Abstract
A transient simulation of shutdown cooling for a gas turbine test rig configuration under ventilated natural convection has been successfully demonstrated using a coupled aero-thermal approach. Large eddy simulation (LES) and finite element analysis (FEA) were employed for fluid domain computational fluid dynamics (CFD) and solid component thermal conduction simulation, respectively. Coupling between LES and FEA was achieved through a plugin communicator. The buoyancy-induced chimney effect under the axially ventilated natural convection is correctly reproduced. The hotter turbulent flow in the upper part of the annular path and the colder laminar-type air movement in the lower part of the annulus are appropriately captured. The heat transfer features in the annular passage are also faithfully replicated, with heat flux of the inner cylinder reaching its maximum and minimum at the bottom dead centre (BDC) and the top dead centre (TDC), respectively. Agreement with experimental measurements is good in terms of both temperature and heat flux, and the result of the transient simulation for the shutdown cooling is encouraging too. In addition, radiation is simulated in the FEA model based on the usual grey body assumptions and Lambert's law for the coupled computation. It has been shown that at the high power (HP) condition, the radiation for the inner cylinder is approximately 11% of its convective heat flux counterpart. The importance of radiation is thus clearly revealed even for the present rig test case with a scaled-down temperature setup. NOMENCLATURE í µí°áreaµí°área [m 2 ] Aref reference area = 0.25í µí¼‹(í µí°· í µí±œ 2 − í µí°· í µí±– 2) [m 2 ] í µí° ¶ í µí±–,í µí±— the radiosity matrix in equation 9 í µí° ¶ í µí± specific heat at constant pressure [J⋅kg-1 ⋅K-1 ] D diameter [m] Dr diameter ratio between the inner and outer cylinders =í µí°· í µí±œ í µí°· í µí±– ⁄ í µí°¹ í µí±–,í µí±— the view factor in equation 9 for radiation g acceleration due to gravity [m⋅s-2 ] H radial depth of the annular test section =(Do-Di)/2 [m] L length [m] í µí±ṧ mass flow rate [kg⋅s-1 ] í µí±š í µí±¥ ̇ mass flow rate in the positive x-direction = 0.5 ∬ í µí¼Œ(í µí±‰ í µí±¥ + |í µí±‰ í µí±¥ |)í µí±‘í µí°´í µí°´í µí°´í µí±¥ [kg⋅s-1 ] m* normalised mass flow rate = í µí±š/í µí±š í µí±Ÿí µí±’í µí±“ NuDi Nusselt number = í µí±ží µí°· í µí±– /(í µí¼…(í µí±‡ í µí±– − í µí±‡ ∞)) Pr Prandtl number = í µí° ¶ í µí± µ/í µí¼… í µí±ž heat flux [W⋅m −2 ] qconv convection heat flux [W⋅m −2 ] qrad radiation heat flux [W⋅m −2 ] qtot total heat flux = í µí±ž í µí±í µí±œí µí±›í µí±£ + í µí±ž í µí±Ÿí µí±Ží µí±‘ [W⋅m −2 ] í µí±„ heat flux integral = ∬ í µí±ží µí±‘í µí°´í µí°´í µí°´í µí±¤ [W] Q* normalised heat flux integral = í µí±„/í µí±„ í µí±Ÿí µí±’í µí±“ í µí±…í µí±Ž í µí°·í µí±– Rayleigh number = í µí¼Œí µí±”í µí»½(í µí±‡ í µí±– − í µí±‡ í µí±œ)í µí°· í µí±– 3 í µí¼‡í µí»¼ ⁄ Re í µí°·í µí±– Reynolds number = í µí¼Œí µí±ˆí µí°· í µí±– /í µí¼‡ í µí±Ÿ * normalised radial coordinate =(í µí±Ÿ − í µí±Ÿ í µí±–) í µí°» ⁄ í µí±‡ temperature [K] í µí±‡ ∞ ambient temperature surrounding the test rig í µí±‡ * normalised temperature =(í µí±‡ − í µí±‡ ∞) (í µí±‡ í µí±– − í µí±‡ ∞) ⁄ t time [s] í µí±¡ 0 shutdown cooling start time [s] í µí±¡ í µí±“ reference flow time =í µí°· í µí±– í µí±ˆ ⁄ [s] í µí±¡ * normalised flow time =í µí±¡ í µí±¡ í µí±“ ⁄ í µí±ˆ reference velocity = √í µí±”í µí»½(í µí±‡ í µí±– − í µí±‡ í µí±œ)í µí°· í µí±– [m⋅s-1 ] í µí±¢ í µí¼ shear or friction velocity = √í µí¼ í µí±¤ /í µí¼Œ [m⋅s-1 ] 2 Copyright © 2024 Rolls-Royce plc. v instantaneous velocity [m⋅s-1 ] í µí±‰ time mean velocity [m⋅s-1 ] í µí±‰ * normalised velocity =í µí±‰ í µí±ˆ ⁄ í µí±¥, í µí±Ÿ, í µí¼ƒ axial, radial and angular coordinates [m,m,º] í µí±¥, í µí±¦, í µí± § Cartesian coordinates [m,m,m] í µí±¥ * normalised axial distance =í µí±¥ í µí°» ⁄ yp wall distance [m] yp + normalised wall distance =ρypuτ/μ Greek í µí»¼ thermal diffusivity = í µí¼…/í µí¼Œí µí° ¶ í µí± [í µí±š 2 ⋅s-1 ] í µí»½ thermal expansion coefficient = 1/í µí±‡ í µí±Ÿí µí±’í µí±“ [K-1 ] í µí»¾ specific heat capacity ratio = í µí° ¶ í µí± /í µí° ¶ í µí±£ Δí µí±‡ temperature difference between the inner and outer cylinders = í µí±‡ í µí±– − í µí±‡ í µí±œ [K] Δ(í µí±¥, í µí±Ÿ, í µí¼ƒ) mesh spacing in axial, radial & angular directions í µí»¿ í µí±–,í µí±— the Kronecker delta ε emissivity for radiation í µí¼ƒ circumferential angle =atan(z/y) [°] í µí¼… thermal conductivity [W⋅í µí±š −1 ⋅K-1 ] í µí¼‡ dynamic viscosity [kg⋅m-1 ⋅s-1 ] í µí¼Œ density [kg⋅m-3 ] í µí¼Œ ∞ ambient density [kg⋅m-3 ] í µí¼Ž the Stefan-Boltzmann constant = 0.56687x10-7 [w⋅m −2 ⋅K −4 ] í µí¼ í µí±¤ wall shear stress [N⋅í µí±š −2 ] Superscript * normalised parameter Subscript av average cone cone i inner cylinder o outer cylinder ref reference parameter í µí±¥, í µí±¦ axial and vertical directions, respectively w wall Acronyms BDC bottom dead centre, θ=180º CFD computational fluid dynamics CHT conjugate heat transfer FEA finite element analysis HP high power condition LES large-eddy simulation URANS unsteady Reynolds-averaged Navier-Stokes simulation TDC top dead centre, θ=0º