Propeller Geometry, Coefficients, Characteristics

Propeller Geometry

A marine propeller consists of a number of blades (2–7) mounted on a boss, Figure 12.1. Normal practice is to cast the propeller in one piece. For special applications, built-up propellers with detachable blades may be employed, such as for controllable pitch propellers or when the blades are made from composite materials.

The propeller is defined in relation to a generator line, sometimes referred to as the directrix, Figure 12.1. This line may be drawn at right angles to the shaft line, but more normally it is raked. For normal applications, blades are raked aft to provide the best clearance in the propeller aperture. For high-speed craft, the blades may be raked forward to balance bending moments due to centrifugal forces against those due to thrust loading.

Physical Components of Main Hull Resistance

An understanding of the components of ship resistance and their behaviour is important as they are used in scaling the resistance of one ship to that of another size or, more commonly, scaling resistance from tests at model size to full size. Such resistance estimates are subsequently used in estimating the required propulsive power.

Observation of a ship moving through water indicates two features of the flow, Figure 3.1, namely that there is a wave pattern moving with the hull and there is a region of turbulent flow building up along the length of the hull and extending as a wake behind the hull.

Both of these features of the flow absorb energy from the hull and, hence, constitute a resistance force on the hull. This resistance force is transmitted to the hull as a distribution of pressure and shear forces over the hull; the shear stress arises because of the viscous property of the water.

Introduction

Ship powering relies on a reliable estimate of the relationship between the shaft torque applied and the net thrust generated by a propulsor acting in the presence of a hull. The propeller provides the main means for ship propulsion. This chapter considers numerical methods for propeller analysis and the hierarchy of the possible methods from the elementary through to those that apply the most recent computational fluid dynamics techniques. It concentrates on the blade element momentum approach as the method best suited to gaining an understanding of the physical performance of propeller action. Further sections examine the influence of oblique flow and tangential wake, the design of wake-adapted propellers and finally the assessment of cavitation risk and effects.

Although other propulsors can be used, Chapter 11, the methods of determining their performance have many similarities to those applied to the conventional ship propeller and so will not be explicitly covered. The main details of the computational fluid dynamic (CFD) based approaches are covered in Chapter 9 as are the methods whereby coupled self-propulsion calculations can be applied, Section 9.6.

New ship types and applications continue to be developed in response to economic, societal and technical factors, including changes in operational speeds and fluctuations in fuel costs. These changes in ship design all depend on reliable estimates of ship propulsive power. There is a growing need to minimise power, fuel consumption and operating costs driven by environmental concerns and from an economic perspective. The International Maritime Organisation (IMO) is leading the shipping sector in efforts to reduce emissions such as NOx, SOx and CO2 through the development of legislation and operational guidelines.

The estimation of ship propulsive power is fundamental to the process of designing and operating a ship. Knowledge of the propulsive power enables the size and mass of the propulsion engines to be established and estimates made of the fuel consumption and likely operating costs. The methods whereby ship resistance and propulsion are evaluated will never be an exact science, but require a combination of analysis, experiments, computations and empiricism. This book provides an up-to-date detailed appraisal of the data sources, methods and techniques for establishing propulsive power.

The estimation of ship propulsive power is fundamental to the process of designing and operating a ship. A knowledge of the propulsive power enables the size and mass of the propulsion engines to be established and estimates made of the fuel consumption and operating costs. The estimation of power entails the use of experimental techniques, numerical methods and theoretical analysis for the various aspects of the powering problem. The requirement for this stems from the need to determine the correct match between the installed power and the ship hull form during the design process. An understanding of ship resistance and propulsion derives from the fundamental behaviour of fluid flow. The complexity inherent in ship hydrodynamic design arises from the challenges of scaling from practical model sizes and the unsteady flow interactions between the viscous ship boundary layer, the generated free-surface wave system and a propulsor operating in a spatially varying inflow.

Up to the early 1860s, little was really understood about ship resistance and many of the ideas on powering at that time were erroneous. Propeller design was very much a question of trial and error. The power installed in ships was often wrong and it was clear that there was a need for a method of estimating the power to be installed in order to attain a certain speed.

General

The hydrodynamic behaviour of the hull over the total speed range may be separated into three broad categories as displacement, semi-displacement and planing. The approximate speed range of each of these categories is shown in Figure 14.1. Considering the hydrodynamic behaviour of each, the displacement craft is supported entirely by buoyant forces, the semi-displacement craft is supported by a mixture of buoyant and dynamic lift forces whilst, when planing, the hull is supported entirely by dynamic lift. The basic development of the hull form will be different for each of these categories.

This chapter concentrates on a discussion of displacement craft, with some comments on semi-displacement craft. Further comments and discussion of semi-displacement and planing craft are given in Chapters 3 and 10.

The field of static aeroelasticity is the study of flight-vehicle phenomena associated with the interaction of aerodynamic loading induced by steady flow and the resulting elastic deformation of the lifting-surface structure. These phenomena are characterized as being insensitive to the rates and accelerations of the structural deflections. There are two classes of design problems that are encountered in this area. The first and most common to all flight vehicles is the effects of elastic deformation on the airloads, as well as effects of airloads on the elastic deformation, associated with normal operating conditions. These effects can have a profound influence on performance, handling qualities, flight stability, structural-load distribution, and control effectiveness. The second class of problems involves the potential for static instability of the lifting-surface structure to result in a catastrophic failure. This instability is often termed “divergence” and it can impose a limit on the flight envelope.

“Aeroelasticity” is the term used to denote the field of study concerned with the interaction between the deformation of an elastic structure in an airstream and the resulting aerodynamic force. The interdisciplinary nature of the field is best illustrated by Fig. 1.1, which originated with Professor A. R. Collar in the 1940s. This triangle depicts interactions among the three disciplines of aerodynamics, dynamics, and elasticity. Classical aerodynamic theories provide a prediction of the forces acting on a body of a given shape. Elasticity provides a prediction of the shape of an elastic body under a given load. Dynamics introduces the effects of inertial forces. With the knowledge of elementary aerodynamics, dynamics, and elasticity, students are in a position to look at problems in which two or more of these phenomena interact. The field of flight mechanics involves the interaction between aerodynamics and dynamics, which most undergraduate students in an aeronautics/aeronautical engineering curriculum have studied in a separate course by their senior year. This text considers the three remaining areas of interaction, as follows:

• between elasticity and dynamics (i.e., structural dynamics)

• between aerodynamics and elasticity (i.e., static aeroelasticity)

• among all three (i.e., dynamic aeroelasticity)

Because of their importance to aerospace system design, these areas are also appropriate for study in an undergraduate aeronautics/aeronautical engineering curriculum. In aeroelasticity, one finds that the loads depend on the deformation (i.e., aerodynamics) and that the deformation depends on the loads (i.e., structural mechanics/dynamics); thus, one has a coupled problem.

The purpose of this chapter is to convey to students a small introductory portion of the theory of structural dynamics. Much of the theory to which the students will be exposed in this treatment was developed by mathematicians during the time between Newton and Rayleigh. The grasp of this mathematical foundation is therefore a goal that is worthwhile in its own right. Moreover, as implied by the da Vinci quotation, a proper use of this foundation enables the advance of technology.

Structural dynamics is a broad subject, encompassing determination of natural frequencies and mode shapes (i.e., the so-called free-vibration problem), response due to initial conditions, forced response in the time domain, and frequency response. In the following discussion, we deal with all except the last category. For response problems, if the loading is at least in part of aerodynamic origin, then the response is said to be aeroelastic. In general, the aerodynamic loading then will depend on the structural deformation, and the deformation will depend on the aerodynamic loading. Linear aeroelastic problems are considered in subsequent chapters, and linear structured dynamics problems are considered in the present chapter. Other important phenomena, such as limit-cycle oscillations of lifting surfaces, must be treated with sophisticated nonlinear-analysis methodology; however, they are beyond the scope of this text.

From First Edition

A senior-level undergraduate course entitled “Vibration and Flutter” was taught for many years at Georgia Tech under the quarter system. This course dealt with elementary topics involving the static and/or dynamic behavior of structural elements, both without and with the influence of a flowing fluid. The course did not discuss the static behavior of structures in the absence of fluid flow because this is typically considered in courses in structural mechanics. Thus, the course essentially dealt with the fields of structural dynamics (when fluid flow is not considered) and aeroelasticity (when it is).

As the name suggests, structural dynamics is concerned with the vibration and dynamic response of structural elements. It can be regarded as a subset of aeroelasticity, the field of study concerned with interaction between the deformation of an elastic structure in an airstream and the resulting aerodynamic force. Aeroelastic phenomena can be observed on a daily basis in nature (e.g., the swaying of trees in the wind and the humming sound that Venetian blinds make in the wind). The most general aeroelastic phenomena include dynamics, but static aeroelastic phenomena are also important. The course was expanded to cover a full semester, and the course title was appropriately changed to “Introduction to Structural Dynamics and Aeroelasticity.”

Aeroelastic and structural-dynamic phenomena can result in dangerous static and dynamic deformations and instabilities and, thus, have important practical consequences in many areas of technology.