DSMC approach to nonstationary Mach reflection of strong incoming shock waves using a smoothing technique

The direct simulation Monte Carlo (DSMC) method is applied to simulation of nonstationary Mach reflection of strong shock waves. Normally the DSMC method is very time consuming in solving unsteady flow field problems especially for high Mach numbers, because of the necessity of iterative calculations to eliminate the inherent statistical fluctuation caused by a finite sample size. A central weighted smoothing technique is introduced to process the DSMC results, so that the iteration time can be significantly reduced. In spite of some relaxations of the shock wave structure, the smoothing technique is verified to be useful to estima te the flow fields qualitatively and even quantitatively by using a relatively small sample size. The comparison between the present approach and the kineticmodel approach (Xu et al. 1991a, 1991b) on the application to unsteady rarefied flow fields was also carried out.This article was processed using Springer-Verlag T_EX Shock Waves macro package 1.0 and the AMS fonts, developed by the American Mathematical Society.     

Radiative heat transfer augmentation of natural gas flames in radiant tube burners with porous ceramic inserts

Experiments were conducted using porous ceramic inserts to enhance the radiative heat transfer from natural gas flames in a straight-through radiant tube burner. The performance of the radiant tube burner with partially stabilized zirconia and silicon carbide inserts is compared to a baseline case of no inserts at three levels of combustion air preheat. Spectral intensities, temperatures within the radiant tube burner, tube wall temperatures, and exhaust temperatures were measured to determine the effectiveness of the enhanced heat transfer due to the inserts. Exhaust emission constituents were also measured to determine the effect that the inserts have on exhaust products. NO_x emissions are reduced by up to 30% with the inserts. The silicon carbide inserts have higher spectral intensities and total radiative energy transfer than partially stabilized zirconia inserts. Both inserts have enhanced radiant heat transfer compared to the no-insert configuration, with the radiative enhancement due to inserts as great as five times that of the no-insert configuration. The net result is increased tube wall temperatures and decreased exhaust temperatures with the ceramic inserts.     

Experimental investigation of creep-crack-tip deformation using moiré interferometry

High-temperature moiré interferometry was applied to obtain full-field creep-crack-tip displacements of a three-point bend Al 2024-T4 specimen uner constant temperature of 200°C up to 720 hr.C ^* was evaluated by the moiré data obtained at discrete time intervals. Test results indicate that under steady-state creep condition, the creepcrack-tipv-displacement rate agrees with the asymptotic solution based on theC ^* integral. However, no creeping behavior was observed for the crack-tipu-displacement field aftert=276 hr. This discrepancy may be due to the initial large creep-crack-tip blunting and cavitation damage which alter the creep-crack-tip singular field such that theC ^* integral is no longer applicable to characterize the steady-state creep-crack-tip field. Postmortem studies of the tested specimen also revealed transgranular fracture path with the ordered grain boundaries perpendicular to the crack line, which may relate to the existence of the substantial crack-tip blunting and noncreeping behavior of theu-displacement field, i.e., the size and shape of material grain boundaries play an important role in the crack-tip-creeping behavior of the material.Paper was preseted at the 1991 SEM Spring Conference on Experimental Mechanics held in Milwaukee, WI on June 9–13.     

Evaluation of creep damage behavior of nickel-base directionally solidified superalloys with different crystallographic orientations

A crystallographic creep damage constitutive model is developed for nickel-base directionally solidified superalloys. The rates of material degradation and grain boundary void growth are considered. The governing parameters are determined from the creep test data of single crystals and directionally solidified superalloys with a crystallographic orientation. A finite element program is used to analyze the creep damage behavior of nickel-base directionally solidified superalloys for different crystallographic orientations. The results depend on the number of grains modelled and compare well with the experimental data.     

Late-Stage Transitional Boundary-Layer Structures. Direct Numerical Simulation and Experiment

This paper is devoted to direct comparisons of related, detailed experimental and numerical studies of the non-linear, late stages of laminar-turbulenttransition in a boundary layer including flow breakdown and the beginning offlow randomization. Preceding non-linear stages of the transition process arealso well documented and compared with previous studies. The experiments wereconducted with the help of a hot-wire anemometer. The numerical study wascarried out by direct numerical simulation (DNS) of the flow employing theso-called spatial approach. Both the experiments and the DNS were performed atcontrolled disturbance conditions with an excitation of instability waves inthe flat-plate boundary layer. In the two cases, the primary disturbanceconsists of a time-harmonic, two-dimensional Tollmien--Schlichting wave thathas a very weak initial spanwise modulation. Despite somewhat differentinitial disturbance conditions used in the experiment and simulation, thesubsequent flow evolution at late non-linear stages is found to be practicallythe same. Detailed qualitative and quantitative comparisons of theinstantaneous velocity and vorticity fields are performed for twocharacteristic stages of the non-linear flow breakdown: (i) “one-spike stage” and (ii) “three-spike stage.” The twoapproaches clearly show in detail the process of development of the Γ-structure, a periodical formation of ring-like vortices, the evolution of the surrounding flow field, and the beginning of flowrandomization. In particular, it is found experimentally and numerically thatthe ring-like vortices (associated with the well-known spikes) induce somerather intensive positive velocity fluctuations (positive spikes) in thenear-wall region which have the same scales as the ring-like vortices and propagate downstream with the same high (almost free-stream) speed. The positive spikes form a new high-shear layer in the near-wall region. In the experiment the induced near-wall perturbationshave a significant irregular low-frequency component. These non-periodicalmotions play an important role in the process of flow randomization and finaltransition to turbulence that starts under the ring-like vortices in thevicinity of the peak position. Received 13 December 2000 and accepted 30 October 2001     

Necessary and sufficient conditions for existence of stationary solutions of some nonlinear stochastic systems

At the state of statistical stationarity, the response of a nonlinear system under multiplicative random excitations can be either trivial or non-trivial, depending on the spectral levels of the excitations and the values of certain system parameters. Assuming that the random excitations are Gaussian white noises, the two types of response may be investigated by way of their stationary densities, which are obtainable for first order dynamical systems and for higher order dynamical systems belonging to the class of generalized stationary potential. Alternatively, the Lyapunov exponents can be computed for perturbation from either the trivial or non-trivial solution, since a negative sign for the greatest Lyapunov exponent provides both the necessary and sufficient conditions for the stability of sample functions with probability one. It is shown in two specific examples, that the boundary at which the greatest Lyapunov exponent changes its sign coincides with the boundary for regularity (or being normalizable) for the probability density in both the trivial and non-trivial solutions. Thus, the stability conditions in the strong sense of probability one and the weak sense in distribution are identical in these cases.     

A Direct Proof of the Uniqueness of the Square-Root of a Positive-Definite Tensor

The uniqueness of the square-root of a positive–definite tensor is shown without using the notion of eigenvalues and eigenvectors. This revised version was published online in August 2006 with corrections to the Cover Date.     

Effect of transverse stress on switch-toughening of ferroelectrics

Testing data indicated that T stress significantly altersR-curves of ferroelectrics. The model of stress-induced polarization switching is adopted to evaluate the fracture toughness of ferroelectrics under K field and T stress. Analytical solution is obtained to estimate the steady state fracture resistance of mono-domain ferroelectrics. The result is generalized to multi-domain ferroelectric ceramics via Reuss approximation, which enables us to explain quantitatively R-curves under two testing configurations.     

Exact Results for the Homogenization of Elastic Fiber-Reinforced Solids at Finite Strain

This work is concerned with the homogenization of solids reinforced by aligned parallel continuous fibers or weakened by aligned parallel cylindrical pores and undergoing large deformations. By alternatively exploiting the nominal and material formulations of the corresponding homogenization problem and by applying the implicit function theorem, it is shown that locally homogeneous deformations can be produced in such inhomogeneous materials and form a differentiable manifold. For every macroscopic strain associated to a locally homogeneous deformation field, the effective nominal or material stress–strain relation is exactly determined and connections are also exactly established between the effective nominal and material elastic tangent moduli. These results are microstructure-independent in the sense that they hold irrespectively of the transverse geometry and distribution of the fibers or pores. A porous medium consisting of a compressible Mooney–Rivlin material with cylindrical pores is studied in detail to illustrate the general results. This work was the first time presented at the Euromech Colloqium 464 on “Fiber-reinforced Solids: Constitutive Laws and Instabilities”, September 28–October 1, 2004, Cantabria, Spain.     

A critical review of dispersion in packed beds

The phenomenon of dispersion (transverse and longitudinal) in packed beds is summarized and reviewed for a great deal of information from the literature. Dispersion plays an important part, for example, in contaminant transport in ground water flows, in miscible displacement of oil and gas and in reactant and product transport in packed bed reactors. There are several variables that must be considered, in the analysis of dispersion in packed beds, like the length of the packed column, viscosity and density of the fluid, ratio of column diameter to particle diameter, ratio of column length to particle diameter, particle size distribution, particle shape, effect of fluid velocity and effect of temperature (or Schmidt number). Empirical correlations are presented for the prediction of the dispersion coefficients (D _T and D _L) over the entire range of practical values of Sc and Pe_m, and works on transverse and longitudinal dispersion of non-Newtonian fluids in packed beds are also considered.