The effects of rate of expansion and injection of water droplets on the entropy generation of nucleating steam flow in a Laval nozzle

The entropy generation due to irreversible heat transfer between vapor and liquid phases in a nucleating steam flow in a Laval nozzle is studied. To calculate the entropy generation due to self-condensation in transonic steam flow, a thermodynamic model is presented. The calculations of nucleating steam flow and the predictions of entropy generation rely on one-dimensional two-phase model. This model shows that the most of the thermodynamic losses take place during the nucleation phenomena. The effect of rate of expansion on the exergy losses is considered by decreasing the divergent angle of nozzle. Also micro-sized pure water droplets is injected theoretically to supercooled steam right after the nozzle throat at the onset of divergent section and the effects of injected droplets on thermodynamic losses and nucleation phenomena are investigated. The results indicate that decreasing the divergent angle and also injection of droplets diminishes the pressure rise in transonic steam flow and decreases the thermal entropy generation due to nucleation.     

A study of thermal nonequilibrium effects in low-pressure wet-steam turbines using a blade-to-blade time-marching technique

A theoretical analysis of the wet-steam flow in the low pressure cylinder of a 500 MW steam turbine using a blade-to-blade time-marching computer program is described. The calculating method can compute most types of wet-steam flow found in LP turbines, including those involving both primary and secondary nucleations in transonic and supersonic blading with shock waves. In particular, condensing flows in highly staggered rotor tip sections can be computed without difficulty. Extensive results are presented showing the effect of departures from thermal equilibrium on the blade surface pressure and velocity distributions, the blade outlet relative flow angle, the mass flow coefficient and the thermodynamic loss coefficient. On the basis of the analysis, recommendations are made concerning the application of nonequilibrium wet-steam theory to steam turbine design.     

Propagation of a pressure wave in two-phase flow with very high void fraction

An experimental and theoretical study of a finite amplitude pressure wave propagating through a two-phase media of about 0.9999–0.99999 void fraction is performed. This two-phase media consists of many parallel liquid films in a gas. The films are perpendicular to the wave propagation direction and result in a two-phase fluid of extremely high void fraction. Experiments are done in a vertical shock tube and show that the shock wave is broken down into an initial sharply rising wave and a second gradually rising wave. The velocity of the first wave agrees well with the theoretical prediction assuming an adiabatic thermal equilibrium change, which approaches the gas sonic velocity in the two-phase flow in the low void fraction region. The second wave is caused by the complex reflection and destruction of the waves.     

Initiation of explosive boiling of a droplet with a shock wave

The role of incident shock waves in the initiation of vapor explosions in volatile liquid hydrocarbons has been investigated. Experiments were carried out on single droplets (1–2 mm diameter) immersed in a host fluid and heated to temperatures at or near the limit of superheat. Shocks generated by spark discharge were directed at previously nonevaporating drops as well as at drops boiling stably at high pressure. Explosive boiling is triggered in previously nonevaporating drops only if the drop temperature is above a threshold temperature that is near the superheat limit. Interaction of a shock with a stably boiling drop immediately causes a transition to violent unstable boiling in which fine droplets are torn from the evaporating interface, generating a two-phase flow downstream. On the previously nonevaporating interface between the drop and the host liquid, multiple nucleation sites appear which grow rapidly and coalesce. Overpressures generated in the surrounding fluid during bubble collapse may reach values on the same level as the pressure jump across the shock wave that initiated the explosive boiling. A simple calculation is given, which suggests that shock focusing may influence the location at which unstable boiling is initiated.     

Hydrodynamical problems of first-order phase transitions

The two-phase liquid-vapor system in a state of thermodynamic equilibrium is considered. If a shock wave propagates in this medium, during its passage the material undergoes shock compression and transforms into a new equilibrium state. Not only the initial velocity changes in this case, but so does the quantitative composition of the phases. Due to the complication of the process, analytic results have practically not been available so far. Calculations of parameters behind the shock discontinuity were carried out approximately by using various tables and nomograms, restricted basically to only one two-phase system, H₂O. Thus, condensation jumps were treated in [1–4] in two-phase supersonic flows within the single-velocity model and a low content of the liquid phase in the mixture. Using the assumptions mentioned, the various parameters were found at the front of the shock wave by numerical solution of the conservation equations of mass, momentum, and energy at the discontinuity. The thermodynamic parameters are usually given in tabulated form as a function of pressure or temperature for equilibrium conditions of the phases.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 81–87, September–October, 1977.     

Origin of droplet size underprediction in modeling of low pressure nucleating flows of steam

This article examines deficiencies in nucleation rate and droplet growth models that impair modeling of low pressure (LP) nucleating flows of steam. It is shown that classical nucleation theory (CNT) exhibits excessive dependence on supersaturation in the operating range of LP condensing (wet-steam) flows. The complex mechanisms of the nucleation-growth model are explained with regard to discrepancies in the modeling results. The discrepancy between modeling results and LP wet-steam experiments is attributed to imprecision in CNT and inadequacies in the employed droplet growth equation. The link between the excessive dependence of CNT on supersaturation and underprediction of the mean droplet size is explained. Two examples are given demonstrating that the inverse correlation between mean droplet size and nucleation rate can be moderated by rectifying and reducing the dependence of CNT on supersaturation. Moreover, prediction of mean droplet size is improved without modifying the location and magnitude of the condensation shock.     

The effect of fine evaporating droplets on the adiabatic-wall temperature in a compressible two-phase boundary layer

A steady-state supersonic flow of a viscous heat-conducting gas with an admixture of small droplets over a flat plate is considered. The plate surface is assumed to be thermally insulated, and its equilibrium temperature is greater than the evaporation point of the droplets. In contrast to previous publications, the case of low-inertia droplets, which do not deposit onto the wall and have time to evaporate in the boundary layer, is considered. Within the two-fluid approximation for the laminar gasdroplet boundary layer with a compressible carrier phase, a parametric numerical study of the effect of evaporating droplets on the boundary layer structure and the temperature of the adiabatic wall is performed. The similarity parameters are found and the range of these parameters is determined, in which the adiabatic-wall temperature is reduced substantially due to the droplet evaporation even for very low initial concentrations of the liquid phase. This makes promising the use of the condensed phase in the schemes of gasdynamic energy separation based on heat transfer between the flows in subsonic and supersonic boundary layers.     

Supersonic Gas Flows in Radial Nozzles

Results of experimental investigations and numerical simulations of supersonic gas flows in radial nozzles with different nozzle widths are presented. It is demonstrated that different types of the flow are formed in the nozzle with a fixed nozzle radius and different nozzle widths: supersonic flows with oblique shock waves inducing boundary layer separation are formed in wide nozzles, and flows with a normal pseudoshock separating the supersonic and subsonic flow domains are formed in narrow nozzles (micronozzles). The pseudoshock structure is studied, and the total pressure loss in the case of the gas flow in a micronozzle is determined.     

Theoretical and experimental investigation of condensation in a centered rarefaction wave

The analysis of the process of spontaneous condensation in one-dimensional formulation is dealt with adequately in many papers. However, in reality supersonic flows are not one-dimensional. The most striking effect of two-dimensionality is manifested in two-phase flows, for example in nozzles, inclined sections of jet turbine grills and rarefaction waves. The investigation of these flows, both in the experimental and theoretical aspect, is a complex problem for which a solution has been found only recently. The results are given in this paper of a theoretical and experimental investigation of spontaneous condensation of water vapor in a centered rarefaction wave formed by flow around a protuberant angle by a hypersonic stream.Translated from Prikladnaya Mekhanika i Tekhnicheskii Fiziki, No. 5, pp. 117–122, September–October, 1971.     

Phase discontinuities in water flows through a porous medium

Flow of a fluid through a porous medium is considered with allowance for heat conduction processes and phase transitions. Discontinuities in flows between both single-phase zones saturated with water and steam and single-and two-phase zones saturated with an equilibrium steam-water mixture are studied. It is shown that only the evaporation fronts are evolutionary for a convex-downward shock adiabat of the discontinuity inside the steam-water mixture. The structure of these fronts is considered and a condition supplementary to the conservation laws and necessary for the well-posed formulation of problems whose solution contains this front is found from the condition of existence of a discontinuity structure between the water (steam) and the steam-water mixture.     

Rarefaction waves in nonequilibrium-boiling fluid flows

The depressurization of a high-pressure vessel initially filled with water heated to below the saturation point is investigated. After depressurization, the pressure in the vessel drops and the boiling fluid flows out into the atmosphere. The experiments [1–3] showed that, when the first rarefaction wave passes through the fluid and the pressure falls below the saturation point, a two-phase mixture with a small steam volume fraction (below 20%) is formed in the vessel. Intense boiling starts only after the arrival of a rarefaction wave traveling at a speed ∼ 10 m/s called the "boiling shock" in [4]. To explain the specific features of this process we developed a mathematical model which takes the difference in the phase velocities into account. Although in bubbly flows this difference is only ∼ 1 m/s, it is enough to cause bubble fragmentation. The calculation showed that the fragmentation proceeds like a chain reaction, i. e. one fragmentation event creates the conditions for the succeeding events. The avalanche-like bubble number growth leads to sharp boiling intensification and the rapid transition of the non-equilibrium mixture to the equilibrium state. This process occurs in a narrow region, namely, in a slow boiling wave which, in the numerical calculations, looks like a shock. The model developed has made it possible to obtain numerical solutions which agree well with the experimental data, to study the wave structure, and to explain the wave mechanism. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 4, pp. 20–33, July–August, 2000. The work received financial support in part from the Russian Foundation for Basic Research (project 99-03-32042) and from INTAS (grant OPEN 97-2027).     

Transient three-dimensional startup side load analysis of a regeneratively cooled nozzle

The objective of this effort is to develop a computational methodology to capture the side load physics and to anchor the computed aerodynamic side loads with the available data by simulating the startup transient of a regeneratively cooled, high-aspect-ratio nozzle, hot-fired at sea level. The computational methodology is based on an unstructured-grid, pressure-based, reacting flow computational fluid dynamics and heat transfer formulation, and a transient inlet history based on an engine system simulation. Emphases were put on the effects of regenerative cooling on shock formation inside the nozzle, and ramp rate on side load reduction. The results show that three types of asymmetric shock physics incur strong side loads: the generation of combustion wave, shock transitions, and shock pulsations across the nozzle lip, albeit the combustion wave can be avoided with sparklers during hot-firing. Results from both regenerative cooled and adiabatic wall boundary conditions capture the early shock transitions with corresponding side loads matching the measured secondary side load. It is theorized that the first transition from free-shock separation to restricted-shock separation is caused by the Coanda effect. After which the regeneratively cooled wall enhances the Coanda effect such that the supersonic jet stays attached, while the hot adiabatic wall fights off the Coanda effect, and the supersonic jet becomes detached most of the time. As a result, the computed peak side load and dominant frequency due to shock pulsation across the nozzle lip associated with the regeneratively cooled wall boundary condition match those of the test, while those associated with the adiabatic wall boundary condition are much too low. Moreover, shorter ramp time results show that higher ramp rate has the potential in reducing the nozzle side loads.

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Two-dimensional mixed flows of a supersaturated and two-phase medium with nonequilibrium phase transitions

The singularities of two-dimensional interchannel flows of a condensing and damp vapor with nonequilibrium phase transitions which contain gas-dynamic discontinuities are investigated. A through-computation difference method is constructed for such flows. The results of the numerical investigation of steam flows with spontaneous condensation in supersonic plane nozzles containing a break in the walls and flow around a wedge are represented. It is shown that nonequilibrium condensation can result in a qualitative rearrangement of the wave structure of the flow which is impossible to obtain within the framework of the one-dimensional approach.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 87–93, July–August, 1978.     

Droplet break-up through an oblique shock wave

The interaction of a two-phase flow with a wedge where a stationary shock wave is initially settled is studied in a two-dimensional configuration. Before the introduction of the dispersed phase, the flow around the wedge is a supersonic one phase flow such as an attached stationary shock wave is present. Then, the dispersed phase is introduced upstream the initial position of the stationary shock wave. The purpose of this study is to point out two-phase and droplets break-up effects on the oblique shock wave. The two-dimensional equations are solved by a TVD scheme where fluxes are computed by using Riemann solver for the gas phase equations and also for the dispersed phase equations wich is an original approach due to the authors (Saurel et al. 1994). In addition to drag forces and heat and mass transfers, the process of droplets fragmentation based on the particle oscillation is considered. Accepted April 28, 1995     

The formation of a secondary shock wave behind a shock wave diffracting at a convex corner

This paper deals with the formation of a secondary shock wave behind the shock wave diffracting at a two-dimensional convex corner for incident shock Mach numbers ranging from 1.03 to 1.74 in air. Experiments were carried out using a 60 mm 150 mm shock tube equipped with holographic interferometry. The threshold incident shock wave Mach number () at which a secondary shock wave appeared was found to be = 1.32 at an 81° corner and = 1.33 at a 120° corner. These secondary shock waves are formed due to the existence of a locally supersonic flow behind the diffracting shock wave. Behind the diffracting shock wave, the subsonic flow is accelerated and eventually becomes locally supersonic. A simple unsteady flow analysis revealed that for gases with specific heats ratio the threshold shock wave Mach number was = 1.346. When the value of is less than this, the vortex is formed at the corner without any discontinuous waves accompanying above the slip line. The viscosity was found to be less effective on the threshold of the secondary shock wave, although it attenuated the pressure jump at the secondary shock wave. This is well understood by the consideration of the effect of the wall friction in one-dimensional duct flows. In order to interpret the experimental results a numerical simulation using a shock adaptive unstructured grid Eulerian solver was also carried out. Received 1 May 1996 / Accepted 12 September 1996     

Supersonic flow of combustible gas mixture past sphere with account for ignition delay time

Assume an axisymmetric blunt body or a symmetric profile is located in a uniform supersonic combustible gas mixture stream with the parameters M₁, p₁, and T₁. A detached shock is formed ahead of the body and the mixture passing through the, shock is subjected to compression and heating. Various flow regimes behind the shock wave may be realized, depending on the freestream conditions. For low velocities, temperatures, or pressures in the free stream, the mixture heating may not be sufficient for its ignition, and the usual adiabatic flow about the body will take place. In the other limiting case the temperature behind the adiabatic shock and the degree of gas compression in the shock are so great that the mixture ignites instantaneously and burns directly behind the shock wave in an infinitesimally thin zone, i. e., a detonation wave is formed. The intermediate case corresponds to the regime in which the width of the reaction zone is comparable with the characteristic linear dimension of the problem, for example, the radius of curvature of the body at the stagnation point.The problem of supersonic flow of a combustible mixture past a body with the formation of a detonation front has been solved in [1, 2]. The initial mixture and the combustion products were considered perfect gases with various values of the adiabatic exponent .These studies investigated the effect of the magnitude of the reaction thermal effect and flow velocity on the flow pattern and the distribution of the gasdynamic functions behind the detonation wave.In particular, the calculations showed that the strong detonation wave which is formed ahead of the sphere gradually transforms into a Chapman-Jouguet wave at a finite distance from the axis of symmetry. For planar flow in the case of flow about a circular cylinder it is shown that the Chapman-Jouguet regime is established only asymptotically, i. e., at infinity.This result corresponds to the conclusions of [3, 4], in which a theoretical analysis is given of the asymptotic behavior of unsteady flows with planar, spherical, and cylindrical detonation waves.Available experimental data show that in many cases the detonation wave does not degenerate into a Chapman-Jouguet wave as it decays, bur rather at some distance from the body it splits into an adiabatic shock wave and a slow combustion front.The position of the bifurcation point cannot be determined within the framework of the zero thickness detonation front theory [1], and for the determination of the location of this point we must consider the structure of the combustion zone in the detonation wave. Such a study was made with very simple assumptions in [5].The present paper presents a numerical solution of the problem of combustible mixture flow about a sphere with a very simple model for the structure of the combustion zone, in which the entire flow behind the bow shock wave consists of two regions of adiabatic flow-an induction region and a region of equilibrium flow of products of combustion separated by the combustion front in which the mixture burns instantaneously. The solution is presented only for subsonic and transonic flow regions.     

Numerical study of the spontaneous nucleation of self-rotational moist gas in a converging–diverging nozzle

Spontaneous nucleation is the primary way of droplet formation in the supersonic gas separation technology, and the converging–diverging nozzle is the condensation and separation unit of supersonic gas separation devices. A three-dimensional geometrical model for the generation of self-rotational transonic gas flow is set up, based on which, the spontaneous nucleation of self-rotational transonic moist gas in the converging–diverging nozzle is carried out using an Eulerian multi-fluid model. The simulated results of the main flow and nucleation parameters indicate that the spontaneous nucleation can occur in the diverging part of the nozzle. However, different from the nucleation flow without self-rotation, the distributions of these parameters are unsymmetrical about the nozzle axis due to the irregular flow form caused by the self-rotation of gas flow. The nucleation region is located on the position where gas flows with intense rotation and the self-rotation impacts much on the nucleation process. Stronger rotation delays the onset of spontaneous nucleation and yields lower nucleation rate and narrow nucleation region. In addition, influences of other factors such as inlet total pressure p ₀, inlet total temperature T ₀, the nozzle-expanding ratio ? and the inlet relative humidity ф ₀ on the nucleation of self-rotational moist gas flow in the nozzle are also discussed.     

超声速气流中雾化燃料喷射的三维数值研究

首次用双流体模型对雾化燃料在扩张形超燃室中沿九喷嘴顺流喷射的混合问题进行了数值研究。气相用迎风 TVD格式求解三维全 Navier- Stokes方程 ,液相用预估、校正 NND格式求解三维 Euler方程。相间相互作用的常微分方程用预估、校正Runge- Kutta法求解。用三维 Poisson方程生成网格。结果表明 :气相较液相的扩散效果好 ,小直径液滴的扩散效果好。相间速度滑移、改变气相喷射压力和喷射速度对液相扩散的贡献不大 ,但调整喷射角度会明显地增强液相的扩散、混合 ,本文结果未出现阻塞。     

Two-phase flow in inclined tubes with specific reference to condensation: A review

Tilting influences the flow patterns and thus the heat transfer and pressure drop during condensation in smooth tubes. However, few studies are available on diabatic two-phase flows in inclined tubes. The purpose of the present paper is to review two-phase flow in inclined tubes, with specific reference to condensation. Firstly, the paper reviews convective condensation in horizontal tubes. Secondly, an overview is given of two-phase flow in inclined tubes. Thirdly, a review is conducted on condensation in inclined tubes. It is shown for convective condensation in inclined tubes that the inclination angle influences the heat transfer coefficient. The heat transfer coefficient can be increased or decreased depending on the experimental conditions, and especially the flow pattern. Under certain conditions, an inclination angle may exist, which leads to an optimum heat transfer coefficient. Furthermore, this paper highlights the lack of experimental studies for the prediction of the inclination angle effect on the flow pattern, the heat transfer coefficient and the pressure drop in two-phase flows during phase change.