CN105279330B - The numerical value emulation method of sea moving ship turbulent wake - Google Patents
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Abstract
The invention belongs to naval hydrodynamics and ocean remote sensing monitoring technical field, specially a kind of numerical value emulation method of sea moving ship turbulent wake.Naval vessel turbulent flow is divided into two classes: stern jet stream and shipboard vortex pair；Naval vessel Numerical Simulation of Turbulent is the semiempirical formula based on turbulent wake width and turbulence energy decay spectra, using the bilinearity addition method.Physical simulation step is: one, turbulent flow width in naval vessel calculates, and by giving naval vessel parameter (length, width, speed of a ship or plane etc.), calculates tail width according to turbulent wake width semiempirical formula；Two, the eddy velocity of naval vessel two sides is calculated according to parameters such as ship length, width, the speed of a ship or plane, form coefficient, hull resistance coefficients；Three, sea is split into grid, calculates the turbulent flow relief height at mesh point with the bilinearity addition method based on the ship Wake spectrum of turbulence.This method principle is simple, calculation amount is small, easy to accomplish, can accurately simulate the main geometrical characteristic of naval vessel turbulent wake, especially turbulent flow relief height, coincide with measured result preferable.
Description
Technical Field
The invention belongs to the technical field of ocean remote sensing monitoring, and particularly relates to a numerical simulation method of a sea surface motion ship turbulence trail.
Background
Turbulence numerical simulation is the leading-edge problem in the field of fluid dynamics at present, and the traditional turbulence simulation methods comprise a direct numerical simulation method, an N-S method and a large vortex simulation method, which are all based on a fussy fluid mechanics formula and a complex differential algorithm, so that the calculation amount is huge, and the calculation accuracy is to be verified.
Although research on ship trails to the end of the nineteenth century, and research on hydrodynamics of ships walks a long road, theoretical research is difficult, in recent years, with the rise and development of Synthetic Aperture Radars (SAR), satellite-borne or airborne SAR image technologies can be used for identifying, detecting and tracking sea surface moving targets, and ship trails often extend for thousands of meters, so that the interest in ship trail research is increasing. The numerical simulation of the ship turbulence trail is a problem which needs to be solved urgently in the field of remote sensing monitoring, a set of method is provided for the simulation of sea waves, the traditional sea wave fluctuation numerical simulation is based on an energy balance equation and describes a sea spectrum, the dynamics of a sea wave field is effectively simplified, and meanwhile, the method has no harsh requirements on time step length and space step length and can be suitable for calculation of a larger area and a long time scale.
Disclosure of Invention
The invention aims to provide a quick, efficient and universal numerical simulation method for a turbulent wake of a sea surface motion ship.
The invention provides a numerical simulation method of a turbulent trail of a sea surface motion ship, which is based on a semi-empirical formula of ship turbulent trail width and a turbulent energy attenuation spectrum and adopts a classical bilinear superposition method. The specific simulation steps are as follows: firstly, calculating turbulence width of a ship, namely calculating the wake width according to a turbulence wake width semi-empirical formula by giving ship parameters (length, width, speed and the like); secondly, calculating the eddy speed of the two sides of the ship according to the length, the width, the navigational speed, the ship shape coefficient, the ship resistance coefficient and other parameters of the ship; and thirdly, dividing the sea surface into grids, and calculating the turbulence fluctuation height at the grid points by using a bilinear superposition method based on the ship wake turbulence spectrum.
The invention provides a numerical simulation method of a turbulent trail of a sea surface motion ship, which comprises the following specific steps:
(1) determining various parameters of the ship: the method comprises the following steps of establishing a geometric model of a moving ship, establishing a coordinate system of simulation calculation, discretizing the sea surface and dividing the sea surface into grid cells, wherein the ship length, transverse width, navigational speed, ship type coefficient, ship resistance coefficient, vortex core depth and the like are adopted;
(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. Specifically, the turbulent wake is regarded as the superposition of an infinite number of simple cosine waves with different amplitudes, frequencies, initial phases and propagation directions.
The following details of each step are described below:
(1) the specific process of the step (1):
setting ship parameters: length ofTransverse widthSpeed of flight；
Establishing two space rectangular coordinate systems, wherein one space rectangular coordinate system is a ship head coordinate system, the origin of coordinates is positioned at the ship head position,the shaft is directed from the bow to the stern,the shaft is parallel to the sea surface and vertical to the ship body,the axis is vertical to the static sea surface; the second is stern coordinate system with origin of coordinates at stern and bow coordinate systemAnd horizontally translating the axis direction by a new coordinate system after the ship body is in length. 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, subdividing the sea surface into grid cells, and setting the sea surface simulation size asThe number of the split nodes isThe selection of the grid step size takes into account the amount of computation.
(2) Calculating the width of a ship turbulent wake:
semi-empirical formula for ship turbulence wake width[1]：
（1）
Wherein the parametersAnddetermined by experimental measurement data, in general. It was found experimentally that the wake width at 4 times the ship's length from the hull was approximately 4 times the ship's width:
（2）
taking equation (2) into equation (1):
（3）
order to
（4）
Then
（5）
Therefore, the size of the ship can be calculatedTo obtain the tail widthThe calculation formula of (2).
(3) Calculating turbulent wake energy attenuation spectrum of a ship and simulating the wake:
the bilinear superposition formula of the sea wave simulation is
（6）
（7）
In the formula,is the height of the sea surface fluctuation,、、、、respectively the amplitude, angular frequency, and frequency of the nth cosine wave,Directional wave number component,The directional wave number component and the initial phase,is composed ofAre uniformly distributed in the random variable, and the random variable,is the acceleration of gravity. The amplitude satisfies Rayleigh distribution and is determined by
（8）
In the formula,is a turbulent energy attenuation spectrum.
Semi-empirical formula of energy attenuation spectrum of stern jet wake[2]：
（9）
In the formula、、Respectively the ship navigation speed, the ship length and the turbulence integral scale.
By making the initial velocity field a uniform isotropic field, the turbulent energy spectrum
（10）
Wherein,are coefficients, determined from experimental measurement data,the wave number corresponding to the peak of the energy spectrum. Integral scale of turbulence
（11）
Semi-empirical formula of ship side eddy current versus wake energy attenuation spectrum:
（12）
in the formulaThe other parameters are the same as above in relation to the vortex speed.
（13）
In the formulaIs the lateral velocity of the vortex pair, the peak value is about 0.1 times of the ship speed,is a proportionality coefficient, taking a value。
The surface horizontal velocity field of the eddy current pair is[3]：
（14）
In the formulaIs the distance between the two vortexes and is,in order to be the depth of the vortex,is the loop flow of the vortex at time t.
（15）
Wherein
（16）
（17）
Parameters in the formula:Lthe length of the ship is taken as the length of the ship,Uthe speed of the ship is taken as the ship speed,Ｂthe transverse width of the ship is large,C p is the coefficient of the ship shape,fis the hull drag coefficient. The ship type coefficient and the ship resistance coefficient of different ships can be consulted with relevant data.
Related parameters are reasonably selected, and a width formula and a turbulence energy attenuation spectrum formula of the ship turbulence wake are accurately calculated, so that the key of simulation is realized; 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.
The method can rapidly and efficiently numerically simulate the turbulent trail of the sea surface motion ship. The method has the advantages of simple principle, small calculated amount and easy realization, and can accurately simulate the main geometric characteristics of the ship turbulence wake, especially the turbulence fluctuation height, and the method is well matched with the actual measurement result.
Drawings
Fig. 1 is a dual coordinate system diagram.
Figure 2 is a schematic diagram of a ship turbulence wake width.
FIG. 3 is a graph of vortex versus lateral velocity.
Fig. 4 is a schematic of the eddy current versus horizontal velocity field.
Fig. 5 is a schematic diagram of three-dimensional simulation of jet wake at the stern of a ship.
FIG. 6 is a schematic diagram of a three-dimensional simulation of a ship vortex versus wake.
Fig. 7 is a schematic diagram of three-dimensional simulation of a ship turbulence wake.
Detailed Description
Ship parameters adopted by simulation: ship lengthTransverse width of rice and shipNavigation speed of rice and naval vesselsMeter/second, ship form factorCoefficient of resistance of ship。
FIG. 1 is a dual coordinate system diagram of turbulence simulation calculation, for calculation convenience, the ship side vortex is used for calculating the wake by adopting a ship head coordinate systemOrigin of coordinatesIs positioned at the position of the ship head,the shaft is directed from the bow to the stern,the shaft is parallel to the sea surface and vertical to the ship body,the axis is vertical to the static sea surface; the stern jet flow trail is calculated by adopting a stern coordinate system and a coordinate originIn the stern, stern coordinate systemIs the bow coordinate systemAnd horizontally translating the axis direction by a new coordinate system after the ship body is in length.
Figure 2 is a schematic diagram of a ship turbulence wake width. According to the formulas (2) to (5) and the ship parameters, a semi-empirical formula for deducing the ship turbulence wake isFig. 2 shows the variation of the width of the wake within 1000 metres behind the bow of the vessel. Visible tail width variation in near fieldLarger, the wake width increases gradually with increasing distance from the vessel, which coincides with the actual observation of the width of the turbulent wake of the vessel.
FIG. 3 shows the lateral velocity of the ship's vortex versus wakeSchematic representation. Calculating wave number corresponding to peak value of energy spectrumGet 4.76, vortex core depthTaking 5 m, the interval between vortex coresAnd (4) rice. The graph shows the lateral speed variation of the vortex at three positions from the back of the bow, the red line shows the lateral speed variation curve at 100 meters, the green line shows the lateral speed variation curve at 200 meters, and the blue line shows the lateral speed variation curve at 400 meters. As can be seen from the lateral speed change curve of a single position, the lateral speed value of the vortex trail above the vortex core is the largest, and the lateral speed is reduced along with the increase of the distance away from the vortex core; comparing the lateral velocity profiles at the three positions shows that the peak value of the lateral velocity decreases with increasing distance from the bow. The calculated results were matched with experimental measurement data.
Fig. 4 is a schematic of the eddy current versus horizontal velocity field. Size of sea surfaceThe weight of the rice is reduced,meter, other calculation parameters are as above, and figure 4 shows the spatial distribution of the ship vortex to the wake lateral velocity, it can be seen that the velocity is large near the bow, the peak velocity is about 2 m/s, and this data is reasonable.
FIG. 5 is an artificial shipTail jet flow trail. According to formulas (6) - (11), wherein. And a stern coordinate system is adopted, the amplitude transformation of the near-field jet flow wake is obvious, and the far field tends to be smooth.
Figure 6 simulates ship side eddy current versus wake. According to equations (6) - (8) and equations (10) - (17), the simulation parameters are as before. Simulation results show that the eddy current is consistent with the eddy current pair velocity field in the figure 4, the near-field wake fluctuation is large, because the lateral velocity is large, the wake fluctuation is large, the energy is rapidly attenuated along with the distance from the ship wake, the lateral velocity is rapidly reduced, and the wake fluctuation is reduced.
FIG. 7 is a simulation result of the ship turbulence wake obtained by synthesizing the ship eddy wake and the stern jet wake. The simulation parameters are as before. The peak value of the fluctuation height of the vortex near the bow to the wake is larger than the peak value of the fluctuation height of the jet wake near the stern, the fluctuation height of the far-field jet wake is slightly larger than the fluctuation height of the vortex to the wake, the total root mean square fluctuation height is about 0.03 meter, and the fluctuation height is matched with experimental measurement data.
Reference documents:
[1]. Gregory Zilman, Anatoli Zapolski, and Moshe Marom. The Speed andBeam 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 ofShips，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 Lx×LyThe number of the split nodes is Nx×NySelecting 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)＝(AxBα-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, zm,nIs the sea surface undulation height, An,m、ωn、kx、ky、φn,mRespectively the amplitude, angular frequency, x-direction wave number component, y-direction wave number component and initial phase phi of the nth cosine waven,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′＝λUvor (13)
in the formula of UvorThe 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, bvThe 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 CpIs 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.
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| CN116415521A (en) * | 2023-03-16 | 2023-07-11 | 中国人民解放军海军潜艇学院 | Vortex trail simulation model of underwater vehicle |
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