CN112199910A - Porous elastic medium heat-flow-solid coupling transient response calculation method and device - Google Patents

Porous elastic medium heat-flow-solid coupling transient response calculation method and device Download PDF

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CN112199910A
CN112199910A CN202011183580.4A CN202011183580A CN112199910A CN 112199910 A CN112199910 A CN 112199910A CN 202011183580 A CN202011183580 A CN 202011183580A CN 112199910 A CN112199910 A CN 112199910A
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杨连枝
何蕃民
朱维耀
宋智勇
樊冰建
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University of Science and Technology Beijing USTB
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Abstract

The disclosure relates to the field of transient response analysis of porous elastic media, and in particular relates to a method and a device for calculating thermal-flow-solid coupling transient response of a porous elastic medium. The method comprises the following steps: acquiring related parameters of the porous elastic medium; establishing a porous elastic medium heat-flow-solid coupling form according to the related parameters of the porous elastic medium; constructing a single-layer porous elastic medium solution form on a Laplace domain or a solution form on any one layer of a multi-layer porous elastic medium based on an eigenvalue theory and a Stroh-like method; obtaining general solutions of all physical quantity Laplace domains of the porous elastic medium based on a propagation matrix method, and determining special solutions of all the physical quantity Laplace domains according to boundary conditions; and acquiring the thermal-fluid-solid coupling transient response of the porous elastic medium based on a Laplace numerical value inverse transformation method. By solving the thermal-fluid-solid coupling transient response of the elastic medium by adopting an analytic method, the calculation amount can be reduced and the calculation speed can be increased.

Description

Porous elastic medium heat-flow-solid coupling transient response calculation method and device
Technical Field
The disclosure relates to the field of transient response analysis of porous elastic media, and in particular relates to a method and a device for calculating thermal-flow-solid coupling transient response of a porous elastic medium.
Background
The seepage effect of the porous medium cannot be ignored in engineering practice, and the influence of the temperature change on the engineering stability is also widely regarded. Therefore, the thermal-fluid-solid coupling effect must be considered when engineering the porous medium transient response problem. However, no effective method for calculating the transient response of the layered saturated porous elastic medium under the heat-flow-solid coupling exists at present.
Disclosure of Invention
In view of the above problems in the prior art, the present disclosure provides a method and an apparatus for calculating a transient response of a thermal-fluid-solid coupling of a porous elastic medium.
In one aspect, an embodiment of the present disclosure provides a method for calculating a transient response of a thermal-fluid-solid coupling of a porous elastic medium, where the method includes:
acquiring relevant parameters of the porous elastic medium, wherein the parameters comprise geometric parameters, temperature field parameters, seepage field parameters, stress field and seepage field coupling parameters and stress field and temperature field coupling parameters of the porous elastic medium;
establishing a porous elastic medium heat-flow-solid coupling form according to the related parameters of the porous elastic medium;
constructing a single-layer porous elastic medium solution form on a Laplace domain or a solution form on any one layer of a multi-layer porous elastic medium based on an eigenvalue theory and a Stroh-like method;
obtaining general solutions of all physical quantity Laplace domains of the porous elastic medium based on a propagation matrix method, and determining specific solutions of all physical quantity Laplace domains according to boundary conditions, wherein the physical quantities comprise temperature, pressure, strain and displacement of the porous elastic medium;
and acquiring the thermal-fluid-solid coupling transient response of the porous elastic medium based on a Laplace numerical value inverse transformation method.
Optionally, the establishing a porous elastic medium thermal-fluid-solid coupling form according to the porous elastic medium related parameters includes: constructing a stress field equation, a temperature field equation and a seepage field equation of the porous elastic medium according to the related parameters of the porous elastic medium;
the stress field equation comprises a stress balance equation (1) and a constitutive equation set (2);
Figure BDA0002750844690000011
wherein, the expression of the pressure term P in the equation set (2) is formula (3);
P＝Mξ-α1Mε11-α2Mε22-α3Mε33+βmMθ (3)
in the above-mentioned formula, the compound of formula,
Figure BDA0002750844690000012
is expressed in relation to a physical quantity σijCalculating a partial derivative of a j axis; sigmaijStress in the direction of the j axis on the plane perpendicular to the i axis, N/m2；εijThe strain in the direction of the j axis on the surface vertical to the i axis is consistent; u. ofiIs the displacement in the plane perpendicular to the i-axis, m; cijThe elastic coefficient in the direction of the j axis on the plane perpendicular to the i axis is N/m2；C44，C55，C66Is shear modulus, N/m2；αiIs the Biot consolidation coefficient on the plane perpendicular to the i-axis, N/(m)2·K)；βiIs the surface stress-temperature coefficient in the plane perpendicular to the i-axis, N/(m)2K); p is pressure, Pa; theta is the temperature, K; m is Biot modulus, N/M2；βmIs the bulk strain-temperature coefficient, 1/K; xi is water content,%; i is 1, 2, 3; j is 1, 2, 3;
the temperature field equation comprises a heat conduction equation (4) and a heat balance equation (5);
Figure BDA0002750844690000021
Figure BDA0002750844690000022
in the above formula, qiHeat flux in the plane perpendicular to the i-axis, W/m2(ii) a Theta is the temperature, K;
Figure BDA0002750844690000023
solving a partial derivative on an x axis for theta; lambda [ alpha ]ijW/(m) is a coefficient of thermal conductivity in the direction of the j axis on a plane perpendicular to the i axis2K); t is time, s;
Figure BDA0002750844690000024
is the second derivative on the x-axis; cθIs the thermal diffusion coefficient, m2·s，cθ＝φρfcf+(1-φ)ρscsWherein, phi is the porosity of the medium,%; rhofFluid density, kg/m3；cfIs the specific heat capacity of the fluid, J/(kg.K); rhosAs the density of the matrix, kg/m3；csThe specific heat capacity of the matrix is J/(kg. K); i is 1, 2, 3; j is 1, 2, 3;
the seepage field equation comprises a motion equation (6) and a mass conservation equation (7);
Figure BDA0002750844690000025
Figure BDA0002750844690000026
in the above formula, viIs the seepage velocity on the plane perpendicular to the i axis, m/s; k is a radical ofijIn the direction of the j axis on the plane perpendicular to the i axisConsistent permeability coefficient, m/s; g is the acceleration of gravity, m/s2(ii) a Xi is water content,%; i is 1, 2, 3; j is 1, 2, 3.
Optionally, the constructing a form of a single-layer porous elastic medium solution on the Laplace domain or a form of a solution on any one layer of a multi-layer porous elastic medium based on eigenvalue theory and a Stroh-like method includes:
performing Laplace transformation on the formulas (5) and (7) to obtain formulas (8) and (9) respectively;
Figure BDA0002750844690000027
Figure BDA0002750844690000028
in the above formula, the superscript represents a physical quantity on the Laplace domain, and w represents a corresponding quantity of time t converted to the Laplace domain on the time domain;
according to the boundary condition form of the four simply-supported side surfaces of the three-dimensional layered medium, the general solution form of the nth layer porous elastic medium meeting the boundary condition form is obtained as follows:
Figure BDA0002750844690000029
Figure BDA00027508446900000210
Figure BDA00027508446900000211
wherein the content of the first and second substances,
Figure BDA0002750844690000031
m and δ are natural numbers in the fourier series expansion terms; a is1、a2、a3、a4、a5、b1、b2、b3、b4、b5、q1、q2、q3、q4、q5、q6、q7Respectively are unknowns to be solved; z is a radical ofnRepresenting the top surface coordinate value of the nth layer of medium; z represents a longitudinal coordinate value of a certain surface in the height direction in the nth layer medium; superscript-denotes an angle-independent physical quantity, z, over the Laplace domainn-1≤z≤znAnd n is a positive integer.
Optionally, the constructing a form of a single-layer porous elastic medium solution on the Laplace domain or a form of a solution on any one layer of a multi-layer porous elastic medium based on eigenvalue theory and a Stroh-like method further includes:
calling a coefficient matrix (13);
a＝[a1，a2，a3，a4，a5]T，b＝[b1，b2，b3，b4，b5]T (13)
substituting the equations (10) and (11) into the constitutive equation set (2) to obtain an equation (14);
b＝(-ET+sD)a (14)
substituting the equations (10) and (12) into the constitutive equation set (2) to obtain an equation (15);
Figure BDA0002750844690000032
substituting the formula (10) into the constitutive equation set (2) according to the formulas (11) to (14) to obtain a formula (16);
[Q+s(E-ET+Ω)+s2D]a＝0 (16)
in the formula (16), E, D, Q and Ω are in the form of a matrix composed of physical parameters; wherein Ω is of the form:
Figure BDA0002750844690000033
according to eigenvalue theory, s is used as the eigenvalue of N, η ═ a, b }TIntrinsic to NConstructing an equivalent relation (18) between the eigenvectors corresponding to the values and the expressions (14) and (16);
Nη＝sη，η＝{a，b}T (18)
wherein the content of the first and second substances,
Figure BDA0002750844690000034
the general form of physical quantity for constructing any nth layer is as follows:
Figure BDA0002750844690000035
wherein the content of the first and second substances,
Figure BDA0002750844690000036
a1-a10，b1-b10is and s1-s10A corresponding feature vector;
obtaining formula (21) from formula (19):
Figure BDA0002750844690000041
substituting equation (21) into equation (19) to obtain the solution of the nth layer of any layer
Figure BDA0002750844690000042
Wherein the content of the first and second substances,
Figure BDA0002750844690000043
optionally, a general solution of each physical quantity Laplace domain of the porous elastic medium is obtained based on a propagation matrix method, and the general solution is determined according to the edges
Determining special solutions of the Laplace domains of the physical quantities by boundary conditions, wherein the special solutions comprise:
obtaining formula (23) according to formula (22):
Figure BDA0002750844690000044
in the formula (I), the compound is shown in the specification,
Figure BDA0002750844690000045
hn＝zn-zn-1，Fn(hn) A transfer matrix being an nth layer;
obtaining formula (24) according to formula (22):
Figure BDA0002750844690000046
obtaining the solution of the outer surface of the Nth layer according to the principle that the pressure, the temperature and the displacement on the contact surface of the N-th layer and the N + 1-th layer are continuous
Figure BDA0002750844690000047
Wherein G is FN(hN)FN-1(hN-1)…F2(h2)F1(h1)；
According to the boundary conditions given by the top surface and the bottom surface, Laplace transformation and Fourier series expansion are carried out on the mathematical expression of the boundary conditions to obtain the physical quantity form on the top Laplace domain
Figure BDA0002750844690000048
And physical quantity form on the bottom Laplace domain
Figure BDA0002750844690000049
Wherein the content of the first and second substances,
Figure BDA00027508446900000410
is in the form of
Figure BDA00027508446900000411
According to equation (25), solve
Figure BDA00027508446900000412
Specific solution of the physical quantity in (1);
determining the physical quantity of any position z according to formula (26) based on a propagation matrix method:
Figure BDA00027508446900000413
the surface of formula (26) satisfies xi ═ F on any nth layern(z-zn-1)…F2(h2)F1(h1) The transfer matrix xi is a constant matrix consisting of physical parameters, Laplace transformation parameters w and Fourier series expansion parameters gamma and beta;
solving according to equation (26)
Figure BDA00027508446900000414
And
Figure BDA00027508446900000415
of
Figure BDA00027508446900000416
Temperature of
Figure BDA00027508446900000417
Pressure of
Figure BDA00027508446900000418
Component of stress
Figure BDA00027508446900000419
Heat flux in z direction
Figure BDA00027508446900000420
And velocity
Figure BDA0002750844690000051
The remaining physical quantities at any position are calculated according to the following formula:
Figure BDA0002750844690000052
Figure BDA0002750844690000053
Figure BDA0002750844690000054
Figure BDA0002750844690000055
Figure BDA0002750844690000056
Figure BDA0002750844690000057
Figure BDA0002750844690000058
wherein
Figure BDA0002750844690000059
In another aspect, the disclosed embodiments provide a transient response calculation apparatus for thermal-fluid-solid coupling of porous elastic medium, the apparatus includes a processor and a memory, the memory stores computer program instructions adapted to be executed by the processor, and the computer program instructions are executed by the processor to perform the steps of the transient response calculation method for thermal-fluid-solid coupling of porous elastic medium.
The technical scheme provided by the embodiment of the disclosure can have the following beneficial effects:
by adopting an analytic method to solve the thermal-fluid-solid coupling transient response of the elastic medium, iterative calculation is not needed by a computer, the calculation amount can be greatly reduced, and the calculation speed is improved; compared with a complex numerical algorithm, the method can effectively reduce the complexity of the algorithm and improve the accuracy of the calculation result.
Drawings
FIG. 1 is a schematic view of a geometric model of a porous elastic medium.
FIG. 2 is a flow chart of a transient response calculation method for thermal-fluid-solid coupling of a porous elastic medium according to an embodiment of the disclosure;
FIG. 3 is a schematic view of a geometric model of another porous elastic medium.
Detailed Description
The present disclosure will be described in further detail with reference to the drawings and embodiments. It is to be understood that the specific embodiments described herein are for purposes of illustration only and are not to be construed as limitations of the present disclosure. It should be further noted that, for the convenience of description, only the portions relevant to the present disclosure are shown in the drawings.
It should be noted that the embodiments and features of the embodiments in the present disclosure may be combined with each other without conflict. It should be noted that, the step numbers in the text are only for convenience of explanation of the specific embodiments, and do not serve to limit the execution sequence of the steps. In addition, the method provided by the present embodiment may be executed by an electronic device such as a server or a computer, and the server is taken as an example for the following description. The present disclosure will be described in detail below with reference to the accompanying drawings in conjunction with embodiments.
The first embodiment of the disclosure provides a transient response calculation method for thermal-fluid-solid coupling of porous elastic media, which will be described below by taking the layered foundation shown in fig. 1 as an example.
In the coordinate system shown in FIG. 1, the length of the three-dimensional porous elastic medium is LxWidth of LyH is high; the origin of coordinates is at any end point of the three-dimensional porous elastic medium, the number of layers is N, the z axis is the thickness direction, and z isnDenotes the top surface of the n-th layer, zn-1Represents the bottom surface of the nth layer (and also the top surface of the (n-1) th layer); in the case of a single layer, N is 1, and N is 0 or 1.
The periphery of the layered foundation shown in the attached figure 1 is simply supported boundary conditions, the bottom surface is fixed boundary conditions, and the boundary conditions and initial conditions in a mathematical form are as follows:
x＝0，0＜y＜Lx：uy＝uz＝0，θ＝0，P＝0
y＝0，0＜x＜Ly：ux＝uz＝0，θ＝0，P＝0
0＜x＜Ly，0＜y＜Lx，z＝H：ux＝uy＝uz＝0，vz＝0，qz＝0
t＝0：ui＝0，θ＝0，P＝0
in the formula ux、uy、uzRespectively displacement in the directions of an x axis, a y axis and a z axis, m; p is pressure, Pa; theta is the temperature, K; q. q.szHeat flux in the z-axis direction, W/m2；vzThe seepage velocity in the z-axis direction is m/s; t is time, s. Wherein x is 0, LxThe left side surface of the layered foundation is shown; y is 0, LyRepresenting the front side of the layered foundation; and z-H represents the bottom surface of the layered foundation.
As shown in fig. 2, the method includes:
(1) acquiring relevant parameters of the porous elastic medium, wherein the relevant parameters of the porous elastic medium comprise geometric parameters, temperature field parameters, seepage field parameters, stress field and seepage field coupling parameters and stress field and temperature field coupling coefficients of the porous elastic medium;
(2) establishing a porous elastic medium heat-flow-solid coupling form according to the related parameters of the porous elastic medium;
(3) constructing a single-layer porous elastic medium solution form on a Laplace domain or a solution form on any one layer of a multi-layer porous elastic medium based on an eigenvalue theory and a Stroh-like method;
(4) obtaining general solutions of all physical quantity Laplace domains of the porous elastic medium based on a propagation matrix method, and determining specific solutions of all the physical quantity Laplace domains according to boundary conditions, wherein the physical quantities of the porous elastic medium comprise temperature, pressure, strain and displacement;
(5) and acquiring the thermal-fluid-solid coupling transient response of the porous elastic medium based on a Laplace numerical value inverse transformation method.
The geometric parameters of the porous elastic medium can comprise the length, width, height and distribution layer number of the porous elastic medium, the temperature field parameters of the porous elastic medium can comprise a heat conduction coefficient and a specific heat capacity, the seepage field parameters of the porous elastic medium can comprise permeability, the stress field and seepage field coupling parameters of the porous elastic medium can comprise a Biot consolidation coefficient, and the stress field and temperature field coupling coefficients of the porous elastic medium can comprise a stress-temperature coupling coefficient. The relevant parameters of the porous elastic medium can be input manually, or can be directly called from a memory, or can be acquired by combining the two modes.
In one possible implementation, the porous elastic medium to which the method disclosed in this embodiment is applied satisfies the following conditions: in a three-dimensional cubic structure, including different properties (e.g., orthotropic, transverseisotropic, isotropic, etc.), in a single or multiple layer arrangement, with continuous variation in physical quantities across the layer interfaces, and with the development of the top and bottom boundary conditions (e.g., point loading, face loading) of the elastic medium in a dual Fourier format.
In one possible implementation, the method for establishing the thermal-fluid-solid coupling form of the porous elastic medium according to the relevant parameters of the porous elastic medium comprises the following steps: and constructing a stress field equation, a temperature field equation and a seepage field equation of the porous elastic medium according to the related parameters of the porous elastic medium.
The stress field equation comprises a stress balance equation (1) and a constitutive equation system (2). The constitutive equation set (2) represents the relationship between stress and deformation, and the relationship between temperature and pressure.
Figure BDA0002750844690000061
Wherein, the expression of the pressure term P in the equation set (2) is formula (3).
P＝Mξ-α1Mε11-α2Mε22-a3Mε33+βmMθ (3)
In the above-mentioned formula, the compound of formula,
Figure BDA0002750844690000062
is expressed in relation to a physical quantity σijCalculating the partial derivative, σ, of the j-axisijStress in the direction of the j axis on the plane perpendicular to the i axis, N/m2；εijThe strain in the direction of the j axis on the surface vertical to the i axis is consistent; u. ofiIs the deformation in the plane perpendicular to the i-axis, m; cijThe elastic coefficient in the direction of the j axis on the plane perpendicular to the i axis is N/m2；C44，C55，C66Is shear modulus, N/m2；αiIs the Biot consolidation coefficient on the plane perpendicular to the i-axis, N/(m)2·K)；βiIs the stress-temperature coefficient in the plane perpendicular to the i-axis, N/(m)2K); p is pressure, Pa; theta is the temperature, K; m is Biot modulus, N/M2；βmIs the bulk strain-temperature coefficient, 1/K; xi is water content,%; i is 1, 2, 3; j is 1, 2, 3. Wherein, three values of i and j can respectively correspond to an x axis, a y axis and a z axis. E.g. σ11Stress in the plane perpendicular to the x-axis, σ22Stress in the plane perpendicular to the y-axis, σ33Stress in the direction of the z-axis in the plane perpendicular to the z-axis, C11Is a coefficient of elasticity in the direction of the x-axis in a plane perpendicular to the x-axis, C22Is a coefficient of elasticity in the y-axis direction in a plane perpendicular to the y-axis, C33Is a coefficient of elasticity in the direction of the z-axis in a plane perpendicular to the z-axis, epsilon11Is the strain in the plane perpendicular to the x-axis, in line with the direction of the x-axis22Is the strain in the plane perpendicular to the y-axis, in line with the y-axis33Is the strain in the plane perpendicular to the z-axis, which coincides with the z-axis direction.
In one possible implementation, when the elastic medium is a transversely isotropic material, C22＝C11，C13＝C23，C66＝(C11-C12)/2，C44＝C55. When the elastic medium is an isotropic material, C11＝C22＝C33，C12＝Ci3＝C23，C44＝C55＝C66。
The temperature field equations include heat conduction equation (4) and heat balance equation (5).
Figure BDA0002750844690000071
Figure BDA0002750844690000072
In the above formula, qiHeat flux in the plane perpendicular to the i-axis, W/m2(ii) a Theta is the temperature, K;
Figure BDA0002750844690000078
solving a partial derivative on an x axis for theta; lambda [ alpha ]ijW/(m) is a coefficient of thermal conductivity in the direction of the j axis on a plane perpendicular to the i axis2K); t is time, s;
Figure BDA0002750844690000079
is the second derivative on the x-axis; cθIs the thermal diffusion coefficient, m2·s，cθ＝φρfcf+(1-φ)ρscsWherein, phi is the porosity of the medium,%; rhofFluid density, kg/m3；cfIs the specific heat capacity of the fluid, J/(kg.K); rhosAs the density of the matrix, kg/m3；csThe specific heat capacity of the matrix is J/(kg. K); i is 1, 2, 3; j is 1, 2, 3.
The seepage field equation comprises a motion equation (6) and a mass conservation equation (7);
Figure BDA0002750844690000073
Figure BDA0002750844690000074
in the above formula, viIs the seepage velocity on the plane perpendicular to the i axis, m/s; k is a radical ofijThe permeability coefficient of the plane perpendicular to the i-axis is in accordance with the j-axis direction, m/s, when i ≠ j, k ij0; g is the acceleration of gravity, m/s2(ii) a Xi is water content,%; i is 1, 2, 3, j is 1, 2, 3.
In a possible implementation manner, the method for constructing a single-layer porous elastic medium solution on a Laplace domain or a solution on any one layer of a multi-layer porous elastic medium based on an eigenvalue theory and a Stroh-like method comprises the following steps:
laplace transformation is carried out on the formulas (5) and (7) to obtain formulas (8) and (9)
Figure BDA0002750844690000075
Figure BDA0002750844690000076
In the above formula, the superscript represents a physical quantity on the Laplace domain, and w represents a corresponding quantity of time t converted to the Laplace domain on the time domain;
obtaining the n-th layer of porous elastic medium (z) meeting the boundary condition form according to the boundary condition form of the four simple side surfaces of the three-dimensional layered mediumn-1≤z≤zn) The general solution form of (A) is as follows:
Figure BDA0002750844690000077
Figure BDA0002750844690000081
Figure BDA0002750844690000082
wherein the content of the first and second substances,
Figure BDA0002750844690000083
m and δ are natural numbers in the fourier series expansion terms; a is1、a2、a3、a4、a5、b1、b2、b3、b4、b5、q1、q2、q3、q4、q5、q6、q7Respectively the introduced unknowns to be solved; z is a radical ofnRepresenting the top surface coordinate value of the nth layer of medium; z represents a longitudinal coordinate value of a certain surface in the height direction in the nth layer medium; the superscript "-" represents an angle-independent physical quantity in the Laplace domain, and n is a positive integer.
Equations (10) - (12) are in the form of the equation solution assumed according to the boundary condition form, that is, the equation solution in this form satisfies the boundary condition form, and then the unknown parameters in the solution are determined according to the equation form, so that the determined form of the equation solution can be obtained.
Because the number of unknowns in the general solution is large, which results in a complicated solution process, in order to facilitate the solution, a coefficient matrix may be introduced to construct a matrix form, that is, a form of a single-layer porous elastic medium solution on a Laplace domain or a form of a solution on any one layer of a multi-layer porous elastic medium may be constructed based on an eigenvalue theory and a Stroh-like method, and the method may further include:
introducing a coefficient matrix (13);
a＝[a1，a2，a3，a4，a5]T，b＝[b1，b2，b3，b4，b5]T (13)
substituting the equations (10) and (11) into the constitutive equation set (2) to obtain the relation between b and a, namely equation (14);
b＝(-ET+sD)a (14)
wherein the superscript "T" represents the transpose of the matrix;
substituting equations (10) and (12) into constitutive equation set (2) to obtain equation (15):
Figure BDA0002750844690000084
substituting the formula (10) into the constitutive equation set (2) according to the formulas (11) to (14) to obtain a formula (16);
[Q+s(E-ET+Ω)+s2D]a＝0 (16)
in the formula (16), E, D, Q and Ω are in the form of a matrix composed of physical parameters.
Figure BDA0002750844690000085
Figure BDA0002750844690000091
Figure BDA0002750844690000092
According to the eigenvalue theory, s is taken as the eigenvalue of N, η ═ a, b }TConstructing an equivalent relation (18) to the expressions (14) and (16) as eigenvectors corresponding to the eigenvalues of N;
Nη＝sη，η＝{a，b}T (18)
wherein the content of the first and second substances,
Figure BDA0002750844690000093
the general form of physical quantity for constructing any nth layer is as follows:
Figure BDA0002750844690000094
wherein the content of the first and second substances,
Figure BDA0002750844690000095
wherein, a1-a10，b1-b10Is obtained from the formula (18) and s1-s10The corresponding feature vector.
Since formula (19) applies to z ═ zn-1Therefore, equation (21) can be obtained from equation (19):
Figure BDA0002750844690000096
substituting equation (21) into equation (19) to obtain the solution of the nth layer of any layer
Figure BDA0002750844690000097
Wherein the content of the first and second substances,
Figure BDA0002750844690000098
if it is
Figure BDA0002750844690000099
Is known, of any position z
Figure BDA00027508446900000910
The average value can be obtained by equation (22).
In a possible implementation manner, obtaining a general solution of each physical quantity Laplace domain of the porous elastic medium based on a propagation matrix method, and determining a special solution of each physical quantity Laplace domain according to a boundary condition, includes:
since the formula (22) applies to z ═ znEquation (23) can be obtained from equation (22):
Figure BDA0002750844690000101
in the formula (I), the compound is shown in the specification,
Figure BDA0002750844690000102
hn＝zn-zn-1，Fn(hn) Referred to as the transfer matrix of the nth layer.
The formula (22) is suitable for any layer, and the same holds true for the n +1 layers, that is, the formula (24) can be obtained from the formula (22)
Figure BDA0002750844690000103
According to the contact surface of the n-th layer and the n + 1-th layer (z ═ z)nFace) principle of pressure, temperature, displacement continuity, equation (23)
Figure BDA0002750844690000104
The formula (22) can be used to obtain the solution of the N-th layer outer surface (z ═ H), and so on
Figure BDA0002750844690000105
Wherein G is FN(hN)FN-1(hN-1)…F2(h2)F1(h1)。
According to the boundary conditions given by the top surface and the bottom surface, Laplace transformation and Fourier series expansion are carried out on the expression of the boundary conditions to obtain the physical quantity form on the top Laplace domain
Figure BDA0002750844690000106
And physical quantity form on the bottom Laplace domain
Figure BDA0002750844690000107
Figure BDA0002750844690000108
Is in the form of
Figure BDA0002750844690000109
According to the given in the specific problemThe boundary conditions can be determined
Figure BDA00027508446900001010
And
Figure BDA00027508446900001011
and (4) a middle part of physical quantities. Expanding the G form in the formula (25) to obtain:
Figure BDA00027508446900001012
in the formula, Mgl(G ═ 1, 2; l ═ 1, 2) is a 3 × 3 submatrix in the G matrix; n is a radical ofgo(G ═ 1, 2; o ═ 1, 2, 3, 4) is a 3 × 1 matrix in the G matrix; egl(G ═ 1, 2; l ═ 1, 2) is a 1 × 3 matrix in the G matrix; j. the design is a squarexoAnd (x is 1, 2, 3, 4; o is 1, 2, 3, 4) is a constant in the G matrix. Determined according to boundary conditions
Figure BDA00027508446900001013
And
Figure BDA00027508446900001014
the value of the partial physical quantity can be determined by (26) as if z is 0.
According to the obtained z-0 plane physical quantity
Figure BDA00027508446900001015
The physical quantity at any position z is determined using the propagation matrix method according to equation (26):
Figure BDA00027508446900001016
the surface of formula (27) is on any nth layer, xi ═ Fn(z-zn-1)…F2(h2)F1(h1) In the formula, the physical quantity of the z-0 plane is known, and the transfer matrix xi is a constant matrix composed of the physical parameters, the Laplace transformation parameters w and the Fourier series expansion parameters γ and β.
Except that
Figure BDA0002750844690000111
And
Figure BDA0002750844690000112
of
Figure BDA0002750844690000113
Temperature of
Figure BDA0002750844690000114
Pressure of
Figure BDA0002750844690000115
Component of stress
Figure BDA0002750844690000116
Heat flux in z direction
Figure BDA0002750844690000117
And velocity
Figure BDA0002750844690000118
The remaining physical quantity (see formula (12)) at any position other than the formula (27) can be calculated by the following method
Figure BDA0002750844690000119
Figure BDA00027508446900001110
Figure BDA00027508446900001111
Figure BDA00027508446900001112
Figure BDA00027508446900001113
Figure BDA00027508446900001114
Figure BDA00027508446900001115
Wherein
Figure BDA00027508446900001116
The method for calculating transient response of thermal-fluid-solid coupling of porous elastic medium provided by the embodiment of the disclosure is further explained by taking the layered foundation shown in fig. 3 as an example.
The three-dimensional porous elastic medium structure shown in FIG. 3 has a length, a width and a height Lx、Ly、ZN. According to the change of the physical parameters of the matrix, the whole material domain can be divided into N layers, and the height h of each layern＝zn-zn-1，LayernA calculation field of the medium representing the n-th layer, znDenotes the upper boundary of the (n + 1) th layer of the medium, where z 00 means that the upper boundary of the first layer of media is the z-0 plane. The porous elastic medium material meets the condition of transverse isotropy, and the physical quantity at the contact surface of the layers is continuously changed. The method for calculating the transient response of the thermal-fluid-solid coupling of the porous elastic medium comprises the following steps:
(1) obtaining relevant parameters of each layer of porous elastic medium material, such as the length (L) of the porous elastic mediumx) Width (L)y) High (H) and number of layers (N) distributed, coefficient of thermal conductivity (lambda)ij) And specific heat capacity (c)θ) Permeability (k)ij) Biot consolidation coefficient (. alpha.)i) Surface stress-temperature coupling coefficient (beta)i) Bulk stress-temperature coefficient of coupling (beta)m) And the obtained parameters are dimensionless by formula (28):
Figure BDA00027508446900001117
Figure BDA00027508446900001118
in the formula, CijThe elastic coefficient in the direction of the j axis on the plane perpendicular to the i axis is N/m2；αiIs the Biot consolidation coefficient on the plane perpendicular to the i-axis, N/(m)2K); m is Biot modulus, N/M2；βmIs the bulk stress-temperature coefficient, 1/K; beta is aiIs the surface stress-temperature coefficient in the plane perpendicular to the i-axis, N/(m)2·K)；CθIs the thermal diffusion coefficient, m2·s；λijW/(m) is a coefficient of thermal conductivity in the direction of the j axis on a plane perpendicular to the i axis2·K)；kijThe permeability coefficient is consistent with the direction of the j axis on the surface vertical to the i axis, and is m/s; x represents the computational domain coordinates, m; the lower right subscript max represents the maximum value in the same physical quantity for each layer; the upper angle mark Λ represents the physical parameters after normalization; i is 1, 2, 3; j is 1, 2, 3. Wherein, the relevant parameters of the porous elastic medium material can be manually input or can be directly called from a memory.
The three-dimensional elastic medium structure shown in fig. 3 has a simple boundary condition around, and the bottom surface is fixed, heat-insulated and impermeable. The boundary conditions and initial conditions are expressed using the physical quantity response values as follows:
Figure BDA00027508446900001119
in the formula ux、uy、uzRespectively displacement in the directions of an x axis, a y axis and a z axis, m; p is pressure, Pa; theta is the temperature, K; q. q.szHeat flux in the z-axis direction, W/m2；vzThe seepage velocity in the z-axis direction is m/s.
The constant sine distribution temperature load is arranged on the top surface of the medium, and the mathematical expression of the load is as follows:
T＝sinxsiny (30)
(2) and constructing a solution form of the single-layer porous elastic medium on the Laplace domain or a solution form on any one layer of the multi-layer porous elastic medium based on an eigenvalue theory and a Stroh-like method.
And constructing a calculation point on the Laplace domain according to the time point on the time domain, wherein the construction form is as follows:
Figure BDA0002750844690000121
wherein, k is 1.,. chi-1; χ is a natural number, and a natural number of 2-10 can be selected.
According to the physical quantity parameters after normalization, a parameter matrix form of the following form is constructed:
Figure BDA0002750844690000122
Figure BDA0002750844690000123
Figure BDA0002750844690000124
constructing the following matrix according to the parameter matrix form:
Figure BDA0002750844690000125
solving all eigenvalues and corresponding eigenvectors of N:
Nη＝sη，η＝{a，b}T (34)
constructing a form matrix according to the 10 obtained eigenvalues and eigenvectors thereof:
A＝[a1，a2，a3，a4，a5，a6，a7，a8，a9，a10]
B＝[b1，b2，b3，b4，b5，b6，b7，b8，b9，b10]
(35)
Figure BDA0002750844690000126
constructing a top-to-bottom transfer matrix form from the above matrix form is as follows:
G＝FN(hN)FN-1(hN-1)…F2(h2)F1(h1) (35)
in the formula (I), the compound is shown in the specification,
Figure BDA0002750844690000127
hn＝zn-zn-1。
zn-1、znthe bottom and top coordinate values of the nth layer medium, respectively.
The physical quantities to be determined are represented in the form of a matrix as follows:
U＝[u，，P]T＝[ux，uy，uz，θ，P]T，Π＝[t，qz，vz]T＝[σzx，σzy，σzz，σzx，σzx]T (36)
and (3) respectively carrying out Fourier series expansion on the top boundary condition and the bottom boundary condition to obtain the following forms:
Figure BDA0002750844690000131
in the formula, superscript denotes a physical quantity in the Laplace domain.
The top and bottom physical quantities have the following relationship:
Figure BDA0002750844690000132
Figure BDA0002750844690000133
the other unknown physical quantities in (a) are respectively:
Figure BDA0002750844690000134
the expression of the physical quantity at any level is:
Figure BDA0002750844690000135
wherein xi is Fn(z-zn-1)…F2(h2)F1(h1)，
Figure BDA0002750844690000136
The expressions for the other physical quantities are:
Figure BDA0002750844690000137
wherein
Figure BDA0002750844690000138
In the formula, superscript denotes a physical quantity in the Laplace domain.
(3) Acquiring the heat-flow-solid coupling transient response of the elastic medium based on a Laplace inverse transformation numerical method, and performing inverse normalization processing on the physical quantity after normalization, wherein the processing mode is as follows:
Figure BDA0002750844690000139
Figure BDA0002750844690000141
in the formula, the upper corner mark ^ represents a physical quantity after the denormalization.
And performing inverse Laplace transformation by adopting an FT numerical integration method, wherein the FT numerical integration method comprises the following steps:
Figure BDA0002750844690000142
wherein the content of the first and second substances,
Figure BDA0002750844690000143
Figure BDA0002750844690000144
and χ is a natural number of 2-10, wherein the higher the value of χ is, the higher the calculation precision is.
According to the method for calculating the thermal-fluid-solid coupling transient response of the porous elastic medium, the thermal-fluid-solid coupling transient response of the elastic medium is solved by adopting an analytic method. Compared with the traditional numerical solving method, the method does not need a computer to carry out iterative computation, can greatly reduce the computation amount and improve the computation speed; compared with a complex numerical algorithm, the method can effectively reduce the complexity of the algorithm; the solving precision of the numerical algorithm is not high as that of the analytic algorithm, so that the method can effectively improve the accuracy of the calculation result.
A second embodiment of the disclosure provides a porous elastic medium thermal-fluid-solid coupling transient response computing device comprising a processor and a memory. Wherein the memory stores computer program instructions adapted to be executed by the processor, and the computer program instructions when executed by the processor perform the steps of the transient response calculation method for thermal-fluid-solid coupling of porous elastic medium in the above embodiment.
A third embodiment of the present disclosure provides a porous elastic medium thermal-fluid-solid coupling transient response computing device, comprising:
the system comprises a first acquisition module, a second acquisition module and a third acquisition module, wherein the first acquisition module is configured to acquire porous elastic medium related parameters, and the porous elastic medium related parameters comprise geometric parameters, temperature field parameters, seepage field parameters, stress field and seepage field coupling parameters and stress field and temperature field coupling parameters of the porous elastic medium;
the first establishing module is configured to establish a porous elastic medium heat-flow-solid coupling form according to the related parameters of the porous elastic medium;
the first construction module is configured to construct a single-layer porous elastic medium solution form on a Laplace domain or a solution form on any one layer of a multi-layer porous elastic medium based on an eigenvalue theory and a Stroh-like method;
the second acquisition module is configured to acquire a general solution of each physical quantity Laplace domain of the porous elastic medium based on a propagation matrix method and determine a specific solution of each physical quantity Laplace domain according to a boundary condition, wherein the physical quantities comprise temperature, pressure, strain and displacement of the porous elastic medium;
and the third acquisition module is configured to acquire the thermal-fluid-solid coupling transient response of the porous elastic medium based on a Laplace numerical value inverse transformation method.
It should be noted that the porous elastic medium thermal-flow-solid coupling transient response calculation apparatus and the porous elastic medium thermal-flow-solid coupling transient response calculation method provided in the foregoing embodiments belong to the same concept, and specific implementation processes thereof are detailed in the method embodiments and are not described herein again.
It should be understood that the various techniques described herein may be implemented in connection with hardware or software or, alternatively, with a combination of both. Thus, the methods and apparatus of the present disclosure, or certain aspects or portions thereof, may take the form of program code (i.e., instructions) embodied in tangible media, such as floppy diskettes, CD-ROMs, hard drives, or any other machine-readable storage medium, wherein, when the program is loaded into and executed by a machine, such as a computer, the machine becomes an apparatus for practicing the disclosure.
In the case of program code execution on programmable computers, the computing device will generally include a processor, a storage medium readable by the processor (including volatile and non-volatile memory and/or storage elements), at least one input device, and at least one output device. Wherein the memory is configured to store program code; the processor is configured to perform the various methods of the present disclosure according to instructions in the program code stored in the memory.
By way of example, and not limitation, computer readable media may comprise computer storage media and communication media. Computer-readable media includes both computer storage media and communication media. Computer storage media store information such as computer readable instructions, data structures, program modules or other data. Communication media typically embodies computer readable instructions, data structures, program modules or other data in a modulated data signal such as a carrier wave or other transport mechanism and includes any information delivery media. Combinations of any of the above are also included within the scope of computer readable media.
It should be appreciated that in the foregoing description of exemplary embodiments of the disclosure, various features of the disclosure are sometimes grouped together in a single embodiment, figure, or description thereof for the purpose of streamlining the disclosure and aiding in the understanding of one or more of the various disclosed aspects. However, the disclosed method should not be interpreted as reflecting an intention that: that is, the claimed disclosure requires more features than are expressly recited in each claim. Rather, as the following claims reflect, disclosed aspects lie in less than all features of a single foregoing disclosed embodiment. Thus, the claims following the detailed description are hereby expressly incorporated into this detailed description, with each claim standing on its own as a separate embodiment of this disclosure.
Those skilled in the art will appreciate that the modules or units or components of the devices in the examples disclosed herein may be arranged in a device as described in this embodiment or alternatively may be located in one or more devices different from the devices in this example. The modules in the foregoing examples may be combined into one module or may be further divided into multiple sub-modules.
Those skilled in the art will appreciate that the modules in the device in an embodiment may be adaptively changed and disposed in one or more devices different from the embodiment. The modules or units or components of the embodiments may be combined into one module or unit or component, and furthermore they may be divided into a plurality of sub-modules or sub-units or sub-components. All of the features disclosed in this specification (including any accompanying claims, abstract and drawings), and all of the processes or elements of any method or apparatus so disclosed, may be combined in any combination, except combinations where at least some of such features and/or processes or elements are mutually exclusive. Each feature disclosed in this specification (including any accompanying claims, abstract and drawings) may be replaced by alternative features serving the same, equivalent or similar purpose, unless expressly stated otherwise.
Moreover, those skilled in the art will appreciate that while some embodiments described herein include some features included in other embodiments, rather than other features, combinations of features of different embodiments are meant to be within the scope of the disclosure and form different embodiments. For example, in the following claims, any of the claimed embodiments may be used in any combination.
Furthermore, some of the described embodiments are described herein as a method or combination of method elements that can be performed by a processor of a computer system or by other means of performing the described functions. A processor having the necessary instructions for carrying out the method or method elements thus forms a means for carrying out the method or method elements. Further, the elements of the apparatus embodiments described herein are examples of the following apparatus: the apparatus is used to implement the functions performed by the elements for the purposes of this disclosure.
As used herein, unless otherwise specified the use of the ordinal adjectives "first", "second", "third", etc., to describe a common object, merely indicate that different instances of like objects are being referred to, and are not intended to imply that the objects so described must be in a given sequence, either temporally, spatially, in ranking, or in any other manner.
While the disclosure has been described with respect to a limited number of embodiments, those skilled in the art, having benefit of this description, will appreciate that other embodiments can be devised which do not depart from the scope of the disclosure as described herein. Moreover, it should be noted that the language used in the specification has been principally selected for readability and instructional purposes, and may not have been selected to delineate or circumscribe the disclosed subject matter. Accordingly, many modifications and variations will be apparent to those of ordinary skill in the art without departing from the scope and spirit of the appended claims. The disclosure of the present disclosure is intended to be illustrative, but not limiting, of the scope of the disclosure, which is set forth in the following claims.

Claims (6)

1. A method for calculating transient response of thermal-fluid-solid coupling of a porous elastic medium is characterized by comprising the following steps:
acquiring relevant parameters of the porous elastic medium, wherein the parameters comprise geometric parameters, temperature field parameters, seepage field parameters, stress field and seepage field coupling parameters and stress field and temperature field coupling parameters of the porous elastic medium;
establishing a porous elastic medium heat-flow-solid coupling form according to the related parameters of the porous elastic medium;
constructing a single-layer porous elastic medium solution form on a Laplace domain or a solution form on any one layer of a multi-layer porous elastic medium based on an eigenvalue theory and a Stroh-like method;
obtaining general solutions of all physical quantity Laplace domains of the porous elastic medium based on a propagation matrix method, and determining specific solutions of all physical quantity Laplace domains according to boundary conditions, wherein the physical quantities comprise temperature, pressure, strain and displacement of the porous elastic medium;
and acquiring the thermal-fluid-solid coupling transient response of the porous elastic medium based on a Laplace numerical value inverse transformation method.
2. The transient response calculation method for porous elastic medium thermal-fluid-solid coupling according to claim 1, wherein the establishing of the form of porous elastic medium thermal-fluid-solid coupling according to the relevant parameters of the porous elastic medium comprises: constructing a stress field equation, a temperature field equation and a seepage field equation of the porous elastic medium according to the related parameters of the porous elastic medium;
the stress field equation comprises a stress balance equation (1) and a constitutive equation set (2);
Figure FDA0002750844680000011
Figure FDA0002750844680000012
wherein, the expression of the pressure term P in the equation set (2) is formula (3);
P＝Mξ-α1Mε11-α2Mε22-α3Mε33+βmMθ (3)
in the above-mentioned formula, the compound of formula,
Figure FDA0002750844680000018
is expressed in relation to a physical quantity σijCalculating a partial derivative of a j axis; sigmaijStress in the direction of the j axis on the plane perpendicular to the i axis, N/m2；εijThe strain in the direction of the j axis on the surface vertical to the i axis is consistent; u. ofiIs the displacement in the plane perpendicular to the i-axis, m; cijThe elastic coefficient in the direction of the j axis on the plane perpendicular to the i axis is N/m2；C44，C55，C66Is shear modulus, N/m2；αiIs the Biot consolidation coefficient on the plane perpendicular to the i-axis, N/(m)2·K)；βiIs the surface stress-temperature coefficient in the plane perpendicular to the i-axis, N/(m)2K); p is pressure, Pa; theta is the temperature, K; m is Biot modulus, N/M2；βmIs the bulk strain-temperature coefficient, 1/K; xi is water content，％；i＝1，2，3；j＝1，2，3；
The temperature field equation comprises a heat conduction equation (4) and a heat balance equation (5);
Figure FDA0002750844680000013
Figure FDA0002750844680000014
in the above formula, qiHeat flux in the plane perpendicular to the i-axis, W/m2(ii) a Theta is the temperature, K;
Figure FDA0002750844680000015
solving a partial derivative on an x axis for theta; lambda [ alpha ]ijW/(m) is a coefficient of thermal conductivity in the direction of the j axis on a plane perpendicular to the i axis2K); t is time, s;
Figure FDA0002750844680000016
is the second derivative on the x-axis; cθIs the thermal diffusion coefficient, m2·s，cθ＝φρfcf+(1-φ)ρscsWherein, phi is the porosity of the medium,%; rhofFluid density, kg/m3；cfIs the specific heat capacity of the fluid, J/(kg.K); rhosAs the density of the matrix, kg/m3；csThe specific heat capacity of the matrix is J/(kg. K); i is 1, 2, 3; j is 1, 2, 3;
the seepage field equation comprises a motion equation (6) and a mass conservation equation (7);
Figure FDA0002750844680000017
Figure FDA0002750844680000021
in the above formula, viIs the seepage velocity on the plane perpendicular to the i axis, m/s; k is a radical ofijThe permeability coefficient is consistent with the direction of the j axis on the surface vertical to the i axis, and is m/s; g is the acceleration of gravity, m/s2(ii) a Xi is water content,%; i is 1, 2, 3; j is 1, 2, 3.
3. The method for calculating transient response of thermal-flow-solid coupling of porous elastic medium according to claim 2, wherein the constructing the solution form of single-layer porous elastic medium on the Laplace domain or the solution form on any layer of the multilayer porous elastic medium based on eigenvalue theory and Stroh-like method comprises:
performing Laplace transformation on the formulas (5) and (7) to obtain formulas (8) and (9) respectively;
Figure FDA0002750844680000022
Figure FDA0002750844680000023
in the above formula, the superscript represents a physical quantity on the Laplace domain, and w represents a corresponding quantity of time t converted to the Laplace domain on the time domain;
according to the boundary condition form of the four simply-supported side surfaces of the three-dimensional layered medium, the general solution form of the nth layer porous elastic medium meeting the boundary condition form is obtained as follows:
Figure FDA0002750844680000024
Figure FDA0002750844680000025
Figure FDA0002750844680000026
wherein the content of the first and second substances,
Figure FDA0002750844680000027
m and δ are natural numbers in the fourier series expansion terms; a is1、a2、a3、a4、a5、b1、b2、b3、b4、b5、q1、q2、q3、q4、q5、q6、q7Respectively are unknowns to be solved; z is a radical ofnRepresenting the top surface coordinate value of the nth layer of medium; z represents a longitudinal coordinate value of a certain surface in the height direction in the nth layer medium; superscript-denotes an angle-independent physical quantity, z, over the Laplace domainn-1≤z≤znAnd n is a positive integer.
4. The method for calculating transient response of thermal-flow-solid coupling of porous elastic medium according to claim 3, wherein the method for constructing the solution form of single-layer porous elastic medium on Laplace domain or the solution form on any layer of multi-layer porous elastic medium based on eigenvalue theory and Stroh-like method further comprises:
calling a coefficient matrix (13);
a＝[a1，a2，a3，a4，a5]T，b＝[b1，b2，b3，b4，b5]T (13)
substituting the equations (10) and (11) into the constitutive equation set (2) to obtain an equation (14);
b＝(-ET+sD)a (14)
substituting the equations (10) and (12) into the constitutive equation set (2) to obtain an equation (15);
Figure FDA0002750844680000031
substituting the formula (10) into the constitutive equation set (2) according to the formulas (11) to (14) to obtain a formula (16);
[Q+s(E-ET+Ω)+s2D]a＝0 (16)
in the formula (16), E, D, Q and Ω are in the form of a matrix composed of physical parameters; wherein Ω is of the form:
Figure FDA0002750844680000032
according to eigenvalue theory, s is used as the eigenvalue of N, η ═ a, b }TConstructing an equivalent relation (18) to the expressions (14) and (16) as eigenvectors corresponding to the eigenvalues of N;
Nη＝sη，η＝{a，b}T (18)
wherein the content of the first and second substances,
Figure FDA0002750844680000033
the general form of physical quantity for constructing any nth layer is as follows:
Figure FDA0002750844680000034
wherein the content of the first and second substances,
Figure FDA0002750844680000035
A＝[a1，a2，a3，a4，a5，a6，a7，a8，a9，a10]
B＝[b1，b2，b3，b4，b5，b6，b7，b8，b9，b10] (20)
Figure FDA0002750844680000036
a1-a10，b1-b10is and s1-s10A corresponding feature vector;
obtaining formula (21) from formula (19):
Figure FDA0002750844680000037
substituting equation (21) into equation (19) to obtain the solution of the nth layer of any layer
Figure FDA0002750844680000038
Wherein the content of the first and second substances,
Figure FDA0002750844680000039
5. the method for calculating the transient response of the thermal-fluid-solid coupling of the porous elastic medium according to claim 4, wherein the method for obtaining the general solution of each Laplace domain of the physical quantity of the porous elastic medium based on a propagation matrix method and determining the specific solution of each Laplace domain of the physical quantity according to the boundary condition comprises the following steps:
obtaining formula (23) according to formula (22):
Figure FDA0002750844680000041
in the formula (I), the compound is shown in the specification,
Figure FDA0002750844680000042
hn＝zn-zn-1，Fn(hn) A transfer matrix being an nth layer;
obtaining formula (24) according to formula (22):
Figure FDA0002750844680000043
obtaining the solution of the outer surface of the Nth layer according to the principle that the pressure, the temperature and the displacement on the contact surface of the N-th layer and the N + 1-th layer are continuous
Figure FDA0002750844680000044
Wherein G is FN(hN)FN-1(hN-1)…F2(h2)F1(h1)；
According to the boundary conditions given by the top surface and the bottom surface, Laplace transformation and Fourier series expansion are carried out on the expression of the boundary conditions to obtain the physical quantity form on the top Laplace domain
Figure FDA0002750844680000045
And physical quantity form on the bottom Laplace domain
Figure FDA0002750844680000046
Wherein the content of the first and second substances,
Figure FDA0002750844680000047
is in the form of
Figure FDA0002750844680000048
According to equation (25), solve
Figure FDA0002750844680000049
Specific solution of the physical quantity in (1);
determining the physical quantity of any position z according to formula (26) based on a propagation matrix method:
Figure FDA00027508446800000410
the surface of formula (26) satisfies xi ═ F on any nth layern(z-zn-1)…F2(h2)F1(h1) The transfer matrix xi is a constant matrix consisting of physical parameters, Laplace transformation parameters w and Fourier series expansion parameters gamma and beta;
solving according to equation (26)
Figure FDA00027508446800000411
And
Figure FDA00027508446800000412
of
Figure FDA00027508446800000413
Temperature of
Figure FDA00027508446800000414
Pressure of
Figure FDA00027508446800000415
Component of stress
Figure FDA00027508446800000416
Heat flux in z direction
Figure FDA00027508446800000417
And velocity
Figure FDA00027508446800000418
The remaining physical quantities at any position are calculated according to the following formula:
Figure FDA00027508446800000419
Figure FDA00027508446800000420
Figure FDA00027508446800000421
Figure FDA00027508446800000422
Figure FDA00027508446800000423
Figure FDA00027508446800000424
Figure FDA0002750844680000051
wherein
Figure FDA0002750844680000052
6. A porous elastic medium thermal-flow-solid coupling transient response calculation device, characterized in that the device comprises a processor and a memory, wherein the memory stores computer program instructions suitable for the processor to execute, and when the computer program instructions are executed by the processor, the steps in the porous elastic medium thermal-flow-solid coupling transient response calculation method according to any one of claims 1 to 5 are executed.
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