Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Stokes”

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 1,765 records · Page 98
All sourcesNASA NTRSDOE OSTI
NASA NTRS1984

Viscous computation of a space shuttle flow field

A procedure is presented, as well as some results, to calculate the flow over the winged orbiter. This necessitates the use of two computer codes. A parabolized marching Navier-Stokes code is used to obtain the solution up to the bow shock-wing shock interaction region and for the region after the interaction. An unsteady Navier-Stokes code is to be used in the region of the shock interaction. Only resuls for the marching code are presented. For the flow conditions calculated, M infinity = 7.9, alpha = 25 deg, T(wall) = 540 R, Re(L) = 60728 per inch, laminar or turbulent, the PNS code was marched up to an X/L = 0.7 which is where the bow shock-wing shock interaction region occurs.

Chaussee, D. S.↗
NASA NTRS1983

Continuation in a parameter - Experience with viscous and free surface flows

The results of modifications in continuation methods applied to obtain solutions to the Navier-Stokes systems of equations for incompressible, two-dimensional, steady flows are reported. It is shown that parameter continuation permits prediction of accurate, initial estimates for iterative processing of nonlinear finite difference and finite element equations of motions. The new parameter steps are derived from values of the preceding parameter steps. The accuracy of the estimates is ensured with appropriate choices of the step size. The continuation predictor/iterative corrector is demonstrated to trace the branches of parameter space along which steady flow states are found, and techniques are available for tracing multiply branching paths. The techniques are applied to solving the Navier-Stokes equations for flow through a rotating square channel, the formation of a falling liquid curtain, and gyrostatic equilibria of rotating cylindrical drops.

Kheshgi, H. S.↗
NASA NTRS1984

Wall mass transfer and pressure gradient effects on turbulent skin friction

The effects of mass injection and pressure gradients on the drag of surfaces were studied theoretically with the aid of boundary-layer and Navier-Stokes codes. The present investigation is concerned with the effects of spatially varying the injection in the case of flat-plate drag. Effects of suction and injection on wavy wall surfaces are also explored. Calculations were performed for 1.2 m long surfaces, one flat and the other sinusoidal with a wavelength of 30.5 cm. Attention is given to the study of the effect of various spatial blowing variations on flat-plate skin friction reduction, local skin friction coefficient calculated by finite difference boundary-layer code and Navier-Stokes code, and the effect of phase-shifting sinusoidal mass transfer on the drag of a sinusoidal surface.

Watson, R. D.↗
NASA NTRS1984

CARS system for turbulent flame measurements

Simultaneous nitrogen number density and rotational-vibrational temperatures were measured in a turbulent diffusion flame with a Coherent Anti-Stokes Raman Scattering (CARS) instrument. The fuel jet was diluted with nitrogen (20 percent by volume) to allow temperature measurements across the entire jet mixing region. These measurements were compared with fluid dynamics computations. The CARS system incorporated a neodymium YAG laser, an intensified silicon photodiode array detector, and unique dynamic range enhancement methods. Theoretical calculations were based on a parabolic Navier-Stokes computer code. The comparison of these techniques will aid their development in the study of complex flowfields.

Antcliff, R. R.↗
NASA NTRS1984

Prediction of transonic separated flows

Johnson et al. (1982) have provided a detailed comparison between a thoroughly documented transonic flow with shock-induced separations and solutions of the flow using the Navier-Stokes equations. According to this comparison, there were several deficiencies in the computations. The present investigation takes into account new experimental data which have been obtained in a larger wind tunnel with the same test model for a wider range of freestream Mach numbers. The results of new Navier-Stokes computations using more compatible boundary conditions are shown, and the effects of the turbulence model choice on predicting Mach number trends are assessed.

Horstman, C. C.↗
NASA NTRS1984

Numerical solution of Space Shuttle Orbiter flow field including real gas effects

The hypersonic, laminar flow around the Space Shuttle Orbiter has been computed for both an ideal gas (gamma = 1.2) and equilibrium air using a real-gas, parabolized Navier-Stokes code. This code employs a generalized coordinate transformation; hence, it places no restrictions on the orientation of the solution surfaces. The initial solution in the nose region was computed using a 3-D, real-gas, time-dependent Navier-Stokes code. The thermodynamic and transport properties of equilibrium air were obtained from either approximate curve fits or a table look-up procedure. Numerical results are presented for flight conditions corresponding to the STS-3 trajectory. The computed surface pressures and convective heating rates are compared with data from the STS-3 flight.

Prabhu, D. K.↗
NASA NTRS1984

Turbulent solutions of the equations of fluid motion

Some turbulent solutions of the unaveraged Navier-Stokes equations (equations of fluid motion) are reviewed. Those equations are solved numerically in order to study the nonlinear physics of incompressible turbulent flow. Initial three-dimensional cosine velocity fluctuations and periodic boundary conditions are used in most of the work considered. The three components of the mean-square velocity fluctuations are initially equal for the conditions chosen. The resulting solutions show characteristics of turbulence such as the linear and nonlinear excitation of small-scale fluctuations. For the stronger fluctuations, the initially nonrandom flow develops into an apparently random turbulence. Thus randomness or turbulence can arise as a consequence of the structure of the Navier-Stokes equations. The cases considered include turbulence which is statistically homogeneous or inhomogeneous and isotropic or anisotropic. A mean shear is present in some cases. A statistically steady-state turbulence is obtained by using a spatially periodic body force. Various turbulence processes, including the transfer of energy between eddy sizes and between directional components, and the production, dissipation, and spatial diffusion of turbulence, are considered. It is concluded that the physical processes occurring in turbulence can be profitably studied numerically.

Deissler, R. G.↗
NASA NTRS1984

Numerical studies of unsteady transonic flow over an oscillating airfoil

A finite-difference solution to the Navier-Stokes equations combined with a time-varying grid-generation technique was used to compute unsteady transonic flow over an oscillating airfoil. These computations were compared with experimental data (obtained at Ames Research Center) which form part of the AGARD standard configuration for aeroelastic analysis. A variety of approximations to the full Navier-Stokes equations was used to determine the effect of frequency, shock-wave motion, flow separation, and airfoil geometry on unsteady pressures and overall air loads. Good agreement is shown between experiment and theory with the limiting factor being the lack of a reliable turbulence model for high-Reynolds-number, unsteady transonic flows.

Chyu, W. J.↗
NASA NTRS1985

Calculation of three-dimensional, viscous flow through turbomachinery blade passages by parabolic marching

The three-dimensional compressible Navier-Stokes equations are formulated in a rotating coordinate system, so as to include centrifugal and Coriolis forces. The equations are parabolized by using a previously calculated inviscid static pressure field. The thin layer Navier-Stokes approximation, which neglects streamwise diffusion, is used. A body-fitted coordinate system is used. The streamwise momentum equation is uncoupled from the cross-stream momentum equation by using contravariant momentum components, and then using the contravariant velocity components as primary unknowns. To reduce problems with small separated regions, the Reyhner and Flugge-Lotz approximation is used. The energy equation is included to allow for calculation of heat transfer. The flow may be laminar, or a simple eddy-viscosity turbulence may be used. A number of curved ducts and an axial stator were analyzed, including cases for which experimental data are available.

Katsanis, T.↗
NASA NTRS1985

Numerical studies of unsteady transonic flow over oscillating airfoil

A finite difference solution to the Navier-Stokes equations combined with a time varying grid generation technique was used to compute unsteady transonic flow over an oscillating airfoil. These computations were compared with experimental data (obtained at Ames Research Center) which form part of the AGARD standard configuration for aeroelastic analysis. A variety of approximations to the full Navier-Stokes equations was used to determine the effect of frequency, shock wave motion, flow separation, and airfoil geometry on unsteady pressures and overall air loads. Good agreement is shown between experiment and theory with the limiting factor being the lack of a reliable turbulence model for high Reynolds number, unsteady transonic flows.

Chyu, W. J.↗
NASA NTRS1985

User's manual for airfoil flow field computer code SRAIR

A two dimensional unsteady Navier-Stokes calculation procedure with specific application to the isolated airfoil problem is presented. The procedure solves the full, ensemble averaged Navier-Stokes equations with turbulence represented by a mixing length model. The equations are solved in a general nonorthogonal coordinate system which is obtained via an external source. Specific Cartesian locations of grid points are required as input for this code. The method of solution is based upon the Briley-McDonald LBI procedure. The manual discusses the analysis, flow of the program, control steam, input and output.

Shamroth, S. J.↗
NASA NTRS1985

Simulation of Multistage Turbine Flows

The numerical simulation of turbine flows serves to enhance the understanding of the flow phenomena within multistage turbomachinery components. The direct benefit of this activity is improved modeling capability, which can be used to improve component efficiency and durability. A hierarchy of equations was formulated to assess the difficulty in analyzing the flow field within multistage turbomachinery components. The Navier-Stokes equations provides the most complete description. The simplest description is given by a set of equations that govern the quasi-one-dimensional flow. The number of unknowns to be solved for increases monotonically above the number of equations. The development of the additional set of equations needed to mathematically close the system of equations forms the closure problem associated with that level of description. For the Navier-Stokes equation there is no closure problem. For the quasi-one-dimensional equation set random flow fluctuations, unsteady fluctuations, nonaxisymmetric flow variations, and hub-to-shroud variations on the quasi-one-dimensional flow must be accounted for.

Celestina, M. L.↗
NASA NTRS1984

Numerical computation of space shuttle orbiter flow field

The complete inviscid viscous real gas flow around the Space Shuttle Orbiter was computed. Real gas effects are important in predicting the reentry environment around the Orbiter because the high temperatures within the shock layer cause the air to dissociate and ionize, thus invalidating the perfect gas assumption. It is shown that real gas effects has a significant influence on the Orbiter aerodynamics. The approach utilizes a time dependent Navier-Stokes code to compute the subsonic nose portion of the flow field. This nose solution provides the initial conditions for the parabolized Navier-Stokes (PNS) code.

Tannehill, J. C.↗
NASA NTRS1985

Diagnostics of vector magnetic fields

It is shown that the vector magnetic fields derived from observations with a filter magnetograph will be severely distorted if the spatially unresolved magnetic structure is not properly accounted for. Thus the apparent vector field will appear much more horizontal than it really is, but this distortion is strongly dependent on the area factor and the temperature line weakenings. As the available fluxtube models are not sufficiently well determined, it is not possible to correct the filter magnetograph observations for these effects in a reliable way, although a crude correction is of course much better than no correction at all. The solution to this diagnostic problem is to observe simultaneously in suitable combinations of spectral lines, and/or use Stokes line profiles recorded with very high spectral resolution. The diagnostic power of using a Fourier transform spectrometer for polarimetry is shown and some results from I and V spectra are illustrated. The line asymmetries caused by mass motions inside the fluxtubes adds an extra complication to the diagnostic problem, in particular as there are indications that the motions are nonstationary in nature. The temperature structure appears to be a function of fluxtube diameter, as a clear difference between plage and network fluxtubes was revealed. The divergence of the magnetic field with height plays an essential role in the explanation of the Stokes V asymmetries (in combination with the mass motions). A self consistent treatment of the subarcsec field geometry may be required to allow an accurate derivation of the spatially averaged vector magnetic field from spectrally resolved data.

Stenflo, J. O.↗
NASA NTRS1985

Dynamic models of flux tubes in the interpretation of polarization measurements

Recent observations of Stokes parameter profiles indicate the presence of mass motions with large velocity gradients associated with small-scale magnetic elements. Dynamic models of flux tubes were used in order to interpret observations of unresolved elements. It is clear that the physical picture of the dynamic models will be quite different from the hydrostatic ones since there is a strong coupling between the magnetic and the velocity field. Polarization measurements have to be interpreted in terms of dynamic models. Two-D steady flow solutions in slender magnetic tubes have been worked out. It was found that the main properties of the intensity line profiles as well as the asymmetries of the V Stokes profiles can be explained best in terms of magnetic elements with moderate field strength.

Ribes-Nesme, E.↗
NASA NTRS1985

Contribution functions for Zeeman-split lines, and line formation in photospheric faculae

The transfer of polarized light in an inhomogeneous stellar atmosphere, and the formation of magnetically sensitive spectral lines, are discussed. A new method for the solution of the transfer equations is proposed. The method gives a natural definition of the contribution functions for Stokes' parameters, i.e., functions describing the contributions from different parts along the line-of-sight (LOS). The formalism includes all magneto-optical effects, and allows for an arbitrary variation of magnetic field, velocity field, temperature, density, etc., along the LOS. The formation of FeI lambda 5250.2 in photospheric faculae is described. A potential-field model of a facular element is presented, and spectra profiles and contribution functions are computed for the Stokes parameters I, Q, and V.

Vanballegooijen, A. A.↗
NASA NTRS1985

The effect of line damping, magneto-optics and parasitic light on the derivation of sunspot vector magnetic fields

The least square fitting of Stokes observations of sunspots using a Milne-Eddington-Unno model appears to lead, in many circumstances, to various inconsistencies such as anomalously large doppler widths and, hence, small magnetic fields which are significantly below those inferred solely from the Zeeman splitting in the intensity profile. It is found that the introduction of additional physics into the model such as the inclusion of damping wings and magneto-optic birefrigence significantly improves the fit to Stokes parameters. Model fits excluding the intensity profile, i.e., of both magnitude as well as spectral shape of the polarization parameters alone, suggest that parasitic light in the intensity profile may also be a source of inconsistencies. The consequences of the physical changes on the vector properties of the field derived from the Fe I lambda 6173 line for the 17 November 1975 spot as well as on the thermodynamic state are discussed. A Doppler width delta lambda (D) - 25mA is bound to be consistent with a low spot temperature and microturbulence, and a damping constant of a = 0.2.

Skumanich, A.↗
NASA NTRS1985

A mixed pseudospectral/finite difference method for a thermally driven fluid in a nonuniform gravitational field

A numerical study of the steady, axisymmetric flow in a heated, rotating spherical shell is conducted to model the Atmospheric General Circulation Experiment (AGCE) proposed to run aboard a later shuttle mission. The AGCE will consist of concentric rotating spheres confining a dielectric fluid. By imposing a dielectric field across the fluid a radial body force will be created. The numerical solution technique is based on the incompressible Navier-Stokes equations. In the method a pseudospectral technique is based on the incompressible Navier-Stokes equations. In the method a pseudospectral technique is used in the latitudinal direction, and a second-order accurate finite difference scheme discretizes time and radial derivatives. This paper discusses the development and performance of this numerical scheme for the AGCE which has been modelled in the past only by pure FD formulations. In addition, previous models have not investigated the effect of using a dielectric force to simulate terrestrial gravity. The effect of this dielectric force on the flow field is investigated as well as a parameter study of varying rotation rates and boundary temperatures. Among the effects noted are the production of larger velocities and enhanced reversals of radial temperature gradients for a body force generated by the electric field.

Macaraeg, M. G.↗