Ship tail duct fin slamming strength evaluation method

Abstract

The invention relates to a slamming strength evaluation method for a duct fin at the tail of a ship, which comprises the following steps of: (1) establishing finite element models of the duct fin and an adjacent ship body structure, and setting boundary conditions; (2) selecting the lower surface of the upper region of the conduit and the lower surface of the fin as slamming pressure acting surfaces, and calculating a slamming pressure peak value of each point; (3) applying slamming pressure to the finite element model, and applying a slamming pressure peak value as a static load to a plurality of local areas of the conduit and the fin to generate different loading conditions; and (4) calculating the structure response, evaluating the Von Mises stress of the plate shell unit and the axial stress of the rod unit, and judging whether the Von Mises stress and the axial stress meet the allowable stress related to the grid size or not. Compared with a method for calculating the slamming load based on CFD, the slamming strength evaluation method has the advantages that the calculation efficiency is extremely high, and the slamming strength of the conduit fin can be quickly evaluated in a short time; the method is more suitable for slamming pressure calculation of the tail conduit fin, and the considered loading mode is more comprehensive.

Description

Technical Field

[0001] The present invention relates to the field of ship engineering structure design, and specifically to a method for evaluating the slamming strength of a ship's aft duct fin based on the finite element method and simplified slamming loads, which is applicable to the structural optimization of energy-saving devices in front of the propeller. Background Art

[0002] With the development of the enlargement of ships and the increasing requirements for energy conservation and environmental protection, more and more ships are equipped with energy-saving devices at the aft to improve or optimize the propulsion efficiency of the propeller by changing the aft flow field.

[0003] The duct fin is a common type of energy-saving device, usually arranged in front of the propeller (see Figure 1 ) and is an appendage structure connected to the hull aft structure. The duct fin includes structures such as a duct, fins, and gussets. Among them, the duct is a ring structure, also known as a guide wheel; the fins are radial structures, also known as guide vanes, connecting the duct and the hull aft; the gussets connect the duct and the hull stern post area. The duct fin is usually located below the water surface and bears complex external environmental loads. Especially when the ship is in extreme working conditions, such as encountering bad sea conditions, the ship undergoes longitudinal rolling, and at the same time, the waves cause the water surface to move up and down, making the duct fin likely to emerge from the water and then re-enter the water. During this process, the duct fin slaps against the water surface, generating a large slamming load, and there is a certain risk of damage. The probability of the duct fin emerging from the water and slamming is small, but it is still a potential risk factor.

[0004] At present, there are no slamming strength assessment standards and guidelines for duct fins in domestic and foreign classification societies. The China Classification Society (CCS) Steel Sea-Going Ship Classification Rules have strength assessment requirements for energy-saving appendages in front of the propeller, but do not include slamming strength; the Norwegian Classification Society (DNV) Rules and the American Bureau of Shipping (ABS) Rules have simplified calculation methods for hull aft slamming pressure and direct strength assessment methods for hull slamming respectively, but do not have strength requirements for energy-saving devices; the Common Structure Rules for Bulk Carriers and Tankers (CSR) have direct strength assessment methods for main supporting members under bow bottom slamming loads, but lack requirements for hull aft slamming and energy-saving devices.

[0005] Papers related to the slamming strength of energy-saving devices include: Liu Yiqian, Xie Xiaolong. Structural Design and Strength Analysis of VLCC Front Duct [J]. Shipbuilding of China, 2013(4):109-119. This paper considered the strength assessment of a front duct without fins under slamming loads, but its slamming load calculation method and loading method may not be applicable to duct fins.

[0006] An important factor in the slamming strength assessment is the slamming load. Using the computational fluid dynamics (CFD) method or the model test method is currently a relatively accurate way to obtain the slamming load of the duct fin. However, calculating such a strongly nonlinear phenomenon as slamming by the CFD method requires a long time and high requirements for computing resources; the model test method also requires a long time and certain financial costs, and has a small scale and great measurement difficulty. For duct fins, especially for the project of retrofitting duct fins on old ships, due to limited time and funds, it is not very suitable to use the above two methods. There is a simplified calculation method for the slamming load of the pre-duct in the aforementioned paper, but this method does not consider the particularity of the wave slamming at the ship's stern, and the research object is not the duct fin, and its loading method is not applicable to the duct fin. The CCS specification has requirements for the strength assessment of the energy-saving appendage in front of the propeller, but there is no slamming load condition, and its allowable stress is not applicable to the slamming strength assessment. Classification societies at home and abroad have slamming strength assessment methods for the hull structure, but there is no slamming strength assessment method for energy-saving devices. The probability of slamming of the duct fin is small, and the phenomenon is different from that of the hull. Directly applying the hull specification method may be too conservative.

[0007] Existing classification society specifications lack slamming strength standards for duct fins. The CFD and test methods are costly and time-consuming. Patent document CN108416133A proposes a method for evaluating the yield strength of ducts (including strength assessment under slamming loads), but the object is not the duct fin. The CFD scheme of CN113408213A is computationally complex, and the structural design of CN113879498A does not involve strength assessment. The present invention fills this technical gap through a simplified formula and a targeted loading method. Summary of the Invention

[0008] Referring to some classification society specifications, the present invention uses a simplified formula to calculate the slamming pressure of the duct fin, considers a suitable loading method for different parts, and considers a suitable allowable stress for different mesh sizes, so as to propose a method for evaluating the slamming strength of the duct fin at the ship's stern, which can realize a rapid and reasonable evaluation of the slamming strength of the duct fin.

[0009] To achieve the above object, the technical solution of the present invention is: a method for evaluating the slamming strength of a duct fin at the ship's stern, including the following steps:

[0010] (1) Establish a finite element model of the duct fin and the adjacent part of the hull structure, and set boundary conditions;

[0011] (2) Select the lower surface of the upper region of the duct and the lower surface of the fin as the slamming pressure acting surface, and calculate the peak slamming pressure P at each point SP ;

[0012] (3) The slamming pressure is applied to the finite element model. The peak value of the slamming pressure is applied as a static load to multiple local areas of the duct and fins, generating different loading conditions, including the duct loading condition, the fin loading condition between the duct and the hull, and the fin loading condition outside the duct;

[0013] (4) Calculate the structural response and evaluate the Von Mises stress of the plate and shell elements and the axial stress of the rod elements to determine whether they meet the allowable stress related to the mesh size.

[0014] Furthermore, the finite element model is established according to the relevant requirements of the CCS specification for the strength analysis of the energy-saving appendage in front of the propeller.

[0015] Furthermore, in the finite element model, rod elements are set at the free edges of the brackets at the mid-longitudinal section, and their cross-sectional area is a minimum value to eliminate the influence on the stiffness.

[0016] Furthermore, the peak value of the slamming pressure P SP is related to the relevant ship parameters, the position and angle of the calculation point, and is reduced relative to the calculated value of the slamming pressure at the stern of the hull specification to consider the relatively low slamming probability of the duct fins relative to the hull. P SP is taken as:

[0017]

[0018] In the formula:

[0019] C - a coefficient related to C W and d p which is between 0 and 1;

[0020] C W - the wave coefficient in the specification;

[0021] d p - the vertical distance from the waterline T to the calculation point;

[0022] L - the specified ship length;

[0023] θ - the transverse angle between the plate and the horizontal plane at the calculation point;

[0024] C B - the block coefficient of the ship;

[0025] T - the minimum draft at the middle position of the duct fins.

[0026] Furthermore, the duct loading conditions include four conditions: conditions SD-1 to SD-4.

[0027] Further, for the working condition SD-1: the loading area extends forward longitudinally from the rear end of the duct by c1 = max(a1 / 2, D / 8), and extends transversely from the mid-longitudinal section to both the left and right by d1 / 2, where d1 = max(b1 / 2, D / 8). Here, a1 is the longitudinal distance from the rear end of the duct to the connection between the hull and the bracket, b1 is the transverse distance between the inner sides of the two duct fins, and D is the propeller diameter.

[0028] Further, for the working conditions SD-2 to SD-4: the loading area covers the entire duct longitudinally, and extends transversely by the range of d2 from the mid-longitudinal section to one side, covers the range of d2 in the middle of the area from the mid-longitudinal section to the connection between the duct and the fin (the range of b2), and covers the range of d2 near the connection between the duct and the fin within the range of b2.

[0029] Further, the fin loading working conditions between the duct and the hull include the working conditions SFn-1 to SFn-3: the loading area covers the entire fin longitudinally, and extends transversely by the range of d3 inward from the connection between the fin and the duct, covers the range of d3 in the middle of the fin, and extends transversely by the range of d3 outward from the connection between the fin and the hull.

[0030] Further, the fin loading working condition outside the duct is the working condition SFn-4, and the loading area covers all diaphragms longitudinally and extends transversely by the range of d4 inward from the outermost end of the fin.

[0031] Further, the allowable stress is adjusted according to the mesh size:

[0032] (1) When the mesh size is 1 / 2×S to 1 / 5×S, the allowable stress is 1.00f sr σ y ~1.18f sr σ y ;

[0033] (2) When the mesh size is t d , the allowable stress is min(1.42f sr σ y , 0.95σ u );

[0034] where S is the average spacing of the transverse diaphragms of the duct, t d is the thickness of the duct outer plate, f sr is the strength reduction coefficient related to the material, σ y and σ u are the minimum yield strength and the tensile strength of the material, respectively.

[0035] The beneficial effects of the present invention are:

[0036] For the fin structure of the ship's stern duct, the present invention proposes a method for evaluating the slamming strength, which has extremely high computational efficiency compared with the method of calculating the slamming load based on CFD, and can quickly evaluate the slamming strength of the duct fin in a short time; compared with the load formula and loading method in the given paper, the load formula of the present invention is more applicable to the calculation of the slamming pressure of the stern duct fin, considering a more comprehensive loading method and having a reasonable mechanical basis; compared with the classification society code, the load calculation, loading method and allowable stress of the present invention are reasonable for the duct fin and avoid overly conservative results. The present invention fills the gap in this part of the classification society code and has good reference significance for the structural design of the duct fin. Brief Description of the Drawings

[0037] Figure 1 is a schematic diagram of the duct fin and its position;

[0038] Figure 2 is a flowchart for evaluating the slamming strength of the duct fin of the present invention;

[0039] Figure 3 is a duct loading area diagram;

[0040] where: (a) Condition SD-1 (longitudinal), (b) Condition SD-1 (transverse), (c) Conditions SD-2 to SD-4 (longitudinal), (d) Condition SD-2 (transverse), (e) Condition SD-3 (transverse), (f) Condition SD-4 (transverse);

[0041] Figure 4 Loading area diagram of the fin between the duct and the hull;

[0042] where: (a) Longitudinal, (b) Condition SFn-1 (transverse), (c) Condition SFn-2 (transverse), (d) Condition SFn-3 (transverse);

[0043] Figure 5 is a loading area diagram of the fin outside the duct; [[ID=,29]]

[0044] where: (a) Longitudinal, (b) (transverse). Detailed Embodiment

[0045] The present invention will be further described below in conjunction with the drawings and embodiments.

[0046] As Figure 2 shown, a method for evaluating the slamming strength of a ship's stern duct fin proposed in an embodiment of the present invention uses the finite element method and a simplified load method, and evaluates the slamming strength of the duct fin according to the following steps:

[0047] The specific description of each step is as follows (the following midship section, longitudinal and transverse all refer to the midship section of the ship, the longitudinal and transverse directions of the ship):

[0048] (1) Establish a finite element model of the duct fin

[0049] Establish a finite element model according to the relevant requirements of the strength analysis of the energy-saving appendage in front of the propeller in the CCS specification, including the duct fin and part of the adjacent hull structure, and set the boundary conditions. For the bracket at the mid-longitudinal section, rod elements are set at the free edge, and the cross-sectional area is a minimum value, which does not affect the stiffness of the bracket.

[0050] (2) Select the pressure surface and calculate the peak slamming pressure

[0051] Select the slamming pressure acting surfaces for the duct and the fin respectively. For the duct, select the lower surface of the upper region, and for the fin, select the lower surface.

[0052] The peak slamming pressure P at a certain calculation point of the duct fin SP , is taken as:

[0053]

[0054] In the formula:

[0055] C——Coefficient related to C W and d p , between 0 and 1

[0056] C W ——Wave coefficient in the specification

[0057] d p ——Vertical distance from the waterline T to the calculation point

[0058] L——Specified ship length

[0059] θ——Transverse angle between the plate and the horizontal plane at the calculation point

[0060] C B ——Ship block coefficient

[0061] T——Minimum draft at the middle position of the duct fin

[0062] (3) Apply the slamming pressure to the finite element model

[0063] The slamming pressure has a moving characteristic and it is impossible to reach the peak value simultaneously on the entire pressure surface. For simplicity, the peak slamming pressure is applied as a static load to a local area on the pressure surface of the duct or the fin, and multiple different loading areas are considered, which are distributed in different working conditions. Each working condition only considers one loading area. The following discussions are carried out for the duct and the fin respectively (the parameter D below is the propeller diameter).

[0064] a) Duct

[0065] Select the lower surface of the upper part of the conduit and consider the following 4 working conditions:

[0066] Working condition SD-1: The loading area extends longitudinally from the rear end of the conduit forward by c1 = max(a1 / 2, D / 8), and transversely extends d1 / 2 to the left and right from the mid-longitudinal section (d1 = max(b1 / 2, D / 8), see a1 and b1 in Figure 3 the (a) and (b) shown in;

[0067] Working condition SD-2: The loading area covers the entire conduit longitudinally, and transversely extends d2 (related to b2 and D) from the mid-longitudinal section towards the adjacent fin direction, see b2 in Figure 3 the (c) and (d) shown in;

[0068] Working condition SD-3: The size of the loading area is the same as that of working condition SD-2, but transversely located in the middle between the mid-longitudinal section and the connection between the conduit and the fin, see Figure 3 the (e) shown in;

[0069] Working condition SD-4: The size of the loading area is the same as that of working condition SD-2, but transversely close to the connection between the conduit and the fin. The loading area is as shown in Figure 3 the (c) and (f) shown in.

[0070] b) The fin between the conduit and the hull

[0071] The loading area is as shown in Figure 4 For the part of a certain fin (such as the nth fin) between the conduit and the hull, select the lower surface of the fin and consider three working conditions (the loading area covers the entire fin longitudinally, see Figure 4 the (a), and transversely as shown in Figure 4 the (b), (c), (d)):

[0072] Working condition SFn-1: Transversely extend d3 (related to b3 and D) inward from the connection between the fin and the conduit, see b3 in Figure 4 the (b) shown in;

[0073] Working condition SFn-2: Transversely in the middle of the fin, covering a range of d3, see Figure 4 the (c);

[0074] Working condition SFn-3: Transversely extend d 3， See Figure 4 the (d). 1]

[0075] c) The fin outside the conduit

[0076] The loading area is as shown in Figure 5 For the part of a certain fin (such as the nth fin) outside the conduit, select the lower surface of the fin and consider working condition SFn-4: The loading area covers all the diaphragms of the fin longitudinally, and the range is shown in Figure 5As shown longitudinally in (a) (c4 is related to D), transversely extend d4 (related to b4 and D) inward from the outermost end of the fin, and b4 is shown in Figure 5 as shown in (b).

[0077] (4) Calculate the structural response and evaluate the slamming strength

[0078] Use the linear static method to calculate the structural response. The evaluation object is the duct fin structure.

[0079] The Von Mises stress of the plate and shell elements and the axial stress of the rod elements do not exceed the allowable stresses listed in the following table.

[0080] Table 1 Allowable stresses

[0081]

[0082] For those with a mesh size different from the above values, the allowable stress can be calculated by the method of linear interpolation or the adjacent smaller allowable stress can be selected. The allowable stress of the smaller mesh size in the above table is only applied to the stress concentration area, otherwise the allowable stress in the first row should be used.

[0083] An efficient evaluation method proposed by the present invention includes the following innovative points:

[0084] (1) Slamming pressure formula: The calculated value of the slamming pressure at the tail of the relative hull specification is reduced to consider the relatively low slamming probability of the duct fin relative to the hull, avoiding overly conservative results;

[0085] (2) Multi-condition loading: Design 8 typical conditions for different regions of the duct and fin, covering the maximum stress regions that may actually occur ( Figures 3 - 5 );

[0086] (3) Dynamic allowable stress: Dynamically adjust the allowable stress according to the mesh size, avoiding the overly conservative criterion (Table 1) caused by mesh refinement in the traditional method.

[0087] Specific application example 1:

[0088] (1) Modeling: Establish a finite element model including the duct, fin and adjacent hull according to the CCS specification, and set rod elements with a cross-sectional area approaching 0 at the free edge of the gusset plate.

[0089] (2) Calculate the peak pressure: Select the lower surface of the upper part of the duct and the lower surface of the fin, and calculate the point P SP , where C = 0.85, C W Take the value according to the DNV specification.

[0090] (3) Loading conditions: Apply SD-1 to SD-4 conditions to the duct and SFn-1 to SFn-4 conditions to the fin, and analyze each condition independently.

[0091] (4) Strength evaluation: Output the Von Mises stress contour plot. If the stress in a certain area exceeds the limit (such as 1.18f when the grid is 1 / 5×S sr σ y ), then optimize the structural thickness at that place.

[0092] Specific application example two:

[0093] Use the linear interpolation method to determine the allowable stress of non-standard grid sizes (such as 1 / 3.5×S): σ allow =(1.06+(1.12 - 1.06) / (1 / 4 - 1 / 3)×(1 / 3.5 - 1 / 3))f sr σ y =1.09f sr σ y , By dynamically adjusting the criterion, while reducing the weight of the structure by 9%, it meets the strength requirements.

Claims

1. A method for evaluating the slamming strength of a duct fin at the stern of a ship, characterized in that, It includes the following steps: (1) Establish a finite element model of the duct fin and the adjacent part of the hull structure, and set boundary conditions; (2) Select the lower surface of the upper region of the duct and the lower surface of the fin as the slamming pressure acting surface, and calculate the peak slamming pressure P at each point. SP ; (3) Apply the peak slamming pressure as a static load to multiple local areas of the duct and the fin in the finite element model to generate different loading conditions, including the duct loading condition, the fin loading condition between the duct and the hull, and the fin loading condition outside the duct; (4) Calculate the structural response and evaluate the Von Mises stress of the plate and shell elements and the axial stress of the rod elements to determine whether they meet the allowable stress related to the mesh size.

2. The method for evaluating the slamming strength of the stern duct fin of a ship according to claim 1, characterized in that The finite element model is established according to the relevant requirements of the CCS specification for the strength analysis of the energy-saving appendage in front of the propeller.

3. The method for evaluating the slamming strength of the stern duct fin of a ship according to claim 1, wherein In the finite element model, rod elements are set at the free edges of the brackets at the mid-longitudinal section, and their cross-sectional areas are set to minimum values to eliminate the influence on stiffness.

4. The method for evaluating the slamming strength of the stern duct fin of a ship according to claim 1, characterized in that The peak slamming pressure P SP is related to relevant ship parameters, the position of the calculation point and the included angle, and is reduced relative to the calculated value of the slamming pressure at the stern of the hull specification to consider the relatively low slamming probability of the duct fin relative to the hull. P SP is taken as: In the formula: C - related to C W and d p The related coefficient ranges from 0 to 1; C W —— Wave coefficient in the specification; d p —— the vertical distance from the waterline T to the calculation point; L —— the specified ship length; θ —— the transverse angle between the plate and the horizontal plane at the calculation point; C B —— Block coefficient of ship; T —— the minimum draft at the middle position of the duct fin.

5. The method for evaluating the slamming strength of the stern duct fin of a ship according to claim 1, wherein The duct loading conditions include four conditions: SD-1 to SD-4.

6. The method for evaluating the slamming strength of the stern duct fin of a ship according to claim 5, characterized in that, For the condition SD-1: The loading area extends forward from the rear end of the duct by c1 = max(a1 / 2, D / 8) longitudinally and extends d1 / 2 to the left and right from the mid-longitudinal section transversely, where d1 = max(b1 / 2, D / 8), a1 is the longitudinal distance from the rear end of the duct to the connection between the hull and the bracket, b1 is the transverse distance between the inner sides of the two duct fins, and D is the propeller diameter.

7. The method for evaluating the slamming strength of the stern duct fin of a ship according to claim 5, wherein, For the conditions SD-2 to SD-4: The loading area covers the entire duct longitudinally and extends a range of d2 to one side from the mid-longitudinal section, covers a range of d2 in the middle of the range of b2 between the mid-longitudinal section and the connection between the duct and the fin, and covers a range of d2 near the connection between the duct and the fin within the range of b2 transversely.

8. The method for evaluating the slamming strength of a ship's aft duct fin according to claim 1, characterized in that, The fin loading conditions between the duct and the hull include conditions SFn-1 to SFn-3: The loading area covers the entire fin longitudinally and extends a range of d3 inward from the connection between the fin and the duct, covers a range of d3 in the middle of the fin, and extends a range of d3 outward from the connection between the fin and the hull transversely.

9. The method for evaluating the slamming strength of the stern duct fin of a ship according to claim 1, wherein The fin loading condition outside the duct is condition SFn-4, and the loading area covers all diaphragms longitudinally and extends a range of d4 inward from the outermost end of the fin transversely.

10. The method for evaluating the slamming strength of the stern duct fin of a ship according to claim 1, wherein The allowable stress is adjusted according to the mesh size: When the mesh size is 1 / 2×S to 1 / 5×S, the allowable stress is 1.00f sr σ y ~1.18f sr σ y ; (2) The mesh size is t d When it is sr σ y , 0.95σ u ); Among them, S is the average spacing of the transverse partitions of the conduit, t d is the thickness of the outer plate of the conduit, f sr is the strength reduction coefficient related to the material, σ y and σ u are the minimum yield strength and the tensile strength of the material, respectively.

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