A B-spline based higher order panel method for analysis of steady flow around marine propellers

An operating propeller is the main source of vibration on the ship hull, especially on the stern. In this article, an improved numerical scheme is presented to predict the pressure fluctuations on the ship hull due to the unsteady sheet cavitation of a propeller. The calculated results are compared with the published results and experimental data carried out in the hydrodynamics and cavitation tunnel of Hamburgische Schiffbau-Versuchsanstalt to verify the improvement. The present method is based on a two-cycle iterating scheme which satisfies the boundary integral equation in time domain. The hull pressure fluctuations calculated by the first-cycle iterations are treated as the initial values for the second-cycle iterations. The solid angles of the elements will deviate from the standard value, .5, as the dramatic variation in geometry appears, and accumulate numerical errors in the calculating process. During the second-cycle iterations, a filter based on the solid angles on hull elements is proposed to minimize the iterating error. A container ship is treated as the computing sample in this study, and evidence is offered regarding the 16% improvement achieved by the present method. 1. Introduction A propeller operating in a nonuniform wake field in the ocean is one of the prime sources of vibration and noise affecting the ship. The prediction of hull pressure fluctuations caused by propellers is an important consideration for many vessels and worthy of being researched. Hull pressure fluctuation caused by the marine propeller has been widely investigated since the 1980s. Huse and Guoqiang (1982) developed a semi-empirical prediction method, in which the cavitation volume on the propeller blade surface can be estimated using experimental data. Breslin et al. (1982) proposed a model based on the potential flow theory, which simulates the ship hull by means of a simple panel method and the propeller by means of a lifting surface vortex lattice method. Kinns and Bloor (2004) used an acoustic boundary element (BE) model to simplify the problem of hull vibration excitation due to propeller sources and dipoles. The convergence of results for a cruise liner model was demonstrated with different element distributions. Kehr and Kao (2004) derived the incident blade rate pressure induced by unsteady sheet cavitation (monopole) and unsteady forces (dipole) of an operating propeller, for calculating the hull pressure fluctuations. Brouwer (2005) applied a stationary set of rings of monopole and dipole sources in the frequency domain to solve the propeller-induced noise and vibrations. Lee et al. (2006) integrated computational fluid dynamics (CFD) and the finite difference method for the computation of propeller-induced hull vibration. It was recommended that the phase difference of the propeller-induced pressure should be considered for preventing overprediction. Kao and Kehr (2006) developed a time domain iteration method to calculate the hull pressure fluctuations induced by the operating propeller. The phase difference is included in the iterating scheme, and the computation is robustly convergent. Seol and Moon (2009) derived the governing equation of pressure fluctuation induced by sheet cavitation according to the Ffowcs Williams approach. In the study by van Wijngaarden (2011), a potential flow boundary element method (BEM) with measured hull pressure data as input was applied to solve the hull pressure fluctuations, and the model experiments were also carried out. It was concluded that the computed hull pressure fluctuations due to non-cavitating propellers is reasonably accurate compared with the experimental data. Kehr and Kao (2011) calculated the pressure fluctuations on ship hull due to propeller sheet cavitation by using the method presented in Kao and Kehr (2006). The numerical result is higher than the experimental data provided by the hydrodynamics and cavitation tunnel (HYKAT) of HSVA (Wiemer 1999) by approximately 27%. The pressure fluctuations on ship stern induced by cavitating propellers were solved by Kanemaru and Ando (2011) with a surface panel method. The maximum amplitude appears in the first blade frequency and overestimates the experimental data by about 30%. Kim et al. (2012) predicted the hull pressure fluctuations induced by marine propeller sheet cavitation, and the Doppler effect was considered at the same time. Wei and Wang (2013) employed CFD to simulate the propulsion of a submarine. The finite element method and BEM were then combined to solve the submarine's structure and acoustic responses under the propeller excitations. The matched-field inversion technique applied in Lee et al. (2014) uses the fluctuating hull pressure field measured by receivers and the acoustic field calculated by BEM to define the sheet cavitation noise, source strengths, source positions, and number of sources. The equivalent source model for the propeller can result in more accurately extrapolated hull pressure distribution. In Wei et al. (2016), the unsteady forces of a submarine propeller were predicted by CFD, and the hull pressure fluctuations due to the non-cavitation propeller were calculated by the method proposed in Kao and Kehr (2006).

In this paper, the hydrodynamic performance of lift-body marine propellers and hydrofoils is analyzed using a B-spline potential-based panel method. The potential panel method, based on a combination of two singularity elements, is proposed, and a B-spline curve interpolation method is integrated with the interpolation of the corner points and collocation points to ensure accuracy and continuity of the interpolation points. The B-spline interpolation is used for the distribution of the singularity elements on a complex surface to ensure continuity of the results for the intensity of the singular points and to reduce the possibility of abrupt changes in the surface velocity potential to a certain extent. A conventional cubic spline method is also implemented as a comparison of the proposed method. The surface pressure coefficient and lift the performance of 2-D and 3-D hydrofoils of sweepback and dihedral type with different aspect ratios are analyzed to verify the rationality and feasibility of the present method. The surface pressure distribution and coefficients of thrust and torque are calculated for different marine propellers and compared with the experimental data. A parametric study on the propeller wake model was carried out. The validated results show that it is practical to improve the accuracy of hydrodynamic performance prediction using the improved potential panel method proposed.

SummaryThree low-order panel methods developed for the analysis of supersonic flows have been used to make calculations for a number of test configurations, with the aim of establishing the range of problems for which this class of computational method yields adequate solutions. The programs investigated were the Woodward USSAERO/C program, the related NLRAERO program, and the British Aerospace Warton supersonic panel program. Results obtained using these programs have been evaluated against theoretical and experimental data for a number of test cases covering wing-alone, body-alone and wing-body geometries. It is concluded that low-order panel methods can provide adequate solutions for supersonic flows about wings, bodies and wing-body combinations, provided the assumptions implicit in the linearised potential flow model are not violated. Examples show that the prediction of lift and pitching moment curve slopes for quite complex configurations may be acceptable, but that the detailed pressure distributions are not always predicted satisfactorily. In particular, serious problems are encountered in calculating the flow about wings with rounded supersonic leading edges due to the linearised flow model which is used.

This paper presents the calculation method of tip cavitation with wake alignment. Tip cavitation consists of tip vortex cavitation and tip super cavitation which means the undeveloped and local super cavitation around blade tip. The feature of this study is that the method applies the wake alignment model in order to express the realistic phenomena of tip cavitation and predict the pressure fluctuation more accurately. In the present method, the wake sheet is deformed according to the induced velocity vector on the vortex lines. The singularity of the potential vortex can be removed by using the Rankine Vortex model. This paper shows the calculated results regarding cavitation pattern, pressure fluctuation etc. comparing with published experimental data and calculated results without wake alignment.

A two-frame PIV (Particle Image Velocimetry) technique is used to investigate the wake characteristics behind a marine propeller with 4 blades at high Reynolds number. For each of 9 different blade phases from <TEX>$ 0^{\circ} $</TEX> to <TEX>$ 80^{\circ} $</TEX>, one hundred and fifty instantaneous velocity fields are measured. They are ensemble averaged to study the spatial evolution of the propeller wake in the region ranging from the trailing edge to one propeller diameter (D) downstream location. The phase-averaged mean velocity shows that the trailing vorticity is related to radial velocity jump, and the viscous wake is affected by boundary layers developed on the blade surfaces and centrifugal force. Both Galilean decomposition method and vortex identification method using swirling strength calculation are very useful for the study of vortex behaviors En the propeller wake legion. The slipstream contraction occurs in the near-wake region up to about X/D : 0.53 downstream. Thereafter, unstable oscillation occurs because of the reduction of interaction between the tip vortex and the wake sheet behind the maximum contraction point.

This paper presents a method to analyze the viscous flow around marine propellers using boundary layer strip theory. A state-of-the-art two-dimensional boundary-layer formulation is coupled to a state-of-the-art perturbation potential panel method used in marine propeller flow analysis. The coupling procedure is applied along strips of the blade where two-dimensional boundary-layer flow is assumed. For this paper these strips were assumed to be constant radial strips of the blade. The resulting method is applied to a conventional marine propeller and comparisons to experiments are given. Results include the global quantities of thrust, torque, and efficiency and the local strip quantities of displacement thickness and section drag coefficient. The resulting comparisons, showing the applicability of the method to conventional marine propellers, are quite good.

The development and evaluation of a gas diffusion flow analysis system for the underway determination of dissolved inorganic carbon in marine and estuarine waters is described. Carbon dioxide produced when sample is injected into an acidic donor stream, diffuses through an efficient hollow fibre microporous membrane into an acceptor stream of ultrapure water, where the resultant changes in electrical conductivity are detected using a contactless capacitively coupled conductivity detector (C4D). The optimal parameters for the construction and operation of the C4D system are reported. Under field operational conditions, the flow analysis method had a linear calibration range for DIC of 0.2–10 mM, a limit of detection of 0.12 mM, repeatability of 0.46% RSD (n = 9 at 6 mM), a sample throughput of 90 h−1 and excellent correlation with comparative analyses (R2 = 0.9951, n = 16). The system was used to perform >250 determinations of DIC measurements underway during a short cruise on the Yarra River estuary, which demonstrated that DIC was conservative over much of the salinity gradient, with the exception of the low salinity region which exhibited the effects of respiratory CO2 and other DIC inputs. The results illustrate the advantages of the use of rapid flow analysis techniques for chemical mapping in transient environments like estuaries.

A naphthalene sublimation technique is employed to study the mass transfer distribution on the suction (convex) surface of a simulated turbine blade. Comparison with a heat transfer study shows good agreement in the general trends in the region of two-dimensional flow on the blade. Near the endwall, local convective coefficients on the suction surface are obtained at 4608 locations from two separate runs. The secondary flows in the passage significantly affect the mass transfer rate on the suction surface and their influence extends to a height of 75% of the chord length, from the endwall, in the trailing edge region. The mass transfer rate in the region near the endwall is extremely high due to small but intense vortices. Thus, a large variation in the mass transfer distribution occurs on the suction surface, from a mass transfer Stanton number of 0.0005 to a maximum of 0.01. In the two-dimensional flow region, the mass transfer distributions at two different Reynolds number are presented.

For the two-dimensional steady and unsteady turbine cascade flows, the Euler/Navier-Stokes equations with Baldwin-Lomax turbulence model are solved in the Cartesian coordinate system. A locally implicit hybrid algorithm on the mixed type of meshes is employed, where the convective dominated part in the flowfield is studied by TVD scheme to obtain high-resolution results on the triangular elements, and the second- and fourth-order dissipative model is introduced on the O-typed quadrilateral grid in the viscous dominated region to minimize the numerical dissipation. When the steady subsonic and transonic turbulent flows are investigated, the distributions of isentropic Mach number on the blade surface, exit flow angle and loss coefficient are obtained. Comparing the present results with the experimental data, the accuracy and reliability of the current approach is confirmed. By giving a moving wake-type total pressure profile at the inlet plane in the rotor-relative frame of reference, the unsteady transonic inviscid and turbulent flows calculations are performed to understand the interaction of the upstream wake with a moving blade row. The Mach number contours, perturbation component of the unsteady velocity vectors, shear stress and pressure distributions on the blade surface are presented. The physical phenomena, which include periodical flow separation on the suction side, bowing, chopping and distortion of incoming wake, negative jet, convection of the vortices and wake segments, and vortex shedding at the trailing edge, are observed. It is concluded that the unsteady aerodynamic behaviors are strongly dependent on the wake/shock/boundary layer interactions.

Visualization of aerodynamic forces and flow field on a straight-bladed vertical axis wind turbine by wind tunnel experiments and panel method

A BEM-isogeometric method for the ship wave-resistance problem

Despite their high manufacturing cost and structural deficiencies especially in tip regions, highly skewed propellers are preferred in the marine industry, where underwater noise is a significant design criterion. However, hydrodynamic performances should also be considered before a decision to use these propellers is made. This study investigates the trade-off between hydrodynamic and hydroacoustic performances by comparing conventional and highly skewed Seiun Maru marine propellers for a noncavitating case. Many papers in the literature focus solely on hydroacoustic calculations for the open-water case. However, propulsive characteristics are significantly different when propeller-hull interactions take place. Changes in propulsion performance also reflect on the hydroacoustic performances of the propeller. In this study, propeller-hull interactions were considered to calculate the noise spectra. Rather than solving the full case, which is computationally demanding, an indirect approach was adopted; axial velocities from the nominal ship wake were introduced as the inlet condition of the numerical approach. A hybrid method based on the acoustic analogy was used in coupling computational fluid dynamics techniques with acoustic propagation methods, implementing the Ffowcs Williams-Hawkings (FW-H) equation. The hydrodynamic performances of both propellers were presented as a preliminary study. Propeller-hull interactions were included in calculations after observing good accordance between our results, experiments, and quasi-continuous method for the open-water case. With the use of the time-dependent flow field data of the propeller behind a non-uniform ship wake as an input, simulation results were used to solve the FW-H equation to extract acoustic pressure and sound pressure levels for several hydrophones located in the near field. Noise spectra results confirm that the highest values of the sound pressure levels are in the low-frequency range and the first harmonics calculated by the present method are in good accordance with the theoretical values. Results also show that a highly skewed propeller generates less noise even in noncavitating cases despite a small reduction in hydrodynamic efficiency.

The applications of surface vortex lattice method to marine propellers are considered. The surface vortex lattice method based on general vortex lattice method is possible to simulate a lifting body including thickness and volume effects by distributing horse-shoe vortices on the surface of the body.The advantages of this method compared to other lifting body theory are the facts that it is easy to simulate a trailing vortex wake geometry behind propeller and that the Kutta-condition is satisfied automatically by convecting the trailing vortices.The geometry of the wake can be calculated by iterative procedure starting from the linear wake model and all vortices are convected to new positions step by step with a small time interval. In this paper, the propeller open characteristics, pressure distribution on the blade and the geometry of the wake concerning to three type propellers have been calculated by the present method. The results of these calculations are good agreements with experiment or other theoretical calculation results.

A finite element method (FEM) for solution of the conservative full potential flow equation is presented as a means for improving the computation of transonic flows about complex geometries. The method does not require an orthogonal mesh, thus removing a major constraint in grid generation. A standard Galerkin finite element formulation is used in conjunction with the artificial compressibility method which stabilizes the algorithm in transonic flow and allows the capture of embedded shock waves. Solution comparisons, including one test case which stresses the'capabilities of state-of-the-art finite difference methods, verify the FEM accuracy and geometric capability. I. Introduction W HILE the computation of inviscid two- and threedimensional flowfields by finite difference methods has now become commonplace in industry, one of the most important technological deficiencies is in the area of geometric modeling, particularly for transonic flows. The finite element method (FEM) is presented as a way of alleviating some problems of geometric modeling which limit the effectiveness of current finite difference methods. Certain specific advantages of the FEM, if fully exploited, may improve greatly the computational state-of-the-art. Since the governing equations of inviscid transonic potential flow are nonlinear, the method of superposition (i.e., panel methods) is insufficient to yield a proper solution, even though solutions have been obtained by a method combining surface singularities and field differences.1 Also, because of the nonlinearity, similarity laws do not exist which allow subsonic flows to be related to transonic flows. Field methods must be used, typically finite difference or finite element methods, requiring a grid of points to be defined, both on the body surface arid in the flowfield, on which solutions to the governing equations are approximated. Finite difference method (FDM) computer codes generally

Purpose.The study involves: 1) formation of 3D propeller models under study; 2) studying of the effect of profiling the blade of the propeller on its hydrodynamic characteristics; 3) development of a methodology for specifying optimal project parameters for modeling the operation of a propeller in free water, which in the future could be recommended when simulating similar tasks in the CFD package Flow Vision. Methodology. The technology of design of propellers of new series was developed. For the first time, the project methodology was proposed in the CFD package Flow Vision for studying the operation of a propeller in free water. Findings. On the example of solving a practical problem for studying the influence of blade profiling on the efficiency of a propeller, the expediency of developing the proposed methodology for setting a propeller design in the CFD package Flow Vision is justified. The using of this technique makes it possible to obtain reliable values of the propeller hydrodynamic characteristics for constructing its action curves, and also to reduce the estimated time. This approach makes it possible to optimize the process of designing propellers. Originality. Through numerous experiments and based on the analysis of the obtained results, it was found that the profiling of the propeller mainly affects its hydrodynamic characteristics. The choice and calculation of the propeller for the projected vessel occurs in the early stages of design. Therefore, the rationale for choosing one or another geometry of the marine propeller is a topical task. A method for specifying project parameters for conducting numerical experiments in studying the operation of propellers in free water was proposed and justified. Thus, it is possible to design not only the serial screws, but also the new series propellers, minimizing the costs of carrying out the research along with the reliability of the resulting calculation results. Practical value. Authors established that the influence of the propeller blade profiling on its hydrodynamic characteristics is greater than the influence of its other general and blade characteristics. The developed design methodology for the calculation of propellers in the CFD package Flow Vision can be used to design the marine propellers of both new series and existing ones, and also in the case of optimizing the shape of the propeller to ensure the greatest efficiency. The application of the technique will allow reducing the time for conducting a numerical experiment due to the convergence of the solution in a relatively short time.