Low-order Panel Method Research Articles

Potential-flow computations in infinite or zero gravity limits via a weakly singular boundary integral equation

Potential flow computations, based on a weakly singular integral equation, are considered in the infinite-gravity limit g=∞ and the zero-gravity limit g=0. The weakly singular integral equation, obtained via a straightforward and rigorous application of Green’s basic identity, involves a distribution of weak dipoles that is continuous across the body surface. The integral equation is solved via a low-order panel method, which is validated for a half sphere and applied to the S60 ship model in translation along the x, y or z-axis. A systematic numerical analysis of the convergence of numerical predictions shows that the number of panels that is required to obtain a 0.1% accuracy is significantly different for the infinite-gravity or zero-gravity flows, and for translation of the S60 hull along the x, y or z-axis. In particular, a very large number of panels is required for translation of the S60 ship model along the horizontal x or y-axis in the zero-gravity limit.

Enhancement of Grid and Face Element Amendment in Aeroelasticity Analysis by Advanced Self-Adaptive Computing Method

This research presents a novel approach for enhancing the accuracy and efficiency of aeroelasticity analysis through the combination of grid optimization and face element amendment techniques. The study focuses on improving the precision of a low order panel method by performing piecewise linear amendment based on Computational Fluid Dynamics (CFD) aerodynamic loads data under varying angles of attack. Additionally, the distribution of face element calculating grid is optimized using visual evoked potential estimation. The proposed method addresses the limitations of traditional panel methods that heavily rely on grid distribution and offers a more robust and accurate solution. The optimized grid not only maintains the computational efficiency of the panel method but also ensures closer approximation of wing stresses to CFD data, thus enhancing the precision and efficiency of aeroelasticity optimized iterative design processes. The results obtained from this research demonstrate effective compensation for the shortcomings of the panel method and a significant improvement in the computational efficiency of aerodynamic loading in the presence of changing structural stiff parameters.

Hydrodynamic Analysis of Twin-Hull Structures Supporting Floating PV Systems in Offshore and Coastal Regions

In this paper, a novel model based on the boundary element method (BEM) is presented for the hydrodynamic analysis of floating twin-hull structures carrying photovoltaic panels, supporting the study of wave responses and their effects on power performance in variable bathymetry regions. The analysis is restricted to two spatial dimensions for simplicity. The method is free of any mild-slope assumptions. A boundary integral representation is applied for the near field in the vicinity of the floating body, which involved simple (Rankine) sources, while the far field is modeled using complete (normal-mode) series expansions that are derived using separation of variables in the constant depth half-strips on either side of the middle, non-uniform domain, where the depth exhibited a general variation, overcoming a mild bottom-slope assumption. The numerical solution is obtained by means of a low-order panel method. Numerical results are presented concerning twin-hull floating bodies of simple geometry lying over uniform and sloping seabeds. With the aid of systematic comparisons, the effects of the bottom slope and curvature on the hydrodynamic characteristics (hydrodynamic coefficients and responses) of the floating bodies are illustrated and discussed. Finally, the effects of waves on the floating PV performance are presented, indicating significant variations of the performance index ranging from 0 to 15% depending on the sea state.

A 3D flow separation model for open propellers with blunt trailing edge

The panel method is widely used in the design and analysis of marine propellers. However, this method cannot handle propellers with a blunt trailing edge due to a lack of proper models for the flow separation downstream. In this study, a numerical scheme, i.e., the three-dimensional flow separation model, is proposed to enable the panel method to be applied to propellers with a blunt trailing edge. In this model, the flow separation zone is represented as an extension of the trailing edge. The criteria of zero local lifts and zero local moments over the extension of all blade sections are used to establish the equations that determine the shape of the flow separation zone. Those equations are solved either by the Newton–Raphson method or as an optimization problem. A low-order panel method coupled with a boundary layer solver (the viscous/inviscid interaction method) is used to predict the pressure distributions and forces for the extended geometry. To validate this model, the pressure distributions of the propeller blade are compared with those from solving the Reynolds-Averaged Navier–Stokes equations. The predicted open water characteristics of a controllable pitch propeller are compared with the experimental measurements at a wide range of advance ratios with different pitches. This model requires much less computational effort while preserving high accuracy, and thus can be used reliably in designing and analyzing propellers with a blunt trailing edge.

An Isogeometric Boundary Element Method for 3D lifting flows using T-splines

In this paper an Isogeometric Boundary Element Method for three-dimensional lifting flows based on Morino’s (Morino and Kuo, 1974) formulation is presented. Analysis-suitable T-splines are used for the representation of all boundary surfaces and the unknown perturbation potential is approximated by the same T-spline basis used for the geometry. A novel numerical application of the so-called Kutta condition is introduced that utilises the advantages of isogeometric analysis with regard to the smoothness of the trailing edge curve basis functions. The method shows good agreement with existing experimental results and superior behaviour when compared to a low order panel method. The effect of the tip singularity on Kutta condition is also investigated for different levels of refinement and positions of the trailing edge collocation points.

삼각형 패널 상에 선형적으로 분포된 다이폴 강도를 갖는 패널법의 정식화

A high-order potential-based panel method based on Green"s theorem, with piecewise-linear dipole strength on triangular panels, is formulated for the analysis of potential flow around a three-dimensional wing. Previous low-order panel methods adopt square panels with piecewise-constant dipole strength, which results in inherent errors. Square panels can not represent a high curvature lifting body, such as propellers, since the four vertices of the square panel do not locate at the same flat plane. Moreover the piecewise-constant dipole strength induces inevitable errors due to the steps in dipole strength between adjacent panels. In this paper a high-order panel method is formulated to improve accuracy by adopting a piecewise linear dipole strength on triangular panels. Firstly, the square panels are replaced by triangular panels in order to increase the geometric accuracy in representing the shape of the object with large curvature. Next, the step difference of the dipole strength between adjacent panels is removed by adopting piecewise-linear dipole strength on the triangular panels. The calculated results by the present method is compared with analytical ones for simple non-lifting geometries, such as ellipsoid. The results for an elliptic wing with zero thickness at finite angle of attack are compared with Jordan"s results. The comparison shows reasonable agreements for the both lifting and non-lifting bodies.

A flow separation model for hydrofoil, propeller and duct sections with blunt trailing edges

The panel method does not apply to hydrofoils, propellers and ducts with blunt trailing edges due to the flow separation downstream. In this paper, a model is proposed to represent the flow separation with an extension, and a low-order panel method coupled with a boundary layer solver is used. The criteria of zero lift and zero moment are adopted to determine the end of the extension zone, and flow separation criteria are used to determine the starting points on either side of the section. The model is applied to hydrofoil, bare duct and ducted propeller sections with blunt trailing edges. The pressure distributions and skin frictions along the hydrofoils and ducts correlate well with those from the Reynolds-averaged Navier–Stokes method. The thrust and torque of the propeller agree much better with experimental measurements when the extension is determined from this model rather than choosing random locations. This model requires much less computational effort while preserving high accuracy, and thus can be used reliably in designing and analysing hydrofoils and propeller ducts with blunt trailing edges.

Panel Method for Ducted Propellers with Sharp Trailing Edge Duct with Fully Aligned Wake on Blade and Duct

A low-order panel method is used to predict the performance of ducted propellers. A full wake alignment (FWA) scheme, originally developed to determine the location of the force-free trailing wake of open propellers, is improved and extended to determine the location of the force-free trailing wakes of both the propeller blades and the duct, including the interaction with each other. The present method is applied on a ducted propeller with sharp trailing edge duct, and the predicted results over a wide range of advance ratios, with or without full alignment of the duct wake, are compared with each other, as well as with results from RANS simulations and with measurements from an experiment.

Spatial Fluctuating Pressure Calculation of Underwater Counter Rotating Propellers under Noncavitating Condition

The spatial fluctuating pressure field (FPF) of counter rotating propeller (CRP) under noncavitating condition is investigated. The hydrodynamic performance and pressure distributions on the blade surfaces are obtained through low-order potential-based panel method, which is also used to analyze the hydrodynamic interaction between the front and rear propellers of CRP as well as the hydrodynamic interference between any solid surface and propeller. The interaction between the given solid spherical surface and propeller is used to simulate the spatial FPF of propeller, and the fluctuating pressure induced by a propeller over one revolution is analyzed in frequency domain through fast Fourier transform. The method proposed is validated through two given propellers by comparing the calculation results with test data. The FPFs of the front and rear propellers are calculated and compared with that of the corresponding single propeller. The result shows that the CRP produces weaker FPF compared with the single propeller.

STUDY ON THE STATIC AND DYNAMIC STABILITY OF A MODULAR AIRPLANE SYSTEM

The purpose of this research is an analysis of the static and dynamic stability of the Modular Airplane System (MAS). The MAS is designed to perform suborbital space flights. The concept assumes that two tailless vehicles bonded together form a conventional aircraft where the wing of the second one is used as the horizontal tail of the whole system. The CFD calculations, and the stability and control derivatives were conducted by the PANUKL package, which uses a low order panel method for the aerodynamic analysis. The analysis of the static and dynamic stability was performed by the SDSA package. Only the selected part of the MAS mission was investigated. The results that will be presented have been divided into three parts: static stability, longitudinal dynamic stability and lateral dynamic stability. The MAS has a few possible applications. The first one is a suborbital space tourism flight. Moreover, it can be used as a lunching vehicle for micro satellites or as a testing platform for new space technology to improve their TRL level. Finally, in the far future, it could be used as a fast point-to-point travel system. The paper presents the results of the static and dynamic stability of a unique aircraft configuration which consists of two tailless vehicles. The research focuses on a situation where the vehicles are just before separation and their mass is similar. Moreover, the influence of the second vehicle’s position with respect to the first one is included.

Prediction of tip vortex cavitation inception with low-order panel method

Tip vortex cavitation is the first type of cavitation to take place in most cases. Because it always produces radiated noise, avoiding or at least delaying tip vortex cavitation is crucial for achieving low radiated noise emissions. The present study aims to predict the tip vortex cavitation inception with the low-order panel method, which is widely used at the early propeller design stage. First, a velocity smoothing parameter varying with the age of vortex is adopted to align the wake. This leads to a wake shape that coincides very well with the wake pattern from a RANS solver. A consistent formula for evaluating the smoothing parameter for different cases is also achieved with the fitting method. Second, the tip vortex circulation is calculated based on the converged wake shape and doublet distribution. This procedure is found to be independent from the panel size. Finally, based on the minimum pressure distribution along the tip vortex, cavitation inception numbers are obtained for the Potsdam Propeller Test Case (PPTC) and the propeller 4383 developed in NSRDC. The results show a good agreement with the experimental measurements.

Computation of hydrodynamic mass and damping coefficients for a cavitating marine propeller flow using a panel method

The present paper deals with the numerical calculation of hydrodynamic mass and damping coefficients under consideration of unsteady sheet cavitation on marine propeller flows. In the first part of the paper, the mathematical and numerical background behind the numerical method is introduced. The numerical calculations carried out in this work are based on a low-order panel method. Panel methods belong to the class of collocation techniques and are applied to obtain a numerical solution of a potential flow based system of boundary integral equations. They are suitable for the present application because of their short computation time which makes them applicable in the design process of marine propellers.Additionally, two different approaches for the determination of hydrodynamic masses and damping are introduced in this work. The hydrodynamic masses and damping are important in studies of the ship motion in seaway and in the analysis of vibrations of a vessel and its appendages. The developed approaches are applied on a propeller flow in heave motion. Hereby, the calculations are performed for a non-rotating and rotating propeller under non-cavitating and cavitating conditions. The results obtained from the simulations are discussed in detail and an outlook is given.

Aeroelastic two-level optimization for preliminary design of wing structures considering robust constraints

An aeroelastic two-level optimization methodology for preliminary design of wing structures is presented, in which the parameters for structural layout and sizes are taken as design variables in the first-level optimization, and robust constraints in conjunction with conventional aeroelastic constraints are considered in the second-level optimization. A low-order panel method is used for aerodynamic analysis in the first-level optimization, and a high-order panel method is employed in the second-level optimization. It is concluded that the design of the abovementioned structural parameters of a wing can be improved using the present method with high efficiency. An improvement is seen in aeroelastic performance of the wing obtained with the present method when compared to the initial wing. Since these optimized structures are obtained after consideration of aerodynamic and structural uncertainties, they are well suited to encounter these uncertainties when they occur in reality.

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

In the present work isogeometric analysis is applied to the solution of the boundary integral equation associated with the Neumann–Kelvin problem and the calculation of the wave resistance of ships. As opposed to low-order panel methods, where the body is represented by a large number of quadrilateral panels and the velocity potential is assumed to be piecewise constant (or approximated by low degree polynomials) on each panel, the isogeometric concept is based on exploiting the same NURBS basis, used for representing exactly the body geometry, for approximating the singularity distribution (and, in general, the dependent physical quantities). In order to examine the accuracy of the present method, numerical results obtained in the case of submerged and surface piercing bodies are compared against analytical solutions, experimental data and predictions provided by the low-order panel or other similar methods appeared in the pertinent literature, illustrating the superior efficiency of the isogeometric approach. The present approach by applying isogeometric analysis and boundary element method to the linear NK problem has the novelty of combining modern CAD systems for ship-hull design with computational hydrodynamics tools.

Robust geometric sizing of a small flying wing planform based on evolutionary algorithms

AbstractIn this paper a geometric sizing method for a small electric powered flying wing is proposed. The geometric sizing method aims to reduce the effects of variations in the power plant characteristics on endurance. This results in a single-objective design optimisation problem where the sensitivity to power plant characteristics of the endurance equation is minimised, constrained to Reynolds number, wing load, wing taper ratio, aircraft size and wing sweep angle. As a result, geometric characteristics of the flying wing such as span, tip chord and root chord are obtained. Flying wing aerodynamic characteristics are obtained by means of an inviscid fluid flow analysis program of the type low-order panel methods, known as CMARC. The optimisation problem involves a non convex function so that it is necessary to rely on heuristic programming methods. In particular an Evolutionary Algorithm based on differential evolution is considered.

A Wake Model for the Prediction of Propeller Performance at Low Advance Ratios

A low order panel method is used to predict the performance of propellers. A wake alignment model based on a pseudounsteady scheme is proposed and implemented. The results from this full wake alignment (FWA) model are correlated with available experimental data, and results from RANS for some propellers at design and low advance ratios. Significant improvements have been found in the predicted integrated forces and pressure distributions.

Static Aeroelastic Response Analysis of Aircrafts Based on CFD Pressure Distribution

An analysis method for static aeroelastic response considering the effect of Computational Fluid Dynamics (CFD) aerodynamic pressure distribution was developed in this paper. The aerodynamic pressure and the steady aerodynamic influence coefficient matrix were computed by the high-order panel method and then were corrected according to CFD pressure distribution on the 3D body-surface panel element. The static aeroelastic response was solved by modal method coupling with the structural model. A high-aspect-ratio wing was taken as an example to evaluate the analysis method, and the aerodynamic pressure obtained by CFD method with Euler equation was used for aerodynamics correction on 3D body-surface panel element in this study case. The method was then evaluated by comparing the results with those from the low-order panel method using external aerodynamic pressure and the high-order panel method. The results indicate that the method could provide correct results. The method could be used in the preliminary stage as well as in the detailed stage of aircraft design to provide design guideline of static aeroelastic response analysis.

Open-Water Thrust and Torque Predictions of a Ducted Propeller System with a Panel Method

This paper discusses several modelling aspects that are important for the performance predictions of a ducted propulsor with a low-order Panel Method. The aspects discussed are the alignment of the wake geometry, the influence of the duct boundary layer on the wake pitch, and the influence of a transpiration velocity through the gap. The analysis is carried out for propeller Ka4-70 operating without and inside a modified duct 19A, in which the rounded trailing edge is replaced by a sharp trailing edge. Experimental data for the thrust and torque are used to validate the numerical results. The pitch of the tip vortex is found to have a strong influence on the propeller and duct loads. A good agreement with the measurements is achieved when the wake alignment is corrected for the presence of the duct boundary layer.

Application of High-order Panel Method in Static Aeroelastic Analysis of Aircraft

A static aeroelastic analysis method based on the high-order panel method and modal method has been recommended through two examples of a high-aspect-ratio wing and a low-aspect-ratio wing. The subsonic aerodynamic forces of a high-aspect-ratio wing and the subsonic/supersonic aerodynamic forces of a low-aspect-ratio wing are investigated in this study. The influences of elastic structural deformation on aerodynamic forces are studied with an emphasis on the aerodynamic coefficients, wing root loads, structural deformation and pressure distribution of different sections, and these results are compared with the results from low-order panel method and the results based on experimental aerodynamic forces. It is concluded that aerodynamic forces can be accurately calculated with the high-order panel method. The method presented in this study is feasible, credible and efficient. Comprehensive static aeroelastic characteristics can be provided by the method for initial phases of aircraft design.

Practical mathematical representation of the flow due to a distribution of sources on a steadily advancing ship hull

A practical mathematical representation of the flow velocity due to a distribution of sources on the mean wetted hull surface and the mean waterline of a ship that steadily advances along a straight path in calm water, of large depth and lateral extent, is presented. A main feature of this flow representation is a simple analytical approximation—valid within the entire flow region—to the local flow component in the expression for the gradient of the Green function associated with the classical Kelvin–Michell linearized free-surface boundary condition. Another notable feature of the flow representation is that the singularity associated with the gradient of the Green function is removed, using a straightforward regularization technique. The flow representation only involves elementary continuous functions (algebraic, exponential and trigonometric) of real arguments. These functions can then be integrated using ordinary Gaussian quadrature rules. Thus, the flow representation is particularly simple and well suited for practical flow calculations. The specific case of a low-order panel method—in which the hull geometry, the source density, and the flow velocity are consistently represented via piecewise linear approximations within flat triangular hull panels or straight waterline segments—is considered.