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NASA NTRS1990

A closed-form solution to HZE propagation

An analytic solution for high energy heavy ion transport assuming straightahead and velocity conserving interactions with constant nuclear cross reactions is given in terms of a Green's function. The series solution for the Green's function is rapidly convergent for most practical applications. The green's function technique can be applied with equal success to laboratory beams as well as to galactic cosmic rays allowing laboratory validation of the resultant space shielding code.

Wilson, John W.↗

NASA NTRS2019

Size and Structure of the Sequence Space of Repeat Proteins

The coding space of protein sequences is shaped by evolutionary constraints set by requirements of function and stability. We show that the coding space of a given protein family— the total number of sequences in that family—can be estimated using models of maximum entropy trained on multiple sequence alignments of naturally occurring amino acid sequences. We analyzed and calculated the size of three abundant repeat proteins families, whose members are large proteins made of many repetitions of conserved portions of *30 amino acids. While amino acid conservation at each position of the alignment explains most of the reduction of diversity relative to completely random sequences, we found that correlations between amino acid usage at different positions significantly impact that diversity. We quantified the impact of different types of correlations, functional and evolutionary, on sequence diversity. Analysis of the detailed structure of the coding space of the families revealed a rugged landscape, with many local energy minima of varying sizes with a hierarchical structure, reminiscent of frustrated energy landscapes of spin glass in physics. This clustered structure indicates a multiplicity of subtypes within each family and suggests new strategies for protein design.

Jacopo Marchi↗

NASA NTRS1998

Nuclear modules for space electric propulsion

Analysis of interplanetary cargo and piloted missions requires calculations of the performances and masses of subsystems to be integrated in a final design. In a preliminary and scoping stage the designer needs to evaluate options iteratively by using fast computer simulations. The Oak Ridge National Laboratory (ORNL) has been involved in the development of models and calculational procedures for the analysis (neutronic and thermal hydraulic) of power sources for nuclear electric propulsion. The nuclear modules will be integrated into the whole simulation of the nuclear electric propulsion system. The vehicles use either a Brayton direct-conversion cycle, using the heated helium from a NERVA-type reactor, or a potassium Rankine cycle, with the working fluid heated on the secondary side of a heat exchanger and lithium on the primary side coming from a fast reactor. Given a set of input conditions, the codes calculate composition. dimensions, volumes, and masses of the core, reflector, control system, pressure vessel, neutron and gamma shields, as well as the thermal hydraulic conditions of the coolant, clad and fuel. Input conditions are power, core life, pressure and temperature of the coolant at the inlet of the core, either the temperature of the coolant at the outlet of the core or the coolant mass flow and the fluences and integrated doses at the cargo area. Using state-of-the-art neutron cross sections and transport codes, a database was created for the neutronic performance of both reactor designs. The free parameters of the models are the moderator/fuel mass ratio for the NERVA reactor and the enrichment and the pitch of the lattice for the fast reactor. Reactivity and energy balance equations are simultaneously solved to find the reactor design. Thermalhydraulic conditions are calculated by solving the one-dimensional versions of the equations of conservation of mass, energy, and momentum with compressible flow.

Difilippo, F. C.↗

NASA NTRS1999

Dynamics and Structure of Dusty Reacting Flows: Inert Particles in Strained, Laminar, Premixed Flames

A detailed numerical study was conducted on the dynamics and thermal response of inert, spherical particles in strained, laminar, premixed hydrogen/air flames. The modeling included the solution of the steady conservation equations for both the gas and particle phases along and around the stagnation streamline of an opposed-jet configuration, and the use of detailed descriptions of chemical kinetics and molecular transport, For the gas phase, the equations of mass, momentum, energy, and species are considered, while for the particle phase, the model is based on conservation equations of the particle momentum balance in the axial and radial direction, the particle number density, and the particle thermal energy equation. The particle momentum equation includes the forces as induced by drag, thermophoresis, and gravity. The particle thermal energy equation includes the convective/conductive heat exchange between the two phases, as well as radiation emission and absorption by the particle. A one-point continuation method is also included in the code that allows for the description of turning points, typical of ignition and extinction behavior. As expected, results showed that the particle velocity can be substantially different than the gas phase velocity, especially in the presence of large temperature gradients and large strain rates. Large particles were also found to cross the gas stagnation plane, stagnate, and eventually reverse as a result of the opposing gas phase velocity. It was also shown that the particle number density varies substantially throughout the flowfield, as a result of the straining of the flow and the thermal expansion. Finally, for increased values of the particle number density, substantial flame cooling to extinction states and modification of the gas phase fluid mechanics were observed. As also expected, the effect of gravity was shown to be important for low convective velocities and heavy particles. Under such conditions, simulations indicate that the magnitude and direction of the gravitational force can substantially affect the profiles of the particle velocity, number density, mass flux, and temperature.

Egolfopoulos, Fokion N.↗

NASA NTRS1999

Dynamics and Structure of Dusty Reacting Flows: Inert Particles in Strained, Laminar, Premixed Flames

A detailed numerical study was conducted on the dynamics and thermal response of inert spherical particles in strained, laminar, premixed hydrogen/air flames. The modeling included the solution of the steady conservation equations for both the gas and particle phases along and around the stagnation streamline of an opposed-jet configuration, and the use of detailed descriptions of chemical kinetics and molecular transport. For the gas phase, the equations of mass, momentum, energy, and species are considered, while for the particle phase, the model is based on conservation equations of the particle momentum balance in the axial and radial direction, the particle number density, and the particle thermal energy equation. The particle momentum equation includes the forces as induced by drag, thermophoresis, and gravity. The particle thermal energy equation includes the convective/conductive heat exchange between the two phases, as well as radiation emission and absorption by the particle. A one-point continuation method is also included in the code that allows for the description of turning points, typical of ignition and extinction behavior. As expected, results showed that the particle velocity can be substantially different than the gas phase velocity, especially in the presence of large temperature gradients and large strain rates. Large particles were also found to cross the gas stagnation plane, stagnate, and eventually reverse as a result of the opposing gas phase velocity. It was also shown that the particle number density varies substantially throughout the flowfield, as a result of the straining of the flow and the thermal expansion. Finally, for increased values of the particle number density, substantial flame cooling to extinction states and modification of the gas phase fluid mechanics were observed. As also expected, the effect of gravity was shown to be important for low convective velocities and heavy particles. Under such conditions, simulations indicate that the magnitude and direction of the gravitational force can substantially affect the profiles of the particle velocity, number density, mass flux, and temperature.

Egolfopoulos, Fokion N.↗

NASA NTRS1989

Simulation studies using multibody dynamics code DART

DART is a multibody dynamics code developed by Photon Research Associates for the Air Force Astronautics Laboratory (AFAL). The code is intended primarily to simulate the dynamics of large space structures, particularly during the deployment phase of their missions. DART integrates nonlinear equations of motion numerically. The number of bodies in the system being simulated is arbitrary. The bodies' interconnection joints can have an arbitrary number of degrees of freedom between 0 and 6. Motions across the joints can be large. Provision for simulating on-board control systems is provided. Conservation of energy and momentum, when applicable, are used to evaluate DART's performance. After a brief description of DART, studies made to test the program prior to its delivery to AFAL are described. The first is a large angle reorientating of a flexible spacecraft consisting of a rigid central hub and four flexible booms. Reorientation was accomplished by a single-cycle sine wave shape torque input. In the second study, an appendage, mounted on a spacecraft, was slewed through a large angle. Four closed-loop control systems provided control of this appendage and of the spacecraft's attitude. The third study simulated the deployment of the rim of a bicycle wheel configuration large space structure. This system contained 18 bodies. An interesting and unexpected feature of the dynamics was a pulsing phenomena experienced by the stays whole playout was used to control the deployment. A short description of the current status of DART is given.

Keat, James E.↗

NASA NTRS1979

Plasma property and performance prediction for mercury ion thrusters

The discharge chambers of mercury ion thrusters are modelled so the principal effects and processes which govern discharge plasma properties and thruster performance are described. The conservation relations for mass, charge and energy when applied to the Maxwellian electron population in the ion production region yield equations which may be made one-dimensional by the proper choice of coordinates. Solutions to these equations with the appropriate boundary conditions give electron density and temperature profiles which agree reasonably well with measurements. It is then possible to estimate plasma properties from thruster design data and those operating parameters which are directly controllable. By varying the operating parameter inputs to the computer code written to solve these equations, perfromance curves are obtained which agree quite well with measurements.

Longhurst, G. R.↗

NASA NTRS1996

Spray Combustion Modeling with VOF and Finite-Rate Chemistry

A spray atomization and combustion model is developed based on the volume-of-fluid (VOF) transport equation with finite-rate chemistry model. The gas-liquid interface mass, momentum and energy conservation laws are modeled by continuum surface force mechanisms. A new solution method is developed such that the present VOF model can be applied for all-speed range flows. The objectives of the present study are: (1) to develop and verify the fractional volume-of-fluid (VOF) cell partitioning approach into a predictor-corrector algorithm to deal with multiphase (gas-liquid) free surface flow problems; (2) to implement the developed unified algorithm in a general purpose computational fluid dynamics (CFD) code, Finite Difference Navier-Stokes (FDNS), with droplet dynamics and finite-rate chemistry models; and (3) to demonstrate the effectiveness of the present approach by simulating benchmark problems of jet breakup/spray atomization and combustion. Modeling multiphase fluid flows poses a significant challenge because a required boundary must be applied to a transient, irregular surface that is discontinuous, and the flow regimes considered can range from incompressible to highspeed compressible flows. The flow-process modeling is further complicated by surface tension, interfacial heat and mass transfer, spray formation and turbulence, and their interactions. The major contribution of the present method is to combine the novel feature of the Volume of Fluid (VOF) method and the Eulerian/Lagrangian method into a unified algorithm for efficient noniterative, time-accurate calculations of multiphase free surface flows valid at all speeds. The proposed method reformulated the VOF equation to strongly couple two distinct phases (liquid and gas), and tracks droplets on a Lagrangian frame when spray model is required, using a unified predictor-corrector technique to account for the non-linear linkages through the convective contributions of VOF. The discontinuities within the sharp interface will be modeled as a volume force to avoid stiffness. Formations of droplets, tracking of droplet dynamics and modeling of the droplet breakup/evaporation, are handled through the same unified predictor-corrector procedure. Thus the new algorithm is non-iterative and is flexible for general geometries with arbitrarily complex topology in free surfaces. The FDNS finite-difference Navier-Stokes code is employed as the baseline of the current development. Benchmark test cases of shear coaxial LOX/H2 liquid jet with atomization/combustion and impinging jet test cases are investigated in the present work. Preliminary data comparisons show good qualitative agreement between data and the present analysis. It is indicative from these results that the present method has great potential to become a general engineering design analysis and diagnostics tool for problems involving spray combustion.

Chen, Yen-Sen↗

NASA NTRS1989

The free-wake prediction of rotor hover performance using a vortex embedding method

A method is developed to predict the rotor hover performance. This method solves the compressible mass conservation equation much like current full potential codes and can therefore predict the transonic flows on a rotor. However, the newly developed approach also allows for the free convection of shed vorticity and permits the computation of the entire hover wake system. The method uses a vortex embedding scheme in potential flow and has been implemented in a computer code, HELIX -I. To predict power we implement a simple boundary layer and two different induced-drag integration schemes. The induced-drag is obtained from surface pressure integration and an energy flux integral. Comparisons between computations and experiment show good agreement for the prediction of power polars, surface pressure distribution, and tip vortex geometry.

Ramachandran, K.↗

NASA NTRS2013

Prediction of Ablation Rates from Solid Surfaces Exposed to High Temperature Gas Flow

A mathematical model and a solution algorithm is developed to study the physics of high temperature heat transfer and material ablation and identify the problems associated with the flow of hydrogen gas at very high temperatures and velocities through pipes and various components of Nuclear Thermal Rocket (NTR) motors. Ablation and melting can be experienced when the inner solid surface of the cooling channels and the diverging-converging nozzle of a Nuclear Thermal Rocket (NTR) motor is exposed to hydrogen gas flow at temperatures around 2500 degrees Kelvin and pressures around 3.4 MPa. In the experiments conducted on typical NTR motors developed in 1960s, degradation of the cooling channel material (cracking in the nuclear fuel element cladding) and in some instances melting of the core was observed. This paper presents the results of a preliminary study based on two types of physics based mathematical models that were developed to simulate the thermal-hydrodynamic conditions that lead to ablation of the solid surface of a stainless steel pipe exposed to high temperature hydrogen gas near sonic velocities. One of the proposed models is one-dimensional and assumes the gas flow to be unsteady, compressible and viscous. An in-house computer code was developed to solve the conservations equations of this model using a second-order accurate finite-difference technique. The second model assumes the flow to be three-dimensional, unsteady, compressible and viscous. A commercial CFD code (Fluent) was used to solve the later model equations. Both models assume the thermodynamic and transport properties of the hydrogen gas to be temperature dependent. In the solution algorithm developed for this study, the unsteady temperature of the pipe is determined from the heat equation for the solid. The solid-gas interface temperature is determined from an energy balance at the interface which includes heat transfer from or to the interface by conduction, convection, radiation, and ablation. Two different ablation models are proposed to determine the heat loss from the solid surface due to the ablation of the solid material. Both of them are physics based. Various numerical simulations were carried out using both models to predict the temperature distribution in the solid and in the gas flow, and then predict the ablation rates at a typical NTR motor hydrogen gas temperature and pressure. Solid mass loss rate per foot of a pipe was also calculated from these predictions. The results are presented for fully developed turbulent flow conditions in a sample SS pipe with a 6 inch diameter.

Akyuzlu, Kazim M.↗

NASA NTRS2017

Modeling Two-Phase Flow and Vapor Cycles Using the Generalized Fluid System Simulation Program

This work presents three new applications for the general purpose fluid network solver code GFSSP developed at NASA's Marshall Space Flight Center: (1) cooling tower, (2) vapor-compression refrigeration system, and (3) vapor-expansion power generation system. These systems are widely used across engineering disciplines in a variety of energy systems, and these models expand the capabilities and the use of GFSSP to include fluids and features that are not part of its present set of provided examples. GFSSP provides pressure, temperature, and species concentrations at designated locations, or nodes, within a fluid network based on a finite volume formulation of thermodynamics and conservation laws. This paper describes the theoretical basis for the construction of the models, their implementation in the current GFSSP modeling system, and a brief evaluation of the usefulness of the model results, as well as their applicability toward a broader spectrum of analytical problems in both university teaching and engineering research.

Smith, Amanda D.↗

NASA NTRS1995

General Fluid System Simulation Program to Model Secondary Flows in Turbomachinery

The complexity and variety of turbomachinery flow circuits created a need for a general fluid system simulation program for test data anomaly resolution as well as design review. The objective of the paper is to present a computer program that has been developed to support Marshall Space Flight Center's turbomachinery internal flow analysis efforts. The computer program solves for the mass. energy and species conservation equation at each node and flow rate equation at each branch of the network by a novel numerical procedure which is a combination of both Newton-Ralphson and successive substitution method and uses a thermodynamic property program for computing real gas properties. A generalized, robust, modular, and 'user-friendly' computer program has been developed to model internal flow rates, pressures, temperatures, concentrations of gas mixtures and axial thrusts. The program can be used for any network for compressible and incompressible flows, choked flow, change of phase and gaseous mixturecs. The code has been validated by comparing the predictions with Space Shuttle Main Engine test data.

Majumdar, Alok K.↗

NASA NTRS2009

Hall-Effect Thruster Simulations with 2-D Electron Transport and Hydrodynamic Ions

A computational approach that has been used extensively in the last two decades for Hall thruster simulations is to solve a diffusion equation and energy conservation law for the electrons in a direction that is perpendicular to the magnetic field, and use discrete-particle methods for the heavy species. This "hybrid" approach has allowed for the capture of bulk plasma phenomena inside these thrusters within reasonable computational times. Regions of the thruster with complex magnetic field arrangements (such as those near eroded walls and magnets) and/or reduced Hall parameter (such as those near the anode and the cathode plume) challenge the validity of the quasi-one-dimensional assumption for the electrons. This paper reports on the development of a computer code that solves numerically the 2-D axisymmetric vector form of Ohm's law, with no assumptions regarding the rate of electron transport in the parallel and perpendicular directions. The numerical challenges related to the large disparity of the transport coefficients in the two directions are met by solving the equations in a computational mesh that is aligned with the magnetic field. The fully-2D approach allows for a large physical domain that extends more than five times the thruster channel length in the axial direction, and encompasses the cathode boundary. Ions are treated as an isothermal, cold (relative to the electrons) fluid, accounting for charge-exchange and multiple-ionization collisions in the momentum equations. A first series of simulations of two Hall thrusters, namely the BPT-4000 and a 6-kW laboratory thruster, quantifies the significance of ion diffusion in the anode region and the importance of the extended physical domain on studies related to the impact of the transport coefficients on the electron flow field.

plasma↗

NASA NTRS1995

Parametric studies of stitching effectiveness for preventing substructure disbond

A methodology is desired that will allow a designer to select appropriate amounts of through-thickness reinforcement needed to meet design requirements. The goal is to use a relatively simple analysis to minimize the amount of testing that needs to be performed, and to make test results from simple configurations applicable to more general structures. Using this methodology one should be able to optimize the selection of stitching materials, the weight of the yarn, and the stitching density. The analysis approach is to treat substructure disbond as a crack propagation problem. In this approach, the stitches have little influence until a delamination begins to grow. Once the delamination reaches, or extends beyond a stitch, the stitch serves to reduce the strain-energy-release-rate (G) at the crack tip for a given applied load. The reduced G can then be compared to the unstitched materials toughness to predict the load required to further extend the crack. The current model treats the stitch as a simple spring which responds to displacements in the vertical (through-thickness) direction. In concept, this approach is similar to that proposed by other authors. Test results indicate that the model should be refined to include the shearing stiffness of the stitch. The strain-energy-release-rate calculations are performed using a code which uses interconnected higher-order plates to model built-up composite cross-sections. When plates are stacked vertically, the interfacial tractions between the plates can be computed. The plate differential equations are solved in closed-form. The code, called SUBLAM, was developed as part of this section in one dimension. Because of this limitation, rows of stitches are treated as a two-dimensional sheet. The spring stiffness of a row of stitches can be estimated from the stitch material, weight, and density. As a practical and conservative approach, we can assume that the stitch is bonded until a crack passes the stitch location. After the crack passes, it is fully bonded. A series of tests were performed to exercise this methodology and incorporated an attached flange such that the sudden change in thickness initiated a delamination. The analysis was used to estimate the materials' critical G from that of the unstitched specimens. With this data, a prediction was made for the load required to delaminate the stitched specimens. Using the methodology, design charts have been created for simplified geometries. These charts give stitch force, along with G(sub 1) and G(sub 2) as as function of the stitch spring stiffness. Using the charts, it should be possible to determine the stitch spring stiffness and strength required to reduce the G to a desired level. From these parameters, the actual stitching material, weight, and density can be computed.

Flanagan, Gerry↗

NASA NTRS1993

Proteus three-dimensional Navier-Stokes computer code, version 1.0. Volume 3: Programmer's reference

A computer code called Proteus 3D was developed to solve the three-dimensional, Reynolds-averaged, unsteady compressible Navier-Stokes equations in strong conservation law form. The objective in this effort was to develop a code for aerospace propulsion applications that is easy to use and easy to modify. Code readability, modularity, and documentation were emphasized. The governing equations are solved in generalized nonorthogonal body fitted coordinates, by marching in time using a fully-coupled ADI solution procedure. The boundary conditions are treated implicitly. All terms, including the diffusion terms, are linearized using second-order Taylor series expansions. Turbulence is modeled using either an algebraic or two-equation eddy viscosity model. The thin-layer or Euler equations may also be solved. The energy equation may be eliminated by the assumption of constant total enthalpy. Explicit and implicit artificial viscosity may be used. Several time step options are available for convergence acceleration. The documentation is divided into three volumes. The Programmer's Reference contains detailed information useful when modifying the program. The program structure, the Fortran variables stored in common blocks, and the details of each subprogram are described.

Towne, Charles E.↗

NASA NTRS1993

Proteus two-dimensional Navier-Stokes computer code, version 2.0. Volume 2: User's guide

A computer code called Proteus 2D was developed to solve the two-dimensional planar or axisymmetric, Reynolds-averaged, unsteady compressible Navier-Stokes equations in strong conservation law form. The objective in this effort was to develop a code for aerospace propulsion applications that is easy to use and easy to modify. Code readability, modularity, and documentation were emphasized. The governing equations are solved in generalized nonorthogonal body-fitted coordinates, by marching in time using a fully-coupled ADI solution procedure. The boundary conditions are treated implicitly. All terms, including the diffusion terms, are linearized using second-order Taylor series expansions. Turbulence is modeled using either an algebraic or two-equation eddy viscosity model. The thin-layer or Euler equations may also be solved. The energy equation may be eliminated by the assumption of constant total enthalpy. Explicit and implicit artificial viscosity may be used. Several time step options are available for convergence acceleration. The documentation is divided into three volumes. This is the User's Guide, and describes the program's features, the input and output, the procedure for setting up initial conditions, the computer resource requirements, the diagnostic messages that may be generated, the job control language used to run the program, and several test cases.

Towne, Charles E.↗

NASA NTRS1993

Proteus two-dimensional Navier-Stokes computer code, version 2.0. Volume 1: Analysis description

A computer code called Proteus 2D was developed to solve the two-dimensional planar or axisymmetric, Reynolds-averaged, unsteady compressible Navier-Stokes equations in strong conservation law form. The objective in this effort was to develop a code for aerospace propulsion applications that is easy to use and easy to modify. Code readability, modularity, and documentation were emphasized. The governing equations are solved in generalized nonorthogonal body-fitted coordinates, by marching in time using a fully-coupled ADI solution procedure. The boundary conditions are treated implicitly. All terms, including the diffusion terms, are linearized using second-order Taylor series expansions. Turbulence is modeled using either an algebraic or two-equation eddy viscosity model. The thin-layer or Euler equations may also be solved. The energy equation may be eliminated by the assumption of constant total enthalpy. Explicit and implicit artificial viscosity may be used. Several time step options are available for convergence acceleration. The documentation is divided into three volumes. This is the Analysis Description, and presents the equations and solution procedure. The governing equations, the turbulence model, the linearization of the equations and boundary conditions, the time and space differencing formulas, the ADI solution procedure, and the artificial viscosity models are described in detail.

Towne, Charles E.↗

NASA NTRS1993

Proteus three-dimensional Navier-Stokes computer code, version 1.0. Volume 2: User's guide

A computer code called Proteus 3D was developed to solve the three-dimensional, Reynolds-averaged, unsteady compressible Navier-Stokes equations in strong conservation law form. The objective in this effort was to develop a code for aerospace propulsion applications that is easy to use and easy to modify. Code readability, modularity, and documentation were emphasized. The governing equations are solved in generalized nonorthogonal body-fitted coordinates, by marching in time using a fully-coupled ADI solution procedure. The boundary conditions are treated implicitly. All terms, including the diffusion terms, are linearized using second-order Taylor series expansions. Turbulence is modeled using either an algebraic or two-equation eddy viscosity model. The thin-layer or Euler equations may also be solved. The energy equation may be eliminated by the assumption of constant total enthalpy. Explicit and implicit artificial viscosity may be used. Several time step options are available for convergence acceleration. The documentation is divided into three volumes. This User's Guide describes the program's features, the input and output, the procedure for setting up initial conditions, the computer resource requirements, the diagnostic messages that may be generated, the job control language used to run the program, and several test cases.

Towne, Charles E.↗