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At least 361 records · Page 20

The generalized drift flux approach: Identification of the void-drift closure law

The main characteristics and the potential advantages of generalized drift flux models are presented. In particular it is stressed that the issue on the propagation properties and on the mathematical nature (hyperbolic or not) of the model and the problem of closure are easier to tackle than in two fluid models. The problem of identifying the differential void-drift closure law inherent to generalized drift flux models is then addressed. Such a void-drift closure, based on wave properties, is proposed for bubbly flows. It involves a drift relaxation time which is of the order of 0.25 s. It is observed that, although wave properties provide essential closure validity tests, they do not represent an easily usable source of quantitative information on the closure laws.

Boure, J. A.↗

Large-eddy simulation of compressible turbulence

The increase in the range of length scales with increasing Reynolds number limits the direct simulation of turbulent flows to relatively simple geometries and low Reynolds numbers. However, since most flows of engineering interest occur at much higher Reynolds number than is currently within the capabilities of full simulation, prediction of these flow fields can only be obtained by solving some suitably-averaged set of governing equations. In the traditional Reynolds-averaged approach, the Navier-Stokes equations are averaged over time. This in turn yields correlations between various turbulence fluctuations. It is these terms, e.g. the Reynolds stresses, for which a turbulence model must be derived. Turbulence modeling of incompressible flows has received a great amount of attention in the literature. An area of research that has received comparatively less attention is the modeling of compressible turbulent flows. An approach to simulating compressible turbulence at high Reynolds numbers is through the use of Large-Eddy Simulation (LES). In LES the dependent variables are decomposed into a large-scale (resolved) component and a sub-grid scale component. It is the small-scale components of the velocity field which are presumably more homogeneous than the large scales and, therefore, more easily modeled. Thus, it seems plausible that simpler models, which should be more universal in character than those employed in second-order closure schemes, may be developed for LES of compressible turbulence. The objective of the present research, therefore, is to explore models for the Large-Eddy Simulation of compressible turbulent flows. Given the recent successes of Zeman in second order closure modeling of compressible turbulence, model development was guided by principals employed in second-order closures.

Squires, Kyle D.↗

Dynamics and structure of turbulent premixed flames

In earlier work (Mantel & Bilger, 1994) the structure of the turbulent premixed flame was investigated using statistics based on conditional averaging with the reaction progress variable as the conditioning variable. The DNS data base of Trouve and Poinsot (1994) was used in this investigation. Attention was focused on the conditional dissipation and conditional axial velocity in the flame with a view to modeling these quantities for use in the conditional moment closure (CMC) approach to analysis of kinetics in premixed flames (Bilger, 1993). Two remarkable findings were made: there was almost no acceleration of the axial velocity in the flame front itself; and the conditional scalar dissipation remained as high, or higher, than that found in laminar premixed flames. The first finding was surprising since in laminar flames all the fluid acceleration occurs through the flame front, and this could be expected also for turbulent premixed flames at the flamelet limit. The finding gave hope of inventing a new approach to the dynamics of turbulent premixed flames through use of rapid distortion theory or an unsteady Bernoulli equation. This could lead to a new second order closure for turbulent premixed flames. The second finding was contrary to our measurements with laser diagnostics in lean hydrocarbon flames where it is found that conditional scalar dissipation drops dramatically below that for laminar flamelets when the turbulence intensity becomes high. Such behavior was not explainable with a one-step kinetic model, even at non-unity Lewis number. It could be due to depletion of H2 from the reaction zone by preferential diffusion. The capacity of the flame to generate radicals is critically dependent on the levels of H2 present (Bilger, et al., 1991). It seemed that a DNS computation with a multistep reduced mechanism would be worthwhile if a way could be found to make this feasible. Truly innovative approaches to complex problems often come only when there is the opportunity to work close at hand with the (in this case numerical) experimental data. Not only can one spot patterns and relationships in the data which could be important, but one can also get to know the limitations of the technique being used, so that when the next experiment is being designed it will address resolvable questions. A three-year grant from the Australian Research Council has enabled us to develop a small capability at the University of Sydney to work on DNS of turbulent reacting flow, and to analyze data bases generated at CTR. Collaboration between the University of Sydney and CTR is essential to this project and finding a workable modus operandum for this collaboration, given the constraints involved, has been a major objective of the past year's effort. The overall objectives of the project are: (1) to obtain a quantitative understanding of the dynamics of turbulent premixed flames at high turbulence levels with a view to developing improved second order closure models; and (2) to carry out new DNS experiments on turbulent premixed flames using a carefully chosen multistep reduced mechanism for the chemical kinetics, with a view to elucidating the laser diagnostic findings that are contrary to the findings for DNS using one-step kinetics. In this first year the objectives have been to make the existing CTR data base more accessible to coworkers at the University of Sydney, to make progress on understanding the dynamics of the flame in this existing CTR data base, and to carefully construct a suitable multistep reduced mechanism for use in a new set of DNS experiments on turbulent premixed flames.

Bilger, R. W.↗

On the prediction of equilibrium states in homogeneous turbulence

A comparison of several commonly used turbulence models (including the Kappa-epsilon and two second-order closures) is made for the test problem of homogeneous turbulent shear flow in a rotating frame. The time evolution of the turbulent kinetic energy and dissipation rate is calculated for a variety of models and comparisons are made with previously published experiments and numerical simulations. Particular emphasis is placed on examining the ability of each model to accurately predict equilibruim states for a range of the parameter Omega/S (the ratio of the rotation rate to the shear rate). It is found that none of the commonly used second-order closure models yield substantially improved predictions for the time evolution of the turbulent kinetic energy and dissipation rate over the somewhat defective results obtained from the simpler Kappa-epsilon model for the turbulent flow regime. There is also a problem with the equilibrium states predicted by the various models. For example, the Kappa-epsilon model erroneously yields equilibrium states that are independent of Omega/S while the Launder, Reece, and Rodi model predicts a flow relaminarization when Omega/S is greater than 0.39 - a result which is contrary to numerical simulations and linear spectral analysis which indicate flow instability for at least the range 0 less than or = Omega/S less than or = 0.5. The physical implications of the results obtained from the various turbulence models considered here are discussed in detail along with proposals to remedy the deficiencies based on a dynamical systems approach.

Speziale, Charles G.↗

On the prediction of equilibrium states in homogeneous turbulence

A comparison of several commonly used turbulence models (including the Kappa-epsilon and two second-order closures) is made for the test problem of homogeneous turbulent shear flow in a rotating frame. The time evolution of the turbulent kinetic energy and dissipation rate is calculated for a variety of models and comparisons are made with previously published experiments and numerical simulations. Particular emphasis is placed on examining the ability of each model to accurately predict equilibrium states for a range of the parameter Omega/S (the ratio of the rotation rate to the shear rate). It is found that none of the commonly used second-order closure models yield substantially improved predictions for the time evolution of the turbulent kinetic energy and dissipation rate over the somewhat defective results obtained from the simpler Kappa-epsilon model for the turbulent flow regime. There is also a problem with the equilibrium states predicted by the various models. For example, the Kappa-epsilon model erroneously yields equilibrium states that are independent of Omega/S while the Launder, Reece, and Rodi model predicts a flow relaminarization when Omega/S is greater than 0.39 - a result which is contrary to numerical simulations and linear spectral analysis which indicate flow instability for at least the range 0 less than or = Omega/S less than or = 0.5. The physical implications of the results obtained from the various turbulence models considered here are discussed in detail along with proposals to remedy the deficiencies based on a dynamical systems approach.

Speziale, C. G.↗

Turbulence energy and diffusion transport of third-moments in a separating and reattaching flow

For accurate prediction of turbulent flow in separated and reattaching regions, it is necessary to incorporate second- and third-moments of turbulent fluctuations. The turbulence energy and the energy dissipation rate equations are modified by incorporating second-order closure. Moreover, a transport equation model for the third-order closure with a near-wall correction is developed for the evaluation of the diffusive action of the second-moments. After comparison of the results with experimental data, it is concluded that the models developed here improve the prediction of triple-velocity correlations in both recirculating and redeveloping flow regions.

Amano, R. S.↗

Mapping Closure Approximation to Conditional Dissipation Rate for Turbulent Scalar Mixing

A novel mapping closure approximation (MCA) technique is developed to construct a model for the conditional dissipation rate (CDR) of a scalar in homogeneous turbulence. It is shown that the CDR model from amplitude mapping closure is incorrect in asymptotic behavior for unsymmetric binary mixing. The correct asymptotic behavior can be described by the CDR model formulated by the MCA technique. The MCA approach is outlined for constructing successive approximation to probability density function (PDF) and conditional moment.

He, Gouwei↗

Jet Noise Diagnostics Supporting Statistical Noise Prediction Methods

The primary focus of my presentation is the development of the jet noise prediction code JeNo with most examples coming from the experimental work that drove the theoretical development and validation. JeNo is a statistical jet noise prediction code, based upon the Lilley acoustic analogy. Our approach uses time-average 2-D or 3-D mean and turbulent statistics of the flow as input. The output is source distributions and spectral directivity. NASA has been investing in development of statistical jet noise prediction tools because these seem to fit the middle ground that allows enough flexibility and fidelity for jet noise source diagnostics while having reasonable computational requirements. These tools rely on Reynolds-averaged Navier-Stokes (RANS) computational fluid dynamics (CFD) solutions as input for computing far-field spectral directivity using an acoustic analogy. There are many ways acoustic analogies can be created, each with a series of assumptions and models, many often taken unknowingly. And the resulting prediction can be easily reverse-engineered by altering the models contained within. However, only an approach which is mathematically sound, with assumptions validated and modeled quantities checked against direct measurement will give consistently correct answers. Many quantities are modeled in acoustic analogies precisely because they have been impossible to measure or calculate, making this requirement a difficult task. The NASA team has spent considerable effort identifying all the assumptions and models used to take the Navier-Stokes equations to the point of a statistical calculation via an acoustic analogy very similar to that proposed by Lilley. Assumptions have been identified and experiments have been developed to test these assumptions. In some cases this has resulted in assumptions being changed. Beginning with the CFD used as input to the acoustic analogy, models for turbulence closure used in RANS CFD codes have been explored and compared against measurements of mean and rms velocity statistics over a range of jet speeds and temperatures. Models for flow parameters used in the acoustic analogy, most notably the space-time correlations of velocity, have been compared against direct measurements, and modified to better fit the observed data. These measurements have been extremely challenging for hot, high speed jets, and represent a sizeable investment in instrumentation development. As an intermediate check that the analysis is predicting the physics intended, phased arrays have been employed to measure source distributions for a wide range of jet cases. And finally, careful far-field spectral directivity measurements have been taken for final validation of the prediction code. Examples of each of these experimental efforts will be presented. The main result of these efforts is a noise prediction code, named JeNo, which is in middevelopment. JeNo is able to consistently predict spectral directivity, including aft angle directivity, for subsonic cold jets of most geometries. Current development on JeNo is focused on extending its capability to hot jets, requiring inclusion of a previously neglected second source associated with thermal fluctuations. A secondary result of the intensive experimentation is the archiving of various flow statistics applicable to other acoustic analogies and to development of time-resolved prediction methods. These will be of lasting value as we look ahead at future challenges to the aeroacoustic experimentalist.

Bridges, James E.↗

Apparent I-Xe Cooling Rates of Chondrules Compared with Silicates from the Colomera Iron Meteorite

In I-Xe dating, a regular pattern of increasing Xe-129/128Xe-128 ratio with increasing extraction temperature is often observed. If one makes the crude assumption that the temperatures at which the Xe is extracted in the laboratory is approximately the same as the temperature at which those sites closed 4.6 Ga ago, a (zeroth order) model cooling rate can be found. In order to test and refine this model we can apply the cooling theory of Dodson to those extraction steps approaching the I-Xe isochrons. Using an Arrhenius plot for these temperature fractions, and assuming that an only single phase is involved, the effective diffusion parameters can be estimated (frequency factor and activation energy). From the apparent (zeroth order) cooling rate, the closure temperature can be estimated from the Dodson equation. This model closure temperature can then be compared with the actual laboratory temperature at which the isochron begins. The ratio of the closure temperature and the temperature corresponding to the start of the isochron provides the ratio of the two temperature scales, incorporation and extraction. The actual cooling rate is then given by the apparent (zeroth order) cooling rate times the temperature scale factor. Figure 1 shows Arrhenius plots for I-Xe data

Hohenberg, C. M.↗

Reactant conversion in homogeneous turbulence - Mathematical modeling, computational validations, and practical applications

The presently obtained closed-form analytical expressions, which predict the limiting rate of mean reactant conversion in homogeneous turbulent flows under the influence of a binary reaction, are derived via the single-point pdf method based on amplitude mapping closure. With this model, the maximum rate of the mean reactant's decay can be conveniently expressed in terms of definite integrals of the parabolic cylinder functions. The results obtained are shown to be in good agreement with data generated by direct numerical simulations.

Madnia, C. K.↗

Studying Turbulence Using Numerical Simulation Databases: Proceedings of the 1996 Summer Program - Part 6

Topics considered include: New approach to turbulence modeling; Second moment closure analysis of the backstep flow database; Prediction of the backflow and recovery regions in the backward facing step at various Reynolds numbers; Turbulent flame propagation in partially premixed flames; Ensemble averaged dynamic modeling. Also included a study of the turbulence structures of wall-bounded shear flows; Simulation and modeling of the elliptic streamline flow.

Source record↗

New results on the realizability of Reynolds stress turbulence closures

The realizability of Reynolds stress models in homogeneous turbulence is critically assessed from a theoretical standpoint. It is proven that a well known second-order closure formulated by Shih and Lumley using the strong realizability constraints of Schumann is, in fact, not a realizable model. The problem arises from the failure to properly satisfy the necessary positive second time derivative constraint when a principal Reynolds stress vanishes - a fatal flaw that becomes apparent when the non-analytic terms in their model are made single-valued as required on physical grounds. It is furthermore shown that the centrifugal acceleration generated by rotations of the principal axes of the Reynolds stress tensor can make the second derivative singular at the most extreme limits of realizable turbulence. This previously overlooked effect appears to make it impossible to identically satisfy the strong form of realizability in any version of the present generation of second-order closures. On the other hand, models properly formulated to satisfy the weak form of realizability - wherein states of one or two component turbulence are not accessible in finite time are found to be realizable. However, unlike the simpler and more commonly used second order closures, these models can be ill-behaved near the extreme limits of realizable turbulence due to the way that higher-degree nonlinearities are often unnecessarily introduced to satisfy realizability. Illustrative computations of homogeneous shear flows are presented to demonstrate these points which can have important implications for turbulence modeling.

Speziale, Charles G.↗

Effects of fineness and closure ratios on boattail drag of circular-arc-afterbody models with jet exhaust at Mach numbers up to 1.3

The effects of variations in fineness ratio and closure ratio on the boattail drag of circular-arc afterbody models were investigated at static conditions and at Mach numbers from 0.40 to 1.30. Jet total-pressure ratio was varied from jet off to about 6, depending on Mach number. Reynolds number based on model maximum diameter varied from about 1.2 million to 2.18 million. Angle of attack was varied from -4 deg to 8 deg. The results indicate that, at subsonic speeds before the drag rise and at a scheduled pressure ratio, the total drag (pressure plus calculated skin friction) is approximately equal for configurations with the same closure ratio. Also, for configurations with the same closure ratio, increasing fineness ratio results in an increased drag-rise Mach number; and for configurations with the same fineness ratio, increasing closure ratio results in an increased drag-rise Mach number.

Reubush, D. E.↗

Simulation of Boundary-Layer Cumulus and Stratocumulus Clouds using a Cloud-Resolving Model With Low- and Third-Order Turbulence Closures

The effects of subgrid-scale condensation and transport become more important as the grid spacings increase from those typically used in large-eddy simulation (LES) to those typically used in cloud-resolving models (CRMs). Incorporation of these effects can be achieved by a joint probability density function approach that utilizes higher-order moments of thermodynamic and dynamic variables. This study examines how well shallow cumulus and stratocumulus clouds are simulated by two versions of a CRM that is implemented with low-order and third-order turbulence closures (LOC and TOC) when a typical CRM horizontal resolution is used and what roles the subgrid-scale and resolved-scale processes play as the horizontal grid spacing of the CRM becomes finer. Cumulus clouds were mostly produced through subgrid-scale transport processes while stratocumulus clouds were produced through both subgrid-scale and resolved-scale processes in the TOC version of the CRM when a typical CRM grid spacing is used. The LOC version of the CRM relied upon resolved-scale circulations to produce both cumulus and stratocumulus clouds, due to small subgrid-scale transports. The mean profiles of thermodynamic variables, cloud fraction and liquid water content exhibit significant differences between the two versions of the CRM, with the TOC results agreeing better with the LES than the LOC results. The characteristics, temporal evolution and mean profiles of shallow cumulus and stratocumulus clouds are weakly dependent upon the horizontal grid spacing used in the TOC CRM. However, the ratio of the subgrid-scale to resolved-scale fluxes becomes smaller as the horizontal grid spacing decreases. The subcloud-layer fluxes are mostly due to the resolved scales when a grid spacing less than or equal to 1 km is used. The overall results of the TOC simulations suggest that a 1-km grid spacing is a good choice for CRM simulation of shallow cumulus and stratocumulus.

Xu, Kuan-Man↗

The mechanics of delamination in fiber-reinforced composite materials. Part 1: Stress singularities and solution structure

The fundamental mechanics of delamination in fiber composite laminates is studied. Mathematical formulation of the problem is based on laminate anisotropic elasticity theory and interlaminar fracture mechanics concepts. Stress singularities and complete solution structures associated with general composite delaminations are determined. For a fully open delamination with traction-free surfaces, oscillatory stress singularities always appear, leading to physically inadmissible field solutions. A refined model is introduced by considering a partially closed delamination with crack surfaces in finite-length contact. Stress singularities associated with a partially closed delamination having frictional crack-surface contact are determined, and are found to be diferent from the inverse square-root one of the frictionless-contact case. In the case of a delamination with very small area of crack closure, a simplified model having a square-root stress singularity is employed by taking the limit of the partially closed delamination. The possible presence of logarithmic-type stress singularity is examined; no logarithmic singularity of any kind is found in the composite delamination problem. Numerical examples of dominant stress singularities are shown for delaminations having crack-tip closure with different frictional coefficients between general (1) and (2) graphite-epoxy composites.

Wang, S. S.↗

The mechanics of delamination in fiber-reinforced composite materials. I - Stress singularities and solution structure

The fundamental mechanics of delamination in fiber composite laminates is studied. Mathematical formulation of the problem is based on laminate anisotropic elasticity theory and interlaminar fracture mechanics concepts. Stress singularities and complete solution structures associated with general composite delaminations are determined. For a fully open delamination with traction-free surfaces, oscillatory stress singularities always appear, leading to physically inadmissible field solutions. A refined model is introduced by considering a partially closed delamination with crack surfaces in finite-length contact. Stress singularities associated with a partially closed delamination having frictional crack-surface contact are determined, and are found to be different from the inverse square-root one of the frictionless-contact case. In the case of a delamination with very small area of crack closure, a simplified model having a square-root stress singularity is employed by taking the limit of the partially closed delamination. The possible presence of logarithmic-type stress singularity is examined; no logarithmic singularity of any kind is found in the composite delamination problem. Numerical examples of dominant stress singularities are shown for delaminations having crack-tip closure with different frictional coefficients between general (1) and (2) graphite-epoxy composites. Previously announced in STAR as N84-13221

Wang, S. S.↗

Simulation and modeling of homogeneous, compressed turbulence

Low Reynolds number homogeneous turbulence undergoing low Mach number isotropic and one-dimensional compression was simulated by numerically solving the Navier-Stokes equations. The numerical simulations were performed on a CYBER 205 computer using a 64 x 64 x 64 mesh. A spectral method was used for spatial differencing and the second-order Runge-Kutta method for time advancement. A variety of statistical information was extracted from the computed flow fields. These include three-dimensional energy and dissipation spectra, two-point velocity correlations, one-dimensional energy spectra, turbulent kinetic energy and its dissipation rate, integral length scales, Taylor microscales, and Kolmogorov length scale. Results from the simulated flow fields were used to test one-point closure, two-equation models. A new one-point-closure, three-equation turbulence model which accounts for the effect of compression is proposed. The new model accurately calculates four types of flows (isotropic decay, isotropic compression, one-dimensional compression, and axisymmetric expansion flows) for a wide range of strain rates.

Wu, C. T.↗

The remarkable ability of turbulence model equations to describe transition

This paper demonstrates how well the k-omega turbulence model describes the nonlinear growth of flow instabilities from laminar flow into the turbulent flow regime. Viscous modifications are proposed for the k-omega model that yield close agreement with measurements and with Direct Numerical Simulation results for channel and pipe flow. These modifications permit prediction of subtle sublayer details such as maximum dissipation at the surface, k approximately y(exp 2) as y approaches 0, and the sharp peak value of k near the surface. With two transition specific closure coefficients, the model equations accurately predict transition for an incompressible flat-plate boundary layer. The analysis also shows why the k-epsilon model is so difficult to use for predicting transition.

Wilcox, David C.↗