Search NASA⌕ Search

SEARCH · Search NASA

Results for “FORMULAS - STRESSES, SHEARING”

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.

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

At least 55 records · Page 3
All sourcesNASA NTRSDOE OSTI
NASA NTRS1986

X-ray observations of clusters - Physical implications

The X-ray properties of clusters of galaxies and elliptical galaxies are reviewed, with an emphasis on cooling flows and their effects on the structure and energetics of radio sources. It is found that the radial profiles of the hot (10 to the 8th K) diffuse (n = about 0.001/cu cm) gas in clusters do not require heating of the intracluster medium after the formation of the cluster. Consideration is given to theoretical formulas for cooling rates, the possible reasons for the observed correlation between cooling flows and the presence of a dominant central galaxy, cooling-flow models of elliptical galaxies, and the significant shear in the velocity field of a cooling flow.

Sarazin, Craig L.↗
NASA NTRS2002

Finite-Strain Fractional-Order Viscoelastic (FOV) Material Models and Numerical Methods for Solving Them

Fraction-order viscoelastic (FOV) material models have been proposed and studied in 1D since the 1930's, and were extended into three dimensions in the 1970's under the assumption of infinitesimal straining. It was not until 1997 that Drozdov introduced the first finite-strain FOV constitutive equations. In our presentation, we shall continue in this tradition by extending the standard, FOV, fluid and solid, material models introduced in 1971 by Caputo and Mainardi into 3D constitutive formula applicable for finite-strain analyses. To achieve this, we generalize both the convected and co-rotational derivatives of tensor fields to fractional order. This is accomplished by defining them first as body tensor fields and then mapping them into space as objective Cartesian tensor fields. Constitutive equations are constructed using both variants for fractional rate, and their responses are contrasted in simple shear. After five years of research and development, we now possess a basic suite of numerical tools necessary to study finite-strain FOV constitutive equations and their iterative refinement into a mature collection of material models. Numerical methods still need to be developed for efficiently solving fraction al-order integrals, derivatives, and differential equations in a finite element setting where such constitutive formulae would need to be solved at each Gauss point in each element of a finite model, which can number into the millions in today's analysis.

Freed, Alan D.↗
NASA NTRS1975

The low frequency sound from multipole sources in axisymmetric shear flows, with applications to jet noise

A closed-form solution for the sound radiation from multipole sources imbedded in an infinite cylindrical jet with an arbitrary velocity profile is obtained. It is valid in the limit where the wavelength is large compared with the jet radius. Simple formulae for the acoustic pressure field due to convected point sources are also obtained. The results show (in a simple way) how the mean flow affects the radiation pattern from the sources. For convected lateral quadrupoles it causes the exponent of the Doppler factor multiplying the far-field pressure signal to be increased from the value of 3 used by Lighthill to 5.

Goldstein, M. E.↗
DOE OSTI2025

Measurements of the polarization of several instabilities in the DIII-D tokamak

Recently, a method to infer the polarization of modes with frequencies much less than the ion cyclotron frequency was published [X.D. Du et al., Phys. Rev. Lett. 132 (2024) 215101]. The method uses measurements of electron temperature and density fluctuations δTₑ and δnₑ at the same spatial position to infer the local ratio of “acoustic polarization,” |δϕ ∥ |/(|δϕ ∥ |+|δψ|), where δϕ ∥ is the effective parallel potential and δψ is related to the parallel magnetic vector potential A ∥ . This paper summarizes key formulas, with emphasis on their range of validity, and elaborates on the workflow required to infer the acoustic polarization from experimental data. The drift-acoustic polarization of ellipticity-induced, toroidicity-induced, and reversed shear Alfvén eigenmodes is nearly zero, as expected for modes with predominately shear-Alfvénic polarization. The polarization of beta-induced Alfvén eigenmodes contains an acoustic component that increases with poloidal wave number. “Low frequency modes,” (instabilities that appear transiently when the minimum of the safety factor qₘᵢₙ passes through rational values) have large and highly variable acoustic polarization. In both experiment and simulation, fishbones have non-zero acoustic polarization that increases as the mode chirps down in frequency.

Alfven eigenmode↗
NASA NTRS1989

Cross correlation and length scales in turbulent flows near surfaces

Two kinds of length scales are used in turbulent flows; 'functional length scales' such as mixing length, dissipation length L(sub epsilon), etc., and 'flow-field length scales' derived from cross correlations of velocity, pressure, etc. in the flow. Some connection between these scales are derived here. We first consider the cross correlation R(sub vv)(y,y(sub 1)) of the normal components u at two heights y, y(sub 1) above a rigid surface, normalized by the velocity y(sub 1) (greater than y). For shear-free boundary layers it is found theoretically, and in field and numerical experiments that R(sub vv) approximately equals y/y(sub 1). For shear layers it is also found that R(sub vv) approximately equals f(y/y(sub 1)) less than or equal to y,y(sub 1). This function f differs slightly between low Reynolds number numerical simulations and field experiments. The lateral structure defined by R(sub vv)(y,r(sub 3); y(sub 1),0) is also self similar and shows that the eddies centered at about y(sub 1) appear to have constant lateral width a(sub 3) above and below y(sub 1), where a(sub 3, sup +) approximately equals 7+1/(1.4dU(sup +)/dy(sup +)), when normalized on u(sub *) and v, where U is the mean velocity. Results for L(sub epsilon, sup -1) from direct numerical simulation are found to compare well with the formula L(sub epsilon, sup -1) = A(sub B)/y + A(sub S)dU/dy/v, for unidirectional and reversing turbulent boundary layers and channel flow, except near where dU/dy approximately equals 0. The conclusion is that the large-scale eddy structure and length scales in these flows are determined by a combination of shear and blocking, and that the vertical component of turbulence has a self-similar structure in both kinds of boundary layer.

Hunt, J. C. R.↗
NASA NTRS1974

The development of experimental techniques for the study of helicopter rotor noise

The features of existing wind tunnels involved in noise studies are discussed. The acoustic characteristics of the MIT low noise open jet wind tunnel are obtained by employing calibration techniques: one technique is to measure the decay of sound pressure with distance in the far field; the other technique is to utilize a speaker, which was calibrated, as a sound source. The sound pressure level versus frequency was obtained in the wind tunnel chamber and compared with the corresponding calibrated values. Fiberglas board-block units were installed on the chamber interior. The free field was increased significantly after this treatment and the chamber cut-off frequency was reduced to 160 Hz from the original designed 250 Hz. The flow field characteristics of the rotor-tunnel configuration were studied by using flow visualization techniques. The influence of open-jet shear layer on the sound transmission was studied by using an Aeolian tone as the sound source. A dynamometer system was designed to measure the steady and low harmonics of the rotor thrust. A theoretical Mach number scaling formula was developed to scale the rotational noise and blade slap noise data of model rotors to full scale helicopter rotors.

Widnall, S. E.↗
NASA NTRS2014

Modeling and Prediction of the Noise from Non-Axisymmetric Jets

The new source model was combined with the original sound propagation model developed for rectangular jets to produce a new version of the rectangular jet noise prediction code. This code was validated using a set of rectangular nozzles whose geometries were specified by NASA. Nozzles of aspect ratios two, four and eight were studied at jet exit Mach numbers of 0.5, 0.7 and 0.9, for a total of nine cases. Reynolds-averaged Navier-Stokes solutions for these jets were provided to the contactor for use as input to the code. Quantitative comparisons of the predicted azimuthal and polar directivity of the acoustic spectrum were made with experimental data provided by NASA. The results of these comparisons, along with a documentation of the propagation and source models, were reported in a journal article publication (Ref. 4). The complete set of computer codes and computational modules that make up the prediction scheme, along with a user's guide describing their use and example test cases, was provided to NASA as a deliverable of this task. The use of conformal mapping, along with simplified modeling of the mean flow field, for noise propagation modeling was explored for other nozzle geometries, to support the task milestone of developing methods which are applicable to other geometries and flow conditions of interest to NASA. A model to represent twin round jets using this approach was formulated and implemented. A general approach to solving the equations governing sound propagation in a locally parallel nonaxisymmetric jet was developed and implemented, in aid of the tasks and milestones charged with selecting more exact numerical methods for modeling sound propagation, and developing methods that have application to other nozzle geometries. The method is based on expansion of both the mean-flowdependent coefficients in the governing equation and the Green's function in series of orthogonal functions. The method was coded and tested on two analytically prescribed mean flows which were meant to represent noise reduction concepts being considered by NASA. Testing (Ref. 5) showed that the method was feasible for the types of mean flows of interest in jet noise applications. Subsequently, this method was further developed to allow use of mean flow profiles obtained from a Reynolds-averaged Navier-Stokes (RANS) solution of the flow. Preliminary testing of the generalized code was among the last tasks completed under this contract. The stringent noise-reduction goals of NASA's Fundamental Aeronautics Program suggest that, in addition to potentially complex exhaust nozzle geometries, next generation aircraft will also involve tighter integration of the engine with the airframe. Therefore, noise generated and propagated by jet flows in the vicinity of solid surfaces is expected to be quite significant, and reduced-order noise prediction tools will be needed that can deal with such geometries. One important source of noise is that generated by the interaction of a turbulent jet with the edge of a solid surface (edge noise). Such noise is generated, for example, by the passing of the engine exhaust over a shielding surface, such as a wing. Work under this task supported an effort to develop a RANS-based prediction code for edge noise based on an extension of the classical Rapid Distortion Theory (RDT) to transversely sheared base flows (Refs. 6 and 7). The RDT-based theoretical analysis was applied to the generic problem of a turbulent jet interacting with the trailing edge of a flat plate. A code was written to evaluate the formula derived for the spectrum of the noise produced by this interaction and results were compared with data taken at NASA Glenn for a variety of jet/plate configurations and flow conditions (Ref. 8). A longer-term goal of this task was to work toward the development of a high-fidelity model of sound propagation in spatially developing non-axisymmetric jets using direct numerical methods for solving the relevant equations. Working with NASA Glenn Acoustics Branch personnel, numerical methods and boundary conditions appropriate for use in a high-resolution calculation of the full equations governing sound propagation in a steady base flow were identified. Computer codes were then written (by NASA) and tested (by OAI) for an increasingly complex set of flow conditions to validate the methods. The NASA-supplied codes were ported to the High-End Computing resources of the NASA Advanced Supercomputing facility for testing and validation against analytical (where possible) and independent numerical solutions. The cases which were completed during the course of this contract were solutions of the two-dimensional linearized Euler equations with no mean flow, a uniform mean flow and a nonuniform mean flow representative of a parallel flow jet.

Leib, Stewart J.↗
NASA NTRS1997

Annual Research Briefs

This report contains the 1997 annual progress reports of the research fellows and students supported by the Center for Turbulence Research (CTR). Titles include: Invariant modeling in large-eddy simulation of turbulence; Validation of large-eddy simulation in a plain asymmetric diffuser; Progress in large-eddy simulation of trailing-edge turbulence and aeronautics; Resolution requirements in large-eddy simulations of shear flows; A general theory of discrete filtering for LES in complex geometry; On the use of discrete filters for large eddy simulation; Wall models in large eddy simulation of separated flow; Perspectives for ensemble average LES; Anisotropic grid-based formulas for subgrid-scale models; Some modeling requirements for wall models in large eddy simulation; Numerical simulation of 3D turbulent boundary layers using the V2F model; Accurate modeling of impinging jet heat transfer; Application of turbulence models to high-lift airfoils; Advances in structure-based turbulence modeling; Incorporating realistic chemistry into direct numerical simulations of turbulent non-premixed combustion; Effects of small-scale structure on turbulent mixing; Turbulent premixed combustion in the laminar flamelet and the thin reaction zone regime; Large eddy simulation of combustion instabilities in turbulent premixed burners; On the generation of vorticity at a free-surface; Active control of turbulent channel flow; A generalized framework for robust control in fluid mechanics; Combined immersed-boundary/B-spline methods for simulations of flow in complex geometries; and DNS of shock boundary-layer interaction - preliminary results for compression ramp flow.

Spinks, Debra↗
NASA NTRS1989

New mixing-length model for turbulent high-speed flows

A modification of Prandtl's mixing-length model is presented which takes into account the effects of compressibility on turbulence for high speed flows. A parameter is introduced into the turbulent transport formula which acts like an effective turbulent Schmidt number for mixtures of gases or a turbulent Prandtl number for a homogeneous gas. Results presented for such cases as high Mach number turbulent boundary layer flows over a flat surface, tangential slot injection problems, and shock/turbulent shear-layer and boundary-layer interactions agree well with experimental data.

Situ, M.↗
NASA NTRS1980

Structural properties of superplastically formed/diffusion-bonded orthogonally corrugated core sandwich plates

This paper describes a new superplastically formed/diffusion-bonded (SPF/DB) orthogonally corrugated sandwich structure, and presents formulae and the associated plots for evaluating the effective elastic constants for the core of this new sandwich structure. Comparison of structural properties of this new sandwich structure with the conventional honeycomb core sandwich structure was made under the condition of equal sandwich density. It was found that the SPF/DB orthogonally corrugated sandwich core has higher transverse shear stiffness than the conventional honeycomb sandwich core. However, the former has lower stiffness in the sandwich core thickness direction than the latter.

Ko, W. L.↗
NASA NTRS2013

Structure of the Small Amplitude Motion on Transversely Sheared Mean Flows

This paper considers the small amplitude unsteady motion of an inviscid non-heat conducting compressible fluid on a transversely sheared mean flow. It extends a previous result given in Goldstein (1978(b) and 1979(a)) which shows that the hydrodynamic component of the motion is determined by two arbitrary convected quantities in the absence of solid surfaces or other external sources. The result is important because it can be used to specify appropriate boundary conditions for unsteady surface interaction problems on transversely sheared mean flows in the same way that the vortical component of the Kovasznay (1953) decomposition is used to specify these conditions for surface interaction problems on uniform mean flows. But unlike the Kovasznay (1953) case the arbitrary convected quantities no longer bear a simple relation to the physical variables. One purpose of this paper is to derive a formula that relates these quantities to the (physically measurable) vorticity and pressure fluctuations in the flow.

Goldstein, Marvin E.↗
DOE OSTI2021

Chiral hydrodynamics in strong external magnetic fields

We construct the general hydrodynamic description of (3+1)-dimensional chiral charged (quantum) fluids subject to a strong external magnetic field with effective field theory methods. We determine the constitutive equations for the energy-momentum tensor and the axial charge current, in part from a generating functional. Furthermore, we derive the Kubo formulas which relate two-point functions of the energy-momentum tensor and charge current to 27 transport coefficients: 8 independent thermodynamic, 4 independent non-dissipative hydrodynamic, and 10 independent dissipative hydrodynamic transport coefficients. Five Onsager relations render 5 more transport coefficients dependent. We uncover four novel transport effects, which are encoded in what we call the shear-induced conductivity, the two expansion-induced longitudinal conductivities and the shear-induced Hall conductivity. Remarkably, the shear-induced Hall conductivity constitutes a novel non-dissipative transport effect. As a demonstration, we compute all transport coefficients explicitly in a strongly coupled quantum fluid via holography.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1991

Passive control of supersonic cavity flowfields

A computational investigation has been conducted to study the effect and mechanisms of the passive control of a supersonic flow over a rectangular two-dimensional cavity. The passive control was included through the use of a porous surface over a vent chamber in the floor of the cavity. The passive control effectively suppressed the low-frequency pressure oscillations for the open type cavity, (length-to-depth ratio = 6.0). The mechanism for the suppression was observed to be the stabilization of the motion of the free shear layer. For the closed type cavity flow, (length-to-depth ratio = 17.5), the passive control modified the flowfield to nearly that of an open type cavity flow; further the cavity drag was reduced by a factor of four. The computational results of both cases showed good agreement with the available experimental data and the predictions of a semiempirical formula. This study demonstrates that the passive control concept can be used to improve the aerodynamic characteristics of open and closed cavity flowfields.

Chokani, N.↗
NASA NTRS2009

Sensitivity of a Cloud-Resolving Model to Bulk and Explicit Bin Microphysical Schemes: Cloud Microphysics and Storm Dynamics Interactions - Part 2

Part I of this paper compares two simulations, one using a bulk and the other a detailed bin microphysical scheme, of a long-lasting, continental mesoscale convective system with leading convection and trailing stratiform region. Diagnostic studies and sensitivity tests are carried out in Part II to explain the simulated contrasts in the spatial and temporal variations by the two microphysical schemes and to understand the interactions between cloud microphysics and storm dynamics. It is found that the fixed raindrop size distribution in the bulk scheme artificially enhances rain evaporation rate and produces a stronger near surface cool pool compared with the bin simulation. In the bulk simulation, cool pool circulation dominates the near-surface environmental wind shear in contrast to the near-balance between cool pool and wind shear in the bin simulation. This is the main reason for the contrasting quasi-steady states simulated in Part I. Sensitivity tests also show that large amounts of fast-falling hail produced in the original bulk scheme not only result in a narrow trailing stratiform region but also act to further exacerbate the strong cool pool simulated in the bulk parameterization. An empirical formula for a correction factor, r(q(sub r)) = 0.11q(sub r)(exp -1.27) + 0.98, is developed to correct the overestimation of rain evaporation in the bulk model, where r is the ratio of the rain evaporation rate between the bulk and bin simulations and q(sub r)(g per kilogram) is the rain mixing ratio. This formula offers a practical fix for the simple bulk scheme in rain evaporation parameterization.

Li, Xiaowen↗
DOE OSTI2022

Study on Emulsification/Demulsification Behavior and Mechanism of Produced Liquid from Polymer Flooding on Alaska North Slope

Heavy oil reservoirs on Alaska North Slope (ANS) are unconsolidated and contain abundant clay minerals, where the first-ever field pilot is currently implemented to validate the use of polymer floods for heavy oil enhanced oil recovery (EOR). The polymer molecules and/or fine clay particles carried with the produced liquid could potentially affect the oil/water separation, which is one of the major concerns for field operators. This dissertation aims to investigate the emulsification behavior of produced liquid, understand the emulsifying mechanism, and seek an adaptive and cost-effective method to treat the produced liquid from polymer flooding. Emulsions were prepared by mechanically mixing the actual heavy oil and the produced water from the pilot site, of which the stability was investigated by bottle test method or multiple light scattering method. Drop size distribution and interfacial properties were measured via microscope and pendant drop technique to probe the stability mechanism further. Results showed that oil-continuous or water-continuous emulsion could be generated depending on the water cut, clay types, clay concentration, and polymer concentration. In the crude oil/water system, the increasing water cut triggered the phase inversion of oil-continuous emulsion to water-continuous emulsion, resulting in faster separation and lower emulsion stability. Whereas, clay particles, no matter added to the oil or water phase, resulted in an unfavorable phase inversion from the loose water-continuous emulsion to the tight oil-continuous emulsion as clay concentration increased. For all four types of clay except Ca-montmorillonite, clay particles added to water led to an earlier phase inversion and higher emulsion stability than that added to the oil. The dual function of polymer on emulsion stability was observed. On the one hand, both sheared and unsheared polymer tended to convert the oil-continuous emulsion formed in either crude oil/water system or complex crude oil/water/clay particle system to the water-continuous emulsion, acting as a weak demulsifier to accelerate the oil/water separation. On the other hand, the addition of polymer to the water-continuous emulsion could result in enhanced emulsion stability, which is primarily attributed to the increased viscosity of the continuous phase and the decreased drop size of the dispersed oil phase. Particularly, the sheared polymer had a weaker ability to stabilize the o/w emulsion than the unsheared polymer due to the lower viscosity of the sheared polymer solution resulting from the breakdown of the polymer macromolecules. As for the chemical demulsification tests, the performance of demulsifiers showed a complex dependency upon the water cut, the shearing intensity, demulsifier type and dosage, and the polymer concentration. A compound emulsion breaker, E12+E18, exhibited the most satisfactory demulsification performance despite the varied test conditions. For severe water-continuous emulsions that might require a multi-fold dosage of demulsifier, a less expensive electrolyte, KCl, was proposed to be used in combination with demulsifier E12+E18 to improve the demulsification performance. In the proposed demulsifier formula, the effectiveness of the commercial demulsifier relied on its destructive effect on the interfacial film, while the efficacy of KCl was mainly dependent on its viscosity reduction effect on the continuous phase. This dissertation illustrates that intermediate layer elimination and water clarification are the major challenges for produced liquid treatment from polymer flooding. It also provides practical and theoretical guidance in advance for the demulsification strategy of the produced liquid from the ongoing first-ever polymer flooding pilot on ANS.

Chang, Hongli↗
NASA NTRS1980

Bifurcation and stability in a model of moist convection in a shearing environment

The truncated spectral system (model I) of shallow moist two-dimensional convection discussed by Shirer and Dutton (1979) is expanded to eleven coefficients (model II) in order to include a basic wind. Cloud streets, the atmospheric analog of the solutions to model II, are typically observed in an environment containing a shearing basic motion field. Analysis of the branching behavior of solutions to mode II shows that, if the basic wind direction varies with height, very complex temporal behavior is possible as the modified Rayleigh number HR is increased sufficiently. The first convective solution is periodic, corresponding to a cloud band that propagates downwind; but secondary branching to a two-dimensional torus can occur for larger values of HR. Orientation band formulas are derived whose predictions generally agree with the results of previous studies.

Shirer, H. N.↗
NASA NTRS1980

Elastic constants for superplastically formed/diffusion-bonded corrugated sandwich core

Formulas and associated graphs for evaluating the effective elastic constants for a superplastically formed/diffusion bonded (SPF/DB) corrugated sandwich core, are presented. A comparison of structural stiffnesses of the sandwich core and a honeycomb core under conditions of equal sandwich core density was made. The stiffness in the thickness direction of the optimum SPF/DB corrugated core (that is, triangular truss core) is lower than that of the honeycomb core, and that the former has higher transverse shear stiffness than the latter.

Ko, W. L.↗
NASA NTRS1976

The effect of adhesive layer on crack propagation in laminates

The effect of the adhesive layer on crack propagation in composite materials is investigated. The composite medium consists of parallel load carrying laminates and buffer strips arranged periodically and bonded with thin adhesive layers. The strips, assumed to be isotropic and linearly elastic, contain symmetric cracks of arbitrary lengths located normal to the interfaces. Two problems are considered: (1) thin adhesive layers are approximated by uncoupled tension and shear springs distributed along the interfaces of the strips for which only the case of internal cracks can be treated rigorously; (2) broken laminates and the true singular behavior in the presence of the adhesive layer are studied. The adhesive is then treated as an isotropic, linearly elastic continuum. General expressions for field quantities are obtained in terms of infinite Fourier integrals. These expressions give a system of singular integral equations in terms of the crack surface displacement derivatives. By using appropriate quadrature formulas, the integral equations reduce to a system of linear algebraic equations which are solved numerically.

Gecit, M. R.↗