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NASA NTRS1978

Equations of motion and two-equation turbulence model for plane or axisymmetric turbulent flows in body-oriented orthogonal curvilinear coordinates and mass-averaged dependent variables

The full Navier-Stokes time-dependent, compressible, turbulent, mean-flow equations in mass-averaged variables for plane or axisymmetric flow are presented. The equations are derived in a body-oriented, orthogonal, curvilinear coordinate system. Turbulence is modelled by a system of two equations for mass-averaged turbulent kinetic energy and dissipation rate proposed. These equations are rederived and some new features are discussed. A system of second order boundary layer equations is then derived which includes the effects of longitudinal curvature and the normal pressure gradient. The Wilcox and Chambers approach is used in considering effects of streamline curvature on turbulence phenomena in turbulent boundary layer type flows. Their two-equation turbulence model with curvature terms are rederived for the cases considered in the present report. The derived system equations serves as a basis for an investigation of problems where streamline curvature is of the order of the characteristic length in the longitudinal direction.

Sislian, J. P.↗

NASA NTRS1977

Implications of Navier-Stokes turbulence theory for plasma turbulence

Plasma turbulence is considered within the framework of the Navier-Stokes turbulence theory. Two-dimensional turbulence is discussed, noting inverse cascades, and compared to three-dimensional turbulence. MHD turbulence is described with reference to applications of the Navier-Stokes theory and the possibility of inverse magnetic cascades. Turbulence in Vlasov plasmas is outlined on the basis of the direct interaction approximation developed for Navier-Stokes fluids (Kraichnan, 1958-1959).

Montgomery, D.↗

NASA NTRS1981

Multiple-scale turbulence modeling of free turbulent flows

As part of an investigation into the application of turbulence models to the computation of flows in advanced scramjet combustors, the multiple-scale turbulence model has been applied to a variety of flowfield predictions. The model appears to have a potential for improved predictions in a variety of areas relevant to combustor problems. This potential exists because of the partition of the turbulence energy spectrum that is the major feature of the model and which allows the turbulence energy dissipation rate to be out of phase with turbulent energy production. To establish the general reliability of the approach, it has been tested through comparison of predictions with experimental data. An appreciable overall improvement in the generality of the predictions is observed, as compared to those of the basic two-equation turbulence model. A Mach number-related correction is found to be necessary to satisfactorily predict the spreading rate of the supersonic jet and mixing layer.

Fabris, G.↗

NASA NTRS1986

Computation of turbulent boundary layer flows with an algebraic stress turbulence model

An algebraic stress turbulence model is presented, characterized by the following: (1) the eddy viscosity expression is derived from the Reynolds stress turbulence model; (2) the turbulent kinetic energy dissipation rate equation is improved by including a production range time scale; and (3) the diffusion coefficients for turbulence equations are adjusted so that the kinetic energy profile extends further into the free stream region found in most experimental data. The turbulent flow equations were solved using a finite element method. Examples include: fully developed channel flow, fully developed pipe flow, flat plate boundary layer flow, plane jet exhausting into a moving stream, circular jet exhausting into a moving stream, and wall jet flow. Computational results compare favorably with experimental data for most of the examples considered. Significantly improved results were obtained for the plane jet flow, the circular jet flow, and the wall jet flow; whereas the remainder are comparable to those obtained by finite difference methods using the standard kappa-epsilon turbulence model. The latter seems to be promising with further improvement of the expression for the eddy viscosity coefficient.

Kim, Sang-Wook↗

NASA NTRS1987

An investigation of turbulence structure in a low-Reynolds-number incompressible turbulent boundary

An existing high turbulence intensity level (5%) atmospheric boundary-layer wind tunnel has been successfully converted to a relatively low level turbulence (0.3%) wind tunnel through extensive modification, testing, and calibration. A splitter plate was designed, built, and installed into the wind-tunnel facility to create thick, mature, two-dimensional turbulent boundary layer flow at zero pressure gradient. Single and cross hot-wire measurements show turbulent boundary layer characteristics of good quality with unusually large physical size, i.e., viscous sublayer of the order of 1 mm high. These confirm the potential ability of the tunnel to be utilized for future high-quality near-wall turbulent boundary layer measurements. It compares very favorably with many low turbulence research tunnels.

White, B. R.↗

NASA NTRS1987

Measurements of the turbulent transport of heat and momentum in convexly curved boundary layers - Effects of curvature, recovery and free-stream turbulence

The effects of streamwise convex curvature, recovery, and freestream turbulence intensity on the turbulent transport of heat and momentum in a mature boundary layer are studied using a specially designed three-wire hot-wire probe. Increased freestream turbulence is found to increase the profiles throughout the boundary layer on the flat developing wall. Curvature effects were found to dominate turbulence intensity effects for the present cases considered. For the higher TI (turbulence intensity) case, negative values of the turbulent Prandtl number are found in the outer half of the boundary layer, indicating a breakdown in Reynolds analogy.

Kim, J.↗

NASA NTRS1987

Prediction of transition on a flat plate under the influence of free-stream turbulence using low-Reynolds-number two-equation turbulence models

The prediction characteristics and capabilities of two popular two-equation low-Reynolds-number turbulence models (Jones, Launder 1972; Lam, Bremhorst 1981) have been evaluated with respect to the prediction of transition of a flat plate under the influence of free-stream turbulence. The sensitivity of the predictions to free-stream turbulence intensity, initial starting location of the calculation, and the assumed initial starting profiles for k and epsilon has been determined and presented. Although both models predict the correct qualitative characteristics of transition, they also exhibit significant quantitative deficiencies with regard to both the predicted location and the length of transition. A modification to the production term in the turbulent kinetic energy equation is proposed which is based on a simple stability criterion and correlated to the free-stream turbulence level. The modification becomes inactive in the fully turbulent regime, but is shown to improve both the qualitative and quantitative characteristics of the transition predictions.

Schmidt, Rodney C.↗

NASA NTRS1988

A multiple-time-scale turbulence model based on variable partitioning of turbulent kinetic energy spectrum

The paper presents a multiple-time-scale turbulence model of a single point closure and a simplified split-spectrum method. Consideration is given to a class of turbulent boundary layer flows and of separated and/or swirling elliptic turbulent flows. For the separated and/or swirling turbulent flows, the present turbulence model yielded significantly improved computational results over those obtained with the standard k-epsilon turbulence model.

Kim, S.-W.↗

NASA NTRS1988

Effects of free-stream turbulence on turbulent boundary layers with mild adverse pressure gradients

The influence of near isotropic free-stream turbulence on the shape factors and skin friction coefficients of turbulent boundary layers is presented for the cases of zero and mild adverse pressure gradients. With free-stream turbulence, improved fluid mixing occurs in boundary layers with adverse pressure gradients relative to the zero pressure gradient condition, with the same free-stream turbulence intensity and length scale. Stronger boundary layers with lower shape factors occur as a result of a lower ratio of the integral scale of turbulence to the boundary layer thickness, and to vortex stretching of the turbulent eddies in the free-stream, both of which act to improve the transmission of momentum from the free-stream to the boundary layers.

Hoffmann, J. A.↗

NASA NTRS1988

The influence of free-stream turbulence on turbulent boundary layers with mild adverse pressure gradients

The influence of near isotropic free-stream turbulence on the shape factors and skin friction coefficients of turbulent bounday layers is presented for the cases of zero and mild adverse pressure gradients. With free-stream turbulence, improved fluid mixing occurs in boundary layers with adverse pressure gradients relative to the zero pressure gradient condition, with the same free-stream turbulence intensity and length scale. Stronger boundary layers with lower shape factors occur as a result of a lower ratio of the integral scale of turbulence to the boundary layer thickness, and to vortex stretching of the turbulent eddies in the free stream, both of which act to improve the transmission of momentum from the free stream to the boundary layers.

Hoffmann, Jon A.↗

NASA NTRS1989

The influence of free-stream turbulence on turbulent boundary layers with mild adverse pressure gradients

Hoffmann, J. A.↗

NASA NTRS1990

Numerical prediction of turbulent flow over airfoil sections with a new nonequilibrium turbulence model

A new nonequilibrium turbulence closure model has been developed for computing wall bounded two-dimensional turbulent flows. This two-layer eddy viscosity model was motivated by the success of the Johnson-King model in separated flow regions. The influence of history effects are described by an ordinary differential equation developed from the turbulent kinetic energy equation. The performance of the present model has been evaluated by solving the flow around three airfoils using the Reynolds time-averaged Navier-Stokes equations. Excellent results were obtained for both attached and separated turbulent flows about the NACA 0012 airfoil, the RAE 2822 airfoil, and the Integrated Technology A 153W airfoil. Based on the comparison of the numerical solutions with the available experimental data, it is concluded that the new nonequilibrium turbulence model accurately captures the history effects of convection and diffusion on turbulence.

Ahmed, S.↗

NASA NTRS1995

Toward a theory of interstellar turbulence. 2: Strong alfvenic turbulence

We continue to investigate the possibility that interstellar turbulence is caused by nonlinear interactions among shear Alfven waves. Here, we restrict attention to the symmetric case where the oppositely directed waves carry equal energy fluxes. This precludes application to the solar wind in which the outward flux significantly exceeds the ingoing one. All our detailed calculations are carried out for an incompressible magnetized fluid. In incompressible magnetohydrodynamics (MHD), nonlinear interactions only occur between oppositely direct waves. We present a theory for the strong turbulence of shear Alfven waves. It has the following main characteristics. (1) The inertial-stage energy spectrum exhibits a critical balance between linear wave periods and nonlinear turnover timescales. (2) The 'eddies' are elongated in the direction of the field on small spatial scales; the parallel and perpendicular components of the wave vector, k(sub z) and k(perpendicular) are related by k(sub z) approximately equals k(sub perpendicular to)(exp 2/3) L(exp -1/3), where L is the outer scale of the turbulence. (3) The 'one-dimensional' energy spectrum is proportional to k(sub perpendicular)(exp -5/3)-an anisotropic Kolmogorov energy spectrum. Shear Alfvenic turbulence mixes specific entropy as a passive contaminant. This gives rise to an electron density power spectrum whose form mimics the energy spectrum of the turbulence. Radio wave scattering by these electron density fluctuations produces anisotropic scatter-broadened images. Damping by ion-neutral collisions restricts Alfvenic turbulence to highly ionized regions of the interstellar medium.

Goldreich, P.↗

NASA NTRS1994

Toward a theory of interstellar turbulence. 1: Weak Alfvenic turbulence

We study weak Alfvenic turbulence of an incompressible, magnetized fluid in some detail, with a view to developing a firm theoretical basis for the dynamics of small-scale turbulence in the interstellar medium. We prove that resonant 3-wave interactions are absent. We also show that the Iroshnikov-Kraichnan theory of incompressible, magnetohydrodynamic turbulence -- which is widely accepted -- describes weak 3-wave turbulence; consequently, it is incorrect. Physical arguments, as well as detailed calculations of the coupling coefficients are used to demonstrate that these interactions are empty. We then examine resonant 4-wave interactions, and show that the resonance relations forbid energy transport to small spatial scales along the direction of the mean magnetic field, for both the shear Alfven wave and the pseudo Alfven wave. The three-dimensional inertial-range energy spectrum of 4-wave shear Alfven turbulence guessed from physical arguments reads E(k(sub z), k(sub perpendicular)) approximately V(sub A)v(sub L)L(exp -1/3)k(sub perpendicular)(exp -10/3), where V(sub A) is the Alfven speed, and v(sub L) is the velocity difference across the outer scale L. Given this spectrum, the velocity difference across lambda(sub perpendicular) approximately k(sub perpendicular exp -1) is v(sub lambda (sub perpendicular)) is approximately v(sub L)(lambda(sub perpendicular)/L)(exp 2/3). We derive a kinetic equation, and prove that this energy spectrum is a stationary solution and that it implies a positive flux of energy in k-space, along directions perpendicular to the mean magnetic field. Using this energy spectrum, we deduce that 4-wave interactions strengthen as the energy cascades to small, perpendicular spatial scales; beyond an upper bound in perpendicular wavenumber, k(sub perpendicular)L is approximately (V(sub A)/v(sub L))(exp 3/2), weak turbulence theory ceases to be valid. Energy excitation amplitudes must be very small for the 4-wave inertial-range to be substantial. When the excitation is strong, the width of the 4-wave inertial-range shrinks to zero. This seems likely to be the case in the interstellar medium.

Sridhar, S.↗

NASA NTRS1999

Double Resonances and Spectral Scaling in the Weak Turbulence Theory of Rotating and Stratified Turbulence

In rotating turbulence, stably stratified turbulence, and in rotating stratified turbulence, heuristic arguments concerning the turbulent time scale suggest that the inertial range energy spectrum scales as k(exp -2). From the viewpoint of weak turbulence theory, there are three possibilities which might invalidate these arguments: four-wave interactions could dominate three-wave interactions leading to a modified inertial range energy balance, double resonances could alter the time scale, and the energy flux integral might not converge. It is shown that although double resonances exist in all of these problems, they do not influence overall energy transfer. However, the resonance conditions cause the flux integral for rotating turbulence to diverge logarithmically when evaluated for a k(exp -2) energy spectrum; therefore, this spectrum requires logarithmic corrections. Finally, the role of four-wave interactions is briefly discussed.

Rubinstein, Robert↗

NASA NTRS2012

Using Indirect Turbulence Measurements for Real-Time Parameter Estimation in Turbulent Air

The use of indirect turbulence measurements for real-time estimation of parameters in a linear longitudinal dynamics model in atmospheric turbulence was studied. It is shown that measuring the atmospheric turbulence makes it possible to treat the turbulence as a measured explanatory variable in the parameter estimation problem. Commercial off-the-shelf sensors were researched and evaluated, then compared to air data booms. Sources of colored noise in the explanatory variables resulting from typical turbulence measurement techniques were identified and studied. A major source of colored noise in the explanatory variables was identified as frequency dependent upwash and time delay. The resulting upwash and time delay corrections were analyzed and compared to previous time shift dynamic modeling research. Simulation data as well as flight test data in atmospheric turbulence were used to verify the time delay behavior. Recommendations are given for follow on flight research and instrumentation.

Martos, Borja↗

DOE OSTI2026

Direct numerical simulations of activation and deactivation in turbulent atmospheric clouds

Significant knowledge gaps remain in our understanding of turbulence–cloud–aerosol interactions in the Earth's atmosphere, and direct numerical simulation (DNS) has increasingly become an indispensable tool to fill such critical knowledge gaps. Here, this study is an extension of our previous DNS model [Gao et al., J. Geophys. Res.: Atmos., 123(4), 2194–2214 (2018)], with a focus on the activation of aerosol particles into cloud droplets and deactivation of cloud droplets into aerosol particles in a microscale cloud environment. The effects of turbulence intensity, particle curvature, and solute, as well as the initial distributions of the aerosol particles (monodisperse or polydisperse) are investigated. The governing equations for the flow of air, temperature, and water vapor mixing ratio are solved numerically in the Eulerian fashion, assuming homogeneous and isotropic turbulence. The dynamics of the aerosol and cloud particles are calculated with the Lagrangian particle tracking method. The results show that the deviations of the thermodynamic variables from their respective means are significantly reduced, the activation process appears to be delayed, and the deactivation process occurs more rapidly, as the turbulence intensity is increased. The inclusion of particle curvature and solute effects, as well as polydispersity, tends to retard the activation of aerosols into cloud droplets. It is also observed that fluctuations in supersaturation broaden the spread of particle radii, and the broadening is followed by a narrowing as turbulent homogenization reduces thermodynamic fluctuations over time.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2024

Hierarchically Informed Engineering Models for Predictive Modeling of Turbulent Premixed Flame Propagation in Pre- chamber Turbulent Jet Ignition

The goal of the project is to improve the predictive accuracy and efficiency of turbulent combustion sub-models for pre-chamber turbulent jet ignition (TJI). This goal is achieved through the development of a hierarchically informed engineering model for turbulent combustion in TJI. The model development starts with the highest level of model description of turbulent combustion with direct numerical simulation (DNS) from which fundamental characteristics and scaling properties of turbulent premixed flame propagation under TJI relevant conditions are obtained.

42 ENGINEERING↗