[...]... turbomachinery designer 1.2 Dimensional analysis An indication of the primary goals of dimensional analysis was given in the introduction to this chapter In the present section attention will be drawn to two different levels of dimensional analysis and consequent dimensionless groups, namely (a) global dimensionless performance variables, artd (b) local dimensionless design and performance variables The first... Section 1.2.3 to illustrate the main ideas and implications of this type of analysis, which involves selection of dimensionless performance coefficients for each meridional streamline such as ~0, Fig 1.5 1.2.1 Overall dimensional analysis and global dimensionless performance parameters The fundamental basis of dimensional analysis is well covered in standard fluiddynamic texts such as Massey (1989)... meridional streamline, thus offering much deeper insights into the detailed performance of turbomachine stages and a much more productive framework for design and performance analysis However, it will be left until Chapters 3, 4, 7 and 8 to develop this in some detail as a primary and most valuable tool for design and performance analysis of a wide range of turbomachines 2 Two.dimensional cascades Introduction... taken as read For the present purpose we will approach the matter from the turbomachinery engineer's viewpoint by considering the performance analysis of a given centrifugal pump, drawing out its main key performance characteristics and showing how global dimensionless performance parameters can help to take advantage of scale model tests For example, let us consider the twofold purpose of the centrifugal... concerned with the key overall or global performance variables of a turbomachine such as flow rate, pressure rise and efficiency in the case of a fan or pump Such global dimensionless groups will be derived in Section 1.2.1 to illustrate the power and scope of dimensional analysis to take advantage of laboratory-scale model testing as a design and 1.2 Dimensional analysis 9 performance predictive tool An extension... model tests to predict the performance of a full scale machine The one feature which we must preserve if these tests are to be truly 'dynamically similar' is its shape The model must be a true geometric scale of the prototype, in which case we can accept Eqn (1.14) as a correct representation of all the other relevant performance factors which will affect 1.2 Dimensional analysis 11 efficiency There... more simplified meridional flow analysis treatments will be given in Chapter 5, followed in Chapter 6 by a detailed discussion of the mechanisms of vorticity production in turbomachines and their influence upon meridional flows In Section 2.1 we will develop the overall fluid dynamic analysis of two-dimensional compressor and fan cascades including the definition of key performance parameters Section...Overall duty Specification Viability check Dimensional analysis Choice of machine type and number of stages FIPSI v - l Thermo-fluid dynamic design Annulus shape Centre-line design Velocity triangles -f Blade design I " "- Meridional Analysis CASCADE I Blade-to-blade cascade design t Profile stacking Stress & vibration Anal~,sis Annulus and secondary... low ~ coefficients Mixed-flow machines would show a compromise performance between these extremes If we were to mark out the best efficiency point for each member of this family of machines we would obtain a curve 9 = f ( ~ ) similar to that shown in Fig 1.9 In reality, if we were to test a very large number of machines and record their performance in this way, we would obtain not a thin curve but a... for compressible flow (1.9a) For incompressible fluids, i.e liquids or low Mach number gases, we may follow the same analysis through, using the incompressible steady flow energy equation instead, namely 0 Vr = (P2 - P l ) / P + ( c2 - c 2 ) / 2 [1.5bl 8 Basic equations and dimensional analysis to obtain the corresponding form of the Euler pump equation, namely (Po2-Pol)/P = U2co2- U1 col for incompressible . 1 Basic equations and dimensional analysis 1 2 Two-dimensional cascades 21 3 Principles of performance analysis for axial turbines 47 4 Performance analysis for axial compressors and fans. viewpoint by considering the performance analysis of a given centrifugal pump, drawing out its main key performance characteristics and showing how global dimensionless performance parameters can. companies towards the use of dimensional analysis for correlation of previous experience or for performance optimisation. Traditionally dimensional analysis has been the province of scale model