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A novel DEM based pore-scale thermo-hydro-mechanical model
Published in Günther Meschke, Bernhard Pichler, Jan G. Rots, Computational Modelling of Concrete and Concrete Structures, 2022
M. Krzaczek, M. Nitka, J. Tejchman
The maximum temperature difference between cooling by diffusion and diffusion with advection was 2.26 K after 400 s of cooling (Figures 6a and 6b). Advection slightly speeded up the cooling process. However, it should be noted that the pressure difference between the lower and upper boundary was very small, 0.05 MPa (Figure 7a). This resulted in very low fluid velocity. The maximum fluid velocity did not exceed 1.8·10-5 m/s (Figure 7c). Generally, the velocity vectors were parallel to the vertical boundaries (Figure 7c) which confirmed a 1D fluid flow in the specimen. The fluid pressure varied almost linearly along the bar (Figure 7a) from the lower boundary to the upper boundary. The fluid density ranged from 1002.3 kg/m3 to 1010.5 kg/m3 (Figure 7b) after 400 s of cooling. The Peng-Robinson equation of state (Eqn. 1) with correction (Eqn. 2) introduced a very small error (less than 1.3%) in the estimation of the density. The fluid density was slightly overestimated.
Gas Turbine
Published in S. Can Gülen, Gas Turbine Combined Cycle Power Plants, 2019
Note that in analyzing gas flow in a turbomachine, one must keep track of “thermal” and “kinetic” energy of the fluid. The former is quantified by the static value of the enthalpy from the static values of pressure and temperature via a suitable equation of state. The equation of state can be as simple as the ideal gas equation of state, i.e., p = ρRT, or quite cumbersome (e.g., JANAF tables or a “real gas” equation of state such as Peng–Robinson or Benedict–Webb–Rubin). The combination of thermal and kinetic components (the latter, per unit mass, is simply v2/2 where v is the gas absolute velocity) gives the total or stagnation enthalpy of the gas in question. In simplified treatment of turbomachinery gas dynamics, as a result of “perfect gas” assumption with constant cp, one frequently encounters the differentiation between static and total/stagnation temperatures. This convention simplifies the flow equations and is pretty accurate for most cases. In the discussion below, static values of p and T are notated without subscript, whereas their total/stagnation values are notated by the subscript tot. In literature, there are many different conventions (e.g., subscript 0 for total/stagnation values, subscript s for static values). In mathematical terms, in US customary system (USCS) units
Special, Second, and Higher-Order Equations
Published in L.M.B.C. Campos, Higher-Order Differential Equations and Elasticity, 2019
Theequation of stateis a relation between any three of the four thermodynamic variables, pressure, temperature, entropy, and mass density (or specific volume), and depends on the substance, for example, gas, liquid, solid, or a mixture. Choosing the equation of state in the form (5.105a) of the pressure as a function of the mass density and entropy:p=pρ,S:dp=cs2dρ+βdS;
A Multiscale and Multiphysics PWR Safety Analysis at a Subchannel Scale
Published in Nuclear Science and Engineering, 2020
H. Y. Yoon, I. K. Park, J. R. Lee, S. J. Lee, Y. J. Cho, S. J. Do, H. K. Cho, J. J. Jeong
After solving the governing equations for the primary variables such as pressure and internal energy, equations of state are used to obtain the physical properties such as temperature, density, viscosity, etc. For mathematical closure of the governing equations, relevant physical models are applied depending on the analysis scale. In a CFD scale, two-equation RANS turbulence models such as the standard , re-normalization group (RNG) , and Menter’s shear stress transport (SST) models are applied and the interface transfer models are determined based on the two-phase topology map.15 In a component scale including the assembly and subchannel scales, a porous medium model is used for the wall friction and heat transfer.
Numerical analysis of density flows in adiabatic two-phase fluids through characteristic finite element method
Published in International Journal of Computational Fluid Dynamics, 2019
Mutsuto Kawahara, Kohei Fukuyama
In previous research studies, to successfully solve these problems, the incompressibility assumption was introduced. However, because the density in this process is variable, the incompressibility assumption is not valid. Therefore, compressibility should be considered. For compressible fluid flows analyses, it is necessary to introduce the equation of conservation of energy. For adiabatic flows, the energy equation cau be reduced to the equation of pressure and density, which is sometimes referred to as the Poisson law. This equation is also referred to as the equation of state. For an adiabatic assumption, the equations of conservations of mass and momentum with a constitutive equation can be employed as governing equations. Here, the main variables are density and velocity because pressure can be transformed into density using the equation of state. The temperature varies with density and pressure. However, with the adiabatic assumption, which is the state that the thermal effect through the boundary is cut off, the temperature inside the closed domain can be eliminated from the main variables. There are various temperature dependent problems in science and engineering, for which the thermal effects should be considered. For such problerms, the energy equation should be introduced.
A discrete multicomponent droplet evaporation model; effects of O2-enrichment, steam injection, and EGR on evaporation of diesel droplet
Published in Numerical Heat Transfer, Part A: Applications, 2018
Rasoul Shahsavan Markadeh, Hojat Ghassemi
Accurate determination of thermophysical and transport properties is of great importance in order to obtain accurate results. Gas density is determined by Peng–Robinson equation of state. NASA polynomials are used for calculation of ambient gases specific heat [43], viscosity, and conductivity [44]. Polynomial by Poling et al. [42] is used for specific heat of vapor hydrocarbons. For viscosity and conductivity of hydrocarbons vapor, Chung method is employed [42]. Chapman–Enskog theory is used to determine gas phase binary diffusion coefficients [45]. Specific heat of species in liquid phase is determined by Lee–Kesler method [46] and their latent heat of vaporization is calculated by relation provided by Yaws [47]. Liquid phase viscosity and thermal conductivity are taken by Daubert and Danner [48] and Wilke–Chung method is used for liquid diffusivity [42].