Method for calculating convective heat transfer coefficient of surface of box girder bridge

Abstract

The invention relates to the technical field of box girder temperature field research, and discloses a method for calculating a convective heat transfer coefficient of a box girder bridge surface, which comprises the following steps of: constructing a wind speed reduction coefficient model, namely fitting height-width ratios of sections of different box girders and wind speed reduction coefficients of different structure surfaces; obtaining a linear function of a height-width ratio and a wind speed reduction coefficient of any section of any box girder; and obtaining a wind speed reduction coefficient of the box girder bridge according to a linear function obtained by a height-width ratio and wind speed reduction coefficient model of the box girder bridge, and further calculating to obtain a convective heat transfer coefficient of the surface of the box girder bridge. According to the method, different wind field distributions faced by different structures on the outer surfaces of different box girders on the whole bridge are considered, a more accurate convective heat transfer coefficient can be obtained, the method can be suitable for a variable-cross-section single-box multi-chamber box girder bridge with a complex and changeable temperature field, and then the applicability and accuracy of bridge temperature field evaluation are improved.

Description

Technical Field

[0001] The invention relates to the technical field of box girder temperature field research, and in particular to a method for calculating the convection heat transfer coefficient of a box girder bridge surface. Background Art

[0002] Box girders are important components of long-span box girder bridges and are often used as the main load-bearing structure, carrying the weight of the bridge and the traffic load of vehicles and pedestrians. Long-span box girder bridges usually include multiple variable-section box girders. Box girder structures are susceptible to drastic temperature changes. When the temperature is too high or too low, the box girder may arch or crack, which will cause changes in the overall performance of the bridge.

[0003] At present, in the numerical simulation of bridge temperature field, the boundary conditions of the box girder single section model (heat convection, heat radiation, heat conduction) are generally set, and then the finite element software is used to solve the bridge temperature field. When setting the thermal convection boundary conditions of the single section of the box girder, the convective heat transfer coefficient is generally calculated directly using a uniform incoming wind speed, without considering that the different structures on the outer surface of the box girder face different wind field distributions on the entire bridge, which leads to large errors in the evaluation of the bridge temperature field.

[0004] Large-span box girder bridges usually use variable-section single-box multi-chamber box girders. Due to the complex structure of the variable-section single-box multi-chamber box girder, the large size of the single unit, the long span, and the multiple box chambers inside, the temperature field distribution of the variable-section single-box multi-chamber box girder is complex and changeable, making it difficult to apply the convective heat transfer coefficient of only a single section of the variable-section single-box multi-chamber box girder to the temperature field analysis of the variable-section single-box multi-chamber box girder bridge.

[0005] Therefore, how to provide a method for calculating the convective heat transfer coefficient of the box girder bridge surface is a problem that technical personnel in this field urgently need to solve. Summary of the invention

[0006] The purpose of the present invention is to propose a method for calculating the convection heat transfer coefficient of the surface of a box girder bridge, thereby solving the problems involved in the background technology.

[0007] In order to achieve the above object, the present invention adopts the following technical solution:

[0008] A method for calculating the convective heat transfer coefficient of a box girder bridge surface, wherein the box girder bridge includes N variable-section box girders, comprising the following steps:

[0009] S1. Construct a wind speed reduction coefficient model, including:

[0010] S11. Obtain wind speed reduction coefficients of different structural surfaces on a cross section of a box girder by using a wind speed reduction coefficient solution method;

[0011] S12, using the same method as described in step S11, respectively obtain the wind speed reduction coefficients of different structural surfaces on a cross section of n different box girders, n≤N;

[0012] S13, obtaining the aspect ratios of all the box girder sections mentioned above;

[0013] S14, fitting the aspect ratios of all the box girder sections and the wind speed reduction coefficients of different structural surfaces to obtain a linear function of the aspect ratio and wind speed reduction coefficient of any section of any box girder;

[0014] S2. According to the height-to-width ratio of the box girder bridge, the wind speed reduction coefficient of the box girder bridge is obtained through the wind speed reduction coefficient model;

[0015] S3. Calculate the convective heat transfer coefficient on the surface of the box girder bridge based on the actual incoming wind speed and the wind speed reduction coefficient of the box girder bridge.

[0016] Furthermore, the method for solving the wind speed reduction coefficient in step S11 specifically includes the following steps:

[0017] A. Set the initial incoming wind speed and the incoming wind speed threshold;

[0018] B. According to the set incoming wind speed, the surface wind field distribution of a box girder is simulated by computational fluid dynamics (CFD), the grid independence is verified, and a box girder surface wind field cross-sectional model is built;

[0019] C. According to the wind field section model on the box girder surface, the wind speed at the thermal boundary layer thickness of different structural surfaces on the box girder section is solved;

[0020] D. Determine the set incoming wind speed; if the incoming wind speed is less than or equal to the preset incoming wind speed threshold, return to step A and set the next incoming wind speed;

[0021] E. If the set incoming wind speed is greater than the preset incoming wind speed threshold, the wind speeds at the thermal boundary layer thickness of different structural surfaces on the box girder section corresponding to different incoming wind speeds are fitted to obtain the wind speed reduction coefficients of different structural surfaces on a section of a box girder.

[0022] Furthermore, the step C comprises the following sub-steps:

[0023] C1. Calculate the velocity boundary layer thickness of different structural surfaces on the box girder section according to the set incoming wind speed;

[0024] C2. Calculate the thermal boundary layer thickness of different structural surfaces on the box girder cross section based on the velocity boundary layer thickness of different structural surfaces on the box girder cross section;

[0025] C3. Based on the box girder surface wind field section model, the wind speed at the thermal boundary layer thickness of different structural surfaces on the box girder section is solved by computational fluid dynamics.

[0026] Furthermore, the velocity boundary layer thickness in step C1 is calculated by the following formulas:

[0027]

[0028] Where δ is the thickness of the velocity boundary layer, x is the distance from the starting point of the calculation boundary on the solid surface to the calculation point, α and β are constants, Re is the Reynolds number, and U is ∞ is the incoming wind speed, l is the characteristic linear dimension, and v is the kinematic viscosity of the fluid.

[0029] Furthermore, the thermal boundary layer thickness in step C2 is calculated by the following formula:

[0030] δ t =Pr -1 / 3 δ

[0031] In the formula, δ t is the thickness of the thermal boundary layer, Pr is the Prandtl number, and δ is the thickness of the velocity boundary layer.

[0032] Furthermore, the convective heat transfer coefficient in step S3 is calculated by the following formulas:

[0033]

[0034] U i =μ·U ∞

[0035] In the formula, h c is the convective heat transfer coefficient, T ∞ is the fluid temperature, T S is the wall temperature, U i is the wind speed at the thickness of the thermal boundary layer, μ is the wind speed reduction factor, U ∞ is the incoming wind speed.

[0036] Compared with the prior art, the present invention has the following advantages:

[0037] 1. The present invention takes into account that different structures on the outer surface of the box girder face different wind field distributions on the entire bridge. Through the wind speed reduction coefficient solution method, the wind speed reduction coefficients of different structural surfaces on a cross section of a box girder are obtained, thereby improving the accuracy of the bridge temperature field assessment.

[0038] 2. The present invention constructs a wind speed reduction coefficient model, that is, fits the aspect ratios of different box girder sections and the wind speed reduction coefficients of different structural surfaces, to obtain a linear function of the aspect ratio and wind speed reduction coefficient of any section of any box girder; then the wind speed reduction coefficient of the box girder bridge is obtained based on the linear function obtained from the aspect ratio and wind speed reduction coefficient model of the box girder bridge, and then a more accurate convective heat transfer coefficient of the surface of the variable-section box girder bridge is calculated, which can be applicable to variable-section single-box multi-chamber box girder bridges with complex and changeable temperature fields, thereby improving the applicability and accuracy of bridge temperature field evaluation. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] Figure 1 This is the layout diagram of the box girder bridge test section.

[0040] Figure 2(a) and Figure 2(b) are cross-sectional views of the box girder temperature field model. Figure 2(a) is a cross-sectional view of the box girder temperature field model; Figure 2(b) is a longitudinal cross-sectional view of the box girder temperature field model.

[0041] Figure 3 This is the overall structure diagram of the box girder temperature field model.

[0042] Figure 4 Schematic diagram of the computational fluid domain.

[0043] Figure 5 Figure 2 shows the division of wind farm into different grid sizes, where (a) is coarse; (b) is relatively coarse; (c) is regular; (d) is relatively fine; and (e) is refined.

[0044] Figure 6(a) and Figure 6(b) are the wind field distribution diagrams of the outer surfaces of different structures of the box girder temperature field model under different grid sizes.

[0045] Among them, Figure 6(a) is the upper surface of the top plate; Figure 6(b) is the lower surface of the bottom plate.

[0046] Figure 7(a) and Figure 7(b) are thermal boundary layer thickness diagrams of different structural outer surfaces of the box girder temperature field model under different incoming wind speeds. Figure 7(a) is the upper surface of the top plate, and Figure 7(b) is the lower surface of the bottom plate.

[0047] Figure 8 This is the steady-state numerical simulation cloud diagram of the wind field near the box girder temperature field model.

[0048] Figure 9(a) to Figure 9(h) The U of different structural outer surfaces of the box girder temperature field model under different incoming wind speeds in working conditions 1 and 2 i Distribution diagram. Among them, Figure 9(a) is the upper surface of the top plate; Figure 9(b) is the lower surface of the bottom plate; Figure 9(c) is the left surface of the web A; Figure 9(d) is the right surface of the web D; Figure 9(e) is the tip of the left flange; Figure 9(f) is the tip of the right flange; Figure 9(g) is the lower side of the left flange; Figure 9(h) is the lower side of the right flange.

[0049] Fig.10 The U of the outer surface of the box girder temperature field model in different structures in working conditions 1 and 2 i with U ∞ Function relationship diagram of .

[0050] Figure 11(a) to Figure 11(d) The temperature field model of the box girder with different absolute sizes has different structural outer surface U i Distribution map.

[0051] Among them, Figure 11(a) is the upper surface of the top plate; Figure 11(b) is the lower surface of the bottom plate; Figure 11(c) is the left surface of the web A; and Figure 11(d) is the right surface of the web D.

[0052] Figure 12(a) to Figure 12(d) The temperature field model of the box girder with different absolute sizes has different structural outer surface U i with U ∞ Figure 12(a) is the upper surface of the top plate; Figure 12(b) is the lower surface of the bottom plate; Figure 12(c) is the left surface of the web A; and Figure 12(d) is the right surface of the web D.

[0053] Figure 13(a) to Figure 13(h) The U of different structures of the No. 36 box girder model under different incoming wind speeds in working conditions 1 and 2 i Distribution diagram. Among them, Figure 13(a) is the upper surface of the top plate; Figure 13(b) is the lower surface of the bottom plate; Figure 13(c) is the left surface of the web A; Figure 13(d) is the right surface of the web D; Figure 13(e) is the tip of the left flange; Figure 13(f) is the tip of the right flange; Figure 13(g) is the lower side of the left flange; Figure 13(h) is the lower side of the right flange.

[0054] Figure 14(a) to Figure 14(h) The U of different structures of the No. 15 box girder model under different incoming wind speeds in working conditions 1 and 2 i Distribution diagram. Among them, Figure 14(a) is the upper surface of the top plate; Figure 14(b) is the lower surface of the bottom plate; Figure 14(c) is the left surface of the web A; Figure 14(d) is the right surface of the web D; Figure 14(e) is the tip of the left flange; Figure 14(f) is the tip of the right flange; Figure 14(g) is the lower side of the left flange; Figure 14(h) is the lower side of the right flange.

[0055] Figure 15(a) to Figure 15(h) The U of different structures of the No. 0 box girder model under different incoming wind speeds in working conditions 1 and 2 i Distribution diagram. Among them, Figure 15(a) is the upper surface of the top plate; Figure 15(b) is the lower surface of the bottom plate; Figure 15(c) is the left surface of the web A; Figure 15(d) is the right surface of the web D; Figure 15(e) is the tip of the left flange; Figure 15(f) is the tip of the right flange; Figure 15(g) is the lower side of the left flange; Figure 15(h) is the lower side of the right flange.

[0056] Figure 16(a) to Figure 16(h) The U of different outer surfaces of the box girder model in different test sections i with U ∞ Figure 16(a) is the upper surface of the top plate; Figure 16(b) is the lower surface of the bottom plate; Figure 16(c) is the left surface of the web A; Figure 16(d) is the right surface of the web D; Figure 16(e) is the tip of the left flange; Figure 16(f) is the tip of the right flange; Figure 16(g) is the lower side of the left flange; Figure 16(h) is the lower side of the right flange.

[0057] Fig.17 This is a comparison chart between μ obtained by simulating the box girder temperature field model and the linear function (μ and the aspect ratio of the box girder) obtained by the final fitting.

[0058] Fig.18 Schematic diagram of fluid flow over a heated plate.

[0059] The meanings of the numbers in the figure are: 1. top plate; 2. bottom plate; 3. web A; 4. web B; 5. web C; 6. web D. DETAILED DESCRIPTION

[0060] In order to make the objectives, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with embodiments and drawings. The exemplary embodiments of the present invention and their description are only used to explain the present invention and are not intended to limit the present invention.

[0061] Example 1

[0062] This example takes a large concrete single-box three-chamber box girder bridge as the research object. Figure 1 As shown in the figure, the box girder bridge is divided into different test sections. The real bridge test box girder section Section I is set, which is equivalent to block 8; the model test reference box girder section Section II is equivalent to block 15.

[0063] After analyzing the dimensions of the model reference box girder section Section II of the actual bridge, the temperature field model of the single-box three-chamber concrete box girder was established. As shown in Figure 2(a) and Figure 2(b), the cross-sectional view and longitudinal view of the box girder temperature field model are shown. The ratio of the model to the actual bridge is 1:2. Figure 3 As shown in the figure, the overall structure of the box girder temperature field model is defined to include top plate 1, bottom plate 2, web A3, web B4, web C5, and web D6. There are 151 temperature sensors in the model, and the temperature sensors are fixed on the steel skeletons of different structures of the box girder temperature field model. Among them, red represents the temperature sensor in the top plate 1, green represents the temperature sensor in the bottom plate 2, and yellow represents the temperature sensor in web A3, web B4, web C5, and web D6.

[0064] This embodiment considers four working conditions:

[0065] Case 1: The average wind speed (w) of the incoming wind is directly used for all the outer surfaces of the box girder bridge, without considering the actual wind field distribution of different structures on the outer surface of the box girder, so CFD simulation is not required. Case 1 is the conventional method used in most current studies and is used as a benchmark in this example;

[0066] Working condition 2: In order to obtain the refined wind field distribution law on the surface of the box girder structure, considering the actual wind field distribution of different structures on the outer surface of the box girder, it is necessary to perform computational fluid dynamics (CFD) simulation on the wind field on the surface of the box girder temperature field model to obtain the wind field distribution on the surface of the box girder temperature field model structure;

[0067] Case 3: In order to study the influence of absolute size change on the wind field distribution on the box girder structure surface, a CFD simulation is performed on the real bridge (1:1) to study the size effect of the box girder temperature field model in the wind field;

[0068] Condition 4: In order to study the wind field on the surface of the entire box girder bridge structure, the wind field distribution of different box girders with different cross sections is analyzed. In addition, since the geometric dimensions of the top plate 1 change slightly, the influence of the beam height on the wind field on the bridge structure surface is mainly analyzed.

[0069] S1. Construct a wind speed reduction coefficient model, including:

[0070] S11. The wind speed reduction coefficients of different structural surfaces on a cross section of a box girder are obtained by using the wind speed reduction coefficient solution method.

[0071] The method for solving the wind speed reduction coefficient specifically includes the following steps:

[0072] A. Set the initial incoming wind speed and the incoming wind speed threshold.

[0073] In addition to analyzing the actual measured data (wind speed), according to the actual bridge construction drawing design instructions, the basic wind speed is 24.9 mm / s when considering wind load, so we directly analyze 10 different incoming wind speeds U in the range of 1 to 30 m / s. ∞ As shown in Table 1, the wind speed range for breeze is 1-5 m / s, increasing by 1 m / s; the wind speed range for strong wind is 10-30 m / s, increasing by 5 m / s.

[0074] Table 1 Working conditions of CFD wind farm simulation

[0075]

[0076] B. According to the set incoming wind speed, the surface wind field distribution of a box girder is simulated by computational fluid dynamics (CFD), the grid independence is verified, and a box girder surface wind field cross-sectional model is built.

[0077] According to the set incoming wind speed, a two-dimensional simulation is performed on the wind field where the box girder is located. Figure 4 As shown, the outer surface structure of the box girder is defined as the upper surface of the top plate (TOP), the lower surface of the bottom plate (BOTTOM), the left surface of web A (WebA), the right surface of web D (WebD), the left flange tip (YYL), the right flange tip (YYR), the lower side of the left flange (YYLD), and the lower side of the right flange (YYRD).

[0078] The top plate upper surface (TOP), the two side flange tips (YYL & YYR), the web surface (WebA, WebD) and the bottom plate lower surface (BOTTOM) are all parallel or perpendicular to the ground, while the lower side of the flange (YYLD & YYRD) has a certain inclination. The difference from the actual bridge shape is that the lane position of the top plate of the actual bridge has a slope of 2.0%.

[0079] The computational fluid domain is a rectangular domain, with the width and height set to 18 times the box beam width (18D) and 40 times the box beam height (40Hver), respectively, and the blocking rate is 2.5%. Figure 4 As shown in the figure, the shear stress transport (SST) k-ω model was used to perform a Reynolds-averaged Navier-Stokes (RANS) numerical simulation of the box girder structure surface.

[0080] In this embodiment, according to the on-site measurement, the local south wind and southerly wind are dominant, so the right side of the box girder (sunny side, south side) is set as the incoming flow direction, the fluid flows from right to left, and the wind attack angle is 0. Then, the right side of the calculation domain is set as the velocity inlet, and the surface of the box girder structure is set as a stationary wall without slip.

[0081] like Figure 4 As shown in the figure, a schematic diagram of the computational fluid domain is shown. Wind field monitoring points are arranged on the surface of the box girder, among which TOP 1-200 Indicates that monitoring points are arranged on the top surface of the roof. The subscript 1-200 indicates that 200 monitoring points are used. 1-200 It means that 200 monitoring points are arranged on the lower surface of the bottom plate. Similarly, WebA represents the left surface of web A, WebD represents the right surface of web D, YYL represents the tip of the left flange, YYLD represents the lower side of the left flange, YYR represents the tip of the right flange, and YYRD represents the lower side of the right flange.

[0082] Verify the independence of the grid. Grid division is crucial in numerical simulation. The grid size directly affects the calculation results of the actual wind field distribution on the box girder surface by fluid dynamics, and is related to the accuracy of the calculation results. Figure 5As shown, in order to discuss the sensitivity of the box girder temperature field model to the mesh size, five different mesh sizes were used, and the number of meshes of each size was counted by FLUENT. The specific size and quantity are shown in Table 2. In order to ensure the mesh quality near the box girder, a 12-layer body-fitted structured quadrilateral mesh was generated in the rigid domain.

[0083] The wind field simulation process was carried out using FLUENT. In order to ensure the accuracy of the wind field distribution around the box girder, 10 -6 Convergence tolerance (including x, y direction speed and ω, etc.).

[0084] Table 2 Wind field analysis grid characteristics

[0085]

[0086] Figure 6(a) and Figure 6(b) show the calculated results of the x-direction velocity distribution on the upper surface of the top plate and the lower surface of the bottom plate of the box girder with different grid sizes.

[0087] By comparing the curves in Figure 6(a) and Figure 6(b), it can be observed that there are differences in wind field distribution even near different positions on the same surface. The upper surface of the top plate and the lower surface of the bottom plate show a wind speed distribution with high in the middle and low on both sides. As shown in Table 3, the deviation between coarse and fine grid sizes is large, which is manifested in the average absolute error of the coarse grid exceeding 0.1m / s, and the maximum absolute error of the fine grid also exceeding 0.1m / s. The wind field distribution patterns of conventional, coarse and fine grid sizes are relatively close. Coarsening the unit grid will lead to an increase in the calculation error, which in turn causes deviations in the calculation results.

[0088] Table 3 Comparison of calculation errors of different mesh sizes

[0089]

[0090] Note: The error is the difference between the calculation results of different mesh size levels and the regular mesh size.

[0091] In order to balance the wind field distribution law on the box girder surface, the accuracy of the calculation results of different grid sizes, and the calculation efficiency (the calculation time of the refined grid is too long), a conventional size grid was finally selected. The grid size is about 1 / 3600 of the box girder width in the main parts of the box girder (top plate 1, bottom plate 2 and web), and half of the grid size of the main parts is used at the flange position.

[0092] After verifying the independence of the grid, a wind field cross-section model of the box girder surface was built.

[0093] C. According to the wind field section model of the box girder surface, the wind speed at the thermal boundary layer thickness of different structural surfaces on the box girder section is solved, including the following steps:

[0094] C1. Calculate the velocity boundary layer thickness of different structural surfaces on the box girder section according to the set incoming wind speed.

[0095] The velocity boundary layer thickness δ can be calculated by the following formula:

[0096]

[0097] Where δ is the thickness of the velocity boundary layer, α and β are constants, Re is the Reynolds number, and x is the distance from the starting point of the calculation boundary of the solid surface to the calculation point (m); constants α and β depend on the incoming wind speed U ∞ , when the incoming wind speed U ∞ ≤5m / s (laminar flow), α=-0.5, β=5; when the incoming wind speed U ∞ When >5m / s (turbulent flow), α=-1 / 5, β=0.37.

[0098] The Reynolds number Re can be calculated by the following formula:

[0099]

[0100] Where l is the characteristic linear dimension and v is the kinematic viscosity of the fluid.

[0101] C2. Calculate the thermal boundary layer thickness of different structural surfaces on the box girder cross section based on the velocity boundary layer thickness of different structural surfaces on the box girder cross section.

[0102] Thermal boundary layer thickness δ t It is usually defined as the temperature in the boundary layer where 99% of the fluid temperature T ∞ The Prandtl number Pr is used to connect the thermal boundary layer and the velocity boundary layer. The thickness of the thermal boundary layer can be calculated by the following formula:

[0103] δ t =Pr -1 / 3 δ

[0104] In the formula, δ t is the thickness of the thermal boundary layer, δ is the thickness of the velocity boundary layer, and Pr is the Prandtl number. The Prandtl number Pr is a parameter used to characterize the relative thickness between the velocity boundary layer and the thermal boundary layer. Except for liquid metals and high-viscosity fluids, the velocity boundary layer thickness and the thermal boundary layer thickness are usually of similar order of magnitude. The Prandtl number can be calculated by the following formula:

[0105]

[0106] Where v is the fluid's kinematic viscosity and α' is the thermal diffusivity. The fluid's kinematic viscosity v and thermal diffusivity α' convey information about the rate at which molecules diffuse through the fluid, and the ratio of the two represents the relative magnitude of momentum and heat diffusion in the fluid. Therefore, Pr can characterize the connection between the velocity field and the temperature field. The Prandtl number Pr and kinematic viscosity v of dry air vary with temperature, as shown in Table 4.

[0107] Table 4 Thermophysical properties of dry air

[0108]

[0109] After preliminary CFD simulation, the upper surface of the box girder top plate and the lower surface of the bottom plate were used as examples to calculate the different incoming wind speeds U ∞ The thickness of the thermal boundary layer around the outer surface of the lower concrete box girder is δ t Figure 7(a) and Figure 7(b) show the different incoming wind speeds U ∞ Thermal boundary layer thickness δ around the outer surface of the lower box girder top structure (upper surface of the top plate, lower surface of the bottom plate) t .

[0110] As shown in Figure 7(a) and Figure 7(b), on the windward side of the box girder, the thermal boundary layer thickness δ t The minimum value is δ, and then gradually increases along the lateral width direction toward the leeward side. This trend applies to all wind conditions. t Generally larger than the thermal boundary layer thickness δ at high wind speeds t When the wind speed is 1m / s, the thickness of the thermal boundary layer δ t reaches a maximum value. As the wind speed increases, the thickness of the thermal boundary layer δ t decreases rapidly; when the wind speed reaches 10m / s, the thickness of the thermal boundary layer δ t The rate of decline slowed down.

[0111] C3. Based on the wind field section model of the box girder surface, the wind speed at the thermal boundary layer thickness of different structural surfaces on the box girder section is solved by computational fluid dynamics (CFD);

[0112] like Figure 9(a) to Figure 9(h) As shown, it shows the average incoming wind speed U ∞ When the speed is 3m / s, 5m / s, 10m / s, 20m / s and 30m / s, the thermal boundary layer thickness δ around the outer surface of the box girder temperature field model of working conditions 1 and 2 is different t Wind speed U i Distribution. At the same time, Figure 8 As shown, it shows the incoming wind speed U ∞=3m / s. The specific parameters of these different working conditions are listed in Table 1. It is worth noting that in this example, the positive wind speed means the wind direction is from left to right, which is different from the incoming wind speed U ∞ On the contrary; on the contrary, negative wind speed indicates that the incoming wind speed U ∞ In addition, at the web and flange tip, the wind speed is positive along the beam height, such as Figure 9(c) to Figure 9(e) , as shown in Figure 9(h), and in Figure 8 Already marked.

[0113] Compare U in Case 1 and Case 2 i distribution, working condition 1 directly adopts the incoming wind speed U ∞ As the U of the outer surface of the entire box girder structure i , while Case 2 considers the actual wind field distribution around the box girder temperature field model. Figure 9(a) to Figure 9(h) It can be seen that:

[0114] (1) The U near the outer surface of the main structural parts (upper surface of the top plate and lower surface of the bottom plate) of the temperature field model of the single-box three-chamber concrete box girder i Generally much smaller than U ∞ ; With the incoming wind speed U ∞ The increase of U on the surface of the model structure i will also increase;

[0115] (2) In general, the U values ​​near the upper surface of the top plate and the lower surface of the bottom plate of the single-box three-chamber concrete box girder temperature field model are i Direction and wind speed U ∞ in the opposite direction;

[0116] (3) At the same incoming wind speed U ∞ The upper surface of the top plate of the box girder and the lower surface of the bottom plate U i The distribution is different, and the U along the width of the plate i The distribution is also different. Specifically, U i Starting from the windward side of the upper surface of the top plate and the lower surface of the bottom plate to the leeward side, the wind speed first gradually increases after a short descending section, and then returns to the wind speed close to the starting position of the boundary layer on the windward side after the descending section, and the wind speed on the leeward side of the lower surface of the bottom plate is U i It will continue to change, but on a smaller scale;

[0117] (4) Box girder web surface U i The highest is at the bottom, and then decreases to about 0 m / s toward the top. The distributions of the right surface of the windward web D and the left surface of the leeward web A are similar but quite different.

[0118] (5) Surface wind speed U at each part of the leeward side i Much lower than the windward side, such as Figure 9(c) to Figure 9(h) shown.

[0119] D. Determine the set incoming wind speed; if the incoming wind speed is less than or equal to the preset incoming wind speed threshold, return to step A and set the next incoming wind speed.

[0120] The wind speed range for breeze is 1-5m / s, increasing by 1m / s. The wind speed range for strong wind is 10-30m / s, increasing by 5m / s.

[0121] E. If the set incoming wind speed is greater than the preset incoming wind speed threshold, the wind speeds at the thermal boundary layer thickness of different structural surfaces on the box girder section corresponding to different incoming wind speeds are fitted to obtain the wind speed reduction coefficients of different structural surfaces on a section of a box girder.

[0122] Previous research objects were streamlined steel box girder cross sections. When designing, it was necessary to reduce the impact of wind on the bridge. The surface wind field distribution was relatively uniform, so different incoming wind speeds U ∞ U of the center surface of each part i The wind reduction coefficient of each part is quantitatively evaluated. However, the object of this example is a concrete box girder, and the cross-sectional design does not consider the influence of the wind field. Compared with the literature, the distribution of the wind field on the same structural surface is quite different (e.g. Figure 8 Therefore, this example uses the average absolute magnitude of the tangential velocity on each surface to quantitatively analyze the actual wind field on the surface of the box girder structure.

[0123] The numerical simulation results of the wind field on the box girder structure surface show that the wind speed U i With the incoming wind speed U ∞ There is a linear relationship between them. The wind speed reduction coefficient μ of the outer surface of each part around the temperature field model of the concrete box girder is defined as the wind speed U at the boundary layer thickness. i With the incoming wind speed U ∞ Therefore, the wind speed reduction factor μ can be calculated by the following formula:

[0124]

[0125] In this example, 10 different incoming wind speeds U in the range of 1 to 30 m / s are directly analyzed. ∞ ,like Fig.10 As shown, fitting different incoming wind speeds U ∞ The wind speed U at the thermal boundary layer thickness of different structural surfaces on the box girder section corresponding to different incoming wind speeds i , the wind speed reduction coefficient μ of different structural surfaces on a section of the box girder temperature field model is obtained, as shown in Table 5.

[0126] Table 5 Summary of wind speed reduction coefficient μ

[0127]

[0128] In addition to the wind speed U at the thermal boundary layer thickness discussed above i In addition to the general trend of Fig.10 From Table 5, we can see that:

[0129] (1) On the top surface of the box girder temperature field model, the wind speed U at the thickness of the thermal boundary layer i Reduce the incoming flow velocity U ∞ The wind speed U at the thermal boundary layer thickness on the right surface of the windward web D is about 20-25% i Correspondingly, the specific wind speed reduction coefficient μ is shown in Table 5;

[0130] (2) Wind speed U at the thickness of the thermal boundary layer on the bottom surface of the base i About U ∞ About 17% of μ, slightly lower than the μ value on the top surface of the top plate;

[0131] (3) Wind speed U at the thermal boundary layer thickness on the left surface of web A (WebA), the left flange tip (YYL), the lower side of the left flange (YYLD), and the lower side of the right flange (YYRD) on the leeward side i At a relatively low level (μ≤0.1);

[0132] (4) Wind speed U at the right flange tip (YYR) at the thermal boundary layer thickness on the entire box girder surface i The highest, but only accounts for U ∞ About 30% of the total area of ​​the box girder, and this part is at the edge of the entire box girder, and its surface area accounts for less than 1% of the entire box girder structure;

[0133] (5) Directly using empirical formulas to analyze the wind field of the box girder structure will greatly overestimate the effect of thermal convection on the surface of the concrete box girder, resulting in a temperature field that is lower than the actual surface temperature.

[0134] This embodiment takes into account that different structures on the outer surface of the box girder face different wind field distributions on the entire bridge, and obtains wind speed reduction coefficients for different structural surfaces on a cross section of a box girder, thereby improving the accuracy of bridge temperature field assessment.

[0135] Due to the influence of the absolute size of working condition 2 on the wind speed reduction factor of the box girder structure surface, the sensitivity analysis includes:

[0136] In order to compare the difference in wind field between the temperature field model of the actual bridge and the box girder with different absolute sizes, the working condition 3 (see Table 1) is set, that is, the 1:2 box girder temperature field model with the same shape but double the absolute size and the 1:1 box girder model of the actual bridge block 15 are analyzed, and an additional 1:4 box girder model is simulated to further clarify the influence of absolute size on the actual wind field of the box girder. The outer surfaces of the main structures such as the top plate 1, bottom plate 2, web A3, web D 6 are selected as the observation objects, and the comparison of the calculation results is as follows Figure 11(a) to Figure 11(d) The width and height of the box girder were normalized before comparison.

[0137] Depend on Figure 11(a) to Figure 11(d) It can be seen that although the change of absolute size will affect the wind speed distribution on the box girder surface, in the field of civil engineering, this effect is not prominent, and the deviation is large in strong winds (20m / s and 30m / s) (as shown in Figure 11(b)), which mainly affects the lower surface of the bottom plate. The wind field fluctuates greatly with the change of absolute size.

[0138] Thermal boundary layer thickness δ of main parts of box girders of various sizes t Wind speed Figure 12(a) to Figure 12(d) shown.

[0139] according to Figure 12(a) to Figure 12(d) Thermodynamic boundary layer thickness δ of the main parts of the box beams with different sizes under different incoming wind speeds t The wind speed reduction coefficients of the main parts of the box girders of various sizes are obtained by fitting, as shown in Table 6.

[0140] Table 6 Wind speed reduction coefficients on the main structure surface of box beam

[0141]

[0142] Note: The calculation of the maximum absolute error is based on the actual bridge, taking the maximum value of the difference between the wind speed reduction coefficients of the 1:2 box girder model and the 1:4 box girder model and the surface wind speed reduction coefficients of the corresponding parts of the actual bridge.

[0143] Depend on Figure 12(a) to Figure 12(d) From Table 6, it can be seen that the determination of wind speed reduction coefficient mainly depends on the incoming wind speed U ∞ The cross-sectional shape and size of the box girder will affect the wind field distribution on the lower surface of the box girder bottom plate under strong winds (10-30 m / s), although such wind conditions rarely occur in practice; even if the actual bridge top plate 1 has a certain slope, the wind speed U at the thickness of the thermal boundary layer on its outer surface iThe influence of the distribution of the wind speed reduction coefficient can be ignored. Since the wind speed reduction coefficient of the reference condition 1 is set to 1, the deviation of the wind speed reduction coefficient relative to the reference condition 1 is still within the acceptable range (less than 0.1). Therefore, from the perspective of the bridge temperature field, the influence of the geometric dimensions on the actual wind field distribution on the box girder surface can be excluded.

[0144] S12. Obtain the wind speed reduction coefficients of different structural surfaces on a cross section of n different box girders respectively by the same method as described in step S11, where n≤N.

[0145] In order to study the actual wind field distribution of different sections of the single-box three-chamber concrete box girder bridge, pay attention to the influence of the beam height on the wind field on the box girder surface, and set working condition 4 (see Table 1). According to the actual bridge block 0 (abutment position), block 8 (actual bridge test box girder section Section I), block 15 (model test reference box girder section Section II, 2 / 5 span), and block 36 (mid-span), the corresponding CFD box girder model sections are set respectively. Through the same method described in step S11 above, the wind speed distribution at the thermal boundary layer thickness of different structural surfaces of each segment box girder model is obtained and plotted, as shown in FIG. Figure 13(a) to Figure 13(h) , Figure 14(a) to Figure 14(h) and Figure 15(a) to Figure 15(h) As shown, different beam height sections are directly represented by corresponding beam section numbers.

[0146] according to Figure 9(a) to Figure 9(h) , Figure 13(a) to Figure 13(h) , Figure 14(a) to Figure 14(h) and Figure 15(a) to Figure 15(h) The data of the same incoming wind speed U ∞ The wind field distribution of the entire bridge will change due to the different box girder heights. For example, the wind direction on the upper surface of the top plate of block 36 on the windward side is opposite to the incoming wind direction, and on the leeward side at the tail end of the boundary layer (within the range of about 0 to 4m) it is the same as the incoming wind direction. This beam section is mainly located in the mid-span of the bridge. The wind field distribution on the lower surface of the bottom plate is most affected by the height of the box girder, and the difference is obvious. Although the height of the box girder web is different, the wind field distribution is relatively similar and the values ​​are close. There are also certain differences in other minor parts, but they are not discussed here.

[0147] like Figure 16(a) to Figure 16(h) As shown, the thermal boundary layer thickness δ of different structural surfaces of the box girder model in different test sections is fitted t Wind speed U i And the incoming flow speed U ∞ , the wind speed reduction coefficients of different structural surfaces on a section of the box girder model in different test sections are obtained, see Table 7.

[0148] Depend on Figure 16(a) to Figure 16(h)It can be seen that under various wind conditions, only block 36 presents a completely linear distribution of wind speed on each structural surface, while other beam sections show different degrees of deviation as the wind speed increases. The change in beam height will affect the boundary layer thickness δ on each surface of the box girder structure. t The distribution of wind speed at the bridge. From block 0 at the abutment to block 15 at the 2 / 5 span, the beam height decreases rapidly, resulting in different degrees of increase in the wind speed reduction coefficients of the main parts of the box beam (top plate 1, bottom plate 2, web A3, web D 6) with the increase of beam height (see Table 7). From block 15 at the 2 / 5 span to block 36 at the 1 / 2 span, the speed of beam height reduction slows down, but the change rules of the wind speed reduction coefficients of the main parts of the box beam are inconsistent, some continue to increase (bottom plate 2, web D 6), and some decrease (top plate 1, web A3).

[0149] Table 7 Structural surface wind speed reduction coefficient

[0150]

[0151] S13. Obtain the aspect ratios of all the above box girder sections.

[0152] The geometric dimensions of the actual bridge sections No. 0 (slab position), No. 8 (box girder section Section I of the actual bridge test), No. 15 (box girder section Section II of the model test reference, 2 / 5 span), and No. 36 (mid-span) are shown in Table 8. The beam heights of blocks 0 to 15 vary greatly, while those of blocks 15 to 36 vary less. Since the geometry of the top plate 1 remains unchanged, the corresponding beam heights and web plate heights are mainly listed.

[0153] Table 8 Geometric dimensions of different segments

[0154]

[0155] S14. Fit the aspect ratios of all the above box girder sections and the wind speed reduction coefficients of different structural surfaces to obtain a linear function of the aspect ratio of any section of any box girder and the wind speed reduction coefficient.

[0156] In order to analyze the wind field of the whole bridge and further obtain the surface convection heat transfer coefficient that can be directly applied to the variable cross-section single-box three-chamber concrete box girder structure, the wind speed reduction coefficient in Table 7 is converted into the height-to-width ratio (H) of the box girder by fitting. ver / D bot ) is a linear function, which is specifically shown in Table 9, where H ver is the height of the box girder, D bot is the width of the box girder bottom plate 2.

[0157] Table 9 Calculation model of wind speed reduction coefficient for the whole bridge

[0158]

[0159] According to the surface simulation and design model of the variable cross-section single-box three-chamber concrete box girder structure, the wind speed reduction coefficient is obtained, such as Fig.17 As shown in the figure, the points represent the wind speed reduction coefficients obtained by simulation, and the dotted line represents the linear function obtained by fitting. The wind speed reduction coefficients are most consistent on the upper surface of the box girder top plate and the lower surface of the bottom plate. Except for the three structural surfaces on the leeward side where the wind speed reduction coefficient μ is set to 0.1, the maximum error between the simulation and the model on the remaining structural surfaces is 0.06, which occurs on the right surface of the web D WebD (H ver / D bot =0.36), however, relative to the reference condition 1 (μ=1), this error is negligible.

[0160] S2. According to the height-to-width ratio of the box girder bridge, the wind speed reduction coefficient of the box girder bridge is obtained through the wind speed reduction coefficient model.

[0161] S3. Calculate the convective heat transfer coefficient on the surface of the box girder bridge based on the actual incoming wind speed and the wind speed reduction coefficient of the box girder bridge.

[0162] The thermal convection boundary conditions of this embodiment are as follows:

[0163] Thermal convection refers to the heat conduction phenomenon that occurs when there is a temperature difference between the surface of an object and the surrounding environment (such as the atmospheric temperature or the temperature of the fluid in the space), which is governed by Newton's cooling equation:

[0164] q c =h c ·(T Bridge -T A )

[0165] In the formula, q c is the heat transfer density of convection (W / m 2 ); T in this embodiment Bridge is the bridge temperature; T A is the ambient temperature; h c is the convective heat transfer coefficient (W / (m 2 ·℃)). The convective heat transfer coefficient is closely related to the wind speed. The greater the wind speed, the greater the convective coefficient. F. Kehlbeck proposed to substitute the Nusselt temperature coefficient (Nu) into the heat transfer coefficient constant term of the surface temperature and the ambient temperature in the windless condition to obtain the convective heat transfer coefficient h for civil engineering. c Calculation formula:

[0166]

[0167] Where, T A is the ambient temperature (℃), T Sis the bridge surface temperature (℃), w is the wind speed, and w≤5m / s. However, due to the different geometric shapes of the bridge, even at the same inflow wind speed, different surfaces are affected by the wind speed to different degrees. In addition, even on the same surface, such as the top plate, the wind speed distribution will be unevenly distributed along the geometric width.

[0168] Just as the hydrodynamic boundary layer is defined as the region in the flow where viscous forces exist, the thermal boundary layer can be defined as the region in the flow where a temperature gradient exists. The temperature gradient in this region is caused by heat exchange processes between the fluid and the wall.

[0169] like Fig.18 As shown in the schematic diagram of velocity boundary and thermodynamic boundary, the wall temperature is T S , the fluid temperature at infinity outside the thermal boundary layer is T ∞ , the thickness of the thermal boundary layer is δ t At the wall, the velocity is zero and heat is transferred to the fluid by heat transfer.

[0170] When a fluid flows over a solid surface at a certain speed, a velocity boundary layer will form on the solid surface. In the velocity boundary layer, since the fluid particles adhere to the solid surface, the velocity on the solid surface is 0, and at the boundary layer thickness δ, the velocity gradually approaches the incoming wind speed U ∞ There is a velocity gradient within the distance range from the solid surface to δ. At the same time, when a fluid with uniform temperature flows through a solid surface with non-uniform temperature, a thermal boundary layer is formed between the fluid and the solid surface. The temperature at the solid surface is infinitely close to the solid surface temperature, and the thickness of the thermal boundary layer δ t At the point, the temperature gradually approaches the fluid temperature T ∞ The thickness of the thermal boundary layer from the solid surface to the t There is a temperature gradient within the range, and convective heat exchange behavior occurs in this range.

[0171] Therefore, the wind speed w in the formula is replaced by the thermal boundary layer thickness δ t Wind speed U i , and the ambient temperature T A Considered as fluid temperature T ∞ In order to study the different structural surfaces of the box girder under the same incoming wind speed U ∞ The convective heat transfer coefficient h of civil engineering is c The calculation formula can be modified as follows:

[0172]

[0173] And the thermal boundary layer thickness δ t Wind speed U i It can be calculated by the following formula:

[0174] U i =μ·U ∞

[0175] In summary, the convective heat transfer coefficient h of civil engineering c The calculation formula can be further modified as follows:

[0176]

[0177] According to the actual incoming wind speed U ∞ and the wind speed reduction coefficient μ of the box girder bridge, a more accurate convective heat transfer coefficient h on the surface of the box girder bridge can be calculated c , which can be applied to variable-section single-box multi-chamber box girder bridges with complex and changeable temperature fields, thereby improving the applicability and accuracy of bridge temperature field evaluation.

[0178] The specific implementation methods described above further illustrate the objectives, technical solutions and beneficial effects of the present invention in detail. It should be understood that the above description is only a specific implementation method of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A method for calculating the convective heat transfer coefficient of a box girder bridge surface, wherein the box girder bridge comprises N variable-section box girders, characterized in that: The following steps are involved: S1. Construct a wind speed reduction coefficient model, including: S11. Obtain wind speed reduction coefficients of different structural surfaces on a cross section of a box girder by using a wind speed reduction coefficient solution method; S12, using the same method as described in step S11, respectively obtain the wind speed reduction coefficients of different structural surfaces on a cross section of n different box girders, n≤N; S13, obtaining the aspect ratios of all the box girder sections mentioned above; S14, fitting the aspect ratios of all the box girder sections and the wind speed reduction coefficients of different structural surfaces to obtain a linear function of the aspect ratio and wind speed reduction coefficient of any section of any box girder; S2. According to the height-to-width ratio of the box girder bridge, the wind speed reduction coefficient of the box girder bridge is obtained through the wind speed reduction coefficient model; S3. Calculate the convective heat transfer coefficient on the surface of the box girder bridge based on the actual incoming wind speed and the wind speed reduction coefficient of the box girder bridge.

2. The method for calculating the convective heat transfer coefficient of a box girder bridge surface according to claim 1, characterized in that: The method for solving the wind speed reduction coefficient in step S11 specifically includes the following steps: A. Set the initial incoming wind speed and the incoming wind speed threshold; B. According to the set incoming wind speed, the surface wind field distribution of a box girder is simulated by computational fluid dynamics, the grid independence is verified, and a box girder surface wind field cross-sectional model is built; C. According to the wind field section model on the box girder surface, the wind speed at the thermal boundary layer thickness of different structural surfaces on the box girder section is solved; D. Determine the set incoming wind speed; if the incoming wind speed is less than or equal to the preset incoming wind speed threshold, return to step A and set the next incoming wind speed; E. If the set incoming wind speed is greater than the preset incoming wind speed threshold, the wind speeds at the thermal boundary layer thickness of different structural surfaces on the box girder section corresponding to different incoming wind speeds are fitted to obtain the wind speed reduction coefficients of different structural surfaces on a section of a box girder.

3. The method for calculating the convective heat transfer coefficient of the box girder bridge surface according to claim 2, characterized in that: The step C comprises the following sub-steps: C1. Calculate the velocity boundary layer thickness of different structural surfaces on the box girder section according to the set incoming wind speed; C2. Calculate the thermal boundary layer thickness of different structural surfaces on the box girder cross section based on the velocity boundary layer thickness of different structural surfaces on the box girder cross section; C3. Based on the box girder surface wind field section model, the wind speed at the thermal boundary layer thickness of different structural surfaces on the box girder section is solved by computational fluid dynamics.

4. The method for calculating the convection heat transfer coefficient of the box girder bridge surface according to claim 3, characterized in that: The velocity boundary layer thickness in step C1 is calculated by the following formulas: Where δ is the thickness of the velocity boundary layer, x is the distance from the starting point of the calculation boundary on the solid surface to the calculation point, α and β are constants, Re is the Reynolds number, and U is ∞ is the incoming wind speed, l is the characteristic linear dimension, and v is the kinematic viscosity of the fluid.

5. The method for calculating the convection heat transfer coefficient of the box girder bridge surface according to claim 3, characterized in that: The thermal boundary layer thickness in step C2 is calculated by the following formula: δ t =Pr -1 / 3 δ In the formula, δ t is the thickness of the thermal boundary layer, Pr is the Prandtl number, and δ is the thickness of the velocity boundary layer.

6. The method for calculating the convection heat transfer coefficient of a box girder bridge surface according to claim 1, characterized in that: The convective heat transfer coefficient in step S3 is calculated by the following formulas: IN i =μ·U ∞ In the formula, h c is the convective heat transfer coefficient, T ∞ is the fluid temperature, T S is the wall temperature, U i is the wind speed at the thickness of the thermal boundary layer, μ is the wind speed reduction factor, U ∞ is the incoming wind speed.

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