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.

Unified analysis for stabilized methods of low-order mixed finite elements for stationary Navier-Stokes equations

A unified analysis is presented for the stabilized methods including the pres- sure projection method and the pressure gradient local projection method of conforming and nonconforming low-order mixed finite elements for the stationary Navier-Stokes equa- tions. The existence and uniqueness of the solution and the optimal error estimates are proved.

OPTIMIZATION OF AUTOBODY PANEL STAMPING PROCESS BASED ON DYNAMIC EXPLICIT FINITE ELEMENT METHOD

Taking CPU time cost and analysis accuracy into account, dynamic explicit finite ele- ment method is adopted to optimize the forming process of autobody panels that often have large sizes and complex geometry. In this paper, for the sake of illustrating in detail how dynamic explicit finite element method is applied to the numerical simulation of the autobody panel forming process,an example of optimization of stamping process pain meters of an inner door panel is presented. Using dynamic explicit finite element code Ls-DYNA3D, the inner door panel has been optimized by adapting pa- rameters such as the initial blank geometry and position, blank-holder forces and the location of drawbeads, and satisfied results are obtained.

An Efficient Method for Local Buckling Analysis of Stiffened Panels

The local buckling of stiffened panels is one of possible failure modes and concerned by engineers in the preliminary design of lightweight structures. In practice,a simplified model,i.e.,a rectangular plate with elastically restrained along its unloaded edges,is established and the Ritz method is usually employed for solutions. To use the Ritz method,however,the loaded edges of the plate are usually assumed to be simply supported. An empirical correction factor has to be used to account for clamped loaded edges. Here,a simple and efficient method,called the quadrature element method(QEM),is presented for obtaining accurate buckling behavior of rectangular plates with any combinations of boundary conditions, including the elastically restrained conditions. Different from the conventional high order finite element method(FEM),non-uniformly distributed nodes are used,and thus the method can achieve an exponential rate of convergence. Formulations are worked out in detail. A computer program is developed. Improvement of solution accuracy can be easily achieved by changing the number of element nodes in the computer program. Several numerical examples are given. Results are compared with either existing solutions or finite element data for verifications. It is shown that high solution accuracy is achieved. In addition,the proposed method and developed computer program can allow quick analysis of local buckling of stiffened panels and thus is suitable for optimization routines in the preliminary design stage.

Numerical-experimental method for elastic parameters identification of a composite panel

A hybrid numerical-experimental approach to identify elastic modulus of a textile composite panel using vibration test data is proposed and investi- gated. Homogenization method is adopted to predict the initial values of elastic parameters of the composite, and parameter identification is transformed to an optimization problem in which the objective function is the minimization of the discrepancies between the experimental and numerical modal data. Case study is conducted employing a woven fabric reinforced composite panel. Three parameters （Ell, E22, G12） with higher sensitivities are selected to be identified. It is shown that the elastic parameters can be accurately identified from experimental modal data.

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.

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.

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.

Dynamic Response of the U-Typed Sandwich Panel Under Explosion Load Based on the SDOF Method

Sandwich panel is commonly used in ship and marine engineering equipment,such as side structure and superstructure deck of a ship,which is of good anti-explosion performance.This paper addresses a study on the dynamic response of the U-typed sandwich panel under explosion load through the numerical simulation and theoretical methods.Based on the orthotropic plate theory,the U-typed sandwich panel is simplified and transformed into a single degree of freedom(SDOF)spring system,the equivalent motion equation of the SDOF system and the expression of triangular explosion load function are established based on the SDOF theory,and the maximum response spectrum of the SDOF system is obtained.Then,the response of the equivalent SDOF system of the U-typed sandwich panel under explosion load is analyzed,and the theoretical results match well with the numerical simulation results,which verifies the accuracy of the theoretical method proposed in this paper.The theoretical method proposed in this paper could have good engineering applications for the structural anti-explosion design,and provide a reference for the evaluation of the anti-explosion performance of ship and offshore platform structures.

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.

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.

Vibration analysis of steel structures including the effect of panel zone flexibility based on the energy method

New approximate formulas are proposed to determine the natural frequencies of structures considering the effects of panel zone flexibility and soil-structure interaction. Several structures with various earthquake resisting systems are idealized as prismatic cantilever flexural-shear beams. Floor masses are considered as lumped masses at each story level and masses of columns are evenly distributed along the cantilever beam. Soil-structure interaction is considered as axial and rotational springs, whose potential energy are formulated and incorporated into overall potential energy of the structure. Subsequently, natural frequency equations are derived on the basis of energy conservation principle. The effect of axial forces on natural frequency is also considered in the proposed formulas. Using the method presented in this study, natural frequencies are computed using a simplified method with no complex numerical modeling. The proposed formulas are verified via experimental and numerical methods. Close agreement between the results from these three approaches are observed. Furthermore, the effects of panel zone flexibility, continuity plates and doubler plates on the natural frequencies of buildings are investigated.

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.

AN IMPROVEMENT FOR LOWER－ORDER PANEL METHOD BASED ON THE DIRICHLET BOUNDARY CONDITION

An improved algorithm for velocity field of general configurations ispresentd for low-order panel method based on the internal Dirichlet boundary condi-tion. A direct calculating method for the velocity distribution by means of a limit pro-cess combining with analytic evaluation of higher-order singular integrals instead of theconventional method of doublet strength gradient is devised in order to avoid the diffi-culty of edge extrapolation of doublet strength. The problem of substantialunderpredictions of the induced drag coefficient obtained from the VSAERO analysisdisappears for the present improved algorithm. Illustrative calculations for several testcases such as swept back wing, swept forward wing and wing-body combination showthat the accuracy of results may be improved and is competitive with high-order panelmethod. In addition, the present direct integral method can be used to evaluate the ve-locity distribution for external flow field correctly, where the method of gradient cannot be used at all.

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.

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.