A setting temperature control method for a water storage type electric water heater based on three-dimensional fluid heat transfer

Abstract

The application discloses a kind of based on three-dimensional fluid heat transfer water storage type electric water heater set temperature control method. Constructing electric water heater water temperature variation function;Three-dimensional fluid heat transfer model is constructed;List energy balance equation and obtain the temperature iteration formula of model;Establish continuity equation;To continuity equation traversal solution to obtain minimum set temperature.The application establishes heat conduction equation and mass exchange equation, and is discretized to solve, through for the up and down flow of water body, the heat transfer and heating effect of adjacent nodes between heating pipe simulate water temperature variation when bathing, real reduction water heater internal temperature variation, solve to obtain suitable set temperature, both guarantee user water temperature comfortable when bathing, save power.The application uses three-dimensional fluid heat transfer equation and combines inner container temperature field heat transfer model, efficiently and reliably predicts electric water heater set temperature, solve to obtain suitable set temperature, both can guarantee user water temperature comfortable when bathing, can save power.

Description

Technical Field

[0001] This invention belongs to the field of electric water heater technology, specifically relating to a method for setting the temperature of a storage-type electric water heater based on three-dimensional fluid heat transfer. Background Technology

[0002] Storage-type electric water heaters are widely used in homes due to their ease of installation and affordability, bringing great convenience to family bathing. However, if the set temperature is not appropriate, it can cause two problems:

[0003] 1) Setting the temperature too high will waste electricity, especially since electric water heaters are widely used and the amount of wasted electricity is difficult to estimate.

[0004] 2) If the temperature is set too low, it may cause discomfort to the user during the shower and may even affect the user's health.

[0005] Most storage-type electric water heaters on the market currently use manual adjustment or constant temperature control methods for temperature setting, which cannot effectively obtain a reasonable and effective set temperature to ensure user comfort while maximizing energy savings. Therefore, regarding the temperature setting issue of storage-type electric water heaters, it is necessary to find a suitable set temperature that allows users to enjoy sufficiently warm water while saving energy consumption. Summary of the Invention

[0006] The purpose of this invention is to address the shortcomings of existing technologies by providing a water heater set temperature control method based on three-dimensional fluid heat transfer. This invention offers a control scheme for the set temperature of electric water heaters, namely, calculating a set temperature that saves electricity while meeting the user's bathing temperature requirements when the water heater is continuously on.

[0007] To address the existing technical problems, the technical solution of the present invention is as follows:

[0008] In a first aspect, the present invention provides a method for controlling the set temperature of a storage-type electric water heater based on three-dimensional fluid heat transfer, comprising the following steps:

[0009] Step (1): Construct the water temperature change function of the electric water heater;

[0010] Step (2): Construct a three-dimensional fluid heat transfer model;

[0011] Step (3): List the energy balance equation and derive the temperature iteration formula for the model;

[0012] Step (4): Establish the continuity equation;

[0013] Step (5): Solve the continuity equation to obtain the minimum set temperature.

[0014] In a second aspect, the present invention provides an electronic device including a processor and a memory, the memory storing machine-executable instructions executable by the processor, the processor executing the machine-executable instructions to implement the method.

[0015] Thirdly, the present invention provides a machine-readable storage medium storing machine-executable instructions that, when invoked and executed by a processor, cause the processor to implement the method.

[0016] The present invention can achieve the following beneficial effects:

[0017] 1) High precision:

[0018] This invention takes into account the different temperatures of the upper and lower layers of an electric water heater, with the lower layer being colder and the upper layer being hotter. It establishes heat conduction equations and mass exchange equations, and solves them by discretization. By simulating the specific water temperature changes during showering through the vertical flow of water, the heat transfer between adjacent nodes, and the heating effect of the heating element, it realistically reproduces the temperature changes inside the water heater. The final calculated set temperature is appropriate, which can ensure a comfortable water temperature for users while saving electricity.

[0019] This invention makes reasonable use of a three-dimensional fluid heat transfer model and discretizes it into a mesh for simulation, instead of using average temperature to replace the actual temperature, which makes the model more accurate and more realistic.

[0020] 2) High efficiency:

[0021] This invention addresses the problem of immature water heater temperature control technology in the current electric water heater field. It uses a three-dimensional fluid heat transfer equation combined with an inner tank temperature field heat transfer model to efficiently and reliably predict the water heater's set temperature. The final calculated set temperature is appropriate, ensuring both comfortable water temperature for users during showers and energy savings.

[0022] This invention proposes a genetic-simulated annealing algorithm based on temperature difference constraints for determining the discretized mesh parameters of the inner tank of a water heater. This algorithm largely overcomes the problem of getting trapped in local optima, making the accuracy of the predicted set temperature higher and the space complexity lower. Attached Figure Description

[0023] Figure 1 This is a flowchart of the method of the present invention;

[0024] Figure 2 The flowchart shows the genetic-simulated annealing algorithm based on temperature difference constraints.

[0025] Figure 3This is a schematic diagram of a water heater structure;

[0026] Figure 4 This is a schematic diagram of a heat transfer model for a temperature field.

[0027] Figure 5 A schematic diagram illustrating the operation of a water heater and changes in water temperature.

[0028] Figure 6 This is a comparison chart of the fitness of the present invention with that of genetic algorithm, Monte Carlo algorithm, and annealing algorithm;

[0029] Figure 7 This is a graph showing the temperature changes of each layer of the water heater predicted by the present invention when taking a shower at room temperature in winter.

[0030] Figure 8 This is a graph showing the actual temperature changes of each layer of the water heater when taking a shower at room temperature in winter.

[0031] Figure 9 A graph showing the daily power consumption of a water heater under different set temperatures in winter.

[0032] Figure 10 This is a comparison chart showing the temperature prediction errors of a multi-node heat transfer model and an energy exchange-based aggregation model, as presented in this invention. Detailed Implementation

[0033] The following description, in conjunction with the accompanying drawings, further illustrates the water heater temperature control scheme based on three-dimensional fluid heat transfer provided by the present invention.

[0034] like Figure 1 A method for setting the temperature of a storage-type electric water heater based on three-dimensional fluid heat transfer includes the following steps:

[0035] Step (1): Construct the water temperature change function of the electric water heater:

[0036] Because water heaters require cold water to be filled before use, heating is necessary before water can be used. Assuming a storage-type electric water heater uses two heating elements (upper and lower) for heating, and considering the water temperature to be approximately uniformly distributed during the heating process... Figure 3 As shown. Let the average heat transfer coefficient of the water heater wall be K, the heat dissipation area of ​​the water heater surface be F, the density and specific heat of water be ρ and c respectively, the temperature of the water during the heating or cooling process be t, and the time variable be τ. The heat balance equation for the water during this heating process is established as follows:

[0037]

[0038] Substituting the initial condition t = t0, where t0 is the initial water temperature, equation (1) can be equivalently transformed into a function of water temperature heating change during the non-outflow period, resulting in:

[0039]

[0040] During the cooling process of the electric water heater, the temperature change equation is similar to that in equation (2). The water temperature cooling change function of the electric water heater is:

[0041] t = t f +[t0-t f ]exp(-KFτ / (VρC p (3)

[0042] Step (2): Construct a three-dimensional fluid heat transfer model;

[0043] Step (2.1): Calculate the flow rates γ of cold water entering and leaving the water storage tank:

[0044] Flow rate μ is the volume of water flowing out of the showerhead per unit time, also known as the amount of water used for showering per unit time. Assuming the water outflow and inflow of a storage-type electric water heater are the same at every moment, ensuring the storage tank is always full, then the flow rates of cold and hot water entering and leaving the storage tank are both γ. Let the flow rate entering the cold and hot water mixing unit from the cold water pipe be β, the total inflow be α, and the total outflow be μ. Then they satisfy the following expression:

[0045]

[0046] Let T be the desired temperature for a person taking a bath. 人 The hot water temperature is T 热 (t), where the temperature of the cold water is T. 冷 The vertical component of the water flow is v. In a hot and cold water mixer, the desired body temperature obtained after mixing cold and hot water, within time t1, follows the following equation:

[0047] (β+γ)t1vρT 人 =βt1vρT 冷 +γt1vρT 热 (t) (5)

[0048] The expression for μ is obtained from equations (4) and (5):

[0049]

[0050] The expression for γ obtained from equation (6) is:

[0051]

[0052] Step (2.2): Establish a three-dimensional fluid heat transfer model:

[0053] Step (2.2.1) Construct the three-dimensional fluid heat transfer equation:

[0054] Assuming the water temperature in a storage-type electric water heater drops to (T0-t1) and then begins to heat, where T0 is the set temperature and t1 is the set value, natural convection occurs due to temperature stratification within the storage tank. Furthermore, during showering, cold water is continuously poured into the tank through the cold water inlet, while hot water flows out from the top outlet, resulting in forced convection from bottom to top. The temperature transfer within the storage-type electric water heater satisfies the three-dimensional fluid heat transfer equation, as shown below:

[0055]

[0056] Where ξ is the thermal diffusivity of the medium, F(x,y,z) is the heat generated by the heat source at point (x,y,z), ρ is the density of water, c is the specific heat capacity of water, and u,v,w are the x, y, and z velocities of water flowing through the particle, respectively.

[0057] Since the water flow direction is only the z-axis direction, i.e., u=0, v=0, in order to further simplify the model, the dimension is reduced to only consider the temperature changes in the x and z directions. Then, equation (8) is further simplified to:

[0058]

[0059] Step (2.2.2) Establish the working state equation of the water heater:

[0060] Assuming that the heat dissipation from the water heater wall is considered a cold source during showering, its effect is equivalent to that of the heater, i.e., F(x,y,z) is the difference between the heating power of the heater and the heat dissipation power of the wall. If the wall is completely insulated, then:

[0061]

[0062] When showering, the water temperature at the bottom of the water heater remains constant at the cold water temperature, which is the room temperature: T z＝0 =t f

[0063] Therefore, the three-dimensional fluid heat transfer model is obtained as follows:

[0064]

[0065] To more clearly describe the entire process of the water heater's operation, control terms a and b are constructed, where:

[0066]

[0067] The working state of the water heater can be represented by the following formula:

[0068]

[0069] in This represents the convective and conductive heat transfer of water during bathing. This indicates heating by a heater. This refers to the natural heat dissipation of the water heater wall.

[0070] Step (3): Construct the energy balance equation and derive the temperature iteration process of the model;

[0071] Dividing the inner tank of the water heater into M columns horizontally and N rows vertically, the entire inner tank can be considered as consisting of N*M nodes. The energy transformation of each node needs to be solved to obtain the temperature iteration process of each node. The temperature field heat transfer model is as follows: Figure 4 As shown.

[0072] Figure 5 This is a diagram illustrating the operation of a water heater and changes in water temperature.

[0073] Step (3.1) Calculate the energy change caused by water flow:

[0074] The water inlet and outlet pipes of the water heater are both installed at the bottom of the inner tank. However, the inlet pipe is shorter, with only a small portion extending out, while the outlet pipe is longer, extending to near the top of the inner tank. Therefore, during the water filling process, the water moves gradually from the bottom to the top of the inner tank, causing the water at each point to change from hot to cold.

[0075] Since cold water flows in from the bottom and hot water flows out from the top during use, the water inside the tank is constantly flowing vertically. Therefore, the energy changes caused by the water flow need to be considered.

[0076]

[0077] Where Δt is the time interval. This represents the energy change at node (i,j) over time Δt caused by the water flow, where i represents the change in the x-direction, j represents the change in the z-direction, c is the specific heat capacity of water, ρ is the density of water, and γ is the calculated inflow rate. Let (i+1,j) represent the temperature of node (i+1,j) at time τ. Let represent the temperature of the (i-1,j)th node at time τ.

[0078] Step (3.2) Calculate the heat transfer between adjacent nodes:

[0079] Because of the temperature difference between adjacent nodes, heat transfer occurs in real time. For node (i,j), the energy change caused by heat transfer between it and its neighboring nodes per unit time is shown below:

[0080]

[0081] in Let S be the energy change at node (i,j) due to heat transfer during time interval Δt, where n is the thermal conductivity of water, and S is the energy change at node (i,j). k1 S is the area of ​​contact between nodes in the vertical direction. k2 Let Δarr represent the horizontal contact area between nodes, Δcol represent the row spacing between nodes, and Δcol represent the column spacing between nodes. Calculate using the following formula:

[0082]

[0083] Header high The height of the inner tank of a storage water heater in the vertical direction. length The width of the inner tank of a storage water heater in the horizontal direction.

[0084] Step (3.3) Calculate the heating effect of the heating element:

[0085] The heating element affects the temperature of each node in the grid. A typical storage-type electric water heater has two heating elements: an upper heating element and a lower heating element. Verification has shown that dual-element heating can be considered uniform heating, meaning that the same amount of heat is distributed to each node in the grid. Treating the two heating elements as a single heat source with a boundary midpoint, the energy change caused by a heating element with a heating power of P is analyzed. It can be represented as:

[0086]

[0087] Step (3.4) Calculate the temperature iteration process:

[0088] The total energy change ΔE of node (i,j) before and after time Δt. i，j for:

[0089]

[0090] Combining steps (3.1)-(3.3), the sum of the energy changes of each node within time Δt equals the total energy change of the node. Therefore:

[0091]

[0092] The temperature iteration process of the nodes in the grid at each time step can be deduced from equation (19):

[0093]

[0094] in

[0095] Step (3.5) as follows Figure 2 As shown, the genetic-simulated annealing algorithm based on temperature difference constraints is used to solve for the number of two-dimensional network partitions M and N in the inner liner of the water storage tank.

[0096] Step (3.5.1) Establishing the objective function for temperature difference

[0097] Assuming z∈[0.8N,N] represents the top layer of the storage water heater and z∈[0,0.2N] represents the bottom layer, the top layer temperature is obtained by averaging the node temperatures calculated in step (3.4). and bottom temperature

[0098] Based on the top temperature and bottom temperature The objective function is constructed as follows:

[0099]

[0100] Dura represents the duration of a bath.

[0101] Step (3.5.2) generates the average number of vertical and horizontal grid divisions for the inner liner of the water storage tank.

[0102] Because storage water heaters come in various sizes, different numbers of two-dimensional grid divisions need to be designed for the inner tank of different sizes. Let Header... high The height (cm) of the inner tank of a storage water heater. length Let be the width (cm) of the inner tank of a storage water heater in the horizontal direction. Then, the average value of the number of vertical divisions of the two-dimensional grid in the inner tank is aver. N and the mean in the horizontal direction M They are respectively:

[0103]

[0104] Step (3.5.3) generates a normally distributed initial population.

[0105] Because the meshing of the inner liner needs to maintain a certain level of precision while minimizing computational complexity, the most effective vertical and horizontal meshing numbers are mostly distributed within the range of aver. N aver M The surrounding area follows a normal distribution, so the initial population can be obtained using normally distributed random numbers.

[0106] First, calculate the values ​​of Aver. N aver M With the central axis, The normal distribution probability density function of the standard deviation:

[0107]

[0108] Then, based on the principle of equal probability, generate a random number u between 0 and 1 for each pair of f(N) and f(M). N u M Then, the inverse transform method is used to calculate the inverse function values ​​F of f(N) and f(M). -1 (u N ) and F -1 (u M Each of them obtains a normally distributed random number, and repeats this process 20 times to ultimately generate their own set of normally distributed random numbers of size 20. and

[0109] set and After performing the Cartesian product, we can obtain the initial population that conforms to a normal distribution.

[0110]

[0111] Step (3.5.4) calculates the objective function of temperature difference for each solution in the population according to formula (21), and then obtains the optimal solution S of the current population. best .

[0112] Step (3.5.5) Iteratively obtains the number of two-dimensional network partitions of the inner tank of the water storage tank.

[0113] After selection, crossover, and mutation, a new population is generated. The determination is made to whether the current optimal solution satisfies the condition that the top-level temperature is less affected by the bottom-level temperature, i.e., the objective function f(S) > f(S). best S represents the solution of the new population; if it is, then update the current optimal solution S. best =S, and continue iterating to obtain a new optimal solution; otherwise, continue to check whether exp(|f(S)-f(S)) is satisfied. best If |) < random(0,1), then do not update and continue searching for the optimal solution; otherwise, update the optimal solution to S. best =S random S random This represents a random solution within the new population, i.e., the number of individuals divided into a two-dimensional network within a water tank.

[0114] If the number of iterations reaches the maximum in step (3.5.6), the iteration stops and the optimal solution is output. The optimal solution (N,M) value is then used in the model temperature iteration process. Otherwise, the process proceeds to step (3.5.3).

[0115] Step (4) Establish the continuity equation:

[0116] Because the lowest temperature at the top of the water heater needs to be higher than the lowest shower temperature T during showering. 温 Based on the three-dimensional heat transfer model (13) and the temperature iteration process (20), the objective function and constraints are as follows:

[0117]

[0118]

[0119] in, This indicates the water temperature change when the power is turned on. This indicates the water temperature changes due to natural heat dissipation. This indicates that the water temperature is changing when taking a shower, but the water temperature is not lower than the set temperature by 5°C. This indicates the change in water temperature when the water temperature is 5°C lower than the set temperature during a shower. T represents the constraint condition. 温 This refers to the minimum hot water temperature required for bathing in different seasons.

[0120] Step (5) Iterate through and solve for the minimum set temperature and power consumption:

[0121] 5-1 Initialize and randomly generate T0;

[0122] 5-2 Assuming that the minimum temperature of the top layer of the water heater at each moment during the shower is the same as the shower water temperature, calculate the temperature of the top layer of the water heater at each moment during the shower according to the objective function (25).

[0123] 5-3 Select the minimum value from the top layer temperatures at each of the above times, and determine whether the minimum value is higher than T. 温 If it is higher than T 温 Then update T0 = T0 - a, where a represents the temperature step size, the iteration count = count + 1, and return to step 5-2. Otherwise, check if the current iteration count is 1. If it is, update T0 = T0 + a, the iteration count = count + 1, and return to step 5-2. Otherwise, output the T0 of the previous iteration as the optimal set temperature T'.

[0124] 5-4 Substituting the optimal set temperature T' into the temperature iteration process (20), the heating time t of the electric water heater on that day is further obtained. 热 ; Relate the power P of the electric water heater to t 热 Multiply to get the power consumption.

[0125] Example

[0126] [1] Implementation conditions

[0127] Based on the present invention, summer and winter were selected as representative seasons. Using a certain brand of 60L and 100L water heaters as experimental conditions, three specifications were selected for the heating power of the two water heaters: 800W, 1200W, and 1500W. It was assumed that each user showered at 8 PM, and the indoor temperature was set to the lowest temperature of the day in summer (24℃) and in winter (4℃). The water temperature at the start of the shower was set to the set temperature minus 5℃. The average shower time was 15 minutes, with a time step of 0.1 seconds. (Summer T...) 温 The temperature is 37℃, and the winter temperature is T. 温 The initial temperature of the water heater is 20℃, the heat transfer coefficient K is 0.879, and the heat dissipation area F is 1.08m². The temperature is 45℃. 2 The thermal conductivity of water, α, is 0.59, and both the outflow and inflow rates are 0.00008 m³ / s. 3 / s, calculates the minimum set temperature and minimum power consumption under this setting and in the case of showering at any time in both summer and winter.

[0128] The following examples are based on a 60L, 1500W water heater and are implemented under winter room temperature conditions. Other specifications will not be discussed further.

[0129] [2] Implementation steps

[0130] Following step (1), we first consider the factors affecting water temperature changes and establish the heat balance equation for water in the non-outlet heating and cooling process. This is based on an initial water temperature of 20℃, an ambient temperature of 4℃, a heat transfer coefficient K of 0.879, and a heat dissipation area F of 1.08m². 2 Substituting the relevant setting parameters into the water temperature heating change function during the non-outflow period in step (1), we can obtain the actual water temperature change over time during water heater heating as follows:

[0131]

[0132] In the formula This is a function representing the change in cooling water temperature of the water heater.

[0133] According to step (2), when cold water is added to the electric water heater, the mixing process of the cold water is regarded as a process of uniform diffusion of the heat source. In order to keep the total amount of water in the electric water heater constant, the total inlet flow rate should be equal to the total outlet flow rate, that is, u = μ. Substituting the corresponding parameters, we can get u = 0.00008 and μ = 0.00008. Since T 热 T 冷 The flow rates of hot and cold water entering and exiting the storage tank are constantly changing, which allows us to solve for the expression of these flow rates. Next, due to the generation of natural convection and forced convection, a three-dimensional heat transfer model can be established. After substituting the inlet and outlet water flow rates into the three-dimensional heat transfer model, the working state equation of the water heater can be obtained:

[0134]

[0135] According to step (3) and its related expressions, the two-dimensional network structure of the inner tank of the water heater can be divided. By discretizing each node according to time, the energy balance equation for the up-and-down flow of water can be obtained as follows:

[0136]

[0137] The energy balance equation for heat transfer between nodes is:

[0138]

[0139] The energy balance equation for the heating effect of the heating tube is:

[0140]

[0141] The total energy change within the specified time step is:

[0142]

[0143] The energy exchange balance equation inside the water heater can be used to obtain:

[0144] ΔE ij =ΔE mij +ΔE cij +ΔE hij (32)

[0145] The above energy balance equations yield the temperature variation curves of the top, middle, and bottom layers within the two-dimensional mesh node division of the water tank liner, related to M and N. Then, the optimal values ​​of M and N are solved using a temperature-constrained genetic-simulated annealing algorithm. First, a random initial water temperature value T0' = 60℃ is obtained, and then aver can be calculated respectively. N =20, aver M =21, and randomly generate the initial population as {(5,9),(11,30),(19,20),(20,21),...} based on the inverse function value of the normal distribution.

[0146] Then, based on the energy balance equation and constraints... Selecting the current optimal solution S best = (N1, M1). In each subsequent iteration, a new generation of temperature node permutations is generated through selection, mutation, and crossover operations. If the optimal solution of the new temperature node permutation is better than the current optimal solution, the optimal solution is changed to the new value; otherwise, if exp(|f(S)-f(S)) is not found, the optimal solution is changed to the new value. bestIf |)≥random(0,1), the optimal solution is replaced with a random arrangement of temperature nodes; otherwise, proceed to the next iteration. After 30 iterations, the optimal solution for the temperature nodes in the x,y grid direction is calculated as (N,M)=(20,20). Substituting (N,M) into the energy balance equation yields the final model temperature iteration process:

[0147]

[0148] Based on the obtained model temperature iteration formula, the curves of the top layer temperature, middle layer temperature, and bottom layer temperature changing with time at a certain initial setting temperature can be calculated.

[0149] Following step (4), and combining the water temperature change function and temperature iteration formula obtained in the above steps, a continuity equation can be derived based on the three-dimensional heat transfer model and the water temperature change curve of the water heater:

[0150]

[0151]

[0152] Following step (5), the water outlet temperature change curve of the water heater during showering at a certain initial set temperature T0 can be obtained based on the first four terms of the continuity equation. Then, starting from a reasonably guessed estimated temperature of 55℃, the solution objective T0 of the continuity equation is searched in a set temperature step of ±0.1℃ until a value satisfying the fifth constraint condition of the continuity equation is found. The initial set temperature T0 (meaning the water temperature from the water heater remains above 45℃ during showering) finally reaches T0 = 61℃, which satisfies the constraint, indicating that the optimal set temperature is 61℃. Based on the water heater's heating power P = 1500W and the heating time of 3.2753 hours due to natural heat dissipation and cold water injection, the daily electricity consumption can be calculated to be 4.913 kWh.

[0153] [3] Measuring instruments and methods

[0154] For the actual measurement of the temperature of each layer of the water heater's inner tank, a patch-type PT1000 temperature sensor was used. Its temperature sensing range is [-50℃, 200℃], and it has high accuracy, making it suitable for measuring the temperature of each layer of the water heater.

[0155] Temperature measurement method: A layer of insulating foam is placed over the inner tank of the water heater. The foam is then peeled off, and a patch-type temperature probe is attached to the upper and lower layers of the inner tank wall. The peeled-off areas are then refilled with foam. Due to the good heat transfer properties of the inner tank wall, the real-time measured temperature of the inner tank wall can be considered the water temperature at the corresponding location within the inner tank. The patch-type PT1000 temperature sensor is connected to an Arduino device for data acquisition to record the temperature at various times.

[0156] For measuring power consumption, the B23111-400 model power meter is used, which has high measurement accuracy, low power consumption and is easy to configure.

[0157] Electricity measurement method: Connect the B23111-400 model electricity meter to the household circuit, turn off other appliances connected to the circuit in the test environment, wait for the water heater to finish working and then read the reading.

[0158] [4] Implementation Results

[0159] Figure 8 The graph shows the temperature change curves of each layer of the water tank in the water heater, measured by the above-mentioned patch-type PT1000 temperature sensor and temperature measurement method during a 15-minute shower at 8 pm when the indoor temperature is 22℃. Figure 7 The water temperature change curve predicted by the model temperature iteration formula provided in step (3) of this invention shows that, with the initial temperature set at 61°C, the actual temperature values ​​of each layer of the water heater from the start of the shower to the end of 15 minutes are basically consistent with the predicted values ​​of this invention. This is because this invention has discretized the inner tank of the water heater into a grid, which effectively divides the top, middle, and bottom layers. Therefore, when using the three-dimensional fluid heat transfer equation to predict the temperature, it can accurately calculate the temperature of each layer that changes over time, indicating that this invention has good accuracy and practical significance.

[0160] Figure 9 This study measured the water heater's power consumption within a day for a set temperature of [61℃, 69℃] using a B23111-400 model power meter at an indoor temperature of 22℃. The data included the natural heat dissipation of hot water during a day and the power consumption of a 15-minute shower at 8 PM. The data showed that power consumption increased with the set temperature, reaching its minimum at this temperature. Setting the temperature below 61℃ might result in hot water temperatures lower than desired, while setting it above 61℃ would lead to wasted electricity. This invention achieves near-consistent temperature prediction by considering the energy exchange effects of water flow and various heat transfer processes. It utilizes a three-dimensional fluid heat transfer equation to summarize these effects, thus highly simulating real-world conditions to multiple degrees.

[0161] Based on the above-mentioned conditions and implementation methods, experiments were repeatedly conducted on water heaters of different capacities and heating powers under simulated summer and winter conditions. Starting with the predicted temperature calculated by this invention, and using a step size of 0.1℃, the water temperature at the top of the water heater was measured in real time using a temperature sensor. The experiment searched for the true initial set temperature of the water heater that ensured the top temperature remained higher than the body's desired temperature for 15 minutes of showering. The power consumption was measured using an electric meter, resulting in the experimental data table shown in Table 1. Table 1 shows that under the test conditions of different seasonal temperatures and water heater capacity and power, the measured and calculated heating energy consumption values ​​showed good consistency, with a maximum relative error of no more than 2%. The actual optimal set temperature also showed good consistency with the calculated value, with a maximum relative error of no more than 1.6%.

[0162] Depend on Figure 6 As shown, compared with other algorithms such as Monte Carlo algorithms and traditional genetic algorithms, the method of this invention makes the model more stable, better able to separate the top and bottom temperatures, and has higher accuracy and effectiveness in solving the problem. Furthermore, the selection of the number of temperature nodes can reduce space complexity while maximizing model accuracy. This is because this invention utilizes the idea of ​​annealing, which allows for the acceptance of temperature node arrangements with poor fitness, enabling them to escape local optima during crossover and mutation. With sufficient iterations, it has a high probability of obtaining the global optimum, significantly separating the temperature layers of the water heater's inner tank.

[0163] Figure 10 The chart compares the actual temperature of the top layer of a 60L, 1500W water heater measured by a temperature sensor during a shower at a set temperature in winter with the percentage error calculated by the temperature iteration formula of this invention and two other heat transfer models at the same time. It shows that this invention outperforms the multi-node-based heat transfer model and the energy exchange-based aggregation model in terms of the percentage deviation between the predicted and actual top layer temperature of the water heater during showering, consistently maintaining an error range within 2%. This demonstrates the effectiveness of this invention. This is because this invention not only considers the energy exchange between various nodes within the water heater and derives the corresponding temperature iteration formula, but also considers the effects of natural convection and forced convection to establish a three-dimensional fluid heat transfer equation, enabling it to accurately predict and calculate the temperature change curves of each layer. This also demonstrates the considerable reliability of this invention.

[0164] Table 1 Comparison of measured and calculated values ​​of set temperature and heating energy consumption

[0165]

Claims

1. A method for controlling the set temperature of a storage-type electric water heater based on three-dimensional fluid heat transfer, characterized in that... Includes the following steps: Step (1): Construct the water temperature change function of the electric water heater; Step (2): Construct a three-dimensional fluid heat transfer model; Step (2.1): Calculate the flow rates γ of cold water entering and leaving the water storage tank; Step (2.2): Establish a three-dimensional fluid heat transfer model; Step (2.2.1) Construct the three-dimensional fluid heat transfer equation: Assuming the water temperature in a storage-type electric water heater drops to (T0-t1) and then begins to heat, where T0 is the set temperature and t1 is the set value, natural convection occurs due to temperature stratification within the storage tank. Furthermore, during showering, cold water is continuously poured into the tank through the cold water inlet, while hot water flows out from the top outlet, resulting in forced convection from bottom to top. The temperature transfer within the storage-type electric water heater satisfies the three-dimensional fluid heat transfer equation, as shown below: Where ξ is the thermal diffusivity of the medium, F(x,y,z) is the heat generated by the heat source at point (x,y,z), ρ is the density of water, c is the specific heat capacity of water, and u,v,w are the x, y, and z velocities of water flowing through the particle, respectively. Since the water flow direction is only the z-axis direction, i.e., u=0, v=0, in order to further simplify the model, the dimension is reduced to only consider the temperature changes in the x and z directions. Then, equation (8) is further simplified to: Step (2.2.2) Establish the working state equation of the water heater: Assuming that the heat dissipation from the water heater wall is considered a cold source during showering, and its effect is equivalent to that of the heater, i.e., F(x,y,z) is the difference between the heating power of the heater and the heat dissipation power of the wall; and if the wall is completely insulated, then: When showering, the water temperature at the bottom of the water heater remains constant at the cold water temperature, which is the room temperature: T z＝0 =t f Therefore, the three-dimensional fluid heat transfer model is obtained as follows: To more clearly describe the entire process of the water heater's operation, control terms a and b are constructed, where: The working state of the water heater can be represented by the following formula: in This represents the convective and conductive heat transfer of water during bathing. This indicates heating by a heater. This refers to the natural heat dissipation from the water heater wall; Step (3): Construct the energy balance equation and derive the temperature iteration process of the model; Divide the inner tank of the water heater into M columns horizontally and N rows vertically. The entire inner tank can be regarded as being composed of N*M nodes. It is necessary to solve the energy transformation of each node and finally obtain the temperature iteration process of each node. Step (4): Establish the continuity equation: Because the lowest temperature at the top of the water heater needs to be higher than the lowest shower temperature T during showering. 温 Based on the three-dimensional heat transfer model (13) and the temperature iteration process, the objective function and constraints are as follows: in, This indicates the water temperature change when the power is turned on. This indicates the water temperature changes due to natural heat dissipation. This indicates that the water temperature is changing when taking a shower, but the water temperature is not lower than the set temperature by 5°C. This indicates the change in water temperature when the water temperature is 5°C lower than the set temperature during a shower. T represents the constraint condition. 温 That is, the minimum hot water temperature required for bathing in different seasons; Step (5): Solve the continuity equation to obtain the minimum set temperature and power consumption: Step (5.1) Initialize and randomly generate T0; Step (5.2) assumes that the minimum temperature of the top layer of the water heater at each moment during the shower is the same as the shower water temperature. Calculate the temperature of the top layer of the water heater at each moment during the shower according to the objective function (25). Step (5.3) selects the minimum value from the top layer temperatures at each of the above times and determines whether the minimum value is higher than T. 温 If it is higher than T 温 Then update T0 = T0 - a, where a represents the temperature step size, the iteration count = count + 1, and return to step (5.2). Otherwise, check if the current iteration count is 1. If it is, update T0 = T0 + a, the iteration count = count + 1, and return to step (5.2). Otherwise, output the T0 of the previous iteration as the optimal set temperature T'. Step (5.4) substitutes the optimal set temperature T' into the temperature iteration process to further obtain the heating time t of the electric water heater on that day. 热 ; Relate the power P of the electric water heater to t 热 Multiply to get the power consumption.

2. The method according to claim 1, characterized in that... Step (1) specifically involves: Assuming a storage-type electric water heater uses two heating elements (upper and lower) for heating, and the water temperature is approximated as uniformly distributed during the heating process, let the average heat transfer coefficient of the water heater wall be K, the heat dissipation area of ​​the water heater surface be F, the density and specific heat of water be ρ and c respectively, the water temperature during the heating or cooling process be t, and the time variable be τ. The heat balance equation for this heating process is established as follows: Substituting the initial condition t = t0, where t0 is the initial water temperature, equation (1) can be equivalently transformed into a function of water temperature heating change during the non-outflow period, resulting in: During the cooling process of the electric water heater, the water temperature change function is as follows: t=t f +[t0-t f ]exp(-KFτ / (VρC p )) (3)。 3. The method according to claim 2, characterized in that... Step (2.1) specifically involves assuming that the water outflow and inflow of the storage-type electric water heater are the same at every moment, ensuring that the water tank is always full, then the flow rates of cold water entering and leaving the water tank are both γ. Let the flow rate entering the cold and hot water mixing unit from the cold water pipe be β, the total inflow be α, and the total outflow be μ, then the following expression is satisfied: Let T be the desired temperature for a person taking a bath. 人 The hot water temperature is T 热 (t), where the temperature of the cold water is T. 冷 The vertical component of the water flow velocity is v; in the hot and cold water mixer, the cold and hot water are mixed to obtain the desired temperature for the human body, and within time t1, it follows the following: (β+γ)t1vρT 人 =βt1vρT 冷 +γt1vρT 热 (t) (5) The expression for μ is obtained from equations (4) and (5): The expression for γ obtained from equation (6) is:

4. The method according to claim 3, characterized in that... Step (3) specifically involves: Step (3.1) Calculate the energy change caused by water flow: Since cold water flows in from the bottom and hot water flows out from the top during use, the water inside the tank is constantly flowing vertically. Therefore, the energy changes caused by the water flow need to be considered. Where Δt is the time interval. This represents the energy change at node (i,j) over time Δt caused by the water flow, where i represents the change in the x-direction, j represents the change in the z-direction, c is the specific heat capacity of water, ρ is the density of water, and γ is the calculated inflow rate. Let (i+1,j) represent the temperature of node (i+1,j) at time τ. Let represent the temperature of the (i-1,j)th node at time τ; Step (3.2) Calculate the heat transfer between adjacent nodes: Because of the temperature difference between adjacent nodes, heat transfer occurs in real time. For node (i,j), the energy change caused by heat transfer between it and its neighboring nodes per unit time is shown below: in Let Δt be the energy change at node (i,j) caused by heat transfer. S is the thermal conductivity of water. k1 S is the area of ​​contact between nodes in the vertical direction. k2 Δarr represents the area of ​​contact between nodes in the horizontal direction, Δcol represents the row spacing between nodes, and Δcol represents the column spacing between nodes. Calculate using the following formula: Header high The height of the inner tank of a storage water heater in the vertical direction. length The width of the inner tank of a storage water heater in the horizontal direction; Step (3.3) Calculate the heating effect of the heating element: The energy change caused by a heating element with heating power P It can be represented as: Step (3.4) Calculate the temperature iteration process: The total energy change ΔE of node (i,j) before and after time Δt. i，j for: Combining steps (3.1)-(3.3), the sum of the energy changes of each node within time Δt equals the total energy change of the node. Therefore: The temperature iteration process of the nodes in the grid at each time step can be deduced from equation (19): in Step (3.5) uses a genetic-simulated annealing algorithm based on temperature difference constraints to solve for the number of two-dimensional network partitions M and N in the inner tank of the water storage tank.

5. The method according to claim 4, characterized in that... Step (3.5) specifically involves: Step (3.5.1) Establishing the objective function for temperature difference Assuming z∈[0.8N,N] represents the top layer of the storage water heater and z∈[0,0.2N] represents the bottom layer, the top layer temperature is obtained by averaging the node temperatures calculated in step (3.4). and bottom temperature Based on the top temperature and bottom temperature The objective function is constructed as follows: Dura represents the duration of the bath; Step (3.5.2) generates the average number of vertical and horizontal grid divisions for the inner liner of the water storage tank. The mean value of the vertical number N of the two-dimensional grid in the inner liner. N The mean of the number of horizontal divisions M M They can be calculated as follows: Step (3.5.3) generates a normally distributed initial population. The best-performing vertical and horizontal divisions are mostly distributed in the aver. N aver M The surrounding area follows a normal distribution, so the initial population can be obtained using normally distributed random numbers. First, calculate the values ​​of Aver. N aver M With the central axis, The normal distribution probability density function of the standard deviation: Then, based on the principle of equal probability, generate a random number u between 0 and 1 for each pair of f(N) and f(M). N u M Then calculate the inverse function value F of f(N) and f(M). -1 (u N ) and F -1 (u M Each of them obtains a normally distributed random number, and repeats this process 20 times to ultimately generate their own set of normally distributed random numbers of size 20. and set and After performing the Cartesian product, we can obtain the initial population that conforms to a normal distribution. Step (3.5.4) calculates the objective function of temperature difference for each solution in the population according to formula (21), and then obtains the optimal solution S of the current population. best ; Step (3.5.5) Iteratively obtains the number of two-dimensional network partitions of the inner tank of the water storage tank. After selection, crossover, and mutation, a new population is generated. The determination is made to whether the current optimal solution satisfies the condition that the top-level temperature is less affected by the bottom-level temperature, i.e., the objective function f(S) > f(S). best S represents the solution of the new population; if it is, then update the current optimal solution S. best =S, and continue iterating to obtain a new optimal solution; otherwise, continue to check whether exp(|f(S)-f(S)) is satisfied. best If |) < random(0,1), then do not update and continue searching for the optimal solution; otherwise, ... The optimal solution is updated to S. best =S random S random This represents a random solution within the new population; If the number of iterations reaches the maximum in step (3.5.6), the iteration stops and the optimal solution is output. The optimal solution (N,M) value is then used in the model temperature iteration process. Otherwise, the process proceeds to step (3.5.3).

6. An electronic device, characterized in that, It includes a processor and a memory, the memory storing machine-executable instructions that can be executed by the processor, the processor executing the machine-executable instructions to implement the method of any one of claims 1-5.

7. A machine-readable storage medium, characterized in that, The machine-readable storage medium stores machine-executable instructions that, when invoked and executed by a processor, cause the processor to implement the method of any one of claims 1-5.

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