Method and device for estimating cold loss of single-tank chilled water storage system and electronic equipment

Abstract

This invention relates to the field of water-based cold storage technology, specifically providing a method, apparatus, and electronic device for estimating the cooling loss of a single-tank water-based cold storage system. The method includes: acquiring initial index data including initial warm water temperature data of the warm water layer and initial cold water temperature data of the cold water layer; constructing a heat transfer differential equation; the heat transfer differential equation characterizing the correlation between the target temperature and the displacement and time changes of the inclined thermocentric layer; based on the initial index data, converting the heat transfer differential equation into an ordinary differential equation for solution, obtaining a relationship function between the target temperature and the displacement and time changes of the inclined thermocentric layer; based on the relationship function, determining the cooling loss function at time t caused by the transfer of warm water from the warm water layer to the cold water layer in the inclined thermocentric layer; and integrating the cooling loss function over the target time period to obtain the cooling loss within the target time period. The technical solution provided by this invention can improve the efficiency of cooling loss estimation.

Description

Technical Field

[0001] This invention relates to the field of water storage technology, and in particular to a method, apparatus and electronic device for estimating the cooling capacity loss of a single-tank water storage system. Background Technology

[0002] Water-based cooling technology involves producing chilled water at full capacity during off-peak electricity hours at night and storing it in a storage tank. During peak electricity hours in the daytime, air conditioning equipment is shut down or operates at reduced load, and the chilled water stored in the storage tank replaces the refrigeration units for cooling. In the operation of a single-tank water-based cooling system, cooling loss is a key factor affecting the system's cooling efficiency and operational economy.

[0003] In existing technologies, cold loss estimation employs numerical calculation methods. This involves decomposing the vertical interface of the cold storage tank into multiple nodal meshes, establishing micro-elements centered on these nodes, and using energy conservation methods to establish a large-scale linear equation system. Finally, software is used to solve the equation system, obtaining the time-varying behavior of each node within the cold storage tank, and then calculating the heat transferred from the warm water layer to the cold water layer. However, numerical simulation requires specialized fluid and heat transfer software, making cold loss estimation time-consuming and labor-intensive.

[0004] Therefore, the existing methods for estimating cooling loss have the technical problem of low estimation efficiency. Summary of the Invention

[0005] The present invention provides a method, apparatus, electronic device, storage medium, and computer program product for estimating the cooling capacity loss of a single-tank water storage cooling system, which improves the efficiency of cooling capacity loss estimation to a certain extent.

[0006] In a first aspect, the present invention provides a method for estimating the cooling capacity loss of a single-tank water-cooled storage system. The method is applied to a single-tank water-cooled storage system, which includes a warm water layer, a temperature gradient layer, and a cold water layer. The method includes:

[0007] Acquire initial index data at the start time; wherein, the initial index data includes the initial warm water temperature data of the warm water layer and the initial cold water temperature data of the cold water layer;

[0008] A heat transfer differential equation is constructed; this equation is used to characterize the correlation between the target temperature and the displacement and time changes of the thermocline.

[0009] Based on the initial index data, the heat transfer differential equation is converted into an ordinary differential equation for solution, and the relationship function between the target temperature and the displacement and time change of the thermocline is obtained.

[0010] Based on the aforementioned relationship function, the cold loss function of the inclined thermosphere at time t, which is the transfer of warm water from the warm water layer to the cold water layer, is determined.

[0011] The cooling loss function is integrated over the target time period to obtain the cooling loss during the target time period.

[0012] In one embodiment of the present invention, assuming the displacement of the inclined temperature layer is 0 at the initial moment, the heat transfer differential equation can be expressed as:

[0013]

[0014] Where a is the thermal diffusivity; T is the target temperature of the oblique temperature layer at displacement x at time t.

[0015] In one embodiment of the present invention, based on the initial index data, the heat transfer differential equation is converted into an ordinary differential equation for solution, yielding a relationship function between the target temperature and the displacement and time variation of the thermocline, including:

[0016] Construct x and t as composite variables ;

[0017] Based on the aforementioned composite variables, the heat transfer differential equation is transformed into an ordinary differential equation. ;

[0018] Solving the above ordinary differential equation yields the relational function: Where T1 and T2 are the initial warm water temperature data and the initial cold water temperature data, respectively. This is the Gaussian error function.

[0019] In one embodiment of the present invention, the heat transfer differential equation is transformed into an ordinary differential equation based on the composite variable. ,include:

[0020] Will Convert to the composite variable Taking the partial derivative, we get ;

[0021] Will Convert to the composite variable Taking the partial derivative, we get ;

[0022] Will Convert to the composite variable Taking the partial derivative, we get = ;

[0023] The heat transfer differential equation Transform into the composite variable Taking the partial derivatives, we obtain the ordinary differential equation. .

[0024] In one embodiment of the present invention, determining the cooling loss function of the temperature gradient layer at time t, from warm water in the warm water layer to cold water in the cold water layer, includes:

[0025] Based on the thermal conductivity k, initial warm water temperature T1, initial cold water temperature T2, and thermal diffusivity a, calculate the cooling loss at time t. ;in, This represents the cooling loss when the displacement of the thermocline is 0.

[0026] In one embodiment of the present invention, the cooling loss function is integrated over a target time period to obtain the cooling loss over the target time period, including:

[0027] Integrating the cooling loss function over the target time period yields the cooling loss over that time period. ;in, ;in, Indicates from the start time to The amount of cold loss at any given moment, where A is the contact area between the hot and cold fluids.

[0028] In one embodiment of the present invention, after the step of integrating the cooling loss function over a target time period to obtain the cooling loss over the target time period, the method further includes:

[0029] According to the aforementioned cooling loss density of liquids Specific heat capacity at constant pressure of liquids Calculate the cold storage efficiency using initial warm water temperature data T1 and initial cold water temperature data T2. ;in, .

[0030] Secondly, the present invention provides a device for estimating the cooling capacity loss of a single-tank water-cooled storage system. The device is applied to a single-tank water-cooled storage system, which includes a warm water layer, a temperature gradient layer, and a cold water layer. The device comprises:

[0031] The indicator acquisition module is used to acquire initial indicator data at the start time; wherein, the initial indicator data includes the initial warm water temperature data of the warm water layer and the initial cold water temperature data of the cold water layer;

[0032] The equation construction module is used to construct the heat transfer differential equation; the heat transfer differential equation is used to characterize the correlation between the target temperature and the displacement and time changes of the thermocline.

[0033] The equation solving module is used to convert the heat transfer differential equation into an ordinary differential equation based on the initial index data, and solve it to obtain the relationship function between the target temperature and the displacement and time change of the thermocline.

[0034] The function determination module is used to determine, based on the relationship function, the cooling loss function of the temperature layer at time t, which is the transfer of warm water from the warm water layer to the cold water layer.

[0035] The cooling loss estimation module is used to perform integral calculation on the cooling loss function within the target time period to obtain the cooling loss within the target time period.

[0036] Thirdly, the present invention provides an electronic device, including a memory and a processor, wherein the memory stores a computer program, and the processor executes the computer program to implement the method for estimating the cooling capacity loss of a single-tank water storage cooling system as described in any of the above claims.

[0037] Fourthly, the present invention provides a computer-readable storage medium having a computer program stored thereon, wherein the computer program, when executed by a processor, implements the method for estimating the cooling capacity loss of a single-tank water storage cooling system as described in any of the preceding claims.

[0038] Fifthly, the present invention provides a computer program product, including a computer program, which, when executed by a processor, causes the computer to perform the cooling capacity loss estimation method for a single-tank water storage cooling system as described in any of the preceding claims.

[0039] This invention provides a method for estimating the cooling loss of a single-tank water-cooled storage system. First, initial index data, including initial warm water temperature data for the warm water layer and initial cold water temperature data for the cold water layer, are obtained. Then, a heat transfer equation is constructed, and the heat transfer differential equation is solved based on the initial index data to obtain the relationship function between the target temperature and the displacement and time change of the inclined temperature layer. Based on this relationship function, the cooling loss function at time t, representing the transfer of warm water from the warm water layer to the cold water layer, is determined. Finally, the cooling loss function is integrated over the target time period to obtain the cooling loss within that period. This simplifies the heat transfer process of the cooling storage tank from three-dimensional unsteady-state heat transfer to one-dimensional unsteady-state heat transfer, thereby improving the efficiency of cooling loss estimation to a certain extent. Attached Figure Description

[0040] To more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the accompanying drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are merely some embodiments of the present invention, and those skilled in the art can obtain other embodiments based on these drawings without creative effort.

[0041] Figure 1 This is a schematic diagram of the operating status of a single-tank water storage cooling system according to an embodiment of the present invention.

[0042] Figure 2 This is a flowchart illustrating a method for estimating the cooling capacity loss of a single-tank water storage cooling system according to an embodiment of the present invention.

[0043] Figure 3 This is a schematic diagram of the structure of a cooling capacity loss estimation device for a single-tank water storage cooling system provided in an embodiment of the present invention.

[0044] Figure 4 This is a schematic diagram of an electronic device provided according to an embodiment of the present invention. Detailed Implementation

[0045] Embodiments of the present invention will now be described in more detail with reference to the accompanying drawings. While some embodiments of the present invention are shown in the drawings, it should be understood that the present invention can be implemented in various forms and should not be construed as limited to the embodiments set forth herein. Rather, these embodiments are provided to provide a more thorough and complete understanding of the present invention. It should be understood that the drawings and embodiments of the present invention are for illustrative purposes only and are not intended to limit the scope of protection of the present invention.

[0046] The production, transmission, and consumption of electricity are instantaneous. Because electricity cannot be stored on a large scale at low cost, electricity production must closely follow demand to achieve real-time balance. People's electricity consumption habits generally exhibit a significant characteristic of "high during the day and low at night." To ensure electricity demand is met, the capacity of generator units must be determined based on meeting maximum electricity demand. However, maximum electricity demand often lasts only a short period, resulting in low utilization rates and waste of generator units. Therefore, reducing maximum electricity load is crucial for improving equipment utilization and enhancing the economics of power plants. Air conditioning and refrigeration equipment constitute a significant electricity load in summer, accounting for up to 40% of the total summer electricity load. Utilizing cold storage technology to reduce the peak-hour electricity load of air conditioning and refrigeration equipment is of great importance.

[0047] Water-based cooling technology involves producing chilled water at full capacity during off-peak hours at night and storing it in storage tanks. During peak hours in the daytime, air conditioning equipment is shut down or operates at reduced load, using the stored chilled water to replace the refrigeration units for cooling. This technology effectively shifts peak-hour load to off-peak hours, achieving a "peak shaving and valley filling" effect on the power grid. Cooling technology is significant for promoting photovoltaic power consumption, driving the construction of new power systems, and achieving "dual-carbon" goals. To facilitate peak shaving and valley filling, the government implements a time-of-use pricing policy, setting higher prices during peak hours and lower prices during off-peak hours, which provides economic feasibility for promoting water-based cooling projects.

[0048] Natural stratification single-tank water storage cooling technology is a currently popular water storage cooling technology. Figure 1 As shown. During the cooling process of the cold storage tank, the cold water at the bottom of the tank can enter the building to cool it down, and then the warm water enters the top of the tank through pipes. In a specific embodiment, during the cold storage process, 7°C cold water from the refrigeration unit enters the bottom of the tank, pushing out the 12°C warm water, which then enters the refrigeration unit for cooling. When releasing the cooling capacity, the 7°C cold water flows from the bottom of the tank to the building's fan coil units, where it rises to 12°C after releasing the cooling capacity, and then flows back into the tank from the top. In short, the cold water (7°C) is always at the bottom of the tank, and the warm water (12°C) after releasing the cooling capacity is always at the top. Since the density of water decreases as the temperature increases, this design always creates a natural stratification phenomenon with cold water at the bottom and warm water at the top. There is a temperature difference heat transfer phenomenon at the interface between the cold and warm water, forming a gradually changing transition layer, namely the thermocline. There is a loss of cooling capacity in the thermocline, and the longer the cooling storage time, the greater the loss of cooling capacity.

[0049] In engineering design, the design capacity of the cold storage tank is determined based on the demand for cold storage and cooling capacity. However, accurate calculation of cold loss is crucial to ensure that the designed cold storage capacity meets actual needs. Currently, estimation and numerical simulation methods are mainly used to calculate cold loss under different conditions. Estimation methods rely on engineering experience to estimate cold loss, but suffer from significant drawbacks such as insufficient engineering experience, large estimation errors, and poor generalizability of the estimation results. Numerical simulation methods decompose the vertical interface of the cold storage tank into multiple node meshes, establish micro-elements centered on the nodes, establish a large-scale linear equation system using the energy conservation method, and finally solve the equation system using software to obtain the time-varying characteristics of each node within the cold storage tank. Then, the heat transferred from the warm water layer to the cold water layer is calculated. Numerical simulation methods offer higher accuracy, but require highly specialized modeling skills, and simulation calculations necessitate specialized fluid and heat transfer software, which is time-consuming and labor-intensive for general engineering designers.

[0050] Based on this, the present invention provides a method for estimating the cooling loss of a single-tank water storage system. First, initial index data, including initial warm water temperature data of the warm water layer and initial cold water temperature data of the cold water layer, are obtained. Then, a heat transfer equation is constructed, and the heat transfer differential equation is solved based on the initial index data to obtain the relationship function between the target temperature and the displacement and time change of the inclined temperature layer. Based on this relationship function, the cooling loss function at time t, where warm water from the warm water layer is transferred to cold water in the cold water layer, is determined. Finally, the cooling loss function is integrated over the target time period to obtain the cooling loss within that period. This simplifies the heat transfer process of the storage tank from three-dimensional unsteady-state heat transfer to one-dimensional unsteady-state heat transfer, thereby improving the efficiency of cooling loss estimation to a certain extent.

[0051] Please see Figure 2 This invention provides a method for estimating the cooling capacity loss of a single-tank water-cooled storage system. The method is applied to a single-tank water-cooled storage system, which includes a warm water layer, a thermocline layer, and a cold water layer. The method may include the following steps.

[0052] Step S110: Obtain initial index data at the start time; wherein, the initial index data includes the initial warm water temperature data of the warm water layer and the initial cold water temperature data of the cold water layer.

[0053] In this embodiment, a single-tank water-based cold storage system refers to a cold storage system that uses only one tank to store both cold and warm water. Its core feature is the utilization of the density difference between water and warm water (cold water is denser than warm water), which naturally creates a stratified structure within the tank, eliminating the need for additional separators. This is equivalent to a dual-tank cold storage system, where two tanks are used for cold and warm water storage respectively, potentially improving tank utilization.

[0054] In this embodiment, the warm water layer, located in the single-tank water storage system, is a water layer with a relatively high temperature, typically close to the ambient temperature or the air conditioning return water temperature. It is situated at the top of the tank, has a lower density, and is separated from the cold water layer by a thermotropic layer. This thermotropic layer is the heat source for cold energy transfer. The thermotropic layer is a transitional water layer between the warm and cold water layers. Its temperature gradually decreases from the warm water layer to the cold water layer, has no clear boundary, and its thickness dynamically changes with time and heat transfer intensity. It is the main area where cold energy loss occurs; that is, cold energy is conducted from the warm water layer to the cold water layer through the thermotropic layer. The cold water layer, located in the single-tank water storage system, has a relatively low temperature, typically 4-7°C, and meets the cooling requirements of the air conditioning system. It is situated at the bottom of the tank, has a higher density, and is the storage layer for cold energy. Cold energy loss will cause its temperature to rise and its cold energy storage effect to decrease.

[0055] In this embodiment, the starting time refers to the initial time point at which the cold loss estimation begins. It is usually the moment when the system completes cold storage and reaches a stable stratification state. At this time, the temperature and height of the warm water layer and the cold water layer are relatively stable, and the thickness of the thermocline layer is in its initial state.

[0056] In this embodiment, the initial index data are the basic parameters used to calculate the cooling loss at the beginning. The core is the temperature of the warm water layer and the cold water layer. These data directly determine the driving force of heat transfer and the basic conditions of the heat transfer zone, which are the premise for solving the subsequent equations.

[0057] Step S120: Construct a heat transfer differential equation; the heat transfer differential equation is used to characterize the correlation between the target temperature and the displacement and time changes of the thermocline.

[0058] In this embodiment, the heat transfer differential equation describes the temperature variation with space (clinospheric displacement) and time. The core of the equation is to characterize the dynamic correlation between the "target temperature", "clinospheric displacement", and "time", which is the core mathematical model for quantifying the cold conduction process.

[0059] Step S130: Based on the initial index data, the heat transfer differential equation is converted into an ordinary differential equation for solution to obtain the relationship function between the target temperature and the displacement and time change of the thermocline.

[0060] In this embodiment, the target temperature refers to the instantaneous temperature (unit: °C) at any location and at any time within the thermocline. It is a core parameter describing the heat transfer state of the thermocline, and its changes directly reflect the intensity and speed of cold conduction.

[0061] In this embodiment, the displacement of the thermocline refers to the offset of a certain characteristic point (such as the midpoint of temperature) within the thermocline relative to its position at the initial moment. It is used to characterize the dynamic movement state of the thermocline, such as moving towards the cold water layer or the warm water layer over time, reflecting the spatial variation law of heat transfer.

[0062] In this embodiment, the ordinary differential equation (ODE) contains only one independent variable. Compared to the heat transfer differential equation (which contains two independent variables, space x and time t), it is easier to solve and can directly yield a clear relationship between the target temperature and the thermocline displacement and time. The relationship function, obtained by solving the ODE, clearly defines the quantitative relationship between the target temperature (T) and the thermocline displacement (x) and time (t), which is the core basis for subsequent calculations of cooling loss.

[0063] In this embodiment, the initial index data is used as boundary conditions to transform the multi-variable heat transfer differential equation into an easily solvable ordinary differential equation. Then, the relationship function between the target temperature and the displacement and time of the thermocline is obtained through mathematical solution. This step realizes the transformation from an abstract heat transfer process to a specific mathematical expression, providing a directly usable basis for calculating cold loss.

[0064] Step S140: Based on the relationship function, determine the cold loss function of the temperature layer at time t, which is the cold water transferred from the warm water layer to the cold water layer.

[0065] In this embodiment, time t refers to any instantaneous point in the process of estimating cold loss. Where t ≥ 0, and t = 0 at the initial moment, is used to calculate the intensity of cold loss at that instant. The cold loss function is a mathematical function used to describe the intensity of cold conduction loss within the thermocline at time t, quantitatively characterizing the amount of cold conducted from the warm water layer to the cold water layer per unit time and per unit area.

[0066] In some embodiments, the cooling loss function is integrated over a target time period to obtain the cooling loss over the target time period.

[0067] In this embodiment, the target time period refers to the time interval in which the total cold loss needs to be estimated. It is usually from the start time t=0 to a certain end time t1, such as the storage period after the system stores cold, the cold release operation period, etc., which can be set according to the actual operation requirements.

[0068] In this embodiment, integrating the cooling loss function over the target time period accumulates the cooling loss intensity at each instant within the target time period, ultimately obtaining the total cooling loss over the target time period, thus quantifying the loss from instantaneous to total.

[0069] The above embodiment provides a method for estimating the cooling loss of a single-tank water-cooled storage system. First, initial index data, including initial warm water temperature data for the warm water layer and initial cold water temperature data for the cold water layer, are obtained. Then, a heat transfer equation is constructed, and the heat transfer differential equation is solved based on the initial index data to obtain the relationship function between the target temperature and the displacement and time change of the inclined temperature layer. Based on this relationship function, the cooling loss function at time t, representing the transfer of warm water from the warm water layer to the cold water layer, is determined. Finally, the cooling loss function is integrated over the target time period to obtain the cooling loss within that period. This simplifies the heat transfer process of the cooling storage tank from three-dimensional unsteady-state heat transfer to one-dimensional unsteady-state heat transfer, thereby improving the efficiency of cooling loss estimation to a certain extent.

[0070] Secondly, by constructing heat transfer differential equations and solving them in combination with initial index data, the dynamic changes of the thermocline, such as displacement and temperature changes over time, are fully considered. This captures the essential laws of cold energy conduction, significantly improves the accuracy of cold energy loss estimation, and provides a reliable basis for optimizing system operating parameters.

[0071] Furthermore, the complete steps from data acquisition to total loss calculation are clearly defined. Each step is clear and operable, requiring no complex experimental equipment. The calculation can be completed simply by collecting initial data using conventional sensors, making it suitable for practical application scenarios of single-tank water storage cooling systems in industries such as industry and construction.

[0072] In some embodiments, assuming the displacement of the inclined thermosphere is 0 at the initial moment, the heat transfer differential equation can be expressed as:

[0073]

[0074] Where a is the thermal diffusivity; T is the target temperature of the oblique temperature layer at displacement x at time t.

[0075] In this embodiment, the displacement of the thermocline is 0, which refers to the initial moment, i.e., t=0. The reference position of the thermocline is set as the displacement origin, i.e., x=0. The subsequent displacement of the thermocline is calculated relative to this origin. For example, if x is positive, it means moving towards the cold water layer, and if x is negative, it means moving towards the warm water layer. This setting is to simplify the equation solution and unify the spatial coordinate reference.

[0076] In this embodiment, the heat transfer differential equation is a one-dimensional unsteady-state heat conduction differential equation, which is the core mathematical model describing the conduction of cold energy within the thermocline. This indicates that the target temperature is a bivariate function of displacement x and time t, meaning that the target temperature is affected by both spatial location and time. Let T be the partial derivative of the target temperature T with respect to time t. It represents the rate of change of the target temperature with time at time t and displacement x, reflecting the time dynamic characteristics of cold conduction. The partial derivative represents the rate of temperature change when only time variation is considered and the displacement is fixed. Let T be the second partial derivative of the target temperature T with respect to displacement x. It represents the second rate of change of the target temperature with respect to spatial displacement at time t and displacement x (unit: ℃ / m²), reflecting the gradient change of temperature distribution within the thermocline. The larger the second partial derivative, the more drastic the temperature change within the thermocline and the higher the heat transfer intensity.

[0077] In this embodiment, thermal diffusivity (unit: m² / s) is an inherent thermophysical parameter of water, characterizing its ability to transfer heat. The higher the thermal diffusivity, the faster the heat transfer rate of water. Where k is the thermal conductivity, W / (m·℃); ρ is the density of the fluid, kg / m³. 3Cp is the specific heat at isobaric pressure of the fluid, in kJ / (kg·℃). Specifically, the thermal conductivity of water is k = 0.598 W / (m·℃), the density of water is 998.2 kg / m³, the specific heat at isobaric pressure of water is Cp = 4.18 kJ / (kg·℃), and the calculated thermal diffusivity is a = 1.43 × 10⁻ 7 m² / s.

[0078] In this embodiment, in the single-tank water storage cooling system, the cooling capacity is mainly conducted along the vertical direction (warm water layer → inclined thermocentric layer → cold water layer), while the horizontal temperature difference is minimal and negligible. Therefore, the heat transfer within the inclined thermocentric layer can be simplified to one-dimensional unsteady-state heat transfer. Consequently, the classic one-dimensional unsteady-state heat conduction differential equation is used as the heat transfer model of this invention. Furthermore, by setting the displacement origin (x=0), the solution process for subsequent equations is simplified. In other words, by setting the displacement origin of the inclined thermocentric layer (x=0), the spatial coordinate reference is unified. Simultaneously, by employing the one-dimensional unsteady-state heat conduction equation and ignoring irrelevant horizontal heat transfer, the complexity of subsequent equation transformation and solution is significantly simplified, ensuring that subsequent steps can be solved using conventional mathematical methods.

[0079] In some embodiments, in step S130, the heat transfer differential equation is converted into an ordinary differential equation and solved according to the initial index data to obtain the relationship function between the target temperature and the displacement and time change of the thermocline, which may include the following steps.

[0080] Step S131: Construct x and t as a composite variable .

[0081] Step S132: Based on the composite variables, transform the heat transfer differential equation into an ordinary differential equation. .

[0082] Step S133: Solve the ordinary differential equation to obtain the relational function: Where T1 and T2 are the initial warm water temperature data and the initial cold water temperature data, respectively. This is the Gaussian error function.

[0083] In this embodiment, composite variables The two independent variables, displacement x and time t, can be combined into a single composite variable η. The core function of this variable is to transform the bivariate function T(x,t) into a univariate function T(η), thereby converting the heat transfer differential equation (a bivariate partial differential equation) into an ordinary differential equation, simplifying the solution process. This composite variable is obtained based on multiple numerical simulations.

[0084] In this embodiment, based on composite variables, the heat transfer differential equation is transformed into an ordinary differential equation and then into a composite variable equation. By taking the derivative, we can obtain the ordinary differential equation. .

[0085] In this embodiment, solving the ordinary differential equation can be done by letting ,but The ordinary differential equation can then be expressed as: .

[0086] Separate variables to obtain .

[0087] Integrating both sides, we get .

[0088] Right now, Then p= .in, It is a constant.

[0089] Then return to the generation .

[0090]

[0091]

[0092] Integrating both sides simultaneously, we get .

[0093] Then, substitute the initial index data to determine the integration constant. and . Condition (1) when At that time, that is , That is, the initial temperature data of the warm water layer. Substituting into the above formula, we get... .in, The conclusion of the Gaussian error integral is as follows: From this, we can deduce .

[0094] Condition (2) When t=0, i.e. hour, .when At that time, that is , That is, the initial temperature data of the warm water layer. Substituting into the above formula, we get... .

[0095] Based on the above conditions, the solution can be obtained. C= .thereby .

[0096] Then, the Gaussian error function is introduced. Gaussian error function It has the following properties: (1) erf(0) = 0, erf( =1. (2) [1-erf( )).

[0097] Based on this = = .

[0098] In this embodiment, by constructing composite variables, the complex bivariate partial differential equation is transformed into a simple univariate ordinary differential equation, avoiding the complex solution process of partial differential equations, reducing computational difficulty, and improving computational efficiency. The relational function can be obtained quickly, meeting the needs of rapid estimation in practical engineering. This relational function is obtained through rigorous mathematical derivation, based on the transformation of the heat transfer differential equation and the solution of the ordinary differential equation, rather than empirical fitting. It accurately reflects the variation of the target temperature within the thermocline with displacement and time, providing a reliable mathematical basis for the subsequent derivation of the cooling loss function and the estimation of cooling loss, further improving the accuracy of cooling loss estimation.

[0099] In some embodiments, in step S132, the heat transfer differential equation is transformed into an ordinary differential equation based on the composite variable. This may include the following steps.

[0100] Step S1321: ... Convert to the composite variable Taking the partial derivative, we get .

[0101] Step S1322: ... Convert to the composite variable Taking the partial derivative, we get .

[0102] Step S1323: ... Convert to the composite variable Taking the partial derivative, we get = .

[0103] Step S1324: Apply the heat transfer differential equation Transform into the composite variable Taking the partial derivatives, we obtain the ordinary differential equation. .

[0104] In this embodiment, the partial derivative is converted into the partial derivative of the target temperature T with respect to time t and displacement x. , , By using the composite variable η, it can be transformed into the total derivative of the target temperature T with respect to η. , The process involves using the chain rule to eliminate the direct influence of the independent variables t and x, thus transforming partial derivatives into total derivatives. This is the core and key to converting partial differential equations into ordinary differential equations. The total derivative of the target temperature T with respect to the composite variable η (i.e. , where represents the rate of change of T with respect to η. Let η be the partial derivative of the composite variable with respect to time t, obtained by... Taking the partial derivative, the calculation result is: Similarly, we can obtain = .

[0105] In this embodiment, through rigorous chain function differentiation and substitution simplification, each step of the derivation conforms to mathematical principles, avoiding derivation errors and ensuring the obtained ordinary differential equation. It can accurately correspond to the original heat transfer differential equation, thereby ensuring the accuracy of subsequent relational function solutions and providing reliable mathematical support for the estimation of cooling loss.

[0106] In some embodiments, in step S140, determining the cold loss function of the temperature layer at time t from the warm water in the warm water layer to the cold water in the cold water layer based on the relationship function may include the following steps.

[0107] Step S141: Calculate the cooling loss at time t based on the thermal conductivity k, initial warm water temperature data T1, initial cold water temperature data T2, and thermal diffusivity a. ;in, This represents the cooling loss when the displacement of the thermocline is 0.

[0108] In this embodiment, the cold loss q(0,t) refers to the cold loss conducted from the warm water layer to the cold water layer per unit time and per unit area at time t and when the displacement of the thermocline is 0. Its physical meaning is the instantaneous cold loss intensity at the reference position of the thermocline, which is the junction of the warm water layer and the thermocline and is the main channel for cold conduction. Its cold loss intensity can characterize the heat transfer intensity of the entire thermocline. This is a formula for calculating cold loss derived from Fourier's law of heat conduction. Fourier's law of heat conduction states that the amount of heat passing through a unit area per unit time is directly proportional to the temperature gradient, but in the opposite direction to the temperature gradient. This represents the first-order partial derivative of the target temperature with respect to displacement x at displacement x=0, reflecting the rate of temperature change with space at x=0.

[0109] In this embodiment, by combining Fourier's law of heat conduction and the relational function, the derived cold loss function can accurately characterize the intensity of cold loss at time t, clarifying the relationship between cold loss and... , The quantitative relationship between t and t is simple in form; only conventional parameters need to be substituted. , The calculation can be completed using k, a, and t, without the need for complex numerical simulations, making it suitable for the need to quickly calculate instantaneous cooling loss in practical engineering applications.

[0110] In some embodiments, step S150, integrating the cooling loss function over a target time period to obtain the cooling loss over the target time period, may include the following steps.

[0111] Step S150: Integrate the cooling loss function over the target time period to obtain the cooling loss over the target time period. ;in, ;in, Indicates from the start time to The amount of cold loss at any given moment, where A is the contact area between the hot and cold fluids.

[0112] In this embodiment, the integral operation refers to the integral operation on the cooling loss function q(0,t) during the target time period [0, Performing definite integral operations within the target time period essentially involves accumulating the cooling loss intensity q(0,t) at each instant within the target time period to obtain the total cooling loss within that period. The target time period refers to the time interval from the start time t=0 to the end time t1 (t1>0, unit: s), and the end time... It can be set according to actual operating needs, such as the duration of cold storage and the duration of cold release operation, which is the calculation range for the total cold loss.

[0113] In this embodiment, the total cooling loss ∆Q refers to the target time period [0, Within the system, the total cold loss conducted from the warm water layer through the thermocline to the cold water layer is the core parameter characterizing the total cold loss of the system. It directly affects the system's cold storage efficiency and operating economy. The larger ∆Q is, the greater the cold loss of the system and the lower the cold storage efficiency.

[0114] In this embodiment, by integrating the cooling loss function, all instantaneous cooling losses within the target time period are accurately accumulated, and the resulting total cooling loss ∆Q accurately reflects the total cooling loss of the system during that time period. The expression for the total cooling loss obtained after integration is concise, requiring only the substitution of conventional parameters such as A, k, T1, T2, a, and t1 to complete the calculation. It eliminates the need for complex numerical integration, thus meeting the practical needs of quickly calculating total cooling loss in engineering applications and improving the method's practicality and operability.

[0115] In addition, the total cooling loss ∆Q is a core indicator for evaluating the system's operating performance. This expression can clearly show the impact of parameters such as heat transfer area A, end time t1, and initial temperature difference T1-T2 on the total cooling loss. It provides a quantitative basis for optimizing the tank structure (adjusting the heat transfer area A), setting a reasonable storage time (adjusting t1), and optimizing the initial temperature parameters (adjusting T1-T2), which helps to reduce the total cooling loss and improve the system's economy.

[0116] In some embodiments, after step S150, the method for estimating the cooling capacity loss of a single-tank water storage cooling system may further include the following steps.

[0117] Step S160: Based on the aforementioned cooling loss density of liquids Specific heat capacity at constant pressure of liquids Calculate the cold storage efficiency using initial warm water temperature data T1 and initial cold water temperature data T2. ;in, .

[0118] In this embodiment, the cold storage efficiency is the core performance indicator of a single-tank water cold storage system, which represents the ratio of the actual cold storage capacity to the theoretical cold storage capacity. The higher the cold storage efficiency, the less cold energy loss the system loses and the better its operating performance.

[0119] In this embodiment, the cold storage efficiency φ is a core indicator that directly reflects the system's performance. This indicator can be used to quickly determine whether the system's cold loss is reasonable and whether its operating performance meets the standards. If φ is too low, it indicates that the cold loss is too large. Based on the cold loss pattern obtained above, relevant parameters can be adjusted, such as optimizing the initial temperature difference, adjusting the storage time, and optimizing the tank structure, to improve the cold storage efficiency.

[0120] In one specific embodiment, the cylindrical cold storage tank has an inner diameter of 6m and a height of 10m. Initially, the lower cold water temperature is 4℃ at a height of 5m, and the upper hot water temperature is 12℃ at a height of 5m. The cold and hot water are in contact at the middle of the tank, where only heat conduction occurs, not convection. The physical properties of the water are shown in the table below:

[0121] Parameter name symbol unit numerical values thermal diffusivity a m² / s <![CDATA[1.43 × 10⁻ 7 ]]> thermal conductivity k W / (m·℃) 0.598 density ρ kg / m³ 998.2 Isobaric specific heat capacity Cp kJ / (kg·℃) 4.18

[0122] After 4 hours of calculation, the cold storage tank experiences a loss of cooling capacity. The approximate algorithm provided in this application is as follows:

[0123] (1) Establish the differential equation and its boundary conditions;

[0124]

[0125]

[0126] (2) Solving the system of differential equations

[0127] When solving differential equations, similarity variables are introduced:

[0128]

[0129] Transforming the partial differential equation into an ordinary differential equation, assuming the temperature field is T(x,t) = f(θ), and substituting it into the equation, we get:

[0130]

[0131] Solution:

[0132]

[0133] Where erf(z) is the error function, defined as:

[0134]

[0135] (3) Calculate the heat transferred from high-temperature water to low-temperature water at a certain moment on the contact surface of the thermocline:

[0136]

[0137] (4) Calculate the cooling loss of the cold storage tank over a period of time:

[0138]

[0139]

[0140] =13.45kWh

[0141] The cold loss calculated using numerical simulation is 14.875 kWh, indicating that the approximate calculation method of the present invention has high accuracy.

[0142] Please see Figure 3 One embodiment of the present invention provides a device for estimating the cooling capacity loss of a single-tank water-cooled storage system. The device is applied to a single-tank water-cooled storage system, which includes a warm water layer, a thermocline layer, and a cold water layer. The device may include: an index acquisition module, an equation construction module, an equation solving module, a function determination module, and a cooling capacity loss estimation module.

[0143] The indicator acquisition module is used to acquire initial indicator data at the start time; wherein, the initial indicator data includes the initial warm water temperature data of the warm water layer and the initial cold water temperature data of the cold water layer.

[0144] The equation construction module is used to construct the heat transfer differential equation; the heat transfer differential equation is used to characterize the correlation between the target temperature and the displacement and time changes of the thermocline.

[0145] The equation solving module is used to convert the heat transfer differential equation into an ordinary differential equation based on the initial index data, and then solve it to obtain the relationship function between the target temperature and the displacement and time change of the thermocline.

[0146] The function determination module is used to determine, based on the relationship function, the cooling loss function of the temperature layer at time t, from the warm water in the warm water layer to the cold water in the cold water layer.

[0147] The cooling loss estimation module is used to perform integral calculation on the cooling loss function within the target time period to obtain the cooling loss within the target time period.

[0148] The specific functions and effects of the cooling capacity loss estimation device for a single-tank water storage cooling system can be explained by referring to other embodiments in this specification, and will not be repeated here. Each module in the cooling capacity loss estimation device for the single-tank water storage cooling system can be implemented entirely or partially through software, hardware, or a combination thereof. Each module can be embedded in or independent of the processor in a computer device in hardware form, or stored in the memory of a computer device in software form, so that the processor can call and execute the operations corresponding to each module.

[0149] Please see Figure 4 One embodiment of the present invention can provide an electronic device, the electronic device comprising:

[0150] A memory, and one or more processors communicatively connected to the memory;

[0151] The memory stores instructions that can be executed by the one or more processors, which, when executed by the one or more processors, enable the one or more processors to implement the cold energy loss estimation method for a single-tank water storage cooling system as described in any of the above embodiments.

[0152] One embodiment of the present invention also provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the method for estimating the cooling capacity loss of a single-tank water storage cooling system as described in any of the above embodiments.

[0153] This specification also provides a computer program product containing instructions that, when executed by a computer, cause the computer to perform the cooling capacity loss estimation method for a single-tank water storage cooling system described in any of the above embodiments.

[0154] It is understood that the specific examples in this document are only intended to help those skilled in the art better understand the embodiments described herein, and are not intended to limit the scope of the invention.

[0155] It is understood that in the various embodiments described in this specification, the sequence number of each process does not imply the order of execution. The execution order of each process should be determined by its function and internal logic, and should not constitute any limitation on the implementation process of the embodiments described in this specification.

[0156] It is understood that the various implementation methods described in this specification can be implemented individually or in combination, and the implementation methods in this specification are not limited in this respect.

[0157] Unless otherwise stated, all technical and scientific terms used in the embodiments of this specification have the same meaning as commonly understood by one of ordinary skill in the art. The terminology used in this specification is for the purpose of describing particular embodiments only and is not intended to limit the scope of this specification. The term "and / or" as used in this specification includes any and all combinations of one or more of the associated listed items. The singular forms "a," "the," and "the" as used in the embodiments of this specification and the appended claims are also intended to include the plural forms unless the context clearly indicates otherwise.

[0158] It is understood that the processor in this invention can be an integrated circuit chip with signal processing capabilities. In implementation, each step of the above method implementation can be completed by the integrated logic circuitry in the processor's hardware or by instructions in software form. The processor can be a general-purpose processor, a digital signal processor (DSP), an application-specific integrated circuit (ASIC), a field-programmable gate array (FPGA), or other programmable logic devices, discrete gate or transistor logic devices, or discrete hardware components. It can implement or execute the methods, steps, and logic block diagrams disclosed in the embodiments of this specification. The general-purpose processor can be a microprocessor or any conventional processor. The steps of the methods disclosed in the embodiments of this specification can be directly embodied in the execution of a hardware decoding processor, or executed by a combination of hardware and software modules in the decoding processor. The software modules can reside in random access memory, flash memory, read-only memory, programmable read-only memory, electrically erasable programmable memory, registers, or other mature storage media in the art. This storage medium is located in memory; the processor reads information from the memory and, in conjunction with its hardware, completes the steps of the above method.

[0159] It is understood that the memory in this invention can be volatile memory or non-volatile memory, or may include both. Specifically, the non-volatile memory can be read-only memory (ROM), programmable read-only memory (PROM), erasable programmable read-only memory (EPROM), electrically erasable programmable read-only memory (EEPROM), or flash memory. The volatile memory can be random access memory (RAM). It should be noted that the memory in the systems and methods described herein is intended to include, but is not limited to, these and any other suitable types of memory.

[0160] The user information (including but not limited to user device information, user personal information, etc.) and data (including but not limited to data used for analysis, data stored, data displayed, etc.) involved in the embodiments of the present invention are all information and data authorized by the user or fully authorized by all parties. Furthermore, the collection, use and processing of the relevant data must comply with the relevant laws, regulations and standards of the relevant countries and regions, and corresponding operation entry points are provided for users to choose to authorize or refuse.

[0161] Those skilled in the art will recognize that the units and algorithm steps of the various examples described in conjunction with the embodiments disclosed herein can be implemented in electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementation should not be considered beyond the scope of this specification.

[0162] Those skilled in the art will clearly understand that, for the sake of convenience and brevity, the specific working processes of the systems, devices, and units described above can be referred to the corresponding processes in the aforementioned method implementations, and will not be repeated here.

[0163] In the several embodiments provided in this specification, it should be understood that the disclosed systems, apparatuses, and methods can be implemented in other ways. For example, the apparatus embodiments described above are merely illustrative; for instance, the division of units is only a logical functional division, and in actual implementation, there may be other division methods. For example, multiple units or components may be combined or integrated into another system, or some features may be ignored or not executed. Furthermore, the coupling or direct coupling or communication connection shown or discussed may be through some interfaces; the indirect coupling or communication connection between devices or units may be electrical, mechanical, or other forms.

[0164] The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the units can be selected to achieve the purpose of this embodiment, depending on actual needs.

[0165] In addition, the functional units in the various embodiments of the present invention can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit.

[0166] If the aforementioned functions are implemented as software functional units and sold or used as independent products, they can be stored in a computer-readable storage medium. Based on this understanding, the technical solutions of this specification, in essence, or the parts that contribute to the prior art, or parts of the technical solutions, can be embodied in the form of software products. These computer software products are stored in a storage medium and include several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of this specification. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0167] The above description is merely a specific embodiment of this specification, but the scope of protection of this invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in this specification should be included within the scope of protection of this specification. Therefore, the scope of protection of this invention should be determined by the scope of the claims.

Claims

1. A method for estimating the cooling capacity loss of a single-tank water storage cooling system, characterized in that, The method is applied to a single-tank water-cooled storage system, which includes a warm water layer, a temperature gradient layer, and a cold water layer. The method includes: Acquire initial index data at the start time; wherein, the initial index data includes the initial warm water temperature data of the warm water layer and the initial cold water temperature data of the cold water layer; A heat transfer differential equation is constructed; this equation is used to characterize the correlation between the target temperature and the displacement and time changes of the thermocline. Based on the initial index data, the heat transfer differential equation is converted into an ordinary differential equation for solution, and the relationship function between the target temperature and the displacement and time change of the thermocline is obtained. Based on the aforementioned relationship function, the cold loss function of the inclined thermosphere at time t, which is the transfer of warm water from the warm water layer to the cold water layer, is determined. The cooling loss function is integrated over the target time period to obtain the cooling loss during the target time period.

2. The method according to claim 1, characterized in that, Assuming the displacement of the thermocline is zero at the initial moment, the heat transfer differential equation can be expressed as: Where a is the thermal diffusivity; T is the target temperature of the oblique temperature layer at displacement x at time t.

3. The method according to claim 2, characterized in that, Based on the initial index data, the heat transfer differential equation is transformed into an ordinary differential equation for solution, yielding a relationship function between the target temperature and the displacement and time variation of the thermocline, including: Construct x and t as composite variables ; Based on the aforementioned composite variables, the heat transfer differential equation is transformed into an ordinary differential equation. ; Solving the above ordinary differential equation yields the relational function: Where T1 and T2 are the initial warm water temperature data and the initial cold water temperature data, respectively. This is the Gaussian error function.

4. The method according to claim 3, characterized in that, Based on the aforementioned composite variables, the heat transfer differential equation is transformed into an ordinary differential equation. ,include: Will Convert to the composite variable Taking the partial derivative, we get ; Will Convert to the composite variable Taking the partial derivative, we get ; Will Convert to the composite variable Taking the partial derivative, we get = ; The heat transfer differential equation Transform into the composite variable Taking the partial derivatives, we obtain the ordinary differential equation. .

5. The method according to claim 3, characterized in that, Based on the aforementioned relationship function, the cold loss function of the temperature gradient layer at time t, which involves the transfer of warm water from the warm water layer to the cold water layer, is determined, including: Based on the thermal conductivity k, initial warm water temperature T1, initial cold water temperature T2, and thermal diffusivity a, calculate the cooling loss at time t. ;in, This represents the cooling loss when the displacement of the thermocline is 0.

6. The method according to claim 5, characterized in that, Integrating the cooling loss function over the target time period yields the cooling loss over that time period, including: Integrating the cooling loss function over the target time period yields the cooling loss over that time period. ;in, ;in, Indicates from the start time to The amount of cold loss at any given moment, where A is the contact area between the hot and cold fluids.

7. The method according to any one of claims 1 to 6, characterized in that, After the step of integrating the cooling loss function over the target time period to obtain the cooling loss over the target time period, the method further includes: According to the aforementioned cooling loss density of liquids Specific heat capacity at constant pressure of liquids Calculate the cold storage efficiency using initial warm water temperature data T1 and initial cold water temperature data T2. ;in, .

8. A device for estimating the cooling capacity loss of a single-tank water storage cooling system, characterized in that, The cooling capacity loss estimation device for a single-tank water-cooled storage system is applied to a single-tank water-cooled storage system, which includes a warm water layer, a temperature gradient layer, and a cold water layer. The cooling capacity loss estimation device for the single-tank water-cooled storage system includes: The indicator acquisition module is used to acquire initial indicator data at the start time; wherein, the initial indicator data includes the initial warm water temperature data of the warm water layer and the initial cold water temperature data of the cold water layer. The equation construction module is used to construct the heat transfer differential equation; the heat transfer differential equation is used to characterize the correlation between the target temperature and the displacement and time changes of the thermocline. The equation solving module is used to convert the heat transfer differential equation into an ordinary differential equation based on the initial index data, and solve it to obtain the relationship function between the target temperature and the displacement and time change of the thermocline. The function determination module is used to determine, based on the relationship function, the cooling loss function of the temperature layer at time t, which is the transfer of warm water from the warm water layer to the cold water layer. The cooling loss estimation module is used to perform integral calculation on the cooling loss function within the target time period to obtain the cooling loss within the target time period.

9. An electronic device, characterized in that, It includes a memory and a processor, the memory storing a computer program, and the processor executing the computer program to implement the method for estimating the cooling capacity loss of a single-tank water storage cooling system according to any one of claims 1 to 7.

10. A computer storage medium, characterized in that, It stores a computer program, which, when executed by a processor, implements the method for estimating the cooling capacity loss of a single-tank water storage cooling system as described in any one of claims 1 to 7.

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