By Rene J. Francillon
Profile guides quantity a hundred and sixty: The Mitsubishi G3M "Nell" through Rene J. Francillon, Ph.D. 14 pages.
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55) where, as usual, U is the vector of conserved physical quantities given by Eq. 2. The Riemann problem is an extension of the typical experimental shock tube apparatus, in which two still gases fill in two compartments and are separated by a diaphragm . At t = 0, the diaphragm is burst and the gases are free to interact. Neglecting viscosity and heat conduction, a solution to the Riemann problem is sought using the compressible Euler equations for a polytropic ideal gas. 6. The vector of conserved quantities therefore does include the term with the transverse momenta.
39) S 31 This definition can be cumbersome to use and a handy expression as a function of readily available quantities is desired. 50) where c p (J K−1 kg−1 ) and cv (J K−1 kg−1 ) are the heat capacities at constant pressure and volume, respectively. 53) where the gas constant r is given by R is the universal gas constant2 and M (kg mol−1 ) is the molar mass of the gas. 54) An ideal gas with a constant γ is said to be polytropic. 3 Real Gas Equations of State Countless equations of state for real gases are available in the scientific literature.
The ideal gas Riemann problem is reduced to a single equation in one unknown, the pressure in the middle region between the left and right waves. This equation is solved iteratively through the Newton-Raphson method. An elaborated initial 19 guess for the unknown pressure allows for a quick convergence in just a few iterations. The real gas case is treated in a similar manner. Details are presented in Chapter 3. Open outflow as well as immobile reflective and gas/liquid boundaries can be specified.