# Thomas Raeder

ul. Studencheskaya 7, Izhevsk, 426069 Russia
Kalashnikov Izhevsk State Technical University

## Publications:

 Raeder T., Tenenev V. A., Chernova A. A. Abstract This paper is concerned with assessing the correctness of applying various mathematical models for the calculation of the hydroshock phenomena in technical devices for modes close to critical parameters of the fluid. We study the applicability limits of the equation of state for an incompressible fluid (the assumption of constancy of the medium density) to the simulation of processes of the safety valve operation for high values of pressures in the valve. We present a scheme for adapting the numerical method of S. K. Godunov for calculation of flows of incompressible fluids. A generalization of the method for the Mie – Grüneisen equation of state is made using an algorithm of local approximation. A detailed validation and verification of the developed numerical method is provided, and relevant schemes and algorithms are given. Modeling of the hydroshock phenomenon under the valve actuation within the incompressible fluid model is carried out by the openFoam software. The comparison of the results for the weakly compressible and incompressible fluid models allows an estimation of the applicability ranges for the proposed schemes and algorithms. It is shown that the problem of the hydroshock phenomenon is correctly solved using the model of an incompressible fluid for the modes characterized by pressure ratios of no more than 1000 at the boundary of media discontinuity. For all pressure ratios exceeding 1000, it is necessary to apply the proposed weakly compressible fluid approach along with the Mie – Grüneisen equation of state. Keywords: hydraulic device, mathematical model, numerical simulation, Godunov’s method, Mie – Grüneisen equation of state, water, weakly compressible fluid approach, incompressible fluid Citation: Raeder T., Tenenev V. A., Chernova A. A.,  Incorporation of Fluid Compressibility into the Calculation of the Stationary Mode of Operation of a Hydraulic Device at High Fluid Pressures, Rus. J. Nonlin. Dyn., 2021, Vol. 17, no. 2, pp.  195-209 DOI:10.20537/nd210205
 Raeder T., Tenenev V. A., Koroleva M. R., Mishchenkova O. V. Nonlinear Processes in Safety Systems for Substances with Parameters Close to a Critical State 2021, Vol. 17, no. 1, pp.  119-138 Abstract The paper presents a modification of the digital method by S. K. Godunov for calculating real gas flows under conditions close to a critical state. The method is generalized to the case of the Van der Waals equation of state using the local approximation algorithm. Test calculations of flows in a shock tube have shown the validity of this approach for the mathematical description of gas-dynamic processes in real gases with shock waves and contact discontinuity both in areas with classical and nonclassical behavior patterns. The modified digital scheme by Godunov with local approximation of the Van der Waals equation by a two-term equation of state was used for simulating a spatial flow of real gas based on Navier – Stokes equations in the area of a complex shape, which is characteristic of the internal space of a safety valve. We have demonstrated that, under near-critical conditions, areas of nonclassical gas behavior may appear, which affects the nature of flows. We have studied nonlinear processes in a safety valve arising from the movement of the shut-off element, which are also determined by the device design features and the gas flow conditions. Keywords: real gas, Van der Waals equation, critical state of substance, Godunov’s method Citation: Raeder T., Tenenev V. A., Koroleva M. R., Mishchenkova O. V.,  Nonlinear Processes in Safety Systems for Substances with Parameters Close to a Critical State, Rus. J. Nonlin. Dyn., 2021, Vol. 17, no. 1, pp.  119-138 DOI:10.20537/nd210109