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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.

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NASA NTRS1979

Computational simulation of turbulent vortex merger and decay

The interaction and eventual merger of corotational vortices and the decay of a single vortex have been studied by employing zero-, one- and two-equation turbulent-flow models in order to gain a better understanding of the role of turbulence. An implicit finite-difference procedure is used to integrate the unsteady, two-dimensional equations in a cross-plane. The zero- and one-equation formulations utilize a mixing-length model, which incorporates the streamline curvature effect by prescribing a spatially-varying mixing-length. In the two-equation model, the turbulence kinetic energy equation and a modified rate of dissipation equation which includes a streamline curvature correction are solved. Computational results of different models applied to various flow-configurations are presented and compared with available experimental data whenever possible.

Raj, P.↗
NASA NTRS1950

Laws of Flow in Rough Pipes

An experimental investigation is made of the turbulent flow of water in pipes with various degrees of relative roughness. The pipes range in size from 25 to 100 millimeters in diameter and from 1800 to 7050 millimeters in length. Flow velocities permitted Reynolds numbers from about 10 (sup. 4) to 10 (sup. 6). The laws of resistance and velocity distributions were obtained as a function of relative roughness and Reynolds number. Mixing length, as described by Prandtl's mixing-length formula, is discussed in relation to the experimental results.

Nikuradse, J↗
NASA NTRS1976

Modeling of three-dimensional mixing and reacting ducted flows

A computer code, based upon a finite element solution algorithm, was developed to solve the governing equations for three-dimensional, reacting boundary region, and constant area ducted flow fields. Effective diffusion coefficients are employed to allow analyses of turbulent, transitional or laminar flows. The code was used to investigate mixing and reacting hydrogen jets injected from multiple orifices, transverse and parallel to a supersonic air stream. Computational results provide a three-dimensional description of velocity, temperature, and species-concentration fields downstream of injection. Experimental data for eight cases covering different injection conditions and geometries were modeled using mixing length theory (MLT). These results were used as a baseline for examining the relative merits of other mixing models. Calculations were made using a two-equation turbulence model (k+d) and comparisons were made between experiment and mixing length theory predictions. The k+d model shows only a slight improvement in predictive capability over MLT. Results of an examination of the effect of tensorial transport coefficients on mass and momentum field distribution are also presented. Solutions demonstrating the ability of the code to model ducted flows and parallel strut injection are presented and discussed.

Zelazny, S. W.↗
NASA NTRS2005

Effects of Multiple Nozzles on Asymmetric Ejector Performance

This paper presents a comparison of a single nozzle and a dual nozzle strut based ejector. The results are focused on the fluid properties in the ejector duct. The research focused on choking mechanisms, mass flow entrainment, and mixing duct pressure distributions. The two ejectors were tests at equivalent primary mass flow rates. This corresponds to chamber pressures ranging from 100 psi to 900 psi in the single nozzle strut and 50 psi to 450 psi in the dual nozzle strut. Secondary flow was drawn from the lab at atmospheric pressure, and was not controlled. The secondary flow was found to choke at a value of 2.3 lb/s for a primary mass flow rate at approximately 2.1 lb/s for both ejectors. This choke was believed to be a mass addition choke rather than a traditional aerodynamic choke. The mixing duct pressure distribution exhibited two distinct trends at "low pressure" trend and at "high pressure" trend. For the low pressure trend, the mixing length for the ejectors remained fixed around 20 inches, regardless of the chamber pressure. For the higher pressure trend, the mixing length was considerably longer and increased with increasing chamber pressure. At high chamber pressures (high mass flow rates), a supersonic core flow was present at the exit of the duct. For these cases, the two streams did not have time to mix by the end of the duct.

Lineberry, D.↗
NASA NTRS1982

Features of a reattaching turbulent shear layer subject to an adverse pressure gradient

Experimental data have been obtained in an incompressible turbulent flow over a rearward-facing step with superimposed adverse pressure gradient. Mean velocities, Reynolds stresses and triple-products measured by a laser Doppler velocimeter are presented for two cases of adverse pressure gradient. Mixing lengths, eddy viscosities, production, convection, turbulent diffusion, and dissipation terms are extracted from the data. These data are compared with various mixing length and eddy-viscosity turbulence models. Numerical calculations incorporating the k-epsilon and the algebraic-stress turbulence models are compared with the data. When determining quantities of engineering interest, the modified algebraic-stress model (ASM) is a significant improvement over the unmodified ASM and the unmodified k-epsilon model

Driver, D. M.↗
NASA NTRS1978

Behavior of a turbulent boundary layer subjected to sudden transverse strain

Data from two experiments on the development of the components of the Reynolds stress tensor after a sudden application of transverse strain are compared. Computations were based on four different turbulence models: a first-order mixing length model, a second-order two-equation eddy viscosity model, and two second-order Reynolds stress models. The second-order models do not produce dramatic improvements over the simple mixing length model. The Reynolds stress models still need development to represent the physics of shear-strained turbulence well. Finally, it is demonstrated that the assumption of a scalar eddy viscosity, often used in engineering calculations of three-dimensional boundary layers, is quite reasonable.

Higuchi, H.↗
NASA NTRS2004

Hydrodynamic Modeling of Oxidizer-Rich Staged Combustion Injector Flow

The main objective of this work is to determine the unsteady hydrodynamic characteristics of coaxial swirl atomizers of interest in oxidizer-rich staged combustion (ORSC) liquid rocket engines. To this end, the pseudo-density (homogeneous flow) treatment combined with the Marker-and-Cell (MAC) numerical algorithm has been used to develop an axisymmetric with swirl, two-phase, unsteady model. The numerical model is capable of assessing the time-dependent orifice exit conditions and internal mixing for arbitrary fuel and oxidizer gas injection conditions. Parametric studies have been conducted to determine the effect of geometry, gas properties, and liquid properties on the exit massflow rate and velocity. It has been found that the frequency at which the liquid film oscillates increases as the density ratio and thickness increase, decreases as film thickness and liquid swirl velocity increase, and is unaffected by the mixing length. Additionally, it has been determined that the variation in the massflow rate increases as the liquid swirl velocity and liquid film thickness increase, and decreases as the density ratio, collar thickness, and mixing length increase.

Canino, J. V.↗
NASA NTRS1976

A complete model of turbulence

A set of constitutive equations suitable for a priori computation of turbulent shear flows has been developed. Since no properties of a given turbulent flow need be known in advance in order to obtain a solution, the equations comprise a complete model of turbulence. Perturbation analysis shows that the model predicts a composite five-layer structure for an incompressible turbulent boundary layer, viz, a defect layer, a law-of-the-wall layer, a viscous sublayer, a near-surface roughness layer, and a viscous superlayer at the boundary-layer edge. Analysis of the defect layer demonstrates the key improvement of the model over its predecessor, the Saffman-Wilcox two-equation model of turbulence. Examination of model-predicted sublayer structure yields model-parameter boundary conditions appropriate for surfaces with roughness and mass injection. Results of numerical computations of compressible and incompressible equilibrium boundary layers show that, for such flows, the model is as accurate as mixing-length theory. Applications to transitional boundary layers and to nonequilibrium relaxation of a boundary layer passing from a rough to a smooth surface indicate that the model's applicability extends far beyond that of mixing-length theory's.

Wilcox, D. C.↗
NASA NTRS1992

Large-scale flows and solar luminosity variations

The influence of a variation of the large-scale flows present in the solar convection zone on solar luminosity is examined. The convection zone is modeled as a plane-parallel fluid layer through which heat is transported by small-scale convection as described by the mixing-length theory, and the large-scale flow is treated as a small perturbation superposed on the layer. The excess energy transported by the flow is calculated and is found to depend critically on the mixing length. The excess luminosity is found to be carried as small-scale convective heat flow rather than bulk enthalpy transport throughout all but the top few percent of the convection zone. The results are applied to the specific examples of supergranules and giant cells.

Arendt, S.↗
NASA NTRS1997

Noise from Supersonic Coaxial Jets: Mean Flow Predictions - Part 1

Recent theories for supersonic jet noise have used an instability wave noise generation model to predict radiated noise. This model requires a known mean flow that has typically been described by simple analytic functions for single jet mean flows. The mean flow of supersonic coaxial jets is not described easily in terms of analytic functions. To provide these profiles at all axial locations, a numerical scheme is developed to calculate the mean flow properties of a coaxial jet. The Reynolds-averaged, compressible, parabolic boundary layer equations are solved using a mixing length turbulence model. Empirical correlations are developed to account for the effects of velocity and temperature ratios and Mach number on the shear layer spreading. Both normal velocity profile and inverted velocity profile coaxial jets are considered. The mixing length model is modified in each case to obtain reasonable results when the two stream jet merges into a single fully developed jet. The mean flow calculations show both good qualitative and quantitative agreement with measurements in single and coaxial jet flows.

Dahl, Milo D.↗
NASA NTRS1980

Full-coverage film cooling. I - Three-dimensional measurements of turbulence structure. II - Prediction of the recovery-region hydrodynamics

Hydrodynamic measurements of turbulence structure were performed with a triaxial hot wire in the full coverage and the recovery regions following an array of injection holes under isothermal conditions at ambient temperature and pressure for blowing ratios of 0.9 and 0.4. High levels of turbulence kinetic energy (TKE) were determined for low blowing, and low TKE levels were found for the high blowing levels; in the recovery region, the flow can be represented by a model with an outer boundary layer and a 2-dimensional inner boundary layer. Recovery region hydrodynamics can be modelled by considering that a new boundary layer started to grow immediately after the end of blowing; the Prandtl mixing length distributions calculated from the values of mean velocity and turbulent shear stresses were consistent with the presence of a dual boundary layer structure in the recovery region. The program used here contains a one-equation model of turbulence, using turbulence kinetic energy with an algebraic mixing length; this 2-dimensional, finite difference program can predict the mean velocity and turbulence kinetic energy profiles based on initial values, boundary conditions, and a closure condition.

Yavuzkurt, S.↗
NASA NTRS1972

Turbulent properties of a compressible boundary layer.

Turbulent shear-stress, eddy-viscosity, mixing-length, heat-flux and Prandtl number distributions across a hypersonic turbulent boundary layer have been determined from the 'time-averaged' conservation equations using experimental mean profile data obtained at several streamwise locations in a fully developed turbulent boundary layer with negligible pressure gradient. The eddy-viscosity, mixing-length and Prandtl number results show general agreement with previous incompressible and adiabatic compressible correlations. However, when the turbulent Prandtl number is defined using total enthalpy as opposed to static enthalpy no clear correlation of the results in the outer portion of the boundary layer could be obtained.

Horstman, C. C.↗
NASA NTRS1973

Thermally driven mass flows in the convection zone of the sun

A formulation of the fluid dynamics of convective regions is developed which leads to an analytical description of the solar rotation, the Evershed flow, and the supergranulation. The starting point of the present formulation is the mixing length picture of convective equilibrium, but the earlier point mass model for convective molecules is replaced here by a model with both inertia and intrinsic moment of inertia. This extension introduces three rotational degrees of freedom into the dynamics of individual convective molecules, which enter into the dynamical equations for a mixing length fluid in the form of a separate vector field which we term the spin field. It is shown that for convective molecules having a spherically symmetric mass distribution, the spin field is proportional to the local vorticity.

Dijkhuis, G. C.↗
NASA NTRS1992

Further improvements of a new model for turbulent convection in stars

The effects of including a variable molecular weight and of using the newest opacities of Rogers and Iglesias (1991) as inputs to a recent model by Canuto and Mazzitelli (1991) for stellar turbulent convection are studied. Solar evolutionary tracks are used to conclude that the the original model for turbulence with mixing length Lambda = z, Giuli's variable Q unequal to 1 and the new opacities yields a fit to solar T(eff) within 0.5 percent. A formulation of Lambda is proposed that extends the purely nonlocal Lambda = z expression to include local effects. A new expression for Lambda is obtained which generalizes both the mixing length theory (MLT) phenomenological expression for Lambda as well as the model Lambda = z. It is argued that the MLT should now be abandoned.

Canuto, V. M.↗
NASA NTRS1993

Why convective heat transport in the solar nebula was inefficient

The radial distributions of the effective temperatures of circumstellar disks associated with pre-main sequence (T Tauri) stars are relatively well-constrained by ground-based and spacecraft infrared photometry and radio continuum observations. If the mechanisms by which energy is transported vertically in the disks are understood, these data can be used to constrain models of the thermal structure and evolution of solar nebula. Several studies of the evolution of the solar nebula have included the calculation of the vertical transport of heat by convection. Such calculations rely on a mixing length theory of transport and some assumption regarding the vertical distribution of internal dissipation. In all cases, the results of these calculations indicate that transport by radiation dominates that by convection, even when the nebula is convectively unstable. A simple argument that demonstrates the generality (and limits) of this result, regardless of the details of mixing length theory or the precise distribution of internal heating is presented. It is based on the idea that the radiative gradient in an optically thick nebula generally does not greatly exceed the adiabatic gradient.

Cassen, P.↗
NASA NTRS1980

Linear modes of convection in the solar envelope

The structure of the solar convective envelope calculated according to mixing-length theory is not consistent with the transport of the convective heat flux by any superposition of the fundamental linear convective modes. If the amplitudes of these modes can be estimated by consideration of the most important nonlinear terms in the equations of motion, it becomes possible to find solar models which are consistent with mode transport of the heat through the convective zone. These models may be characterized by a mixing length which varies from point to point through the envelope. The linear modes in such models show peaks in velocity at certain preferred length scales, but these scales do not necessarily correspond to those of the solar motions, such as the supergranulation.

Bogart, R. S.↗
NASA NTRS1994

On sound generation by turbulent convection: A new look at old results

We have revisited the problem of acoustic wave generation by turbulent convection in stellar atmospheres. The theory of aerodynamically generated sound, originally developed by Lighthill and later modified by Stein to include the effects of stratification, has been used to estimate the acoustic wave energy flux generated in solar and stellar convection zones. We correct the earlier computations by incorporating an improved description of the spatial and temporal spectrum of the turbulent convection. We show the dependence of the resulting wave fluxes on the nature of the turbulence, and compute the wave energy spectra and wave energy fluxes generated in the Sun on the basis of a mixing-length model of the solar convection zone. In contrast to the previous results, we show that the acoustic energy generation does not depend very sensitively on the turbulent energy spectrum. However, typical total acoustic fluxes of order F(sub A) = 5 x 10(exp 7) ergs/sq cm/s with a peak of the acoustic frequency spectrum near omega = 100 mHz are found to be comparable to those previously calculated. The acoustic flux turns out to be strongly dependent on the solar model, scaling with the mixing-length parameter alpha as alpha(exp 3.8). The computed fluxes most likely constitute a lower limit on the acoustic energy produced in the solar convection zone if recent convection simulations suggesting the presence of shocks near the upper layers of the convection zone apply to the Sun.

Musielak, Z. E.↗
NASA NTRS1991

Stellar turbulent convection - A new model and applications

Improvements of the mixing-length theory (MLT) of turbulent convection in stellar atmospheres are developed theoretically. It is pointed out that inaccuracies are introduced into MLT by the approximating assumptions of a single large eddy (rather than many eddies of different sizes) and of incompressibility. In the proposed new model, the full spectrum of turbulent eddies is determined using more recent turbulence models (e.g., the eddy-damped quasi-normal Markovian model of Orszag, 1977), and a new formula for the convective flux is obtained which gives values up to 10 times greater than those of the MLT at high convective efficiencies. The problem of compressibility is addressed by adding one of two new expressions (one with no free parameters) for the mixing length. Numerical results from simulations of a solar-type star and a 0.8-solar-mass globular-cluster star are presented in tables and graphs and discussed in detail; the agreement with observations is found to be better than with the MLT.

Canuto, V. M.↗