Variational calculus as a foundation of medium flow with allowance for real gases state equation

Fluid, gas and plasma mechanics


Nazyrova R. R.

Keldysh Research Centre, 8, Onezhskaya str., Moscow, 125438, Russia



The modern phase of competitive liquid-propellant engines design is based on employing various mathematical models, including the knowledge of both fluid mechanics and thermochemistry.

Mathematical models provide a number of possibilities to study both the most idealized processes and of the special phenomenons, such as the intermolecular reaction of substances, by the equation for real gas state process. Well-known works on the studies of fluid by real gas are based on the accentuate of the amount of virial coefficients in the equation. The presented work is dedicated both to define the each mathematical model as an element of variational calculus tasks class, and to explore mathematical models to find the identical to the initial theories confirmations.

The formal expression for the chemical potentials correlation for any substance of the thermodynamic system, described by the equation of the ideal gas state and by the equation of the real gas state, has the integral form. Thus, the mathematical model for any equilibrium state is the task of the variational calculus. Special mathematical technologies (the equivalent transformation, structuring, averaging of integrals) define the task or the subtask of models as the element of classes for the linear or the convex programming. Thus, there is compared to the correct technology of calculations, describing criteria of the identical with model and the acceptable precision of the solution, for the mathematical model of any equilibrium state. The results of mathematical calculations confirm the efficiency of technologies and present the variations of fundamental properties of fluid mechanics.


nozzle, the liquid-propellant rocket chamber, equilibrium state, real gas


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