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NASA NTRS2004

Computations of Flow Over a Hump Model Using Higher Order Method With Turbulence Modeling

Turbulent separated flow over a two-dimensional hump is computed by solving the RANS equations with k-omega (SST) turbulence model for the baseline, steady suction and oscillatory blowing/suction flow control cases. The flow equations and the turbulent model equations are solved using a fifth-order accurate weighted essentially nonoscillatory (WENO) scheme for space discretization and a third order, total variation diminishing (TVD) Runge-Kutta scheme for time integration. Qualitatively the computed pressure distributions exhibit the same behavior as they are observed in the experiments. The computed separation regions are much longer than that are observed. However, the percentage reduction in the separation region in the steady suction case is closer to that was measured in the experiment. The computations did not predict the expected reduction in the separation length in the oscillatory case. The predicted turbulent quantities are two to three times smaller than that are measured and it points towards the deficiencies in the existing turbulent models when they are applied to strong steady/unsteady separated flows.

Balakumar, Ponnampalam↗
NASA NTRS2004

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 106/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 5th-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.

Balakumar, Ponnampalam↗
NASA NTRS2004

On the Total Variation of High-Order Semi-Discrete Central Schemes for Conservation Laws

We discuss a new fifth-order, semi-discrete, central-upwind scheme for solving one-dimensional systems of conservation laws. This scheme combines a fifth-order WENO reconstruction, a semi-discrete central-upwind numerical flux, and a strong stability preserving Runge-Kutta method. We test our method with various examples, and give particular attention to the evolution of the total variation of the approximations.

Bryson, Steve↗
NASA NTRS2006

Control of Supersonic Boundary Layers Using Steady Suction

Control of supersonic boundary layers using steady suction through a series of very small two-dimensional strips is numerically investigated at a free stream Mach number of 1.8. The mean flow induced by rows of suction holes is also computed. Both the steady and unsteady solutions are obtained by solving the full Navier-Stokes equations using the 5th-order accurate weighted essentially non-oscillatory (WENO) scheme for space discretization and using third-order total-variationdiminishing (TVD) Runge-Kutta scheme for time integration. Computations for the two-dimensional cases are performed at suction coefficients 0.001 and 0.002 to investigate the stabilizing effects of suction. The simulation showed that a series of shock waves are generated at the slots. The stability results showed that the total amplification is reduced up to the end of the computational domain. However, the growth rates become larger at downstream distances away from the suction region. The computations for the suction holes showed the generation of Mach waves from each hole and the formation of longitudinal vortices.

Balakumar, P.↗
NASA NTRS2006

Stability of Supersonic Boundary Layers Over Blunt Wedges

Receptivity and stability of supersonic boundary layers over blunt flat plates and wedges are numerically investigated at a free stream Mach number of 3.5 and at a high Reynolds number of 10(exp 6)/inch. Both the steady and unsteady solutions are obtained by solving the full Navier-Stokes equations using the 5th-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. Computations are performed for a flat plate with leading edge thicknesses of 0.0001, 0.001, 0.005 and 0.01 inches that give Reynolds numbers based on the leading edge thickness ranging from 1000 to 10000. Calculations are also performed for a wedge of 10 degrees half angle with different leading edge radii 0.001 and 0.01 inches. The linear stability results showed that the bluntness has a strong stabilizing effect on the stability of two-dimensional boundary layers. The transition Reynolds number for a flat plate with a leading edge thickness of 0.01 inches is about 3.5 times larger than it is for the Blasius boundary layer. It was also revealed that boundary layers on blunt wedges are far more stable than on blunt flat plates.

Balakumar, Ponnampalam↗
NASA NTRS2007

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

The transition process induced by the interaction of acoustic disturbances in the free-stream 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 5th -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.

Kara, K.↗
NASA NTRS2007

Effects of Nose Bluntness on Stability of Hypersonic Boundary Layers over 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 5th-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 it is very small, approx.10(exp -3), for large bluntness.

Kara, K.↗
NASA NTRS2007

Receptivity of Supersonic Boundary Layers Due To Acoustic Disturbances Over Blunt Cones

Receptivity and stability of supersonic boundary layers over a 5-degree straight cone with a blunt tip are numerically investigated at a free stream Mach number of 3.5 and at a high Reynolds number of 106/inch. Both the steady and unsteady solutions are obtained by solving the full Navier-Stokes equations using the 5th-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 linear stability results showed that bluntness has less stabilizing effects on the stability of boundary layers over cones than on flat plates and wedges. The unsteady simulations of the interaction of plane threedimensional acoustic waves with the cone showed that the modulation of wavelength and the generation of instability waves first occurred near the leading edge in the plane where the constant acoustic phase lines are perpendicular to the cone axis. Further downstream, this instability region spreads in the azimuthal direction from this plane.

Balakumar, P.↗
NASA NTRS2008

Boundary Layer Receptivity due to Roughness and Freestream Sound for Supersonic Flows over Axisymmetric Cones

The receptivity of supersonic boundary layers due to the interaction of a two-dimensional acoustic wave with a three-dimensional roughness is numerically investigated over a 5-degree sharp tipped straight cone at a free stream Mach number of 3.5 and a high Reynolds number of 10(exp 6)/inch. 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 spatial discretization and using third-order total-variation-diminishing (TVD) Runge-Kutta scheme for temporal integration. The simulations are performed with different roughness heights and roughness locations. The steady computations with the roughness reveal that the perturbations induced by the roughness remain very close to the wall and do not penetrate to the outer part of the boundary layer. The effects of the roughness persist for about 10 boundary layer thicknesses downstream of each element. The unsteady simulation shows the generation of unstable three-dimensional first mode disturbances within a short distance from the roughness. However, the amplitudes of the instability waves are very small near the neutral point, on the order of 10(exp -4) compared to the free stream disturbances. The receptivity coefficients due to the roughness elements located very close to the tip are one order of magnitude smaller than those due to the roughness elements located closer to the neutral point.

Balakumar, P.↗
NASA NTRS2008

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).

Kara, K.↗
NASA NTRS2009

Stability of Supersonic Boundary Layers on a Cone at an Angle of Attack

The stability and receptivity of three-dimensional supersonic boundary layers over a 7deg sharp tipped straight cone at an angle of attack of 4.2deg is numerically investigated at a free stream Mach number of 3.5 and at two high Reynolds numbers, 0.25 and 0.50x10(exp 6)/inch. The generation and evolution of stationary crossflow vortices are also investigated by performing simulations with three-dimensional roughness elements located on the surface of the cone. The flow fields with and without the roughness elements are obtained by solving the full Navier-Stokes equations in cylindrical coordinates using the fifth-order accurate weighted essentially non-oscillatory (WENO) scheme for spatial discretization and using the third-order total-variation-diminishing (TVD) Runge-Kutta scheme for temporal integration. Stability computations reveal that the azimuthal wavenumbers are in the range of m approx. 25-50 for the most amplified traveling disturbances and in the range of m approx. 40-70 for the stationary disturbances. The N-Factor computations predicted that transition would occur further forward in the middle of the cone compared to the transition fronts near the windward and the leeward planes. The simulations revealed that the crossflow vortices originating from the nose region propagate towards the leeward plane. No perturbations were observed in the lower part of the cone.

Balakumar, Ponnampalam↗
NASA NTRS2010

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 flow fields were obtained by solving the two-dimensional Navier-Stokes equations in axi-symmetric coordinates using the 5th 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 mean boundary layer profiles were analyzed using local stability and non-local parabolized stability equations (PSE) 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. Firstly, the frequency of the most amplified second-mode disturbance was increased relative to the zero pressure gradient case. Secondly, the amplification of first- and second-mode disturbances was increased. Although an adverse pressure gradient enhances instability wave growth rates, small nose-tip bluntness was found to delay transition due to the low receptivity coefficient and the resulting weak initial amplitude of the instability waves. The computed and measured amplitude-frequency spectrums in all three cases agree very well in terms of frequency and the shape except for the amplitude.

Balakumar, Ponnampalam↗
NASA NTRS2010

Stability of Hypersonic Boundary Layers on a Cone at an Angle of Attack

The stability and receptivity of a three-dimensional hypersonic boundary layer over a 7deg half-angle straight cone at an angle of attack of 6deg is numerically investigated at a freestream Mach number of 6.0 and a Reynolds number of 10.4x10(exp 6)/m. The generation and evolution of stationary crossflow vortices are also investigated by performing simulations with three-dimensional roughness elements located on the surface of the cone. The flow fields with and without the roughness elements are obtained by solving the full Navier- Stokes equations in cylindrical coordinates using a fifth-order accurate weighted essentially non-oscillatory (WENO) scheme for spatial discretization and a third-order total-variation-diminishing (TVD) Runge-Kutta scheme for temporal integration. Stability computations produced azimuthal wavenumbers in the range of m approx. 20-50 for the most amplified traveling disturbances and in the range of m approx.30-70 for the stationary disturbances. The frequency of the unstable second-mode ranges from 400 kHz to 900 kHz along the windward ray. The N-Factor computations predicted transition would occur more forward on the sides of the cone as compared to the transition fronts near the windward and the leeward rays. The simulations also show the crossflow vortices originating from the nose region propagate towards the leeward ray. No perturbations were observed toward the windward half of the cone.

Balakumar, P.↗
NASA NTRS2009

Construction of Low Dissipative High Order Well-Balanced Filter Schemes for Non-Equilibrium Flows

The goal of this paper is to generalize the well-balanced approach for non-equilibrium flow studied by Wang et al. [26] to a class of low dissipative high order shock-capturing filter schemes and to explore more advantages of well-balanced schemes in reacting flows. The class of filter schemes developed by Yee et al. [30], Sjoegreen & Yee [24] and Yee & Sjoegreen [35] consist of two steps, a full time step of spatially high order non-dissipative base scheme and an adaptive nonlinear filter containing shock-capturing dissipation. A good property of the filter scheme is that the base scheme and the filter are stand alone modules in designing. Therefore, the idea of designing a well-balanced filter scheme is straightforward, i.e., choosing a well-balanced base scheme with a well-balanced filter (both with high order). A typical class of these schemes shown in this paper is the high order central difference schemes/predictor-corrector (PC) schemes with a high order well-balanced WENO filter. The new filter scheme with the well-balanced property will gather the features of both filter methods and well-balanced properties: it can preserve certain steady state solutions exactly; it is able to capture small perturbations, e.g., turbulence fluctuations; it adaptively controls numerical dissipation. Thus it shows high accuracy, efficiency and stability in shock/turbulence interactions. Numerical examples containing 1D and 2D smooth problems, 1D stationary contact discontinuity problem and 1D turbulence/shock interactions are included to verify the improved accuracy, in addition to the well-balanced behavior.

Wang, Wei↗
NASA NTRS2013

DNS, Enstrophy Balance, and the Dissipation Equation in a Separated Turbulent Channel Flow

The turbulent flows through a plane channel and a channel with a constriction (2-D hill) are numerically simulated using DNS and RANS calculations. The Navier-Stokes equations in the DNS are solved using a higher order kinetic energy preserving central schemes and a fifth order accurate upwind biased WENO scheme for the space discretization. RANS calculations are performed using the NASA code CFL3D with the komega SST two-equation model and a full Reynolds stress model. Using DNS, the magnitudes of different terms that appear in the enstrophy equation are evaluated. The results show that the dissipation and the diffusion terms reach large values at the wall. All the vortex stretching terms have similar magnitudes within the buffer region. Beyond that the triple correlation among the vorticity and strain rate fluctuations becomes the important kinematic term in the enstrophy equation. This term is balanced by the viscous dissipation. In the separated flow, the triple correlation term and the viscous dissipation term peak locally and balance each other near the separated shear layer region. These findings concur with the analysis of Tennekes and Lumley, confirming that the energy transfer terms associated with the small-scale dissipation and the fluctuations of the vortex stretching essentially cancel each other, leaving an equation for the dissipation that is governed by the large-scale motion.

Balakumar, Ponnampalam↗
NASA NTRS2014

Parallel Adaptive High-Order CFD Simulations Characterizing Cavity Acoustics for the Complete SOFIA Aircraft

This paper presents one-of-a-kind MPI-parallel computational fluid dynamics simulations for the Stratospheric Observatory for Infrared Astronomy (SOFIA). SOFIA is an airborne, 2.5-meter infrared telescope mounted in an open cavity in the aft of a Boeing 747SP. These simulations focus on how the unsteady flow field inside and over the cavity interferes with the optical path and mounting of the telescope. A temporally fourth-order Runge-Kutta, and spatially fifth-order WENO-5Z scheme was used to perform implicit large eddy simulations. An immersed boundary method provides automated gridding for complex geometries and natural coupling to a block-structured Cartesian adaptive mesh refinement framework. Strong scaling studies using NASA's Pleiades supercomputer with up to 32,000 cores and 4 billion cells shows excellent scaling. Dynamic load balancing based on execution time on individual AMR blocks addresses irregularities caused by the highly complex geometry. Limits to scaling beyond 32K cores are identified, and targeted code optimizations are discussed.

Acoustics↗
NASA NTRS2016

Parallel Adjective High-Order CFD Simulations Characterizing SOFIA Cavity Acoustics

This paper presents large-scale MPI-parallel computational uid dynamics simulations for the Stratospheric Observatory for Infrared Astronomy (SOFIA). SOFIA is an airborne, 2.5-meter infrared telescope mounted in an open cavity in the aft fuselage of a Boeing 747SP. These simulations focus on how the unsteady ow eld inside and over the cavity interferes with the optical path and mounting structure of the telescope. A temporally fourth-order accurate Runge-Kutta, and spatially fth-order accurate WENO- 5Z scheme was used to perform implicit large eddy simulations. An immersed boundary method provides automated gridding for complex geometries and natural coupling to a block-structured Cartesian adaptive mesh re nement framework. Strong scaling studies using NASA's Pleiades supercomputer with up to 32k CPU cores and 4 billion compu- tational cells shows excellent scaling. Dynamic load balancing based on execution time on individual AMR blocks addresses irregular numerical cost associated with blocks con- taining boundaries. Limits to scaling beyond 32k cores are identi ed, and targeted code optimizations are discussed.

CFD↗
NASA NTRS2016

Transition Prediction in Hypersonic Boundary Layers Using Receptivity and Freestream Spectra

Boundary-layer transition in hypersonic flows over a straight cone can be predicted using measured freestream spectra, receptivity, and threshold values for the wall pressure fluctuations at the transition onset points. Simulations are performed for hypersonic boundary-layer flows over a 7-degree half-angle straight cone with varying bluntness at a freestream Mach number of 10. The steady and the unsteady flow fields are obtained by solving the two-dimensional Navier-Stokes equations in axisymmetric coordinates using a 5th-order accurate weighted essentially non-oscillatory (WENO) scheme for space discretization and using a third-order total-variation-diminishing (TVD) Runge-Kutta scheme for time integration. The calculated N-factors at the transition onset location increase gradually with increasing unit Reynolds numbers for flow over a sharp cone and remain almost the same for flow over a blunt cone. The receptivity coefficient increases slightly with increasing unit Reynolds numbers. They are on the order of 4 for a sharp cone and are on the order of 1 for a blunt cone. The location of transition onset predicted from the simulation including the freestream spectrum, receptivity, and the linear and the weakly nonlinear evolutions yields a solution close to the measured onset location for the sharp cone. The simulations over-predict transition onset by about twenty percent for the blunt cone.

Balakumar, P.↗