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NASA NTRS2022

Combined Bluntness and Roughness Effects on Cones at Hypersonic Speeds

This computational study investigates the effects of discrete roughness elements on a blunt cone at zero degrees angle of attack in a Mach 6 flow. Motivation was provided by experiments conducted in the Air Force Research Laboratory Mach 6 High Reynolds Number facility on a 7-degree half-angle cone with a roughness array located at 45 degrees from the apex on two nose tips of different blutness but equivalent roughness Reynolds number. Transition was only affected on the blunter cone, indicating that the transition onset is associated with the combined effects of bluntness and roughness. The present study investigates the 15.24 mm nose radius, 420 azimuthal wavenumber case via Navier-Stokes computations of the laminar base flow and instability analysis. Plane-marching parabolized stability equations (PSE) and inflow-resolvent analysis based on the three-dimensional, harmonic linearized Navier-Stokes equations (HLNSE) are used to calculate the amplification of disturbances along the roughness wake as well as over the roughness nearfield. Results show that the roughness shape can have a great impact on the characteristics of the most amplified wake instabilities. For the experimental configuration with cubic roughness elements of 15 μ m height, the flow is marginally unstable. For prismatic elements of 20 μ m height, the PSE predicts a logarithmic disturbance amplification ratio of N = 5.6 along its wake, but this ratio increases to N = 9.6 when the amplification over the roughness and separation regions is included in the inflow-resolvent analysis.

Boundary-layer transition↗

NASA NTRS2022

Combined Bluntness and Roughness Effects on Cones at Hypersonic Speeds

Boundary-layer transition↗

NASA NTRS1994

Combined LAURA-UPS solution procedure for chemically-reacting flows

A new procedure seeks to combine the thin-layer Navier-Stokes solver LAURA with the parabolized Navier-Stokes solver UPS for the aerothermodynamic solution of chemically-reacting air flowfields. The interface protocol is presented and the method is applied to two slender, blunted shapes. Both axisymmetric and three dimensional solutions are included with surface pressure and heat transfer comparisons between the present method and previously published results. The case of Mach 25 flow over an axisymmetric six degree sphere-cone with a noncatalytic wall is considered to 100 nose radii. A stability bound on the marching step size was observed with this case and is attributed to chemistry effects resulting from the noncatalytic wall boundary condition. A second case with Mach 28 flow over a sphere-cone-cylinder-flare configuration is computed at both two and five degree angles of attack with a fully-catalytic wall. Surface pressures are seen to be within five percent with the present method compared to the baseline LAURA solution and heat transfers are within 10 percent. The effect of grid resolution is investigated and the nonequilibrium results are compared with a perfect gas solution, showing that while the surface pressure is relatively unchanged by the inclusion of reacting chemistry the nonequilibrium heating is 25 percent higher. The procedure demonstrates significant, order of magnitude reductions in solution time and required memory for the three dimensional case over an all thin-layer Navier-Stokes solution.

Wood, William A.↗

NASA NTRS1972

Boundary-Layer Edge Conditions and Transition Reynolds Number Data for a Flight Test at Mach 20 (Reentry F)

A flight experiment, designated Reentry F, was conducted to measure heat-transfer rates for laminar, transitional, and turbulent boundary layers on a 5 deg half-angle cone 3.962 m (13 ft) long with a preflight nose radius of 2.54 mm (0.10 in.). Data were obtained over an altitude range from 36.58 to 18.29 km (120 000 to 60 000 ft) at a flight velocity of about 6.096 km/sec (20 000 ft/sec). The nominal values of the free-stream total enthalpy, sharp-cone Mach number, and the wall-to-total enthalpy ratio were 18 MJ/kg (8000 Btu/lb), 15, and 0.03, respectively. Calculated boundary-layer edge conditions that account for effects of the entropy layer and corresponding local transition Reynolds numbers are reported in the present paper. Fully developed turbulent flow occurred with essentially constant boundary-layer edge conditions near the sharp-cone values. Transition data were obtained with local edge Mach numbers ranging from about 5.55 to 15. Transition Reynolds numbers, based on local condition, were as high as 6.6 x 10(exp 7) with an edge Mach number of about 14.4 at an altitude of 24.38 km (80 000 ft). The transition could be correlated with previous flight data taken over a Mach number range from 3 to 12 in terms of parameters including the effects of local unit Reynolds number, boundary-layer wall-to-edge enthalpy ratio, and local Mach number.

Johnson, Charles B.↗

NASA NTRS1966

Transonic aerodynamic investigation of tension shell and blunted 100 deg conical shapes for unmanned entry vehicles

An experimental investigation of a spherically blunted 100° cone and two tension shell configurations with varying nose-bluntness ratios for use in unmanned entry into low -density planetary atmospheres has been conducted by the National Aeronautics and Space Administration at Mach numbers from 0.30 to 1.20 and at angles of attack from approximately O° to 40°. The results show that the models were longitudinally stable, with centers of pressure located rearward of the base at all test conditions. The tension shell configurations exhibited substantially higher axial-force coefficients than the 100° cone although the variation of axial-force coefficient with Mach number at zero angle of attack was similar for all configurations. An increase in tension shell body length resulted in a reduction of the axial-force coefficients and a more forward center-of-pressure location. Variation in nose bluntness had no significant effect on the longitudinal aerodynamic characteristics of the tension shell configurations.

TRANSONIC SPEED↗

NASA NTRS1989

Optimum shape of a blunt forebody in hypersonic flow

The optimum shape of a blunt forebody attached to a symmetric wedge or cone is determined. The length of the forebody, its semi-thickness or base radius, the nose radius and the radius of the fillet joining the forebody to the wedge or cone are specified. The optimum shape is composed of simple curves. Thus experimental models can be built readily to investigate the utilization of aerodynamic heating for boundary layer control. The optimum shape based on the modified Newtonian theory can also serve as the preliminary shape for the numerical solution of the optimum shape using the governing equations for a compressible inviscid or viscous flow.

Maestrello, L.↗

NASA NTRS1954

Theoretical and experimental investigation of additive drag

The significance of additive drag is discussed and equations for determining its approximate value are derived for annular and open-nose inlets. Charts are presented giving values of additive drag coefficient over a range of free-stream Mach numbers for open and for annular-nose inlets with conical flow at the inlet. The effects on additive drag of variable inlet-total-pressure recovery and static pressures on the centerbody are investigated and an analytical method of predicting the variation of pressure on the centerbody with mass-flow ratio is given. Experimental additive-drag values are presented for a series of 20 degree and 25 degree cone half-angle inlets and one open-nose inlet operating at free-stream Mach numbers of 1.8 and 1.6. A comparison with the theoretical values of additive drag shows excellent agreement for the open-nose inlet and moderately good agreement for the annular inlets. (author)

Sibulkin, Merwin↗

NASA NTRS1983

Subsonic high-angle-of-attack aerodynamic characteristics of a cone and cylinder with triangular cross sections and a cone with a square cross section

Experiments were conducted in the 12-Foot Pressure Wind Tunnel at Ames Research Center on three models with noncircular cross sections: a cone having a square cross section with rounded corners and a cone and cylinder with triangular cross sections and rounded vertices. The cones were tested with both sharp and blunt noses. Surface pressures and force and moment measurements were obtained over an angle of attack range from 30 deg to 90 deg and selected oil-flow experiments were conducted to visualize surface flow patterns. Unit Reynolds numbers ranged from 0.8x1,000,000/m to 13.0x1,000,000/m at a Mach number of 0.25, except for a few low-Reynolds-number runs at a Mach number of 0.17. Pressure data, as well as force data and oil-flow photographs, reveal that the three dimensional flow structure at angles of attack up to 75 deg is very complex and is highly dependent on nose bluntness and Reynolds number. For angles of attack from 75 deg to 90 deg the sectional aerodynamic characteristics are similar to those of a two dimensional cylinder with the same cross section.

Clarkson, M. H.↗

NASA NTRS1961

Exploratory Study of the Reduction in Friction Drag Due to Streamwise Injection of Helium

The effects on average skin-friction drag and pressure drag of the streamwise injection of helium into the boundary layer near the nose of a 6 deg. half-angle cone at Mach numbers of 3 to 5 are presented. Large reductions in skin friction are shown to be possible with relatively small amounts of helium injection.

Swenson, Byron L.↗

NASA NTRS2012

On Heatshield Shapes for Mars Entry Capsules

The 70deg sphere-cone - the standard geometry for all US Mars entry missions - is thoroughly examined via flow field simulations at a select few peak heating points along candidate flight trajectories. Emphasis is placed on turbulent heating based on the Baldwin- Lomax turbulence model. It is shown that increased leeward turbulent heating for a 70 sphere-cone flying at angle of attack is primarily due to the discontinuity in curvature between the spherical nose cap and the conical frustum - the attachment of the sonic line at this sphere-cone junction leads to a supersonic edge Mach number over the leeward acreage. In an attempt to mitigate this problem of elevated turbulent heating, alternate geometries, without any curvature discontinuities in the acreage, are developed. Two approaches, one based on nonlinear optimization with constraints, and one based on the use of non-uniform rational B-splines, are considered. All configurations examined remain axisymmetric. The aerothermal performance of alternate geometries is shown to be superior to that of the 70 sphere-cone.

Prabhu, DInesh K.↗

NASA NTRS1979

Measured and predicted shock shapes and aerodynamic coefficients for blunted cones at incidence in helium at Mach 20.3

Experimental values of shock shapes (alpha = 0 degrees and 10 degrees) and static aerodynamic coefficients (alpha = -4 degrees to 12 degrees) for sharp and spherically blunted cones having cone half-angles of 30, 45, 60, and 70 degrees and nose bluntness ratios of 0, 0.25, and 0.50 are presented. Shock shapes were also measured at 0 degree angle of attack by using a flat-faced cylinder (90 degree cone) and a hemispherically blunted cylinder (sphere). All tests were conducted in helium (gamma = 5/3) at a free-stream Mach number of 20.3 and a unit free-stream Reynolds number of 22,400,000 per meter. Comparisons between measured values and predicted values were made by using several numerical and simple engineering methods.

Calloway, R. L.↗

NASA NTRS1995

Dual-Code Solution Strategy for Chemically-Reacting Hypersonic Flows

A new procedure seeks to combine the thin-layer Navier-Stokes solver LAURA with the parabolized Navier-Stokes solver UPS for the aerothermodynamic solution of chemically-reacting air flow fields. The interface protocol is presented and the method is applied to two slender, blunted shapes. Both axisymmetric and three-dimensional solutions are included with surface pressure and heat transfer comparisons between the present method and previously published results. The case of Mach 25 flow over an axisymmetric six degree sphere-cone with a non-catalytic wall is considered to 100 nose radii. A stability bound on the marching step size was observed with this case and is attributed to chemistry effects resulting from the non-catalytic wall boundary condition. A second case with Mach 28 flow over a sphere-cone-cylinder-flare configuration is computed at both two and five degree angles of attack with a fully-catalytic wall. Surface pressures are seen to be within five percent with the present method compared to the baseline LAURA solution and heat transfers are within 10 percent. The effect of grid resolution is investigated in both the radial and streamwise directions. The procedure demonstrates significant, order of magnitude reductions in solution time and required memory for the three-dimensional case in comparison to an all thin-layer Navier-Stokes solution.

Wood, William A.↗

NASA NTRS1961

Measurements of Aerodynamic Heat Transfer and Boundary-Layer Transition on a 15 deg. Cone in Free Flight at Supersonic Mach Numbers up to 5.2

Measurements of aerodynamic heat transfer have been made at several stations on the 15 deg total-angle conical nose of a rocket-propelled model in free flight at Mach numbers up to 5.2. Data are presented for a range of local Mach number just outside the boundary layer from 1.40 to 4.65 and a range of local Reynolds number from 3.8 x 10(exp 6) to 46.5 x 10(exp 6), based on length from the nose tip to a measurement station. Laminar, transitional, and turbulent heat-transfer coefficients were measured. The laminar data were in agreement with laminar theory for cones, and the turbulent data agreed well with turbulent theory for cones using Reynolds number based on length from the nose tip. At a nearly constant ratio of wall to local static temperature of 1.2 the Reynolds number of transition increased from 14 x 10(exp 6) to 30 x 10(exp 6) as Mach number increased from 1.4 to 2.9 and then decreased to 17 x 10(exp 6) as Mach number increased to 3.7. At Mach numbers near 3.5, transition Reynolds numbers appeared to be independent of skin temperature at skin temperatures very cold with respect to adiabatic wall temperature. The transition Reynolds number was 17.7 x 10(exp 6) at a condition of Mach number and ratio of wall to local static temperature near that for which three-dimensional disturbance theory has been evaluated and has predicted laminar boundary-layer stability to very high Reynolds numbers (approximately 10(exp 12)).

Rumsey, Charles B.↗

NASA NTRS1952

Forces and Moments on Pointed Blunt-nosed Bodies of Revolution at Mach Numbers from 2.75 to 5.00

Results of tests to determine the aerodynamic forces and moments on bodies of revolution at angles of attack from 0 degrees to 25 degrees are presented and compared with theory. Cones and ogives of fineness ratios 3 to 7 and two blunt-nosed body shapes with fineness ratios 3 and 5 were tested at Mach numbers from 2.75 to 5.00. Reynolds numbers were from 0.5 million to 6.4 million, depending on Mach number and body fineness ratio.

Dennis, David H↗

NASA NTRS1971

Analysis of Free-Flight Laminar, Transitional, and Turbulent Heat-Transfer Results at Free-Stream Mach Numbers Near 20 (Reentry F)

Laminar, transitional, and turbulent heat-transfer data were measured during a reentry flight at a Mach number of 20 on a 5 deg half-angle cone 3.962 m (13 ft) long with an initial nose tip radius of 0.254 cm (0.1 in.). The free-stream Reynolds number increased during the prime data period from 7.0 x 10(exp 6) to 51.5 x 10(exp 6) per meter (2.1 x 10(exp 6) to 15.7 x 10(exp 6) per foot) and the ratio of wall to total temperature varied from 0.053 to 0.12. The angle of attack was less than 1deg for the prime data period. The experimental laminar and turbulent heating rates are compared with results from existing flat-plate prediction methods. At conditions of minimal tip blunting and angle of attack (above 26.8 km (88 000 ft)), values from a flat-plate laminar method agreed within 20 percent with the laminar data. The Schultz-Grunow skin-friction equation with reference enthalpy; conditions, with the Reynolds number based on distance from the transition location, and with the Colburn Reynolds analogy agreed within 10 percent with the experimental turbuleiit heating data. The Van Driest n skin-friction equation with Reynolds number greater than 10(exp 7) based on distance from the peak heating point and the Colburn Reynolds analogy was also within approximately 10 percent of the experimental turbulent heating data. A data correlation jbf the extent of transition and a simple empirical transition-zone heating correlation were also presented.

Zoby, Ernest V.↗

NASA NTRS1975

Second-order small-disturbance solutions for hypersonic flow over power-law bodies

Similarity solutions were found which give the adiabatic flow of an ideal gas about two-dimensional and axisymmetric power-law bodies at infinite Mach number to second order in the body slenderness parameter. The flow variables were expressed as a sum of zero-order and perturbation similarity functions for which the axial variations in the flow equations separated out. The resulting similarity equations were integrated numerically. The solutions, which are universal functions, are presented in graphic and tabular form. To avoid a singularity in the calculations, the results are limited to body power-law exponents greater than about 0.85 for the two-dimensional case and 0.75 for the axisymmetric case. Because of the entropy layer induced by the nose bluntness (for power-law bodies other than cones and wedges), only the pressure function is valid at the body surface. The similarity results give excellent agreement with the exact solutions for inviscid flow over wedges and cones having half-angles up to about 20 deg. They give good agreement with experimental shock-wave shapes and surface-pressure distributions for 3/4-power axisymmetric bodies, considering that Mach number and boundary-layer displacement effects are not included in the theory.

Townsend, J. C.↗

NASA NTRS1980

Measured and predicted shock shapes and aerodynamic coefficients for blunted cones at incidence in air at Mach 5.9

Experimental values of shock shapes (angles of attack of 0 deg and 10 deg) and static aerodynamic coefficients (angles of attack of -4 deg to 12 deg for sharp and spherically blunted cones having cone half angles of 30 deg, 45 deg, 60 deg, and 70 deg, and nose bluntness ratios of 0, 0.25, and 0.50 are presented. Shock shapes were measured at 0 deg angle of attack by using a flat faced cylinder (90 deg cone) and a hemispherically blunted cylinder (sphere). All tests were conducted in air at a free stream Mach number of 5.9 and a unit free stream Reynolds number of 2,800,000 per meter. Comparisons between measured values and predicted values were made by using several numerical and simple engineering methods.

Calloway, R. L.↗

NASA NTRS1961

Low-Subsonic-Speed Static Stability of Right-Triangular-Pyramid and Half-Cone Lifting Reentry Configurations

An investigation has been made to determine the low-subsonic-speed static stability characteristics of several right-triangular-pyramid and half-cone configurations. Also studied were the effects of various modifications, such as base extensions, nose shape, nose incidence, and ridge-line shape. The investigation showed that, in general, the models had satisfactory longitudinal and lateral stability. The basic pyramid model and the conical ridge-line model with or without a rounded nose had almost identical longitudinal and lateral stability characteristics and lift-drag ratios. The lift-drag ratios of the cylindrical ridge-line and half-cone models were considerably lower than those of the conical ridge-line model. The addition of a 20 degree boattail to the models increased the lift-drag ratios but decreased the directional stability, whereas a streamwise base extension was more effective in increasing the lift-drag ratios and increased the directional stability.

Ware, George M.↗