Method for calculating wall temperature and heat compensation power of vertical shaft type gravity energy storage lower bin in winter

Abstract

The invention discloses a vertical shaft type gravity energy storage lower bin winter cave wall temperature and heat compensation power calculation method, which comprises a concept model and a mathematical model, and the mathematical model comprises a cave wall one-dimensional heat conduction definite solution problem and a heat conduction definite solution problem in a weight block body. Convection heat exchange of the surface of the lower bin wall, the surface of a weight and air in the lower bin causes air temperature change in the lower bin, a change curve of the temperature of the surface of the lower bin wall along with time is obtained through the method, when the temperature of the surface of the lower bin wall is reduced to 0 DEG C or below, it is considered that freezing risks exist, and heat compensation is needed; the heat compensation power is calculated according to the average power of the total power before the surface temperature of the tunnel wall is reduced to 0 DEG C or below. According to the method, the change rule of the tunnel wall concrete lining temperature and the heat compensation power along with time is analyzed, technical support is provided for heat compensation or heat preservation design, construction of a gravity energy storage system in a cold region is facilitated, and the structural strength and durability of a lower bin of the gravity energy storage system are guaranteed.

Description

Technical Field

[0001] The invention belongs to the technical field of gravity energy storage, and in particular relates to a method for calculating the winter cave wall temperature and heating power of a lower warehouse of a vertical shaft type gravity energy storage. Background Art

[0002] As the proportion of new energy continues to increase and the electricity trading market gradually improves, various energy storage technologies have ushered in huge development opportunities. The gravity energy storage technology based on the shaft is a large-scale, long-term physical energy storage power generation technology that can achieve peak shaving and valley filling of electric energy. Its technical principles are as follows: Figure 1 As shown. During the off-peak electricity price stage, the power station uses electric energy to drive the motor to lift the heavy objects in the lower warehouse to the upper warehouse through the shaft in sequence, and the electric energy is converted into potential energy stored in the heavy objects in the upper warehouse, realizing the energy storage process; during the peak electricity consumption period, the heavy objects in the upper warehouse on the surface are lowered to the lower warehouse through the shaft in sequence. During the lowering process, the potential energy of the heavy objects is converted into rotational kinetic energy, driving the generator to generate electricity, realizing the energy release process.

[0003] In gravity energy storage projects, the lower warehouse generally adopts a crisscross tunnel scheme. The rail transit tunnel is connected to the vertical shaft, and the vertical shaft realizes the vertical path of gravity energy storage. The volume of the lower warehouse is generally thousands to tens of thousands of cubic meters. The heavy objects are concrete blocks or cast iron blocks. The single heavy object is several tons to tens of tons, and the total number is hundreds.

[0004] The gravity energy storage shaft is deep and the surrounding rock temperature is high. Generally, the temperature of the surrounding rock of the cave wall is higher than the air temperature of the lower chamber. There is a convection heat exchange process between the surrounding rock of the cave wall and the air, and a heat conduction process from the surrounding rock to the cave wall occurs in the surrounding rock of the cave wall. It is generally necessary to adopt necessary heat removal measures in the chamber to ensure that the air temperature reaches the required temperature.

[0005] Since the upper warehouse contains a large number of heavy objects and a large volume, it generally only has a maintenance structure, no insulation structure or heating measures. For cold areas, the air temperature in the upper warehouse is relatively low in winter. If the heavy objects are stored in the upper warehouse for a long time, the temperature will also drop significantly. During the energy release process of the energy storage power station, a large number of cold heavy objects enter the lower warehouse in a short period of time. Heat conduction and convection heat transfer processes also occur inside and on the surface of the heavy objects, which will cause the air temperature in the lower warehouse to drop rapidly. Under extreme temperature conditions in winter, the air temperature in the lower warehouse may drop below zero, and the surface of the cave wall lining will freeze. In the subsequent energy storage process, the heavy objects are lifted to the ground, the cave wall lining is heated by the surrounding rock, the temperature rises, and the freeze melts. Under this reciprocating cycle, the strength and durability of the concrete lining will be greatly affected.

[0006] Therefore, it is necessary to analyze the variation of the wall temperature of the lower warehouse in winter over time, calculate the winter heating power, and provide a basis for heating or insulation design. From an engineering perspective, the available insulation measures include: upper warehouse insulation, heavy object insulation, or lower warehouse wall insulation measures. Specific measures need to be determined through technical and economic comparative analysis, but analyzing the variation of the concrete lining temperature of the cave wall and the heating power over time is the most basic data and basis. The present invention proposes a method for calculating the variation of the wall temperature and heating power over time in the lower warehouse of a vertical shaft gravity energy storage in cold areas, and performs calculations and analyses on typical working conditions. Summary of the invention

[0007] The technical problem to be solved by the present invention is to provide a method for calculating the winter cave wall temperature and heating power of the lower warehouse of a vertical shaft gravity energy storage, solve the problem that the lower warehouse temperature in cold areas changes repeatedly in winter and thus affects the structural strength and durability, fill the gap in the prior art, and analyze the changes in the cave wall concrete lining temperature and heating power over time, providing a basis for heating or insulation design.

[0008] According to the technical scheme of the present invention, the present invention provides a method for calculating the winter wall temperature and supplementary heat power of the lower warehouse of a vertical shaft gravity energy storage, and the conceptual model used for the calculation includes the following assumptions: after the heavy object is retained and placed in the upper warehouse, the temperature inside the heavy object is evenly distributed, and the temperature of the heavy object is lower than the air temperature and the wall temperature of the lower warehouse; when releasing energy, the heavy object moves instantly between the upper warehouse and the lower warehouse and enters the warehouse completely, and the temperature remains unchanged before and after the movement; the wall of the lower warehouse includes surrounding rock and lining arranged on the surface of the wall, and the thermophysical parameters of the surrounding rock are consistent with the parameters of the lining; the heat conduction of the wall is one-dimensional heat conduction, and the boundary outside the influence range is a constant temperature boundary; the heat conduction in the heavy object block is one-dimensional heat conduction, and the influence depth is limited to the equivalent depth, and the equivalent depth boundary is adiabatic; the convective heat transfer coefficients of the lower warehouse wall surface and the heavy object surface in all directions are consistent; Based on the above conceptual model, the mathematical model used for calculation includes the following: The solution to the one-dimensional heat conduction problem of the cave wall is as follows: , In the formula, T c is the cave wall temperature; x It is the distance between a certain position of the cave wall and the surface of the cave wall; t For time; a c is the thermal diffusion coefficient of the cave wall; L cr is the distance between the outer constant temperature boundary of the assumed heat conduction of the cave wall and the cave wall surface; T cm is the surface temperature of the cave wall; T R0 is the initial temperature of the cave wall; f ( x) is the initial temperature distribution of surrounding rock; The heat conduction problem in the heavy block is solved as follows: , In the formula, T w is the temperature inside the weight; y is the distance between a certain point of the weight and the surface of the weight, in meters; t For time; a w is the thermal diffusion coefficient of the weight; L wr is the equivalent depth of heat conduction of heavy objects, calculated according to formula 9; , V w is the sum of the volumes of the weights, A w is the sum of the surface areas of all the weights; T wm is the surface temperature of the weight; T w0 is the initial temperature of the weight; g ( y ) is the initial temperature distribution inside the weight; The convection heat exchange between the lower chamber wall surface, the heavy object surface and the air in the lower chamber causes the air temperature in the lower chamber to change. The change of the lower chamber air temperature over time is expressed by the following formula 10: , In the formula, T a is the lower warehouse air temperature; c p is the isobaric specific heat of air; ρ a is the atmospheric pressure in the lower chamber; V k It is the remaining space volume after the lower warehouse is fully loaded; T a0 is the initial temperature of the air in the lower chamber; h c is the convective heat transfer coefficient; The total power of convective heat exchange between the lower chamber wall surface, the heavy object surface and the air in the lower chamber is calculated according to the following formula 11: , In the formula, w cwd ( t ) is the convective heat transfer power of the lower chamber wall surface, the heavy object surface and the air in the lower chamber; The curve of the change of the cave wall surface temperature over time is obtained by the above method. When the cave wall surface temperature drops below 0°C, it is considered that there is a risk of freezing and supplementary heat is needed. The supplementary heat power is the average power of the total convective heat transfer power before the cave wall surface temperature drops below 0°C, that is: , In the formula, w is the heating power; t ice It is the time when the surface temperature of the cave wall drops to 0℃.

[0009] Furthermore, the method of discretizing time is adopted in the calculation and solution. It is assumed that in each time step, the boundary conditions of heat conduction in the cave wall and the heavy object and the convection heat transfer with the air in the lower warehouse are all constant conditions, and the analytical solution is calculated under the constant boundary conditions. The calculation process for each time step includes: for the cave wall side, the convective heat transfer power between the lower chamber air and the cave wall surface is calculated, and the heat conduction power is obtained based on the temperature distribution inside the cave wall, and then the cave wall surface temperature is obtained based on the equality of the convective heat transfer power and the heat conduction power. T cm ; For the heavy object side, calculate the convection heat transfer power between the lower warehouse air and the heavy object surface, and calculate the heat conduction power based on the temperature distribution inside the heavy object, and then calculate the surface temperature of the heavy object based on the power equality T wm ; Then, T cm The temperature distribution inside the cave wall is calculated based on one-dimensional heat conduction as the boundary condition. T wm The temperature distribution inside the heavy object is calculated based on one-dimensional heat conduction as the boundary condition; then the air temperature in the lower chamber and the convective heat transfer power between the wall surface, the heavy object surface and the air in the lower chamber are calculated. w cwd .

[0010] Furthermore, for the solution of the one-dimensional heat conduction equation, the problem of heat conduction in the surrounding rock of the cave wall is decomposed into the following two problems: Steady-state nonhomogeneous problem: , The solution to this problem is: , In the formula, T cw The surrounding rock temperature of the lower chamber for the steady-state nonhomogeneous problem; Unsteady Homogeneous Problem: , The solution to this problem is: , In the formula,T cf The surrounding rock temperature of the lower chamber for the non-steady-state homogeneous problem; The solutions of the original solution formula 1 to formula 4 are: ; Substituting Formula 15 and Formula 20 into Formula 21 and rearranging them, we obtain: , In the formula, β m is the eigenvalue, , m is a natural number, m =1, 2, 3, ..., ∞; A similar method is used to obtain the solutions of equations 5 to 8 of the fixed-solution problem:

[0011] In the formula, β n is the eigenvalue, , n is a natural number, n =1, 2, 3, ..., ∞.

[0012] Compared with the prior art, the beneficial technical effects of the present invention are as follows: In view of the problems faced in constructing gravity energy storage systems in cold regions, the present invention proposes a method for calculating the winter cave wall temperature and heating power of the lower warehouse of a vertical shaft gravity energy storage, which fills the gap in the prior art and realizes the analysis of the temporal variation patterns of the cave wall concrete lining temperature and heating power, providing technical support for heating or insulation design, facilitating the construction of gravity energy storage systems in cold regions and ensuring the structural strength and durability of their lower warehouses. BRIEF DESCRIPTION OF THE DRAWINGS

[0013] Figure 1 It is a basic structural diagram of a vertical shaft gravity energy storage system.

[0014] Figure 2 It is a schematic diagram of the conceptual model for calculating the wall temperature and supplementary heating power of the lower warehouse in winter according to the present invention.

[0015] Figure 3 It is a calculation flow chart of each time step in the preferred embodiment of the present invention.

[0016] Figure 4 It is a curve diagram of the temperature changes of the cave wall surface, the weight surface and the air in the lower bin according to an embodiment of the present invention.

[0017] Figure 5 1 is a graph showing thermal power variation over time according to an embodiment of the present invention.

[0018] Figure 6 This is a curve diagram of the total thermal power of a warehouse changing with time according to an embodiment of the present invention. DETAILED DESCRIPTION

[0019] The present invention provides a method for calculating the winter cave wall temperature and heating power of the lower warehouse of a vertical shaft gravity energy storage, which solves the problem that the lower warehouse temperature in cold areas changes repeatedly in winter and thus affects the structural strength and durability, fills the gap in the prior art, and realizes the analysis of the temporal variation of the cave wall concrete lining temperature and heating power, thus providing a basis for heating or insulation design.

[0020] The basic structure of the vertical shaft gravity energy storage system described in the present invention is as follows: Figure 1 As shown, it includes an upper warehouse 1 located above the ground, a gravity turbine system 2 and a plant 3, and a lower warehouse 6 located below the ground. The upper warehouse 1 and the lower warehouse 6 are connected by a shaft 4. The gravity turbine system 2 realizes the lifting and movement of a heavy object 7 (usually a block) in the shaft 4 by, for example, a wire rope transmission, and the heavy object 7 can be moved and stored by the transmission system in the upper and lower warehouses; the lower warehouse 6 is surrounded by surrounding rock 5 (the part close to the internal space of the lower warehouse 6 is called the cave wall, and the surface has a concrete lining structure layer). This basic structure is a prior art, and this solution can also be applied to other similar gravity energy storage systems to analyze and solve the related problems of the lower warehouse temperature changing due to heat exchange with the heavy object.

[0021] The computational models used in this scheme include conceptual models and mathematical models.

[0022] The conceptual model includes the following contents.

[0023] Under normal operating conditions, one energy storage and one energy release process are generally completed within one day to achieve the so-called standard cycle. In the standard cycle, the heavy objects are stored in the upper warehouse for no more than one day. However, under extreme conditions of long-term power outages, the heavy objects will be stored in the upper warehouse for a long time. In winter, its temperature will gradually decrease, approaching the local winter temperature. It should be noted that even if the storage time in the upper warehouse is long, the temperature distribution inside the heavy objects is not uniform, and there are slight fluctuations with the changes in temperature within a day. In order to simplify the calculation, this calculation method assumes that the temperature of the heavy objects is uniformly distributed.

[0024] During the energy release process, the heavy objects enter the lower warehouse through the shaft in turn and are arranged neatly. The total energy release process generally takes several hours. The time for the heavy objects to pass through the shaft is about tens of seconds to several minutes, and their surface will have a slight temperature rise. In order to simplify the calculation, this calculation method assumes that the heavy objects enter the lower warehouse instantly at one time and maintain the temperature they had when they were in the upper warehouse on the ground. After the heavy objects enter the lower warehouse from the upper warehouse, the temperature of the heavy objects will gradually increase, and the air temperature of the lower warehouse and the temperature of the cave wall will gradually decrease.

[0025] In order to maintain the stability of the lower warehouse wall, a layer of concrete lining structure is generally built on the wall of the lower warehouse rough hole after excavation. In other words, the wall of the lower warehouse includes the surrounding rock and the lining set on the surface of the wall. However, considering that the thermal conductivity and isobaric specific heat of the concrete lining [2.94W / (m•K), 0.96kJ / (kg•K)] are close to those of the surrounding rock [2~5W / (m•K), 0.75~1.14kJ / (kg•K)], the concrete lining and the surrounding rock can be regarded as the same heat transfer medium, and the two have the same thermal physical parameters.

[0026] The temperature distribution of the surrounding rock before the lower warehouse is excavated can be considered to be uniform. After the lower warehouse is put into operation, the air temperature in the lower warehouse will fluctuate with the seasons, and the temperature distribution of the surrounding rock will also change. In summer, ventilation measures will be taken to maintain the required temperature. In winter, the entry and exit of cold and heavy objects will cause the air temperature and the surrounding rock temperature to drop. The change in the air temperature of the lower warehouse has a limited impact on the surrounding rock temperature. The heat conduction of the surrounding rock of the cave wall can be regarded as one-dimensional heat conduction, and the boundary outside the impact range is a constant temperature boundary.

[0027] This calculation method assumes that the air temperature in the lower bin is constant during the period when the heavy objects are detained in the upper bin, and the convection heat exchange of the cave wall and the heat conduction in the surrounding rock have corresponding changes in the surrounding rock temperature. And this surrounding rock temperature distribution is used as the initial condition for the subsequent calculation after the cold heavy objects enter the lower bin.

[0028] After the heavy object enters the lower bin, the temperature of the heavy object is lower than the air temperature in the lower bin, and convection heat transfer occurs on its surface and heat conduction occurs inside. In order to simplify the calculation, the heat conduction in the heavy object block is assumed to be one-dimensional heat conduction, the influence depth is limited to the equivalent depth, and the equivalent depth boundary is adiabatic; and the ratio of the volume of the heavy object block to its surface area is taken as its equivalent depth.

[0029] The surface of the lower chamber wall and the surface of the object weight exchange heat with the air in the lower chamber. The convective heat transfer coefficient varies depending on the surface orientation. Under the same wind speed, the convective heat transfer coefficient of the vertical surface is greater than that of the horizontal surface. However, in order to simplify the calculation, this calculation method assumes that the convective heat transfer coefficients of the surfaces in all directions are the same.

[0030] After the cold heavy objects enter the lower warehouse, the heavy objects absorb the heat of the air in the lower warehouse through heat conduction and convection heat exchange, and the air temperature will decrease; the surrounding rock supplements the air with heat through heat conduction and convection heat exchange, and the temperature of the cave wall decreases. Calculate the convection heat transfer power of the cave wall (positive) and the convection heat transfer power of the heavy object surface (negative), and add the two to get the total power of the lower warehouse. When the total power is positive, the air temperature in the lower warehouse rises, and when it is negative, the air temperature in the lower warehouse drops.

[0031] According to the above analysis, we can propose Figure 2 The conceptual model for calculating the lower warehouse wall temperature and heating power in winter is shown.

[0032] Based on the above conceptual model, the following assumptions are used in the calculation model of this scheme: 1) After the heavy objects are placed in the upper warehouse, the internal temperature is evenly distributed, and the temperature of the heavy objects is lower than the air temperature and the wall temperature of the lower warehouse; 2) When releasing energy, the heavy objects move instantly between the upper and lower bins and all enter the bins, and the temperature remains unchanged before and after the movement; 3) The surrounding rock thermal physical parameters are consistent with the lower warehouse lining parameters; 4) The heat conduction of the surrounding rock of the cave wall can be regarded as one-dimensional heat conduction, and the area outside the influence range is a constant temperature boundary; 5) The heat conduction in the heavy object is assumed to be one-dimensional, the influence depth is limited to the equivalent depth, and the equivalent depth boundary is adiabatic; 6) The convective heat transfer coefficients of the lower bin surface and the heavy object surface are consistent in all directions.

[0033] Based on the above conceptual model, the mathematical model of this scheme includes the following contents.

[0034] The solution to the one-dimensional heat conduction problem of the cave wall is as follows: , In the formula, T c is the wall temperature, which is a function of position and time, in K; x It is the distance from a certain position of the cave wall to the surface of the cave wall, in m; t is the time, in seconds; a c is the thermal diffusion coefficient of the cave wall, for example, the thermal diffusion coefficient of the surrounding rock, the unit is m 2 ⁄s; L cr is the distance between the outer constant temperature boundary of the assumed heat conduction of the cave wall and the cave wall surface, in meters; T cm is the surface temperature of the cave wall, which is a function that changes with time and is in K; T R0 is the initial temperature of the cave wall, in K; f ( x ) is the temperature distribution of the cave wall at the end of the heavy object retention.

[0035] The heat conduction problem in the heavy block is solved as follows: , In the formula, T wis the temperature inside the mass, a function of position and time, in K; y is the distance from a point inside the weight to the surface of the weight, in meters; t is the time, calculated from the end time of the short position, in seconds; a w is the thermal diffusion coefficient of the weight, in m 2 ⁄s; L wr is the equivalent depth of heat conduction of heavy objects, in meters, calculated according to formula 9; , V w is the sum of the volumes of the weights, in m 3 ; A w is the sum of the surface areas of all the weights, in m 2 ; T wm is the surface temperature of the weight, in K; T w0 is the initial temperature of the weight, in K; g ( y ) is the initial temperature distribution inside the weight.

[0036] The convection heat exchange between the lower bin wall surface (lining inner surface), the weight surface and the air in the lower bin causes the air temperature in the lower bin to change. The change of the lower bin air temperature over time is expressed by the following formula 10: , In the formula, T a is the lower bin air temperature. When the lower bin is full, this value changes with time. The unit is K. c p is the isobaric specific heat of air, in J ⁄ (kg⋅K); ρ a is the atmospheric pressure in the lower chamber, in Pa; V k The remaining space volume after the lower warehouse is fully loaded, in m 3 ; T a0 is the initial temperature of the air in the lower chamber; hc is the convective heat transfer coefficient.

[0037] The total power of convective heat exchange between the lower chamber wall surface, the heavy object surface and the air in the lower chamber is calculated according to the following formula 11: , In the formula, w cwd ( t ) is the convective heat transfer power of the lower chamber wall surface, the heavy object surface and the air in the lower chamber, and the unit is W.

[0038] The above method is used to obtain the curve of the change of the cave wall surface temperature over time. When the cave wall surface temperature drops below 0°C, it is considered that there is a risk of freezing and supplementary heat is needed. The supplementary heat power is the average power of the total convective heat transfer power before the cave wall surface temperature drops below 0°C, that is: , In the formula, w is the heating power; t ice It is the time when the surface temperature of the cave wall drops to 0℃.

[0039] As for the solution method, whether it is the empty warehouse stage or the full warehouse stage, the initial conditions and boundary conditions of the solution problem are relatively complex, and it is very difficult to directly solve the above solution problems. In the calculation model, the convection heat exchange between the cave wall, the heavy object and the air is considered. The air temperature in the cave is not constant and changes with time. The surface temperature of the cave wall and the surface temperature of the heavy object also change with time. Therefore, due to the boundary conditions of the solution problem of formulas 1 to 8 T cm and T wm As it is a function that changes with time, it is difficult to directly solve the above fixed-point problem.

[0040] This embodiment adopts a method of discretizing time when solving the problem. It is assumed that in each time step, the boundary conditions of heat conduction inside the cave wall and the heavy object and the convective heat transfer between the cave wall and the air in the lower warehouse are all constant conditions, and the analytical solution can be calculated under the constant boundary conditions.

[0041] like Figure 3 As shown in the figure, the calculation process for each time step includes: for the cave wall side, the convection heat transfer power between the lower chamber air and the cave wall surface is calculated, and the heat conduction power is obtained based on the temperature distribution inside the cave wall, and then the cave wall surface temperature is obtained based on the power equality. T cm ; For the heavy object side, calculate the convection heat transfer power between the lower warehouse air and the heavy object surface, and obtain the heat conduction power based on the internal temperature distribution of the heavy object. Then, based on the equality of convection heat transfer power and heat conduction power, obtain the surface temperature of the heavy object. T wm ; Then, Tcm The temperature distribution inside the cave wall is calculated based on one-dimensional heat conduction as the boundary condition. T wm The temperature distribution inside the heavy object is calculated based on one-dimensional heat conduction as the boundary condition, and then the air temperature in the lower chamber and the convection heat transfer power between the wall surface, the heavy object surface and the air in the lower chamber are calculated. w cwd (After obtaining the air temperature and the temperature distribution of the surrounding rock of the cave wall, the total convective heat transfer power of the cave wall and heavy objects to the air can be calculated).

[0042] Furthermore, for the solution of the one-dimensional heat conduction equation, the problem of heat conduction in the surrounding rock of the cave wall can be decomposed into the following two problems: (1) Steady-state nonhomogeneous problem: , The solution to this problem is: , In the formula, T cw The surrounding rock temperature of the chamber for a steady-state non-homogeneous problem.

[0043] (2) Non-steady-state homogeneous problem: , The solution to this problem is: , In the formula, T cf The surrounding rock temperature of the chamber for the non-steady-state homogeneous problem.

[0044] The solutions of the original solution formula 1 to formula 4 are: .

[0045] Substituting Formula 15 and Formula 20 into Formula 21 and rearranging them, we obtain: , In the formula, β m is the eigenvalue, , m is a natural number, m =1, 2, 3, ..., ∞.

[0046] The solution to the fixed-point problem contains infinite series summation operations. In actual calculations, the cutoff value can be determined through trial calculations. For example, m can be taken as 30 in subsequent calculations.

[0047] A similar method can be used to obtain the solutions of equations 5 to 8 of the fixed-solution problem:

[0048] In the formula, β n is the eigenvalue, , n is a natural number, n =1, 2, 3, ..., ∞.

[0049] In order to facilitate a more intuitive understanding of this calculation method and its function, a specific example is given below.

[0050] The parameters required for calculating the wall temperature and heating power of the lower warehouse of the vertical gravity energy storage in cold regions in winter are divided into three parts: lower warehouse, heavy objects and air parameters, as shown in Tables 1 to 3. The heavy objects are made of iron, and the retention time of the heavy objects in the upper warehouse is 30 days, the length of time after entering the lower warehouse is 30 days, and the time step is 30 seconds.

[0051] Table 1 Lower warehouse parameters

[0052] Table 2 Heavy object parameters

[0053] Table 3 Air parameters

[0054] According to the above mathematical model and solution method, the temperature change curves of the cave wall surface, the heavy object surface and the air in the lower chamber at each time point after the heavy object is placed in the chamber can be obtained. Figure 4 As can be seen from the figure, the surface temperature of the cave wall and the air dropped rapidly in the early stage, and gradually slowed down after 0.2 days. The weight is made of iron, which has a large thermal conductivity and the surface temperature rises slowly. The temperature of the cave wall dropped below 0℃ at 1.3 days, and there was a risk of freezing.

[0055] The convection heat transfer between the surface temperature of the cave wall, the surface of the weight and the air temperature generates positive heat flow and negative heat flow respectively (see Figure 5 ). Since the surface temperature of the heavy object, the surface temperature of the cave wall and the air temperature are quite different at the beginning of the heavy object going down to the warehouse, the initial thermal power is relatively large. As the air temperature in the warehouse decreases, the thermal power decreases rapidly. Figure 5 It shows that in the initial period, due to the full loading of cold heavy objects, the temperature of the lower warehouse dropped sharply, and the power of the cave wall increased rapidly to about 6MW. Then, as the temperature of the cave surface decreased, the thermal power of the cave wall decreased. The thermal surface temperature of the heavy object was low at the beginning, and the absolute value of the thermal power was large. As the surface temperature decreased, the thermal power of the heavy object also decreased. However, in terms of overall size, the absolute value of the positive thermal power generated by the cave wall is basically the same as the negative thermal power generated by the heavy object. The absolute value of the negative thermal power is slightly larger than the positive thermal power of the cave wall, and the total power is negative ( Figure 6 ).

[0056] analyze Figure 6 The data show that the total heat power of convection heat transfer is relatively large before 0.2 days, especially in the first 6 minutes, when the total heat power reaches -1000kW. After 21 minutes, the total heat power drops below -50kW. After 1 day, it drops to about -2.7kW. Figure 4 It can be seen that at 1.3 days, the surface temperature of the cave wall dropped to 0°C. Therefore, if the cave wall temperature is to be kept above 0°C, supplementary heating measures need to be taken, and the supplementary heating power is determined by the average value of the average total thermal power within 1.3 days, that is, 46kW.

Claims

1. A method for calculating the wall temperature and heating power of the lower warehouse of a vertical shaft gravity energy storage in winter, characterized in that: The conceptual model used in the calculation includes the following assumptions: after the heavy objects are placed in the upper bin, the temperature inside the heavy objects is evenly distributed, and the temperature of the heavy objects is lower than the air temperature and the wall temperature of the lower bin; when releasing energy, the heavy objects move instantly between the upper bin and the lower bin, and all enter the bin, and the temperature remains unchanged before and after the movement; The wall of the lower warehouse includes surrounding rock and lining arranged on the surface of the wall. The thermophysical parameters of the surrounding rock are consistent with those of the lining. The heat conduction of the wall is one-dimensional, and the temperature outside the influence range is a constant temperature boundary. The heat conduction in the heavy object block is one-dimensional, and the influence depth is limited to the equivalent depth, and the equivalent depth boundary is adiabatic. The convection heat transfer coefficients of the lower warehouse wall surface and the heavy object surface are consistent in all directions. Based on the above conceptual model, the mathematical model used for calculation includes the following: The solution to the one-dimensional heat conduction problem of the cave wall is as follows: ， In the formula, T c is the cave wall temperature; x It is the distance between a certain position of the cave wall and the surface of the cave wall; t For time; a c is the thermal diffusion coefficient of the cave wall; L cr is the distance between the outer constant temperature boundary of the assumed heat conduction of the cave wall and the cave wall surface; T cm is the surface temperature of the cave wall; T R0 is the initial temperature of the cave wall; f ( x ) is the initial temperature distribution of surrounding rock; The heat conduction problem in the heavy block is solved as follows: ， In the formula, T w is the temperature inside the weight; y is the distance between a certain point of the weight and the surface of the weight, in meters; t For time; a w is the thermal diffusion coefficient of the weight; L wr is the equivalent depth of heat conduction of heavy objects, calculated according to formula 9; , V w is the sum of the volumes of the weights, A w is the sum of the surface areas of all the weights; T wm is the surface temperature of the weight; T w0 is the initial temperature of the weight; g ( y ) is the initial temperature distribution inside the weight; The convection heat exchange between the lower chamber wall surface, the heavy object surface and the air in the lower chamber causes the air temperature in the lower chamber to change. The change of the lower chamber air temperature over time is expressed by the following formula 10: ， In the formula, T a is the lower warehouse air temperature; c p is the isobaric specific heat of air; ρ a is the atmospheric pressure in the lower chamber; V k It is the remaining space volume after the lower warehouse is fully loaded; T a0 is the initial temperature of the air in the lower chamber; h c is the convective heat transfer coefficient; The total power of convective heat exchange between the lower chamber wall surface, the heavy object surface and the air in the lower chamber is calculated according to the following formula 11: ， In the formula, w cwd ( t ) is the convective heat transfer power of the lower chamber wall surface, the heavy object surface and the air in the lower chamber; The curve of the change of the cave wall surface temperature over time is obtained by the above method. When the cave wall surface temperature drops below 0°C, it is considered that there is a risk of freezing and supplementary heat is needed. The supplementary heat power is the average power of the total convective heat transfer power before the cave wall surface temperature drops below 0°C, that is: ， In the formula, w is the heating power; t ice It is the time when the surface temperature of the cave wall drops to 0℃.

2. The method for calculating the wall temperature and heating power of the lower warehouse of the vertical shaft gravity energy storage in winter according to claim 1 is characterized in that: The method of discretizing time is adopted in the calculation and solution. It is assumed that in each time step, the boundary conditions of heat conduction in the cave wall and the heavy object and the convection heat exchange with the air in the lower warehouse are all constant value conditions, and the analytical solution is calculated under the constant value boundary conditions. The calculation process for each time step includes: for the cave wall side, the convective heat transfer power between the lower chamber air and the cave wall surface is calculated, and the heat conduction power is obtained based on the temperature distribution inside the cave wall, and then the cave wall surface temperature is obtained based on the equality of the convective heat transfer power and the heat conduction power. T cm ; For the heavy object side, calculate the convection heat transfer power between the lower warehouse air and the heavy object surface, and calculate the heat conduction power based on the temperature distribution inside the heavy object, and then calculate the surface temperature of the heavy object based on the power equality T wm ; Then, T cm The temperature distribution inside the cave wall is calculated based on one-dimensional heat conduction as the boundary condition. T wm The temperature distribution inside the heavy object is calculated based on one-dimensional heat conduction as the boundary condition; then the air temperature in the lower chamber and the convective heat transfer power between the wall surface, the heavy object surface and the air in the lower chamber are calculated. w cwd .

3. The method for calculating the wall temperature and heating power of the lower warehouse of the vertical shaft gravity energy storage in winter according to claim 1 or 2, characterized in that: For the solution of the one-dimensional heat conduction equation, the problem of heat conduction in the surrounding rock of the cave wall is decomposed into the following two problems: Steady-state nonhomogeneous problem: ， The solution to this problem is: ， In the formula, T cw The surrounding rock temperature of the lower chamber for the steady-state nonhomogeneous problem; Unsteady Homogeneous Problem: ， The solution to this problem is: ， In the formula, T cf The surrounding rock temperature of the lower chamber for the non-steady-state homogeneous problem; The solutions of the original solution formula 1 to formula 4 are: ； Substituting Formula 15 and Formula 20 into Formula 21 and rearranging them, we obtain: ， In the formula, β m is the eigenvalue, , m is a natural number, m =1, 2, 3, ..., ∞; A similar method is used to obtain the solutions of equations 5 to 8 of the fixed-solution problem: In the formula, β n is the eigenvalue, , n is a natural number, n =1, 2, 3, ..., ∞.

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