Water temperature calculation method for water conveyance tunnel

Abstract

This invention relates to a method for calculating the water temperature of a water conveyance tunnel, comprising: for pressurized tunnels: calculation of the temperature of the outer surface of the lining; calculation of the equivalent thermal conductivity of the tunnel; calculation of the net heat flux of the inner surface of the tunnel lining; calculation of the water temperature at the tunnel exit; for unpressurized tunnels: calculation of the air temperature above the water body in the tunnel; calculation of the tunnel inner wall temperature; calculation of the water temperature at the tunnel exit. This invention first establishes a parameterized equation and water temperature model for heat exchange between the water body and the tunnel wall in pressurized tunnels, and analyzes the spatiotemporal variation of water temperature; then, it establishes a parameterized equation and water temperature model for heat exchange between the water body and the tunnel wall and gas in unpressurized tunnels, and analyzes the spatiotemporal variation of air and water temperatures, considering the heat exchange between the water body and the riverbed and related factors, thus forming a more accurate method for calculating tunnel temperature, providing a scientific basis for accurately predicting the icing of water conveyance tunnels.

Description

Technical Field

[0001] This invention relates to a method for calculating the water temperature in a water conveyance tunnel, which is a heat exchange calculation method and a method for measuring and calculating the water temperature in a water conveyance tunnel. Background Technology

[0002] Water conveyance tunnels are a crucial component of long-distance canal systems, and variations in their water temperature significantly impact ice conditions downstream. Besides open channels and aqueducts, long-distance canal systems also rely on hydraulic structures such as tunnels and inverted siphons for water transport. Taking the central canal project as an example, with a total length of approximately 1277 km, many sections utilize tunnels for water conveyance: the Chuanhuang Tunnel (3450 m long, maximum depth 35 m, minimum depth 23 m); the Wushan Tunnel (2509 m long); the Wushan Tunnel (2207 m long); and the Gangtou Tunnel (1800 m long), among others. Because tunnels and inverted siphons are deeply buried underground waterways, the ice conditions in long-distance canal systems differ significantly from those in natural river channels.

[0003] Since its full operation in 2014, the Central Route Canal has undergone continuous ice condition monitoring for many years. Except for the severe ice conditions during the extreme cold wave of 2015-2016, other winters have been predominantly mild. For example, in the winter of 2019-2020, the average daily temperature ranged from -0.5 to -2.7℃, the minimum temperature from -7.3 to -14.7℃, and the water temperature ranged from 0.82 to 8.5℃. The average water temperature at each monitoring station ranged from 2.97 to 5.34℃, and the lowest measured water temperature ranged from 0.82 to 4.24℃. The main ice conditions were bank ice and drifting ice, with no continuous ice cover forming. However, numerical simulations using the river ice-hydraulic theory model predict the formation of a continuous and thick ice cover. This raises a pressing scientific question: what are the main reasons for this significant discrepancy between theory and reality?

[0004] In past ice-hydraulic calculations and analyses, traditional linear heat exchange models were generally used to analyze ice conditions, neglecting the heat exchange between the water body and the riverbed. To understand the reasons for the significant discrepancy between theoretical calculations and actual conditions in the central route project, this study investigated the heat exchange between the water body and the atmosphere and bed of open channels and aqueducts during the ice season. It considered solar radiation and albedo, long-wave radiation between the ground and the atmosphere, heat exchange from water surface evaporation and convection, and ground reflection. The study analyzed the spatiotemporal variations of these factors on water temperature and ice content at cross-sections during ice bloom. The results show that: 1) correctly considering the influence of various factors on heat exchange between the water surface and the atmosphere is the direction for improving the accuracy of ice condition prediction; 2) the heat exchange between the water body and the canal bed and aqueduct must be considered, otherwise the water temperature cannot be determined. Currently, the problem is the lack of mathematical models describing the spatiotemporal variations of water temperature in water conveyance tunnels in ice-hydraulic research. Water conveyance tunnels can be divided into pressurized tunnels and unpressurized tunnels. When water passes through a pressurized tunnel, it only exchanges heat with the tunnel wall, and the water temperature depends on the ground temperature of the surrounding rock. However, when water passes through an unpressurized tunnel, it exchanges heat not only with the tunnel walls but also with the air above the water surface. The water temperature depends on the changes in the ground temperature and air temperature of the surrounding rock. Calculating these heat exchanges is a problem that needs to be solved. Summary of the Invention

[0005] To overcome the problems of existing technologies, this invention proposes a method for calculating the water temperature of water conveyance tunnels. The method establishes parameterized equations and water temperature models for heat exchange between water and tunnel walls in pressurized tunnels, and for heat exchange between water and tunnel walls and gases in unpressurized tunnels, thus forming a more accurate method for calculating the temperature of water conveyance tunnels.

[0006] The objective of this invention is achieved as follows: a method for calculating the water temperature of a water conveyance tunnel, comprising calculation methods for pressurized tunnels and calculation methods for unpressurized tunnels:

[0007] I. Calculations for pressurized tunnels:

[0008] The pressurized tunnel has a circular cross-sectional shape, and its dimensions are as follows: the inner radius of the tunnel lining is R, and the outer radius of the tunnel lining is... The tunnel is a deep-buried tunnel, and the temperature distribution around the tunnel is divided into three layers: the first layer is the lining layer. The second layer is the temperature-varying surrounding rock layer. ,in The outer diameter of the variable-temperature layer; the third layer is the constant-temperature layer of the surrounding rock. The constant temperature layer of the surrounding rock is set as the geothermal temperature. It is a constant;

[0009] 1) Temperature of the outer surface of the lining Calculation:

[0010]

[0011] in: Temperature of the tunnel inner wall; The thermal conductivity of the lining; The thermal conductivity of the surrounding rock temperature-varying layer;

[0012] 2) The lining layer and the surrounding rock temperature-changing layer can be divided into: When the tunnel is layered, the equivalent thermal conductivity is... Calculation:

[0013]

[0014] Where: m is a positive integer greater than or equal to 2, and j is the j-th layer in the m layers;

[0015] 3) Net heat flux of the inner surface of the tunnel lining Calculation:

[0016]

[0017] In the formula: The heat exchange coefficient between the water body and the tunnel; The average cross-sectional temperature of the water in the tunnel;

[0018] 4) Calculate the tunnel section Exit time water temperature calculate:

[0019] The tunnel is divided into multiple sections along its length, denoted by the subscript "". "Numbering the tunnel section"

[0020] ,

[0021] In the formula: For the tunnel section Import time Water temperature; For the tunnel section Exit time Water temperature; ; ; The density of water; The specific heat of water; For tunnel segment i, the cross-sectional area of ​​the tunnel through which water flows is denoted.

[0022] when :

[0023] , ;

[0024] In the formula: For tunnel flow rate; Let be the flow velocity in tunnel segment i; For the tunnel section Length;

[0025] II. Calculation of Unpressurized Tunnels:

[0026] The cross-sectional shape of the pressureless tunnel is that of a city gate, that is, the upper part is an arched top and the lower part is a straight wall;

[0027] 5) Calculate the air temperature above the water body in the tunnel. ;

[0028]

[0029] In the formula: for Temperature at any given moment;

[0030] , , ;

[0031] In the formula:

[0032] , ,

[0033] , ,

[0034]

[0035] In the formula: The coefficient of heat exchange between air and water convection; The velocity of the gas inside the cave relative to the water flow; Local atmospheric pressure;

[0036] And the temperature distribution pattern along the route:

[0037] ;

[0038] in: x is the velocity of the gas; x is the distance. for The starting point of Section 1 of the tunnel;

[0039] 6) Calculate the temperature of the tunnel inner wall. :

[0040]

[0041] In the formula: The convective heat exchange coefficient between the air and the cave wall;

[0042] 7) Calculate the tunnel section Exit time water temperature :

[0043] ,

[0044] ,

[0045] In the formula: For tunnel segment i ; For tunnel segment i ; For tunnel segment i .

[0046] The advantages and beneficial effects of this invention are as follows: First, this invention establishes parameterized equations and a water temperature model for heat exchange between water and tunnel walls in pressurized tunnels, and analyzes the spatiotemporal variation of water temperature. Then, it establishes parameterized equations and a water temperature model for heat exchange between water and tunnel walls and gas in unpressurized tunnels, analyzes the spatiotemporal variation of air and water temperatures, and considers heat exchange between water and riverbed as well as related factors, forming a more accurate method for calculating tunnel temperature, providing a scientific basis for accurately predicting the freezing of water conveyance tunnels. If a water conveyance inverted siphon is considered a special case of a pressurized tunnel, then the parameterized method for heat exchange in pressurized tunnels and the water temperature model are also applicable to water conveyance inverted siphons. Attached Figure Description

[0047] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0048] Figure 1 This is a schematic diagram of the computational framework of the method described in the embodiments of the present invention;

[0049] Figure 2 This is a schematic diagram of the cross-sectional shape of the pressurized tunnel targeted by the method described in the embodiments of the present invention;

[0050] Figure 3 This is a schematic diagram of the cross-sectional shape of the unpressurized tunnel targeted by the method described in the embodiments of the present invention;

[0051] Figure 4 This is the tunnel air temperature distribution along the tunnel in the winter water conveyance operation in the application example described in the embodiments of the present invention;

[0052] Figure 5 This refers to the tunnel air temperature distribution along the tunnel under different water flow rates in the application examples described in this embodiment of the invention.

[0053] Figure 6This is a simulation of the tunnel water temperature distribution along the tunnel under different surrounding rock constant temperature layer temperatures and atmospheric temperatures during winter water conveyance, as described in the application example of this invention. Detailed Implementation

[0054] Example:

[0055] This embodiment describes a method for calculating the water temperature of a water conveyance tunnel. The method includes calculations for pressurized tunnels and unpressurized tunnels, with the calculation framework as follows: Figure 1 As shown.

[0056] I. Heat exchange in pressurized tunnels:

[0057] At the Earth's surface, due to the influence of solar radiation, the temperature often exhibits diurnal, seasonal, and multi-year cycle variations; this layer is called the exothermic layer. At the lower boundary of the exothermic layer, the temperature remains constant year-round, equal to or slightly higher than the annual average temperature; this depth zone is called the isothermal layer or isothermal zone. Below the isothermal layer, due to the influence of the Earth's internal heat sources, the temperature begins to gradually increase with depth.

[0058] The tunnel body is usually located in a constant temperature layer. As the tunnel is excavated and water is introduced, the original thermal balance between the tunnel lining and the surrounding rock is broken, and a new thermal balance is formed. The tunnel lining and the surrounding rock near the tunnel become a variable temperature layer within a certain range.

[0059] To avoid complex calculations of unstable temperature fields, a stable temperature field is used to analyze the heat exchange between the water body and the tunnel. Studies have shown that for tunnels buried at depths exceeding 10m, the ground temperature is generally unaffected by annual fluctuations in surface temperature and can be considered as a deep-buried tunnel.

[0060] like Figure 1 The circular cross-section of the pressurized deep-buried tunnel shown can be divided into three layers in terms of temperature distribution. The first layer is the lining layer 1, see... Figure 2 , ,in and These are the inner diameter of the tunnel and the outer diameter of the lining, respectively; the second layer is the temperature-changing surrounding rock layer 2. ,in The outer diameter of the variable temperature layer; the third layer is the constant temperature layer of the surrounding rock. Ground temperature It is a constant.

[0061] Assuming that the temperatures at the same radius of the lining layer and the surrounding rock temperature-varying layer are the same and independent of the ordinate, the heat conduction equation for the steady-state temperature field in cylindrical coordinates is:

[0062] (1)

[0063] In the formula: The temperature of the lining or surrounding rock, ; Let be the radius, in meters (m).

[0064] Solving the ordinary differential equation (1) yields:

[0065] (2)

[0066] (3)

[0067] Lining layer boundary conditions: when hour, ;when hour, ,in: The temperature of the tunnel inner wall. ; The temperature of the outer surface of the lining. Substituting these boundary conditions into equations (2) and (3), we get:

[0068] (4)

[0069] (5)

[0070] (6)

[0071] Boundary conditions of variable temperature layer in surrounding rock: when hour, ;when hour, The temperature outside the thermosphere can be considered as the ground temperature. , are known numbers. Substituting these boundary conditions into equations (2) and (3), we get:

[0072] (7)

[0073] (8)

[0074] According to the principle of heat balance, at the interface between the lining layer and the temperature-variable layer Solving equations (6) and (8) simultaneously yields the temperature on the outer side of the lining:

[0075] (9)

[0076] Heat flux of the inner surface of the tunnel lining:

[0077] (10)

[0078] In the formula: This refers to the net heat flux of the inner surface of the tunnel lining. ; The thermal conductivity of the lining, ; The thermal conductivity of the surrounding rock temperature-varying layer is... ;

[0079] Substituting equation (9) into equation (10), we get:

[0080] (11)

[0081] (12)

[0082] In the formula: The equivalent thermal conductivity of the tunnel, [ In the calculation process, the outer diameter of the temperature-changing layer of the surrounding rock can generally be taken as the value. = (2~3)R, or the thickness of the temperature-variable layer = (1~2)R.

[0083] Similarly, when the lining layer and the surrounding rock temperature-changing layer can be divided into When the tunnel is layered, the equivalent thermal conductivity is:

[0084] (13)

[0085] Due to the average cross-sectional temperature of the water in the tunnel Approximately equal to the water temperature of the inner surface of the tunnel lining. ,Right now: Therefore, equation (11) can be rewritten as:

[0086] (14)

[0087] In the formula: The heat exchange coefficient between the water body and the tunnel represents the heat exchange capacity between the water body and the tunnel surface. , .

[0088] II. Calculation of water temperature in pressurized tunnels:

[0089] As the water in the pressurized tunnel exchanges heat with the tunnel walls, heat is transferred downstream and throughout the entire cross-section through the movement and turbulence of the water flow. Under one-dimensional conditions, the convection-heat diffusion equation along the flow direction is:

[0090] (15)

[0091] In the formula: The average cross-sectional temperature of the water is ℃; For time, s; Let m be the distance. The density of water is kg / m³. 3 At room temperature 1000 kg / m³; The specific heat of water at 0°C =4217.7 J / kg℃; The cross-sectional area of ​​the tunnel under water passage is in meters. 2 ; The average cross-sectional velocity of the water is denoted as ρ, in m / s. The thermal diffusivity; For wetted perimeter, m.

[0092] The first term on the left side of equation (15) represents the change in heat across the cross-section of the water over time; the second term represents the change in heat across the cross-section of the water as the water moves, also known as the convective transfer of heat; and the third term represents the change in heat across the cross-section of the water as the water diffuses. The right side of equation (15) represents the amount of heat exchange between the water and the tunnel.

[0093] In the analysis of ice-water dynamics, the thermal diffusion term of the water body can be ignored, and equation (15) can be rewritten as:

[0094] (16)

[0095] (17)

[0096] In the formula: ; <0, ; Indicates the change of liquid particles over time The changing trajectory of motion is called a characteristic line.

[0097] When the tunnel is divided into Segment, in each segment parameter , , If is a constant, then integrating equation (16) along the characteristic line yields the recursive formula for calculating water temperature:

[0098] , (18)

[0099] In the formula: subscript " "This is the tunnel section number; For the tunnel section Import time Water temperature, °C; For the tunnel section Exit time Water temperature, °C; ,s; , , Let i be a constant for tunnel segment i.

[0100] Integrating equation (17) yields Therefore, equation (18) can be rewritten as:

[0101] , (19)

[0102] In the formula: For tunnel flow rate, m 3 / s; Let be the flow velocity in tunnel segment i.

[0103] Due to the coefficient It always holds true, therefore, regardless of the water temperature at the tunnel inlet. Is the water temperature in segment i greater than or less than 0℃? As time goes by or distance The increase in temperature follows an exponential pattern, gradually approaching the temperature of a constant-temperature layer in a certain section of the tunnel.

[0104] (20)

[0105] In summary, an important conclusion can be drawn: if a pressurized tunnel is long enough that the outlet water temperature is greater than 0℃ during the ice season, then ice flow will not occur in a certain length of the downstream channel from the tunnel outlet.

[0106] III. Temperature Calculation in Unpressurized Tunnels:

[0107] The entrance and exit of a pressureless tunnel are connected to the atmosphere. Changes in atmospheric temperature inevitably affect the distribution and temporal variation of air temperature within the tunnel. Furthermore, tunnel wall temperature and water temperature also influence air temperature changes within the tunnel. Simultaneously, air temperature changes within the tunnel affect water temperature changes. Therefore, understanding the patterns of air temperature variation within the tunnel is fundamental to analyzing water temperature variation patterns. The following analysis uses a portal-type pressureless tunnel, commonly used in water conveyance projects, as an example to analyze the patterns of air temperature variation within the tunnel. The portal-type tunnel described in this embodiment has an arched top and a straight wall at the bottom, and is buried 10 meters underground. Based on temperature analysis requirements, the tunnel is divided into multiple temperature distribution zones: lining layer 4, surrounding rock temperature-changing layer 5, and surrounding rock constant-temperature layer 6, as shown below. Figure 3 As shown.

[0108] Winter ice condition observations indicate that the relative humidity in open channel water conveyance projects is relatively high. Taking the Beijing-Shijiazhuang section of the central route as an example, the daily average relative humidity is 57.5%-71.1%, with the highest daily relative humidity reaching 81.5%-96.10%. Considering the limited gas space inside the unpressurized tunnel, the atmosphere entering the tunnel easily reaches saturation due to water evaporation, i.e., the relative humidity... =100%. Under these conditions, the effect of water surface evaporation is negligible. The heat exchange between gas and water in the unpressurized tunnel is mainly affected by convection. Based on the Russian winter formula, the heat flux of convection is:

[0109] (twenty one)

[0110] (twenty two)

[0111] In the formula: Net heat flux for air-water heat exchange, W / m 2 ; The air-water convection heat exchange coefficient, ; The velocity of the gas inside the cave relative to the water flow is expressed in m / s. The local atmospheric pressure is given in hPa. Assuming the airflow and water flow tunnels are of the same size and direction, then... .

[0112] Equation (21) can be rewritten as

[0113] (twenty three)

[0114] In the formula: , , .

[0115] The convective heat exchange between the gas and the upper tunnel wall surface can be described as follows:

[0116] (twenty four)

[0117] In the formula: Net heat flux of the tunnel wall, W / m 2 ; The convective heat exchange coefficient between air and the cave wall The following empirical formula can be used for calculation.

[0118] (25)

[0119] In the formula: Let be the velocity of the gas, in m / s.

[0120] Considering the heat conduction of the tunnel lining and surrounding rock, we can obtain:

[0121] (26)

[0122] Solving equations (24) and (26) simultaneously, we get:

[0123] (27)

[0124] Substituting equation (27) into equation (26), we obtain the net heat flux of the tunnel wall:

[0125] (28)

[0126] (29)

[0127] In the formula: This represents the heat exchange coefficient between the gas and the tunnel. For the arched roof of a portal-type unpressurized tunnel, Determined by equation (13), denoted as For straight walls:

[0128] (30)

[0129] The temperature of the air inside the tunnel is affected by the temperature of the tunnel walls and the water temperature along the tunnel. Assuming that the gas in the unpressurized tunnel is an incompressible fluid and neglecting the effect of thermal diffusion, the one-dimensional convection equation for the gas is:

[0130] (31)

[0131] In the formula: The density of air at 0°C and 1 atmosphere. =1.29kg / m³; Let m be the area of ​​air on the cross-section of the tunnel. 2 ; Assuming the specific heat of air is 1000 J / (kg℃), a preliminary calculation suggests this value can be taken. Let be the perimeter of the arched dome, in meters (m). The length of the tunnel wall in contact with the gas, in meters; The width of the water surface is in meters (m).

[0132] The first term on the right side of equation (31) is the heat flux conducted to the gas by the constant temperature layer of the surrounding rock of the tunnel, while the second term is the heat flux conducted to the gas by the thermal convection of the water surface.

[0133] Under normal circumstances, the water depth for normal water conveyance in a city gate-type tunnel is... Less than the height of the straight wall When the water depth at the tunnel cross-section is known. , crown radius and central angle (radians), then

[0134] , , (32)

[0135] Given the water flow rate and the width of the tunnel bottom The following methods can be used to calculate the water depth. Assuming the flow is uniform, the average velocity V across the cross-section is:

[0136]

[0137] Right now:

[0138] (33)

[0139] In the formula: The average flow velocity is given in m / s. The Manning roughness coefficient of the tunnel wall is generally taken as [value missing]. ; Let be the hydraulic radius, in meters. This refers to the hydraulic gradient or bottom slope. The water depth can be calculated from equation (33) using numerical methods. .

[0140] Using the characteristic line method, equation (31) can be rewritten as:

[0141] (34)

[0142] (35)

[0143] In the formula: ,

[0144] , ,

[0145] Due to the actual engineering This always holds true. Let's analyze a typical case:

[0146] 1) The flow in the unpressurized tunnel is a quasi-steady-state uniform flow, and the water flow velocity is... The water temperature remains constant throughout the journey. The change is small and can be considered a constant;

[0147] 2) Assuming that the gas flow in the unpressurized tunnel is caused by the movement of water, and taking that the wind speed and water flow velocity are in the same direction, then That is, gas flow rate ;

[0148] 3) The properties of the lining and surrounding rock remain constant along the route, including lining thickness, thermal conductivity, and surrounding rock temperature. wait.

[0149] Under the above assumptions, the solution to the ordinary differential equation (34) is:

[0150]

[0151] The temperature changes over time:

[0152] (36)

[0153] In the formula: for Temperature at any given moment

[0154] , ,

[0155] The solution to the ordinary differential equation (35) is:

[0156] (37)

[0157] Substitute equation (37) into equation (36) to eliminate The distribution pattern of temperature along the path:

[0158] (38)

[0159] When the tunnel entrance is taken as ,but This refers to the atmospheric temperature at the tunnel inlet. When... , This indicates that regardless of the temperature at the tunnel entrance... Greater than or less than the tunnel surrounding rock temperature and water temperature, air temperature As the distance from the cave entrance increases, the temperature tends to reach a constant temperature exponentially. Its size is related to the temperature of the surrounding rock. Water temperature It is related to the tunnel structure and thermodynamic parameters.

[0160] IV. Temperature Variation Patterns in Unpressurized Tunnels:

[0161] For example Figure 2 The unpressurized tunnel shown, considering that the normal water level in the tunnel is generally within the vertical wall range, the heat exchange between the water and the tunnel can be described as follows:

[0162] (39)

[0163] (40)

[0164] In the formula: The thickness, in meters, is the thickness of the lining wall or base slab. Let be the thickness of the temperature-varying layer of the surrounding rock, in meters (m). In preliminary calculations, we can take... = (1~2)R.

[0165] According to equation (21), the net heat flux from gas convection received by the water surface of an unpressurized tunnel is... It can be described as:

[0166] (41)

[0167] In the formula: , , , .

[0168] The heat exchange between the tunnel water and the surrounding environment includes convective heat exchange between the water surface and the air, and heat exchange between the water and the tunnel, namely:

[0169] (42a)

[0170] , , , (42b)

[0171] Put the right side of equation (15) Using the right side of equation (42a) Instead, ignoring the thermal diffusivity term and using the characteristic line method, we can obtain:

[0172] (43)

[0173] For actual water conveyance projects, This always holds true. When the tunnel is divided into... Segment, in each segment parameter , , , If is a constant, then integrating equation (43) along the characteristic line yields:

[0174] , (44)

[0175] , (45)

[0176] In the formula: subscript " "This is the tunnel section number; is the number of hole sections; For the tunnel section The length, in meters; For the tunnel section The average flow velocity, m / s; ,s; For the tunnel section Import time Water temperature, °C; For the tunnel section Exit time Water temperature, °C;

[0177] , , (46)

[0178] At a known time Starting point of tunnel section 1 water temperature Under the given conditions, the tunnel segment can be recursively calculated using equation (44) or equation (45). exit During the period The final water temperature Due to the coefficient Always true, water temperature Over time or distance The increase in follows an exponential law, approaching 0. .

[0179] Calculation example:

[0180] The following section takes the Wuzhuang Tunnel on the Beijing-Shijiazhuang section of the central route as an example to quantitatively analyze the spatiotemporal changes of air and water temperature inside the tunnel.

[0181] 1) Changes in air temperature inside the cave with varying inlet atmospheric temperatures and flow rates:

[0182] The Wuzhuang Tunnel is 2373m long, with a tunnel body length of 2207m and a bottom slope of 1 / 5870. It adopts a twin-tube layout and has a design flow rate of 125m³ / h. 3 / s, verification flow rate 150 m³ / s 3 / s; The tunnel cross-section is a circular arch with straight walls, and the net width is... 7.8m, hole height =8.15m; the tunnel section mainly uses concrete lining, with a lining thickness of... 0.25m, with a single layer of steel mesh inside. When the check flow rate is 150 m³ / h. 3 With a roughness coefficient n=0.014, the uniform flow velocity V=1.64m / s and water depth H=5.85m inside the tunnel. The water conveyance flow rate during the winter of 2015-2016 was 45.72m³ / s. 3 When n = 0.014 and s = 1.22 m / s, V = 2.41 m. The height of the straight wall is calculated. 5.9m, crown radius R=4.5m, lining outer diameter = 4.75m, taking the radius of the temperature-changing layer of the surrounding rock. =2.0 =9.0m, reinforced concrete =1.74 W / m.℃, thickness of the variable temperature layer in the surrounding rock = 4.25m, assuming the surrounding rock is granite with a thermal conductivity of . =3.0W / (m℃), gas density = 1.29 kg / m³, specific heat of air =1000J / (kg℃).

[0183] The temperature of the constant-temperature layer is directly proportional to altitude and can be estimated using the following empirical formula.

[0184] (47)

[0185] In the formula: Z is the altitude of the ground point, in meters. When the constant temperature layer temperature is taken... 10.0℃ Wind speed relative to water flow and gas Table 1 shows the calculated characteristic parameter values, where V=1.22m / s and V=1.64 m / s represent winter water conveyance and check water conveyance, respectively.

[0186] Table 1 Calculation of characteristic parameter values

[0187]

[0188] Figure 4 The simulation shows different atmospheric temperatures during winter water transport. The air temperature distribution along the tunnel under the condition (x=0). When the atmospheric temperature at the tunnel inlet is greater than 0℃, the air temperature inside the tunnel decreases approximately linearly with increasing distance from the tunnel entrance. When the atmospheric temperature at the tunnel inlet is less than 0℃, the air temperature inside the tunnel increases rapidly and exponentially with increasing distance from the tunnel entrance, approaching or even exceeding 0℃. For example: atmospheric temperature =-18℃, water temperature =1℃ and the temperature of the surrounding rock constant temperature layer At 10℃, the air temperature at the tunnel exit It rose to around -0.4℃; =-18℃ =4℃ and At 10℃, the air temperature at the tunnel exit It rose to around 1.7℃.

[0189] Figure 5 The simulation shows the tunnel air temperature distribution along the tunnel under different water flow rates, where: gas cross-sectional area =39.64m 2 The corresponding winter water conveyance flow rate is 45.72 m³. 3 / s, =12.81m 2 The corresponding verification operating condition water flow rate is 150.0 m³.3 / s. Obviously, the gas space inside the tunnel decreases as the water flow rate increases; the larger the gas space, the more gradual the temperature distribution along the tunnel, while the smaller the gas space, the greater the temperature distribution, especially near the tunnel entrance. For example, under the check flow condition, the temperature at the entrance of Wuzhuang Tunnel is -18℃, while at a distance of 500m from the tunnel entrance, the temperature rises by more than -7℃.

[0190] 2) Changes in water temperature inside the cave with varying temperatures of the surrounding rock constant-temperature layer and the inlet atmospheric temperature:

[0191] Assuming there is an ice cap at the entrance of the Wuzhuang Tunnel, the water temperature beneath the ice... =0.00℃. The water temperature will be analyzed below. During the change process, the temperature inside the unpressurized tunnel It can be calculated using formula (36) or formula (38), and is a known quantity. Figure 6 The diagram illustrates the tunnel water temperature distribution under simulated winter water conveyance conditions with varying surrounding rock isothermal layer temperatures and atmospheric temperatures (x = 0), where the water flow rate is 150.0 m³ / s. 3 / s, atmospheric temperature at tunnel inlet 18~ 6℃, temperature of the constant temperature layer in the tunnel The temperatures are 5℃ and 10℃, respectively.

[0192] observe Figure 6 It is evident that, regardless of 5℃ or 10℃, water temperature Distance from the tunnel entrance The increase from water temperature =0.00℃ first drops to below 0℃, then as The temperature gradually increased, even exceeding 0°C, because the air temperature at the tunnel inlet was negative and as... The increase was rapid, and it even turned positive (see [reference]). Figure 4 From this, we can draw the following conclusion: when there is an ice cap at the entrance of an unpressurized tunnel, and the atmospheric temperature is less than zero, the water temperature in the tunnel section at the entrance will drop below 0°C, becoming supercooled water, which may produce ice flowers. However, as the distance from the tunnel entrance increases, the ice flowers will disappear as the water temperature rises.

[0193] Finally, it should be noted that the above is only used to illustrate the technical solution of the present invention and not to limit it. Although the present invention has been described in detail with reference to preferred arrangements, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solution of the present invention (such as the form of the tunnel, the application of various formulas, the derivation process and conclusions, etc.) without departing from the spirit and scope of the technical solution of the present invention.

Claims

1. A method for calculating the water temperature of a water conveyance tunnel, the method comprising a calculation method for pressurized tunnels and a calculation method for unpressurized tunnels, characterized in that: I. Calculations for pressurized tunnels: The pressurized tunnel has a circular cross-sectional shape, with the following dimensions: the inner radius of the tunnel lining is R, and the outer radius of the tunnel lining is R1. The tunnel is a deep-buried tunnel, and the temperature distribution around the tunnel is divided into three layers: the first layer is the lining layer. ; The second layer is the temperature-varying layer of the surrounding rock. ,in The outer diameter of the variable-temperature layer; the third layer is the constant-temperature layer of the surrounding rock. The constant temperature layer of the surrounding rock is set as the geothermal temperature. It is a constant; 1) Temperature of the outer surface of the lining Calculation: in: Temperature of the tunnel inner wall; The thermal conductivity of the lining layer; The thermal conductivity of the surrounding rock temperature-varying layer; 2) The lining layer and the surrounding rock temperature-changing layer are divided into: When the tunnel is layered, the equivalent thermal conductivity is... Calculation: Where: m is a positive integer greater than or equal to 2, and j is the j-th layer in the m layers; 3) Net heat flux of the inner surface of the tunnel lining Calculation: In the formula: The heat exchange coefficient between the water body and the tunnel; The average cross-sectional temperature of the water in the tunnel; 4) Calculate the tunnel section Exit time water temperature calculate: The tunnel is divided into multiple sections along its length, denoted by the subscript "". "Numbering the tunnel section" ， In the formula: For the tunnel section Import time Water temperature; For the tunnel section Exit time Water temperature; ; , Let i be a constant for tunnel segment i; The density of water; The specific heat of water; For tunnel segment i, the cross-sectional area of ​​the tunnel through which water flows is denoted. when : ， ； In the formula: For tunnel flow rate; Let be the flow velocity in tunnel segment i; For the tunnel section Location along the route; II. Calculation of Unpressurized Tunnels: The cross-sectional shape of the pressureless tunnel is that of a city gate, that is, the upper part is an arched top and the lower part is a straight wall; 5) Calculate the air temperature above the water body in the tunnel. ; In the formula: for Temperature at any given moment; ， ， ； In the formula: , , Transition coefficient; And the temperature distribution pattern along the route: ； in: x is the velocity of the gas; x is the distance; x0 is... The starting point of Section 1 of the tunnel; 6) Calculate the temperature of the tunnel inner wall : In the formula: The convective heat exchange coefficient between the air and the cave wall; 7) Calculate the tunnel section Exit time water temperature : , , In the formula: For tunnel segment i ; For tunnel segment i ; For tunnel segment i .

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