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NASA NTRS2001

The Numerical Analysis of a Turbulent Compressible Jet

A numerical method to simulate high Reynolds number jet flows was formulated and applied to gain a better understanding of the flow physics. Large-eddy simulation was chosen as the most promising approach to model the turbulent structures due to its compromise between accuracy and computational expense. The filtered Navier-Stokes equations were developed including a total energy form of the energy equation. Subgrid scale models for the momentum and energy equations were adapted from compressible forms of Smagorinsky's original model. The effect of using disparate temporal and spatial accuracy in a numerical scheme was discovered through one-dimensional model problems and a new uniformly fourth-order accurate numerical method was developed. Results from two- and three-dimensional validation exercises show that the code accurately reproduces both viscous and inviscid flows. Numerous axisymmetric jet simulations were performed to investigate the effect of grid resolution, numerical scheme, exit boundary conditions and subgrid scale modeling on the solution and the results were used to guide the three-dimensional calculations. Three-dimensional calculations of a Mach 1.4 jet showed that this LES simulation accurately captures the physics of the turbulent flow. The agreement with experimental data was relatively good and is much better than results in the current literature. Turbulent intensities indicate that the turbulent structures at this level of modeling are not isotropic and this information could lend itself to the development of improved subgrid scale models for LES and turbulence models for RANS simulations. A two point correlation technique was used to quantify the turbulent structures. Two point space correlations were used to obtain a measure of the integral length scale, which proved to be approximately 1/2 D(sub j). Two point space-time correlations were used to obtain the convection velocity for the turbulent structures. This velocity ranged from 0.57 to 0.71 U(sub j).

DeBonis, James R.↗

NASA NTRS1999

Polar Spacecraft Observations of the Turbulent Outer Cusp/Magnetopause Boundary Layer of Earth

The orbit of the Polar spacecraft has been ideally suited for studying the turbulent region of the cusp that is located near or just outside the magnetopause current sheet at 7-9 R(sub E). The wave data obtained in this region show that electromagnetic turbulence is dominant in the frequency range 1-10 Hz. The waves responsible for this turbulence usually propagate perpendicular to the local magnetic field and have an index of refraction that generally falls between the estimated cold plasma theoretical values of the electromagnetic lower hybrid and whistler modes and may be composed of both modes in concert with kinetic Alfven waves and/or fast magnetosonic waves. Fourier spectra of the higher frequency wave data also show the electromagnetic turbulence at frequencies up to and near the electron cyclotron frequency. This higher frequency electromagnetic turbulence is most likely associated with whistler mode waves. The lower hybrid drift and current gradient instabilities are suggested as possible mechanisms for producing the turbulence. The plasma and field environment of this turbulent region is examined and found to be extremely complex. Some of the wave activity is associated with processes occurring locally, such as changes in the DC magnetic field, while others are associated with solar wind and interplanetary magnetic field changes.

Pickett, J. S.↗

NASA NTRS2002

Turbulence Measurements of Separate Flow Nozzles with Mixing Enhancement Features

Comparison of turbulence data taken in three separate flow nozzles, two with mixing enhancement features on their core nozzle, shows how the mixing enhancement features modify turbulence to reduce jet noise. The three nozzles measured were the baseline axisymmetric nozzle 3BB, the alternating chevron nozzle, 3A12B, with 6-fold symmetry, and the flipper tab nozzle 3T24B also with 6-fold symmetry. The data presented show the differences in turbulence characteristics produced by the geometric differences in the nozzles, with emphasis on those characteristics of interest in jet noise. Among the significant findings: the enhanced mixing devices reduce turbulence in the jet mixing region while increasing it in the fan/core shear layer, the ratios of turbulence components are significantly altered by the mixing devices, and the integral lengthscales do not conform to any turbulence model yet proposed. These findings should provide guidance for modeling the statistical properties of turbulence to improve jet noise prediction.

Bridges, James↗

NASA NTRS2002

Meteorology Associated with Turbulence Encounters During NASA's Fall-2000 Flight Experiments

Initial flight experiments have been conducted to investigate convectively induced turbulence and to test technologies for its airborne detection. Turbulence encountered during the experiments is described with sources of data measured from in situ sensors, groundbased and airborne Doppler radars, and aircraft video. Turbulence measurements computed from the in situ system were quantified in terms of RMS normal loads (sigma(sub Delta n)), where 0.20 g is less than or equal to sigma(sub Delta n) is less than or equal to 0.30 g is considered moderate and sigma(sub Delta n) is greater than 0.30 g is severe. During two flights, 18 significant turbulence encounters (sigma(sub Delta) is greater than or equal to 0.20 g) occurred in the vicinity of deep convection; 14 moderate and 4 severe. In all cases, the encounters with turbulence occurred along the periphery of cumulus convection. These events were associated with relatively low values of radar reflectivity, i.e. RRF is less than 35 dBz, with most levels being below 20 dBz. The four cases of severe turbulence occurred in precipitation and were centered at the interface between a cumulus updraft turret and a downwind downdraft. Horizontal gradients of vertical velocity at this interface were found to be strongest on the downwind side of the cumulus turrets. Furthermore, the greatest loads to the aircraft occurred while flying along, not orthogonal to, the ambient environmental wind vector. During the two flights, no significant turbulence was encountered in the clear air (visual meteorological conditions), not even in the immediate vicinity of the deep convection.

Hamilton, David W.↗

NASA NTRS2002

X-33 Turbulent Aeroheating Measurements and Predictions

Measurements and predictions of the X-33 turbulent aeroheating environment have been performed for Mach 6, perfect-gas air conditions. The purpose of this investigation was to compare turbulent aeroheating predictions from two Navier-Stokes codes, LAURA and GASP, with each other and with experimental data in which turbulent flow was produced through either natural transition or forced transition using roughness elements. The wind tunnel testing was conducted at free stream Reynolds numbers of 0.72 x 10(exp 7)/m to 2.4 x 10(exp 7)/m (2.2 x 10(exp 6)/ft to 7.3 x 10(exp 6)/ft) on 0.254 m (10.0-in.) X-33 models at alpha = 40 deg with smooth surfaces, smooth surfaces with discrete trips, and surfaces with simulated bowed thermal protection system panels. Turbulent flow was produced by the discrete trips and bowed panels for all but the lowest Reynolds number, while turbulent flow on the smooth model was produced only at the highest Reynolds number. Turbulent aeroheating levels on each of the three model types were measured using global phosphor thermography and agreed to within the experimental accuracy (+/= 15%) of the test technique. Computations were performed at the wind tunnel free stream conditions using both codes. Turbulent aeroheating levels predicted using the LAURA code were generally 5%-10% lower than those from GASP, although both sets of predictions fell within the experimental accuracy of the wind tunnel data.

Hollis, Brian R.↗

NASA NTRS2002

Experimental Investigation of Transition to Turbulence as Affected by Passing Wakes

Experimental results from a study of the effects of passing wakes upon laminar-to-turbulent transition in a low-pressure turbine passage are presented. The test section geometry is designed to simulate the effects of unsteady wakes resulting from rotor-stator interaction upon laminar-to-turbulent transition in turbine blade boundary layers and separated flow regions over suction surfaces. Single-wire, thermal anemometry techniques were used to measure time-resolved and phase-averaged, wall-normal profiles of velocity, turbulence intensity, and intermittency at multiple streamwise locations over the turbine airfoil suction surface. These data are compared to steady state, wake-free data collected in the same geometry to identify the effects of wakes upon laminar-to-turbulent transition. Results are presented for flows with a Reynolds number based on suction surface length and exit velocity of 50,000 and an approach flow turbulence intensity of 2.5 percent. From these data, the effects of passing wakes and associated increased turbulence levels and varying pressure gradients on transition and separation in the near-wall flow are presented. The results show that the wakes affect transition both by virtue of their difference in turbulence level from that of the free-stream but also by virtue of their velocity deficit relative to the freestream velocity, and the concomitant change in angle of attack and temporal pressure gradients. The results of this study seem to support the theory that bypass transition is a response of the near-wall viscous layer to pressure fluctuations imposed upon it from the free-stream flow. The data also show a significant lag between when the wake is present over the surface and when transition begins. The accompanying CD-ROM includes tabulated data, animations, higher resolution plots, and an electronic copy of this report.

Kaszeta, Richard W.↗

NASA NTRS1958

Statistical Study of Turbulence: Spectral Functions and Correlation Coefficients

In reading the publications on turbulence of different authors, one often runs the risk of confusing the various correlation coefficients and turbulence spectra. We have made a point of defining, by appropriate concepts, the differences which exist between these functions. Besides, we introduce in the symbols a few new characteristics of turbulence. In the first chapter, we study some relations between the correlation coefficients and the different turbulence spectra. Certain relations are given by means of demonstrations which could be called intuitive rather than mathematical. In this way we demonstrate that the correlation coefficients between the simultaneous turbulent velocities at two points are identical, whether studied in Lagrange's or in Euler's systems. We then consider new spectra of turbulence, obtained by study of the simultaneous velocities along a straight line of given direction. We determine some relations between these spectra and the correlation coefficients. Examining the relation between the spectrum of the turbulence measured at a fixed point and the longitudinal-correlation curve given by G. I. Taylor, we find that this equation is exact only when the coefficient is very small.

Frenkiel, Francois N.↗

NASA NTRS2004

Annual Research Briefs, 2004: Center for Turbulence Research

This report contains the 2004 annual progress reports of the Research Fellows and students of the Center for Turbulence Research in its eighteenth year of operation. Since its inception in 1987, the objective of the CTR has been to advance the physical understanding of turbulent flows and development of physics based predictive tools for engineering analysis and turbulence control. Turbulence is ubiquitous in nature and in engineering devices. The studies at CTR have been motivated by applications where turbulence effects are significant; these include a broad range of technical areas such as planetary boundary layers, formation of planets, solar convection, magnetohydrodynamics, environmental and eco systems, aerodynamic noise, propulsion systems and high speed transportation. Numerical simulation has been the predominant research tool at CTR which has required a critical mass of researchers in numerical analysis and computer science in addition to core disciplines such as applied mathematics, chemical kinetics and fluid mechanics. Maintaining and promoting this interdisciplinary culture has been a hallmark of CTR and has been responsible for the realization of the results of its basic research in applications. The first group of reports in this volume are directed towards development, analysis and application of novel numerical methods for ow simulations. Development of methods for large eddy simulation of complex flows has been a central theme in this group. The second group is concerned with turbulent combustion, scalar transport and multi-phase ows. The nal group is devoted to geophysical turbulence where the problem of solar convection has been a new focus of considerable attention recently at CTR.

Moin, Parviz↗

NASA NTRS1999

Unlocking the Keys to Vortex/Flame Interactions in Turbulent Gas-Jet Diffusion Flames--Dynamic Behavior Explored on the Space Shuttle

Most combustion processes in industrial applications (e.g., furnaces and engines) and in nature (e.g., forest fires) are turbulent. A better understanding of turbulent combustion could lead to improved combustor design, with enhanced efficiency and reduced emissions. Despite its importance, turbulent combustion is poorly understood because of its complexity. The rapidly changing and random behavior of such flames currently prevents detailed analysis, whether experimentally or computationally. However, it is possible to learn about the fundamental behavior of turbulent flames by exploring the controlled interaction of steady laminar flames and artificially induced flow vortices. These interactions are an inherent part of turbulent flames, and understanding them is essential to the characterization of turbulent combustion. Well-controlled and defined experiments of vortex interaction with laminar flames are not possible in normal gravity because of the interference of buoyancy- (i.e., gravity) induced vortices. Therefore, a joint microgravity study was established by researchers from the Science and Technology Development Corp. and the NASA Lewis Research Center. The experimental study culminated in the conduct of the Turbulent Gas-Jet Diffusion Flames (TGDF) Experiment on the STS-87 space shuttle mission in November 1997. The fully automated hardware, shown in photo, was designed and built at Lewis. During the mission, the experiment was housed in a Get Away Special (GAS) canister in the cargo bay.

Stocker, Dennis P.↗

NASA NTRS2005

Plasma sheet turbulence observed by Cluster II

Cluster fluxgate magnetometer (FGM) and ion spectrometer (CIS) data are employed to analyze magnetic field fluctuations within the plasma sheet during passages through the magnetotail region in the summers of 2001 and 2002 and, in particular, to look for characteristics of magnetohydrodynamic (MHD) turbulence. Power spectral indices determined from power spectral density functions are on average larger than Kolmogorov's theoretical value for fluid turbulence as well as Kraichnan's theoretical value for MHD plasma turbulence. Probability distribution functions of the magnetic fluctuations show a scaling law over a large range of temporal scales with non-Gaussian distributions at small dissipative scales and inertial scales and more Gaussian distribution at large driving scales. Furthermore, a multifractal analysis of the magnetic field components shows scaling behavior in the inertial range of the fluctuations from about 20 s to 13 min for moments through the fifth order. Both the scaling behavior of the probability distribution functions and the multifractal structure function suggest that intermittent turbulence is present within the plasma sheet. The unique multispacecraft aspect and fortuitous spacecraft spacing allow us to examine the turbulent eddy scale sizes. Dynamic autocorrelation and cross correlation analysis of the magnetic field components allow us to determine that eddy scale sizes fit within the plasma sheet. These results suggest that magnetic field turbulence is occurring within the plasma sheet resulting in turbulent energy dissipation.

Weygand, James M.↗

NASA NTRS2006

Relationship Between Vortex Meander and Ambient Turbulence

Efforts are currently underway to increase the capacity of airports by use of closely-spaced parallel runways. If such an objective is to be achieved safely and efficiently during both visual and instrument flight conditions, it will be necessary to develop more precise methods for the prediction of the motion and spread of the hazard posed by the lift-generated vortex-wakes of aircraft, and their uncertainties. The purpose of the present study is to relate the motion induced in vortex filaments by turbulence in the ambient flow field to the measured turbulence in the flow field. The problem came about when observations made in the two largest NASA wind tunnels indicated that extended exposure of vortex wakes to the turbulence in the wind tunnel air stream causes the centers of the vortices to meander about with time at a given downstream station where wake measurements are being made. Although such a behavior was expected, the turbulence level based on the maximum amplitude of meander was much less than the root-mean-squared value measured in the free-stream of the wind tunnel by use of hot-film anemometers. An analysis of the time-dependent motion of segments of vortex filaments as they interact with an eddy, indicates that the inertia of the filaments retards their motion enough in the early part of their travel to account for a large part of the difference in the two determinations of turbulence level. Migration of vortex filaments from one turbulent eddy to another (probably with a different orientation), is believed to account for the remainder of the difference. Methods that may possibly be developed for use in the measurement of the magnitude of the more intense eddies in turbulent flow fields and how they should be adjusted to predict vortex meander are then discussed.

Rossow, Vernon J.↗

NASA NTRS2008

Diagnosis of Magnetic Structures and Intermittency in Space Plasma Turbulence using the Method of Surrogate Data

Several observations in space plasmas have reported the presence of coherent structures at different plasma scales. Structure formation is believed to be a direct consequence of nonlinear interactions between the plasma modes, which depend strongly on phase synchronization of those modes. Despite this important role of the phases in turbulence, very limited work has been however devoted to study the phases as a potential tracers of nonlinearities in comparison with the wealth of literature on power spectra of turbulence where phases are totally missed. We present a method based on surrogate data to systematically detect coherent structures in turbulent signals. The new method has been applied successfully to magnetosheath turbulence (Sahraoui, Phys. Rev. E, 2008, in press), where the relationship between the identified phase coherence and intermittency (classically identified as non Gaussian tails of the PDFs) as well as the energy cascade has been studied. Here we review the main results obtained in that study and show further applications to small scale solar wind turbulence. Implications of the results on theoretical modelling of space turbulence (applicability of weak/wave turbulence, its validity limits and its connection to intermittency) will be discussed.

Sahraoui, Fouad↗

NASA NTRS2003

The Statistical Mechanics of Ideal MHD Turbulence

Turbulence is a universal, nonlinear phenomenon found in all energetic fluid and plasma motion. In particular. understanding magneto hydrodynamic (MHD) turbulence and incorporating its effects in the computation and prediction of the flow of ionized gases in space, for example, are great challenges that must be met if such computations and predictions are to be meaningful. Although a general solution to the "problem of turbulence" does not exist in closed form, numerical integrations allow us to explore the phase space of solutions for both ideal and dissipative flows. For homogeneous, incompressible turbulence, Fourier methods are appropriate, and phase space is defined by the Fourier coefficients of the physical fields. In the case of ideal MHD flows, a fairly robust statistical mechanics has been developed, in which the symmetry and ergodic properties of phase space is understood. A discussion of these properties will illuminate our principal discovery: Coherent structure and randomness co-exist in ideal MHD turbulence. For dissipative flows, as opposed to ideal flows, progress beyond the dimensional analysis of Kolmogorov has been difficult. Here, some possible future directions that draw on the ideal results will also be discussed. Our conclusion will be that while ideal turbulence is now well understood, real turbulence still presents great challenges.

Shebalin, John V.↗

NASA NTRS2010

Establishing Consensus Turbulence Statistics for Hot Subsonic Jets

Many tasks in fluids engineering require knowledge of the turbulence in jets. There is a strong, although fragmented, literature base for low order statistics, such as jet spread and other meanvelocity field characteristics. Some sources, particularly for low speed cold jets, also provide turbulence intensities that are required for validating Reynolds-averaged Navier-Stokes (RANS) Computational Fluid Dynamics (CFD) codes. There are far fewer sources for jet spectra and for space-time correlations of turbulent velocity required for aeroacoustics applications, although there have been many singular publications with various unique statistics, such as Proper Orthogonal Decomposition, designed to uncover an underlying low-order dynamical description of turbulent jet flow. As the complexity of the statistic increases, the number of flows for which the data has been categorized and assembled decreases, making it difficult to systematically validate prediction codes that require high-level statistics over a broad range of jet flow conditions. For several years, researchers at NASA have worked on developing and validating jet noise prediction codes. One such class of codes, loosely called CFD-based or statistical methods, uses RANS CFD to predict jet mean and turbulent intensities in velocity and temperature. These flow quantities serve as the input to the acoustic source models and flow-sound interaction calculations that yield predictions of far-field jet noise. To develop this capability, a catalog of turbulent jet flows has been created with statistics ranging from mean velocity to space-time correlations of Reynolds stresses. The present document aims to document this catalog and to assess the accuracies of the data, e.g. establish uncertainties for the data. This paper covers the following five tasks: Document acquisition and processing procedures used to create the particle image velocimetry (PIV) datasets. Compare PIV data with hotwire and laser Doppler velocimetry (LDV) data published in the open literature. Compare different datasets acquired at roughly the same flow conditions to establish uncertainties. Create a consensus dataset for a range of hot jet flows, including uncertainty bands. Analyze this consensus dataset for self-consistency and compare jet characteristics to those of the open literature. One final objective fulfilled by this work was the demonstration of a universal scaling for the jet flow fields, at least within the region of interest to aeroacoustics. The potential core length and the spread rate of the half-velocity radius were used to collapse of the mean and turbulent velocity fields over the first 20 jet diameters in a highly satisfying manner.

Bridges, James↗

NASA NTRS2002

Experimental Investigation of Transition to Turbulence as Affected by Passing Wakes

Experimental results from a study of the effects of passing wakes upon laminar-to-turbulent transition in a low-pressure turbine passage are presented. The test section geometry is designed to simulate the effects of unsteady wakes resulting from rotor-stator interaction upon laminar-to-turbulent transition in turbine blade boundary layers and separated flow regions over suction surfaces. Single-wire, thermal anemometry techniques were used to measure time- resolved and phase-averaged, wall-normal profiles of velocity, turbulence intensity, and intermittency at multiple streamwise locations over the turbine airfoil suction surface. These data are compared to steady state, wake-free data collected in the same geometry to identify the effects of wakes upon laminar-to-turbulent transition. Results are presented for flows with a Reynolds number based on suction surface length and exit velocity of 50,000 and an approach flow turbulence intensity of 2.5 percent. From these data, the effects of passing wakes and associated increased turbulence levels and varying pressure gradients on transition and separation in the near-wall flow are presented. The results show that the wakes affect transition both by virtue of their difference in turbulence level from that of the free-stream but also by virtue of their velocity deficit relative to the freestream velocity, and the concomitant change in angle of attack and temporal pressure gradients. The results of this study seem to support the theory that bypass transition is a response of the near-wall viscous layer to pressure fluctuations imposed upon it from the free-stream flow. The data also show a significant lag between when the wake is present over the surface and when transition begins. The accompanying CD-ROM includes tabulated data, animations, higher resolution plots, and an electronic copy of this report.

Kaszeta, Richard W.↗

NASA NTRS2012

Three-Dimensional Magnetohydrodynamic Modeling of the Solar Wind Including Pickup Protons and Turbulence Transport

To study the effects of interstellar pickup protons and turbulence on the structure and dynamics of the solar wind, we have developed a fully three-dimensional magnetohydrodynamic solar wind model that treats interstellar pickup protons as a separate fluid and incorporates the transport of turbulence and turbulent heating. The governing system of equations combines the mean-field equations for the solar wind plasma, magnetic field, and pickup protons and the turbulence transport equations for the turbulent energy, normalized cross-helicity, and correlation length. The model equations account for photoionization of interstellar hydrogen atoms and their charge exchange with solar wind protons, energy transfer from pickup protons to solar wind protons, and plasma heating by turbulent dissipation. Separate mass and energy equations are used for the solar wind and pickup protons, though a single momentum equation is employed under the assumption that the pickup protons are comoving with the solar wind protons.We compute the global structure of the solar wind plasma, magnetic field, and turbulence in the region from 0.3 to 100 AU for a source magnetic dipole on the Sun tilted by 0 deg - .90 deg and compare our results with Voyager 2 observations. The results computed with and without pickup protons are superposed to evaluate quantitatively the deceleration and heating effects of pickup protons, the overall compression of the magnetic field in the outer heliosphere caused by deceleration, and the weakening of corotating interaction regions by the thermal pressure of pickup protons.

Usmanov, Arcadi V.↗

NASA NTRS2013

Cloud Simulations in Response to Turbulence Parameterizations in the GISS Model E GCM

The response of cloud simulations to turbulence parameterizations is studied systematically using the GISS general circulation model (GCM) E2 employed in the Intergovernmental Panel on Climate Change's (IPCC) Fifth Assessment Report (AR5).Without the turbulence parameterization, the relative humidity (RH) and the low cloud cover peak unrealistically close to the surface; with the dry convection or with only the local turbulence parameterization, these two quantities improve their vertical structures, but the vertical transport of water vapor is still weak in the planetary boundary layers (PBLs); with both local and nonlocal turbulence parameterizations, the RH and low cloud cover have better vertical structures in all latitudes due to more significant vertical transport of water vapor in the PBL. The study also compares the cloud and radiation climatologies obtained from an experiment using a newer version of turbulence parameterization being developed at GISS with those obtained from the AR5 version. This newer scheme differs from the AR5 version in computing nonlocal transports, turbulent length scale, and PBL height and shows significant improvements in cloud and radiation simulations, especially over the subtropical eastern oceans and the southern oceans. The diagnosed PBL heights appear to correlate well with the low cloud distribution over oceans. This suggests that a cloud-producing scheme needs to be constructed in a framework that also takes the turbulence into consideration.

Yao, Mao-Sung↗

NASA NTRS2018

Development and Documentation of kL-Based Linear, Nonlinear, and Full Reynolds Stress Turbulence Models

The development and implementation of kL-based Reynolds Average Navier-Stokes (RANS) turbulence models are reported herein. The kL is based on Abdol-Hamid's closure and Menter's modi cation to Rotta's two-equation model. Rotta shows that a reliable transport equation can be formed from the turbulent length scale L, and the turbulent kinetic energy k. Rotta's kL equation is well suited for term-by-term modeling and displays useful features compared to other scale formulation. One of the important di erences is the inclusion of higher order velocity derivatives in the source terms of the scale equation. This can enhance the ability of RANS solvers to simulate unsteady ows in URANS mode. The present report documents the formulation of three model levels of turbulence models as implemented in the CFD code FUN3D. Methodology and calibration examples are shown in detail. The levels are the linear k-kL and the two-equation algebraic Reynolds stress model (ARSM) as well as the full Reynolds Stress Model (RSM). Attached, separated and corner ow cases are documented and compared with experimental, theoretical and other turbulence model data. The results show generally very good comparisons with canonical and experimental data. The results from this formulation are similar or better than results using the SST two- equation turbulence model. ARSM shows great promise with similar level of computational resources as general two equation turbulence models.

Abdol-Hamid, Khaled S.↗