A comparative investigation of hydrofoil at angles of attack

Abstract

SUMMARYIn this paper, a numerical investigation of incompressible flow around a hydrofoil is presented. The laminar flow was modeled at different angles of attack. Momentum and continuity equations were coupled by the artificial compressibility scheme. In finite-volume method, convective fluxes were calculated and compared by four schemes. Flux averaging with pressure correction was used. The other characteristic-based (CB) methods consisted of Roe scheme and original CB scheme. A revised CB scheme was implemented in this research, which demonstrated very accurate solutions with respect to others. The results confirmed the superiority of the revised upwind scheme regarding accuracy and convergence without any requirement to artificial viscosity. The problem was studied at high Reynolds numbers at the onset of turbulence. For time discretization, the fifth-order Runge-Kutta scheme was used. Results were compared with those of others in which good agreement was observed. Numerical experiments were performed on the NACA0012 hydrofoil.

Genuinely characteristic-based scheme for the incompressible turbulent flows

“…The number of iterations to achieve steady state is reduced by using a variable time step that depends on the local flow changes and the grid spacing as [13] Dt ¼…”

Incompressible Roe‐like scheme for turbulent flows

“…The pressure‐based modification for the convective fluxes includes where, R and L indicate right and left cells respectively and p is used as a driving force . The first and higher accuracy can be achieved in Equation .…”

“…The fifth‐order Runge–Kutta has a higher stability range ( CFL ≤ 3), which has been used for time discretization in the present study where Q includes the discretized form of integral convective and viscous terms. The number of iterations to achieve steady state is reduced by using a variable time step that depends on the local flow changes and the grid spacing as where Δ t shows the local time step.…”

“…where, R and L indicate right and left cells respectively and p is used as a driving force [7]. The first and higher accuracy can be achieved in Equation (12).…”

Pseudo-characteristic upwind scheme for incompressible flows

“…The comparative studies of the original and revised CBM revealed that both the methods demonstrate the same performances in terms of accuracy and convergence rate. 16,17 Razavi et al 13 suggested that the slow convergence of the CBM originates from the assumption of local one-dimensionality of wave propagation parallel to the grid normals, in which the effects of disturbances traveling along other directions are excluded. Their hypothesis was based on the similar problem observed previously in the gridaligned compressible upwind schemes.…”