SEARCH · Engineering Papers

Results for “Boundary value problem”

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.

SourceResearch connectionFrom yearThrough year

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 1,135 records · Page 63

All sources NASA NTRS DOE OSTI

NASA NTRS2004

On Nonlinear Combustion Instability in Liquid Propellant Rocket Motors

All liquid propellant rocket instability calculations in current use have limited value in the predictive sense and serve mainly as a correlating framework for the available data sets. The well-known n-t model first introduced by Crocco and Cheng in 1956 is still used as the primary analytical tool of this type. A multitude of attempts to establish practical analytical methods have achieved only limited success. These methods usually produce only stability boundary maps that are of little use in making critical design decisions in new motor development programs. Recent progress in understanding the mechanisms of combustion instability in solid propellant rockets"' provides a firm foundation for a new approach to prediction, diagnosis, and correction of the closely related problems in liquid motor instability. For predictive tools to be useful in the motor design process, they must have the capability to accurately determine: 1) time evolution of the pressure oscillations and limit amplitude, 2) critical triggering pulse amplitude, and 3) unsteady heat transfer rates at injector surfaces and chamber walls. The method described in this paper relates these critical motor characteristics directly to system design parameters. Inclusion of mechanisms such as wave steepening, vorticity production and transport, and unsteady detonation wave phenomena greatly enhance the representation of key features of motor chamber oscillatory behavior. The basic theoretical model is described and preliminary computations are compared to experimental data. A plan to develop the new predictive method into a comprehensive analysis tool is also described.

Sims, J. D.↗

NASA NTRS1989

Automatic control of cryogenic wind tunnels

Inadequate Reynolds number similarity in testing of scaled models affects the quality of aerodynamic data from wind tunnels. This is due to scale effects of boundary-layer shock wave interaction which is likely to be severe at transonic speeds. The idea of operation of wind tunnels using test gas cooled to cryogenic temperatures has yielded a quantrum jump in the ability to realize full scale Reynolds number flow similarity in small transonic tunnels. In such tunnels, the basic flow control problem consists of obtaining and maintaining the desired test section flow parameters. Mach number, Reynolds number, and dynamic pressure are the three flow parameters that are usually required to be kept constant during the period of model aerodynamic data acquisition. The series of activity involved in modeling, control law development, mechanization of the control laws on a microcomputer, and the performance of a globally stable automatic control system for the 0.3-m Transonic Cryogenic Tunnel (TCT) are discussed. A lumped multi-variable nonlinear dynamic model of the cryogenic tunnel, generation of a set of linear control laws for small perturbation, and nonlinear control strategy for large set point changes including tunnel trajectory control are described. The details of mechanization of the control laws on a 16 bit microcomputer system, the software features, operator interface, the display and safety are discussed. The controller is shown to provide globally stable and reliable temperature control to + or - 0.2 K, pressure to + or - 0.07 psi and Mach number to + or - 0.002 of the set point value. This performance is obtained both during large set point commands as for a tunnel cooldown, and during aerodynamic data acquisition with intrusive activity like geometrical changes in the test section such as angle of attack changes, drag rake movements, wall adaptation and sidewall boundary-layer removal. Feasibility of the use of an automatic Reynolds number control mode with fixed Mach number control is demonstrated.

Balakrishna, S.↗

NASA NTRS1991

The effects of suction on the nonlinear stability of the three-dimensional boundary layer above a rotating disc

There exist two types of stationary instability of the flow over a rotating disc corresponding to the upper branch, inviscid mode and the lower branch mode, which has a triple deck structure, of the neutral stability curve. A theoretical study of the linear problem and an account of the weakly nonlinear properties of the lower branch modes have been undertaken by Hall and MacKerrell respectively. Motivated by recent reports of experimental sightings of the lower branch mode and an examination of the role of suction on the linear stability properties of the flow here, the effects are studied of suction on the nonlinear disturbance described by MacKerrell. The additional analysis required in order to incorporate suction is relatively straightforward and enables the derivation of an amplitude equation which describes the evolution of the mode. For each value of the suction, a threshold value of the disturbance amplitude is obtained; modes of size greater than this threshold grow without limit as they develop away from the point of neutral stability.

Bassom, Andrew P.↗

NASA NTRS1975

Nonlinear vibration of cylindrical shells

The large amplitude vibration of a thin-walled cylindrical shell is analyzed. A perturbation method is used to solve the steady-state forced vibration problem. The simply-supported boundary conditions and the circumferential periodicity condition are satisfied. The resulting solution indicates that in addition to the fundamental mode, the response contains asymmetric modes as well as axisymmetric modes with the frequency twice that of the fundamental mode. Vibrations involving a single driven mode response are investigated. The results indicate that the nonlinearity is either softening or hardening depending on the mode. The vibrations involving both a driven mode and a companion mode are also investigated. An experimental investigation is conducted, and the results are in qualitative agreement with the theory. 'Nonstationary' response is detected at some frequencies for large amplitude response in which the amplitude drifts from one value to another. Various nonlinear phenomena are observed and comparisons with the theoretical results are made.

Chen, J. C.↗

NASA NTRS1999

Electrical Impact of SiC Structural Crystal Defects on High Electric Field Devices

Commercial epilayers are known to contain a variety of crystallographic imperfections. including micropipes, closed core screw dislocations. low-angle boundaries, basal plane dislocations, heteropolytypic inclusions, and non-ideal surface features like step bunching and pits. This paper reviews the limited present understanding of the operational impact of various crystal defects on SiC electrical devices. Aside from micropipes and triangular inclusions whose densities have been shrinking towards manageably small values in recent years, many of these defects appear to have little adverse operational and/or yield impact on SiC-based sensors, high-frequency RF, and signal conditioning electronics. However high-power switching devices used in power management and distribution circuits have historically (in silicon experience) demanded the highest material quality for prolonged safe operation, and are thus more susceptible to operational reliability problems that arise from electrical property nonuniformities likely to occur at extended crystal defects. A particular emphasis is placed on the impact of closed-core screw dislocations on high-power switching devices, because these difficult to observe defects are present in densities of thousands per cm,in commercial SiC epilayers. and their reduction to acceptable levels seems the most problematic at the present time.

Neudeck, Philip G.↗

NASA NTRS1953

Method for Calculation of Laminar Heat Transfer in Air Flow Around Cylinders of Arbitrary Cross Section (including Large Temperature Differences and Transpiration Cooling)

The solution of heat-transfer problems has become vital for many aeronautical applications. The shapes of objects to be cooled can often be approximated by cylinders of various cross sections with flow normal to the axis as, for instance heat transfer on gas-turbine blades and on air foils heated for deicing purposes. A laminar region always exists near the stagnation point of such objects. A method previously presented by E. R. G. Eckert permits the calculation of local heat transfer around the periphery of cylinders of arbitrary cross section in the laminar region for flow of a fluid with constant property values with an accuracy sufficient for engineering purposes. The method is based on exact solutions of the boundary-layer equations for incompressible wedge-type flow and on the postulate that at any point on the cylinder the boundary-layer growth is the same as that on a wedge with comparable flow conditions. This method is extended herein to take into account the influence of large temperature differences between the cylinder wall and the flow as well as the influence of transpiration cooling when the same medium as the outside flow is used as coolant.

Eckert, E R↗

NASA NTRSDate not supplied

Evaluating Subgrid-Scale Properties of Low Clouds over the Beaufort Sea in Arctic System Reanalysis using ARISE Airborne In Situ Observations

Arctic low clouds influence the evolution of the Arctic system through their effects on radiative fluxes, boundary layer mixing, stability, turbulence, humidity, and precipitation. Unfortunately, atmospheric models and retrospective analysis (reanalysis) products struggle to accurately simulate the occurrence and properties of low clouds in the Arctic. To better understand the magnitude and possible causes of this problem, we analyze the disagreements between the Arctic System Reanalysis version 2 (ASR) and data taken during the September 2014 Arctic Radiation-IceBridge Sea and Ice Experiment (ARISE) airborne campaign conducted over the Beaufort Sea. Previous analysis of grid scale-averaged meteorological variables revealed a lack of cloud water produced in ASR, related to warm/dry biases, a failure to produce sufficient cloud water in conditions that are observed to be favorable for large cloud water values, and sampling issues with the ARISE flight paths. However, ARISE collected meteorological observations at one second intervals, offering spatial data resolution comparable to the subgrid scale of ASR. Subgrid scale properties and processes must be parameterized in conventional atmospheric models and reanalyses such as ASR, and often rely on assumed distributions of meteorological variables about the grid box mean state. To enable an examination of the realism of ASR’s subgrid scale properties, we use high resolution data from ARISE determine the “subgrid scale” distributions of cloud water and thermodynamic variables in the real atmosphere. Preliminary results show that the subgrid scale distribution of thermodynamic variables about the grid scale mean resembles the triangular distribution assumed in many bulk microphysical parameterization schemes, but also with tails resembling Gaussian distributions. The main goal is to understand the partitioning of the total available atmospheric water into water vapor and cloud water. Models typically covert some percentage of total water in a grid box to cloud water based on the estimated amount of supersaturation from the assumed vapor distribution. The ARISE measurements can reveal the relationship between subgrid scale supersaturation and the partition between cloud water and water vapor.

Jason Brant Dodson↗

DOE OSTI2023

Hydro-Code Implementation and Testing of a Kinetic Phase Transition Framework

In this report we describe the Kinetic Phase Transition (KPT) framework that has been worked out over the last 10 years (from around 2014) and the implementation of it into three different codes, the one-dimensional hydro- LASLO and the three-dimensional magneto-hydro- ALEGRA, Sandia codes, via subroutines in the LAMBDA Equations of State and constitutive models package, and Flag, an arbitrary Lagrangian-Eulerian multiphysics code developed within the Lagrangian Applications project (LAP) at LANL. We discuss the introduction of phase mass (and/or volume) fractions that are needed in a code for it to be ‘phase aware’, that is, not only the thermodynamic state is known in each point but also the mixture of the materials’ phases in that point. Further we point to the need of a full Equations of State for each phase in a material to achieve phase awareness and we review the equilibrium phase model, where a phase mixture is at its lowest Gibbs free energy state, to make this point clear. Contrasting the kinetic phase transition to this equilibrium model seamlessly introduce us to the KPT framework that is subsequently thoroughly discussed. While the determination of the total state and the states and mass fractions of phases in each point is a problem that can borrow many of its numerical details from Eulerian codes and mixture of materials (not phases), the update of mass fractions with time in a KPT framework needs a new set of considerations. General for any update model is that we need to prevent mass fractions from becoming unphysical (negative or their sum to be larger than one). We have solved this problem by implementing a subdivision of the hydro time step that prevents the phase from being fully present to not present at all in one subdivided time step by limiting the size of the subdivided time step. This scheme also corrects numerical problems from abrupt changes in parameter values, the so called Gibbs phenomena, that gives rise to slushing between phases in the KPT framework. Interspersed throughout the report are discussions on different thermodynamics considerations. EOS validity windows, limitations on the EOS phase space, are needed for the KPT framework and are discussed separately and exemplified. The KPT framework described in this report has been verified by code comparison, but validation is still an active area of research. There is room for improvement in the update model, both in the model for determination of rates and in how to prevent the mass fractions from becoming unphysical. In addition, the parameters in the KPT update model and the placement of the phase boundary in the EOS phase space, and interactions with other constitutive models, are closely related and interfering with each other. One possible way forward is to simultaneously develop KPT parameters, EOS, and constitutive models for each material.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

NASA NTRS2014

Mean Flow Augmented Acoustics in Rocket Systems

Oscillatory motion in solid rocket motors and liquid engines has long been a subject of concern. Many rockets display violent fluctuations in pressure, velocity, and temperature originating from the complex interactions between the combustion process and gas dynamics. The customary approach to modeling acoustic waves inside a rocket chamber is to apply the classical inhomogeneous wave equation to the combustion gas. The assumption of a linear, non-dissipative wave in a quiescent fluid remains valid while the acoustic amplitudes are small and local gas velocities stay below Mach 0.2. The converging section of a rocket nozzle, where gradients in pressure, density, and velocity become large, is a notable region where this approach is not applicable. The expulsion of unsteady energy through the nozzle of a rocket is identified as the predominate source of acoustic damping for most rocket systems. An accurate model of the acoustic behavior within this region where acoustic modes are influenced by the presence of a steady mean flow is required for reliable stability predictions. Recently, an approach to address nozzle damping with mean flow effects was implemented by French [1]. This new approach extends the work originated by Sigman and Zinn [2] by solving the acoustic velocity potential equation (AVPE) formulated by perturbing the Euler equations [3]. The acoustic velocity potential (psi) describing the acoustic wave motion in the presence of an inhomogeneous steady high-speed flow is defined by, (del squared)(psi) − (lambda/c)(exp 2)(psi) − M(dot)[M(dot)(del)(del(psi))] − 2(lambda(M/c) + (M(dot)del(M))(dot)del(psi)−2(lambda)(psi)[M(dot)del(1/c)]=0 (1) with M as the Mach vector, c as the speed of sound, and lambda as the complex eigenvalue. French apply the finite volume method to solve the steady flow field within the combustion chamber and nozzle with inviscid walls. The complex eigenvalues and eigenvector are determined with the use of the ARPACK eigensolver. The present study employs the COMSOL Multphysics framework to solve the coupled eigenvalue problem using the finite element approach. The study requires one way coupling of the CFD High Mach Number Flow (HMNF) and mathematics module. The HMNF module evaluated the gas flow inside of a solid rocket motor using St. Robert's law modeling solid propellant burn rate, slip boundary conditions, and the supersonic outflow condition. Results from the HMNF model are used by the coefficient form of the mathematics module to determine the eigenvalues of the AVPE. The mathematics model is truncated at the nozzle sonic line, where a zero flux boundary condition is self-satisfying. The remaining boundaries are modeled with a zero flux boundary condition, assuming zero acoustic absorption on all surfaces. Pertinent results from these analyses are the complex valued eigenvalue and eigenvectors. Comparisons are made to the French results to evaluate the modeling approach. A comparison of the French results with that of the present analysis is displayed in figures 1 and 2, respectively. The graphic shows the first tangential eigenvector's real (a) and imaginary (b) values.

Fischbach, Sean R.↗

DOE OSTI2022

Physics‐Informed Machine Learning Method for Large‐Scale Data Assimilation Problems

Abstract We develop a physics‐informed machine learning approach for large‐scale data assimilation and parameter estimation and apply it for estimating transmissivity and hydraulic head in the two‐dimensional steady‐state subsurface flow model of the Hanford Site given synthetic measurements of said variables. In our approach, we extend the physics‐informed conditional Karhunen‐Loéve expansion (PICKLE) method to modeling subsurface flow with unknown flux (Neumann) and varying head (time‐dependent Dirichlet) boundary conditions. We demonstrate that the PICKLE method is comparable in accuracy with the standard maximum a posteriori (MAP) method, but is significantly faster than MAP for large‐scale problems. Both methods use a mesh to discretize the computational domain. In MAP, the parameters and states are discretized on the mesh; therefore, the size of the MAP parameter estimation problem directly depends on the mesh size. In PICKLE, the mesh is used to evaluate the residuals of the governing equation, while the parameters and states are approximated by the truncated conditional Karhunen‐Loéve expansions with the number of parameters controlled by the smoothness of the parameter and state fields, and not by the mesh size. For a considered example, we demonstrate that the computational cost of PICKLE increases near linearly (as N 1.15 ) with the number of grid nodes N , while that of MAP increases much faster (as N 3.28 ). We also show that once trained for one set of Dirichlet boundary conditions (i.e., one river stage), the PICKLE method provides accurate estimates of the hydraulic head for any value of the Dirichlet boundary conditions (i.e., for any river stage).

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1974

Relaxation of an unsteady turbulent boundary layer on a flat plate in an expansion tube

An analysis is presented for the relaxation of a turbulent boundary layer on a semi-infinite flat plate after passage of a shock wave and a trailing driver gas-driven gas interface. The problem has special application to expansion-tube flows. The flow-governing equations have been transformed into the Crocco variables, and a time-similar solution is presented in terms of the dimensionless distance-time variable alpha and the dimensionless velocity variable beta. An eddy-viscosity model, similar to that of time-steady boundary layers, is applied to the inner and outer regions of the boundary layer. A turbulent Prandtl number equal to the molecular Prandtl number is used to relate the turbulent heat flux to the eddy viscosity. The numerical results, obtained by using the Gauss-Seidel line-relaxation method, indicate that a fully turbulent boundary layer relaxes faster to the final steady-state values of heat transfer and skin friction than a laminar boundary layer. The results also give a fairly good estimate of the local skin friction and heat transfer for near steady-flow conditions.

Gurta, R. N.↗

NASA NTRS1985

Vibration and buckling of rotating, pretwisted, preconed beams including Cooriolis effects

The effects of pretwist, precone, setting angle and Coriolis forces on the vibration and buckling behavior of rotating, torsionally rigid, cantilevered beams were studied. The beam is considered to be clamped on the axis of rotation in one case, and off the axis of rotation in the other. Two methods are employed for the solution of the vibration problem: (1) one based upon a finite-difference approach using second order central differences for solution of the equations of motion, and (2) based upon the minimum of the total potential energy functional with a Ritz type of solution procedure making use of complex forms of shape functions for the dependent variables. The individual and collective effects of pretwist, precone, setting angle, thickness ratio and Coriolis forces on the natural frequencies and the buckling boundaries are presented. It is shown that the inclusion of Coriolis effects is necessary for blades of moderate to large thickness ratios while these effects are not so important for small thickness ratio blades. The possibility of buckling due to centrifugal softening terms for large values of precone and rotation is shown.

Subrahmanyam, K. B.↗

NASA NTRS1985

Vibration and buckling of rotating, pretwisted, preconed beams including Coriolis effects

Subrahmanyam, K. B.↗

NASA NTRS1999

Pulsating Hydrodynamic Instability and Thermal Coupling in an Extended Landau/Levich Model of Liquid-Propellant Combustion

Hydrodynamic (Landau) instability in combustion is typically associated with the onset of wrinkling of a flame surface, corresponding to the formation of steady cellular structures as the stability threshold is crossed. In the context of liquid-propellant combustion, such instability has recently been shown to occur for critical values of the pressure sensitivity of the burning rate and the disturbance wavenumber, significantly generalizing previous classical results for this problem that assumed a constant normal burning rate. Additionally, however, a pulsating form of hydrodynamic instability has been shown to occur as well, corresponding to the onset of temporal oscillations in the location of the liquid/gas interface. In the present work, we consider the realistic influence of a nonzero temperature sensitivity in the local burning rate on both types of stability thresholds. It is found that for sufficiently small values of this parameter, there exists a stable range of pressure sensitivities for steady, planar burning such that the classical cellular form of hydrodynamic instability and the more recent pulsating form of hydrodynamic instability can each occur as the corresponding stability threshold is crossed. For larger thermal sensitivities, however, the pulsating stability boundary evolves into a C-shaped curve in the disturbance-wavenumber/ pressure-sensitivity plane, indicating loss of stability to pulsating perturbations for all sufficiently large disturbance wavelengths. It is thus concluded, based on characteristic parameter values, that an equally likely form of hydrodynamic instability in liquid-propellant combustion is of a nonsteady, long-wave nature, distinct from the steady, cellular form originally predicted by Landau.

Margolis, S. B.↗

NASA NTRS1999

Pulsating Hydrodynamic Instability in a Dynamic Model of Liquid-Propellant Combustion

Margolis, Stephen B.↗

DOE OSTI2025

The transition from resistance to acceptance: Managing a marine invasive species in a changing world

Abstract Marine invasive species can transform coastal ecosystems, yet mitigating their effects can be difficult, and even impractical. Often, marine invasive species are managed at poorly matched spatial scales, and at the same time, rates of spread and establishment are increasing under climate change and can outpace resources available for population suppression. These circumstances challenge traditional conservation goals of maintaining a historic environmental state, especially for a species like the European green crab ( Carcinus maenas ), a formidable invader with few examples of successful long‐term removal programs. A management paradigm where decision alternatives include resisting or accepting a new ecological trajectory may be needed. We apply mathematical concepts from decision theory to develop a quantitative framework for navigating management decisions in this new resist‐accept paradigm. We develop a model of European green crab growth, removal and colonization, and we find optimal levels of removal effort that minimize both ecological change and removal cost. We establish a benchmark of colonization pressure at which green crab density becomes decoupled from a decision maker's actions, such that population control can no longer shape the invasion trajectory. For informing the decision boundary between resistance and acceptance, our results highlight that a decision maker's understanding of how removal cost scales with removal effort is more important than understanding the density‐impact relationship. We show that assuming stationary system dynamics can result in sub‐optimal levels of species removal effort, highlighting the importance of developing anticipatory management strategies by accounting for non‐stationary dynamics. Policy implications . For marine invasive species that can disperse across long distances and recolonize rapidly after removal, the focus of conservation policy should shift away from understanding how to resist change to understanding when to stop resisting change. Navigating this decision problem involves trade‐offs among competing objectives, highlighting the need for structured approaches to elicit objective weights that reflect the values of the decision maker. For natural resource managers facing possible ecosystem transformation, this decision framework can enable proactive and strategic decisions made under uncertainty in a changing world.

Keller, Abigail G. [Department of Environment Scie↗

NASA NTRS1999

Pulsating Hydrodynamic Instability and Thermal Coupling in an Extended Landau/Levich Model of Liquid-Propellant Combustion: Inviscid Analysis - 1

Hydrodynamic (Landau) instability in combustion is typically associated with the onset of wrinkling of a flame surface, corresponding to the formation of steady cellular structures as the stability threshold is crossed. In the context of liquid-propellant combustion, such instability has recently been shown to occur for critical values of the pressure sensitivity of the burning rate and the disturbance wavenumber, significantly generalizing previous classical results for this problem that assumed a constant normal burning rate. Additionally, however, a pulsating form of hydrodynamic instability has been shown to occur as well, corresponding to the onset of temporal oscillations in the location of the liquid/gas interface. In the present work, we consider the realistic influence of a non-zero temperature sensitivity in the local burning rate on both types of stability thresholds. It is found that for sufficiently small values of this parameter, there exists a stable range of pressure sensitivities for steady, planar burning such that the classical cellular form of hydrodynamic instability and the more recent pulsating form of hydrodynamic instability can each occur as the corresponding stability threshold is crossed. For larger thermal sensitivities, however, the pulsating stability boundary evolves into a C-shaped curve in the (disturbance-wavenumber, pressure-sensitivity) plane, indicating loss of stability to pulsating perturbations for all sufficiently large disturbance wavelengths. It is thus concluded, based on characteristic parameter values, that an equally likely form of hydrodynamic instability in liquid-propellant combustion is of a non-steady, long-wave nature, distinct from the steady, cellular form originally predicted by Landau.

Margolis, Stephen B.↗

NASA NTRS1971

On propagation of long waves in curved ducts.

Propagation of waves in curved ducts and pipes belong to the class of motion which is characterized by wave patterns totally different from those known in straight ducts or in unlimited space. The curvilinear boundaries are responsible for the appearance of a continuous standing radial wave which in turn affects the transmitted tangential waves. The purpose of this paper is to solve the problem of propagation of long acoustic waves in slightly and sharply bent ducts. This problem has been only partially analyzed by various authors. In this study two acoustic systems are considered which allow determination of the basic modes of motion and describe the transition and distortion of plane waves as they propagate down the curved channel. A detailed study of the behavior of waves in junctions between straight and curved ducts is also given. Solutions and expressions for principal modes of the wave are obtained by using the linearized equation of motion solved for its characteristic values. This original approach required a novel use of Bessel functions to determine the characteristic values of the steady and the decaying fields of motion.

Rostafinski, W.↗