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At least 253 records · Page 14

A composite velocity procedure for the compressible Navier-Stokes equations

A new boundary-layer relaxation procedure is presented. In the spirit of the theory of matched asymptotic expansions, a multiplicative composite of the appropriate velocity representations for the inviscid and viscous regions is prescribed. The resulting equations are structured so that far from the surface of the body the momentum equations lead to the Bernoulli relation for the pressure, while the continuity equation reduces to the familiar compressible potential equation. Close to the body surface, the governing equations and solution techniques are characteristic of those describing interacting boundary-layers; although, the full Navier-Stokes equations are considered here. Laminar flow calculations for the subsonic flow over an axisymmetric boattail simulator geometry are presented for a variety of Reynolds and Mach numbers. A strongly implicit solution method is applied for the coupled velocity components.

Khosla, P. K.↗

Rethinking Use of the OML Model in Electric Sail Development

In 1924, Irvin Langmuir and H. M. Mott-Smith published a theoretical model for the complex plasma sheath phenomenon in which they identified some very special cases which greatly simplified the sheath and allowed a closed solution to the problem. The most widely used application is for an electrostatic, or "Langmuir," probe in laboratory plasma. Although the Langmuir probe is physically simple (a biased wire) the theory describing its functional behavior and its current-voltage characteristic is extremely complex and, accordingly, a number of assumptions and approximations are used in the LMS model. These simplifications, correspondingly, place limits on the model's range of application. Adapting the LMS model to real-life conditions is the subject of numerous papers and dissertations. The Orbit-Motion Limited (OML) model that is widely used today is one of these adaptions that is a convenient means of calculating sheath effects. Since the Langmuir probe is a simple biased wire immersed in plasma, it is particularly tempting to use the OML equation in calculating the characteristics of the long, highly biased wires of an Electric Sail in the solar wind plasma. However, in order to arrive at the OML equation, a number of additional simplifying assumptions and approximations (beyond those made by Langmuir-Mott-Smith) are necessary. The OML equation is a good approximation when all conditions are met, but it would appear that the Electric Sail problem lies outside of the limits of applicability.

Stone, Nobie H.↗

Estimation of homogeneous nucleation flux via a kinetic model

The proposed kinetic model for condensation under homogeneous conditions, and the onset of unidirectional cluster growth in supersaturated gases, does not suffer from the conceptual flaws that characterize classical nucleation theory. When a full set of simultaneous rate equation is solved, a characteristic time emerges, for each cluster size, at which the production rate, and its rate of conversion to the next size (n + 1) are equal. Procedures for estimating the essential parameters are proposed; condensation fluxes J(kin) exp ss are evaluated. Since there are practical limits to the cluster size that can be incorporated in the set of simultaneous first-order differential equations, a code was developed for computing an approximate J(th) exp ss based on estimates of a 'constrained equilibrium' distribution, and identification of its minimum.

Wilcox, C. F.↗

Discussion of Boundary-Layer Characteristics Near the Wall of an Axial-Flow Compressor

The boundary-layer velocity profiles in the tip region of an axial-flow compressor downstream of the guide vanes and downstream of the rotor were measured by use of total-pressure and claw-type yaw probes. These velocities were resolved into two components: one along the streamline of the flow outside the boundary layer, and the other perpendicular to it. The affinity among all profiles was thus demonstrated with the boundary-layer thickness and the deflection of the boundary layer at the wall as the generalizing parameters. By use of these results and the momentum-integral equations, boundary-layer characteristics on the walls of an axial-flow compressor were qualitatively evaluated.

Mager, Artur↗

Multiple steady states for characteristic initial value problems

The time dependent, isentropic, quasi-one-dimensional equations of gas dynamics and other model equations are considered under the constraint of characteristic boundary conditions. Analysis of the time evolution shows how different initial data may lead to different steady states and how seemingly anamolous behavior of the solution may be resolved. Numerical experimentation using time consistent explicit algorithms verifies the conclusions of the analysis. The use of implicit schemes with very large time steps leads to erroneous results.

Salas, M. D.↗

Vibration of thermally buckled composite plates with initial deflections using triangular elements

A consistent finite element formulation is presented for the analysis of thermal postbuckling and free vibration of thermally buckled thin, laminated composite plates subjected to large temperature change. The influence of moderately large initial imperfections in deflection on the thermal postbuckling deflection and the vibration characteristics of the buckled plate is also investigated. The finite element equations of motion are derived from the principle of virtual work. These equations can be mathematically separated into two sets and solved in sequence. The first set of equations yields the particular solution of static thermal postbuckling deflection, and the second set of equations gives the homogeneous solution of vibration characteristics on the buckled plate. The first set of static equations is solved by using Newton-Raphson iteration method. The tangent stiffness matrix in the final iteration is equal to the total stiffness matrix of the second set of dynamic equations. This feature saves tremendous computation time in comparing with using the conventional approach. The influence of lamination angle, temperature distribution, plate planform of arbitrary shape, and boundary support conditions on postbuckling and vibration behavior are investigated.

Zhou, R. C.↗

Heat pipe modeling and simulation

Presented herein is a parametric study of the defining equations which govern the steady state operational characteristics of the Grumman Monogroove Dual Passage Heat Pipe. These defining equations are combined to develop a mathematical model which describes and predicts the operational and performance capabilities of a specific heat pipe, given the necessary physical characteristics and working fluid. Included is a brief review of the current literature, a discussion of the governing equations, and a description of both the mathematical and computer model. Final results of preliminary test runs of the model are presented and compared with experimental tests performed by Grumman on actual prototypes.

Peterson, G. P.↗

Anti-Ultralocality and Plateau Models of Inflation

Anti-ultralocality refers to the growth of spatial gradient terms relative to velocity terms in the coupled Einstein--scalar field equations. It is a characteristic feature of decelerated expansion before the onset of inflation. Previous numerical relativity studies have shown that anti-ultralocality prevents the onset of inflation in models with power-law inflaton potentials. In this paper, we show that models with plateau-shaped inflaton potentials, which are considered to be the simplest way to generate a tensor-to-scalar ratio below current observational upper limits, are especially vulnerable to anti-ultralocality effects. The reasons are the flatness of the plateau and the energy density gap of $\sim 10$ orders of magnitude between the Planck density and the plateau potential energy. To study the problem, we develop a protocol for assessing the viability of inflationary models in general, and we apply it to a plateau potential using a previously validated numerical relativity code. We find that, starting from generic initial conditions, the growth of gradient terms in the Einstein equations relative to non-gradient terms either prevents inflation from lasting for enough $e$-folds or triggers a phase of quantum runaway. We show that the fine-tuning of initial conditions necessary to avoid these issues becomes more severe as the energy scale of inflation is made smaller, disfavoring common approaches for reducing the tensor-to-scalar ratio.

FOS: Physical sciences↗

Vibration of Shells

The vibrational characteristics and mechanical properties of shell structures are discussed. The subjects presented are: (1) fundamental equations of thin shell theory, (2) characteristics of thin circular cylindrical shells, (3) complicating effects in circular cylindrical shells, (4) noncircular cylindrical shell properties, (5) characteristics of spherical shells, and (6) solution of three-dimensional equations of motion for cylinders.

Leissa, A. W.↗

Main Chamber Injectors for Advanced Hydrocarbon Booster Engines

Achieving the highest possible specific impulse has long been a key driver for space launch systems. Recently, more importance has been placed on the need for increased reliability and streamlined launch operations. These general factors along with more specific mission requirements have provided a new focus that is centered on the oxidizer rich staged combustion (ORSC) cycle. Despite a history of use in Russia that extends back to the 1960's, a proven design methodology for ORSC cycle engines does not exist in the West. This lack of design expertise extends to the main chamber injector, a critical subcomponent that largely determines the engine performance and main chamber life. The goals of the effort described here are to establish an empirical knowledge base to provide a fundamental understanding of main chamber injectors and for verification of an injector design methodology for the ORSC cycle. The design of a baseline injector element, derived from information on Russian engines in the open literature, is presented. The baseline injector comprises a gaseous oxidizer core flow and an annular swirling fuel flow. Sets of equations describing the steady-state and the dynamic characteristics of the injector are presented; these equations, which form the basis of the design analysis methodology, will be verified in tests later this year. On-going cold flow studies, using nitrogen and water as simulants, are described which indicate highly atomized and symmetric sprays.

Long, Matthew R.↗

Coupling Between Electrons and Charge Density Wave Fluctuation and its Possible Role in Superconductivity

In most charge density wave (CDW) systems of different material classes, ranging from traditional correlated systems in low-dimension to recent topological systems with Kagome lattice, superconductivity emerges when the system is driven toward the quantum critical point (QCP) of CDW via external parameters of doping and pressure. Despite this rather universal trend, the essential hinge between CDW and superconductivity has not been established yet. Here, the evidence of coupling between electron and CDW fluctuation is reported, based on a temperature- and intercalation-dependent kink in the angle-resolved photoemission spectra of 2H-Pd x TaSe 2 . Kinks are observed only when the system is in the CDW phase, regardless of whether a long- or short-range order is established. Notably, the coupling strength is enhanced upon long-range CDW suppression, albeit the coupling energy scale is reduced. Interestingly, the estimation of the superconducting critical temperature by incorporating the observed coupling characteristics into McMillan's equation yields results closely resembling the known values of the superconducting dome. The results thus highlight a compelling possibility that this new coupling mediates Cooper pairs, which provides new insights into the competing relationship not only for CDW but also for other competing orders.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Assessment of integral models for non-Boussinesq lazy plumes using numerical simulations

Integral modelling of turbulent buoyant plumes is crucial for rapid predictions of plume characteristics. While the governing equations are typically derived using self-similarity and a Boussinesq approximation, these assumptions may not hold for plumes originating from finite-area sources with large density ratios. Here, this work evaluates the accuracy of integral-scale models for non-Boussinesq lazy plumes using high-fidelity numerical simulations of turbulent helium plumes. We analyse the plume kinematics by computing vertical fluxes, plume radius and radial profiles, establishing some disparities between common practice and physical accuracy. We identify how the definition of the plume radius changes the perception of the plume structure when the flow is not self-similar and derive a relationship between the flux-based and threshold-based definitions without requiring self-similarity. We then examine the plume dynamics by evaluating the source terms from the governing plume equations. Our results support neglecting diffusive and viscous effects but emphasise the importance of the mean pressure gradient, even in the self-similar regime. Two coefficients need to be modelled: the well-known entrainment coefficient and the lesser-known momentum correction coefficient, which is a correction required for the momentum equation to account for self-similar and slender approximations. The momentum correction coefficient is found to be approximately constant and slightly greater than the assumed value of 1. The standard entrainment coefficient models perform well up to a local Richardson number three times the asymptotic value but overpredict entrainment for larger Richardson numbers. We propose a correction using the known finite limit of entrainment at infinite Richardson number.

Meehan, Michael Alexander [Sandia National Laborat↗

Generation of entangled-photons by a quantum dot cascade source in polarized cavities: Using cavity resonances to boost signals and preserve the entanglements

Motivated by recent advances in the development of single photon emitters for quantum information sciences, here we design and formulate a quantum cascade model that describes cascade emission by a quantum dot (QD) in a cavity structure while preserving entanglement that stores information needed for single photon emission. The theoretical approach is based on a photonic structure that consists of two orthogonal cavities in which resonance with either the first or second of the two emitted photons is possible, leading to amplification and rerouting of the entangled light. The cavity–QD scheme uses a four-level cascade emitter that involves three levels for each polarization, leading to two spatially entangled photons for each polarization. By solving the Schrodinger equation, we identify the characteristic properties of the system, which can be used in conjunction with optimization techniques to achieve the “best” design relative to a set of prioritized criteria or constraints in our optical system. The theoretical investigations include an analysis of emission spectra in addition to the joint spectral density profile, and the results demonstrate the ability of the cavities to act as frequency filters for the photons that make up the entanglements and to modify entanglement properties. The results provide new opportunities for the experimental design and engineering of on-demand single photon sources.

Chemistry↗

An experimental-analytical method to study steady spray combustion.

Description of a method for determining the local parameters of the gas mixture resulting from the combustion of sprayed fuel in a gaseous oxidizer. The method is based on the measurement of local static pressures in the gas mixture and does not require the knowledge of the droplet distribution function, drag, and vaporization characteristics. A set of equations with substituted local pressure values is used for calculations. Application of the method is demonstrated on a liquid oxygen-ethanol rocket fuel.

Bracco, F. V.↗

Analysis and design of three dimensional supersonic nozzles. Volume 2: Numerical program for analysis of nozzle-exhaust flow fields

The FORTRAN IV Program developed to analyze the flow field associated with scramjet exhaust systems is presented. The instructions for preparing input and interpreting output are described. The program analyzes steady three dimensional supersonic flow by the reference plane characteristic technique. The governing equations and numerical techniques employed are presented in Volume 1 of this report.

Kalben, P.↗

Calculation of eddy viscosity in a compressible turbulent boundary layer with mass injection and chemical reaction, volume 1

The turbulent kinetic energy equation is coupled with boundary layer equations to solve the characteristics of compressible turbulent boundary layers with mass injection and combustion. The Reynolds stress is related to the turbulent kinetic energy using the Prandtl-Wieghardt formulation. When a lean mixture of hydrogen and nitrogen is injected through a porous plate into the subsonic turbulent boundary layer of air flow and ignited by external means, the turbulent kinetic energy increases twice as much as that of noncombusting flow with the same mass injection rate of nitrogen. The magnitudes of eddy viscosity between combusting and noncombusting flows with injection, however, are almost the same due to temperature effects, while the distributions are different. The velocity profiles are significantly affected by combustion; that is, combustion alters the velocity profile as if the mass injection rate is increased, reducing the skin-friction as a result of a smaller velocity gradient at the wall. If pure hydrogen as a transpiration coolant is injected into a rocket nozzle boundary layer flow of combustion products, the temperature drops significantly across the boundary layer due to the high heat capacity of hydrogen. At a certain distance from the wall, hydrogen reacts with the combustion products, liberating an extensive amount of heat. The resulting large increase in temperature reduces the eddy viscosity in this region.

Omori, S.↗

Calculation of eddy viscosity in a compressible turbulent boundary layer with mass injection and chemical reaction

The turbulent kinetic energy equation is coupled with boundary layer equations to solve the characteristics of compressible turbulent boundary layers with mass injection and combustion. The Reynolds stress is related to the turbulent kinetic energy using the Prandtl-Wieghardt formulation. When a lean mixture of hydrogen and nitrogen is injected through a porous plate into the subsonic turbulent boundary layer of air flow and ignited by external means, the turbulent kinetic energy increases twice as much as that of noncombusting flow with the same mass injection rate of nitrogen. The magnitudes of eddy viscosity between combusting and noncombusting flows with injection, however, are almost the same due to temperature effects, while the distributions are different. The velocity profiles are significantly affected by combustion. If pure hydrogen as a transpiration coolant is injected into a rocket nozzle boundary layer flow of combustion products, the temperature drops significantly across the boundary layer due to the high heat capacity of hydrogen. At a certain distance from the wall hydrogen reacts with the combustion products, liberating an extensive amount of heat.

Omori, S.↗