CN111380906A - Refinement method for converting phase change latent heat of frozen soil into equivalent specific heat - Google Patents

Refinement method for converting phase change latent heat of frozen soil into equivalent specific heat Download PDF

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CN111380906A
CN111380906A CN202010234198.5A CN202010234198A CN111380906A CN 111380906 A CN111380906 A CN 111380906A CN 202010234198 A CN202010234198 A CN 202010234198A CN 111380906 A CN111380906 A CN 111380906A
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陈之祥
郭晓霞
邵龙潭
李顺群
高凌霞
田筱剑
张翻
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Abstract

A refinement method for converting the phase change latent heat of frozen soil into equivalent specific heat is characterized in that the change rate of the unfrozen water content and the phase change latent heat of the frozen soil are determined by a calculus method through fitting a change curve of the unfrozen water content along with the temperature of the frozen soil; on the basis, a curve equation of the transformation latent heat to specific heat to phase change along with the temperature change is determined by assuming that a transformation latent heat to specific heat curve of the phase change is parallel to a change curve of the unfrozen water content along with the frozen soil temperature, and then the transformation latent heat to specific heat of any temperature point is determined. The method considers the correlation between the latent heat of phase change of the frozen soil and the content of unfrozen water, reflects the evolution trend of the phase change heat along with the negative temperature, reduces the test quantity of the soil samples at the intermediate temperature point, and improves the consistency evolution relation between the latent heat of phase change and the specific heat. The actual measurement and calculation show that the prediction accuracy of the calculation method is improved by 45.72% on average and can be improved by 189.7% to the maximum extent compared with the literature method. The most real equivalent specific heat value can be obtained to the maximum extent by improving the precision, and a basis is provided for the refined prediction of the frozen soil temperature field.

Description

Refinement method for converting phase change latent heat of frozen soil into equivalent specific heat
Technical Field
The invention belongs to the field of determination of calculation parameters of a frozen soil temperature field, and relates to a fine method for converting phase change latent heat of frozen soil into equivalent specific heat, which can be used for converting the phase change latent heat of the frozen soil into equivalent specific heat of a soil body.
Background
The heat propagation form in frozen earth is divided into sensible heat and latent heat. Sensible heat refers to the heat required by the temperature rise or decrease of frozen soil without phase change; for example, the soil body at 10 ℃ is raised to 15 ℃. Latent heat refers to the heat required for the melting of ice in frozen earth or the freezing of liquid water. In most cases, particularly under negative temperature conditions, both sensible and latent heat transfer modes exist in frozen earth. Influenced by the nonlinear change of the content of unfrozen water in the freezing and thawing process of the soil body, and the latent heat of phase change is changed along with the nonlinear change of the unfrozen water. Therefore, sensible heat and latent heat exist simultaneously in the process of lowering or raising the temperature of the frozen soil.
Generally, the specific heat of the mixture can be determined by adopting a mass weighted average calculation method, so that the specific heat of the frozen soil mixture can be directly determined on the premise that the compositions of various phases of the frozen soil and the specific heat value thereof are known. And sensible heat and latent heat in the frozen soil can be separately considered through latent heat calculation. In the conventional temperature field calculation software, only one latent heat release interval can be set, and the latent heat is evenly distributed to each section in the interval, which is inconsistent with the non-linear change of the unfrozen water content of the frozen soil with the negative temperature. Therefore, some studies try to convert the latent heat of the frozen soil into equivalent specific heat, and then substitute the equivalent specific heat into temperature field simulation software for calculation. For example, patent No. 2018105205434 discloses a method for calculating the phase change latent heat of frozen earth into equivalent specific heat, which is to divide the latent heat in a certain temperature interval by the length of the temperature interval as the average specific heat of the temperature interval, and then to take the weighted calculation value of the average specific heat of two adjacent intervals as the specific heat of the temperature points of the two adjacent intervals. The method is characterized in that the heat in the interval is averaged and does not accord with the nonlinear change of latent heat along with the temperature, and two unequal specific heat values exist at the temperature points of adjacent intervals, so that certain error exists in the calculation. Therefore, a refinement method for converting the phase change latent heat of the frozen soil into the equivalent specific heat is needed to be provided, so as to meet the actual phase change latent heat change of the frozen soil and improve the prediction precision of the temperature field.
Disclosure of Invention
The invention aims to provide a refining method for converting phase change latent heat of frozen soil into equivalent specific heat, so as to be beneficial to determining the equivalent specific heat of the frozen soil.
In order to achieve the purpose, the invention provides a refining method for converting the phase change latent heat of frozen soil into equivalent specific heat, which comprises the following steps:
1) fitting the mass percent content W of unfrozen water of frozen soiluThe change curve along with the frozen soil temperature T is in the form of a formula (1), and the formula (1) is as follows:
Wu＝aebT+K (1)
in the formula, WuIs the content of unfrozen water of frozen soil in percentage by mass; a. b and K are fitting coefficients; e is a natural constant; t is the frozen soil temperature in units of;
2) obtaining the mass percent content W of the unfrozen water by respectively calculating the derivative of the frozen soil temperature T at two ends of the formula (1)uRate of change W with frozen soil temperature Tu', i.e.:
W′u＝abebT(2)
in the formula, Wu' is the content W of unfrozen water in mass percentuRate of change with frozen soil temperature T; a. b is a fitting coefficient; e is a natural constant; t is the frozen soil temperature in units of;
3) the change dQ of the latent heat of the frozen soil is expressed by a formula (3), wherein the formula (3) is as follows:
Figure RE-GDA0002489092570000021
in the formula, dQ is the variation of the latent heat of the frozen soil, and the unit is kJ/kg; l is phase change heat of water, and the unit is kJ/kg; rhodIs the dry density of the soil sample in kg/m3(ii) a Rho is the density of the soil sample and has the unit of kg/m3(ii) a a. b is a fitting coefficient; e is a natural constant; dT is the temperature variation of the frozen soil, and the unit is;
4) the negative temperature interval [ Tn～Tj]Total amount of latent heat Q in segmentj～nExpressed as:
Figure RE-GDA0002489092570000022
in the formula, Qj～nIs a negative temperature interval [ Tn～Tj]The total latent heat in the section is kJ/kg, where 0 > Tj＞Tn(ii) a L is phase transition heat of water, kJ/kg; rhodIs the dry density of the soil sample in kg/m3(ii) a Rho is the density of the soil sample and has the unit of kg/m3(ii) a a. b is a fitting coefficient; t isn、TjIs a negative temperature interval [ Tn～Tj]The boundary temperature of (c); e is a natural constant; dT is the frozen soil temperature variation in units of ℃.
5) Arranged in space with a curve CLThe mass percent of the water in the frozen soil is WuThe change curves along with the frozen soil temperature T are parallel, then the curve CLExpressed as:
CL＝aebT+I (5)
in the formula, CLIs a curve in space; a. b is a fitting coefficient; e is a natural constant; i is a fitting constant; t is the frozen soil temperature in units of;
6) let equation (6) hold, equation (6) is:
Figure RE-GDA0002489092570000031
in the formula, Tn、TjIs a negative temperature interval [ Tn～Tj]In ° C, where 0 > Tj＞ Tn(ii) a a. b is a fitting coefficient; e is a natural constant; i is a fitting constant; t is the frozen soil temperature in units of; dT is the temperature variation of the frozen soil, and the unit is;
7) solving the value of I by using a formula (6), substituting I into a formula (5), and respectively enabling T to be TiWherein T isn＜Ti＜TjThen temperature interval [ Tn～Tj]Temperature point T in zoneiOrdinate C ofL(i)Can be determined, then CL(i)I.e. the temperature point TiThe phase change of (a) induces a latent heat equivalent specific heat value.
8) Frozen earth at temperature point TiThe equivalent specific heat C at that time is calculated by the formula (7), and the formula (7) is:
C＝CL(i)+Csms+Cimi+Cwmw(7)
wherein C is frozen soil at temperature point TiThe equivalent specific heat in kJ/(kg. DEG C); cL(i)Is a temperature point TiThe phase change of (A) induces a latent heat equivalent specific heat value in kJ/(kg. DEG C); cs、Ci、CwThe specific heat values of soil particles, ice and water are respectively expressed in kJ/(kg DEG C); w is as、wi、wwRespectively frozen earth at temperature point TiThe mass percent ratio content of soil particles, ice and unfrozen water is expressed in unit.
According to the method, the true specific heat of the frozen soil can be converted into the equivalent specific heat of the frozen soil, and a foundation is laid for calculating the temperature field of the frozen soil.
The invention has the beneficial effects that: the provided method takes the correlation between the phase change latent heat of the frozen soil and the content of unfrozen water into consideration, reflects the evolution trend of the phase change heat along with negative temperature, reduces the test quantity of soil samples at intermediate temperature points, and improves the consistency evolution relation between the phase change latent heat and the specific heat. The actual measurement and calculation show that the prediction accuracy of the calculation method is improved by 45.72% on average compared with the literature method, and can be improved by 189.7% to the maximum extent. The most real equivalent specific heat value can be obtained to the maximum extent by improving the precision, and a basis is provided for the refined prediction of the frozen soil temperature field.
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FIG. 1 is a graph of temperature versus various parameters.
Detailed Description
A refinement method for converting the phase change latent heat of the frozen soil into the equivalent specific heat of the invention is described with reference to fig. 1.
The invention discloses a refinement method principle for converting phase change latent heat of frozen soil into equivalent specific heat, which comprises the following steps: determining the change rate of the unfrozen water content and the phase change latent heat of the frozen soil by a calculus method by fitting a change curve of the unfrozen water content along with the temperature of the frozen soil; on the basis, a curve equation of the transformation latent heat to specific heat to phase change along with the temperature change is determined by assuming that a transformation latent heat to specific heat curve of the phase change is parallel to a change curve of the unfrozen water content along with the frozen soil temperature, and then the transformation latent heat to specific heat of any temperature point is determined.
The invention provides a calculation method for converting phase change latent heat of frozen soil into equivalent specific heat, which comprises the following steps:
1) fitting the mass percent content W of unfrozen water of frozen soiluThe variation curve with the frozen soil temperature T is in the form of formula (8), as shown in FIG. 1, formula (8) is:
Wu＝aebT+K (8)
in the formula, WuIs the content of unfrozen water of frozen soil in percentage by mass; a. b and K are fitting coefficients; e is a natural constant; t is the frozen soil temperature in units of;
2) the derivative of the frozen soil temperature T is respectively obtained at two ends of the formula (8), and the mass percent content W of the unfrozen water can be obtaineduRate of change W with frozen soil temperature Tu', i.e. that
W′u＝abebT(9)
In the formula, Wu' is the content W of unfrozen water in mass percentuRate of change with frozen soil temperature T; a. b is a fitting coefficient; e is natureA constant; t is the frozen soil temperature in units of;
3) the change dQ of the latent heat of the frozen soil can be expressed by the formula (10), and the formula (10) is:
Figure RE-GDA0002489092570000051
in the formula, dQ is the variation of the latent heat of the frozen soil, and the unit is kJ/kg; l is phase change heat of water, and the unit is kJ/kg; rhodIs the dry density of the soil sample in kg/m3(ii) a Rho is the density of the soil sample and has the unit of kg/m3(ii) a a. b is a fitting coefficient; e is a natural constant; dT is the temperature variation of the frozen soil, and the unit is;
4) the negative temperature interval [ Tn～Tj](0＞Tj＞Tn) Total amount of latent heat Q in segmentj～nExpressed as:
Figure RE-GDA0002489092570000052
in the formula, Qj～nIs a negative temperature interval [ Tn～Tj](0＞Tj＞Tn) The total latent heat in the section is kJ/kg; l is phase transition heat of water, kJ/kg; rhodIs the dry density of the soil sample in kg/m3(ii) a Rho is the density of the soil sample and has the unit of kg/m3(ii) a a. b is a fitting coefficient; t isn、TjIs a negative temperature interval [ Tn～Tj](0＞Tj＞Tn) The boundary temperature of (c); e is a natural constant; dT is the frozen soil temperature variation in units of ℃.
5) Arranged in space with a curve CLThe mass percent of the water in the frozen soil is WuThe curves are parallel with the change of the frozen soil temperature T, and as shown in figure 1, the curve C isLCan be expressed as:
CL＝aebT+I (12)
in the formula, CLIs a curve in space; a. b is a fitting coefficient; e is a natural constant; i is a fitting constant; t is the frozen soil temperature in units of;
6) let equation (13) hold, equation (13) is:
Figure RE-GDA0002489092570000053
in the formula, Tn、TjIs a negative temperature interval [ Tn～Tj](0＞Tj＞Tn) The boundary temperature of (c); a. b is a fitting coefficient; e is a natural constant; i is a fitting constant; t is the frozen soil temperature in units of; dT is the temperature variation of the frozen soil, and the unit is;
7) solving the value of I by using a formula (13), substituting I into a formula (12) and respectively enabling T to be Ti(Tn＜Ti＜Tj) Then temperature interval [ Tn～Tj]Temperature point T in zoneiOrdinate C ofL(i)Can be determined, then CL(i)I.e. the temperature point TiThe phase change of (a) induces a latent heat equivalent specific heat value.
8) Frozen earth at temperature point TiThe equivalent specific heat C at that time can be calculated by equation (14), equation (14) being:
C＝CL(i)+Csms+Cimi+Cwmw(14)
wherein C is frozen soil at temperature point TiThe equivalent specific heat in kJ/(kg. DEG C); cL(i)Is a temperature point TiThe phase change of (A) induces a latent heat equivalent specific heat value in kJ/(kg. DEG C); cs、Ci、CwThe specific heat values of soil particles, ice and water are respectively expressed in kJ/(kg DEG C); w is as、wi、wwRespectively frozen earth at temperature point TiThe mass percent ratio content of soil particles, ice and unfrozen water is expressed in unit. According to the method, the true specific heat of the frozen soil can be converted into the equivalent specific heat of the frozen soil, and a foundation is laid for calculating the temperature field of the frozen soil.
Example (b): the dry density of the sample was 1.8g/cm using the method of the present application, the mass weighted average method and the method provided by the conventional transformation method (patent 2018105205434)3，dsIs 2.72The specific heat value of the saturated mealy clay is determined, and the calculation result is shown in table 1.
TABLE 1 calculation of the conversion of the latent heat of phase change of certain frozen soils into equivalent specific heat
Figure RE-GDA0002489092570000061
Calculated value C by comparison with the conventional transformation method in Table 1kAnd the calculation value of the refinement method for converting the phase change latent heat of the frozen soil into the equivalent specific heat is found to be improved by 45.72 percent and the maximum prediction precision is improved by 189.7 percent compared with the average prediction precision of the conventional method at the temperature of between 5 ℃ below zero and 20 ℃ below zero.
The above description is only for the purpose of illustration in conjunction with the present calculation process, and it will be apparent to those skilled in the art that various changes and modifications may be made in the present invention. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims (1)

1. A refinement method for converting phase change latent heat of frozen soil into equivalent specific heat is characterized by comprising the following steps:
1) fitting the mass percent content W of unfrozen water of frozen soiluThe change curve along with the frozen soil temperature T is in the form of a formula (1), and the formula (1) is as follows:
Wu＝aebT+K (1)
in the formula, WuIs the content of unfrozen water of frozen soil in percentage by mass; a. b and K are fitting coefficients; e is a natural constant; t is the frozen soil temperature in units of;
2) obtaining the mass percent content W of the unfrozen water by respectively calculating the derivative of the frozen soil temperature T at two ends of the formula (1)uRate of change W with frozen soil temperature Tu', i.e.:
W'u＝abebT(2)
in the formula, Wu' is the content W of unfrozen water in mass percentuRate of change with frozen soil temperature T; a. b is a fitting coefficient; e is a natural constant; t is the temperature of the frozen soilThe position is as follows;
3) the change dQ of the latent heat of the frozen soil is expressed by a formula (3), wherein the formula (3) is as follows:
Figure FDA0002430418260000011
in the formula, dQ is the variation of the latent heat of the frozen soil, and the unit is kJ/kg; l is phase change heat of water, and the unit is kJ/kg; rhodIs the dry density of the soil sample in kg/m3(ii) a Rho is the density of the soil sample and has the unit of kg/m3(ii) a a. b is a fitting coefficient; e is a natural constant; dT is the temperature variation of the frozen soil, and the unit is;
4) the negative temperature interval [ Tn～Tj]Total amount of latent heat Q in segmentj～nExpressed as:
Figure FDA0002430418260000012
in the formula, Qj～nIs a negative temperature interval [ Tn～Tj]The total latent heat in the section is kJ/kg, where 0 > Tj＞Tn(ii) a L is phase transition heat of water, kJ/kg; rhodIs the dry density of the soil sample in kg/m3(ii) a Rho is the density of the soil sample and has the unit of kg/m3(ii) a a. b is a fitting coefficient; t isn、TjIs a negative temperature interval [ Tn～Tj]The boundary temperature of (c); e is a natural constant; dT is the temperature variation of the frozen soil, and the unit is;
5) arranged in space with a curve CLThe mass percent of the water in the frozen soil is WuThe change curves along with the frozen soil temperature T are parallel, then the curve CLExpressed as:
CL＝aebT+I (5)
in the formula, CLIs a curve in space; a. b is a fitting coefficient; e is a natural constant; i is a fitting constant; t is the frozen soil temperature in units of;
6) let equation (6) hold, equation (6) is:
Figure FDA0002430418260000021
in the formula, Tn、TjIs a negative temperature interval [ Tn～Tj]In ° C, where 0 > Tj＞Tn(ii) a a. b is a fitting coefficient; e is a natural constant; i is a fitting constant; t is the frozen soil temperature in units of; dT is the temperature variation of the frozen soil, and the unit is;
7) solving the value of I by using a formula (6), substituting I into a formula (5), and respectively enabling T to be TiWherein T isn＜Ti＜TjThen temperature interval [ Tn～Tj]Temperature point T in zoneiOrdinate C ofL(i)Can be determined, then CL(i)I.e. the temperature point TiThe phase change of (a) induces a latent heat equivalent specific heat value;
8) frozen earth at temperature point TiThe equivalent specific heat C at that time is calculated by the formula (7), and the formula (7) is:
C＝CL(i)+Csms+Cimi+Cwmw(7)
wherein C is frozen soil at temperature point TiThe equivalent specific heat in kJ/(kg. DEG C); cL(i)Is a temperature point TiThe phase change of (A) induces a latent heat equivalent specific heat value in kJ/(kg. DEG C); cs、Ci、CwThe specific heat values of soil particles, ice and water are respectively expressed in kJ/(kg DEG C); w is as、wi、wwRespectively frozen earth at temperature point TiThe mass percent ratio content of soil particles, ice and unfrozen water is expressed in unit;
according to the method, the true specific heat of the frozen soil can be converted into the equivalent specific heat of the frozen soil, and the temperature field of the frozen soil can be further researched.
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