Numerical Uncertainty Analysis Research Articles

Study on Pure Roll Test of a Ship Using CFD Simulation

Roll moment usually is ignored when analyzing the maneuverability of surface ships. However, it is well known that the influence of roll moment on maneuverability is significant for ships with small metacentric height such as container ships, passenger ships, etc. In this study, a pure roll test is performed to determine the hydrodynamic derivatives with respect to roll motion as added mass and damping. The target ship is an autonomous surface ship designed to carry containers with a small drift and large freeboard. The commercial code of STAR CCM+ software is applied as a specialized tool in naval hydrodynamic based on RANS equation for simulating the pure roll of the ship. The numerical uncertainty analysis is conducted to verify the numerical accuracy. By distinguishing the in-phase and out-of-phase from hydrodynamic forces and moments due to roll motion, added mass derivatives and damping derivatives relative to roll angular velocity are obtained.

Comparison of self-propulsion performance between vessels with single-screw propulsion and hybrid contra-rotating podded propulsion

The present work compares the self-propulsion performance between vessels with single-screw propulsion and hybrid contra-rotating podded propulsion. The viscous flow fields of 4000 TEU container vessels with single-screw, single-rudder propulsion and hybrid contra-rotating propeller (CRP) podded propulsion systems were solved numerically by the Reynolds-averaged Navier–Stokes equations (RANS), the shear stress transport (SST) k−ω turbulence model, and the sliding mesh method. Numerical uncertainty analysis of the resistance and self-propulsion factor were employed according to ITTC Quality Manual 7.5-03-01-01. Self-propulsion factor, viscous flow field, and pressure distribution at the stern of the vessels were analyzed in detail. Numerical results suggested that the vessel with the hybrid CRP podded propulsion showed a 17.59% larger effective wake fraction, a 40.2% smaller thrust deduction fraction, a 15.1% higher hull efficiency, and a 4.12% higher overall propulsive efficiency compared with the single-screw vessel. In addition, the vessel with the hybrid CRP podded propulsion showed a basically symmetric, smaller velocity gradient and more uniform flow field at the stern, resulting in a much smaller propeller-induced fluctuating pressure on the hull, compared with the single-screw vessel. In conclusion, the hybrid CRP podded propulsion system exhibited high efficiency and low vibration levels.

A finite volume formulation for magnetostatics of discontinuous media within a multi-region OpenFOAM framework

In this article we present a formulation for the numerical computation of static magnetic fields in discontinuous media. Focusing on solving magneto-fluid-structure interaction problems, we developed a finite volume multi-region framework capable of treating an arbitrary number of magnetized, permeable and current carrying bodies. The balance equations are written in terms of the magnetic vector potential leading to a formulation with discontinuous boundary conditions at interfaces between regions. We derived a consistent formulation of the discrete interface boundary conditions which guarantee accurate results for the magnetic field. The computational framework is based on a multi-region implementation that relies on non-conformal field mapping between and an implicit-explicit iterative solution procedure. Several numerical experiments show that the formulation gives good results for orthogonal meshes in terms of magnitude and direction of the magnetic field. We executed a numerical uncertainty analysis for a test case where a volumetric current, a permanent magnet and a ferromagnetic material interact between each other; we report apparent orders of accuracy, grid convergence indexes and grid convergence curves for several points of the computational domain.

A Study on the Air Cavity under a Stepped Planing Hull

Based on the FVM (finite volume method) numerical method, the flow field around the stepped planing hull in Taunton series was simulated. According to the general procedure of numerical uncertainty analysis, the numerical uncertainty in the high-speed flow field simulation of the stepped planing hull was discussed. Combined with the wave-making characteristics of the hull, the generation mechanism, shape evolution of air cavity, and the pressure distribution characteristics under the influence of the cavity, focuses on the variation of the flow around the stepped planing when the hull is in the triangle planing stage. Numerical results suggest that, as the air cavity enlarges, the cover rate of the air cavity can rise up to 77.8% of the whole wetted surface of the planing hull bottom. While, in the triangle planing stage, there is additional wetting at the aft bilge, which leads to the decrease of the air cavity rate and the increase of the wetted area. At the same time, the pressure distribution concentrates to the center of gravity.

Predictions of ship maneuverability based on virtual captive model tests

Maneuverability is an important hydrodynamic performance of a ship, and should be taken into account during the ship design stage. The present study of Computational Fluid Dynamic (CFD) calculations aims to offer a numerical tool for maneuvering prediction with high accuracy. The virtual captive model tests for a model scale KCS container ship are conducted using unsteady Reynolds-averaged Navier–Stokes (RANS) computation to obtain the full set of linear and nonlinear hydrodynamic derivatives in the 3rd-order Abkowitz model. The numerical uncertainty analysis is carried out for the pure sway and yaw–drift tests to verify the numerical accuracy. It is concluded that the lower order Fourier coefficients are preferred in the computation of the hydrodynamic derivatives. Moreover, part of the computed hydrodynamic forces and moments are compared with the available captive model test data, and good agreement is obtained. By substituting the computed hydrodynamic derivatives into the mathematical model, the standard turning and zigzag maneuvers are predicted. By comparing the predicted maneuvering results with the available experimental data and the prediction results by others, it is demonstrated that acceptable prediction accuracy can be achieved with the present method, which shows the effectiveness of the present method in predicting ship maneuverability.

Numerical uncertainty analysis of active and passive structures in the structural design phase

The active approach is nowadays well developed and widely used for various kinds of structures for vibration control or compensation. However, it makes the structure more complex than a passive structure. In this study, active and passive beam structures with the same designed size are compared with regard to uncertainty analysis of the system. The purpose of the comparison is to find a comprehensive way to decide whether an active or a passive approach should be used in the structural design phase. An active beam structure used in this study is a beam structure with one sensor, one actuator, and one controller. The controller is designed to reduce the structural vibration. An active beam structure with a properly designed controller can reduce the structural vibration without changing the structure’s physical dimensions. In contrast, a passive approach can also reduce the structural vibration without additional electric energy for active components, e.g., by changing the material. The comparison of the active and the passive beam structure is based on a beam structure with the same boundary conditions. It is well known that after manufacture and assembly the input parameters of the structure do not exactly correspond to the designed values. Therefore, the input parameters are assumed to be normally or uniformly distributed according to the manufacture tolerance class. They are varied according to the Monte Carlo method to compare the vibration reduction ability of the active and the passive approaches. Finally, uncertainty analysis supports the decision if an active or a passive approach should be used in the structural design phase.

Numerical study on scale effect of nominal wake of single screw ship

A 4000TEU container ship was studied without considering free surface effect, and the viscous flow fields of ship at different scales were solved numerically by RANS method, numerical uncertainty analysis was employed according to factors of safety method for Richardson extrapolation, scale effect of axial nominal wake field was analyzed in details. It shows that the reciprocal of mean axial wake fraction of propeller disc exhibits a near linear dependence on Reynolds number in logarithmic scale. For the single screw ship without bilge vortex, linear function is fit perfectly for the relationship between the reciprocal of mean axial wake fraction at each radius, reciprocal of amplitude of wake peak right above propeller disc and Reynolds number in logarithmic scales. In inner area of propeller disc, the reciprocal of amplitude of wake valley and wake peak right down propeller disc reveal nearly linear dependence on Reynolds number in logarithmic scales. While in outer area, the amplitude of wake peak and valley decline rapidly to potential wake fraction, and the wake width reveals negative exponent power function dependence on Reynolds number in logarithmic scales. On this basis, an extrapolated wake field scaling method is proposed.

A survey of non-probabilistic uncertainty treatment in finite element analysis

The objective of this paper is to critically review the emerging non-probabilistic approaches for uncertainty treatment in finite element analysis. The paper discusses general theoretical and practical aspects of both the interval and fuzzy finite element analysis. First, the applicability of the non-probabilistic concepts for numerical uncertainty analysis is discussed from a theoretical viewpoint. The necessary conditions for a useful application of the non-probabilistic concepts are determined, and are proven to be complementary rather than competitive to the classical probabilistic approach. The second part of the paper focuses on numerical aspects of the interval finite element method. It describes two principal strategies for the implementation, i.e., the anti-optimisation and the interval arithmetic approach, and gives a state-of-the-art of the interval finite element algorithms available from literature. It is shown how the application of the interval arithmetic approach to the classical finite element procedure can result in a severe overestimation of the uncertainty on the output, and the main sources of this conservatism are identified. A numerical example in the final part of the paper illustrates the capabilities of the different strategies on an eigenfrequency analysis of a built-up benchmark structure.

Relating error bounds for maximum concentration estimates to diffusion meteorology uncertainty

The intent of this paper is to relate the magnitude of the error bounds of data, used as inputs to a Gaussian dispersion model, to the magnitude of the error bounds of the model output, which include the estimates of the maximum concentration and the distance to that maximum. The research specifically addresses the uncertainty in estimating the maximum concentrations from elevated buoyant sources during unstable atmospheric conditions, as these are most often of practical concern in regulatory decision making. A direct and quantitative link between the nature and magnitude of the input uncertainty and modeling results has not been previously investigated extensively. The ability to develop specific error bounds, tailored to the modeling situation, allows more informed application of the model estimates to the air quality issues. In this study, a numerical uncertainty analysis is performed using the Monte-Carlo technique to propagate the uncertainties associated with the model input. Uncertainties were assumed to exist in four model input parameters: (1) wind speed, (2) standard deviation of lateral wind direction fluctuations, (3) standard deviation of vertical wind direction fluctuations, and (4) plume rise. For each simulation, results were summarized characterizing the uncertainty in four features of the ground-level concentration pattern predicted by the model: (1) the magnitude of the maximum concentration, (2) the distance to the maximum concentration, and (3) and (4) the areas enclosed within the isopleths of 50% and 25% of the error-free estimate of maximum concentration. The authors conclude that the error bounds for the estimated maximum concentration and the distance to the maximum can be double that of the error bounds for individual model input parameters. The model output error bounds for the areas enclosed within isopleth values can be triple the error bounds of the input. It was not our intent to cover all possible combinations for the error in the input parameters. Ours was a much more limited goal of providing a lower bound estimate of model uncertainty in which we assume the input is reasonably well characterized and there is no bias in the input. These results allow estimation of minimum bounds on errors in model output when considering reasonable input error bounds.