CN-121997561-A - Moon surface heat flow inversion method based on three-layer steady-state heat conduction model

CN121997561ACN 121997561 ACN121997561 ACN 121997561ACN-121997561-A

Abstract

The invention discloses a moon surface heat flow inversion method based on a three-layer steady-state heat conduction model, which comprises the steps of 1, calculating the total mass heat generation rate by using the specific heat generation rate and the mass heat generation rate of radioactive elements in a moon, 2, constructing the three-layer steady-state heat conduction model comprising a giant weathering layer, a moon shell and a moon veil, setting the condition of boundary and heat flow continuity, 3, solving the coefficient of a heat conduction equation of the three-layer steady-state heat conduction model to obtain a temperature profile and a temperature gradient, 4, calculating the brittle strength and the plastic strength envelope by using the temperature profile, calculating the predicted bending moment by using the envelope integral, 5, calculating the target bending moment by using the effective elastic thickness of a rock ring, 6, continuously adjusting the thickness of the giant weathering layer, reducing the deviation of the predicted bending moment and the target bending moment to obtain a converged temperature structure, 7, calculating the surface temperature gradient from the converged temperature structure, and 8, and calculating the moon surface heat flow according to the surface temperature gradient. The invention improves the estimation precision of the moon surface heat flow.

Inventors

ZHANG WENSONG
YE MAO
WANG YONG
LI KEZHAO
CHEN LIN
LIANG NAN

Assignees

河南省科学院空天信息研究所
河南省科学院
河南理工大学

Dates

Publication Date: 20260508
Application Date: 20251229

Claims (4)

1. The moon surface heat flow inversion method based on the three-layer steady-state heat conduction model is characterized by comprising the following steps of: step 1, taking radioactive elements as radioactive heat sources, and obtaining the total mass heat production rate according to the specific heat production rate and the mass heat production rate of the radioactive elements Th, U and K in the lunar shell and the lunar valance ; Step 2, constructing a three-layer steady-state heat conduction model, and setting boundary and heat flow continuity conditions, wherein the specific process is as follows: step 2.1, dividing a lunar near-surface area into a giant weathering layer, a lunar shell and a lunar veil, and constructing a three-layer steady-state heat conduction model, wherein a heat conduction equation is expressed as follows: Wherein: 、、 And Respectively representing the temperature of the giant weathering layer, the moon shell, the moon curtain and the moon surface, 253K; 、 And Respectively represents the heat generated by the giant weathering layer, the moon shell and the moon mantle in unit volume, and 、 And The thermal conductivity density and the total mass heat generation rate corresponding to the giant weathering layer, the lunar shell and the lunar veil respectively Is a product of (2); 、 And Respectively representing the heat conductivity of the giant weathering layer, the moon shell and the moon curtain; 、、、 And Are all coefficients; 、 And The thickness of the giant weathering layer, the thickness of the moon shell and the thickness of the moon curtain are respectively shown; Representing a depth vertically downward from the moon surface; Step 2.2, setting the boundary and heat flow continuity conditions of the three-layer steady-state heat conduction model, wherein the conditions comprise conditions that the heat flux and the temperature at the boundary of the giant weathering layer and the lunar shell need to be met, conditions that the heat flux and the temperature at the boundary of the lunar shell and the lunar veil need to be met, and conditions that the temperature at the boundary of the lunar veil and the lunar core need to be met; Step 3, taking the temperature of the lunar surface, the boundary temperature of the lunar veil and the lunar nucleus as boundary conditions for solving the heat conduction equation, and solving coefficients 、、、 And Substituting it into the heat conduction equation Solving the temperature structural parameters of the giant weathering layer, the lunar shell and the lunar veil, including the temperature profile And temperature gradient ; And 4, calculating the brittle strength and the plastic strength envelope by using the temperature profile, wherein the concrete process comprises the following steps: Step 4.1, brittle Strength of rock ring And plastic strength Expressed as: Wherein: Is the density of the rock ring; gravitational acceleration; Is the depth vertically downward from the moon surface; Is the strain rate; is the grain size of the rock ring; is a gas constant; Is a temperature profile; 、、 And Are all rheological parameters; Step 4.2, for brittle Strength And plastic strength Envelope is performed, expressed as: Step 4.3, utilizing intensity envelope integration according to Calculating the predicted bending moment Expressed as: Wherein: represents the neutral plane depth; Step 5, target bending rigidity Expressed as: Wherein: And Respectively representing the elastic modulus and poisson ratio; Representing the effective elastic thickness of the rock ring; Then the target bending moment Expressed as: Wherein: representing the curvature, and taking the value of 1.0 multiplied by 10 -9 ; step6, predicting bending moment Bending moment with target Comparing, continuously adjusting the thickness of the giant weathering layer Thereby reducing And Obtaining a converged temperature structure; step 7, obtaining the surface temperature gradient from the converged temperature structure, namely, converging the temperature profile Expressed as: The temperature gradient is expressed as: Step 8, under the constraint that the boundary and the heat flow continuity condition of the three-layer steady-state heat conduction model are met, the heat flow of the lunar surface is carried out Expressed as: Wherein: Representing the thermal conductivity of the giant weathered layer.
2. The lunar surface heat flow inversion method based on three-layer steady state heat conduction model according to claim 1, wherein the total mass heat generation rate of step1 The calculation formula of (2) is as follows: Wherein: 、、 And The specific heat generation rates of the radioactive elements 238 U、 235 U、 232 Th and 40 K are respectively shown; 、、 And The mass heat generation rates of the radioactive elements 238 U、 235 U、 232 Th and 40 K are shown, respectively.
3. The lunar surface heat flow inversion method based on the three-layer steady-state heat conduction model as claimed in claim 1, wherein the specific process of the step 2.2 is as follows: 1) At the boundary of the giant weathering layer and the lunar shell: 1.1 Conditions that the heat flux needs to meet are expressed as: 1.2 Conditions that the temperature needs to meet are expressed as: 2) At the boundary of the moon shell and the moon veil: 2.1 Conditions that the heat flux needs to meet are expressed as: 2.2 Conditions that the temperature needs to meet are expressed as: 3) At the boundary of the moon curtain and the moon core, the conditions that the temperature needs to satisfy are expressed as: Wherein: the boundary temperature between the moon curtain and the moon core is 1900K.
4. The lunar surface heat flow inversion method based on the three-layer steady-state heat conduction model according to claim 3, wherein the specific process of the step 3 is as follows: step 3.1, formula 、、、 And Written in matrix form, expressed as: Wherein: 、、、 And Expressed as: Step 3.2, elimination of coefficients And Expressed as: Step 3.3, solving the coefficients Expressed as: Step 3.4, solving the coefficients And Expressed as: step 3.5, solving the coefficients And Expressed as: By solving for 、、、 And Substituting it into the heat conduction equation Solving the temperature structural parameters of the giant weathering layer, the lunar shell and the lunar veil in the moon, including the temperature profile ) And temperature gradient 。

Description

Moon surface heat flow inversion method based on three-layer steady-state heat conduction model Technical Field The invention relates to planetary science and geophysics, in particular to a moon surface heat flow inversion method based on a three-layer steady-state heat conduction model. Background The current method for directly acquiring the heat flow on the lunar surface mainly depends on limited actual measuring points of an Apollo task, the data are concentrated in a lunar frontal storm ocean area and cannot represent global characteristics, the current heat flow estimation is mostly based on an elastic thickness or radioactive element distribution model, the heat insulation effect of a surface giant weathering layer (Megaregolith) and the existence of larger uncertainty of the elastic thickness of a rock ring are ignored, the giant weathering layer has the characteristics of low density, low heat conductivity and high porosity, the heat resistance of the giant weathering layer is as high as 1-km at the lunar altitude, the heat resistance of the giant weathering layer obviously influences the heat flow conduction on the surface, however, the heat flow estimation result is greatly deviated because the heat insulation influence of the giant weathering layer and the uncertainty of the elastic thickness of the rock ring are not considered in the current heat flow estimation model. Therefore, how to introduce the thickness of the giant weathering layer and the effective elastic thickness of the rock ring to realize effective constraint on the heat flow on the moon surface is a key problem in the current planetary heat evolution research. Disclosure of Invention The invention aims to provide a moon surface heat flow inversion method based on a three-layer steady-state heat conduction model, which improves the estimation accuracy of moon surface heat flow by introducing the thickness of a giant weathering layer and the effective elastic thickness of a rock ring. The invention is realized by the following technical scheme: A moon surface heat flow inversion method based on a three-layer steady-state heat conduction model comprises the following steps: step 1, taking radioactive elements as radioactive heat sources, and obtaining the total mass heat production rate according to the specific heat production rate and the mass heat production rate of the radioactive elements Th, U and K in the lunar shell and the lunar valance ; Step 2, constructing a three-layer steady-state heat conduction model, and setting boundary and heat flow continuity conditions, wherein the specific process is as follows: step 2.1, dividing a lunar near-surface area into a giant weathering layer, a lunar shell and a lunar veil, and constructing a three-layer steady-state heat conduction model, wherein a heat conduction equation is expressed as follows: Wherein: 、、 And Respectively representing the temperature of the giant weathering layer, the moon shell, the moon curtain and the moon surface,253K;、 And Respectively represents the heat generated by the giant weathering layer, the moon shell and the moon mantle in unit volume, and、AndThe thermal conductivity density and the total mass heat generation rate corresponding to the giant weathering layer, the lunar shell and the lunar veil respectivelyIs a product of (2);、 And Respectively representing the heat conductivity of the giant weathering layer, the moon shell and the moon curtain;、、、 And Are all coefficients;、 And The thickness of the giant weathering layer, the thickness of the moon shell and the thickness of the moon curtain are respectively shown; Representing a depth vertically downward from the moon surface; Step 2.2, setting the boundary and heat flow continuity conditions of the three-layer steady-state heat conduction model, wherein the conditions comprise conditions that the heat flux and the temperature at the boundary of the giant weathering layer and the lunar shell need to be met, conditions that the heat flux and the temperature at the boundary of the lunar shell and the lunar veil need to be met, and conditions that the temperature at the boundary of the lunar veil and the lunar core need to be met; Step 3, taking the temperature of the lunar surface, the boundary temperature of the lunar veil and the lunar nucleus as boundary conditions for solving the heat conduction equation, and solving coefficients 、、、AndSubstituting it into the heat conduction equationSolving the temperature structural parameters of the giant weathering layer, the lunar shell and the lunar veil, including the temperature profileAnd temperature gradient; And 4, calculating the brittle strength and the plastic strength envelope by using the temperature profile, wherein the concrete process comprises the following steps: Step 4.1, brittle Strength of rock ring And plastic strengthExpressed as: Wherein: Is the density of the rock ring; gravitational acceleration; Is the depth vertically downward fr