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At least 163 records · Page 9

The solution of the Navier-Stokes equations using Gauss-Seidel line relaxation

The Navier-Stokes equations in an implicit flux-split difference formulation are solved numerically using a Gauss-Seidel line-relaxation procedure. Particular attention is given to the selection of flux-vector splitting method and flux splitting in boundary layers. Results for sample problems involving (1) turbulent supersonic flow over a cone and (2) the viscous hypersonic flow of a chemically reacting gas in thermal nonequilibrium past a blunted cone are presented in extensive graphs and briefly characterized. The present flux-split procedures are shown to provide accurate shear-layer calculations.

Maccormack, Robert W.↗

A three-dimensional upwind parabolized Navier-Stokes code for chemically reacting flows

A new upwind, parabolized Navier-Stokes (PNS) code has been developed to compute the three-dimensional flow of chemically reacting air around hypersonic vehicles. The code is a modification of the perfect gas, three-dimensional UPS code of Lawrence et al. (1986) which has been extended in the present study to permit the calculation of hypersonic, viscous flows in chemical nonequilibrium. The algorithm solves the PNS equations using a finite-volume, upwind TVD method based on Roe's approximate Riemann solver that has been modified to account for real gas effects. The present code solves the fluid dynamic and species continuity equations in a loosely-coupled manner. The fluid medium is assumed to be a chemically reacting mixture of thermally perfect (but calorically imperfect) gases in thermal equilibrium. Results are presented for the hypersonic laminar flow over a cone at 0- and 10-deg angles of attack and for a generic hypersonic vehicle. Calculations are performed assuming either perfect gas, equilibrium air, or finite-rate chemistry.

Buelow, Philip E.↗

Nonequilibrium effects for hypersonic transitional flows

Presented are the results of numerical simulations of hypersonic flow about blunt cones and hemispherical nose configurations for reentry velocities of 7.5 and 10 km/s. Cone half angles 0, 5, and 10 deg are considered at zero angle of incidence; however, the focus is for the 5 deg cone. The body size and altitude ranges considered (70 to 110 km) are such that the flow is in the transitional regime. Translational, thermodynamic, and chemical nonequilibrium effects are considered in the numerical simulation by utilizing the direct simulation Monte Carlo (DSMC) method of Bird. The DSMC results are compared with those obtained with viscous shock-layer and Navier-Stokes methods. Comparisons between the DSMC and continuum calculations show the altitude range where differences in flowfield structure and surface quantities become significant. The current calculations show that the binary scaling similitude provides a means of correlating the blunt body surface quantities in the hypersonic, transitional regime. Furthermore, for the higher velocity entry conditions, the results highlight some of the concerns in the application of multitemperature continuum formulations, particularly the use of some proposed functional relations for the chemical rate constants under thermodynamic nonequilibrium conditions.

Moss, James N.↗

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.↗

Hypersonic Transition Analysis for HIFiRE Experiments

The HIFiRE-1 flight experiment provided a valuable database pertaining to boundary layer transition over a 7-degree half-angle, circular cone model from supersonic to hypersonic Mach numbers, and a range of Reynolds numbers and angles of attack. This paper reports selected findings from the ongoing computational analysis of the measured in-flight transition behavior. Transition during the ascent phase at nearly zero degree angle of attack is dominated by second mode instabilities except in the vicinity of the cone meridian where a roughness element was placed midway along the length of the cone. The growth of first mode instabilities is found to be weak at all trajectory points analyzed from the ascent phase. For times less than approximately 18.5 seconds into the flight, the peak amplification ratio for second mode disturbances is sufficiently small because of the lower Mach numbers at earlier times, so that the transition behavior inferred from the measurements is attributed to an unknown physical mechanism, potentially related to step discontinuities in surface height near the locations of a change in the surface material. Based on the time histories of temperature and/or heat flux at transducer locations within the aft portion of the cone, the onset of transition correlated with a linear N-factor, based on parabolized stability equations, of approximately 13. Due to the large angles of attack during the re-entry phase, crossflow instability may play a significant role in transition. Computations also indicate the presence of pronounced crossflow separation over a significant portion of the trajectory segment that is relevant to transition analysis.

Li, Fei↗

Time-resolved unsteady shock motion and spectral analysis of a hypersonic shock-wave/boundary-layer interaction over a double-cone

Direct experimental measurements of double-cone shock-wave/boundary-layer interaction dynamics at Mach 7.2 were collected using a schlieren-based shock-detection algorithm at the University of Texas at San Antonio. The points of flow separation and reattachment were spatially and spectrally evaluated at 300 kHz for time-resolved characterization of the unsteadiness of this flow field. The separation bubble was found to rapidly expand and contract about a large mean length. Spectral analysis of the velocity fluctuations of this motion revealed this behavior to be a turbulent phenomenon, with spectral energy trends consistent with the Kolmogorov theory for the turbulent energy cascade.

Glasby, Ryan [ORNL]↗

Thermochemical Nonequilibrium Modeling in a Continuous-Galerkin, Finite-Element Framework

The presented work discusses the implementation, verification, and validation of Park's two-temperature model in a scalable, computational fluid dynamics (CFD) code developed at the US Department of Energy's Oak Ridge National Laboratory (ORNL). The implementation of Park's two-temperature model was verified through 0D test cases involving an adiabatic reactor and a nitrogen thermal bath. The implementation was then validated through comparisons with other validated CFD codes and experimental data on a hypersonic cylinder and double cones. These are standard benchmark test cases for thermochemical non-equilibrium (TCNE) modeling, and all data are shared publicly. The verification and validation results showed that ORNL's in-house CFD code could model complex, high-speed flow problems with and without TCNE modeling. This work is essential for future research involving 3D shock wave/boundary layer interactions (SBLIs).

Nutter, Nicole↗

Hypersonic Shock Interactions About a 25 deg/65 deg Sharp Double Cone

This paper presents the results of a numerical study of shock interactions resulting from Mach 10 air flow about a sharp double cone. Computations are made with the direct simulation Monte Carlo (DSMC) method by using two different codes: the G2 code of Bird and the DAC (DSMC Analysis Code) code of LeBeau. The flow conditions are the pretest nominal free-stream conditions specified for the ONERA R5Ch low-density wind tunnel. The focus is on the sensitivity of the interactions to grid resolution while providing information concerning the flow structure and surface results for the extent of separation, heating, pressure, and skin friction.

Moss, James N.↗

Low-to-high altitude predictions of three-dimensional ablative reentry flowfields

A new coupled-chemistry PNS scheme has been developed to study 3D hypersonic reentry flows over sphere cones at small angles of attack. A new quasi-steady ablation model for Teflon was used to predict ablative reentry flow fields under laminar, transitional, and turbulent conditions. This solution scheme uses a new two-step solution scheme for solving the species conservation equations under low-altitude conditions. As an example, the scheme is used to study hypersonic flow over a 6-deg sphere-cone configuration at 50 and 125 kft conditions under zero and nonzero angle of attack conditions.

Bhutta, Bilal A.↗

Improved tangent-cone method for the Aerodynamic Preliminary Analysis System (APAS) version of the hypersonic arbitrary-body program

The Aerodynamic Preliminary Analysis System (APAS) utilizes a modified version of the Hypersonic Arbitrary-Body Program (HABP) Mark 3 code in its analysis rationale. Four methods are considered for incorporation into the code as the tangent-cone method. The combination of second-order slender body theory and the approximate solution of Hammitt and Murthy shows the best agreement with the exact numerical solutions and is thus included in the APAS production version of the HABP code.

Cruz, Christopher I.↗

Stability Analysis for HIFiRE Experiments

The HIFiRE-1 flight experiment provided a valuable database pertaining to boundary layer transition over a 7-degree half-angle, circular cone model from supersonic to hypersonic Mach numbers, and a range of Reynolds numbers and angles of attack. This paper reports selected findings from the ongoing computational analysis of the measured in-flight transition behavior. Transition during the ascent phase at nearly zero degree angle of attack is dominated by second mode instabilities except in the vicinity of the cone meridian where a roughness element was placed midway along the length of the cone. The growth of first mode instabilities is found to be weak at all trajectory points analyzed from the ascent phase. For times less than approximately 18.5 seconds into the flight, the peak amplification ratio for second mode disturbances is sufficiently small because of the lower Mach numbers at earlier times, so that the transition behavior inferred from the measurements is attributed to an unknown physical mechanism, potentially related to step discontinuities in surface height near the locations of a change in the surface material. Based on the time histories of temperature and/or heat flux at transducer locations within the aft portion of the cone, the onset of transition correlated with a linear N-factor, based on parabolized stability equations, of approximately 13.5. Due to the large angles of attack during the re-entry phase, crossflow instability may play a significant role in transition. Computations also indicate the presence of pronounced crossflow separation over a significant portion of the trajectory segment that is relevant to transition analysis. The transition behavior during this re-entry segment of HIFiRE-1 flight shares some common features with the predicted transition front along the elliptic cone shaped HIFiRE-5 flight article, which was designed to provide hypersonic transition data for a fully 3D geometric configuration. To compare and contrast the crossflow dominated transition over the HIFiRE-1 and HIFiRE-5 configurations, this paper also analyzes boundary layer instabilities over a subscale model of the HIFiRE-5 flight configuration that was tested in the Mach 6 quiet tunnel facility at Purdue University.

Li, Fei↗

Effects of wind-tunnel disturbances on hypersonic boundary-layer transition. I, II.

An experimental investigation of the dependence on facility disturbance of transition on sharp cones has been made. In Part I, the sound radiated from the turbulent boundary layer on the walls of several facilities was measured with pressure transducers mounted flush with the cone surface. In Part II, a constant current hot-wire anemometer measured free-stream and cone shock layer disturbances in two hypersonic helium tunnels. Comparison of hot-wire results with surface pressure measurements in one of the helium tunnels indicate the latter data provide an accurate indication of the facility disturbance levels. Both studies show that transition Reynolds numbers correlate in terms of facility rms sound disturbance levels provided the laminar boundary layers on the models are similar.

Stainback, P. S.↗

Interaction of a Tunnel-like Acoustic Disturbance Field with a Blunt Cone Boundary Layer at Mach 8

The existing measurements of laminar-to-turbulent transition over circular cones in conventional (i.e., “noisy”) hypersonic wind tunnels have established that the transition location moves downstream when the nose radius is increased from zero. However, this initially downstream movement slows down and ultimately reverses beyond a critical value of the nose radius, and may be related to external forcing in the form of freestream disturbances and/or surface roughness. To understand the effects of freestream acoustic disturbances on transition reversal over a blunt body, hypersonic boundary-layer receptivity to broadband freestream acoustic disturbances from the nozzle wall of a digital conventional wind tunnel is investigated by both direct numerical simulations (DNS) and modal and nonmodal stability analysis. A Mach 8 flow over a 7 deg half-angle cone with a nose radius of 𝑅 𝑛 = 5.2mm and freestream Reynolds number of 12.2 × 10 6 m -1 is considered. The results show that the broadband tunnel noise in the free stream of a convectional hypersonic wind tunnel (i.e., outside of the nozzle-wall turbulent boundary layer) can be well represented by an acoustic model with an ansatz of slow acoustic waves. With successful calibration of the model parameters against the precursor tunnel DNS, such an acoustic ansatz can successfully reproduce both the frequency-wavenumber spectra and the temporal evolution of the broadband tunnel noise radiated from the nozzle wall. Additionally, the DNS of the Mach 8 blunt cone with tunnel-like acoustic input above the bow shock showed that the spectra of wall-pressure and heat-transfer fluctuations recovers the signature of the axisymmetric waves predicted by the nonmodal analysis. Furthermore, the azimuthal wavenumber and frequency spectrum of the temperature fluctuations as a function of the wall-normal distance show higher amplitudes for three-dimensional waves above the boundary-layer edge. The numerical schlieren contours show the inclined structures commonly observed in blunt cone experiments, demonstrating that they correspond to three-dimensional structures due to freestream disturbances in the presence of an entropy layer.

Boundary layer transition↗