Supersonic flow past a flat lattice of cylindrical rods

Abstract

Two-dimensional supersonic laminar ideal gas flows past a regular flat lattice of identical circular cylinders lying in a plane perpendicular to the free-stream velocity are numerically simulated. The flows are computed by applying a multiblock numerical technique with local boundary-fitted curvilinear grids that have finite regions overlapping the global rectangular grid covering the entire computational domain. Viscous boundary layers are resolved on the local grids by applying the Navier-Stokes equations, while the aerodynamic interference of shock wave structures occurring between the lattice elements is described by the Euler equations. In the overlapping grid regions, the functions are interpolated to the grid interfaces. The regimes of supersonic lattice flow are classified. The parameter ranges in which the steady flow around the lattice is not unique are detected, and the mechanisms of hysteresis phenomena are examined.

Hysteresis in Supersonic Flow Past a Plane Cascade of Cylindrical Rods

“…The free-stream Mach number M 1 is varied from 2.4 to 4.2. The lattice period h = 5D ensures the fairly high degree of the screen permeability σ = 1 -D/h = 0.8 for which the shock waves ahead of the lattice elements remain local and do not form a global bow shock ahead of the permeable screen [12]. In this case a secondary supersonic stream which is the result of confluence of discrete small jets formed between the lattice elements is formed behind the screeen [2,10].…”

“…A very simple model of the permeable screen is the plane cascade (lattice) of parallel circular cylinders located at an identical distance from each other. In this case the flow past a permeable screen can be described in detail on all scales-from the local dimension of lattice elements to the global dimension of screen [11][12][13]. In the regime without stand-off bow shock ahead of the screen the perturbations from the windward side of lattice are limited by the fronts of local shock waves ahead of the rigid lattice elements, while a discrete system of small supersonic jets develops on the leeward side.…”

“…In such a regime the general lattice dimension has no value and the lattice can be considered as an infinite permeable screen [11]. In this case, to describe flow on the scale of the lattice step the attention can be restricted to calculations in the strip that contains a single cylindrical element, so that the boundary conditions of periodicity of flow should be fulfilled on the parallel side faces of the strip [12].…”

“…The investigations [11,12] showed that complex shock-wave flow structures develop in the near-wake region behind the cylindrical lattice elements. In these structures the shock waves propagating from the neighboring lattice elements interact between themselves and with inhomogeneous domains of the near aerodynamic wake.…”

“…In [11] the hysteresis related to the well-known ambivalence of the possible schemes of intersection of shock waves in accordance with the Mach-type or regular interaction was described. In [12] a new type of hysteresis related to restructuring of the near wake behind the lattice as a result of the action of shock waves from the neighboring elements directly to the rear flow region behind intermediate lattice element was identified. Recently, the time-dependent flow regimes with formation of a discrete vortex street in the supersonic wake behind the lattice were reported [13,14].…”