Introduction

Monohulls and catamarans, often equipped with foils, trim tabs, and/or interceptors that control the trim angle and minimize wave-induced motions, are nowadays the most established concepts for high-speed vessels. Interceptors are relatively new concepts and are illustrated in Figure 7.5. The vessels have transom sterns, that is, there is a flat part of the aft ship below the mean free surface that is perpendicular to the centerplane. Catamaran designs include the wave-piercing and semi-SWATH (small waterplane area twin hull)-style hulls. The length of high-speed catamarans used for passenger transportation in coastal water is typically 30 to 40 m. Both monohulls and catamarans longer than 100 m have been built. Trimarans and pentamarans are new types of multihull vessels that are considered. They consist of a long center hull with smaller outrigger hulls. The outrigger hulls are important for static heeling stability. The larger vessels are typically ro-pax ferries, which means they carry passengers and allow roll-on/roll-off payloads, most often cars.

Calm water resistance of semi-displacement vessels is dealt with in Chapters 2 and 4. This chapter concentrates on linear wave-induced motions and loads; however, added resistance in waves is also handled. Common statistical procedures for calculating short- and long-term responses based on linear results in regular waves are also shown. One important load aspect is slamming, which is relevant for all high-speed vessels. This is dealt with in detail in Chapter 8. Maneuvering is considered in Chapter 10.

Introduction

Figure 5.1 shows an example of a surface effect ship (SES). Figure 1.8 gives a fish-eye view. The vessel is supported by an air cushion that is bounded by flexible seal systems at the bow and stern and by two side hulls. The aft seal is usually a flexible bag consisting of a loop of flexible material open against the side hulls, with one or two internal webs restraining the aft face of the loop into a two- or three-loop configuration. In equilibrium position, there is a very small gap between the bottom of the bag and the water surface. An example is a gap height of 3 cm. The bow seal (skirt) is usually a finger seal consisting of a row of vertical loops of flexible material. Details are shown in Figures 5.2 and 5.3. The seal material is rubber.

There is an air fan system (Figure 5.4) that provides the excess pressure in the air cushion and lifts the SES up, thereby reducing the water resistance. The excess pressure in the air cushion causes a water level inside the cushion lower than the level outside. Typically, the air cushion carries 80% of the weight of the vessel. The buoyancy of the side hulls carries the rest of the weight at zero speed. When the vessel speed increases, the vertical side hull forces due to the water are caused by both hydrostatic (buoyancy) and hydrodynamic pressures.

Introduction

Before we can describe wave resistance in detail, we need to introduce wave theory. This theory is also needed in the description of wave-induced motions and loads on a high-speed vessel. We first present linear wave theory in regular harmonic waves in deep and finite water depths. This includes analysis of wave refraction. An irregular sea state can be represented as a sum of regular waves of different frequencies and wave propagation directions. Recommended wave spectra that describe the frequency content in irregular waves are then given.

Linear wave theory assumes that the wave slope is asymptotically small. Not all waves occurring in reality can be described by linear wave theory; an extreme example is breaking waves. Figure 3.1 illustrates plunging, breaking waves generated in a wave flume. We see breaking waves on a beach, but they can also occur in the open sea in deep water. A strong current in the opposite direction of the wave propagation steepens the waves. This is a phenomenon known in connection with the Agulhas current off the east coast of Africa. A typical feature of a nonlinear wave is that the vertical distance between the wave crest and the mean water level is larger than the distance between the mean water level and the wave trough.

Scatter diagrams of significant wave heights and mean wave periods are needed in operational and design studies. These diagrams describe the probability of occurrence of different sea states for a given operational area.

Introduction

Planing vessels are used as patrol boats, sportfishing vessels, service craft, ambulance craft, recreational craft, and for sport competitions. The Italian vessel Distriero, designed by Donald L. Blount and Associates, won in 1992 the Blue Riband Award for the fastest transatlantic passage without refueling. The average speed was 53.1 knots. The vessel is a 67 m–long planing monohull equipped with gas turbines and three waterjets with a combined horsepower of 60,000. Use of hydrodynamic test facilities was an important part of the design. However, the amount of research on planing vessels is relatively small, considering the large amount of different recreational craft that exist. Our focus is on monohull vessels, but catamaran types also exist. Most of the planing vessels have lengths smaller than 30 m. Recreational craft are typically smaller than that.

A vessel is planing when the length Froude number Fn > 1.2 (Savitsky 1992). However, Fn = 1.0 is also used as a lower limit for planing; that is, we cannot set a clear line of demarcation between planing and nonplaning conditions just by referring to the Froude number. During planing, the weight of the vessel is mainly supported by hydrodynamic pressure loads, with buoyancy having less importance. The hydrodynamic pressure both lifts the vessel and affects the trim angle.

Figure 9.1 shows a typical high-speed planing hull.

In this chapter, we summarize and expand somewhat on those results from quantum mechanics and spectroscopy most germane to our study of statistical thermodynamics. We then prepare for revisiting intensive properties in Chapter 9 by considering the nature of thermodynamic calculations before the advent of quantum mechanics. From a pedagogical point of view, the previous three chapters have focused on the properties of a single atom or molecule. For our purposes, the most important such properties are the allowed energy levels and degeneracies corresponding to the translational, rotational, vibrational, and electronic energy modes of an independent particle. Exploiting this knowledge, we proceed to a macroscopic assembly of atoms or molecules, with a focus on calculations of thermodynamic properties for any pure ideal gas. Assemblies composed of different particle types subsequently permit the evaluation of properties for both nonreacting and reacting gaseous mixtures, including equilibrium constants for various chemical reactions. Finally, re-applying spectroscopy to such mixtures, we examine the utility of statistical thermodynamics for experimentally determining temperature or concentrations in realistic gaseous mixtures at high temperatures and pressures.

Energy and Degeneracy

Our foray into quantum mechanics and spectroscopy has led to relations giving the energy and degeneracy for all four energy modes – translation, rotation, vibration, and electronic. If we insist on mode independence, any consideration of diatomic molecules also mandates the simplex model, which presumes a combined rigid rotor and harmonic oscillator.

The thermochemical data for the ideal gases of this appendix are taken directly from the Third Edition of the JANAF Thermochemical Tables, as tabulated by Chase et al. (1985). The twelve atoms and molecules selected are frequently cited in papers dealing with the chemistry and physics of flames and plasmas. For the sake of brevity, the plethora of possible hydrocarbons are not included in this appendix, but many of them can, of course, be found in the complete JANAF tables, which are available in the reference section of most science and engineering libraries.

The ordered listing of the twelve chosen gases is as follows: H2, H, O2, O, H2O, OH, CO, CO2, N2, N, NO, and NO2. Each table describes the formation of one mole of the subject species from its elements in their natural physical state at 298.15 K and 1 bar. The reader should refer to the original JANAF tables for a listing of the quantum mechanical and spectroscopic data used to effect the statistical mechanical calculations for each species. The reference state for all of these compounds is the hypothetical ideal gas at a temperature of 298.15 K (Tr) and a pressure of 1 bar (0.1 MPa). The logarithm of the equilibrium constant is to the base 10. By definition, both the enthalpy and Gibbs free energy of formation are identically zero for any ideal gas reference compound, such as H2, O2, or N2.

The atomic number (top left) is the number of protons in the nucleus. The atomic mass (bottom) is weighted by mean isotopic abundances in the earth's surface. Atomic masses are relative to the mass of the carbon-12 isotope, defined to be exactly 12 atomic mass units (amu). If sufficiently stable isotopes do not exist for an element, the mass of its longest-lived isotope is indicated in parentheses. For elements 110–112, the mass numbers of the known isotopes are given. Reference: Schroeder (2000) as extracted from The European Physical JournalC3, 73 (1998).

Now that we have reviewed the essentials of probability and statistics, we are mathematically prepared to pursue our primary goal, which is to understand at a basic statistical level the fundamental laws and relations of classical thermodynamics. To avoid unnecessary complications, we will begin by evaluating the macroscopic properties of simple compressible systems composed of independent particles. The most important thermodynamic systems of this type are those describing the behavior of ideal gases. Recall that all gases behave as independent particles at sufficiently low density because of their weak intermolecular interactions combined with their extremely short-range intermolecular potentials. Such gaseous systems constitute a propitious place to begin our study of statistical thermodynamics because by invoking the assumption of independent particles, our upcoming statistical analyses can be based rather straightforwardly on probability theory describing independent events, as summarized in Chapter 2.

While considering assemblies of independent particles, we will pursue new insight with respect to three basic concepts important to classical thermodynamics. First, we will seek a whole new statistical understanding of entropy. Second, we will develop a related statistical definition of thermodynamic equilibrium. Third, in so doing, we will gain new perspective concerning the significance of temperature in properly defining thermal equilibrium. Once we understand these three major concepts, we will be in a position to develop statistical expressions allowing us to evaluate the thermodynamic properties of an assembly from the quantum mechanical properties of its individual particles.

To this point in your career, you have probably dealt almost exclusively with the behavior of macroscopic systems, either from a scientific or engineering viewpoint. Examples of such systems might include a piston–cylinder assembly, a heat exchanger, or a battery. Typically, the analysis of macroscopic systems uses conservation or field equations related to classical mechanics, thermodynamics, or electromagnetics. In this book, our focus is on thermal devices, as usually described by thermodynamics, fluid mechanics, and heat transfer. For such devices, first-order calculations often employ a series of simple thermodynamic analyses. Nevertheless, you should understand that classical thermodynamics is inherently limited in its ability to explain the behavior of even the simplest thermodynamic system. The reason for this deficiency rests with its inadequate treatment of the atomic behavior underlying the gaseous, liquid, or solid states of matter. Without proper consideration of constituent microscopic systems, such as a single atom or molecule, it is impossible for the practitioner to understand fully the evaluation of thermodynamic properties, the meaning of thermodynamic equilibrium, or the influence of temperature on transport properties such as the thermal conductivity or viscosity. Developing this elementary viewpoint is the purpose of a course in statistical thermodynamics. As you will see, such fundamental understanding is also the basis for creative applications of classical thermodynamics to macroscopic devices.

The Statistical Foundation of Classical Thermodynamics

Since a typical thermodynamic system is composed of an assembly of atoms or molecules, we can surely presume that its macroscopic behavior can be expressed in terms of the microscopic properties of its constituent particles.