CN105279330B - The numerical value emulation method of sea moving ship turbulent wake - Google Patents

Abstract

The invention belongs to the technical field of marine fluid mechanics and marine remote sensing monitoring, in particular to a numerical simulation method of turbulent wake of ships moving on the sea surface. Ship turbulence is divided into two categories: stern jet and side vortex pairs; ship turbulence numerical simulation is a semi-empirical formula based on turbulent wake width and turbulent energy attenuation spectrum, using the bilinear superposition method. The specific simulation steps are: 1. Calculate the turbulent width of the ship. From the given ship parameters (length, width, speed, etc.), calculate the wake width according to the semi-empirical formula of the width of the turbulent wake; The eddy current velocity on both sides of the ship is calculated by parameters such as ship shape coefficient and hull resistance coefficient. Third, the sea surface is divided into grids, and the turbulent fluctuation height at the grid points is calculated by the bilinear superposition method based on the ship wake turbulence spectrum. The method is simple in principle, small in computation and easy to implement, and can accurately simulate the main geometric features of the ship's turbulent wake, especially the turbulent undulation height, which is in good agreement with the measured results.

Description

Numerical simulation method of turbulent wake for ships moving on the sea surface

Field of Invention

The invention belongs to the technical field of ocean remote sensing monitoring, and in particular relates to a numerical simulation method of turbulent wake of ships moving on the sea surface.

Background technique

Turbulence numerical simulation is currently a frontier problem in the field of fluid dynamics. The traditional turbulence simulation methods include direct numerical simulation method, N-S method and large eddy simulation method. These methods are all based on tedious fluid mechanics formulas and complex differential algorithms. Huge, and the computational accuracy has yet to be verified.

Although the study of ship wake can be traced back to the end of the nineteenth century, the hydrodynamic research of ships has come a long way, and theoretical research is relatively difficult. In recent years, with the rise and development of synthetic aperture radar (SAR) , the spaceborne or airborne SAR image technology can be used to identify, detect and track moving targets on the sea surface, and ship wakes often extend for thousands of meters, so there is an increasing interest in the study of ship wakes. Numerical simulation of ship turbulent wake is an urgent problem that needs to be solved in the field of remote sensing monitoring, and there is already a set of methods for wave simulation. The dynamics of the field, and at the same time it has no strict requirements on the time step and space step, and can be applied to the calculation of large areas and long time scales.

SUMMARY OF THE INVENTION

The purpose of the present invention is to provide a fast, efficient and general numerical simulation method of the turbulent wake of a ship moving on the sea surface.

The numerical simulation method of the turbulent wake of the ship moving on the sea surface proposed by the present invention is based on the semi-empirical formula of the width of the ship's turbulent wake and the turbulent energy attenuation spectrum, and adopts the classical bilinear superposition method. The specific simulation steps are: 1. Calculate the turbulent width of the ship. From the given ship parameters (length, width, speed, etc.), calculate the wake width according to the semi-empirical formula of the width of the turbulent wake; The eddy current velocity on both sides of the ship is calculated by parameters such as ship shape coefficient and hull resistance coefficient. Third, the sea surface is divided into grids, and the turbulent fluctuation height at the grid points is calculated by the bilinear superposition method based on the ship wake turbulence spectrum.

The numerical simulation method of the turbulent wake of a ship moving on the sea surface proposed by the present invention includes the following specific steps:

(1) Determine various parameters of the ship: ship length, transverse width, speed, ship shape coefficient, hull resistance coefficient, vortex core depth, etc., establish a geometric model of the moving ship, and establish a coordinate system for simulation calculation, Discretization, divided into grid cells;

(2) According to the ship parameters and the semi-empirical formula of ship turbulent wake width, calculate the wake width formula of the ship at a specific speed;

(3) According to the semi-empirical formula of the turbulence spectrum of the ship wake, the energy attenuation spectrum of the stern jet and the side vortex pair is calculated respectively, and the bilinear superposition method is used to simulate the turbulent wake. Specifically, the turbulent wake is regarded as the superposition of infinitely many simple cosine waves with different amplitudes, frequencies, initial phases and propagation directions.

The specific details of each step are described below:

(1) The specific process of step (1):

Set ship parameters: length , horizontal width , speed ;

Two space Cartesian coordinate systems are established, one is the bow coordinate system, and the coordinate origin is located at the bow position, The shaft goes from the bow to the stern, axis parallel to the still sea and perpendicular to the hull, The axis is perpendicular to the still sea surface; the second is the stern coordinate system, the coordinate origin is at the stern, and the stern coordinate system is the bow coordinate system at The new coordinate system after the axis direction is horizontally translated by one hull length. The bow coordinate system is used to calculate the fluctuation height of the side vortex, and the stern coordinate system is used to calculate the fluctuation height of the stern jet;

The sea surface is discretized and divided into grid cells, and the simulation size of the sea surface is set as , the number of split nodes is , the selection of grid step should consider the amount of calculation.

(2) Calculation of ship turbulent wake width:

The semi-empirical formula for the width of ship turbulent wake ^[1] :

(1)

Among them, the parameter and Determined by experimental measurement data, generally . The experiment found that the wake width at 4 times the length of the hull is about 4 times the width of the ship:

(2)

, put formula (2) into formula (1) to get:

(3)

make

(4)

but

(5)

Therefore, according to the size of the ship, it can be calculated , and then get the trail width calculation formula.

(3) Calculation of energy attenuation spectrum of ship turbulent wake and simulation of wake:

The bilinear superposition formula for ocean wave simulation is

(6)

(7)

In the formula, is the undulation height of the sea surface, , , , , are the amplitude, angular frequency, and directional wavenumber components, direction wavenumber component and initial phase, for uniformly distributed random variables between is the acceleration of gravity. The amplitude satisfies the Rayleigh distribution and is determined by

(8)

In the formula, is the turbulent energy decay spectrum.

The semi-empirical formula of the wake energy attenuation spectrum of the stern jet ^[2] :

(9)

in the formula , , are the speed of the ship, the length of the ship and the turbulence integral scale, respectively.

Let the initial velocity field be a uniform isotropic field, then the turbulent energy spectrum

(10)

in, is the coefficient, determined according to the experimental measurement data, is the wavenumber corresponding to the peak of the energy spectrum. Turbulence integral scale

(11)

The semi-empirical formula of the ship's side vortex to the wake energy attenuation spectrum:

(12)

in the formula Related to eddy current speed, other parameters are the same as above.

(13)

in the formula is the lateral speed of the vortex pair, with a peak value of about 0.1 times the ship speed, is the scale factor, the value .

The surface horizontal velocity field of the vortex pair is ^[3] :

(14)

in the formula is the distance between the two vortices, is the vortex depth, is the circulating flow of the vortex at time t.

(15)

in

(16)

(17)

Parameters in the formula: L is the length of the ship, U is the speed of the ship, B is the transverse width of the ship, C _p is the ship shape coefficient, and f is the hull resistance coefficient. For different ships, their hull type coefficient and hull resistance coefficient can be found in the relevant information.

Reasonable selection of relevant parameters, accurate calculation of the width formula of the ship's turbulent wake and the formula of the turbulent energy attenuation spectrum is the key to the simulation; the stern coordinate system and the bow coordinate system are used to simulate the stern jet wake and the ship's side vortex pair wake, and two types of linear superposition are used. wake.

The method of the invention can numerically simulate the turbulent wake of ships moving on the sea surface quickly and efficiently. The method is simple in principle, small in computation and easy to implement, and can accurately simulate the main geometric features of the ship's turbulent wake, especially the turbulent undulation height, which is in good agreement with the measured results.

Description of drawings

FIG. 1 is a dual coordinate system diagram.

Figure 2 is a schematic diagram of the width of the ship's turbulent wake.

Figure 3 is a schematic diagram of eddy current versus lateral velocity.

Figure 4 is a schematic diagram of the eddy current versus the horizontal velocity field.

Figure 5 is a schematic diagram of the three-dimensional simulation of the wake of the jet at the stern of the ship.

Figure 6 is a schematic diagram of the three-dimensional simulation of ship vortex pair wake.

Figure 7 is a schematic diagram of a three-dimensional simulation of a ship's turbulent wake.

Detailed ways

Ship parameters used for simulation: ship length m, the width of the ship meters, the speed of the ship m/s, ship shape factor , the hull resistance coefficient .

Figure 1 shows the dual coordinate system of turbulence simulation calculation. For the convenience of calculation, the bow coordinate system is used for the calculation of the wake caused by the side eddy current. ,Coordinate origin in the bow position, The shaft goes from the bow to the stern, axis parallel to the still sea and perpendicular to the hull, The axis is perpendicular to the still sea surface; the calculation of the wake of the stern jet adopts the stern coordinate system, the coordinate origin At the stern, the stern coordinate system is the bow coordinate system in The new coordinate system after the axis direction is horizontally translated by one hull length.

Figure 2 is a schematic diagram of the width of the ship's turbulent wake. According to formulas (2)-(5) and ship parameters, the semi-empirical formula of ship turbulent wake is derived as: , Figure 2 shows the change in the width of the wake within 1000 meters behind the bow. It can be seen that the wake width varies greatly in the near field. With the increase of the distance from the ship, the increase of the wake width tends to be gentle, which is consistent with the actual observed width of the ship's turbulent wake.

Figure 3 shows the lateral velocity of ship vortex versus wake Schematic. The wavenumber corresponding to the peak of the energy spectrum in the calculation Take 4.76, the depth of the vortex core Take 5 meters, the vortex core spacing Meter. The figure shows the lateral velocity changes of the vortex at three positions behind the bow. The red line represents the lateral velocity curve at 100 meters, the green line represents the lateral velocity curve at 200 meters, and the blue line represents the lateral velocity at 400 meters. Curve. It can be seen from the variation curve of lateral velocity at a single position that the lateral velocity value of the vortex wake above the vortex core is the largest, and as the distance from the vortex core increases, the lateral velocity decreases. Comparing the lateral velocity curves of the three positions, it can be seen that with As the distance from the bow increases, the peak lateral velocity decreases. The calculated results are in good agreement with the experimental measurement data.

Figure 4 is a schematic diagram of the eddy current versus the horizontal velocity field. sea surface size Meter, m, and other calculation parameters are the same as above. Figure 4 shows the spatial distribution of ship eddy current to the lateral velocity of the wake. It can be seen that the velocity near the bow is larger, and the peak velocity is about 2 m/s. This data is reasonable.

Figure 5 simulates the wake of the ship's stern jet. According to formulas (6)-(11), where . Using the stern coordinate system, the amplitude of the jet wake in the near field changes obviously, and the far field tends to be gentle.

Figure 6 simulates the ship side vortex pair wake. According to formula (6)-(8) and formula (10)-(17), the simulation parameters are the same as before. The simulation results show that the vortex pair velocity field is consistent with Fig. 4. The near-field wake fluctuates greatly, because the lateral velocity is large and the wake fluctuation is large. .

Figure 7. The simulation results of the ship turbulent wake are obtained by combining the ship vortex pair wake and the stern jet wake. The simulation parameters are the same as before. The peak value of the fluctuation height of the vortex pair wake near the bow is greater than the peak value of the jet wake fluctuation height near the stern, and the fluctuation height of the jet wake in the far field is slightly larger than that of the vortex pair wake. The measured data are in good agreement.

references:

[1]. Gregory Zilman, Anatoli Zapolski, and Moshe Marom. The Speed and Beam of a Ship From Its Wake’s SAR Images,” IEEE Trans. Geosci. Remote Sens., vol. 42, no. 10, Oct 2004.

[2]. J. H. Milgram, Richard A. Skop, Rodney D. Peltzer and Owen M. Griffin. Modeling Short Sea Wave Energy Distributions in the Far Wakes of Ships, Journal of Geophysical Research, Vol. 98, no. c4, pages 7115- 7124, April 15, 1993.

[3]. A. Skoelv, T. Wahl, S. Eriksen. Simulation of SAR Imaging of ShipWakes. IGARSS’88 Symposium, I3-I6 Sept.1988, pp.1525.

Claims (4)

1. A numerical simulation method of sea surface ship turbulence wake is characterized by comprising the following specific steps:

(1) determining various parameters of the ship: the method comprises the steps of building a geometric model of a moving ship, building a simulation calculation coordinate system, discretizing a sea surface and subdividing the sea surface into grid cells, wherein the ship length, the transverse width, the navigational speed, the ship type coefficient, the ship resistance coefficient and the vortex core depth are used for calculating the ship movement; the specific process comprises the following steps:

setting ship parameters: the ship length L, the ship transverse width B and the ship speed U;

establishing two space rectangular coordinate systems, wherein one space rectangular coordinate system is a ship head coordinate system, the origin of coordinates of the ship head coordinate system is located at the ship head position, the x axis points to the ship tail from the ship head, the y axis is parallel to the static sea surface and is vertical to the ship body, and the z axis is vertical to the static sea surface; the stern coordinate system is a new coordinate system after the bow coordinate system horizontally translates by a ship body length in the x-axis direction; the bow coordinate system is used for calculating the fluctuation height of the ship side vortex pair, and the stern coordinate system is used for calculating the fluctuation height of the stern jet flow;

discretizing the sea surface, dividing the sea surface into grid cells, and setting the sea surface simulation size to be L_x×L_yThe number of the split nodes is N_x×N_ySelecting the grid step length by considering the calculated amount;

(2) calculating a wake width formula at a specific speed of the ship according to ship parameters and a ship turbulence wake width semi-empirical formula;

(3) respectively calculating the energy attenuation spectrums of stern jet flow and ship side vortex flow pairs according to a semi-empirical formula of a ship wake turbulence spectrum, and simulating the turbulence wake by adopting a bilinear superposition method, namely, regarding the turbulence wake as the superposition of infinite simple cosine waves with different amplitudes, frequencies, initial phases and propagation directions.

2. The numerical simulation method of a sea surface vessel turbulence wake of claim 1, characterized in that: the specific process of the step (2) is as follows:

semi-empirical formula of ship turbulence wake width:

W(x)＝(AxB^α-1)^1/α (1)

wherein B is the transverse width of the ship, α belongs to [4,5], and the trail width at the position 4 times the ship length away from the ship is found to be 4 times the ship width through experiments;

will be publicThe formula (2) brings the formula (1) into the formula:

order:

then:

therefore, the values of a and b can be calculated according to the size of the ship, and a calculation formula of the width W of the turbulent wake of the ship is further obtained.

3. The numerical simulation method of a sea surface vessel turbulence wake of claim 2, characterized in that: the specific process of the step (3) is as follows:

the bilinear superposition formula of the sea wave simulation is as follows:

in the formula, z_m,nIs the sea surface undulation height, A_n,m、ω_n、k_x、k_y、φ_n,mRespectively the amplitude, angular frequency, x-direction wave number component, y-direction wave number component and initial phase phi of the nth cosine wave_n,mIs [0,2 π ]]Random variables are uniformly distributed, and g is gravity acceleration;

the amplitude satisfies the rayleigh distribution, determined by the following equation:

wherein S (ω, θ) is a turbulent energy attenuation spectrum;

calculating the energy attenuation spectrum of the stern jet flow:

the semi-empirical formula of the energy attenuation spectrum of the stern jet wake:

u, L, l is ship speed, ship length and turbulence integral scale, E (k) is turbulence spectrum;

let the initial velocity field be a uniform isotropic field, then the turbulent energy spectrum:

wherein k can be determined from experimental measurement data₀The wave number corresponding to the peak value of the energy spectrum; integral scale of turbulence:

calculation of the ship side eddy current energy attenuation spectrum:

semi-empirical formula of ship side eddy current versus wake energy attenuation spectrum:

wherein U' is related to the vortex velocity, and other parameters are as above;

U′＝λU_vor (13)

in the formula of U_vorThe peak value is 0.1 time of the ship speed, and the lambda is a proportionality coefficient and takes a value of 10 +/-5;

the surface horizontal velocity field of the eddy current pair is:

in the formula, b_vThe distance between two vortexes is h is the depth of the vortexes, and gamma (t) is the circulation volume of the vortexes at time t;

wherein

The parameters in the formula are: l is ship length, U is ship speed, B is ship transverse width and C_pIs the ship shape coefficient, and f is the ship body resistance coefficient.

4. The numerical simulation method of a sea surface vessel turbulence wake of claim 3, characterized in that: reasonably selecting related parameters, and accurately calculating a width formula and a turbulence energy attenuation spectrum formula of a ship turbulence wake; and respectively adopting a stern coordinate system and a bow coordinate system to simulate a stern jet wake and a ship side vortex pair wake, and linearly superposing the two wakes.