Design and calibration of a wind tunnel with a two dimensional contraction

A low speed, open circuit, laboratory wind tunnel has been redesigned for use in turbine blade cooling experiments. The two dimensional contraction was designed using a sixth order polynomial. This paper outlines the process of design optimisation, using Computational Fluid Dynamics (CFD) to model the contraction. The parameters that were varied were the location of the point of inflection and the curvature at the contraction inlet. The optimisation was based on flow uniformity at the working section midplane, prevention of separation in the contraction and minimising the boundary layer thickness at entrance to the working section. Calibration of the wind tunnel after construction has demonstrated the value of the design process and validated the CFD predictions. Nomenclature P Pressure, reference pressure (Pa) a, b, c, d, e, f, g Polynomial coefficients h Contraction inlet half height-exit half height (m) i Axial distance to point of inflection (m) l Total length of contraction (m) ρ Density (kg/m) τw Wall shear stress u* u*=(τw/ρ) 1/2 w Parameter vector x, y,z Cartesian coordinates (streamwise, vertical, transverse) y+ y=yu*/ν α Curvature at inlet (/m) ‘ d/dx Introduction Based on evidence in current literature, aerodynamic research is poised between experimental and computation techniques. The two are closely linked and as progress is made in the development of more advanced computational fluid models, more comprehensive experimental data are required to validate the models. In the present situation a wind tunnel was remodelled for the purpose of turbine blade cooling research. The new facility is required for detailed studies of turbulent mixing processes associated with the injection of a simulated cooling jet through the wall of the working section. The data obtained will be used to improve CFD modelling of these complex flows. Traditionally, the design of wind tunnel contractions has been based on a pair of cubic polynomials, and the parameter used to optimise the design for a fixed length and contraction ratio, has been the location of the joining point [2, 3]. The computation of flow field within the contraction has previously utilised incompressible, inviscid flow equations and co-ordinate transformation techniques to solve the difference equations. Published, parameterised data in the form of design charts [2] are also available to avoid the need to repeat these computations, for axisymmetric contractions. Currently, more flexibility in the design of wind tunnel contractions can be exhibited, with the use of CFD to enable rapid testing of designs to optimise contractions of arbitrary cross-section and wall profile. The use of CFD allows for the use of higher order polynomials, and non-zero curvature or slope at inlet to the contraction. However, the performance of the contraction still requires testing after construction, as the level of CFD used for this application is typically insufficient to detect the development of longitudinal vortices through the working section such as were measured by [4]. This paper describes the design of a 2D contraction with 6 degree polynomial wall profile for a wind tunnel with a square working section and its subsequent experimental validation. Description of the facility The purpose of this work was to design a wind tunnel using the inlet, honeycomb and, potentially, screens of an existing facility. The working section dimensions were increased from 125 x 225 mm to 225 x 225 mm, requiring an increase in the exit area of the contraction. The contraction inlet was 1200 x 225 mm resulting in a new area ratio of 5.3. This was lower than the limit of recommended area ratios [1], and a full analysis of the design was considered necessary. The maximum velocity in the working section was 20 m/s. The original contraction length of 2 m was retained, but the profile definition was changed from a pair of cubic curves to a 6 order polynomial. The wall curvature at inlet and the location of the point of inflection in the wall profile were chosen as design parameters. Parameterisation of the profile The coordinate system for the contraction profile is defined with origin on the tunnel centre line at the contraction inlet plane, and x coordinate increasing in the downstream direction. The y coordinate defines the contraction profile and z is in the spanwise direction. A sixth order polynomial was chosen to define the profile shape: g fx ex dx cx bx ax y + + + + + + = 2 3 4 5 6 (1) The chosen profile has 7 parameters (a-g). Five of these are specified by the inlet and outlet height, zero slope at the inlet and outlet and zero curvature at outlet. This leaves two parameters available for optimisation. These are specified by the inlet curvature and the axial position of the point of inflection relative to the contraction length. The 7 conditions defining the profile are thus: