Condensation Waves Research Articles

A comprehensive analysis of the moist air transonic flow in a nozzle with a very low expansion rate

• Experimental study of the moist air transonic flow in a nozzle with a low expansion rate. • Mathematical models of homogeneous condensation. • The study of the effect of air relative humidity on the expansion process. • The study of the interaction between condensation and pressure waves. Inevitable and undesirable as it is, phase transition has a significant impact on the fluid flow efficiency in many energy processes. This paper deals with the impact of water vapour condensation and liquid water evaporation in the moist air expansion in a nozzle with a low expansion rate. The presented comprehensive analysis includes a numerical study supported by analytical and experimental research. The experimental study concerning measurements of atmospheric air transonic flows was carried out using an in-house experimental test rig. A nozzle with a low expansion rate of P ̇ ≈ 1000 s - 1 was investigated experimentally at different inlet air relative humidity values included in the range of 25 to 51 %. The nozzle was measured for supersonic outlet conditions, as well as with elevated back pressure (78 kPa). The technique of Schlieren photography and static pressure measurement on the nozzle wall were used for qualitative identification of both condensation and shock waves. The presented numerical modelling was conducted using commercial computational fluid dynamics software extended with an in-house condensation model. The code was validated against experimental data and data available in the literature. The analysis of the flow in the nozzle with a very low expansion rate revealed very interesting structures of pressure waves. The impact of relative air humidity on the condensation process and the interaction of the condensation wave with aerodynamic oblique as well as normal shock waves were investigated. It is observed that the higher the air relative humidity value, the more difficult it is to identify aerodynamically induced oblique shock waves in the flow. Finally, considering that the efficiency drop induced by the phase change can reach up to 10 %, the impact of condensation on the expansion process efficiency is presented.

Analysis of the moist air transonic flow in the symmetric and asymmetric nozzle of the low expansion

Condensation has a negative impact on turbomachinery efficiency in many energy processes. This paper compares the expansion of moist air in symmetric and asymmetric nozzles with a low expansion rate. The presented numerical study is supported by analytical and experimental research. The experimental tWesting was carried out using an in-house experimental test rig where two nozzles were examined for moist air with relative humidity of about 25%. The nozzles were tested for a supersonic outlet, as well as for the outlet condition with elevated pressure, which resulted in the occurrence of a normal shock in the test section. The asymmetric nozzle profile is congruent with the symmetric nozzle. However, the nozzle walls are shifted linearly in the flow direction. The Schlieren photography technique and static pressure measurements on the nozzle wall were used for qualitative identification of both condensation and shock waves. The presented numerical modelling was conducted using commercial computational fluid dynamics software extended with an in-house condensation model. The code was validated against in-house experiment as well as against the data available in the literature. The analysis of the flow in the considered two types of nozzles with a very low expansion rate revealed very interesting structures of pressure waves. The impact of the linear shift of the nozzle walls on the condensation process and the interaction of the condensation wave with aerodynamic oblique as well as normal shock waves were investigated.

A modified Euler-Lagrange-Euler approach for modelling homogeneous and heterogeneous condensing droplets and films in supersonic flows

The phase change in supersonic flows is of great interest in many industrial applications including steam turbines, nozzles, ejectors and aircraft. However, the phase change phenomenon is still not fully understood due to the completed flow behavior including nucleation, condensation, film generation and shock waves in supersonic flows. In the present study, we proposed a modified Euler-Lagrange-Euler model to explore the internal flow mechanism within supersonic separators. The mutual heat and mass transfer of the gaseous phase, droplets, and liquid film were simulated in supersonic flows. The homogeneous nucleation and growth model was innovatively added to ensure the model's comprehensiveness. The feasibility of the proposed model was validated by experiments. Then, the interaction of heterogeneous and homogeneous condensation in supersonic condensation flow was excavated for the first time. The results show the heterogeneous droplet diameter's decrease or concentration's increase had a significant inhibitory effect on homogeneous condensation. Subsequently, the supersonic swirl field's generation, the dynamic evolution of the homogeneous/heterogeneous droplet condensation and deposition, the liquid film development, and the heat-mass transfer between them in the supersonic separator were analyzed using the proposed model. Furthermore, the separation capacity of the supersonic separator was evaluated considering the co-action of homogeneous and heterogeneous condensation. Results show that increasing inlet droplet concentration from 0.0001 kg/s to 0.0025 kg/s can increase vapor separation efficiency and dew point depression from 61.39 % to 84.74 % and 19.03 K to 28.28 K, respectively.

Condensation properties of water vapor under different back pressures in nozzle

The existence of back pressure at outlet has a direct impact on the separation performance of the separation separator. However, the influence of back pressure is not understood well due to the complicated interaction of the supersonic flow, condensation and shock waves. In this study, the condensation flow models of water vapor were established, the influence of back pressure on supersonic condensation properties of water vapor was investigated. The results show that when the back pressure exists, the position of the shock wave is more forward than that without condensation, and the strength of shock wave is weaker. The nucleation rate is generated around the position of x = 115 mm and increases sharply from 0 to 1025 m−3 s−1. The shock wave is generated at x = 145 mm and x = 122 mm when the outlet back pressure is 20 kPa and 30 kPa, respectively. The condensed droplets evaporate again with the effect of shock wave, and then the secondary condensation of droplets occurs owing to the cooling effect of nozzle. When the back pressure is higher than a certain value, the refrigeration environment in the nozzle is completely destroyed with the effect of shock wave, and the condensed droplets evaporate again.

Chemical Condensation Wave Initiating Oxygen-Free Combustion and Detonation

It is well known that the propagation of traditional combustion and detonation waves was determined by the branched chain reactions discovered by Academician N.N. Semenov. This article discusses a new type of detonation waves initiated by chemical condensation processes. Chemical condensation waves arise as a result of the heat released during the explosive condensation of a highly supersaturated carbon vapor formed as a result of the dissociation of the initial carbon-containing molecules behind the front of the initiating shock wave. Unlike traditional combustion and detonation waves, the mechanism of chemical condensation does not include branched chain reactions; nevertheless, the laws of propagation of detonation waves of condensation are clearly described by the Zel’dovich–Neumann–Döring theory.

Non-equilibrium condensation of water vapour in supersonic flows with shock waves

The fluid flow and heat and mass transfer in a supersonic separator are not understood well due to the complicated interaction of the supersonic flow, swirling flow, phase transition and shock waves. In the present study, we develop a wet steam model to investigate the flow structure inside a supersonic separator with the co-existence of non-equilibrium condensation and shock waves. A study of the effect of the inlet subcooling and inlet saturation on the condensation behaviour is conducted to evaluate the performance of the supersonic separation with a focus on the shock wave. The numerical result shows that the degree of supersaturation of the water vapour can reach a maximum value of 4.28 within the designed supersonic separator and generate a peak nucleation rate of approximately 1021 kg m−3 s−1. The occurrence of the shock wave changes the equilibrium thermodynamic state, which leads to the re-evaporation of the condensed droplet. Higher inlet subcooling and inlet saturation not only shift downstream the position of the shock wave, but also induce an earlier condensation and higher liquid fraction. For the present nozzle, when the inlet subcooling and inlet saturation are about 34 K and 0.28 respectively, the shock wave intersects the region of the intense nucleation process, the non-equilibrium condensation process is terminated due to the increase of the pressure and temperature downstream the shock wave. Stronger swirling flow results in non-uniform distribution of the static pressure and decreases the nucleation rate of water vapour. The high swirling flow with a maximum swirl velocity of 150 m/s weakens the liquid fraction by 25% compared to the no swirling flow. This indicates that it is important to balance the swirling flow and condensation process to achieve an efficient performance of the supersonic separator.

Abstract 3724: Molecular mechanisms of TTField action determined by measurements and modelling of electro-conductive properties of microtubules

Abstract Biological effects of AC electric fields at frequencies between 100-300 kHz discovered a decade ago are being applied to cancer cells as a therapeutic modality in the treatment of glioblastoma multiforme (GBM). They are called Tumor Treating Fields (TTFields) as they disrupt cell division. Based on our electro-conductive measurements and modeling, we provide an assessment of possible molecular-level mechanisms. Computer simulations and experimental measurements carried out for microtubules and actin filaments are presented. Charge and dipole values for monomers and dimers as well as polymerized forms of these proteins are summarized. Continuum approximations for cable equations describing actin filaments and microtubules compare favorably to measurements in buffer solutions showing soliton waves and transistor-like amplification of ionic signals, respectively. AC Conductivity and capacitance of tubulin and microtubules have been measured and modeled in the range of frequencies between 1 Hz and 1 MHz. A dramatic change in conductivity occurs when tubulin forms microtubules. In living cells, this signals a conductive phase transition coinciding with mitosis in dividing cells. This process is allowed by TTField penetration into the cleavage furrow in dividing cells and provides the most significant mechanistic explanation of the observed effects. We provide estimates of the forces, energies and power involved in the action of TTFields on microtubules and kinesin motors. These calculations are compared and contrasted with typical values experienced at a cell level and provide strong arguments for real physical effects of TTFields in dividing cells. We also show results of DLS and TEM measurements on microtubules and tubulin oligomers in solution, which allow us to quantify these processes under controlled conditions. In conclusion, the most likely candidates to provide a quantitative explanation of these effects are ionic condensation waves around microtubules as well as dielectrophoretic effects on the dipole moments of microtubules. Citation Format: Aarat P. Kalra, Sahil Patel, Asadullah Bhuiyan, Jordane Preto, Vahid Rezania, John D. Lewis, Karthik Shankar, Jack Tuszynski. Molecular mechanisms of TTField action determined by measurements and modelling of electro-conductive properties of microtubules [abstract]. In: Proceedings of the American Association for Cancer Research Annual Meeting 2019; 2019 Mar 29-Apr 3; Atlanta, GA. Philadelphia (PA): AACR; Cancer Res 2019;79(13 Suppl):Abstract nr 3724.

An Overview of Sub-Cellular Mechanisms Involved in the Action of TTFields.

Long-standing research on electric and electromagnetic field interactions with biological cells and their subcellular structures has mainly focused on the low- and high-frequency regimes. Biological effects at intermediate frequencies between 100 and 300 kHz have been recently discovered and applied to cancer cells as a therapeutic modality called Tumor Treating Fields (TTFields). TTFields are clinically applied to disrupt cell division, primarily for the treatment of glioblastoma multiforme (GBM). In this review, we provide an assessment of possible physical interactions between 100 kHz range alternating electric fields and biological cells in general and their nano-scale subcellular structures in particular. This is intended to mechanistically elucidate the observed strong disruptive effects in cancer cells. Computational models of isolated cells subject to TTFields predict that for intermediate frequencies the intracellular electric field strength significantly increases and that peak dielectrophoretic forces develop in dividing cells. These findings are in agreement with in vitro observations of TTFields’ disruptive effects on cellular function. We conclude that the most likely candidates to provide a quantitative explanation of these effects are ionic condensation waves around microtubules as well as dielectrophoretic effects on the dipole moments of microtubules. A less likely possibility is the involvement of actin filaments or ion channels.

Shock wave-boundary layer interactions at the supersonic flow around three-dimensional configurations

The study suggests that the problems of interactions of turbulent flows at the supersonic flow around aircraft elements be solved by numerical analysis methods aided by a mathematical model that is based on the system of the Reynolds-averaged Navier-Stokes equations. The system includes the k-ω SST turbulence model for viscous compressible medium (with two scalar equations of turbulent kinetic energy and relative velocity of its dissipation with the modification that takes into account the transfer of shear stress). The paper presents applied testing and verification of the model along with examples of the problems on supersonic flows around a flat wall and a sphenoid superstructure as well as a perpendicular gas stream. We have identified physical characteristics of interactions between the condensation wave and the boundary turbulent layer, which manifest themselves in the formation of a complex structure of disconnecting and connecting zones of a boundary turbulent layer, which are characterized by respective lines of separation and joining on the wrap surface. The solutions adequately reflect the pattern of the supersonic flow of a compressible medium, condensation waves and vortex zones that are commonly observed during field studies. The comparative analysis of the results of numerical modeling and experimental data confirms the applicability of the mathematical model for complex tasks of the supersonic gas-dynamic state.

Numerical study of non-equilibrium condensation and shock waves in transonic moist-air and steam flows

Transonic condensing/evaporating moist-air flow through converging-diverging nozzles is investigated numerically using non-equilibrium thermodynamic model. In this study, the results of moist-air and pure steam flows through nozzles are compared, in other words, carrier gas effects are investigated numerically. It is observed that, under similar operating conditions for steam, the wetness fraction and droplet nucleation rate along the nozzle in the case of moist-air flow is more than pure steam case. That is due to the internal flow of heat from steam portion towards the air that enhances the wetness fraction and droplet nucleation rate in moist-air case. In this study, the influence of the normal aerodynamic shocks is also studied. It is interestingly observed that, although the entropy of the mixture (steam+air) and steam portion increases along the shock, the entropy of the air portion can be reduced in response to evaporation of the liquid phase. Validation of the results is performed versus the experimental data for pure steam and moist-air flows, which show relatively good agreements.

Quantum effects in the kinetics of the initiation of detonation condensation waves

The features of the kinetics of the initiation of detonation condensation waves in carbon suboxide and acetylene have been experimentally studied at high pressures near the low-temperature limits. The role of quantum effects in the expansion of detonation limits has been analyzed. Quantum corrections to the endothermic reaction rates, which are caused by an increase in the high-energy tails of the momentum distribution functions at high pressures due to the manifestation of the uncertainty principle for the energy of colliding particles at a high collision frequency, have been quantitatively estimated. It has been shown that experimentally observed deviations in Arrhenius dependences of the induction periods of the initiation of detonation condensation waves are well described by the proposed quantum corrections.

ファン・デル・ワールス流体でみられる蒸発波および凝縮波

ファン・デル・ワールス流体でみられる蒸発波および凝縮波

STOCHASTIC DYNAMICS OF VISCOELASTIC SKEINS: CONDENSATION WAVES AND CONTINUUM LIMITS

Skeins (one-dimensional queues) of migrating birds show typical fluctuations in swarm length and frequent events of "condensation waves" starting at the leading bird and traveling backward within the moving skein, similar to queuing traffic waves in car files but more smooth.These dynamical phenomena can be fairly reproduced by stochastic ordinary differential equations for a "multi-particle" system including the individual tendency of birds to attain a preferred speed as well as mutual interaction "forces" between neighbors, induced by distance-dependent attraction or repulsion as well as adjustment of velocities. Such a one-dimensional system constitutes a so-called "stochastic viscoelastic skein."For the simple case of nearest neighbor interactions we define the density between individualsu = u(t, x) as a step function inversely proportional to the neighbor distance, and the velocity function v = v(t, x) as a standard piecewise linear interpolation between individual velocities. Then, in the limit of infinitely many birds in a skein of finite length, with mean neighbor distance δ converging to zero and after a suitable scaling, we obtain continuum mass and force balance equations that constitute generalized nonlinear compressible Navier–Stokes equations. The resulting density-dependent stress functions and viscosity coefficients are directly derived from the parameter functions in the original model.We investigate two different sources of additive noise in the force balance equations: (1) independent stochastic accelerations of each bird and (2) exogenous stochastic noise arising from pressure perturbations in the interspace between them. Proper scaling of these noise terms leads, under suitable modeling assumptions, to their maintenance in the continuum limit δ → 0, where they appear as (1) uncorrelated spatiotemporal Gaussian noise or, respectively, (2) certain spatially correlated stochastic integrals. In both cases some a priori estimates are given which support convergence to the resulting stochastic Navier–Stokes system.Natural conditions at the moving swarm boundaries (along characteristics of the hyperbolic system) appear as singularly perturbed zero-tension Neumann conditions for the velocity function v. Numerical solutions of this free boundary value problem are compared to multi-particle simulations of the original discrete system. By analyzing its linearization around the constant swarm state, we can characterize several properties of swarm dynamics. In particular, we compute approximating values for the averaged speed and length of typical condensation waves.

Radiative Hydrodynamic Models of Optical and Ultraviolet Emission from M Dwarf Flares

We report on radiative hydrodynamic simulations of M dwarf stellar flares and compare the model predictions to observations of several flares. The flares were simulated by calculating the hydrodynamic response of a model M dwarf atmosphere to a beam of non-thermal electrons. Radiative backwarming through numerous soft X-ray, extreme ultraviolet, and ultraviolet transitions are also included. The equations of radiative transfer and statistical equilibrium are treated in non-LTE for many transitions of hydrogen, helium and the Ca II ion allowing the calculation of detailed line profiles and continuum radiation. Two simulations were carried out, with electron beam fluxes corresponding to moderate and strong beam heating. In both cases we find the dynamics can be naturally divided into two phases: an initial gentle phase in which hydrogen and helium radiate away much of the beam energy, and an explosive phase characterized by large hydrodynamic waves. During the initial phase, lower chromospheric material is evaporated into higher regions of the atmosphere causing many lines and continua to brighten dramatically. The He II Lya line is especially enhanced, becoming the brightest line in the flaring spectrum. The hydrogen Balmer lines also become much brighter and show very broad line widths, in agreement with observations. We compare our predicted Balmer decrements to decrements calculated for several flare observations and find the predictions to be in general agreement with the observations. During the explosive phase both condensation and evaporation waves are produced. The moderate flare simulation predicts a peak evaporation wave of 130 km/s and a condensation wave of 30 km/s. The velocity of the condensation wave matches velocities observed in several transition region lines.

Steam condensation waves in water-saturated porous rock

We formulate balance laws governing condensation of steam injected into a linear porous medium containing water. Heat losses to the outside are neglected. Longitudinal heat conduction and capillary effects are taken into account. The condensation process is modeled by a rate equation based on a simple heat-transfer model. We study the condensation front as a traveling wave, under the approximation that pressure variations are negligible within the front. We find this traveling wave for the case of injection of high-quality steam using a combination of phase-plane analysis and numerical calculation of orbits.

Nonsteady condensation and evaporation waves

We study the motion of a phase transition (PT) front at a constant temperature between stable and metastable states in fluids with the van der Waals equation of state. We focus on a case of relatively large metastability and low viscosity, when no steadily moving PT front exists. Simulating the one-dimensional hydrodynamic equations, we find that the PT front generates acoustic shocks in forward and backward directions. Through this mechanism, the nonsteady PT front drops its velocity and eventually stops. The shock wave may shuttle between the PT front and the system's edge, rarefaction waves appearing in the shuttle process. If the viscosity is below a certain threshold, a turbulent state sets in.

Computation, analysis and theory of two-phase flows

AbstractThe non-equilibrium fluid mechanics and thermodynamics of two-phase vapour-droplet and gas-particle flow are considered. The formation of the droplets as well as their subsequent interaction with the vapour are discussed. Five topics have been given particular attention: (i) CFD application to unsteady condensation waves, (ii) CFD application to shock waves moving through a vapour-droplet mixture, (iii) a new theory of nucleation of water droplets in steam turbines based on Monte Carlo simulation (steam turbines are responsible for 80% of global electricity production and the presence of moisture significantly reduces the turbine efficiency costing £50m per annum in the UK alone), (iv) a unified theory for the interpretation of total pressure and total temperature in two-phase flows and, (v) a unified theory of particle transport in a turbulent flowfield.

Wave splitting in a fluid of large heat capacity

The splitting of a single pressure discontinuity into a propagating two-wave system is studied for the case of saturated-liquid expansion (liquid-evaporation wave splitting) and vapour compression (vapour-condensation wave splitting). Experimental results from the Max-Planck-Institut für Strömungsforschung and from Rensselaer Polytechnic Institute show that splitting occurs in test fluids of large molar heat capacity, such as iso-octane (Cv0/R≈ 37). Each of the two forms of splitting results in a single-phase forerunner wave carrying a pressure discontinuity followed by a phase-change wave, also with a pressure discontinuity. The thermodynamic state between the forerunner wave and the phase-change wave is metastable (supersaturated liquid or vapour). The waves are quantitatively described by systems of adiabats, e.g. shock adiabats. It appears that nucleation processes are predominantly homogeneous.In vapour-compression shock-wave splitting, a combined wave (liquefaction shock) splits into discrete forerunner and condensation waves at a triple point, the intersection of a liquefaction shockfront, forerunner shock and condensation discontinuity: such a point occurs just at critical supersaturation (i.e. the Wilson-line state), where condensation is spontaneous and immediate. For shock waves that produce a metastable state of subcritical supersaturation, condensation is delayed, that is, the condensation discontinuity propagates more slowly; for a split-shock system, the condensation discontinuity propagates subsonically. The pressure amplitude of a real split-shock system is much larger than that predicted by an equilibrium model.In liquid-evaporation wave splitting, the forerunner wave is an acoustic expansion wave and the second wave an evaporation wave with a propagation velocity approximately determined by the Chapman-Jouguet condition for deflagration. Such evaporation wavefronts are increasingly distinct as the temperature approaches the critical-point value. The evaporation rates across the wavefront are comparable to those found in vapour explosions.

Shock waves and phase changes in a large-heat-capacity fluid emerging from a tube

The emergence of a shockwave from the open end of a shock tube is studied, with special emphasis on test fluids of high molar heat capacity, i.e. retrograde fluids. A variety of wavelike vapour-liquid phase changes are observed in such fluids, including the liquefaction shock, mixture-evaporation shock, condensation waves associated with shock splitting and liquid-evaporation waves (these phenomena have analogues in the polymorphic phase changes of solids; only the first two are treated in this paper). The open end of the shock-tube test section discharges into an observation chamber where photographs of the emerging flow are taken. Calculations were performed with the Benedict-Webb-Rubin, van der Waals and other equations of state. Numerical (finite-difference) predictions of the flow were made for single-phase and two-phase flows: solutions were tested against the experimental shock diffraction and vortex data of Skews. The phase-change properties of the test fluid can be quantified by the ‘retrogradicity’ r(T), measuring the difference in slope between the P, T isentrope and the vapour-pressure curve, and the ‘kink’ k(T), measuring the difference between the single-phase and mixture sound speeds. Mixture-evaporation (i.e. rarefaction) shocks appear to have a sonic-sonic or double Chapman-Jouguet structure and show agreement with amplitude predictions based on k(T). Liquefaction shocks are found to show a reproducible transition from regular, smooth shock fronts to irregular, chaotic shock fronts with increasing shock Mach number. This transition can be correlated with published stability limits.

Shock Waves in Aerodynamics

This paper reviews some of the physical aspects of shock waves as they affect the high-velocity performance of airfoils. I t is shown tha t the conventional frictionless, adiabatic, irrotational fluid motion can admit shocks only as an added discontinuity. Real fluids with viscosity and thermal conductivity will admit shocks as a necessary part of the complete solution of highvelocity problems. A brief discussion is given of oblique shock waves and of the necessarily rotational motion in the region behind a shock wave. A few words are included on the subject of the critical Mach Number for airfoils. Finally, combustion, detonation, and condensation waves are mentioned.