number is 7.8x10(exp 6)/ft. Both the steady and unsteady solutions are obtained by solving the full Navier-Stokes equations using 5th-order accurate weighted essentially non-oscillatory (WENO) scheme for space discretization and using 3rd-order total variation diminishing (T VD) Runge-K utta scheme for time integration. Computations are performed for a cone with nose radius of 0.001 inch for adiabatic wall temperature (T(sub aw)), 0.75*T(sub aw), 0.5*T(sub aw), 0.40*T(sub aw), 0.30*T(sub aw), and 0.20*T(sub aw). Once the mean flow field is computed, disturbances are introduced at the upstream end of the computational domain. Generation of instability waves from leading edge region and receptivity of boundary layer to slow acoustic waves are investigated. Computations showed that wall cooling has strong stabilization effect on the first mode disturbances as was observed in the experiments. T ransition location moved to upstream when wall cooling was applied It is also found that the boundary layer is much more receptive to fast acoustic wave (by almost a factor of 50). When simulations performed using the same forcing frequency growth of the second mode disturbances are delayed with wall cooling and they attained values two times higher than that of adiabatic case. In 0.20*T(sub aw) case the transition Reynolds number is doubled compared to adiabatic conditions. The receptivity coefficient for adiabatic wall case (804 R) is 1.5225 and for highly cooled cones (241, and 161 R); they are in the order of 10(exp -3).

Nonlinear Disturbance Evolution Across a Hypersonic Compression Corner

The nonlinear evolution of the second-mode disturbance across a compression comer under the hypersonic flow condition is studied by spatial direct numerical simulation in this investigation. A fifth-order weighted essentially nonoscillating scheme is employed for this simulation. After the mean flow is obtained, the two- and three-dimensional mono- or random-frequency disturbances are added into the mean flow at the beginning of the computational domain. The nonlinear simulations show that two-dimensional disturbance will become saturated downstream of the separation region when its amplitude grows to a quite large value. For three-dimensional monofrequency disturbance evolution, with appropriate initial disturbance amplitude, the nonlinear interactions of the oblique disturbance will first happen at the beginning of the separation region, and some superharmonics will begin to appear in this region, but only downstream of the separation region do these harmonics begin to grow rapidly