Combination of Gibbs and Helmholtz Energy Equations of State in a Multiparameter Mixture Model Using the IAPWS Seawater Model as an Example

For carbon capture and storage (CCS) applications different sets of equations of state are used to describe the whole CCS-chain. While for the transport and pipeline sections highly accurate equations of state (EOS) explicit in the Helmholtz energy are used, properties under typical geological storage conditions are described by more simple, mostly cubic EOS, and brines are described by Gibbs energy models. Combining the transport and storage sections leads to inconsistent calculations. Since the used models are formulated in different independent variables (temperature and density versus temperature and pressure), mass and energy balances are challenging and equilibria in the injection region are difficult to model. To overcome these limitations, a predictive combination of the Gibbs energy-based IAPWS seawater model (IAPWS R13-08, 2008) with Helmholtz energy-based multi-parameter EOS is presented within this work. The Helmholtz energy model used in this work is based on the EOS-CG-2016 of Gernert and Span (J Chem Thermodyn 93:274–293, 10.1016/j.jct.2015.05.015, 2016). The results prove that a consistent combination of the two different models is possible. Furthermore, it is shown, that a more complex brine model needs to be combined with Helmholtz energy EOS for calculations at storage conditions.

Analysis of Thermal Performances in a Ventilated Room Using LBM-MRT: Effect of a Porous Separation

This article demonstrates the feasibility of porous separation on the performance of displacement ventilation in a rectangular enclosure. A jet of fresh air enters the cavity through an opening at the bottom of the left wall and exits through an opening at the top of the right wall. The porous separation is placed in the center of the cavity and its height varies between 0.2 and 0.8 with three values of thickness, 0.1, 0.2, and 0.3. The heat transfer rate was calculated for different intervals of Darcy (10−6 ≤ Da ≤ 10), Rayleigh (10 ≤ Ra ≤ 106), and Reynolds (50 ≤ Re ≤ 500) numbers. The momentum and the energy equations were solved by the lattice Boltzmann method with multiple relaxation times (LB-MRT). Schemes D2Q9 and D2Q5 were chosen for the velocity and temperature fields, respectively. For porous separation, the generalized Darcy–Brinkman–Forchheimer model was adopted. It is represented by a term added in the standard LB equations. For the dynamic domain, numerical simulations revealed complex flow structures depending on all control parameters. The results showed that the thermal field, mainly in the second compartment, is very dependent on the size and permeability of the porous separation. However, they have no influence on the transfer rate.

Upper tropospheric energetics of standing eddies In wave number domain during contrasting Monsoon activity over India

The upper tropospheric energetics of the standing eddies in wave number domain during contrasting monsoon' activity over India have been investigated. Two normal monsoon years (1970. 1971) and two drought monsoon years (1972, 1979) are considered for a comparative study, Energy equations of Saltzman (1957) are used to compute wave-wave Interaction and wave to zonal mean flow Interaction. Analysis of the results show that the standing eddies in the region of tropical easterlies (5°S-24 .2°N) have larger kinetic energy than those in the region of southern hemispheric, westerlies (24.2°S-5°S). Wave to zonal mean flow interaction of all waves (waves 1-15) Indicate that the standing eddies are a source of kinetic energy to zonal mean flow ID the region of easterlies and there sink of kinetic energy to zonal mean flow in the region of westerlies. In the region of easterlies planetary standing waves (waves 1-2) are the major kinetic energy source to other standing waves and wave-wave Interaction of all waves leads to positive Imbalance of kinetic energy during normal monsoon years (1970, 1971) and negative imbalance, of kinetic, energy during drought monsoon years (1972, 19~9). In the region of westerlies the imbalance of kinetic energy IS negative during normal monsoon years and positive during drought monsoon years.

The Effects of Electrical Conductivity on Fluid Flow between Two Parallel Plates in a Porous Medioum

This paper deals with a mathematical model of a fluid flowing between two parallel plates in a porous medium under the influence of electromagnetic forces (EMF). The continuity, momentum, and energy equations were utilized to describe the flow. These equations were stated in their nondimensional forms and then processed numerically using the method of lines. Dimensionless velocity and temperature profiles were also investigated due to the impacts of assumed parameters in the relevant problem. Moreover, we investigated the effects of Reynolds number , Hartmann number M, magnetic Reynolds number , Prandtl number , Brinkman number , and Bouger number , beside those of new physical quantities (N , ). We solved this system by creating a computer program using MATLAB.

Mechanical improvement in solar aircraft by using tangent hyperbolic single-phase nanofluid

Solar power is the primary thermal energy source from the sunlight. This research has carried out the study of solar aircraft with solar radiation in enhancing efficiency. The thermal transfer inside the solar aircraft wings using a nanofluid past a parabolic surface trough collector (PTSC) is investigated thoroughly. The source of heat is regarded as solar radiation. For several impacts, such as porous medium, thermal radiation, and varying heat conductivity, the heat transmission performance of the wings is examined. By using the tangent hyperbolic nanofluid (THNF), the entropy analysis has been performed. The modeled momentum and energy equations are managed using the well-established numerical methodology known as the finite difference method. Two distinct kinds of nano solid-particles have been examined, such as Copper (Cu) and Zirconium dioxide (ZrO2), while Engine Oil (EO) being regarded as a based fluid. Different diagram parameters will be reviewed and revealed as figures and tables on speed, shear stress, temperature, and the surface drag coefficient and Nüselt number. It is observed that in terms of heat transfer for amplification of thermal radiation and changeable thermal conductance parameters, the performance of the aircraft wings raises. In contrast to traditional fluid, nanofluid is the best source of heat transmission. Cu-EO's thermal efficiency over ZrO2-EG falls to the minimum level of 12.6% and has reached a peak of 15.3%.

Calculation of evaporation length of a liquid bridge flowing between inclined hot tubes

The bridge consists of liquid held by surface tension forces between two inclined tubes in an LNG heat exchanger. The shape of the bridge is calculated by the hydrostatic equation, which is reduced to a nonlinear integral equation and resolved by the Newton method. The velocity and temperature fields in the bridge are described by the Navier-Stokes and energy equations, respectively. They are reduced to the boundary integral equations and calculated by the method of boundary elements. Heat transfer coefficient is calculated for evaporating bridge and the length of total bridge evaporation is estimated.

Gas flow modeling in wells

The topic of research is gas flow modeling in wells. The subject of the study is to determine the dynamic parameters of gas in a gas well, taking into account changes in the ambient temperature and gravity. Mathematical and numerical modeling of gas flow in a gas well is performed; a numerical algorithm to determine gas pressure in a gas well is built. This algorithm allows studying the state of production and injection wells with varying conditions at the wellhead and at the lower end of the well. Research methods are based on the energy equations of the transported gas; the mass conservation equation, which are the basic equations of gas flow; the methods of numerical and mathematical modeling. In the article, numerical and mathematical models of gas flow in a gas well are obtained, taking into account changes in the ambient temperature and gravity. A numerical algorithm and a program were built to determine the gas-dynamic characteristics of wells. The computational process was based on the “cycle in cycle” principle. Provisions were made to study the state of production and injection wells with varying conditions at the wellhead and at the bottom end of the well.

Power Law Fluid Model for Thermal Elastohydrodynamic Lubrication

The aim of this paper is to analyse thermal elastohydrodynamic lubrication (TEHL) line contact of rolling a bearing using a non-Newtonian uid that is described by the power law model. The performance characteristics of the rolling bearing are determined for various index for dilatant, Newtonian and pseudo plastic uids. The one-dimensional Reynolds and energy equations are both modied to incorporate the non-Newtonian nature of the lubricant. The coupled system of governing equations are discretized using the finite difference method and solved simultaneously. The results show that the pressure, film thickness and temperature for dilatant uids increased with increase in the ow index as compared to pseudo plastic uids. The in uence of thermal effects on pressure and lm thickness is more significant compared with that under isothermal elastohydrodynamic lubrication especially on the case of dilatant uids. The viscosity of the lubricant increases with increase in pressure and reduces with increment in temperature. The surface roughness in the bearing surface increases the lm thickness of the lubricant. The uid pressure, film thickness and temperature increases with increase in the bearing speed. To truly re ect the characteristics of EHL models, thermal effects should be considered.

THEORETICAL MATHEMATICAL MODELING OF HEAT EXCHANGE IN PIPES WITH TRIANGULAR AND SQUARE TURBULATORS WITH d/D=0.95÷0.90, t/D=0.25÷1.00 AND HIGH REYNOLDS NUMBERS Re=106

Mathematical modeling of heat exchange process in straight and round horizontal pipes with protrusions and d/D=0.95...0.90, t/D=0.25...1.00 of triangular and square sections with large Reynolds numbers (RE=106) are carried out on the basis of multiblock computing technologies based on solutions of factored and finite-volume algorithm of RANS equations and energy equations. It is shown that for higher square protrusions and at higher Reynolds numbers, a limited increase in NU/NUgl is accompanied by a significant increase in relative hydro resist ance in accordance with the higher Reynolds number; for triangular turbulators, this persists and even deepens.

Modeling of the dynamics of tornado structures in a pipe with turbulators of square, semicircular and triangular profiles

Objectives. To carry out mathematical simulations of changes in time of tornado compositions in channels with projections of semicircular, triangular, square profiles for average Reynolds criteria based on multiblock computing technology with the solution of finite- volume factorized methods of the Reynolds equation and energy equations.Method. The calculations were carried out on the basis of theoretical approaches based on the solution of Reynolds equations by finite-volume factorized methods, which were closed using the simulation of Menter stresses, and the energy of a structured grid.Result. The calculations of time-dependent flow and heat transfer parameters carried out in the article showed that the excess dissipation of turbulence generation for projections of sharp profiles - square profile, triangular profile - and rounded profiles - semicircular profile, segment profile - is provided with radically different hydraulic losses: channels with protrusions of rounded profiles, for example, semicircular, have much lower hydraulic resistance coefficients than channels with protrusions with sharp profiles, for example, triangular or square, rectangular.Conclusion. In the article, mathematical simulations of time-dependent tornado compositions were performed in channels with transversal profiles in the form of a square, triangle and semicircle, which is as informative as possible in terms of studying turbulent flows and heat transfer arising under average Reynolds criteria based on computer multiblock technology when using solutions of finite-volume factorized methods (FCOM-am) Reynolds equations and energy equations. The following protrusions were considered in the article: square transversal profiles, in which tornadoes are most pronounced, and side tornadoes affect the flow in the maximum way; triangular transversal profiles, where tornadoes are not so strong, and side tornadoes affect the main flow weaker than with square protrusions; semicircular transversal profiles, in which the incoming main tornado moves along the stream with the generation of limited side tornadoes. The calculated information obtained in the article correlates to a high degree with the available experimental data, which indicates the verification of the mathematical modeling involved in the article.