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.

SourceResearch connectionFrom yearThrough year

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

At least 37 records · Page 2

All sources NASA NTRS DOE OSTI

NASA NTRS1990

Fastener Design Manual

This manual was written for design engineers to enable them to choose appropriate fasteners for their designs. Subject matter includes fastener material selection, platings, lubricants, corrosion, locking methods, washers, inserts, thread types and classes, fatigue loading, and fastener torque. A section on design criteria covers the derivation of torque formulas, loads on a fastener group, combining simultaneous shear and tension loads, pullout load for tapped holes, grip length, head styles, and fastener strengths. The second half of this manual presents general guidelines and selection criteria for rivets and lockbolts.

Barrett, Richard T.↗

DOE OSTI2020

Improving the Physical Basis for Updraft Dynamics in Deep Convection Parameterizations

This article presents a new deep convective parameterization that determines cloud characteristics based on a specified cloud size distribution. The vertical profiles of cloud properties are determined by analytic equations, which formulate entrainment with an inverse relationship to cloud width. In line with recent studies of large eddy simulations (LES), cloud widths are assumed to be constant with height and vertical mass flux (M) characteristics of the clouds are therefore regulated by the vertical velocity profile. The parameterization is configured to work with existing cloud base M closure formulations, with the closure predicting the total cloud area rather than the cloud base M directly. Analytic formula are also used to connect the vertical wind shear magnitude to the cloud size distribution, wherein larger shear magnitudes result in more numerous large updrafts than weaker shear magnitudes, which is in line with recent research results. The parameterization is compared against 10 deep convective LES with varying thermodynamic and vertical wind shear profiles. Results show dramatic improvements in the prediction of normalized M, detrainment, and the properties of detrained air over the existing Zhang and McFarlane (1995) scheme. In particular, the new model is able to correctly portray the transition from a bottom-heavy M profile in weakly sheared environments, to a top-heavy M profile in strongly sheared environments.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2022

Pseudogauge dependence of the spin polarization and of the axial vortical effect

The mean spin polarization vector of spin 1/2 particles in a relativistic fluid at local thermal equilibrium (LTE) in different pseudogauges (PGs), i.e., with different choices for the decomposition of orbital and spin angular momentum, is obtained. The spin polarization obtained in the canonical PG differs from the one obtained in the Belinfante PG. It is found that this difference can not be written by replacing the thermal vorticity with the spin potential in the usual polarization formula. Other PG choices affect the contribution of thermal shear to the spin polarization. So, the choice of a PG affects the predictions for the polarization measured in heavy-ion collisions. In general, it is shown that the Wigner function of a noninteracting Dirac field at LTE is affected by the PG transformations. Explicit expressions of the mean axial current are also calculated and it is found that even the axial vortical effect conductivity depends on the PG.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

NASA NTRS1985

Constraints on short-term mantle rheology from the J2 observation and the dispersion of the 18.6 y tidal Love number

Information derived from data recently acquired from the LAGEOS satellite is used to place some constraints on the rheological parameters of short-term mantle rheology. The validity of Lambeck and Nakiboglu's (1983) rheological model is assessed by formally developing an expression for the transformed shear modulus using a truncated retardation spectrum. This analytical formula is used to show that the parameters of the above mentioned model are not consistent at all with the amount of anelastic dispersion expected in the Chandler wobble and with the attenuation of seismic normal modes. The feasibility of a standard linear solid (SLS) rheology operating over intermediate timescales between 1 and 100 yr is investigated to determine whether the tidal dispersion at 18.6 yr can be explained by this model. An attempt is made to place some constraints on the parameters of the SLS model and the nature of short-term mantle rheology for timescales of less than 100 yr is discussed.

Sabadini, R.↗

NASA NTRS1989

Navier-Stokes analysis of cold scramjet-afterbody flows

The progress of two efforts in coding solutions of Navier-Stokes equations is summarized. The first effort concerns a 3-D space marching parabolized Navier-Stokes (PNS) code being modified to compute the supersonic mixing flow through an internal/external expansion nozzle with multicomponent gases. The 3-D PNS equations, coupled with a set of species continuity equations, are solved using an implicit finite difference scheme. The completed work is summarized and includes code modifications for four chemical species, computing the flow upstream of the upper cowl for a theoretical air mixture, developing an initial plane solution for the inner nozzle region, and computing the flow inside the nozzle for both a N2/O2 mixture and a Freon-12/Ar mixture, and plotting density-pressure contours for the inner nozzle region. The second effort concerns a full Navier-Stokes code. The species continuity equations account for the diffusion of multiple gases. This 3-D explicit afterbody code has the ability to use high order numerical integration schemes such as the 4th order MacCormack, and the Gottlieb-MacCormack schemes. Changes to the work are listed and include, but are not limited to: (1) internal/external flow capability; (2) new treatments of the cowl wall boundary conditions and relaxed computations around the cowl region and cowl tip; (3) the entering of the thermodynamic and transport properties of Freon-12, Ar, O, and N; (4) modification to the Baldwin-Lomax turbulence model to account for turbulent eddies generated by cowl walls inside and external to the nozzle; and (5) adopting a relaxation formula to account for the turbulence in the mixing shear layer.

Baysal, Oktay↗

NASA NTRS2008

Improved Design Formulae for Buckling of Orthotropic Plates under Combined Loading

Simple, accurate buckling interaction formulae are presented for long orthotropic plates with either simply supported or clamped longitudinal edges and under combined loading that are suitable for design studies. The loads include 1) combined uniaxial compression (or tension) and shear, 2) combined pure inplane bending and 3) shear and combined uniaxial compression (or tension) and pure inplane bending. The interaction formulae are the results of detailed regression analysis of buckling data obtained from a very accurate Rayleigh-Ritz method.

Weaver, Paul M.↗

DOE OSTI2020

A Formula for the Maximum Vertical Velocity in Supercell Updrafts

In supercell environments, previous authors have shown strong connections between the vertical wind shear magnitude, updraft width, and entrainment. Based on these results, it is hypothesized that the influences of entrainment-driven dilution on buoyancy and maximum updraft vertical velocity w in supercell environments are a predictable function of the vertical wind shear profile. It is also hypothesized that the influences of pressure perturbation forces on maximum updraft w are small because of a nearly complete offset between upward dynamic pressure forces and downward buoyant pressure forces. To address these hypotheses, we derive a formula for the maximum updraft w that incorporates the effects of entrainment-driven dilution on buoyancy but neglects pressure gradient forces. Solutions to this formula are compared with output from previous numerical simulations. This formula substantially improves predictions of maximum updraft w over past CAPE-derived formulas for maximum updraft w, which supports the first hypothesis. Furthermore, integrated vertical accelerations along trajectories show substantial offsets between dynamic and buoyant pressure forces, supporting the second hypothesis. It is argued that the new formula should be used in addition to CAPE-derived measures for w in forecast and research applications when accurate diagnosis of updraft speed is required.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

NASA NTRS1987

A general form for the dissipation length scale in turbulent shear flows

It has been found that, for a wide range of turbulent wall-bounded shear flows with mean velocity profile U(y), the scale length L-epsilon determining the dissipation is approximately described in terms of distance from the wall (y), the mean shear (dU/dy), and the variance of the normal component of turbulence (bar u-squared), by the formula: L-epsilon to the -1 power is approximately equal to (A sub B / y) + A sub S (dU/dy / square root of bar u-squared) where L-epsilon = epsilon/(bar u-squared) to the 3/2 power. To match with shear-free boundary layers, A sub B is approximately 0.27, and to match with the log layer, A sub S is approximately 0.46. The shear flows tested here were: boundary layers over a flat plate, sink flow, oscillatory flow, and channel flow. The use of the square root of bar u-squared as a velocity scale minimizes the effects of Reynolds number. However, the formula fails within a distance of order L-epsilon for the regions where dU/dy = 0.

Hunt, J. C. R.↗

NASA NTRS1979

Laminar boundary-layer flow of non-Newtonian fluid

A solution for the two-dimensional and axisymmetric laminar boundary-layer momentum equation of power-law non-Newtonian fluid is presented. The analysis makes use of the Merk-Chao series solution method originally devised for the flow of Newtonian fluid. The universal functions for the leading term in the series are tabulated for n from 0.2 to 2. Equations governing the universal functions associated with the second and the third terms are provided. The solution together with either Lighthill's formula or Chao's formula constitutes a simple yet general procedure for the calculation of wall shear and surface heat transfer rate. The theory was applied to flows over a circular cylinder and a sphere and the results compared with published data.

Lin, F. N.↗

NASA NTRS1954

Formulas for the elastic constants of plates with integral waffle-like stiffening

Formulas are derived for the fifteen elastic constants associated with bending, stretching, twisting, and shearing of plates with closely spaced integral ribbing in a variety of configurations and proportions. In the derivation the plates are considered, conceptually, as more uniform orthotropic plates somewhat on the order of plywood. The constants, which include the effectiveness of the ribs for resisting deformations other than bending and stretching in their longitudinal directions, are defined in terms of four coefficients, and theoretical and experimental methods for the evaluation of these coefficients are discussed. Four of the more important elastic constants are predicted by these formulas and are compared with test results. Good correlation is obtained. (author)

Dow, Norris R↗

NASA NTRS1957

A discussion of cone and flat-plate Reynolds numbers for equal ratios of the laminar shear to the shear caused by small velocity fluctuations in a laminar boundary layer

By use of the linear theory of boundary-layer stability and Schlichting's formula for the maximum amplification of a disturbance, an approximate relation is derived between the Reynolds number on a cone and the Reynolds number on a flat plate for equal closeness to transition. The indication is that the ratio of the cone Reynolds number for transition, based on the distance to the cone apex, to the plate Reynolds number for transition, based on the distance to the leading edge, is not in general equal to 3, as has been suggested by other investigators, but varies from 3 when transition occurs at the minimum critical Reynolds number to unity when transition occurs at a large multiple of the critical Reynolds number.

FLOW, TURBULENT↗

NASA NTRS1981

Organized motion in turbulent flow

A review of organized motion in turbulent flow indicates that the transport properties of most shear flows are dominated by large-scale vortex nonrandom motions. The mean velocity profile of a turbulent boundary layer consists of a viscous sublayer, buffer layer, and a logarithmic outer layer; an empirical formula of Coles (1956) applies to various pressure gradients. The boundary layer coherent structure was isolated by the correlation methods of Townsend (1956) and flow visualization by direct observations of complex unsteady turbulent motions. The near-wall studies of Willmart and Wooldridge (1962) used the space-time correlation for pressure fluctuations at the wall under a thick turbulent boundary layer; finally, organized motion in free shear flows and transition-control of mixing demonstrated that the Reynolds number invariance of turbulence shows wide scatter.

Cantwell, B. J.↗

DOE OSTI2021

A theory of localized excitations in supercooled liquids

Here, a new connection between the structure and dynamics in glass-forming liquids is presented. We show how the origin of spatially localized excitations, as defined by the dynamical facilitation (DF) theory, can be understood from a structure-based framework. This framework is constructed by associating excitation events in the DF theory to hopping events between energy minima in the potential energy landscape (PEL). By reducing the PEL to an equal energy well picture and applying a harmonic approximation, we develop a field theory to describe elastic fluctuations about inherent states, which are energy minimizing configurations of the PEL. We model an excitation as a shear transformation zone (STZ) inducing a localized pure shear deformation onto an inherent state. We connect STZs to T1 transition events that break the elastic bonds holding the local structure of an inherent state. A formula for the excitation energy barrier, denoted as J σ , is obtained as a function of inherent-state elastic moduli and the radial distribution function. The energy barrier from the current theory is compared to the one predicted by the DF theory where good agreement is found in various two-dimensional continuous poly-disperse atomistic models of glass formers. These results strengthen the role of structure and elasticity in driving glassy dynamics through the creation and relaxation of localized excitations.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

NASA NTRS1984

A current generation by Compton scattering in a relativistic plasma with velocity shear and temperature gradient

Current generation by Thomson scattering in a non-relativistic plasma with the velocity shear and the temperature gradient (Hinata and Daneshvar, 1983) is extended to a relativistic plasma by replacing Thomson cross section by the Klein-Nishina formula. Because of the energy dependence of the cross-section, a numerical rather than analytic result is presented. The present calculation may be applied to a supernova implosion where the temperature may reach several MeV and a strong differential rotation is expected. It may also find applications in the early universe, and laser-pellet interaction.

Hinata, S.↗

DOE OSTI2021

Relativistic spin hydrodynamics with torsion and linear response theory for spin relaxation

Using the second law of local thermodynamics and the first-order Palatini formalism, we formulate relativistic spin hydrodynamics for quantum field theories with Dirac fermions, such as QED and QCD, in a torsionful curved background. We work in a regime where spin density, which is assumed to relax much slower than other non-hydrodynamic modes, is treated as an independent degree of freedom in an extended hydrodynamic description. Spin hydrodynamics in our approach contains only three non-hydrodynamic modes corresponding to a spin vector, whose relaxation time is controlled by a new transport coefficient: the rotational viscosity. We study linear response theory and observe an interesting mode mixing phenomenon between the transverse shear and the spin density modes. We propose several field-theoretical ways to compute the spin relaxation time and the rotational viscosity, via the Green-Kubo formula based on retarded correlation functions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

NASA NTRS1972

Rayleigh wave effects in an elastic half-space.

Consideration of Rayleigh wave effects in a homogeneous isotropic linearly elastic half-space subject to an impulsive uniform disk pressure loading. An approximate formula is obtained for the Rayleigh wave effects. It is shown that the Rayleigh waves near the center of loading arise from the portion of the dilatational and shear waves moving toward the axis, after they originate at the edge of the load disk. A study is made of the vertical displacement due to Rayleigh waves at points on the axis near the surface of the elastic half-space.

Aggarwal, H. R.↗

NASA NTRS1974

Secondary vorticity in axial compressor blade rows

A theoretical investigation of secondary flow in compressor blade rows is presented. Formulas for calculating secondary flows in annular cascade blade passages are derived. The influence of the relative rotation vector on secondary velocity perturbations, using recent developments in shear-flow theory, is examined. A method of calculating the flow through successive blade rows is given and a comparison is made with experimental results.

Dixon, S. L.↗

NASA NTRS2004

A Model for Shear Layer Effects on Engine Noise Radiation

Prediction of aircraft engine noise is an important aspect of addressing the issues of community noise and cabin noise control. The development of physics based methodologies for performing such predictions has been a focus of Computational Aeroacoustics (CAA). A recent example of code development in this area is the ducted fan noise propagation and radiation code CDUCT-LaRC. Included within the code is a duct radiation model that is based on the solution of FfowcsWilliams-Hawkings (FW-H) equation with a penetrable data surface. Testing of this equation for many acoustic problems has shown it to provide generally better results than the Kirchhoff formula for moving surfaces. Currently, the data surface is taken to be the inlet or exhaust plane for inlet or aft-fan cases, respectively. While this provides reasonable results in many situations, these choices of data surface location lead to a few limitations. For example, the shear layer between the bypass ow and external stream can refract the sound waves radiated to the far field. Radiation results can be improved by including this effect, as well as the rejection of the sound in the bypass region from the solid surface external to the bypass duct surrounding the core ow. This work describes the implementation, and possible approximation, of a shear layer boundary condition within CDUCT-LaRC. An example application also illustrates the improvements that this extension offers for predicting noise radiation from complex inlet and bypass duct geometries, thereby providing a means to evaluate external treatments in the vicinity of the bypass duct exhaust plane.

Nark, Douglas M.↗