There are two main approaches to the problem of aerodynamic design of turbomachinery blades, the direct and the inverse approach. In the direct approach, the flow is computed for a given blade geometry, while in the inverse design approach the required flow distribution is specified and the corresponding blade geometry is computed.
In recent years, as a result of development in computational fluid dynamics, considerable progress has been made in the numerical solution of the direct concern of turbomachinery design. Such methods are of substantial value to the designer, who can use them to analyse the flow conditions along vanes and blades. In practice, however, there are difficulties in determining the degree and blade shape at any location affects the flow at other parts of the blade.
This is particularly so in the case of radial turbomachinery, where the blade geometry and the flow field are complicated and three-dimensional. As a result, the most rational approach for designing radial turbomachinery blades is to use a three-dimensional inverse design method.
A large number of inverse design methods are available in two dimensions and are widely used in the design of axial turbomachinery blades. Ideally, one would like to prescribe the pressure or velocity distribution on the pressure and suction surfaces so that the blades are designed with optimized boundary layers. However, this type of design specification has no control over blade thickness and could result in an ill-posed problem.
In three dimensions, additional constraints on the choice of the design specification are required in order to avoid this issue. For instance, the value of the pressure along the hub of a radial turbomachinery vane is affected by the pressure along the shroud and as a result it is not possible to specify the pressure on the hub and shroud independently. The main implication of this fact is that very few three-dimensional inverse design methods are available now. In all these methods, either the blade loading or the circulation distribution is prescribed together with a thickness distribution. However, all these methods are affected by shortcomings which limit their application to problems of practical interest.
This paper is concerned with the development of a three-dimensional inverse design method applicable to radial and mixed flow machines in subsonic compressible flow. This method not only computes the blade shape but can also provide detailed information about the flow distribution (i.e. velocity, pressure, etc.) through the designed blade-row.
This paper 'A Compressible Three-Dimensional Design Method for Radial and Mixed-Flow Turbomachinery Blades' described how the calculation for compressible flow can be performed by computing velocities and density throughout the 3D flow field. A second, approximate, approach to solve the compressible flow problem is also presented. In this approach, the variation of density in the pitchwise direction is neglected and an approximate form of the continuity equation is used. In both approaches, the partial differential equations modelling the flow field and the blade boundary condition are solved numerically by a using finite difference method on a body-fitted curvilinear computational plane.
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