Virginie Daru

Evaluation of TVD high resolution schemes for unsteady viscous shocked flows

Abstract The goal of this study is to evaluate the accuracy of several high resolution total variation diminishing schemes in solving complex unsteady viscous shocked flows. Two types of discretization, namely a combined time and space discretization, and an independent time and space discretization are considered. Both methods are associated with several limiters, among which a more accurate new family of limiters depending on the local wave velocity. The accuracy properties of each scheme are first reviewed on inviscid 1D and 2D test cases, in order to establish a ranking with respect to their dissipative error. We then study the flow produced by the interaction of a reflected shock wave with the incident boundary layer in a shock tube. The calculations are performed for two values of the Reynolds number. At Re=200, convergence is attained and it is shown that the combined time and space discretization method converges faster. Good classical limiters do almost the same job as the new family of limiters. When the Reynolds number is increased to the value of 1000, the flow becomes much more complex. Although convergence is hard to reach, the close examination of the results leads us to conclude that the combined time and space discretization method associated with the new limiter gives from far the best results.

Fast acoustic streaming in standing waves : Generation of an additional outer streaming cell

Rayleigh streaming in a cylindrical acoustic standing waveguide is studied both experimentally and numerically for nonlinear Reynolds numbers from 1 to 30 [Re(NL)=(U0/c0)(2)(R/δν)(2), with U0 the acoustic velocity amplitude at the velocity antinode, c0 the speed of sound, R the tube radius, and δν the acoustic boundary layer thickness]. Streaming velocity is measured by means of laser Doppler velocimetry in a cylindrical resonator filled with air at atmospheric pressure at high intensity sound levels. The compressible Navier-Stokes equations are solved numerically with high resolution finite difference schemes. The resonator is excited by shaking it along the axis at imposed frequency. Results of measurements and of numerical calculation are compared with results given in the literature and with each other. As expected, the axial streaming velocity measured and calculated agrees reasonably well with the slow streaming theory for small ReNL but deviates significantly from such predictions for fast streaming (ReNL>1). Both experimental and numerical results show that when ReNL is increased, the center of the outer streaming cells are pushed toward the acoustic velocity nodes until counter-rotating additional vortices are generated near the acoustic velocity antinodes.

A conservative coupling algorithm between a compressible flow and a rigid body using an Embedded Boundary method

This paper deals with a new solid-fluid coupling algorithm between a rigid body and an unsteady compressible fluid flow, using an Embedded Boundary method. The coupling with a rigid body is a first step towards the coupling with a Discrete Element method. The flow is computed using a finite volume approach on a Cartesian grid. The expression of numerical fluxes does not affect the general coupling algorithm and we use a one-step high-order scheme proposed by Daru and Tenaud V. Daru, C. Tenaud, J. Comput. Phys. (2004)]. The Embedded Boundary method is used to integrate the presence of a solid boundary in the fluid. The coupling algorithm is totally explicit and ensures exact mass conservation and a balance of momentum and energy between the fluid and the solid. It is shown that the scheme preserves uniform movement of both fluid and solid and introduces no numerical boundary roughness. The efficiency of the method is demonstrated on challenging one- and two-dimensional benchmarks.

A numerical method for the simulation of low Mach number liquid-gas flows

This work is devoted to the numerical simulation of liquid-gas flows. The liquid phase is considered as incompressible, while the gas phase is treated as compressible in the low Mach number approximation. A single fluid two pressure model is developed and the front-tracking method is used to track the interface. Navier-Stokes equations coupled with that of temperature are solved in the whole computational domain. Velocity, pressure and temperature fields are computed yielding a complete description of the dynamics for both phases. We show that our method is much more efficient than the so-called all-Mach methods involving a single pressure, since large time steps can be used while retaining time accuracy. The model is first validated on a reference test problem solved using an accurate ALE technique to track the interface. Numerical examples in two space dimensions are next presented. They consist of air bubbles immersed in a closed cavity filled up with liquid water. The forced oscillations of the system consisting of the air bubbles and the liquid water are investigated. They are driven by a heat supply or a thermodynamic pressure difference between the bubbles.

Multi-Zone Quasi-Dimensional Combustion Models for Spark-Ignition Engines

The present work aims at improving the predictive capabilities of quasi-dimensional combustion models for fast and accurate automated design of spark engines. The models are based on mass and energy conservation principles supplemented by sub models based on experimental correlations. Here, we improve the accuracy of the classical two-zone model by means of two successive modifications. First, we generate a three-zone model by introducing a reacting zone near the walls. In the third zone, the gases burn at a lower temperature than in the main reacting zone, due to heat losses to the walls. Secondly, a multi-zone model is built by dynamically adding new reacting zones at given crank-angle intervals. The use of multiple zones allows to take into account temperature and concentrations gradients in the flame. To validate our models, the energy release rates and pressures time histories predicted by the three-zone and by the multi-zone models are compared to experimental data and to the standard two-zone approach for several operating conditions.

A time semi-implicit scheme for the energy-balanced coupling of a shocked fluid flow with a deformable structure

The objective of this work is to present a conservative coupling method between an inviscid compressible fluid and a deformable structure undergoing large displacements. The coupling method combines a cut-cell Finite Volume method, which is exactly conservative in the fluid, and a symplectic Discrete Element method for the deformable structure. A time semi-implicit approach is used for the computation of momentum and energy transfer between fluid and solid, the transfer being exactly balanced. The coupling method is exactly mass-conservative (up to round-off errors in the geometry of cut-cells) and exhibits numerically a long-time energy-preservation for the coupled system. The coupling method also exhibits consistency properties, such as conservation of uniform movement of both fluid and solid, absence of numerical roughness on a straight boundary, and preservation of a constant fluid state around a wall having tangential deformation velocity. The performance of the method is assessed on test cases involving shocked fluid flows interacting with two and three-dimensional deformable solids undergoing large displacements.

Inertial effects on non linear acoustic streaming

The effect of inertia on nonlinear streaming generated inside a cylindrical resonator where a mono-frequency standing wave is imposed, is investigated numerically using two codes: A code solving the full Navier-Stokes compressible equations, assuming that the flow is isentropic in order to exclude thermal effects, and a code solving the time-averaged equations where the linear acoustic flow field is used as a source term. It is shown that the sole effect of inertia cannot be responsible for the acoustic streaming behavior observed for large values of the nonlinear Reynolds number.

Evolution of Rayleigh streaming flow velocity components in a resonant waveguide at high acoustic levels

The interaction between an acoustic wave and a solid wall generates a mean steady flow called Rayleigh streaming, generally assumed to be second order in a Mach number expansion. This flow is well known in the case of a stationary plane wave at low amplitude: it has a half-wavelength spatial periodicity and the maximum axial streaming velocity is a quadratic function of the acoustic velocity amplitude at the antinode. For higher acoustic levels, additional streaming cells have been observed. In the present study, results of LDV and PIV measurements are compared to direct numerical simulations. The evolution of axial and radial velocity components for both acoustic and streaming flows is studied from low to high acoustic amplitudes. Two streaming flow regimes are pointed out, the axial streaming dependency upon acoustics going from quadratic to linear. The hypothesis of the radial streaming velocity being of second order in a Mach number expansion is shown to be invalid at high amplitudes. The change of re...

Acoustic and streaming velocity components in a resonant waveguide at high acoustic levels

Rayleigh streaming is a steady flow generated by the interaction between an acoustic wave and a solid wall, generally assumed to be second order in a Mach number expansion. Acoustic streaming is well known in the case of a stationary plane wave at low amplitude: it has a half-wavelength spatial periodicity and the maximum axial streaming velocity is a quadratic function of the acoustic velocity amplitude at antinode. For higher acoustic levels, additional streaming cells have been observed. Results of laser Doppler velocimetry measurements are here compared to direct numerical simulations. The evolution of axial and radial velocity components for both acoustic and streaming velocities is studied from low to high acoustic amplitudes. Two streaming flow regimes are pointed out, the axial streaming dependency on acoustics going from quadratic to linear. The evolution of streaming flow is different for outer cells and for inner cells. Also, the hypothesis of radial streaming velocity being of second order in a Mach number expansion, is not valid at high amplitudes. The change of regime occurs when the radial streaming velocity amplitude becomes larger than the radial acoustic velocity amplitude, high levels being therefore characterized by nonlinear interaction of the different velocity components.

Acoustic Rayleigh streaming: Comprehensive analysis of source terms and their evolution with acoustic level

Rayleigh streaming is a second order mean flow generated by the interaction between a standing wave and a solid wall. At moderate acoustic levels, the streaming flow is slow, composed of two cells along a quarter wavelength: an inner cell close to the tube wall and an outer cell in the core. When increasing the acoustic level, the streaming flow inside the inner cells is marginally modified, while the outer cells are strongly distorted. The emergence of an extra cell was observed both in previous numerical simulations and experiments and it has been shown that inertia is not responsible for this behavior, which is rather due to nonlinear interactions between streaming and acoustics. In the present work these interactions are analyzed both numerically and theoretically. The averaged Navier-Stokes equations are numerically solved with acoustic correlation source terms obtained from previous full instantaneous simulations. The effect of each source term is highlighted and the source term responsible for the ...