Method for calculating maximum water supply interval for preventing canal icing based on external high-temperature water into canal

Abstract

The application discloses a kind of maximum water replenishing interval calculation methods of preventing canal icing based on external high-temperature water into channel, it is characterized in that, including the actual flow of channel, channel water temperature, reservoir water temperature into channel, air temperature and reservoir inflow;According to the actual flow of channel, channel water temperature, reservoir water temperature into channel and reservoir inflow, the mixed water temperature after channel water replenishing is calculated;According to the actual flow of channel and reservoir inflow, total flow and water depth after water replenishing are calculated;According to air temperature and total flow, water depth and mixed water temperature after water replenishing, prevent canal icing maximum water replenishing interval is calculated using channel unfreezing length model wherein Q and respectively total flow and water depth after water replenishing;T a For air temperature;T0 for mixed water temperature;R 2 For goodness of fit.

Description

Technical Field

[0001] This invention belongs to the field of water conveyance technology, specifically relating to a method for calculating the maximum water replenishment interval for preventing canal freezing based on external high-temperature water entering the canal. Background Technology

[0002] Long-distance water conveyance projects are the most effective and direct means of addressing the uneven spatial and temporal distribution of water resources. In high-latitude regions of northern China, the accumulated negative temperature is high in winter, leading to varying degrees of ice formation in canals. Water conveyance under the ice cover is the most common winter water conveyance method for long-distance water conveyance channels. Through hydraulic regulation, a stable ice cover is formed on the water surface, isolating the water body from the outside atmosphere. Under the ice cover, no new ice will form in the water, thus ensuring safe water conveyance during the ice season.

[0003] In order to ensure that ice cover can form smoothly in the channel and to prevent downstream ice from sinking into the leading edge of the ice cover or in front of the ice-blocking cable and causing ice blockage, it is necessary to limit the channel flow velocity and Froude number within a certain range (usually requiring v<0.6m / s, Fr<0.08) by using control gates. Although this operation ensures the safe operation of the channel, it also limits the channel's water transport capacity during the ice period.

[0004] Based on thermodynamic principles, drawing high-temperature water into the canal along its length reduces ice formation, transforming water transport under the ice cover into a two-phase flow of ice and water, or even ice-free transport, fundamentally solving the problem of reduced water transport capacity during ice periods. Currently, drawing groundwater into the canal to achieve ice-free water transport has been successfully applied in some power plants. By placing a pumping station at regular intervals along the power plant's water intake canal, high-temperature groundwater is drawn into the canal, ensuring the canal water temperature remains above freezing, achieving ice-free water transport in winter. This not only improves water transport capacity during ice periods but also eliminates the need for ice removal water consumption, reduces the difficulty of ice period management, and greatly improves the efficiency of the power plant.

[0005] Currently, the technology of using high-temperature water to regulate the thermal temperature during the ice-period is only applied to power station water diversion canals that are only a few tens of kilometers long. Furthermore, there are no universally applicable theoretical results for determining the inflow rate, water temperature, and pump station intervals. The determination is still mainly based on estimation and manual experience. Pump stations are then set up at the estimated locations to replenish the external high-temperature water. Since the intervals of the pump stations are set based on experience, there are situations where the water replenishment intervals are not set reasonably: if the intervals are set too short, the pump stations will be built too densely, resulting in high investment costs; if the intervals are set too short, the water temperature in the canal will drop below the freezing point before it reaches the next pump station, causing freezing and affecting the normal water transport in the canal. Summary of the Invention

[0006] In view of the above-mentioned shortcomings in the prior art, the maximum water replenishment interval calculation method for preventing canal freezing based on external high-temperature water inflow provided by the present invention solves the problem that the existing technology uses empirical water replenishment intervals, resulting in unreasonable pump station installation location settings.

[0007] A method for calculating the maximum water replenishment interval for preventing canal freezing based on external high-temperature water inflow is provided, which includes the following steps:

[0008] Obtain the actual flow rate of the channel, the channel water temperature, the reservoir inlet water temperature, the air temperature, and the reservoir inlet flow rate;

[0009] Calculate the mixed water temperature after replenishment of the channel based on the actual flow rate of the channel, the channel water temperature, the reservoir inlet water temperature and the reservoir inlet flow rate;

[0010] Calculate the total flow and water depth after replenishment based on the actual flow rate of the channel and the inflow rate of the reservoir into the channel;

[0011] Based on the air temperature, total flow rate after water replenishment, water depth, and mixed water temperature, the maximum water replenishment interval L0 for preventing canal freezing is calculated using the canal non-freezing length model.

[0012]

[0013] Among them, Q and These represent the total flow rate and water depth after replenishment; T a T0 is the air temperature; R is the mixed water temperature. 2 The goodness of fit is denoted as .

[0014] Furthermore, when the canal replenishment method involves unidirectional extraction of deep water from the reservoir and injection into the canal, the formula for calculating the mixed water temperature is:

[0015]

[0016] When the canal replenishment method involves drawing deep water from the reservoir and injecting it into the canal, and simultaneously drawing an equal amount of low-temperature water from the canal upstream of the replenishment point and injecting it into the reservoir, the formula for calculating the mixed water temperature is:

[0017]

[0018] Where T is the channel water temperature; q is the reservoir inflow rate; Q1 is the actual channel flow rate; and t is the reservoir inflow water temperature.

[0019] Furthermore, the method for constructing the channel non-freezing length model includes:

[0020] Obtain the water temperature equation for the channel;

[0021] When the inlet water temperature, channel water depth, and channel water flow rate are constant, and the initial water temperature along the channel is equal to the inlet water temperature, the channel water temperature decrease rate along the channel under different air temperatures is simulated based on the water temperature equation to obtain the unfrozen length of the channel under different air temperatures.

[0022] Based on multiple air temperatures and their corresponding unfrozen channel lengths, a formula for the relationship between the unfrozen channel length and the outside air temperature is obtained through fitting:

[0023] L0 = 252.6(-T) a ) -1 (R 2 =0.9988);

[0024] When the air temperature, channel water depth and channel water flow are constant, and the initial water temperature along the channel is equal to the inlet water temperature, the rate of decrease of channel water temperature along the channel under different inlet temperatures is simulated based on the water temperature equation to obtain the unfrozen length of the channel under different inlet temperatures.

[0025] Based on multiple different inlet temperatures and their corresponding unfrozen channel lengths, a fitted formula was obtained to determine the relationship between the unfrozen channel length and the inlet water temperature:

[0026] L0 = 35.66t0(R) 2 =0.9999);

[0027] When the air temperature, channel water depth and reservoir water temperature are constant, and the initial water temperature along the channel is equal to the inlet water temperature, the rate of decrease of channel water temperature along the channel under different channel water flow rates is simulated based on the water temperature equation to obtain the unfrozen length of the channel under different channel water flow rates.

[0028] Based on the water flow rates of multiple different channels and their corresponding unfrozen lengths, a fitting formula was obtained to determine the relationship between the unfrozen length and the water flow rate of the channels:

[0029] L0 = 0.67Q(R) 2 =0.9935);

[0030] When the air temperature, channel water flow rate and reservoir inlet water temperature are constant, and the initial water temperature along the channel is equal to the inlet water temperature, the rate of decrease of channel water temperature along the channel at different channel depths is simulated based on the water temperature equation to obtain the unfrozen length of the channel at different channel depths.

[0031] Based on multiple different channel water depths and their corresponding unfrozen lengths, a fitting formula was obtained to determine the relationship between the unfrozen length and the channel water depth:

[0032]

[0033] Multivariate fitting was performed on the relationships between the unfrozen length of the canal and the outside temperature, the unfrozen length of the canal and the inlet water temperature, the unfrozen length of the canal and the water flow rate, and the unfrozen length of the canal and the water depth to obtain the final model of the unfrozen length of the canal:

[0034]

[0035] Furthermore, the formula for calculating the water temperature equation is as follows:

[0036]

[0037] S = S1 + S2, S1 = h wa (1-C a (T) w -T a S2=h wi (T w -t i )

[0038] Among them, C p E is the specific heat of water. x h is the longitudinal diffusion coefficient. wa h is the heat exchange coefficient between the water body and the outside atmosphere. wi The heat exchange coefficient between the water body and the ice sheet; C a The ice-covered rate of the canal surface; T w The temperature of the channel water; T i ρ is the temperature at the bottom of the ice cap; S is the density of water; S is the total heat exchange per unit surface area of ​​the water body; S1 is the heat exchange between the water body and the outside atmosphere; S2 is the heat exchange between the water body and the ice cap; A is the cross-sectional area of ​​the channel; B is the width of the channel surface; t is time; x is the distance along the channel.

[0039] Furthermore, the formula for calculating the heat exchange coefficient between the water body and the ice sheet is as follows:

[0040] h wi =1622v 0.8 y -0.2

[0041] Where v is the average flow velocity of the channel cross section and y is the channel water depth.

[0042] The beneficial effects of this invention are as follows: This solution combines the adjustable reservoir water temperature along the channel that needs to be controlled to obtain a relatively accurate mixed water temperature and water depth. Combined with the channel non-freezing length model, a relatively accurate maximum water replenishment interval can be obtained, so as to obtain the construction distance of the pumping station relatively accurately. In this way, after the external high temperature water enters the channel, the anti-freezing effect can be reduced, and the risks of water freezing, ice blockage and other risks can be avoided, thus ensuring the normal transportation of water in the channel.

[0043] Because this scheme fully considers the effects of multiple factors such as total flow rate, water depth, air temperature, and mixed water temperature, it can ensure that the intervals are just right, avoid the waste of external heat resources or insufficient heat supply to the channel, and avoid the problems of unreasonable planning of water pumping stations due to the reliance on experience in existing technologies, which could lead to increased water transmission costs or poor anti-freezing effects. Attached Figure Description

[0044] Figure 1 This is a flowchart illustrating the calculation method for the maximum water replenishment interval to prevent canal freezing based on external high-temperature water entering the canal.

[0045] Figure 2 This shows the temperature drop along the canal water path under different air temperature conditions.

[0046] Figure 3 This relates the length of the ice-free zone to the temperature.

[0047] Figure 4 This shows the temperature drop along the canal under different reservoir inlet water temperatures.

[0048] Figure 5 This relates the length of the unfrozen section to the water temperature at the reservoir's inlet.

[0049] Figure 6 The variation of channel water temperature along the channel under different water flow conditions is shown.

[0050] Figure 7 This relates the unfrozen length to the water flow rate.

[0051] Figure 8 The variation of channel water temperature along the channel under different average water depth conditions at different cross sections.

[0052] Figure 9 This represents the relationship between the unfrozen length and the average water depth of the cross-section. Detailed Implementation

[0053] The specific embodiments of the present invention are described below to enable those skilled in the art to understand the present invention. However, it should be understood that the present invention is not limited to the scope of the specific embodiments. For those skilled in the art, various changes are obvious as long as they are within the spirit and scope of the present invention as defined and determined by the appended claims. All inventions utilizing the concept of the present invention are protected.

[0054] refer to Figure 1 , Figure 1 A flowchart illustrating the calculation method for the maximum water replenishment interval to prevent canal icing based on external high-temperature water inflow is shown; Figure 1 As shown, the method S includes steps S1 to S4.

[0055] In step S1, the actual flow rate of the channel, the channel water temperature, the reservoir inlet water temperature, the air temperature, and the reservoir inlet flow rate are obtained. The reservoir mentioned in this scheme can be an underground reservoir or an underground aquifer, or it can be a water storage reservoir along the channel.

[0056] In step S2, the mixed water temperature after replenishment of the channel is calculated based on the actual flow rate of the channel, the channel water temperature, the reservoir inlet water temperature and the reservoir inlet flow rate.

[0057] In implementation, this scheme is preferred when the channel replenishment method is unidirectional extraction of deep water from the reservoir and injection into the channel. The formula for calculating the mixed water temperature is as follows:

[0058]

[0059] When the canal replenishment method involves drawing deep water from the reservoir and injecting it into the canal, and simultaneously drawing an equal amount of low-temperature water from the canal upstream of the replenishment point and injecting it into the reservoir, the formula for calculating the mixed water temperature is:

[0060]

[0061] Where T is the channel water temperature; q is the reservoir inflow rate; Q1 is the actual channel flow rate; and t is the reservoir inflow water temperature.

[0062] In step S3, the total flow and water depth after replenishment are calculated based on the actual flow rate of the channel and the inflow rate of the reservoir into the channel;

[0063] In step S4, based on the air temperature, total flow rate after water replenishment, water depth, and mixed water temperature, the maximum water replenishment interval L0 for preventing canal freezing is calculated using the canal non-freezing length model.

[0064]

[0065] Among them, Q and These represent the total flow rate and water depth after replenishment; T a T0 is the air temperature; R is the mixed water temperature. 2 The goodness of fit is denoted as .

[0066] To facilitate understanding of the non-freezing length model, the construction process of the channel non-freezing length model will be explained in detail below, taking into account the relevant parameters of the channel:

[0067] To facilitate the sensitivity analysis of channel water temperature to various thermal and hydraulic factors, this scheme first constructs a relatively simple mathematical model of the channel. The channel is 60 km long with no branching points. The channel head is a reservoir-gate boundary, and the reservoir water level upstream of the gate remains constant (66.0 m). The channel head is a pumping station, and it is assumed that the pumping flow rate of the pumping station remains constant. During the simulated ice-period water conveyance process, the opening of the head gate remains unchanged from its initial opening. The channel cross-section is trapezoidal, and the specific parameters of the channel are shown in Table 1. The specific parameters of the upstream gate are shown in Table 2.

[0068] Table 1 Channel Parameter Table

[0069]

[0070] Table 2 Gate Parameter Table

[0071]

[0072] Construct a formula relating the length of the canal without freezing to the outside temperature.

[0073] First, the influence of air temperature on canal water temperature is analyzed using a canal mathematical model. It is assumed that the reservoir inlet water temperature is constant at 0.5℃, and that the initial water temperature along the canal is also equal to the reservoir inlet water temperature of 0.5℃. A single constant ambient air temperature is used (i.e., calculations are performed under different constant air temperature conditions: -2.5℃, -5.0℃, -7.5℃, -10℃, -12.5℃, and -15.0℃). The temperature decay law along the canal under different air temperature conditions is analyzed. The canal water flow rate is taken as its design value, i.e., 85 m³ / h. 3 / s.

[0074] Figure 2 To obtain a channel water temperature attenuation diagram along the channel through numerical simulation under different air temperature conditions, combined with the water temperature equation. Figure 2 As shown in the figure, when the air temperature is lower than the water temperature, the water temperature in the channel decreases along the channel. The lower the outside air temperature, the greater the difference between the water and air temperatures, and the faster the water temperature decreases along the channel. When the air temperatures are -2.5℃, -5.0℃, -7.5℃, -10.0℃, -12.5℃, and -15.0℃, the water temperature decay rates along the channel are 0.0051℃ / km, 0.0094℃ / km, 0.0139℃ / km, 0.0184℃ / km, 0.0228℃ / km, and 0.0273℃ / km, respectively; the unfrozen lengths of the channels are 98.0km, 53.0km, 35.9km, 27.2km, 21.9km, and 18.3km, respectively (derived from the water temperature decrease rate along the channel). Figure 3 To understand the relationship between the unfrozen length of the canal and the air temperature, we can determine the absolute value of the unfrozen length relative to the negative air temperature (-T). a They are inversely proportional. According to... Figure 3 The relationship between the unfrozen length and the outside temperature can be obtained by fitting the equation as follows: L0=252.6(-T a ) -1 (R 2 =0.9988).

[0075] The formula for calculating the water temperature equation is as follows:

[0076]

[0077] S = S1 + S2, S1 = h wa (1-C a (T) w -Y a S2=h wi (T w -T i )

[0078] Among them, C p E is the specific heat of water. x h is the longitudinal diffusion coefficient. wah is the heat exchange coefficient between the water body and the outside atmosphere. wi The heat exchange coefficient between the water body and the ice sheet; C a The ice-covered rate of the canal surface; T w The temperature of the channel water; T i ρ is the temperature at the bottom of the ice cap; S is the density of water; S is the total heat exchange per unit surface area of ​​the water body; S1 is the heat exchange between the water body and the outside atmosphere; S2 is the heat exchange between the water body and the ice cap; A is the cross-sectional area of ​​the channel; B is the width of the channel surface; t is time; x is the distance along the channel.

[0079] The formula for calculating the heat exchange coefficient between water bodies and ice sheets is:

[0080] h wi =1622v 0.8 y -0.2

[0081] Where v is the average flow velocity of the channel cross section and y is the channel water depth.

[0082] Construct the relationship between the length of the canal without freezing and the inlet water temperature.

[0083] The water conveyance flow rate of the channel is 85m³ / h (design flow rate). 3 Assuming that the initial water temperature along the canal is equal to the reservoir inlet water temperature, and the air temperature is a single value of -15.0℃, the influence of different reservoir inlet water temperatures on the water temperature changes along the canal is calculated and analyzed.

[0084] Figure 4 This paper presents the canal water temperature attenuation along the canal under different reservoir inlet water temperatures, using numerical simulation based on the water temperature equation. Figure 4 As can be seen, the higher the water temperature entering the canal from the reservoir, the greater the rate at which the water temperature decreases along the canal, but the difference is very small. Figure 5 The relationship between the unfrozen length of the canal and the inlet water temperature of the reservoir is shown. It is evident that the inlet water temperature significantly affects the unfrozen length; the higher the inlet water temperature, the more heat energy the inlet water contains, and the longer the unfrozen length. When the inlet water temperatures are 0.50℃, 0.75℃, 1.00℃, 1.25℃, and 1.50℃, the corresponding rates of temperature decrease along the canal are 0.0273℃ / km, 0.0276℃ / km, 0.0279℃ / km, 0.0281℃ / km, and 0.0283℃ / km; the unfrozen lengths of the canals are 18.3km, 27.2km, 35.9km, 44.5km, and 53.0km, respectively. Based on... Figure 5 The relationship between the unfrozen length and the inlet water temperature of the reservoir can be obtained by fitting, as follows: L0=35.66T0(R 2 =0.9999).

[0085] Construct the relationship between the unfrozen length of the channel and the water flow rate of the channel.

[0086] Assuming the reservoir inlet water temperature is constant at 0.5℃ and the air temperature is a single value of -15.0℃, the impact of different canal flow rates on the canal water temperature decay is calculated and analyzed. Figure 6 and Figure 7 As shown in the figure, the larger the water flow rate in the channel, the more total heat energy the water in the channel contains, resulting in a smaller rate of temperature decay along the channel and a longer unfrozen length. When the channel water flow rate is 17.0 m³ / s... 3 / s, 34.0m 3 / s, 51.0m 3 / s, 68.0m 3 / s, 85.0m 3 At a speed of / s, combined with the water temperature equation, the water temperature attenuation rates along the channel obtained through numerical simulation were 0.0336℃ / km, 0.0192℃ / km, 0.0140℃ / km, 0.0112℃ / km, and 0.0094℃ / km, respectively; the unfrozen lengths of the channels were 14.9km, 26.0km, 35.7km, 44.6km, and 53.0km, respectively. According to... Figure 7 The relationship between the unfrozen length and the water flow rate can be obtained by fitting, as follows: L0=0.67Q(R) 2 =0.9935).

[0087] Construct the relationship between the length of the canal that does not freeze and the depth of the canal water.

[0088] The water conveyance flow rate of the channel is 85m³ / h (design flow rate). 3 With a water temperature of 0.5℃ at the reservoir inlet and a single air temperature of -15.0℃, different channel bottom slopes were used to vary the water depth at the channel head. The temperature decay pattern along the channel under different water depths was analyzed. When the channel bottom slopes were 1 / 5000, 1 / 10000, 1 / 15000, 1 / 20000, and 1 / 25000, the average water depth at the channel head was 2.11m, 2.46m, 2.69m, 2.86m, and 2.99m, respectively. Figure 8 This is a diagram showing the variation of channel water temperature along the channel through numerical simulation under different water depth conditions, combined with the water temperature equation. The diagram shows that the greater the average water depth at the cross-section, the wider the water surface, the higher the heat dissipation rate along the channel, the greater the rate of temperature decrease along the channel, and the shorter the unfrozen length of the channel. When other conditions are the same, with average water depths at the channel head of 2.11m, 2.46m, 2.69m, 2.86m, and 2.99m, the corresponding rates of temperature decrease along the channel are 0.0080℃ / km, 0.0087℃ / km, 0.0091℃ / km, 0.0094℃ / km, and 0.0097℃ / km; the corresponding unfrozen lengths of the channel are 62.5km, 57.5km, 54.7km, 53.0km, and 51.8km. Figure 9The graph shows the relationship between the unfrozen length of the canal and the average water depth of the cross-section. Analysis reveals that the unfrozen length of the canal and the average water depth of the cross-section have a power function relationship, as shown below:

[0089]

[0090] The above analysis shows that the unfrozen length of a canal is affected by multiple factors, including air temperature, reservoir inlet water temperature, water flow rate, and canal water depth. The unfrozen length is directly proportional to the water flow rate and reservoir inlet water temperature, and inversely proportional to the absolute value of the negative air temperature and the square root of the average water depth at the cross-section. A multivariate fitting of these influencing factors yields the formula for calculating the unfrozen length of a canal:

[0091]

[0092] In summary, this solution can accurately determine the maximum water replenishment interval to prevent channel freezing, thus avoiding the risks of water freezing and blockage in long-distance water conveyance channels during winter. Moreover, it fundamentally solves the problem of reduced water conveyance capacity during the ice season, thereby ensuring normal water conveyance in northern channels during winter.

Claims

1. A method for calculating the maximum water replenishment interval for preventing canal freezing based on external high-temperature water inflow, characterized in that, Including the following steps: Obtain the actual flow rate of the channel, the channel water temperature, the reservoir inlet water temperature, the air temperature, and the reservoir inlet flow rate; Calculate the mixed water temperature after replenishment of the channel based on the actual flow rate of the channel, the channel water temperature, the reservoir inlet water temperature and the reservoir inlet flow rate; Calculate the total flow and water depth after replenishment based on the actual flow rate of the channel and the inflow rate of the reservoir into the channel; Based on the air temperature, total flow rate after water replenishment, water depth, and mixed water temperature, the maximum water replenishment interval L0 for preventing canal freezing is calculated using the canal non-freezing length model. Among them, Q and These represent the total flow rate and water depth after replenishment; T a T0 is the air temperature; R is the mixed water temperature. 2 The goodness of fit is denoted as .

2. The method for calculating the maximum water replenishment interval according to claim 1, characterized in that, When the water replenishment method for the channel is unidirectional extraction of deep water from the reservoir and injection into the channel, the formula for calculating the mixed water temperature is: When the canal replenishment method involves drawing deep water from the reservoir and injecting it into the canal, and simultaneously drawing an equal amount of low-temperature water from the canal upstream of the replenishment point and injecting it into the reservoir, the formula for calculating the mixed water temperature is: Where T is the channel water temperature; q is the reservoir inflow rate; Q1 is the actual channel flow rate; and t is the reservoir inflow water temperature.

3. The method for calculating the maximum water replenishment interval according to claim 1, characterized in that, The method for constructing the channel non-freezing length model includes: Obtain the water temperature equation for the channel; When the inlet water temperature, channel water depth, and channel water flow rate are constant, and the initial water temperature along the channel is equal to the inlet water temperature, the channel water temperature decrease rate along the channel under different air temperatures is simulated based on the water temperature equation to obtain the unfrozen length of the channel under different air temperatures. Based on multiple air temperatures and their corresponding unfrozen channel lengths, a formula for the relationship between the unfrozen channel length and the outside air temperature is obtained through fitting: L0=252.6(-T a ) -1 (R 2 =0.9988); When the air temperature, channel water depth and channel water flow are constant, and the initial water temperature along the channel is equal to the inlet water temperature, the rate of decrease of channel water temperature along the channel under different inlet temperatures is simulated based on the water temperature equation to obtain the unfrozen length of the channel under different inlet temperatures. Based on multiple different inlet temperatures and their corresponding unfrozen channel lengths, a fitted formula was obtained to determine the relationship between the unfrozen channel length and the inlet water temperature: L0=35.66T0(R 2 =0.9999); When the air temperature, channel water depth and reservoir water temperature are constant, and the initial water temperature along the channel is equal to the inlet water temperature, the rate of decrease of channel water temperature along the channel under different channel water flow rates is simulated based on the water temperature equation to obtain the unfrozen length of the channel under different channel water flow rates. Based on the water flow rates of multiple different channels and their corresponding unfrozen lengths, a fitting formula was obtained to determine the relationship between the unfrozen length and the water flow rate of the channels: L0=0.67Q(R 2 =0.9935); When the air temperature, channel water flow rate and reservoir inlet water temperature are constant, and the initial water temperature along the channel is equal to the inlet water temperature, the rate of decrease of channel water temperature along the channel at different channel depths is simulated based on the water temperature equation to obtain the unfrozen length of the channel at different channel depths. Based on multiple different channel water depths and their corresponding unfrozen lengths, a fitting formula was obtained to determine the relationship between the unfrozen length and the channel water depth: Multivariate fitting was performed on the relationships between the unfrozen length of the canal and the outside temperature, the unfrozen length of the canal and the inlet water temperature, the unfrozen length of the canal and the water flow rate, and the unfrozen length of the canal and the water depth to obtain the final model of the unfrozen length of the canal:

4. The method for calculating the maximum water replenishment interval according to claim 3, characterized in that, The formula for calculating the water temperature equation is as follows: S=S1+S 2， S1=h wa (1-C a )(T w -T a ),S2=h wi (T w -T i ) Among them, C p E is the specific heat of water. x h is the longitudinal diffusion coefficient. wa h is the heat exchange coefficient between the water body and the outside atmosphere. wi The heat exchange coefficient between the water body and the ice sheet; C a The ice-covered rate of the canal surface; T w The temperature of the channel water; T i ρ is the temperature at the bottom of the ice cap; S is the density of water; S is the total heat exchange per unit surface area of ​​the water body; S1 is the heat exchange between the water body and the outside atmosphere; S2 is the heat exchange between the water body and the ice cap; A is the cross-sectional area of ​​the channel; B is the width of the channel surface; t is time; x is the distance along the channel.

5. The method for calculating the maximum water replenishment interval according to claim 4, characterized in that, The formula for calculating the heat exchange coefficient between the water body and the ice sheet is: h wi =1622v 0.8 y -0.2 Where v is the average flow velocity of the channel cross section and y is the channel water depth.

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