Asymptotic behaviour at the wall in compressible turbulent channels

The asymptotic behaviour of Reynolds stresses close to walls is well established in incompressible flows owing to the constraint imposed by the solenoidal nature of the velocity field. For compressible flows, thus, one may expect a different asymptotic behaviour, which has indeed been noted in the literature. However, the transition from incompressible to compressible scaling, as well as the limiting behaviour for the latter, is largely unknown. Thus, we investigate the effects of compressibility on the near-wall, asymptotic behaviour of turbulent fluxes using a large direct numerical simulation (DNS) database of turbulent channel flow at higher than usual wall-normal resolutions. We vary the Mach number at a constant friction Reynolds number to directly assess compressibility effects. We observe that the near-wall asymptotic behaviour for compressible turbulent flow is different from the corresponding incompressible flow even if the mean density variations are taken into account and semi-local scalings are used. For Mach numbers near the incompressible regimes, the near-wall asymptotic behaviour follows the well-known theoretical behaviour. When the Mach number is increased, turbulent fluxes containing wall-normal components show a decrease in the slope owing to increased dilatation effects. We observe that $R_{vv}$ approaches its high-Mach-number asymptote at a lower Mach number than that required for the other fluxes. We also introduce a transition distance from the wall at which turbulent fluxes exhibit a change in scaling exponents. Implications for wall models are briefly presented.

Acceleration of Solar Energetic Particles by the Shock of Interplanetary Coronal Mass Ejection

Interplanetary coronal mass ejection (ICME) shocks are known to accelerate particles and contribute significantly to solar energetic particle events. We have performed magnetohydrodynamic-particle in cell simulations of ICME shocks to understand the acceleration mechanism. These shocks vary in Alfvénic Mach numbers as well as in magnetic field orientations (parallel and quasi-perpendicular). We find that diffusive shock acceleration plays a significant role in accelerating particles in a parallel ICME shock. In contrast, shock drift acceleration (SDA) plays a pivotal role in a quasi-perpendicular shock. High-Mach shocks are seen to accelerate particles more efficiently. Our simulations suggest that background turbulence and local particle velocity distribution around the shock can indirectly hint at the acceleration mechanism. Our results also point toward a few possible in situ observations that could validate our understanding of the topic.

Localized time accurate sampling of nonequilibrium and unsteady hypersonic flows: methods and horizons

Modern “non-intrusive” optical methods are providing revolutionary capabilities for diagnostics of hypersonic flow fields. They generate accurate information on the performance of ground test facilities and provide local time accurate measurements of near-wall and off-body flow fields surrounding hypersonic test articles. They can follow the true molecular motion of the flow and detect nonequilibrium states and gas mixtures. They can be used to capture a wide range of turbulent scales and can produce highly accurate velocity, temperature and density measurements as well as time-frozen images that provide intuitive understanding of flow phenomena. Recent review articles address many of these methods and their applications. The methods highlighted in this review are those that have been enabled or greatly improved by new, versatile laser systems, particularly including kHz rate femtosecond lasers and MHz rate pulse burst lasers. Although these methods can be applied to combusting environments, the focus of this review is on external high Mach number flows surrounding test articles and wind tunnel core flow properties. The high repetition rates enable rapid time evolving flows to be analyzed and enable the collection of large data sets necessary for statistical analysis. Future capabilities based on the use of atomic vapor filters and on frequency tunable, injection locked MHz rate lasers are promising.

Self-Consistent Cathode–Plasma Coupling and Role of the Fluid Flow Approach in Torch Modeling

A two-dimensional and stationary magnetohydrodynamic model of a plasma spray torch operated with argon is developed to predict the plasma properties in a steady operating mode. The model couples a submodel of a refractory cathode and its non-equilibrium boundary layer to a submodel of the plasma in local thermodynamic equilibrium in a self-consistent manner. The Navier–Stokes equations for a laminar and compressible flow are solved in terms of low and high Mach number numerical approaches. The results show that the Mach number can reach values close to one. Simulations are performed for electric currents of 600 A and 800 A, and gas flow rates of 40, 60, and 80 NLPM. The plasma parameters obtained by the two approaches differ, and the differences become more pronounced for higher currents and gas flow rates. The arc voltage, the electric power, and the thermal efficiency from both the low and high Mach number models of the plasma agree well with experimental findings for a current of 600 A and a flow rate of 40 NLPM. For higher currents and gas flow rates, the results of the low and high Mach number models gradually differ and underline the greater appropriateness of the high Mach number model.

Entropy Stable Discontinuous Galerkin Finite Element Method with Multi-Dimensional Slope Limitation for Euler Equations

We present an entropy stable Discontinuous Galerkin (DG) finite element method to approximate systems of 2-dimensional symmetrizable conservation laws on unstructured grids. The scheme is constructed using a combination of entropy conservative fluxes and entropy-stable numerical dissipation operators. The method is designed to work on structured as well as on unstructured meshes. As solutions of hyperbolic conservation laws can develop discontinuities (shocks) in finite time, we include a multidimensional slope limitation step to suppress spurious oscillations in the vicinity of shocks. The numerical scheme has two steps: the first step is a finite element calculation which includes calculations of fluxes across the edges of the elements using 1-D entropy stable solver. The second step is a procedure of stabilization through a truly multi-dimensional slope limiter. We compared the Entropy Stable Scheme (ESS) versus Roe’s solvers associated with entropy corrections and Osher’s solver. The method is illustrated by computing solution of the two stationary problems: a regular shock reflection problem and a 2-D flow around a double ellipse at high Mach number.