CN111579434B - Method for establishing soil heat-moisture coupling model test similarity criterion - Google Patents
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Abstract
The invention discloses a method for establishing a similarity criterion of a soil thermal-wet coupling model test, which uses a non-linear relation between soil thermal physical property parameters and a similarity third theorem design idea to deduce the similarity criterion between a soil thermal-wet coupling model test model and a test prototype by using a similarity conversion method. The method combines the accuracy of the nonlinear heat conduction differential equation, and also integrates the soil moisture motion basic equation under the hydrothermal coupling effect into the similarity criterion, thereby making up the defect that the nonlinear heat conduction differential equation analysis method does not consider the influence of moisture motion on soil heat and humidity migration.
Description
Technical Field
The invention belongs to the technical field of geotechnical engineering tests, and particularly relates to a method for establishing a similarity criterion of a soil heat and moisture coupling model test.
Background
The model test is a common method for scientific research, and is widely applied in various subject fields by carrying out geometric scaling on a prototype in a certain proportion, establishing the relationship between the prototype and the model by using corresponding similarity criteria and further simplifying the complicated large-scale prototype test. The similarity criterion is used as a link between the model and the prototype and is a theoretical basis for model test.
The urban buried heat pipe network is used as a pipeline system for conveying and distributing heat supply media to heat users as an urban centralized heat supply source, and the pipeline is directly buried in soil, so that urban traffic and urban appearance are not influenced, the pipeline directly bears external load, the manufacturing cost is low, and the construction is simple and convenient, so that the urban buried heat pipe network can be widely applied. Because the temperature and the water content of the soil around the leakage point are increased due to the leakage of the buried heat distribution pipe network, and the temperature and the water movement of the soil in the area above the leakage point are influenced, the influence of the buried heat distribution pipe network on the soil heat and moisture migration rule is researched, and the method is particularly important for quickly and accurately positioning the leakage point of the buried heat distribution pipe network.
At present, a nonlinear heat conduction differential equation analysis method is a common method for solving a soil heat and moisture migration model test similarity criterion, but the method does not consider the influence of water movement involved in actual engineering on the soil heat and moisture migration rule, and the similarity criterion is established in an ideal state with soil thermophysical property parameters as constants, which is greatly different from the actual situation that the soil thermophysical property parameters continuously change along with the influence of factors such as temperature, water content and the like, so that the method cannot objectively describe the actual soil heat and moisture migration rule.
Disclosure of Invention
Aiming at the defects of the prior art, the invention aims to solve the technical problem of establishing a soil heat-moisture coupling model test similarity criterion.
The technical scheme adopted by the invention for solving the technical problems is as follows:
a method for establishing a similarity criterion of a soil heat-moisture coupling model test is characterized in that the similarity criterion between a soil heat-moisture coupling test model and a test prototype is derived by a similarity conversion method according to a nonlinear relation between soil thermophysical parameters and based on a similar third theorem design idea; the method comprises the following steps:
s1, under the action of heat-moisture coupling, a soil vertical one-dimensional water motion basic equation is expressed as a formula (1):
in the formula: d T Is the water diffusion coefficient under the action of temperature difference, D W Is the water and water vapor diffusion coefficient, theta is the soil water content, T is the time, T is the temperature, k is the soil water conductivity, and z is the soil depth;
under the effect of heat-moisture coupling, the heat transfer basic equation of soil can be expressed as follows:
in the formula: c V Is the soil thermal capacity, lambda is the soil thermal conductivity, L is water vaporLatent heat of generation, D W/V Thermal diffusivity due to moisture movement;
wherein the thermal conductivity of the soil is lambda and the thermal capacity of the soil is C V The functional relation with the soil moisture content theta satisfies the formulas (3) and (4):
C V ＝θ+Dε+E(4)
in the formula: A. b, C, D and E are fitting constants, and epsilon is the porosity of the soil;
water and vapor diffusion coefficient D W The empirical formula of (2) is formula (5), and the water diffusion coefficient D under the action of temperature difference T Is the formula (6):
D W ＝0.0004e 0.14611θ (5)
D T ＝6×10 -16 T 5.9146 (6)
s2, deducing a similarity criterion based on a similarity transformation method; defining the similarity transformation between the test prototype and each parameter of the test model in the formulas (1) to (4) to meet the formula (7), namely the corresponding parameters are proportional;
wherein p represents a physical quantity of a prototype; m represents a physical quantity of the test model; k represents the scaling of the corresponding coefficients of the test prototype and the test model, wherein K A 、K B 、K C 、K D 、K E The scaling of the corresponding fitting constants in formula (3) and formula (4); k θ The shrinkage ratio of the water content of the soil is,
is the water diffusion coefficient contraction ratio under the action of temperature difference,
is the water and water vapor diffusion coefficient scaling, K L Is water vaporThe heat-generating capacity is reduced by the heat-generating capacity,
thermal diffusivity shrinkage caused by moisture movement, K l In geometric scale, K t To scale time, K T Is a temperature scaling, K k Is the soil water conductivity scaling, K ε The shrinkage ratio of the porosity of the soil is adopted;
the basic equations of motion of moisture and heat transfer of the test prototype obtained by respectively substituting the formulas (3), (4) and (7) into the formulas (1) and (2) are respectively the formulas (8) and (9), and the basic equations of motion of moisture and heat transfer of the test model are the formulas (10) and (11):
according to a similar third theorem, the basic equation of water movement and the basic equation of heat transfer between the test prototype and the test model are correspondingly equal, i.e. equations (8) and (10) are equal, and equations (9) and (11) are equal, so that 9 similar indexes of equation (12) are obtained:
further processing the above 9 similarity index formulas to obtain the following 9 similarity criterion numbers pi 1 -π 9 ：
The derivation result shows that 9 similarity criteria between the test prototype and the test model are established according to the relationship between the similarity criteria numbers between the test model and the physical quantities of the test prototype; in the practical application process, if several similar criterion numbers in the test model are known, other similar criterion numbers of the test model can be obtained.
Compared with the prior art, the invention has the beneficial effects that:
the method is based on the soil heat-moisture coupling equation, and the similarity criterion between the soil heat-moisture coupling test model and the test prototype is deduced by using the similarity of single-value conditions of two similar phenomena similar to the third theorem, so that the accuracy of the nonlinear heat-conduction differential equation is combined, the soil moisture motion basic equation under the hydrothermal coupling action is integrated into the similarity criterion, and the defect that the influence of moisture motion on soil heat-moisture migration is not considered in the nonlinear heat-conduction differential equation analysis method is overcome.
The similarity criterion of the invention is established on the basis of the non-linear relationship (specifically, formulas (3) - (6)) between the soil thermophysical parameters, and is more in line with the change rule of the soil thermophysical parameters in the actual engineering, thereby overcoming the defect of over-ideal thermophysical parameters in the past similarity criterion and providing necessary conditions for the actual soil thermophysical migration model test. The similarity criterion established by the method can accurately convert the prototype test into the model test, and has great reference value for modeling of the prototype test.
Detailed Description
The present invention will be described in detail below, but the scope of the present invention is not limited thereto.
The method for establishing the soil heat-moisture coupling model test similarity criterion is based on the design idea of a similar third theorem, namely that the single-value conditions of two phenomena are similar, and the numerical values of the same-name similarity criterion composed of single-value quantities are the same, so that the two phenomena are similar, and the two similar physical phenomena can be described by using the same differential equation. The soil heat-moisture coupling equation is used as a basis, single-value conditions of two similar phenomena in the aspects of geometric and physical elements are similar, the similarity criterion between the soil heat-moisture coupling test model and the test prototype is deduced by using a similarity conversion method, and the similarity criterion is applied to the large-scale soil heat-moisture coupling test model, so that the large-scale test prototype can be modeled and simplified, the test prototype is reversely deduced according to the result obtained by the test model, and the heat-moisture migration rule of the test prototype can be accurately obtained.
The invention relates to a method for establishing a soil heat-moisture coupling model test similarity criterion (method for short), which comprises the following steps:
s1, under the action of heat-moisture coupling, a soil vertical one-dimensional water motion basic equation can be expressed as follows:
in the formula: d T Is the water diffusion coefficient under the action of temperature difference, D W Is the water and water vapor diffusion coefficient, theta is the soil water content, T is the time, T is the temperature, k is the soil water conductivity, and z is the soil depth;
under the effect of heat and moisture coupling, the basic equation of heat transfer of soil can be expressed as follows:
in the formula: c V Is the soil thermal capacity, lambda is the soil thermal conductivity, L is the water evaporation latent heat, D W/V Thermal diffusivity due to moisture movement;
wherein the thermal conductivity of the soil is lambda and the thermal capacity of the soil is C V The functional relation with the soil moisture content theta satisfies the formulas (3) and (4):
C V ＝θ+Dε+E(4)
in the formula: A. b, C, D and E are fitting constants, and epsilon is the porosity of the soil;
water and water vapor diffusion coefficient D W The empirical formula of (2) is formula (5), and the water diffusion coefficient D under the action of temperature difference T Is the formula (6):
D W ＝0.0004e 0.14611θ (5)
D T ＝6×10 -16 T 5.9146 (6)
s2, deducing a similarity criterion based on a similarity transformation method; defining the similarity transformation of each parameter of the test prototype and the test model in the formulas (1) to (4) to meet the formula (7), namely the corresponding parameters are proportional;
wherein p represents a physical quantity of a prototype (prototype); m represents a physical quantity of a model (model); k represents the scaling of the corresponding coefficients of the test prototype and the test model, wherein K A 、K B 、K C 、K D 、K E Is the scaling of the corresponding fitting constants in formula (3) and formula (4); k θ The shrinkage ratio of the water content of the soil is shown,
is the water diffusion coefficient contraction ratio under the action of temperature difference,
is the water and water vapor diffusion coefficient scaling, K L In order to reduce the latent heat of water evaporation,
thermal diffusivity shrinkage caused by moisture movement, K l For geometric scaling, K t To scale time, K T Is a temperature scaling, K k Is the soil water conductivity scaling, K ε The soil porosity scaling;
the water motion basic equation and the heat transfer basic equation of the experimental prototype obtained by respectively substituting the formulas (3), (4) and (7) into the formulas (1) and (2) are respectively expressed as formulas (8) and (9), and the water motion basic equation and the heat transfer basic equation of the experimental model are expressed as formulas (10) and (11):
according to a third theorem, the two phenomena are similar in terms of single-valued conditions and the same-name similarity criterion number composed of single-valued quantities is the same, and the two phenomena are similar, and the two similar physical phenomena can be described by using the same differential equation, that is, the basic equation of water movement and the basic equation of heat transfer between the test prototype and the test model are correspondingly equal, that is, equations (8) and (10) are equal, and equations (9) and (11) are equal, so that 9 similar indexes of equation (12) can be obtained:
further processing the above 9 similarity index formulas to obtain the following 9 similarity criterion numbers pi 1 -π 9 ：
Specifically, from
The material is pushed out of the mould,
the other similar index formulas can be obtained in the same way;
the derivation result shows that the similarity criterion number between the test model and each physical quantity of the test prototype has the relation shown in the formula (13), and 9 similarity criteria between the test prototype and the test model are established; in the practical application process, if the number of the similarity criteria of several items in the test model is known, the number of the other similarity criteria of the test model can be obtained, so that the complicated test prototype is simplified.
The above-mentioned push result is explained with reference to specific examples;
setting the soil depth z of a certain test prototype to be 3 meters, and arranging a constant heat source with the temperature of 30 ℃ at the soil depth z of-3 meters; the initial temperature of the soil layer is 2 ℃, and the initial water content is 0.3m 3 /m 3 To study the temperature and humidity change of the soil within a certain period of time; the concrete parameters of the soil which are actually measured are shown in the following table 1, and because the soil is thick in depth, complex in-situ field test and difficult to realize, a test model is established by utilizing the similarity criterion of the soil heat-moisture coupling model test of the method for research;
TABLE 1 values of prototype parameters
Knowing that the soil depth z of the test model is 1m, and a constant heat source with the temperature of 30 ℃ is arranged at the soil depth z of-1 m; the initial temperature of the soil layer is 2 ℃, and the initial water content is 0.3m 3 /m 3 ；
The original soil is adopted as a test model material, so the soil thermal conductivity lambda and the soil thermal capacity C of the test prototype and the test model V Equal to each fitting constant of the functional relationship between the soil water content theta, i.e. A p ＝A m ，B p ＝B m ，C p ＝C m ，D p ＝D m ，E p ＝E m ；
By number of similarity criteria
Can obtain the product
From C p ＝C m ，D p ＝D m ，E p ＝E m Can obtain theta p ＝θ m ，ε p ＝ε m ，
Because the soil depth of the test prototype is 3m and the soil depth of the test model is 1m, the soil depth of the test prototype is 1m p ＝3l m And then t is obtained p ＝9t m ；
By
Can obtain the product
Is prepared from p ＝3l m ，t p ＝9t m Can be obtained by D Wp ＝D Wm ；
T is obtained from constant temperature p ＝T m ，L p ＝L m ；
By number of similarity criteria
The following can be obtained:
By number of similarity criteria
Can obtain the product
Is prepared from p ＝3l m ，t p ＝9t m ，θ p ＝θ m Available k p ＝1/3k m ；
The physical quantities of the test model obtained according to the above formulas and the similarity criteria are shown in table 2, and a soil heat-moisture coupling test model is established according to the physical quantities in table 2 to study the heat-moisture migration rule of prototype soil.
TABLE 2 test model parameter values
Nothing in this specification is said to apply to the prior art.
Claims (1)
1. A method for establishing a similarity criterion of a soil thermal-wet coupling model test is characterized in that the method uses a non-linear relation between soil thermal physical property parameters, and utilizes a similarity conversion method to derive the similarity criterion between a soil thermal-wet coupling test model and a test prototype based on a similar third theorem design idea; the method comprises the following steps:
s1, under the action of heat-moisture coupling, a soil vertical one-dimensional water motion basic equation is expressed as a formula (1):
in the formula: d T Is the water diffusion coefficient under the action of temperature difference, D W Is the water and water vapor diffusion coefficient, theta is the soil water content, T is the time, T is the temperature, k is the soil water conductivity, and z is the soil depth;
under the effect of heat-moisture coupling, the heat transfer basic equation of soil can be expressed as follows:
in the formula: c V Is the soil thermal capacity, lambda is the soil thermal conductivity, L is the water evaporation latent heat, D W/V Thermal diffusivity due to moisture movement;
wherein the thermal conductivity of the soil is lambda and the thermal capacity of the soil is C V The functional relation with the soil moisture content theta satisfies the formulas (3) and (4):
C V ＝θ+Dε+E (4)
in the formula: A. b, C, D and E are fitting constants, and epsilon is the porosity of the soil;
water and water vapor diffusion coefficient D W The empirical formula of (2) is formula (5), and the water diffusion coefficient D under the action of temperature difference T Is the formula (6):
D W ＝0.0004e 0.14611θ (5)
D T ＝6×10 -16 T 5.9146 (6)
s2, deducing a similarity criterion based on a similarity transformation method; defining the similarity transformation of each parameter of the test prototype and the test model in the formulas (1) to (4) to meet the formula (7), namely the corresponding parameters are proportional;
wherein p represents a physical quantity of a prototype; m represents a physical quantity of the test model; k represents the contraction ratio of the corresponding coefficients of the test prototype and the test modelIn which K is A 、K B 、K C 、K D 、K E Is the scaling of the corresponding fitting constants in formula (3) and formula (4); k θ The shrinkage ratio of the water content of the soil is,
is the water diffusion coefficient contraction ratio under the action of temperature difference,
is the water and water vapor diffusion coefficient scaling, K L In order to reduce the latent heat of water evaporation,
thermal diffusivity shrinkage caused by moisture movement, K l In geometric scale, K t To scale time, K T Is a temperature scaling, K k Is the soil water conductivity scaling, K ε The shrinkage ratio of the porosity of the soil is adopted;
the basic equations of motion of moisture and heat transfer of the test prototype obtained by respectively substituting the formulas (3), (4) and (7) into the formulas (1) and (2) are respectively the formulas (8) and (9), and the basic equations of motion of moisture and heat transfer of the test model are the formulas (10) and (11):
according to a similar third theorem, the basic equation of water movement and the basic equation of heat transfer between the test prototype and the test model are correspondingly equal, i.e. equations (8) and (10) are equal, and equations (9) and (11) are equal, so that 9 similar indexes of equation (12) are obtained:
further processing the above 9 similarity index formulas to obtain the following 9 similarity criterion numbers pi 1 -π 9 ：
The derivation result shows that 9 similarity criteria between the test prototype and the test model are established according to the relationship between the similarity criteria numbers between the test model and the physical quantities of the test prototype; in the practical application process, if several similar criterion numbers in the test model are known, other similar criterion numbers of the test model can be obtained.
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