Submarine Hydrodynamics

Submarines are very specialised vehicles, and their design is extremely complex. This book deals with only the hydrodynamics aspects of submarines, and a knowledge of ship hydrodynamics is assumed. The principles of submarine geometry are outlined in this chapter, covering those terms which are not common to naval architecture, such as: axisymmetric hull; sail; aft body; fore body; control surfaces; casing; and propulsor. Over the years a number of different unclassified submarine geometries have been developed to enable organisations to benchmark results of their hydrodynamics studies in the open literature. These geometries have also been used to provide initial input to the design of new submarine shapes. A summary of some of the more widely used geometries is given, along with references to enable the reader to obtain further information as required.

A submarine must conform to Archimedes’ Principle, which states that a body immersed in a fluid has an upward force on it (buoyancy) equal to the weight of the displaced fluid, (displacement). There are two different definitions of submerged displacement: one that doesn’t include the mass of fluid in the free flooding spaces (hydrostatic displacement), which is used by submarine naval architects, and one that does include the mass of the fluid in the free flooding spaces (form displacement), which is used by submarine hydrodynamicists. For equilibrium in the vertical plane the mass must be balanced exactly by the buoyancy force. As compressibility affects the buoyancy, it is not possible for a submarine to be in stable equilibrium in the vertical plane. Submarines are fitted with ballast tanks to enable the mass to be changed. Ballast tanks fit into two categories: those used for major adjustment of mass (main ballast tanks); and those used for minor adjustments (trim tanks). The effect of each tank is plotted and this is compared with the changes in mass and trimming moment possible during operations using a trim polygon to determine whether the ballast tanks are adequate. Transverse stability of a submarine is discussed, including particular issues that arise when passing through the free surface, when on the seabed, or when surfacing through ice. On the water surface, metacentric height (GM) is important, whereas below the surface it is the distance between the centre of buoyancy and the centre of gravity (BG) which governs the transverse stability of a submarine. Various transverse stability criteria are presented, both for surfaced and submerged submarines.

The equations of motion for submarine manoeuvring are presented and discussed together with a non-linear coefficient based approach for determining the forces and moments on the submarine. Means of determining the coefficients using model tests, including a rotating arm and a planar motion mechanism, are detailed. In addition, the use of Computational Fluid Dynamics; and empirical techniques for determining the manoeuvring coefficients are discussed. Empirical equations for determining the manoeuvring coefficients are presented, and the results compared to published results from experiments. Issues associated with manoeuvring in the horizontal and vertical planes are explained, including: stability in the horizontal plane; the Pivot Point; heel during a turn, including snap roll; the effect of the sail, including the stern dipping effect; the Centre of Lateral Resistance; stability in the vertical plane; the Neutral Point; and the Critical Point, including the effect of speed, and issues at very low speed. Manoeuvring close to the surface, including surface suction, is discussed. Suggested criteria for stability in the horizontal and vertical planes, along with rudder and plane effectiveness are given. The concept of Safe Operating Envelopes, including Manoeuvring Limitation Diagrams and Safe Manoeuvring Envelopes together with the associated Standard Operating Procedures in event of credible failures are presented. Free running model experiments and manoeuvring trials, including submarine definitive manoeuvres and submarine trials procedures are discussed.

The resistance of a submarine will have a major influence on its top speed, endurance, and acoustic signature. The various components of resistance include: surface friction; form drag; induced drag; and wave making resistance. The latter only becomes important when the submarine is operating on, or close to, the water surface. The flow over a submarine will influence its top speed, its acoustic signature, and the effectiveness of its own sensors. In particular, flow separation should be avoided. A submarine hull is usually considered in three parts: fore body; parallel middle body; and aft body. The main driver for the hydrodynamic design of the fore body is to control the flow such that there is laminar flow over the sonar array. A fuller fore body may be beneficial for this. The length of the parallel middle body influences the length to diameter ratio, and it is shown that there is an optimum value of the L/D to minimise resistance, depending on the hull form. The aft body shape can be characterised by the half tail cone angle, which defines its fullness. The primary aim of the design of the aft body is to avoid flow separation, and ensure good flow into the propulsor. Appendages contribute significantly to the hull resistance. In addition, they generate vortices which can have a detrimental effect on the flow around the hull, and in particular into the propulsor. Model testing and Computational Fluid Dynamics techniques are discussed. In addition, an empirical method of predicting the resistance of a submarine, suitable for use in the early stage of the design, is presented.

The efficiency and acoustic performance of any propulsor will be affected by the flow into it. This is determined by: the hull shape, particularly the aft body and the tail cone angle; the casing; the sail; and the aft appendages. There will be an uneven wake field into the propulsor which will depend on the sail design and aft control surface configuration. This will result in fluctuating forces, causing vibration and noise. The quality of the flow into the propulsor can be assessed quantitatively using either the Distortion Coefficient, or the Wake Objective Function, and these are both explained. Results are presented to estimate the Taylor wake fraction, and the thrust deduction fraction as functions of the tail cone angle and the ratio of propeller diameter to hull diameter. The hull efficiency, which is the ratio of effective power to thrust power, can be estimated. The relative rotative efficiency is the ratio of the open water propulsive efficiency to the efficiency of the propulsor when operating in the wake. The Quasi Propulsive Coefficient (QPC) is the ratio of useful power to the power delivered to the propeller. Submarines are often propelled by a large optimum diameter single propeller. It is important to avoid cavitation, and the Cavitation Inception Speed depends on depth of submergence. Blade number is important, and this is discussed. Many submarines use pumpjets, which comprise two or more blade rows within a duct. The principles of pumpjets are discussed, along with some design guidance. The diameter of a pumpjet is usually smaller than that of a propeller, resulting in a lower rotor tip speed. Contra-rotating propulsion; twin propellers; podded propulsion; and rim driven propulsion are also discussed. Propulsor performance can be assessed using either the thrust identity or torque identity method, and both are described.

Submarines usually have three groups of appendages: sail; forward control surfaces; and aft control surfaces. Appendages contribute a considerable increase in drag, and need to be considered carefully. There are two approaches to sail design: a foil type; and a blended type. The blended type of sail has a larger volume than the foil type, and is better faired into the hull. If the sail is at an angle of attack it will generate a side force high up resulting in a heel angle (particularly snap roll) and a force and moment in the vertical plane on the hull, resulting in a stern dipping tendency. The magnitude of the side force when manoeuvring will depend on the distance of the sail from the Pivot Point. The location of the sail will also affect the turning radius. The forward planes can be located in three different positions: midline; eyebrow; and sail. The pros and cons of each of these are discussed. The aft control surfaces may include fixed and movable surfaces, with the fixed surfaces increasing stability, and the movable surfaces used to change trim, and hence to make large depth changes, and to turn the submarine. Different aft control surface configurations include: cruciform; X-form; inverted Y; and pentaform. The pros and cons of these different configurations are discussed.

The propulsor is the most important source of hydrodynamic noise. Low rotational speed and low tip speed are generally considered advantageous from a hydro-acoustic point of view. Hydroacoustic noise generated directly by a propulsor can be categorized into: cavitation noise; narrowband, (or tonal), noise; and broadband noise. Each of these is discussed briefly. It is noted that if cavitation occurs it will dominate all other sources of noise. Cavitation Inception Speed is the lowest speed at which cavitation will occur. Four different operating regimes can be identified: ultra-quiet operation at low speed; normal operation at patrol speed; high speed operation; and operation close to the surface when snorkeling. Each of these is discussed briefly.