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NASA NTRS1996

An Optimal Order Nonnested Mixed Multigrid Method for Generalized Stokes Problems

A multigrid algorithm is developed and analyzed for generalized Stokes problems discretized by various nonnested mixed finite elements within a unified framework. It is abstractly proved by an element-independent analysis that the multigrid algorithm converges with an optimal order if there exists a 'good' prolongation operator. A technique to construct a 'good' prolongation operator for nonnested multilevel finite element spaces is proposed. Its basic idea is to introduce a sequence of auxiliary nested multilevel finite element spaces and define a prolongation operator as a composite operator of two single grid level operators. This makes not only the construction of a prolongation operator much easier (the final explicit forms of such prolongation operators are fairly simple), but the verification of the approximate properties for prolongation operators is also simplified. Finally, as an application, the framework and technique is applied to seven typical nonnested mixed finite elements.

Deng, Qingping↗

NASA NTRS1996

Conditional Moment Closure of Mixing and Reaction in Turbulent Nonpremixed Combustion

Nonpremixed combustion is the process whereby fuel and oxidizer species, which are each nonflammable in isolation, concurrently mix to burn a flammable mixture, and chemically react in the flammable mixture. In cases of practical industrial interest, the bulk of nonpremixed combustion occurs in a turbulent mixing regime where enhanced mass transfer rates flow the maximum power density to be achieved in any given thermochemical device.

Smith, Nigel S. A.↗

NASA NTRS1996

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.↗

NASA NTRS1996

Asymptotic solution of the turbulent mixing layer for velocity ratio close to unity

The equations describing the first two terms of an asymptotic expansion of the solution of the planar turbulent mixing layer for values of the velocity ratio close to one are obtained. The first term of this expansion is the solution of the well-known time-evolving problem and the second, which includes the effects of the increase of the turbulence scales in the stream-wise direction, obeys a linear system of equations. Numerical solutions of these equations for a two-dimensional reacting mixing layer show that the correction to the time-evolving solution may explain the asymmetry of the entrainment and the differences in product generation observed in flip experiments.

Higuera, F. J.↗

NASA NTRS1997

Mixing of Multiple Jets With a Confined Subsonic Crossflow: Opposed Rows of Orifices in Rectangular Ducts - Part 2

This paper summarizes experimental and computational results on the mixing of opposed rows of jets with a confined subsonic crossflow in rectangular ducts. The studies from which these results were excerpted investigated flow and geometric variations typical of the complex 3-D flowfield in the combustion chambers in gas turbine engines. The principal observation was that the momentum-flux ratio, J, and the orifice spacing, S/H, were the most significant flow and geometric variables. Jet penetration was critical, and penetration decreased as either momentum-flux ratio or orifice spacing decreased. It also appeared that jet penetration remained similar with variations in orifice size, shape, spacing, and momentum-flux ratio when the orifice spacing was inversely proportional to the square-root of the momentum-flux ratio. It was also seen that planar averages must be considered in context with the distributions. Note also that the mass-flow ratios and the offices investigated were often very large (jet-to-mainstream mass-flow ratio greater than 1 and the ratio of orifices-area-to-mainstream-cross-sectional-area up to 0.5 respectively), and the axial planes of interest were often just downstream of the orifice trailing edge. Three-dimensional flow was a key part of efficient mixing and was observed for all configurations.

Holdeman, James D.↗

NASA NTRS1997

Mixing of Pure Air Jets with a Reacting Fuel-Rich Crossflow

Jets in a crossflow play an integral role in practical combustion systems such as can and annular gas turbine combustors in conventional systems, and the Rich-burn/Quick-mix/Lean-burn (RQL) combustor utilized in stationary applications and proposed for advanced subsonic and supersonic transports. The success of the RQL combustor rests with the performance of the quick-mixing section that bridges the rich and lean zones. The mixing of jet air with a rich crossflow to bring the reaction to completion in the lean zone must be performed rapidly and thoroughly in order to decrease the extent of near-stoichiometric fluid pocket formation. Fluid pockets at near-stoichiometric equivalence ratios are undesirable because the high temperatures attained accelerate pollutant formation kinetics associated with nitric oxide (NO). The present study develops a model experiment designed to reveal the processes that occur when jet air is introduced into hot effluent emanating from a fuel-rich reaction zone.

Leong, M. Y.↗

NASA NTRS1997

Optimization of Jet Mixing Into a Rich, Reacting Crossflow

Radial jet mixing of pure air into a fuel-rich, reacting crossflow confined to a cylindrical geometry is addressed with a focus on establishing an optimal jet orifice geometry. The purpose of this investigation was to determine the number of round holes that most effectively mixes the jets with the mainstream flow, and thereby minimizes the residence time of near-stoichiometric and unreacted packets. Such a condition might reduce pollutant formation in axially staged, gas turbine combustor systems. Five different configurations consisting of 8, 10, 12, 14, and 18 round holes are reported here. An optimum number of jet orifices is found for a jet-to-mainstream momentum-flux ratio (J) of 57 and a mass-flow ratio (MR) of 2.5. For this condition, the 14-orifice case produces the lowest spatial unmixedness and the most uniformly-distributed species concentrations and temperature profiles at a plane located one duct diameter length from the jet orifice inlet.

Leong, M. Y.↗

NASA NTRS1960

Mixing Characteristics Downstream of Core Region of High-Temperature Axisymmetric Jets Exhausting Into Transonic and Supersonic Streams

A series of rocket motors with varying exit to throat area ratios was tested in the 8- by 6-foot wind tunnel to determine the effects of mixing on jet diameter and temperature decay at large distances (x/d > 30) from the nozzle exit. An approximate method to account for effects of the initial expansion was evolved. It was determined that the combustion efficiency has an important effect on jet spreading, since the unburned products can burn downstream of the nozzle. The data showed considerable scatter; however, mixing rates were, in general, lower than those observed for subsonic jets. Data for angles of attack of 5 and 10 deg are also presented, giving the respective centerline shift and temperature decay as a function of axial distance.

Huff, Ronald G.↗

NASA NTRS1998

Process-Parameter-Dependent Optical and Structural Properties of ZrO2MgO Mixed-Composite Films Evaporated from the solid Solution

The process-parameter-dependent optical and structural properties of ZrO2MgO mixed-composite material have been investigated. Optical properties were derived from spectrophotometric measurements. By use of atomic force microscopy, x-ray diffraction analysis, and energy-dispersive x-ray (EDX) analysis, the surface morphology, grain size distributions, crystallographic phases, and process-dependent material composition of films have been investigated. EDX analysis made evident the correlation between the oxygen enrichment in the films prepared at a high level of oxygen pressure and the very low refractive index. Since oxygen pressure can be dynamically varied during a deposition process, coatings constructed of suitable mixed-composite thin films can benefit from continuous modulation of the index of refraction. A step modulation approach is used to develop various multilayer-equivalent thin-film devices.

Sahoo, N. K.↗

NASA NTRS1998

Models of Plumes: Their Flow, Their Geometric Spreading, and Their Mixing with Interplume Flow

There are two types of plume flow models: (1) 1D models using ad hoc spreading functions, f(r); (2) MagnetoHydroDynamics (MHD) models. 1D models can be multifluid, time dependent, and incorporate very general descriptions of the energetics. They confirm empirical results that plume flow is slow relative to requirements for high speed wind. But, no published 1 D model incorporates the rapid local spreading at the base (fl(r)) which has an important effect on mass flux. The one published MHD model is isothermal, but confirms that if b=8*pi*p/absolute value(B)2<<l then the field is nearly potential below -70,000 km. Building on the MHD result, we apply a two scale approximation to calculate fl(r). We also compute the global spreading (fg(r)) out to 5.0 RSUN imposed by coronal hole geometry. Global MHD models provide a potent method of calculating fg(r). Unambiguous plume signatures have not yet been found in the solar wind. This is probably due to strong mixing of plume and interplume flows near the Sun. We describe a physical source for strong mixing due to the observed flows being unstable to shear instabilities that lead to rapid disruption.

Suess, Steven T.↗

NASA NTRS1999

A Mixed-Mode I/II Fracture Criterion and Its Application in Crack Growth Predictions

A crack tip opening displacement (CTOD)-based, mixed mode fracture criterion is developed for predicting the onset and direction of crack growth. The criterion postulates that crack growth occurs in either the Mode I or Mode II direction, depending on whether the maximum in either the opening or the shear component of CTOD, measured at a specified distance behind the crack tip, attains a critical value. For crack growth direction prediction, the proposed CTOD criterion is shown to be equivalent to seven commonly used crack growth criteria under linearly elastic and asymptotic conditions. Under elastic-plastic conditions the CTOD criterion's prediction of the dependence of the crack growth direction on the crack-up mode mixity is in excellent agreement with the Arcan test results. Furthermore, the CTOD criterion correctly predicts the existence of a crack growth transition from mode I to mode II as the mode mixity approaches the mode II loading condition. The proposed CTOD criterion has been implemented in finite element crack growth simulation codes Z1P2DL and FRANC2DL to predict the crack growth paths in (a) a modified Arcan test specimen and fixture made of AL 2024-T34 and (b) a double cantilever beam (DCB) specimen made of AL 7050. A series of crack growth simulations have been carried out for the crack growth tests in the Arcan and DCB specimens and the results further demonstrate the applicability of the mixed mode CTOD fracture criterion crack growth predictions and residual strength analyses for airframe materials.

Sutton, Michael A.↗

NASA NTRS1997

The Use of a Lidar Forward-Looking Turbulence Sensor for Mixed-Compression Inlet Unstart Avoidance and Gross Weight Reduction on a High Speed Civil Transport

Inlet unstart causes a disturbance akin to severe turbulence for a supersonic commercial airplane. Consequently, the current goal for the frequency of unstarts is a few times per fleet lifetime. For a mixed-compression inlet, there is a tradeoff between propulsion system efficiency and unstart margin. As the unstart margin decreases, propulsion system efficiency increases, but so does the unstart rate. This paper intends to first, quantify that tradeoff for the High Speed Civil Transport (HSCT) and second, to examine the benefits of using a sensor to detect turbulence ahead of the airplane. When the presence of turbulence is known with sufficient lead time to allow the propulsion system to adjust the unstart margin, then inlet un,starts can be minimized while overall efficiency is maximized. The NASA Airborne Coherent Lidar for Advanced In-Flight Measurements program is developing a lidar system to serve as a prototype of the forward-looking sensor. This paper reports on the progress of this development program and its application to the prevention of inlet unstart in a mixed-compression supersonic inlet. Quantified benefits include significantly reduced takeoff gross weight (TOGW), which could increase payload, reduce direct operating costs, or increase range for the HSCT.

Soreide, David↗

NASA NTRS1999

Effects of Passive Fuel-Air Mixing Control on Burner Emissions Via Lobed Fuel Injectors

The present experimental study examines the effects of differing levels of passive fuel-air premixing on flame structures and their associated NO(x) and CO emissions. Four alternative fuel injector geometries were explored, three of which have lobed shapes. These lobed injectors mix fuel and air and strain species inter-faces to differing extents due to streamwise vorticity generation, thus creating different local or core equivalence ratios within flow regions upstream of flame ignition and stabilization. Prior experimental studies of two of these lobed injector flowfields focused on non-reactive mixing characteristics and emissions measurements for the case where air speeds were matched above and below the fuel injector, effectively generating stronger streamwise vorticity than spanwise vorticity. The present studies examine the effects of airstream mismatch (and hence additional spanwise vorticity generation), effects of confinement of the crossflow to reduce the local equivalence ratio, and the effects of altering the geometry and position of the flameholders. NO(x) and CO emissions as well as planar laser-induced fluorescence imaging (PLIF) of seeded acetone are used to characterize injector performance and reactive flow evolution.

Mitchell, M. G.↗

NASA NTRS1998

The Applicability of Jet-Shear-Layer Mixing and Effervescent Atomization for Low-NO(x) Combustors

An investigation has been conducted to develop appropriate technologies for a low-NO(x), liquid-fueled combustor. The combustor incorporates an effervescent atomizer used to inject fuel into a premixing duct. Only a fraction of the combustion air is used in the premixing process. This fuel-rich mixture is introduced into the remaining combustion air by a rapid jet-shear-layer mixing process involving radial fuel-air jets impinging on axial air jets in the primary combustion zone. Computational modeling was used as a tool to facilitate a parametric analysis appropriate to the design of an optimum low-NO(x) combustor. A number of combustor configurations were studied to assess the key combustor technologies and to validate the three-dimensional modeling code. The results from the experimental testing and computational analysis indicate a low-NO(x) potential for the jet-shear-layer combustor. Key features found to affect NOx emissions are the primary combustion zone fuel-air ratio, the number of axial and radial jets, the aspect ratio and radial location of the axial air jets, and the radial jet inlet hole diameter. Each of these key parameters exhibits a low-NO(x) point from which an optimized combustor was developed Also demonstrated was the feasibility of utilizing an effervescent atomizer for combustor application. Further developments in the jet-shear-layer mixing scheme and effervescent atomizer design promise even lower NO(x) with high combustion efficiency.

Colantonio, R. O.↗

NASA NTRS1999

A Stratospheric Mixing and Transport Sampler

The mixing and transport of stratospheric chemical species occurs by a variety of physical mechanisms on a range of length and time scales. Slow vertical diffusion resembles Taylor diffusion in pipe flow, while rapid stirring by chaotic advection is essentially a "baker's transformation", via the stretching and folding of material lines in the flow. Other examples include global scale transport by large organized flow structures, such as the winter stratospheric "eggbeater" that brings tropical air to the north pole. This presentation is a survey of these different mixing and transport phenomena and how we see their signatures in observations of chemical tracers.

Sparling, Lynn↗

NASA NTRS1999

Mixing Characteristics of Coaxial Injectors at High Gas to Liquid Momentum Ratios

A study of the spray of a swirl coaxial gas-liquid injector operating at high gas to liquid momentum ratios is reported. Mixing and droplet size characteristics of the swirl injector are also compared to a shear coaxial injector, currently being used in the Space Shuttle Main Engine fuel preburner. The injectors were tested at elevated chamber pressures using water as a LOX simulant and nitrogen and helium as gaseous hydrogen simulants. The elevated chamber pressure allowed for matching of several of the preburner injector conditions including; gas to liquid momentum ratio, density ratio and Mach number. Diagnostic techniques used to characterize the spray included; strobe back-light imaging, laser sheet spray imaging, mechanical patternation, and a phase Doppler interferometry. Results thus far indicate that the radial spreading of the swirl coaxial spray is much less than was reported in previous studies of swirl injectors operating at atmospheric back-pressure. The swirl coaxial spray does, however, exhibit a smaller overall droplet size which may be interpreted as an increase in local mixing.

Strakey, P. A.↗

NASA NTRS1999

Supersonic Jet Mixing Enhancement due to Natural and Induced Screech

Outline of presentation are: (1) Review of experimental apparatus. (2) Effect of natural screech of jet mixing; converging nozzle, underexpanded jet and converging-diverging nozzle, design pressure.(3) Effect of induced screech on jet mixing: produced by paddles in shear layers, similar to edge tones, and converging-diverging nozzle, design pressure. (4) Effect of paddles on near-field jet noise. and (5) Concluding remarks.

Rice, E. J.↗

NASA NTRS1999

Application of a Flip-Flop Nozzle on Plume Mixing Enhancement

Mach wave radiation is a major source of noise in high speed jets. It is created by turbulent eddies which travel at supersonic speed within the shear layer of the jet. Downstream of the potential core, the convection speed of the eddies decays and noise production is reduced. Once the convection speeds drops below the speed of sound, eddy Mach wave radiation ceases. Mach wave radiation may be reduced by shortening the core length of the jet. This requires a faster growth of the shear layer, i.e. enhanced mixing in the jet. We investigated the possibility of mixing enhancement by the excitation of the instability waves in a supersonic rectangular jet.

Schreck, Stefan↗