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The Ideal Gas
Published in Irving Granet, Jorge Luis Alvarado, Maurice Bluestein, Thermodynamics and Heat Power, 2020
Irving Granet, Jorge Luis Alvarado, Maurice Bluestein
Note that in the equations for polytropic processes, they may be stated in terms of temperatures only by invoking the ideal gas law pv = RT as in Equation 6.100 with n instead of k. For problems involving turbomachinery, the most commonly used equation for work is Equation 6.103 with n instead of k:w=nRT11−n[(P2P1)n−1n−1]
Pulse Tube Cryocoolers
Published in David A. Cardwell, David C. Larbalestier, Aleksander I. Braginski, Handbook of Superconductivity, 2023
John M. Pfotenhauer, Xiaoqin Zhi
Because it inherently applies to sinusoidal oscillating systems that relate an oscillating driving force to its associated flow, there are many features of the analysis that mirror equivalent terms in AC electrical systems. Both types of systems draw extensively from wave behavior, but in the field of thermo-acoustics the additional relationships defined by the ideal gas law, polytropic relations, and heat transfer provide additional information relating pressure, temperature, and volume (or mass) flow rates.
Hydrodynamic Aspects on Sonoluminescence
Published in Sanjay J. Dhoble, B. Deva Prasad Raju, Vijay Singh, Phosphors Synthesis and Applications, 2018
Consider a trapped bubble that oscillates synchronous to the ultrasonic wave. As is well known, one cannot obtain the instantaneous properties such as density, pressure, and temperature for the gas inside the bubble using the ideal gas law with a polytropic relation [11]. Instead, one should solve the mass, momentum, and energy equations to understand the gas behavior inside a bubble. In spherical symmetry, the mass and momentum equations for the gas inside the bubble are given by ∂pg∂τ+1r2∂∂r(pgugr2)=0, $$ \frac{{\partial p_{g} }}{{\partial \tau }} + \frac{1}{{r^{2} }}\frac{\partial }{{\partial r}}(p_{g} u_{g} r^{2} ) = 0, $$ ∂∂τ(pgug)+1r2∂∂r(pgug2r2)+∂Pb∂r=0, $$ \frac{\partial }{{\partial \tau }}(p_{g} u_{g} ) + \frac{1}{{r^{2} }}\frac{\partial }{{\partial r}}(p_{g} u_{g}^{2} r^{2} ) + \frac{{\partial P_{b} }}{{\partial r}} = 0, $$
Development and validation of a Riemann solver in OpenFOAM® for non-ideal compressible fluid dynamics
Published in Engineering Applications of Computational Fluid Mechanics, 2022
Jianhui Qi, Jinliang Xu, Kuihua Han, Ingo H. J. Jahn
Several CFD solvers exist to solve NICFD problems, including ANSYS, SU2 and zFlow (Colonna & Rebay, 2004; Head et al., 2017; Vitale et al., 2015). SU2 obtains real gas properties by selecting a polytropic Equation of State (EoS), e.g. the polytropic ideal gas, polytropic Van der Waals or polytropic Peng–Robinson models. When solving the Riemann problem, the Vinokur–Montagnè approximate Riemann solver with the averaged-gradient formulation for the viscous counterpart is used (Vitale et al., 2015). In the most recent work, SU2 (v6.1.0) has been validated by comparing the numerical data with experimental results from the Test-Rig for Organic VApours (TROVA) (Gori et al., 2017). zFlow simulates inviscid dense gas flows with real gas properties calculated from the Peng–Robinson real gas equation of state. Flux is calculated by a Roe approximate Riemann flux calculator.
Backflow air and pressure analysis in emptying a pipeline containing an entrapped air pocket
Published in Urban Water Journal, 2018
Mohsen Besharat, Oscar E. Coronado-Hernández, Vicente S. Fuertes-Miquel, Maria Teresa Viseu, Helena M. Ramos
A polytropic expression is used to simulate the air pocket behaviour using the polytropic equation, i.e. , which relates the air pocket pressure with the air volume (). The polytropic exponent or polytropic index (n) can vary from 1 for the isothermal process to 1.4 for adiabatic process depending on temperature change and heat transfer (Besharat and Ramos 2015). An algebraic-differential system (ADS) describes the entire process, which is composed by the momentum equation, a moving interface air-water position, and the polytropic model. The resolution of the ADS gives the information of the hydraulic variables (air pocket pressure, water velocity and length of the water column). To solve the ADS a constant friction coefficient was considered (f= 0.018) with a non-variable polytropic coefficient of n = 1.1. The minor loss coefficients were calibrated based on the experiments. The Simulink tool in Matlab was used to solve the algebraic-differential equations system.
Numerical Modeling of a Wicked Heat Pipe Using Lumped Parameter Network Incorporating the Marangoni Effect
Published in Heat Transfer Engineering, 2021
Jibin Joy Kolliyil, Naresh Yarramsetty, Chakravarthy Balaji
Following the ideal gas assumption, the vapor present inside vapor storage follows the equation Hence, applying the continuity equation to the control volume of the vapor storage, we obtain the following equations where V is the storage volume, P is the pressure, R* is the ideal gas constant, T is the temperature of the vapor in the vapor storage, is the mass flow rate, γ is the polytropic constant (assumption 3) and is the flow capacitance.