On the behavior of nonlinear hydrodynamic coefficients of a submerged cylinder beneath the water surface

This study aims at numerically exploring the behavior of flow fields and nonlinear hydrodynamic coefficients of a horizontal cylinder beneath the free surface flow considering the effects of nonlinear surface waves and various cylinder shapes. The computational model is based on two-dimensional incompressible Navier-Stokes solvers along with the treatment of the free surface flow using the volume of fluid method. The effect of the turbulent flow is also considered by using the shear stress transport turbulence model. The simulation result of a benchmark case study of the submerged cylinder is first validated with available experiment data, where a mesh convergence analysis is also performed. Afterward, the flow fields and hydrodynamic force coefficients around the cylinder surface are analyzed, and the influences of various cylinder shapes and Reynolds numbers on the hydrodynamic coefficients are investigated. A state diagram representing the hydrodynamic behavior including stable and unstable stages is finally proposed; this is an important criterion for the practice design of submerged civil structures under the free surface flow.

RANS-BASED CFD PREDICTION OF THE HYDRODYNAMIC COEFFICIENTS OF DARPA SUBOFF GEOMETRY IN STRAIGHT-LINE AND ROTATING ARM MANOEUVRES

Computational Fluid Dynamics (CFD) simulations using Reynolds Averaged Navier-Stokes (RANS) equations are increasingly adopted as an analysis tool to predict the hydrodynamic coefficients of underwater vehicles. These simulations have shown to offer both a high degree of accuracy comparable to experimental methods and a greatly reduced computational cost compared to Large Eddy Simulation (LES) and Direct Numerical Simulation (DNS). However, one of the major challenges faced with CFD simulations is that the results can vary greatly depending on the numerical model settings. This paper uses the DARPA SUBOFF hull form undergoing straight-line and rotating arm manoeuvres at different drift angles to analyse the hydrodynamic forces and moments on the vehicle against experimental data, showing that the selection of the boundary conditions and turbulence models, and the quality of the mesh model can have a considerable and independent effect on the computational results. Comparison between the Baseline Reynolds Stress Model (BSLRSM) and Shear Stress Transport with Curvature Correction (SSTCC) were carried out for both manoeuvres, showing that with a sufficiently fine mesh, appropriate mesh treatment, and simulation conditions matching the experiments; the BSLRSM predictions offer good agreement with experimental measurements, while the SSTCC predictions are agreeable with the longitudinal force but fall outside the experimental uncertainty for both the lateral force and yawing moment.

DETERMINATION OF DRAG AND LIFT RELATED COEFFICIENTS OF AN AUV USING COMPUTATIONAL AND EXPERIMENTAL FLUID DYNAMICS METHODS

Determination of hydrodynamic coefficients is a vital part of predicting the dynamic behavior of an Autonomous Underwater Vehicle (AUV). The aim of the present study was to determine the drag and lift related hydrodynamic coefficients of a research AUV, using Computational and Experimental Fluid Dynamics methods. Experimental tests were carried out at AUV speed of 1.5 m s-1 for two general cases: I. AUV without control surfaces (Hull) at various angles of attack in order to calculate Hull related hydrodynamic coefficients and II. AUV with control surfaces at zero angle of attack but in different stern angles to calculate hydrodynamic coefficients related to control surfaces. All the experiments carried out in a towing tank were also simulated by a commercial computational fluid dynamics (CFD) code. The hydrodynamic coefficients obtained from the numerical simulations were in close agreement with those obtained from the experiments.

QUANTIFICATION OF UNCERTAINTY IN MANOEUVRING CHARACTERISTICS FOR DESIGN OF UNDERWATER VEHICLES

The prediction of manoeuvring characteristics of underwater vehicles during design involves approximations at various stages. This paper attempts to quantify some of the uncertainties involved in the manoeuvring characteristics of underwater vehicles. The first source of uncertainty is in idealization of mathematical model selected for trajectory simulation. This is illustrated for alternative mathematical models in trajectory simulation programs. Next, the values of the hydrodynamic coefficients (HDCs) in the equations of motion have their own levels of uncertainty, depending upon the methods used to determine them. The sensitivity of trajectory simulation results to uncertainty levels in various HDCs is examined. Finally, the level of uncertainty in full-scale measurements of manoeuvres of underwater vehicles is discussed and estimated. It emerges that the cumulative errors in the prediction process during design need to be reduced further, in order to maintain their levels of uncertainty below those of the validation process.

VISCOSITY IN SEAKEEPING

Application of strip theory for the prediction of ship motions in waves relies on sectional hydrodynamic coefficients; i.e. the added mass and damping coefficients. These coefficients apply to linearised problems and are normally computed for inviscid fluids. It is possible to account for viscosity but this cannot be done by the RANS equations, as in linear problems there is no room for turbulence. The hydrodynamic coefficients can include the effect of viscosity but this can be done rightly through the classic Navier–Stokes equations for laminar (non-turbulent) flows. For solving these equations commercial RANS software can be used, assuming no Reynolds stresses.

ESTIMATION OF HYDRODYNAMIC COEFFICIENTS OF A NONLINEAR MANOEUVRING MATHEMATICAL MODEL WITH FREE-RUNNING SHIP MODEL TESTS

Free-running model tests have been carried out based on a scaled chemical tanker ship model, having a guidance, control and navigation system developed and implemented in LabVIEW. In order to make the modelling more flexible and physically more realistic, a modified version of Abkowitz model was introduced. During the identification process, the model’s structure is fixed and its parameters have been obtained using system identification. A global optimization algorithm has been used to search the optimum values and minimize the loss functions. In order to reduce the effect of noise in the variables, different loss functions considering the empirical errors and generalization performance have been defined and implemented in the system identification program. The hydrodynamic coefficients have been identified based on the manoeuvring test data of free-running ship model. Validations of the system identification algorithm were also carried out and the comparisons with experiments demonstrated the effectiveness of the proposed system identification method.

Identification of hydrodynamic coefficients of AUV in the presence of measurement biases

This paper mainly presents the parameter identification method developed from a Least Square Estimation (LSE) algorithm to estimate hydrodynamic coefficients of Autonomous Underwater Vehicle (AUV) in the presence of measurement biases. LSE based parameter determination method is developed to obtain unbiased estimated values of hydrodynamic coefficients of AUV from biased Inertial Navigation System (INS) measurements. The proposed parameter identification method consists of two phases: in the first phase, high precision INS and its auxiliary instrument including compass, pressure depth sensor, and Doppler Velocity Log (DVL) are designed as Integrated Navigational System coupled with Complementary Kalman Filter (CKF) to determine hydrodynamic coefficients of AUV by removing the INS measurement biases; in the second phase, LSE based parameter identification method is applied to the model in the first phase for obtaining unbiased estimated values of hydrodynamic coefficients of AUV. In this paper, a method for identifying the yaw and sway motion dynamic parameters of an AUV is given. Various maneuvering scenarios are verified to assess the parameter identification method employed. The simulation results indicate that using the CKF based Integrated Navigation System together with unbiased measurement conversion could produce better results for estimating the hydrodynamic coefficients of AUV.

Robust Parameter Estimation of an Empirical Manoeuvring Model Using Free-Running Model Tests

The work presents the identification and validation of the hydrodynamic coefficients for the surge, sway, and yaw motion. This is performed in two ways: using simulated data and free-running test data. The identification and validation with the simulation data are carried out using a 25° turning test and a 20°−20° zigzag manoeuvring test. For the free-running test data, two zigzag manoeuvres are used: 30°−30° zigzag for identification and 20°−20° zigzag for validation. A nonlinear manoeuvring model is proposed based on the standard Euler equations, and the hydrodynamic coefficients are computed using empirical equations. To obtain robust results, the truncated singular value decomposition is employed to diminish the multicollinearity and the parameter uncertainties due to noise. The validation is carried out by comparing the result of the measured values with the predictions obtained using the manoeuvring models. Finally, a sensitivity analysis for the simulation data is performed to understand the influence of the parameters in the manoeuvres.