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NASA NTRS1976

Repeated-cascade theory of strong turbulence in a magnetized plasma

A two-dimensional Navier-Stokes equation of vorticity in fluid turbulence is used to model drift turbulence in a plasma with a strong constant magnetic field and a constant mean density gradient. The nonlinear eddy diffusivity is described by a time-integrated Lagrangian correlation of velocities, and the repeated-cascade method is employed to choose the rank accounting for nearest-neighbor interactions, to calculate the Lagrangian correlation, and to close the correlation hierarchy. As a result, the diffusivity becomes dependent on the plasma's induced diffusion and is represented by a memory chain that is cut off by similarity and inertial randomization. Spectral laws relating the kinetic-energy spectrum to the -5, -5/2, -3, and -11 powers of wavenumber are derived for the velocity subranges of production, approach to inertia, inertia, and dissipation, respectively. It is found that the diffusivity is proportional to some inverse power of the magnetic field, that power being 1, 2/3, 5/6, and 2, respectively, for the four velocity subranges.

Tchen, C. M.↗

NASA NTRS1976

Flux-corrected transport techniques for transient calculations of strongly shocked flows

New flux-corrected transport algorithms are described for solving generalized continuity equations. These techniques were developed by requiring that the finite difference formulas used ensure positivity for an initially positive convected quantity. Thus FCT is particularly valuable for fluid-like problems with strong gradients or shocks. Repeated application of the same subroutine to mass, momentum, and energy conservation equations gives a simple solution of the coupled time-dependent equations of ideal compressible fluid dynamics without introducing an artificial viscosity. FCT algorithms span Eulerian, sliding-rezone, and Lagrangian finite difference grids in several coordinate systems. The latest FCT techniques are fully vectorized for parallel/pipeline processing.

Boris, J. P.↗

NASA NTRS1978

Seismic structure of the lunar mantle - An overview

The direct P and S wave arrival times from natural lunar seismic events are the most complete and reliable data set for determining the structure of the lunar mantle. A total of 40 events provide sufficiently well-observed arrivals to permit the extraction of structural information. Using this arrival time data set, the average velocities in a two-layered mantle with an assumed crustal structure (from Toksoz et al., 1974) have been obtained. Reflected phases arriving after direct S are then used to calculate the depth of the boundary between the two mantle layers, and to demonstrate that it is probably a complex transition zone approximately 80 km thick between 400 and 480 km depth. To determine velocity gradients in the upper mantle it is required that the model explain the pronounced decrease in shear wave amplitudes and accompanying delay in shear wave arrival times beyond a distance of about 90 deg. The final model is well-constrained.

Goins, N. R.↗

NASA NTRS1980

Calculation of skin-friction coefficients for low Reynolds number turbulent boundary layer flows

An analysis is presented of the reliability of various generally accepted empirical expressions for the prediction of the skin-friction coefficient C/sub f/ of turbulent boundary layers at low Reynolds numbers in zero-pressure-gradient flows on a smooth flat plate. The skin-friction coefficients predicted from these expressions were compared to the skin-friction coefficients of experimental profiles that were determined from a graphical method formulated from the law of the wall. These expressions are found to predict values that are consistently different than those obtained from the graphical method over the range 600 Re/sub theta 2000. A curve-fitted empirical relationship was developed from the present data and yields a better estimated value of C/sub f/ in this range. The data, covering the range 200 Re/sub theta 7000, provide insight into the nature of transitional flows. They show that fully developed turbulent boundary layers occur at Reynolds numbers Re/sub theta/ down to 425. Below this level there appears to be a well-ordered evolutionary process from the laminar to the turbulent profiles. These profiles clearly display the development of the turbulent core region and the shrinking of the laminar sublayer with increasing values of Re/sub theta/.

Barr, P. K.↗

NASA NTRS1987

Navier-Stokes analysis of two- and three-dimensional flow field in solid rocket motors with segment joints

A multidimensional implicit Navier-Stokes analysis which uses numerical solution of ensemble-averaged Navier-Stokes equations in a nonorthogonal bodyfitted cylindrical-polar coordinate system has been applied to simulation of the internal flow field in solid-propellant rocket motor chambers with segment joints. The calculation procedure incorporates a two-equation (k-epsilon) turbulence model and utilizes a consistently split, linearized block-implicit algorithm for numerical solution of the governing equations. Computations performed to simulate the axisymmetric flow field in the vicinity of the aft field joint in the Space Shuttle SRB using 14,725 grid points show the presence of a region of reversed axial flow near the downstream edge of the slot. Calculations were also performed for two cases involving asymmetric three-dimensional flow in the vicinity of the aft field joint in the SRB using 721,525 grid points to estimate circumferential velocities and pressure gradients at the joint.

Sabnis, J. S.↗

NASA NTRS1984

Thermal convection during Bridgman crystal growth

Numerical experiments are used to study thermally driven flows which occur during vertical Bridgman crystal growth of a single component fluid. The solid-liquid interface was specified as parabolic and flow patterns were calculated for various insulation thicknesses, Grashof, Prandtl, and Biot numbers. When the melt is on top and the gravity vector is axially downward it is shown that flow persists as long as a radial temperature gradient is present. If the interface is convex, as viewed from the liquid, a single cell is observed. A concave interface exhibits multiple counterrotating cells. The insulation thickness and Grashof, Prandtl, and Biot numbers influence the flow in a quantitative manner.

Carlson, Frederick M.↗

NASA NTRS1988

Relaxation of impact basins on icy satellites

The problem of relaxation of very large impact craters on icy satellites is addressed and the extent to which such studies can help place constraints on the nature of such satellite interiors is investigated. Very general calculations aimed at understanding the nature of relaxation of large impact structures, including the directions, relaxation velocities, and stress levels, are presented. The dependence of relaxation on such factors as silicate core size and viscosity gradients in the ice is examined. The general results are used to address whether comparing the current morphology of impact basins to estimates of their original shape will yield an understanding of the thermal and mechanical structure of the interiors of the icy satellites. It is found that the relaxation rates derived from models of satellite interiors can provide constraints on viscous layer thicknesses. High thermal gradients can permit substantial relaxation even in thin viscous layers. Finally, the constraints on the internal structure of Tethys arising from the extremely relaxed state of the Odysseus basin and the existence of Ithaca Chasma are discussed.

Thomas, Paul J.↗

NASA NTRS1991

Effect of suction on controlling the secondary instability of boundary layers

The effect of suction on controlling the three-dimensional secondary instability is investigated for a boundary layer with a pressure gradient in the presence of a small but finite-amplitude Tollmien-Schlichting wave. The focus is on the principal parametric resonance responsible for the strong growth of subharmonics in a low disturbance environment. Calculations are presented for the effect of suction on the onset and amplification of the secondary instability in Blasius and Falkner-Skan flows, as well as its effect on controlling the production of the vortical structure.

El-Hady, Nabil M.↗

NASA NTRS1992

Numerical simulation of aerothermal loads in hypersonic engine inlets due to shock impingement

The effect of shock impingement on an axial corner simulating the inlet of a hypersonic vehicle engine is modeled using a finite-difference procedure. A three-dimensional dynamic grid adaptation procedure is utilized to move the grids to regions with strong flow gradients. The adaptation procedure uses a grid relocation stencil that is valid at both the interior and boundary points of the finite-difference grid. A linear combination of spatial derivatives of specific flow variables, calculated with finite-element interpolation functions, are used as adaptation measures. This computational procedure is used to study laminar and turbulent Mach 6 flows in the axial corner. The description of flow physics and qualitative measures of heat transfer distributions on cowl and strut surfaces obtained from the analysis are compared with experimental observations. Conclusions are drawn regarding the capability of the numerical scheme for enhanced modeling of high-speed compressible flows.

Ramakrishnan, R.↗

NASA NTRS1995

Stellar models with microscopic diffusion and rotational mixing. 1: Application to the Sun

The Yale stellar evolution code has been modified to include the combined effects of diffusion and rotational mixing on H-1, H-4, and the trace elements He, Li-6, Li-7, and Be-9. The interaction between rotational mixing and diffusion is studied by calculating a number of calibrated solar models. The rotational mixing inhibits the diffusion in the outer parts of the models, leading to a decrease in the envelope diffusion by 25%-50%. Conversely, diffusion leads to gradients in mean molecular weight which can inhibit the rotational mixing. The degree to which gradients in mean molecular weight inhibit the rotational mixing is somewhat uncertain. A comparison with the observed solar oblateness suggests that gradients in the mean molecular weight play a smaller role in inhibiting the rotational mixing than previously believed. This is reinforced by the fact that the model with the standard value for the inhibiting effect of mean molecular weight on the rotational mixing depletes no Li on the main sequence. This is clear in contrast to the observations. A reduction in the inhibiting effect of mean molecular weight gradients by a factor of 10 loads to noticeable main-sequence Li depletion.

Chaboyer, Brian↗

NASA NTRS1996

Nonstationary Gravity Wave Forcing of the Stratospheric Zonal Mean Wind

The role of gravity wave forcing in the zonal mean circulation of the stratosphere is discussed. Starting from some very simple assumptions about the momentum flux spectrum of nonstationary (non-zero phase speed) waves at forcing levels in the troposphere, a linear model is used to calculate wave propagation through climatological zonal mean winds at solstice seasons. As the wave amplitudes exceed their stable limits, a saturation criterion is imposed to account for nonlinear wave breakdown effects, and the resulting vertical gradient in the wave momentum flux is then used to estimate the mean flow forcing per unit mass. Evidence from global, assimilated data sets are used to constrain these forcing estimates. The results suggest the gravity-wave-driven force is accelerative (has the same sign as the mean wind) throughout most of the stratosphere above 20 km. The sense of the gravity wave forcing in the stratosphere is thus opposite to that in the mesosphere, where gravity wave drag is widely believed to play a principal role in decelerating the mesospheric jets. The forcing estimates are further compared to existing gravity wave parameterizations for the same climatological zonal mean conditions. Substantial disagreement is evident in the stratosphere, and we discuss the reasons for the disagreement. The results suggest limits on typical gravity wave amplitudes near source levels in the troposphere at solstice seasons. The gravity wave forcing in the stratosphere appears to have a substantial effect on lower stratospheric temperatures during southern hemisphere summer and thus may be relevant to climate.

Alexander, M. J.↗

NASA NTRS2003

Improvement in diastolic intraventricular pressure gradients in patients with HOCM after ethanol septal reduction

We sought to validate measurement of intraventricular pressure gradients (IVPG) and analyze their change in patients with hypertrophic obstructive cardiomyopathy (HOCM) after ethanol septal reduction (ESR). Quantitative analysis of color M-mode Doppler (CMM) images may be used to estimate diastolic IVPG noninvasively. Noninvasive IVPG measurement was validated in 10 patients undergoing surgical myectomy. Echocardiograms were then analyzed in 19 patients at baseline and after ESR. Pulsed Doppler data through the mitral valve and pulmonary venous flow were obtained. CMM was used to obtain the flow propagation velocity (Vp) and to calculate IVPG off-line. Left atrial pressure was estimated with the use of previously validated Doppler equations. Data were compared before and after ESR. CMM-derived IVPG correlated well with invasive measurements obtained before and after surgical myectomy [r = 0.8, P < 0.01, Delta(CMM - invasive IVPG) = 0.09 +/- 0.45 mmHg]. ESR resulted in a decrease of resting LVOT systolic gradient from 62 +/- 10 to 29 +/- 5 mmHg (P < 0.001). There was a significant increase in the Vp and IVPG (from 48 +/- 5to 74 +/- 7 cm/s and from 1.5 +/- 0.2 to 2.6 +/- 0.3 mmHg, respectively, P < 0.001 for both). Estimated left atrial pressure decreased from 16.2 +/- 1.1 to 11.5 +/- 0.9 mmHg (P < 0.001). The increase in IVPG correlated with the reduction in the LVOT gradient (r = 0.6, P < 0.01). Reduction of LVOT obstruction after ESR is associated with an improvement in diastolic suction force. Noninvasive measurements of IVPG may be used as an indicator of diastolic function improvement in HOCM.

NASA Program Biomedical Research and Countermeasur↗

NASA NTRS2018

Predicting Global Ground Geoelectric Field With Coupled Geospace and Three-Dimensional Geomagnetic Induction Models

We forecast the global effects of space weather on the geoelectric and geomagnetic fields using a novel combination of methods. We use a realistic three-dimensional (3-D) model of Earth's electrical conductivity and a realistic representation of magnetospheric and ionospheric current systems. Our scheme involves the following steps: (1) We run a global magnetohydrodynamic model of the magnetosphere coupled to an electrostatic model of the ionosphere. (2) We calculate a global time series of the ground magnetic field resulting from the ionospheric, field-aligned, and magnetospheric currents of the global magnetohydrodynamic model. (3) We approximate this external field by an equivalent source current flowing in a thin shell above Earth. (4) We calculate a global time series of geoelectric and geomagnetic fields from the equivalent current and a 3-D conductivity model of Earth that also takes into account the coast effect due to large horizontal conductivity gradient. We verify our implementation by comparing the results against known analytic and numeric solutions, and then apply our scheme to the geomagnetic storm of 14 and 15 December 2006. In particular, we show that accounting for 3-D structure of Earth's conductivity results in significantly enhanced geoelectric field at large lateral gradients of conductivity, especially in coastal regions, both at middle and high latitudes. In the studied geomagnetic storm the largest values of 3-D geoelectric field are detected at high latitudes reaching 2.5 volts per kilometer and the 3-D effect extends inland by a few hundred kilometers.

Honkonen, I.↗

NASA NTRS2021

Aircraft Flaps Modeling in OpenMDAO

The goal of this project was to develop a model for a single subsystem in the aerodynamics discipline, in this case the flaps of an aircraft. Flaps are high-lift devices used by planes to allow for quicker takeoffs, and slower landings. A computer-based aircraft model of the flaps of an aircraft was developed using the Python based open-source framework OpenMDAO. OpenMDAO is used to develop multi-disciplinary aircraft models using gradient-based optimization; design optimization (MDO) is concerned with solving design problems involving numerical models of complex engineering systems. There were 4 components in the model; each has input values, output variables, and equations to calculate said outputs. The variables and equations are sourced from NASA Fortran code from the 1970s, in a project called the General Aviation Synthesis Program (GASP). These variables and equations which create the model are being converted to Python for ease of use. The flaps model developed will be integrated into a larger model of a conventional aircraft’s flight phases. All subsystems of the model will first be built using the parameters of a Boeing 737 MAX-8, to validate its functionality and accuracy. Then, the aircraft model will be used for hybrid-electric research; running optimizations to improve efficiency, minimize fuel burn, and advance hybrid-electric technology in the aerospace field.

Computer-based aircraft modeling↗

NASA NTRSDate not supplied

Using Thermal Desktop to Determine Equivalent Solar Hours on Spacecraft Surfaces

Equivalent solar hours (ESH) are the duration of exposure of a surface to solar radiation, particularly ultraviolet (UV) radiation. Since UV light causes degradation to optical properties of thermal control surfaces, the determination of ESH is important to calculate end of life (EOL) optical properties for spacecraft external surfaces. A higher ESH value generally correlates to greater UV degradation experienced by the surface, resulting in an increase in solar absorptivity. This paper details a novel approach for calculating ESH using Thermal Desktop. Since the ESH value is useful for thermal analysts, this technique is beneficial to quickly perform the analysis internally with tools readily available without relying on external support and funding. The example presented in this paper shows how this method was developed and used for NASA's lunar Gateway spacecraft. This method of analysis is used to calculate ESH for the transit, assembly in orbit, and operational phases for Gateway, utilizing each of the program’s planned configurations throughout its 15-year lifetime. ESH values were calculated using the Monte-Carlo ray tracing capability of Thermal Desktop using both direct solar heating and indirect solar heating due to reflections from other surfaces. The output of this analysis includes an ESH gradient map across the spacecraft. Post-processing of these results enabled identification of the average and maximum ESH on critical surfaces such as radiators. The final ESH values for each surface are then used for determination of EOL optical properties.

Thermal Control↗

NASA NTRS1984

Convergent-tapered annular seals - Analysis and testing for rotordynamic coefficients

A combined analytical-computational method has been developed to calculate the pressure field and dynamic coefficients for tapered high-pressure annular seals. Completely developed turbulent flow is assumed in both the circumferential and axial directions, according to Hirs' (1973) bulk-flow turbulent-lubrication equations. In a numerical experiment with the method, a short bearing approximation is used to derive an analytical expression for the first-order (dynamic) pressure gradient. This expression is integrated numerically to define dynamic coefficients of the seal. Numerical results of the integration are compared with previous results for straight and tapered seals. It is found that direct stiffness and leakage coefficients increase in the present seal, while the remaining coefficients decrease. An optimal taper angle is shown to exist with respect to: (1) the direct stiffness and (2) the ratio of direct stiffness to leakage. On the basis of the optimal taper angle calculations, stiffness increases on the order of 40 to 50 percent are predicted. Experimental results for three taper angles are presented, and are found to be in good agreement with the theoretical predictions.

Childs, D. W.↗

NASA NTRS1990

Materials with periodic internal structure: Computation based on homogenization and comparison with experiment

The combination of thermal and mechanical loading expected in practice means that constitutive equations of metal matrix composites must be developed which deal with time-independent and time-dependent irreversible deformation. Also, the internal state of composites is extremely complicated which underlines the need to formulate macroscopic constitutive equations with a limited number of state variables which represent the internal state at the micro level. One available method for calculating the macro properties of composites in terms of the distribution and properties of the constituent materials is the method of homogenization whose formulation is based on the periodicity of the substructure of the composite. A homogenization procedure was developed which lends itself to the use of the finite element procedure. The efficiency of these procedures, to determine the macroscopic properties of a composite system from its constituent properties, was demonstrated utilizing an aluminum plate perforated by directionally oriented slits. The selection of this problem is based on the fact that, extensive experimental results exist, the macroscopic response is highly anisotropic, and that the slits provide very high stress gradients which severely test the effectiveness of the computational procedures. Furthermore, both elastic and plastic properties were investigated so that the application to practical systems with inelastic deformation should be able to proceed without difficulty. The effectiveness of the procedures was rigorously checked against experimental results and with the predictions of approximate calculations. Using the computational results it is illustrated how macroscopic constitutive equations can be expressed in forms of the elastic and limit load behavior.

Jansson, S.↗

DOE OSTI2023

Tree-Based Ensemble Learning Models for Wall Temperature Predictions in Post-Critical Heat Flux Flow Regimes at Subcooled and Low-Quality Conditions

Accurately predicting post-critical heat flux (CHF) heat transfer is an important but challenging task in water-cooled reactor design and safety analysis. Although numerous heat transfer correlations have been developed to predict post-CHF heat transfer, these correlations are only applicable to relatively narrow ranges of flow conditions due to the complex physical nature of the post-CHF heat transfer regimes. In this paper, a large quantity of experimental data is collected and summarized from the literature for steady-state subcooled and low-quality film boiling regimes with water as the working fluid in vertical tubular test sections. In addition, a low-quality water film boiling (LWFB) database is consolidated with a total of 22,813 experimental data points, which cover a wide flow range of the system pressure from 0.1 to 9.0 MPa, mass flux from 25 to 2750 kg/m 2 s, and inlet subcooling from 1 to 70 °C. Two machine learning (ML) models, based on random forest (RF) and gradient boosted decision tree (GBDT), are trained and validated to predict wall temperatures in post-CHF flow regimes. The trained ML models demonstrate significantly improved accuracies compared to conventional empirical correlations. To further evaluate the performance of these two ML models from a statistical perspective, three criteria are investigated and three metrics are calculated to quantitatively assess the accuracy of these two ML models. For the full LWFB database, the root-mean-square errors between the measured and predicted wall temperatures by the GBDT and RF models are 5.7% and 6.2%, respectively, confirming the accuracy of the two ML models.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗