A method for simulating and calculating the surface supersaturation of KDP crystals based on UDS

Abstract

The invention discloses a KDP crystal surface supersaturation simulation calculation method based on UDS, which relates to the technical field of crystal growth numerical simulation, and comprises: establishing a physical geometric model of a crystal growth groove, meshing the physical geometric model, and then importing it into Fluent simulation software; based on a user-defined scalar equation UDS, coupling fluid turbulence and energy equations, establishing a solute transport equation of a KDP crystal growth system; based on a KDP crystal surface solute reaction boundary condition, writing a user-defined function UDF, and based on a user-defined storage UDM, storing the equilibrium concentration of a KDP solution, mounting a custom function of equilibrium concentration varying with temperature, thereby constructing a self-consistent function of crystal surface growth rate; coupling the established equations and functions, establishing a mathematical model of the KDP crystal growth system, setting a calculation domain condition and a boundary condition of the mathematical model, and calculating and solving to obtain the supersaturation distribution of the KDP crystal growth system.

Description

Technical Field

[0001] The invention relates to the technical field of crystal growth numerical simulation, and in particular to a KDP crystal surface supersaturation simulation calculation method based on UDS. Background Art

[0002] At present, potassium dihydrogen phosphate (chemical formula KH2PO4, referred to as KDP) and its deuteride (chemical formula K(D X H 1-X )2PO4, referred to as DKDP) crystal, as a nonlinear and electro-optical crystal with good performance, has the advantages of wide transmission band, high transmittance, large electro-optic coefficient, low half-wave voltage and good optical uniformity, and is widely used in the laser field. Inertial confinement fusion (ICF) is considered to be one of the important ways to solve the energy problem of mankind in the 21st century. Among them, strong laser frequency conversion crystal is an important optical component of high-power laser in ICF system. Large-aperture KDP crystal is mainly used as electro-optical switch and frequency doubling device, and large-aperture DKDP crystal is mainly used as triple frequency doubling device. KDP / DKDP crystal is the only nonlinear optical crystal that can be used in ICF device due to its excellent optical properties and easy growth of large-size blocks.

[0003] Usually, KDP crystals grow in aqueous solution, and the growth mechanism is step-by-step growth based on screw dislocations or two-dimensional nuclei. The convection of the solution in the growth system can effectively improve material transport and crystal growth rate, but at the same time it has a certain impact on the uniformity of supersaturation on the crystal surface and the stability of the step morphology. Specifically, the instability of fluid flow, such as the distribution of shear force and the generation of convection vortex cells, leads to the instability of the step morphology on the crystal surface, causing the step to coalesce and the mismatch of the growth hillocks. This is the main reason for the formation of inclusion defects and the impact on the optical quality of the crystal. At present, due to the closed nature of the KDP growth system and the complexity of the large-diameter crystal growth system, it is difficult to perform in-situ surface observation of the actual growing crystals, and it is impossible to obtain the supersaturation distribution of the crystal surface, so that the control of KDP crystal growth is limited to empirical judgment and lacks theoretical support, which also limits the precise regulation during the crystal growth process. Summary of the invention

[0004] In order to solve the shortcomings of the above-mentioned prior art, the present invention provides a UDS-based KDP crystal surface supersaturation simulation calculation method, based on the existing Fluent software and the UDS (User Defined Scalar) and UDF (User Defined Function) modules in the software, numerical simulation is performed on various growth parameters in a large-diameter KDP crystal growth system, and the surface supersaturation distribution during the KDP crystal growth process is simulated and calculated, so as to provide an effective basis and data support for the precise regulation of the growth of KDP crystals.

[0005] The invention provides a KDP crystal surface supersaturation simulation calculation method based on UDS.

[0006] A method for simulating and calculating KDP crystal surface supersaturation based on UDS, comprising:

[0007] According to the KDP crystal growth system, a physical geometric model of the crystal growth tank is established;

[0008] Mesh the physical geometric model and import the meshed model into the Fluent simulation software;

[0009] Based on the user-defined scalar equation UDS, coupled with the fluid turbulence and energy equations, the solute transport equation of the KDP crystal growth system is established;

[0010] Based on the solute reaction boundary conditions on the KDP crystal surface, a user-defined function (UDF) is written, and based on the user-defined storage (UDM), the equilibrium concentration of the KDP solution is stored, and a custom function of the equilibrium concentration changing with temperature is mounted to construct a self-consistent function of the crystal surface growth rate.

[0011] The established equations and functions are coupled to establish a mathematical model of the KDP crystal growth system, and the calculation domain conditions and boundary conditions of the mathematical model are set to calculate and solve the velocity, shear force, temperature, solute concentration and supersaturation distribution of the KDP crystal growth system.

[0012] A further technical solution is to mesh the physical geometry model, including:

[0013] The established physical geometric model of the KDP crystal growth trough is divided into three parts: crystal domain, inner flow domain and outer flow domain. The crystal domain is meshed using an encrypted hexahedral structured grid, and the inner flow domain and outer flow domain are meshed using a tetrahedral unstructured grid.

[0014] A further technical solution is to merge the meshes of various parts of the physical geometry model of the KDP crystal growth trough, check the mesh quality, and import the meshed physical geometry model of the KDP crystal growth trough into the Fluent simulation software, set the model size scaling, establish the computational domain mesh interface, and check whether the mesh volume is correct.

[0015] A further technical solution is to construct the solute scalar transport equation in a single-phase flow solution based on the user-defined scalar equation UDS, which is:

[0016]

[0017] In the formula, c is the solute concentration of the solution, D is the solute diffusion coefficient, S c is the source term; is a non-steady-state term, is the convection term, is the diffusion term, x j Represents the coordinate components of the rectangular coordinate system, u j Represents the velocity vector of the fluid.

[0018] A further technical solution is to construct the crystal surface solute transport flux expression based on the solute reaction boundary conditions on the KDP crystal surface, which is:

[0019]

[0020] In the formula, ρ s is the crystal density, c eq is the equilibrium concentration of the solution, and n is the normal direction of the crystal plane.

[0021] In a further technical solution, the normal growth rate R of the crystal plane is determined based on the crystal surface type, solution supersaturation, fluid flow conditions and crystal surface temperature, and conforms to the kinetic law of the screw dislocation mechanism of solution-grown crystals; the expression of the normal growth rate R of the crystal plane is:

[0022] R = k g σ g

[0023] In the formula, k g is the growth rate coefficient, and the supersaturation of the growth driving force σ is defined as (cc eq ) / c eq , g is the growth order, g is 1 when the supersaturation is high, and g is 2 when the supersaturation is low, c is the solute concentration of the solution, c eq is the equilibrium concentration of the solution.

[0024] As a further technical solution, the solute transport boundary conditions on the KDP crystal surface are discretized using the Over-Relaxed method, and the discretization format is:

[0025]

[0026]

[0027] Where φ is a user-defined scalar, the subscript f represents the boundary surface, and eq represents the equilibrium state. is the crystal surface boundary transmission flux, The boundary surface vector is decomposed into and Two portions, is the unit vector from the neighboring grid cell to the boundary grid cell, c0 represents the boundary adjacent grid cell, dr is the distance between the grid cell centers, Γ φ is the diffusion coefficient, h c is the solute transfer coefficient.

[0028] Further technical solutions include setting the calculation domain conditions and boundary conditions of the mathematical model and adding the physical properties of potassium dihydrogen phosphate solution, including:

[0029] The crystal rotation speed is set according to the specific process parameters. The inlet adopts a velocity inlet, the outlet is a free outflow boundary, the wall is a no-slip boundary condition, the inlet and outlet and container wall temperatures are set to constant temperature boundary conditions, and the remaining walls are adiabatic walls. The solute scalar boundary conditions on the crystal surface are set using a UDF custom function, and the solute concentrations on the remaining walls are set according to actual needs.

[0030] In a further technical solution, the process of constructing the self-consistent function of the crystal surface growth rate includes:

[0031] First, a global computational domain grid cell traversal cycle is performed in the computational node to obtain the grid cell temperature value;

[0032] Secondly, the grid cell equilibrium concentration is calculated based on the solubility curve, and the user-defined storage UDM is enabled to store the equilibrium concentration of the KDP solution;

[0033] Finally, the equilibrium concentration value is distributed among nodes, and a custom function is mounted to complete the automatic update of the solute equilibrium concentration with the crystal surface temperature. Combined with the user-defined function UDF, a self-consistent function of the crystal surface growth rate is constructed.

[0034] Further technical solutions to solve the mathematical model include:

[0035] Initialize the mathematical model, monitor the average temperature of each surface of the KDP crystal and the average solute concentration, set the iteration parameters, and perform simulation calculations;

[0036] Whether the multiple iterative calculations are completed is determined based on whether the monitored values ​​are stable or the calculated residual values ​​are converged; when the monitored values ​​are stable or the calculated residual values ​​are converged, the calculation is completed and the distribution of liquid flow, shear force, temperature and supersaturation cloud maps and vector diagrams on the crystal surface and the overall flow field profile are output.

[0037] The above technical solution has the following beneficial effects:

[0038] 1. The present invention provides a method for simulating and calculating the supersaturation of a KDP crystal surface based on UDS. On the basis of the Fluent general module, the flow and heat transfer problems are solved, and a custom function of the change of the equilibrium concentration of the solution with the temperature is constructed, thereby solving the problem of different growth driving forces, i.e., supersaturations, on various surfaces of the crystal caused by uneven temperature. The UDS module is called and combined with a user-defined function (UDF) to solve the solute transport equation on the crystal surface, thereby realizing the numerical simulation of the KDP crystal growth process, and finally calculating and solving the speed, shear force, temperature, solute concentration and supersaturation distribution of the KDP crystal growth system, realizing the calculation of the supersaturation distribution on the surface of the KDP crystal that is difficult to observe, and providing effective guidance for analyzing defect generation, optimizing process parameters and improving crystal quality.

[0039] 2. The numerical simulation method proposed in the present invention can be used to evaluate the influence of various growth process parameters on the crystal growth process, optimize various process parameters, reduce crystal defects, and thus improve the optical quality and utilization rate of the crystal, thus strongly supporting the stable operation of high-power laser devices. BRIEF DESCRIPTION OF THE DRAWINGS

[0040] The accompanying drawings in the specification, which constitute a part of the present invention, are used to provide a further understanding of the present invention. The exemplary embodiments of the present invention and their descriptions are used to explain the present invention and do not constitute improper limitations on the present invention.

[0041] Figure 1 This is a flow chart of a method for simulating and calculating the supersaturation of a KDP crystal surface based on UDS according to an embodiment of the present invention;

[0042] Figure 2 A schematic diagram of a physical geometric model of a KDP crystal growth tank in an embodiment of the present invention;

[0043] Figure 3 This is a cloud diagram of the temperature distribution on the surface of the KDP crystal in an embodiment of the present invention;

[0044] Figure 4 This is a cloud diagram of the supersaturation distribution of the KDP crystal surface in an embodiment of the present invention. DETAILED DESCRIPTION

[0045] It should be noted that the following detailed descriptions are exemplary only, are intended to describe specific embodiments, are intended to provide further explanation of the present invention, and are not intended to limit exemplary embodiments according to the present invention. Unless otherwise specified, all technical and scientific terms used herein have the same meanings as those of ordinary skill in the art to which the present invention belongs. In addition, it should also be understood that when the terms "comprising" and / or "including" are used in this specification, it indicates the presence of features, steps, operations, devices, components and / or combinations thereof.

[0046] Embodiment 1

[0047] In order to realize in-situ surface observation of actual growing crystals and obtain the supersaturation distribution of the crystal surface, this embodiment provides a KDP crystal surface supersaturation simulation calculation method based on UDS. On the basis of the Fluent general module, it solves the flow and heat transfer problems, constructs a custom function of the solution equilibrium concentration changing with temperature, and thereby solves the problem of different growth driving forces, i.e., supersaturation, on different crystal surfaces caused by uneven temperature; calls the UDS module and combines it with the user-defined function (UDF) to solve the crystal surface solute transport equation, thereby realizing the numerical simulation of the KDP crystal growth process, and obtaining surface physical quantity information that is difficult to observe experimentally, such as solution flow direction, shear force distribution, supersaturation distribution, etc., to provide a basis for analyzing the generation of crystal defects. The KDP crystal surface supersaturation simulation calculation method based on UDS proposed in this embodiment, such as Figure 1 As shown, the specific steps include:

[0048] According to the KDP crystal growth system, a physical geometric model of the crystal growth tank is established;

[0049] Mesh the physical geometric model and import the meshed model into the Fluent simulation software;

[0050] Based on the user-defined scalar equation UDS, coupled with the fluid turbulence and energy equations, the solute transport equation of the KDP crystal growth system is established;

[0051] Based on the solute reaction boundary conditions on the KDP crystal surface, a user-defined function (UDF) is written, and based on the user-defined storage (UDM), the equilibrium concentration of the KDP solution is stored, and a custom function of the equilibrium concentration changing with temperature is mounted to construct a self-consistent function of the crystal surface growth rate.

[0052] The established equations and functions are coupled to establish a mathematical model of the KDP crystal growth system, and the calculation domain conditions and boundary conditions of the mathematical model are set to calculate and solve the velocity, shear force, temperature, solute concentration and supersaturation distribution of the KDP crystal growth system.

[0053] The following content introduces in more detail the UDS-based KDP crystal surface supersaturation simulation calculation method proposed in this embodiment.

[0054] Step S1, according to the KDP crystal growth system, establish a physical geometric model of the crystal growth tank. Specifically, according to the large-diameter KDP crystal traditional growth system, use 3D drawing software such as UG, SolidWorks or DesignModeler to establish a physical geometric model of the KDP crystal growth tank (i.e., a 3D geometric model), such as Figure 2 As shown, the geometric model is established in the Cartesian coordinate system, with the Z axis as the axial direction and the X and Y axes as the radial directions. The KDP crystal growth tank model is actually a rotation model. The calculation of this rotation model adopts the multi-reference frame model (MRF), in which the fluid calculation domain (i.e., fluid domain) is divided into an inner flow domain and an outer flow domain. In order to solve the crystal near-wall concentration boundary layer, a crystal domain is also set outside the crystal wall. That is, the KDP crystal growth tank model is divided into three parts: the crystal domain, the inner flow domain, and the outer flow domain.

[0055] Step S2: mesh the physical geometric model and import the meshed model into the Fluent simulation software.

[0056] Step S2.1, mesh the physical geometry model and check the mesh quality. Specifically, use ICEM and other software physical geometry models for meshing, where an encrypted hexahedral structured grid is used to mesh the crystal domain to solve the crystal near-wall concentration boundary layer; a tetrahedral unstructured grid is used to mesh the inner and outer flow domains. Afterwards, the meshes of the various parts of the physical geometry model of the KDP crystal growth trough are merged, and the mesh quality is checked. Here, by checking whether the mesh quality meets the Fluent calculation requirements (i.e., greater than 0.2), the problem of iterative calculation divergence caused by too low mesh quality is avoided.

[0057] Step S2.2, import the meshed physical geometry model of the KDP crystal growth trough into the Fluent simulation software, set the model size scaling, establish the computational domain mesh interface, and check whether the mesh volume is correct.

[0058] The above computational domain mesh interface is mainly used to process data transfer between regional interfaces in multi-region computational models. Specifically, the overall fluid computational domain is divided into three parts: the crystal domain, the inner flow domain, and the outer flow domain. Combined with the above step S2.1, meshes are constructed for these three parts respectively. If the overall computational domain remains fluid, an interface needs to be created on the mutually contacting boundaries to achieve data transfer.

[0059] On this basis, after the meshed model is imported into Fluent, it is necessary to perform necessary mesh checking operations. This checking function is provided in the "Setting Up Domain" menu and "Mesh" tab in Fluent software. The checking mainly feedbacks the following information: a. Coordinate information of the calculation domain; b. Mesh information, such as the maximum and minimum volume (area) of the mesh unit; c. Report any mesh errors. Among them, the mesh checking mainly examines the minimum volume to ensure that it cannot be negative, otherwise it will lead to subsequent calculation errors.

[0060] Step S3, based on the user-defined scalar equation UDS, coupled with the fluid turbulence and energy equations, establish the solute transport equation of the KDP crystal growth system. That is, set the fluid turbulence model, energy model and user-defined scalar equation (User-Defined Scalars, UDS) model to establish the solute transport equation of the KDP growth system.

[0061] Specifically, the solubility of KDP crystals in water increases with increasing temperature, so the aqueous solution cooling method is often used for growth, and the cooling rate is generally 0.01-0.05°C per day. Considering that the growth of KDP crystals is very slow at a certain moment, it can be regarded as a quasi-static system. When growing crystals in low-temperature aqueous solutions, it is usually necessary to rotate the crystals or stir the solution to ensure sufficient supply of raw materials on each crystal surface. The flow state of the solution during rotation is determined by the Reynolds number, which can be expressed as:

[0062]

[0063] Where ρ is the density of the KDP solution, ω is the crystal rotation speed, L is the characteristic length of the KDP crystal, which is half the length of the diagonal edge of the crystal, and μ is the dynamic viscosity of the KDP solution.

[0064] In this embodiment, a conventional growth system is used to grow a large-diameter KDP crystal, with a rotation speed as low as 2 rpm and a Reynolds number of 4.8×10 4 , which is greater than the critical Reynolds number (Re=1000) of the flow field in the rotating cylinder, so the turbulence model adopts the RNG k-ε model. On this basis, the crystal wall adopts enhanced wall treatment, combined with the turbulent viscosity differential equation provided by the RNG k-ε turbulence model, which can better handle the low Reynolds number area near the wall and effectively solve the solute boundary layer.

[0065] Furthermore, the basic control equations of numerical simulation calculations include: the mass conservation equation (continuity equation), the momentum conservation equation (motion equation), and the energy conservation equation (energy equation), among which the motion equation has different expressions based on the selection of the turbulence model. Since Fluent provides general modules for turbulence and energy, the equations are not listed separately here. In addition, Fluent additionally provides a user-defined scalar equation (UDS) module, which can be used to solve the solution solute concentration transport equation in this embodiment. The above four equations are combined to form the control equation group of this embodiment. Specifically, assuming that the KDP solution is an incompressible fluid, based on the user-defined scalar equation UDS, a solute transport equation in which the solute concentration in a single-phase flow solution varies with space and time can be constructed, which can be expressed as:

[0066]

[0067] In the formula, c is the solute concentration of the solution, D is the solute diffusion coefficient, S c is the source term; is a non-steady-state term, is the convection term, is the diffusion term, x j Represents the coordinate components of the rectangular coordinate system, u j Represents the velocity vector of the fluid, where the effect of fluid convection on solute transport is considered.

[0068] Furthermore, by coupling the above energy equation to solve the temperature, the temperature is actually also a scalar, and its conservation equation has the same form as the solute transport equation. The temperature affects the boundary conditions of solute transport, thereby affecting the solute transport.

[0069] Step S4, based on the solute reaction boundary conditions on the KDP crystal surface, write a user-defined function UDF, and based on the user-defined storage UDM, store the equilibrium concentration of the KDP solution, and mount a custom function of the equilibrium concentration changing with temperature, so as to construct a self-consistent function of the crystal surface growth rate.

[0070] Step S4.1: Based on the solute reaction boundary condition on the KDP crystal surface, write a user-defined function (UDF) program and load the program into the Fluent example file.

[0071] Specifically, the crystal surface growth process can be divided into two stages: (1) solutes are supplied to the crystal surface through the diffusion boundary layer between the growing crystal and the solution by convection transport and molecular diffusion; (2) solute ions or molecules are integrated into the crystal, i.e., the surface reaction stage. Based on the solute reaction boundary conditions on the KDP crystal surface, depending on the growth system, flow state, and supersaturation, the solute transport flux toward the crystal surface during the crystal growth process can be expressed as:

[0072]

[0073] In the formula, ρ s is the crystal density, c eq is the equilibrium concentration of the solution, and n is the normal direction of the crystal plane.

[0074] In the above formula, the normal growth rate R of the crystal plane is determined by the crystal surface type, solution supersaturation, fluid flow conditions and crystal surface temperature. The Burton-Cabrera-Frank (BCF) crystal growth model and crystal growth experiments have obtained the growth kinetics of the screw dislocation mechanism of solution-grown crystals. The normal growth rate of the crystal surface can be expressed as:

[0075] R = k g σ g

[0076] In the formula, k g is the growth rate coefficient, and the supersaturation of the growth driving force σ is defined as (cc eq ) / c eq , g is the growth order. At high supersaturation, g is 1, and the kinetic law is linear; at low supersaturation, it weakens to a parabolic law, and g is 2.

[0077] Preferably, the Over-Relaxed method is used to discretize the solute transport boundary conditions on the crystal surface to obtain the solute boundary analytical solution, and the discretization format is:

[0078]

[0079] Where φ is a user-defined scalar, the subscript f represents the boundary surface, and eq represents the equilibrium state. is the crystal surface boundary transmission flux, The boundary surface vector is decomposed into and Two portions, is the unit vector from the neighboring grid cell to the boundary grid cell, c0 represents the boundary adjacent grid cell, dr is the distance between the grid cell centers, Γ φ is the diffusion coefficient, h c is the solute transfer coefficient.

[0080] After completing the above steps, for user-defined functions (UDF), the solute transport boundary conditions on the crystal surface are compiled into UDF code using C language, and the source file can be compiled and loaded into the Fluent software by interpretation or compilation. The software automatically builds the UDF shared library and target file, and dynamically connects with the solver. The UDF can be used to control some model parameters, boundary conditions or calculation processes in the Fluent calculation process, thereby realizing the complex functions required by users.

[0081] Step S4.2, enable user-defined memory (UDM) to store the equilibrium concentration of KDP solution, and mount a custom function of the equilibrium concentration changing with temperature to construct a self-consistent function of the crystal surface growth rate.

[0082] Specifically, the solubility of KDP crystals increases with increasing temperature, and the solute equilibrium concentrations corresponding to the uneven crystal surface temperature are different, which in turn causes changes in the crystal surface driving force and the surface solute flux. In this embodiment, the function of the solute equilibrium concentration changing with the crystal surface temperature is implemented by the DEFINE_ADJUST macro; DEFINE_ADJUST is a general macro provided by Fluent to adjust and modify variables. The solver can execute the macro defined by DEFINE_ADJUST in each iteration and call it in each iteration before solving the transport equation.

[0083] The construction process of the self-consistent function of the crystal surface growth rate specifically includes: first, performing a global computational domain grid cell traversal cycle in the computational node to obtain the grid cell temperature value; second, calculating the grid cell equilibrium concentration according to the solubility curve, and enabling the user-defined storage (UDM) to store the KDP solution equilibrium concentration. The equilibrium concentration c is achieved through the above two steps. eq As the temperature changes, the change of the equilibrium concentration on the crystal surface will affect the solute transport flux at the crystal surface boundary, which is stored through UDM. Finally, the equilibrium concentration value is distributed among nodes using the data communication macro, and a custom function is mounted to complete the automatic update of the solute equilibrium concentration with the crystal surface temperature. Combined with step S4.1, the equilibrium concentration is passed to the boundary condition in step S4.1 (written as UDF code), so as to construct a self-consistent function of the crystal surface growth rate.

[0084] Step S5, coupling the established equations and functions, establishing a mathematical model of the KDP crystal growth system, setting the calculation domain conditions and boundary conditions of the mathematical model, and calculating and solving the velocity, shear force, temperature, solute concentration and supersaturation distribution of the KDP crystal growth system.

[0085] Step S5.1, setting the calculation domain conditions and boundary conditions of the established mathematical model, and adding the physical properties of the potassium dihydrogen phosphate solution material.

[0086] Furthermore, the crystal rotation speed is set according to specific process parameters, the inlet adopts velocity inlet, the outlet is a free outflow boundary, the wall is a no-slip boundary condition, the inlet and outlet and container wall temperatures are set to constant temperature boundary conditions, the remaining walls are adiabatic walls, the solute scalar boundary conditions on the crystal surface are set using a UDF custom function program, and the solute concentrations on the remaining walls are set according to actual needs.

[0087] Step S5.2, solving the mass, momentum, temperature and solute transport control equations based on the separation solution SIMPLEC algorithm, and the physical quantity discretization format adopts the second-order upwind form.

[0088] Step S5.3, initialize the model, monitor the average temperature of each surface of the KDP crystal and the average solute concentration, set the iteration parameters, and perform simulation calculations.

[0089] Step S5.4, judging whether the multiple iterative calculations are completed according to whether the monitored value reaches stability or whether the calculated residual value converges; when the monitored value reaches stability or the calculated residual value converges, the calculation is completed, and the crystal surface and overall flow field profile liquid flow, shear force, temperature and supersaturation cloud map and vector map distribution are output.

[0090] Furthermore, based on the above calculation results, the calculation results are analyzed: growth streaks (growth layers) are one of the common macroscopic defects in the crystal growth process. The existence of this defect destroys the uniformity of the crystal's physical properties, especially the optical properties; a temperature fluctuation of 0.05°C can lead to growth streak defects. Therefore, when growing KDP crystals, the temperature should be controlled within the range of ±0.01°C, and the corresponding standard deviation should be less than 3.3×10 -3 When the KDP crystal prism height is 400 mm, the crystal rotation rate is 2 rpm, the inlet velocity is 1.02 cm / s, the inlet temperature is 52 ° C, the growth temperature is 50 ° C, and the initial supersaturation is 2%, the surface temperature distribution of the KDP crystal is as follows: Figure 3 As shown in the figure, the cone region of the crystal is impacted by the solution heat flow, while the column region crystal surface is affected by the cooling flow. The maximum surface temperature difference is about 0.04℃, and the standard deviation SD of the cone surface temperature is 4.1×10 -3 , which indicates that growth stripe defects may occur on the surface of KDP crystal. Based on the above settings, the supersaturation distribution cloud of KDP crystal surface is shown in Figure 4As shown, due to the rotation, the supersaturation at the edge of the cone is larger than that at the center of the cone, and a low supersaturation zone is formed in the center of the cone. The uneven supersaturation on the crystal surface will lead to different growth step rates. The rate at the edge is faster than that in the center, causing the growth step to bend, encapsulating the mother liquid and forming inclusion defects.

[0091] In the above manner, the proposed numerical simulation method can be used to evaluate the influence of various growth process parameters on the crystal growth process, optimize various process parameters, reduce crystal defects, and thus improve the crystal optical quality and utilization rate, strongly supporting the stable operation of high-power laser devices.

[0092] The above description is only a preferred embodiment of the present invention. Although the specific implementation mode of the present invention is described in conjunction with the accompanying drawings, it is not intended to limit the scope of protection of the present invention. Those skilled in the art should understand that on the basis of the technical solution of the present invention, various modifications or variations that can be made by those skilled in the art without creative work are still within the scope of protection of the present invention.

Claims

1. A method for simulating and calculating the supersaturation of a KDP crystal surface based on UDS, characterized in that: include: According to the KDP crystal growth system, a physical geometric model of the crystal growth tank is established; Mesh the physical geometric model and import the meshed model into the Fluent simulation software; Based on the user-defined scalar equation UDS, coupled with the fluid turbulence and energy equations, the solute transport equation of the KDP crystal growth system is established; Based on the solute reaction boundary conditions on the KDP crystal surface, a user-defined function (UDF) is written, and based on the user-defined storage (UDM), the equilibrium concentration of the KDP solution is stored, and a custom function of the equilibrium concentration changing with temperature is mounted to construct a self-consistent function of the crystal surface growth rate. The established equations and functions are coupled to establish a mathematical model of the KDP crystal growth system, and the calculation domain conditions and boundary conditions of the mathematical model are set to calculate and solve the velocity, shear force, temperature, solute concentration and supersaturation distribution of the KDP crystal growth system; Among them, based on the user-defined scalar equation UDS, the solute scalar transport equation in the single-phase flow solution is constructed as follows: In the formula, c is the solute concentration of the solution, D is the solute diffusion coefficient, S c is the source term; is a non-steady-state term, is the convection term, is the diffusion term, x j Represents the coordinate components of the rectangular coordinate system, u j represents the velocity vector of the fluid; The process of constructing the self-consistent function of the crystal surface growth rate includes: First, a global computational domain grid cell traversal cycle is performed in the computational node to obtain the grid cell temperature value; Secondly, the grid cell equilibrium concentration is calculated based on the solubility curve, and the user-defined storage UDM is enabled to store the equilibrium concentration of the KDP solution; Finally, the equilibrium concentration value is distributed among nodes, and a custom function is mounted to complete the automatic update of the solute equilibrium concentration with the crystal surface temperature. Combined with the user-defined function UDF, a self-consistent function of the crystal surface growth rate is constructed.

2. The method for simulating and calculating the supersaturation of the KDP crystal surface based on UDS as claimed in claim 1, characterized in that: Meshing of physical geometry models, including: The established physical geometric model of the KDP crystal growth trough is divided into three parts: crystal domain, inner flow domain and outer flow domain. The crystal domain is meshed using an encrypted hexahedral structured grid, and the inner flow domain and outer flow domain are meshed using a tetrahedral unstructured grid.

3. The method for simulating and calculating the supersaturation of the KDP crystal surface based on UDS as claimed in claim 2, characterized in that: The meshes of various parts of the physical geometry model of the KDP crystal growth trough are merged, the mesh quality is checked, and the physical geometry model of the KDP crystal growth trough after mesh division is imported into the Fluent simulation software, the model size scaling is set, the computational domain mesh interface is established, and the mesh volume is checked to see if it is correct.

4. The method for simulating and calculating the supersaturation of the KDP crystal surface based on UDS as claimed in claim 1, characterized in that: Based on the solute reaction boundary conditions on the KDP crystal surface, the expression for the solute transport flux on the crystal surface is constructed as follows: In the formula, ρ s is the crystal density, c eq is the equilibrium concentration of the solution, n is the normal direction of the crystal plane, c is the solute concentration of the solution, D is the solute diffusion coefficient, and R is the growth rate normal to the crystal plane.

5. The method for simulating and calculating the supersaturation of the KDP crystal surface based on UDS as claimed in claim 4, characterized in that: The normal growth rate R of the crystal plane is determined based on the crystal surface type, solution supersaturation, fluid flow conditions and crystal surface temperature, and conforms to the kinetic law of the screw dislocation mechanism of solution-grown crystals; the expression of the normal growth rate R of the crystal plane is: R=k g s g In the formula, k g is the growth rate coefficient, and the supersaturation of the growth driving force σ is defined as (cc eq ) / c eq , g is the growth order, g is 1 when the supersaturation is high, and g is 2 when the supersaturation is low, c is the solute concentration of the solution, c eq is the equilibrium concentration of the solution.

6. The method for simulating and calculating the supersaturation of the KDP crystal surface based on UDS as claimed in claim 1, characterized in that: The solute transport boundary conditions on the KDP crystal surface are discretized using the Over-Relaxed method. The discretization format is: Where φ is a user-defined scalar, subscript f indicates the boundary surface, and eq indicates the equilibrium state. is the crystal surface boundary transmission flux, is the boundary surface vector, which can be decomposed into and Two portions, is the unit vector from the neighboring grid cell to the boundary grid cell, c0 represents the boundary adjacent grid cell, dr is the distance between the grid cell centers, Γ φ is the diffusion coefficient, h c is the solute transfer coefficient.

7. The method for simulating and calculating the supersaturation of the KDP crystal surface based on UDS as claimed in claim 1, characterized in that: Set the computational domain conditions and boundary conditions of the mathematical model, and add the physical properties of potassium dihydrogen phosphate solution, including: The crystal rotation speed is set according to the specific process parameters. The inlet adopts a velocity inlet, the outlet is a free outflow boundary, the wall is a no-slip boundary condition, the inlet and outlet and container wall temperatures are set to constant temperature boundary conditions, and the remaining walls are adiabatic walls. The solute scalar boundary conditions on the crystal surface are set using a UDF custom function, and the solute concentrations on the remaining walls are set according to actual needs.

8. The method for simulating and calculating the supersaturation of the KDP crystal surface based on UDS as claimed in claim 1, characterized in that: Solving mathematical models, including: Initialize the mathematical model, monitor the average temperature of each surface of the KDP crystal and the average solute concentration, set the iteration parameters, and perform simulation calculations; Whether the multiple iterative calculations are completed is determined based on whether the monitored values ​​are stable or the calculated residual values ​​are converged; when the monitored values ​​are stable or the calculated residual values ​​are converged, the calculation is completed and the distribution of liquid flow, shear force, temperature and supersaturation cloud maps and vector diagrams on the crystal surface and the overall flow field profile are output.

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