A rapid calculation method for hydroplaning loads of water surface aircraft considering aerodynamic lift

Abstract

This invention discloses a rapid calculation method for the hydroplaning load of a surface vehicle considering aerodynamic lift, comprising (1) calculating the damping coefficient, added mass, and lift magnitude of the surface vehicle; and (2) calculating all forces by considering nonlinear factors in the motion process of the surface vehicle through nonlinear slicing theory, and then performing calculations based on torque balance. This method can significantly reduce computation time and computational resources, effectively improving the design efficiency and calculation accuracy of surface vehicles, and greatly reducing human and computational resources.

Description

Technical Field

[0001] This invention belongs to the field of load calculation technology for surface aircraft, and particularly relates to a rapid calculation method for the water skidding load of surface aircraft that takes into account aerodynamic lift. Background Technology

[0002] Compared to traditional land-based aircraft, waterplanes can take off and land in various scenarios, including rivers, lakes, and seas, making them suitable for multiple applications such as transportation, firefighting, and water rescue. However, when waterplanes perform takeoffs and landings in complex water environments, the overloads on their components far exceed those on land. The interaction between the aircraft's bottom and even the sides, where they wade through water, and the waves causes the model to experience various forces during the waterplane landing process, including wind and wave drag, hydrodynamic drag, wave-making drag, and aerodynamic lift. This results in excessive loads on the fuselage components, potentially damaging parts of the aircraft's structure. Furthermore, when moving through waves, waterplanes experience significant turbulence, generating substantial waterplane loads. These loads are primarily used to check and control the overall strength of the wings and fuselage, and are one of the main load conditions for waterplanes. On the other hand, the fuselage also generates significant bending moments, especially during forced landings on wavy water surfaces. These bending moments, coupled with those generated by low-frequency waves, can lead to a loss of overall longitudinal strength of the fuselage. Therefore, it is feasible and necessary to conduct numerical calculations on the water skidding characteristics, water skidding loads, and attitude changes of surface vehicles in high sea states, and to study the load variation laws of the model. Simultaneously, surface vehicles generate upward lift during the water skidding process; considering the influence of lift on the water skidding loads better reflects the model's state during water skidding. Furthermore, most of the influences experienced by surface vehicles during water skidding are nonlinear; employing nonlinear calculation methods can improve the accuracy of water skidding load calculations. Numerical calculations to study the overall water skidding performance of surface vehicles, as well as overload and bottom pressure during water skidding, can further improve the safety and reliability of surface vehicles during water skidding, reduce design costs and design cycles, and have significant guiding significance and practical value for surface vehicle research. In previous studies on water skidding loads, there are many numerical calculation methods, the most common being: the original slice theory, the high-speed slender body theory, the three-dimensional surface element method, and the nonlinear slice theory.

[0003] The original slice theory, with its advantages of simple modeling, high computational efficiency, and accuracy meeting engineering requirements, is widely used in ship design. However, it has significant errors in predicting the motion response and wave loads of ships with low encounter frequencies, wide hulls, and high Froude numbers. The high-speed slender-hull ship model is an extension of the conventional slice method. This theory considers the three-dimensional flow field effect of the free surface and can accurately predict the wave loads and motion response of high-speed ships, but it is not suitable for wide, bulky hulls with relatively low speeds.

[0004] The three-dimensional surface element method (3FEM) is a numerical method based on the boundary element method (BEM) and is suitable for solving boundary value problems in fluid flow. It divides the flow field into many small surface elements, assuming constant flow variables on each element. By solving the boundary conditions on these surface elements, the solution for the entire flow field is obtained. It is applicable to ships and marine structures of arbitrary shapes, but its analysis process is relatively complex and computationally intensive, requiring high numerical computational capabilities. Secondly, for high Reynolds number flows, the presence of vortices necessitates more frequency domain modes to obtain accurate results. Furthermore, the 3FEM requires highly precise mesh generation when dealing with viscous flows.

[0005] Nonlinear slice theory employs an analytical method based on the original slice theory, taking into account various nonlinear factors and the change of the instantaneous wetted surface of the fuselage over time. This theory is widely used in the calculation of wave loads on ships, but it does not involve the calculation of aerodynamic lift, added mass, and damping coefficients generated during the motion of surface aircraft. Summary of the Invention

[0006] Purpose of the invention

[0007] To address the shortcomings and problems in existing methods for calculating hydroplaning loads, this invention provides a rapid calculation method for hydroplaning loads of water surface vehicles that takes aerodynamic lift into account. This method can quickly and accurately calculate the wave hydroplaning loads of water surface vehicles, meeting technical requirements.

[0008] Invention Technology Solutions

[0009] A rapid calculation method for the hydroplaning load of a surface aircraft that takes into account aerodynamic lift includes the following steps:

[0010] (1) Calculate the damping coefficient, added mass, and lift of the surface aircraft;

[0011] (2) By using nonlinear slice theory, considering the nonlinear factors in the motion process of the water surface aircraft, all forces are calculated and then calculated based on torque balance.

[0012] Preferably, step (1) is calculated using the two-dimensional source-sink method, specifically including the following process:

[0013] Let p(x,y) be any point in the flow field, and q(ξ,η) on the surface C be the location of the strong source; the Green's function in two-dimensional finite water depth is represented by G(x,y,ξ,η,t), which satisfies the continuity equation, as well as the boundary conditions at infinity, the seabed condition, and the free surface condition. Then, the integral form of the Green's function can be obtained:

[0014] G(x,y,ξ,η,t)=g(x,y,ξ,η)·e -iωt

[0015] Where: e-iωt Let g(x,y,ξ,η) be the time term and g(x,y,ξ,η) be the spatial Green's function.

[0016]

[0017] The mixture model is derived using the Green's function as follows:

[0018]

[0019] Where D represents the fluid domain. Let G(p,q) be the stream function on the surface boundary, and let it be a point source. For point dipoles, S q The area of ​​the surface element on the perimeter;

[0020] Within the watershed R, there must exist certain Green's functions P and Q that satisfy Green's theorem, the potential flow assumption, and the boundary conditions. Therefore:

[0021]

[0022] make Applying Green's theorem to the two-dimensional source-emission theory within a watershed, the integral equation is:

[0023]

[0024] Where: the watershed R is a simply connected domain with boundary L;

[0025] L = C' + C + C a ;

[0026] C'=C F +C -∞ +C B +C ∞ +C F ;

[0027] C a For the finite domain boundary of the fluid particles;

[0028] C is the boundary of the object surface.

[0029] By dividing the area into line integrals, we can obtain:

[0030]

[0031] therefore:

[0032] Diffraction problem:

[0033] Radiation issues: in It is the unit normal vector;

[0034] Divide the wet boundary of the object surface C into N segments, with endpoints (ξ). j ,η j The midpoint coordinates are (x, y). j ,y j ), where node number j = 1, 2, ..., N+1, segment number i = 1, 2, ..., N;

[0035] The cross-section can then be discretized into:

[0036]

[0037] Matrix it:

[0038]

[0039] but:

[0040] Diffraction problem:

[0041] Radiation issues:

[0042] From the above formula, we can see that by first obtaining the radiation potential, we can then obtain the added mass and damping coefficient.

[0043]

[0044] Where A ij For added mass, B ij is the damping coefficient.

[0045] Preferably, the forces in step (2) include buoyancy, gravity, inertial force, damping force, additional wave hydrodynamic force, slamming force, and wave forcing force.

[0046] Preferably, in step (2), by analyzing the forces acting on the micro-segment, the overall equation of motion can be obtained, and then the steady-state solution ζ and pitch θ of the water surface aircraft's motion, as well as the magnitude of the center of gravity acceleration a, can be obtained.

[0047] Preferably, the calculation process in steps (1) and (2) is implemented by writing code.

[0048] Preferably, the lift is calculated using the following formula:

[0049]

[0050] Where L represents lift; ρ represents air density; V represents flight speed; S represents the reference area of ​​the wing; C L This represents the lift coefficient.

[0051] The preferred formula for buoyancy is:

[0052] fs =-ρgA(x,t)

[0053] Where: ρ is the density of seawater, g is the gravitational acceleration, and A(x,t) is the draft area of ​​the seaplane.

[0054] The preferred formula for inertial force is:

[0055]

[0056] in: For the first-order partial derivative of rise and fall with respect to time, Let x be the second-order partial derivative of the pan / tilt motion with respect to time, and let x represent the longitudinal position of the slice. G Represents the vertical position of the center of gravity.

[0057] The preferred formula for damping force is:

[0058]

[0059] in: For the first-order partial derivative of rise and fall with respect to time, Let x be the first-order partial derivative of the pan / tilt motion with respect to time, and let x represent the longitudinal position of the slice. G The longitudinal position of the center of gravity is represented by U, the speed of the waterplane is represented by θ, the pitch is represented by N(x,t) and the damping coefficient of the current slice is represented by v. z The wave speed.

[0060] The preferred formula for impact force is:

[0061]

[0062] Where: M H (x,t) represents the added quality of the current slice. V(x,t) is the z-direction partial derivative of the added mass, and is the relative sailing speed under the wave.

[0063] Advantages of this invention: This method takes into account accessory mass, lift and nonlinear factors. It can reduce a lot of computing time and computing resources, effectively improve the design efficiency and calculation accuracy of surface aircraft, and greatly reduce human resources and computing resources. Attached Figure Description

[0064] Figure 1 This is a diagram illustrating lift.

[0065] Figure 2 This is a conceptual diagram of the source-sink method.

[0066] Figure 3 It is a schematic diagram of the discrete cross-section.

[0067] Figure 4This is a flowchart of the source-sink method calculation.

[0068] Figure 5 This is a schematic diagram of the nonlinear slice theory principle that takes into account aerodynamic lift.

[0069] Figure 6 This is a schematic diagram of the calculation process. Detailed Implementation

[0070] The present invention is achieved through the following technical solution.

[0071] A rapid calculation method for the hydroplaning load of a surface aircraft that takes into account aerodynamic lift includes the following steps:

[0072] a) Considering model lift

[0073] like Figure 1 As shown, the lift formula is used to calculate the lift force generated when an object moves in a fluid in fluid dynamics. The most common lift formula is based on Bernoulli's principle and fluid mechanics theory, especially for airfoils, fan blades, and other fluid power equipment.

[0074]

[0075] Where L represents lift; ρ represents air density; V represents flight speed; S represents the reference area of ​​the wing; C L The lift coefficient is a dimensionless coefficient that is related to wing shape, angle of attack, and aerodynamic characteristics.

[0076] b) Calculation of damping coefficient and added mass using the two-dimensional sink method

[0077] When the fuselage moves at high speed in waves, the added mass effect and damping effect have a significant impact. (Appendix) Figure 2 This diagram illustrates the calculation of damping coefficients and added mass using the two-dimensional source-sink method. Let p(x,y) be any point in the flow field, and q(ξ,η) on the surface C be the location of the strong source. The Green's function in two-dimensional finite water depth is represented by G(x,y,ξ,η,t), which satisfies the continuity equation and also the boundary conditions at infinity, the seabed condition, and the free surface condition. Therefore, the integral form of the Green's function can be obtained:

[0078] G(x,y,ξ,η,t)=g(x,y,ξ,η)·e -iωt

[0079] Where: e -iωt Let g(x,y,ξ,η) be the time term and g(x,y,ξ,η) be the spatial Green's function.

[0080]

[0081] Where: k is the wave number, h is the water depth, d is the draft, and v is the speed.

[0082] r 2 =(x-ξ) 2 +(y-η) 2

[0083] r1=(x-ξ) 2 +(y+2d+η) 2

[0084]

[0085] The mixture model is derived using the Green's function as follows:

[0086]

[0087] Where D represents the fluid domain. Let G(p,q) be the stream function on the surface boundary, and let it be a point source. For point dipoles, S q It represents the area of ​​the surface element on the perimeter.

[0088] Within the watershed R, there must exist certain Green's functions P and Q that satisfy Green's theorem, the potential flow assumption, and the boundary conditions. Therefore:

[0089]

[0090] make Applying Green's theorem to the two-dimensional source-emission theory within a watershed, the integral equation is:

[0091]

[0092] Where: the watershed R is a simply connected domain with boundary L;

[0093] L = C' + C + C a ;

[0094] C'=C F +C -∞ +C B +C ∞ +C F ;

[0095] C a C represents the finite domain boundary of the fluid particle; C represents the surface boundary.

[0096] By dividing the area into line integrals, we can obtain:

[0097]

[0098] therefore:

[0099] Diffraction problem:

[0100] Radiation issues: in φ is the unit normal vector. D For diffraction potential, φ R It represents the radiation potential.

[0101] Appendix Figure 3 As a profile discretization method, the wetted boundary of the object surface C is divided into N segments, with endpoints at (ξ). j ,η j The midpoint coordinates are (x, y). j ,y j ), where node number j = 1, 2, ..., N+1, and segment number i = 1, 2, ..., N.

[0102] Then it can be discretized into:

[0103]

[0104] Matrix it:

[0105]

[0106] but:

[0107] Diffraction problem:

[0108] Radiation issues:

[0109] From the above formula, we can see that by first obtaining the radiation potential, we can then obtain the added mass and damping coefficient.

[0110]

[0111] Where A ij For added mass, B ij The damping coefficient is... Let ω be the normal partial derivative of the velocity potential, and ω be the wave angular velocity.

[0112] The calculation process of the two-dimensional source-sink method is attached. Figure 4 As shown.

[0113] c) Application of nonlinear slicing to surface aircraft models

[0114] Traditional slicing theory divides an object along its length into several segments, each denoted as dx. b It is assumed that the fluid in each cross-section flows only in a plane, neglecting the interference between the slices. When the force f on each slice is calculated according to the planar flow assumption... i After that, it acts on the entire ship. i for:

[0115] f i =∫ L f i 'dx b

[0116] Nonlinear slice theory determines the fluid forces acting on a ship in waves by analyzing the velocity potential of the flow field around the fuselage and calculating the fluid pressure components of each part. It takes into account the nonlinear slamming load generated by the fuselage.

[0117] Based on the loads acting on the fuselage slices, they can be divided into several types of forces:

[0118] Buoyancy: The buoyancy of the fuselage in waves is proportional to the submerged area of ​​the fuselage, reflecting the static term of the fluid.

[0119] f s =-ρgA(x,t)

[0120] Where: ρ is the density of seawater, g is the gravitational acceleration, and A(x,t) is the draft area of ​​the seaplane.

[0121] gravity:

[0122] f g =W(x)

[0123] Where: W(x) is the slice quality of the surface aircraft.

[0124] Inertial force:

[0125]

[0126] in: For the first-order partial derivative of rise and fall with respect to time, Let x be the second-order partial derivative of the pan / tilt motion with respect to time, and let x represent the longitudinal position of the slice. G Represents the vertical position of the center of gravity.

[0127] Damping force:

[0128]

[0129] in: For the first-order partial derivative of rise and fall with respect to time, Let x be the first-order partial derivative of the pan / tilt motion with respect to time, and let x represent the longitudinal position of the slice. G The longitudinal position of the center of gravity is represented by U, the speed of the waterplane is represented by θ, the pitch is represented by N(x,t) and the damping coefficient of the current slice is represented by v. z The wave speed.

[0130] The hydrodynamic forces of waves acting on the fuselage can be classified into additional wave hydrodynamic forces and slamming forces.

[0131]

[0132] Impact force:

[0133]

[0134] Where: M H (x,t) represents the added quality of the current slice. V(x,t) is the z-direction partial derivative of the added mass, and is the relative sailing speed under the wave.

[0135] Additional wave hydrodynamics:

[0136]

[0137] in: This is the longitudinal partial derivative of the wave velocity. The longitudinal partial derivative of the added mass.

[0138] Wave forcing force is the sum of the Froude-Krylov force and diffraction force acting on a ship. Their expressions are:

[0139] F i DI =F i F-K +F i D

[0140]

[0141] Due to the instantaneous wet surface S of the fuselage B (t) and its average wetted surface S B The difference is small, therefore, when accurate to the first-order quantity, S in the above two equations... B (t) can be used by S B Replace. (Incident potential) Substituting (diffraction potential) into the above equation, we can obtain the expression for wave disturbance in the frequency domain:

[0142]

[0143] in: For heave and sag, ω is the wave angular velocity, ω e For the frequency of encounters, For radiation velocity potential,

[0144] The numbers below represent different directions, with β representing pitch.

[0145] By analyzing the forces acting on the infinitesimal segment dx, the equations of motion for the entire system can be obtained:

[0146]

[0147] In the above formula, f m To add wave hydrodynamics, f slam For impact force, f i For inertial force, f r For damping force, f g For gravity, f s For buoyancy, f F-K For Froude-Krylov force, f d For diffraction force, f a It is aerodynamic lift.

[0148] Using the above equations, we obtain the steady-state solutions ζ (heave) and θ (pitch) for the motion of the water surface vehicle, as well as the magnitude of a (acceleration at the center of gravity). The specific process is as follows: Figure 5 As shown.

[0149] d) Modular solution

[0150] like Figure 6 As shown, the nonlinear slice theory that takes into account aerodynamic lift, as well as the additional mass and damping coefficient, are modularly integrated and solved by formula. Only the required parameters need to be input, and the hydroplaning load of the model can be calculated quickly, which greatly improves the calculation efficiency and accuracy.

[0151] This method, based on the regular wave formula system, ensures the stability and periodicity of wave morphology during the calculation process, effectively avoiding the wave attenuation phenomenon commonly seen in experimental environments. When compared with experimental data and CFD analysis results, the predicted results shown by this invention maintain a small deviation from both, which not only verifies the scientific validity and accuracy of the method but also fully demonstrates its ability to accurately predict the dynamic response and hydroplaning loads of surface vehicles. Its prediction accuracy fully meets the acceptable standards for engineering applications.

[0152] The scope of protection of this invention is not limited to the embodiments described above. Obviously, those skilled in the art can make various modifications and variations to this invention without departing from its scope. If such modifications and variations fall within the scope of the claims of this invention and their equivalents, then the intent of this invention also includes these modifications and variations.

Claims

1. A method for rapidly calculating the hydroplaning load of a water surface vehicle considering aerodynamic lift, characterized in that, Includes the following steps: (1) Calculate the damping coefficient, added mass, and lift of the surface aircraft; (2) By using nonlinear slice theory, considering the nonlinear factors in the motion process of the water surface aircraft, all forces are calculated and then calculated based on torque balance. Step (1) is calculated using the two-dimensional source-sink method, specifically including the following process: Let p(x,y) be any point in the flow field, and q(ξ,η) on the surface C be the location of the strong source; the Green's function in two-dimensional finite water depth is represented by G(x,y,ξ,η,t), which satisfies the continuity equation, as well as the boundary conditions at infinity, the seabed condition, and the free surface condition. Then, the integral form of the Green's function can be obtained: G(x,y,ξ,η,t)=g(x,y,ξ,η)·e -iωt Where: e -iωt Let g(x,y,ξ,η) be the time term and g(x,y,ξ,η) be the spatial Green's function. The mixture model is derived using the Green's function as follows: Where D represents the fluid domain. Let G(p,q) be the stream function on the surface boundary, and let it be a point source. For point dipoles, S q The area of ​​the surface element on the perimeter; Within the watershed R, there must exist certain Green's functions P and Q that satisfy Green's theorem, the potential flow assumption, and the boundary conditions. Therefore: make Applying Green's theorem to the two-dimensional source-emission theory within a watershed, the integral equation is: Where: the watershed R is a simply connected domain with boundary L; L=C'+C+C a ; C'=C F +C -∞ +C B +C ∞ +C F ; C a For the finite domain boundary of the fluid particles; C is the boundary of the object surface. By dividing the area into line integrals, we can obtain: therefore: Diffraction problem: Radiation issues: in It is the unit normal vector; Divide the wet boundary of the object surface C into N segments, with endpoints (ξ). j ,η j The midpoint coordinates are (x, y). j ,y j ), where node number j = 1, 2, ..., N+1, segment number i = 1, 2, ..., N; The cross-section can then be discretized into: Matrix it: but: Diffraction problem: Radiation issues: From the above formula, we can see that by first obtaining the radiation potential, we can then obtain the added mass and damping coefficient. Where A ij For added mass, B ij is the damping coefficient.

2. The method for rapid calculation of hydroplaning load of a water surface vehicle considering aerodynamic lift as described in claim 1, characterized in that, The forces in step (2) include buoyancy, gravity, inertial force, damping force, additional wave hydrodynamic force, slamming force, and wave coercive force.

3. The method for rapid calculation of hydroplaning load of a water surface vehicle considering aerodynamic lift as described in claim 1, characterized in that, In step (2), by analyzing the forces acting on the micro-segment, the equation of motion of the whole can be obtained, and then the steady-state solution ζ and pitch θ of the motion of the water surface aircraft, as well as the magnitude of the acceleration a of the center of gravity, can be obtained.

4. The method for rapid calculation of hydroplaning load of a water surface vehicle considering aerodynamic lift as described in claim 1, characterized in that, The calculation process in steps (1) and (2) is implemented by writing code.

5. The method for rapid calculation of the hydroplaning load of a water surface vehicle considering aerodynamic lift as described in claim 1, characterized in that, The magnitude of lift is calculated using the following formula: Where L represents lift; ρ represents air density; V represents flight speed; S represents the reference area of ​​the wing; C L This represents the lift coefficient.

6. The method for rapid calculation of the hydroplaning load of a water surface vehicle considering aerodynamic lift as described in claim 2, characterized in that, The formula for buoyancy is: f s =-ρgA(x,t) Where: ρ is the density of seawater, g is the gravitational acceleration, and A(x,t) is the draft area of ​​the seaplane.

7. The method for rapid calculation of the hydroplaning load of a water surface vehicle considering aerodynamic lift as described in claim 2, characterized in that, The formula for inertial force is: in: For the first-order partial derivative of rise and fall with respect to time, Let x be the second-order partial derivative of the pan / tilt motion with respect to time, and let x represent the longitudinal position of the slice. G Represents the vertical position of the center of gravity.

8. The method for rapid calculation of hydroplaning load of a water surface vehicle considering aerodynamic lift as described in claim 2, characterized in that, The formula for damping force is: in: For the first-order partial derivative of rise and fall with respect to time, Let x be the first-order partial derivative of the pan / tilt motion with respect to time, and let x represent the longitudinal position of the slice. G The longitudinal position of the center of gravity is represented by U, the speed of the waterplane is represented by θ, the pitch is represented by N(x,t) and the damping coefficient of the current slice is represented by v. z The wave speed.

9. The method for rapid calculation of hydroplaning load of a water surface vehicle considering aerodynamic lift as described in claim 2, characterized in that, The formula for impact force is: Where: M H (x,t) represents the added quality of the current slice. V(x,t) is the z-direction partial derivative of the added mass, and is the relative sailing speed under the wave.

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