Abstract

This chapter describes a three-dimensional simulation technology for physical processes in concentric hydraulic brakes with a throttling-groove partly filled hydraulic cylinder. The technology is based on the numerical solution of a system of Navier–Stokes equations. Free surface tracking is provided by the volume of fluid (VOF) method. Recoiling parts are simulated by means of moving transformable grids. Numerical solution of the equations is based on the finite-volume discretization on an unstructured grid. Our technology enables simulations of the whole working cycle of the hydraulic brake. Results of hydraulic brake simulations in the counter-recoil regime are reported. The results of the simulations are compared with experimental data obtained on JSC "KBP" test benches. The calculated and the experimental sets of data are compared based on the piston velocity as a function of distance. The performance of the hydraulic brake is studied as a function of the fluid mass and firing elevation of the gun.

Keywords: hydraulic brake, Navier-stokes equations, multi-phase flow, volume of fluid, moving rigid body, turbulent flow

### 1. Introduction

This chapter describes our three-dimensional simulation technology for physical processes in hydraulic brakes with a throttling-groove partly filled hydraulic cylinder. The technology is based on the numerical solution of a system of Navier-Stokes equations with an additional transport equation to track the working fluid/ free volume interface by the volume of fluid (VOF) method [1, 2]. As a solver, we use an iterative algorithm, PISO [1, 3], combined with a SLAE solver based on the algebraic multigrid method [4]. To improve the accuracy of solution, we use interface capturing schemes, HRIC [1, 4], near the interface between the phases. Moving parts are simulated by means of moving deforming meshes [5], the motion of which is represented in the initial equations with the Lagrange-Eulerian approximation [6]. Our technology enables modeling of the whole working cycle of the hydraulic brake.

To demonstrate the performance of our technology, we are considering simulation of a hydraulic brake with a throttling-groove partly filled hydraulic cylinder. The simulation outputs are compared with experimental data obtained on the test benches at JSC "KBP." The calculated and the experimental sets of data are compared based on the piston velocity as a function of displacement. The performance of the hydraulic brake is studied as a function of the fluid mass and hydraulic brake angle.
