Two-phase Instability Research Articles

Direct Simulation Monte Carlo for astrophysical flows – II. Ram-pressure dynamics

We use the Direct Simulation Monte Carlo (DSMC) method combined with an n-body code to study the dynamics of the interaction between a gas-rich spiral galaxy and intracluster or intragroup medium, often known as the ram pressure scenario. The advantage of this gas kinetic approach over traditional hydrodynamics is explicit treatment of the interface between the hot and cold, dense and rarefied media typical of astrophysical flows and the explicit conservation of energy and momentum and the interface. This approach yields some new physical insight. Owing to the shock and backward wave that forms at the point ICM--ISM contact, ICM gas is compressed, heated and slowed. The shock morphology is Mach-disk-like. In the outer galaxy, the hot turbulent post-shock gas flows around the galaxy disk, while heating and ablating the initially cool disk gas. The outer gas and angular momentum are lost to the flow. In the inner galaxy, the hot gas pressurizes the neutral ISM gas causing a strong two-phase instability. As a result, the momentum of the wind is no longer impulsively communicated to the cold gas as assumed in the Gunn-Gott (1972) formula, but oozes through the porous disk, transferring its linear momentum to the disk en masse. The escaping gas mixture has a net positive angular momentum and forms a slowly rotating sheath. The shear flow caused by the post-shock ICM flowing through the porous multiphase ISM creates a strong Kelvin-Helmholtz instability in the disk that results in Cartwheel-like ring and spoke morphology.

Clump formation due to the gravitational instability of a multiphase medium in a massive protoplanetary disc

Planetary systems form in gas–dust protoplanetary discs via the growth of solid bodies. In this paper, we show that the most intriguing stage of such growth, namely the transformation of 1–10 m boulders into kilometre-sized planetesimals, can be explained by a mechanism of gravitational instability. The present work focused on the origin of self-gravitating clumps in which planetesimal formation could take place. Our computer simulations demonstrated that such clumps of gas and boulders formed due to the development of a two-phase instability. This instability revealed a so-called ‘mutual influence effect’ in the protoplanetary disc, where the dynamics of the system were determined by the collisionless collective motion of a low-mass subdisc composed of primary solids. We found that a 0.1cs velocity dispersion in the boulder subdisc was sufficient to cause the formation of self-gravitating clumps of gas and boulders. In such regimes, the time needed for the formation of the collapsing objects was less than the boulders’ dissipation time in the density waves of the medium.

Experimental Investigation of Two-Phase Flow Instabilities in Low-Mass-Flux Water Wall Tubes of Supercritical Circular Fluidized Bed Boilers

For the purpose of disclosing the hydrodynamic flow characteristics, under the low mass velocity conditions of the 600-MW supercritical circular fluidized beds boilers, experimental studies on instability of two-phase flow in parallel vertical internally ribbed tubes were conducted. Two kinds of oscillations, pressure-drop oscillation and density-wave oscillation, have been observed. In the range of test parameters the effects of pressure, mass flux, inlet subcooling, compressible volume, exit throttle, and asymmetric heat flux to the two-phase instability were explored and analyzed. Indications from experiment data are: To increase system pressure, mass flux and inlet subcooling will intensify the stability of water wall tubes. To increase exit throttle will intensify the instability of water wall tubes. The bounding pressure and bounding mass flux of density-wave oscillations and the bounding pressure of pressure-drop oscillation have been obtained. Based on the results of testing and using a homogeneous model, the threshold relational expressions of instability were obtained. The results may be used for the design and safe operation of parallel vertical rifled water wall tubes of supercritical circular fluidized beds boilers.

Experimental study of complex two-phase instabilities during the start-up of a vertical thermosyphon reboiler operating under vacuum

This paper reports experimental studies of the start-up at reduced pressures (0.105–0.171 bar) and low heat fluxes (1.23–1.55 kW m −2) of the thermosyphon reboiler research facility in the Morton Laboratory at the University of Manchester. This is a full scale replica of an industrial sized natural circulation thermosyphon reboiler comprising 50 vertically mounted 25 mm OD tubes of 3 m length with water as the process fluid in the tubes and with steam condensing in the shell side of the reboiler. Unstable behaviour is obtained at start-up with flow-induced instabilities (geysering) when the level of the liquid within the tubes of the bundle is up to the top tubesheet (100% submergence) and also at 83% submergence of the tubes irrespective of the process pressure. At 100% submergence of the tubes, intermittent reversed flows in the entire loop with substantial vibrations are obtained. Chaotic behaviour is obtained at the lower submergence level of 83%. However, start-up at process pressures of 0.22 and 1.04 bar, and low heat fluxes with the entire thermosyphon loop flooded with liquid completely alleviated the flow-induced instabilities observed at the lower submergence levels within the tubes. The flow in the closed loop of liquid is induced very soon after the steam is introduced into the reboiler due to the buoyancy forces emanating from differences in density around the loop. The start-up is smooth and relatively quick, but further instrumentation and control are required for the introduction of the feed to the thermosyphon system once vapour is generated. A control strategy and procedure is proposed which will avoid the instabilities that inherently occur with start-up procedures currently practised in industry.

A SIMPLE ANALYTICAL METHOD FOR NONLINEAR DENSITY WAVE TWO-PHASE INSTABILITY IN A SODIUM-HEATED AND HELICALLY COILED STEAM GENERATOR

A simple model to analyze non-linear density-wave instability in a sodium-cooled helically coiled steam generator is developed. The model is formulated with three regions with moving boundaries. The homogeneous equilibrium flow model is used for the two-phase region and the shell-side energy conservation is also considered for the heat flux variation in each region. The proposed model is applied to the analysis of two-phase instability in a JAEA (Japan Atomic Energy Agency) 50MWt No.2 steam generator. The steady state results show that the proposed model accurately predicts the six cases of operating temperatures on the primary and secondary sides. The sizes of three regions, the secondary side pressure drop according to the flow rate, and the temperature variation in the vertical direction are also predicted well. The temporal variations of the inlet flow rate according to the throttling coefficient, the boiling and superheating boundaries and the pressure drop in the two-phase and superheating regions are obtained from the unsteady analysis.

Analysis of flow instabilities in forced-convection steam generator

Because of the practical importance of two-phase instabilities, substantial efforts have been made to date to understand the physical phenomena governing such instabilities and to develop computational tools to model the dynamics. The purpose of this study is to present a numerical model for the analysis of flow-induced instabilities in forced-convection steam generator. The model is based on the assumption of homogeneous two-phase flow and ther-modynamic equilibrium of the phases. The thermal capacity of the heater wall has been included in the analysis. The model is used to analyze the flow instabilities in the steam generator and to study the effects of system pressure, mass flux, inlet temperature and inlet/outlet restriction, gap size, the ratio of d o/ d i, and the ratio of q i/ q o on the system behavior.

05/02510 Two-phase instability analysis in natural circulation loops of China advanced research reactor

Two-phase flow instability in natural circulation loops of China Advanced Research Reactor was investigated.The homogeneous flow model is used to establish the system control equations.Gear method is employed to solve the system equations documented in form of ordinary differential equations numerically.The boundaries of the instability of natural circulation loops were obtained.The variations of flux,pressure difference,wall temperature,fluid temperature and the boiling boundary were analyzed.Especially,the phase-space trajectory of boiling boundary at various flux was discussed.The calculated results have great significance for the safety operation of China Advanced Research Reactor and its accident analysis.

Two-phase instability analysis in natural circulation loops of China advanced research reactor

In this paper, two-phase flow instability in natural circulation loops of China Advanced Research Reactor (CARR) has been investigated. CARR is a low pressure and low power density research reactor. A natural circulation instability analysis model is developed for the natural circulation loop of CARR. The homogeneous flow model is used to establish the system control equations. The non-uniform heating and subcooled boiling heat transfer is included. The accumulation heat of the wall is also included. Numerical method of Gear is employed to solve the system equations documented in terms of ordinary differential equations. According to the calculation results, stability maps of the natural circulation loop, which confirm the presence of an instability region under the conditions of low equilibrium quality in the outlet and low pressure, are obtained. It is a special kind of density wave oscillation (DWO) that occurs in very low equilibrium quality region with the characteristics of geysering and ‘Type-I’ DWO at the same time. The calculation results show such oscillation course clearly. The variations of the mass flow rate, the pressure drop and the boiling boundary are analyzed separately. Especially, the phase-space trajectory of the boiling boundary and the mass flow rate is discussed. Finally the oscillation frequency is discussed. The calculated results have important significance for the safety operation and accidental analysis of CARR.

Microstructural change in gravity cast Mg−Ni alloys with Ni contents

The effects of Ni content on the microstructures of gravity cast Mg−Ni alloys were examined. Different shapes of primary solid particles and microstructures of the eutectic matrix were observed with varying Ni content. The eutectic matrix in the hypoeutectic alloy consisted of rod-like Mg2Ni phase with a small amount of α-Mg phase. The eutectic matrix in the near-eutectic and hypereutectic alloys consisted of eutectic cells oriented in different directions. A transition of lamellae to fiber occurred. The formation of cellular structure and transition of lamellae to fiber resulted from two-phase instability in the coupled region induced by constitutional undercooling.

TWO-PHASE FLOW THERMAL INSTABILITIES IN A HORIZONTAL IN-TUBE BOILING SYSTEM WITH ENHANCED SURFACES

This study is aimed at presenting the experimental results on two-phase flow thermal instabilities in a horizontal pipe with enhanced surfaces. Five different heat transfer surface configurations including one bare tube and four tubes with different enhancement inserts were used. Two types of thermal oscillations were observed: independent thermal oscillations and compound thermal oscillations. Independent thermal oscillations occurred due to the oscillatory behavior of the mixture-vapor transition point. Compound thermal oscillations are system-induced fluctuations and occur in a region of pressure drop oscillations where film boiling is occurring. The results reveal that the tubes with no enhanced surface give the smallest amplitudes and periods on the basis of the thermal oscillations in comparison to the all enhanced surfaces. Both the period and the amplitude of the independent thermal oscillations decrease with increasing inlet mass flow rate and with increasing inlet temperature. Heat transfer enhancement devices affected the thermal oscillation characteristics.

An insight into thermo-hydrodynamic coupling in closed loop pulsating heat pipes

A Closed Loop Pulsating Heat Pipe (CLPHP) is a complex heat transfer device with a strong thermo-hydrodynamic coupling governing its thermal performance. To better understand its operational characteristics, a two-phase loop is constructed with a capillary tube (ID = 2.0 mm) having no internal wick structure. The loop is heated at one end and cooled at the other and partially made up of glass to assist visualization. The working fluid employed is ethanol. It is concluded from the study that a two-phase loop does represent the thermo-fluidic characteristics of a multi-turn CLPHP. Dynamic two-phase instabilities are present in a two-phase loop also; although the number of turns in a CLPHP increases the level of internal perturbations. The existence of an optimum number of turns for a given heat throughput requirement is explained. Also, it is shown that classical thermodynamics based on quasi-equilibrium theory seems not to be sufficient for complete system analysis. The performance (i.e., overall thermal resistance) is strongly dependent on the flow pattern existing inside the tubes. The role of gravity in the operation characteristics is clarified.

Axisymmetric Instability of Fluid Saturated Pervious Cylinders

The emergence of two-phase instability is investigated analytically for the axisymmetric cylinders made of a pervious solid matrix with pores filled with an interstitial fluid. General analytical solutions are derived for a broad range of constitutive models, and are illustrated for a few specific types of solids. For particular combinations of stresses and material moduli, saturated hypoelastic and elastoplastic solids are found to undergo two-phase instability, whereas their dry solid matrices remain stable. Two-phase instability can emerge within stable single-phase solids due to the interaction between solid matrix and fluid flow. The present analysis provides general analytical solutions useful for investigating the instabilities of axisymmetric soil samples subjected to the undrained triaxial tests of geomechanics.

Plane strain instability of saturated elasto-plastic soils

The two-phase instability of saturated elasto-plastic soils is investigated under plane strain conditions. This type of material instability is characterised by a non-homogeneous field of solid deformation with vortex-like patterns, which grows rapidly and is accompanied by a non-uniform flow of interstitial water exhibiting source–sink flow patterns. Three simple criteria are established to define the conditions for the onset of two-phase instability within elasto-plastic soils saturated with an incompressible fluid and subjected to plane-strain undrained loadings. The simplest criterion states that the onset of instability almost coincides with the peak deviator stress during undrained loading. This analysis shows that two-phase instability in elasto-plastic soils is different from strain localisation, strain softening and con-stitutive singularities. Two-phase instability is likely to emerge before shear bands in contractant elasto-plastic soils of the Mohr–Coulomb type. The study suggests that two-phase instability may disrupt numerical liquefaction analyses using elasto-plastic soil models, and thus prompts the need for further analytical and experimental investigations.

Plane strain instability of saturated elasto–plastic soils

The two-phase instability of saturated elasto-plastic soils is investigated under plane strain conditions. This type of material instability is characterised by a non-homogeneous field of solid deformation with vortex-like patterns, which grows rapidly and is accompanied by a non-uniform flow of interstitial water exhibiting source–sink flow patterns. Three simple criteria are established to define the conditions for the onset of two-phase instability within elasto-plastic soils saturated with an incompressible fluid and subjected to plane-strain undrained loadings. The simplest criterion states that the onset of instability almost coincides with the peak deviator stress during undrained loading. This analysis shows that two-phase instability in elasto-plastic soils is different from strain localisation, strain softening and con-stitutive singularities. Two-phase instability is likely to emerge before shear bands in contractant elasto-plastic soils of the Mohr–Coulomb type. The study suggests that two-phase instability may disrupt numerical liquefaction analyses using elasto-plastic soil models, and thus prompts the need for further analytical and experimental investigations.

Flow excursion instability in downward flow systems part II: two-phase instability

A mechanistic model is presented in this paper to predict the onset of flow excursion in downward flows at low-pressure conditions. The model is represented in a graphical form on the subcooling number versus the Zuber (phase-change) number plane. The subcooling number and the Zuber number are measures of integral system parameter such as fluid properties, inlet subcooling, heat flux, channel geometry and coolant flow rate (all measurable quantities) resulting in an easy extrapolation of the predictive correlation to the physical system. The model addresses the distinction between the point of significant void and the onset of flow excursion and provides an analytical method for its evaluation. The model is compared with flow excursion data for downward flows and the agreement is satisfactory.

Plane-Strain Instability of Saturated Porous Media

Herein, we investigate the plane-strain instability of rectangular blocks that are made of porous materials saturated with a fluid. We model the material behavior with rate-type constitutive equations, and study the instability generated by the interaction of nearly incompressible solid and fluid constituents. Our investigation, although it applies to a broad range of materials, is limited to hypoelastic and elastoplastic models. Elastoplastic models are found to undergo two-phase instability even though the solid phase remains stable. Two-phase instability is more likely to occur in contractant hardening materials than in dilatant materials. Its emergence is triggered by the solid-fluid interaction, and is delayed by the grain-fluid compressibility. Two-phase instability also takes place in dilatant materials, but is less catastrophic than in contractant materials. The present analysis is useful for distinguishing the physical from the artificial origins of instabilities, which is an important issue in the numerical solutions of soil-liquefaction problems.