ЧИСЕЛЬНЕ МОДЕЛЮВАННЯ ТЕЧІЇ РІДИНИ У ЦИЛІНДРИЧНОМУ КАНАЛІ, ЩО МІСТИТЬ ДВІ ДІАФРАГМИ ЗІ ЗМІННИМ ДІАМЕТРОМ ОТВОРІВ

The flow of a viscous incompressible fluid in a cylindrical duct containing two serial diaphragms with variable orifice diameters was studied based on the numerical solution of the unsteady Navier-Stokes equations. The solution algorithm was based on the finite volume method using second-order accurate difference schemes in both space and time. The TVD (Total-Variation Diminishing) form of a central-difference scheme with a flux limiter was used to interpolate the convective terms. The combined evaluation of the velocity and pressure fields was performed using the PISO (Pressure Implicit Split Operator) procedure. It was shown that at relatively low Reynolds numbers, the flow in the region between the diaphragms remains stationary regardless of the diameter of the diaphragm orifice. The surface layer separates from the leading edge of the first diaphragm, forming an annular shear layer. A circulation motion is established inside the cavity formed by the diaphragms. At higher Reynolds numbers, the flow becomes unsteady. As the flow approaches the second diaphragm, a sequence of ring vortices forms in the shear layer, interacting with the diaphragm surface and potentially leading to the emergence of tonal sound. When the diameter of the diaphragm orifice increases, the separation angle of the boundary layer at the leading edge of the first diaphragm increases. As a result, the share of the jet’s kinetic energy participating in the circulation motion inside the cavity between the diaphragms decreases. Simultaneously, the critical Reynolds number at which the tonal sound begins to excite increases, as does the Strou- hal number, while the frequency of the generated sound decreases. When the diameter of the diaphragm orifice reaches a critical value, the circulation motion becomes destabilized, causing the formation of ring vortices in the shear layer to lose periodicity, and the generated sound acquires a noisy character.