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Gnoffo, P. A.

Publications and source records attributed to Gnoffo, P. A..

35 records · Page 2
All sourcesNASA NTRSDOE OSTI
NASA NTRS1984

Heat-transfer distributions for biconics at incidence in hypersonic-hypervelocity real-gas flows

Laminar heat-transfer distributions were measured on spherically blunted, 13/7 deg straight and bent biconics at freestream velocities from 4.5 to 6.9 km/s and Mach numbers from 6 to 9. The flows were generated in the NASA's Langley Expansion Tube using helium, nitrogen, air, and carbon dioxide; angle of attack, referenced to the axis of the aft cone, was varied from zero to 20 deg. The penalty in windward heating to the fore cone due to the 7-deg nose bend diminished rapidly with increasing angle of attack and was only 10 to 20 percent at the design trim angle of attack of 20 deg. Leeward heating initially decreased, then increased, with increasing angle of attack. Windward heating rates predicted with a computer code that solves the parabolized Navier-Stokes equations were in good agreement with measurements for helium and air. The study used a 1.9-percent scale model of the proposed generic planetary vehicle and is directly applicable to the orbital transfer vehicle, which incorporates a spherically blunted biconic.

Miller, C. G.↗
NASA NTRS1983

Hypersonic flows over biconics using a variable-effective-gamma, Parabolized-Navier-Stokes code

Hypersonic flows over straight and bent biconics are calculated for a range of freestream conditions in which the gas behind the shock is treated as either perfect or real. The Parabolized-Navier-Stokes (PNS) equations form the basis of the approximation scheme. Good comparisons with experimental data for pressures, forces and moments, heat transfer, and oil-flow patterns serve to validate the perfect-gas version of the code. Circumferential velocity vector plots further aid in the interpretation of leeside oil-flow patterns. A variable-effective-gamma (VEG) option is implemented for the real-gas calculations. Gamma, now defined as the ratio of enthalpy to internal energy, is determined from a locally valid linear relation in enthalpy and pressure at every mesh point which in turn is calculated from a benchmark equilibrium code. The VEG option is easily incorporated into a host PNS code because it uses the underlying perfect-gas structure of the code. Comparisons to experimental data for heat transfer and shock shape in high enthalpy air have been obtained using the VEG option.

Gnoffo, P. A.↗
NASA NTRS1983

Viscous shock-layer flowfield analysis by an explicit-implicit method

The present work extends the recently reported implicit analogue of MacCormack's earlier widely-used explicit method to external axisymmetric laminar flows with strong entropy gradients. The details of the 'numerics' of the implicit part are provided in a body-oriented coordinate system with a moving outer (shock) boundary during the transient part of the solutions. The limiting values of the Courant number are obtained when the shock boundary is treated explicitly. The solution algorithm outlined includes the treatment of the source term associated with the equations in weak conservation form. From the results obtained for two sample problems, it becomes clear that accuracy of predictions is, indeed, very good at higher values of the Courant number. There is a significant saving in overall computing time, depending on the Courant number used and the flow Reynolds number. These properties combined with the simplicity of programming the implicit analogue may appeal to researchers for using it in the analysis of three-dimensional flow problems.

Gupta, R. N.↗
NASA NTRS1983

Heat-transfer distributions on biconics at incidence in hypersonic-hypervelocity He, N2, air, and CO2 flows

Laminar heat-transfer rates were measured on spherically blunted, 13 degrees/F degrees on-axis and bent biconics (fore cone bent 7 degrees upward relative to aft cone) at hypersonic-hypervelocity flow conditions in the Langley Expansion Tube. Freestream velocities from 4.5 to 6.9 km/sec and Mach numbers from 6 to 9 were generated using helium, nitrogen, air, and carbon dioxide test gases, resulting in normal shock density ratios from 4 to 19. Angle of attack, referenced to the axis of the aft cone, was varied from zero to 20 degrees in 4 degree increments. The effect of nose bend, angle of attack, and real-gas phenomena on heating distributions are presented along with comparisons of measurement to prediction from a code which solves the three-dimensional 'parabolized Navier-Stokes' equations.

Miller, C. G.↗
NASA NTRS1983

A viscous shock-layer flowfield analysis by an explicit-implicit method

An implicit analogue of a widely used explicit method to external axisymmetric laminar flows with strong entropy gradients is extended. The details of the "numerics" of the implicit part are provided in a body oriented coordinate system with a moving outer (shock) boundary during the transient part of the solutions. The limiting values of the Courant number are obtained when the shock boundary is treated explicitly. The solution algorithm outlined includes the treatment of the source term associated with the equations in weak conservation form. From the results obtained for two sample problems, it becomes clear that accuracy of predictions is, indeed, very good at higher values of the Courant number. There is a significant saving in overall computing time, depending on the Courant number used and the flow Reynolds number. These properties combined with the simplicity of programming the implicit analog may appeal to researchers for using it in the analysis of 3-D flow problems.

Gupta, R. M.↗
NASA NTRS1983

Heat-transfer distributions on biconics at incidence in hypersonic-hypervelocity He, N2, air, and CO2 flows

Laminar heat transfer rates were measured on spherically blunted, 13 deg/7 deg on axis and bent biconics (fore cone bent 7 deg upward relative to aft cone) at hypersonic hypervelocity flow conditions in the Langley Expansion Tube. Freestream velocities from 4.5 to 6.9 km/sec and Mach numbers from 6 to 9 were generated using helium, nitrogen, air, and carbon dioxide test gases, resulting in normal shock density ratios from 4 to 19. Angle of attack, referenced to the axis of the aft cone, was varied from 0 to 20 deg in 4 deg increments. The effect of nose bend, angle of attack, and real gas phenomena on heating distributions are presented along with comparisons of measurement to prediction from a code which solves the three dimensional parabolized Navier-Stokes equations.

Miller, C. G.↗
NASA NTRS1982

Pressure distributions and shock shapes for a bent-nose biconic at incidence

Initial results of a NASA study of the lift-drag characteristics of a 12.84/7 deg biconic model intended for airbraking during atmospheric entry of probes to Mars, Venus, Saturn, and Titan are reported. Pressure distributions and shock shapes were measured in the Langley 20 in. Mach 6 tunnel with the spherically blunted bent-nose model set at angles from 0-25 deg. Pressure distributions and shock shapes where computed using the STEIN flowfield code, which features a MacCormack scheme to integrate the three-dimensional Euler equations, the Rankine-Hugoniot jump conditions to model shock waves as discontinuities, and requires a supersonic condition at every step. A comparison was made between measured and predicted values. The leeward shock angle was found to be predictable to within 3% for all angles of attack, while parabolized Navier-Stokes equations are regarded as offering more accurate results than the STEIN code for surface pressure distributions.

Miller, C. G., III↗
NASA NTRS1982

An experimental investigation of hypersonic flow over biconics at incidence and comparison to prediction

Pressure distributions, aerodynamic coefficients, shock shapes, and oil-flow patterns were measured on spherically blunted, 12.84 deg/7 deg on-axis and bent biconics at Mach 6 in air. The angle of attack, referenced to the axis of the aft-cone, was varied from -10 to 40 deg in nominal 5 deg increments. Predictions from an inviscid flowfield computer code referred to as STEIN and codes which solve the three-dimensional parabolized Navier Stokes (PNS) equations were compared with measurement. Three PNS codes were found which provided accurate predictions of windward and leeward pressure distributions for angles of attack to 25 deg.

Miller, C. G.↗
NASA NTRS1982

A vectorized, finite-volume, adaptive grid algorithm applied to planetary entry problems

An adaptive grid, finite-volume method has been applied to problems in planetary entry for computing complete flowfields. The adaption algorithm is implicit in nature and is keyed to resolve user specified gradients. The finite-volume algorithm is explicit, utilizing a maximum time step advancement at each grid point to accelerate convergence to the steady state. The present version of the code is for the laminar flow of a perfect gas. The role of the adaption algorithm in resolving various features of blunt body/wake flow for planetary entry conditions is emphasized.

Gnoffo, P. A.↗
NASA NTRS1982

A vectorized, finite-volume, adaptive-grid algorithm for Navier-Stokes calculations

An adaptive grid, finite-volume method has been used to solve the Navier-Stokes equations for complete (forebody and afterbody) flowfields around blunt bodies. The code, which is applicable for axisymmetric or two-dimensional flows, allows the mesh to adjust during the computation to provide a closer spacing of mesh points in regions of high gradients, thus minimizing the number of required computational points. The solution technique is explicit, utilizing a maximum time-step advancement at each grid point to accelerate convergence to the steady state. The code has been fully vectorized for efficient solution on the CYBER 203 computer. A very flexible rezoning routine is used to concentrate mesh points anywhere in the field, either by a user-defined weighting function or by allowing high gradient regions to adjust the grid. The grid adjustment routine is implicit in nature and represents a very small portion of the total computational cost. Currently, the code runs in approximately 0.000016 seconds per grid point per iteration.

Gnoffo, P. A.↗
NASA NTRS1979

Complete supersonic flowfields over blunt bodies in a generalized orthogonal coordinate system

A general orthogonal coordinate system is used to describe various axisymmetric and two-dimensional shapes. Close approximations to planetary probe configurations are possible. The full Navier-Stokes equations are discretized in this coordinate system in a manner based on Allen and Cheng's numerical procedure. The blow shock is treated as a discontinuity which floats between grid points. Completely coupled flows over the forebody, base, and near wake were calculated over a cylinder, sphere, and an approximation to the Viking Aeroshell. Some problem areas in determining the base flow for increasing Reynolds number are discussed. In particular, it is found that the mean free path of the fluid near the wall immediately below the corner of the Viking Aeroshell, which experiences a severe expansion, can become greater than the local mesh size required to resolve the boundary layer in the forebody.

Gnoffo, P. A.↗
NASA NTRS1978

Forebody and afterbody solutions of the Navier-Stokes equations for supersonic flow over blunt bodies in a generalized orthogonal coordinate system

A coordinate transformation, which can approximate many different two-dimensional and axisymmetric body shapes with an analytic function, is used as a basis for solving the Navier-Stokes equations for the purpose of predicting 0 deg angle of attack supersonic flow fields. The transformation defines a curvilinear, orthogonal coordinate system in which coordinate lines are perpendicular to the body and the body is defined by one coordinate line. This system is mapped in to a rectangular computational domain in which the governing flow field equations are solved numerically. Advantages of this technique are that the specification of boundary conditions are simplified and, most importantly, the entire flow field can be obtained, including flow in the wake. Good agreement has been obtained with experimental data for pressure distributions, density distributions, and heat transfer over spheres and cylinders in supersonic flow. Approximations to the Viking aeroshell and to a candidate Jupiter probe are presented and flow fields over these shapes are calculated.

Gnoffo, P. A.↗
NASA NTRS1978

Inviscid, nonadiabatic flow fields over blunt, sonic corner bodies for outer planet entry conditions by a method of integral relations

An investigation has been made into the ability of a method of integral relations to calculate inviscid zero degree angle of attack, radiative heating distributions over blunt, sonic corner bodies for some representative outer planet entry conditions is investigated. Comparisons have been made with a more detailed numerical method, a time asymptotic technique, using the same equilibrium chemistry and radiation transport subroutines. An effort to produce a second order approximation (two-strip) method of integral relations code to aid in this investigation is also described and a modified two-strip routine is presented. Results indicate that the one-strip method of integral relations cannot be used to obtain accurate estimates of the radiative heating distribution because of its inability to resolve thermal gradients near the wall. The two-strip method can sometimes be used to improve these estimates; however, the two-strip method has only a small range of conditions over which it will yield significant improvement over the one-strip method.

Gnoffo, P. A.↗
NASA NTRS1977

A generalized orthogonal coordinate system for describing families of axisymmetric and two-dimensional bodies

A generalized curvilinear orthogonal coordinate system is presented which can be used for approximating various axisymmetric and two-dimensional body shapes of interest to aerodynamicists. Such body shapes include spheres, ellipses, spherically capped cones, flat-faced cylinders with rounded corners, circular disks, and planetary probe vehicles. A set of transformation equations is also developed whereby a uniform velocity field approaching a body at any angle of attack can be resolved in the transformed coordinate system. The Navier-Stokes equations are written in terms of a generalized orthogonal coordinate system to show the resultant complexity of the governing equations.

Gnoffo, P. A.↗
NASA NTRS1976

Correlations for determining thermodynamic properties of hydrogen-helium gas mixtures at temperatures from 7,000 to 35,000 K

Simple relations for determining the enthalpy and temperature of hydrogen-helium gas mixtures were developed for hydrogen volumetric compositions from 1.0 to 0.7. These relations are expressed as a function of pressure and density and are valid for a range of temperatures from 7,000 to 35,000 K and pressures from 0.10 to 3.14 MPa. The proportionality constant and exponents in the correlation equations were determined for each gas composition by applying a linear least squares curve fit to a large number of thermodynamic calculations obtained from a detailed computer code. Although these simple relations yielded thermodynamic properties suitable for many engineering applications, their accuracy was improved significantly by evaluating the proportionality constants at postshock conditions and correlating these values as a function of the gas composition and the product of freestream velocity and shock angle. The resulting equations for the proportionality constants in terms of velocity and gas composition and the corresponding simple realtions for enthalpy and temperature were incorporated into a flow field computational scheme. Comparison was good between the thermodynamic properties determined from these relations and those obtained by using a detailed computer code to determine the properties. Thus, an appreciable savings in computer time was realized with no significant loss in accuracy.

Zoby, E. V.↗