Method of Ship Ice Resistance Model Experiment Based on Non-refrigerated Model Ice

Abstract

The present disclosure discloses a method of ship ice resistance model experiment based on non-refrigerated model ice, including the following steps: determining the overall length L.sub.1, breadth B and scale ratio λ of a selected ship model; determining the size A.sub.1 of an experimental area for placing broken ice in the ship ice resistance model experiment; determining the characteristic length of model ice; determining the quantitative proportion of the model ice for each size under the target coverage ratio c of the model; obtaining the number of the model ice for each size under the target coverage ratio according to the quantitative proportion of the model ice for each size under the target coverage ratio c and the total area A.sub.2 of the model ice; determining the geometrical shape and parameters of each size under the target coverage ratio c of the model ice. The present disclosure solves the problems of poor economy and poor operability in a freezing model ice experiment of an ice basin, and provides a design method for carrying out a ship ice resistance model experiment in a towing tank.

Claims

1. A method of ship ice resistance model experiment based on non-refrigerated model ice, comprising the following steps: S1. determining an overall length L.sub.1, a breadth B, and a scale ratio λ of a selected ship model; determining a size A.sub.1 of an experimental area for placing broken ice in the ship ice resistance model experiment: according to the overall length L.sub.1 and the breadth B of the selected ship model, determining the minimum size of the experimental area, further determining the size of the experimental area:
L.sub.2≥5L.sub.1=21.8m,
W≥3B=1.968m,
A.sub.1=WL.sub.2, wherein, L.sub.2 represents a length of the experimental area, and W represents a width of the experimental area; S2. determining a characteristic length of model ice: S21. determining a target coverage ratio c of the model ice; S22. according to the experimental area size A.sub.1 obtained in step S1 and the target ice coverage ratio c obtained in step S21, determining a total area A.sub.2 of the model ice:
A.sub.2=cA.sub.1; S23. according to the bending theory of thin plate sitting on elastic foundation, determining a critical characteristic length L.sub.c of the broken ice without bending failure: $L_c=\sqrt[4]{\frac{D}{k}},$ wherein, D represents a flexural rigidity of ice, satisfying the following equation: $D=\frac{{\mathrm{Et}}^3}{12.Math.\left(1-v^2\right)},$ E represents an elastic modulus of ice, with the unit of Pa; t represents an actual thickness of the broken ice, with the unit of m; ν is Poisson's ratio; and k represents an elastic stiffness of the base, satisfying the following equation:
k=ρ.sub.wg, ρ.sub.w is the density of water, with the unit of kg/m.sup.3; and g is the acceleration of gravity, with the unit of kg/m.sup.2; S24. determining the critical characteristic length l: $l=\frac{L}{\lambda },$ wherein, L represents a characteristic length of the broken ice, satisfying the following condition:
L≤L.sub.c; S25. according to the critical characteristic length l of the model ice, determining a characteristic length l.sub.n of each size of the model ice in the ship ice resistance model experiment; S3. determining a quantitative proportion of the model ice for each size under the target coverage ratio c of the model ice: $N\left(l_n\right)=\{\begin{array}{c}{\beta }_1.Math.{l_n}^{-{\alpha }_1},l_n\in \left[1,40\right]\\ {\beta }_2.Math.{l_n}^{-{\alpha }_2},l_n\in \left[40,1500\right]\end{array}$ wherein, N(l.sub.n) represents a number of the model ice with the size l.sub.n, α.sub.1, a.sub.2, β.sub.1 and β.sub.2 are coefficients, α.sub.1=1.15, α.sub.2=1.87; when the characteristic length l.sub.n of the model ice is in a range of [l.sub.1,l.sub.2], the total area of the model ice satisfies the following equation: $A=\underset{l_1}{\stackrel{l_2}{\int }}.Math.n_a\left(x\right).Math.s\left(x\right).Math.\mathrm{dx}=\frac{-\mathrm{\pi \beta \alpha }}{4.Math.\left(\alpha -2\right)}.Math.\left(l_2^{\left(-\alpha +2\right)}-l_1^{\left(-\alpha +2\right)}\right),$ solving the following set of equations to obtain β.sub.1 and β.sub.2, $\{\begin{array}{cc}\mathrm{cA}=\stackrel{1500}{\underset{1}{\int }}.Math.n_a\left(x\right).Math.s\left(x\right).Math.\mathrm{dx},& A=1.Math.{\mathrm{km}}^2\\ {\beta }_1.Math.l^{-{\alpha }_1}={\beta }_2.Math.l^{-{\alpha }_2},& l=40.Math.m\end{array};$ S4. according to the quantitative proportion of the model ice of each size under the target coverage ratio c obtained in step S3, and the total area A.sub.2 of the model ice to obtain the number of the model ice of each size under the target coverage ratio c; and S5. determining a geometrical shape and parameters of the model ice for each size under the target coverage ratio c: a roundness R of the model ice satisfies the following equation: $R=\frac{d_p}{d}=\frac{\frac{P}{\pi }}{l_n}=\frac{P}{{\pi .Math.l}_n};$ wherein, d.sub.p represents a perimeter-equivalent diameter, d represents a area-equivalent diameter, and d is equal to l.sub.n, P represents a perimeter of geometrical shape of the model ice; an area S of the geometrical shape of the model ice satisfies the following equation: $S=\frac{{{\pi .Math.l}_n}^2}{4};$ a caliper diameter ratio R.sub.a of the model ice satisfies the following equation:
R.sub.a=D.sub.max/D.sub.min; determining P according to the value of R; determining the geometrical shape of the model ice according to P, S, and R.sub.a.

2. The method according to claim 1, wherein an actual construction method of the experimental area is to build a fence with PVC pipes connected by tee pipes, and an outer wall of the PVC pipe located under the water is pasted with pearl cotton board.

3. The method according to claim 1, wherein the model ice is made of H-type PP material.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0036] In order to more clearly illustrate the embodiments of the present disclosure or the technical solutions in the prior art, the drawings required in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings in the following descriptions are some embodiments of the present disclosure. For those of ordinary skilled in the art, other drawings can be obtained based on these drawings without inventive effort.

[0037] FIG. 1 is a flow diagram of the design method of ship ice resistance model experiment based on non-refrigerated model ice in the embodiment of the present disclosure.

[0038] FIG. 2 is a function curve of the size distribution law of broken ice.

[0039] FIG. 3 is a distribution diagram of cumulative quantity of the model ice for each size under the target coverage ratio c of the model ice in the embodiments of the present disclosure (c=0.6).

[0040] FIG. 4 is a schematic diagram of the geometric shape (30 cm) of the model ice in the embodiment of the present disclosure.

[0041] FIG. 5 shows the installation effect of the fence in the embodiment of the present disclosure.

[0042] FIG. 6 is an assembly diagram of PVC pipe and pearl cotton board in the embodiment of the present disclosure.

[0043] FIG. 7 is a picture of an experimental area in the embodiment of the present disclosure.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0044] To make the objectives, technical solutions and advantages of the present disclosure clearer, a clear and complete description in the embodiments of the present disclosure may be given herein after in combination with the accompany drawings in the embodiment of the present disclosure. Obviously, the described embodiments are parts of the embodiments of the present disclosure, but not all of them. Based on the embodiments in the present disclosure, all other embodiments obtained by those of ordinary skilled in the art without inventive effort are within the scope of the present disclosure.

[0045] As shown in FIG. 1 to FIG. 7, a design method of ship ice resistance model experiment based on non-refrigerated model ice, includes the following steps:

[0046] S1. The overall length L.sub.1, breadth B and scale ratio λ of the selected ship model were determined.

[0047] A FPSO ship model was used in this embodiment, with a scale ratio A=50 and the main size of the ship model is shown in the table below.

TABLE-US-00002 Overall Length (m) 4.36 Length between 4.2 Perpendiculars (m) Breadth (m) 0.656 Depth (m) 0.364 Draft (m) 0.16

[0048] L.sub.1=4.36 m, B=0.656 m.

[0049] The size A.sub.1 of the experimental area for placing broken ice in the ship ice resistance model experiment was determined:

[0050] According to the overall length L.sub.1 and the breadth B of the selected ship model, the minimum size of the experimental area was determined, and the size of the experimental area was further determined:

L.sub.2≥5L.sub.1=21.8m,

W≥3B=1.968m,

A.sub.1=WL.sub.2,

wherein, L.sub.2 represents the length of the experimental area, and W represents the breadth of the experimental area.

[0051] According to the minimum size of the experimental area and the actual size of the towing tank (170 m×7.0 m×4.0 m), the size of the experimental area of 29 m×3.0 m×4.0 m was finally selected.

[0052] S2. The characteristic length of the model ice was determined

[0053] S21. The target coverage ratio c was determined

[0054] The ratio c was set to 90%, 80%, and 60% respectively.

[0055] S22. According to the experimental area size A.sub.1 obtained in step S1 and the target ice coverage ratio c obtained in step S21, a total area A.sub.2 of the model ice was determined:

A.sub.2=cA.sub.1,

[0056] When c was equal to 90%, 80%, and 60%, the corresponding A.sub.2 was 67.5 m.sup.2, 60 m.sup.2 and 45 m.sup.2.

[0057] S23. According to the bending theory of thin plate sitting on elastic foundation, the critical characteristic length L.sub.c of the broken ice without bending failure was determined:

[00009]$L_c=\sqrt[4]{\frac{D}{k}},$

wherein, D represents a flexural rigidity of the ice, which satisfies the following equation:

[00010]$D=\frac{{\mathrm{Et}}^3}{12.Math.\left(1-v^2\right)},$

[0058] E represents an elastic modulus of the ice, E=5 GPa; and t represents an actual thickness of the broken ice, t=1 m; ν represents Poisson's ratio, ν=0.3; k represents an elastic stiffness of the base, which satisfies the following equation:

k=ρ.sub.wg,

[0059] ρ.sub.w is the density of water, ρ.sub.w=1025 kg/m.sup.3; and g is the acceleration of gravity, g=9.81 kg/m.sup.2.

[0060] S24. The critical characteristic length l was determined:

[00011]$l=\frac{L}{\lambda };$

wherein, L represents the characteristic length of the broken ice, which satisfies the following equation:

L≤L.sub.c.

[0061] So,

[00012]$l=\frac{L}{\lambda }\le \frac{L_c}{\lambda }=0.3.Math.m$

[0062] S25. According to the critical characteristic length l of the model ice, the characteristic length l.sub.n of each size of the model ice in the ship ice resistance model experiment was determined to be 10 cm, 15 cm, 20 cm, 25 cm, and 30 cm respectively.

[0063] S3. the quantitative proportion of the model ice for each size under the target coverage ratio c of the model ice was determined:

[00013]$N\left(l_n\right)=\{\begin{array}{c}{\beta }_1.Math.{l_n}^{-{\alpha }_1},l_n\in \left[1,40\right]\\ {\beta }_2.Math.{l_n}^{-{\alpha }_2},l_n\in \left[40,1500\right]\end{array},$

wherein, this equation is the size distribution law function of the broken ice.

[0064] Wherein, N(l.sub.n) represents a number of the model ice with the size l.sub.n, α.sub.1, α.sub.2, β.sub.1 and ρ.sub.2 are coefficients, α.sub.1=1.15, α.sub.2=1.87, when the characteristic length l of the model ice is in the range of [l.sub.1,l.sub.2], the total area of the model ice satisfies the following equation:

[00014]$A=\underset{l_1}{\stackrel{l_2}{\int }}.Math.n_a\left(x\right).Math.s\left(x\right).Math.\mathrm{dx}=\frac{-\mathrm{\pi \beta \alpha }}{4.Math.\left(\alpha -2\right)}.Math.\left(l_2^{\left(-\alpha +2\right)}-l_1^{\left(-\alpha +2\right)}\right)$

[0065] The following equation set was solved to find β.sub.1 and β.sub.2.

[00015]$\{\begin{array}{cc}\mathrm{cA}=\frac{-{\mathrm{\pi \beta }}_1.Math.{\alpha }_1}{4.Math.\left({\alpha }_1-2\right)}.Math.\left({40}^{\left(-{\alpha }_1+2\right)}-1^{\left(-{\alpha }_2+2\right)}\right)+\frac{-{\mathrm{\pi \beta }}_2.Math.{\alpha }_2}{4.Math.\left({\alpha }_2-2\right)}.Math.\left({1500}^{\left(-{\alpha }_1+2\right)}-{40}^{\left(-{\alpha }_2+2\right)}\right),& A=1.Math.{\mathrm{km}}^2\\ {\beta }_1.Math.l^{-{\alpha }_1}={\beta }_2.Math.l^{-{\alpha }_2},& l=40.Math.m\end{array}\hspace{1em}$

[0066] The ratio c was equal to 90%, 80% and 60%, and the corresponding β.sub.3 and β.sub.2 values were respectively solved, as shown in the table below:

TABLE-US-00003 Target Coverage 0.9 0.8 0.6 β.sub.1 1.776261 1.578899 1.184174 β.sub.2 0.17498 0.155538 0.11665378

[0067] β.sub.1 and β.sub.2 were plugged into the size distribution law function of the broken ice to obtain a cumulative distribution function of the corresponding target coverage. According to the obtained cumulative distribution function and the scale ratio λ, the quantitative proportion of the model ice with different sizes under the target coverage c of the model ice was calculated (In order to get a quantity of 30 cm by interpolation, calculating the cumulative quantity of 35 cm).

TABLE-US-00004 35 cm 30 cm 25 cm 20 cm 15 cm 10 cm Full Dimension 0.0175 0.015 0.0125 0.01 0.0075 0.005 (km) 0.9 Accumulation 186 222 274 354 493 786 Current 36 52 80 139 293 0.8 Accumulation 166 198 244 315 439 699 Current 32 46 71 124 261 0.6 Accumulation 124 148 183 236 329 524 Current 24 35 53 93 195

[0068] S4. According to the quantitative proportion of the model ice of each size under the target coverage ratio c obtained in step S3, and the total area A.sub.2 of the model ice, the number of the model ice of each size under the target coverage ratio c was obtained, as shown in the table below:

TABLE-US-00005 Target Coverage 30 cm 25 cm 20 cm 15 cm 10 cm 0.9 197 283 437 758 1598 0.8 175 251 389 674 1421 0.6 131 189 292 505 1066

[0069] The cumulative quantity distribution with target coverage ratio of 0.6 is shown in FIG. 3.

[0070] S5. The geometrical shape and parameters of the model ice for each size under target coverage ratio c were determined:

[0071] The roundness R of the model ice satisfies the following formula:

[00016]$R=\frac{d_p}{d}=\frac{\frac{P}{\pi }}{l_n}=\frac{P}{{\pi .Math.l}_n};$

wherein, d.sub.p represents a perimeter-equivalent diameter, d represents a area-equivalent diameter, and d is equal to l.sub.n, P represents a perimeter of geometrical shape of the model ice.

[0072] An area S of the geometrical shape of the model ice satisfies the following equation:

[00017]$S=\frac{{{\pi .Math.l}_n}^2}{4};$

[0073] A caliper diameter ratio R.sub.a of the model ice satisfies the following equation:

R.sub.a=D.sub.max/D.sub.min

[0074] The statistic data showed that the R of the broken ice behaves as a linear function, which was about 1.145±0.002, meanwhile, the smaller the characteristic length L of the ice floe was, the smaller the fluctuation was. The caliper diameter ratio R.sub.a was about 1.78±0.4, and the smaller the maximum caliper diameter D.sub.max, the smaller the fluctuation of R.sub.a was. Thus, took R=1.145, R.sub.a=1.78.

[0075] P was determined according to the value of R;

TABLE-US-00006 30 cm 25 cm 20 cm 15 cm 10 cm P (cm) 107.91 89.93 71.94 53.96 35.97 S (m2) 0.070686 0.0491 0.0314 0.0177 0.00785 D.sub.min (cm) 19.93 16.6 13.28 9.96 6.64 D.sub.max (cm) 35.47 29.56 23.65 17.74 11.8

[0076] The geometrical shape of the model ice was determined according to P, S, and R.sub.a.

[0077] The geometric shape of the model ice was selected as polygon to satisfy the relationship of perimeter, area and side length of the shape in the table above, so as to determine the detailed geometric shape parameters of the regular polygon. Each polygon calculation method is different, and there are non-unique geometric parameters according to the above conditions, so there is no detailed calculation here. Only a set of diagrams of long trapezoid, flat trapezoid, rectangle, pentagon, hexagon, and ellipses (30 cm) with assumption of symmetry are listed here, as shown in FIG. 4.

[0078] After the experimental area was selected, a fence with a size of 29 m×3.0 m should be installed in the towing tank to fence the broken ice field for ship navigation. The fence was made of standard PVC pipe with a length of 4 m and a external diameter of 75 mm. The PVC pipes were connected with tee pipes. In order to strengthen the connection between the pipe fittings and the tee pipes, two holes were drilled in the overlap part of PVC pipe and the tee pipe, and the iron wire was tightened through the two holes. The whole installation effect of the fence is shown in FIG. 5. In addition, due to the PVC pipe is hollow structure, in order to make the PVC pipe floating on the water surface and achieve good ice blocking effect, a little modification should be made to PVC pipe. Different from the method of inserting would weight into the pipe and then blocking the two ends of the pipe fitting, a pearl cotton board with 2 cm×2 cm was pasted on the outer wall of the PVC pipe located under the water along its length direction, and the side of the pearl cotton board was installed right below the water surface. The installation diagram is shown in FIG. 6. The pearl cotton board with smaller density provides buoyancy, so as to avoid the problem of the model ice sliding out due to the PVC pipe sinks below the water surface, which can not only make the complete set of fence device has the expected ice blocking effect, but also save the cost and reduce the construction quantity.

[0079] Finally, according to the above calculation results, the picture of the experimental area with a target coverage ratio of 0.6 is shown in FIG. 7.

[0080] At last, it should be stated that the above embodiments are only used to illustrate the technical solutions of the present disclosure without limitation; and despite reference to the aforementioned embodiments to make a detailed description of the present disclosure, those of ordinary skilled in the art should understand: the described technical solutions in above various embodiments may be modified or the part of or all technical features may be equivalently substituted; while these modifications or substitutions do not make the essence of their corresponding technical solutions deviate from the scope of the technical solutions of the embodiments of the present disclosure.