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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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NASA NTRS2002

Prediction of Shock Wave Structure in Weakly Ionized Gas Flow by Solving MGD Equation

This paper reports the recent research results of shockwave structure predictions using a new developed code. The modified Rankine-Hugoniot relations across a standing normal shock wave are discussed and adopted to obtain jump conditions. Coupling a electrostatic body force to the Burnett equations, the weakly ionized flow field across the shock wave was solved. Results indicated that the Modified Rankine-Hugoniot equations for shock wave are valid for a wide range of ionization fraction. However, this model breaks down with small free stream Mach number and with large ionization fraction. The jump conditions also depend on the value of free stream pressure, temperature and density. The computed shock wave structure with ionization provides results, which indicated that shock wave strength may be reduced by existence of weakly ionized gas.

Deng, Z. T.↗
NASA NTRS1976

Frequency modulation at a moving material interface and a conservation law for wave number

An integral conservation law for wave numbers is considered. In order to test the validity of the proposed conservation law, a complete solution for the reflection and transmission of an acoustic wave impinging normally on a material interface moving at a constant speed is derived. The agreement between the frequency condition thus deduced from the dynamic equations of motion and the frequency condition derived from the jump condition associated with the integral equation supports the proposed law as a true conservation law. Additional comparisons such as amplitude discontinuities and Snells' law in a moving media further confirm the stated proposition. Results are stated concerning frequency and wave number relations across a shock front as predicted by the proposed conservation law.

Kleinstein, G. G.↗
NASA NTRS1977

Boundary-value problem of configurations with compressible free vortex flow

A self-consistent version of the compressible boundary-value problem for configurations with leading-edge vortex separation is formulated, based on the assumption that the compressible flow field is controlled by the linearized potential equation. The stream surface boundary condition and the zero pressure jump condition of the compressible free vortex flows are analyzed; application of the Goethert rule permits the compressible nonlinear boundary-value problem for the subsonic flow domain to be transformed into an equivalent nonlinear incompressible problem. The compressibility corrections developed are used in numerical calculations of subsonic leading-edge vortex flows about planar wing geometries. The sample calculations, employing an inviscid flow model in which the wing and vortex sheets are represented by piecewise continuous quadratic doublet sheet distributions, are applicable to high subsonic Mach numbers.

Brune, G. W.↗
NASA NTRS1988

Energized winds

The general theory of winds whose energy flux increases along the flow trajectories, but without momentum deposition, is developed. It is shown that the sonic point is generally within the region of significant energy deposition or at its boundary. Assuming that the energy is deposited into a thin layer, it is shown that the jump conditions across the layer imply that the fluid jumps to a Mach number of one just downstream of the deposition layer if the deposited energy per unit area exceeds some critical amount. This result is used to estimate the incident flux needed to excite wind from a stellar surface in terms of the star's mass and the penetration grammage of the incident flux. The expected mass flux from the star bombarded by a 'supercritical' energy flux is calculated, and the results are compared to the measured P-dot/P of Cyg X-3.

Eichler, David↗
NASA NTRS1995

Kinetic structure of intermediate shocks: Implications for the magnetopause

A general study of the structure and stability of intermediate shocks (IS) in an isotropic plasma is presented using a hybrid as well as a resistive Hall MHD code. Special emphasis is put on the question of whether the rotational layers observed at the magnetopause can be intermediate shocks. The shocks are formed dynamically by the interaction between a flowing plasma and a stationary piston. Coplanar ISs (both strong and weak) are found to be stable in a collisionless plasma. The existence of slow shocks in a high beta plasma is also established for the first time. Noncoplanar ISs are found to be time-dependent, evolving toward a rotational discontinuity (RD) after some characteristic time tau which can be quite long (1000 Omega(exp -1), where Omega is the ion gyrofrequency). The value tau is larger the closer the rotation angle is to 180 deg. Rotations larger than 180 deg are found to be unstable, decaying into a state of minimum shear (i.e., rotation angle less than 180 deg). There are various length scales associated with an IS in the kinetic regime. The shortest scale is found to be the length scale over which rotation of the transverse component of the magnetic field takes place. This scale can have a half width as small as one ion inertial length (c/omega(sub p)) for electron sense rotations and 3c/omega(sub p) for ion sense rotations, for an upstream ion beta of unity. Both of these scales are consistent with the observed thickness at the magnetopause and identical to the corresponding RD scales. A detailed study of the mode conversion of the Alfven ion cyclotron waves (A/IC) waves across both slow and intermediate shocks and the resulting downstream wave spectrum are presented. The possibility that the large number of relfected ions observed at the magnetopause may be due to the presence of strong ISs is considered. The identification of strong ISs and their distinction from RDs should be possible in observations due to significant differences that exist between jump conditions and overall structure of the two discontinuities. The jumps in the plasma parameters across a weak IS are typically small. This together with the fact that the weak ISs and RDs have very similar thickness and other overall properties makes the distinction between weak ISs and RDs in the observations largely inconsequential. However, at large noncoplanarity angles the weak IS approaches the RD limit in a relatively short time (approximately less than 100 Omega (exp -1)). Thus, magnetopause rotations with large noncoplanarity angles are most likely either RDs or strong ISs. Finally, direct comparisons between fluid (resistive Hall MHD) and kinetic simulations show that fluid theory is not applicable to study of ISs in a collisionless plasma.

Karimabadi, H.↗
NASA NTRS1986

Necessary conditions for maximax problems with application to aeroglide of hypervelocity vehicles

This paper presents the necessary conditions for solving Chebyshev minimax (or maximax) problems with bounded control. The jump conditions obtained are applicable to problems with single or multiple maxima. By using Contensou domain of maneuverability, it is shown that when the maxima are isolated single points the control is generally continuous at the jump point in the minimax problems and discontinuous in the maximax problems in which the first time derivative of the maximax function contains the control variable. The theory is applied to the problem of maximizing the flight radius in a closed circuit glide of a hypervelocity vehicle and to a maximax optimal control problem in which the control appears explicitly with the first time derivative of the maximax function.

Vinh, N. X.↗
NASA NTRS1984

Structure of the November 12, 1978, quasi-parallel interplanetary shock

The jump in plasma parameters exhibited by the intense interplanetary shock event of Nov. 12, 1978 is analyzed using ISEE 1, 2 and 3 data. Magnetic and electric field measurements indicated that the shock magnetic field profile was similar to the earth bow shock profile. Data on the electron and proton densities, temperatures, bulk velocities and alpha particles showed a steady electron temperature increase across the shock on a 12 earth radii scale. The upstream and downstream flow parameters are found to be within 10 percent of Rankin-Hugoniot jump conditions. The shock moved at 614 km/sec and had three dissipative scales, one a few Larmor radii determined by the magnetic field jump, a second 10 earth radii correlated with the electron equilibrium and the other 30 earth radii connected to the energetic proton foreshock.

Kennel, C. F.↗
NASA NTRS1972

Bounded state space

This investigation is divided functionally into three different areas: (1) study of bounded state space, (2) nonlinear smoothing theory, and (3) system identification. (1) Study of bounded state space: necessary and sufficient conditions for an optimal control are obtained for a bounded state space optimal control problem. The difficulty of determining the so-called jump conditions is eliminated; however, the problem of determining the points where the response either enters or leaves the boundary still remains unsolved. (2) Nonlinear smoothing theory: nonlinear fixed-interval, fixed-point and fixed-lag smoothing of a random signal generated by a stochastic differential equation are investigated. Results on the asymptotic stability of a linear constant-parameter fixed-interval smoothing filter are obtained. (3) System identification: a particular stochastic modelling problem is solved. An Ito stochastic integral equation is used to mathematically model a black box having multiple inputs and multiple outputs. A new method for identifying system parameters is presented.

Eyman, E. D.↗
NASA NTRS1991

Hypersonic merged layer blunt body flows with wakes

An attempt is made here to understand the basic physics of the flowfield with wake on a blunt body of revolution under hypersonic rarefied conditions. A merged layer model of flow is envisioned. Full steady-state Navier-Stokes equations in spherical polar coordinate system are computed from the surface with slip and temperature jump conditions to the free stream by the Accelerated Successive Replacement method of numerical integration. Analysis is developed for bodies of arbitrary shape, but actual computations have been carried out for a sphere and sphere-cone body. Particular attention is paid to set the limit of the onset of separation, wake closure, shear-layer impingement, formation and dissipation of the shocks in the flowfield. Validity of the results is established by comparing the present results for sphere with the corresponding results of the SOFIA code in the common region of their validity and with the experimental data.

Jain, Amolak C.↗
NASA NTRS1979

Axisymmetric internal flows with shocks

Internal flow problems with supersonic entrance conditions and subsonic exit conditions are studied. The suitability of applying the transonic-small disturbance theory to internal flows is examined and found to be very limited. The full inviscid equations in nonconservative form are solved by relaxation. Jump conditions which conserve mass and normal momentum are applied explicitly at shock waves. This method is suitable for solving flows which include supersonic-subsonic shock waves nearly normal to the streamlines.

Rizk, M. H.↗
NASA NTRS1990

Electromagnetic axisymmetric finite elements based on a gauged four-potential variational principle

Electromagnetic finite elements are derived based on a variational principle that uses the electromagnetic four-potential as a primary variable. The Lorentz gage normalization is incorporated as a constraint condition through a Lagrange multiplier field to construct elements suitable for downstream coupling with mechanical and thermal finite elements for the analysis of high-temperature superconductor devices with aerospace applications. The main advantages are: jump discontinuities on interfaces are naturally handled; no a priori approximations are invoked; and the number of degrees of freedom per node remains modest as the problem dimensionality increases. The new elements are tested on two magnetostatic axisymmetric problems. The results are in excellent agreement with analytical solutions and previous solutions for the 1D problem of a conducting infinite wire, in which case the multiplier field has no effect. For materials of widely different permeability, jump conditions are naturally accommodated by the present formulation.

Schuler, J.↗
NASA NTRS1987

Investigation of hypersonic rarefied flow on a spherical nose of the AOTV

The Navier-Stokes (NS) equations were integrated numerically for investigating the flow characteristics on the forepart of the spherical nose of a space vehicle such as the AOTV or AFE by a modified Accelerated Successive Replacement (ASR) scheme under hypersonic rarefied conditions. Technical feasibility of the mathematical approach was demonstrated by computing the flowfield on a spherical nose under conditions that the AFE encounters at times t = 15 and 20 seconds after its reentry into the atmosphere. Local similar solutions for the merged layer flow along the stagnation line of the sphere were developed. These are correct to the same degree of accuracy as the NS equations. These solutions provided stagnation line boundary conditions for the domain of integration on the spherical noise. Also, a parametric study of the stagnation line solution was made with a view to understand the flow characteristics in tunnels with different ambient fluids. Analytical expressions for surface slip temperature, jump conditions, and concentration level in the presence of the real gas effects at the top of the Knudsen layer were derived and used to calculate the stagnation line flowfield with nonequilibrium dissociation and ionization. A number of graphics were drawn to illustrate the basic physics of the flowfields. The present analysis can be extended to include real gas effects and to bodies of arbitrary shapes. It can further provide boundary conditions for integrating the NS equations in the near wake region.

Jain, Amolak C.↗
NASA NTRS1987

A linearized Euler analysis of unsteady flows in turbomachinery

A method for calculating unsteady flows in cascades is presented. The model, which is based on the linearized unsteady Euler equations, accounts for blade loading shock motion, wake motion, and blade geometry. The mean flow through the cascade is determined by solving the full nonlinear Euler equations. Assuming the unsteadiness in the flow is small, then the Euler equations are linearized about the mean flow to obtain a set of linear variable coefficient equations which describe the small amplitude, harmonic motion of the flow. These equations are discretized on a computational grid via a finite volume operator and solved directly subject to an appropriate set of linearized boundary conditions. The steady flow, which is calculated prior to the unsteady flow, is found via a Newton iteration procedure. An important feature of the analysis is the use of shock fitting to model steady and unsteady shocks. Use of the Euler equations with the unsteady Rankine-Hugoniot shock jump conditions correctly models the generation of steady and unsteady entropy and vorticity at shocks. In particular, the low frequency shock displacement is correctly predicted. Results of this method are presented for a variety of test cases. Predicted unsteady transonic flows in channels are compared to full nonlinear Euler solutions obtained using time-accurate, time-marching methods. The agreement between the two methods is excellent for small to moderate levels of flow unsteadiness. The method is also used to predict unsteady flows in cascades due to blade motion (flutter problem) and incoming disturbances (gust response problem).

Hall, Kenneth C.↗
NASA NTRS1989

Calculation of unsteady flows in turbomachinery using the linearized Euler equations

A method for calculating unsteady flows in cascades is presented. The model, which is based on the linearized unsteady Euler equations, accounts for blade loading shock motion, wake motion, and blade geometry. The mean flow through the cascade is determined by solving the full nonlinear Euler equations. Assuming the unsteadiness in the flow is small, then the Euler equations are linearized about the mean flow to obtain a set of linear variable coefficient equations which describe the small amplitude, harmonic motion of the flow. These equations are discretized on a computational grid via a finite volume operator and solved directly subject to an appropriate set of linearized boundary conditions. The steady flow, which is calculated prior to the unsteady flow, is found via a Newton iteration procedure. An important feature of the analysis is the use of shock fitting to model steady and unsteady shocks. Use of the Euler equations with the unsteady Rankine-Hugoniot shock jump conditions correctly models the generation of steady and unsteady entropy and vorticity at shocks. In particular, the low frequency shock displacement is correctly predicted. Results of this method are presented for a variety of test cases. Predicted unsteady transonic flows in channels are compared to full nonlinear Euler solutions obtained using time-accurate, time-marching methods. The agreement between the two methods is excellent for small to moderate levels of flow unsteadiness. The method is also used to predict unsteady flows in cascades due to blade motion (flutter problem) and incoming disturbances (gust response problem).

Hall, Kenneth C.↗
NASA NTRS1996

A Multigrid Algorithm for Immersed Interface Problems

Many physical problems involve interior interfaces across which the coefficients in the problem, the solution, its derivatives, the flux, or the source term may have jumps. These interior interfaces may or may not align with a underlying Cartesian grid. Zhilin Li, in his dissertation, showed how to discretize such elliptic problems using only a Cartesian grid and the known jump conditions to second order accuracy. In this paper, we describe how to apply the full multigrid algorithm in this context. In particular, the restriction, interpolation, and coarse grid problem will be described. Numerical results for several model problems are given to demonstrate that good rates can be obtained even when jumps in the coefficients are large and do not align with the grid.

Adams, Loyce↗
NASA NTRS1993

Termination shock - Solar cycle variations of location and speed

Plasma and magnetic field data from Voyagers 1 and 2 over an 11-year period (1978-1988) together with a one-fluid MHD model are used to study the motion of the termination shock. The observed large fluctuations in solar wind parameters cause variations in the speed, in the jump conditions, and in the location of the termination shock. If the interstellar stagnation pressure is equivalent to a magnetic field of 0.5 nT plus draping enhancements, the termination shock moves between 88 AU and 102 AU. The location of the termination shock is anticorrelated with the sunspot number. The termination shock is very strong with pressure ratios of a few thousands, the fast Mach number is about 12, and the plasma beta ratio jumps from about 0.1 to about 14. During the declining phase of the solar cycle, the shock speed is often greater than or comparable to the spacecraft speed. If the crossing of the termination shock by a spacecraft occurs during the declining phase, the spacecraft will cross the termination shock 3 or more times over a period of about 4 years.

Whang, Y. C.↗
NASA NTRS2018

Modeling and Flight Performance of Supersonic Disk-Gap-Band Parachutes in Slender Body Wakes

NASA's ASPIRE (Advanced Supersonic Parachute Inflation Research and Experiments) project is investigating the supersonic deployment and inflation of full-scale parachutes. To achieve Mars-relevant conditions, the parachutes are deployed at high altitudes over Earth on a sounding rocket platform. During the flight test, Disk-Gap-Band parachutes of 21.5 meter diameter are deployed behind a slender payload 1/6th the diameter of the blunt Mars2020 capsule. Due to the differences in leading body geometry between the test flight and a parachute deployment at Mars, high fidelity numerical simulations of slender and blunt bodywakes, and of rigid parachutes behind them, were used to understand differences and similarities in the flow and the effect on parachute drag. The slender body wake is thinner, closes earlier, and presents a smaller wake deficit. Thus, a parachute deployed in the wake of a slender body is more likely to see a higher dynamic pressure than a parachute deployed behind a blunt body. In the presence of a parachute, the interaction of the unsteady wake with the parachute bow shock is stronger behind the blunt body. Simulations yield highly unsteady forces on the parachute, which was modeled as a rigid body. The mean parachute force behind a slender body is between 3 and 12 percent higher than behind a blunt body, depending on the angle of the parachute with the flow. As the angle of incidence increases, more of the parachute moves out of the leading body wakes, decreasing the sensitivity to leading body shape. To compare the flow past parachutes in Earth's and Mars' atmospheres, simulations were also performed in CO2. At the Mach number considered (1.75), the shock standoff distance ahead of the parachute, post-shock jump conditions, and the resulting parachute forces were found to be very similar in both air and CO2, indicating that a high altitude test is a good proxy for a Mars descent. The results of these numerical simulations and available data on past flight and wind tunnel tests of supersonic Disk-Gap-Band parachutes behind slender bodies were used to generate a parachute drag model for ASPIRE, which in turn was used to help design the flight test. The first flight test occurred in October 2017. The parachute was successfully deployed at Mach 1.77 and an altitude of 42 kilometers. Test instrumentation provided the atmospheric conditions, test vehicle trajectory, and the loads on the parachute along with detailed high-resolution imagery of the inflation process. Reconstruction of the flight test indicated that the measured forces on the parachute were within the model's bounds, although the model over-predicted the parachute force during the first few seconds. The parachute forces during the long subsonic period were well-predicted by the ASPIRE drag model.

Muppidi, Suman↗