Sensitivity analysis of spacecraft in micrometeoroids and orbital debris environment based on panel method

To reduce the risk of mission failure caused by the MM/OD impact of the spacecraft,it is necessary to optimize the design of the spacecraft.Spacecraft survivability assessment is the key technology in the optimal design of spacecraft.Spacecraft survivability assessment includes spacecraft impact sensitivity analysis and spacecraft component vulnerability analysis under MM/OD environment.The impact sensitivity refers to the probability of a spacecraft encountering an MM/OD impact while in orbit.Vulnerability refers to the probability that each component of a spacecraft may fail or malfunction when impacted by space debris.Yet this paper mainly analyzes the impact sensitivity and proposes a spacecraft sensitivity assessment method under the MM/OD environment based on a panel method.Under this panel method,a spacecraft geometric model is discretized into small panels,and whether they are impacted by MM/OD or not is determined through the analysis of the shielding or shadowing relationships between panels.The number of impacts on each panel is obtained through calculation,and accordingly the probability of each spacecraft component encountering MM/OD impact can be acquired,thus generating the impact sensibility.This paper extracts data from the NASA’s ORDEM2000,the ESA’s MASTER8 as well as the SDEEM2015(Space Debris Environmental Engineering Model developed by HIT),and uses the PCHIP(Piecewise Cubic Hermite Interpolating Polynomial)method to interpolate and fit the size-flux relationship of space debris.Compared with linear interpolation and cubic spline interpolation,the fitting results through the method are relatively more accurate.The feasibility of this method is also demonstrated through two actual examples shown in this paper,whose results are close to those from ESABASE,although there are some minor errors mainly due to different debris data input.Through the cross-check by three risk assessment software-BUMPER,MDPANTO and MODAOST-under standard operating conditions,the feasibility of this method is again verified.

Using the surface panel method to predict the steady performance of ducted propellers

A new numerical method was developed for predicting the steady hydrodynamic performance of ducted propellers. A potential based surface panel method was applied both to the duct and the propeller, and the interaction between them was solved by an induced velocity potential iterative method. Compared with the induced velocity iterative method, the method presented can save programming and calculating time. Numerical results for a JD simplified ducted propeller series showed that the method presented is effective for predicting the steady hydrodynamic performance of ducted propellers.

A Havelock Source Panel Method for Near-surface Submarines

A panel method is described for calculating potential flow around near-surface submarines. The method uses Havelock sources which automatically satisfy the linearized free-surface boundary condition. Outputs from the method include pressure field, pressure drag, wave resistance, vertical force, trim moment and wave pattern. Comparisons are made with model tests for wave resistance of Series 58 and DARPA SUBOFF hulls, as well as with wave resistance, lift force and trim moment of three length-to-diameter variants of the DSTO Joubert submarine hull. It is found that the Havelock source panel method is capable of determining with reasonable accuracy wave resistance, vertical force and trim moment for submarine hulls. Further experimental data are required in order to assess the accuracy of the method for pressure field and wave pattern prediction. The method is implemented in the computer code“HullWave”and offers potential advantages over RANS-CFD codes in terms of speed, simplicity and robustness.

Analysis of Influencing Factors on Lift Coefficients of Autonomous Sailboat Double Sail Propulsion System Based on Vortex Panel Method

Sail is the core part of autonomous sailboat and wing sail is a new type of sail. Wing sail generates not only propulsion but also lateral force and heeling moment. The latter two will affect the navigation status and bring resistance. Double sail can effectively reduce the center of wind pressure and heeling moment. In order to study the effect of distance between two sails, airfoil and attack angle on the total lift coefficient of double sail propulsion system, pressure coefficient distribution and lift coefficient calculation model have been established based on vortex panel method. By using the basic finite solution, the fluid dynamic forces on the two-dimensional sails are computed.The results show that, the distance in the range of 0 to 1 time chord length, when using the same airfoil in the fore and aft sail, the total lift coefficient of the double sail increases with the increase of distance, finally reaches a stable value in the range of one to three times chord length. Lift coefficients of thicker airfoils are more sensitive to the change of distance. The thicker the airfoil, the longer distance is required of the total lift coefficient toward stable.When different airfoils are adopted in fore and aft sail, the total lift coefficient increases with the increase of the thickness of aft sail. The smaller the thickness difference is, the more sensitive to the distance change the lift coefficient is. The thinner the fore sail is, the lower the influence will be on the lift coefficient of aft sail.

Study on Wave Added Resistance of a Deep-V Hybrid Monohull Based on Panel Method

In this paper, a panel method based on three dimensional potential flow theory is used to study the problem of wave added resistance. The time-domain motion response of Wigely III ship in head waves is calculated by AQWA, and then the wave added resistance of ship is obtained by near-field pressure integration method. By comparing the calculated results with the experimental data in literature, it is shown that the variation trend and peak value are in good agreement, and the accuracy and efficiency meet the research requirements. Based on the above mentioned method, the wave added resistance of a deep-V hybrid monohull in head waves is studied. The motions and wave added resistances of the deep-V hybrid monohull and the deep-V original ship advancing in head waves with various forward speed and wave frequencies are calculated and analyzed. The results show that the longitudinal motion response of the deep-V hybrid monohull is effectively suppressed and the wave added resistance is obviously reduced, the new type of ship has good engineering application prospects. The present method provides an approach of satisfactory accuracy and efficiency to predict wave added resistance of ships voyaging in waves.

Prediction of Hydrodynamic Performance of Marine Propellers by Surface Panel Method

The potential based low order surface panel method is used to predict the hydrodynamic performance of marine propellers. In present method the hyperboloidal quadrilateral panels are employed to avoid the gap between the panels. The influence coefficients of panels are calculated by Morino’s analytical formulations for increasing numerically calculating speed. The pressure Kutta condition is satisfied on the trailing edge of propeller blade by Newton-Raphson iterative procedure. Therefore the pressure coefficients of the suction and pressure faces of blade are equal on trailing edge. The method developed by Yanagizawa is used to determine the velocities on propeller surface, and to avoid the singularity in the numerical differentiation. The predicted pressure distributions and open water performances of general propellers and highly skewed propellers have a good agreement with experimental dat and other calculation results.

Propulsion Performance of Spanwise Flexible Wing Using Unsteady Panel Method

In this paper, the propulsion performance of a spanwise flexible oscillating wing, which is broadly similar to the undulation of a fin fluke, is investigated. The geometry of the fluke underwent three prescribed harmonic oscillating motions simultaneously while surging with constant velocity. The effect of deflection phase angle, flexibility parameter, and wing tip deflection amplitude on thrust coefficient and swimming efficiency was studied. A low-order unsteady panel method coupled with a time stepping algorithm for free wake alignment is implemented in a computer program to estimate the propulsion efficiency of lifting bodies. A novel approach is introduced to evaluate the singular integrals of line vortices by using an adaptive mollifier function. This method is an efficient way to accelerate computational speed by reducing the order of problem from R^3 to body boundaries. Results present the significant effect of phase angle on the propulsion characteristics of oscillating fluke.

Study on Wave Added Resistance of Ships in Oblique Waves Based on Panel Method

When the ship is sailing at sea,wave added resistance has great influence on the rapidity and economy of the ship.With the increasing pressure of energy and environmental protection,IMO has proposed the EEDI formula of the newly built ships,which restricts the energy consumption standard of civil ships more strictly.Therefore,a panel method based on three dimensional potential flow theory is proposed to study the problem of wave added resistance in this paper.Firstly,the method solves the motion responses of the ship in the time domain,and then calculates the wave added resistance of the ship by near-field pressure integration method.The wave added resistance of S175 container ship in head and oblique waves are calculated and compared with the experimental data,and the accuracy of the proposed method are verified.At last,the influence of Froude number and wave direction angle on wave added resistance is studied.The proposed method provides an approach of satisfactory accuracy and efficiency for the development of high-performance new ship forms,optimization of ship hull lines,comprehensive performance evaluation of ships and practical navigation guidance.

Aerodynamic Performances of Wind Turbine Airfoils Using a Panel Method

One of the key features of Laplace＇s Equation is the property that allows the equation governing the flow field to be converted from a 3D problem throughout the field to a 2D problem for finding the potential on the surface. The solution is then found using this property by distributing ＂singularities＂ of unknown strength over discretized portions of the surface： panels. Hence the flow field solution is found by representing the surface by a number of panels, and solving a linear set of algebraic equations to determine the unknown strengths of the singularities. In this paper a Hess-Smith Panel Method is then used to examine the aerodynamics of NACA 4412 and NACA 23015 wind turbine airfoils. The lift coefficient and the pressure distribution are predicted and compared with experimental result for low Reynolds number. Results show a good agreement with experimental data.

Numerical Computation of Motions and Structural Loads for Large Containership using 3D Rankine Panel Method

In this paper, we present the results of our numerical seakeeping analyses of a 6750-TEU containership, which were subjected to the benchmark test of the 2 nd ITTC–ISSC Joint Workshop held in 2014. We performed the seakeeping analyses using three different methods based on a 3D Rankine panel method, including 1) a rigid-body solver, 2) a flexible-body solver using a beam model, and 3) a flexible-body solver using the eigenvectors of a 3D Finite Element Model(FEM). The flexible-body solvers adopt a fully coupled approach between the fluid and structure. We consider the nonlinear Froude–Krylov and restoring forces using a weakly nonlinear approach. In addition, we calculate the slamming loads on the bow flare and stern using a 2D generalized Wagner model. We compare the numerical and experimental results in terms of the linear response, the time series of the nonlinear response, and the longitudinal distribution of the sagging and hogging moments. The flexible-body solvers show good agreement with the experimental model with respect to both the linear and nonlinear results, including the high-frequency oscillations due to springing and whipping vibrations. The rigid-body solver gives similar results except for the springing and whipping.

Multigrid ILU Panel Method for the Calculation of Wavemaking Resistance

Panel methods for the calculation of wavemaking resistance result in a linear equation system for the unknown singularities.The coefficient matrix is full but not well conditioned.In this paper an incomplete LU decomposition (ILU) method and a combined multigrid ILU method are used to solve the linear system.Systematic computations using the ILU method have shown that the CPU time can be reduced to 30% to 40% of that using an incomplete Gaussian elimination method. In the proposed multigrid ILU method an averaged restriction and a piecewise constant prolongation are used.The construction of the coefficient matrix at coarse levels is based on geometrical considerations.It turns out that the condition of the relative consistency is fulfilled.Comparison computations have shown that nearly the same results were obtained.However,due to additional CPU time needed for the execution of the matrix vector products in the restriction and the prolongation proceses of the multigrid method,a further reduction of the total CPU time could not be reailized.

RADAR CROSS-SECTION COMPUTATIONS OF ARBITRARILY COMPLICATED TARGETS BY APPLYING THE PANEL METHOD

The present paper deals with the method for the radar cross-section (RCS)computations of arbitrarily complicated targets based on the work by D. Klement et al.(1988).This method is convenient in use, fast in operation and precise in calculating RCS of a complicatedtarget. With this method, the RCS of classic scatterers, for example, a cone and a cylinder, arecomputed with the result of good agreement with experimental data. Furthermore, the RCS’of an aircraft model at various attitudes are calculated with the result of good agreement withexperimental data also.

Non-Dimensional Values for Convergence of Lift Prediction Using Panel Method

This paper presents an implementation and posterior analysis of the convergence of the panel method. The implemented panel method is based on vortex lines and an unsteady wake on a flat plate as a wing. The main goal of the study was to discover parameters and their values range to obtain convergence of the solution. Results of lift convergence in function of control panel’s position, the effect of the size of the wake panels, the dimension of the wake, and the computation time are quantitatively described. The lift results are similar to the predictions by the lifting-line theory and the wake exhibited an expected shape, showing wingtip, and start vortices. Geometric parameters and non-dimensional values were developed to increase accuracy and stability of the method.

PREDICTION OF UNSTEADY CAVITATION OF PROPELLER USING SURFACE PANEL METHOD

This paper has predicted the range and volume of unsteady sheet cavitation of a propeller by using the surface panel method. The linearization in cavity thickness is adopted to reduce the computing time and storage space. The iteration scheme between chordwise strips has been used because the range and volume of cavitation are both unknown. The propeller cavitation range determined by the calculation method presented in this paper agrees with the observation results of cavity image at cavitation tunnel very well, and this proves the practicability of the method.

NUMERICAL SIMULATIONS OF WAVE-INDUCED SHIP MOTIONS IN TIME DOMAIN BY A RANKINE PANEL METHOD

A time domain prediction of wave-induced ship motions by a Rankine panel method is investigated. Linear boundary conditions on free surface and mean wetted body surface are adopted, while the numerical damping method is used for the radiation conditions. The motions of two ships in regular head waves are computed by the present method. The related numerical results are compared with the experiment data and those from linear strip theory. The comparison shows satisfactory agreements for pitch and heave transfer functions.

PREDICTION OF PODDED PROPELLER CAVITATION USING AN UNSTEADY SURFACE PANEL METHOD

The unsteady sheet cavitation of podded propeller was predicted by using a surface panel method. The interaction between propeller and pod was treated with the iterative calculation of induced velocity potential, and the method of induced velocity potential can save a great deal of storage and computation time compared to the method of induced velocity. The induced velocity potential of unit singularity on every pod panel to every key blade panel and of unit singularity on every key blade panel and its wake panel to every pod panel were calculated when the key blade is at every angle position. Based on the wake model of the conventional single propeller, a new wake model of podded propeller was constructed. The propeller is analyzed only on the key blade in order to save computation time and memory space. The method can be used to calculate the hydrodynamics performance and cavitation of propeller in uniform and non-uniform inflows. It can give the unsteady force and cavitation shape of propeller. The propeller cavitation range determined by the present method agrees with the observation results of cavity image given in cavitation tunnel well, and this proves the practicability of the method.

A method for static aeroelastic analysis based on the high-order panel method and modal method

A method for static aeroelastic analysis based on the high-order panel method and modal method is presented. The static aeroelastic characteristics of flexible wings are investigated using this method. Three-dimensional aerodynamic models of flexible wings are constructed based on the geometry of wing configuration, and the modal method is adopted to achieve the fluid-structure coupling. The static aeroelastic characteristics of the AGARD445.6 wing and a low-aspect-ratio wing are investigated in this study. The influences of elastic structural deformation on aerodynamic forces are studied with an emphasis analyzing the aerodynamic coefficients, wing root loads, structural deformation and pressure distribution of different sections, and results are compared with the results from wind-tunnel tests and the elastic 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 early phases of aircraft design.

A THREE-DIMENSIONAL DESINGULARIZED HIGH ORDER PANEL METHOD BASED ON NURBS

A desingularized high order panel method based on Non-Uniform Rational B-Spline （NURBS） was developed to deal with three-dimensional potential flow problems. A NURBS surface was used to precisely represent the body geometry. Velocity potential on the body surface was described by the B-spline after the source density distribution on the body surface had been solved. The collocation approach was employed to satisfy the Neurnann boundary condition and Gaussian quadrature points were chosen as both the collocation points and the source points. The singularity was removed by a combined method, so the process of the numerical computation was non-singular. In order to verify the method proposed, the unbounded flow problems of sphere and ellipsoid, the wave-making problem of a submerged ellipsoid were chosen as computational examples. It is shown that the numerical results are in good agreement with analytical solutions and other numerical results in all cases, and sufficient accuracy of numerical solution can be reached with a small number of panels.

A RAISED PANEL METHOD BASED ON NURBS FOR FREE-SURFACE POTENTIAL FLOWS WITH FORWARD SPEED

A raised panel method based on NURBS (Non-Uniform Rational B-Splines) forfree-surface flows with forward speed is presented. In this generalized panel method, NURBS areemployed to represent the body geometry, disturbed free surface, and to express the unknown sourcestrength distribution, on the body surface and above the free surface. Compared with commonhigher-order panel methods, it has no need of adopting local coordinates. NURBS make the geometryrepresentation of the body shape and the wave pattern more precise. Raised panels above the freesurface produce less numerical dispersion error, need less CPU consumption and are helpful andcombined with collocation-point shifting up-stream, can satisfy the radiation condition numerically.By using continuous and discrete Fourier analysis, numerical errors of this method are discussedand a general expression for the errors of numerical damping and dispersion, including the effectsof the vertical distance of singularities to the free surface, the order of singularity distributionrepresented by B-splines in panels, and collocation-point shifting is derived.

Prediction of Hydrodynamic Forces on a Moored Ship Induced by a Passing Ship in Shallow Water Using a High-Order Panel Method

A three-dimensional high-order panel method based on non-uniform rational B-spline(NURBS) is developed for predicting the hydrodynamic interaction forces on a moored ship induced by a passing ship in shallow water. An NURBS surface is used to precisely represent the hull geometry. Velocity potential on the hull surface is described by B-spline after the source density distribution on the boundary surface is determined. A collocation approach is applied to the boundary integral equation discretization. Under the assumption of low passing speed, the effect of free surface elevation is neglected in the numerical calculation, and infinite image method is used to deal with the finite water depth effect. The time stepping method is used to solve the velocity potential at each time step. Detailed convergence study with respect to time step, panel size and Green function is undertaken. The present results of hydrodynamic forces are compared with those obtained by slender-body theory to show the validity of the proposed numerical method. Calculations are conducted for different water depths and lateral distances between ships, and the detail results are presented to demonstrate the effects of these factors.