Instability of Combustion

THE following equations governing the phenomenon of intrinsic instability of combustion, leading to low frequency oscillations in a rocket motor using a single liquid propellant, were derived and investigated by L. Crocco.

A cyclostationary multi-domain analysis of fluid instability in Kaplan turbines

Hydraulic instabilities represent a critical problem for Francis and Kaplan turbines, reducing their useful life due to increase of fatigue on the components and cavitation phenomena. Whereas an exhaustive list of publications on computational fluid-dynamic models of hydraulic instability is available, the possibility of applying diagnostic techniques based on vibration measurements has not been investigated sufficiently, also because the appropriate sensors seldom equip hydro turbine units. The aim of this study is to fill this knowledge gap and to exploit fully, for this purpose, the potentiality of combining cyclostationary analysis tools, able to describe complex dynamics such as those of fluid-structure interactions, with order tracking procedures, allowing domain transformations and consequently the separation of synchronous and non-synchronous components. This paper will focus on experimental data obtained on a full-scale Kaplan turbine unit, operating in a real power plant, tackling the issues of adapting such diagnostic tools for the analysis of hydraulic instabilities and proposing techniques and methodologies for a highly automated condition monitoring system. © 2015 Elsevier Ltd.

Nonlinear saturation of ion-acoustic instability

It is proposed that the wave mediated indirect wave-particle interaction may be responsible for nonlinear saturation of current driven low frequency ion-acoustic turbulence. This process decreases the growth rate and increases the damping rate of the wave. Comparison has been made with some experiments.

Global lopsided instability in a purely stellar galactic disc

It is shown that pure exponential discs in spiral galaxies are capable of supporting slowly varying discrete global lopsided modes, which can explain the observed features of lopsidedness in the stellar discs. Using linearized fluid dynamical equations with the softened self-gravity and pressure of the perturbation as the collective effect, we derive self-consistently a quadratic eigenvalue equation for the lopsided perturbation in the galactic disc. On solving this, we find that the ground-state mode shows the observed characteristics of the lopsidedness in a galactic disc, namely the fractional Fourier amplitude A(1), increases smoothly with the radius. These lopsided patterns precess in the disc with a very slow pattern speed with no preferred sense of precession. We show that the lopsided modes in the stellar disc are long-lived because of a substantial reduction (approximately a factor of 10 compared to the local free precession rate) in the differential precession. The numerical solution of the equations shows that the groundstate lopsided modes are either very slowly precessing stationary normal mode oscillations of the disc or growing modes with a slow growth rate depending on the relative importance of the collective effect of the self-gravity. N-body simulations are performed to test the spontaneous growth of lopsidedness in a pure stellar disc. Both approaches are then compared and interpreted in terms of long-lived global m = 1 instabilities, with almost zero pattern speed.

Surface instability of confined elastic bilayers: Theory and simulations

The surface of a soft elastic film becomes unstable and forms a self-organized undulating pattern because of adhesive interactions when it comes in contact proximity with a rigid surface. For a single film, the pattern length scale lambda, which is governed by the minimization of the elastic stored energy, gives lambda similar to 3h, where h is the film thickness. Based on a linear stability analysis and simulations of adhesion and debonding, we consider the contact instability of an elastic bilayer, which provides greater flexibility in the morphological control of interfacial instability. Unlike the case of a single film, the morphology of the contact instability patterns, debonding distance, and debonding force in a bilayer can be controlled in a nonlinear way by varying the thicknesses and shear moduli of the films. Interestingly, the pattern wavelength in a bilayer can be greatly increased or decreased compared to a single film when the adhesive contact is formed by the stiffer or the softer of the two films, respectively. In particular, lambda as small as 0.5h can be obtained. This indicates a new strategy for pattern miniaturization in elastic contact lithography.

Instability of Coupled Longitudinal and Transverse Electromagnetic Modes of Wave‐Propagation in Bounded Streaming Plasmas

The instability of coupled longitudinal and transverse electromagnetic modes associated with long wavelengths is studied in bounded streaming plasmas. The main conclusions are as follows: (i) For long waves for which O (k 2)=0, in the absence of relative streaming motion of electrons and ions and aωp/c<0.66, the whole spectrum of harmonic waves is excited due to finite temperature and boundary effects consisting of two subseries. One of these subseries can be identified with Tonks-Dattner resonance oscillations for the electrons, and arises primarily due to the electrons with frequencies greater than the electrostatic plasma frequency corresponding to the electron density in the midplane in the undisturbed state. The other series arises primarily due to ion motion. When aωp/c>0.66, in addition to the above spectrum of harmonic waves, the system admits an infinite number of growing and decaying waves. The instability associated with these modes is found to arise due to the interaction of the waves inside the plasma with the external electromagnetic field. (ii) For modes with comparatively shorter wavelengths for which O (k3)=0, the coupling due to finite temperature sets in, and it is found that the two series of harmonic waves obtained in (i) deriving energy from the transverse modes also become unstable. Thus, for these wavelengths the system admits three sets of growing and decaying modes, first two for all values of aωp/c and the third for (aωp/c) > 0.66. (iii) The presence of streaming velocities introduces various other coupling mechanisms, and we find that even for the wavelengths for which O (k2)=0, we get three sets of growing and decaying waves. The numerical values for the growth rates show that the streaming velocities enhance the growth rates of instability significantly.

Two-stream instability in plasma

The problem of two-stream instability in plasma is studied by specifying the importance of initial magnetic field associated with the motion of the charged particles and the boundary effects. In Part I the accurate initial steady state is studied when the streams of electrons and ions move with different uniform speeds in plasmas with plane and cylindrical geometry. In Part II, in order to show the effects of finiteness and inhomogeneity of the system, small transverse plasma oscillations are studied in the case of plane plasmas. The role of plasma-sheath oscillations at the boundaries is found to be very important in driving the instabilities associated with the electromagnetic modes. The numerical estimates of the growth rates of the instability are given for the specific case of the physical data in discharge tubes.

MECHANISMS AND EFFECTS OF MITOCHONDRIAL DNA INSTABILITY AND COPY NUMBER MANIPULATION

Defects in mitochondrial DNA (mtDNA) maintenance cause a range of human diseases, including autosomal dominant progressive external ophthalmoplegia (adPEO). This study aimed to clarify the molecular background of adPEO. We discovered that deoxynucleoside triphosphate (dNTP) metabolism plays a crucial in mtDNA maintenance and were thus prompted to search for therapeutic strategies based on the modulation of cellular dNTP pools or mtDNA copy number. Human mtDNA is a 16.6 kb circular molecule present in hundreds to thousands of copies per cell. mtDNA is compacted into nucleoprotein clusters called nucleoids. mtDNA maintenance diseases result from defects in nuclear encoded proteins that maintain the mtDNA. These syndromes typically afflict highly differentiated, post-mitotic tissues such as muscle and nerve, but virtually any organ can be affected. adPEO is a disease where mtDNA molecules with large-scale deletions accumulate in patients tissues, particularly in skeletal muscle. Mutations in five nuclear genes, encoding the proteins ANT1, Twinkle, POLG, POLG2 and OPA1, have previously been shown to cause adPEO. Here, we studied a large North American pedigree with adPEO, and identified a novel heterozygous mutation in the gene RRM2B, which encodes the p53R2 subunit of the enzyme ribonucleotide reductase (RNR). RNR is the rate-limiting enzyme in dNTP biosynthesis, and is required both for nuclear and mitochondrial DNA replication. The mutation results in the expression of a truncated form of p53R2, which is likely to compete with the wild-type allele. A change in enzyme function leads to defective mtDNA replication due to altered dNTP pools. Therefore, RRM2B is a novel adPEO disease gene. The importance of adequate dNTP pools and RNR function for mtDNA maintenance has been established in many organisms. In yeast, induction of RNR has previously been shown to increase mtDNA copy number, and to rescue the phenotype caused by mutations in the yeast mtDNA polymerase. To further study the role of RNR in mammalian mtDNA maintenance, we used mice that broadly overexpress the RNR subunits Rrm1, Rrm2 or p53R2. Active RNR is a heterotetramer consisting of two large subunits (Rrm1) and two small subunits (either Rrm2 or p53R2). We also created bitransgenic mice that overexpress Rrm1 together with either Rrm2 or p53R2. In contrast to the previous findings in yeast, bitransgenic RNR overexpression led to mtDNA depletion in mouse skeletal muscle, without mtDNA deletions or point mutations. The mtDNA depletion was associated with imbalanced dNTP pools. Furthermore, the mRNA expression levels of Rrm1 and p53R2 were found to correlate with mtDNA copy number in two independent mouse models, suggesting nuclear-mitochondrial cross talk with regard to mtDNA copy number. We conclude that tight regulation of RNR is needed to prevent harmful alterations in the dNTP pool balance, which can lead to disordered mtDNA maintenance. Increasing the copy number of wild-type mtDNA has been suggested as a strategy for treating PEO and other mitochondrial diseases. Only two proteins are known to cause a robust increase in mtDNA copy number when overexpressed in mice; the mitochondrial transcription factor A (TFAM), and the mitochondrial replicative helicase Twinkle. We studied the mechanisms by which Twinkle and TFAM elevate mtDNA levels, and showed that Twinkle specifically implements mtDNA synthesis. Furthermore, both Twinkle and TFAM were found to increase mtDNA content per nucleoid. Increased mtDNA content in mouse tissues correlated with an age-related accumulation of mtDNA deletions, depletion of mitochondrial transcripts, and progressive respiratory dysfunction. Simultaneous overexpression of Twinkle and TFAM led to a further increase in the mtDNA content of nucleoids, and aggravated the respiratory deficiency. These results suggested that high mtDNA levels have detrimental long-term effects in mice. These data have to be considered when developing and evaluating treatment strategies for elevating mtDNA copy number.

Instability of the self-similar flow into a cavity

In this paper we have investigated the instability of the self-similar flow behind the boundary of a collapsing cavity. The similarity solutions for the flow into a cavity in a fluid obeying a gas law p = Kργ, K = constant and 7 ≥ γ > 1 has been solved by Hunter, who finds that for the same value of γ there are two self-similar flows, one with accelerating cavity boundary and other with constant velocity cavity boundary. We find here that the first of these two flows is unstable. We arrive at this result only by studying the propagation of disturbances in the neighbourhood of the singular point.

The effect of viscosity and surface tension on the Taylor instability of the surface of a cavitation bubble*

This paper is devoted to a consideration of the following problem: A spherical mass of fluid of density varrho1, viscosity μ1 and external radius R is surrounded by a fluid of density varrho2 and viscosity μ2.The fluids are immiscible and incompressible. The interface is accelerated radially by g1: to study the effect of viscosity and surface tension on the stability of the interface. By analyzing the problem in spherical harmonics the mathematical problem is reduced to one of solution of the characteristic determinant equation. The particular case of a cavity bubble, where the viscosity μ1 of the fluid inside the bubble is negligible in comparison with the viscosity μ2 of the fluid outside the bubble, is considered in some detail. It is shown that viscosity has a stabilizing role on the interface; and when g1 > T(n − 1) (n + 2)/R2(varrho2 − varrho1) the stabilizing role of both viscosity and surface tension is more pronounced than would result when either of them is taken individually.

Localised instability in unsteady separation bubbles

We propose in experimental method to study the instability of thin unsteady separation bubbles, i.e. of unsteady boundary layers with reverse flow. The unsteady boundary layer is created by controlled temporal and spatial variations of the velocity external to the boundary layer. We present results of the evolution of instability in different temporally varying flows in a shallow angle diffuser. Depending on the extent of reverse flow in the boundary we observe that instability can be spatially localised.

Monetary Policy, Stock Price Misalignments and Macroeconomic Instability

Perhaps the most fundamental prediction of financial theory is that the expected returns on financial assets are determined by the amount of risk contained in their payoffs. Assets with a riskier payoff pattern should provide higher expected returns than assets that are otherwise similar but provide payoffs that contain less risk. Financial theory also predicts that not all types of risks should be compensated with higher expected returns. It is well-known that the asset-specific risk can be diversified away, whereas the systematic component of risk that affects all assets remains even in large portfolios. Thus, the asset-specific risk that the investor can easily get rid of by diversification should not lead to higher expected returns, and only the shared movement of individual asset returns – the sensitivity of these assets to a set of systematic risk factors – should matter for asset pricing. It is within this framework that this thesis is situated. The first essay proposes a new systematic risk factor, hypothesized to be correlated with changes in investor risk aversion, which manages to explain a large fraction of the return variation in the cross-section of stock returns. The second and third essays investigate the pricing of asset-specific risk, uncorrelated with commonly used risk factors, in the cross-section of stock returns. The three essays mentioned above use stock market data from the U.S. The fourth essay presents a new total return stock market index for the Finnish stock market beginning from the opening of the Helsinki Stock Exchange in 1912 and ending in 1969 when other total return indices become available. Because a total return stock market index for the period prior to 1970 has not been available before, academics and stock market participants have not known the historical return that stock market investors in Finland could have achieved on their investments. The new stock market index presented in essay 4 makes it possible, for the first time, to calculate the historical average return on the Finnish stock market and to conduct further studies that require long time-series of data.

Nonlinear intrinsic instability of solid propellant combustion including gas-phase thermal inertia

The problem of homogeneous solid propellant combustion instability is studied with a one-dimensional flame model, including the effects of gas-phase thermal inertia and nonlinearity. Computational results presented in this paper show nonlinear instabilities inherent in the equations, due to which periodic burning is found even under steady ambient conditions such as pressure. The stability boundary is obtained in terms of Denison-Baum parameters. It is found that inclusion of gas-phase thermal inertia stabilizes the combustion. Also, the effect of a distributed heat release in the gas phase, compared to the flame sheet model, is to destabilize the burning. Direct calculations for finite amplitude pressure disturbances show that two distinct resonant modes exist, the first one near the natural frequency as obtained from intrinsic instability analysis and a second mode occurring at a much higher driving frequency. It is found that er rn in the low frequency region, the response of the propellant is significantly affected by the specific type of gas-phase chemical heat-release model employed. Examination of frequency response function reveals that the role of gas-phase thermal inertia is to stabilize the burning near the first resonant mode. Calculations made for different amplitudes of driving pressure show that the mean burning rate decreases with increasing amplitude. Also, with an increase in the driving amplitude, higher harmonics are generated in the burning rate.

Adhesion-Induced Instability in Asperities

Adhesive forces between two approaching asperities will deform the asperities, and under certain conditions this will result in a sudden runaway deformations leading to a jump-to-contact instability. We present finite element-based numerical studies on adhesion-induced deformation and instability in asperities. We consider the adhesive force acting on an asperity, when it is brought near a rigid half-space, due to van der Waals interaction between the asperity and the half-space. The adhesive force is considered to be distributed over the volume of the asperity (body force), thus resulting in more realistic simulations for the length scales considered. Iteration scheme based on a ``residual stress update'' algorithm is used to capture the effect of deformation on the adhesion force, and thereby the equilibrium configuration and the corresponding force. The numerical results are compared with the previous approximate analytical solutions for adhesion force, deformation of the asperity and adhesion-induced mechanical instability (jump-to-contact). It is observed that the instability can occur at separations much higher,and could possibly explain the higher value of instability separation observed in experiments. The stresses in asperities, particularly in case of small ones, are found to be high enough to cause yielding before jump -to-contact. The effect of roughness is considered by modeling a spherical protrusion on the hemispherical asperity.This small-scale roughness at the tip of the asperities is found to control the deformation behavior at small separations, and hence are important in determining the friction and wear due to the jump-to-contact instability.