Doubly Perfect Nonlinear Boolean Permutations

Due to implementation constraints the XOR operation is widely used in order to combine plaintext and key bit-strings in secret-key block ciphers. This choice directly induces the classical version of the differential attack by the use of XOR-kind differences. While very natural, there are many alternatives to the XOR. Each of them inducing a new form for its corresponding differential attack (using the appropriate notion of difference) and therefore block-ciphers need to use S-boxes that are resistant against these nonstandard differential cryptanalysis. In this contribution we study the functions that offer the best resistance against a differential attack based on a finite field multiplication. We also show that in some particular cases, there are robust permutations which offers the best resistant against both multiplication and exponentiation base differential attacks. We call them doubly perfect nonlinear permutations

The actual impedance of non-reflecting boundary conditions : implications for the computation of resonators

Non-reflecting boundary conditions are essential elements in the computation of many compressible flows: such simulations are very sensitive to the treatment of acoustic waves at boundaries. Non-reflecting conditions allow acoustic waves to propagate through boundaries with zero or small levels of reflection into the domain. However, perfectly non-reflecting conditions must be avoided because they can lead to ill-posed problems for the mean flow. Various methods have been proposed to construct boundary conditions which can be sufficiently non-reflecting for the acoustic field while still making the mean-flow problem well posed. This paper analyses a widely-used technique for non-reflecting outlets (Rudy and Strikwerda, Poinsot and Lele). It shows that the correction introduced by these authors can lead to large reflection levels and non-physical resonant behaviors. A simple scaling is proposed to evaluate the relaxation coefficient used in theses methods for a non-reflecting outlet. The proposed scaling is tested for simple cases (ducts) both theoretically and numerically

DNS and modeling of the interaction between turbulent premixed flames and walls

The interaction between turbulent premixed flames and walls is studied using a two-dimensional full Navier-Stokes solver with simple chemistry. The effects of wall distance on the local and global flame structure are investigated. Quenching distances and maximum wall heat fluxes during quenching are computed in laminar cases and are found to be comparable to experimental and analytical results. For turbulent cases, it is shown that quenching distances and maximum heat fluxes remain of the same order as for laminar flames. Based on simulation results, a 'law-of-the-wall' model is derived to describe the interaction between a turbulent premixed flame and a wall. This model is constructed to provide reasonable behavior of flame surface density near a wall under the assumption that flame-wall interaction takes place at scales smaller than the computational mesh. It can be implemented in conjunction with any of several recent flamelet models based on a modeled surface density equation, with no additional constraints on mesh size or time step

Lorenz integrable system moves \`a la Poinsot

A transformation is derived which takes Lorenz integrable system into the well-known Euler equations of a free-torque rigid body with a fixed point, i.e. the famous motion \`a la Poinsot. The proof is based on Lie group analysis applied to two third order ordinary differential equations admitting the same two-dimensional Lie symmetry algebra. Lie's classification of two-dimensional symmetry algebra in the plane is used. If the same transformation is applied to Lorenz system with any value of parameters, then one obtains Euler equations of a rigid body with a fixed point subjected to a torsion depending on time and angular velocity. The numerical solution of this system yields a three-dimensional picture which looks like a "tornado" whose cross-section has a butterfly-shape. Thus, Lorenz's {\em butterfly} has been transformed into a {\em tornado}.Comment: 14 pages, 6 figure

Numerical simulations of turbulent premixed H2/O2/N2 flames with complex chemistry

Premixed stoichiometric H2/O2/N2 flames propagating in two-dimensional turbulence were studied using direct numerical simulation (simulations in which all fluid and thermochemical scales are fully resolved) including realistic chemical kinetics and molecular transport. Results are compared with earlier zero-chemistry (flame sheet) and one-step chemistry simulations. Consistent with the simpler models, the turbulent flame with realistic chemistry aligns preferentially with extensive strain rates in the tangent plane and flame curvature probability density functions are close to symmetric with near-zero means. By contrast to simple-chemistry results with non-unity Lewis numbers (ratio of thermal to species diffusivity), local flame structure does not correlate with curvature but rather with tangential strain rate. Turbulent straining results in substantial thinning of the flame relative to the steady unstrained laminar case. Heat release and H2O2 contours remain thin and connected ('flamelet-like') while species including H-atom and OH are more diffuse. Peak OH concentration occurs well behind the peak heat-release zone. The feasibility of incorporating realistic chemistry into full turbulence simulations to address issues such as pollutant formation in hydrocarbon-air flames is suggested

Using LES to Study Reacting Flows and Instabilities in Annular Combustion Chambers

Great prominence is put on the design of aeronautical gas turbines due to increasingly stringent regulations and the need to tackle rising fuel prices. This drive towards innovation has resulted sometimes in new concepts being prone to combustion instabilities. In the particular field of annular combustion chambers, these instabilities often take the form of azimuthal modes. To predict these modes, one must compute the full combustion chamber, which remained out of reach until very recently and the development of massively parallel computers. Since one of the most limiting factors in performing Large Eddy Simulation (LES) of real combustors is estimating the adequate grid, the effects of mesh resolution are investigated by computing full annular LES of a realistic helicopter combustion chamber on three grids, respectively made of 38, 93 and 336 million elements. Results are compared in terms of mean and fluctuating fields. LES captures self-established azimuthal modes. The presence and structure of the modes is discussed. This study therefore highlights the potential of LES for studying combustion instabilities in annular gas turbine combustors

LES and acoustic analysis of thermo-acoustic instabilities in a partially premixed model combustor

Numerical simulations were performed using Large Eddy Simulation (LES) and acoustic analysis tools to study thermo-acoustic instabilities in an academic burner. The configuration studied corresponds to a methane/air burner installed at the University of Twente (The Netherlands). It operates under fuel-lean partially premixed conditions at atmospheric pressure, and was built to study thermo-acoustic instabilities in conditions representative of gas turbine Lean Premixed systems: gaseous fuel is injected upstream of the combustor and has a limited time to mix with air. Even though the objective is to burn in a premixed mode, the actual regime corresponds to a partially premixed flame where strong equivalence ratio variations are created especially during combustion instabilities. Capturing these modes with LES is a challenge: here, simulations for both stable and unstable regimes are performed. In the unstable case, the limit cycle oscillations (LCO) are characterized and compared to experimental results. Reasonable agreement is found between simulations and experiments

Can Deflagration-Detonation-Transitions occur in Type Ia Supernovae?

The mechanism for deflagration-detonation-transition (DDT) by turbulent preconditioning, suggested to explain the possible occurrence of delayed detonations in Type Ia supernova explosions, is argued to be conceptually inconsistent. It relies crucially on diffusive heat losses of the burned material on macroscopic scales. Regardless of the amplitude of turbulent velocity fluctuations, the typical gradient scale for temperature fluctuations is shown to be the laminar flame width or smaller, rather than the factor of thousand more required for a DDT. Furthermore, thermonuclear flames cannot be fully quenched in regions much larger than the laminar flame width as a consequence of their simple ``chemistry''. Possible alternative explosion scenarios are briefly discussed.Comment: 8 pages, uses aastex; added references. Accepted by ApJ Letter

Lie point symmetries and first integrals: the Kowalevsky top

We show how the Lie group analysis method can be used in order to obtain first integrals of any system of ordinary differential equations. The method of reduction/increase of order developed by Nucci (J. Math. Phys. 37, 1772-1775 (1996)) is essential. Noether's theorem is neither necessary nor considered. The most striking example we present is the relationship between Lie group analysis and the famous first integral of the Kowalevski top.Comment: 23 page

Numerical Benchmark for High-Reynolds-Number Supercritical Flows with Large Density Gradients

Because of the extreme complexity of physical phenomena at high pressure, only limited data are available for solver validation at device-relevant conditions such as liquid rocket engines, gas turbines, or diesel engines. In the present study, a two-dimensional direct numerical simulation is used to establish a benchmark for supercritical flow at a high Reynolds number and high-density ratio at conditions typically encountered in liquid rocket engines. Emphasis has been placed on maintaining the flow characteristics of actual systems with simple boundary conditions, grid spacing, and geometry. Results from two different state-of-the-art codes, with markedly different numerical formalisms, are compared using this benchmark. The strong similarity between the two numerical predictions lends confidence to the physical accuracy of the results. The established database can be used for solver benchmarking and model development at conditions relevant to many propulsion and power systems