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NASA NTRS1991

Mixing transition and the cascade to small scales in a plane mixing layer

Direct numerical simulations of time-developing plane mixing layers have been performed using a variety of initial conditions. Up to two pairings of the dominant spanwise rollers have been simulated. When the flow is sufficiently three-dimensional, a pairing can cause the mixing layer to undergo a transition to small-scale turbulence. This small-scale transition is accompanied by increased mixing of a passive scalar, similar to observations of the mixing transition in experiments. As part of the transition process, thin vortex sheets are generated by vortex stretching and roll up in a two-dimensional mixing layer. This higher-order rollup is part of the cascade to small-scale turbulence. Estimates are obtained for the degree of three-dimensionality required for the pairing to initiate the transition.

Moser, R. D.↗

NASA NTRS1991

Preferential concentration of particles by turbulence

Direct numerical simulation of isotropic turbulence was used to investigate the effect of turbulence on the concentration fields of heavy particles. The hydrodynamic field was computed using 64-cubed points, and a statistically stationary flow was obtained by forcing the low-wave-number components of the velocity field. The particles used in the simulations were time advanced according to Stokes drag law and were also assumed to be much more dense than the fluid. Properties of the particle cloud were obtained by following the trajectories of 1,000,000 particles through the simulated flow fields. Three values of the ratio of the particle time constant to large-scale turbulence time scale were used in the simulations: 0.075, 0.15, and 0.52. The simulations show that the particles collect preferentially in regions of low vorticity and high strain rate. This preferential collection was most pronounced for particles with the instantaneous number density as much as 25 times the mean value. The fact that dense particles collect in regions of low vorticity and high strain in turn implies that turbulence may actually inhibit rather than enhance mixing of particles.

Squires, Kyle D.↗

NASA NTRS1991

Scalar dissipation and mixing in turbulent reacting flows

The mixing term that appears in probability density function-based formulations of the statistical behavior of turbulent reacting flows was studied with the use of direct numerical simulations of an irreversible, second-order, isothermal chemical reaction between initially segregated reactants in decaying, homogeneous turbulence. Three-dimensional, time-dependent pseudospectral calculations with 64-cubed Fourier modes were made as well as were Monte Carlo simulations of the joint concentration pdf equations for coalescence-dispersion (C/D) models. It was found that the development of the scalar microscales depends largely on the initial concentration distributions (both isotropic and nonisotropic distributions were used) and is relatively independent of the reaction rate constant. Joint concentration probability density functions were compared to predictions of D/D models that make use of parameters evaluated from the nonreacting or inert system.

Leonard, Andy D.↗

NASA NTRS1990

Numerical investigation of the spreading of self-excited stratified jets

The structure and evolution of self-excited subsonic periodic arrays of jets of constant and variable density are studied using spectral-element direct numerical simulations. The governing equation of motion is presented, and a method based on spectral element discretizations appropriate for simulating arbitrarily complex geometry jets and large density variations for subsonic flows is developed. Variable density fields are found to be more unstable than the corresponding uniform density fields with much higher rms values; as a result, their spreading is also considerably larger. There is a dramatic increase in spreading after a few pairings occur. Findings presented for low and high side-momentum flux reveal a shifting of the origin of instability from the near-field to the far-field, respectively, and suggest possible routes of stabilization.

Batcho, P. F.↗

NASA NTRS1991

Asymptotic behavior of curvature of surface elements in isotropic turbulence

The asymptotic behavior of the curvature of material elements in turbulence is investigated using Lagrangian velocity-gradient time series obtained from direct numerical simulations of isotropic turbulence. Several material-element ensembles of different initial curvatures and shapes are studied. It is found that, at long times, the (first five) moments of the logarithm of characteristic curvature and shape factor asymptote to values that are independent of the initial curvature or shape. This evidence strongly suggests that the asymptotic pdf's of the curvature and shape of material elements are stationary and independent of initial conditions. Irrespective of initial curvature or shape, the asymptotic shape of a material surface is cylindrical with a high probability.

Girimaji, S. S.↗

NASA NTRS1989

The topology and vorticity dynamics of a three-dimensional plane compressible wake

The three-dimensional aspects of transition in a low Mach number plane compressible wake are studied numerically. Comparisons are made between the topology of the velocity field and the vorticity dynamics of the flow based on results from direct numerical simulations of the full compressible Navier-Stokes equations. The velocity field is integrated to obtain instantaneous streamlines at different stages in the evolution. A generalized three-dimensional critical point theory is applied to classify the critical points of the velocity field.

Chen, Jacqueline H.↗

NASA NTRS1991

Motion of particles with inertia in a compressible free shear layer

The effects of the inertia of a particle on its flow-tracking accuracy and particle dispersion are studied using direct numerical simulations of 2D compressible free shear layers in convective Mach number (Mc) range of 0.2 to 0.6. The results show that particle response is well characterized by tau, the ratio of particle response time to the flow time scales (Stokes' number). The slip between particle and fluid imposes a fundamental limit on the accuracy of optical measurements such as LDV and PIV. The error is found to grow like tau up to tau = 1 and taper off at higher tau. For tau = 0.2 the error is about 2 percent. In the flow visualizations based on Mie scattering, particles with tau more than 0.05 are found to grossly misrepresent the flow features. These errors are quantified by calculating the dispersion of particles relative to the fluid. Overall, the effect of compressibility does not seem to be significant on the motion of particles in the range of Mc considered here.

Samimy, M.↗

NASA NTRS1991

Reynolds shear stress and heat flux calculations in a fully developed turbulent duct flow

The use of a modified form of the Van Driest mixing length for a fully developed turbulent channel flow leads to mean velocity and Reynolds stress distributions that are in close agreement with data obtained either from experiments or direct numerical simulations. The calculations are then extended to a nonisothermal flow by assuming a constant turbulent Prandtl number, the value of which depends on the molecular Prandtl number. Calculated distributions of mean temperature and lateral heat flux are in reasonable agreement with the simulations. The extension of the calculations to higher Reynolds numbers provides some idea of the Reynolds number required for scaling on wall variables to apply in the inner region of the flow.

Antonia, R. A.↗

NASA NTRS1991

On turbulent spots in plane Poiseuille flow

Turbulence characteristics inside a turbulent spot in plane Poiseuille flow are investigated by analyzing a database obtained from a direct numerical simulation. The spot is found to consist of two distinct regions - a turbulent area and a wave area. The flow inside the turbulent area has a strong resemblance to that found in the fully developed turbulent channel. Suitably defined mean and r.m.s. fluctuations as well as the internal shear-layer structures are found to be similar to the turbulent counterpart. In the wave area the inflexional mean spanwise profiles cause a rapid growth of oblique waves, which break down to turbulence. The breakdown process of the oblique waves is reminiscent of the secondary instability observed during transition to turbulence in channel and boundary-layer flows. Other detailed characteristics associated with the Poiseuille spot are presented and are compared with experimental results.

Henningson, Dan S.↗

NASA NTRS1990

Enstrophy budget in decaying compressible turbulence

The interaction of vorticity and shock waves in decaying compressible turbulence is investigated by direct numerical simulation of the Navier-Stokes equation using a spectral method with 64-cubed collocation points. The Taylor microscale Reynolds number decreases from 36 to 17 and the rms Mach number from 0.8 to 0.4 during the decay. It is observed that vorticity is created inside curved shocks through baroclinic interaction and intensified by the compression of fluid elements. Vortex stretching is, on the other hand, dominant outside shocks and is responsible for enhancing the strength of vorticity. A dipole of vorticity is typically created at the vertex of curved shocks, the structure of which is explained in terms of jump relations of velocity derivatives across a curved shock.

Kida, Shigeo↗

NASA NTRS1991

Spectral methods for the Navier-Stokes equations with one infinite and two periodic directions

The time-dependent, 3D incompressible Navier-Stokes equations in (1) boundary layers, the semiinfinite domain, and (2) mixing layers or wakes, the fully infinite domain, are respectively solved by two numerical methods which employ rapidly decaying spectral basis functions to approximate the vertical dependence of the solutions. These functions are then combined with one, for method (1), and two, for method (2), slowly decaying 'extra functions' for each wave vector. Each extra function can exactly represent the solution's irrotational component at large distances. The two methods have been applied to extensive direct-numerical simulation of transition and turbulence.

Spalart, Philippe R.↗

NASA NTRS1991

The effects of rotation on initially anisotropic homogeneous flows

Rotation of initially anisotropic homogeneous flows is studied using a model spectral tensor. It is shown that the anisotropy changes because of the influence of rotation through phase scrambling. Phase scrambling causes the Reynolds stresses to develop with damped oscillations. The final Reynolds stress anisotropy is found to be proportional to the initial structural tensor anisotropy. Closure models for the rapid pressure strain terms should reflect this change in anisotropy, and should drive the anisotropy to reach its final predicted state. Finally, it is shown that long-time integration using direct numerical simulations should be treated with care because phase scrambling effects on a discrete wave space can cause loss of resolution when time becomes large.

Mansour, Nagi N.↗

NASA NTRS1991

On the wall-normal velocity of the compressible boundary-layer equations

Numerical methods for the compressible boundary-layer equations are facilitated by transformation from the physical (x,y) plane to a computational (xi,eta) plane in which the evolution of the flow is 'slow' in the time-like xi direction. The commonly used Levy-Lees transformation results in a computationally well-behaved problem for a wide class of non-similar boundary-layer flows, but it complicates interpretation of the solution in physical space. Specifically, the transformation is inherently nonlinear, and the physical wall-normal velocity is transformed out of the problem and is not readily recovered. In light of recent research which shows mean-flow non-parallelism to significantly influence the stability of high-speed compressible flows, the contribution of the wall-normal velocity in the analysis of stability should not be routinely neglected. Conventional methods extract the wall-normal velocity in physical space from the continuity equation, using finite-difference techniques and interpolation procedures. The present spectrally-accurate method extracts the wall-normal velocity directly from the transformation itself, without interpolation, leaving the continuity equation free as a check on the quality of the solution. The present method for recovering wall-normal velocity, when used in conjunction with a highly-accurate spectral collocation method for solving the compressible boundary-layer equations, results in a discrete solution which is extraordinarily smooth and accurate, and which satisfies the continuity equation nearly to machine precision. These qualities make the method well suited to the computation of the non-parallel mean flows needed by spatial direct numerical simulations (DNS) and parabolized stability equation (PSE) approaches to the analysis of stability.

Pruett, C. David↗

NASA NTRS1992

Effective equations and the inverse cascade theory for Kolmogorov flows

We study the two dimensional Kolmogorov flows in the limit as the forcing frequency goes to infinity. Direct numerical simulation indicates that the low frequency energy spectrum evolves to a universal kappa (exp -4) decay law. We derive effective equations governing the behavior of the large scale flow quantities. We then present numerical evidence that with smooth initial data, the solution to the effective equation develops a kappa (exp -4) type singularity at a finite time. This gives a convenient explanation for the kappa (exp -4) decay law exhibited by the original Kolmogorov flows.

Weinan, E.↗

NASA NTRS1991

Turbulence modeling

The performance of existing two-equation eddy viscosity models was examined. An effort was made to develop better models for near-wall turbulence using direct numerical simulations of plane channel and boundary layer flows. The asymptotic near-wall behavior of turbulence was used to examine the problems of current second order closure models and develop new models with the correct near-wall behavior. Rapid Distortion Theory was used to analytically study the effects of mean deformation on turbulence, obtain analytical solutions for the spectrum tensor, Reynolds stress tensor, anisotropy tensor and its invariants, which can be used in the turbulence model development. The potential of the renormalization group theory in turbulence modeling was studied, as well as compressible turbulent flows, and modeling of bypass transition.

Shih, Tsan-Hsing↗

NASA NTRS1991

RNG in turbulence and modeling of bypass transition

Two projects are considered: the Renormalization Group (RNG) analysis of turbulence modeling, and the calculation of bypass transition through turbulence modeling. RNG is a process which eliminates small scales on the uneliminated large scales as the change in the transport properties. It is because of this property of RNG that it was previously suggested that RNG could be used as a model builder in turbulence modeling. The possibility is studied of constructing RNG based turbulence models, and to try to proceed to do the modeling through RNG in parallel with the classical approach. The numerical predictions made by RNG models and by classical models is compared against data from Direct Numerical Simulation. While in an environment with freestream turbulence, the transition initiated by the instability of the laminar boundary layer to Tollmien-Schlichting waves is found to be a bypass one in which turbulent spots are formed without T-S wave amplification. The formation is a random process, and flow within a turbulent spot is almost fully turbulent. This suggests the possibility of using turbulence modeling to describe and predict the bypass transition.

Yang, Zhigang↗

NASA NTRS1991

An improved k-epsilon model for near wall turbulence

An improved k-epsilon model for low Reynolds number turbulence near a wall is presented. In the first part of this work, the near-wall asymptotic behavior of the eddy viscosity and the pressure transport term in the turbulent kinetic energy equation are analyzed. Based on these analyses, a modified eddy viscosity model with the correct near-wall behavior is suggested, and a model for the pressure transport term in the k-equation is proposed. In addition, a modeled dissipation rate equation is reformulated, and a boundary condition for the dissipation rate is suggested. In the second part of the work, one of the deficiencies of the existing k-epsilon models, namely, the wall distance dependency of the equations and the damping functions, is examined. An improved model that does not depend on any wall distance is introduced. Fully developed turbulent channel flows and turbulent boundary layers over a flat plate are studied as validations for the proposed new models. Numerical results obtained from the present and other previous k-epsilon models are compared with data from direct numerical simulation. The results show that the present k-epsilon model, with added robustness, performs as well as or better than other existing models in predicting the behavior of near-wall turbulence.

Shih, T. H.↗

NASA NTRS1991

Advancements in engineering turbulence modeling

Some new developments in two-equation models and second order closure models are presented. Two-equation models (k-epsilon models) have been widely used in computational fluid dynamics (CFD) for engineering problems. Most of low-Reynolds number two-equation models contain some wall-distance damping functions to account for the effect of wall on turbulence. However, this often causes the confusion and difficulties in computing flows with complex geometry and also needs an ad hoc treatment near the separation and reattachment points. A set of modified two-equation models is proposed to remove the aforementioned shortcomings. The calculations using various two-equation models are compared with direct numerical simulations of channel flow and flat boundary layers. Development of a second order closure model is also discussed with emphasis on the modeling of pressure related correlation terms and dissipation rates in the second moment equations. All the existing models poorly predict the normal stresses near the wall and fail to predict the 3-D effect of mean flow on the turbulence (e.g. decrease in the shear stress caused by the cross flow in the boundary layer). The newly developed second order near-wall turbulence model is described and is capable of capturing the near-wall behavior of turbulence as well as the effect of 3-D mean flow on the turbulence.

Shih, T.-H.↗