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NASA NTRS1994

Modification of the MML turbulence model for adverse pressure gradient flows

Computational fluid dynamics is being used increasingly to predict flows for aerospace propulsion applications, yet there is still a need for an easy to use, computationally inexpensive turbulence model capable of accurately predicting a wide range of turbulent flows. The Baldwin-Lomax model is the most widely used algebraic model, even though it has known difficulties calculating flows with strong adverse pressure gradients and large regions of separation. The modified mixing length model (MML) was developed specifically to handle the separation which occurs on airfoils and has given significantly better results than the Baldwin-Lomax model. The success of these calculations warrants further evaluation and development of MML. The objective of this work was to evaluate the performance of MML for zero and adverse pressure gradient flows, and modify it as needed. The Proteus Navier-Stokes code was used for this study and all results were compared with experimental data and with calculations made using the Baldwin-Lomax algebraic model, which is currently available in Proteus. The MML model was first evaluated for zero pressure gradient flow over a flat plate, then modified to produce the proper boundary layer growth. Additional modifications, based on experimental data for three adverse pressure gradient flows, were also implemented. The adapted model, called MMLPG (modified mixing length model for pressure gradient flows), was then evaluated for a typical propulsion flow problem, flow through a transonic diffuser. Three cases were examined: flow with no shock, a weak shock and a strong shock. The results of these calculations indicate that the objectives of this study have been met. Overall, MMLPG is capable of accurately predicting the adverse pressure gradient flows examined in this study, giving generally better agreement with experimental data than the Baldwin-Lomax model.

Conley, Julianne M.↗

NASA NTRS1989

Cross correlation and length scales in turbulent flows near surfaces

Two kinds of length scales are used in turbulent flows; 'functional length scales' such as mixing length, dissipation length L(sub epsilon), etc., and 'flow-field length scales' derived from cross correlations of velocity, pressure, etc. in the flow. Some connection between these scales are derived here. We first consider the cross correlation R(sub vv)(y,y(sub 1)) of the normal components u at two heights y, y(sub 1) above a rigid surface, normalized by the velocity y(sub 1) (greater than y). For shear-free boundary layers it is found theoretically, and in field and numerical experiments that R(sub vv) approximately equals y/y(sub 1). For shear layers it is also found that R(sub vv) approximately equals f(y/y(sub 1)) less than or equal to y,y(sub 1). This function f differs slightly between low Reynolds number numerical simulations and field experiments. The lateral structure defined by R(sub vv)(y,r(sub 3); y(sub 1),0) is also self similar and shows that the eddies centered at about y(sub 1) appear to have constant lateral width a(sub 3) above and below y(sub 1), where a(sub 3, sup +) approximately equals 7+1/(1.4dU(sup +)/dy(sup +)), when normalized on u(sub *) and v, where U is the mean velocity. Results for L(sub epsilon, sup -1) from direct numerical simulation are found to compare well with the formula L(sub epsilon, sup -1) = A(sub B)/y + A(sub S)dU/dy/v, for unidirectional and reversing turbulent boundary layers and channel flow, except near where dU/dy approximately equals 0. The conclusion is that the large-scale eddy structure and length scales in these flows are determined by a combination of shear and blocking, and that the vertical component of turbulence has a self-similar structure in both kinds of boundary layer.

Hunt, J. C. R.↗

NASA NTRS1957

Experimental evaluation of methods for improving diffuser-exit total-pressure profiles for a side-inlet model at Mach number 1.91

Distortion effects of the following model additions or changes were studied: (1) constant-area mixing lengths at the end of the subsonic diffuser, (2) screens with systematic variations in mesh and flow-area blockage, (3) bleeds slots on the inlet cowl, and (4) a simulated compressor hub. Data at a diffuser-exit Mach number of 0.36 are compared with data of a similar study at Mach 0.20. At the higher Mach number, the same length of constant-area mixing was less effective in reducing total-pressure distortions, while the use of screens was more effective.

Klann, John L↗

NASA NTRS1965

On the magneto-hydrostatic theory of sunspots.

Sunspot models used to derive relations between coolness of spot and its magnetic field strength and between magnetic field strength and ratio of mixing length to pressure scale height

SUNSPOT↗

NASA NTRS1982

Curvature effects and turbulent boundary layers

Results are examined from an experiment conducted to determine quantitatively the secondary factors which affect the response of a turbulent boundary layer to convex curvature and to examine the recovery process after curvature ended. The variation of Stanton number with streamwise distance and with enthalpy thickness Reynolds number for the baseline case is shown. The effect of delta sub .99/R on the velocity of the potential core would have if we extended to the wall with no viscous effects, of free stream acceleration, of an unheated starting length, and of boundary layer maturity are discussed. Mixing length and turbulent Prandtl number models are reviewed.

Moffat, R. J.↗

NASA NTRS1990

Effect of radiative transfer on convection in the deep photosphere of late-type dwarfs

A method is proposed to eliminate the compressional instability of a shallow layer in the upper part of stellar convective zones in standard mixing-length models. By equating the radiative cooling time of mixing eddies to their convective turnover time, the effective sizes of the eddies are assumed to be the smallest of those which are not eliminated by radiative transfer. Computations of the models with this assumption leads to smooth temperature profiles in the previously unstable layers and reductions of the convective velocity above its maximum value.

Fontenla, J. M.↗

NASA NTRS1977

A length-scale model for developing turbulent flow in a rectangular duct

A three-dimensional mixing length model is proposed for modeling local Reynolds stress behavior in rectangular ducts of arbitrary aspect ratio. The model is applicable to both developing and fully-developed flows, and can be applied to other 90-degree corner flows with mild streamwise pressure gradients. Comparisons between theory and experiment show that all components of the Reynolds stress tensor are modeled reasonably well, both in the vicinity of a corner and in two-dimensional regions away from the corner.

Gessner, F. B.↗

NASA NTRS1999

Development of a 12-Thrust Chamber Kerosene /Oxygen Primary Rocket Sub-System for an Early (1964) Air-Augmented Rocket Ground-Test System

Airbreathing/Rocket combined-cycle, and specifically rocket-based combined- cycle (RBCC), propulsion systems, typically employ an internal engine flow-path installed primary rocket subsystem. To achieve acceptably short mixing lengths in effecting the "air augmentation" process, a large rocket-exhaust/air interfacial mixing surface is needed. This leads, in some engine design concepts, to a "cluster" of small rocket units, suitably arrayed in the flowpath. To support an early (1964) subscale ground-test of a specific RBCC concept, such a 12-rocket cluster was developed by NASA's Marshall Space Flight Center (MSFC). The small primary rockets used in the cluster assembly were modified versions of an existing small kerosene/oxygen water-cooled rocket engine unit routinely tested at MSFC. Following individual thrust-chamber tests and overall subsystem qualification testing, the cluster assembly was installed at the U. S. Air Force's Arnold Engineering Development Center (AEDC) for RBCC systems testing. (The results of the special air-augmented rocket testing are not covered here.) While this project was eventually successfully completed, a number of hardware integration problems were met, leading to catastrophic thrust chamber failures. The principal "lessons learned" in conducting this early primary rocket subsystem experimental effort are documented here as a basic knowledge-base contribution for the benefit of today's RBCC research and development community.

Pryor, D.↗

NASA NTRS1973

A kinematic eddy viscosity model including the influence of density variations and preturbulence

A model for the kinematic eddy viscosity was developed which accounts for the turbulence produced as a result of jet interactions between adjacent streams as well as the turbulence initially present in the streams. In order to describe the turbulence contribution from jet interaction, the eddy viscosity suggested by Prandtl was adopted, and a modification was introduced to account for the effect of density variation through the mixing layer. The form of the modification was ascertained from a study of the compressible turbulent boundary layer on a flat plate. A kinematic eddy viscosity relation which corresponds to the initial turbulence contribution was derived by employing arguments used by Prandtl in his mixing length hypothesis. The resulting expression for self-preserving flow is similar to that which describes the mixing of a submerged jet. Application of the model has led to analytical predictions which are in good agreement with available turbulent mixing experimental data.

Cohen, L. S.↗

NASA NTRS1995

Supersonic coaxial jet noise predictions

Predictions are made for the noise radiation from supersonic, coaxial jets. These predictions are based on the assumption that the noise radiation in the downstream direction of supersonic jets is dominated by sound generated by instability waves with supersonic phase velocities relative to ambient. Since the analysis requires a known mean flow and the coaxial jet mean flow is not described easily in terms of analytical functions, a numerical prediction is made for its development. The compressible, Reynolds averaged, boundary layer equations are solved with a modified mixing length turbulence model. The model has been calibrated to account for compressibility and temperature effects on the rate of mixing. Both normal and inverted velocity profile jets are considered. Predictions are made for the differences between the noise radiated by coaxial jets with difference operating conditions and a single reference jet with the same thrust, mass flow, and exit area. The effects of area ratio changes and simulated enhanced mixing on noise radiation are also considered.

Dahl, Milo D.↗

NASA NTRS1974

Calculation of compressible turbulent free shear layers

Rudy and Bushnell's (1972) mixing length theory for the prediction of mean velocity fields in turbulent shear layers is extended to include supersonic free turbulent mixing. The normal momentum equation is coupled with the conventional equations of motion and is solved iteratively. Results show that transverse static pressure variation has very little effect on the mean flow variables in compressible free turbulent shear layers.

Oh, Y. H.↗

NASA NTRS2000

Mixing of an Airblast-atomized Fuel Spray Injected into a Crossflow of Air

The injection of a spray of fuel droplets into a crossflow of air provides a means of rapidly mixing liquid fuel and air for combustion applications. Injecting the liquid as a spray reduces the mixing length needed to accommodate liquid breakup, while the transverse injection of the spray into the air stream takes advantage of the dynamic mixing induced by the jet-crossflow interaction. The structure of the spray, formed from a model plain-jet airblast atomizer, is investigated in order to determine and understand the factors leading to its dispersion. To attain this goal, the problem is divided into the following tasks which involve: (1) developing planar imaging techniques that visualize fuel and air distributions in the spray, (2) characterizing the airblast spray without a crossflow, and (3) characterizing the airblast spray upon injection into a crossflow. Geometric and operating conditions are varied in order to affect the atomization, penetration, and dispersion of the spray into the crossflow. The airblast spray is first characterized, using imaging techniques, as it issues into a quiescent environment. The spray breakup modes are classified in a liquid Reynolds number versus airblast Weber number regime chart. This work focuses on sprays formed by the "prompt" atomization mode, which induces a well-atomized and well-dispersed spray, and which also produces a two-lobed liquid distribution corresponding to the atomizing air passageways in the injector. The characterization of the spray jet injected into the crossflow reveals the different processes that control its dispersion. Correlations that describe the inner and outer boundaries of the spray jet are developed, using the definition of a two-phase momentum-flux ratio. Cross-sections of the liquid spray depict elliptically-shaped distributions, with the exception of the finely-atomized sprays which show kidney-shaped distributions reminiscent of those obtained in gaseous jet in crossflow systems. A droplet trajectory analysis overpredicts the liquid mass penetration, and indicates a need for a more rigorous model to account for the three-dimensional mixing field induced by the jet-crossflow interaction. Nonetheless, the general procedures and criteria that are outlined can be used to efficiently assess and compare the quality of sprays formed under different conditions.

Leong, May Y.↗

NASA NTRS1982

Turbulent compressible convection in a deep atmosphere. I - Preliminary two-dimensional results

The turbulent convection of a compressible fluid in a deep atmosphere is simulated by two-dimensional numerical computations, displaying coexisting 'cells' whose sizes range from the total depth of the convection zone to the smallest scale height at the top. While the largest cells traverse the entire zone, smaller ones are clustered near the top. The vertical correlation length of the vertical velocity is proportional to the local pressure or density scale height, in a way reminiscent of the concept of mixing length.

Chan, K. L.↗

NASA NTRS1972

Some effects of swirl on turbulent mixing and combustion

A general formulation of some effects of swirl on turbulent mixing is given. The basis for the analysis is that momentum transport is enhanced by turbulence resulting from rotational instability of the fluid field. An appropriate form for the turbulent eddy viscosity is obtained by mixing length type arguments. The result takes the form of a corrective factor that is a function of the swirl and acts to increase the eddy viscosity. The factor is based upon the initial mixing conditions implying that the rotational turbulence decays in a manner similar to that of free shear turbulence. Existing experimental data for free jet combustion are adequately matched by using the modifying factor to relate the effects of swirl on eddy viscosity. The model is extended and applied to the supersonic combustion of a ring jet of hydrogen injected into a constant area annular air stream. The computations demonstrate that swirling the flow could: (1) reduce the burning length by one half, (2) result in more uniform burning across the annulus width, and (3) open the possibility of optimization of the combustion characteristics by locating the fuel jet between the inner wall and center of the annulus width.

Rubel, A.↗

NASA NTRS1975

Analytical study of mixing and reacting three-dimensional supersonic combustor flow fields

An analytical investigation is presented of mixing and reacting hydrogen jets injected from multiple orifices transverse and parallel to a supersonic airstream. The COMOC computer program, based upon a finite-element solution algorithm, was developed to solve the governing equations for three-dimensional, turbulent, reacting, boundary-region, and confined flow fields. The computational results provide a three-dimensional description of the velocity, temperature, and species-concentration fields downstream of hydrogen injection. Detailed comparisons between cold-flow data and results of the computational analysis have established validity of the turbulent-mixing model based on the elementary mixing-length hypothesis. A method is established to initiate computations for reacting flow fields based upon cold-flow correlations and the appropriate experimental parameters of Mach number, injector spacing, and pressure ratio. Key analytical observations on mixing and combustion efficiency for reacting flows are presented and discussed.

Baker, A. J.↗

NASA NTRS1978

Characteristics of Mach 10 transitional and turbulent boundary layers

Measurements of the mean flow properties of transitional and turbulent boundary layers in helium on 4 deg and 5 deg wedges were made for flows with edge Mach numbers from 9.5 to 11.3, ratios of wall temperature to total temperature of 0.4 to 0.95, and maximum length Reynolds numbers of one hundred million. The data include pitot and total temperature surveys and measurements of heat transfer and surface shear. In addition, with the assumption of local similarity, turbulence quantities such as the mixing length were derived from the mean flow profiles. Low Reynolds number and precursor transition effects were significant factors at these test conditions and were included in finite difference boundary layer predictions.

Watson, R. D.↗

NASA NTRS2001

Development of a Hybrid RANS/LES Method for Turbulent Mixing Layers

Significant research has been underway for several years in NASA Glenn Research Center's nozzle branch to develop advanced computational methods for simulating turbulent flows in exhaust nozzles. The primary efforts of this research have concentrated on improving our ability to calculate the turbulent mixing layers that dominate flows both in the exhaust systems of modern-day aircraft and in those of hypersonic vehicles under development. As part of these efforts, a hybrid numerical method was recently developed to simulate such turbulent mixing layers. The method developed here is intended for configurations in which a dominant structural feature provides an unsteady mechanism to drive the turbulent development in the mixing layer. Interest in Large Eddy Simulation (LES) methods have increased in recent years, but applying an LES method to calculate the wide range of turbulent scales from small eddies in the wall-bounded regions to large eddies in the mixing region is not yet possible with current computers. As a result, the hybrid method developed here uses a Reynolds-averaged Navier-Stokes (RANS) procedure to calculate wall-bounded regions entering a mixing section and uses a 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. With this technique, closure for the RANS equations is obtained by using the Cebeci-Smith algebraic turbulence model in conjunction with the wall-function approach of Ota and Goldberg. The LES equations are closed using the Smagorinsky subgrid scale model. Although the function of the Cebeci-Smith model to replace all of the turbulent stresses is quite different from that of the Smagorinsky subgrid model, which only replaces the small subgrid turbulent stresses, both are eddy viscosity models and both are derived at least in part from mixing-length theory. The similar formulation of these two models enables the RANS and LES equations to be solved with a single solution scheme and computational grid. The hybrid RANS-LES method has been applied to a benchmark compressible mixing layer experiment in which two isolated supersonic streams, separated by a splitter plate, provide the flows to a constant-area mixing section. Although the configuration is largely two dimensional in nature, three-dimensional calculations were found to be necessary to enable disturbances to develop in three spatial directions and to transition to turbulence. The flow in the initial part of the mixing section consists of a periodic vortex shedding downstream of the splitter plate trailing edge. This organized vortex shedding then rapidly transitions to a turbulent structure, which is very similar to the flow development observed in the experiments. Although the qualitative nature of the large-scale turbulent development in the entire mixing section is captured well by the LES part of the current hybrid method, further efforts are planned to directly calculate a greater portion of the turbulence spectrum and to limit the subgrid scale modeling to only the very small scales. This will be accomplished by the use of higher accuracy solution schemes and more powerful computers, measured both in speed and memory capabilities.

Georgiadis, Nicholas J.↗

NASA NTRS1995

Advanced k-epsilon modeling of heat transfer

This report describes two approaches to low Reynolds-number k-epsilon turbulence modeling which formulate the eddy viscosity on the wall-normal component of turbulence and a length scale. The wall-normal component of turbulence is computed via integration of the energy spectrum based on the local dissipation rate and is bounded by the isotropic condition. The models account for the anisotropy of the dissipation and the reduced mixing length due to the high strain rates present in the near-wall region. The turbulent kinetic energy and its dissipation rate were computed from the k and epsilon transport equations of Durbin. The models were tested for a wide range of turbulent flows and proved to be superior to other k-epsilon models, especially for nonequilibrium anisotropic flows. For the prediction of airfoil heat transfer, the models included a set of empirical correlations for predicting laminar-turbulent transition and laminar heat transfer augmentation due to the presence of freestream turbulence. The predictions of surface heat transfer were generally satisfactory.

Kwon, Okey↗