This chapter deals with loads related to the hull structure, the operation of mechanical equipment as well as those related to cargoes. The loads related to the hull structure include hull weight, inertial loads, loads induced during the fabrication process (residual stresses) as well as loads acting during occasional circumstances. These include drydocking, launching, and conversion procedures. Grounding and collision that are undesirable events are also discussed. Loads that are induced by the operation of mechanical equipment are considered, the most important of these being propeller-induced vibration and vibration of the main propulsion machinery. Cargo-induced loads are discussed next. These relate to both cargo and ballast water and include weight, inertial loads and the effect of cargo shifting. Lastly thermal gradients are considered the most important cases being the heating of crude oil using heating coils and ensuring low temperature in the case of gas carriers. The loads acting on the hull girder are summarised in tabular form in which their relative importance is assessed. In the last section load action is described with the principal loads acting on the hull girder discussed as well as the different load systems (primary, secondary and tertiary).

This chapter deals with the application of structural reliability theory in the field of ship structural analysis and design. Sources of uncertainty in the marine environment are discussed, followed by the probability theory dealing with combined loads (still-water bending and wave-induced bending). Three applications of reliability theory are then presented: the development of the IACS reliability-based code for the strength of oil tankers, a comparison of ships designed before and after the introduction of the IACS Common Structural Rules and lastly the risk-based structural design of an oil tanker.

In this chapter the probabilistic modelling of hull girder primary loading and response are presented. In the first part the probabilistic modelling of the sea environment is described. The nature of the sea surface is described in qualitative terms, following which the short-term description is presented. Deterministic modelling is discussed and statistics descriptors of ocean wave records defined. The concept of the wave spectrum is introduced and spectra for moderate and rough sea states described and differentiated, as well as wave spectra for ship design. Ship response to wave loading is discussed. The importance of linear response is underlined and structural considerations described. The basis of extreme value theory is presented and the Fisher-Tippett-Gnedenko theorem is introduced. Extreme as well as combined loads in short-term seas are described. Long-term analysis of sea loads is considered next. Differences with short-term analysis are mentioned and the use of full-scale measurements at sea described. The statistical description of a critical wave height is described using firstly the return period, and probability of occurrence method and secondly the wave height and period approach (scatter diagram). Two methods used to conduct long-term analysis of sea states are described: the long-term cumulative distribution (LTCD) method and the simulation method.

Hull girder vibration is treated in this chapter using mathematical methods (differential equation and energy approach). In the first part elementary vibration theory is presented, progressing from the SDOF system to the undamped vibration of the Timoshenko beam. The energy approach to vibration is presented next. In the next part ship vibration is presented. The types of vibration encountered in ships are discussed and classified, following which the distinguishing features of ship vibration compared to that of a uniform beam are presented. These relate to structural layout, design and operational aspects and the marine environment (added mass effect). In the next section vibration arising from steady-state excitation is described. This concerns vertical, horizontal and torsional vibration. Expressions for natural frequencies in each mode are given. In the case of vertical vibration the differential equations of vibration of a ship hull girder are obtained and expressions for natural frequency included in various publications compared. The differential equations of coupled vertical and horizontal vibration are obtained and springing is discussed. Vibration arising from transient loading is discussed and includes slam-induced whipping and whipping induced by bow flare impact.

The different types of uncertainty and the theories developed to account for them are presented in this chapter. The concepts of risk and reliability are introduced and defined following which basic probability ideas are discussed. The methods used to determine structural reliability are described (the direct integration method, Level II reliability methods and the Level I method). Level II reliability methods include the mean value first-order second-moment method and variants of it based on the Hasofer-Lind reliability index used in the case of nonlinear limit state functions and the Rackwitz-Fiessler procedure that has to be followed in the case of non-normal distributions. The Level I reliability method is discussed and the approach followed to determine partial safety factors described. In the next section fuzzy logic and fuzzy set theory are described. They are introduced by distinguishing between classical logic and fuzzy logic, following which fuzzy sets and fuzzy inference are described. In the last section the steps in the fuzzy inference system are presented and examples of such systems mentioned.

The nonlinear response of the hull girder to global loads is treated in this chapter. These include torsional loads, the result of major damage leading to loss of longitudinal strength of part of the hull girder, and hull girder collapse. In the case of torsional loads, of critical importance is the position of the shear centre, and this depends on hull girder geometry (closed or open section). The effect of structural arrangements is then described in relation to longitudinal warping. The effect of discontinuities is discussed and design issues are considered. Combined and coupled horizontal bending and torsion are treated next. The next section deals with the determination of reserve strength of the hull girder following damage. The approach followed by a classification society to calculating residual strength is described and the use of IACS Common Structural Rules in calculating residual strength of oil tankers is presented. The topic of the last part of the chapter is the ultimate strength of the hull girder in longitudinal bending. The need to calculate ultimate strength is discussed, followed by the calculation of ultimate strength using a simplified, upper bound approach. Progressive collapse analysis is presented and this allows for the gradual spread of elasto-plastic behaviour in individual stiffened plate elements of the hull girder.

Quantifying and assessing the computational accuracy of coarse-graining simulations of turbulence is challenging and imperative to achieve prediction – computations and results with a quantified and adequate degree of uncertainty that can be confidently used in projects without reference data. Verification, validation, and uncertainty quantification (VVUQ) provide the tools and metrics to accomplish such an objective. This chapter reviews these methods and illustrates their importance to coarse-graining models. Toward this end, we first describe the sources of computational errors and uncertainties in coarse-graining simulations of turbulence, followed by the concepts of VVUQ. Next, we utilize the modified equation analysis and the physical interpretation of a complex problem to demonstrate the role of VVUQ in evaluating and enhancing the fidelity and confidence in numerical simulations. This is crucial to achieving predictive rather than postdictive simulations.

Using high-order simulations, we have shed light on complex chemically reacting flow processes and identified new mechanisms of the supersonic combustion process. We have employed 11th-order accurate implicit large eddy simulation (ILES) in conjunction with a finite-rate (Arrhenius) thermochemistry model using a reduced reaction mechanism for the combustion of hydrogen and air. We compare the coarse-grained computations with available experiments from the German Aerospace Centre (DLR) and discuss the accuracy and uncertainties. A supersonic combustion chamber can be accurately modelled using high-order ILES without a specific turbulence-chemistry model. The simulations reveal that the flame intermittently propagates upstream behind the wedge-shaped flame holder, alternating between the upper and lower turbulent free shear layers at a frequency of ≃ 7,990 Hz. This can be a leading cause of unsteady pressure loadings on the interior surfaces downstream of the combustion chamber and is a crucial structural design parameter. Furthermore, the simulations reveal that high temperatures are sustained long distances downstream of the combustion onset. A barycentric map for the Reynolds stresses is employed to analyze the turbulent anisotropy. The results correlate the axisymmetric contraction and expansion of turbulence with the interaction of the reflected shock waves and the supersonic combustion hydroxyl production regions. The physics insights presented in this study could potentially lead to more efficient supersonic combustion and engineering designs.

This chapter gives an overview of data-driven methods applied to turbulence closure modeling for coarse graining. A non-exhaustive introduction of the various data-driven approaches that have been used in the context of closure modeling is provided which includes a discussion of model consistency, which is the ultimate indicator of a successful model, and other key concepts. More details are then presented for two specific methods, one a neural-network representative of nontransparent black-box approaches and one specific type of evolutionary algorithm representative of transparent approaches yielding explicit mathematical expressions. The importance of satisfying physical constraints is emphasized and methods to choose the most relevant input features are suggested. Several recent applications of data-driven methods to subgrid closure modeling are discussed, both for nonreactive and reactive flow configurations. The chapter is concluded with current trends and an assessment of what can be realistically expected of data-driven methods for coarse graining.

A nuclear detonation’s energy release can be approximately broken up into blast (50%), thermal (35%), and radiation (15%). If a detonation occurs significantly above ground (airburst) and various factors are favorable, for example, few clouds and no snow on the ground, then thermal radiation can ignite surface fires. These fires will first commence within fine fuels, such as paper and leaves on vegetation, but given time, these small-scale fires can upscale to larger fires that burn entire houses, trees, and possibly a city. Depending on weather conditions, the fires may continue to spread within a city and impact first responders or civilians sheltering in place to avoid fallout. This chapter highlights the coarse-graining of turbulence, combustion, and cloud physics associated with ignition, spread, and possible interaction of fires with nuclear fallout plumes. In particular, examples are given to illustrate the complex relationship between fallout and fires, an idealized detonation over Dallas (Texas, USA) and Hiroshima (Japan). For both examples, even though the nuclear airburst was at a fallout-free height of burst, the complex and turbulent interaction of the fires with clouds induced significant fallout on the ground.