An experimental and numerical investigation of heat transfer downstream of a normal film cooling injection slot
Creators: name: Sun, Yuping
Publisher: name: University of British Columbia
Year: 2009

description: This thesis presents an experimental and numerical investigation of turbulent heat transfer associated with film cooling from a 2D slot. To determine the film cooling heat transfer coefficient, detailed mass transfer measurements have been carried out downstream of a normal film cooling injection slot. The plate downstream of the injection location is porous and air contaminated with propane or methane is bled through the plate beneath it. By measuring the propane or methane concentration very close to the wall, mass transfer measurements are conducted for film cooling mass flow ratios ranging from zero to 0.5. The mass transfer coefficients are calculated using a wall function correction formula, which corrects the measurements for displacement from the surface, and are then related directly to corresponding heat transfer coefficients using the mass/heat transfer analogy. The validity of the method and the wall function correction formula are checked by examining the case with zero film coolant injection, a situation analogous to the well-known turbulent boundary layer mass/heat transfer with impermeable/unheated starting length. Good agreement with data in the literature is obtained for this experiment. For film cooling with low mass flow ratios (M 0.1), heat transfer coefficients close to those of a conventional turbulent boundary layer are obtained. At high values of mass flow ratio (M &gt; 0.1) heat transfer coefficients similar to those of turbulent separated flows are observed, reflecting the important effect of the separation bubble just downstream of injection. Numerical calculations of turbulent flow and heat transfer associated with film cooling have been carried out to validate the present mass transfer method and to ensure that the heat transfer coefficients obtained using the mass/heat transfer analogy are valid. In the present study, the time-averaged continuity equation, Navier Stokes equations and thermal energy equation, together with the k-ε a turbulence model, are used to describe the turbulent flow and heat transfer. This system of governing equations is discretized using the control volume method. To obtain the numerical solution of the resulting finite difference equations, a novel multi-grid method with no boundary correction is proposed. This method differs from the FAS multi-grid method in that it employs a special multi-grid procedure to ensure that the correction on the coarse grids vanishes along the boundary, and it offers an easier procedure to overcome difficulties arising from the boundary treatment in both discretization and the multi-grid algorithm. The performance of the method is examined using the laminar cavity flow and the turbulent boundary layer flow, which indicates that it is efficient and can overcome difficulties resulting from the near-wall treatment and the discrete vorticity boundary condition. Numerical simulation of turbulent flow and heat transfer associated with film cooling are conducted using the proposed multigrid method. Detailed turbulent flow field and heat transfer results are obtained for film cooling mass flow ratios ranging from zero to 0.5. The numerical results show that the standard k-ε a turbulence model, together with the standard wall function, underpredicts considerably the heat transfer coefficients of film cooling at high mass flow ratio, and therefore, is not appropriate for accurate prediction of turbulent heat transfer in the region of flow separation. However, with a modified near-wall treatment, predictions of heat transfer coefficients compare well with the experimental results obtained using the mass/heat transfer analogy. Numerical calculations also show that the overall effect of the wall transpiration for the blowing rates used for the mass transfer measurements on heat transfer is negligible. The present study finally concludes that both the numerical and mass transfer method can be used to investigate film cooling heat transfer with fair accuracy.