CN110096744B - Wave rich depth calculation method based on ship length wavelength ratio - Google Patents
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Abstract
The invention relates to a method for calculating the wave rich depth based on a ship length wavelength ratio, which comprises the following steps of: firstly, determining a ship scale parameter; secondly, determining wave elements; thirdly, determining a ship wave included angle psi; fourth, confirm keel subsidence response amplitude operator Z K /H S (ii) a Fifthly, calculating the maximum sinking amount Z under the keel K (ii) a Sixthly, calculating the maximum roll angle theta m (ii) a Seventhly, calculating the maximum sinking amount Z at the bilge keel BK (ii) a Eighthly, taking the larger as the wave rich depth (Z) 2 ) ψj (ii) a Ninthly, when the included angle of the ship waves is not unique, calculating the wave rich depth corresponding to the included angle of the ship waves for a plurality of times, and taking the largest one as the final wave rich depth Z 2 . Compared with the traditional technology, the method fills the blank of wave rich depth calculation under the condition of medium-long period waves in domestic specifications, and can calculate the wave rich depth of any angle within the range of a ship wave included angle psi of 0-180 degrees.
Description
Technical Field
The invention relates to the field of water conservancy science and technology, in particular to a wave rich depth calculation method based on a ship length wavelength ratio.
Background
The wave surplus depth refers to the surplus depth which needs to be reserved for the channel because the ship generates vertical motion response under the action of waves, and is one of important parameters for designing the water depth of the channel. At present, the calculation of the wave rich depth in the domestic specification is only suitable for the condition of short-period waves (the wave period is less than or equal to 8s), which meets the requirements in the sea areas around China or other short-period sea areas. However, in the fields of oceanic reefs, africa, southeast asia, south america and the like, many project constructions suffer from the influence of medium-long period waves. The medium-long period wave has longer wavelength, high propagation speed and quite high energy, and has non-negligible influence on the navigation of large ships.
The vertical motion response of the ship under the action of waves is mainly caused by heaving, pitching and rolling. At present, two methods of physical model test and numerical simulation are mainly used as research means, wherein the physical model test method has high precision, but the cost of expenditure and time is high; the numerical simulation method has low time and expense cost and relatively high calculation accuracy, and becomes the current mainstream, wherein a Response Amplitude Operator (RAO) method based on a linear theory is widely applied to channel specifications of various countries.
At present, the research on the ship motion response under the medium and long period wave conditions mainly focuses on the ship mooring state, the research on the ship motion response under the sailing state is less, and no mature calculation method exists at home for the wave rich depth under the medium and long period wave conditions.
In order to solve the above problems, we have made a series of improvements.
Disclosure of Invention
The invention aims to provide a method for calculating the wave rich depth based on the ship length-wavelength ratio, which considers the maximum vertical motion response of a ship under the conditions of the most unfavorable rolling and the most unfavorable pitching, and can respectively calculate the wave rich depth of bulk freighters of 10 ten thousand, 20 ten thousand and 30 ten thousand tons under the working conditions of different wave heights, different ship wave included angles (0-180 degrees) and different wave periods (8-30 s) so as to overcome the defects and shortcomings in the prior art.
A wave rich depth calculation method based on a ship length wavelength ratio comprises the following steps:
the method comprises the following steps: determining the dimension parameter of the ship and determining the length L of the ship PP Dimension parameters of the ship width B and the full-load draft T;
step two: determining wave design elements including effective wave height H S Spectrum peak period T p Wave direction angle and wavelength lambda, wherein the wavelength lambda can be solved iteratively by a linear dispersion relation;
step three: determining a ship wave included angle psi, and determining at least one corresponding ship wave included angle according to the inconsistency of the normal wave direction and the strong wave direction of the engineering sea area;
step four: operator Z for calculating and determining keel subsidence response amplitude K /H S ；
Step five: calculating the maximum subsidence Z of the keel K ；
Step six: calculating the maximum roll angle theta m ；
Step seven: calculating the maximum sinking amount Z of the bilge keel BK ；
Step eight: the greater is the wave margin depth (Z) 2 ) ψj ；
Step nine: when the included angle of the ship waves is not unique, calculating the wave rich depth (Z) corresponding to the included angle of the ship waves for a plurality of times 2 ) ψj Taking the largest one as the final wave rich depth Z 2 。
Further, the formula of the included angle of the ship waves in the third step is formula 1
V of the formula 1 is a ship navigation direction angle, and an absolute value of a difference value between a course angle and a wave direction angle is obtained
The ship wave angle psi is obtained by comparison with 180 deg..
Further, in the fourth step, an envelope method is adopted for calculating the keel subsidence response amplitude operator, specifically, two modes of a graph checking method and a formula method are adopted, and the graph checking method comprises the steps of firstly determining the ship length wavelength ratio L PP And lambda, then making a vertical line from the abscissa to the upper part in the corresponding RAO envelope diagram, finding an intersection point of an included angle curve of the ship waves under the corresponding working condition, making a horizontal line from the intersection point to the left, and reading out a keel sinking response amplitude operator value Z K /H S 。
Further, in the fourth step, the calculation method of the formula method is formula 2
In formula 2, τ is the ratio L of the length of the ship to the wavelength PP A/lambda, alpha is the maximum value of the logic curve, the range of the value range is 0-alpha, beta is the connecting curve between the logic curve 0 and alphaThe slope of the line, beta being greater, slope being steeper, tau 0 And determining the position of the abscissa of the median of the logic curve, determining the position of the abscissa of the vertex of the Gaussian curve by mu, determining the size of the peak value and the width of the region of the Gaussian curve by sigma, wherein the larger the sigma is, the smaller the peak value of the curve is, the wider the width is, and the gradient of two sides of the peak value is gentle.
Further, the keel response amplitude operator in the fifth step is multiplied by the effective wave height H S Calculating the maximum sinking Z under the keel under the most unfavorable condition of pitching K 。
Further, the maximum roll angle θ in the sixth step m Is the formula 3
further, in the seventh step, when the rolling is the most unfavorable condition, the sinking amount of bilge keels at two sides of the ship bottom reaches the maximum, and the calculation formula is formula 4
Further, in the eighth step, the larger of the most unfavorable condition of the pitching in the fifth step and the most unfavorable condition of the rolling in the seventh step is taken as the wave rich depth (Z) corresponding to the ship wave included angle 2 ) ψj The calculation method of the step eight is formula 5, where formula 5:
further, in the ninth step, when the included angle of the ship wave is not unique, the wave rich depth (Z) corresponding to the included angle of the ship wave is calculated for a plurality of times 2 ) ψj Taking the maximum as the final wave affluence depth Z 2 Said step (c)The calculation method of nine is formula 6, wherein the formula 6
The invention has the beneficial effects that:
compared with the traditional technology, the method fills the blank of wave rich depth calculation under the condition of long-period waves in domestic specifications; the maximum vertical motion response of the ship under the conditions of the worst pitching and the worst rolling is considered, and the RAO curve of the response amplitude operator is fitted by adopting an envelope line, so that the design value is safer; the RAO curve of the adopted response amplitude operator is drawn according to data obtained by a large-scale ship manipulation simulator test, and the test is added with the influence of artificial manipulation on the basis of numerical simulation, so that the result is closer to the practical significance; the wave rich depth of any angle in the range of 0-180 degrees of the ship wave included angle psi can be calculated, and the design value precision is higher.
Description of the drawings:
FIG. 1 is a flow chart of a calculation method.
Fig. 2 is a schematic view of the included angle of the waves.
Fig. 3 is a response amplitude operator-envelope for the keel sag of a 10-ten-thousand-ton bulk carrier.
Fig. 4 is a response amplitude operator-envelope for 20-ten-thousand-ton bulk carrier keel sag.
Fig. 5 is a response amplitude operator-envelope for the 30-ten-thousand-ton bulk carrier keel sag.
Fig. 6 is a distribution diagram of the included angle of the wave rich depth value with the ship waves calculated by the case.
Detailed Description
The present invention will be further described with reference to the following examples. It should be understood that the following examples are illustrative only and are not intended to limit the scope of the present invention.
FIG. 1 is a flow chart of a calculation method. Fig. 2 is a schematic view of the included angle of the waves. Fig. 3 is a response amplitude operator-envelope for the keel sag of a 10-ten-thousand-ton bulk carrier. Fig. 4 is a response amplitude operator-envelope for keel subsidence for a 20-ten-thousand-ton bulk carrier. Figure 5 is an amplitude operator-envelope of a 30-ten-thousand-ton bulk carrier keel sag response. Fig. 6 is a distribution diagram of the wave rich depth value along with the ship wave included angle calculated by the case.
Example 1
As shown in fig. 1, a method for calculating a wave rich depth based on a ship length wavelength ratio includes the following steps:
the method comprises the following steps: determining the dimension parameter of the ship and determining the length L of the ship PP Dimension parameters of the width B and the full-load draft T.
Step two: determining wave design elements including effective wave height H S Spectrum peak period T p Wave direction angle and wavelength lambda, wherein wavelength lambda can be solved iteratively by a linear dispersion relation. Determining wave design elements, comprising: effective wave height H s Spectrum peak period T P Angle of wave direction
And a wavelength lambda. (a) The wave height is defined as the vertical distance between adjacent peaks and valleys of the undulating water surface. Effective wave height H s The statistical wave height of the actually measured water level data of the engineering local sea area is equal to the average value of the first third wave height or equal to the zero order moment wave height H m0 And calculating the wave spectrum and solving the zero order moment of the wave spectrum to obtain the wave spectrum. The conversion between different statistical wave heights can be obtained by consulting the engineering design manual of seaports. (b) The wave period is defined as the adjacent identical phase of the wave surface, for example: two adjacent peaks, the time required to pass a certain position. Period of spectral peak T P The statistical wave period of the actually measured water level data of the engineering local sea area is equal to the corresponding period of the spectrum peak frequency of the wave spectrum. The conversion of different statistical wave cycle periods can be obtained by consulting the harbor engineering design manual. (c) Wave direction is the direction of travel of wave propagation, wave angle
The value of (a) is a vector angle between the wave velocity vector and the true north direction, and the north direction, the east direction, the south direction and the west direction are respectively 0 degree, 90 degrees, 180 degrees and 270 degrees. The wave directions include normal wave directions and strong wave directions in different seasons, and thus there may be one or more different wave directions, i.e. normal wave directions and strong wave directions
Or
(d) The wavelength λ is defined as the adjacent identical phase of the wave surface, for example: the horizontal distance between two adjacent wave crests along the wave propagation direction can be solved iteratively through a linear dispersion relation according to the effective wave height and the spectrum peak period. The calculation formula is shown in table 1, wherein the iterative formula can be simplified according to the relative magnitude relation of variables in the following formula under the respective working conditions for solving the wavelength under the deep water and shallow water working conditions.
TABLE 1 formula for calculating wavelength under different water depth
Note: d is beach water depth, g is local gravity acceleration
Step three: determining a ship wave included angle psi, determining at least one corresponding ship wave included angle according to the inconsistency of the normal wave direction and the strong wave direction of the engineering sea area, wherein the calculation process is as follows: (a) firstly, determining a sailing direction angle v of a ship, taking the value of the sailing direction angle v as a vector angle between the sailing direction and the positive north, wherein the north, east, south and west directions are respectively 0 degree, 90 degrees, 180 degrees and 270 degrees; (b) secondly, the absolute value of the difference between the course angle and the wave direction angle is obtained
And compared to 180 °; (c) and finally, solving the ship wave included angle psi, and calculating as shown in formula (1). The ship's wave angle psi is shown in fig. 2, and it can be seen that the ship's travel direction is opposite, perpendicular and the same as the wave direction, and the ship's wave angles are equal to 0 °, 90 ° and 180 °, respectively. In addition, since the normal wave direction and the strong wave direction of the engineering sea area may not be consistent, and the sailing direction may have different line selection schemes, one or more corresponding ship wave included angles, i.e., psi or psi, may be provided j . The ship wave included angle formula obtained in the third step is formula 1
Step four: operator Z for calculating and determining keel subsidence response amplitude K /H S Length L of ship determined according to the ton class of ship and previous steps PP Wavelength lambda and ship wave angle psi or psi j Determining keel subsidence response amplitude operator Z K /H S . Keel subsidence response amplitude operator is defined as ship keel subsidence Z K Divided by the effective wave height H under the corresponding working condition S . The keel subsidence response amplitude operator can be determined by an envelope curve method, and specifically comprises a graph checking method and a formula method. The image checking method comprises the following steps: first, the ratio L of the length of the ship to the wavelength is determined PP The/lambda is the horizontal coordinate value of the determined envelope curve diagram; secondly, selecting corresponding envelope graphs according to the tonnage of the ship, wherein the envelope graphs correspond to ships with 10 ten thousand, 20 ten thousand and 30 ten thousand tonnage respectively as shown in fig. 3, 4 and 5; thirdly, finding out an operator curve corresponding to the ship wave included angle psi in the envelope chart, and determining the coordinate value L of the ship wave included angle psi on the abscissa in the envelope chart PP Making a vertical line upwards from the lambda, and finding an intersection point of the vertical line and the operator curve; finally, a horizontal line is drawn leftwards from the intersection point, and the intersection point of the horizontal line and the vertical coordinate of the envelope diagram is found, namely the keel subsidence response amplitude operator value Z K /H S . The formula method comprises the following calculation steps: first, the ratio L of the length of the ship to the wavelength is determined PP The/lambda is the independent variable value tau of the envelope equation; secondly, selecting corresponding envelope equation coefficient tables according to the ton class of the ship, wherein the corresponding envelope equation coefficient tables are respectively corresponding to 10 ten thousand ships, 20 ten thousand ships and 30 ten thousand ships as shown in tables 2, 3 and 4; thirdly, finding a corresponding coefficient column in an equation coefficient table according to the ship wave included angle psi; finally, substituting the coefficient into formula 2 to obtain a keel subsidence response amplitude operator Z K /H S . Equation 2:
wherein tau is the ratio L of the length of the ship to the wavelength PP /λ(ii) a Alpha is the maximum value of the logic curve, and the range of the value range is 0-alpha; beta is the slope of a connecting curve between the logic curve 0 and alpha, and the larger beta is, the steeper the slope is; tau is 0 Determining the position of the abscissa of the median of the logic curve; determining the vertex abscissa position of the Gaussian curve; the sigma determines the peak value size and the area width of a Gaussian curve, and the larger the sigma is, the smaller the curve peak value is, the wider the width is, and the slopes on two sides of the peak value are gentle.
Table 210 ten thousand ton level bulk carrier keel sinking response amplitude operator envelope equation coefficient
Envelope equation coefficient of keel sinking response amplitude operator of bulk cargo ship with 320-ten-thousand-ton scale in table
Envelope equation coefficient of response amplitude operator of keel sinking of bulk cargo ship with table 430 ten-thousand-ton level
Step five: calculating the maximum subsidence Z under the keel K The keel sinking amount is the larger value between the bow sinking amount and the stern sinking amount and is equal to the keel sinking amount response amplitude operator Z obtained in the fourth step K /H s Multiplied by the effective wave height H s . Calculating the maximum sinking Z under the keel under the condition of the worst pitching K 。
Step six: calculating the maximum roll angle theta m Maximum roll angle θ in step six m Is the formula 3
In equation 3:
ψ p 90 ° is set. Other coefficient values are shown in table 5.
Table 5 maximum roll angle coefficient value reference.
Step seven: calculating the maximum sinking amount Z of the bilge keel BK And the maximum sinking Z of the bilge keel needs to be calculated under the most unfavorable rolling condition BK . The maximum sinking amount of the bilge keels is composed of two parts, namely a heaving sinking amount and a rolling sinking amount, the heaving sinking amount is conservatively estimated by pi/16 times of effective wave height, and the rolling sinking amount is the product of 0.5 times of the width of the ship and the maximum rolling angle. Bilge keel maximum sinking Z BK The calculation expression is formula 4
Step eight: taking the larger of the most unfavorable condition of the pitching in the step five and the most unfavorable condition of the rolling in the step seven as the wave rich depth (Z) corresponding to the ship wave included angle 2 ) ψj The calculation mode of the step eight is formula 5, and the formula 5
Step nine: if the included angle of the ship waves has the only value, the seventh step is the final wave rich depth, namely Z 2 ＝(Z 2 ) ψj (ii) a If a plurality of ship wave included angles exist, repeating the steps from four to seven to obtain a plurality of ship wave included angles psi j Corresponding multiple wave rich depth (Z) 2 ) ψj The maximum value between them is taken as the final wave affluence depth. The calculation method is shown in formula 6, formula 6
In the embodiment 1 of the invention, a 10-kiloton bulk cargo ship developed in a certain sea area of the east coast of south Africa enters a port channel, the length is about 50km, the width is 240m, and the depth is 21.8 m. The effective wave height of the local waves is 1m, and the average wave period is 15 s. The normal wave direction and the strong wave direction of the sea area are both SE direction (the vector angle with the due north direction is 1353), and three route selection schemes are provided for the sailing direction, and the vector angles with the due north direction are 135 degrees, 180 degrees and 225 degrees respectively. The design ship type selects a standard bulk cargo ship with the 10 ten thousand ton class, the length of the ship is 250m, the type width is 43m, and the full-load draught is 14.5 m.
The method comprises the following steps: determining a ship scale parameter: according to the appendix of the general design specification of the harbor, the design ship length is 250m, the profile width is 43m, and the full draft is 14.5 m.
Step two: determining wave design elements:
therefore, the wave in the sea area belongs to the finite water depth wave, and the wavelength lambda is 204.84m by solving by adopting a linear dispersion relation iterative method; effective wave height H S 1m, wave period T p 15S. The wave direction angle is SE direction, i.e. 135 °.
Step three: the ship-wave included angle ψ is determined, and as is known from the above, the heading angle v is 135 °, 180 °, 225 °, the wave direction angle is 135 °, and the ship-wave included angle ψ is 0 °, 45 °, 90 ° calculated by equation 4. Considering that the heading directions of the ship entering and exiting the port are opposite, the included angles psi of the ship waves are respectively 0 degrees, 45 degrees, 90 degrees, 135 degrees and 180 degrees.
Step four: keel subsidence response amplitude operator Z under corresponding working conditions is determined by utilizing graph checking method in envelope curve method K /H S : calculating the ratio L of the length of the ship to the wavelength PP As shown in fig. 3, the response amplitude operators RAO corresponding to the ship's wave angle ψ of 0 °, 45 °, 90 °, 135 °, 180 ° are 1.21, 1.20, 0.59, 0.97, and 1.09, respectively.
Step five: calculating the maximum sinking amount (the most unfavorable condition of pitching) Z of the keel K : multiplying the RAO operators obtained in the third step by the effective wave height H respectively S The maximum sinking Z of the fore and the stern under the conditions that the included angle psi of the ship waves is 0 degrees, 45 degrees, 90 degrees, 135 degrees and 180 degrees can be obtained K 1.21m, 1.20m, 0.59m, 0.97m and 1.09m, respectively.
Step six: calculating the maximum roll angle theta m : calculating the maximum roll angle theta under the conditions that the ship wave included angle psi is 0 degrees, 45 degrees, 90 degrees, 135 degrees and 180 degrees by using a formula 3 m Respectively at 0 °, 0.25 °, 3.26 °, 0.88 °, 0 °.
Step seven: calculating the maximum sinking amount (the most unfavorable condition of rolling) Z at the bilge keel BK : calculating the maximum sinking amount Z of the bilge keel under the conditions that the ship wave included angle psi is 0 degrees, 45 degrees, 90 degrees, 135 degrees and 180 degrees by using a formula 3 BK 0.20m, 0.25m, 0.94m, 0.4m and 0.2m, respectively.
Step eight: the greater is the wave margin depth (Z) 2 ) ψj : taking the larger sinking amount respectively corresponding to the ship waves with the included angles psi of 0 deg., 45 deg., 90 deg., 135 deg. and 180 deg. in the fourth step and the sixth step as the wave rich depth (Z) by using the calculation formula 5 2 ) ψj 1.21m, 1.20m, 0.94m, 0.97m and 1.09m, respectively, and the distribution is shown in FIG. 6.
Step nine: the maximum value of the wave rich depth corresponding to each ship wave included angle in the seventh step is taken by using a calculation formula 6 as the final wave rich depth Z 2 The final wave slack depth was 1.21 m.
While the present invention has been described with reference to the specific embodiments, the present invention is not limited thereto, and various changes may be made without departing from the spirit of the present invention.
Claims (2)
1. A wave abundance depth calculation method based on a ship length wavelength ratio is characterized by comprising the following steps of:
the method comprises the following steps: determining the dimension parameter of the ship and determining the length L of the ship PP Dimension parameters of the ship width B and the full-load draft T;
step (ii) ofII, secondly, the method comprises the following steps: determining wave design elements including effective wave height H S Spectrum peak period T p Wave direction angle
And a wavelength λ, wherein the wavelength λ is iteratively solved by a linear dispersion relation;
step three: determining a ship wave included angle psi, and determining at least one corresponding ship wave included angle according to the inconsistency of the normal wave direction and the strong wave direction of the engineering sea area; the ship wave included angle formula is formula 1
V in the formula 1 is a ship navigation direction angle, and the value is a vector angle between the navigation direction and the right north;
step four: operator Z for calculating and determining keel subsidence response amplitude K /H S (ii) a The calculation of the keel subsidence response amplitude operator adopts an envelope method, and the envelope method comprises the following steps: two modes of a graph checking method and a formula method are adopted, wherein the graph checking method comprises the steps of firstly determining the ship length wavelength ratio L PP And a/lambda, then making a vertical line from the abscissa to the upper part in the corresponding RAO enveloping diagram, finding an intersection point of an angle curve between the intersection point and the corresponding working condition ship wave, making a horizontal line from the intersection point to the left, and reading out a keel sinking response amplitude operator value Z K /H S (ii) a The calculation method of the formula method is formula 2
In formula 2, τ is the ratio L of the length of the ship to the wavelength PP A/lambda, alpha is the maximum value of the logic curve, the range of the value is 0-alpha, beta is the slope of the connecting curve between the logic curve 0 and alpha, the larger beta is, the steeper the slope is, and tau 0 Determining the position of the abscissa of the median of the logic curve, determining the position of the abscissa of the vertex of the Gaussian curve, determining the peak value and the region width of the Gaussian curve by sigma, wherein the larger the sigma, the smaller the curve peak value and the wider the curveThe wider the degree is, the slower the slopes of two sides of the peak value are;
step five: calculating the maximum sinking Z of the keel under the condition of the worst pitching K (ii) a Wherein the operator value of response amplitude under keel is multiplied by the effective wave height H S Equal to the maximum subsidence Z below the keel K ；
Step six: calculating the maximum roll angle theta m (ii) a The calculation formula is formula 3
In the formula 3:
ψ p ＝90°；
step seven: calculating the maximum sinking amount Z of the bilge keel when the rolling is the most unfavorable condition BK (ii) a Wherein, the sinking amount of bilge keels at two sides of the ship bottom reaches the maximum, and the calculation formula is formula 4
Step eight: the greater is the wave margin depth (Z) 2 ) ψj (ii) a Wherein, the larger of the worst condition of the pitching in the step five and the worst condition of the rolling in the step seven is taken as the wave margin depth (Z) corresponding to the ship wave included angle 2 ) ψj The calculation mode of the step eight is formula 5, and the formula 5
Step nine: when the included angle of the ship waves is not unique, calculating the wave rich depth (Z) corresponding to the included angle of the ship waves for a plurality of times 2 ) ψj Taking the maximum as the final wave affluence depth Z 2 。
2. The method of claim 1, wherein the method comprises: in the ninth step, when the included angle of the ship waves is not unique, the wave rich depth (Z) corresponding to the included angle of the ship waves for a plurality of times is calculated 2 ) ψj Taking the maximum as the final wave affluence depth Z 2 The calculation method of the step nine is shown in formula 6, and the formula 6
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| CN87105881A (en) * | 1986-09-12 | 1988-03-23 | 苏舍兄弟有限公司 | Boats and ships and method of operation thereof that stern propeller is arranged |
| JPH10325765A (en) * | 1997-05-23 | 1998-12-08 | Yokohama Rubber Co Ltd:The | Method for measuring wave compelling force while taking account of bay water oscillation |
| CN106652565A (en) * | 2015-10-29 | 2017-05-10 | 华北电力大学 | Method for calculating ship navigable areas by use of hydrodynamic model |
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| CN87105881A (en) * | 1986-09-12 | 1988-03-23 | 苏舍兄弟有限公司 | Boats and ships and method of operation thereof that stern propeller is arranged |
| JPH10325765A (en) * | 1997-05-23 | 1998-12-08 | Yokohama Rubber Co Ltd:The | Method for measuring wave compelling force while taking account of bay water oscillation |
| CN106652565A (en) * | 2015-10-29 | 2017-05-10 | 华北电力大学 | Method for calculating ship navigable areas by use of hydrodynamic model |
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