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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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All sourcesNASA NTRSDOE OSTI
NASA NTRS1964

Tables for Supersonic Flow Around Right Circular Cones at Small Angle of Attack

The solution of supersonic flow fields by the method of characteristics requires that starting conditions be known. Ferri, in reference 1, developed a method-of-characteristics solution for axially symmetric bodies of revolution at small angles of attack. With computing machinery that is now available, this has become a feasible method for computing the aerodynamic characteristics of bodies near zero angle of attack. For sharp-nosed bodies of revolution, the required starting line may be obtained by computing the flow field about a cone at a small angle of attack. This calculation is readily performed using Stone's theory in reference 2. Some solutions of this theory are available in reference 3. However, the manner in which these results are presented, namely in a wind-fixed coordinate system, makes their use somewhat cumbersome. Additionally, as pointed out in reference 4, the flow component perpendicular to the meridian planes was computed incorrectly. The results contained herein have been computed in the same basic manner as those of reference 3 with the correct velocity normal to the meridian planes. Also, all results have been transferred into the body-fixed coordinate system. Therefore, the values tabulated herein may be used, in conjunction with the respective zero-angle-of-attack results of reference 5, as starting conditions for the method-of-characteristics solution of the flow field about axially symmetric bodies of revolution at small angles of attack. As in the zero-angle-of-attack case (ref. 5) the present results have been computed using the ideal gas value of 1.4 for the ratio of the specific heats of air. Solutions are given for cone angles from 2.5 deg to 30 deg in increments of 2.5 deg. For each cone angle, results were computed for a constant series of free-stream Mach numbers from 1.5 to 20. In addition, a solution was computed which yielded the minimum free-stream Mach number for a completely supersonic conical flow field. For cone angles of 27.5 deg and 30 deg, this minimum free-stream Mach number was above 1.5. Consequently, solutions at this Mach number were not computed for these two cone angles.

SUPERSONIC FLOW↗
NASA NTRSDate not supplied

Hypersonic Boundary-Layer Transition over a Blunt Circular Cone in a Mach 8 Digital Wind Tunnel

To understand the effects of freestream acoustic disturbances on transition reversal over a blunt body, three-dimensional direct numerical simulations (DNS) were conducted to investigate the interaction of a tunnel-like acoustic disturbance field with a Mach 8 laminar boundary layer over a 7 deg half-angle blunt cone with a nose radius of 𝑅 𝑛 = 5.2 mm. The flow conditions and the axisymmetric cone geometry matched those measured in the Sandia Hypersonic Wind Tunnel at Mach 8 (Sandia HWT-8), and the incident freestream acoustic disturbances in the DNS were generated by acoustic radiation from the nozzle-wall turbulent boundary layer in the same tunnel. Consistent with the predictions of the nonmodal instability analysis, the study shows the emergence of a second spectral peak for moderately oblique waves between 150 kHz and 200 kHz in the aft part of the cone. The spectral energy of temperature and streamwise velocity fluctuations is initially concentrated within the entropy layer. These fluctiations are eventually “swallowed” by the boundary layer as the entropy-layer thickness 𝛿 𝑆 becomes similar to the boundary-layer thickness 𝛿h𝑡 at downstream locations. The numerical schlieren contours show the same inclined structures commonly observed in blunt cone experiments, and these structures are found to be three dimensional and advect with a constant speed approximately equal to the mean flow speed near the edge of the boundary layer.

Hypersonic Flow↗
NASA NTRSDate not supplied

Hypersonic Boundary-Layer Transition over a Blunt Circular Cone in a Mach 8 Digital Wind Tunnel

To understand the effects of freestream acoustic disturbances on transition reversal over a blunt body, three-dimensional direct numerical simulations (DNS) were conducted to investigate the interaction of a tunnel-like acoustic disturbance field with a Mach 8 laminar boundary layer over a 7 deg half-angle blunt cone with a nose radius of 𝑅 𝑛 = 5.2 mm. The flow conditions and the axisymmetric cone geometry matched those measured in the Sandia Hypersonic Wind Tunnel at Mach 8 (Sandia HWT-8), and the incident freestream acoustic disturbances in the DNS were generated by acoustic radiation from the nozzle-wall turbulent boundary layer in the same tunnel. Consistent with the predictions of the nonmodal instability analysis, the study shows the emergence of a second spectral peak for moderately oblique waves between 150 kHz and 200 kHz in the aft part of the cone. The spectral energy of temperature and streamwise velocity fluctuations is initially concentrated within the entropy layer. These fluctiations are eventually “swallowed” by the boundary layer as the entropy-layer thickness 𝛿 𝑆 becomes similar to the boundary-layer thickness 𝛿h𝑡 at downstream locations. The numerical schlieren contours show the same inclined structures commonly observed in blunt cone experiments, and these structures are found to be three dimensional and advect with a constant speed approximately equal to the mean flow speed near the edge of the boundary layer.

Hypersonic Flow↗
NASA NTRS1972

Numerical calculations of flow fields

The solutions to the equations of motion for inviscid fluid flow around a pointed elliptic cone at incidence are presented. The numerical method used, MacCormack's second order preferential predictor-corrector finite difference approximation, is applied to the fluid flow equations derived in conservation-law form. The entropy boundary condition, hitherto unused for elliptic cone problems, is investigated and compared to reflection boundary condition solutions. The stagnation streamline movement of the inclined elliptic cone is noted and surface pressure coefficients are plotted. Also presented are solutions for an elliptic cone and a circular cone at zero incidence and a circular cone at a small angle of attack. Comparisons are made between these present solutions and previously published theory.

Anderson, D. M.↗
NASA NTRS2018

Nonlinear Evolution and Breakdown of Azimuthally Compact Crossflow Vortex Pattern over a Yawed Cone

Hypersonic boundary-layer flows over a circular cone at moderate angle of incidence can support strong crossflow instability in between the windward and leeward rays on the plane of symmetry. Due to the more efficient excitation of stationary crossflow vortices by surface roughness, a possible path to transition in such flows corresponds to rapid amplification of the high-frequency secondary instabilities of finite amplitude stationary crossflow vortices. In the present paper, the previous analyses of crossflow instability over a 7- degree half-angle, yawed circular cone in a Mach 6 free stream have been extended to the nonlinear evolution of azimuthally localized crossflow vortex packets and the amplification characteristics and nonlinear breakdown of high-frequency secondary instabilities associated with those packets. A comparison between plane marching PSE and direct Navier-Stokes simulations (DNS) reveals favorable agreement in regard to mode shapes, most amplified disturbance frequencies, and N-factor evolution. In contrast, the quasi-parallel predictions are found to result in severe underprediction of the N-factors. The direct numerical simulations also indicate that the breakdown of secondary instabilities in a 3D hypersonic boundary layer shares certain common features with the previous computations of crossflow transition over subsonic swept wings.

Vortex structure↗
NASA NTRS2010

Analysis of Instabilities in Non-Axisymmetric Hypersonic Boundary Layers Over Cones

Hypersonic flows over circular cones constitute one of the most important generic configurations for fundamental aerodynamic and aerothermodynamic studies. In this paper, numerical computations are carried out for Mach 6 flows over a 7-degree half-angle cone with two different flow incidence angles and a compression cone with a large concave curvature. Instability wave and transition-related flow physics are investigated using a series of advanced stability methods ranging from conventional linear stability theory (LST) and a higher-fidelity linear and nonlinear parabolized stability equations (PSE), to the 2D eigenvalue analysis based on partial differential equations. Computed N factor distribution pertinent to various instability mechanisms over the cone surface provides initial assessments of possible transition fronts and a guide to corresponding disturbance characteristics such as frequency and azimuthal wave numbers. It is also shown that strong secondary instability that eventually leads to transition to turbulence can be simulated very efficiently using a combination of advanced stability methods described above.

Li, Fei↗
NASA NTRS1989

Aerobraking orbital transfer vehicle

An aerobraking orbital transfer vehicle which includes an aerobraking device which also serves as a heat shield in the shape of a raked-off elliptic or circular cone with a circular or elliptical base, and with an ellipsoid or other blunt shape nose. The aerobraking device is fitted with a toroid-like skirt and is integral with the support structure of the propulsion system and other systems of the space vehicle. The vehicle is intended to be transported in components to a space station in lower earth orbit where it is assembled for use as a transportation system from low earth orbit to geosynchronous earth orbit and return. Conventional guidance means are included for autonomous flight.

Scott, Carl D.↗
NASA NTRS1958

Elliptic Cones Alone and with Wings at Supersonic Speed

To help fill the gap in the knowledge of aerodynamics of shapes intermediate between bodies of revolution and flat triangular wings, force and moment characteristics for elliptic cones have been experimentally determined for Mach numbers of 1.97 and 2.94. Elliptic cones having cross-sectional axis ratios from 1 through 6 and with lengths and base areas equal to circular cones of fineness ratios 3.67 and 5 have been studied for angles of bank of 0 degree and 90 degrees. Elliptic and circular cones in combination with triangular wings of aspect ratios 1 and 1.5 also have been considered. The angle-of-attack range was from 0 degree to about 16 degrees, and the Reynolds number was 8 x 10(6), based on model length. In addition to the forces and moments at angle of attack, pressure distributions for elliptic cones at zero angle of attack have been determined. The results of this investigation indicate that there are distinct aerodynamic advantages to the use of elliptic cones.

Jorgensen, Leland H↗
NASA NTRS2021

Hypersonic Boundary-Layer Transition on Blunted Cones at Angle of Attack

Experimental studies of cones at several high-speed facilities have demonstrated that, for small nosetip bluntness, transition onset over a circular cone moves upstream along the leeward side and downstream along the windward side, but this trend may be reversed at large bluntness values, where transition onset moves downstream along the leeward side and upstream along the windward side. A theoretical and numerical investigation is performed to characterize the effects of nose bluntness on disturbance amplification over the circular cone for several angles of attack, with the goal of understanding the potential physical mechanisms behind the experimental observations. The three-dimensional laminar basic states over a 1.5 m long, 7-degree half-angle cone with 9.525 mm nosetip radius are computed for selected angles of attack values and freestream conditions that are selected to match the Mach 10 experiments conducted within the Hypervelocity Wind Tunnel 9 at the Arnold Engineering Development Complex (AEDC). The solutions at a freestream unit Reynolds number of 17.1 million per meter are used to perform detailed instability analyses for angles of attack equal to 0, 1, 3, and 5 degrees. Results indicate that the linear amplification of stationary crossflow waves along inflection lines may begin to influence transition along the acreage of the cone for angles of attack equal to or larger than 5 degrees. The measured trend in transition front with respect to increasing angle of attack is found to be consistent with the predicted increase in the amplification factors for Mack mode disturbances along the streamline trajectories. The increase in Mack mode amplification along the windward ray for higher angles of attack is shown to be the result of a progressively earlier entropy-layer swallowing. Computations also indicate that the transition amplification factor along the windward ray is not constant and increases with the angle of attack and that the transition #-factors along the leeward ray are rather small. The nonmodal analysis for zero degrees angle of attack shows that entropy-layer disturbances with appreciably strong energy growth can coexist with Mack mode instabilities at the measured transition location.

boundary layer transition↗
NASA NTRS2021

Hypersonic Boundary-Layer Transition on Blunted Cones at Angle of Attack

Experimental studies of cones at several high-speed facilities have demonstrated that, for small nosetip bluntness, transition onset over a circular cone moves upstream along the leeward side and downstream along the windward side, but this trend may be reversed at large bluntness values, where transition onset moves downstream along the leeward side and upstream along the windward side. A theoretical and numerical investigation is performed to characterize the effects of nose bluntness on disturbance amplification over the circular cone for several angles of attack, with the goal of understanding the potential physical mechanisms behind the experimental observations. The three-dimensional laminar basic states over a 1.5 m long, 7-degree half-angle cone with 9.525 mm nosetip radius are computed for selected angles of attack values and freestream conditions that are selected to match the Mach 10 experiments conducted within the Hypervelocity Wind Tunnel 9 at the Arnold Engineering Development Complex (AEDC). The solutions at a freestream unit Reynolds number of 17.1 million per meter are used to perform detailed instability analyses for angles of attack equal to 0, 1, 3, and 5 degrees. Results indicate that the linear amplification of stationary crossflow waves along inflection lines may begin to influence transition along the acreage of the cone for angles of attack equal to or larger than 5 degrees. The measured trend in transition front with respect to increasing angle of attack is found to be consistent with the predicted increase in the amplification factors for Mack mode disturbances along the streamline trajectories. The increase in Mack mode amplification along the windward ray for higher angles of attack is shown to be the result of a progressively earlier entropy-layer swallowing. Computations also indicate that the transition amplification factor along the windward ray is not constant and increases with the angle of attack and that the transition #-factors along the leeward ray are rather small. The nonmodal analysis for zero degrees angle of attack shows that entropy-layer disturbances with appreciably strong energy growth can coexist with Mack mode instabilities at the measured transition location.

Boundary Layer Transition↗
NASA NTRS1971

Calculation of stability derivatives for slowly oscillating bodies of revolution at Mach 1.0

A parabolic method for steady transonic flow is extended to bodies of revolution oscillating in a sonic flow field. A Laplace transform technique is employed to derive the dipole solution, and the Adams-Sears iterative technique is used in the stability derivative calculation. A computer program is developed to perform the stability derivative calculation for the slowly oscillating cone and parabolic ogive. Inputs for the program are body geometry thickness ratio, acceleration constant, and pitch axis location. Sample calculations were performed for the parabolic ogive and circular cone and results are compared with those obtained by using other techniques and the available experimental data for circular cones.

Ruo, S. Y.↗
NASA NTRS1992

Prediction of asymmetric vortical flows around slender bodies using Navier-Stokes equations

Steady and unsteady asymmetric vortical flows around slender bodies at high angles of attack are solved using the unsteady, compressible, thin-layer Navier-Stokes equations. An implicit, upwind-biased, flux-difference splitting, finite-volume scheme is used for the numerical computations. For supersonic flows past point cones, the locally conical flow assumption have been used for efficient computational studies of this phenomenon. Asymmetric flows past a 5-deg semiapex-angle circular cone at different angles of attack, free-stream Mach numbers, and Reynolds numbers have been studied in responses to different sources of disturbances. The effects of grid fineness and computational domain size have also been investigated. Next, the responses of three-dimensional supersonic asymmetric flow around a 5-deg circular cone at different angles of attack and Reynolds numbers to short-duration sideslip disturbances are presented. The results show that flow asymmetry becomes stronger as the Reynolds number and angles of attack are increased. One of the cases of flow over a cone-cylinder configuration is validated fairly well by experimental data.

Liu, C. H.↗