Prediction method for melting duration of ice blocks in circulating water tank of air purification vehicle

Abstract

The invention discloses a method for predicting the melting time of ice blocks in a circulating water tank of an air purification vehicle, and the method comprises the steps: building a three-dimensional Cartesian coordinate system at the center of the ice blocks, and enabling the distance between the center of the ice blocks and the wall surface in the x direction to be x; calculating the internal energy variation of the ice block in unit time; calculating the convective heat exchange amount between the ice block and the outside in unit time; according to energy conservation, the internal energy variable quantity of the ice blocks in unit time is equal to the convective heat exchange quantity of the ice blocks and the external environment, and a function relational expression of dx / dt and dT / dx is obtained; the temperature gradient dT / dx in the ice block is solved through a cubic heat balance integral method, and a temperature distribution formula in the x-axis positive direction of the ice block is calculated; the temperature distribution formula of the ice block in the positive direction of the x axis and x = X are substituted into a function relational expression of dx / dt and dT / dx, X is the thickness of the current ice block, special solutions x = 0 and t = 0 are substituted into the equation, and a relational expression between the melting duration and x is obtained. According to the method, the melting time of the rectangular ice blocks in the circulating water tank can be quickly predicted, and the operation parameters of the ice adding process of the crawler-type string grid air purification vehicle are perfected.

Description

Technical Field

[0001] The invention belongs to the technical field of heat damage control in plateau high ground temperature construction tunnels, and in particular relates to a method for predicting the melting time of ice in a circulating water tank of an air purification vehicle. Background Art

[0002] In western my country, the Qinghai-Tibet Plateau, Yunnan-Guizhou Plateau and other regions are rich in geothermal resources, with strong hydrothermal activities and a wide distribution of underground hot springs. In the process of tunnel construction, it is inevitable to encounter high temperature heat damage. The temperature of the tunnel body can reach 60°C, which makes the commonly used ventilation cooling, spray water cooling and ice cooling unable to meet the occupational safety needs. The use of mechanical refrigeration to cool long tunnels requires the laying of long-distance cables, and the power loss is as high as 1000V per 6km, which will cause huge energy loss. In this regard, a crawler-type string grid air purification vehicle is proposed for dust removal and cooling in construction tunnels. Its cold source comes from ice making outside the tunnel, which is then brought into the tunnel by construction personnel, which can greatly reduce energy loss. In tunnel construction, the working time of the template second lining trolley operation team is about 4 hours. The rhythm of transporting ice to the face should be in line with the construction cycle. When the template second lining trolley operation team changes shifts, ice cubes are brought into the tunnel to add ice cubes to the air purification vehicle. Therefore, in order to ensure the cooling effect of the air purification vehicle during construction, the melting time of the ice in its circulating water tank needs to be controlled. However, the construction environment of the tracked string-type air purification vehicle is changeable, there is a medium of water and iron shell between the ice and the external environment, and the thermal environment inside the circulating water tank is complex. As a result, it is impossible to determine the input power of the external environment to the ice, and the existing ice melting time calculation formula cannot be used.

[0003] In view of the problems existing in the prior art, a tracked string-grid air purification vehicle used for dust removal and cooling in construction tunnels is combined to solve the problems of large limitations of the existing ice melting time prediction method and unclear ice adding operation parameters of the tracked string-grid air purification vehicle, which has become a key research direction for technical personnel in this field. Summary of the invention

[0004] In order to solve the above problems, the present invention provides a method for predicting the melting time of ice cubes in the circulating water tank of an air purification vehicle, so as to quickly predict the melting time of rectangular ice cubes in the circulating water tank and improve the operating parameters of the ice adding process of the crawler type string grid air purification vehicle.

[0005] To achieve the above object, the present invention provides the following technical solutions.

[0006] A method for predicting the melting time of ice in a circulating water tank of an air purification vehicle comprises: establishing a three-dimensional Cartesian coordinate system at the center of the ice, wherein the distance from the center of the ice to the wall in the x direction is x; calculating the change in the internal energy of the ice per unit time; calculating the convective heat exchange between the ice and the outside world per unit time; according to the law of conservation of energy, the change in the internal energy of the ice per unit time is equal to the convective heat exchange between the ice and the outside environment, and obtaining a functional relationship between dx / dt and dT / dx, wherein dx / dt represents the change in the melting thickness of the ice in the positive direction x with time t, and dT / dx is the temperature gradient in the x direction inside the ice; solving the temperature gradient dT / dx inside the ice by a triple heat balance integration method, and the calculation formula is:

[0007] T(x,t)=A+Bx+Cx 3

[0008] Wherein A, B, and C are polynomial coefficients. Based on the assumption that the temperature penetration depth has reached the center of the rectangular ice block after the start of heat transfer, the values ​​of A, B, and C are obtained, thereby calculating the temperature distribution formula in the positive direction of the x-axis of the ice block; the temperature distribution formula in the positive direction of the x-axis of the ice block and x=X are substituted into the functional relationship between dx / dt and dT / dx, X is the current thickness of the ice block, and the special solution x=0, t=0 is substituted into the equation to obtain the relationship between the melting time and x.

[0009] Preferably, the ice cubes are rectangular ice cubes.

[0010] Preferably, the air purification vehicle is a tracked string-type air purification vehicle.

[0011] A method for predicting the melting time of ice in a circulating water tank of an air purification vehicle, wherein the ice is a rectangular ice with a length, width and height ratio of 2:2:1, and the calculation formula of the melting time is: Where: t is the melting time, s; ρ is the density of ice, kg / m 3 ; c is the specific heat capacity of ice, J / (kg·℃); T m is the melting temperature of ice, °C; T n The center temperature of the ice cube, ℃; L is the latent heat of phase change, J / kg; h is the convection heat transfer coefficient, W / (m 2 ·K); T ∞ is the incoming flow temperature of the environment where the ice cube is located, ℃; x is the distance from the center of the ice cube to the wall in the X direction, m.

[0012] Preferably, the initial temperature of the ice cube is taken as the center temperature Tn of the ice cube.

[0013] Preferably, the air purification vehicle is a tracked string-type air purification vehicle.

[0014] Compared with the prior art, the method for predicting the melting time of ice cubes in the circulating water tank of an air purification vehicle of the present invention simplifies the temperature gradient term in the mathematical relationship of ice-water solid-flow conversion of rectangular ice cubes by the triple heat balance integration method, separates the time and ice cube length in the relationship as variables, and enables the melting time of ice cubes under the boundary conditions of the circulating water tank of the air purification vehicle to be predicted by the size of the ice cubes and the water temperature, thereby quickly predicting the melting time of rectangular ice cubes in the circulating water tank, and improving the operating parameters of the ice-adding process of the crawler-type string-grid air purification vehicle. BRIEF DESCRIPTION OF THE DRAWINGS

[0015] Figure 1 The schematic diagram of the structure of an air purification vehicle involved in the method for predicting the melting time of ice in the circulating water tank of an air purification vehicle according to an embodiment of the present invention.

[0016] Figure 2 It is a structural schematic diagram of a circulating water tank involved in a method for predicting the melting time of ice in a circulating water tank of an air purification vehicle according to an embodiment of the present invention.

[0017] Figure 3 The diagram is a schematic diagram of the structure of ice blocks involved in the method for predicting the melting time of ice blocks in the circulating water tank of an air purification vehicle according to an embodiment of the present invention.

[0018] Figure 4 This is a schematic diagram of the temperature distribution in the x-direction of ice in the method for predicting the melting time of ice in the circulating water tank of an air purification vehicle according to an embodiment of the present invention.

[0019] Figure 5 This is a schematic diagram of the error caused by the difference between the initial temperature and the average central temperature in the method for predicting the melting time of ice in the circulating water tank of an air purification vehicle according to an embodiment of the present invention.

[0020] Figure 6 This is a schematic diagram of the melting time of ice cubes at different sizes, water flow temperatures and initial temperatures in the method for predicting the melting time of ice cubes in the circulating water tank of an air purification vehicle according to an embodiment of the present invention. DETAILED DESCRIPTION

[0021] The present invention will be further described below in conjunction with the accompanying drawings and examples.

[0022] like Figures 1 to 6 As shown, an embodiment of the present invention provides a method for predicting the melting time of ice cubes in a circulating water tank of an air purification vehicle. The air purification vehicle is a tracked chord air purification vehicle, comprising a circulating water tank 1, an axial flow exhaust fan 2, an air purification section 3, a tracked chassis 4, and a control room 5. The size of the circulating water tank 1 is 6m×2m×0.8m, the diameter of the circulating water tank inlet 11 is DN80, the diameter of the outlet 12 is DN60, and the inlet flow rate is 0.0024m 3 / s, the cross-sectional flow rate of the circulating water tank is 0.0015m / s. The ice cubes used in the circulating water tank are the most common rectangular ice cubes in industry (such as Figure 3 As shown in A in the figure, the length, width and height ratio is 2:2:1. Rectangular ice cubes with other ratios can also be obtained by the calculation method of the present invention.

[0023] The process of obtaining the calculation formula for the melting time of the rectangular ice block includes the following steps.

[0024] 1) Assume that at the end of the melting of the rectangular ice cube, its shape approaches that of a small ball (e.g. Figure 3 As shown in B), if the required result focuses on the total melting time, the melting rate of the ice cube during the melting process is not considered. It can be considered that the melting rates of the rectangular ice cube in different directions of the xyz axis are proportional. Taking a rectangular ice cube with a length, width and height ratio of 2:2:1 as an example, a three-dimensional Cartesian coordinate system is established at the center of the ice cube, and the distance from the center of the ice cube to the wall in the x, y, and z directions is x, x, and 0.5x. When the melting thickness in the positive direction of x at time dt is dx, the melting thickness in the positive direction of the y axis and the positive direction of the z axis is dx and 0.5dx.

[0025] 2) Based on the assumptions made in step (1), calculate the change in the internal energy of the ice cube per unit time. The calculation formula is:

[0026] dQ=4cρx 3 dT+12ρLx 2 dx (1)

[0027] Where:

[0028] L is the latent heat of phase change, J / kg; ρ is the density of ice, kg / m 3 ; c is the specific heat of ice, J / (kg·℃); 4x 3 is the volume of ice, m 3 ; dT is the change in temperature inside the ice cube at time dt, ℃; 12x 2 dx is the volume change of the ice cube at time dt, m 3 ;

[0029] 3) Calculate the convective heat exchange between the ice cube and the outside world per unit time. The calculation formula is:

[0030] Q d =16hx 2 (T ∞ -T m ) (2)

[0032] Where:

[0033] Q d is the convective heat transfer per unit time, J / s; h is the convective heat transfer coefficient, W / (m 2K); 16x 2 is the surface area of ​​the ice cube, m 2 ; T ∞ is the incoming flow temperature of the environment where the ice cube is located, ℃; T m is the melting temperature of ice, ℃.

[0034] 4) According to the law of conservation of energy, the change in the internal energy of the ice cube per unit time is equal to the convective heat exchange between the ice cube and the external environment. Combining formula (1) and formula (2), we can get:

[0035]

[0036] The derivative of temperature T with respect to time t in formula (3) is converted into the derivative with respect to the spatial function x:

[0037]

[0038] Extract similar items:

[0039]

[0040] Where:

[0041] dT / dx is the temperature gradient in the x-direction inside the ice cube.

[0042] 5) The temperature gradient dT / dx inside the ice block is solved by the triple heat balance integration method, and the calculation formula is:

[0043] T(x, t)=A+Bx+Cx 3 (6)

[0044] Where:

[0045] A, B, C are polynomial coefficients.

[0046] For the convenience of research, the present invention assumes that after the heat transfer begins, the temperature penetration depth has reached the center of the rectangular ice block, and the temperature distribution state of the ice block in the x direction is as follows: Figure 4 shown.

[0047] The boundary conditions and solutions of the ice block at a certain time are as follows:

[0048] T=T n x=0 (7)

[0049]

[0050] T=T m x=X (9)

[0051] Where:

[0052] T n is the center temperature of the ice block, and X is the current thickness of the ice block.

[0053] Substituting formulas (7), (8), and (9) into (6), we obtain: A = T n , B=0,

[0054] The temperature distribution of the rectangular ice cube in the positive x-axis direction is calculated as:

[0055]

[0056] 6) Substituting the temperature gradient in the x direction obtained in step (5) and x=X into formula (5), the calculation formula is:

[0057]

[0058] Simplify the equation and substitute the particular solution x=0, t=0 into the equation.

[0059]

[0060] Where:

[0061] t is the melting time, s; ρ is the density of ice, kg / m 3 ; c is the specific heat capacity of ice, J / (kg·℃); T m is the melting temperature of ice, °C; T n The center temperature of the ice cube, ℃; L is the latent heat of phase change, J / kg; h is the convection heat transfer coefficient, W / (m 2 ·K); T ∞ is the incoming flow temperature of the environment where the ice cube is located, ℃; x is the distance from the center of the ice cube to the wall in the X direction, m.

[0062] 7) Calculate the melting time of the rectangular ice block in the circulating water tank of the crawler type string grid air purification vehicle, and the specific operation is as follows:

[0063] a) Determine the constant term in the calculation formula. Among them, ρ = 920kg / m 3 , c = 2100 J / (kg·℃), T m =0℃, L=335000J / kg.

[0064] b) The convective heat transfer coefficient of a rectangular ice block with a ratio of 2:2:1 under the boundary conditions of the circulating water tank of a tracked chord air purification vehicle is 620 W / (m 2 ·K). The cross-sectional flow velocity in the circulating water tank of the crawler type string grid air purification vehicle is 0.0015m / s. Through simulation and experiment, it is found that in the low flow water area with a flow velocity of 0.0015m / s, the change of ice size and the change of temperature difference between ice and water within a certain range have little effect on the convective heat transfer coefficient and can be ignored.

[0065] c) Take the initial temperature of the ice cube as the average center temperature of the ice cube. ① The present invention is a calculation formula for the total melting time of the ice cube. Therefore, regardless of the change of the center temperature over time, the melting time of the ice cube is calculated using the average center temperature through formula (12). In the later stage of ice melting, the outside temperature can penetrate into the center of the ice cube, and the center temperature rises very slowly until the volume of the ice cube is small enough, and the center temperature rises rapidly, so that the calculated average center temperature of the ice cube is very close to the initial temperature of the ice cube; ② The sensible heat change c (T m -T n ) is quite different from the value of the latent heat change L. When the initial temperature is -10℃ and the center temperature of the ice cube does not change, its value is 21000J / kg, and the value of the latent heat change L is 335000J / kg. The sensible heat change only accounts for 5.89% of the internal energy change. The center temperature of the ice cube has little effect on the total melting time. Combining ① and ②, it can be seen that the error caused by taking the initial temperature as the average center temperature of the ice cube is very small. Calculate the error caused by taking the initial temperature as the average center temperature of the ice cube as follows Figure 5 shown.

[0066] d) The water flow temperatures in the circulating water tank of the tracked string-type air purification vehicle are 15°C, 20°C, 25°C, 30°C, 35°C, 40°C, and 45°C, respectively; the distances from the center of the rectangular ice block to the wall in the x-direction are 0.05m, 0.10m, 0.15m, 0.20m, and 0.25m, respectively; and the initial temperatures of the ice block are 5°C, 10°C, 15°C, and 20°C, respectively.

[0067] e) Substitute the above values ​​into formula (12) and the result is as follows: Figure 6 As shown in (a) to (d).

[0068] By analyzing the specific implementation plan, the following conclusions can be drawn:

[0069] The melting time of a certain proportion of ice cubes under the boundary conditions of the circulating water tank of a tracked string-grid air purification vehicle is obtained by model test. The convective heat transfer coefficient of the ice cubes of this proportion can be calculated using formula (12). At a low flow rate of 0.0015 m / s, the convective heat transfer coefficient is less affected by the size of the ice cubes and the temperature difference. The convective heat transfer coefficient of the ice cubes of this proportion can be regarded as a fixed value. The melting time of ice cubes of this proportion under different sizes, initial temperatures and water body temperatures can be calculated according to formula (12). Therefore, the embodiment of the present invention proposes a method for predicting the melting time of ice cubes in the circulating water tank of a tracked string-grid air purification vehicle that is simple, reliable and low in investment.

[0070] The important innovation of the present invention is to simplify the temperature gradient term in the mathematical relationship of the conversion of rectangular ice cubes into ice-water solid flow through the triple heat balance integration method, separate the time and ice cube length in the relationship into variables, so that the melting time of ice cubes under the boundary conditions of the circulating water tank of the tracked string-grid air purification vehicle can be predicted by the size of the ice cubes and the water temperature. In addition, the calculation formula obtaining method of the present invention is also applicable to ice cubes of other shapes and sizes, preferably rectangular ice cubes, which are easy to implement and relatively simple to calculate. In previous inventions, it is necessary to determine the input power of the external environment to the ice cubes to predict the melting time of ice cubes, which is also what distinguishes the present invention from other inventions.

[0071] The above description of the disclosed embodiments enables one skilled in the art to make or use the invention. Various modifications to these embodiments will be apparent to one skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the invention. Therefore, the invention will not be limited to the embodiments shown herein, but rather to the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A method for predicting the melting time of ice in a circulating water tank of an air purification vehicle, characterized in that: include: A three-dimensional Cartesian coordinate system is established at the center of the ice block, and the distance from the center of the ice block to the wall in the x direction is x; Calculate the change in internal energy of the ice cube per unit time; Calculate the convective heat exchange between the ice cube and the outside world per unit time; according to the law of conservation of energy, the change in the internal energy of the ice cube per unit time is equal to the convective heat exchange between the ice cube and the outside world, and obtain the functional relationship between dx / dt and dT / dx. dx / dt represents the change in the melting thickness of the ice cube in the positive direction x with time t, and dT / dx is the temperature gradient in the x direction inside the ice cube; solve the temperature gradient dT / dx inside the ice cube by the triple heat balance integration method, and the calculation formula is: T(x,t)=A+Bx+Cx 3 Wherein A, B, and C are polynomial coefficients. Based on the assumption that the temperature penetration depth has reached the center of the rectangular ice block after the start of heat transfer, the values ​​of A, B, and C are obtained, thereby calculating the temperature distribution formula in the positive direction of the x-axis of the ice block; the temperature distribution formula in the positive direction of the x-axis of the ice block and x=X are substituted into the functional relationship between dx / dt and dT / dx, X is the current thickness of the ice block, and the special solution x=0, t=0 is substituted into the equation to obtain the relationship between the melting time and x.

2. The method for predicting the melting time of ice in the circulating water tank of an air purification vehicle according to claim 1, characterized in that: The air purification vehicle is a tracked string-grid air purification vehicle.

3. The method for predicting the melting time of ice in the circulating water tank of an air purification vehicle according to claim 1, characterized in that: The ice cubes are rectangular ice cubes.

4. A method for predicting the melting time of ice in a circulating water tank of an air purification vehicle, characterized in that: The ice cube is a rectangular ice cube with a length, width and height ratio of 2:2:

1. The calculation formula for the melting time is: Where: t is the melting time, s; ρ is the density of ice, kg / m 3 ; c is the specific heat capacity of ice, J / (kg·℃); T m is the melting temperature of ice, °C; T n The center temperature of the ice cube, ℃; L is the latent heat of phase change, J / kg; h is the convection heat transfer coefficient, W / (m 2 ·K); T ∞ is the incoming flow temperature of the environment where the ice cube is located, ℃; x is the distance from the center of the ice cube to the wall in the x direction, m.

5. The method for predicting the melting time of ice in the circulating water tank of an air purification vehicle according to claim 4, characterized in that: Take the initial temperature of the ice cube as the center temperature T of the ice cube n .

6. The method for predicting the melting time of ice in the circulating water tank of an air purification vehicle according to claim 5 or 6, characterized in that: The air purification vehicle is a tracked string-grid air purification vehicle.

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