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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 NTRS2009

Adiabatic Shock Capturing in Perfect Gas Hypersonic Flows

This paper considers the streamline-upwind Petrov/Galerkin (SUPG) method applied to the compressible Euler and Navier-Stokes equations in conservation-variable form. The spatial discretization, including a modified approach for interpolating the inviscid flux terms in the SUPG finite element formulation, is briefly reviewed. Of particular interest is the behavior of the shock capturing operator, which is required to regularize the scheme in the presence of strong, shock-induced gradients. A standard shock capturing operator which has been widely used in previous studies by several authors is presented and discussed. Specific modifications are then made to this standard operator which are designed to produce a more physically consistent discretization in the presence of strong shock waves. The actual implementation of the term in a finite dimensional approximation is also discussed. The behavior of the standard and modified scheme is then compared for several supersonic/hypersonic flows. The modified shock capturing operator is found to preserve enthalpy in the inviscid portion of the flowfield substantially better than the standard operator.

Kirk, Benjamin S.↗
NASA NTRS2013

MHD Simulations of the Plasma Flow in the Magnetic Nozzle

The magnetohydrodynamic (MHD) flow of plasma through a magnetic nozzle is simulated by solving the governing equations for the plasma flow in the presence of an static magnetic field representing the applied nozzle. This work will numerically investigate the flow and behavior of the plasma as the inlet plasma conditions and magnetic nozzle field strength are varied. The MHD simulations are useful for addressing issues such as plasma detachment and to can be used to gain insight into the physical processes present in plasma flows found in thrusters that use magnetic nozzles. In the model, the MHD equations for a plasma, with separate temperatures calculated for the electrons and ions, are integrated over a finite cell volume with flux through each face computed for each of the conserved variables (mass, momentum, magnetic flux, energy) [1]. Stokes theorem is used to convert the area integrals over the faces of each cell into line integrals around the boundaries of each face. The state of the plasma is described using models of the ionization level, ratio of specific heats, thermal conductivity, and plasma resistivity. Anisotropies in current conduction due to Hall effect are included, and the system is closed using a real-gas equation of state to describe the relationship between the plasma density, temperature, and pressure.A separate magnetostatic solver is used to calculate the applied magnetic field, which is assumed constant for these calculations. The total magnetic field is obtained through superposition of the solution for the applied magnetic field and the self-consistently computed induced magnetic fields that arise as the flowing plasma reacts to the presence of the applied field. A solution for the applied magnetic field is represented in Fig. 1 (from Ref. [2]), exhibiting the classic converging-diverging field pattern. Previous research was able to demonstrate effects such as back-emf at a super-Alfvenic flow, which significantly alters the shape of the magnetic field in both the near- and far-field regions. However, in that work the downstream domain was constrained to a channel of constant cross-sectional area. In the present work we seek to address this issue by modeling the downstream region with a domain that permits free expansion of the plasma, permitting a better evaluation of the downstream effects the applied field has on the plasma. The inlet boundary conditions and applied magnetic field values will also be varied to determine the effect the initial plasma energy content and applied magnetic field energy density have on the near- and far-field plasma properties on the MHD code. This will determine the effect of inlet boundary conditions on the results downstream and address issues related to the restrictive numerical domain previously used.

Smith, T. E. R.↗
NASA NTRS1983

On the joint bimodality of temperature and moisture near stratocumulus cloud tops

The observed distributions of the thermodynamic variables near stratocumulus top are highly bimodal. Two simple models of sub-grid fractional cloudiness motivated by this observed bimodality are examined. In both models, certain low order moments of two independent, moist-conservative thermodynamic variables are assumed to be known. The first model is based on the assumption of two discrete populations of parcels: a warm-day population and a cool-moist population. If only the first and second moments are assumed to be known, the number of unknowns exceeds the number of independent equations. If the third moments are assumed to be known as well, the number of independent equations exceeds the number of unknowns. The second model is based on the assumption of a continuous joint bimodal distribution of parcels, obtained as the weighted sum of two binormal distributions. For this model, the third moments are used to obtain 9 independent nonlinear algebraic equations in 11 unknowns. Two additional equations are needed to determine the covariance within the two subpopulations. In case these two internal covariance vanish, the system of equations can be solved analytically.

Randall, D. A.↗
NASA NTRS1983

A fully vectorized numerical solution of the incompressible Navier-Stokes equations

A vectorizable algorithm is presented for the implicit finite difference solution of the incompressible Navier-Stokes equations in general curvilinear coordinates. The unsteady Reynolds averaged Navier-Stokes equations solved are in two dimension and non-conservative primitive variable form. A two-layer algebraic eddy viscosity turbulence model is used to incorporate the effects of turbulence. Two momentum equations and a Poisson pressure equation, which is obtained by taking the divergence of the momentum equations and satisfying the continuity equation, are solved simultaneously at each time step. An elliptic grid generation approach is used to generate a boundary conforming coordinate system about an airfoil. The governing equations are expressed in terms of the curvilinear coordinates and are solved on a uniform rectangular computational domain. A checkerboard SOR, which can effectively utilize the computer architectural concept of vector processing, is used for iterative solution of the governing equations.

Patel, N.↗
NASA NTRS1990

Stratus: An interactive steady state mixed layer model for personal computers

A steady-state, horizontally homogeneous, cloud-topped marine boundary layer model based primarily on the work of Lilly (1968) and Schubert et al., (1979) is presented. The conservative thermodynamic variables are equivalent potential temperature, theta(sub e), and total water mixing ratio, q + l. Some of the differences between this and Lilly's (1968) model are: radiation is allowed to penetrate into the boundary layer; cloud top values of longwave radiation, equivalent potential temperature, and water vapor mixing ratio are linear functions of height derived from climatological data at California coastal stations; and the closure assumption assumes a weighted average of Lilly's (1968) maximum and minimum entrainment theories. This model was programmed in FORTRAN and will run interactively on an IBM-compatible personal computer. The program allows the user to specify the geographical location, the wind speed, the sea-surface temperature, the large scale horizontal divergence, and the initial guess for cloud top height. Output includes the steady state values of cloud top and cloud base height, mixed layer equivalent potential temperature and total water mixing ratio, and the associated convective and radiative fluxes.

Guinn, Thomas A.↗
NASA NTRS1992

Gravitational influences on the behavior of confined diffusion flames

Closed form, mathematical representations for the shapes of laminar diffusion flames stabilized on two-dimensional slot burners are derived for arbitrary gravitational levels. The solution technique employs the Schvab-Zeldovich conserved species variable. Effects of gravity on the velocity field are incorporated through the momentum equation; these effects, in turn, influence the species field. The results reduce smoothly to the classical Burke-Schumann solution as gravity approaches zero. It is shown that both flame height and width increase with decreasing gravity levels. Several interesting cases are considered explicitly; these include effects of negative and extremely high values of gravity. In the latter case, it is shown that the flame collapses onto the burner surface. The analysis finds application in the modeling of steady and unsteady gas and solid propellant diffusion flames.

Hegde, U.↗
NASA NTRS1993

Effects of spatial order of accuracy on the computation of vortical flowfields

The effect of the order-of-accuracy, used for the spatial discretization, on the resolution of the leading edge vortices over sharp-edged delta wings is investigated. The flowfield is computed using a viscous/inviscid zonal approach. The viscous flow in the vicinity of the wing is computed using the conservative formulation of the compressible, thin-layer Navier-Stokes equations. The leeward-side vortical flowfield and the other flow regions away from the surface are computed as inviscid. The time integration is performed with both an explicit fourth-order Runge-Kutta scheme and an implicit, factorized, iterative scheme. High-order-accurate inviscid fluxes are computed using both a conservative and a non-conservative (primitive variable) formulation. The nonlinear, inviscid terms of the primitive variable form of the governing equations are evaluated with a finite-difference numerical scheme based on the sign of the eigenvalues. High-order, upwind-biased, finite difference formulas are used to evaluate the derivatives of the nonlinear convective terms. Computed results are compared with available experimental data, and comparisons of the flowfield in the vicinity of the vortex cores are presented.

Ekaterinaris, J. A.↗
NASA NTRS1996

Three Dimensional Flow and Pressure Patterns in a Hydrostatic Journal Bearing

The flow in a hydrostatic journal bearing (HJB) is described by a mathematical model that uses the three dimensional non-orthogonal form of the Navier-Stokes equations. Using the u, v, w, and p, as primary variables, a conservative formulation, finite volume multi-block method is applied through a collocated, body fitted grid. The HJB has four shallow pockets with a depth/length ratio of 0.067. This paper represents a natural extension to the two and three dimensional studies undertaken prior to this project.

Braun, M. Jack↗
NASA NTRS2001

Coarse Grid Modeling of Turbine Film Cooling Flows Using Volumetric Source Terms

The recent trend in numerical modeling of turbine film cooling flows has been toward higher fidelity grids and more complex geometries. This trend has been enabled by the rapid increase in computing power available to researchers. However, the turbine design community requires fast turnaround time in its design computations, rendering these comprehensive simulations ineffective in the design cycle. The present study describes a methodology for implementing a volumetric source term distribution in a coarse grid calculation that can model the small-scale and three-dimensional effects present in turbine film cooling flows. This model could be implemented in turbine design codes or in multistage turbomachinery codes such as APNASA, where the computational grid size may be larger than the film hole size. Detailed computations of a single row of 35 deg round holes on a flat plate have been obtained for blowing ratios of 0.5, 0.8, and 1.0, and density ratios of 1.0 and 2.0 using a multiblock grid system to resolve the flows on both sides of the plate as well as inside the hole itself. These detailed flow fields were spatially averaged to generate a field of volumetric source terms for each conservative flow variable. Solutions were also obtained using three coarse grids having streamwise and spanwise grid spacings of 3d, 1d, and d/3. These coarse grid solutions used the integrated hole exit mass, momentum, energy, and turbulence quantities from the detailed solutions as volumetric source terms. It is shown that a uniform source term addition over a distance from the wall on the order of the hole diameter is able to predict adiabatic film effectiveness better than a near-wall source term model, while strictly enforcing correct values of integrated boundary layer quantities.

Heidmann, James D.↗
NASA NTRS1998

Mixing of Multiple Jets With a Confined Subsonic Crossflow

Results from a recently completed enhanced mixing program are summarized in the two technical papers. These studies were parts of a High Speed Research (HSR)-supported joint Government/industry/university program that involved, in addition to the NASA Lewis Research Center, researchers at United Technologies Research Center, Allison Engine Company, CFD Research Corporation, and the University of California, Irvine. The studies investigated the mixing of jets injected normal to a confined subsonic mainsteam in both rectangular and cylindrical ducts. Experimental and computational studies were performed in both nonreacting and reacting flows. The orifice geometries and flow conditions were selected as typical of the complex three-dimensional flows in the combustion chambers in low-emission gas turbine engines. The principal conclusion from both the experiments and modeling was that the momentum-flux ratio J and orifice spacing S/H were the most significant flow and geometry variables, respectively. Conserved scalar distributions were similar-independent of reaction, orifice diameter H/d, and shape-when the orifice spacing and the square root of the momentum-flux ratio were inversely proportional. Jet penetration was critical, and penetration decreased as either momentum-flux ratio or orifice spacing decreased. We found that planar averages must be considered in context with the distributions. The mass-flow ratios and the orifices investigated were often very large. The jet-to-mainstream mass-flow ratio was varied from significantly less than 1 to greater than 1. The orifice-area to mainstream-cross-sectional-area was varied from approx. 0 to 0.5, and the axial planes of interest were often just downstream of the orifice trailing edge. Three-dimensional flow was a key part of efficient mixing and was observed for all configurations. As an example of the results, the accompanying figure shows the effects of different rates of mass addition on the opposite walls of a rectangular duct.

Holdeman, James D.↗
NASA NTRS2006

Accuracy Quantification of the Loci-CHEM Code for Chamber Wall Heat Transfer in a GO2/GH2 Single Element Injector Model Problem

A robust rocket engine combustor design and development process must include tools which can accurately predict the multi-dimensional thermal environments imposed on solid surfaces by the hot combustion products. Currently, empirical methods used in the design process are typically one dimensional and do not adequately account for the heat flux rise rate in the near-injector region of the chamber. Computational Fluid Dynamics holds promise to meet the design tool requirement, but requires accuracy quantification, or validation, before it can be confidently applied in the design process. This effort presents the beginning of such a validation process for the Loci-CHEM CFD code. The model problem examined here is a gaseous oxygen (GO2)/gaseous hydrogen (GH2) shear coaxial single element injector operating at a chamber pressure of 5.42 MPa. The GO2/GH2 propellant combination in this geometry represents one the simplest rocket model problems and is thus foundational to subsequent validation efforts for more complex injectors. Multiple steady state solutions have been produced with Loci-CHEM employing different hybrid grids and two-equation turbulence models. Iterative convergence for each solution is demonstrated via mass conservation, flow variable monitoring at discrete flow field locations as a function of solution iteration and overall residual performance. A baseline hybrid was used and then locally refined to demonstrate grid convergence. Solutions were obtained with three variations of the k-omega turbulence model.

West, Jeff↗
NASA NTRS2006

Accuracy Quantification of the Loci-CHEM Code for Chamber Wall Heat Fluxes in a G02/GH2 Single Element Injector Model Problem

A robust rocket engine combustor design and development process must include tools which can accurately predict the multi-dimensional thermal environments imposed on solid surfaces by the hot combustion products. Currently, empirical methods used in the design process are typically one dimensional and do not adequately account for the heat flux rise rate in the near-injector region of the chamber. Computational Fluid Dynamics holds promise to meet the design tool requirement, but requires accuracy quantification, or validation, before it can be confidently applied in the design process. This effort presents the beginning of such a validation process for the Loci- CHEM CPD code. The model problem examined here is a gaseous oxygen (GO2)/gaseous hydrogen (GH2) shear coaxial single element injector operating at a chamber pressure of 5.42 MPa. The GO2/GH2 propellant combination in this geometry represents one the simplest rocket model problems and is thus foundational to subsequent validation efforts for more complex injectors. Multiple steady state solutions have been produced with Loci-CHEM employing different hybrid grids and two-equation turbulence models. Iterative convergence for each solution is demonstrated via mass conservation, flow variable monitoring at discrete flow field locations as a function of solution iteration and overall residual performance. A baseline hybrid grid was used and then locally refined to demonstrate grid convergence. Solutions were also obtained with three variations of the k-omega turbulence model.

West, Jeff↗
NASA NTRS2012

Calculating Soil Wetness, Evapotranspiration and Carbon Cycle Processes Over Large Grid Areas Using a New Scaling Technique

Soil wetness typically shows great spatial variability over the length scales of general circulation model (GCM) grid areas (approx 100 km ), and the functions relating evapotranspiration and photosynthetic rate to local-scale (approx 1 m) soil wetness are highly non-linear. Soil respiration is also highly dependent on very small-scale variations in soil wetness. We therefore expect significant inaccuracies whenever we insert a single grid area-average soil wetness value into a function to calculate any of these rates for the grid area. For the particular case of evapotranspiration., this method - use of a grid-averaged soil wetness value - can also provoke severe oscillations in the evapotranspiration rate and soil wetness under some conditions. A method is presented whereby the probability distribution timction(pdf) for soil wetness within a grid area is represented by binning. and numerical integration of the binned pdf is performed to provide a spatially-integrated wetness stress term for the whole grid area, which then permits calculation of grid area fluxes in a single operation. The method is very accurate when 10 or more bins are used, can deal realistically with spatially variable precipitation, conserves moisture exactly and allows for precise modification of the soil wetness pdf after every time step. The method could also be applied to other ecological problems where small-scale processes must be area-integrated, or upscaled, to estimate fluxes over large areas, for example in treatments of the terrestrial carbon budget or trace gas generation.

Sellers, Piers↗
NASA NTRS2026

Spacecraft Disposal Rosetta Stone: Parametric Tool for Orbital Lifetime, Disposal, and Cost Assessment

This Technical Memorandum documents a simplified, parametric method for evaluating spacecraft orbital lifetime, disposal compliance, and disposal-related cost impacts during early mission formulation and preliminary design. The method captures the dominant drivers of orbital decay—effective ballistic coefficient, operating altitude, and solar-cycle variability—using conservative bounding assumptions. Solar maximum conditions are used to bound achievable mission lifetime, while solar minimum conditions are used to bound disposal timelines and compliance with orbital debris requirements. A single tabulated dataset provides orbital lifetime under both solar-cycle extremes together with representative disposal ΔV required to ensure compliant disposal, enabling rapid assessment of disposal feasibility, cost sensitivity, and system-level impacts prior to committing to higher-fidelity analyses.

Orbital debris mitigation↗
NASA NTRS1993

Variable-Volume Flushing (V-VF) device for water conservation in toilets

Thirty five percent of residential indoor water used is flushed down the toilet. Five out of six flushes are for liquid waste only, which requires only a fraction of the water needed for solid waste. Designers of current low-flush toilets (3.5-gal. flush) and ultra-low-flush toilets (1.5-gal. flush) did not consider the vastly reduced amount of water needed to flush liquid waste versus solid waste. Consequently, these toilets are less practical than desired and can be improved upon for water conservation. This paper describes a variable-volume flushing (V-VF) device that is more reliable than the currently used flushing devices (it will not leak), is simple, more economical, and more water conserving (allowing one to choose the amount of water to use for flushing solid and liquid waste).

Jasper, Louis J., Jr.↗
NASA NTRS1981

Numerical approximation of boundary conditions with applications to inviscid equations of gas dynamics

A comprehensive overview of the state of the art of well-posedness and stability analysis of difference approximations for initial boundary value problems of the hyperbolic type is presented. The applicability of recent theoretical development to practical calculations for nonlinear gas dynamics is examined. The one dimensional inviscid gas dynamics equations in conservation law form are selected for numerical experiments. The class of implicit schemes developed from linear multistep methods in ordinary differential equations is chosen and the use of linear extrapolation as an explicit or implicit boundary scheme is emphasized. Specification of boundary data in the primitive variables and computation in terms of the conservative variables in the interior is discussed. Some numerical examples for the quasi-one-dimensional nozzle are given.

Yee, H. C.↗
NASA NTRS2003

A Discrete Constraint for Entropy Conservation and Sound Waves in Cloud-Resolving Modeling

Ideal cloud-resolving models contain little-accumulative errors. When their domain is so large that synoptic large-scale circulations are accommodated, they can be used for the simulation of the interaction between convective clouds and the large-scale circulations. This paper sets up a framework for the models, using moist entropy as a prognostic variable and employing conservative numerical schemes. The models possess no accumulative errors of thermodynamic variables when they comply with a discrete constraint on entropy conservation and sound waves. Alternatively speaking, the discrete constraint is related to the correct representation of the large-scale convergence and advection of moist entropy. Since air density is involved in entropy conservation and sound waves, the challenge is how to compute sound waves efficiently under the constraint. To address the challenge, a compensation method is introduced on the basis of a reference isothermal atmosphere whose governing equations are solved analytically. Stability analysis and numerical experiments show that the method allows the models to integrate efficiently with a large time step.

Zeng, Xi-Ping↗
NASA NTRS2001

High Order Difference Method for Low Mach Number Aeroacoustics

A high order finite difference method with improved accuracy and stability properties for computational aeroacoustics (CAA) at low Mach numbers is proposed. The Euler equations are split into a conservative and a symmetric non- conservative portion to allow the derivation of a generalized energy estimate. Since the symmetrization is based on entropy variables, that splitting of the flux derivatives is referred to as entropy splitting. Its discretization by high order central differences was found to need less numerical dissipation than conventional conservative schemes. Owing to the large disparity of acoustic and stagnation quantities in low Mach number aeroacoustics, the split Euler equations are formulated in perturbation form. The unknowns are the small changes of the conservative variables with respect to their large stagnation values. All nonlinearities and the conservation form of the conservative portion of the split flux derivatives can be retained, while cancellation errors are avoided with its discretization opposed to the conventional conservative form. The finite difference method is third-order accurate at the boundary and the conventional central sixth-order accurate stencil in the interior. The difference operator satisfies the summation by parts property analogous to the integration by parts in the continuous energy estimate. Thus, strict stability of the difference method follows automatically. Spurious high frequency oscillations are suppressed by a characteristic-based filter similar to but without limiter. The time derivative is approximated by a 4-stage low-storage second-order explicit Runge-Kutta method. The method has been applied to simulate vortex sound at low Mach numbers. We consider the Kirchhoff vortex, which is an elliptical patch of constant vorticity rotating with constant angular frequency in irrotational flow. The acoustic pressure generated by the Kirchhoff vortex is governed by the 2D Helmholtz equation, which can be solved analytically using separation of variables.

Mueller, B.↗