CN110070919B - Melting model related to crystalline phase reaction and numerical simulation method thereof - Google Patents
Melting model related to crystalline phase reaction and numerical simulation method thereof Download PDFInfo
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Abstract
The invention discloses a melting model relating to crystal phase reaction and a numerical simulation method thereof, relating to the field of numerical simulation of binary alloy melting and comprising the following steps: step 1: establishing a constant temperature diffusion model; step 2: establishing a diffusion equation on the basis of a constant temperature diffusion model; and 3, step 3: establishing a heating melting model; and 4, step 4: if the alloy is not positioned in the phase change region, calculating the alloy temperature by adopting a heat conduction equation without an internal heat source; if the alloy is located in the phase change region, the temperature and the liquid phase portion of the alloy in the melting process are calculated by adopting an internal heat source heat conduction equation. The invention discloses a fusion model which effectively and feasible relates to a crystalline phase reaction and a simulation method thereof by combining diffusion mass transfer and a phase diagram theory.
Description
Technical Field
The invention relates to the field of numerical simulation of binary alloy melting, in particular to a melting model for crystal phase reaction and a numerical simulation method thereof.
Background
Solid-liquid phase change occurs in the melting process, different materials can also generate crystalline phase reaction in the melting process, and the crystalline phase reaction can change the crystal structure of the materials and further influence the inherent characteristics of the materials, such as thermal property, mechanical property and chemical property, so that the materials are aged in advance, and the safety and the economical efficiency of actual production are influenced. Therefore, the research on the crystal phase reaction in the melting process is significant in improving the safety of material application and developing new materials to research the performance of the material.
The solid-liquid phase change model used for simulating the melting phenomenon is based on an enthalpy value, the temperature is kept unchanged in the melting process theoretically, and the liquid phase share and the specific enthalpy value are in a linear relation. The calculation flow is as follows: firstly, an enthalpy value is obtained according to an energy equation:
then obtaining the temperature distribution and the liquid phase fraction according to the following formula, and determining the position of a phase interface according to the liquid phase fraction:
in the formula, T m Is the phase transition temperature, H s And H L Respectively is solid phase enthalpy and liquid phase enthalpy, C p,s And C p,L The constant pressure specific heat capacity of the solid phase and the liquid phase respectively, and epsilon is the liquid phase share.
The relation between the temperature and the liquid phase fraction and the enthalpy value in the solid-liquid phase change model used for simulating the melting phenomenon is an empirical formula, and the melting process related to the crystal phase reaction can not be simulated, and only can be used for simulating the melting of a single-component substance.
Regarding the simulation of the reaction phenomenon of the crystal phase, mustar, A.P.A., et al, 3D correlation of electronic interaction of Pb-Sn system using Moving Particle Semi-interference (MPS) method, annals of Nuclear Energy,2015.81 p.26-33. The simulation and experiment of the eutectic reaction phenomenon of Pb-Sn at constant temperature are described. At a constant temperature of 225 ℃, mass diffusion occurs at the interface of the lead block and the tin block, and the mass diffusion equation is as follows:
according to the Pb-Sn phase diagram, eutectic melting occurs at the phase interface when the mass fraction of tin reaches the corresponding liquefaction value.
Accordingly, those skilled in the art have been devoted to developing a melting model involving the reaction of crystal phases and a numerical simulation method thereof, which can effectively simulate the melting process with the reaction of crystal phases.
Disclosure of Invention
In view of the above-mentioned drawbacks of the prior art, the technical problem to be solved by the present invention is that the empirical relationship of temperature and liquid phase fraction with enthalpy in a phase transition model of enthalpy does not allow to correctly simulate the melting phenomenon and that there is no melting model that can simulate reactions involving crystalline phases.
In order to achieve the above object, the present invention also provides a melting numerical simulation method involving a reaction of a crystal phase, comprising the steps of:
step 1: establishing a constant temperature diffusion model;
step 2: establishing a diffusion equation on the basis of the constant temperature diffusion model, and calculating the total mass fraction w of the alloy element A in the alloy 0 ；
And 3, step 3: establishing a heating melting model: according to the mass fraction of the alloy element A and the alloy temperature T 0 And an alloy binary phase diagram, judging whether the alloy enters a phase change region;
and 4, step 4: if the alloy is not positioned in the phase change region, calculating the alloy temperature T by adopting a heat conduction equation without an internal heat source 1 (ii) a If the alloy is positioned in the phase change area, calculating the temperature T of the alloy in the melting process by adopting an internal heat source heat conduction equation 1 And a liquid phase fraction;
and 5: if the alloy is completely melted, stopping the iterative calculation process; if the alloy is not completely melted, repeating the steps 2 to 4.
Further, the constant temperature diffusion model in the step 1 includes an alloy element a and a metal element B: the alloy element A is in a solid state, and the metal element B is in a liquid state; the alloy element A and the metal element B are in contact with each other and the temperature of the contact surface is kept constant.
Further, the diffusion equation in the step 2 is:
wherein n is the amount of the substance, t is the time, and D is the diffusion coefficient in a solid or liquid;
a crystal phase reaction occurs on the alloy solid-liquid phase interface, and the crystal phase reaction is described as a diffusion behavior with a large diffusion coefficient in calculation, wherein the diffusion equation is as follows:
wherein K is the interfacial diffusion coefficient.
Further, the total mass fraction of the alloying element a in the temperature-increasing melting model in the step 3 is kept constant.
Further, in the step 4, the heat conduction equation of the internal heat source-free heat source is as follows:
wherein ρ is the density of the alloy, C p Is the constant pressure specific heat capacity of the alloy, T is the temperature, T is the time, and k is the heat transfer coefficient.
Further, in the step 4, the liquid phase fraction is calculated by the formula:
in the formula, x L Is the liquid phase fraction of the alloy, omega L Is the mass fraction, omega, of the alloying element A in the liquid phase of the alloy s The superscript n is the mass fraction of the alloying element A in the alloy solid phase and denotes the nth time step,
is the mass fraction of element A in the alloy phase at the nth time step.
Further, in the step 4, the heat conduction equation of the internal heat source is as follows:
wherein ρ is the density of the alloy, C p Is the constant pressure specific heat capacity of the alloy, T is the temperature, T is the time, k is the heat transfer systemNumber, x L Is the liquid phase fraction of the alloy, h sL Is the latent heat of solid-liquid fusion phase change.
Further, in the step 4, the heat conduction equation of the internal heat source is obtained through the following steps:
step 4.1: in the (n-1) th step, melting is started, and the mass fraction of the alloying element A in the liquid phase is
Step 4.2: in the n-th step, the liquid phase fraction is
The liquid phase portion is increased by an amount of
Is marked as
The heat absorption of the liquefaction part of this time step is
The mass fractions of the alloy element A in the solid phase and the liquid phase are respectively
And
step 4.3: in the (n + 1) th step, the remaining solid phase portion is melted, and the liquid phase portion is increased by an amount
Is marked as
The heat absorption of the liquefied fraction in this time step is
At this time, the mass fraction of the element alloying element A in the solid phase and the liquid phase becomes
And
step 4.4: repeating said steps 4.1 to 4.2 until complete liquefaction.
Further, the density of the alloy is calculated by the formula:
in the formula, M A Is the molar mass of the alloying element A, n A For one calculation of the amount of said substance of the alloying element A, M B Is the molar mass of the metal element B, n B Calculating the amount of the metal element B in a calculation grid, and V is the volume of the calculation grid;
the calculation formula of the constant-pressure specific heat capacity of the alloy is as follows:
in the formula, C pA Is the constant pressure specific heat capacity of the alloy element A, C pB Is the constant pressure specific heat capacity of the metal element B.
The invention also provides a melting model related to the crystal phase reaction, which comprises a constant-temperature diffusion part and a heating melting part, wherein the constant-temperature diffusion part and the heating melting part are represented by the following formulas:
where ρ is the density of the alloy, C p Is a stand forThe constant pressure specific heat capacity of the alloy, T is temperature, T is time, k is heat transfer coefficient, x L Is the liquid phase fraction of the alloy, h sL Is the latent heat of solid-liquid fusion phase change.
Compared with the prior art, the invention has at least the following beneficial effects:
1. the invention discloses a melting model relating to crystalline phase reaction and a numerical simulation method thereof, which combine diffusion mass transfer and phase diagram theory and provide a melting process capable of simulating the crystalline phase reaction;
2. the invention discloses a melting model related to a crystalline phase reaction and a numerical simulation method thereof, which overcome the defect that the conventional enthalpy model neglects to enter a phase change region, only a part of solid phase is liquefied at a certain temperature, and each temperature rise corresponds to the increase of the liquid phase fraction.
The conception, the specific structure and the technical effects of the present invention will be further described with reference to the accompanying drawings to fully understand the objects, the features and the effects of the present invention.
Drawings
FIG. 1 is a computational flow diagram of the present invention;
FIG. 2 is a schematic view of a constant temperature diffusion model according to a preferred embodiment of the present invention;
FIG. 3 is a peritectic phase diagram of a preferred embodiment of the present invention;
FIG. 4 is a schematic view of a temperature-increasing melting model in accordance with a preferred embodiment of the present invention;
FIG. 5 is an equilibrium phase diagram of a temperature-increasing melting model in accordance with a preferred embodiment of the present invention.
Detailed Description
The technical contents of the preferred embodiments of the present invention will be more clearly and easily understood by referring to the drawings attached to the specification. The present invention may be embodied in many different forms of embodiments and the scope of the invention is not limited to the embodiments set forth herein.
In the drawings, elements that are structurally identical are represented by like reference numerals, and elements that are structurally or functionally similar in each instance are represented by like reference numerals. The size and thickness of each component shown in the drawings are arbitrarily illustrated, and the present invention is not limited to the size and thickness of each component. The thickness of the components may be exaggerated where appropriate in the figures to improve clarity.
The peritectic phase diagram of Cu-Ni alloy is taken as an example to explain the phenomenon that solid nickel blocks are melted in liquid copper.
As shown in FIG. 2, the temperature of the solid nickel 1 is 1100 deg.C, the temperature of the liquid copper 2 is 1450 deg.C, and the liquid copper 2 melts the solid nickel 1 at 1100 deg.C, during which the Cu-Ni peritectic reaction occurs. The entire melting process can be divided into two phenomena: the melting caused by the reaction of the crystal phases caused by diffusion and the melting caused by heating are simultaneously carried out in the whole process, the melting caused by the reaction of the crystal phases is simulated by a constant-temperature diffusion model, and the melting caused by heating is simulated by a temperature-increasing melting model. The two processes are explained below separately by means of phase diagrams.
As shown in FIG. 1 and FIG. 3, after the constant temperature diffusion model is established, firstly, the diffusion equation is solved to obtain the mass fraction w of the Ni element in the alloy 0， And obtaining a solidus and a liquidus under the mass fraction by a phase diagram, then judging whether to enter a phase change region (namely whether the temperature is greater than the solidus and less than the liquidus), if so, calculating the temperature and the liquid phase share by using a heat conduction equation of an internal heat source, otherwise, calculating the temperature by using the heat conduction equation without the internal heat source, and carrying out the melting process according to the rule until the melting is completely liquefied.
As shown in FIG. 2, the constant temperature diffusion model reflects the constant temperature diffusion process of melting, the temperature of the contact surface of the two metals is controlled to be kept constant and maintained at 1450 ℃, the influence of the temperature is not considered, only the melting caused by the crystal phase reaction is considered, and the concentration gradient is the only influencing factor.
The diffusion equation due to gradient differences in the solid or liquid phase is:
wherein n is the amount of the substance, t is the time, and D is the diffusion coefficient in a solid or liquid;
in the Cu-Ni solid-liquid phase interface, a crystal phase reaction occurs, which is described as a diffusion behavior with a large diffusion coefficient in calculation, and the diffusion equation is as follows:
wherein K is the interfacial diffusion coefficient.
The diffusion at the interface simulates the equation of the crystal phase reaction, and the diffusion coefficient K of the interface is far larger than the diffusion coefficient D in solid or liquid (namely non-interface).
As shown in FIG. 3, the x-axis is the mass fraction of Ni content and the y-axis is temperature. At the constant temperature of 1450 ℃, mass diffusion occurs at the phase interface, the Ni content in the solid phase is reduced along with the diffusion, and when the Ni content is lower than omega L When this occurs, the solid phase changes to a liquid phase.
The temperature-rising melting model is shown in FIG. 4, a solid alloy Cu-Ni block 3 is arranged on a heating plate 4, the Cu-Ni ratio of the alloy is fixed at the moment of the alloy Cu-Ni block 3, and the initial temperature is 1000 ℃; the temperature of the heating plate 4 was 1500 ℃. The whole melting process is divided into two parts according to whether phase change occurs or not, and pure solid phase or pure liquid phase heat conduction is calculated according to a heat conduction equation without an internal heat source:
where ρ is the density of the alloy, C p The constant pressure specific heat capacity of the alloy, T is temperature, T is time and k is heat transfer coefficient.
The solid-liquid coexisting phase in the phase change region generates crystalline phase reaction to absorb heat, the heat absorption capacity is related to the liquid phase fraction according to an equation with an internal heat source, a control equation is established by utilizing a phase diagram and a lever law to obtain the temperature and the liquid phase fraction:
in the formula, x L Is the liquid phase fraction of the alloy, omega L Is the mass fraction of the alloying element Ni in the liquid phase of the alloy, omega s Is the mass fraction of the alloying element Ni in the solid phase of the alloy, omega L Is the mass fraction of an alloy element Ni in an alloy liquid phase,
the mass fraction of the element Ni in the alloy phase at the nth time step is shown by the superscript n sL Is the latent heat of solid-liquid fusion phase change.
As shown in the equilibrium phase diagram of fig. 5, assuming an equilibrium state at each time step of the simulation, the contents of Ni in the solid phase and the liquid phase are uniform, and the liquid phase fraction increases with an increase in temperature during melting.
The heat conduction equation of the internal heat source is obtained by the following steps:
step 4.1: in the (n-1) th step, melting is started, and the mass fraction of the alloy element Ni in the liquid phase is
Step 4.2: in the n-th step, the liquid phase fraction is
The liquid phase fraction is increased by
Is marked as
The heat absorption of the liquefaction part of this time step is
The mass fractions of the alloy element Ni in the solid phase and the liquid phase are respectively
And
step 4.3: in step n +1, the remaining solid phase is partially melted and the liquid phase fraction is increased by
Is marked as
The heat absorption of the liquefied fraction in this time step is
At this time, the mass fraction of the element alloying element Ni in the solid phase and the liquid phase becomes
And
step 4.4: step 4.1 to step 4.2 are repeated until complete liquefaction.
According to the amount of Cu and Ni substances in each particle, thermodynamic parameters such as density, thermal conductivity coefficient, specific heat capacity and the like can be obtained through weighted average of the following equations:
in the formula, M A Is the molar mass of the alloying element Ni, n A For one calculation of the amount of substance of the alloying element Ni in the grid, M B Is the molar mass of the metallic element Cu, n B Calculating the amount of a metal element Cu substance in a calculation grid, and V is the volume of the calculation grid;
the calculation formula of the constant-pressure specific heat capacity of the Cu-Ni alloy is as follows:
in the formula, C pA Is the constant pressure specific heat capacity of the alloying element Ni, C pB Is the constant pressure specific heat capacity of the metallic element Cu.
In the formula, λ pA Is the thermal conductivity of the alloying element Ni, lambda pB Is the thermal conductivity of the metallic element Cu.
The foregoing detailed description of the preferred embodiments of the invention has been presented. It should be understood that numerous modifications and variations could be devised by those skilled in the art in light of the present teachings without departing from the inventive concept. Therefore, the technical solutions that can be obtained by a person skilled in the art through logical analysis, reasoning or limited experiments based on the prior art according to the concepts of the present invention should be within the scope of protection determined by the claims.
Claims (5)
1. A method of melt numerical simulation involving reaction of crystalline phases, comprising the steps of: the method comprises the following steps:
step 1: establishing a constant temperature diffusion model; the constant-temperature diffusion model comprises an alloy element A and a metal element B: the alloy element A is in a solid state, and the metal element B is in a liquid state; the alloy element A and the metal element B are mutually contacted, and the temperature of a contact surface keeps the temperature of the metal element B unchanged;
step 2: establishing a diffusion equation on the basis of the constant-temperature diffusion model, and calculating the total mass fraction w of the alloy element A in the alloy 0 (ii) a The diffusion equation is:
wherein n is the amount of the substance, t is the time, and D is the diffusion coefficient in a solid or liquid;
a crystal phase reaction occurs on the alloy solid-liquid phase interface, and the crystal phase reaction is described as a diffusion behavior with a large diffusion coefficient in calculation, wherein the diffusion equation is as follows:
in the formula, K is an interface diffusion coefficient;
and step 3: establishing a heating melting model: according to the mass fraction of the alloy element A and the alloy temperature T 0 And an alloy binary phase diagram, judging whether the alloy enters a phase change region;
and 4, step 4: if the alloy is not positioned in the phase change region, calculating the alloy temperature T by adopting a heat conduction equation without an internal heat source 1 (ii) a If the alloy is positioned in the phase change area, calculating the temperature T of the alloy in the melting process by adopting an internal heat source heat conduction equation 1 And a liquid phase fraction;
the liquid phase fraction calculation formula is as follows:
in the formula, x L Is the liquid phase fraction of the alloy, omega L Is the mass fraction of the alloy element A in the alloy liquid phase,
the superscript n is the mass fraction of the alloying element A in the solid phase of the alloy and denotes the nth time step, ω A Is the mass fraction of the element A in the alloy phase at the nth time step;
the heat conduction equation of the internal heat source is as follows:
wherein ρ is the density of the alloy, C p Is the constant pressure specific heat capacity of the alloy, T is the temperature, T is the time, k is the heat transfer coefficient, h sL Is the phase change latent heat of solid-liquid fusion;
the heat conduction equation of the internal heat source is obtained through the following steps:
step 4.1: in the (n-1) th step, melting is started, and the mass fraction of the alloying element A in the liquid phase is
Step 4.2: in the n-th step, the liquid phase fraction is
The liquid phase portion is increased by an amount of
Is marked as
The heat absorption of the liquefaction part of this time step is
The mass fractions of the alloy element A in the solid phase and the liquid phase are respectively
And
step 4.3: in step (n + 1), the remaining solid phase portion is melted, and the liquid phase portion is increased by an amount of
Is marked as
The heat absorption of the liquefied fraction in this time step is
At this time, the mass fraction of the element alloying element A in the solid phase and the liquid phase becomes
And
step 4.4: repeating said steps 4.1 to 4.2 until complete liquefaction;
and 5: if the alloy is completely melted, stopping the iterative calculation process; if the alloy is not completely melted, repeating the steps 2 to 4.
2. The melting numerical simulation method involving a crystal phase reaction according to claim 1, wherein the total mass fraction of the alloying element a in the temperature-increasing melting model is kept constant in the step 3.
3. A melting numerical simulation method involving a crystal phase reaction according to claim 2, wherein the heat conduction equation of the non-internal heat source in the step 4 is:
where ρ is the density of the alloy, C p Is the constant pressure specific heat capacity of the alloy, T is the temperature, T is the time, and k is the heat transfer coefficient.
4. A melting numerical simulation method involving a crystal phase reaction according to claim 3, wherein the density of the alloy is calculated by the formula:
in the formula, M A Is the molar mass of the alloying element A, n A For one calculation of the amount of said substance of the alloying element A, M B Is the molar mass of the metal element B, n B Calculating the amount of the metal element B in a calculation grid, and V is the volume of the calculation grid;
the calculation formula of the constant-pressure specific heat capacity of the alloy is as follows:
in the formula, C pA Is the constant pressure specific heat capacity of the alloy element A, C pB Is the constant pressure specific heat capacity of the metal element B.
5. A melting model relating to a reaction of crystal phases for use in a numerical melting simulation method relating to a reaction of crystal phases according to any one of claims 1 to 2, comprising a constant-temperature diffusing part, a temperature-increasing melting part, the constant-temperature diffusing part and the temperature-increasing melting part being represented by the following formulae:
wherein ρ is the density of the alloy, C p Is the constant pressure specific heat capacity of the alloy, T is the temperature, T is the time, k is the heat transfer coefficient, x L Is the liquid phase fraction of the alloy, h sL Is the latent heat of solid-liquid fusion phase change.
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