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At least 595 records · Page 33
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

BISON TRISO Modeling Advancements and Validation to AGR-1 Data

BISON is a finite element-based nuclear fuel performance code. Among its unique characteristics are its ability to model 1D, 2D, and 3D geometries and its applicability to a wide variety of nuclear fuels. For the last eight years, BISON has included a beginning capability to model tri-structural isotropic (TRISO) fuel. Recently, interest in TRISO fuel has grown, and a significant effort has been made to improve BISON’s capabilities in this area. Capability development has occurred for each material present in TRISO fuel particles: the buffer, inner pyrolytic carbon, silicon carbide, and outer pyrolytic carbon layers, as well as the fuel kernel. New elastic, creep, swelling, thermal expansion, thermal conductivity, and fission gas release (FGR) models are available. New models for the graphite matrix are also now available. Another important addition is the ability to perform statistical failure analysis of large samples of fuel particles. This new capability, which continues to grow, enables evaluation of failure due to pressure or crack formation by analyzing many thousands of particles. This enables realistic calculations of fission product release from the many particles in a TRISO-fueled reactor. These capabilities were checked via regression and verification tests. A large number of code benchmarking problems were also run, showing that BISON’s results closely match those of other software tools. Finally, a significant validation effort was completed in which fission product release, measured as part of the AGR-1 capsule experiments, was compared to BISON outputs. BISON outputs compared very well to the experimental data and to PARFUME results. Interest in BISON’s TRISO capabilities is growing, with the U.S. Nuclear Regulatory Commission (NRC) and Westinghouse Electric Company receiving training during the past year. Multiple other entities have expressed interest in or are actively using BISON. Kairos Power, LLC, has a strong partnership with Idaho National Laboratory (INL) regarding the use of BISON for TRISO analysis. While its capabilities still continue to grow, BISON has already become a powerful tool for TRISO analysis.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
NASA NTRS1992

Model reduction in a subset of the original states

A model reduction method is investigated to provide a smaller structural dynamic model for subsequent structural control design. A structural dynamic model is assumed to be derived from finite element analysis. It is first converted into the state space form, and is further reduced by the internal balancing method. Through the co-ordinate transformation derived from the states that are deleted during reduction, the reduced model is finally expressed with the states that are members of the original states. Therefore, the states in the final reduced model represent the degrees of freedom of the nodes that are selected by the designer. The procedure provides a more practical implementation of model reduction for applications in which specific nodes, such as sensor and/or actuator attachment points, are to be retained in the reduced model. Thus, it ensures that the reduced model is under the same input and output condition as the original physical model. The procedure is applied to two simple examples and comparisons are made between the full and reduced order models. The method can be applied to a linear, continuous and time-invariant model of structural dynamics with nonproportional viscous damping.

Yae, K. H.↗
NASA NTRS1993

Numerical simulation using vorticity-vector potential formulation

An accurate and efficient computational method is needed for three-dimensional incompressible viscous flows in engineering applications. On solving the turbulent shear flows directly or using the subgrid scale model, it is indispensable to resolve the small scale fluid motions as well as the large scale motions. From this point of view, the pseudo-spectral method is used so far as the computational method. However, the finite difference or the finite element methods are widely applied for computing the flow with practical importance since these methods are easily applied to the flows with complex geometric configurations. However, there exist several problems in applying the finite difference method to direct and large eddy simulations. Accuracy is one of most important problems. This point was already addressed by the present author on the direct simulations on the instability of the plane Poiseuille flow and also on the transition to turbulence. In order to obtain high efficiency, the multi-grid Poisson solver is combined with the higher-order, accurate finite difference method. The formulation method is also one of the most important problems in applying the finite difference method to the incompressible turbulent flows. The three-dimensional Navier-Stokes equations have been solved so far in the primitive variables formulation. One of the major difficulties of this method is the rigorous satisfaction of the equation of continuity. In general, the staggered grid is used for the satisfaction of the solenoidal condition for the velocity field at the wall boundary. However, the velocity field satisfies the equation of continuity automatically in the vorticity-vector potential formulation. From this point of view, the vorticity-vector potential method was extended to the generalized coordinate system. In the present article, we adopt the vorticity-vector potential formulation, the generalized coordinate system, and the 4th-order accurate difference method as the computational method. We present the computational method and apply the present method to computations of flows in a square cavity at large Reynolds number in order to investigate its effectiveness.

Tokunaga, Hiroshi↗
DOE OSTI2020

Development and Validation of SAM Multi-dimensional Flow Model for Thermal Mixing and Stratification Modeling

Thermal mixing and stratification in large pools or enclosures are very important phenomena that are critical to nuclear reactor safety. Because of the wide ranges of time and length scales associated with such phenomena, accurate modeling and simulation of thermal mixing and stratification remain as the key unresolved, challenging problems for reactor transient analyses. In traditional system analysis codes, simplified zero-dimensional (0-D) models are widely used for their high numerical efficiency, but they generally suffer from very limited prediction accuracies or range of applicability. Like traditional system analysis codes, the current version of the SAM code has implemented such simplified 0-D and one-dimensional mixing models. On the other hand, high-resolution Computational Fluid Dynamics (CFD) tools are often used to model complex thermal mixing and stratification phenomena. They are, however, generally numerically expensive, and they require large amounts of computational resources. It is therefore desirable to implement advanced and efficient thermal mixing and stratification modeling capabilities embedded in a system analysis code. This approach will improve the accuracy of reactor safety analyses when thermal mixing and stratification are involved, and also avoid using the large computational resources needed for high-resolution CFD analysis. Currently, with the support of the U.S. DOE Office of Nuclear Energy’s Nuclear Energy Advanced Modeling and Simulation program, an effort has been launched to develop and implement a multi-dimensional flow model in the system analysis code SAM, and demonstrate its applications to model thermal mixing and stratification phenomena in large enclosures. The main outcomes of this research and development activity are summarized in this report, which presents an attempt to include a built-in advanced multi-dimensional flow model in a system analysis code with the focus on overcoming the simulation challenges of thermal mixing and stratification phenomena. In this report, we start with the introduction of existing SAM code capabilities to simulate thermal mixing and stratification phenomena, which is followed by a short summary of the multi-dimensional model implemented in the SAM code, including both the physical model and the Finite Element Method code implementation. In this study, two options were implemented in the SAM code to model turbulent flows: a relatively simple built-in turbulence model and an interface to accept externally computed turbulent viscosities (e.g., from a high- resolution CFD simulation). Code validation studies on this newly added capability were then carried out to compare SAM simulation results with experimental data from the SUPERCAVNA facility, which was designed to study the complex flow recirculation and thermal stratification phenomena relevant to sodium fast reactor designs. In this study, one transient and two steady-state test cases were used for code validation. Different approaches have been used to model the complex turbulence flow fields in the SUPERCAVNA facility. A highly simplified zero-equation turbulence model was first used, but it was determined that it is too simple to capture the complex turbulence flow fields in these test cases. Subsequently, the code validation continued with the use of turbulent viscosity data from high-resolution STAR-CCM+ CFD simulations to improve the accuracy of the results. Using this approach, the SAM simulation results showed very good agreement with both the SUPERCAVNA experimental data and STAR-CCM+ simulation results. In this report, we demonstrate the development, implementation, and successful validation of a multi-dimensional flow model in the SAM code, which aims to improve the simulation accuracy for complex thermal mixing and stratification phenomena. Lessons have also been learned, including that in cases where the flow fields are not well predicted by the zero-equation model, the iinput of turbulent viscosities from an external source can enhance the overall predictive capabilities needed to accurately capture complex thermal-hydraulic phenomena. Therefore, future research will be needed to further improve the code’s capabilities, such as by developing a more efficient and robust approach to capture the turbulence effects in the SAM code.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
NASA NTRS1987

Further generalization of an equivalent plate representation for aircraft structural analysis

Recent developments from a continuing effort to provide an equivalent plate representation for aircraft structural analysis are described. Previous work provided an equivalent plate analysis formulation that is capable of modeling aircraft wing structures with a general planform such as cranked wing boxes. However, the modeling is restricted to representing wing boxes having symmetric cross sections. Further developments, which are described, allow modeling of wing cross sections having asymmetries that can arise from airfoil camber or from thicknesses being different in the upper and lower cover skins. An implementation of thermal loadings, which are described as temperature distributions over the planform of the cover skins, has been included. Spring supports have been added to provide for a more general set of boundary conditions. Numerical results are presented to assess the effect of wing camber on the static and dynamic response of an example wing structure under pressure and thermal loading. These results are compared with results from a finite element analysis program to indicate how well a cambered wing box can be represented with an equivalent plate formulation.

Giles, Gary L.↗
DOE OSTI2025

A simple introduction to the SiMPL method for density-based topology optimization

We introduce a novel method for solving density-based topology optimization problems: Sigmoidal Mirror descent with a Projected Latent variable (SiMPL). The SiMPL method (pronounced as “the simple method”) optimizes a design using only first-order derivative information of the objective function. The bound constraints on the density field are enforced with the help of the (negative) Fermi–Dirac entropy, which is also used to define a non-symmetric distance function called a Bregman divergence on the set of admissible designs. This Bregman divergence leads to a simple update rule that is further simplified with the help of a so-called latent variable. Because the SiMPL method involves discretizing the latent variable, it produces a sequence of pointwise-feasible iterates, even when high-order finite elements are used in the discretization. Numerical experiments demonstrate that the method outperforms other popular first-order optimization algorithms. In conclusion, to outline the general applicability of the technique, we include examples with (self-load) compliance minimization and compliant mechanism optimization problems.

Calculus of Variations and Optimization↗
DOE OSTI2021

A solution framework for linear PDE-constrained mixed-integer problems

Abstract We present a general numerical solution method for control problems with state variables defined by a linear PDE over a finite set of binary or continuous control variables. We show empirically that a naive approach that applies a numerical discretization scheme to the PDEs to derive constraints for a mixed-integer linear program (MILP) leads to systems that are too large to be solved with state-of-the-art solvers for MILPs, especially if we desire an accurate approximation of the state variables. Our framework comprises two techniques to mitigate the rise of computation times with increasing discretization level: First, the linear system is solved for a basis of the control space in a preprocessing step. Second, certain constraints are just imposed on demand via the IBM ILOG CPLEX feature of a lazy constraint callback. These techniques are compared with an approach where the relations obtained by the discretization of the continuous constraints are directly included in the MILP. We demonstrate our approach on two examples: modeling of the spread of wildfire and the mitigation of water contamination. In both examples the computational results demonstrate that the solution time is significantly reduced by our methods. In particular, the dependence of the computation time on the size of the spatial discretization of the PDE is significantly reduced.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1987

Further generalization of an equivalent plate representation for aircraft structural analysis

Recent developments from a continuing effort to provide an equivalent plate representation for aircraft structural analysis are described. Previous work provided an equivalent plate analysis formulation that is capable of modeling aircraft wing structures with a general planform such as cranked wing boxes. However, the modeling is restricted to representing wing boxes having symmetric cross sections. Further developments, which are described in this paper, allow modeling of wing cross section having asymmetries that can arise from airfoil camber or from thicknesses being different in the upper and lower cover skins. An implementation of thermal loadings, which are described as temperature distributions over the planform of the cover skins, has been included. Spring supports have been added to provide for a more general set of boundary conditions. Numerical results are presented to assess the effect of wing camber on the static and dynamic response of an example wing structure under pressure and thermal loading. These results are compared with results from a finite element analysis program to indicate how well a cambered wing box can be represented with an equivalent plate formulation.

Giles, Gary L.↗
NASA NTRS1992

Development of 3D electromagnetic modeling tools for airborne vehicles

The main goal of this project is to develop methodologies for scattering by airborne composite vehicles. Although our primary focus continues to be the development of a general purpose code for analyzing the entire structure as a single unit, a number of other tasks are also pursued in parallel with this effort. These tasks are important in testing the overall approach and in developing suitable models for materials coatings, junctions and, more generally, in assessing the effectiveness of the various parts comprising the final code. Here, we briefly discuss our progress on the five different tasks which were pursued during this period. Our progress on each of these tasks is described in the detailed reports (listed at the end of this report) and the memoranda included. The first task described below is, of course, the core of this project and deals with the development of the overall code. Undoubtedly, it is the outcome of the research which was funded by NASA-Ames and the Navy over the past three years. During this year we developed the first finite element code for scattering by structures of arbitrary shape and composition. The code employs a new absorbing boundary condition which allows termination of the finite element mesh only 0.3 lambda from the outer surface of the target. This leads to a remarkable reduction of the mesh size and is a unique feature of the code. Other unique features of this code include capabilities to model resistive sheets, impedance sheets and anisotropic materials. This last capability is the latest feature of the code and is still under development. The code has been extensively validated for a number of composite geometries and some examples are given. The validation of the code is still in progress for anisotropic and larger non-metallic geometries and cavities. The developed finite element code is based on a Galerkin's formulation and employs edge-based tetrahedral elements for discretizing the dielectric sections and the region between the target and the outer mesh termination boundary (ATB). This boundary is placed in conformity with the target's outer surface, thus resulting in additional reduction of the unknown count.

Volakis, John L.↗
NASA NTRS1993

A study of fiber volume fraction effects in notched unidirectional SCS-6/Ti-15V-3Cr-3Al-3Sn composite

Notched unidirectional SCS-6/Ti-15-3 composite of three different fiber volume fractions (vf = 0.15, 0.37, and 0.41) was investigated for various room temperature microstructural and material properties including: fatigue crack initiation, fatigue crack growth, and fracture toughness. While the matrix hardness is similar for all fiber volume fractions, the fiber/matrix interfacial shear strength and matrix residual stress increases with fiber volume fraction. The composite fatigue crack initiation stress is shown to be matrix controlled and occurs when the net maximum matrix stress approaches the endurance limit stress of the matrix. A model is presented which includes residual stresses and presents the composite initiation stress as a function of fiber volume fraction. This model predicts a maximum composite initiation stress at vf approximately 0.15 which agrees with the experimental data. The applied composite stress levels were increased as necessary for continued crack growth. The applied Delta(K) values at crack arrest increase with fiber volume fraction by an amount better approximated using an energy based formulation rather than when scaled linear with modulus. After crack arrest, the crack growth rate exponents for vf37 and vf41 were much lower and toughness much higher, when compared to the unreinforced matrix, because of the bridged region which parades with the propagating fatigue crack. However, the vf15 material exhibited a higher crack growth rate exponent and lower toughness than the unreinforced matrix because once the bridged fibers nearest the crack mouth broke, the stress redistribution broke all bridged fibers, leaving an unbridged crack. Degraded, unbridged behavior is modeled using the residual stress state in the matrix ahead of the crack tip. Plastic zone sizes were directly measured using a metallographic technique and allow prediction of an effective matrix stress intensity which agrees with the fiber pressure model if residual stresses are considered. The sophisticated macro/micro finite element models of the 0.15 and 0.37 fiber volume fractions presented show good agreement with experimental data and the fiber pressure model when an estimated effective fiber/matrix debond length is used.

Covey, Steven J.↗
NASA NTRS1997

The International Space Station Assembly on Schedule

As engineers continue to prepare the International Space Station (ISS) for in-orbit assembly in the year 2002, ANSYS software has proven instrumental in resolving a structural problem in the project's two primary station modules -- Nodes 1 and 2. Proof pressure tests performed in May revealed "low temperature, post-yield creep" in some of the Nodes' gussets, which were designed to reinforce ports for loads from station keeping and reboost motion of the entire space station. An extensive effort was undertaken to characterize the creep behavior of the 2219-T851 aluminum forging material from which the gussets were made. Engineers at Sverdrup Technology, Inc. (Huntsville, AL) were responsible for conducting a combined elastic-plastic-creep analysis of the gussets to determine the amount of residual compressive stress which existed in the gussets following the proof pressure tests, and to determine the stress-strain history in the gussets while on-orbit. Boeing, NASA's Space Station prime contractor, supplied the Finite Element Analysis (FEA) model geometry and developed the creep equations from the experimental data taken by NASA's Marshall Space Flight Center and Langley Research Center. The goal of this effort was to implement the uniaxial creep equations into a three dimensional finite element program, and to determine analytically whether or not the creep was something that the space station program could live with. The objective was to show analytically that either the creep rate was at an acceptable level, or that the node module had to be modified to lower the stress levels to where creep did not occur. The elastic-plastic-creep analysis was performed using the ANSYS finite element program of ANSYS, Inc. (Houston, PA). The analysis revealed that the gussets encountered a compressive stress of approximately 30,000 pounds per square inch (psi) when unloaded. This compressive residual stress significantly lowered the maximum tension stress in the gussets which decreased the creep strain rate. The analysis also showed that the gussets would not experience a great deal of creep from future pressure tests if braces or struts proposed by Boeing were installed to redistribute stress away from them. Subsequent analysis of on-orbit station keeping and reboost loads convinced Boeing that the gussets should be removed altogether.

Source record↗
NASA NTRS1975

On a numerical sufficiency test for monotonic convergence of finite element models

Finite element analyses characterized by monotonic convergence include the discipline for meaningful measurements of convergence rate and consequently economical extrapolation. Few proposers of element models guarantee monotonic convergence for their elements. Thus, a need exists for an automatic test to classify available element models. This paper describes such a test - a test can be performed using a digital computer to guarantee that a particular element model imbues monotonicity. It describes the test and its basis. It examines seven element models for a rectangular membrane to illustrate the value of the tests. Besides confirming results already known, the application yields new data. It 'proves' monotonicity for two improved models, defines the range of element proportions for which another element can be guaranteed to exhibit monotonicity, and suggests that another element is deficient. In the special case of absolutely convergent membrane displacement models, proof of monotonicity is a necessary and sufficient condition to insure that upper bound estimates of strain energy are developed. Accordingly, the test furnishes a proof of bound solutions independently of requirements on displacement continuity the element basis may or may not satisfy.

Melosh, R. J.↗
DOE OSTI2021

VERA-Grizzly Ex-Core Calculations: Watts Bar Unit 1 Cycles 1-2

The critical structures that comprise light-water reactor (LWR) nuclear power plants are subjected to operating environments that can challenge their integrity. Structures in close proximity to the reactor core, such as the reactor pressure vessel (RPV) and the biological shield wall, are subjected to high levels of radiation emanating from the core, as well as elevated temperatures. As the US fleet of operating LWRs ages, the effects of these operating environments on the integrity of these structures must be considered to ensure their continued safe operation. Extending the lifetime of commercial reactors and maintaining the aging reactor fleet require accurate prediction of the exposure of ex-core components to neutron and photon radiation. In particular, concrete degradation studies must be performed to evaluate the safety and long-term operation of reactors with lifetime extensions. The concrete reactor bioshield is important for providing radiological protection during operation and must last for the entire lifetime of the reactor. Recent interest in lifetime extensions furthers the need to accurately simulate concrete material degradation in the reactor bioshield. As a result of this need, the Nuclear Energy Advanced Modeling and Simulation (NEAMS) program has funded this study to couple its tools, Virtual Environment for Reactor Applications (VERA) and Grizzly. VERA allows users to set up models to calculate time-dependent and fully coupled solutions (with thermal feedback) for ex-core quantities of interest such as vessel and coupon fluence and detector responses for multiple statepoints and cycles. Grizzly is a finite-element application based on the Multiphysics Object Oriented Simulation Environment (MOOSE) framework that is used to enable aging materials calculations. This report highlights the work performed to calculate the fluence in the vessel and concrete for Watts Bar Nuclear Plant Unit 1 (WBN1) Cycles 1 and 2. The fluences obtained from VERA were successfully transferred to Grizzly using a Python script. Four simulations were run with Grizzly: (1) the Mazars model with the initial Young’s modulus being the instantaneous modulus, (2) the Mazars model with the initial Young’s modulus being the delayed modulus, (3) the Mazars model with the initial Young’s modulus being the delayed modulus with the addition of the effects of micro-damage caused by irradiation, and (4) the Mazars model with the initial Young’s modulus being the instantaneous modulus, and with the addition of micro-damage and creep. Details regarding the methods used to obtain the fluence and the statistical errors associated with the VERA Monte Carlo Shift calculations are discussed in greater detail in this report. The results obtained from the four Grizzly models are also presented in this report.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
NASA NTRS1986

Correlation of data on strain accumulation adjacent to the San Andreas Fault with available models

Theoretical and numerical studies of deformation on strike slip faults were performed and the results applied to geodetic observations performed in the vicinity of the San Andreas Fault in California. The initial efforts were devoted to an extensive series of finite element calculations of the deformation associated with cyclic displacements on a strike-slip fault. Measurements of strain accumulation adjacent to the San Andreas Fault indicate that the zone of strain accumulation extends only a few tens of kilometers away from the fault. There is a concern about the tendency to make geodetic observations along the line to the source. This technique has serious problems for strike slip faults since the vector velocity is also along the fault. Use of a series of stations lying perpendicular to the fault whose positions are measured relative to a reference station are suggested to correct the problem. The complexity of faulting adjacent to the San Andreas Fault indicated that the homogeneous elastic and viscoelastic approach to deformation had serious limitations. These limitation led to the proposal of an approach that assumes a fault is composed of a distribution of asperities and barriers on all scales. Thus, an earthquake on a fault is treated as a failure of a fractal tree. Work continued on the development of a fractal based model for deformation in the western United States. In order to better understand the distribution of seismicity on the San Andreas Fault system a fractal analog was developed. The fractal concept also provides a means of testing whether clustering in time or space is a scale-invariant process.

Turcotte, Donald L.↗
DOE OSTI2024

Vertical z-axis discontinuous carbon fibers for improved lightning strike performance of continuous fiber-reinforced polymer composites

Effective lightning strike protection for critical aerospace and wind applications requires high electrical conductivity to dissipate current efficiently. However, polymer matrix composites face a challenge due to their inherently insulating nature. While conventional carbon fiber-reinforced composites (CFRP) exhibit electrical conductivity in the planar direction, achieving through-thickness conductivity remains an ongoing challenge. In this work, we have undertaken the fabrication of CFRP interleaved with vertically oriented carbon fibers (Z-fiber) to impart higher electrical conductivity along the thickness direction. Two Z-fiber composite variations are prepared: Z-1 with a single layer of Z-fiber and Z-5 with five interleaved layers and compared with no Z-fiber layer (Z-0) composite. The composite panels were subjected to lab-scale lightning strike tests with a current magnitude of 100 kA. To emulate real-world service conditions, an aerospace-grade paint coating was applied to the composite laminates. Comparative analysis shows Z-1 reduces damage diameter to ∼22 mm compared to Z-0 (∼26 mm), while Z-5 exhibits the least damage (∼16.7 mm), confirmed by optical microscopy. Z-5 demonstrates nine times higher through-thickness electrical conductivity than Z-0, reducing electrical anisotropy substantially. Thermal-electric finite element damage modeling predicts surface damage within 6% of experimental values for both Z-0 and Z-5 composites. Flexural tests post-lightning reveal Z-5 retains 66% flexural strength and 86% modulus, significantly better than Z-0, which retains less than 40% for both properties. This study highlights the efficacy of Z-fiber composites in lightning strike protection, offering improved through-thickness conductivity and mechanical property retention.

36 MATERIALS SCIENCE↗
DOE OSTI2020

An adaptive space-time phase field formulation for dynamic fracture of brittle shells based on LR NURBS

Here, we present an adaptive space-time phase field formulation for dynamic fracture of brittle shells. Their deformation is characterized by the Kirchhoff–Love thin shell theory using a curvilinear surface description. All kinematical objects are defined on the shell’s mid-plane. The evolution equation for the phase field is determined by the minimization of an energy functional based on Griffith’s theory of brittle fracture. Membrane and bending contributions to the fracture process are modeled separately and a thickness integration is established for the latter. The coupled system consists of two nonlinear fourth-order PDEs and all quantities are defined on an evolving two-dimensional manifold. Since the weak form requires C 1 -continuity, isogeometric shape functions are used. The mesh is adaptively refined based on the phase field using Locally Refinable (LR) NURBS. Time is discretized based on a generalized-α method using adaptive time-stepping, and the discretized coupled system is solved with a monolithic Newton–Raphson scheme. Finally, the interaction between surface deformation and crack evolution is demonstrated by several numerical examples showing dynamic crack propagation and branching.

42 ENGINEERING↗
NASA NTRS1984

Natural convection in steady solidification - Finite element analysis of a two-phase Rayleigh-Benard problem

Galerkin finite-element approximations and Newton's method for solving free boundary problems are combined with computer-implemented techniques from nonlinear perturbation analysis to study solidification problems with natural convection in the melt. The Newton method gives rapid convergence to steady state velocity, temperature and pressure fields and melt-solid interface shapes, and forms the basis for algebraic methods for detecting multiple steady flows and assessing their stability. The power of this combination is demonstrated for a two-phase Rayleigh-Benard problem composed of melt and solid in a veritical cylinder with the thermal boundary conditions arranged so that a static melt with a flat melt-solid interface is always a solution. Multiple cellular flows bifurcating from the static state are detected and followed as Rayleigh number is varied. Changing the boundary conditions to approach those appropriate for the vertical Bridgman solidification system causes imperfections that eliminate the static state. The flow structure in the Bridgman system is related to those for the Rayleigh-Benard system by a continuous evolution of the boundary conditions.

Chang, C. J.↗
NASA NTRS1989

Hypervelocity atmospheric flight: Real gas flow fields

Flight in the atmosphere is examined from the viewpoint of including real gas phenomena in the flow field about a vehicle flying at hypervelocity. That is to say, the flow field is subject not only to compressible phenomena, but is dominated by energetic phenomena. There are several significant features of such a flow field. Spatially, its composition can vary by both chemical and elemental species. The equations which describe the flow field include equations of state and mass, species, elemental, and electric charge continuity; momentum; and energy equations. These are nonlinear, coupled, partial differential equations that have been reduced to a relatively compact set of equations in a self-consistent manner (which allows mass addition at the surface at a rate comparable to the free-stream mass flux). The equations and their inputs allow for transport of these quantities relative to the mass-average behavior of the flow field. Thus transport of mass by chemical, thermal, pressure, and forced diffusion; transport of momentum by viscosity; and transport of energy by conduction, chemical considerations, viscosity, and radiative transfer are included. The last of these complicate the set of equations by making the energy equations a partial integrodifferential equation. Each phenomenon is considered and represented mathematically by one or more developments. The coefficients which pertain are both thermodynamically and chemically dependent. Solutions of the equations are presented and discussed in considerable detail, with emphasis on severe energetic flow fields. Hypervelocity flight in low-density environments where gaseous reactions proceed at finite rates chemical nonequilibrium is considered, and some illustrations are presented. Finally, flight where the flow field may be out of equilibrium, both chemically and thermodynamically, is presented briefly.

Howe, John T.↗