A review of the ONR/NAVAIR research option combustion instabilities in compact ramjets, 1983-1988

This paper consists of two parts summarizing two portions of the ONR/NAVAIR Research Option. The option began in 1983 and continued for five years, involving 11 organizations. Simultaneously, similar or related programs supported by other agencies or institutions were being carried out in several other places. Results of those programs have been briefly summarized in five papers collected in a document to be published by C.P.L.A. This paper contains two of the five papers in that document. Here we cover the subjects of approximate analyses and stability; and large-scale structures and passive control. The first is concerned chiefly with an analytical framework constructed on the basis of observations; it is intended to provide a means of correlating and interpreting data, and predicting the stability of motions in a combustion chamber. The second is a summary of recent experimental work directed to understanding the flows in dump combustors of the sort used in modern ramjet engines. Much relevant material is not included here, but may be found in the remaining papers of the document cited above. For completeness, we note briefly the substance of those reports. In their summary "Spray Combustion Processes in Ramjet Combustion Instability," Bowman (Stanford), Law (University of California, Davis) and Sirignano (University of California, Irvine) review several aspects of spray combustion relevant to combustion instabilities. The objectives of the works were: (1) to determine the effect of spray characteristics on the energy release pattern in a dump combustor and the subsequent effects on combustion instability; (2) to gain a fundamental understanding of the coupling of the spray vaporization process with an unsteady flow field; and (3) to investigate methods for controlling and enhancing spray vaporization rates in liquid-fueled ramjets. During the past five years considerable progress has been made in applying methods of computational fluid dynamics to the flow in a dump combustor including consequences of energy release due to combustion processes. Jou has summarized work done at Flow Research, Inc. and at the Naval Research Laboratory in his paper "A Summary Report on Large-Eddy Simulations of Pressure Oscillations in a Ramjet Combustor." The serious effects of combustion instabilities on the inlets of ramjet engines were discovered in the late 1970's in experimental work at the Aeropropulsion Laboratory, Wright Field, the Naval Weapons Center and the Marquardt Company. The most thorough laboratory work on the unsteady behavior of inlets has been accomplished at the McDonnell-Douglas Research Laboratory by Sajben who has reviewed the subject in his paper "The Role of Inlet in Ramjet Pressure Oscillations.

Numerical solution of a non-linear conservation law applicable to the interior dynamics of partially molten planets

The energy balance of a partially molten rocky planet can be expressed as a non-linear diffusion equation using mixing length theory to quantify heat transport by both convection and mixing of the melt and solid phases. In this formulation the effective or eddy diffusivity depends on the entropy gradient, $\partial S/\partial r$, as well as entropy. First we present a simplified model with semi-analytical solutions, highlighting the large dynamic range of $\partial S/\partial r$, around 12 orders of magnitude, for physically-relevant parameters. It also elucidates the thermal structure of a magma ocean during the earliest stage of crystal formation. This motivates the development of a simple, stable numerical scheme able to capture the large dynamic range of $\partial S/\partial r$ and provide a flexible and robust method for time-integrating the energy equation. We then consider a full model including energy fluxes associated with convection, mixing, gravitational separation, and conduction that all depend on the thermophysical properties of the melt and solid phases. This model is discretised and evolved by applying the finite volume method (FVM), allowing for extended precision calculations and using $\partial S/\partial r$ as the solution variable. The FVM is well-suited to this problem since it is naturally energy conserving, flexible, and intuitive to incorporate arbitrary non-linear fluxes that rely on lookup data. Special attention is given to the numerically challenging scenario in which crystals first form in the centre of a magma ocean. Our computational framework is immediately applicable to modelling high melt fraction phenomena in Earth and planetary science research. Furthermore, it provides a template for solving similar non-linear diffusion equations arising in other disciplines, particularly for non-linear functional forms of the diffusion coefficient

Entropy production selects nonequilibrium states in multistable systems

Far-from-equilibrium thermodynamics underpins the emergence of life, but how has been a long-outstanding puzzle. Best candidate theories based on the maximum entropy production principle could not be unequivocally proven, in part due to complicated physics, unintuitive stochastic thermodynamics, and the existence of alternative theories such as the minimum entropy production principle. Here, we use a simple, analytically solvable, one-dimensional bistable chemical system to demonstrate the validity of the maximum entropy production principle. To generalize to multistable stochastic system, we use the stochastic least-action principle to derive the entropy production and its role in the stability of nonequilibrium steady states. This shows that in a multistable system, all else being equal, the steady state with the highest entropy production is favored, with a number of implications for the evolution of biological, physical, and geological systems.Comment: 15 pages, 4 figure

First-principles prediction of a decagonal quasicrystal containing boron

We interpret experimentally known B-Mg-Ru crystals as quasicrystal approximants. These approximant structures imply a deterministic decoration of tiles by atoms that can be extended quasiperiodically. Experimentally observed structural disorder corresponds to phason (tile flip) fluctuations. First-principles total energy calculations reveal that many distinct tilings lie close to stability at low temperatures. Transfer matrix calculations based on these energies suggest a phase transition from a crystalline state at low temperatures to a high temperature state characterized by tile fluctuations. We predict B$_{38}$Mg$_{17}$Ru$_{45}$ forms a decagonal quasicrystal that is metastable at low temperatures and may be thermodynamically stable at high temperatures.Comment: 4 pages, 3 figures, submitted to Phys. Rev. Let

Phase behavior of flowerlike micelles in a SCF cell model

We study the interactions between flowerlike micelles, self-assembled from telechelic associative polymers, using a molecular self-consistent field (SCF) theory and discuss the corresponding phase behavior. In these calculations we do not impose properties such as aggregation number, micellar structure and number of bridging chains. Adopting a SCF cell model, we calculate the free energy of interaction between a central micelle surrounded by others. Based on these results, we predict the binodal for coexistence of dilute and dense liquid phases, as a function of the length of the hydrophobic and hydrophilic blocks. In the same cell model we compute the number of bridges between micelles, allowing us to predict the network transition. Several quantitative trends obtained from the numerical results can be rationalized in terms of transparent scaling argument