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At least 73 records · Page 4

PAN AIR - A higher order panel method for predicting subsonic or supersonic linear potential flows about arbitrary configurations

PAN AIR is a computer program for predicting subsonic or supersonic linear potential flow about arbitrary configurations. It uses linear source and quadratic doublet strength distributions. These higher-order distributions have been implemented in a manner that greatly reduces the numerical stability problems that have plagued earlier attempts to make surface paneling methods work successfully for supersonic flow. PAN AIR's problem-solving capability, numerical approach, modeling features, and program architecture are described. Numerical results are presented for a variety of geometries at supersonic Mach numbers.

Carmichael, R. L.↗

Efficient computer algebra algorithms for polynomial matrices in control design

The theory of polynomial matrices plays a key role in the design and analysis of multi-input multi-output control and communications systems using frequency domain methods. Examples include coprime factorizations of transfer functions, cannonical realizations from matrix fraction descriptions, and the transfer function design of feedback compensators. Typically, such problems abstract in a natural way to the need to solve systems of Diophantine equations or systems of linear equations over polynomials. These and other problems involving polynomial matrices can in turn be reduced to polynomial matrix triangularization procedures, a result which is not surprising given the importance of matrix triangularization techniques in numerical linear algebra. Matrices with entries from a field and Gaussian elimination play a fundamental role in understanding the triangularization process. In the case of polynomial matrices, matrices with entries from a ring for which Gaussian elimination is not defined and triangularization is accomplished by what is quite properly called Euclidean elimination. Unfortunately, the numerical stability and sensitivity issues which accompany floating point approaches to Euclidean elimination are not very well understood. New algorithms are presented which circumvent entirely such numerical issues through the use of exact, symbolic methods in computer algebra. The use of such error-free algorithms guarantees that the results are accurate to within the precision of the model data--the best that can be hoped for. Care must be taken in the design of such algorithms due to the phenomenon of intermediate expressions swell.

Baras, J. S.↗

A New Approach for a Wider Class of Entropy Split Methods for Compressible Gas Dynamics and MHD

The high order entropy split methods of Sjögreen & Yee [1, 2] by entropy splitting of the compressible Euler (inviscid) flux derivatives for a thermally-perfect gas are based on Harten’s entropy function [3, 4, 5]. Their derivation takes advantage of the homogeneity property of Euler flux, symmetrizable Euler flux derivatives and energy-norm stability in conjunction with high order classical spatial central, DRP (dispersion relation-preserving) [6, 7, 8] or Padé (compact) spatial discretizations [9] with summation-by-parts (SBP) operators [10]. Our entropy split methods have been proven entropy conserving and stable [1, 11, 12]. Our proofs do not rely on a two-point numerical flux, but rather only a linear difference operator is required to derive these methods. To extend the entropy split method for the MHD, we used the Godunov symmetrizable non-conservative MHD form [12, 13, 14]. These high order entropy split methods not only preserve certain physical properties of the chosen governing equations but are also known to either improve numerical stability, and/or minimize aliasing errors in long time integration of turbulent flow computations without the aid of added numerical dissipation. In our previous published work, extensive error norm comparison with grid refinement was performed to show the high accuracy performance of these methods. These studies also showed how well the entropy split methods conserve the entropy, momentum and mass, and preserve the kinetic energy for long time integration of the various flows [1, 2, 12, 13, 14]. The objective of the present work is to use a new approach to obtain a wider class of entropy split methods consisting of a two-point numerical flux portion and a non-conservative portion in such a way that the homogeneity property of the compressible Euler flux is not required. For high order classical spatial central, DRP (dispersion relation-preserving) or Padé (compact) spatial discretizations, this new approach can be proven to be entropy conservative with conservative spatial dsicretizations while at the same time allowing a wider class of symmetrizable inviscid flux derivatives. We also use this generalization to derive an entropy split scheme that is entropy conserving for the equations of MHD without the homogeneity property using the Godunov symmetrizable ideal MHD formulation [15].

High Order Physical Preserving Methods↗

UDU/T/ covariance factorization for Kalman filtering

There has been strong motivation to produce numerically stable formulations of the Kalman filter algorithms because it has long been known that the original discrete-time Kalman formulas are numerically unreliable. Numerical instability can be avoided by propagating certain factors of the estimate error covariance matrix rather than the covariance matrix itself. This paper documents filter algorithms that correspond to the covariance factorization P = UDU(T), where U is a unit upper triangular matrix and D is diagonal. Emphasis is on computational efficiency and numerical stability, since these properties are of key importance in real-time filter applications. The history of square-root and U-D covariance filters is reviewed. Simple examples are given to illustrate the numerical inadequacy of the Kalman covariance filter algorithms; these examples show how factorization techniques can give improved computational reliability.

Thornton, C. L.↗

Analytical treatment of gas flows through multilayer insulation, project 1

A theoretical investigation of gas flow inside a multilayer insulation system was made for the case of the broadside pumping process. A set of simultaneous first-order differential equations for the temperature and pressure of the gas molecules through the perforations on the insulation layers. A modified Runge-Kutta method was used for numerical experiment. The numerical stability problem was also investigated. It was shown that when the relaxation time is less than the time period over which the gas properties change appreciably, the set of differential equations can be replaced by a set of algebraic equations for solution. Numerical examples were given and comparisons with experimental data were made.

Lin, J. T.↗

Analysis of gas flow through a multilayer insulation system.

A theoretical investigation of gas flow inside a multilayer insulation system has been made for the case of the broadside pumping process. A set of simultaneous first-order differential equations for the temperature and pressure of the gas mixture was obtained by considering the diffusion mechanism of the gas molecules through the perforations on the insulation layers. A modified Runge-Kutta method was used for numerical experiment. The numerical stability problem was investigated. It has been shown that when the relaxation time is small compared with the time period over which the gas properties change appreciably, the set of differential equations can be replaced by a set of algebraic equations for solution. Numerical examples were given and comparison with experimental data was made.

Lin, J. T.↗

Thermal engineering research

A theoretical investigation of gas flow inside a multilayer insulation system has been made for the case of the broadside pumping process. A set of simultaneous first-order differential equations for the temperature and pressure of the gas mixture was obtained by considering the diffusion mechanism of the gas molecules through the perforations on the insulation layers. A modified Runge-Kutta method was used for numerical experiment. The numerical stability problem was investigated. It has been shown that when the relaxation time is small compared with the time period over which the gas properties change appreciably, the set of differential equations can be replaced by a set of algebraic equations for solution. Numerical examples were given, and comparisons with experimental data were made.

Shih, C. C.↗

A numerical comparison of discrete Kalman filtering algorithms - An orbit determination case study

An improved Kalman filter algorithm based on a modified Givens matrix triangularization technique is proposed for solving a nonstationary discrete-time linear filtering problem. The proposed U-D covariance factorization filter uses orthogonal transformation technique; measurement and time updating of the U-D factors involve separate application of Gentleman's fast square-root-free Givens rotations. Numerical stability and accuracy of the algorithm are compared with those of the conventional and stabilized Kalman filters and the Potter-Schmidt square-root filter, by applying these techniques to a realistic planetary navigation problem (orbit determination for the Saturn approach phase of the Mariner Jupiter-Saturn Mission, 1977). The new algorithm is shown to combine the numerical precision of square root filtering with the efficiency of the original Kalman algorithm.

Thornton, C. L.↗

Externally pressurized gas-lubricated journal bearings with herringbone grooves - Load capacity and stability analysis.

A small eccentricity analysis was performed to predict load capacity and stability. Numerical results were obtained for a range of feeding parameter, pressure ratio, groove length and orifice recess volume for compressibility numbers from 0 to 50. These results were obtained from a digital computer program. Results showed that the addition of herringbone grooving to an externally pressurized bearing increases stability, but reduces load capacity at low compressibility numbers. A fully-grooved bearing is more stable than a partially-grooved bearing. Orifice recesses reduce stability, especially at high compressibility numbers.

Fleming, D. P.↗

Numerical studies of transverse curvature effects on transonic flow stability

A numerical study of transverse curvature effects on compressible flow temporal stability for transonic to low supersonic Mach numbers is presented for axisymmetric modes. The mean flows studied include a similar boundary-layer profile and a nonsimilar axisymmetric boundary-layer solution. The effect of neglecting curvature in the mean flow produces only small quantitative changes in the disturbance growth rate. For transonic Mach numbers (1-1.4) and aerodynamically relevant Reynolds numbers (5000-10,000 based on displacement thickness), the maximum growth rate is found to increase with curvature - the maximum occurring at a nondimensional radius (based on displacement thickness) between 30 and 100.

Macaraeg, M. G.↗

Mathematical Model of a Regenerative Fuel Cell for System Optimization

This thesis developed a system-level optimization model of a regenerative fuel cell (RFC) system for long-duration, off-world energy storage applications. Prior RFC design studies have typically been limited to reduced parameter sets and simplified constraints due to computational limitations relative to the number of relevant degrees of freedom. As a result, important nonlinear interactions between subsystems have not been fully captured. This work began to address that gap by developing a higher-fidelity, nonlinear optimization framework that incorporates a broader set of design variables and coupled constraints, enabling a multidimensional model that captures the coupled behavior of RFC subsystems and demonstrates the feasibility of applying optimization to such systems. An expanded system-level optimization approach was established that captures interactions between electrochemical performance, structural requirements, and storage design. This enabled a more comprehensive evaluation of trade-offs than conventional formulations. The model integrates four coupled subsystems: a fuel cell, an electrolyzer, reactant gas, and high-pressure storage tanks, and was formulated to accommodate a wide range of mission parameters, including operational time and required output power. It incorporates constraints on available solar array power, reactant mass balance between production and consumption, and pressure-dependent storage requirements. To enable reliable convergence, the optimization problem was reformulated to reduce dimensionality and improve numerical stability, with subsystem models organized for efficient evaluation. Problem dimensionality was reduced by consolidating lower-level design variables into higher-level representative quantities, and subsystem behavior was evaluated within the optimization loop. A multi-start initialization strategy was employed to mitigate sensitivity to local minima and improve solution quality, while nonlinear relationships were solved using robust numerical methods. The results showed that convergence was achieved across a range of required output power values. Specific energy reached a maximum at a critical mission power level, where the electrolyzer power matched the available solar input and operated near its voltage and current density limits. Beyond this point, further increases in required power resulted in less mass-efficient operation, increasing total system mass and reducing overall performance. The developed model represents an advancement in RFC system-level optimization by enabling analysis of a broader and more tightly coupled design space than previous considerations. While convergence behavior and computational cost remain challenges, the methods introduced improve solvability and allow inclusion of additional design variables with minimal loss of physical fidelity. However, the numerical results should not be interpreted as definitive design recommendations, as the model includes simplifying assumptions and omits several higher-order effects. Future work should extend this framework by incorporating additional subsystems and loss mechanisms, such as thermal management, parasitic power consumption, and reactant losses, to improve fidelity and ensure more representative design conclusions.

Electrochemistry↗

Numerical spatial marching techniques for estimating duct attenuation and source pressure profiles

A numerical method was developed that could predict the pressure distribution of a ducted source from far field pressure inputs. Using an initial value formulation, the two-dimensional homogeneous Helmholtz wave equation (no steady flow) was solved using explicit marching techniques. The Von Neumann method was used to develop relationships which describe how sound frequency and grid spacing effect numerical stability. At the present time, stability considerations limit the approach to high frequency sound. Sample calculations for both hard and soft wall ducts compare favorably to known boundary value solutions. In addition, assuming that reflections in the duct are small, this initial value approach was successfully used to determine the attenuation of a straight soft wall duct. Compared to conventional finite difference or finite element boundary value approaches, the numerical marching technique is orders of magnitude shorter in computation time and required computer storage and can be easily employed in problems involving high frequency sound.

Baumeister, K. J.↗

Numerical spatial marching techniques for estimating duct attenuation and source pressure profiles

A numerical method is developed that could predict the pressure distribution of a ducted source from far-field pressure inputs. Using an initial value formulation, the two-dimensional homogeneous Helmholtz wave equation (no steady flow) is solved using explicit marching techniques. The Von Neumann method is used to develop relationships which describe how sound frequency and grid spacing effect numerical stability. At the present time, stability considerations limit the approach to high frequency sound. Sample calculations for both hard and soft wall ducts compare favorably to known boundary value solutions. In addition, assuming that reflections in the duct are small, this initial value approach is successfully used to determine the attenuation of a straight soft wall duct. Compared to conventional finite difference or finite element boundary value approaches, the numerical marching technique is orders of magnitude shorter in computation time and required computer storage and can be easily employed in problems involving high frequency sound.

Baumeister, K. J.↗

Euler solvers for transonic applications

The 1980s may well be called the Euler era of applied aerodynamics. Computer codes based on discrete approximations of the Euler equations are now routinely used to obtain solutions of transonic flow problems in which the effects of entropy and vorticity production are significant. Such codes can even predict separation from a sharp edge, owing to the inclusion of artificial dissipation, intended to lend numerical stability to the calculation but at the same time enforcing the Kutta condition. One effect not correctly predictable by Euler codes is the separation from a smooth surface, and neither is viscous drag; for these some form of the Navier-Stokes equation is needed. It, therefore, comes as no surprise to observe that the Navier-Stokes has already begun before Euler solutions were fully exploited. Moreover, most numerical developments for the Euler equations are now constrained by the requirement that the techniques introduced, notably artificial dissipation, must not interfere with the new physics added when going from an Euler to a full Navier-Stokes approximation. In order to appreciate the contributions of Euler solvers to the understanding of transonic aerodynamics, it is useful to review the components of these computational tools. Space discretization, time- or pseudo-time marching and boundary procedures, the essential constituents are discussed. The subject of grid generation and grid adaptation to the solution are touched upon only where relevant. A list of unanswered questions and an outlook for the future are covered.

Vanleer, Bram↗

A Transient Hydrodynamic Model of Screen Channel Liquid Acquisition Devices for In-Space Cryogenic Propellant Management

Screen channel liquid acquisition devices (LADs) will play a crucial role in future deep space travel. It is essential that vapor-free delivery of propellants during tank-to-tank transfer is ensured to maximize yield from storage tanks and prevent potential combustion instabilities. The screen channel LAD utilizes a fine screen wire mesh that can separate phases in a low Bond number (i.e. microgravity) environment using surface tension forces. This study presents the development and verification of a new model for transient screen compliance, one of the influential factors for screen channel LAD design. Screen compliance is crucial during LAD channel outflow transients because the slight deflection of the screen can provide needed mass to satisfy rapid outflow demands and reduce the pressure difference across the screen. The model is successfully verified against CFD simulations. In addition, the characteristic speed for the governing screen compliance equations is derived which allows for numerical stability criteria to be established. As shown in this study, the transient maximum pressure difference across the screen can greatly exceed the steady state maximum pressure difference across the screen in many cases.

Hydrodynamics Simulations↗

Magnetohydrodynamic instabilities in coronal arcades

The MHD stability of coronal arcades is studied with and without a detached flux using a two-dimensional linear MHD stability numerical model. Two-dimensional magnetohydrostatic equilibria with and without gravity are computed. A coronal arcade without a detached flux tube is found to be stable for any magnetic shear and for any longitudinal mode. On the other hand, an arcade with a detached flux tube is unstable for perturbations with nonzero longitudinal wave number n and the instability mode structure and growth rate vary depending on the field twist and n. All the equilibria studied are stable to n = 0 perturbations. Gravity has a stabilizing effect on the equilibria. As the ratio lambda of the standard arcade width to the gravitational scale height increases from zero to 0.2, the m = 0 transverse mode growth rate decreases, but high m modes are stabilized. The equilibria studied here are completely stabilized for lambda larger than 0.33.

An, Chang-Hyuk↗

Pterodactyl: Aerodynamic and Aerothermal Modeling for a Symmetric Deployable Earth Entry Vehicle with Flaps

NASA’s Pterodactyl project has investigated a deployable atmospheric entry vehicle integrated with a flap control system that provides precision targeting during reentry. The control system consists of eight flaps mounted at the edge of a heatshield that can deflect in and out of the flow. An aerodynamic and aerothermodynamic analysis process was developed for preliminary vehicle design and aerodynamic database generation using engineering and CFD tools with varying levels of fidelity. The objective of this analysis was to: 1) understand the inherent aerodynamics, 2) provide an aerodynamics database for stability and control analysis, and 3) provide qualitative and quantitative aeroheating analysis for Thermal Protection System modeling of the flaps. A high fidelity Euler code, Cart3D, was used to resolve complex flow features such as secondary shocks and shock impingement. A wide range of supersonic (Mach 2) and hypersonic Mach numbers (up to Mach 40) were tested with an Earth atmosphere model. A process was developed to utilize the adaptive volume mesh generator utility of the perfect gas model of Cart3D to create meshes with high cell efficiency and numerical stability prior to running a 2nd order accurate solution with a real gas model. High-fidelity aerothermal CFD simulations were performed using US3D to further improve the aerothermal analysis on hypersonic flow around a complex entry vehicle shape including viscosity, chemical reactions of air species, vibrational energy, and catalytic surface reactions. In this process, it was found that the flap control system provided multi-axis control that can be utilized for entry precision targeting. Additionally, the Pterodactyl vehicle can achieve up to a trim L/D of 0.2. Finally, the increased fidelity of the aerothermal heating environments revealed that the shear stress contributes to increasing the heating on the flaps.

Deployable Entry Vehicle↗