KR101975798B1 - Method of inundation analysis in ship - Google Patents

Abstract

The present invention relates to an analyzing method of ship inundation, and more specifically, to an analyzing method of ship static inundation, which considers fluid spill such as oil in a damaged ship to apply a dynamic orifice equation and considers cargo loaded in a section to apply a polyhedron integral method, thereby providing more accurate inundation simulation.

Description

[0001] METHOD OF INUNDATION ANALYSIS IN SHIP [0002]

The present invention relates to a method of immersion analysis of a ship, and more particularly, to a dynamic orifice equation considering fluid outflow such as oil in a damaged ship, and more particularly, to a quasi-static immersion analysis method that provides a more accurate immersion simulation by applying a polyhedron integral method.

If an accident occurs at sea due to collision, stranding, etc., the ship may be sunked due to flooding or leakage of oil in the compartment, which can cause enormous human, material and environmental damage. If it is possible to simulate and predict the time of sinking of the damaged vessel and the time of sinking, equilibrium attitude and equilibrium attitude, oil spillage and discharge rate in a comparatively short time, Minimizing the casualties caused by the execution, identifying the causes after the accident and constructing countermeasures.

So far, several quasi-static inundation analysis methods have been studied for flood simulation. However, previous studies have considered the damage of the ship, but did not consider leakage of other fluids (eg oil) except gas and water.

In order to analyze the flooding, it is necessary to calculate the inflow and outflow of the fluid between the damaged part and the partition in the ship. In addition, the damaged vessel moves its weight and center of gravity due to the inflow of external seawater, which causes a change in the posture of the vessel, and the fluid surface in the vessel changes every hour. It is therefore necessary to calculate the exact volume of the fluid. In addition, for accurate immersion analysis, it is necessary to consider not only the inflow and outflow of fluids but also various solid cargoes in the ship.

Therefore, existing flood analysis methods have limitations that can not reflect realistic and accurate flood situation.

Published patent 2015-0008286

SUMMARY OF THE INVENTION The present invention has been made in order to solve the above problems, and it is an object of the present invention to apply a dynamic orifice equation in consideration of fluid outflow such as oil in a damaged vessel, apply a polyhedron integration method To provide a quasi-static immersion analysis method that provides more accurate immersion simulation.

A method for analyzing flooded water of a ship according to an embodiment of the present invention is a method for analyzing a flooded water of a ship, comprising the steps of: a first space divided from each other by a predetermined partition wall and a first fluid and a second fluid And a flow rate of the fluid flowing between the first fluid and the second fluid facing each other with the cross-sectional area of the opening formed in the partition wall as a boundary, the method comprising the steps of: Applying a mechanical orifice equation; .

Preferably, the cross-sectional area is divided into at least one separation area having a predetermined area according to the kind of the first fluid and the second fluid facing each other with the cross-sectional area interposed therebetween, Apply the above kinetic orifice equations respectively.

Preferably, the kinetic orifice equation is as follows.

(식 1)

(Equation 1)

(A ₁ : cross-sectional area of the separation region,

p ₁ is the fluid pressure of the first fluid in the first space,

P ₂ : fluid pressure of the second fluid in the second space,

ρ = density of the first fluid when u ≥ 0, ρ = density of the second fluid when u <0)

Preferably, the equation (1) is summarized by the time variation of the flow velocity,

(식2)

(Equation 2)

A _opening : Sectional area of the separation area (= A ₁ ))

Integrating equation (2) by the Euler method to derive equation (3) representing the flow rate at the next time unit at the flow rate in the current time unit, and

(식 3)

(Equation 3)

(p ₀ is the pressure of the first fluid in the first space at the current time (u _n )

p ₁ is the pressure of the fluid in the second space at the current time (u _n )

: 다음 시간 단위에서의 유속,

: Flow rate at the next time unit,

:현재 시간 단위에서의 유속

: Flow rate in the current time unit

: 시간 간격)

: Time interval)

And the step of deriving the flow rate per hour by substituting the flow velocity derived from the above-mentioned equation (3) into the following equation (4).

(식 4)

(Equation 4)

: 유량(

: Flow

: 유속

: Flow rate

: 흐르는 유체의 밀도 계수

: Density coefficient of flowing fluid

: 시간 간격)

: Time interval)

는, 유체의 종류에 따라서 상이한 값을 갖는다.Preferably, in formula

Have different values depending on the kind of the fluid.

는 0.6 ~ 0.7 이다.Preferably, when the first fluid or the second fluid is oil,

Is 0.6 to 0.7.

Preferably, the step of applying the flooding rate of each compartment according to the solid cargo present in the compartment in the vessel.

Preferably, the step of calculating the inflow amount of the fluid by deriving the shape of the inflowed fluid by using the polyhedral integration method.

The method of immersion analysis of a ship according to the present invention provides a more accurate flooding simulation by applying a dynamic orifice equation considering fluid outflow such as oil in a damaged vessel and applying a polyhedron integration method considering the cargo in a compartment do.

1 is a view showing a dynamic orifice equation used in a method of immersion analysis of a ship according to the present invention.
2 is a graph showing the relationship between t / T and u / u _f in the dynamic orifice equation used in the method of immersion analysis of a ship according to the present invention.
3 is an enlarged view of a portion of a ship when only a water-gas exists in a damaged ship, and Fig. 4 is an enlarged view of an area where an opening is formed.
5 is a view showing each case of the cross-sectional area of the opening in the case where only the water-gas exists in the damaged vessel.
FIG. 6 is an enlarged view of a portion of the ship when water, gas, and oil are present in the damaged vessel, and FIG. 7 is an enlarged view of an area where the openings are formed.
Fig. 8 is a view showing each case of the cross-sectional area of the opening when water, gas, and oil are present in the damaged vessel. Fig.
9 is a view showing the flooding rate of the ship compartment when solid cargo is present in the compartment.
FIG. 10A is a view showing a polyhedral integration method, and FIG. 10B is a view showing application of a polyhedral integration method to the calculation of the volume of fluid immersed in an inclined ship.
FIG. 11 shows a comparison between the fluid plane based method and the polyhedron integral method among the fluid volume calculation methods.
12 (a) is a diagram showing a model line used in Ruponen's study, and FIG. 12 (b) is a diagram showing a model line of the present invention modeled in the same way.
13 is a view showing main specifications of a model line in Fig.
Fig. 14 is a view showing a case of a ship damaged on the starboard or bottom. Fig.
15 and 16 are respectively the results of the analysis of the first case by Ruponen (2007) and the results of the experiment and the analysis of the present invention by the pitch and heave of the ship.
Figures 17 and 18 compare the results of the analysis by Ruponen (2007) and the experimental results and the analysis results of the present invention, respectively, with the pitch and heave of the ship in the second case.
Figure 19 shows the model used for experiments in a study by Debra (2001).
20 is a table summarizing the characteristics of the oil used in the experiment in the study of Debra (2001).
FIG. 21 shows a case in which oil flows out in the air, and FIG. 22 shows a case in which oil flows out in water.
Figures 23 and 24 compare the analytical results of the present invention for the two cases shown in Figures 21 and 22 and the values measured by experiments in a study of Debra (2001).
25 shows a model modeled for verifying the accuracy of the immersion analysis method in which the solid cargo of the present invention is taken into consideration through comparison with a commercial program.

Hereinafter, preferred embodiments of the present invention will be described with reference to the accompanying drawings.

For inundation analysis, it is necessary to calculate the flow of fluid through openings such as damaged vessel outer walls, doors between compartments, windows, and vents. In the present invention, the flow of fluid flowing through such openings is calculated according to the dynamic orifice equation.

The dynamic orifice equation used in the method of immersion analysis of a ship according to the present invention is given by the following Equation (0).

(식 0)

(Expression 0)

First, for the purpose of the present invention, the kinetic orifice equation will be described. Here, it is assumed that the fluid is imcompressible, the fluid flowing in the opening is the same in velocity and pressure distribution in the control volume, is inviscous, and the fluid flow in the opening is always perpendicular to the opening .

The momentum conservation law in the fluid region is expressed by the Euler equation as shown in the following equation A1, A1 '.

(식 A1)

(Formula A1)

(식 A1')

(Formula A1 ')

: 속도벡터,

: 단위질량에 작용하는 외력(body force))(

: Velocity vector,

: Body force acting on unit mass)

Integral version When describing the momentum conservation law in the fluid region by using the Euler equation, it is expressed by the following equation A2, A2 '. This is an equation equivalent to the formula A1 and the formula A1 'expressed by the above differential form.

(식 A2)

(Formula A2)

(식 A2')

(Formula A2 ')

는 관심의 영역이 되는 유체영역이고,

는 이 영역의 경계이다. 직교벡터

의 방향은 선박 내부 영역에서 선박 외부인 바깥으로 향하는 방향을 양의 방향으로 한다.here

Is a fluid region that is an area of interest,

Is the boundary of this area. Orthogonal vector

The direction from the inside of the ship to the outside of the ship is the positive direction.

은 개구부의 단면에서 떨어진 거리로 충분히 크게 잡아 유동이 거의 없는 경계가 되도록 택한다. 이곳에서는 압력이

로 일정하고, 또한 속도의 방향은 직교방향이 된다. This is shown in Fig. 1 as a picture. 1,

Lt; RTI ID = 0.0 &gt; a &lt; / RTI &gt; Here,

And the direction of the velocity is the orthogonal direction.

로 표기하며, 개구부의 단면에 직교하는 속도는

로 표기하고 전체속도는

으로 표기한다. When the notation of velocity is represented by a vector

, And the velocity orthogonal to the cross section of the opening is expressed by

And the overall speed is

.

이고 단면을 제외한 벽면의 면적을

라고 가정한다. 유체영역은 개구부 단면의 왼쪽부분을

로 하고 오른쪽을

으로 한다. 단면의 형상이 축대칭이라고 가정하면, 옆방향 즉 x 방향 속도를 제외한 속도성분은 단면의 중심선을 지나는 선에 반대칭(asymmetric)하게 된다.It is assumed that the velocity is constant and the pressure is uniformly distributed at the right end of the cross section of the opening. The area of the cross-

And the area of the wall surface excluding the cross section is

. The fluid region is defined by the left side of the cross-

And to the right

. Assuming that the shape of the cross section is axisymmetric, the velocity components other than the lateral or x-direction velocity are asymmetric to the line passing through the centerline of the cross section.

에 대하여 연속방정식을 적용시키면 다음 식 A3 과 같다.Fluid region

The following equation A3 is obtained.

(식 A3)

(Formula A3)

는 개구부 단면에서의 체적유량(volumetric flux)이다. 모멘텀 보존법칙을

에 적용시키고

의 위치에서 압력이

으로 일정하게 유지된다고 가정한다. 이때, x 방향 속도를 제외한 속도성분은 서로 상쇄되어 사라지고, x 방향 속도성분에 대한 식만 존재한다. 따라서, 아래 식 A4, A5 가 도출된다.here

Is the volumetric flux at the cross-section of the opening. Momentum conservation law

Apply and

The pressure in the

. &Lt; / RTI &gt; At this time, the velocity components other than the x-direction velocity cancel each other and only the equation for the x-direction velocity component exists. Therefore, the following equations A4 and A5 are derived.

(식 A4)

(Formula A4)

(식 A5)

(Formula A5)

에 대하여 질량 보존법칙을 적용하면 식 A6 이 도출되며, 이를 변형하면 식 A7 이 도출된다.In addition,

, The equation A6 is derived by applying the law of conservation of mass.

(식 A6)

(Formula A6)

(식 A7)

(Formula A7)

Accordingly, the velocity can be expressed as the following equation A8.

(식 A8)

(Formula A8)

에 적용시키면, 반대칭성(asymmetry) 때문에 x 방향 성분만 남고, 다른 방향 성분은 서로 상쇄되어 사라진다. 따라서, 다음과 같은 식 A9 를 얻는다.The equation A2 representing the momentum conservation law

, Only the x-direction component is left because of the asymmetry, and the other direction components cancel each other out. Therefore, the following expression A9 is obtained.

(식 A9)

(Formula A9)

과

에서 발생되는데,

에서의 적분은

의 거동을 하므로

이 클 때 사라진다. 남는 적분은 개구부 단면적

에서의 적분이다. Looking at the second integral of the above equation A9,

and

, &Lt; / RTI &gt;

The integral at

The behavior of

It disappears when it is big. The remaining integral is the cross-

.

에서

로 일정하므로 아래 식 A10 과 같은 관계가 성립된다.The pressure

in

Therefore, the following relation is established as in the formula A10.

(식 A10)

(Formula A10)

Therefore, the pressure integral is given by the following equation A11.

(식 A11)

(Formula A11)

보다 약간 작다. 거리가 멀어지면

와 거의 같고, 개구부 단면 근처에서만 달라져서 단면에서의 압력에 가까이 가게 된다.The final integral of the above equation A11 is the integration at the wall. The pressure on the wall

Lt; / RTI &gt; As the distance goes away

And is close to the pressure at the cross section only at the vicinity of the cross section of the opening.

로 표기하면 모멘텀 보존법칙은 다음 식 A12 와 같이 표현할 수 있다.Thus, the final integral has a positive value and is smaller than the second integral. this

, The momentum conservation law can be expressed as the following equation A12.

(식 A12)

(Formula A12)

를

으로 바꾸어 표현할 수 있다. 따라서 아래 식 A13 이 도출된다.When the equation A5 is substituted for the above equation,

To

. Therefore, the following equation A13 is derived.

(식 A13)

(Formula A13)

에서 속도는 거의 일정하게 유지되므로 대표 속도와 그 안에 있는 질량으로 표현할 수 있다. 또한 개구부 단면

에서의 적분은 속도가 면적상의 위치에 따라 변하는데, 이것의 평균개념을 사용하면 아래 식 A14 와 같다.Considering the second integral of the above equation A13,

The velocity is kept almost constant and can be expressed by the representative velocity and the mass in it. Also,

The integral at the velocity changes with the position on the area, and its mean concept is shown in the following equation A14.

(식 A14)

(Formula A14)

The over bar in equation A14 means the mean value. Gastroesophage is the result of applying equations for conservation of momentum.

Since the fluid is assumed to be an incompressible non-viscous fluid, the velocity field can be expressed using the velocity potential. Using the velocity potential, the pressure integral at the wall surface can be expressed in terms of velocity and potential using the Bernoulli equation. Therefore, it is expressed as the expression A15.

(식 A15)

(Formula A15)

Substituting this into equation A14 yields the following equation A16.

(식 A16)

(Formula A16)

The momentum conservation law is confirmed by using the above equation A2 '.

(식 A17)

(Formula A17)

에서는 속도의 거동 때문에 적분값이 사라지고, 결국 개구부 단면과 벽면에서의 적분만으로 표현된다.The difference of the above equation A17 from the previous equation A9 is in the second integration. Looking at the second integral,

The integral value disappears due to the behavior of the velocity, and is expressed only by the integral of the opening section and the wall surface.

(식 A18)

(Formula A18)

Substituting Equation A18 and Equation A11 into Equation A17 yields the following Equation A19.

(식 A19)

(Formula A19)

은 x 방향의 속도만이 아니라 전체 속도의 제곱이란 점이고, 또한 벽면에서의 적분도 고려하여야 한다는 점이다. 식 A16 과 식 A19 는 같은 문제에 대한 다른 표현식이다.The above formula A19 differs from the above formula A16 in that the velocity square

Is not only the velocity in the x direction but also the square of the total velocity, and also the integration on the wall must be taken into consideration. Expression A16 and Expression A19 are different expressions for the same problem.

The concept of added mass is used to briefly express the equation. The above three items of A16 and A19 are related to mass. In the absence of viscosity and no free surface wave, the velocity changes instantaneously as the velocity in the cross section of the aperture changes. This flow is not time dependent but is formed proportional to the flow rate at the opening cross section. Therefore, the inertial force term can be expressed by the following equation A20.

(식 A20)

(Formula A20)

Here, the following expression A21 is established.

(식 A21)

(Formula A21)

The representative speed at the cross section of the opening is defined as the average speed as follows.

(식 A22)

(Formula A22)

만큼 떨어진 곳에서의 속도는 다음처럼 표현된다. 이것은 위 식 A7 에서 도출된 것이다.The integration of the velocity squared on the wall is as follows.

The speed at the distance is expressed as follows. This is derived from equation A7 above.

(식 A23)

(Formula A23)

에서의 적분을 살펴보면 아래와 같다.Of the formula A16

The integration in the following is as follows.

(식 A24)

(Formula A24)

는 개구부 단면의 반지름과 같게 택한다. 따라서, 아래 식 A25 와 같은 관계가 성립한다.here,

Is equal to the radius of the cross-section of the opening. Therefore, the relationship shown in the following equation A25 is established.

(식 A25)

(Formula A25)

Using Equation A21 and Equation A25 and using the mean value at the cross section of the opening, the two equations of momentum conservation law A16 and A19 are expressed as follows.

(식 A26)

(Formula A26)

(식 A27)

(Formula A27)

Here, the mean square of the square and the square of the mean square on the cross section of the opening are slightly different, but this difference is judged to be small and can be treated equally. Then the above equation is expressed as

(식 A28)

(Formula A28)

(식 A29)

(Formula A29)

Since the above equations A28 and A29 are the same, the relationship between the orthogonal velocity and the total velocity can be obtained. That is, the following equation A30 can be obtained.

(식 A30)

(Formula A30)

The shrinkage coefficient of a circular orifice with a right angle edge is theoretically equal to the following value.

This is of course for non-viscous fluids. Also, the term shrinkage coefficient is used because it establishes the relationship between the orthogonal velocity and the overall velocity.

는 개구부 단면에서의 속도가 있을 때 이것에 비례하여 주위의 유체가 같이 움직이는 양을 의미한다. 즉 부가질량이다. 여기서는 근사적으로 원판의 부가질량을 사용하며, 원판의 부가질량은 아래와 같이 알려져 있다.A28, A29

Means the amount of movement of the surrounding fluid in proportion to the velocity at the cross section of the opening. That is, the added mass. Here, the added mass of the disk is approximately used, and the added mass of the disk is known as follows.

는 원판의 반지름으로서, 아래와 같다.here,

Is the radius of the disc, as shown below.

Therefore, the following equation A31 is established.

(식 A31)

(Formula A31)

를 약간 큰 값으로 근사하여 1/2로 사용하는 것이 바람직하다. 이에 따르면, 아래 식 A32, A33 이 도출된다.However, the additional masses considered here also include the effect of blocking fluid flow on the wall, so it is reasonable to use slightly larger values than this. Therefore,

It is preferable to approximate it to a slightly larger value and use it as 1/2. According to this, the following equations A32 and A33 are derived.

(식 A32)

(Formula A32)

(식 A33)

(Formula A33)

?이어서

인 경우에 해당하는 방정식이다. 두 식 A중 어느 것을 사용하여도 되지만, 첫 번째 식을 사용하는 것이 편리하다.The above formula is the same. Also

?next

Is an equation corresponding to the case of. Either formula A may be used, but it is convenient to use the first formula.

The final speed of the steady state is given by the following equation A34.

(식 A34)

(Formula A34)

The velocity according to equation A34 is the velocity orthogonal to the orifice. To calculate the flow rate through the orifice it is reasonable to calculate the velocity perpendicular to the orifice.

The rate of change at the beginning, that is, at t = 0, is as follows.

(식 A35)

(Formula A35)

The time to reach the final speed by the initial rate of change of speed is shown in the following equation A36.

(식 A36)

(Formula A36)

The relationship between t / T and u / u _f is shown in FIG. 2 as a graph. After this time, u / u _f is 0.765, and u / u _f is 0.965 when 2T is passed, and it can be seen that t / T = 2.5 should be enough for u / u _f to be 0.99.

)가

보다 클 때는 계산을 하는 것이 바람직하지 않다.

를 적절히 작게 택하여 이런 경우가 나타나지 않도록 한다. 그러나

를 작게 택했을 경우라도 면적이 작아지면 이런 경우가 발생하게 된다. 이럴 때는 계산 값이 정상상태 값을 넘어가지 않게 제한을 두거나, 이곳에서만

를 작게 택하여 계산을 한다. (5개로 나누고 다섯 번 하는 식으로) 또한 여기서 보면 압력차가 작아지면 도달시간이 길어진다. 이것이 의미하는 바는 처음에는

가 작아서 문제가 될 수도 있으나 이때는 유동의 속도가 커서 공기압력의 진동현상은 발생하지 않는다. 압력차가 작아지면 도달시간이 길어지기 때문에 당연히 위의 동역학적 모델이 사용될 것이므로 압력의 진동현상을 줄일 수 있을 것이다. 이렇게 u 를 구하고 유량을 계산할 때는 유출계수

를 곱하여야 하는데, 앞에서 보았듯이 0.756이 이미 곱해져 있으므로

는 0.9정도를 사용하는 것이 좋다.Referring to FIG. 2,

)end

It is not desirable to do calculations when larger.

So that this case does not occur. But

Even if it is small, this case occurs when the area becomes small. In this case, you can limit the calculation so that it does not exceed the steady state value,

And the calculation is performed. (5 times divided into 5 times) In addition, as the pressure difference becomes smaller, the reaching time becomes longer. What this means is that at first

Is small, but at this time, the velocity of the flow is large, so that the air pressure does not oscillate. As the pressure difference becomes smaller, the above dynamic model will be used because of the longer reaching time, so that the vibration phenomenon of the pressure can be reduced. When u is obtained and the flow rate is calculated,

. As we have seen, 0.756 has already been multiplied

Is about 0.9.

The density is determined according to the sign of u. It is not determined according to the sign of the pressure difference. The equation derived above is the equation for flowing in one direction only, and the same equation for flowing in the opposite direction. The equation for the case of flowing in both directions using this is expressed as follows.

(식 A37)

(Formula A37)

For large area orifices:

(식 A38)

(Formula A38)

The process of deriving the above dynamic orifice equation is summarized as follows.

의 control volume 을 반구형 형상으로 정의한다. 그러면 해당 control volume 에서의 질량 보존에 관한 식 B1 과 모멘트 보존에 관한 식 B2 를 얻을 수 있다.From Fig. 1, in which the fluid flow of the opening is shaped,

The control volume of the hemispherical shape is defined as a hemispherical shape. We can then obtain equation B1 for mass conservation and equation B2 for moment conservation in the corresponding control volume.

(식 B1)

(Formula B1)

(식 B2)

(Formula B2)

의 control volume을 개구부의 수직한 방향의 직육면체 형상으로 가정하고,

와 마찬가지로 질량 보존에 관한 식과 모멘트 보존에 관한 식을 유도할 수 있다. 앞서 밝힌 바와 같이 유체는 비압축성이라고 가정하고, 침수 해석 동안의 control volume 은 일정하므로 위 식 B1 은 식 B3 과 같이 유도될 수 있다. 또한, 개구부에서의 유체 흐름은 항상 개구부에 수직하고, 수직 방향의 체적력(body force)은 없다고 가정하면, 식 B2 는 식 B4 와 같이 유도될 수 있다.In addition,

Assuming that the control volume of the opening is a rectangular parallelepiped shape in the vertical direction of the opening,

The equation for conservation of mass and the equation for conservation of moment can be derived. As previously stated, assuming that the fluid is incompressible and the control volume during the immersion analysis is constant, the above equation B1 can be derived as in equation B3. Further, assuming that the fluid flow in the openings is always perpendicular to the openings and that there is no body force in the vertical direction, equation B2 can be derived as in equation B4.

(식 B3)

(Formula B3)

(식 B4)

(Formula B4)

에 적용하면 개구부로부터 유출되는 유체의 유량

를 식 B5 와 같이 유도할 수 있다. 또한 유입되는 쪽의 control volume 내에서의 속도와 압력 분포가 동일하다는 가정과 유체는 비점성이라는 가정 하에 식 B4 를

에 적용하면 식 B6 과 같이 유도할 수 있다.Expression B3

The flow rate of the fluid flowing out from the opening portion

Can be derived as shown in equation B5. Assuming that the velocity and pressure distributions in the control volume on the inflow side are the same and that the fluid is inviscid,

Can be derived as shown in Equation B6.

(식 B5)

(Formula B5)

(식 B6)

(Formula B6)

를 대입하면 식 B7 과 같이 유량에 대한 속도벡터를 유도할 수 있다. 또한 식 B4 를 C₂ 에 적용하여, 식 B6 과 식 B7 을 대입하면 식 B8 과 같이 개구부를 지나는 유체의 양을 계산할 수 있는 동역학적 오리피스 방정식을 얻을 수 있다. 즉, 위에서 유도한 식 A37 과 같은 식을 얻을 수 있다.Then, the formula B3 is applied to C ₂ , and the formula

, The velocity vector for the flow rate can be derived as shown in Equation B7. Applying equation B4 to C ₂ and substituting equation B6 and equation B7, we obtain a dynamic orifice equation that can calculate the amount of fluid passing through the opening as in equation B8. That is, the same expression as the above-mentioned expression A37 can be obtained.

(식 B7)

(Formula B7)

(식 B8)

(Formula B8)

This explains the derivation process of the dynamical orifice equation.

The dynamic orifice equation derived as described above is applied to the immersion analysis of a damaged ship as follows.

FIG. 3 is an enlarged view of a portion of a damaged ship, and FIG. 4 is an enlarged view of an area in which an opening appears as a circle in FIG. In FIG. 3, it is assumed that a vessel having a compartment is formed by a predetermined partition, and an opening is formed in the compartment, so that fluid outflow occurs. In Fig. 3, the first space S1 and the second space S2 are shown. The first space and the second space may each be a compartment in the ship, the opening may be the damage caused by the partition in the ship, or the first space may be inside the vessel and the second space outside the vessel, It may be something that happened.

First, it is assumed that only two kinds of fluids are present in the first space and the second space, that is, water and gas. That is, as shown in Fig. 3, there are the gas A1 and the water B1 in the first space, and the gas A2 and the water B2 in the second space. Under these assumptions, the cross-sectional area of the opening in the compartment where the opening is formed and the fluid outflow occurs is defined by the gas-gaseous cross-sectional area I, the water-gas cross-sectional area J, , And a cross-sectional area (K) by water-water.

According to this, the cross-sectional area of the opening may have nine cases as shown in Fig.

The derived kinetic orifice equations are applied differently for each cross-sectional area according to the type of fluid.

First, the kinetic orifice equation in the cross-sectional area by gas-gas is applied as in the following equation C1.

(식 C1)

(Formula C1)

는 기체-기체로 이루어진 단면 영역의 넓이를 뜻한다. 또한,

과

는 각각 제1 공간과 제2 공간의 기체 압력을 의미한다. 또한, 동역학적 오리피스 방적식에 의해서,

는 두 제1 공간과 제2 공간 중 더 높은 기체 압력을 가진 공간의 기체의 밀도를 의미한다.In the above equation C1,

Is the width of the cross-sectional area of the gas-gas. Also,

and

Mean the gas pressure in the first space and the second space, respectively. Further, by the kinetic orifice spinning type,

Means the density of the gas in the space having the higher gas pressure of the two first spaces and the second space.

Next, the kinetic orifice equation in the cross-sectional area by the water-gas is applied as in the following equation C2.

(식 C2)

(Formula C2)

는 물- 기체에 의한 단면 영역의 넓이를 의미한다.

은 제1 공간의 물의 압력을 의미한다. 또한,

는 두 공간내의 유체 중 더 높은 유체 압력을 가진 공간의 유체의 밀도를 의미한다.In the above equation C2,

Means the area of the cross-sectional area due to the water-gas.

Quot; means the pressure of water in the first space. Also,

Means the density of the fluid in the space having the higher fluid pressure in the fluid in the two spaces.

Next, the kinetic orifice equation in the cross-sectional area by the water-gas is applied as in the following expression C3.

(식 C3)

(Formula C3)

는 물-물에 의한 단면 영역의 넓이를 의미한다.

은 제1 공간의 물의 압력을 의미하며,

는 제2 공간의 물의 압력을 의미한다. 또한,

는 두 공간 내의 유체 중 더 높은 유체 압력을 가진 공간의 물의 밀도를 의미한다.In the above formula C3,

Means the width of the cross-sectional area due to water-water.

Means the pressure of water in the first space,

Means the pressure of water in the second space. Also,

Means the density of water in the space having higher fluid pressure in the fluid in the two spaces.

,

,

의 면적을 계산하고, 제 1 공간과 제 2공간의 압력 차이를 함께 동역학적 오리피스 방정식에 대입하여 각 단면에서의 속도를 계산한다. 위 과정을 매 시간단위 마다 반복하여 물 또는 기체의 유입, 유출량을 계산할 수 있다. In order to calculate the inflow and outflow of water or gas at every hour unit through the kinetic orifice equation, we need to take into account the total of 9 cross-sectional areas shown in Fig. Every hour about the cross-sectional situation of the opening

,

,

And calculates the velocity at each cross section by substituting the pressure difference between the first space and the second space into the dynamic orifice equation. The above process can be repeated every hour unit to calculate the inflow and outflow of water or gas.

In summary, the above equations C1, C2, and C3 are expressed as the time variation of the flow velocity, respectively. Accordingly, the equations C1 to C3 are derived as shown by the following formula C4. Here, each cross-sectional area is represented by A _opening .

(식 C4)

(Formula C4)

을 현재 시간 단위에서의 유속

로 나타내면 아래 식 C5와 같다.Expression C4 is integrated by the Euler method, and the flow rate at the next time unit

To the current time unit

Is expressed by the following expression C5.

(식 C5)

(Formula C5)

In formula C5, and p _0, p ₁ indicates the first space and the fluid pressure of the second space at the current time (u _n), respectively.

를 통해 유량

를 구하면 아래의 식 C6 과 같다.The flow rate of the next time can be calculated through the flow rate calculated every hour as shown in equation C5. That is, the flow rate per hour derived from the above equation

Through flow

Is given by Equation C6 below.

(식 C6)

(Formula C6)

는 흐르는 유체의 밀도 계수,

는 계산된 유량,

는 유체가 흐르는 개구부의 단면적,

는 시간 간격을 나타낸다. 식 C6 에 의해서, 매 시간 단위마다 유체의 유입, 유출량을 도출할 수 있다.In the above equation C6

Is the density coefficient of the flowing fluid,

Is the calculated flow rate,

Sectional area of the opening through which the fluid flows,

Represents the time interval. By the formula C6, it is possible to derive the inflow and outflow amount of the fluid every time unit.

However, if other fluids are taken into consideration, another number of cases will occur.

Fig. 6 is an enlarged view of a portion of a damaged ship, and Fig. 7 is an enlarged view of an area where an opening of Fig. 6 occurs. 6 and 7 As shown in FIGS. 3 and 4, it is assumed that a ship having a predetermined section is assumed, and an opening is formed in the section, so that a fluid outflow occurs. The first space S1 and the second space S2 in Fig. 6 may also be a partition in the ship or a space outside the ship, respectively.

In addition to water and gas, oil exists in the first space and the second space. 6 and 7, the gas A1, the water B1 and the oil C1 are present in the first space S1 and the gas A2 and the oil C2 are present in the second space S2. Lt; / RTI &gt;

Under this assumption, the cross-sectional area of the opening in the compartment where the opening is formed and the fluid outflow occurs, for example, as shown in Fig. 7, is defined as the cross-sectional area P by the oil- (Q), and water-oil cross-sectional area (R).

In this way, when the oil is included in the immersion analysis process, the cross section of the opening can be divided into three sections: the oil-gas cross-sectional area, the oil-oil cross-sectional area, and the water- Additional consideration will be given. In addition, the kinematic orifice equation derived above is also applied independently for each cross-sectional area.

First, the kinetic orifice equation in the cross-sectional area P between the oil and gas is utilized as shown in the following equation C7.

(식 C7)

(Formula C7)

는 기름-기체로 이루어진 단면 영역의 넓이를 뜻한다.

은 제1 공간의 기름의 압력이며,

는 제2 공간의 기체의 압력이다. In the above equation

Means the width of the cross-sectional area of the oil-gas.

Is the pressure of the oil in the first space,

Is the pressure of the gas in the second space.

Next, the dynamic orifice equation in the oil-oil cross-sectional area (Q) is used as shown in the following equation (C8).

(식 C8)

(Formula C8)

는 기름-기름에 의한 단면 영역의 넓이를 뜻한다.

은 제1 공간의 기름의 압력이며,

는 제2 공간의 기름의 압력이다.In the above equation

Means the area of the cross-sectional area due to oil-oil.

Is the pressure of the oil in the first space,

Is the pressure of the oil in the second space.

The dynamic orifice equation at the cross-sectional area (R) by water-oil is used as shown in the following equation (C9).

(식 C9)

(Formula C9)

는 물-기름에 의한 단면 영역의 넓이를 뜻한다.

은 제1 공간의 물의 압력을 의미하며,

는 제2 공간의 기름의 압력이다.In the above equation

Means the area of the cross-sectional area due to water-oil.

Means the pressure of water in the first space,

Is the pressure of the oil in the second space.

The derivation of the inflow and outflow of fluids by the above equations C7, C8 and C9 can be derived through the same process as the above-mentioned equations C4 to C6.

In addition, as described above, three dynamic orifice equations for the cross-sectional area shown in FIG. 5 are additionally considered by considering three dynamic orifice equations for the cross-sectional area shown in FIG. 8 in the three dynamic equilibrium orifice equations, . As shown in Fig. 8, there are 35 kinds of openings including oil, water, and gas.

에 대해 변경 사항을 반영하였고, 본 발명에서 기름에 적용한 실시 예는 약 0.6 ~ 0.7 로 기름의 종류에 따라 다르게 적용되어야 한다는 것을 확인하였다.And, preferably, when applying the equation C6 to calculate the flow rate, the density coefficient of the fluid can also be applied differently depending on the flowing fluid. In the conventional method, the density coefficient of the fluid is given as 0.9 considering the viscosity. (Ruponen, 2007). However, in this study, it was applied to oil and various fluids. As a result, it was found that it did not fit well with the experimental results. Thus, in the present invention,

And the embodiment applied to the oil according to the present invention is about 0.6 to 0.7, and it is confirmed that the embodiment should be applied differently depending on the type of oil.

Therefore, in the presence of gas-water-oil, a total of 44 situations should be considered. In addition, it is desirable to change the density coefficient of the fluid for each kind of fluid in 44 situations. Of course, it is also possible to add a kinetic orifice equation for multiple fluids by taking into account the outflow of fluids other than just considering the water-oil-gas as above.

Below, the immersion analysis of a ship considering solid cargo will be explained.

There are various types of solid cargo in the ship as well as fluids such as water and oil. Therefore, it is necessary to analyze the immersion of the ship in consideration of this. It is considered that the fluid does not flow into the space where the solid cargo exists.

In the immersion analysis method so far, only the flooding rate of the compartment was considered when considering the solid cargo, and there was no flooding analysis considering the shape and arrangement of the actual solid cargo. The flooding rate of a compartment is a method of limiting the fluid inflow volume of the compartment in consideration of the fact that the fluid can not flow into the volume of the solid cargo when the solid cargo exists in the compartment. The flooding rate of a general ship segment is shown in the table shown in Fig.

However, when such a simple consideration is taken, it can not be calculated considering the inflow situation of the fluid due to the arrangement of the solid cargo. Therefore, accurate hydrostatic pressure and the center of gravity of the fluid in the compartment can not be derived.

In other words, when seawater enters the submerged compartment, the weight and attitude of the ship change every hour. Accordingly, the increased weight and changed posture through calculation of inflow of seawater influences the shape of the fluid in the ship by the free water surface effect. Therefore, it is necessary to accurately consider the shape of the changed fluid.

Accordingly, in the present invention, the calculation is performed by using the polyhedron integral method in order to calculate the fluid volume and the center of gravity according to the inflow amount of the fluid, taking into account the shape and the volume of the solid body.

According to the polyhedral integration method, the shape of the fluid and the solid is formed into a tri-mesh shape, and then the volume and the volume center thereof are calculated. Referring to FIG. 10A, a triangular mesh is assumed to be a tetrahedron with respect to an arbitrary point, and a volume thereof is calculated. Here, the volume of the tetrahedron can be calculated according to the following expression C10.

(식 C10)

(Formula C10)

When the polyhedron integration method is applied, the shape of the ship is formed of a set of triangular meshes, and thus the volume, shape center, and shape moment can be calculated using the triangular mesh. Fig. 10B is a view showing the application of the polyhedron integration method in the calculation of the volume of the fluid immersed in the inclined ship. Fig. For example, as shown in FIG. 10B, when the shape of the ship is cut into a specific cross section, that is, when the ship is inclined to a specific height and the fluid is inside the ship, the shape of the fluid inside the ship, Volume, volume center, etc. can be accurately calculated.

According to such a polyhedron integration method, the shape of the fluid inside the vessel can be defined as a set of triangular meshes, and accurate fluid shape can be derived through accumulation of the volume calculations of a plurality of tetrahedrons. That is, the volume of the shape can be calculated by calculating the volume using the above-mentioned C10 formula for all the triangular meshes with respect to an arbitrary point, and then adding all together.

FIG. 11 shows a comparison between the fluid plane based method and the polyhedron integral method among the fluid volume calculation methods.

Conventionally, as shown in FIG. 11 (a), a method of adding a fluid inflow amount on a water surface assuming a fluid inflow amount by using a fluid plane based method is adopted. However, as described above, this method does not reflect the shape change of the fluid in the vessel due to the change of attitude of the vessel.

However, by using the polyhedron integration method as in the present invention, it is possible to accurately describe the inflow amount of the free shape. In addition, there is an advantage that the inflow shape and the center of gravity of the fluid can be accurately calculated considering the shape of the solid body as described above.

Hereinafter, verification results of the immersion analysis method using the dynamic orifice equation as described above will be described.

In Ruponen 's work, we conducted a model line test to verify the immersion method using the hydraulic orifice equation and compared the results. In this study, the immersion analysis method using the dynamical orifice equation was verified by comparing the experimental results obtained from Ruponen 's research with the results of inundation analysis using dynamic orifice equations. The model line used in Ruponen's study is shown in Figure 12 (a), and the model line of this study, which is modeled in the same way, is shown in Figure 12 (b). The main specifications of the model line are shown in the table shown in FIG.

In this study, we compared the experimental results of two cases performed by Ruponen (2007). In the first case, the posture of the ship over time was compared in case of starboard damage. In the second case, the ship's posture was compared with time when the bottom was damaged. Details of the two cases are as shown in Fig.

Figures 15 to 18 show the results of the analysis by Ruponen (2007), the experimental results, and the analysis results of the present invention through the pitch and heave of the ship.

FIGS. 15 and 16 are respectively a comparison of the results of the analysis by the Ruponen (2007) and the experimental results and the analysis results of the present invention in the first case through the pitch and heave of the ship, and FIGS. 17 and 18 respectively show Ruponen ) And the experimental result and the analysis result of the present invention are compared with the pitch and heave of the ship.

 In the comparison results shown in FIGS. 15 to 18, the solid line A represents the result of Ruponen 2007, the solid line B represents the analysis result of Ruponen 2007, The results of the analysis using the mechanical orifice equation are shown. Also, the green solid line (D) represents the CFD interpretation (Strasser et al., 2009) for the same case. However, in FIGS. 15 to 18, the black solid line and the blue solid line are substantially overlapped.

As shown in FIGS. 15 to 18, the analysis results according to the present invention are not significantly different from each other in comparison with the three analysis results, and the analysis results according to the present invention are most similar to the experimental results. Therefore, it can be predicted that the analysis method according to the present invention secures reliability.

Next, the analysis method of oil spill is verified by comparison with Debra (2001) study. In the present invention, the dynamic orifice equation used for immersion analysis is confirmed to be reliable by comparing with the experimental results of Ruponen (2007). However, inundation analysis considering liquid cargo (oil) was not considered in the experiment of Ruponen (2007). In the present invention, an oil spill experiment in a tank conducted by Debra (2001) is compared with an analysis result according to the present invention for verification of oil spill analysis method.

Figure 19 shows the model used for experiments in a study by Debra (2001). The table in Fig. 20 also summarizes the characteristics of the oil used in the experiment. The oil spill analysis method according to the present invention is verified through comparison with two experiments conducted by Debra (2001). In the first case shown in FIG. 21, oil flows out from the air, and in the second case shown in FIG. 22, oil flows out in the water. In Fig. 22, the model of Fig. 19 is inserted into the water tank of a predetermined height to analyze the oil spill state.

As shown in FIGS. 21 and 22, the analysis results of the present invention for two cases and the values measured by experiments in the study of Debra (2001) are as shown in FIGS. 23 and 24, respectively. As shown in FIGS. 23 and 24, in the case of the first case, the oil height over time is very similar to the experimental result, and the final result shows a relatively small error of about 1 mm. The analysis results of the second case show that the amount of oil spill over time is very similar to the experimental results, but the water shows a slight difference at the beginning. This is expected in the present invention as a result of not considering the viscosity of the fluid. Nevertheless, it can be seen that the outflow and inflow of water and oil are very similar in the final state. Therefore, it can be understood that the oil spill analysis method used in the present invention has a certain degree of reliability.

Next, referring to Fig. 25, the accuracy of the immersion analysis method considering the solid cargo of the present invention is verified through comparison with a commercial program.

In order to verify the immersion analysis method considering the solid cargo utilized in the present invention, the results with commercial CAD programs were compared. The model modeled for comparison is shown in Fig. As shown in the figure, it is assumed that a cube-shaped cargo with a length of 5 m is loaded in a 10-m box. And that it was damaged at the same height as the cargo. When water is introduced through the damaged opening, water having the same hydrostatic pressure, that is, equal to the height of the opening, will enter. Therefore, the volume excluding solid cargo within 5m height will be occupied by water. Calculated using commercial CAD programs, the volume of water taking up solid cargo is 375m ³ . As a result of analyzing the flood analysis method considering the solid cargo proposed in the present invention, the same result can be obtained exactly. Therefore, it can be confirmed that the immersion analysis method considering the solid cargo used in the present invention leads to accurate calculation results.

While the present invention has been particularly shown and described with reference to exemplary embodiments thereof, it is to be understood that the invention is not limited to the disclosed exemplary embodiments, but, on the contrary, It should be understood that various modifications may be made by those skilled in the art without departing from the spirit and scope of the present invention.

S1: First space
S2: the second space
A1, A2: Gas
B1, B2: Water
C1, C2: Oil

Claims (8)

The fluid inflow amount between the first fluid and the second fluid respectively located in the first space S1 and the second space S2 which are divided from each other with a predetermined partition therebetween and the outflow amount are calculated to analyze the submersion of the ship In a method of flooding analysis of a ship,
Applying a dynamic orifice equation to the first fluid and the second fluid facing each other with the cross-sectional area of the opening formed in the partition wall as a boundary; / RTI &gt;
The cross-
A first fluid that faces each other across the cross-sectional area, and at least one separation area that has a predetermined area in accordance with the type of the second fluid,
Wherein the dynamic orifice equation is applied to each of the separation regions. delete The method according to claim 1,
The kinetic orifice equation may be expressed as:
A method for analyzing flooded water of a ship,

(Equation 1)
(A ₁ : cross-sectional area of the separation region,
p ₁ : the fluid pressure of the first fluid in the first space S1,
P ₂ : the fluid pressure of the second fluid in the second space S2,
ρ = density of the first fluid when u ≥ 0, ρ = density of the second fluid when u <0) The method of claim 3,
Applying the kinetic orifice equation to the first fluid and the second fluid facing each other with the cross-sectional area of the opening formed in the partition wall as a boundary,
Calculating the equation (2) by summing the equation (1) with the time variation of the flow velocity,

(Equation 2)
(A _opening : cross-sectional area of the separation area (= A ₁ ))
Integrating equation (2) by the Euler method to derive equation (3) representing the flow rate at the next time unit at the flow rate in the current time unit, and

(Equation 3)
(p _0: pressure of the first fluid in the first space (S1) at the current time (u _n),
p ₁ is the pressure of the fluid in the second space S2 at the current time u _n ,

: Flow rate at the next time unit,

: Flow rate in the current time unit

: Time interval)
And calculating a flow rate of each time by substituting the flow velocity derived from the equation (3) into the following equation (4).

(Equation 4)
(

: Flow rate,

: Flow rate,

: Density coefficient of flowing fluid,

: Time interval) The method of claim 4,
In Equation 4,

Is a method of immersion analysis of a ship having different values depending on the type of fluid. The method of claim 4,
When the first fluid or the second fluid is oil,
In Equation 4,

Is a method of inundation analysis of a ship of 0.6 to 0.7. The method according to claim 1,
And applying a flooding rate of each compartment according to the solid cargo present in the compartment within the vessel. The method of claim 7,
And calculating the inflow amount of the fluid by deriving the shape of the inflow fluid using the polyhedral integration method.

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