Numerical simulation of turbulent combustion of subsonic gas jet flows

A physical and mathematical model of turbulent combustion of subsonic gas fuel jet flows flowing into an air space is proposed. The processes are described by averaged equations of the boundary layer with a turbulent viscosity model and a combustion diffusion model. As turbulent viscosity models, the well-known two-parameter k-? standard and k-?? models are taken. The results of the averaged and pulsating flow characteristics?? comparison of numerical calculations with the experimental data are presented.     

Local Discontinuous Galerkin Method for Surface Diffusion and Willmore Flow of Graphs

In this paper, we develop a local discontinuous Galerkin (LDG) finite element method for surface diffusion and Willmore flow of graphs. We prove L ² stability for the equation of surface diffusion of graphs and energy stability for the equation of Willmore flow of graphs. We provide numerical simulation results for different types of solutions of these two types of the equations to illustrate the accuracy and capability of the LDG method.     

The effect of the earth pressure coefficients on the runout of granular material

In the framework of a better territory risk assessment and decision making, numerical simulation can provide a useful tool for investigating the propagation phase of phenomena involving granular material, like rock avalanches, when realistic geological contexts are considered.Among continuum mechanics models, the numerical model SHWCIN uses the depth averaged Saint Venant approach, in which the avalanche thickness (H) is very much smaller than its extent parallel to the bed (L). The material is assumed to be incompressible and the mass and the momentum equations are written in a depth averaged form.The SHWCIN code, based on the hypothesis of isotropy of normal stresses (σ_xx = σ_yy = σ_zz), has been modified (new code: RASH^3D) in order to allow for the assumption of anisotropy of normal stresses (σ_xx = Kσ_zz; σ_yy = Kσ_zz).A comparison among the results obtained by assuming isotropy or anisotropy is given through the back analysis of a set of laboratory experiments [Gray, J.M.N.T., Wieland, M., Hutter, K., 1999. Gravity-driven free surface flow of granular avalanches over complex basal topography. Proceedings of the Royal Society of London, Series A 455(1841)] and of a case history of rock avalanche (Frank slide, Canada).The carried out simulations have also underlined the importance of using a different earth pressure coefficient value (K) for directions of convergence and of divergence of the flux.     

Parallel performance of a lattice-Boltzmann/finite element cellular blood flow solver on the IBM Blue Gene/P architecture

We discuss the parallel implementation and scaling results of a hybrid lattice-Boltzmann/finite element code for suspension flow simulations. This code allows the direct numerical simulation of cellular blood flow, fully resolving the two-phase nature of blood and the deformation of the suspended phase. A brief introduction to the numerical methods employed is given followed by an outline of the code structure. Scaling results obtained on Argonne National Laboratories IBM Blue Gene/P (BG/P) are presented. Details include performance characteristics on 512 to 65,536 processor cores.     

Development of a Variational Multiscale Large-Eddy Simulation Code ‘MISTRAL’ Using Double-Scale Finite Elements

A variational multiscale large-eddy simulation (VMS-LES) code, named MISTRAL, has been developed based upon the finite element method (FEM) for accurate and practical computation of geometrically complicated turbulent flow problems. The numerical strategy of the FEM-based VMS-LES is explained, especially focusing on the double-scale approximation for velocity and pressure in the incompressible Navier-Stokes equations, a pressure stabilization technique and a multiscale turbulence modeling. A unique technique is also employed in the time integration to realize an efficient inversion of the multiscale mass matrix and to form the multiscale pressure Poisson equation used in the approximate projection method for divergence-free constraint of velocity. As a numerical demonstration, a 2D driven cavity flow problem has been solved with the MISTRAL code in a wide range of Reynolds number (Re=1000 to 50000). The results are compared with reference data to quantitatively estimate the accuracy (magnitude of errors in terms of L ² norms) of the proposed VMS-LES method.     

A Linear Energy Stable Scheme for a Thin Film Model Without Slope Selection

We present a linear numerical scheme for a model of epitaxial thin film growth without slope selection. The PDE, which is a nonlinear, fourth-order parabolic equation, is the L ² gradient flow of the energy $\int_{\Omega}( - \frac{1}{2} \ln(1 + |\nabla\phi|^{2} ) + \frac{\epsilon^{2}}{2}|\Delta\phi(\mathbf{x})|^{2})\,\mathrm{d}\mathbf{x}$ . The idea of convex-concave decomposition of the energy functional is applied, which results in a numerical scheme that is unconditionally energy stable, i.e., energy dissipative. The particular decomposition used here places the nonlinear term in the concave part of the energy, in contrast to a previous convexity splitting scheme. As a result, the numerical scheme is fully linear at each time step and unconditionally solvable. Collocation Fourier spectral differentiation is used in the spatial discretization, and the unconditional energy stability is established in the fully discrete setting using a detailed energy estimate. We present numerical simulation results for a sequence of ? values ranging from 0.02 to?0.1. In particular, the long time simulations show the ?log(t) decay law for the energy and the t ^1/2 growth law for the surface roughness, in agreement with theoretical analysis and experimental/numerical observations in earlier works.     

Optimization of a synthetic jet actuator for aerodynamic stall control

The numerical simulation of aerodynamic stall control using a synthetic jet actuator is presented and the automatic optimization of the control parameters is investigated. Unsteady Reynolds-averaged Navier-Stokes equations are solved on unstructured grids using a near-wall low-Reynolds number turbulence closure to simulate the effects of a synthetic jet, located at 12% of the chord from the leading edge of a NACA 0015 airfoil, for a Reynolds number Re = 8.96 × 10⁵ and incidences between 12° and 24°. Then, an automatic optimization procedure coupled with the flow solver is employed to optimize the parameters of the actuator (momentum coefficient, frequency, angle with respect to the wall) at each incidence in order to increase the time-averaged lift. A significant increase of the maximum lift is obtained (+52% with respect to the baseline airfoil) and the stall delayed from 16° to 22° for optimal parameters. The flow characteristics and the influence of the respective control parameters are analysed.     

A global collisionless PIC code in magnetic coordinates

A global plasma turbulence simulation code, ORB5, is presented. It solves the gyrokinetic electrostatic equations including zonal flows in axisymmetric magnetic geometry. The present version of the code assumes a Boltzmann electron response on magnetic surfaces. It uses a Particle-In-Cell (PIC), δf scheme, 3D cubic B-splines finite elements for the field solver and several numerical noise reduction techniques. A particular feature is the use of straight-field-line magnetic coordinates and a field-aligned Fourier filtering technique that dramatically improves the performance of the code in terms of both the numerical noise reduction and the maximum time step allowed. Another feature is the capability to treat arbitrary axisymmetric ideal MHD equilibrium configurations. The code is heavily parallelized, with scalability demonstrated up to 4096 processors and 10⁹ marker particles. Various numerical convergence tests are performed. The code is validated against an analytical theory of zonal flow residual, geodesic acoustic oscillations and damping, and against other codes for a selection of linear and nonlinear tests.     

Eduction of near wall flow structures responsible for large deviations of the momentum-heat transfer analogy and fluctuations of wall transfer rates in turbulent channel flow

In this paper we analyze the flow structures responsible for large local instantaneous deviations of the conventional momentum-heat transfer analogy and large fluctuations of the wall shear stress and the wall heat flux in a forced convection turbulent channel flow at low-Reynolds numbers (Re = 4570, Pr = 0.7). The analysis was carried out using a database obtained from a direct numerical simulation performed with a second-order finite volume code. The ensemble averaged velocity and temperature profiles and profiles of the turbulence intensities and turbulent heat fluxes agree well with direct numerical simulations available in the literature. When the flow was statistically fully developed, we recorded the time evolution of the velocities and temperatures near one wall of the channel. The near wall structures responsible for the extreme values of the deviations were educed by a conditional sampling technique. Results show that extreme values of the wall shear stress and wall heat transfer rates, as well as departures from the conventional analogy between momentum and heat transfer, occur within the high-speed streaks on the wall and are associated with fluctuations of the streamwise pressure gradient. These large fluctuations on the wall are produced by the combined effect of two quasi-parallel counterrotating streamwise vortices.     

Numerical simulation of interaction between turbulent flow and a vibrating airfoil

The subject of this paper is the numerical simulation of the interaction of two-dimensional incompressible viscous flow and a vibrating airfoil. A solid elastically supported airfoil with two degrees of freedom, which can rotate around the elastic axis and oscillate in the vertical direction, is considered. The numerical simulation consists of the stabilized finite element treatment of the Reynolds averaged Navier–Stokes (RANS) approach, the use of turbulence models and the solution of the system of ordinary differential equations describing the airfoil motion. The time dependent computational domain and a moving grid are taken into account with the aid of the Arbitrary Lagrangian–Eulerian (ALE) formulation of the Navier–Stokes equations. High Reynolds numbers up to 10⁶ require to use a suitable stabilization of the finite element discretization and the application of a turbulence model. We apply the algebraic turbulence model, which was designed by Baldwin and Lomax and modified by Rostand. The developed technique was tested by the simulation of flow past a flat rigid plate and the computation of pressure distribution around a rotating airfoil with prescribed motion. Finally, the method was applied to the simulation of flow induced airfoil vibrations. This research was supported under the Grant No. IAA200760613 of the Grant Agency of Academy of Sciences of the Czech Republic. The research of M. Feistauer was partly supported by the research project MSM 0021620839 financed by the Ministry of Education of the Czech Republic and the research of L. Dubcová was partly supported by the grant No. 48607 of the Grant Agency of the Charles University. The authors acknowledge the support of these institutions.     

Neural networks based subgrid scale modeling in large eddy simulations

In this paper a multilayer feed-forward neural network (NN) is used as subgrid scale (SGS) model in a large eddy simulation (LES). The NN was previously off-line trained using numerical data generated by a LES of a channel flow at Re_τ=180 with Bardina's scale similar (BFR) SGS model. Results show the ability of NNs to identify and reproduce the highly nonlinear behavior of the turbulent flows, and therefore the possibility of using NN techniques in numerical simulations of turbulent flows.     

Numerical simulation of the transonic turbulent flow around a wedge-shaped body with a backward-facing step

A fully three-dimensional near-wall complex turbulent flow around a wedge-shaped body with a backward-facing step is considered with the transonic flow regime (Mach number M = 0.913) at the Reynolds number Re = 7.2 × 10⁶. The technology of the numerical simulation of problems of the class under study is represented in detail. A series of preliminary auxiliary calculations is carried out for choosing the optimal computational algorithm. The numerical results of the problem simulation based on the eddy-resolving hybrid RANS-LES approach IDDES are finally given for the full configuration. The validity of the results obtained is confirmed by comparing them to the corresponding experimental data.     

Higher order finite difference solutions to non-shallow hyperbolic paraboloidal shells

This paper presents the numerical results on the mechanical characteristics of a non-shallow hyperbolic paraboloidal shell obtained by means of the finite difference method. In order to obtain accurate solutions with a small number of meshes, higher order finite difference operators with error terms of o(h⁴) are applied not only to the equilibrium equations but also to the boundary conditions. The applicability range of the shallow shell theory to a non-shallow hyperbolic paraboloidal shell is clarified through the numerical examples.     

Simulating flows with moving rigid boundary using immersed-boundary method

The present study is to apply the immersed-boundary method to simulate 2- and 3-D viscous incompressible flows interacting with moving solid boundaries. Previous studies indicated that for stationary-boundary problems, different treatments inside the solid body did not affect the external flow. However, the relationship between internal treatment of the solid body and external flow for moving-boundary problems was not studied extensively and is investigated here. This is achieved via direct-momentum forcing on a Cartesian grid by combining “solid-body forcing” at solid nodes and interpolation on neighboring fluid nodes. The influence of the solid body forcing within the solid nodes is first examined by computing flow induced by an oscillating cylinder in a stationary square domain, where significantly lower amplitude oscillations in computed lift and drag coefficients are obtained compared with those without solid-body-forcing strategy. Grid-function convergence tests also indicate second-order accuracy of this implementation with respect to the L¹ norm in time and the L² norm in space. Further test problems are simulated to examine the validity of the present technique: 2-D flows over an asymmetrically-placed cylinder in a channel, in-line oscillating cylinder in a fluid at rest, in-line oscillating cylinder in a free stream, two cylinders moving with respect to one another, and 3-D simulation of a sphere settling under gravity in a static fluid. All computed results are in generally good agreement with various experimental measurements and with previous numerical simulations. This indicates the capability of the present simple implementation in solving complex-geometry flow problems and the importance of solid body forcing in computing flows with moving solid objects.     

Microcapillary electrophoresis chip with a bypass channel for autonomous compensation of hydrostatic pressure flow

The application of chip-based microcapillary electrophoresis (µCE) to determine the electrophoretic mobility of molecules and particles has been intensively studied in the last two decades. Balancing the hydrostatic pressure between both ends of the microchannel is essential for free-zone electrophoresis and highly accurate measurement. This balancing operation appears simple on a macroscale (e.g., >?10^?3 m); however, on a microscale (e.g., 10^?6–10^?3 m), it is not straightforward because of the complexity of the interface dynamics at the meniscus. The hydrostatic pressure flow is unstable because of the small size of the microchannel, which is smaller than a single droplet of water. In this study, a µCE chip design was proposed by adding an extra bypass channel to balance the fluid level of the two open reservoirs and inhibit the generation of hydrostatic pressure flow within the microchannel. The fluid behaviors in the microchannel and current and voltage (I–V) characterization were experimentally studied. In addition, a numerical simulation of the electroosmotic flow and hydrostatic flow in the µCE chip was performed. The comparison between the µCE chip with and without the bypass channel showed that the bypass channel did not produce a disturbance in the microchannel for the electrophoretic measurement. The simple microchannel design enabled autonomous compensation of the hydrostatic pressure from the instability of the meniscus, and thus improved the usability of the chip-based µCE chip and the accuracy in the electrophoretic measurement.     

The data from the numerical investigation of turbulent combustion in jet flows

The data from the numerical calculations are represented for free subsonic and supersonic turbulent jets subject to chemical reactions (combustion) of the flowing components. The calculations are carried out using averaged Navier–Stokes equations with various turbulent-viscosity models (k–ε, SST, Secundov model) and the large eddy simulation (LES). The Magnussen model and the Zeldovich model are regarded as turbulent combustion models. The calculation data are compared with the experimental data.     

Hardware-oriented numerics and concepts for PDE software

Processor technology is still dramatically advancing and promises further enormous improvements in processing data for the next decade. On the other hand, much lower advances in moving data are expected such that the efficiency of many numerical software tools for partial differential equations (PDEs) are restricted by the cost for memory access. We demonstrate how data locality and pipelining can achieve a significant percentage of the available huge computing power, and we explain the influence of processor technology on recent and future numerical PDE simulation tools. Exemplarily, we describe hardware-oriented concepts for adaptive error control, multigrid/domain decomposition schemes and incompressible flow solvers and discuss their numerical and computational characteristics.     

Direct numerical simulation of flow separation around a NACA 0012 airfoil

Direct numerical simulation (DNS) for the flow separation and transition around a NACA 0012 airfoil with an attack angle of 4° and Reynolds number of 10⁵ based on free-stream velocity and chord length is presented. The details of the flow separation, detached shear layer, vortex shedding, breakdown to turbulence, and re-attachment of the boundary layer are captured in the simulation. Though no external disturbances are introduced, the self-excited vortex shedding and self-sustained turbulent flow may be related to the backward effect of the disturbed flow on the separation region. The vortex shedding from the separated free shear layer is attributed to the Kelvin-Helmholtz instability.     

Non-body-fitted Cartesian-mesh simulation of highly turbulent flows using multi-relaxation-time lattice Boltzmann method

This paper presents a lattice Boltzmann method (LBM) based study aimed at numerical simulation of highly turbulent and largely inclined flow around obstacles of curved geometry using non-body-fitted Cartesian meshes. The approach features (1) combining the interpolated bounce-back scheme with the LBM of multi-relaxation-time (MRT) type to enable the use of simple Cartesian mesh for the flow cases even with complex geometries; and (2) incorporating the Spalart–Allmaras (SA) turbulence model into LBM in order to represent the turbulent flow effect. The numerical experiments are performed corresponding to flows around an NACA0012 airfoil at Re=5×10⁵ and around a flat plate at Re=2×10⁴, respectively. The agreement between all simulation results obtained from this study and the data provided by other literature demonstrates the reliability of the enhanced LBM proposed in this paper for simulating, simply on Cartesian meshes, complex flows that may involve bodies of curved boundary, high Reynolds number, and large angle of attack.     

Numerical simulations of solutions of a two-level averaged Navier–Stokes system

An averaging procedure for the Navier–Stokes equations has been proposed in an earlier article [I. Moise, R.M. Temam, Renormalization group method. Application to Navier–Stokes Equation, Discrete Contin. Dyn. Syst. 6 (1) (2000) 191–210]. This averaging procedure is based on a two-level decomposition of the solution into low and high frequencies. The aim of the present article is to investigate, with the help of numerical simulations, the behavior of the small scales of the corresponding system. Space-periodic solutions with a non-resonant period are considered. The time evolution of the averaged and standard (non-averaged) small scales are compared at different Reynolds numbers and for different values of the cut-off level used to separate large and small scales of the flow variables. The numerical results illustrate the efficiency of the proposed averaging procedure for the Navier–Stokes equations. The averaged small scales provide an accurate prediction of the time-averaged small scales of the Navier–Stokes solutions. As the computational cost is reduced for the averaged equations, long time integrations on more than 50 eddy-turnover times have been performed for cut-off levels ensuring a proper resolution of the large scales. In these cases, development of instabilities in the averaged small scale equation is observed.