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NASA NTRS2001

A Hybrid Numerical Method for Turbulent Mixing Layers

A hybrid method has been developed for simulations of compressible turbulent mixing layers. Such mixing layers dominate the flows in exhaust systems of modern day aircraft and also those of hypersonic vehicles currently under development. The method configurations in which a dominant structural feature provides an unsteady mechanism to drive the turbulent development in the mixing layer. The hybrid method uses a Reynolds-averaged Navier-Stokes (RANS) procedure to calculate wall bounded regions entering a mixing section, and a Large Eddy Simulation (LES) procedure to calculate the mixing dominated regions. A numerical technique was developed to enable the use of the hybrid RANS-LES method on stretched, non-Cartesian grids. Closure for the RANS equations was obtained using the Cebeci-Smith algebraic turbulence model in conjunction with the wall-function approach of Ota and Goldberg. The wall-function approach enabled a continuous computational grid from the RANS regions to the LES region. The LES equations were closed using the Smagorinsky subgrid scale model. The hybrid RANS-LES method is applied to a benchmark compressible mixing layer experiment. Preliminary two dimensional calculations are used to investigate the effects of axial grid density and boundary conditions. Vortex shedding from the base region of a splitter plate separating the upstream flows was observed to eventually transition to turbulence. The location of the transition, however, was much further downstream than indicated by experiments. Actual LES calculations, performed in three spatial directions, also indicated vortex shedding, but the transition to turbulence was found to occur much closer to the beginning of the mixing section. which is in agreement with experimental observations. These calculations demonstrated that LES simulations must be performed in three dimensions. Comparisons of time-averaged axial velocities and turbulence intensities indicated reasonable agreement with experimental data.

Georgiadis, Nicholas J.↗
NASA NTRS2020

Turbulent mixing in supercritical jets: effect of compressibility factor and inflow condition

Fuel injection and turbulent mixing at supercritical pressures determines ignition and combustion in numerous engineering applications. Flow evolution under such conditions is characterized by strong non-linear coupling between dynamics, transport coefficients, and thermodynamics. Experimental studies observe that the jets injected at supercritical pressures exhibit significantly different dynamics from the jets at subcritical conditions, owing to the lack of distinct liquid and gas phases in supercritical state. Thus, the averaged flow quantities such as the potential core length, jet spatial growth rate and velocity decay profiles differ in the two conditions, resulting in different mixed-fluid distributions. In this study, turbulent jet direct numerical simulations (DNS) are performed to examine the variations in flow statistics between injection of Nitrogen (N₂) in Nitrogen (N₂) at both subcritical (perfect-gas) and supercritical conditions. In all cases, isothermal round jets at Reynolds number (Re_{D}), based on jet diameter (D) and jet orifice velocity (U₀), of 5000 are considered. For mixing analyses, a passive scalar transported with the flow is examined.

Sharan, Nek↗
NASA NTRS1990

Interaction of a streamwise vortex with a turbulent mixing layer

The interaction of a single streamwise vortex with a plane turbulent mixing layer is experimentally studied. Initially, near the mixing layer origin, the vortex rides just below the layer and only affects the mixing layer properties near the bottom side of the mixing layer. Once the vortex starts to become embedded within the mixing layer and active interaction has begun, the effect of the vortex is to grossly distort the mean velocity and turbulence contours over the whole width of the mixing layer. The induced cross-flow velocities in the mixing layer result in the production of additional normal Reynolds stresses which in turn act with mean flow gradients to generate extra shear stresses. In particular, the secondary shear stress (SSS) achieves an absolute peak value equivalent to about 40 percent of the maximum primary shear stress. The position and decay of the SSS peak are then found to be strongly correlated with those of the streamwise vortex.

Bell, James H.↗
NASA NTRS1986

Direct numerical simulations of chemically reacting turbulent mixing layers

The results of direct numerical simulations of chemically reacting, turbulent mixing layers are presented. The reaction considered is a binary, irreversible reaction with no heat release, so that only the effect of the turbulence on the chemical reaction is investigated. The simulation results are shown to be consistent with similarity theory, and are found to be in approximate agreement with laboratory data, even though there are no adjustable parameters in the method.

Riley, J. J.↗
NASA NTRS1993

Turbulent mixing layers in the interstellar medium of galaxies

We propose that turbulent mixing layers are common in the interstellar medium (ISM). Injection of kinetic energy into the ISM by supernovae and stellar winds, in combination with density and temperature inhomogeneities, results in shear flows. Such flows will become turbulent due to the high Reynolds number (low viscosity) of the ISM plasma. These turbulent boundary layers will be particularly interesting where the shear flow occurs at boundaries of hot (approximately 10(exp 6) K) and cold or warm (10(exp 2) - 10(exp 4) K) gas. Mixing will occur in such layers producing intermediate-temperature gas at T is approximately equal to 10(exp 5.0) - 10(exp 5.5) that radiates strongly in the optical, ultraviolet, and EUV. We have modeled these layers under the assumptions of rapid mixing down to the atomic level and steady flow. By including the effects of non-equilibrium ionization and self-photoionization of the gas as it cools after mixing, we predict the intensities of numerous optical, infrared, and ultraviolet emission lines, as well as absorption column densities of C 4, N 5, Si 4, and O 6.

Slavin, J. D.↗
NASA NTRS1994

Direct Simulation of a Self-Similar Turbulent Mixing Layer

Three direct numerical simulations of incompressible turbulent plane mixing layers have been performed. All the simulations were initialized with the same two velocity fields obtained from a direct numerical simulation of a turbulent boundary layer with a momentum thickness Reynolds number of 300 computed by Spalart (J. Fluid Mech. 187, 61, 1988). In addition to a baseline case with no additional disturbances, two simulations were begun with two-dimensional disturbances of varying strength in addition to the boundary layer turbulence. After a development stage, the baseline case and the case with weaker additional two-dimensional disturbances evolve self-similarly, reaching visual thickness Reynolds numbers of up to 20 000. This self-similar period is characterized by a lack of large-scale organized pairings, a lack of streamwise vortices in the 'braid' regions, and scalar mixing that is characterized by 'marching' Probability Density Functions (PDFs). The case begun with strong additional two-dimensional disturbances only becomes approximately self-similar, but exhibits sustained organized large-scale pairings, clearly defined braid regions with streamwise vortices that span them, and scalar PDFs that are 'nonmarching.' It is also characterized by much more intense vertical velocity fluctuations than the other two cases. The statistics and structures in several experiments involving turbulent mixing layers are in better agreement with those of the simulations that do not exhibit organized pairings.

Rogers, Michael M.↗
NASA NTRS1991

Some effects of swirl on turbulent mixing layer development

Effects of swirl on the development of an axisymmetric turbulent mixing layer have been studied. The development of the zero swirl case is found to be consistent with that of a single-stream mixing layer developing from a tripped boundary layer. In particular, the consistency of the measured stress levels shows the accuracy of the measurement system. Swirl increases all the Reynolds stress levels with the increased scaling with swirl number. The shear stresses are found to be affected significantly more than the normal stresses. The stress increases are partly explained by considering extra production terms in the transport equations that are activated by the presense of the swirl. The thickness and growth rate for the lower swirl rate are found to be comparable to the zero swirl case, while those for the higher swirl rate are increased significantly, in line with the increased Reynolds stresses.

Mehta, R. D.↗
NASA NTRS1993

Turbulent mixing layers in the interstellar medium of galaxies

It is proposed that turbulent mixing layers are common in the ISM of the Milky Way and selected external galaxies, with many layers per kiloparsec along typical lines of sight. All of the diffuse C I 1550-A background emission and a significant fraction of the diffuse H-alpha background at high latitude can be explained by mixing layers cooling at pressure of about 3000/cu cm K. These models also produce the correct ratio of semiforbidden C IV 15500 III 1663-A emission. Only 10 percent of the disk H-alpha is likely to arise from mixing layers. The observed Galactic absorption-line column densities of C IV, N V, Si IV, and O VI are roughly consistent with mixing-layer models with an intermediate temperature of about 10 exp 5.3 K and depleted abundances.

Slavin, Jonathan D.↗
NASA NTRS1988

Direct simulations of chemically reacting turbulent mixing layers, part 2

The results of direct numerical simulations of chemically reacting turbulent mixing layers are presented. This is an extension of earlier work to a more detailed study of previous three dimensional simulations of cold reacting flows plus the development, validation, and use of codes to simulate chemically reacting shear layers with heat release. Additional analysis of earlier simulations showed good agreement with self similarity theory and laboratory data. Simulations with a two dimensional code including the effects of heat release showed that the rate of chemical product formation, the thickness of the mixing layer, and the amount of mass entrained into the layer all decrease with increasing rates of heat release. Subsequent three dimensional simulations showed similar behavior, in agreement with laboratory observations. Baroclinic torques and thermal expansion in the mixing layer were found to produce changes in the flame vortex structure that act to diffuse the pairing vortices, resulting in a net reduction in vorticity. Previously unexplained anomalies observed in the mean velocity profiles of reacting jets and mixing layers were shown to result from vorticity generation by baroclinic torques.

Metcalfe, Ralph W.↗
NASA NTRS1975

Supersonic free turbulent mixing layers

A mean turbulent closure method with a length scale function is developed for predicting the reduced spreading rate in high Mach number, high Reynolds number free shear layers. The new feature of the method is the inclusion of effects of the pressure-dilation term which appears in the compressible form of the turbulence energy equation. The model indicates that the pressure-dilation correlation may act as a turbulence energy sink or source depending on whether the transverse gradients of mean Mach number and mean density have the same or opposite signs.

Oh, Y. H.↗
NASA NTRS1984

Direct simulations of chemically reacting turbulent mixing layers

The report presents the results of direct numerical simulations of chemically reacting turbulent mixing layers. The work consists of two parts: (1) the development and testing of a spectral numerical computer code that treats the diffusion reaction equations; and (2) the simulation of a series of cases of chemical reactions occurring on mixing layers. The reaction considered is a binary, irreversible reaction with no heat release. The reacting species are nonpremixed. The results of the numerical tests indicate that the high accuracy of the spectral methods observed for rigid body rotation are also obtained when diffusion, reaction, and more complex flows are considered. In the simulations, the effects of vortex rollup and smaller scale turbulence on the overall reaction rates are investigated. The simulation results are found to be in approximate agreement with similarity theory. Comparisons of simulation results with certain modeling hypotheses indicate limitations in these hypotheses. The nondimensional product thickness computed from the simulations is compared with laboratory values and is found to be in reasonable agreement, especially since there are no adjustable constants in the method.

Riley, J. J.↗
NASA NTRS2008

Toward Better Modeling of Supercritical Turbulent Mixing

study was done as part of an effort to develop computational models representing turbulent mixing under thermodynamic supercritical (here, high pressure) conditions. The question was whether the large-eddy simulation (LES) approach, developed previously for atmospheric-pressure compressible-perfect-gas and incompressible flows, can be extended to real-gas non-ideal (including supercritical) fluid mixtures. [In LES, the governing equations are approximated such that the flow field is spatially filtered and subgrid-scale (SGS) phenomena are represented by models.] The study included analyses of results from direct numerical simulation (DNS) of several such mixing layers based on the Navier-Stokes, total-energy, and conservation- of-chemical-species governing equations. Comparison of LES and DNS results revealed the need to augment the atmospheric- pressure LES equations with additional SGS momentum and energy terms. These new terms are the direct result of high-density-gradient-magnitude regions found in the DNS and observed experimentally under fully turbulent flow conditions. A model has been derived for the new term in the momentum equation and was found to perform well at small filter size but to deteriorate with increasing filter size. Several alternative models were derived for the new SGS term in the energy equation that would need further investigations to determine if they are too computationally intensive in LES.

Selle, Laurent↗
NASA NTRS1983

Combustion in a turbulent mixing layer formed at a rearward-facing step

A premixed propane/air flame was stabilized in a turbulent mixing layer formed at a rearward-facing step. The mean and rms averages of the turbulent velocity flowfield were determined by laser velocimetry for both reacting (phi = 0.57) and nonreacting flows (Re = 15,000-37,000 based on step height). The reacting-flow was visualized by high-speed schlieren photography. Large-scale structures dominate the reacting mixing layer. The growth of the large-scale structures was tied to the propagation of the flame. The linear growth rate of the reacting mixing layer defined by the mean velocity profiles was unchanged by combustion but the virtual origin moves downstream. The reacting mixing layer boundaries based on the mean velocity profiles were shifted toward the recirculation zone and reattachment lengths were shortened by 30 percent. The edge of the flame controlled by the large-scale structure development propagated faster into the incoming reactants than the boundary of the mixing layer given by the mean velocity flowfield. Thus, the region of high velocity gradient did not coincide with the region of high reaction and heat transfer.

Pitz, R. W.↗