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All sourcesNASA NTRSDOE OSTI
NASA NTRS1987

Two-component LDV investigation of 3-dimensional shock/turbulent boundary layer interactions

Mean-velocity and turbulence measurements obtained by two-component laser Doppler velocimetry are presented, together with numerical predictions, for the shock-related separation of a turbulent boundary layer at Mach 2.85. The basic geometry, a 30 deg half-angle flare mounted on a long cylinder, is made three-dimensional by tipping the flare at an angle of attack, alpha. The separation length and general upstream influence increase with alpha. A recirculating vortex in the separated zone becomes stronger as three-dimensionality increases. A large-scale unsteadiness of the separation shock wave and surrounding flowfields grows in amplitude with alpha, and appears to strongly influence the amplification of turbulence correlations ahead of detachment. Scaling of the streamwise coordinate by separation length causes two-dimensional and three-dimensional data profiles on the cylinder to collapse for most measured quantities.

Brown, J. D.↗
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 NTRS1985

An interplanetary magnetic field ensemble at 1 AU

A method for calculation ensemble averages from magnetic field data is described. A data set comprising approximately 16 months of nearly continuous ISEE-3 magnetic field data is used in this study. Individual subintervals of this data, ranging from 15 hours to 15.6 days comprise the ensemble. The sole condition for including each subinterval in the averages is the degree to which it represents a weakly time-stationary process. Averages obtained by this method are appropriate for a turbulence description of the interplanetary medium. The ensemble average correlation length obtained from all subintervals is found to be 4.9 x 10 to the 11th cm. The average value of the variances of the magnetic field components are in the approximate ratio 8:9:10, where the third component is the local mean field direction. The correlation lengths and variances are found to have a systematic variation with subinterval duration, reflecting the important role of low-frequency fluctuations in the interplanetary medium.

Matthaeus, W. H.↗
NASA NTRS1986

An interplanetary magnetic field ensemble at 1 AU

A method for calculation ensemble averages from magnetic field data is described. A data set comprising approximately 16 months of nearly continuous ISEE-3 magnetic field data is used in this study. Individual subintervals of this data, ranging from 15 hours to 15.6 days comprise the ensemble. The sole condition for including each subinterval in the averages is the degree to shich it represents a weakly time-stationary process. Averages obtained by this method are appropriate for a turbulence description of the interplanetary medium. The ensemble average correlation length obtained from all subintervals is found to be 4.9 x 10 to the 11th cm. The average value of the variances of the magnetic field components are in the approximate ratio 8:9:10, where the third component is the local mean field direction. The correlation lengths and variances are found to have a systematic variation with subinterval duration, reflecting the important role of low-frequency fluctuations in the interplanetary medium.

Matthaeus, W. H.↗
NASA NTRS1982

Measurement of the rugged invariants of magnetohydrodynamic turbulence in the solar wind

Measurements of the total energy, cross helicity, and magnetic helicity of the solar wind at 1, 2.8, and 5 AU are presented. These quantities are the three rugged invariants of three-dimensional ideal incompressible MHD turbulence theory. The theoretical technique for measuring the magnetic helicity from the matrix of two-point correlations is shown. The length scales characterizing the magnetic helicity are found to be equal to or greater than those which characterize the magnetic energy. The magnetic helicity typically lies at scales larger than the magnetic correlation length, consistent with the expectations of the inverse cascade and selective decay hypotheses of three-dimensional MHD turbulence. At smaller scales, the magnetic helicity oscillates in sign. Measurements of the cross helicity are not fully consistent with the usual interpretation in terms of outward propagating Alfvenic functions. Especially during the interval at 5 AU the cross helicity is found to oscillate in sign indicating fluctuations propagating both outward and inward.

Matthaeus, W. H.↗
NASA NTRS1992

Coherent 1-micron lidar measurements of atmospheric-turbulence-induced spatial decorrelation using a multielement heterodyne detector array

A coherent 1-micron Nd:YAG lidar system is employed to measure directly the reduced spatial coherence length rho 0 of the lidar returns caused by atmospheric turbulence. The experiments were conducted by using a 2 x 2 heterodyne detector array, which permitted real-time spatial correlation measurements of the lidar returns at two different detector spacings. The spatial correlation coefficients and spatial coherence length of the lidar returns from a hard target were measured during a day-to-night time period when the atmospheric turbulence parameter, Cn-squared, was measured to vary from 2 x 10 exp -13 to 2 x 10 exp -4 m exp -2/3. These directly measured values of rho 0 as a function of Cn-squared were found to be in good agreement with theoretical predictions.

Chan, Kin P.↗
NASA NTRS1972

Turbulent properties of a compressible boundary layer.

Turbulent shear-stress, eddy-viscosity, mixing-length, heat-flux and Prandtl number distributions across a hypersonic turbulent boundary layer have been determined from the 'time-averaged' conservation equations using experimental mean profile data obtained at several streamwise locations in a fully developed turbulent boundary layer with negligible pressure gradient. The eddy-viscosity, mixing-length and Prandtl number results show general agreement with previous incompressible and adiabatic compressible correlations. However, when the turbulent Prandtl number is defined using total enthalpy as opposed to static enthalpy no clear correlation of the results in the outer portion of the boundary layer could be obtained.

Horstman, C. C.↗
NASA NTRS1958

On the statistical theory of turbulence

A study is made of the spectrum of isotropic turbulence with the aid of the customary method of Fourier analysis. The spectrum of the turbulent motion is derived to the smallest wave lengths, that is, into the laminar region, and correlation functions and pressure fluctuations are calculated. A comparison with experimental results is included. Finally, an attempt is made to derive the numerical value of a constant characteristic of the energy dissipation in isotropic turbulence.

Heisenberg, W↗
NASA NTRS1994

The asymptotic state of rotating homogeneous turbulence at high Reynolds numbers

The long-time, asymptotic state of rotating homogeneous turbulence at high Reynolds numbers has been examined using large-eddy simulation of the incompressible Navier-Stokes equations. The simulations were carried out using 128 x 128 x 512 collocation points in a computational domain that is four times longer along the rotation axis than in the other directions. Subgrid-scale motions in the simulations were parameterized using a spectral eddy viscosity modified for system rotation. Simulation results show that in the asymptotic state the turbulence kinetic energy undergoes a power-law decay with an exponent which is independent of rotation rate, depending only on the low-wavenumber form of the initial energy spectrum. Integral lengthscale growth in the simulations is also characterized by power-law growth; the correlation length of transverse velocities exhibiting much more rapid growth than observed in non-rotating turbulence.

Squires, Kyle D.↗
NASA NTRS2022

Isotropization and Evolution of Energy-Containing Eddies in Solar Wind Turbulence: Parker Solar Probe, Helios 1, ACE, WIND, and Voyager 1

We examine the radial evolution of correlation lengths perpendicular (l^ C) and parallel (  lC) to the magnetic-field direction, computed from solar wind magnetic-field data measured by Parker Solar Probe (PSP) during its first eight orbits, Helios 1, Advanced Composition Explorer (ACE), WIND, and Voyager 1 spacecraft. Correlation lengths are grouped by an interval’s alignment angle; the angle between the magnetic-field and solar wind velocity vectors (ΘBV). Parallel and perpendicular angular channels correspond to angles 0° < ΘBV < 40° and 50° < ΘBV < 90°, respectively. We observe an anisotropy in the inner heliosphere within 0.40 au, with  l l »^ 0.75 C C at 0.10 au. This anisotropy reduces with increasing heliocentric distance and the correlation lengths roughly isotropize within 1 au. Results from ACE and WIND support a reversal of the anisotropy, such that  l l »^ 1.29 C C at 1 au. The ratio does not appear to change significantly beyond 1 au, although the small number of parallel intervals in the Voyager data set precludes unambiguous conclusions from being drawn. This study provides insights regarding the radial evolution of the large, most energetic interacting turbulent fluctuations in the heliosphere. We also emphasize the importance of tracking the changes in sampling direction in PSP measurements as the spacecraft approaches the Sun, when using these data to study the radial evolution of turbulence. This can prove to be vital in understanding the more complex dynamics of the solar wind in the inner heliosphere and can assist in improving related simulations.

Manuel Enrique Cuesta↗
NASA NTRS1981

Predicting aerodynamic sound utilizing a two-point, two-time turbulence theory

The feasibility of determining two-point, two-time turbulent velocity correlations based on extending closure models for one-point, one-time turbulence correlations is demonstrated. The procedure used is based on a spatial moment integral formulation of the governing equations using approximate, parameterized trial functions for the two-point, two-time velocity correlations. Solution of the equations is shown to give a set of anisotropic length scales and the separation-time-dependent decorrelation of the ensemble averaged turbulent velocities. The analysis is simplified using the assumption of homogeneous stationary turbulence and a constant shear, unidirectional mean flow. It is shown that the anisotropic behavior of measured turbulence correlations can be characterized through this technique.

Hecht, A. M.↗
NASA NTRS2005

Prediction of Turbulence-Generated Noise in Unheated Jets: JeNo Technical Manual (Version 1.0) - Part 1

The model-based approach, used by the JeNo code to predict jet noise spectral directivity, is described. A linearized form of Lilley's equation governs the non-causal Green s function of interest, with the non-linear terms on the right hand side identified as the source. A Reynolds-averaged Navier-Stokes (RANS) solution yields the required mean flow for the solution of the propagation Green s function in a locally parallel flow. The RANS solution also produces time- and length-scales needed to model the non-compact source, the turbulent velocity correlation tensor, with exponential temporal and spatial functions. It is shown that while an exact non-causal Green s function accurately predicts the observed shift in the location of the spectrum peak with angle as well as the angularity of sound at low to moderate Mach numbers, the polar directivity of radiated sound is not entirely captured by this Green s function at high subsonic and supersonic acoustic Mach numbers. Results presented for unheated jets in the Mach number range of 0.51 to 1.8 suggest that near the peak radiation angle of high-speed jets, a different source/Green s function convolution integral may be required in order to capture the peak observed directivity of jet noise. A sample Mach 0.90 heated jet is also discussed that highlights the requirements for a comprehensive jet noise prediction model.

Khavaran, Abbas↗
NASA NTRS1987

On the saturation of the refractive index structure function. II - Influence of the correlation length on astronomical 'seeing'

A physical length scale in the wavefront corresponding to the parameter (r sub 0) characterizing the loss in detail in a long exposure image is identified, and the influence of the correlation scale of turbulence as r sub 0 approaches this scale is shown. Allowing for the effect of 2-point correlations in the fluctuations of the refractive index, Venkatakrishnan and Chatterjee (1987) proposed a modified law for the phase structure function. It is suggested that the departure of the phase structure function from the 5/3 power law for length scales in the wavefront approaching the correlation scale of turbulence may lead to better 'seeing' at longer wavelengths.

Venkatakrishnan, P.↗
NASA NTRS1989

Non-WKB evolution of solar wind fluctuations - A turbulence modeling approach

Recent observations indicate systematic changes in the interplanetary inertial range velocity-magnetic field correlation with increasing heliocentric distance. Here, a multiple length scale model for the evolution of the small scale fluctuations due to local nonlinear couplings as well as couplings to large scale gradients is outlined, which is similar to that used in turbulence modeling of inhomogeneous shear flows. A simple special case solution is given, indicating that couplings to large scale flow gradients can cause radial evolution of the type seen in observations. The strongest couplings of this type are linear and do not appear in the usual WKB orderings. The relationship of the present approach to WKB theory is not fully understood at present.

Ye, Zou↗
NASA NTRS1993

Vortex generation and mixing in three-dimensional supersonic combustors

The generation and evolution of the flow vorticity established by instream injector ramps in a high Mach number/high enthalpy scramjet combustor flow-field are described in detail for a number of computational cases. Classical fluid dynamic circulation is presented for these cases in order to clarify the spatial distribution and convection of the vorticity. The ability of the simulations to accurately represent Stokes Law of circulation is discussed and shown. In addition, the conservation of swirl (effectively the moment-of-momentum theorem) is presented for these flows. The impact of both turbulent diffusion and the vortex/ramp non-uniformity on the downstream mixing rate is clearly illustrated. A correlation over the length of the combustor between fuel-air mixing and a parameter called the vortex stirring length is demonstrated. Finally, computational results for a representative ramp injector are compared with experimental data. Influence of the stream vorticity on the effective turbulent Prandtl number used in the simulation is discussed.

Riggins, D. W.↗
NASA NTRS1985

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.↗
NASA NTRS2003

Fluid Dynamics of a High Aspect-Ratio Jet

Circulation control wings are a type of pneumatic high-lift device that have been extensively researched as to their aerodynamic benefits. However, there has been little research into the possible airframe noise reduction benefits of a circulation control wing. The key element of noise is the jet noise associated with the jet sheet emitted from the blowing slot. High aspect-ratio jet acoustic results (aspect-ratios from 100 to 3,000) from a related study showed that the jet noise of this type of jet was proportional to the slot height to the 3/2 power and slot width to the 1/2 power. Fluid dynamic experiments were performed in the present study on the high aspect-ratio nozzle to gain understanding of the flow characteristics in an effort to relate the acoustic results to flow parameters. Single hot-wire experiments indicated that the jet exhaust from the high aspect-ratio nozzle was similar to a 2-d turbulent jet. Two-wire space-correlation measurements were performed to attempt to find a relationship between the slot height of the jet and the length-scale of the flow noise generating turbulence structure. The turbulent eddy convection velocity was also calculated, and was found to vary with the local centerline velocity, and also as a function of the frequency of the eddy.

Munro, Scott E.↗
NASA NTRS1980

Cycle II.5 aircraft aero-optical turbulent boundary-layer/shear-layer measurements

The aero-optical effects associated with propagating a laser beam through aircraft turbulent boundary layers and shear layers were examined. Observed laser optical performance levels were compared with those inferred from aerodynamic measurements of unsteady densities and correlation lengths within these random flows. Optical instrumentation included a fast shearing interferometer (FSI). A 9 cm diameter collimated helium neon laser beam made a double pass through the aircraft random flow via an airfoil mirror located one meter from the fuselage. Typical aircraft turbulent boundary layer thickness measured 0.3 meters. Averaging many FSI generated modulation transfer functions (MTFs) and Fourier transforming, this average yields the expected far field intensity degradation associated with an aircraft mounted laser system. Aerodynamic instrumentation included fine wire probes to measure unsteady temperature and mass flux. A laser doppler velocimeter measured unsteady velocity within the flows. An analysis of these data yielded point measurements of unsteady density and correlation length.

Gilbert, K.↗