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NASA NTRS1992

Miniature high temperature plug-type heat flux gauges

The objective is to describe continuing efforts to develop methods for measuring surface heat flux, gauge active surface temperature, and heat transfer coefficient quantities. The methodology involves inventing a procedure for fabricating improved plug-type heat flux gauges and also for formulating inverse heat conduction models and calculation procedures. These models and procedures are required for making indirect measurements of these quantities from direct temperature measurements at gauge interior locations. Measurements of these quantities were made in a turbine blade thermal cycling tester (TBT) located at MSFC. The TBT partially simulates the turbopump turbine environment in the Space Shuttle Main Engine. After the TBT test, experiments were performed in an arc lamp to analyze gauge quality.

Liebert, Curt H.↗

NASA NTRS1992

A boundary integral method for an inverse problem in thermal imaging

An inverse problem in thermal imaging involving the recovery of a void in a material from its surface temperature response to external heating is examined. Uniqueness and continuous dependence results for the inverse problem are demonstrated, and a numerical method for its solution is developed. This method is based on an optimization approach, coupled with a boundary integral equation formulation of the forward heat conduction problem. Some convergence results for the method are proved, and several examples are presented using computationally generated data.

Bryan, Kurt↗

NASA NTRS1991

Two-dimensional hydrodynamic calculations of the nonlinear development of the Goldreich-Schubert-Fricke instability in a rotating annulus

Two-dimensional nonlinear hydrodynamic calculations are presented which may help assess the effectiveness of the instability in transporting angular momentum in the equatorial zones of stars and planets which are stably stratified with respect to convection. The calculations were made by numerically integrating the 2D axisymmetric Navier-Stokes equations, including viscosity and heat conduction. The instability was followed into the nonlinear regime. The maximum rms velocity amplitude was found to correlate well with the product of the linear growth rate and radial length scale of the instability, consistent with the idea that the instability grows to an amplitude such that an eddy turnover time becomes equal to the growth time defined by the inverse of the growth rate. The time scale for angular momentum to be redistributed to a state of marginal stability was consistent with this picture. The results suggest that in physical situations a state of marginal stability will be maintained, since departures from such a state will be rapidly corrected.

Korycansky, D. G.↗

NASA NTRS1991

Theoretical and computational dynamics of a compressible flow

An introduction to the theoretical and computational fluid dynamics of a compressible fluid is presented. The general topics addressed include: thermodynamics and physical properties of compressible fluids; 1D flow of an inviscid compressible fluid; shock waves; fundamental equations of the dynamics of a compressible inviscid non-heat-conducting and radiating fluid, method of small perturbations, linearized theory; 2D subsonic steady potential flow; hodograph and rheograph methods, exact solutions of 2D insentropic steady flow equations, 2D steady transonic and hypersonic flows, method of characteristics, linearized theory of 3D potential flow, nonlinear theory of 3D compressibe flow, anisentropic (rotational) flow of inviscid compressible fluid, electromagnetogasdynamics, multiphase flows, flows of a compressible fluid with transport phenomena.

Pai, Shih-I↗

NASA NTRS1992

Analysis of surface roughness generation in aircraft ice accretion

Patterns of roughness evolution have been studied analysis of high magnification video observations of accreting ice surfaces provided by the NASA Lewis Research Center. Three distinct patterns of surface roughness generation have been identified within the parametric regions studied. They include: Rime, Multi-Zone Glaze, and Uniform Glaze. Under most icing conditions, a brief period of transient rime ice growth was observed caused by heat conduction into the body. The resulting thin rime layer explains previously observed insensitivity of some ice accretions to substrate insensitivity of some ice accretions to substrate surface chemistry and may provide justification for simplifying assumptions in ice accretion sailing and modeling effects.

Hansman, R. J., Jr.↗

NASA NTRS1992

Mechanical energy flow models of rods and beams

It has been proposed that the flow of mechanical energy through a structural/acoustic system may be modeled in a manner similar to that of flow of thermal energy/in a heat conduction problem. If this hypothesis is true, it would result in relatively efficient numerical models of structure-borne energy in large built-up structures. Fewer parameters are required to approximate the energy solution than are required to model the characteristic wave behavior of structural vibration by using traditional displacement formulations. The energy flow hypothesis is tested in this investigation for both longitudinal vibration in rods and transverse flexural vibrations of beams. The rod is shown to behave approximately according to the thermal energy flow analogy. However, the beam solutions behave significantly differently than predicted by the thermal analogy unless locally-space-averaged energy and power are considered. Several techniques for coupling dissimilar rods and beams are also discussed. Illustrations of the solution accuracy of the methods are included.

Wohlever, J. C.↗

NASA NTRS1992

An efficient finite element method for aircraft de-icing problems

In this paper, a finite element formulation based on an assumed states method is proposed for the solution of heat conduction problems with phase change at a fixed temperature. Attention is directed toward reduction of computer cost through the use of an efficient formulation, solver and algorithm. The procedure is applied to the analysis of an electrothermally deiced aircraft surface.

Huang, J. R.↗

NASA NTRS1992

Optimal moving grids for time-dependent partial differential equations

Various adaptive moving grid techniques for the numerical solution of time-dependent partial differential equations were proposed. The precise criterion for grid motion varies, but most techniques will attempt to give grids on which the solution of the partial differential equation can be well represented. Moving grids are investigated on which the solutions of the linear heat conduction and viscous Burgers' equation in one space dimension are optimally approximated. Precisely, the results of numerical calculations of optimal moving grids for piecewise linear finite element approximation of PDE solutions in the least-squares norm are reported.

Wathen, A. J.↗

NASA NTRS1992

Properties of thermospheric gravity waves on earth, Venus and Mars

A spectral model with spherical harmonics and Fourier components that can simulate atmospheric perturbations in the global geometry of a multiconstituent atmosphere is presented. The boundaries are the planetary surface where the transport velocities vanish and the exobase where molecular heat conduction and viscosity dominate. The time consuming integration of the conservation equations is reduced to computing the transfer function (TF) which describes the dynamic properties of the medium divorced from the complexities in the temporal and horizontal variations of the excitation source. Given the TF, the atmospheric response to a chosen source distribution is then obtained in short order. Theoretical studies are presented to illuminate some properties of gravity waves on earth, Venus and Mars.

Mayr, H. G.↗

NASA NTRS1992

A PC-based collapse factor analysis for high pressure cryogenic systems

A collapse factor simulation computer program, suitable for use on personal computers, for supercritical cryogen system pressurization is examined. The available literature is previewed, individual component models are developed, and the overall simulation program logic is examined. Extensive use is made of existing thermodynamic and transport property evaluation packages. Heat transfer is estimated using natural convection correlations, and transient wall heat conduction is considered. Examples of the simulation are demonstrated for two facilities. Partial validation is achieved by comparing the simulation output with data from an existing test facility. Preliminary results indicate that the collapse factors will seldom exceed 1.15 during supercritical operation of high-pressure cryogenic systems. Recommendations for improvements in the component models and the simulation are made.

Hodge, B. K.↗

NASA NTRS1992

A variational method for finite element stress recovery: Applications in one-dimension

It is well-known that stresses (and strains) calculated by a displacement-based finite element analysis are generally not as accurate as the displacements. In addition, the calculated stress field is typically discontinuous at element interfaces. Because the stresses are typically of more interest than the displacements, several procedures have been proposed to obtain a smooth stress field, given the finite element stresses, and to improve the accuracy. Hinton and Irons introduced global least squares smoothing of discrete data defined on a plane using a finite element formulation. Tessler and co-workers recently developed a conceptually similar formulation for smoothing of two-dimensional data based on a discrete least square approximation with a penalty constraint. The penalty constraint results in a stress field which is C(exp 1)-continuous, a result not previously obtained. The approach requires additional, 'smoothing' finite element analysis and for their two-dimensional application, they used a conforming C(exp 0)-continuous triangular finite element based on a conforming plate element. This paper presents the results of a detailed investigation into the application of Tessler's smoothing procedure to the smoothing of finite element stresses from one-dimensional problems. Although the one-dimensional formulation has some practical applicability, such as in truss, beam, axisymmetric mechanics, and one-dimensional heat conduction, the primary motivation for developing the one-dimensional smoothing case is to explore the characteristics of the general smoothing strategy. In particular, it is used to describe the behavior of the method and to explore the suitability of criteria proposed for the smoothing analysis. Prior to presenting numerical results, the variational formulation of the smoothing strategy is presented and a criterion for the smoothing analysis is described.

Riggs, H. Ronald↗

NASA NTRS1992

Forced precession of the cometary nucleus with randomly placed active regions

The cometary nucleus is assumed to be triaxial or axisymmetric spheroid rotating about its axis of maximum moment of inertia and is forced to precess due to jets of ejected material. Randomly placed regions of exposed ice on the surface of the nucleus are assumed to produce gas and dust. The solution of the heat conduction equation for each active region is used to find the gas sublimation rate and the jet acceleration. Precession of the comet nucleus is followed numerically using a phase-averaged system of equations. The gas production curves and the variation of the spin axis during the orbital motion of the comet are presented.

Szutowicz, Slawomira↗

NASA NTRS1993

Flow instability in particle-bed nuclear reactors

The particle-bed core offers mitigation of some of the problems of solid-core nuclear rocket reactors. Dividing the fuel elements into small spherical particles contained in a cylindrical bed through which the propellant flows radially, may reduce the thermal stress in the fuel elements, allowing higher propellant temperatures to be reached. The high temperature regions of the reactor are confined to the interior of cylindrical fuel assemblies, so most of the reactor can be relatively cool. This enables the use of structural and moderating materials which reduce the minimum critical size and mass of the reactor. One of the unresolved questions about this concept is whether the flow through the particle-bed will be well behaved, or will be subject to destructive flow instabilities. Most of the recent analyses of the stability of the particle-bed reactor have been extensions of the approach of Bussard and Delauer, where the bed is essentially treated as an array of parallel passages, so that the mass flow is continuous from inlet to outlet through any one passage. A more general three dimensional model of the bed is adopted, in which the fluid has mobility in three dimensions. Comparison of results of the earlier approach to the present one shows that the former does not accurately represent the stability at low Re. The more complete model presented should be capable of meeting this deficiency while accurately representing the effects of the cold and hot frits, and of heat conduction and radiation in the particle-bed. It can be extended to apply to the cylindrical geometry of particle-bed reactors without difficulty. From the exemplary calculations which were carried out, it can be concluded that a particle-bed without a cold frit would be subject to instability if operated at the high temperatures desired for nuclear rockets, and at power densities below about 4 megawatts per liter. Since the desired power density is about 40 megawatts per liter, it can be concluded that operation at design exit temperature but at reduced power could be hazardous for such a reactor. But the calculations also show that an appropriate cold frit could very likely cure the instability. More definite conclusions must await calculations for specific designs.

Kerrebrock, Jack L.↗

NASA NTRS1993

Composite micromechanical modeling using the boundary element method

The use of the boundary element method for analyzing composite micromechanical behavior is demonstrated. Stress-strain, heat conduction, and thermal expansion analyses are conducted using the boundary element computer code BEST-CMS, and the results obtained are compared to experimental observations, analytical calculations, and finite element analyses. For each of the analysis types, the boundary element results agree reasonably well with the results from the other methodologies, with explainable discrepancies. Overall, the boundary element method shows promise in providing an alternative method to analyze composite micromechanical behavior.

Goldberg, Robert K.↗

NASA NTRS1992

Modeling the Martian seasonal CO2 cycle. I - Fitting the Viking Lander pressure curves. II - Interannual variability

The present diurnal and seasonal thermal model for Mars, in which surface CO2 frost condensation and sublimation are determined by the net effects of radiation, latent heat, and heat conduction in subsurface soil layers, in order to simulate seasonal exchanges of CO2 between the polar caps and atmosphere, successfully reproduces the measured pressured variations at the Viking Lander 1 site. In the second part of this work, the year-to-year differences between measured surface pressures at Viking sites as a function of season are used as upper limits on the potential magnitudes of interannual variations in the Martian atmosphere's mass. Simulations indicate that the dust layers deposited onto the condensing north seasonal polar cap during dust storms can darken seasonal frost deposits upon their springtime uncovering, while having little effect on seasonal pressure variations.

Wood, Stephen E.↗

NASA NTRS1992

A mapping closure for turbulent scalar mixing using a time-evolving reference field

A general mapping-closure approach for modeling scalar mixing in homogeneous turbulence is developed. This approach is different from the previous methods in that the reference field also evolves according to the same equations as the physical scalar field. The use of a time-evolving Gaussian reference field results in a model that is similar to the mapping closure model of Pope (1991), which is based on the methodology of Chen et al. (1989). Both models yield identical relationships between the scalar variance and higher-order moments, which are in good agreement with heat conduction simulation data and can be consistent with any type of epsilon(phi) evolution. The present methodology can be extended to any reference field whose behavior is known. The possibility of a beta-pdf reference field is explored. The shortcomings of the mapping closure methods are discussed, and the limit at which the mapping becomes invalid is identified.

Girimaji, Sharath S.↗

NASA NTRS1993

Computational solution of the defect stream-function equation for nonequilibrium turbulent boundary layers

The derivation of the accurate, second-order, almost linear, approximate equation governing the defect stream function for nonequilibrium compressible turbulent boundary layers is reviewed. The similarity of this equation to the heat conduction equation is exploited in the development of an unconditionally stable, tridiagonal computational method which is second-order accurate in the marching direction and fourth-order accurate in the surface-normal direction. Results compare well with experimental data. Nonlinear effects are shown to be small. This two-dimensional method is simple and has been implemented on a programmable calculator.

Barnwell, Richard W.↗

NASA NTRS1992

A one-dimensional modeling study of carbonaceous haze effects on the springtime Arctic environment

The effect of carbonaceous Arctic haze on the surface energy balance was investigated using a specially developed one-dimensional three-component numerical model which accounts for the transfer of IR and solar radiation through the atmosphere, turbulent mixing within the boundary layer, and heat conduction through snow-capped sea ice. The results of calculations indicate that, when haze is present, the surface temperature increases, provided the relative humidity through the column does not change. The increase is due to an increase in the absorbed radiation at the surface.

Emery, Christopher A.↗