Introduction

In the study of fluid mechanics, Newton's second law of motion enables the Eulerian equations of motion of a fluid to be applied to a study of the forces acting on a fluid particle at a particular point at a particular time. The solution of these equations with the true boundary conditions in a pump is a formidable task, because within a pump there are rotating and stationary blades that change in their orientation and cross-sectional geometry from hub to tip. There also are boundary layers on the annulus walls and the blade surfaces, wakes from the trailing edges of the blade, over-tip leakage flows etc, so the flow is unsteady, three-dimensional, and viscous.

A brief reference has already been made to empirical approaches in the chapter on axial and mixed flow machines principles. In this chapter the empirical approach to determining passage shapes will first be outlined, and then the more analytical techniques made possible by the computer will be outlined.

Stream-surfaces

Where pumps are of radial, of Francis type or completely mixed flow layout, the principles for centrifugal pumps already covered are often used, once the stream-surfaces are established. In the following sections the approach to the shape of stream surfaces is discussed, and then empirical solutions are outlined.

Stream-surface design

Solutions are described in some detail in texts such as that by Wisclicenus (1965) and in less detail by Turton (1984a).

Introduction

Chapters 1 to 7 have outlined the principles that underlie the successful design of the elements of the flow path in centrifugal, axial and mixed flow machines, and with the help of worked examples the logic to be followed has been explained. Chapter 8 has introduced the background to shaft design, seal and bearing system selection, and Chapter 9 has introduced the problems posed by difficult liquids, and the principles to be followed in choosing the correct materials and thickness of machine elements.

The first stage in the process of developing a pump is the establishing of the pump duty, which does not just mean the duty point but the fluid properties and other matters. Detail design is only complete when all the relevant standards and codes of practice are observed and satisfied. The discussion which follows covers these matters, and concludes with a brief discussion of test provisions and procedures.

Establishing the pump duty

An important factor in the process of producing the right pump design is the establishment of the pump duty. This demands a full interchange of information between the customer and the pump maker.

The pump designer requires to know, in addition to the rated flow rate, head and NPSHA, the environment in which the machine is to be operated, the probable range of flow rates and heads that are to be presented to the machine in the plant.

Introduction

Axial and mixed flow pumps will be treated as members of the same family, as they are high specific speed machines, even though the ‘Francis’ type of centrifugal machine has a mixed flow path. Both types exhibit the same characteristic behaviour, with a rise of specific energy towards shut valve which can be high in axials and in some mixed flow machines, and share a distinct tendency to unstable behaviour at part flow, and a power requirement which rises as flow reduces.

Energy is imparted to the fluid by blades rather than passages, and instability arises from flow breakdown over the blade profiles (giving rise to stall effects as described in Chapter 4). The interaction of fluid and pump components is complex, and performance is affected by blade profiles, surface finish, small variations in blade spacing and setting, and intake disturbances.

The principles underlying isolated blade profiles and blades in close proximity were described in Chapter 4, and simple but reasonably effective design techniques can be applied to the axial flow pump when the inlet flow is undisturbed. Quite efficient machines have been designed in the empirical way outlined in Section 7.3, but higher performance axial machines and all mixed flow machines require more sophisticated approaches, discussed in Section 7.4. Computer based methods were discussed in outline in Chapter 5.

Introduction

Typical flow paths for axial and mixed flow machines are shown in Figure 4.1. Axial flow pumps are usually fitted with a rotor only, so that there is very little pressure recovery after the impeller and even where outlet guide vanes are fitted their main function is to remove any outlet swirl from the flow. Mixed flow pumps may either be as shown in Figure 4.1(b) without outlet guide vanes, or as in many machines, for example in the bulb or bore hole pumps, guide vanes are fitted to improve the flow into the second stage of the assembly.

Unlike the centrifugal pump, the performance in axial machines in particular is a function of the action of blade profiles. Only in mixed flow pumps with many blades is the dominant fluid dynamic action that of the passages as in centrifugal machines.

The fundamental relations have been introduced in Chapter 1, and the application of the Euler equation was demonstrated. In this chapter data for isolated aerofoils is discussed, as it applies to axial machinery, and the concepts of radial equilibrium and stall are introduced. This material forms the basis of empirical design techniques, where it is assumed that all stream surfaces are cylindrical. This is only approximately true in axial machines, and in mixed flow machines it is necessary to establish a number of stream surfaces and then either use the axial data along each surface, or use more advanced analytic fluid dynamic solutions based on the surfaces. This chapter therefore outlines an approach to stream surface shape determination and to mixed flow empirical and analytic solutions.

Introduction

It is not possible to cover anything in this book but the most basic considerations that underly the choice of shaft bearing seal and drive, so that the reader is referred to the literature and to pump handbooks that give more information. In this chapter the very basic principles are introduced, and the conventional terms used are defined.

Shaft design is first introduced, it being commented that this must involve the whole rotating system. Rolling element and plain bearings are then discussed, the basic seal designs are introduced and some design rules for good service are outlined. The chapter concludes with references to the selection of drive arrangement.

Shaft design

The shaft in a pump must sustain torsional effects, bending forces due to both the mechanical parts and hydraulic loads, and axial loads due to weight in the vertical plane and to hydraulic loads.

The empirical approach to shaft design is well documented in such texts as Stepannof (1976), Karassik et al. (1976) and the engineering handbooks. If the weight of the impeller system is known, and the axial and radial hydraulic loads determined, the shaft sizes can be determined and checked. Consider Figure 8.1, showing the rotating assembly for a horizontal centrifugal pump. Simple statics allow the determination of the reactions R1 and R2 and the resulting moment applied to the bearing system can be calculated.

Introduction

When designing a pump a number of design variables need to be determined:

• impeller rotational speed

• impeller inlet or suction dimensions

• impeller outlet diameter

• impeller blade number

• impeller blade passage geometry, including inlet and outlet blade angles

• impeller position relative to the casing

• collector leading dimensions (volute throat area or diffuser geometry)

• pump construction and materials.

There are a number of approaches to design, chief among which are: small changes from existing designs to give a slight change in head or flow range; design using empirical information, tabular and graphical; and computer based approaches which are in some instances based on empirical data and more recently use finite element or finite difference approaches. The use of these techniques will be discussed later. The sections which now follow survey some of the empirical information available. Typical pump cross-sections of single-stage end suction, and double suction designs and of a multi-stage machine are shown in Figures 3.1, 3.2 and 3.3.

Choice of rotational speed

As will be clear from a reading of the later chapters on design, the choice of rotational speed is interlocked with other parameters, but there are empirical speed limits as given, for example, by the American Hydraulic Institute Standards (1983) reproduced in many handbooks. Clearly the rotational speed is limited to a range of synchronous speeds when using electric motor on a 50 or 60 HZ supply frequency. For large pumps, turbine or diesel drive is used, and the eventual rotational speed is a compromise between hydraulic design and driver considerations.

Great increases in the cost of fuel and the advent of very large tankers and bulk carriers have focused the attention, during the last decades, on means to enhance the efficiency of ship propulsion. An obvious way of obtaining an efficiency increase is to use propellers of large diameter driven by engines at low revolutions, as can be deduced from the developments in Chapter 9. Such a solution is, however, in many cases not practically possible. This has then given impetus to the study and adoption of unconventional propulsion arrangements, consisting, in general, of static or moving surfaces in the vicinity of propellers.

A distinct indication of the serious and extensive activity in the development and use of unconventional propulsors may be seen in the report of the Propulsor Committee of the 19th ITTC (1990b) which lists seven devices including large diameter, slower turning propellers. Here we summarize the hydrodynamic characteristics of six of these devices omitting larger-diameter propellers. The six devices are: Coaxial contrarotating propellers, propeller with vane wheel, with pre-swirl stators, with postswirl stators, ducted propellers and propellers operating behind flowsmoothing devices.

Emphasis is given in the following to a variational procedure which, in a unified fashion enables nearly optimum design of several of these configurations.

Propulsive Efficiency

Propulsive efficiency is conventionally thought of as the product of the open-water efficiency of the propulsor, the hull efficiency and a factor termed the relative-rotative efficiency.

The flows about wings of finite span are sufficiently analogous to those about propeller blades to warrant a brief examination before embarking on the construction of a mathematical model of propellers. A more detailed account of wing theory is given for example by von K ármán & Burgers (1935).

A basic feature of the flow about a straight upward-lifting wing of finite span and starboard-port symmetry in a uniform axial stream is that the velocity vectors on both the lower and upper surfaces are not parallel to the longitudinal plane of symmetry. On the lower side the vectors are inclined outboard and on the upper side they are inclined inwardly in any vertical plane or section parallel to the vertical centerplane. This is a consequence of the pressure relief at the wing tips and the largest increase in pressure being in the centerplane on the lower side and the greatest decrease in pressure being in the centerplane on the upper or suction side. Thus there are positive spanwise pressure gradients on the lower side and negative spanwise gradients on the upper side which give rise to spanwise flow components which are obviously not present in two-dimensional flows.

In many treatments of wing theory one finds figures purporting to show the flow about a wing of finite aspect ratio in which there is a continuous line of stagnation points near the leading edge, extending from one wing tip to the other.

The number of comparisons that have been made of calculated and measured blade-frequency thrust, torque and other force and moment components are very few because of the paucity of data. In this chapter comparisons of theoretical predictions with experimental data will be given. Results obtained by various theories will also be compared. The chapter concludes with presentation of a simple procedure, based upon the KT-J curve of the steady case, for a quick estimate of the varying thrust at blade frequency.

The measurement of blade-frequency forces on model propellers requires great care in the design of the dynamometer which must have both high sensitivity and high natural frequencies well above the model blade frequency. After a number of failures a successful blade-frequency propeller dynamometer capable of measuring six components (three forces, three moments) was evolved at David Taylor Research Center (DTRC) about 1960.

Measurements were made with a triplet of three-bladed propellers of different blade-area ratio designed to produce the same mean thrust. This set was tested in the DTRC 24-inch water tunnel alternately abaft threeand four-cycle wake screens which produced large harmonic amplitudes of the order of 0.25-U in order to obtain strong output-to-“noise” levels! The three-cycle screens give rise to blade-frequency thrust and torque whereas the four-cycle wake produces transverse and vertical forces and moments about the y- and z-axes which in general come from the fourth and second harmonic orders of blade loading on a three-bladed propeller, as was demonstrated on p. 367.

The non-symmetrical flow generated by flat and cambered laminae at angles of attack is at first modelled by vorticity distributions via classical linearized theory. Here, in contrast to the analysis of symmetrical sections, we encounter integral equations in the determination of the vorticity density because the local transverse component of flow at any one point depends upon the integrated or accumulated contributions of all other elements of the distribution. Pressure distributions at non-ideal incidence yield a square-root-type infinity at the leading edge because of the approximations of first order theory. Lighthill's (1951) leading edge correction is applied to give realistic pressure minima at non-ideal angles of incidence.

Our interest in pressure minima of sections is due to our concern for cavitation which can occur when the total or absolute pressure is reduced to the vapor pressure of the liquid at the ambient temperature. Since cavitation may cause erosion and noise it should be avoided or at least mitigated which may possibly be done by keeping the minimum pressure above the vapor pressure. This corresponds to maintaining the (negative) minimum-pressure coefficient Cpmin higher than the negative of the cavitation index.

At this point we shall not go deeper into the details of cavitation which is postponed until Chapter 8. Instead we shall continue our theoretical development with flat and cambered sections.

THE FLAT PLATE

We now seek the pressure distributions and the lift on sections having zero thickness but being cambered and, in general, set at any arbitrary (but small) angle of attack to the free stream, U. Consider a flat plate at small angle α.