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NASA NTRS1995

The sensitivity of various mode sets for probing differential rotation shear zones

The potential of future data sets from global oscillations network group (GONG) and solar oscillations investigation (SOI) for resolving long-lived azimuthal jets and shearing flows, is investigated. Various artificial data sets are constructed, containing noise resembling that of a one-year observation run. These are inverted using a two dimensional regularized least squares inversion. The ability of this method to form well localized averages of the rotation rate, as measured by the averaging kernels, is investigated using an extensive mode set and subsets. It is shown that it is possible to keep the noise in the solution down to a few nHz in much of the solar interior, while obtaining a reasonable resolution for a GONG-like data set. At low latitudes in the middle of the convection zone, an angular resolution of less than 10 deg and a radial resolution of about 0.04 solar radii, are obtained. The averaging kernels depend on the mode set, and a reduction in the number of modes tends to introduce small-scale near surface structures into the averaging kernels which would adversely affect the inferred rotation rate.

Christensen-Dalsgaard, Joergen↗
NASA NTRS1995

An extended structure-based model based on a stochastic eddy-axis evolution equation

We have proposed and implemented an extension of the structure-based model for weak deformations. It was shown that the extended model will correctly reduce to the form of standard k-e models for the case of equilibrium under weak mean strain. The realizability of the extended model is guaranteed by the method of its construction. The predictions of the proposed model were very good for rotating homogeneous shear flows and for irrotational axisymmetric contraction, but were seriously deficient in the case of plane strain and axisymmetric expansion. We have concluded that the problem behind these difficulties lies in the algebraic constitutive equation relating the Reynolds stresses to the structure parameters rather than in the slow model developed here. In its present form, this equation assumes that under irrotational strain the principal axes of the Reynolds stresses remain locked onto those of the eddy-axis tensor. This is correct in the RDT limit, but inappropriate under weaker mean strains, when the non-linear eddy-eddy interactions tend to misalign the two sets of principal axes and create some non-zero theta and gamma.

Kassinos, S. C.↗
NASA NTRS1995

Distorted turbulence submitted to frame rotation: RDT and LES results

The objective of this effort is to carry the analysis of Lee et al. (1990) to the case of shear with rotation. We apply the RDT approximation to turbulence submitted to frame rotation for the case of a uniformly sheared flow and compare its mean statistics to results of high resolution DNS of a rotating plane channel flow. In the latter, the mean velocity profile is modified by the Coriolis force, and accordingly, different regions in the channel can be identified. The properties of the plane pure strain turbulence submitted to frame rotation are, in addition, investigated in spectral space, which shows the usefulness of the spectral RDT approach. This latter case is investigated here. Among the general class of quadratic flows, this case does not follow the same stability properties as the others since the related mean vorticity is zero.

Godeferd, Fabien S.↗
NASA NTRS1996

Shear Stabilization of a Solidifying Front

The manufacturing of multi-component single crystals with uniform material properties is frequently hampered by the presence of morphological instabilities during the solidification. We discuss the influence of shear flows on the linear and nonlinear stability of the solid/liquid interface during the directional solidification of binary alloys. The flows are generated by nonplanar harmonic translations of the crystal parallel to the mean interface position. Oscillations with physically realizable amplitudes and frequencies are found useful for stabilization purposes.

Davis, Stephen H.↗
NASA NTRS1996

Computations of Drop Collision and Coalescence

Computations of drops collisions, coalescence, and other problems involving drops are presented. The computations are made possible by a finite difference/front tracking technique that allows direct solutions of the Navier-Stokes equations for a multi-fluid system with complex, unsteady internal boundaries. This method has been used to examine the various collision modes for binary collisions of drops of equal size, mixing of two drops of unequal size, behavior of a suspension of drops in linear and parabolic shear flows, and the thermal migration of several drops. The key results from these simulations are reviewed. Extensions of the method to phase change problems and preliminary results for boiling are also shown.

Tryggvason, Gretar↗
NASA NTRS1997

Towards Perfectly Absorbing Boundary Conditions for Euler Equations

In this paper, we examine the effectiveness of absorbing layers as non-reflecting computational boundaries for the Euler equations. The absorbing-layer equations are simply obtained by splitting the governing equations in the coordinate directions and introducing absorption coefficients in each split equation. This methodology is similar to that used by Berenger for the numerical solutions of Maxwell's equations. Specifically, we apply this methodology to three physical problems shock-vortex interactions, a plane free shear flow and an axisymmetric jet- with emphasis on acoustic wave propagation. Our numerical results indicate that the use of absorbing layers effectively minimizes numerical reflection in all three problems considered.

Hayder, M. Ehtesham↗
NASA NTRS1996

Ion Viscosity Mediated by Tangled Magnetic Fields: An Application to Black Hole Accretion Disks

We examine the viscosity associated with the shear stress exerted by ions in the presence of a tangled magnetic field. As an application, we consider the effect of this mechanism on the structure of black hole accretion disks. We do not attempt to include a self-consistent description of the magnetic field. Instead, we assume the existence of a tangled field with coherence length lambda(sub coh), which is the average distance between the magnetic 'kinks' that scatter the particles. For simplicity, we assume that the field is self-similar, and take lambda(sub coh) to be a fixed fraction zeta of the local disk height H. Ion viscosity in the presence of magnetic fields is generally taken to be the cross-field viscosity, wherein the effective mean free path is the ion Larmor radius lambda(sub L), which is much less than the ion-ion Coulomb mean free path A(sub ii) in hot accretion disks. However, we arrive at a formulation for a 'hybrid' viscosity in which the tangled magnetic field acts as an intermediary in the transfer of momentum between different layers in the shear flow. The hybrid viscosity greatly exceeds the standard cross-field viscosity when (lambda/lambda(sub L)) much greater than (lambda(sub L)/lambda(sub ii)), where lambda = ((lambda(sub ii)(sup -1) + lambda(sub (coh)(sup -1))(sup -1) is the effective mean free path for the ions. This inequality is well satisfied in hot accretion disks, which suggests that the ions may play a much larger role in the momentum transfer process in the presence of magnetic fields than was previously thought. The effect of the hybrid viscosity on the structure of a steady-state, two-temperature, quasi-Keplerian accretion disk is analyzed. The hybrid viscosity is influenced by the degree to which the magnetic field is tangled (represented by zeta = lambda(sub coh)), and also by the relative accretion rate M/M(sub E), where M(sub E) = L(sub E)/c(sup 2) and L(sub E) is the Eddington luminosity. We find that ion viscosity in the presence of magnetic fields (hybrid viscosity) can dominate over conventional magnetic viscosity for fields that are tangled on sufficiently small scales.

Subramanian, Prasad↗
NASA NTRS1981

Numerical Simulation of Three-Dimensional Boattail Afterbody Flowfields

The thin shear-layer approximations of the three-dimensional, compressible Navier-Stokes equations are solved for subsonic, transonic, and supersonic now over axisymmetric boattail bodies at moderate angles of attack. The plume is simulated by a solid body configuration identical to those used In experimental tests. An implicit algorithm of second-order accuracy is used to solve the equations on the ILLIAC 4 computer. The turbulence is expressed by an algebraic model applicable to three-dimensional flowfields with moderate separation. The formulation used is attractive in its independence of boundary-layer parameters. Such a simple model, however, is incapable of supporting detailed quantitative descriptions of complex shear flows. Never-the-less, good qualitative comparisons are found with three different sets of experimental date. Quantitative improvement will depend on improved turbulence transport descriptions.

Deiwert, G. S.↗
NASA NTRS1997

Annual Research Briefs

This report contains the 1997 annual progress reports of the research fellows and students supported by the Center for Turbulence Research (CTR). Titles include: Invariant modeling in large-eddy simulation of turbulence; Validation of large-eddy simulation in a plain asymmetric diffuser; Progress in large-eddy simulation of trailing-edge turbulence and aeronautics; Resolution requirements in large-eddy simulations of shear flows; A general theory of discrete filtering for LES in complex geometry; On the use of discrete filters for large eddy simulation; Wall models in large eddy simulation of separated flow; Perspectives for ensemble average LES; Anisotropic grid-based formulas for subgrid-scale models; Some modeling requirements for wall models in large eddy simulation; Numerical simulation of 3D turbulent boundary layers using the V2F model; Accurate modeling of impinging jet heat transfer; Application of turbulence models to high-lift airfoils; Advances in structure-based turbulence modeling; Incorporating realistic chemistry into direct numerical simulations of turbulent non-premixed combustion; Effects of small-scale structure on turbulent mixing; Turbulent premixed combustion in the laminar flamelet and the thin reaction zone regime; Large eddy simulation of combustion instabilities in turbulent premixed burners; On the generation of vorticity at a free-surface; Active control of turbulent channel flow; A generalized framework for robust control in fluid mechanics; Combined immersed-boundary/B-spline methods for simulations of flow in complex geometries; and DNS of shock boundary-layer interaction - preliminary results for compression ramp flow.

Spinks, Debra↗
NASA NTRS2000

Theory of the lattice Boltzmann Method: Dispersion, Dissipation, Isotropy, Galilean Invariance, and Stability

The generalized hydrodynamics (the wave vector dependence of the transport coefficients) of a generalized lattice Boltzmann equation (LBE) is studied in detail. The generalized lattice Boltzmann equation is constructed in moment space rather than in discrete velocity space. The generalized hydrodynamics of the model is obtained by solving the dispersion equation of the linearized LBE either analytically by using perturbation technique or numerically. The proposed LBE model has a maximum number of adjustable parameters for the given set of discrete velocities. Generalized hydrodynamics characterizes dispersion, dissipation (hyper-viscosities), anisotropy, and lack of Galilean invariance of the model, and can be applied to select the values of the adjustable parameters which optimize the properties of the model. The proposed generalized hydrodynamic analysis also provides some insights into stability and proper initial conditions for LBE simulations. The stability properties of some 2D LBE models are analyzed and compared with each other in the parameter space of the mean streaming velocity and the viscous relaxation time. The procedure described in this work can be applied to analyze other LBE models. As examples, LBE models with various interpolation schemes are analyzed. Numerical results on shear flow with an initially discontinuous velocity profile (shock) with or without a constant streaming velocity are shown to demonstrate the dispersion effects in the LBE model; the results compare favorably with our theoretical analysis. We also show that whereas linear analysis of the LBE evolution operator is equivalent to Chapman-Enskog analysis in the long wave-length limit (wave vector k = 0), it can also provide results for large values of k. Such results are important for the stability and other hydrodynamic properties of the LBE method and cannot be obtained through Chapman-Enskog analysis.

Lallemand, Pierre↗
NASA NTRS2001

Vorticity and Wave Motion in a Compressible Protoplanetary Disk

The impact of an isolated vortex in a compressible Keplerian disk is examined using higher order numerical solutions of the Euler and entropy-conserving Energy equations. The vortex is stretched by the background shear flow with longer lasting anticyclonic vortices persisting for about 10 vortex revolutions. Simultaneously, the vortex emits transient radial waves consisting mainly of axisymmetrical weak shock waves and a slower, nonaxisymmetric Rossby wave. These waves may contribute to certain transient events in protoplanetary disks. The vortex stretching and waves were found to have little long-term feedback on the baseline 'standard solar nebula' disk structure and confirm the extremely stable structure of non self-gravitating disks.

Davis, Sanford S.↗
NASA NTRS2004

Recent Progress in Understanding the Sun's Magnetic Dynamo

100 years ago we thought that the Sun and stars shone as a result of slow gravitational contraction over a few tens of millions of years - putting astronomers at odds with geologists who claimed that the Earth was much, much older. That mystery was solved in the 1920s and 30s with the discovery of nuclear energy (proving that the geologists had it right all along). Other scientific mysteries concerning the Sun have come and gone but three major mysteries remain: 1) How does the Sun produce sunspots with an 11-year cycle? 2) What produces the huge explosions that result in solar flares, prominence eruptions, and coronal mass ejections? and 3) Why is the Sun's outer atmosphere, the corona, so darned hot? Recent progress in solar astronomy reveals a single key to understanding all three of these mysteries.The 11-year time scale for the sunspot cycle indicates the presence of a magnetic dynamo within the Sun. For decades this dynamo was though to operate within the Sun's convection zone - the outmost 30% of the Sun where convective currents transport heat and advect magnetic lines of force. The two leading theories for the dynamo had very different models for the dynamics of the convection zone. Actual measurements of the dynamics using the techniques of helioseismology showed that both of these models had to be wrong some 20 years ago. A thin layer of strongly sheared flow at the base of the convection zone (now called the tachocline) was then taken to be the seat of the dynamo. Over the last 10 years it has become apparent that a weak meridional circulation within the convection zone also plays a key role in the dynamo. This meridional circulation has plasma rising up from the tachocline in the equatorial regions, spreading out toward the poles at a top speed of about 10-20 m/s at the surface, sinking back down to the tachocline in the polar regions, and then flowing back toward the equator at a top speed of about 1-2 m/s in the tachocline itself. Recent dynamo models that include this meridional flow now appear to have some power for predicting the size of future sunspot cycles.

Hathaway, David. H.↗
NASA NTRS2008

Spatially Developing Secondary Instabilities and Attachment Line Instability in Supersonic Boundary Layers

This paper reports on progress towards developing a spatial stability code for compressible shear flows with two inhomogeneous directions, such as crossflow dominated swept-wing boundary layers and attachment line flows. Certain unique aspects of formulating a spatial, two-dimensional eigenvalue problem for the secondary instability of finite amplitude crossflow vortices are discussed. A primary test case used for parameter study corresponds to the low-speed, NLF-0415(b) airfoil configuration as tested in the ASU Unsteady Wind Tunnel, wherein a spanwise periodic array of roughness elements was placed near the leading edge in order to excite stationary crossflow modes with a specified fundamental wavelength. The two classes of flow conditions selected for this analysis include those for which the roughness array spacing corresponds to either the naturally dominant crossflow wavelength, or a subcritical wavelength that serves to reduce the growth of the naturally excited dominant crossflow modes. Numerical predictions are compared with the measured database, both as indirect validation for the spatial instability analysis and to provide a basis for comparison with a higher Reynolds number, supersonic swept-wing configuration. Application of the eigenvalue analysis to the supersonic configuration reveals that a broad spectrum of stationary crossflow modes can sustain sufficiently strong secondary instabilities as to potentially cause transition over this configuration. Implications of this finding for transition control in swept wing boundary layers are examined. Finally, extension of the spatial stability analysis to supersonic attachment line flows is also considered.

Li, Fei↗
NASA NTRS2008

Topological Evolution of a Fast Magnetic Breakout CME in 3-Dimensions

W present the extension of the magnetic breakout model for CME initiation to a fully 3-dimensional, spherical geometry. Given the increased complexity of the dynamic magnetic field interactions in 3-dimensions, we first present a summary of the well known axisymmetric breakout scenario in terms of the topological evolution associated with the various phases of the eruptive process. In this context, we discuss the completely analogous topological evolution during the magnetic breakout CME initiation process in the simplest 3-dimensional multipolar system. We show that an extended bipolar active region embedded in an oppositely directed background dipole field has all the necessary topological features required for magnetic breakout, i.e. a fan separatrix surface between the two distinct flux systems, a pair of spine fieldlines, and a true 3-dimensional coronal null point at their intersection. We then present the results of a numerical MHD simulation of this 3-dimensional system where boundary shearing flows introduce free magnetic energy, eventually leading to a fast magnetic breakout CME. The eruptive flare reconnection facilitates the rapid conversion of this stored free magnetic energy into kinetic energy and the associated acceleration causes the erupting field and plasma structure to reach an asymptotic eruption velocity of greater than or approx. equal to 1100 km/s over an approx.15 minute time period. The simulation results are discussed using the topological insight developed to interpret the various phases of the eruption and the complex, dynamic, and interacting magnetic field structures.

Lynch, B. J.↗
NASA NTRS2011

Spatially Developing Secondary Instabilities in Compressible Swept Airfoil Boundary Layers

Two-dimensional eigenvalue analysis is used on a massive scale to study spatial instabilities of compressible shear flows with two inhomogeneous directions. The main focus of the study is crossflow dominated swept-wing boundary layers although the methodology can also be applied to study other type of flows, such as the attachment-line flow. Certain unique aspects of formulating a spatial, two-dimensional eigenvalue problem for the secondary instability of finite amplitude crossflow vortices are discussed, namely, fixing the spatial growth direction unambiguously through a non-orthogonal formulation of the linearized disturbance equations. A primary test case used for parameter study corresponds to the low-speed, NLF-0415(b) airfoil configuration as tested in the ASU Unsteady Wind Tunnel, wherein a spanwise periodic array of roughness elements was placed near the leading edge in order to excite stationary crossflow modes with a specified fundamental wavelength. The two classes of flow conditions selected for this analysis include those for which the roughness array spacing corresponds to either the naturally dominant crossflow wavelength, or a subcritical wavelength that serves to reduce the growth of the naturally excited dominant crossflow modes. Numerical predictions are compared with the measured database, both as indirect validation for the spatial instability analysis and to provide a basis for comparison with a higher Reynolds number, supersonic swept-wing configuration. Application of the eigenvalue analysis to the supersonic configuration reveals that a broad spectrum of stationary crossflow modes can sustain sufficiently strong secondary instabilities as to potentially cause transition over this configuration. Implications of this finding for transition control in swept wing boundary layers are examined.

Li, Fei↗
NASA NTRS2003

Growing Three-Dimensional Corneal Tissue in a Bioreactor

Spheroids of corneal tissue about 5 mm in diameter have been grown in a bioreactor from an in vitro culture of primary rabbit corneal cells to illustrate the production of optic cells from aggregates and tissue. In comparison with corneal tissues previously grown in vitro by other techniques, this tissue approximates intact corneal tissue more closely in both size and structure. This novel three-dimensional tissue can be used to model cell structures and functions in normal and abnormal corneas. Efforts continue to refine the present in vitro method into one for producing human corneal tissue to overcome the chronic shortage of donors for corneal transplants: The method would be used to prepare corneal tissues, either from in vitro cultures of a patient s own cells or from a well-defined culture from another human donor known to be healthy. As explained in several articles in prior issues of NASA Tech Briefs, generally cylindrical horizontal rotating bioreactors have been developed to provide nutrient-solution environments conducive to the 30 NASA Tech Briefs, October 2003 growth of delicate animal cells, with gentle, low-shear flow conditions that keep the cells in suspension without damaging them. The horizontal rotating bioreactor used in this method, denoted by the acronym "HARV," was described in "High-Aspect-Ratio Rotating Cell-Culture Vessel" (MSC-21662), NASA Tech Briefs, Vol. 16, No. 5 (May, 1992), page 150.

Spaulding, Glen F.↗
NASA NTRS2014

Hi-C Observations of an Active Region Corona, and Investigation of the Underlying Magnetic Structure

The solar corona is much hotter (>=10(exp 6) K) than its surface (approx 6000 K), puzzling astrophysicists for several decades. Active region (AR) corona is again hotter than the quiet Sun (QS) corona by a factor of 4-10. The most widely accepted mechanism that could heat the active region corona is the energy release by current dissipation via reconnection of braided magnetic field structure, first proposed by E. N. Parker three decades ago. The first observational evidence for this mechanism has only recently been presented by Cirtain et al. by using High-resolution Coronal Imager (Hi-C) observations of an AR corona at a spatial resolution of 0.2 arcsec, which is required to resolve the coronal loops, and was not available before the rocket flight of Hi-C in July 2012. The Hi-C project is led by NASA/MSFC. In the case of the QS, work done by convection/granulation on the inter-granular feet of the coronal field lines translates into the heat observed in the corona. In the case of the AR, as here, there could be flux emergence, cancellation/submergence, or shear flows generating large stress and tension in coronal field loops which is released as heat in the corona. We are currently investigating the changes taking place in photospheric feet of the magnetic field involved with brightenings in the Hi-C AR corona. For this purpose, we are also using SDO/AIA data of +/- 2 hours around the 5 minutes Hi-C flight. In the present talk, I will first summarize some of the results of the Hi-C observations and then present some results from our recent analysis on what photospheric processes feed the magnetic energy that dissipates into heat in coronal loops.

Tiwari, S. K.↗
NASA NTRS2016

Velocity Statistics and Spectra in Three-Stream Jets

Velocimetry measurements were obtained in three-stream jets at the NASA Glenn Research Center Nozzle Acoustics Test Rig using the time-resolved Doppler global velocimetry technique. These measurements afford exceptional frequency response, to 125 kHz bandwidth, in order to study the detailed dynamics of turbulence in developing shear flows. Mean stream-wise velocity is compared to measurements acquired using particle image velocimetry for validation. Detailed results for convective velocity distributions throughout an axisymmetric plume and the thick side of a plume with an offset third-stream duct are provided. The convective velocity results exhibit that, as expected, the eddy speeds are reduced on the thick side of the plume compared to the axisymmetric case. The results indicate that the time-resolved Doppler global velocimetry method holds promise for obtaining results valuable to the implementation and refinement of jet noise prediction methods being developed for three-stream jets.

Three-Stream Jets↗