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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.↗

Interactive phenomena in supersonic jet mixing problems. II - Numerical studies

Applications of the numerical techniques discussed in Part I of this article are presented. Fundamental wave/shear-layer interaction calculations are performed exhibiting the waves produced by high-speed turbulent mixing processes and the interactions of an expansion fan and shock wave with a developing shear layer. Calculations for an underexpanded supersonic jet into a supersonic external stream at different velocity ratios are presented which delineate betweeen weakly interactive and strongly interactive processes in the jet near field. Calculations for the multiple-cell shock structure of an underexpanded jet into still air exhibit the damping of wave intensities by the turbulence and compare quite favorably with available data.

Dash, S. M.↗

A first-order Green's function approach to supersonic oscillatory flow: A mixed analytic and numeric treatment

A frequency domain Green's Function Method for unsteady supersonic potential flow around complex aircraft configurations is presented. The focus is on the supersonic range wherein the linear potential flow assumption is valid. In this range the effects of the nonlinear terms in the unsteady supersonic compressible velocity potential equation are negligible and therefore these terms will be omitted. The Green's function method is employed in order to convert the potential flow differential equation into an integral one. This integral equation is then discretized, through standard finite element technique, to yield a linear algebraic system of equations relating the unknown potential to its prescribed co-normalwash (boundary condition) on the surface of the aircraft. The arbitrary complex aircraft configuration (e.g., finite-thickness wing, wing-body-tail) is discretized into hyperboloidal (twisted quadrilateral) panels. The potential and co-normalwash are assumed to vary linearly within each panel. The long range goal is to develop a comprehensive theory for unsteady supersonic potential aerodynamic which is capable of yielding accurate results even in the low supersonic (i.e., high transonic) range.

Freedman, M. I.↗

A numerical study of mixing enhancement in supersonic reacting flow fields

NASA Langley has intensively investigated the components of ramjet and scramjet systems for endoatmospheric, airbreathing hypersonic propulsion; attention is presently given to the optimization of scramjet combustor fuel-air mixing and reaction characteristics. A supersonic, spatially developing and reacting mixing layer has been found to serve as an excellent physical model for the mixing and reaction process. Attention is presently given to techniques that have been applied to the enhancement of the mixing processes and the overall combustion efficiency of the mixing layer. A fuel injector configuration has been computationally designed which significantly increases mixing and reaction rates.

Drummond, J. Philip↗

A numerical study of mixing enhancement in a supersonic combustor

This investigation describes an application of the Langley Research Center (LaRC) SPARK family of computer codes to swept and unswept ramp fuel injectors in a reacting highly vortical flow. Both mixing and reacting studies are performed. They show substantially higher mixing as well as flow losses for the swept ramp case. Computational results are compared both qualitatively and quantitatively with experimental results.

Riggins, D. W.↗

A Parametric Numerical Study of Mixing in a Cylindrical Duct

The interaction is described of some of the important parameters affecting the mixing process in a quick mixing region of a rich burn/quick mix/lean burn (RQL) combustor. The performance of the quick mixing region is significantly affected by the geometric designs of both the mixing domain and the jet inlet orifices. Several of the important geometric parameters and operating conditions affecting the mixing process were analytically studied. Parameters such as jet-to-mainstream momentum flux ratio (J), mass flow ratio (MR), orifice geometry, orifice orientation, and number of orifices/row (equally spaced) around the circumferential direction were analyzed. Three different sets of orifice shapes were studied: (1) square, (2) elongated slots, and (3) equilateral triangles. Based on the analytical results, the best mixing configuration depends significantly on the penetration depth of the jet to prevent the hot mainstream flow from being entrained behind the orifice. The structure in a circular mixing section is highly weighted toward the outer wall and any mixing structure affecting this area significantly affects the overall results. The increase in the number of orifices per row increases the mixing at higher J conditions. Higher slot slant angles and aspect ratios are generally the best mixing configurations at higher momentum flux ratio (J) conditions. However, the square and triangular shaped orifices were more effective mixing configurations at lower J conditions.

Oechsle, V. L.↗

A parametric numerical study of mixing in a cylindrical duct

The interaction is described of some of the important parameters affecting the mixing process in a quick mixing region of a rich burn/quick mix/lean burn (RQL) combustor. The performance of the quick mixing region is significantly affected by the geometric designs of both the mixing domain and the jet inlet orifices. Several of the important geometric parameters and operating conditions affecting the mixing process were analytically studied. Parameters such as jet-to-mainstream momentum flux ratio (J), mass flow ratio (MR), orifice geometry, orifice orientation, and number of orifices/row (equally spaced around the circumferential direction were analyzed. Three different sets of orifice shapes were studied: (1) square, (2) elongated slots, and (3) equilateral triangles. Based on the analytical results, the best mixing configuration depends significantly on the penetration depth of the jet to prevent the hot mainstream flow from being entrained behind the orifice. The structure in a circular mixing section is highly weighted toward the outer wall and any mixing structure affecting this area significantly affects the overall results. The increase in the number of orifices per row increases the mixing at higher J conditions. Higher slot slant angles and aspect ratios are generally the best mixing configurations at higher momentum flux ratio (J) conditions. However, the square and triangular shaped orifices were more effective mixing configurations at lower J conditions.

Oechsle, V. L.↗

A numerical study of mixing and combustion in hypervelocity flows through a scramjet combustor model

Interest in high speed, air-breathing propulsion systems such as scramjets has revived in recent years fueled to a large extent by the National Aerospace Plane (NASP) program. These vehicles are expected to fly trans-atmospheric and as a consequence, the Mach number level within the engine/combustor would be rather high (M greater than 5). Ground based testing of such scramjet engines requires a facility that can not only achieve the right Mach number, but also have the proper pressures and temperatures to simulate the combustion processes. At present, only pulse type facilities can provide such high enthalpy flows. The newest of these is the free-piston shock tunnel, T5 located at GALCIT. Recently, a generic combustor model was tested in T5, and the experimental data from that study is analyzed in the present report. The available experimental data from T5 are essentially the static pressures on the injection wall and the one opposite to it. Thus, a principal aim of the present study was to validate the available experimental data by using a proven CFD tool and then investigate the performance characteristics of the combustor model, such as, the mixing efficiency and combustion efficiency. For this purpose, in this study, the code GASP has been used.

Krishamurthy, Ramesh↗

Numerical Simulation of Mixing Enhancement in a Hot Supersonic Jet

Experimental observations show that the presence of small tabs on the edge of a hot, compressible jet exiting into a slower moving, colder ambient flow can increase the rate of spreading of the jet. This suggests that the rate of mixing of the jet and the ambient fluid is also increased. In order to elucidate the physical mechanism responsible for the increased spreading rate a set of calculations were carried out within the framework of the compressible three dimensional Navier-Stokes equations. A series of grid refinements were made to assess the accuracy of the results. The first simulated the flow without the tabs, obtaining reasonable agreement with experimental measurements of the velocity. We then simulated the flow, without tabs, over a range of values of the convective Mach number in order to determine the dependence of the mixing on this parameter. Simulations with modeled tabs were also carried out. In these calculations the effect of the tabs on the flow was modeled by pairs of counter rotating vortices. The results of these calculations indeed show that the presence of the tabs increase the spreading rate of the jet. The basic physical mechanism responsible for the enhanced spreading rate is discussed and qualitative comparisons with flow visualizations are made.

Grosch, C. E.↗

Passive scalar entrainment and mixing in a forced, spatially-developing mixing layer

Numerical simulations are performed for the forced, spatially-developing plane mixing layer in two and three dimensions. Transport of a passive scalar field is included in the computation. This, together with the allowance for spatial development in the simulations, affords the opportunity for study of the asymmetric entrainment of irrotational fluid into the layer. The inclusion of a passive scalar field provides a means for simulating the effect of this entrainment asymmetry on the generation of 'products' from a 'fast' chemical reaction. Further, the three-dimensional simulations provide useful insight into the effect of streamwise structures on these entrainment and 'fast' reaction processes. Results from a two-dimensional simulation indicate 1.22 parts high-speed fluid are entrained for every one part low-speed fluid. Inclusion of streamwise vortices at the inlet plane of a three-dimensional simulation indicate a further increase in asymmetric entrainment - 1.44:1. Results from a final three-dimensional simulation are presented. In this case, a random velocity perturbation is imposed at the inlet plane. The results indicate the 'natural' development of the large spanwise structures characteristic of the mixing layer.

Lowery, P. S.↗

Vorticity generation mechanisms in parallel injection schemes for supersonic mixing

A numerical study is reported of the three-dimensional nonreacting supersonic flow field produced by three parallel fuel injection schemes. Such injections are being considered as a means of enhancing fuel mixing in future Scramjet engine designs. The strength of vortex structures produced by ramp injectors and by rocket/jet interactions are quantified and their relative effectiveness in enhancing the fuel mixing process is addressed. An experimental setup for validation of the above numerical results has been constructed and preliminary results are presented. For the flow field parameters chosen, the ramp generated vorticity is found to be considerably larger than that generated by the shock. The unsteady recirculating flow field in the wake of the injector appears also to give rise to important additional vorticity and mixing.

Donohue, James M.↗

Mixed convection in a horizontal rectangular channel - Experimental and numerical velocity distributions

Mixed convection in a rectangular channel (width/height = 2) with bottom-heated and top-cooled sections is studied by laser Doppler anemometry in nitrogen at Ra = 22,200 and Re = 18.75, 36, and 54. At the lower Re values, symmetry breaking is observed in steady but spatially oscillating flows that prevail over a certain distance from the leading edge of the differentially heated section. Further downstream, unsteady flows are found even for Re = 18.75. Numerical models are used to investigate the effects of adiabatic, conducting (with a conductive-convective heat transfer coefficient), and perfectly conducting side walls; channel tilts and Prandtl number dependence. Good agreement between calculations and experiment is obtained for longitudinal convective roll velocities. The transverse velocities are found to be independent of Re.

Nyce, Thomas A.↗

Interactive phenomena in supersonic jet mixing problems. I Phenomenology and numerical modeling techniques

The interactive phenomena that occur in supersonic jet mixing flowfields, and numerical modeling techniques developed to analyze such phenomena are discussed. A spatial marching procedure based on solving the parabolized Navier-Stokes jet mixing equations is presented. This procedure combines shock-capturing methodology for the analysis of supersonic mixing regions with pressure-split methodology for the analysis of subsonic mixing regions. The two regions are coupled at viscous sonic lines utilizing a viscous-characteristic coupling procedure. Specialized techniques for the treatment of jet boundary growth, strong discontinuties (Mach disks), and small embedded subsonic zones (behind Mach disks) are presented. Turbulent processes are represented by two-equation turbulence model formulations. In Part II of this article, numerical studies are presented for a variety of supersonic jet interactive phenomena.

Dash, S. M.↗

Numerical Analysis of Mixed-Phase Icing Cloud Simulations in the NASA Propulsion Systems Laboratory

This presentation describes the development of a numerical model that couples the thermal interaction between ice particles, water droplets, and the flowing gas of an icing wind tunnel for simulation of NASA Glenn Research Centers Propulsion Systems Laboratory (PSL). The ultimate goal of the model is to better understand the complex interactions between the test parameters and have greater confidence in the conditions at the test section of the PSL tunnel. The model attempts to explain the observed changes in test conditions by coupling the conservation of mass and energy equations for both the cloud particles and flowing gas mass. Model predictions were compared to measurements taken during May 2015 testing at PSL, where test conditions varied gas temperature, pressure, velocity and humidity levels, as well as the cloud total water content, particle initial temperature, and particle size distribution.

NASA PSL↗

Numerical Analysis of Mixed-Phase Icing Cloud Simulations in the NASA Propulsion Systems Laboratory

This paper describes the development of a numerical model that couples the thermal interaction between ice particles, water droplets, and the flowing gas of an icing wind tunnel for simulation of NASA Glenn Research Centers Propulsion Systems Laboratory (PSL). The ultimate goal of the model is to better understand the complex interactions between the test parameters and have greater confidence in the conditions at the test section of the PSL tunnel. The model attempts to explain the observed changes in test conditions by coupling the conservation of mass and energy equations for both the cloud particles and flowing gas mass. Model predictions were compared to measurements taken during May 2015 testing at PSL, where test conditions varied gas temperature, pressure, velocity and humidity levels, as well as the cloud total water content, particle initial temperature, and particle size distribution.

NASA PSL↗

Numerical solution of laminar jet mixing with and without free stream.

Systematic numerical solutions of two-dimensional and axisymmetrical laminar jet of an incompressible fluid with and without free stream have been obtained. For the case without free stream, the exact numerical solutions have been obtained for different initial velocity profiles and compared with experimental results and similarity solutions. For the case with free stream, the numerical solutions have been compared with the linearized analytical solutions. An approximate numerical solution for the axial velocity distribution of the three-dimensional laminar jet is proposed. The accuracy of the method has been determined from the exact solutions of the two limiting cases of three-dimensional jets, i.e., the two-dimensional and axisymmetric cases.

Pai, S. I.↗