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NASA NTRSDate not supplied

Assessment of Turbulence Models for a Single-Injector Cooling Flow

This work assesses the ability of Reynolds-averaged Navier-Stokes turbulence models to predict a fundamental thermal cooling flow configuration. This geometry consists of a plate with a single cooling hole positioned downstream of a heated exhaust nozzle. The linear Shear Stress Transport (SST), non-linear Quadratic Constitutive Relation (QCR), and differential SSG/LRR Reynolds Stress Model (RSM) turbulence models were investigated for flow conditions with a blowing ratio of 1.0 and 2.0. Despite significant differences in turbulence model complexity, the results miss important details observed in the data and large eddy simulation (LES). Injection penetration is over-predicted. Mixing and centerline wake recovery is too slow. Temperature predictions are worse than velocity, suggesting that perhaps the simple gradient diffusion approximation used to model the turbulent heat flux may be to blame. These observations are put into context using other studies to identify shortcomings in the modeling of both the turbulent stress and turbulent heat flux.

Film Cooling↗

NASA NTRS1995

Flame-vortex interactions imaged in microgravity

The scientific objective is to obtain high quality color-enhanced digital images of a vortex exerting aerodynamic strain on premixed and nonpremixed flames with the complicating effects of buoyancy removed. The images will provide universal (buoyancy free) scaling relations that are required to improve several types of models of turbulent combustion, including KIVA-3, discrete vortex, and large-eddy simulations. The images will be used to help quantify several source terms in the models, including those due to flame stretch, flame-generated vorticity, flame curvature, and preferential diffusion, for a range of vortex sizes and flame conditions. The experiment is an ideal way to study turbulence-chemistry interactions and isolate the effect of vortices of different sizes and strengths in a repeatable manner. A parallel computational effort is being conducted which considers full chemistry and preferential diffusion.

Driscoll, James F.↗

NASA NTRS1977

Vertical and horizontal fluxes of ozone at the tropopause from the first year of GASP data

Ozone measurements taken from commercial airlines (GASP data) are used to estimate the vertical and horizontal fluxes of ozone near the tropopause. The annual average flux of O3 into the troposphere at 30 to 50 deg N is nearly the same as indirect estimates based on surface O3 data, thus supporting the hypothesis that the amount of ozone in the troposphere is essentially controlled by injection from the stratosphere. The present GASP estimates of the total flux of O3 into the troposphere verify the model results of Cunnold et al. (1975), although the distribution of flux between mean motions and diffusion is different and suggests that models with coarse horizontal resolution must continue to parameterize much vertical transport by diffusion coefficients. A significant variation in the east-west spatial autocorrelation function of O3 near the tropopause is found to be about 1900 km. Monthly estimates of the horizontal transient eddy flux of ozone are generally smaller than seasonal or yearly results based on ozonesonde data. This is perhaps because the present estimates are made over monthly periods to reduce the influence of correlation between the annual variations in ozone and meridional wind. The available data support the hypothesis that transient eddy fluxes of O3 have large longitudinal variations.

Nastrom, G. D.↗

NASA NTRS1985

Numerical simulation of compressible, turbulent, two-phase flow

A computer program for numerically simulating compressible, turbulent, two-phase flows is described and applied. Special attention is given to flows in which dust is ingested into the turbulent boundary layer behind shock waves moving over the earth's surface. it is assumed that the two phases are interpenetrating continua which are coupled by drag forces and heat transfer. The particle phase is assumed to be dilute, and turbulent effects are modeled by zero- and two-equation eddy viscosity models. An important feature of the turbulence modeling is the treatment of surface boundary conditions which control the ingestion of particles into the boundary layer by turbulent friction and diffusion. The numerical method uses second-order implicit upwind differencing of the inviscid terms of the equations and second-order central differencing of the viscous terms. A diagonal form of the implicit algorithm is used to improve efficiency, and the transformation to a curvilinear coordinate system is accomplished by the finite volume techniques. Applications to a series of representative flows include a two-phase nozzle flow, the steady flow of air over a sand bed, and the air flow behind a normal shock wave in uniform motion over a sand bed. Results of the latter two applications are compared with experimental results.

Coakley, t. J.↗

NASA NTRS1985

A critical evaluation of various turbulence models as applied to internal fluid flows

Models employed in the computation of turbulent flows are described and their application to internal flows is evaluated by examining the predictions of various turbulence models in selected flow configurations. The main conclusions are: (1) the k-epsilon model is used in a majority of all the two-dimensional flow calculations reported in the literature; (2) modified forms of the k-epsilon model improve the performance for flows with streamline curvature and heat transfer; (3) for flows with swirl, the k-epsilon model performs rather poorly; the algebraic stress model performs better in this case; and (4) for flows with regions of secondary flow (noncircular duct flows), the algebraic stress model performs fairly well for fully developed flow, for developing flow, the algebraic stress model performance is not good; a Reynolds stress model should be used. False diffusion and inlet boundary conditions are discussed. Countergradient transport and its implications in turbulence modeling is mentioned. Two examples of recirculating flow predictions obtained using PHOENICS code are discussed. The vortex method, large eddy simulation (modeling of subgrid scale Reynolds stresses), and direct simulation, are considered. Some recommendations for improving the model performance are made. The need for detailed experimental data in flows with strong curvature is emphasized.

Nallasamy, M.↗

NASA NTRSDate not supplied

Quantitative Approach for the Accurate CFD Simulation of Hover in Turbulent Flow

Time-dependent Navier-Stokes simulations have been carried out for a V22 rotor in hover using an improved, low-diffusion, HLLE++ upwind algorithm in the OVERFLOW code. Emphasis is placed on lessons learned over the past decade regarding the effects of high-order spatial accuracy, grid resolution, and the use of detached eddy simulation in predicting the rotor performance, i.e., figure-of-merit (FM). A quick-start procedure is described together with a statistical measure of FM convergence that reduces hover computations by 5 times, similar in computational work for forward flight. Furthermore, Cartesian adaptive mesh refinement in the rotor wake revealed a complex turbulent flow with worm-like structures of various scales. These turbulent worms, found computationally more than a decade ago, have recently been observed in a separate German Aerospace Center (DLR) experiment. Moreover, adaptive mesh refinement has been used to resolve the tip-vortex to its correct physical size.

Neal M. Chaderjian↗

NASA NTRS2002

Discontinuous Galerkin Methods for Turbulence Simulation

A discontinuous Galerkin (DG) method is formulated, implemented, and tested for simulation of compressible turbulent flows. The method is applied to turbulent channel flow at low Reynolds number, where it is found to successfully predict low-order statistics with fewer degrees of freedom than traditional numerical methods. This reduction is achieved by utilizing local hp-refinement such that the computational grid is refined simultaneously in all three spatial coordinates with decreasing distance from the wall. Another advantage of DG is that Dirichlet boundary conditions can be enforced weakly through integrals of the numerical fluxes. Both for a model advection-diffusion problem and for turbulent channel flow, weak enforcement of wall boundaries is found to improve results at low resolution. Such weak boundary conditions may play a pivotal role in wall modeling for large-eddy simulation.

Collis, S. Scott↗

NASA NTRS1999

Ocean Turbulence I: One-Point Closure Model Momentum and Heat Vertical Diffusivities

Since the early forties, one-point turbulence closure models have been the canonical tools used to describe turbulent flows in many fields. In geophysics, Mellor and Yamada applied such models using the 1980 state-of-the art. Since then, no improvements were introduced to alleviate two major difficulties: 1) closure of the pressure correlations, which affects the correct determination of the critical Richardson number Ri(sub cr) above which turbulent mixing is no longer possible and 2) the need to express the non-local third-order moments (TOM) in terms of lower order moments rather than via the down-gradient approximation as done thus far, since the latter seriously underestimates the TOMs. Since 1) and 2) are still being dealt with adjustable parameters which weaken the credibility of the models, alternative models, not based on turbulence modeling, have been suggested. The aim of this paper is to show that new information, partly derived from the newest 2-point closure model discussed, can be used to solve these shortcomings. The new one-point closure model, which in its simplest form is algebraic and thus simple to implement, is first shown to reproduce a variety of data. Then, it is used in a Ocean-General Circulation Model (O-GCM) where it reproduces well a large variety of ocean data. While phenomenological models are specifically tuned to ocean turbulence, the present model is not. It is first tested against laboratory data on stably stratified flows and then used in an O-GCM. It is more general, more predictive and more resilient, e.g., it can incorporate phenomena like wave-breaking at the surface, salinity diffusivity, non-locality, etc. One important feature that naturally comes out of the new model is that the predicted Richardson critical value Ri(sub cr) is Ri (sub cr approx. = 1) in agreement with both Large Eddy Simulations (LES) and empirical evidence while all previous models predicted Ri (sub cr approx. = 0.2) which led to a considerable underestimate of the extent of turbulent mixing and thus to an incorrect mixed layer depth. The predicted temperature and salinity profiles (vs. depth) are presented and compared with those of the Kolmogorov-Petruvsky-Piskunuv (KPP) model and Levitus data.

Canuto, V. M.↗

NASA NTRS1999

A Theory of Oscillating Edge Flames

It has been known for some years that when a near-limit flame spreads over a liquid pool of fuel, the edge of the flame can oscillate relative to a frame moving with the mean speed. Each period of oscillation is characterized by long intervals of modest motion during which the edge gases radiate like those of a diffusion flame, punctuated by bursts of rapid advance during which the edge gases radiate like those in a deflagration. Substantial resources have been brought to bear on this issue within the microgravity program, both experimental and numerical. It is also known that when a near-asphyxiated candle-flame burns at zero gravity, the edge of the (hemispherical) flame can oscillate violently prior to extinction. Thus a web-surfer, turning to the NASA web-site at http://microgravity.msfc.nasa.gov, and following the trail combustion science/experiments/experimental results/candle flame, will find photographs and a description of candle burning experiments carried out on board both the Space-shuttle and the Russian space station Mir. A brief report can also be found in the proceedings of the Fourth Workshop. And recently, in a third microgravity program, the leading edge of the flame supported by injection of ethane through the porous surface of a plate over which air is blown has been found to oscillate when conditions are close to blow-off. A number of important points can be made with respect to these observations: It is the edge itself which oscillates, advancing and retreating, not the diffusion flame that trails behind the edge; oscillations only occur under near limit conditions; in each case the Lewis number of the fuel is significantly larger than 1; and because of the edge curvature, the heat losses from the reacting edge structure are larger than those from the trailing diffusion flame. We propose a general theory for these oscillations, invoking Occam's 'Law of Parsimony' in an expanded form, to wit: The same mechanism is responsible for the oscillations in all three experiments; and no new mechanism is invoked (Occam's original 'Razor'). Such a strategy eliminates Marangoni effects as the source, for these are absent in the second and third experiments. And it eliminates arguments that point to numerically predicted gas eddies as the source, a new mechanism, unelucidated. Indeed, we hypothesize that the essential driving mechanism for the instability is a combination of large Lewis number and heat losses from the reacting structure near the flame edge. Instabilities driven by these mechanisms are commonplace in 1D configurations. Chemical reactor theory, for example, leads to system responses which mimic the response of the candle flame - steady flame, oscillations, extinction. In a combustion context, oscillating instabilities were first reported for diffusion flames in a theoretical study by Kirkby and Schmitz, and here also the instabilities are associated with near-extinction conditions, large Lewis numbers, and heat losses. And deflagrations will oscillate if the Lewis number is large enough, oscillations that are exacerbated when heat losses are present, whether global or to a surface.

Buckmaster, J.↗

NASA NTRS1972

Mass diffusion in a self-confined rotating flow

The effectiveness of fluid containment near an interior stagnation point and within a self-confined stagnation region is determined by numerically solving the species conservation equation for a bi-component mixture. The flow geometry is that of a swirling fluid stream containing a stationary eddy on the axis of rotation. The base flow is axisymmetric, and the Reynolds number is equal to 50. Schmidt numbers range from 0.1 to 10.

Torrance, K. E.↗

NASA NTRS1991

Examination of various turbulence models for application in liquid rocket thrust chambers

There is a large variety of turbulence models available. These models include direct numerical simulation, large eddy simulation, Reynolds stress/flux model, zero equation model, one equation model, two equation k-epsilon model, multiple-scale model, etc. Each turbulence model contains different physical assumptions and requirements. The natures of turbulence are randomness, irregularity, diffusivity and dissipation. The capabilities of the turbulence models, including physical strength, weakness, limitations, as well as numerical and computational considerations, are reviewed. Recommendations are made for the potential application of a turbulence model in thrust chamber and performance prediction programs. The full Reynolds stress model is recommended. In a workshop, specifically called for the assessment of turbulence models for applications in liquid rocket thrust chambers, most of the experts present were also in favor of the recommendation of the Reynolds stress model.

Hung, R. J.↗

NASA NTRS2008

Development of Eddy Current Techniques for Detection of Deep Fatigue Cracks in Multi-Layer Airframe Components

Thick, multi-layer aluminum structure has been widely used in aircraft design in critical wing splice areas. The multi-layer structure generally consists of three or four aluminum layers with different geometry and varying thickness, which are held together with fasteners. The detection of cracks under fasteners with ultrasonic techniques in subsurface layers away from the skin is impeded primarily by interlayer bonds and faying sealant condition. Further, assessment of such sealant condition is extremely challenging in terms of complexity of structure, limited access, and inspection cost. Although Eddy current techniques can be applied on in-service aircraft from the exterior of the skin without knowing sealant condition, the current eddy current techniques are not able to detect defects with wanted sensitivity. In this work a series of low frequency eddy current probes have been designed, fabricated and tested for this application. A probe design incorporating a shielded magnetic field sensor concentrically located in the interior of a drive coil has been employed to enable a localized deep diffusion of the electromagnetic field into the part under test. Due to the required low frequency inspections, probes have been testing using a variety of magnetic field sensors (pickup coil, giant magneto-resistive, anisotropic magneto-resistive, and spin-dependent tunneling). The probe designs as well as capabilities based upon a target inspection for sub-layer cracking in an airframe wing spar joint is presented.

Wincheski, Russell A.↗

NASA NTRS1981

Numerical simulation of transonic flows in diffusers

Numerical simulations were made of two-dimensional transonic flows in diffusers, including flow separation induced by a shock or adverse pressure gradient. The mass-averaged, time-dependent, compressible Navier-Stokes equations, simplified by the thin-layer approximation, were solved using MacCormack's hybrid method. The eddy-viscosity formulation was described by the Wilcox-Rubesin's two-equation, k-omega model. Detailed comparison of the computed results with measurements showed good agreement in all cases, including one with massive separation induced by a strong shock. The computation correctly predicted the details of a distinct lambda shock pattern, closely duplicating the configuration observed experimentally in spark-schlieren photographs.

Liou, M.-S.↗

NASA NTRS2011

Comparison of Four Mixed Layer Mesoscale Parameterizations and the Equation for an Arbitrary Tracer

In this paper we discuss two issues, the inter-comparison of four mixed layer mesoscale parameterizations and the search for the eddy induced velocity for an arbitrary tracer. It must be stressed that our analysis is limited to mixed layer mesoscales since we do not treat sub-mesoscales and small turbulent mixing. As for the first item, since three of the four parameterizations are expressed in terms of a stream function and a residual flux of the RMT formalism (residual mean theory), while the fourth is expressed in terms of vertical and horizontal fluxes, we needed a formalism to connect the two formulations. The standard RMT representation developed for the deep ocean cannot be extended to the mixed layer since its stream function does not vanish at the ocean's surface. We develop a new RMT representation that satisfies the surface boundary condition. As for the general form of the eddy induced velocity for an arbitrary tracer, thus far, it has been assumed that there is only the one that originates from the curl of the stream function. This is because it was assumed that the tracer residual flux is purely diffusive. On the other hand, we show that in the case of an arbitrary tracer, the residual flux has also a skew component that gives rise to an additional bolus velocity. Therefore, instead of only one bolus velocity, there are now two, one coming from the curl of the stream function and other from the skew part of the residual flux. In the buoyancy case, only one bolus velocity contributes to the mean buoyancy equation since the residual flux is indeed only diffusive.

Canuto, V. M.↗

NASA NTRS2023

Stratospheric Water Vapor Affecting Atmospheric Circulation

Water vapor plays an important role in many aspects of the climate system, by affecting radiation, cloud formation, atmospheric chemistry and dynamics. Even the low stratospheric water vapor content provides an important climate feedback, but current climate models show a substantial moist bias in the lowermost stratosphere. Here we report crucial sensitivity of the atmospheric circulation in the stratosphere and troposphere to the abundance of water vapor in the lowermost stratosphere. We show from a mechanistic climate model experiment and inter-model variability that lowermost stratospheric water vapor decreases local temperatures, and thereby causes an upward and poleward shift of subtropical jets, a strengthening of the stratospheric circulation, a poleward shift of the tropospheric eddy-driven jet and regional climate impacts. The mechanistic model experiment in combination with atmospheric observations further shows that the prevailing moist bias in current models is likely caused by the transport scheme, and can be alleviated by employing a less diffusive Lagrangian scheme. The related effects on atmospheric circulation are of similar magnitude as climate change effects. Hence, lowermost stratospheric water vapor exerts a first order effect on atmospheric circulation and improving its representation in models offers promising prospects for future research.

stratosphere↗

NASA NTRS1993

A Realizable Reynolds Stress Algebraic Equation Model

The invariance theory in continuum mechanics is applied to analyze Reynolds stresses in high Reynolds number turbulent flows. The analysis leads to a turbulent constitutive relation that relates the Reynolds stresses to the mean velocity gradients in a more general form in which the classical isotropic eddy viscosity model is just the linear approximation of the general form. On the basis of realizability analysis, a set of model coefficients are obtained which are functions of the time scale ratios of the turbulence to the mean strain rate and the mean rotation rate. The coefficients will ensure the positivity of each component of the mean rotation rate. These coefficients will ensure the positivity of each component of the turbulent kinetic energy - realizability that most existing turbulence models fail to satisfy. Separated flows over backward-facing step configurations are taken as applications. The calculations are performed with a conservative finite-volume method. Grid-independent and numerical diffusion-free solutions are obtained by using differencing schemes of second-order accuracy on sufficiently fine grids. The calculated results are compared in detail with the experimental data for both mean and turbulent quantities. The comparison shows that the present proposal significantly improves the predictive capability of K-epsilon based two equation models. In addition, the proposed model is able to simulate rotational homogeneous shear flows with large rotation rates which all conventional eddy viscosity models fail to simulate.

Shih, Tsan-Hsing↗

NASA NTRS2002

Large Eddy Simulation of Cryogenic Injection Processes at Supercritical Pressure

This paper highlights results from the first of a series of hierarchical simulations aimed at assessing the modeling requirements for application of the large eddy simulation technique to cryogenic injection and combustion processes in liquid rocket engines. The focus is on liquid-oxygen-hydrogen coaxial injectors at a condition where the liquid-oxygen is injected at a subcritical temperature into a supercritical environment. For this situation a diffusion dominated mode of combustion occurs in the presence of exceedingly large thermophysical property gradients. Though continuous, these gradients approach the behavior of a contact discontinuity. Significant real gas effects and transport anomalies coexist locally in colder regions of the flow, with ideal gas and transport characteristics occurring within the flame zone. The current focal point is on the interfacial region between the liquid-oxygen core and the coaxial hydrogen jet where the flame anchors itself.

Oefelein, Joseph C.↗

NASA NTRS2002

Large Eddy Simulation of Cryogenic Injection Processes at Supercritical Pressure

Oefelein, Joseph C.↗