A simulation method for determining different snow storage material coverage options

Abstract

This invention discloses a simulation method for determining different snow storage material cover options. The method includes: a simulation method for snow storage experiments, including mathematical methods for calculating the total amount of solar radiation on any slope and mathematical methods for unsteady-state heat transfer; and a numerical method for simulating the performance of snow storage cover options, including finite difference methods and economic analysis methods. This method solves the existing problem of selecting snow storage cover material options for different regions and climate conditions.

Description

Technical Field

[0001] The invention relates to a technology for screening snow storage materials, and in particular to a simulation method for determining covering schemes of different snow storage materials. Background Art

[0002] With the rapid development of my country's snow and ice industry, snow storage research is bound to expand, and various related scientific studies will continue to deepen. Snowdrift storage is a type of engineering project in the natural environment. It not only faces the complexities of an open system, but also constantly changes in external meteorological and environmental factors. As the insulating structure exchanges matter and energy with the external environment, its own state also undergoes changes, such as temperature fields and thermal properties. Furthermore, snow is a unique substance, with its shape and physical parameters constantly changing and prone to phase transitions. This leads to various changes in the snowdrift, especially in its geometry, snow layer structure, and thermal parameters, which have a significant impact on the heat transfer process within the snowdrift. The heat transfer performance of the snowdrift cover scheme is a major factor in determining the effectiveness of artificial snow storage. Research both domestically and internationally has focused on the selection and comparison of cover schemes.

[0003] At present, the evaluation of the thermal insulation performance of the covering scheme is still mainly based on experiments, and has not risen to the theoretical and simulation level. The geographical location and meteorological conditions of each snow storage site are different, which determines that the thermal insulation performance of different snow storage covering schemes will also be different. Therefore, the performance data obtained from most snow storage covering scheme experiments are only applicable to Europe. The covering scheme that has achieved good snow storage effects in Europe may be poorly applied in Asia, and its experience and results are difficult to match different regions. The external environment transfers heat to the snow pile through the thermal insulation structure mainly through heat conduction of the covering layer. The heat transfer of thermal insulation materials is a complex non-steady-state process. The ideas and methods of non-steady-state heat transfer have been very mature and are widely used. For example, building insulation, food heating, and aerospace, etc., but the application of non-steady-state heat transfer methods in snow storage is very rare. Therefore, it is a technical problem that people in this field need to solve urgently to invent a snow storage material optimal covering solution that can be applied to different regions, different temperatures and other different conditions. Summary of the Invention

[0004] The main purpose of the present invention is to provide a simulation method for determining different snow storage material covering schemes, so as to solve the problem of screening snow storage covering material schemes in different regions and climatic conditions in the prior art.

[0005] The technical solution adopted by the present invention is: a simulation method for determining different snow storage material coverage schemes, comprising:

[0006] Simulation methods for snow storage experiments, including mathematical methods for total solar radiation on arbitrary slopes and mathematical methods for unsteady-state heat transfer;

[0007] Numerical simulation methods for the performance of snow storage cover schemes, including finite difference methods and economic analysis methods.

[0008] Furthermore, the finite difference method includes:

[0009] Use a grid of finite discrete points instead of a continuous solution region;

[0010] The function of continuous variables on the continuous solution area is approximated by the function of discrete variables defined on the grid;

[0011] Approximate the heat conduction differential equation and the equations in the boundary conditions using difference equations;

[0012] A finite number of discrete points are solved iteratively using a system of differential equations. The iteration can be stopped when the temperature difference between the corresponding nodes of the two previous and subsequent iterations reaches the initial conditions and boundary conditions. The result of the last iteration is used as the final solution to the system of equations, and the temperature values ​​of all discrete points are obtained.

[0013] Furthermore, the finite difference method is specifically:

[0014] The governing equation for one-dimensional heat transfer of a homogeneous insulation structure in Cartesian coordinates is:

[0015]

[0016] For thermal insulation structures, discrete grid and Temperature at the location (°C); To calculate time; is the distance from the coordinate origin; is the density of the material (kg / m 3 ); is the specific heat capacity of the material (KJ / (kg·K)); is the thermal conductivity of the material (W / (m·K));

[0017]

[0018] m represents the moment;

[0019] The solution of heat transfer problems requires initial conditions and boundary conditions to proceed smoothly;

[0020] The expressions for the initial and boundary conditions are as follows:

[0021] Initial conditions

[0022]

[0023] The initial temperature of the insulation structure is set to 0 °C.

[0024] The third type of boundary condition (Robin condition)

[0025]

[0026] and It is the heat transfer coefficient of the inner and outer surfaces of the thermal insulation structure taking into account convection and radiation (W / (m 2 K)); is the external integrated air temperature (°C); is the temperature of the air layer surrounding the snow pile (0°C); 0 represents the first boundary of the insulation structure, that is, the outer surface of the insulation structure; L represents the second boundary, that is, the inner surface of the insulation structure; is the temperature of the outer surface of the thermal insulation structure at time m; is the temperature of the inner surface of the thermal insulation structure at time m;

[0027] formula The expression converted to difference format is:

[0028]

[0029] k represents the kth layer (1, 2······n) of the thermal insulation structure.

[0030] formula It can be written as the following expression:

[0031]

[0032] Boundary condition formula The expression converted to difference format is:

[0033]

[0034] The formula and The difference equations that together form the implicit format of the temperature of each node of the adiabatic structure are:

[0035]

[0036] By the formula The resulting matrix equation is:

[0037]

[0038] The set iteration stop threshold is that the temperature difference between the two iterations is less than 10 -5 ;

[0039] Delay time and attenuation multiple are parameters that reflect the performance of thermal insulation structures. The calculation formula is:

[0040]

[0041] and are the delay time and attenuation multiple respectively.

[0042] Furthermore, the economic analysis method includes:

[0043] The economic analysis of the thermal insulation structure is carried out by using the ratio of the cost of the thermal insulation structure to the average temperature of the outer and inner surfaces of the thermal insulation structure. The calculation equation is:

[0044]

[0045] is the cost per unit ratio (RMB); and Respectively represent Volume price of layer material (RMB / m 3 ) and volume (m 3 ); ℃) and (℃) represent the average temperatures of the outer and inner surfaces of the insulation structure respectively.

[0046] Advantages of the present invention:

[0047] This study uses the finite difference method, a non-steady-state heat transfer simulation method for evaluating the performance of snow storage cover solutions. It is one of the most popular methods for solving non-steady-state problems in thermodynamics and can determine the temperature and heat transfer at any location and time within an insulating structure. This method has broad applicability, as insulating materials are commonly used for glacier protection, building refrigeration, and snow storage in the snow and ice industry.

[0048] In addition to the above-described objects, features and advantages, the present invention has other objects, features and advantages. The present invention will be further described in detail below with reference to the accompanying drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0049] The drawings constituting a part of this application are used to provide a further understanding of the present invention. The illustrative embodiments of the present invention and their descriptions are used to explain the present invention and do not constitute improper limitations on the present invention.

[0050] Figure 1This is a diagram of the external integrated air temperature of the south-facing slope of a snow pile according to the present invention (the circle and square represent the external integrated air temperature with sawdust and geotextile as the outer surface, respectively). DETAILED DESCRIPTION

[0051] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention.

[0052] refer to Figure 1 , a simulation method for determining different snow storage material cover options, including:

[0053] Simulation methods for snow storage experiments, including mathematical methods for total solar radiation on arbitrary slopes and mathematical methods for unsteady-state heat transfer;

[0054] Numerical simulation methods for the performance of snow storage cover schemes, including finite difference methods and economic analysis methods.

[0055] The finite difference method includes:

[0056] Use a grid of finite discrete points instead of a continuous solution region;

[0057] The function of continuous variables on the continuous solution area is approximated by the function of discrete variables defined on the grid;

[0058] Approximate the heat conduction differential equation and the equations in the boundary conditions using difference equations;

[0059] A finite number of discrete points are solved iteratively using a system of differential equations. The iteration can be stopped when the temperature difference between the corresponding nodes of the two previous and subsequent iterations reaches the initial conditions and boundary conditions. The result of the last iteration is used as the final solution to the system of equations, and the temperature values ​​of all discrete points are obtained.

[0060] The finite difference method is specifically:

[0061] The governing equation for one-dimensional heat transfer of a homogeneous insulation structure in Cartesian coordinates is:

[0062] For thermal insulation structures, discrete grid and Temperature at the location (°C); To calculate time; is the distance from the coordinate origin; is the density of the material (kg / m 3 ); is the specific heat capacity of the material (KJ / (kg·K)); is the thermal conductivity of the material (W / (m·K));

[0063]

[0064] m represents the moment;

[0065] The solution of heat transfer problems requires initial conditions and boundary conditions to proceed smoothly;

[0066] The expressions for the initial and boundary conditions are as follows:

[0067] Initial conditions

[0068]

[0069] The initial temperature of the insulation structure is set to 0 °C.

[0070] The third type of boundary condition (Robin condition)

[0071]

[0072] and It is the heat transfer coefficient of the inner and outer surfaces of the thermal insulation structure taking into account convection and radiation (W / (m 2 K)); is the external integrated air temperature (°C); is the temperature of the air layer surrounding the snow pile (0°C); 0 represents the first boundary of the insulation structure, that is, the outer surface of the insulation structure; L represents the second boundary, that is, the inner surface of the insulation structure; is the temperature of the outer surface of the thermal insulation structure at time m; is the temperature of the inner surface of the thermal insulation structure at time m;

[0073] formula The expression converted to difference format is:

[0074]

[0075] k represents the kth layer (1, 2······n) of the thermal insulation structure.

[0076] formula It can be written as the following expression:

[0077]

[0078] Boundary condition formula The expression converted to difference format is:

[0079] The formula and The difference equations that together form the implicit format of the temperature of each node of the adiabatic structure are:

[0080]

[0081] By the formula The resulting matrix equation is:

[0082]

[0083] The set iteration stop threshold is that the temperature difference between the two iterations is less than 10 -5 ;

[0084] Delay time and attenuation multiple are parameters that reflect the performance of thermal insulation structures. The calculation formula is:

[0085]

[0086] and are the delay time and attenuation multiple respectively.

[0087] The economic analysis method includes:

[0088] The economic analysis of the thermal insulation structure is carried out by using the ratio of the cost of the thermal insulation structure to the average temperature of the outer and inner surfaces of the thermal insulation structure. The calculation equation is:

[0089]

[0090] is the cost per unit ratio (RMB); and Respectively represent Volume price of layer material (RMB / m 3 ) and volume (m 3 ); (℃) and (℃) represent the average temperatures of the outer and inner surfaces of the insulation structure respectively.

[0091] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A simulation method for determining different snow storage material coverage schemes, characterized in that: include: Simulation methods for snow storage experiments, including mathematical methods for total solar radiation on arbitrary slopes and mathematical methods for unsteady-state heat transfer; Numerical simulation methods for the performance of snow storage cover schemes, including finite difference methods and economic analysis methods; The finite difference method includes: Use a grid of finite discrete points instead of a continuous solution region; The function of continuous variables on the continuous solution area is approximated by the function of discrete variables defined on the grid; Approximate the heat conduction differential equation and the equations in the boundary conditions using difference equations; The differential equations are used to iterate a finite number of discrete points. The iteration is stopped when the temperature difference between the corresponding nodes of the two iterations reaches the initial conditions and boundary conditions. The result of the last iteration is used as the final solution of the equations to obtain the temperature values ​​of all discrete points. The finite difference method is specifically: The governing equation for one-dimensional heat transfer of a homogeneous insulation structure in Cartesian coordinates is: T(x, t) is the temperature of the thermal insulation structure at the discrete grid positions x and t, in °C; t is the calculation time; x is the distance from the coordinate origin; ρ is the density of the material, in kg / m 3 ; c is the specific heat capacity of the material, in KJ / (kg·K); λ is the thermal conductivity of the material, in W / (m·K); m represents the moment; The solution of heat transfer problems requires initial conditions and boundary conditions to proceed smoothly; The expressions for the initial and boundary conditions are as follows: Initial conditions T(x, 0) = 0 (3) The initial temperature of the thermal insulation structure is set to 0°C; The third type of boundary condition is the Robin condition; α i and α e It is the heat transfer coefficient of the inner and outer surfaces of the thermal insulation structure taking into account convection and radiation, and the unit is W / (m 2 ·K); T e is the external integrated air temperature, in °C; T i is the temperature of the air layer around the snow pile, which is 0℃; 0 represents the first boundary of the insulation structure, which is the outer surface of the insulation structure; L represents the second boundary, which is the inner surface of the insulation structure; is the temperature of the outer surface of the thermal insulation structure at time m; is the temperature of the inner surface of the thermal insulation structure at time m; The expression converted from formula (1) into differential format is: k represents the kth layer of the thermal insulation structure, k = 1, 2······n; Formula (5) is written as follows: The boundary condition formula (4) is converted into the differential format expression: Formulas (6) and (7) are combined to form the implicit difference equations for the temperature of each node of the adiabatic structure: The matrix equation obtained from formula (8) is: The set iteration stop threshold is when the temperature difference between the two iterations is less than 10 -5 ; Delay time and attenuation multiple are parameters that reflect the performance of thermal insulation structures. The calculation formula is: ξ and υ are the delay time and attenuation multiple respectively.

2. The simulation method for determining different snow storage material coverage schemes according to claim 1, characterized in that: The economic analysis method includes: The economic analysis of the thermal insulation structure is carried out by using the ratio of the cost of the thermal insulation structure to the average temperature of the outer and inner surfaces of the thermal insulation structure. The calculation equation is: C u is the cost per unit ratio, in RMB; C k and V k Represents the volume price and volume of the k-th layer material, in RMB / m 3 and m 3 ;T x＝0 (average), in °C and T x＝L (average), in °C, represents the average temperature of the outer and inner surfaces of the insulation structure respectively.

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