Search NASA⌕ Search

SEARCH · Search NASA

Results for “MIXING LENGTH”

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 127 records · Page 7
All sourcesNASA NTRSDOE OSTI
NASA NTRS1976

The relativistic equations of stellar structure and evolution. Stars with degenerate neutron cores. 1: Structure of equilibrium models

The general relativistic equations of stellar structure and evolution are reformulated in a notation which makes easy contact with Newtonian theory. Also, a general relativistic version of the mixing-length formalism for convection is presented. Finally, it is argued that in previous work on spherical systems general relativity theorists have identified the wrong quantity as "total mass-energy inside radius r."

Thorne, K. S.↗
NASA NTRS1975

A grid of model atmospheres for metal-deficient giant stars. I

A grid of flux-constant model atmospheres for stars with effective temperatures between 3750 and 6000 K, log g between 0.75 and 3.0, and (A/H) between -3.0 and 0.0 has been constructed. The line absorption is approximated by opacity distribution functions. Metal lines and molecular lines, including those from the infrared bands of CO and CN, are taken into account. The variation of the structure of the models with metal abundance and microturbulence parameter is found to be quite regular and not very drastic. The surface cooling produced by CO is important for all the models with a maximum temperature of 5000 K, while CN mainly causes a backwarming effect but is not very important for solar CNO abundances. The effects of convection, estimated by using the mixing-length approximation, are important only for the coldest models. The models compare very well with models from overlapping regions of other grids. A solar model consistent with the grid models is found to agree satisfactorily with empirical solar model atmospheres. The careful use of scaled solar models for stars with (A/H) approximately equal to zero is justified.

Gustafsson, B.↗
NASA NTRS1976

Modeling of three-dimensional mixing and reacting ducted flows

A computer code based on a finite-element solution algorithm is developed to perform an analytical investigation on the turbulent mixing and reaction of hydrogen jets injected from multiple orifices transverse and parallel to a supersonic airstream. A laser optical cavity flow field was also analyzed to demonstrate the generality of the proposed model. Computational results provide a three-dimensional description of velocity, temperature, and species-concentration fields downstream of injection. Major conclusions are that the analysis has immediate utility in evaluating the mixing effectiveness of transverse H2 injection data since it has been tested in its ability to model this type of data and that turbulent mixing length theory, constant effective Prandtl number, and a Lewis number of unity provide reasonable agreement with transverse H2 injection data downstream of the near-injection region. Efforts are presently being directed toward using the code in modeling laser and scramjet data for a wide range of flow conditions.

Zelazny, S. W.↗
NASA NTRS1976

Excitation of pulsations in the CNO ionization zone of luminous stars

Homogeneous models of luminous hydrogen-and-helium burning stars were constructed on the basis of Carson's new radiative opacities. These opacities exhibit a large 'bump' at moderate temperatures and low densities as a result of the ultimate ionization of the CNO group of elements and they induce in the envelopes of the more massive stars a strong local convection zone, a high central condensation and pulsational instability by means of the kappa-mechanism above a certain stellar mass. This critical mass for Population I hydrogen-burning stars is probably greater than 45 solar masses for the fundamental radial mode, with the overtones being more stable, while for the homogeneous helium-burning stars, the critical mass lies in the range 2-6 solar masses for all modes up to at least the third overtone. Convection is alternately treated by means of the mixing length theory and the assumption of strict adiabaticity.

Stothers, R.↗
NASA NTRS1976

Heat transfer to a full-coverage film-cooled surface with 30 degree slant-hole injection

Heat transfer behavior was studied in a turbulent boundary layer with full coverage film cooling through an array of discrete holes and with injection 30 deg to the wall surface in the downstream direction. Stanton numbers were measured for a staggered hole pattern with pitch-to-diameter ratios of 5 and 10, an injection mass flux ratio range of 0.1 to 1.3, and a range of Reynolds number Re sub x of 150,000 to 5 million. Air was used as the working fluid, and the mainstream velocity varied from 9.8 to 34.2 m/sec (32 to 112 ft/sec). The data were taken for secondary injection temperature equal to the wall temperature and also equal to the mainstream temperature. The data may be used to obtain Stanton number as a continuous function of the injectant temperature by use of linear superposition theory. The heat transfer coefficient is defined on the basis of a mainstream-to-wall temperature difference. This definition permits direct comparison of performance between film cooling and transpiration cooling. A differential prediction method was developed to predict the film cooling data base. The method utilizes a two-dimensional boundary layer program with routines to model the injection process and turbulence augmentation. The program marches in the streamwise direction, and when a row of holes is encountered, it stops and injects fluid into the boundary layer. The turbulence level is modeled by algebraically augmenting the mixing length, with the augmentation keyed to a penetration distance for the injected fluid.

Crawford, M. E.↗
NASA NTRS1977

Vorticity interaction effects on blunt bodies

Numerical solutions of the viscous shock layer equations governing laminar and turbulent flows of a perfect gas and radiating and nonradiating mixtures of perfect gases in chemical equilibrium are presented for hypersonic flow over spherically blunted cones and hyperboloids. Turbulent properties are described in terms of the classical mixing length. Results are compared with boundary layer and inviscid flowfield solutions; agreement with inviscid flowfield data is satisfactory. Agreement with boundary layer solutions is good except in regions of strong vorticity interaction; in these flow regions, the viscous shock layer solutions appear to be more satisfactory than the boundary layer solutions. Boundary conditions suitable for hypersonic viscous shock layers are devised for an advanced turbulence theory.

Anderson, E. C.↗
NASA NTRS1977

Full-scale altitude engine test of a turbofan exhaust-gas-forced mixer to reduce thrust specific fuel consumption

The specific fuel consumption of a low-bypass-ratio, confluent-flow, turbofan engine was measured with and without a mixer installed. Tests were conducted for flight Mach numbers from 0.3 to 1.4 and altitudes from 10,670 to 14,630 meters (35,000 to 48,000 ft) for core-stream-to-fan-stream temperature ratios of 2.0 and 2.5 and mixing-length-to-diameter ratios of 0.95 and 1.74. For these test conditions, the reduction in specific fuel consumption varied from 2.5 percent to 4.0 percent. Pressure loss measurements as well as temperature and pressure surveys at the mixer inlet, the mixer exit, and the nozzle inlet were made.

Cullom, R. R.↗
NASA NTRS1976

Similarity theory of the buoyantly interactive planetary boundary layer with entrainment

A similarity model is developed for the vertical profiles of turbulent flow variables in an entraining turbulent boundary layer of arbitrary buoyant stability. In the general formulation the vertical profiles, internal rotation of the velocity vector, discontinuities or jumps at a capping inversion and bulk aerodynamic coefficients of the boundary layer are given by solutions to a system of ordinary differential equations in the similarity variable. To close the system, a formulation for buoyantly interactive eddy diffusivity in the boundary layer is introduced which recovers Monin-Obukhov similarity near the surface and incorporates a hypothesis accounting for the observed variation of mixing length throughout the boundary layer. The model is tested in simplified versions which depend only on roughness, surface buoyancy, and Coriolis effects by comparison with planetary-boundary-layer wind- and temperature-profile observations, measurements of flat-plate boundary layers in a thermally stratified wind tunnel and observations of profiles of terms in the turbulent kinetic-energy budget of convective planetary boundary layers. On balance, the simplified model reproduced the trend of these various observations and experiments reasonably well, suggesting that the full similarity formulation be pursued further.

Hoffert, M. I.↗
NASA NTRS1977

A critique of some recent second-order turbulence closure models for compressible boundary layers

Computations based on two recently developed second-order turbulence closure models are compared with a series of boundary-layer experiments and with predictions of these experiments using an algebraic mixing length model. One of the models employs an eddy viscosity, whereas the other evaluates components of the Reynolds stress tensor. For flat plates, the computations are compared with the van Driest skin-friction transformation to assess the handling of compressibility. For boundary layers in pressure gradients, four experiments at Mach 4 and one at Mach 6.7 are used as the bases for comparison. In general, both models represent mean velocities and skin friction reasonably well, but represent the turbulence shear stress less accurately.

Rubesin, M. W.↗
NASA NTRS1977

The relativistic equations of stellar structure and evolution

The general-relativistic equations of stellar structure and evolution are reformulated in a notation which makes easy contact with Newtonian theory. Also, a general-relativistic version of the mixing-length formalism for convection is presented.

Thorne, K. S.↗
NASA NTRS1977

Altitude engine test of a turbofan exhaust gas mixer to conserve fuel

A comparison of the specific fuel consumption was made with and without an internal mixer installed in a low bypass ratio, confluent flow turbofan engine. Tests were conducted at several Mach numbers and altitudes for core to fan stream total temperature ratios of 2.0 and 2.5 and mixing lengths of L/D = 0.95 and 1.74. For these test conditions, the specific fuel consumption improvement varied from 2.5 to 4.0 percent.

Cullom, R. R.↗
NASA NTRS1977

Numerical solution of three-dimensional free turbulent shear flows

Numerical results are presented for three-dimensional compressible turbulent jet and wake flows. An alternating direction implicit numerical procedure is used to solve the finite-difference form of the parabolic elliptic Navier-Stokes equations. A coordinate transformation maps the boundaries at infinity into a finite computational domain in order to properly specify infinity boundary conditions as well as contain the downstream growth of the viscous flow field in a fixed computational grid. Turbulence closure is achieved through an algebraic mixing length eddy viscosity model. Numerical results for supersonic flow are presented for an axisymmetric jet, an elliptical jet, an elliptical wake, and two interacting rectangular jets. Experimental data were not available for comparison with the numerical results. However, the results compare well with empirical results for free shear flows.

Oh, Y. H.↗
NASA NTRS1977

Experimental evaluation of fuel preparation systems for an automotive gas turbine catalytic combustor

Spatial fuel distributions, degree of vaporization, pressure drop and air velocity profiles were measured. Three airblast injectors and an air-assist nozzle were tested. Air swirlers were used to improve the spatial fuel-air distribution. The work was done in a 12 cm tubular duct. Test conditions were: a pressure of 0.3 and 0.5 MPa, inlet air temperatures up to 800 K, air velocities of 10 20 m/s and fuel-air ratios up to 0.020. The fuel was Jet A. The best results were obtained with an airblast configuration that used multiple cones to provide high velocity air for atomization and also straightened the inlet airflow. With this configuration, uniform spatial fuel-air distributions were obtained with mixing lengths greater than 17.8 cm. In this length, vaporization of the fuel was 98.5 percent complete at an inlet air temperature of 700 K. The total pressure loss was 1.0 percent with a reference velocity of 20 m/s and 0.25 percent at 10m/s. The air velocity was uniform across the duct and no autoignition reactions were observed.

Tacina, R. R.↗
NASA NTRS1978

Computational studies of turbulent merger of corotational vortices

A computational study has been conducted to gain a better understanding of the criteria governing the merger of corotating vortices. The zero-equation and one-equation turbulent-flow models are used to model the interaction of two rolled-up, corotational vortices. A model appropriate for the swirling flow under consideration has been proposed to prescribe the algebraic variation of mixing-length in the flow field. The unsteady, two-dimensional equations in a cross-plane are solved for primitive variables using an implicit finite-difference code. The computed downstream merging distances are in good agreement with available wind tunnel data.

Raj, P.↗
NASA NTRS1978

Reynolds number and pressure gradient effects on compressible turbulent boundary layers

A detailed investigation of attached supersonic turbulent boundary layers over an extensive range of Reynolds numbers (12 x 10 to the 6th to 314 x 10 to the 6th) is presented. Experimental measurements were obtained for adverse pressure gradients ranging in magnitude from those of previous investigations to those approaching separation. The measurements include mean values of surface pressure and skin-friction, mean-flow profiles, and profiles of the three turbulent velocity fluctuation components and turbulent shear stress. Numerical solutions, employing three turbulence models of various degrees of complexity have been compared with the details of the measured flow fields. Generally, it was found that the more sophisticated turbulence models are superior to a mixing length model for predicting the Reynolds number and pressure gradient effects. However, some details of the turbulent fluctuations as well as the exact Reynolds number trends indicated by the data were not accurately predicted with any of the turbulence models considered.

Acharya, M.↗
NASA NTRS1977

Experimental evaluation of fuel preparation systems for an automotive gas turbine catalytic combustor

Premixing-prevaporizing fuel systems were evaluated for use with a catalytic reactor for possible automotive gas turbine application. Spatial fuel-air distributions, degree of vaporization, pressure drop and air velocity profiles were measured. Three airblast injectors and an air-assist nozzle were tested. Air swirlers were used to improve the spatial fuel-air distribution. The work was done in a 12 cm tubular duct. Test conditions were: a pressure of 0.3 and 0.5 MPa, inlet air temperatures up to 800 K, air velocities of 10 and 20 m/s and fuel-air ratios up to 0.020. The fuel was Jet A. The best results were obtained with an air-blast configuration that used multiple cones to provide high velocity air for atomization and also straightened the inlet airflow. With this configuration, uniform spatial fuel-air distributions were obtained with mixing lengths greater than 17.8 cm. In this length, vaporization of the fuel was 98.5 percent complete at an inlet air temperature of 700 K. The total pressure loss was 1.0 percent with a reference velocity of 20 m/s and 0.25 percent at 10 m/s. The air velocity was uniform across the duct and no autoignition reactions were observed.

Tacina, R. R.↗
NASA NTRS1978

Effect of wall temperature on a supersonic turbulent boundary layer

Measurement of mean flow profiles in a fully developed Mach 3 turbulent boundary layer with negligible pressure gradient is reported. Data were acquired at several streamwise locations for wall-to-total temperature ratios of 0.94, 0.71, and 0.54. The results demonstrate that the velocity defect formulation of the law-of-the-wake, which successfully correlates compressible, adiabatic boundary layers, is also valid for nonadiabatic flows. It is also shown that for adiabatic walls, the linear Crocco relation between total temperature and velocity does not provide a valid test of the nature of the boundary-layer flow for practical cases where the Prandtl number departs from unity. Finally, the turbulent shear stress, mixing length, and eddy viscosity were extracted from the 'time-averaged' conservation equations using the measured mean flow profiles and found to be insensitive to wall temperature. In particular, the latter properties are in good agreement with earlier compressible, adiabatic correlations of turbulent transport properties.

Laderman, A. J.↗
NASA NTRS1978

On the angular momentum loss of late-type stars

The observed surface angular velocity of main-sequence stars shows a sharp decrease at about spectral type F6. It is suggested that stars more massive than F6 cannot experience an appreciable angular-momentum loss because their convection zones cannot sustain a magnetic dynamo: without a magnetic field the angular-momentum loss is very small. The influence of rotation on the convective motions is essential for the existence of a solar-type dynamo. Rotation can influence these convective motions only if the typical convective time is larger than the rotation time. For main-sequence stars of different masses and chemical compositions the dimensionless parameter (convective velocity/sum's angular velocity times mixing length in the lower part of the convection zone) is evaluated. It is shown that this parameter increases very sharply for stars whose mass exceeds that defined by the relation log(star mass/solar mass) is of the order of 0.1. Thus even for large angular velocities, magnetic dynamos are not feasible if log(star mass/solar mass) appreciably exceeds 0.1.

Durney, B. R.↗