EFFECTS OF ADVERSE PRESSURE GRADIENT ON A TURBULENT BOUNDARY LAYER Joung-Ho Lee Department of Mechanical Engineering, Korea Advanced Institute of Science and Technology, 373-1, Guseong-dong, Yuseong-gu, Daejeon, 305-701, Korea leejh34@kaist.ac.kr Hyung Jin Sung Department of Mechanical Engineering, Korea Advanced Institute of Science and Technology, 373-1, Guseong-dong, Yuseong-gu, Daejeon, 305-701, Korea hjsung@kaist.ac.kr ABSTRACT Direct numerical simulations were performed to investigate the physics of turbulent boundary layer flows subjected to adverse pressure gradient. A fully implicit fractional step method was employed to simulate the flows. To avoid generating an inflow with adverse pressure gradient, the sufficient streamwise length was placed from the inlet to the sudden change of free-stream velocity. The spatially-developing characteristics of turbulent boundary layer with adverse pressure gradient were examined. The present results were in good agreement with previous experimental ones. The visualization results showed that the adverse pressure gradient weakens the vortical structures. This causes a reduction in turbulence intensity near the wall. NOMENCLATURE p C = Pressure coefficient, normalized by the inlet free-stream velocity, 0 U G = Shape factor, = ( ) 2 0 1 ( )/ U u u dy τ ∞ − Δ ∫ P = Mean pressure P + = 3 ( / )/ dP dx u τ ν ρ β = Clauser pressure gradient parameter, = * ( / ) / w dP dx δ τ Δ = Defect thickness = 0 ( )/ U u u dy τ ∞ − ∫ in θ = Inlet momentum thickness INTRODUCTION Turbulent boundary layers with adverse pressure gradient are found in many engineering applications including diffusers, turbine blades and the trailing edges of airfoils etc. It is of both fundamental and practical significance to understand the structure of turbulent boundary layer affected by adverse pressure gradient. Clauser (1954) suggested a new class of the equilibrium boundary layer with adverse pressure gradient, where the profiles of velocity-defect and of turbulent stresses at different streamwise stations show a similarity when properly scaled. Following Clauser, a number of theoretical and experimental studies on adverse pressure gradient flows were made throughout the past decades. However, the physics of adverse pressure gradient flows and the interaction with turbulence and structures are not fully understood. In the present study, we simulated a spatially developing turbulent boundary layer with adverse pressure gradient using direct numerical simulation in order to elucidate the effect on the near-wall and outer layer turbulent structures of adverse pressure gradient. First the numerical method is described briefly and some results are compared with the flows with zero pressure gradient. NUMERICAL METHODS Direct numerical simulations are performed to investigate the physics of spatially developing turbulent boundary layer flows subjected to adverse pressure gradient. A schematic diagram of the computational domain is displayed in Fig. 1. Time-dependent zero pressure gradient turbulent inflow data are provided at the inlet based on the method of Lund et al. (1998). A convective boundary condition at the exit has the form ( / ) ( / ) 0 u t c u x ∂ ∂ + ∂ ∂ = , where c is the local bulk velocity. The no-slip condition is imposed at the solid wall. Periodic boundary conditions are applied in the spanwise direction. Townsend (1961) and Mellor & Gibson (1966) showed that an approximate equilibrium flow is obtained when the variation of free- stream has the form of a power-law relation in the streamwise direction. A free-stream velocity () U x ∞ along the upper boundary of the computational domain is prescribed as,