Novel heat-flow-force coupling simulation method based on near-field dynamics differential operator

Abstract

The invention discloses a novel heat-flow-force coupling simulation method based on a near-field dynamics differential operator, and the method comprises the steps: defining the geometric dimension of a material, and setting initial parameters; fluid and solid areas are divided into a plurality of near-field dynamic points, a fluid point family and a solid point family are divided, and a discrete model is generated; calculating a temperature field of the fluid; calculating dimensionless heat related parameters of the fluid, and applying boundary conditions of dimensionless temperature, heat insulation and speed of a flow field; calculating a temperature field of the solid material; calculating the dimensionless heat flux density of the fluid-solid interface; calculating dimensionless thermal parameters of the solid material, and applying adiabatic boundary conditions and displacement boundary conditions; calculating the mechanical parameters of the material to comprehensively evaluate the mechanical properties of the system; updating a displacement field and a temperature field of the fluid point and the solid point through iterative calculation by adopting a self-adaptive dynamic relaxation method; in the iteration process, whether the system reaches a steady state or not is judged, and heat-flow-force coupling simulation is completed after the system reaches the steady state.

Description

Technical Field

[0001] The invention belongs to the technical field of building material performance analysis, and in particular relates to a novel heat-fluid-force coupling simulation method based on peridynamic differential operators. Background Art

[0002] With the rapid development of social economy, more and more new building materials are being developed and applied to engineering structures. Fiber-reinforced cementitious composites (ECC) have excellent tensile properties and crack control capabilities, and have broad application prospects in the reinforcement and repair of engineering structures. When an accidental fire occurs, the structural bearing capacity of the engineering structure in a high temperature environment will face great damage. At present, the application of peridynamics (PD) models in solving the problem of thermal failure in ECC and concrete bonded specimens is still insufficient. Traditional methods are difficult to fully consider the performance degradation of materials in high temperature environments and the complex multi-field coupling effects. Therefore, it is particularly important to propose a simulation method that can comprehensively consider the material microstructure, high temperature performance degradation and fire dynamics response. Summary of the invention

[0003] In order to solve the above technical problems, the present invention proposes a novel thermal-fluid-mechanical coupling simulation method and system based on peridynamic differential operators, which are used to effectively simulate the response of concrete and ECC under high temperature loads.

[0004] To achieve the above object, the present invention provides a novel thermal-fluid-mechanical coupling simulation method based on peridynamic differential operators, comprising:

[0005] Define the material geometry and set initial parameters, including temperature, density, velocity, and pressure of fluid and solid materials;

[0006] Dividing the fluid and solid regions into a plurality of peridynamic points, and classifying them according to different properties to divide them into fluid point families and solid point families, and generating discrete models based on the fluid point families and the solid point families;

[0007] Calculating the temperature field of the fluid, updating the temperature value of each point, and converting it into a dimensional form as needed; calculating the dimensionless heat-related parameters of the fluid, and applying the dimensionless temperature, adiabatic and velocity boundary conditions of the flow field;

[0008] Calculate the temperature field of the solid material; calculate the dimensionless heat flux density of the fluid-solid interface; calculate the dimensionless thermal parameters of the solid material, and apply adiabatic boundary conditions and displacement boundary conditions; calculate and update the temperature of each point, and convert it into a dimensional form; calculate the bond force density of each point;

[0009] Calculate the mechanical parameters of the material to comprehensively evaluate the mechanical properties of the system; apply displacement boundary conditions, and use the adaptive dynamic relaxation method to iteratively calculate and update the displacement field and temperature field of the fluid and solid points; during the iteration process, determine whether the system has reached a steady state, and complete the thermal-fluid-force coupling simulation after reaching a steady state.

[0010] Optionally, set the initial temperatures of the fluid and solid materials as follows:

[0011]

[0012] Among them, T fire (t) is the initial temperature of the fluid and solid material, t is the elapsed time, and K is the temperature unit Kelvin.

[0013] Optionally, set the initial pressure calculations for fluid and solid materials as follows:

[0014]

[0015] Among them, ρ 0 is the initial density of the fluid, C s is the artificial speed of sound, and γ is the heat capacity ratio.

[0016] Optionally, generate a discrete model including:

[0017] Dividing the simulation area into a plurality of peridynamic points; the number and distribution density of the peridynamic points are determined according to the accuracy of the simulation and the computing resources;

[0018] According to the type and property of the material, the near-field dynamic points are divided into a fluid point family and a solid point family in the discrete model, wherein the fluid point family includes hot gas or other fluid media in the fire, and the solid point family includes fiber-reinforced cement-based composite materials and concrete solid materials;

[0019] Assign the set initial parameters to each peridynamic point.

[0020] Optionally, a method for calculating the temperature field of the fluid is:

[0021] The explicit integration method is used to solve the peridynamic heat conduction equation, and its discretized form is:

[0022]

[0023] Among them, t n represents the current time step, x i Represents x j Material point in the near field, N i Represents x i The total number of material points in the near field, Vj Represents a particle x j The approximate volume of

[0024] The temperature value of the next time step is calculated using the forward difference method as follows:

[0025]

[0026] Among them, Δt TH To calculate the time step of heat diffusion, the conditions are selected as follows:

[0027]

[0028] in, For x i and x j The micro thermal conductivity function between hot bonds is given by K(T) is the thermal conductivity of the material; For x i and x j The relative distance between .

[0029] Optionally, the method for calculating the dimensionless heat-related parameters of the fluid is:

[0030] Obtain the dimensionless nonlocal form of the Navier–Stokes equations:

[0031]

[0032] Among them, the parameters with subscript 0 are reference variables, the parameters with superscript * are dimensionless variables, g represents the acceleration due to gravity, For mass x 1 The dimensionless form of For mass x 2 The dimensionless form of L 0 is the reference length, For mass x 1 The dimensionless form of velocity, For mass x 2 The dimensionless form of velocity, v 0 is the initial velocity, t * is the dimensionless form of time, is the dimensionless form of fluid density, ρ f is the fluid density, is the dimensionless form of the fluid point temperature, T f is the fluid point temperature, T 0 is the initial temperature, p * is the dimensionless form of fluid pressure, p is the fluid pressure, p 0 is the initial fluid pressure, g *is the dimensionless form of gravitational acceleration, g is the gravitational acceleration, is the dimensionless value of dynamic viscosity, μ f is the dynamic viscosity, is the dimensionless value of thermal conductivity, k f is the thermal conductivity;

[0033] The parameter calculation formulas involved in calculating the mass conservation, momentum conservation and energy conservation equations are as follows:

[0034]

[0035] Where Re is the Reynolds number, Pr is the Prandtl number, Ec is the Eckert number, μ 0 is the initial dynamic viscosity, C 0 is the initial specific heat, k 0 is the initial thermal conductivity, T 0 is the initial temperature;

[0036] The dimensionless gravitational acceleration is approximately:

[0037]

[0038] where β f is the thermal expansion coefficient of the fluid, β 0 is the initial thermal expansion coefficient, T * is the dimensionless form of temperature, Ra is the Rayleigh number, and is calculated as:

[0039]

[0040] Sutherland's law reflects the effect of temperature on viscosity and thermal conductivity, and is expressed in dimensionless form as:

[0041]

[0042] in, is the dimensionless value of dynamic viscosity, is the dimensionless value of thermal conductivity, T f is the fluid point temperature, S μ is the dimensionless value of the fluid dynamic viscosity, S k is the dimensionless value of the thermal conductivity of the fluid.

[0043] Optionally, dimensionless temperature, adiabatic, and velocity boundary conditions are imposed on the flow field including

[0044] Temperature boundary conditions:

[0045] Add a virtual layer with a thickness of δ near-field radius, and apply a temperature boundary to the particles in the virtual layer according to the following formula:

[0046]

[0047] The adiabatic boundary condition is applied as follows:

[0048]

[0049] in, Indicates t n Boundary temperature value at time, Indicates t n The point x in the virtual layer at time i The temperature, Indicates t n Real material point x j The temperature of the virtual point x i The distance to the boundary and the real particle x j The distances to the border are equal;

[0050] Flow boundary conditions:

[0051] For the no-slip solid wall boundary condition, the virtual layer in peridynamics is used;

[0052] Add a thickness of δ to the fluid domain boundary f The rigid solid wall virtual layer R c，f , set the velocity and displacement of the particle in the virtual layer to:

[0053] v f (x f )=0,u f (x f )=0,x f ∈R c，f

[0054] The pressure value of the virtual layer is defined as:

[0055]

[0056] where x f，i is a particle in the virtual layer, x f，j is x f，j The real fluid point in the near field belongs to the flow field, N c，f is x f，i The total number of real fluid particles in the near field.

[0057] Optionally, applying adiabatic boundary conditions and displacement boundary conditions includes:

[0058] Displacement and velocity boundary conditions:

[0059] For displacement and velocity boundary conditions, it is also necessary to add a virtual layer R with a thickness of δ c , for R c The particles in the region exert a forced displacement vector U0 Or velocity vector V 0 ;

[0060]

[0061] Heat transfer conditions at fluid-solid interface:

[0062] The heat flux density generated by thermal convection is in the form of:

[0063]

[0064] Where h is the convective heat transfer coefficient, t n Time interface point x interface The temperature, t n Time step particle x interface The temperature of the surrounding medium;

[0065] The form is as follows:

[0066]

[0067] in, Represents the interface point x interface The total number of points belonging to the fluid in the near field, T f (x f，j , t n ) is t n Time step fluid point x f，j Temperature;

[0068] The heat flux generated by thermal radiation is in the form of:

[0069]

[0070] Where σ is the emissivity of the boundary surface:

[0071]

[0072] Optionally, the adaptive dynamic relaxation method is used to update the displacement field and temperature field of the fluid point and the solid point through iterative calculation, including:

[0073] Adaptive dynamic relaxation method is used. By introducing virtual mass matrix and damping term, the equation of motion is:

[0074] Where D is the virtual mass matrix, c is the damping coefficient, which are obtained by Reschgorin's law and Rayleigh quotient, respectively; u represents the displacement, and F is the sum of the bond force density and the body force density;

[0075] The explicit central difference method is used to solve this equation:

[0076]

[0077] Among them, Δt M is the time step;

[0078] When the iteration starts:

[0079]

[0080] c 1 =0

[0081] By calculating the root mean square Ru of the displacement of each particle, and comparing the root mean square with a relatively small number Ω(, we can determine whether the numerical solution converges. When Ru≤Ω, the system is considered to have reached a steady state. Otherwise, we continue to iterate to find the steady-state solution of the motion equation.

[0082] The calculation form of Ru is as follows:

[0083]

[0084] Where M is the total number of discrete model particles.

[0085] Technical effect of the invention: The invention discloses a novel heat-fluid-mechanical coupling simulation method based on peridynamic differential operators, which solves the limitation of the existing numerical methods in dealing with complex multi-field coupling effects involving temperature field, flow field and stress field, and it is difficult to fully reflect the actual response of materials under extreme conditions such as fire, and the existing models often ignore the microstructural characteristics of ECC and concrete, such as fiber distribution in ECC, aggregate distribution in concrete, etc., resulting in low accuracy of simulation results. PDDO is introduced into the heat-fluid-mechanical coupling simulation, and the Navier-Stokes equations (mass, momentum and energy conservation equations) describing fluid flow and heat transfer are converted into non-local integral form and the microstructural characteristics of concrete are targeted. A heterogeneous peridynamic model including cement mortar phase, aggregate phase and interface phase is constructed, and the interaction between different phases and the technical means of interface treatment are considered. The technical effects of significantly improving the accuracy and reliability of the simulation results, realizing the simulation of multi-field coupling effects, and expanding the application scope of performance evaluation of other multiphase composite materials and complex structures in high temperature environments. BRIEF DESCRIPTION OF THE DRAWINGS

[0086] The drawings constituting a part of the present application are used to provide a further understanding of the present application. The illustrative embodiments and descriptions of the present application are used to explain the present application and do not constitute an improper limitation on the present application. In the drawings:

[0087] Figure 1A schematic flow chart of a novel thermal-fluid-mechanical coupling simulation method based on peridynamic differential operators according to an embodiment of the present invention;

[0088] Figure 2 A geometrical schematic diagram of a fiber-reinforced cement-based composite material under a fire scenario according to an embodiment of the present invention;

[0089] Figure 3 Schematic diagram of the PD discrete model of an embodiment of the present invention, wherein (a) is the fluid domain and (b) is the ECC specimen;

[0090] Figure 4 Schematic diagram of temperature distribution in the fluid domain at different times in the embodiment of the present invention, where (a) is t=100s (t * =0.05), (b) is t=200s(t * =0.1), (c) is t=400s(t * =0.2), (d) is t=600s(t * =0.3), (e) is t=800s(t * =0.4), (f) is t=900s(t * =0.45);

[0091] Figure 5 Schematic diagram of horizontal velocity distribution of heat flow in the fluid domain at different times in the embodiment of the present invention, where (a) is t=100s (t * =0.05), (b) is t=200s(t * =0.1), (c) is t=400s(t * =0.2), (d) is t=600s(t * =0.3), (e) is t=800s(t * =0.4), (f) is t=900s(t * =0.45);

[0092] Figure 6 Schematic diagram of the vertical velocity distribution of hot gas in the fluid domain at different times in the embodiment of the present invention, where (a) is t=100s (t * =0.05), (b) is t=200s(t * =0.1), (c) is t=400s(t * =0.2), (d) is t=600s(t * =0.3), (e) is t=800s(t * =0.4), (f) is t=900s(t * =0.45);

[0093] Figure 7The temperature distribution cloud diagram of the ECC board at different times in the embodiment of the present invention, where (a) is t=100s (t * =0.05), (b) is t=200s(t * =0.1), (c) is t=400s(t * =0.2), (d) is t=600s(t * =0.3), (e) is t=800s(t * =0.4), (f) is t=900s(t * =0.45);

[0094] Figure 8 The horizontal displacement cloud diagram of the ECC board at different times in the embodiment of the present invention, where (a) is t=100s (t * =0.05), (b) is t=200s(t * =0.1), (c) is t=400s(t * =0.2), (d) is t=600s(t * =0.3), (e) is t=800s(t * =0.4), (f) is t=900s(t * =0.45);

[0095] Fig. 9 The vertical displacement cloud diagram of the ECC board at different times in the embodiment of the present invention, where (a) is t=100s (t * =0.05), (b) is t=200s(t * =0.1), (c) is t=400s(t * =0.2), (d) is t=600s(t * =0.3), (e) is t=800s(t * =0.4), (f) is t=900s(t * =0.45);

[0096] Fig.10 Schematic diagram of the convergence of the displacement field (t=100s) calculated by the ADR algorithm according to an embodiment of the present invention;

[0097] Fig.11 Schematic diagram of the evolution of the temperature of the bottom surface of the test piece of the embodiment of the present invention over time;

[0098] Fig.12 Schematic diagram of the numerical results of crack extension of the ECC plate of the embodiment of the present invention, where (a) is t=100s (t * =0.05), (b) is t=200s(t * =0.1), (c) is t=400s(t* =0.2), (d) is t=600s(t * =0.3), (e) is t=800s(t * =0.4), (f) is t=900s(t * =0.45). DETAILED DESCRIPTION

[0099] It should be noted that, in the absence of conflict, the embodiments and features in the embodiments of the present application can be combined with each other. The present application will be described in detail below with reference to the accompanying drawings and in combination with the embodiments.

[0100] It should be noted that the steps shown in the flowcharts of the accompanying drawings can be executed in a computer system such as a set of computer executable instructions, and that, although a logical order is shown in the flowcharts, in some cases, the steps shown or described can be executed in an order different from that shown here.

[0101] like Figure 1 As shown, this embodiment provides a novel thermal-fluid-mechanical coupling simulation method based on peridynamic differential operators, including:

[0102] S1: Initialization settings: define the material geometry and set the initial parameters, including the temperature, density, velocity, pressure, etc. of the fluid and solid materials;

[0103] S2: Generate discrete model: Divide the fluid and solid areas into multiple PD (peri-field dynamics) points, and classify them according to different properties to divide them into fluid point families and solid point families.

[0104] S3: Fluid-solid interface processing: Calculate the fluid temperature field cyclically, update the temperature value of each point, and convert it into dimensional form as needed; calculate the dimensionless thermal related parameters of the fluid, such as thermal conductivity, thermal expansion coefficient, etc.; and apply the dimensionless temperature, adiabatic and velocity boundary conditions of the flow field; calculate the temperature field of the solid material; calculate the dimensionless heat flux density at the fluid-solid interface; calculate the dimensionless thermal parameters of the solid material, and apply adiabatic boundary conditions and displacement boundary conditions; then, calculate and update the temperature of each point, and convert it into dimensional form; calculate the bond force density at each point.

[0105] S4: Application of dynamic relaxation algorithm: Calculate the mechanical parameters of the material, such as stress and strain, to comprehensively evaluate the mechanical properties of the system; apply displacement boundary conditions, and use the adaptive dynamic relaxation method (Adaptive Dynamic Relaxation, ADR algorithm) to update the displacement field, temperature field and other parameters of the fluid and solid points through iterative calculation; during the iteration process, determine whether the system has reached a steady state based on the condition "If Ru≤Ω".

[0106] S5: Result output: Output the calculated temperature field, mechanical parameters and other results for subsequent analysis and application.

[0107] Furthermore, the specific method of step S1 is as follows:

[0108] S1.1: Define material geometry: First, the geometry of the simulation object needs to be defined. For example, when simulating an ECC board or an ECC-concrete bi-material board, its length, width, and thickness need to be defined. These dimensions should be determined based on the specific research objectives and experimental conditions.

[0109] S1.2: Temperature of fluid and solid materials: Set the initial temperature of fluid (such as hot air in fire) and solid (ECC and concrete) according to the initial conditions of the simulation. For example, when simulating a fire scene, the initial ambient temperature can be set to normal temperature (such as 20°C), while the initial temperature of the fire hot air can be set according to the fire model (such as ISO834 standard temperature rise curve), and its function form is as follows:

[0110]

[0111] Among them, T fire (t) is the initial temperature of the fluid and solid material, t is the elapsed time, and K is the temperature unit Kelvin.

[0112] The above formula can be expressed in dimensionless form as:

[0113]

[0114] S1.3: Density: According to the physical properties of ECC and concrete, set their densities respectively. The density of ECC may vary slightly due to its fiber reinforcement, while the density of concrete is relatively stable; Velocity: At the initial moment, it is usually assumed that all fluid and solid points are at rest, so the velocities are set to 0; Pressure: In the fluid domain, it is necessary to set the initial pressure field, which is usually related to the initial state of the fluid and the boundary conditions; Introduce the state equation to estimate the pressure of the density field:

[0115]

[0116] where ρ 0 is the initial density of the fluid, C s is the artificial sound velocity, and its value must be at least 10 times higher than the maximum flow rate of the fluid. γ is the heat capacity ratio, and the heat capacity ratio of gas is usually 1. In the solid domain, the initial pressure can be set to 0.

[0117] Furthermore, the specific method of step S2 is as follows:

[0118] S2.1: Divide the simulation area into multiple peridynamic points (PD points); the number and distribution density of PD points should be determined based on the simulation accuracy and computing resources.

[0119] S2.2: Attribute classification: According to the type and properties of the material, in the discrete model, PD points are divided into fluid point families and solid point families; the fluid point family represents hot gas or other fluid media in the fire, while the solid point family represents solid materials such as ECC and concrete.

[0120] S2.3: Initial parameter assignment: Assign the previously set initial parameters (such as temperature, density, speed, pressure, etc.) to each PD point. In this way, each PD point carries its own physical state and attribute information.

[0121] Furthermore, the specific method of step S3 is as follows:

[0122] S3.1: Fluid-solid interface processing: First, calculate the PD differential operator of the fluid point according to the divided fluid point family and solid point family, and enter Figure 1 Cycle 1 shown calculates the temperature fields of the fluid and solid materials;

[0123] The explicit integration method is used to solve the peridynamic heat conduction equation, and its discretized form is:

[0124]

[0125] where t n represents the current time step, x i Represents x j Material point in the near field, N i Represents x i The total number of material points in the near field, V j Represents a particle x j The approximate volume of

[0126] The forward difference method is used to calculate the temperature value of the next time step. The algorithm is expressed as:

[0127]

[0128] Where Δt TH To calculate the time step of heat diffusion, the conditions are selected as follows:

[0129]

[0130] in, For x i and x j The micro thermal conductivity function between hot bonds is calculated as follows: K(T) is the thermal conductivity of the material; For x i and x j The relative distance between .

[0131] S3.2 then calculates dimensionless heat-related parameters for the fluid and solid;

[0132] The dimensionless nonlocal form of the Navier-Stokes equations can be obtained using the following parameters:

[0133]

[0134] Among them, the parameters with subscript 0 are reference variables, the parameters with superscript * are dimensionless variables, g represents the acceleration due to gravity, For mass x 1 The dimensionless form of For mass x 2 The dimensionless form of L 0 is the reference length, For mass x 1 The dimensionless form of velocity, For mass x 2 The dimensionless form of velocity, v 0 is the initial velocity, t* is the dimensionless form of time, is the dimensionless form of fluid density, ρ f is the fluid density, is the dimensionless form of the fluid point temperature, T f is the fluid point temperature, T 0 is the initial temperature, p * is the dimensionless form of fluid pressure, p is the fluid pressure, p 0 is the initial fluid pressure, g * is the dimensionless form of gravitational acceleration, g is the gravitational acceleration, is the dimensionless value of dynamic viscosity, μ f is the dynamic viscosity, is the dimensionless value of thermal conductivity, k f is the thermal conductivity;

[0135] The parameter calculation formulas involved in calculating the mass conservation, momentum conservation and energy conservation equations are as follows:

[0136]

[0137] Where Re is the Reynolds number, Pr is the Prandtl number, Ec is the Eckert number, μ 0 is the initial dynamic viscosity, C 0 is the initial specific heat, k 0 is the initial thermal conductivity, T 0 is the initial temperature;

[0138] The dimensionless gravitational acceleration can be approximated as:

[0139]

[0140] Among them, β f is the thermal expansion coefficient of the fluid, β 0 is the initial thermal expansion coefficient, T * is the dimensionless form of temperature, and Ra is the Rayleigh number, which is calculated as:

[0141]

[0142] In addition, Sutherland's law reflects the effect of temperature on viscosity and thermal conductivity, and their dimensionless forms are expressed as:

[0143]

[0144] in, is the dimensionless value of dynamic viscosity, is the dimensionless value of thermal conductivity, T f is the fluid point temperature, S μ is the dimensionless value of the fluid dynamic viscosity, S k is the dimensionless value of the thermal conductivity of the fluid, the dimensionless value S μ = 0.368 and S k =0.648.

[0145] S3.3 and apply fluid and solid boundary conditions;

[0146] S3.3.1 Application of flow field boundary conditions:

[0147] Temperature boundary conditions:

[0148] In order to ensure that the specified boundary temperature can be accurately reflected in the real material area, it is necessary to add a virtual layer with a thickness of δ near-field radius, and apply a temperature boundary to the particles in the virtual layer according to the following formula:

[0149]

[0150] The adiabatic boundary condition is applied as follows:

[0151]

[0152] in Indicates t n Boundary temperature value at time, Indicates t n The point x in the virtual layer at time i The temperature, Indicates t n Real material point x iThe temperature of the virtual point x i The distance to the boundary and the real particle x j The distances to the border are equal.

[0153] Flow boundary conditions:

[0154] For the no-slip solid wall boundary condition, the virtual layer in peridynamics is used; a thickness of δ is added to the fluid domain boundary. f The rigid solid wall virtual layer R c，f , set the velocity and displacement of the particle in the virtual layer to:

[0155] v f (x f )=0,u f (x f )=0,x f ∈R c，f (14)

[0156] The pressure value of the virtual layer is defined as:

[0157]

[0158] where x f，i is a particle in the virtual layer, x f，j is x f，i The real fluid point in the near field belongs to the flow field, N c，f is x f，i The total number of real fluid particles in the near field.

[0159] S3.3.2 Application of boundary conditions for solid materials:

[0160] Displacement and velocity boundary conditions: For displacement and velocity boundary conditions, it is also necessary to add a virtual layer R with a thickness of δ c , for R c The particles in the region exert a forced displacement vector U 0 Or velocity vector V 0 ;

[0161]

[0162] Heat transfer conditions at fluid-solid interface:

[0163] The heat flux density generated by thermal convection is in the form of:

[0164]

[0165] Where h is the convective heat transfer coefficient, t n Time interface point x interface The temperature, t nTime step particle x interface The temperature of the surrounding medium. The form is as follows:

[0166]

[0167] Since the thermal fluid is the heat transfer source to the solid, Represents the interface point x interface The total number of points belonging to the fluid in the near field, T f (x f，j , t n ) is t n Time step fluid point x f，j temperature.

[0168] The heat flux generated by thermal radiation is in the form of:

[0169]

[0170] Where σ is the Stefan-Boltzmann constant and is the emissivity (also known as blackness) of the boundary surface:

[0171]

[0172] Furthermore, the specific method of step S4 is as follows:

[0173] S4.1 uses the adaptive dynamic relaxation method (ADR algorithm). By introducing the virtual mass matrix and damping terms, the numerical solution can converge quickly. At this time, the motion equation is:

[0174]

[0175] Where D is the virtual mass matrix, c is the damping coefficient, which is obtained by Reschgorin's law and Rayleigh quotient respectively; u represents displacement, and F is the sum of bond force density and body force density. The explicit central difference method is used to solve this equation:

[0176]

[0177] Δt M is the time step, Δt in the adaptive dynamic relaxation method M It has no physical meaning. For the convenience of calculation, Δt is usually taken M =1.

[0178] When the iteration starts:

[0179]

[0180] c 1 =0 (26)

[0181] To determine whether the numerical solution converges, the root mean square of the displacement of each particle, Ru, is calculated and compared with a fairly small number, Ω. The smaller the value, the higher the accuracy of the calculation result, but the greater the calculation cost. In this paper, 1×10 -10 ) is compared. When Ru≤Ω, the system is considered to have reached a steady state. Otherwise, the steady-state solution of the motion equation is continuously iterated. The calculation form of Ru is as follows:

[0182]

[0183] Where M is the total number of discrete model particles.

[0184] Furthermore, the specific method of step S5 is as follows:

[0185] S5.1 determines whether the system has reached a steady state based on the condition "If Ru≤Ω". If so, the damage is updated and the next fluid-solid family is calculated. If the steady state has not been reached, the result is re-submitted into the calculation of the solid displacement field, the displacement boundary conditions are applied and the bond force density of each point is recalculated, and then re-submitted into the ADR algorithm for solution.

[0186] A specific application example of the present invention is as follows:

[0187] Initialization settings: Define material geometry: The dimensionless geometry of the model is as follows: Figure 2 As shown, the geometric dimensions of the ECC board with a fiber content of 2% are 0.5 in length and 0.4 in width; the board is placed in an air square cavity with a size of 1×1, a fire load is applied to the bottom of the fluid domain, and its distance from the bottom of the ECC specimen is 0.3.

[0188] Temperature of fluid and solid material: reference temperature and initial temperature are taken as T 0 =293K.

[0189] Other parameters: reference length is L 0 = 0.2m, the dimensionless Rayleigh number and Prandtl constant of air are taken as Ra = 10 3 and Pr = 0.71, viscosity coefficient α f，0 =2×10 -5 m / s, the reference speed is usually calculated as v 0 =α f，0 / L 0 , artificial sound speed c sound =10v 0 The thermal conductivity of air is 0.24W / (w·K) and the density is 1.29kg / m 3 , specific heat capacity 1100 J / (kg·K).

[0190] Generate a discrete model:

[0191] PD Discrete: PD Discrete model is as follows Figure 3 As shown, the near field radius δ * =0.02, particle spacing dx * =dy * =δ * / 4, the dimensionless time step for temperature field calculation is Compute the displacement field using the adaptive dynamic relaxation method with a time step of Δt M =1.

[0192] Fluid-solid interface treatment:

[0193] Fluid material processing: First, according to the divided fluid point family and solid point family, the PD differential operator of the fluid point is calculated and entered Figure 1 The cycle 1 shown calculates the temperature field of the fluid; then the dimensionless heat-related parameters of the fluid are calculated, and the dimensionless temperature, adiabatic and velocity boundary conditions of the flow field are applied;

[0194] Fluid temperature boundary conditions:

[0195]

[0196]

[0197] Fluid virtual wall boundary conditions:

[0198]

[0199] The dimensionless density, velocity, pressure, and temperature of the fluid point are then calculated and updated.

[0200] Solid material processing: Calculate the temperature field of the solid material according to the divided fluid point families and solid point families; then calculate the dimensionless heat flux density at the fluid-solid interface and the dimensionless thermal parameters of the solid material, and apply adiabatic boundary conditions;

[0201] Temperature boundary conditions of ECC specimens:

[0202]

[0203] x * =0.5,0.3≤y * 0.7; 0≤x * ≤0.5,y * = 0.3 and y * =0.7; (33)

[0204]

[0205] Finally, the temperature of each point is calculated and updated and converted into dimensional form.

[0206] Dynamic relaxation algorithm application:

[0207] Calculate the mechanical parameters of the material and enter Figure 1 Loop 2 in Calculates the displacement field of the solid material and applies displacement boundary conditions.

[0208] Displacement boundary conditions for ECC:

[0209]

[0210] Then the bond force density of each point is calculated; the adaptive dynamic relaxation algorithm calculates the displacement and determines whether "If Ru≤Ω". If the condition is not met, it is re-entered into loop 2 for iteration; if the condition is met, the damage is updated, and the new fluid and solid point families are brought into loop 1 for a new round of iterative calculation.

[0211] Result analysis:

[0212] like Figure 4 , Figure 5 and Figure 6 As shown in the figure, in the early stage of heat transfer, the bottom of the fluid domain is affected by the fire heat source, and the temperature is significantly higher than the top, resulting in significant pressure and density differences, which prompts the hot air to flow from bottom to top. The maximum horizontal velocity appears at the ECC and the upper and lower boundaries of the fluid domain, and the maximum vertical velocity is at the right boundary of the ECC and the right boundary of the fluid domain. As the heat transfer deepens, the temperature difference decreases, the buoyancy effect weakens, and the hot air velocity gradually decreases and tends to be stable.

[0213] like Figure 7 , Figure 8 and Fig. 9 The temperature cloud map, horizontal and vertical displacement cloud map of the ECC plate are given. It can be seen that the temperature rise of the ECC plate in contact with the heat flow is significant. Due to the low thermal conductivity of the material, the internal temperature rises slowly, forming a large temperature gradient. As the heat transfer proceeds, the edge of the plate accumulates damage, the high temperature is concentrated on the outer edge, and the damage has limited effect on heat transfer. The displacement cloud map shows that the specimen expands toward the high temperature side, the deformation is non-uniform, the deformation on the high temperature side is large, and the displacement on both sides of the crack is discontinuous.

[0214] Fig.10 It shows the convergence of the ADR algorithm in calculating the displacement field. The number of ADR steps is basically around 4000 steps, and the calculation results converge.

[0215] Fig.12 The thermal damage mode of the ECC plate is shown: at 400s, the bottom edge and the right boundary are decomposed by the high temperature (>700K), and the fiber is brittlely damaged with the matrix peeling off. The high temperature is concentrated at the boundary, and the peeling zone expands along the high temperature gradient network crack, while the interior remains intact. Compared with Li Hongbing's test, the ECC specimens show different degrees of damage at different temperatures. Fig.11 and Fig.12The comparison of the results shows that at 500s, the bottom edge temperature reaches 850K, with a small amount of spalling and microcracks; at 800s, it exceeds 1050K, the spalling increases, and the network cracks expand significantly.

[0216] The present invention discloses a novel heat-fluid-mechanical coupling simulation method based on peridynamic differential operators, which solves the shortcomings of the prior art in dealing with the problem of thermal failure in fiber-reinforced cement-based composite materials and concrete bonding specimens, especially the simulation difficulties of material performance degradation and complex multi-field coupling effects in high-temperature environments. The peridynamic differential operator is introduced into the heat-fluid-mechanical coupling simulation, which realizes the comprehensive consideration of the material microstructure, high-temperature performance degradation and fire dynamics response, and provides a more accurate and comprehensive simulation method for the performance evaluation of fiber-reinforced cement-based composite materials and concrete bonding specimens in high-temperature environments, which has important engineering application value and scientific research significance.

[0217] The above are only preferred specific implementations of the present application, but the protection scope of the present application is not limited thereto. Any changes or substitutions that can be easily thought of by a person skilled in the art within the technical scope disclosed in the present application should be included in the protection scope of the present application. Therefore, the protection scope of the present application should be based on the protection scope of the claims.

Claims

1. A novel thermal-fluid-mechanical coupling simulation method based on peridynamic differential operators, characterized in that: include: Define the material geometry and set initial parameters, including temperature, density, velocity, and pressure of fluid and solid materials; Dividing the fluid and solid regions into a plurality of peridynamic points, and classifying them according to different properties to divide them into fluid point families and solid point families, and generating discrete models based on the fluid point families and the solid point families; Calculating the temperature field of the fluid, updating the temperature value of each point, and converting it into a dimensional form as needed; calculating the dimensionless heat-related parameters of the fluid, and applying the dimensionless temperature, adiabatic and velocity boundary conditions of the flow field; calculating a temperature field of the solid material; Calculate the dimensionless heat flux at the fluid-solid interface; Calculate dimensionless thermal parameters of solid materials and apply adiabatic and displacement boundary conditions; Calculate and update the temperature of each point and convert it into dimensional form; calculate the bond force density of each point; Calculate the mechanical parameters of the material to comprehensively evaluate the mechanical properties of the system; apply displacement boundary conditions, and use the adaptive dynamic relaxation method to update the displacement field and temperature field of the fluid point and solid point through iterative calculation; During the iteration process, it is determined whether the system has reached a steady state, and after reaching a steady state, the thermal-fluid-force coupling simulation is completed.

2. The novel thermal-fluid-mechanical coupling simulation method based on peridynamic differential operators as claimed in claim 1 is characterized in that: Set the initial temperature of the fluid and solid materials to be calculated as follows: Among them, T fine (t) is the initial temperature of the fluid and solid material, t is the elapsed time, and K is the temperature unit Kelvin.

3. The novel thermal-fluid-mechanical coupling simulation method based on peridynamic differential operators as claimed in claim 1 is characterized in that: Set the initial pressure calculations for the fluid and solid materials as follows: Where ρ0 is the initial density of the fluid, C s is the artificial speed of sound, and γ is the heat capacity ratio.

4. The novel thermal-fluid-mechanical coupling simulation method based on peridynamic differential operators as claimed in claim 1 is characterized in that: Generating a discrete model involves: Dividing the simulation area into a plurality of peridynamic points; the number and distribution density of the peridynamic points are determined according to the accuracy of the simulation and the computing resources; According to the type and property of the material, the near-field dynamic points are divided into a fluid point family and a solid point family in the discrete model, wherein the fluid point family includes hot gas or other fluid media in the fire, and the solid point family includes fiber-reinforced cement-based composite materials and concrete solid materials; Assign the set initial parameters to each peridynamic point.

5. The novel thermal-fluid-mechanical coupling simulation method based on peridynamic differential operators as claimed in claim 1 is characterized in that: The method for calculating the temperature field of the fluid is: The explicit integration method is used to solve the peridynamic heat conduction equation, and its discretized form is: Among them, t n represents the current time step, x i Represents x j Material point in the near field, N i Represents x i The total number of material points in the near field, V j Represents a particle x j The approximate volume of The temperature value of the next time step is calculated using the forward difference method as follows: Among them, Δt TH To calculate the time step of heat diffusion, the conditions are selected as follows: in, For x i and x j The micro thermal conductivity function between hot bonds is given by K(T) is the thermal conductivity of the material; For x i and x j The relative distance between .

6. The novel thermal-fluid-mechanical coupling simulation method based on peridynamic differential operators as claimed in claim 1 is characterized in that: The method for calculating the dimensionless heat-related parameters of the fluid is: Obtain the dimensionless nonlocal form of the Navier–Stokes equations: Among them, the parameters with subscript 0 are reference variables, the parameters with superscript * are dimensionless variables, g represents the acceleration due to gravity, is the dimensionless form of the particle x1, is the dimensionless form of the particle x2, L0 is the reference length, is the dimensionless form of the velocity of particle x1, is the dimensionless form of the velocity of particle x2, v0 is the initial velocity, t * is the dimensionless form of time, is the dimensionless form of fluid density, ρ f is the fluid density, is the dimensionless form of the fluid point temperature, T f is the fluid point temperature, T0 is the initial temperature, p * is the dimensionless form of fluid pressure, p is the fluid pressure, p0 is the initial fluid pressure, g * is the dimensionless form of gravitational acceleration, g is the gravitational acceleration, is the dimensionless value of dynamic viscosity, μ f is the dynamic viscosity, is the dimensionless value of thermal conductivity, k f is the thermal conductivity; The parameter calculation formulas involved in calculating the mass conservation, momentum conservation and energy conservation equations are as follows: Where Re is the Reynolds number, Pr is the Prandtl number, Ec is the Eckert number, μ0 is the initial dynamic viscosity, C0 is the initial specific heat capacity, k0 is the initial thermal conductivity, and T0 is the initial temperature; The dimensionless gravitational acceleration is approximately: Among them, β f is the thermal expansion coefficient of the fluid, β0 is the initial thermal expansion coefficient, T * is the dimensionless form of temperature, Ra is the Rayleigh number, and is calculated as: Sutherland's law reflects the effect of temperature on viscosity and thermal conductivity, and is expressed in dimensionless form as: in, is the dimensionless value of dynamic viscosity, is the dimensionless value of thermal conductivity, T f is the fluid point temperature, S μ is the dimensionless value of the fluid dynamic viscosity, S k is the dimensionless value of the thermal conductivity of the fluid.

7. The novel thermal-fluid-mechanical coupling simulation method based on peridynamic differential operators as claimed in claim 1 is characterized in that: The dimensionless temperature, adiabatic and velocity boundary conditions that impose the flow field include Temperature boundary conditions: Add a virtual layer with a thickness of δ near-field radius, and apply a temperature boundary to the particles in the virtual layer according to the following formula: The adiabatic boundary condition is applied as follows: in, Indicates t n Boundary temperature value at time, Indicates t n The point x in the virtual layer at time i The temperature, Indicates t n Real material point x j The temperature of the virtual point x i The distance to the boundary and the real particle x j The distances to the border are equal; Flow boundary conditions: For the no-slip solid wall boundary condition, the virtual layer in peridynamics is used; Add a thickness of δ to the fluid domain boundary f The rigid solid wall virtual layer R c，f , set the velocity and displacement of the particle in the virtual layer to: v f (x f )=0,u f (x f )=0,x f ∈R c，f The pressure value of the virtual layer is defined as: where x f，i is a particle in the virtual layer, x f，j is x f，j The real fluid point in the near field belongs to the flow field, N c，f is x f，i The total number of real fluid particles in the near field.

8. The novel thermal-fluid-mechanical coupling simulation method based on peridynamic differential operators as claimed in claim 1 is characterized in that: Applying adiabatic boundary conditions and displacement boundary conditions includes: Displacement and velocity boundary conditions: For displacement and velocity boundary conditions, it is also necessary to add a virtual layer R with a thickness of δ c , for R c The particles in the region exert a forced displacement vector U0 or velocity vector V0; Heat transfer conditions at fluid-solid interface: The heat flux density generated by thermal convection is in the form of: Where h is the convective heat transfer coefficient, t n Time interface point x interface The temperature, t n Time step particle x interface The temperature of the surrounding medium; The form is as follows: in, Represents the interface point x interface The total number of points belonging to the fluid in the near field, T f (x f，j , t n ) is t n Time step fluid point x f，j Temperature; The heat flux generated by thermal radiation is in the form of: Where σ is the emissivity of the boundary surface:

9. The novel thermal-fluid-mechanical coupling simulation method based on peridynamic differential operators as claimed in claim 1, characterized in that: The adaptive dynamic relaxation method is used to iteratively calculate and update the displacement field and temperature field of fluid points and solid points, including: Adaptive dynamic relaxation method is used. By introducing virtual mass matrix and damping term, the equation of motion is: Where D is the virtual mass matrix, c is the damping coefficient, which are obtained by Reschgorin's law and Rayleigh quotient, respectively; u represents the displacement, and F is the sum of the bond force density and the body force density; The explicit central difference method is used to solve this equation: Among them, Δt M is the time step; When the iteration starts: c1＝0 By calculating the root mean square Ru of the displacement of each particle, and comparing the root mean square with a relatively small number Ω(, we can determine whether the numerical solution converges. When Ru≤Ω, the system is considered to have reached a steady state. Otherwise, we continue to iterate to find the steady-state solution of the motion equation. The calculation form of Ru is as follows: Where M is the total number of discrete model particles.

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