Conservation Of Internal Energy Research Articles

DYNAMIC MODEL OF THERMAL PROCESSES IN A LIQUID FLOWING THROUGH A CHANNEL

The article presents a dynamic thermal process model for an incompressible fluid moving through a channel of arbitrary cross-sectional shape. The study focuses on expressing the non-steady law of conservation of internal energy of the fluid by considering the dependence of parameters on both spatial coordinates and time. The one-dimensional spatial formulation of the problem is simplified by disregarding any changes in flow parameters in the direction perpendicular to the channel axis. The resulting equation represents a non-stationary, non-homogeneous, quasi-linear hyperbolic partial differential equation, which can be solved with the method of characteristics in the case of constant coefficients. The solution consists of two distinct solutions that are glued along the line x/t=v, with isolines shown in the figure provided. The research is relevant for the design of heat exchangers, rocket and aircraft engines, and other heat engineering devices.

DIRETRIZES GERAIS PARA DESENVOLVIMENTO DE UM PLANO DE AÇÃO QUE BUSQUE A REDUÇÃO DOS GASTOS COM O INSUMO ENERGIA ELÉTRICA NO ÂMBITO DO PODER PÚBLICO

DIRETRIZES GERAIS PARA DESENVOLVIMENTO DE UM PLANO DE AÇÃO QUE BUSQUE A REDUÇÃO DOS GASTOS COM O INSUMO ENERGIA ELÉTRICA NO ÂMBITO DO PODER PÚBLICO

The soil heat flux sensor functioning checks, imbalances' origins, and forgotten energies

Abstract. Soil heat flux is an important component of the surface energy balance (SEB) equation. Measuring it requires an indirect measurement. Every used technique may present some possible errors tied with the utilized specific technique, soil inhomogeneities, or physical phenomena such as latent heat conversion beneath the plates, especially in desiccation cracking soil or vertisol. The installation place may also induce imbalances. Finally, some errors resulting from the physical sensor presence, vegetation presence, or soil inhomogeneities may occur and are not avoidable. For all these reasons it is important to check the validity of the measurements. A quick and easy way is to integrate results over 1 year. By consideration of the inert core internal energy conservation law, it is shown that the corresponding integration should be close to zero after a necessary geothermal heat efflux subtraction. However, below-plate evaporation and vegetation-absorbed water or rainwater infiltration may also contribute to the observed short-scale and/or long-scale imbalance generating convective heat fluxes not sensed by the heat flux sensors. Another energy source is usually not included in the SEB equation: rainfall or irrigation. Yet its importance for short- and long-term integration is notable. As an example, the most used sensor, soil heat flux plates (SHFPs), is given.

Development of singular value decomposition based solution scheme for a numerical simulation of multiphase flow

This paper presents an innovative solution scheme that may resolve the numerical challenges of simulating the phase appearance and disappearance phenomena in multiphase flow. In this study, a least square problem for the mass and internal energy conservation equations is reviewed, and its inherent ill-posedness, originating from the rank deficiency of the coefficient matrix, in the inverse problem is introduced. Since building mathematically well-conditioned matrices is essential to avoiding the numerical instability as well as the singularity of matrices, first of all, a new solution scheme for the mass and internal energy conservation equations for the simulation of multiphase flow in which phase can appear and disappear under various flow conditions is derived based on a truncated Singular Value Decomposition (SVD)-based low rank approximation. The truncated SVD-based low rank approximation is then used to solve the mass and internal energy conservation equations by computing the pseudo inverse of the low rank approximation matrix. The field equations and closure relations currently being developed by introducing arbitrary values, which replace an extremely low volume fraction of fluids, are redefined in this study. As such, the physical phenomena themselves are directly considered without any modifications to the mathematical equations to compute phase transitions. The characteristics of phase transition are classified into convection, vaporization, and condensation over a wide range of fluid conditions, and the verification of the proposed solution method is completed through simulations of the 3 phase transition mechanisms. The SVD-based low rank approximation method improves computations of phase transition as simulation results indicate that the proposed solution scheme describes the physics better than the conventional one.

A numerical derivation of internal energy equation under a staggered mesh system for 1-D thermal hydraulic system analysis codes

This paper introduces a modified internal energy equation derived for multiphase flow in various flow conditions for a staggered mesh system. The pressure drop and heat dissipation terms in the internal energy conservation equation currently being developed based on the assumption that the scalar and momentum variables, which originate from the total energy and mechanical energy equations, respectively, are all located in the cell center of the control volume were redefined such that two different pressures and velocities stored in both cell centers and faces were imposed for the internal energy conservation. To achieve this, first, a modified internal energy conservation equation for a staggered mesh was derived by subtracting the mechanical energy equation from the total energy equation. The equation was then discretized classifying each term by its origin; variables that originated from the total energy equation were defined in the cell center, whereas terms that came from the mechanical energy equation were identified at faces. Since the discretized form of the proposed equation contained face velocity and cell pressure for the heat dissipation and pressure drop terms, respectively, these two terms were calculated implicitly leading to enhanced numerical stability. The accuracy of the modified internal energy equation in predicting the system pressure, fluid temperature, and heat balance for various flow channels was assessed. The verification of the proposed equation was completed through simulations of multiple theoretical problems including saturated liquid depressurization, adiabatic expansion of hydrogen, heat transfer in a helical steam generator, and energy transfer in a converging pipe. An improved result was obtained with the modified equation as the numerical calculation results agreed well with the analytic solutions with relative deviations less than 0.1% for most cases, while the solution obtained by the conventional internal energy equation showed a significant amount of deviation from the analytic solution.

Comparison of the numerical and self-similar solutions of Sedov’s problem on a point explosion in gas

Comparative analysis of solutions of Sedov’s problem of a point explosion in gas for the plane case, obtained by the analytical method and using the open software package of computational fluid dynamics OpenFOAM, is carried out. A brief analysis of methods of dimensionality and similarity theory used for the analytical self-similar solution of point explosion problem in a perfect gas (nitrogen) which determined by the density of uncompressed gas, magnitude of released energy, ratio of specific heat capacities and by the index of geometry of the explosion is given. The system of one-dimensional gas dynamics equations for a perfect gas includes the laws of conservation of mass, momentum, and energy is used. It is assumed that at the initial moment of time there is a point explosion with instantaneous release of energy. Analytical self-similar solutions for the Euler and Lagrangian coordinates, mass velocity, pressure, temperature, and density in the case of plane geometry are given. The numerical simulation of considered process in sonicFoam solver of OpenFOAM package built on the PISO algorithm was performed. For numerical modeling the system of differential equations of gas dynamics is used, including the equations of continuity, Navier-Stokes motion for a compressible medium and conservation of internal energy. Initial and boundary conditions were selected in accordance with the obtained analytical solution using the setFieldsDict, blockMeshDict, and uniformFixedValue utilities. The obtained analytical and numerical solutions have a satisfactory agreement.

Simulation the formation process of boiling water flow during depressurization of a high pressure vessel using OpenFoam open source

A numerical study of the initial stage of water outflow process through a thin nozzle from a supercritical state in a two-dimensional axisymmetric setting is performed using the OpenFOAM software open source with the sonicFoam solver. The mathematical model of sonicFoam solver includes the equation of mass conservation, Navier-Stokes equation, internal energy conservation and equation of state of water vapor in the form of a perfect gas. Visualization of calculation results was carried out by the ParaView graphic platform. The features of supersonic high-speed flow regime in a jet accompanied by the formation of a hollow jet in a form close to parabolic are investigated.

Numerical model of the electro-gas-dynamics of a gas–particle system based on the equations of motion of a two-velocity two-temperature gas–particle mixture

A mathematical model of the electro-gas-dynamics of a gas–particle system is described. A numerical method for solving the system of equations is proposed, and an analysis is made of the motion of charged solid aerosol particles in gas–particle flow in the electric field produced by the corona electrode of the atomizer, the grounded surface on which deposition is performed, and the charge of the aerosol particles in the interelectrode space. The solution is based on the two-velocity two-temperature model of a monodisperse medium without phase transitions and coagulation assuming that only the carrier medium, described by the Navier–Stokes equations for a compressible gas, has viscosity. The dispersed phase is defined by the equation of conservation of mass, the equations of conservation of momentum components taking into account the Coulomb force and aerodynamic friction, and the equation of conservation of internal energy. The system is written in generalized coordinates in dimensionless form and solved using the explicit McCormack method with splitting over the spatial coordinates and a conservative correction scheme. The velocity and density fields of the gas–particle mixture were investigated in the interelectrode space and near the surface on which solid aerosol particles in the gas–particle flow are deposited.

Numerical investigation of the evolution of a shock wave in a gas suspension with consideration for the nonuniform distribution of the particles

In this paper we present the results of investigating the process of evolution of a shock wave in a gas suspension whose dynamics are simulated by the continuous system of motion equations of a two-temperature and two-speed monodispersive medium in the two-dimensional case. The carrier medium is described by the system of Navier–Stokes equations. The dispersive phase is simulated by the mass, momentum, and internal-energy conservation equations. The system is brought into the dimensionless form and is solved by the explicit McCormack method with the conservative correction scheme applied to each phase in order to obtain a monotonic solution. The obtained solutions are compared with the results known from the literature.

Numerical study of shock wave dynamics in a gas suspension

We describe a process of pressure discontinuity breakdown in a gas suspension, dynamics of which is simulated by a system of equations of motion for a two-temperature two-speed monodisperse medium without phase transition and coagulation. The carrying medium is described by the Navier-Stokes equation system. A disperse phase is simulated by equations of mass, momentum and internal energy conservation. The system is reduced to a dimensionless form, it is written in the generalized coordinates and is solved by the explicit MacCormack method with a conservative correction scheme applied to each phase to obtain a monotonous solution. We describe an effect of decreasing the time intensity of a shock wave when its attitude is retained. The time of the pressure differential value relaxation at the direct shock wave front depends on the volumetric content and dispersion degree of the gas suspension.

An implementation of the HLL Scheme on a hyperbolic two-fluid model for two-phase flow simulations

In this manuscript, we discuss the implementation of an upwind method for a new two-dimensional two-fluid model by including the surface tension effect in the momentum equations. This model consists of a complete set of eight equations including two mass, four momentum, and two internal energy conservation equations, all with real eigenvalues. Based on this equation system, we first made a characteristic analysis for investigating mathematical properties. Next, we made a two-dimensional pilot code based on the HLL scheme to solve some benchmark problems in order to determine whether this model and numerical method can simulate a fundamental two-dimensional two-phase flow problem as well as one-dimensional problems.

Vibrational energy transfer in ultracold molecule-molecule collisions

We present a rigorous study of vibrational relaxation in $\text{para}\text{\ensuremath{-}}{\mathrm{H}}_{2}+\text{para}\text{\ensuremath{-}}{\mathrm{H}}_{2}$ collisions at cold and ultracold temperatures and identify an efficient mechanism of rovibrational energy transfer. If the colliding molecules are in different rotational and vibrational levels, the internal energy may be transferred between the molecules through an extremely state-selective process involving simultaneous conservation of internal energy and total rotational angular momentum. The same transition in collisions of distinguishable molecules corresponds to the rotational energy transfer from one vibrational state of the colliding molecules to another.

On the existence of weak solutions to the equations of non-stationary motion of heat-conducting incompressible viscous fluids

This paper is concerned with the equations of non-stationary motion in 3D of heat-conducting incompressible viscous fluids with temperature-dependent viscosity. The conservation of internal energy includes the usual dissipation term. We prove the existence of a ‘weak solution with defect measure’ to the system of PDEs under consideration. Our method of proof is based on a regularization of the equations of conservation of momentum. Copyright © 2006 John Wiley & Sons, Ltd.

Thermodynamic basis for a variational model for crystal growth.

Variational models provide an alternative approach to standard sharp interface models for calculating the motion of phase boundaries during solidification. We present a correspondence between objective functions used in variational simulations and specific thermodynamic functions. We demonstrate that variational models with the proposed identification of variables are consistent with nonequilibrium thermodynamics. Variational models are derived for solidification of a pure material and then generalized to obtain a model for solidification of a binary alloy. Conservation laws for internal energy and chemical species and the law of local entropy production are expressed in integral form and used to develop variational principles in which a "free energy," which includes an interfacial contribution, is shown to be a decreasing function of time. This free energy takes on its minimum value over any short time interval, subject to the laws of conservation of internal energy and chemical species. A variational simulation based on this model is described, and shown for small time intervals to provide the Gibbs-Thomson boundary condition at the solid-liquid interface.

Spectroscopic Constraints on Models of Ion Cyclotron Resonance Heating in the Polar Solar Corona and High‐Speed Solar Wind

Using empirical ion velocity distributions derived from Ultraviolet Coronagraph Spectrometer (UVCS) and Solar Ultraviolet Measurements of Emitted Radiation (SUMER) ultraviolet spectroscopy, we construct theoretical models of the nonequilibrium plasma state of the polar solar corona. The primary energy deposition mechanism we investigate is the dissipation of high-frequency (10-10,000 Hz) ion cyclotron resonant Alfven waves which can heat and accelerate ions differently depending on their charge and mass. We solve the internal energy conservation equations for the ion temperature components parallel and perpendicular to the superradially expanding magnetic field lines and use empirical constraints for the remaining parameters. We find that it is possible to explain many of the kinetic properties of the plasma (such as high perpendicular ion temperatures and strong temperature anisotropies) with relatively small amplitudes for the resonant waves. There is suggestive evidence for steepening of the Alfven wave spectrum between the coronal base and the largest heights observed spectroscopically, and it is important to take Coulomb collisions into account to understand observations at the lowest heights. Because the ion cyclotron wave dissipation is rapid, the extended heating seems to demand a constantly replenished population of waves over several solar radii. This indicates that the waves are generated gradually throughout the wind rather than propagated up from the base of the corona.

Level-to-level vibrationally inelastic rate constants for Li2* –X (X=He, Ne, Ar, Xe) collisions

We present 1088 level resolved rate constants for the vibrotationally inelastic collisions Li*2(vi=9, ji)+X →Li*2(vf, jf)+X with Li2 in the A 1∑+u state, ji =8, 22, and 42 and X=He, Ne, Ar, and Xe at T∼600 °C. At high ji, the results display a quasiresonant enhancement of vibrational transfer and a striking lack of dependence on target gas (X). At ji=42, the jf distributions for Δv≡vf−vi≠0 are quite narrow and peak at jf=ji+Δj with Δj=−4Δv. Internal energy conservation would require Δj=−6Δv; hence our use of the prefix ‘‘quasi’’ above. At high ji, the vibrationally inelastic cross sections are large: e.g., 4.5 Å2 into the single final level Δv=−1, jf =46 and over 80 Å2 total for Xe. Absolute errors as small as 6% have been routinely attained by using an analysis procedure which averages data from several fluorescence bands after correcting for variation of Franck–Condon factors with j.