Mathematical Modeling of the Workflows of a Reciprocating Compressor with Intensive Cooling of the Cylindrical Piston Group

Calculation of the Incompressible Viscous Fluid Flow in Piston Seals of Piston Hybrid Power Machines

“…The classic piston seal connecting the compressor and pump sections is a smooth gap of constant clearance along the length formed by the piston and cylinder [14,15], while the piston has a concentric or eccentric arrangement. When using a smooth gap seal, the flow rate of the fluid in the forward and reverse direction is the same.…”

“…The system of Equations (13) and (14) in the general case has no analytical solution and can be solved only numerically. Currently, three main methods are used to solve such systems of equations: the finite difference method, the finite volume method, and the finite element method.…”

“…The idea of this method is to replace infinitely small volumes of fluid with volumes of finite sizes-cells. Equations (13) and (14) are written for each created cell, and the totality of all cells is called the computational grid. The theory of turbulent motions proves that turbulent fluid motions consist of many vortex formations having different geometric dimensions [26,27].…”

“…In this way the number of cells in the grid can be significantly reduced. In this case, a certain number of turbulent structures will fall inside each of the grid cells, and, therefore, their characteristics cannot be determined on the basis of Equations (13) and (14), i.e., additional equations are required to calculate turbulence characteristics. To date, several empirical methods for calculating turbulence characteristics have been developed.…”

“…The proposed averaging of Reynolds does not solve the problem, because it adds six additional unknowns to the system of equations, which are called "Reynolds stress". Using the Boussinesq hypothesis simplifies significantly the Navier-Stokes Equation (14) and reduces the number of unknowns characterizing turbulence from six to one, turbulent viscosity. Turbulent viscosity is not a constant value, like molecular viscosity, but depends both on time and on spatial coordinates, and its value is calculated for each cell of the design string at each step of integration over time.…”