有固相析出的多效两段蒸发 系统模型与过程模拟

建立了带有冷凝水闪蒸的有固相析出的多效两段蒸发系统的常规设计数学模型,模型将系统的相平衡关系用回归式表达,使模型可以用计算机编程求解,避免了手工计算结合查相图的烦琐的计算过程;利用矩阵方程具有结构清晰和高度模块化的特点,将系统的物料衡算和热量衡算方程组写成矩阵方程的形式,只要保留或舍弃矩阵方程中的相关块矩阵,模型就能代表没有冷凝水闪蒸或没有固相析出的多效两段蒸发系统常规设计模型;采用迭代法结合矩阵法来求解模型,算例表明,冷凝水闪蒸对多效两段蒸发系统是有效的节能措施,算法收敛速度快、收敛稳定性好。     

The Convective Instabilities in a Liquid–Vapor System with a Non-equilibrium Evaporation Interface

Rayleigh–Marangoni–Bénard instability in a system consisting of a horizontal liquid layer and its own vapor has been investigated. The two layers are separated by a deformable evaporation interface. A linear stability analysis is carried out to study the convective instability during evaporation. In previous works, the interface is assumed to be under equilibrium state. In contrast with previous works, we give up the equilibrium assumption and use Hertz–Knudsen’s relation to describe the phase change under non-equilibrium state. The influence of Marangoni effect, gravitational effect, degree of non-equilibrium and the dynamics of the vapor on the instability are discussed.     

一种低饱和蒸气压润滑脂的真空蒸发特性测试

针对一种国外进口的空间活动部件用低饱和蒸气压润滑脂,应用真空物理的基础理论,以及现有的试验设备和仪器条件,设计了蒸发速率测试方案,评价了该润滑脂的真空蒸发损失特性,回归出饱和蒸气压随温度变化的方程。为预测其在真空下长期使用中的蒸发损失量,以及验证在常温下的饱和蒸气压指标提供了一种方法。     

Gravitational Effects on Multi-component Droplet Evaporation

This paper focuses on the analysis of multi-component droplet heating and evaporation under microgravity and normal gravity conditions. This analysis is based on the conventional conservation equations of species and energy for the gas phase, and the energy balance equation at the liquid?Cgas interface. The species diffusion is based on the Hirschfelder law, rather than on the less general Fick??s equation. Moreover, the heat flux due to species diffusion is taken into account in addition to the classical conduction heat flux between the gas and the liquid droplets. The liquid phase analysis is based on the infinite thermal conductivity liquid phase model, which has been justified by a reasonably good agreement between the predicted and experimental results. Indeed, the developed evaporation model has been validated against experimental data reported by Chauveau et al. (2008), where the droplets evaporation has been observed in microgravity and normal gravity conditions. The effects of gravity have been taken into account by introducing the Grashof number in the expressions of the Sherwood and Nusselt numbers. This model has been implemented in the multidimensional IFP-C3D industrial software. The modeling and experimental results have been shown to be reasonably close and the gravitational effects have been revealed to be significant especially for multi-component liquids including heavy components.     

支承运动情况下旋转梁的刚-柔耦合振动分析

利用哈密顿原理建立了支承运动情况下旋转梁的刚-柔耦合振动非线性动力学方程组及边界条件。根据假设模态法，利用边界条件以及模态函数的性质，得到一组模态坐标与刚性角位移耦合时变系数常微分方程，运用数值方法比较了非耦合和耦合时刚性角位移的结果，计算了梁的动力响应并分析了模态截断的影响，最后运用梁端部弹性振动的相轨迹分析了该时变系统的稳定性。     

Slow evaporation of a drop of solution

A method is proposed for determining the degree of evaporation of a drop of solution under conditions where the evaporation is slow and the effect of diffusion within the drop can be neglected. An equation and criterion are derived which determine the evaporation of a drop of solution under these conditions. The range of criterial values corresponding to these conditions was determined experimentally.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 34, No. 2, pp. 205–211, February, 1978.     

Mechanical behavior of a FGM micro-beam subjected to a nonlinear electrostatic pressure

The present article studies the mechanical behavior of a FGM micro-beam subjected to a nonlinear electrostatic pressure. The FGM micro-beam is made of metal and ceramic and material properties vary continuously along the beam thickness according to a power-law. The nonlinear equation of dynamic motion of the FGM micro-beam is derived. By solving the equation of the static deflection, equilibrium positions of the micro-beam are determined and shown in the state control space. To study the stability of the fixed points, the trajectories of the beam motion are illustrated in the phase plane for different initial conditions. In order to find the response of the micro-beam to a step DC applied voltage, the nonlinear equation of motion is solved using a Galerkin based reduced order model. Moreover, time histories and phase portraits for different applied voltages are illustrated. The effect of different power law exponent on the stability of the micro-beam is studied.     

Weak evaporation (condensation) with an arbitrary evaporation coefficient in gases with a constant frequency of molecular collisions

We have obtained an exact solution of the problem on determination of temperature and concentration jumps of a rarefied elementary (monoatomic) gas in the case of weak evaporation from the gas-condensed phase interface into the half-space of a saturated vapor. Use is made of a model kinetic equation with a collision integral in the BGK (Bhatnagar, Gross, and Krook) form. Accurate coefficients of the temperature and concentration jumps are found. It is shown that at low evaporation coefficients the dependence of the concentration of the vapor on its evaporation (concentration) rate at a large distance from the interface is linear even at low (as compared to sonic) vapor velocities. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 73, No. 3, pp. 542–549, May–June, 2000.     

An approximate method for evaporation problem with mushy zone

In the present paper, a simple mushy zone model is used to track the moving boundaries in an evaporation problem in which the vapor is removed upon formation. Two main parameters for the mushy zone model are analyzed as well as their effect on the movement of the moving boundaries and the thickness of the mushy zone. A new approximate method is developed for analysis and tracking the moving boundaries appears throughout the process. The proposed method mainly based on applying the boundary integral equation corresponding to each phase in such a way that the associated boundary and initial conditions as well as energy equations at the moving boundaries achieved with minimum error and low number of iterations. The results of the present paper seem to be good because there are neither analytical or numerical solutions available.     

Evaporation kinetics of volatile liquids and release kinetics of water from a smectite clay: Comparison between experiments and finite element calculations

Numerical calculations of the evaporation kinetics of bulk volatile liquids and of water from smectite clay granules are compared with experimental results. The weight loss of the volatiles is analyzed by thermogravimetry and differential calorimetry. Under the thermodynamic conditions of the experiments, finite element calculations are in good agreement with the experimental data, and an approximate semi-analytical model is developed in order to explain the dependence of the rate of evaporation on the temperature, the chemical species and the carrier gas flow rate. The initial rate of evaporation of water from the clay granule is close to that for bulk water. Its decrease with time is determined mainly by changes in the gas/condensed phase partition given by the equilibrium desorption isotherm, with little limitations due to internal diffusion effects for the present experimental conditions. Its temperature dependence could also be approximately described by an Arrhenius-type equation derived from the semi-analytical model. Further analysis of the experimental measurements reveals steps in the heat of vaporization of water as a function of water concentration, that could be related to the equilibrium desorption isotherm.     

The Stability of a Condensate Film Moving under the Effect of Gravity and Turbulent Flow of Vapor

The linear stability of a condensate film moving along a vertical isothermal plate under the effect of gravity and turbulent vapor flow is investigated. The cases of both cocurrent and countercurrent motion of phases are treated with regard for phase transformation. An analytical solution for the distribution of film thickness along the plate taking into account the film inertia is obtained using the integral method. A two-wave equation is deduced for the film thickness, and dispersion relations are derived. The effect of moving vapor on the film stability in a wide range of flow parameters is shown.     

Effects of nonuniform heating and thermocapillarity in evaporating films falling down an inclined plate

Summary. The dynamics of a thin evaporating liquid film falling down an inclined plate is studied in the cases of both uniformly and nonuniformly heated plates. The film flow is influenced by gravity, mean surface tension, thermocapillary force and mass loss. The dynamics of the two-dimensional evaporating film is studied by the use of long-wavelength theory. Numerical solution of the evolution equation indicates that the evaporation has a strong stabilizing effect on the film instability and that a sequence of instability, stability and then instability of the falling film during its evaporation exists. The effect of nonuniform heating is dominant prior to film disappearance and it enforces film rupture. Due to the joint action of thermocapillarity and evaporating mass loss, the film evolution exhibits the formation of multi-hump structures, the downstream propagation of which is suppressed. When the nonuniformities in the imposed temperature differences are increased, large deformations of the liquid-vapor interface occur that lead to an enhancement of the heat transfer processes.     

On the existence of periodic solution for equation of motion of thick beams having arbitrary cross section with tip mass under harmonic support motion

A cantilever beam having arbitrary cross section with a lumped mass attached to its free end while being excited harmonically at the base is fully investigated. The derived equation of vibrating motion is found to be a non-linear parametric ordinary differential equation, having no closed form solution for it. We have, therefore, established the sufficient conditions for the existence of periodic oscillatory behavior of the beam using Green’s function and employing Schauder’s fixed point theorem. The derived equation of vibration motion is found to be a non-linear parametric ordinary differential equation, having no closed form solution for it. To formulate a simple, physically correct dynamic model for stability and periodicity analysis, the general governing equations are truncated to only the first mode of vibration. Using Green’s function and Schauder’s fixed point theorem, the necessary and sufficient conditions for periodic oscillatory behavior of the beam are established. Consequently, the phase domain of periodicity and stability for various values of physical characteristics of the beam-mass system and harmonic base excitation are presented.     

Modeling evaporation using models that are not boundary-layer regulated

Experimentation shows that oil is not strictly air boundary-layer regulated. The fact that oil evaporation is not strictly boundary-layer regulated implies that a simplistic evaporation equation suffices to describe the process. The following processes do not require consideration: wind velocity, turbulence level, area, thickness, and scale size. The factors important to evaporation are time and temperature. The equation parameters found experimentally for the evaporation of oils can be related to commonly available distillation data for the oil. Specifically, it has been found that the distillation percentage at 180 degrees C correlates well with the equation parameters. Relationships have been developed enabling calculation of evaporation equations directly from distillation data: percentage evaporated = 0.165 (%D)ln(t) where %D is the percentage (by weight) distilled at 180 degrees C and t is the time in minutes. These equations were combined with the equations generated to account for the temperature variations: percentage evaporated = [0.165(%D)+0.045(T-15))ln(t) The results have application in oil spill prediction and modeling. The simple equations can be applied using readily available data such as sea temperature and time. Old equations required oil vapour pressure, specialized distillation data, spill area, wind speed, and mass transfer coefficients, all of which are difficult to obtain.     

Stability of superconducting states out of thermal equilibrium

Quasiparticles of superconductors can be manipulated either by irradiation or tunnel injection such that substantial changes of the gap (order parameter) occur which are most pronounced close to the transition temperature. These phenomena are investigated by a theory which is based on the combined system of the Boltzmann equation and the BCS gap equation. Several stationary, spatially homogeneous states are found in some range of temperatures. A linear stability analysis reveals two types of behavior, depending, essentially, on whether quasiparticle diffusion increases or decreases the stability. In a representative situation of the first type, two states turn out to be locally stable. An investigation of a nonlinear equation of motion for the order parameter leads to the conclusion that a first-order phase transition between these two states occurs at a given temperature. In a situation of the second type, one finds that fluctuations of a definite wave vector destroy the spatially homogeneous state and lead to a stable state of layered structure.     

Unique Bond Breaking in Crystalline Phase Change Materials and the Quest for Metavalent Bonding

Laser‐assisted field evaporation is studied in a large number of compounds, including amorphous and crystalline phase change materials employing atom probe tomography. This study reveals significant differences in field evaporation between amorphous and crystalline phase change materials. High probabilities for multiple events with more than a single ion detected per laser pulse are only found for crystalline phase change materials. The specifics of this unusual field evaporation are unlike any other mechanism shown previously to lead to high probabilities of multiple events. On the contrary, amorphous phase change materials as well as other covalently bonded compounds and metals possess much lower probabilities for multiple events. Hence, laser‐assisted field evaporation in amorphous and crystalline phase change materials reveals striking differences in bond rupture. This is indicative for pronounced differences in bonding. These findings imply that the bonding mechanism in crystalline phase change materials differs substantially from conventional bonding mechanisms such as metallic, ionic, and covalent bonding. Instead, the data reported here confirm a recently developed conjecture, namely that metavalent bonding is a novel bonding mechanism besides those mentioned previously.     

Phase separation and surface morphology of spin-coated films of polyetherimide/polycaprolactone immiscible polymer blends

The surface morphology in thin films of immiscible polyetherimide and polycaprolactone blends was studied using scanning electron and atomic force microscopy. The thin films were obtained by spin-coating from dichloromethane solution. A self-assembled periodic pattern of phase separated domains was observed, which was induced by capillary effects along with the solution radial flow and the unsteady air flow field above the film during the initial stages of spin-coating. A secondary phase separation was observed during the solvent evaporation stage of spin-coating. The differences in surface topographies of the two distinct phases are attributed to different solvent evaporation rates within each phase. In addition, a great variety of domain structures and surface morphologies were observed as a function of polymer blend composition.     

Condensation and evaporation heat transfer of R410A inside internally grooved horizontal tubes

Heat transfer coefficient and pressure drop were measured for condensation and evaporation of R410A and HCFC22 inside internally grooved tubes. The experiments were performed for a conventional spiral groove tube of 8.01 mm o.d. and 7.30 mm mean i.d., and a herring-born groove tube of 8.00 mm o.d. and 7.24 mm mean i.d. To measure the local heat transfer coefficients and pressure drop, the test section was subdivided into four small sections having 2 m working length. The ranges of refrigerant mass flow density was from 200 to 340 kg/(m² s) for both condensation and evaporation of R410A and HCFC22, and the vapour pressure was 2.41 MPa for condensation and 1.09 MPa for the evaporation of R410A. The obtained heat transfer data for R410A and HCFC22 indicate that the values of the local heat transfer coefficients of the herring-bone grooved tube are about twice as large as those of spiral one for condensation and are slightly larger than those of spiral one for the evaporation. The measured local pressure drop in both condensation and evaporation is well correlated with the empirical equation proposed by the authors.     

An Indirect Method for Vapor Pressure and Phase Change Enthalpy Determination by Thermogravimetry

Vapor pressure is a fundamental property of a pure substance. This property is the pressure of a compound’s vapor in thermodynamic equilibrium with its condensed phase (solid or liquid). When phase equilibrium condition is met, phase coexistence of a pure substance involves a continuum interplay of vaporization or sublimation to gas and condensation back to their liquid or solid form, respectively. Thermogravimetric analysis (TGA) techniques are based on mass loss determination and are well suited for the study of such phenomena. In this work, it is shown that TGA method using a reference substance is a suitable technique for vapor pressure determination. This method is easy and fast because it involves a series of isothermal segments. In contrast to original Knudsen’s approach, where the use of high vacuum is mandatory, adopting the proposed method a given experimental setup is calibrated under ambient pressure conditions. The theoretical framework of this method is based on a generalization of Langmuir equation of free evaporation: The real strength of the proposed method is the ability to determine the vapor pressure independently of the molecular mass of the vapor. A demonstration of this method has been performed using the Clausius–Clapeyron equation of state to derive the working equation. This algorithm, however, is adaptive and admits the use of other equations of state. The results of a series of experiments with organic molecules indicate that the average difference of the measured and the literature vapor pressure amounts to about 5 %. Vapor pressure determined in this study spans from few mPa up to several kPa. Once the p versus T diagram is obtained, phase transition enthalpy can additionally be calculated from the data.     

自同步振动系统的稳定性与分岔

用偏心转子相位差角微分方程代替双激振器反向回转式自同步振动系统的运动方程，讨论了系统的平衡点稳定性和分岔特性。首先，根据振动系统的运动方程推导出关于偏心转子相位差角的微分方程。然后，基于该方程建立了同步运动的必要性条件，应用Lyapunov稳定性理论，讨论系统的平衡点稳定性及其分岔特性，最后，结合仿真，考察了系统质量、刚度参数和激振器参数的影响规律。