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High-amplitude pressure oscillations in solid propellant rocket motor combustion chambers display nonlinear effects including: (1) limit cycle behavior in which the fluctuations may dwell for a considerable period of time near their peak amplitude, (2) elevated mean chamber pressure (DC shift), and (3) a triggering amplitude above which pulsing will cause an apparently stable system to transition to violent oscillations. Along with the obvious undesirable vibrations, these features constitute the most damaging impact of combustion instability on system reliability and structural integrity. The physical mechanisms behind these phenomena and their relationship to motor geometry and physical parameters must, therefore, be fully understood if instability is to be avoided in the design process, or if effective corrective measures must be devised during system development. Predictive algorithms now in use have limited ability to characterize the actual time evolution of the oscillations, and they do not supply the motor designer with information regarding peak amplitudes or the associated critical triggering amplitudes. A pivotal missing element is the ability to predict the mean pressure shift; clearly, the designer requires information regarding the maximum chamber pressure that might be experienced during motor operation. In this paper, a comprehensive nonlinear combustion instability model is described that supplies vital information. The central role played by steep-fronted waves is emphasized. The resulting algorithm provides both detailed physical models of nonlinear instability phenomena and the critically needed predictive capability. In particular, the origin of the DC shift is revealed. [ABSTRACT FROM AUTHOR]

Further development of large-eddy simulation (LES) faces as major obstacles the strong coupling between subgrid-scale (SGS) modeling and the truncation error of the numerical discretization. One can exploit this link by developing discretization methods where the truncation error itself functions as an implicit SGS model. The name “implicit LES” is used for approaches that merge the SGS model and numerical discretization. In this paper, the implicit SGS modeling environment provided by the adaptive local deconvolution method is extended to LES of passive-scalar mixing. The resulting adaptive advection algorithm is discussed with respect to its numerical and turbulence-theoretical background. We demonstrate that the new method allows for reliable predictions of the turbulent transport of passive scalars in isotropic turbulence and in turbulent channel flow for a wide range of Schmidt numbers. [ABSTRACT FROM AUTHOR]

It is known that the wavelength of the ripples on icicles in nature is of the centimeter scale. Such study on morphological instability of ice-water interface during ice growth from flowing supercooled water film with one side being a free surface has recently been made [K. Ueno, Phys. Rev. E 68, 021603 (2003)]. This is the first theoretical study taking into account the influence of the shape of the water-air surface on the growth condition of infinitesimal disturbances of the ice-water interface. A simpler formula to determine the wavelength of the ripples than that in the previous paper is derived. It seems that the wavelength of ripples is insensitive to the water supply rates, diameters of the icicles, and surrounding air temperatures. The details of dependence of the wavelength of ripples on these parameters are investigated. [ABSTRACT FROM AUTHOR]

Taylor’s incompressible and rotational profile is extended to a porous cylinder with arbitrary headwall injection. This profile, often referred to as Culick’s mean flow, is now generalized to permit the imposition of reactive headwall conditions. Starting with Euler’s steady equations, the solution that we derive is approximate, being exact only at the sidewall, the centerline, or for similarity-conforming inlet profiles. Furthermore, the approximation is quasiviscous, being observant of the no slip requirement at the sidewall. Based on numerical experiments under inviscid flow conditions, the closed-form approximation that we obtain appears to be well suited to describe the bulk flow field in basic models of solid and hybrid rockets where uniform sidewall injection is imposed at the propellant surface. For similarity-nonconforming profiles, the approximation becomes more accurate as we move away from the headwall. Results are verified using computational fluid dynamics for several headwall injection patterns. [ABSTRACT FROM AUTHOR]

Numerical simulations of a model of plane Couette flow focusing on its in-plane spatio-temporal properties are used to study the dynamics of turbulent spots. While the core of a spot is filled with small-scale velocity fluctuations, a large-scale flow extending far away and occupying the full gap between the driving plates is revealed upon filtering out small scales. It is characterized by streamwise inflow towards the spot and spanwise outflow from the spot, giving it a quadrupolar shape. A correction to the base flow is present within the spot in the form of a spanwise vortex with vorticity opposite in sign to that of the base flow. The Reynolds stresses are shown to be at the origin of this recirculation, whereas the quadrupolar shape of the in-plane flow results from the transport of this recirculation by the base flow that pumps it towards the spot in the streamwise direction and flushes it in the spanwise direction to insure mass conservation. These results shed light on earlier observations in plane Couette flow or other wall flows experiencing a direct transition to turbulence by spot nucleation. [ABSTRACT FROM AUTHOR]

We study the nonlinear evolution of the magnetic Rayleigh-Taylor instability using three-dimensional magnetohydrodynamic simulations. We consider the idealized case of two inviscid, perfectly conducting fluids of constant density separated by a contact discontinuity perpendicular to the effective gravity g, with a uniform magnetic field B parallel to the interface. Modes parallel to the field with wavelengths smaller than λc=B·B/(ρh-ρl)g are suppressed (where ρh and ρl are the densities of the heavy and light fluids, respectively), whereas modes perpendicular to B are unaffected. We study strong fields with λc varying between 0.01 and 0.36 of the horizontal extent of the computational domain. Even a weak field produces tension forces on small scales that are significant enough to reduce shear (as measured by the distribution of the amplitude of vorticity), which in turn reduces the mixing between fluids, and increases the rate at which bubbles and finger are displaced from the interface compared to the purely hydrodynamic case. For strong fields, the highly anisotropic nature of unstable modes produces ropes and filaments. However, at late time flow along field lines produces large scale bubbles. The kinetic and magnetic energies transverse to gravity remain in rough equipartition and increase as t4 at early times. The growth deviates from this form once the magnetic energy in the vertical field becomes larger than the energy in the initial field. We comment on the implications of our results to Z-pinch experiments, and a variety of astrophysical systems. [ABSTRACT FROM AUTHOR]

Flow-induced forces on two identical nearby spheres at Re=300 were numerically studied. We consider all possible arrangements of the two spheres in terms of the distance between the spheres and the angle inclined with respect to the main flow direction. It turns out that significant changes in the characteristics of vortex shedding are noticed depending on how the two spheres are positioned, resulting in quantitative changes of force coefficients on both spheres. Collecting all the numerical results obtained, we present the diagrams for the force coefficients on the distance versus angle plane for each of the two spheres. The perfect geometrical symmetry implied in the flow configuration allows one to use those diagrams to estimate flow-induced forces on two identical spheres arbitrarily positioned in physical space with respect to the main flow direction. [ABSTRACT FROM AUTHOR]

We describe an asymptotic model for long large-amplitude internal solitary waves with a trapped core, propagating in a narrow layer of nearly uniformly stratified fluid embedded in an infinitely deep homogeneous fluid. We consider the case of a mode one asymmetric wave with an amplitude slightly greater than the critical amplitude, for which there is incipient overturning, that is wave-breaking. We then incorporate a vortex core located near the point at which this incipient breaking occurs. The effect of the vortex core is to introduce into the governing equation for the wave amplitude an extra nonlinear term proportional to the 3/2 power of the difference between the wave amplitude and the critical amplitude. Thus the derived new equation for the wave amplitude incorporates both the nonlinearity arising due to the flow over the recirculation core, and the nonlinearity associated with the ambient stratification; the dispersion term however remains of the Benjamin-Ono-type. We find that as the wave amplitude increases above the critical amplitude, the wave broadens, which is in marked contrast to the case of small amplitude waves where a sharpening of the wave crest normally occurs. The limiting form of the broadening wave is “a deep fluid bore.” The wave speed is found to depend nonlinearly on the wave amplitude and the traditional linear dependence underestimates this speed. [ABSTRACT FROM AUTHOR]

Numerical solutions are presented for a modified form of the canonical jet in crossflow (JICF) in which a steady round jet issues into a crossflow stream oscillating with a sinusoidal velocity profile. The numerical model uses large eddy simulation to simulate turbulent flow and mixing. This system is used to represent the dynamics and flow fields present during subsurface addition of reactants in stirred tanks. Thus, two variables associated with the oscillating crossflow velocity profile were manipulated to simulate the effects of impeller design and operation. Variation of the amplitude of crossflow oscillation had little effect on the trajectory of the jet plume, while variation in the frequency of crossflow oscillation was found to have a significant effect on plume trajectory. Additionally, oscillation of the crossflow affected the contiguity of the plume when compared with a steady crossflow JICF, resulting in mixing enhancement. The numerical solutions were validated using empirical data collected during a previous investigation of a steady crossflow JICF system. This research suggests that mixing during subsurface reagent addition could potentially be enhanced by optimizing impeller operating conditions and draft tube location, and the model presented here may offer a tractable computational method for optimization of these systems. [ABSTRACT FROM AUTHOR]