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Recent analysis of databases generated by direct numerical simulations of homogeneous turbulent shear flows have revealed the presence of coherent structures similar to those in turbulent boundary layers. In this paper these findings and tentative conclusions on their significance are discussed.
Abstract Sawteeth are one of the concerning instabilities in ITER and future burning plasma experiments. Sawtooth dynamics and its interaction with broadband plasma turbulence has been a challenge for predictive simulations of core transport in future fusion devices. This study provides new observations of core turbulence behavior during sawtooth oscillations in DIII-D hydrogen L-mode neutral beam injection heated plasmas in an inner wall limited configuration. A strong correlation of electron temperature and density turbulence levels with the sawtooth oscillation phase has been observed at locations inside the T e inversion radius and/or safety factor q = 1 magnetic surface. The T e turbulence amplitude in the core during the sawtooth ramp exhibits a critical T e gradient behavior inside but not near the T e inversion radius/ q = 1 magnetic surface. The most unstable mode calculated from the trapped gyro-landau fluid turbulence simulations reveal a change from low- k ion-type to low-k electron-type modes from pre- to post- sawtooth crash time periods.
ABSTRACT In this work, we find empirical evidence that the scale-dependent statistical properties of solar wind and magnetohydrodynamic (MHD) turbulence can be described in terms of a family of parametric probability distribution functions (PDFs) known as Normal Inverse Gaussian (NIG). Understanding these PDFs is one of the most important goals in turbulence theory, as they are inherently connected to the intermittent properties of solar wind turbulence. We investigate the properties of PDFs of Elsasser increments based on a large statistical sample from solar wind observations and high-resolution numerical simulations of MHD turbulence. In order to measure the PDFs and their corresponding properties, three experiments are presented: fast and slow solar wind for experimental data and a simulation of reduced MHD (RMHD) turbulence. Conditional statistics on a 23-yr-long sample of WIND data near 1 au and high-resolution pseudo-spectral simulation of steadily driven RMHD turbulence on a $2048^3$ mesh are used to construct scale-dependent PDFs. The empirical PDFs are fitted to NIG distributions, which depend on four free parameters. Our analysis shows that NIG distributions accurately capture the evolution of the PDFs, with scale-dependent parameters, from large scales characterized by a Gaussian distribution, turning to exponential tails within the inertial range and stretched exponentials at dissipative scales. We also show that empirically-measured NIG parameters exhibit well-defined scaling properties that are similar across the three empirical data sets, which may be indicative of universal behaviour.
Mesoscale-to-microscale coupling is an important tool for conducting turbulence-resolving multiscale simulations of realistic atmospheric flows, which are crucial for applications ranging from wind energy to wildfire spread studies. Different techniques are used to facilitate the development of realistic turbulence in the large-eddy simulation (LES) domain while minimizing computational cost. Here, we explore the impact of a simple and computationally efficient Stochastic Cell Perturbation method using momentum perturbation (SCPM-M) to accelerate turbulence generation in boundary-coupled LES simulations using the Weather Research and Forecasting model. We simulate a convective boundary layer (CBL) to characterize the production and dissipation of turbulent kinetic energy (TKE) and the variation of TKE budget terms. Furthermore, we evaluate the impact of applying momentum perturbations of three magnitudes below, up to, and above the CBL on the TKE budget terms. Momentum perturbations greatly reduce the fetch associated with turbulence generation. When applied to half the vertical extent of the boundary layer, momentum perturbations produce an adequate amount of turbulence. However, when applied above the CBL, additional structures are generated at the top of the CBL, near the inversion layer. The magnitudes of the TKE budgets produced by SCPM-M when applied at varying heights and with different perturbation amplitudes are always higher near the surface and inversion layer than those produced by No-SCPM, as are their contributions to the TKE. This study provides a better understanding of how SCPM-M reduces computational costs and how different budget terms contribute to TKE in a boundary-coupled LES simulation.
An experimental investigation was made on a simulated reusable-surface-insulation tile array in a turbulent boundary layer to determine aerodynamic-heating distributions representative of those expected on the surface of the shuttle orbiter during earth entry due to the presence of longitudinal and transverse surface gaps. The tests were conducted in an 8-foot high-temperature structures tunnel in a test medium of methane-air combustion products at a nominal Mach number of 6.6 and over a free-stream Reynolds number range from 2,000,000 to 4,900,000 per meter (600,000 to 1,500,000 per foot). The results were used to assess the aerodynamic heating effects produced by parameters that include gap width, boundary-layer displacement thickness, in-line and staggered tile arrangement, and tile protrusion.
Wall-pressure fluctuations are a practically robust input for real-time control systems aimed at modifying wall-bounded turbulence. The scaling behaviour of the wall-pressure–velocity coupling requires investigation to properly design a controller with such input data so that it can actuate upon the desired turbulent structures. A comprehensive database from direct numerical simulations (DNS) of turbulent channel flow is used for this purpose, spanning a Reynolds-number range$Re_\tau \approx 550\unicode{x2013}5200$. Spectral analysis reveals that the streamwise velocity is most strongly coupled to the linear term of the wall pressure, at a Reynolds-number invariant distance-from-the-wall scaling of$\lambda _x/y \approx 14$(and$\lambda _x/y \approx 8$for the wall-normal velocity). When extending the analysis to both homogeneous directions in$x$and$y$, the peak coherence is centred at$\lambda _x/\lambda _z \approx 2$and$\lambda _x/\lambda _z \approx 1$for$p_w$and$u$, and$p_w$and$v$, respectively. A stronger coherence is retrieved when the quadratic term of the wall pressure is concerned, but there is only little evidence for a wall-attached-eddy type of scaling. An experimental dataset comprising simultaneous measurements of wall pressure and velocity complements the DNS-based findings at one value of$Re_\tau \approx 2$k, with ample evidence that the DNS-inferred correlations can be replicated with experimental pressure data subject to significant levels of (acoustic) facility noise. It is furthermore shown that velocity-state estimations can be achieved with good accuracy by including both the linear and quadratic terms of the wall pressure. An accuracy of up to 72 % in the binary state of the streamwise velocity fluctuations in the logarithmic region is achieved; this corresponds to a correlation coefficient of$\approx$0.6. This thus demonstrates that wall-pressure sensing for velocity-state estimation – e.g. for use in real-time control of wall-bounded turbulence – has merit in terms of its realization at a range of Reynolds numbers.
Without resort to any modeling, subgrid-scale eddy viscosity is computed from the results of high-resolution (64 cubed and 128 cubed grid points) direct numerical simulations of three-dimensional homogeneous isotropic decaying turbulence. In these simulations the eddy viscosity peaks sharply at the cutoff wavenumber, in rough agreement with the results of Kraichnan (1976). In addition, in the low-wavenumber range the eddy viscosity may be negative, contrary to the generally accepted concept of subgrid-scale eddy viscosity. Some possible explanations of this behavior are discussed.
The National Full-Scale Aerodynamics Complex 80- by 120-Foot Wind Tunnel (80x120) was dedicated in 1987 and rated at 100 knots for full-scale aircraft testing at NASA Ames Research Center. The 80x120 is the world’s largest wind tunnel, designed as an open circuit tunnel with a large aerodynamically treated inlet open to the ambient atmospheric air. In 2017, damage was sustained within the wind tunnel drive system, opening a window to do testing using the existing 1/50th-scale model of the 80- by 120-Foot Wind Tunnel within the full-scale 80- by 120-Foot Wind tunnel test section. The objective of the research was to quantify the turbulence levels within the 1/50th-scale test section as a function of onset atmospheric wind direction (± 90 deg from tunnel center-line), variable test section speed (5 – 50 m/s) and purposeful obtrusion of wind flow into the inlet. The model wind tunnel inlet, contraction, and test section are geometrically identical to that of the full-scale wind tunnel and model testing provides aerodynamic performance characteristics under controlled test conditions allowing for insight into the full-scale test section flow quality. The test section turbulence levels are minimally affected by the onset direction of the ambient atmospheric wind, but are dramatically affected by the speed in the tunnel while operated in the presence of winds. Original design specifications were axial/vertical/lateral turbulence ≤ 0.5% at maximum test section speed, though early full scale tunnel testing determined that lateral turbulence would be ≤ 0.6%. For test section speeds ≥ 30 m/s the tunnel is within the design specification limits. Between 5 m/s and 30 m/s, the test section turbulence levels are dependent on the onset wind direction and test section speed where test section turbulence in the axial, vertical and lateral directions was seen to be between 0.5% and 1% and, at times, greater than 1%. Finally, testing was performed with blockage designs at the inlet to disrupt the wind flow quality entering the tunnel contraction zone in an attempt to create higher levels of turbulence for high turbulent test conditions simulating the earth’s boundary layer. The highest turbulence levels measured were 6% in the axial direction by use of large spires designed to obstruct ≈ 50% of the inlet area.
Two multi-scale-type turbulence models are implemented in the PAB3D solver. The models are based on modifying the Reynolds Averaged Navier-Stokes (RANS) equations. The first scheme is a hybrid RANS/LES model utilizing the two-equation (k(epsilon)) model with a RANS/LES transition function dependent on grid spacing and the computed turbulence length scale. The second scheme is a modified version of the Partially Averaged Navier-Stokes (PANS) model, where the unresolved kinetic energy parameter (f(sub k)) is allowed to vary as a function of grid spacing and the turbulence length scale. This parameter is estimated based on a novel two-stage procedure to efficiently estimate the level of scale resolution possible for a given flow on a given grid for Partial Averaged Navier-Stokes (PANS). It has been found that the prescribed scale resolution can play a major role in obtaining accurate flow solutions. The parameter f(sub k) varies between zero and one and equal to one in the viscous sub layer, and when the RANS turbulent viscosity becomes smaller than the LES viscosity. The formulation, usage methodology, and validation examples are presented to demonstrate the enhancement of PAB3D's time-accurate and turbulence modeling capabilities. The accurate simulations of flow and turbulent quantities will provide valuable tool for accurate jet noise predictions. Solutions from these models are compared to RANS results and experimental data for high-temperature jet flows. The current results show promise for the capability of hybrid RANS/LES and PANS in simulating such flow phenomena.
A subgrid electron–temperature–gradient (ETG) model is demonstrated here which averages local electron-scale turbulence over intermediate scales in space and time to include in global ion–temperature–gradient (ITG) simulations. This approach results in ion-scale equations, which incorporate the electron heat transport from ETG turbulence and the effects of electron-scale turbulence on the ion scale. Flux-tube ETG Cyclone Base Case simulations are performed at different radial locations and a kinetic form of the flux is added to global ion-scale (IS) simulations as a source term. Analytic radial profiles of ETG heat flux are constructed and compared to flux-tube results at multiple radial locations. Different ratios of ITG to ETG heat flux levels are considered and the results of capturing ETG heat transport in global ion-scale simulations are discussed. The potential coupling of the ETG streamer potential and intermediate-scale zonal flows to the ion scale is further addressed.
Large eddy simulations of three convective turbulence events are investigated and compared with observational data. Two events were characterized with severe turbulence and the other with moderate turbulence. Two of the events occurred during NASA s turbulence flight experiments during the spring of 2002, and the third was an event identified by the Flight Operational Quality Assurance (FOQA) Program. Each event was associated with developing or ongoing convection and was characterized by regions of low to moderate radar reflectivity. Model comparisons with observations are favorable. The data sets from these simulations can be used to test turbulence detection sensors.
In the context of Large Eddy Simulations (LES), the effects of inflow turbulence are investigated through the Synthetic Eddy Method (SEM). The growth rate of a turbulent compressible mixing layer corresponding to operating conditions of GeobelDutton Case 2 is investigated herein. The effects of spanwise width on the growth rate of the mixing layer is investigated such that spanwise width independence is reached. The error in neglecting inflow turbulence effects is quantified by comparing two methodologies: (1) Hybrid-RANS-LES methodology and (2) SEM-LES methodology. Best practices learned from Case 2 are developed herein and then applied to a higher convective mach number corresponding to Case 4 experiments of GeobelDutton.
The low-edge rotation, intrinsically ELM-free, and improved confinement wide-pedestal quiescent H-mode (QH-mode), discovered in DIII-D tokamak, has pedestal widths exceeding the EPED-kinetic-ballooning mode (KBM) model scaling typically by at least 25%. Ion-scale ($k_yp_s$ < 1) microturbulence and its role in setting the pedestal structure is investigated using the radially local δ$f$ gyrokinetic code CGYRO. The electromagnetic trapped electron mode (TEM) is unstable at the pedestal top, while plasma beta (β$_e$) is ∼60% below the KBM onset threshold and the electron temperature gradient mode is found to be unstable in the peak gradient region. Nonlinear simulation reveals that the ion-scale turbulence could produce electron energy flux consistent with the flux inferred from power balance at the pedestal top, with a reasonable variation of the local shearing rate; and the local neoclassical transport from NEO is dominant over the simulated turbulent transport in the ion energy flux channel. The simulated ion-scale turbulence produces much lower electron energy flux than inferred from experiment in the pedestal peak gradient region. A correction to the EPED-KBM pedestal width scaling is obtained based on the two-dimensional scan of pedestal top plasma beta (β$_e$) and normalized electron density and temperature scale lengths,${a}$/${L_n}_e$, ${a}$/${L_T}_n$using CGYRO linear simulations. Mode transitions among TEM, micro-tearing mode, ion-temperature gradient mode and KBM, are observed in the 2D scan at the pedestal top. A fixed normalized growth rate for these drift-type modes is taken to determine the pedestal width scaling, which shows good consistency with the QH experimental database on pedestal heights and widths. The onset of KBM instabilities and the local E × B shear suppression criterion set the lower and upper limit for the pedestal width of standard QH-mode, wide-pedestal QH-mode and type-I ELMy H mode. A potentially higher and wider pedestal is expected from the new scaling of pedestal width. This work presents an improved understanding of the ion-scale micro-turbulence of wide-pedestal QH-mode and sheds light on a promising scenario for future reactors, including ITER and beyond.
Compressibility effects were studied on turbulence by direct numerical simulation of homogeneous shear flow. A primary observation is that the growth of the turbulent kinetic energy decreases with increasing turbulent Mach number. The sinks provided by compressible dissipation and the pressure dilatation, along with reduced Reynolds shear stress, are shown to contribute to the reduced growth of kinetic energy. Models are proposed for these dilatational terms and verified by direct comparison with the simulations. The differences between the incompressible and compressible fields are brought out by the examination of spectra, statistical moments, and structure of the rate of strain tensor.
Compressibility effects were studied on turbulence by direct numerical simulation of homogeneous shear flow. A primary observation is that the growth of the turbulent kinetic energy decreases with increasing turbulent Mach number. The sinks provided by compressible dissipation and the pressure dilatation, along with reduced Reynolds shear stress, are shown to contribute to the reduced growth of kinetic energy. Models are proposed for these dilatational terms and verified by direct comparison with the simulations. The differences between the incompressible and compressible fields are brought out by the examination of spectra, statistical moments, and structure of the rate of strain tensor.
Gyrokinetic simulation of a dedicated pedestal density ramping-up discharge on DIII-D can reproduce the enhancement of magnetic turbulence in the pedestal, which is identified to be caused by micro-tearing modes (MTMs). Here, an increase of MTM amplitude results in higher electron thermal diffusivity, consistent with experimentally observed lower electron temperature gradient and degraded pedestal height. Gyrokinetic simulation identifies the major cause of MTM enhancement to be the increase of collisionality, which has a significant impact on the MTM intensity and is beyond the description of any (quasi-)linear theory.
Two new approaches are discussed in this paper for application in the Scramjet inlet of an air-breathing propulsion system: 1) In the first approach, the pylon set is installed in the rectangular inlet near the cowl front edge. For a quasi-axisymmetric inlet, a similar set is installed along the Star-shaped forebody axis. This set contains 3 - 4 airfoil-shaped strips or cross-sectional rings depending on the type of inlet. The inlets: rectangular, axisymmetric or star-shaped, are located at different distances from the forebody. Fuel injection takes place through these pylons, which provides for uniform mixing downstream. The locations, sizes and angles of these pylons are very important for efficient application. Optimal values of geometrical parameters were determined from multi-parametric NSE-based numerical simulations of the laminar and turbulent external/internal flows. These simulations have shown significant benefits for mixing, combustion and thrust of the proposed approach by comparison with traditional well-known designs. Experimental tests will be conducted soon at the NASA LaRC and Institute of Mechanics at Moscow State University. Preliminary estimates are very promising.
The improved simulation of sonic boom propagation through the real atmosphere requires greater understanding of how the transient acoustic pulses popularly termed sonic booms are affected by atmospheric turbulence. A nonlinear partial differential equation that can be used to simulate the effects of smaller-scale atmospheric turbulence on sonic boom waveforms is described. The equation is first order in the time derivative and involves an extension of geometrical acoustics to include diffraction phenomena. Various terms in the equation are explained in physical terms. Such terms include those representing convection at the wave speed, diffraction, molecular relaxation, classical dissipation, and nonlinear steepening. The atmospheric turbulence enters through an effective sound speed, which varies with all three spatial coordinates, and which is the sum of the local sound speed and the component of the turbulent flow velocity projected along a central ray that connects the aircraft trajectory with the listener.