Zone conditional analysis of a freely propagating one-dimensional turbulent premixed flame

The zone conditional conservation equations are derived and validated against the DNS data of a freely propagating one-dimensional turbulent premixed flame. Conditional flow velocities are calculated by the conditional continuity and momentum equations, and a modeled transport equation for the Reynolds average reaction progress variable. An asymptotic formula for turbulent burning velocity is obtained with the effects of a finite Damköhler number accounted for as an additional factor. It is shown that flame generated turbulence is primarily due to correlations between fluctuating gas velocities and fluctuating unit normal vector on a flame surface. More investigation is required to validate general predictive capability of the derived conditional conservation equations and the relationships modeled for closure.     

Mechano-chemistry; diffusion in multicomponent compressible mixtures

In the present work we derive the volume continuity equation and demonstrate its use to define the volume frame of reference in the multicomponent, compressible systems. The volume velocity (material velocity) is a unique frame of reference for all internal forces and processes, e.g., the mass diffusion, heat flow, etc. No basic changes are required in the foundations of linear irreversible thermodynamics except recognizing the need to add volume to the usual list of extensive physical properties undergoing transport in every continuum. The volume fixed frame of reference allows the translation of the Newton’s discrete mass-point molecular mechanics into continuum mechanics and the use of the Cauchy linear momentum equation of fluid mechanics and Navier-Lamé equation of mechanics of solids.Our proposed modifications of Navier-Lamé and energy conservation equations are self-consistent with the literature for solid-phase continua dating back to the classical interdiffusion experiments of Kirkendall and their subsequent interpretation by Darken in terms of diffuse volume transport. We do show that the local diffusion processes do not change the centre of mass of the system and that the stress and viscosity depend only on the local volume velocity.     

Transport of volume in a binary liquid

In this paper, the transport of volume in a binary liquid mixture is theoretically investigated in three steps, with strong implications for the measurement of mutual diffusivities in non-dilute mixtures. In a first step, the velocity of volume transport is determined from the transport velocities of the two components and the thermodynamic relation of state of the liquid mixture in equilibrium. The role played by Galilean invariance and the choice of a rigid frame of reference for reckoning current densities is highlighted. The divergence of the volume-transport velocity field is found to involve the isothermal compressibility and the thermal expansivity of the liquid together with the spatiotemporal variations of pressure and temperature. In a second step, a linear-response relation is introduced between the interdiffusion current density and the gradient of composition; this relation phenomenologically defines the mutual diffusivity of the binary liquid in a manifestly Galilean-invariant way. In a third step, it is examined whether the practical measurement of that diffusivity in a constant-volume container entails a vanishing mass-transport or volume-transport velocity. From a singular-perturbation analysis of the hydrodynamic equations, it is shown that the mass-transport velocity vanishes in the limit of a diffusion of composition that is much slower than the diffusion of momentum. As a consequence, the volume-transport velocity does not vanish during interdiffusion even though the law of additive volumes of the components holds. The physical meaning of the non-vanishing volume velocity is interpreted by means of the thermodynamic results obtained in the second step. Some of the conclusions carry over to multicomponent liquid mixtures.     

Calibration of a Gardon Sensor in a High-Temperature High Heat Flux Stagnation Facility

A calibration methodology developed for custom-made heat flux sensors used for the investigation of hydrothermal spallation drilling is presented. An air jet stagnation convection calibration system allowing independent control of jet velocity and temperature, cooling water flow and temperature, stand off distance, and nozzle diameter was built. A thermopile device was used as reference heat flux sensor. Air jets with velocities up to 400 m/s, exit temperatures of 760°C, and heat fluxes up to 0.6 MW/m² can be reached. The standard deviation of a reference heat flux measurement is below 2%, and overall uncertainty achieved is less than 5.5%.     

Extension of Hydrodynamic Balance Equations for Simple Fluids

A systematic approach to derivation of hydrodynamic-like balance equations for systems with a smooth continuous potential as well as hard sphere repulsion is represented. Cases of many-particle local and two-particle nonlocal hydrodynamic densities are considered. The results are applied for construction of balance equations for fluxes of momentum and energy, which form the first extension of conventional hydrodynamics. Explicit balance equations for the stress tensor and the heat flux in the local frame of reference are obtained.     

Energy–momentum tensor for the electromagnetic field in a dielectric

The total momentum of a thermodynamically closed system is unique, as is the total energy. Nevertheless, there is continuing confusion concerning the correct form of the momentum and the energy–momentum tensor for an electromagnetic field interacting with a linear dielectric medium. Rather than construct a total momentum from the Abraham momentum or the Minkowski momentum, we define a thermodynamically closed system consisting of a propagating electromagnetic field and a negligibly reflecting dielectric and we identify the Gordon momentum as the conserved total momentum by the fact that it is invariant in time. In the formalism of classical continuum electrodynamics, the Gordon momentum is therefore the unique representation of the total momentum in terms of the macroscopic electromagnetic fields and the macroscopic refractive index that characterizes the material. We also construct continuity equations for the energy and the Gordon momentum, noting that a time variable transformation is necessary to write the continuity equations in terms of the densities of conserved quantities. Finally, we use the continuity equations and the time–coordinate transformation to construct an array that has the properties of a traceless, symmetric energy–momentum tensor.     

The Gravitational Energy–Momentum Density of Radially Accelerated Observers in Schwarzschild Spacetime

A hybrid machinery that is useful for calculations in teleparallel theories when the spacetime is spherically symmetric is developed. Using this machinery, the gravitational energy–momentum tensor density of the Schwarzschild spacetime is evaluated in a frame adapted to observers that accelerate in the radial direction. The energy density, the total energy, and the gravitational energy-momentum flux are obtained. The regularization procedure and the limit where gravity is absent is discussed. It turns out that the regularized energy and energy–momentum flux are consistent in the whole spacetime. The continuity equation for the gravitational energy–momentum also holds for any point outside the black hole. Finally, the static and freely falling cases are discussed. It is found that a static observer measures a negative gravitational energy density, while a freely falling one measures a vanishing density.     

On gravitational radiation and the energy flux of matter

A suitable derivative of Einstein's equations in the framework of the teleparallel equivalent of general relativity (TEGR) yields a continuity equation for the gravitational energy‐momentum. In particular, the time derivative of the total gravitational energy is given by the sum of the total fluxes of gravitational and matter fields energy. We carry out a detailed analysis of the continuity equation in the context of Bondi and Vaidya's metrics. In the former space‐time the flux of gravitational energy is given by the well known expression in terms of the square of the news function. It is known that the energy definition in the realm of the TEGR yields the ADM (Arnowitt‐Deser‐Misner) energy for appropriate boundary conditions. Here we show that the same energy definition also describes the Bondi energy. The analysis of the continuity equation in Vaidya's space‐time shows that the variation of the total gravitational energy is determined by the energy flux of matter only.     

New drift modes in a nonuniform quantum magnetoplasma

We report the existence of two new drift modes in a nonuniform quantum magnetoplasma. By using the electron and ion fluid velocities deduced from the quantum momentum equations, together with the continuity and Poisson equations, we derive the governing equations for the low-frequency drift modes. The equations are then Fourier transformed to obtain linear dispersion relations, which admit new drift modes. The results are relevant for identifying electrostatic fluctuations that can cause cross-field charged particle transport in an inhomogeneous, ultracold magnetized quantum plasma.     

A simple classical derivation of spin-orbit couplings

A general derivation of spin-orbit couplings for arbitrary velocities is given which is based only on the definition of spin as the angular momentum in a rest frame of the particle and on the equation of motion in a non-inertial frame of reference.     

Nonlinear dynamics of a continuum Heisenberg spin chain with an anisotropy and an external magnetic field

By stereographically projecting the spin vector onto a complex plane in the equations of motion for a continuum Heisenberg spin chain with an anisotropy (an easy plane and an easy axis) and an external magnetic field, the effect of the magnetic field for integrability of the system is discussed. Then, introducing an auxiliary parameter, the Lax equations for Darboux matrices are generated recursively. By choosing the constants, the Jost solutions are satisfied the corresponding Lax equations. The exact soliton solutions are investigated, then the total magnetic momentum and its z-component are obtained. These results show that the solitary waves depend essentially on two velocities which describe a spin configuration deviating from a homogeneous magnetization. The depths and widths of solitary waves vary periodically with time. The center of an inhomogeneity moves with a constant velocity, while the shape of soliton also changes with another velocity and this shape is not symmetrical with respect to the center. The total magnetic momentum and its z-component vary with time.     

Linear time domain model of the acoustic potential field

A new time domain formulation of the acoustic wave is developed to avoid approximating assumptions of the linearized scalar wave equation that limit its validity to low Mach particle velocity modeling or to a smooth potential field in a stationary medium. The proposed model offers precision of the moving frame while retaining the form of the widely used linearized scalar wave equation although with respect to modified coordinates. It is applicable to field calculations involving transient waves with unlimited particle velocity, propagating in inhomogenous fluids or in those with time varying density. The model is based on the exact flux continuity equation and the equation of motion, both using the moving reference frame. The resulting closed-form free space scalar wave equation employing total derivatives is converted back to the partial differential form by using modified independent variables. The modified variables are related to the common coordinates of space and time following integral expressions involving transient particle velocity representing wave radiated by each point of a stationary source. Consequently, transient field produced by complex surface velocity sources can be calculated following existing surface integrals of the radiation theory although using modified coordinates. The use of the proposed model is presented in a numerical simulation of a transient velocity source vibrating at selected magnitudes, leading to the determination of the propagating pressure and velocity wave at any point.     

高密度和高粘度比率下气液两相流动的数值模拟

本文在VOF方法的基础上,采用粗细两套网格对高密度和高粘度比率下的气液两相流动模拟进行了研究分析.在细网格中求解流体体积函数方程,在粗网格中采用交错网格求解动量方程和压力修正方程,通过粗细网格间的数据传递获得求解动量方程时需要的准确的界面密度和粘度及控制体密度,克服了高密度和高粘度比率下通过插值方法计算界面密度和粘度及控制体密度带来较大误差的困难,保证了质量和动量同时守恒.高密度和高粘度比率下气液两相流动中气液交界面处密度、速度和压力急剧变化,为了保证格式的有界性和稳定性,采用稳定的有界高阶组合格式STOIC.最后模拟了不同工况下气泡在液体中的运动,并通过实验和模拟结果验证了方法的可行性及准确性.     

黏弹性流体充模过程中凝固现象的数值模拟

建立了黏弹性流体在充模过程中带有相变的气一液两相模型,该模型分别由气、液两相的质量守恒方程、动量守恒方程、能量守恒方程描述,并通过引入Heaviside函数将气一液两相的方程组统一为一个方程组;建立了一个对型腔内熔体和气体都适用的修正的焓方法来描述充模过程中的相变,采用基于同位网格的有限体积方法对模型进行求解,水平集方法捕捉充模过程中的界面演化,模拟出了黏弹性流体在充模过程中的凝固现象,得出了充模过程中型腔内的温度、压力、第一法向应力差等随时间的变化;并讨论了型腔壁面温度、熔体温度、注射速度对充模过程中凝固现象的影响,研究结果表明:型腔壁面温度越高,凝固层越薄;熔体温度越高,凝固层越薄;注射速度越高,凝固层越薄,故提高型腔壁面温度、熔体温度、注射速度可以减少或消除型腔壁面附近的凝固层。     

三维混合沙输运数值模拟

采用计算流体力学和颗粒离散元耦合的方法模拟了三维混合沙输运过程。采用体平均的Navier-stokes方程来描述气相运动,考虑了气相和颗粒相的相互作用。颗粒运动通过求解牛顿运动方程来求解,采用硬球模型描述颗粒和颗粒及颗粒和壁面的碰撞。本模型中,颗粒运动是三维的而气相运动是二维的。计算结果表明:总输沙率沿高度方向在大于2cm以上按照指数衰减,在2 cm以下则偏大;各粒径颗粒具有不同的输沙率分布,粗粒径颗粒按指数规律衰减,其它粒径颗粒输沙率随高度先指数增加后减少;各粒径颗粒平均水平速度随高度对数函数增加且同高度时随粒径增大而减小,1 cm高度以下则相反;沙粒平均粒径沿高度线性递减,2 cm以下粒径偏大。     

Optical activity induced by rotation of atomic spin

Summary Physical systems or processes invariant under mirror reflection are not expected to exhibit intrinsically chiral asymmetries. Thus, it is ordinarily the case that unbounded and unexcited atoms (in the absence of weak nuclear interactions) should not manifest circular birefringence. It is shown, however, that in a rotating reference frame the coupling of atomic spin angular momentum to the angular velocity of the rest frame gives to optical activity even in the absence of contributions from nuclear interactions and the classical Coriolis force. Ground-state atomic hydrogen is predicted to be optically active in the microwave region near the hyperfine splitting frequency of 1420 MHz. Under appropriate circumstances, this spin-associated rotational circular birefringence can be some ten orders of magnitude larger than that previously estimated for virtual electronic transitions falling within the visible and UV portions of the spectrum.     

Computation of fluid flows in non-inertial contracting, expanding, and rotating reference frames

We present the method for computation of fluid flows that are characterized by the large degree of expansion/contraction and in which the fluid velocity is dominated by the bulk component associated with the expansion/contraction and/or rotation of the flow. We consider the formulation of Euler equations of fluid dynamics in a homologously expanding/contracting and/or rotating reference frame. The frame motion is adjusted to minimize local fluid velocities. Such approach allows to accommodate very efficiently large degrees of change in the flow extent. Moreover, by excluding the contribution of the bulk flow to the total energy the method eliminates the high Mach number problem in the flows of interest. An important practical advantage of the method is that it can be easily implemented with virtually any Eulerian hydrodynamic scheme and adaptive mesh refinement (AMR) strategy.We also consider in detail equation invariance and existence of conservative formulation of equations for special classes of expanding/contracting reference frames. Special emphasis is placed on extensive numerical testing of the method for a variety of reference frame motions, which are representative of the realistic applications of the method. We study accuracy, conservativity, and convergence properties of the method both in problems which are not its optimal applications as well as in systems in which the use of this method is maximally beneficial. Such detailed investigation of the numerical solution behavior is used to define the requirements that need to be considered in devising problem-specific fluid motion feedback mechanisms.     

Sound waves in a liquid with polydisperse vapor–gas bubbles

A mathematical model is presented for the propagation of plane, spherical, and cylindrical sound waves in a liquid containing polydisperse vapor–gas bubbles with allowance for phase transitions. A system of integro-differential equations is constructed to describe perturbed motion of a two-phase mixture, and a dispersion relation is derived. An expression for equilibrium sound velocity is obtained for a gas–liquid or vapor–liquid mixture. The theoretical results agree well with the known experimental data. The dispersion curves obtained for the phase velocity and the attenuation coefficient in a mixture of water with vapor–gas bubbles are compared for various values of vapor concentration in the bubbles and various bubble distributions in size. The evolution of pressure pulses of plane and cylindrical waves is demonstrated for different values of the initial vapor concentration in bubbles. The calculated frequency dependence of the phase sound velocity in a mixture of water with vapor bubbles is compared with experimental data.     

The dominant “heating” mode: bending excitation of water molecules by low-energy positron impact

We report a quantum dynamical treatment of the vibrational excitation of the bending mode of water molecules by collision with low energy positrons in the energy regions close to threshold openings. The exact vibrationally coupled-channel equations derived for the total e+-H2O system are solved in a Body-Fixed-Vibrational-Coupled-Channels (BF-VCC) reference frame, using a single-center expansion of the total wavefunction and of the interaction potential. The vibrationally inelastic cross-sections for transitions from the ground to the lowest excited state of the bending mode clearly show the bending excitation channel to be the dominant inelastic process at low collision energies. Comparisons with our earlier calculations for the other modes and for the excited processes induced by electron impact are also presented and analysed.     

Predicted flow characteristics of a wire-nonparallel plate type electrohydrodynamic gas pump using the Finite Element Method

The aim of this paper is to numerically investigate the interaction between the electrostatic field and the fluid flow in a wire-nonparallel plate configuration of electrodes. The governing equations: Poisson equation for electric field, continuity equation for charge transport and the momentum equation for gas flow were solved using the Finite Element Method assuming a highly non-uniform mesh distribution. The main outcome of this study is the determination of velocity versus pressure characteristics of the pump, which provides useful information for predicting the pump performance and for control purposes. In addition, the efficiency and optimum geometric configuration are evaluated using this model. The numerical results show that a higher voltage leads to larger velocity and higher pressure, where the gas velocity is a linear, but pressure is a non-linear function of the supplied voltage. It was also found that there is an optimum wall angle for which the air volumetric flow rate from the outlet of the pump reaches the maximum value.