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At least 1,243 records · Page 69

An analysis of supersonic flows with low-Reynolds number compressible two-equation turbulence models using LU finite volume implicit numerical techniques

A generalized flow solver using an implicit Lower-upper (LU) diagonal decomposition based numerical technique has been coupled with three low-Reynolds number kappa-epsilon models for analysis of problems with engineering applications. The feasibility of using the LU technique to obtain efficient solutions to supersonic problems using the kappa-epsilon model has been demonstrated. The flow solver is then used to explore limitations and convergence characteristics of several popular two equation turbulence models. Several changes to the LU solver have been made to improve the efficiency of turbulent flow predictions. In general, the low-Reynolds number kappa-epsilon models are easier to implement than the models with wall-functions, but require much finer near-wall grid to accurately resolve the physics. The three kappa-epsilon models use different approaches to characterize the near wall regions of the flow. Therefore, the limitations imposed by the near wall characteristics have been carefully resolved. The convergence characteristics of a particular model using a given numerical technique are also an important, but most often overlooked, aspect of turbulence model predictions. It is found that some convergence characteristics could be sacrificed for more accurate near-wall prediction. However, even this gain in accuracy is not sufficient to model the effects of an external pressure gradient imposed by a shock-wave/ boundary-layer interaction. Additional work on turbulence models, especially for compressibility, is required since the solutions obtained with base line turbulence are in only reasonable agreement with the experimental data for the viscous interaction problems.

Lee, J.↗

Localized phase contrast imaging at the Wendelstein 7-X stellarator

In its basic form, phase contrast imaging (PCI) provides line-integrated measurements of electron density fluctuations in plasmas. As turbulent fluctuations in magnetically confined plasmas have wave vectors almost perpendicular to the background magnetic field, the signals scattered by fluctuations from different parts of the PCI line-of-sight (LoS) are spatially separated in focal planes of the plasma. This allows localized PCI measurements by placing a mask in such a plane, to only permit signals from specific parts of the LoS to reach the PCI detectors. The present paper describes modeling and design of localization masks for the PCI system at the Wendelstein 7-X (W7-X) stellarator as well as the first results obtained using the masks in the recent long-pulse W7-X experimental campaign. During this project, we have extended the theory describing the mask response within the Fraunhofer diffraction model. As a novel development, we show from first principles that the mask response is determined by the fraction of power of the scattered beam spots that passes the mask. These insights have been used to select the W7-X mask design, consisting of a circular cutout, allowing the unscattered beam spot to pass the mask, with wedges covering a fixed angular range outside the central cutout. In the recent W7-X experimental campaign, the masks have verified the location of the main turbulence features observed by the PCI system and provided new information about the location of short-wavelength magnetohydrodynamic modes.

Physics↗

Modeling rf sheath formation in turbulent tokamak boundary plasma

During ICRF antenna operation, complex interactions between turbulent density profiles, nonlinear RF sheaths, and RF-induced convective transport are observed to alter plasma density in the tokamak edge [D’Ippolito et al., Nucl. Fusion 38, 1543 (1998)]. In this work, we explore the physics of such interactions via numerical modeling, using a nonlinear EM/plasma/sheath code (VSim) and profiles obtained from a fluid plasma turbulence code (Hermes) in a 3D slab domain containing biased side-wall limiters. RF-rectified sheath formation on antenna and limiter surfaces is observed as electromagnetic waves launched by the antenna are refracted through the turbulent density profile. On transport timescales, such sheath potentials have been shown to influence both the mean species density and its RMS fluctuation spectrum [Smithe et al., these proceedings]. On the faster RF timescales, we demonstrate that the converse is also true – regions of high plasma density near material surfaces give rise to the highest sheath potential amplitudes. When density is turbulent and spatially nonuniform, localized regions of high sheath potential (hotspots) may develop where high-density filaments intersect material surfaces. Such hotspots are of particular concern as sources of impurity sputtering, and we explore their behavior in response to changes both to the local plasma density and to antenna operating parameters and structure. Related results exploring the role of Faraday shields and/or enclosing structures in suppressing high sheath potentials for other devices (e.g. SPARC) will also be shown.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Langmuir turbulence in the auroral ionosphere 2: Nonlinear theory and simulations

A theoretical interpretation of sounding rocket measurements of intense Langmuir wave fields (less than or equal to 500 mV/m) driven by a stream of 20 eV to 4 keV electrons in the lower auroral zone is developed. This interpretation is based on the ability of the 10 microseconds sampling rate of the wave detector to temporally resolve the structure of the Langmuir wave field envelope. A modified form of the Zakharov equations is used to numerically study beam-driven Langmuir turbulence in the presence of a moderate magnetic field (OMEGA (sub e) approximately equals Omega (sub pe). Strong Landau damping on observed nonthermal scattered electrons, which is treated in a companion paper (Newman et al., this issue), plays an important role by inhibiting backscatter cascade and the development of strong turbulence. A parameterized model of the linear electron stream-driven wave instability is introduced, which incorporates limited quasilinear plateau formation. A reasonable set of parameters is found that yields semiquantitative agreement between observed properties of the Langmuir fields and the results of Zakharov equation simulations, including the amplitude and characteristic frequency of the electric field envelope modulations.

Newman, D. L.↗

Nonlinear dynamics of small-scale Alfvén waves

Herein we study the nonlinear evolution of very oblique small-scale Alfvén waves with k ⊥ d i ≳1. At these scales, the waves become significantly compressive, unlike in magnetohydrodynamics, due to the Hall term in the equations. We demonstrate that when frequencies are small compared to the ion gyrofrequency and amplitudes are small compared to unity, no new nonlinear interaction appears due to the Hall term alone at the lowest non-trivial order, even when k ⊥ d i ~1. However, at the second non-trivial order, we discover that the Hall physics leads to a slow but resonant nonlinear interaction between co-propagating Alfvén waves, an inherently three-dimensional effect. Including the effects of finite temperature, finite frequency, and electron inertia, the two-fluid Alfvén wave also becomes dispersive once one or more of k ⊥ ρ s , k ⊥ d e , or k ∥ d i becomes significant: for oblique waves at low β as studied here, this can be at a much smaller scale than d i . We show that the timescale for one-dimensional steepening of two-fluid Alfvén waves is only significant at these smaller dispersive scales, and also derive an expression for the amplitude of driven harmonics of a primary wave. Importantly, both new effects are absent in gyrokinetics and other commonly used reduced two-fluid models. Our calculations have relevance for the interpretation of laboratory Alfvén wave experiments, as well as shedding light on the physics of turbulence in the solar corona and inner solar wind, where the dominant nonlinear interaction between counter-propagating waves is suppressed, allowing these new effects to become important.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

On the physics of waves in the solar atmosphere: Wave heating and wind acceleration

This paper presents work performed on the generation and physics of acoustic waves in the solar atmosphere. The investigators have incorporated spatial and temporal turbulent energy spectra in a newly corrected version of the Lighthill-Stein theory of acoustic wave generation in order to calculate the acoustic wave energy fluxes generated in the solar convective zone. The investigators have also revised and improved the treatment of the generation of magnetic flux tube waves, which can carry energy along the tubes far away from the region of their origin, and have calculated the tube wave energy fluxes for the sun. They also examine the transfer of the wave energy originated in the solar convective zone to the outer atmospheric layers through computation of wave propagation and dissipation in highly nonhomogeneous solar atmosphere. These waves may efficiently heat the solar atmosphere and the heating will be especially significant in the chromospheric network. It is also shown that the role played by Alfven waves in solar wind acceleration and coronal hole heating is dominant. The second part of the project concerned investigation of wave propagation in highly inhomogeneous stellar atmospheres using an approach based on an analytic tool developed by Musielak, Fontenla, and Moore. In addition, a new technique based on Dirac equations has been developed to investigate coupling between different MHD waves propagating in stratified stellar atmospheres.

Musielak, Z. E.↗

On the physics of waves in the solar atmosphere: Wave heating and wind acceleration

This paper presents work performed on the generation and physics of acoustic waves in the solar atmosphere. The investigators have incorporated spatial and temporal turbulent energy spectra in a newly corrected version of the Lighthill-Stein theory of acoustic wave generation in order to calculate the acoustic wave energy fluxes generated in the solar convective zone. The investigators have also revised and improved the treatment of the generation of magnetic flux tube waves, which can carry energy along the tubes far away from the region of their origin, and have calculated the tube energy fluxes for the sun. They also examine the transfer of the wave energy originated in the solar convective zone to the outer atmospheric layers through computation of wave propagation and dissipation in highly nonhomogeneous solar atmosphere. These waves may efficiently heat the solar atmosphere and the heating will be especially significant in the chromospheric network. It is also shown that the role played by Alfven waves in solar wind acceleration and coronal hole heating is dominant. The second part of the project concerned investigation of wave propagation in highly inhomogeneous stellar atmospheres using an approach based on an analytic tool developed by Musielak, Fontenla, and Moore. In addition, a new technique based on Dirac equations has been developed to investigate coupling between different MHD waves propagating in stratified stellar atmospheres.

Musielak, Z. E.↗

Theory of the tertiary instability and the Dimits shift within a scalar model

The Dimits shift is the shift between the threshold of the drift-wave primary instability and the actual onset of turbulent transport in magnetized plasma. It is generally attributed to the suppression of turbulence by zonal flows, but developing a more detailed understanding calls for consideration of specific reduced models. The modified Terry--Horton system has been proposed by St-Onge [J. Plasma Phys. {\bf 83}, 905830504 (2017)] as a minimal model capturing the Dimits shift. Here, we use this model to develop an analytic theory of the Dimits shift and a related theory of the tertiary instability of zonal flows. We show that tertiary modes are localized near extrema of the zonal velocity $U(x)$, where $x$ is the radial coordinate. By approximating $U(x)$ with a parabola, we derive the tertiary-instability growth rate using two different methods and show that the tertiary instability is essentially the primary drift-wave instability modified by the local $U''$. Then, depending on $U''$, the tertiary instability can be suppressed or unleashed. The former corresponds to the case when zonal flows are strong enough to suppress turbulence (Dimits regime), while the latter corresponds to the case when zonal flows are unstable and turbulence develops. This understanding is different from the traditional paradigm that turbulence is controlled by the flow shear $U'$. Our analytic predictions are in agreement with direct numerical simulations of the modified Terry--Horton system.

fusion plasmas↗

Auroral kilometric radiation - A theoretical review

Auroral kilometric radiation (AKR) is a high-density radio wave radiation in the frequency band from 50 to 750 kHz, with a peak around 250 kHz, that has been observed emanating from the auroral zone. In connection with its low frequency, the radiation can not penetrate through the ionosphere to earth, so all observations have been made by satellite. The AKR is closely correlated with the occurrence of discrete auroral arcs, which are believed to be generated by intense inverted V electron precipitation bands. A review is presented of several theories which have been proposed to explain the observed AKR. Attention is given to the conversion of electron cyclotron wave to O mode, the coherent amplification of gyroemission by velocity space instabilities, beam-driven electromagnetic instability via low-frequency turbulence, soliton radiation, loss cone instability, nonlinear beating of electrostatic waves, and the beam amplification of electromagnetic wave via coherent EIC density fluctuations.

Grabbe, C. L.↗

Langmuir turbulence in the auroral ionosphere 1: Linear theory

Intense bursts of Langmuir waves with electric fields of 50 to 500 mV / m have been frequently observed at altitudes greater than 500 km in the auroral ionosphere. These bursts are driven by 20 eV to 4 keV field-aligned electrons, which are embedded in an approximately isotropic nonthermal tail of scattered electrons. The Langmuir bursts are often observed at altitudes where the ionosphere is moderately magnetized (OMEGA (sub e) approximately equals omega (sub pe)). Both the moderate magnetization and the scattered electrons have a major influence on the linear dispersion and damping of Langmuir waves. In particular, the linear dispersion is topologically different depending on whether the magnetic field is subcritical (OMEGA (sub e) less than omega (sub pe)) or supercritical (OMEGA (sub e) greater than omega (sub pe)). The correct dispersion and damping can account for the observed polarization of the Langmuir waves, which is very nearly parallel to the geomagnetic field. Inferred properties of the linear instability driven by the field-aligned electrons are discussed. The linear dispersion and damping derived here provide the basis for a nonlinear turbulence study described in a companion paper (Newman et al., this issue).

Newman, D. L.↗

The effect of turbulence on the loudness of minimized sonic boom signatures

An important issue for shaped minimized sonic booms is whether turbulence-induced distortions will adversely affect the benefits gained by shaping. This question was considerably simplified by two recent results. The first is the finding that the loudness of sonic booms is well quantified by loudness. The second is that loudness of a shaped boom is dominated by the shock waves. The issue is now the effect of turbulence on weak (1 psf or less) sonic booms. Since it is clear that molecular relaxation effects have a significant effect on shock structure and loudness, turbulence effects must be examined in conjunction with relaxation-thickened shocks. This analysis must be directed toward loudness calculations and include all pertinent mechanisms.

Plotkin, Kenneth J.↗

New Insight into Short-Wavelength Solar Wind Fluctuations from Vlasov Theory

The nature of solar wind (SW) turbulence below the proton gyroscale is a topic that is being investigated extensively nowadays, both theoretically and observationally. Although recent observations gave evidence of the dominance of kinetic Alfven waves (KAWs) at sub-ion scales with omega < omega(sub ci), other studies suggest that the KAW mode cannot carry the turbulence cascade down to electron scales and that the whistler mode (i.e., omega > omega (sub ci)) is more relevant. Here, we study key properties of the short-wavelength plasma modes under limited, but realistic, SW conditions, Typically Beta(sub i) approx. > Beta (sub e) ∼ 1 and for high oblique angles of propagation 80 deg <= Theta (sub kB) < 90 deg as observed from the Cluster spacecraft data. The linear properties of the plasma modes under these conditions are poorly known, which contrasts with the well-documented cold plasma limit and/or moderate oblique angles of propagation (Theta (sub kB) < 80 deg). Based on linear solutions of the Vlasov kinetic theory, we discuss the relevance of each plasma mode (fast, Bernstein, KAW, whistler) in carrying the energy cascade down to electron scales. We show, in particular, that the shear Alfven mode (known in the magnetohydrodynamic limit) extends at scales kappa rho (sub i) approx. > 1 to frequencies either larger or smaller than omega (sub ci), depending on the anisotropy kappa (parallel )/ kappa(perpendicular). This extension into small scales is more readily called whistler (omega > omega (sub ci)) or KAW (omega < omega (sub ci)) although the mode is essentially the same. This contrasts with the well-accepted idea that the whistler branch always develops as a continuation at high frequencies of the fast magnetosonic mode. We show, furthermore, that the whistler branch is more damped than the KAW one, which makes the latter the more relevant candidate to carry the energy cascade down to electron scales. We discuss how these new findings may facilitate resolution of the controversy concerning the nature of the small-scale turbulence, and we discuss the implications for present and future spacecraft wave measurements in the SW.

waves↗

A model for broadband jet noise amplification

A model is proposed for the change in turbulent structure of a round jet in the presence of an acoustic excitation. The excitation is assumed to trigger instability waves of a known initial amplitude at the jet exit. As these waves propagate downstream they extract energy from the mean flow and transfer it to the random turbulence. This results in an increase in the levels of the turbulence and a resulting increase in the radiated broadband noise. No calculations are presented for the noise radiation; however, an examination is made of the effect of excitation level and frequency on the jet flow. The numerical procedure allows for radial as well as axial variations in the averaged properties of jet to be calculated. The results indicate that the presence of a finite amplitude instability wave increases the spreading of the jet. It does not vary the characteristic radial shapes of both the axial mean velocity and the turbulent kinetic energy. An energy budget for the random turbulence shows that it is fed energy from the excited wave predominantly on each side of the jet lip line. This results in a broader radial shape for the turbulent kinetic energy.

Morris, P. J.↗

Multi-scale Dynamics of Kinetic Turbulence in Weakly Collisional, High-Beta Plasmas (Final Report for DOE Grant DE-SC0019046)

This grant was a collaborative grant between Prof Matt Kunz (Princeton) and Prof. Eliot Quataert. Quataert was initially a faculty member at UC Berkeley when the grant was funded but moved to Princeton during the timeframe of this grant. Over the course of this grant we made major progress on understanding turbulence and multi-scale dynamics in weakly collisional high-beta plasmas. The most important contributions included: We developed one of the most compelling theoretical explanations for a decades-old puzzle at the heart of our understanding of the origin of the solar wind. The puzzle is that many of the observations of ion temperatures and distribution functions in the solar wind are consistent with cyclotron resonant heating. However, theoretical models of MHD turbulence in the solar wind show that most of the turbulent energy remains at low frequencies below the cyclotron frequency. In Squire et al. (2022), we showed, however, that in imbalanced turbulence (in which there is an asymmetry in the Alfven-wave flux in opposite directions along the magnetic field), which is the norm in the fast solar wind, the turbulent energy reaches a ‘bottleneck’ near the ion Larmor radius, and the amplitude and characteristic frequency of the fluctuations grow until the cyclotron frequency is reached.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Observations of velocity shear driven plasma turbulence

Electrostatic and magnetic turbulence observations from Hawkeye 1 during the low-altitude portion of its elliptical orbit over the Southern Hemisphere are presented. The magnetic turbulence is confined near the auroral zone and is similar to that seen at higher altitudes by Heos 2 in the polar cusp. The electrostatic turbulence is composed of a background component with a power spectral index of 1.89 + or - 0.26 and an intense component with a power spectral index of 2.80 + or - 0.34. The intense electrostatic turbulence and the magnetic turbulence correlate with velocity shears in the convective plasma flow. Since velocity-shear instabilities are most unstable to wave vectors perpendicular to the magnetic field, the shear-correlated turbulence is anticipated to be two-dimensional in character and to have a power spectral index of 3, which agrees with that observed in the intense electrostatic turbulence.

Kintner, P. M., Jr.↗

CFD Validation Experiment of a Mach 2.5 Axisymmetric Shock-Wave Boundary-Layer Interaction

Preliminary results of an experimental investigation of a Mach 2.5 two-dimensional axisymmetric shock-wave/boundary-layer interaction (SWBLI) are presented. The purpose of the investigation is to create a SWBLI dataset specifically for CFD validation purposes. Presented herein are the details of the facility and preliminary measurements characterizing the facility and interaction region. The results will serve to define the region of interest where more detailed mean and turbulence measurements will be made.

Superonic Flow↗

Acoustic Insights into Flow Condensation Mechanisms

Two-phase thermal management systems, with both boiling and condensation processes, offer great potential and heat transfer coefficients that are orders of magnitude higher than traditional single-phase systems. However, two-phase flows can suffer from a wide range of interfacial instabilities leading to significant thermal performance degradation. In this study, we aim to detect regime transitions and characterize dominating physical mechanisms of flow condensation, such as turbulent diffusion in annular liquid film and interfacial waves, using an integrated system of acoustic, modal, and optical sensing techniques and thermofluidic characterizations. A wideband acoustic emissions sensor and high-sensitivity accelerometer are utilized to capture acoustic and vibrational signatures that signal the onset of liquid film formation and interfacial waves during flow pattern transitions. Compared to optical imaging, wideband acoustic emission sensing allows for higher sampling rates to capture high-frequency interface oscillations critical to the flow regime transitions and works well even for condensation in opaque tubes. Acoustic features (e.g., amplitude, frequency, energy, duration) are correlated with thermofluidic processes (e.g., capillary flows, turbulent flows, boiling, condensation). By relating thermal performance metrics with these dynamic signatures in acoustic and modal regimes, we explore the ability to probe and monitor critical flow regime transitions and transport efficiency in flow condensation.

Acoustic Modal Regimes↗