Directional solidification apparatus and heat compensation method for the same

Abstract

A directional solidification device and a heat compensation method for the device, the device comprising a crucible; a heat-conducting pad arranged at the bottom of the crucible; a plurality of heat compensation vertical pipe groups, each of which comprises a plurality of heat compensation vertical pipes arranged in parallel with the sidewall of the crucible; a main liquid storage tank in contact with the heat-conducting pad, below which a buffer air chamber is arranged; a plurality of auxiliary liquid storage tanks equal in number to the heat compensation vertical pipe groups and arranged at the side of the main liquid storage tank, the top of each auxiliary liquid storage tank being in communication with the plurality of heat compensation vertical pipes of a heat compensation vertical pipe group; a gate valve type piston being arranged inside each auxiliary liquid storage tank, an inflatable diaphragm box being arranged above the gate valve type piston; the inflatable diaphragm box being connected with the buffer air chamber through an air pipe provided with a one-way air valve; each auxiliary liquid storage tank being in communication with the main liquid storage tank through a heat compensation horizontal pipe; and the top of the main liquid storage tank being in communication with all the heat compensation vertical pipes. The heat compensation method can dynamically adjust the liquid level height in the heat compensation vertical pipes, so that the net heat exchange amount of the sidewall tends to be zero.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of directional solidification technology, in particular to a directional solidification device and a heat compensation method for the device. BACKGROUND

[0002] The core of directional solidification technology is to realize directional phase change of melt by precisely regulating temperature field. The existing technology generally adopts a scheme combining passive heat insulation and active heat dissipation, for example, heat insulation of the side wall and top of the crucible is carried out through multi-layer heat insulation material or composite heat insulation structure, and a specific heat dissipation channel is formed by auxiliary heat dissipation (air cooling, liquid cooling, etc.) at the bottom of the crucible to create a one-way temperature gradient, so as to realize the construction of temperature field for directional solidification.

[0003] However, the thermal resistance of the heat insulation structure in the above-mentioned existing technology will change with directional solidification at different temperatures, causing unstable heat insulation performance. Moreover, the heat dissipation at the bottom of the crucible accounts for 70%-80% of the total energy consumption of the device, and the existing technology does not feedback the waste heat to the side wall for dynamic compensation, resulting in low energy utilization rate.

[0004] In summary, the existing technology cannot realize self-adaptive heat compensation in the whole solidification process, resulting in poor process stability and high energy consumption. SUMMARY

[0005] To solve the above technical problems, the present application provides a directional solidification device and a heat compensation method for the device.

[0006] The present application provides a directional solidification device, comprising:

[0007] a crucible;

[0008] a heat-conducting pad arranged at the bottom of the crucible;

[0009] a plurality of heat compensation vertical pipe groups, each heat compensation vertical pipe group comprising a plurality of heat compensation vertical pipes arranged in parallel with the side wall of the crucible;

[0010] a main liquid storage tank in contact with the heat-conducting pad, and a buffer air chamber is arranged below the main liquid storage tank;

[0011] a plurality of auxiliary liquid storage tanks arranged beside the main liquid storage tank and equal in number to the heat compensation vertical pipe groups, and the top of each auxiliary liquid storage tank is in communication with the plurality of heat compensation vertical pipes of a heat compensation vertical pipe group;

[0012] a gate valve type piston is arranged in each auxiliary liquid storage tank, and an inflatable diaphragm box is arranged above the gate valve type piston;

[0013] the inflatable diaphragm box is connected with the buffer air chamber through an air pipe provided with a one-way air valve;

[0014] each auxiliary liquid storage tank is in communication with the main liquid storage tank through a heat compensation horizontal pipe;

[0015] The top part of the main liquid storage tank is in communication with all the heat compensation vertical pipes.

[0016] Optionally, the directional solidification device further comprises:

[0017] The heat insulation cover covers the top and side of the crucible;

[0018] The heat insulation layer of the heat compensation vertical pipe is arranged between the crucible and the heat insulation cover.

[0019] The application also provides a heat compensation method for the directional solidification device, which comprises the following steps:

[0020] The inside of the main liquid storage tank, the auxiliary liquid storage tank, the heat compensation horizontal pipe and the heat compensation vertical pipe is vacuumized;

[0021] The main liquid storage tank is filled with heat-conducting liquid, and the heat-conducting liquid in the main liquid storage tank is driven to expand by the heat emitted from the bottom of the crucible during the directional solidification process;

[0022] The temperature change of the bottom of the crucible is sensed by the inflatable bellows, and the inflatable bellows and the gate valve piston are combined to make the heat-conducting liquid in the main liquid storage tank flow into the auxiliary liquid storage tank through the heat compensation horizontal pipe;

[0023] The morphological change of the phase change interface is monitored in real time during the directional solidification process;

[0024] Based on the first formula of the morphological change of the phase change interface and the heat exchange amount of the side wall of the crucible, the temperature change and the morphological change, the liquid level height in the heat compensation vertical pipe is dynamically adjusted to make the net heat exchange amount of the side wall tend to zero and maintain the phase change interface level;

[0025] The first formula is as follows:

[0026] ;

[0027] Wherein, the vertical symmetry axis of the melt is taken as the y axis, the width of the melt is taken as W, the lower boundary of the region with a height of Δ where the phase change interface is located is taken as the x axis, the height Δ is taken as the calculation region, q is the heat flux density of the side wall of the crucible, t is the temperature of the calculation region, is the temperature of the lower edge of the calculation region, is the temperature of the upper edge of the calculation region, s is the latent heat released in the solidification process, and λ is the thermal conductivity of the melt, n is an odd number.

[0028] Optionally, when the heat loss of the side wall of the crucible increases, the phase change interface appears to be concave, the inflatable bellows becomes smaller, the gate valve piston is driven to rise, the liquid level in the heat compensation vertical pipe is raised to strengthen the heat preservation and inhibit the concave of the phase change interface;

[0029] When the crucible sidewall heat surplus, phase transition interface appears convex, inflatable membrane box volume increases, drive gate valve piston to reduce, make the heat compensation standpipe liquid level to reduce to reduce the heat preservation, inhibit the phase transition interface convex.

[0030] Optionally, the first formula is obtained based on a temperature field formula and a boundary condition formula in a calculation region, and at least includes the following steps:

[0031] The temperature field formula and the boundary condition formula are transformed to obtain a temperature field first formula, a temperature field second formula, a temperature field third formula, a boundary condition first formula, a boundary condition second formula and a boundary condition third formula.

[0032] The temperature field formula is: ;

[0033] The boundary condition formula is: ; wherein, is a temperature distribution function of a lower edge of the calculation region, is a temperature distribution function of an upper edge of the calculation region.

[0034] The first formula is obtained by solving the temperature field first formula and the boundary condition first formula, the temperature field second formula and the boundary condition second formula, and the temperature field third formula and the boundary condition third formula, respectively.

[0035] Optionally, the first formula is obtained by solving the temperature field first formula and the boundary condition first formula, the temperature field second formula and the boundary condition second formula, and the temperature field third formula and the boundary condition third formula, respectively, and at least includes the following steps:

[0036] The second formula is obtained by solving the temperature field first formula and the boundary condition first formula.

[0037] The temperature field first formula is: ;

[0038] The boundary condition first formula is: ;

[0039] The third formula is obtained by solving the temperature field second formula and the boundary condition second formula.

[0040] The temperature field second formula is: ;

[0041] The boundary condition second formula is: ;

[0042] The fourth formula is obtained by solving the temperature field third formula and the boundary condition third formula.

[0043] The temperature field third formula is: ;

[0044] The third formula of the boundary condition is: ;

[0045] Based on the second formula, the third formula, the fourth formula, the boundary condition formula, and the sum of the first formula of the temperature field, the second formula of the temperature field and the third formula of the temperature field, the first formula is solved.

[0046] Optionally, based on the first formula of the temperature field and the first formula of the boundary condition, the second formula is solved, including the following steps:

[0047] Let , then u satisfies the fifth formula: ;

[0048] And the boundary condition satisfies the sixth formula: ;

[0049] By Fourier expansion, the analytical solution of u is solved as:

[0050] ;

[0051] According to u and the analytical solution, the second formula is solved as follows:

[0052] .

[0053] Optionally, based on the second formula of the temperature field and the second formula of the boundary condition, the third formula is solved by using the separation of variables method as follows:

[0054] ;

[0055] Wherein, is a periodic constant factor.

[0056] Optionally, based on the third formula of the temperature field and the third formula of the boundary condition, the fourth formula is solved by using the separation of variables method as follows:

[0057] .

[0058] Optionally, based on the second formula, the third formula, the fourth formula, the boundary condition formula, and the sum of the first formula of the temperature field, the second formula of the temperature field and the third formula of the temperature field, the first formula is solved, including the following steps:

[0059] Based on the sum of the first formula of the temperature field, the second formula of the temperature field and the third formula of the temperature field, the following formula is obtained:

[0060] ;

[0061] Based on the second formula, the third formula and the fourth formula, the boundary condition formula is transformed to obtain the fifth formula as follows:

[0062] ;

[0063] Based on the second formula, the third formula, the fourth formula, the fifth formula, and the sum of the temperature field first formula, the temperature field second formula and the temperature field third formula, a separation variable method is used to solve to obtain the first formula.

[0064] Compared with the prior art, the present application can realize real-time compensation for the heat loss of the crucible sidewall by setting multiple auxiliary liquid storage tanks and corresponding control heat compensation vertical pipe groups combined with a linkage mechanism, thereby solving the problem of fixed heat preservation structure and inability to realize real-time regulation and control in the prior art.

[0065] Compared with the prior art, the present application further reduces heat loss and improves the heat preservation effect of the entire directional solidification process by setting a heat preservation cover on the top and side of the crucible and a heat insulation layer between the crucible and the heat preservation cover.

[0066] Compared with the prior art, the present application can accurately control the morphology of the phase change interface and maintain its level by dynamically adjusting the liquid level height in the heat compensation vertical pipe based on the first formula of the phase change interface morphology and the heat exchange amount of the crucible sidewall, thereby improving the solidification quality.

[0067] Compared with the prior art, the present application can automatically adjust the liquid level height in the heat compensation vertical pipe to strengthen or reduce heat preservation when the heat loss of the crucible sidewall increases or heat is excessive, thereby realizing automatic control of the solidification process and improving the automation level of the process.

[0068] Compared with the prior art, the first formula of the present application is based on the temperature field formula and the boundary condition formula in the calculation region, providing accurate theoretical support for heat compensation, making heat compensation more scientific and accurate.

[0069] Compared with the prior art, the present application obtains the first formula through a multi-step accurate solving process, further improving the accuracy and reliability of heat compensation.

[0070] Compared with the prior art, the analytic solution obtained by Fourier expansion provides accurate control parameters for heat compensation, so that the morphology of the phase change interface can be controlled more accurately.

[0071] Compared with the prior art, the first formula is obtained based on the second formula, the third formula, the fourth formula and the fifth formula, the influence of multiple factors is comprehensively considered, and the accuracy of the phase change interface morphology control is improved. BRIEF DESCRIPTION OF DRAWINGS

[0072] The drawings described herein are used to provide further understanding of the present application, and form a part of the present application. The illustrative embodiments of the present application and their description serve to explain the present application, and do not constitute an improper limitation on the present application. In the drawings:

[0073] Figure 1 a structure diagram of an embodiment of the directional solidification device of the present application;

[0074] Figure 2 a flowchart of an embodiment of the heat compensation method for the directional solidification device of the present application;

[0075] Figure 3 a phase change interface diagram of an embodiment of the heat compensation method for the directional solidification device of the present application;

[0076] Figure 4 a diagram of the first formula of an embodiment of the heat compensation method for the directional solidification device of the present application;

[0077] Figure 5 a solidification initial stage diagram of an embodiment of the heat compensation method for the directional solidification device of the present application;

[0078] Figure 6 a diagram of an embodiment of the heat compensation method for the directional solidification device of the present application, in which the heat compensation vertical pipe is filled with heat-conducting liquid;

[0079] Figure 7 a structure diagram of an embodiment of the directional solidification device of the present application, in which eight groups of heat compensation vertical pipes are independent of each other;

[0080] Figure 8 a principle diagram of an embodiment of the heat compensation method for the directional solidification device of the present application, in which the phase change interface is concave;

[0081] Figure 9 another principle diagram of an embodiment of the heat compensation method for the directional solidification device of the present application, in which the phase change interface is concave;

[0082] Figure 10A schematic diagram of a heat compensation process when the phase change interface is convex in an embodiment of the heat compensation method for directional solidification equipment of the present application;

[0083] Figure 11 Another schematic diagram of a heat compensation process when the phase change interface is convex in an embodiment of the heat compensation method for directional solidification equipment of the present application;

[0084] Figure 12 A schematic diagram of the phase change interface being horizontal in an embodiment of the heat compensation method for directional solidification equipment of the present application;

[0085] Figure 13 Another schematic diagram of the phase change interface being horizontal in an embodiment of the heat compensation method for directional solidification equipment of the present application.

[0086] The reference signs: 10, crucible; 20, heat-conducting pad; 30, heat compensation vertical pipe; 40, main liquid storage tank; 50, buffer air chamber; 60, auxiliary liquid storage tank, 61, inflatable film box, 62, gate valve piston; 70, air pipe, 71, one-way air valve; 80, heat preservation cover; 90, heat insulation layer. DETAILED DESCRIPTION

[0087] To make the objectives, technical solutions and advantages of the embodiments of the present application clearer, the technical solutions in the embodiments of the present application will be described clearly and completely below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are some but not all of the embodiments of the present application. It should be understood that the specific embodiments described herein are only used to explain the present application and not used to limit the present application. Based on the embodiments in the present application, all other embodiments obtained by those of ordinary skill in the art without creative work fall within the scope of protection of the present application.

[0088] As shown in Figure 1 , the present application provides a directional solidification equipment, comprising:

[0089] a crucible 10;

[0090] a heat-conducting pad 20 arranged at the bottom of the crucible 10;

[0091] a plurality of heat compensation vertical pipe groups, each of which comprises a plurality of heat compensation vertical pipes 30 arranged in parallel with the sidewall of the crucible 10;

[0092] a main liquid storage tank 40 attached to the heat-conducting pad 20, below which a buffer air chamber 50 is arranged;

[0093] a plurality of auxiliary liquid storage tanks 60 equal in number to the heat compensation vertical pipe groups and arranged at the side of the main liquid storage tank 40, the top of each auxiliary liquid storage tank 60 being in communication with the plurality of heat compensation vertical pipes 30 of a heat compensation vertical pipe group;

[0094] The inside of each auxiliary liquid storage tank 60 is provided with a gate valve type piston 62, and an air-filled diaphragm box 61 is arranged above the gate valve type piston 62;

[0095] The air-filled diaphragm box 61 is connected with the buffer air chamber 50 through an air pipe 70 provided with a one-way air valve 71;

[0096] Each auxiliary liquid storage tank 60 is communicated with the main liquid storage tank 40 through a thermal compensation vertical pipe;

[0097] The top of the main liquid storage tank 40 is communicated with all the thermal compensation vertical pipes 30.

[0098] The present application can realize real-time compensation for the heat loss of the sidewall of the crucible 10 by arranging a plurality of auxiliary liquid storage tanks 60 and a corresponding control thermal compensation vertical pipe group in combination with a linkage mechanism, thereby solving the problem of fixed heat preservation structure and the inability to realize real-time regulation and control in the prior art. The directional solidification equipment can effectively transfer the heat emitted from the bottom of the crucible 10 to the sidewall for heat preservation and control of the phase change interface form, thereby recycling and reusing the originally wasted heat energy and improving the energy utilization efficiency.

[0099] Preferably, the directional solidification equipment further comprises:

[0100] A heat preservation cover 80 covering the top of the crucible 10;

[0101] A heat insulation layer 90 covering the thermal compensation vertical pipe 30, which is arranged between the crucible 10 and the heat preservation cover 80.

[0102] The present application further reduces the heat loss and improves the heat preservation effect of the entire directional solidification process by arranging the heat preservation cover 80 on the top and side of the crucible 10 and arranging the heat insulation layer 90 between the crucible 10 and the heat preservation cover 80, which helps to reduce the energy that must be input to maintain the required temperature, thereby reducing the overall energy consumption.

[0103] As shown in the accompanying drawings, Figure 2 The present application also provides a heat compensation method for any of the above-mentioned directional solidification equipment, characterized in that it comprises the following steps:

[0104] The inside of the main liquid storage tank 40, the auxiliary liquid storage tank 60, the thermal compensation horizontal pipe and the thermal compensation vertical pipe 30 is vacuumized;

[0105] The main liquid storage tank 40 is filled with a heat-conducting liquid, and the heat-conducting liquid in the main liquid storage tank 40 is driven to expand by the heat emitted from the bottom of the crucible 10 during the directional solidification process;

[0106] The temperature change at the bottom of the crucible 10 is sensed by the inflatable diaphragm 61, and the heat-conductive liquid in the main liquid tank 40 flows into the auxiliary liquid tank 60 through the heat-compensated horizontal pipe in combination with the linkage mechanism of the inflatable diaphragm 61 and the gate valve piston 62;

[0107] During the directional solidification process, the morphological change of the phase interface is monitored in real time;

[0108] Based on the first formula of the phase interface morphology and the heat exchange amount of the crucible 10 sidewall, the temperature change and the morphological change, the liquid level height in the heat-compensated vertical pipe 30 is dynamically adjusted, so that the net heat exchange amount of the sidewall tends to be zero, and the phase interface is maintained to be horizontal;

[0109] The first formula is as follows:

[0110] ;

[0111] Wherein, since the phase interface only occupies a small area in the melt, the vertical symmetry axis of the melt is taken as the y axis by virtue of symmetry, the lower boundary of the small thin area with a height of delta where the phase interface is located is taken as the x axis, and the height delta is taken as the calculation region (refer to Figure 3 ), because the height delta is very small, the solidification latent heat energy released by the melt at the phase interface is uniformly distributed in the entire calculation region; q is the heat flux density of the crucible 10 sidewall, t is the temperature of the calculation region, is the temperature of the lower edge of the calculation region, is the temperature of the upper edge of the calculation region, s is the solidification latent heat released during the solidification process, and lambda is the thermal conductivity of the melt, n is an odd number.

[0112] The present application can accurately control the morphology of the phase interface, maintain it to be horizontal, and improve the solidification quality by dynamically adjusting the liquid level height in the heat-compensated vertical pipe 30 based on the first formula of the phase interface morphology and the heat exchange amount of the crucible 10 sidewall; the stability of the directional solidification process is improved by monitoring the morphological change of the phase interface in real time and dynamically adjusting, and the defects caused by temperature fluctuation are reduced.

[0113] The present application can be used for directional solidification purification of polycrystalline silicon, directional solidification of titanium-aluminum alloy precision casting or aluminum alloy precision casting, and can dynamically adjust the phase interface morphology under the premise of meeting the basic temperature field of directional solidification, and can reduce thermal stress and prevent ingot cracking.

[0114] For example, in the practical application of the directional solidification purification of polycrystalline silicon or the precision casting process of titanium-aluminum alloy, the bottom main liquid storage tank 40, the auxiliary liquid storage tank 60, the inflatable diaphragm capsule 61, the heat-compensating horizontal pipe and the heat-compensating vertical pipe 30 are all made of nickel alloy (Inconel 600), the inflatable diaphragm capsule 61 is filled with argon, and Galinstan liquid metal alloy (melting point of 6℃, boiling point > 1400℃) composed of 68.5% Ga (gallium) + 21.5% In (indium) + 10% Sn (tin) is used as the heat-compensating liquid working medium.

[0115] For another example, in the directional solidification process of the precision casting of aluminum alloy, the bottom main liquid storage tank 40, the auxiliary liquid storage tank 60, the inflatable diaphragm capsule 61, the heat-compensating horizontal pipe and the heat-compensating vertical pipe 30 are all made of titanium alloy, the inflatable diaphragm capsule 61 is filled with nitrogen, and high-temperature silicone oil is used as the heat-compensating liquid working medium.

[0116] The design concept of the present application is that since the heat loss and dissipation of the directional solidification of the melt cannot be avoided, it is better to guide the heat loss to the side wall of the crucible 10 for full utilization, which is equivalent to side heat preservation and control. At the same time, the overall temperature field of the melt is kept above the phase transition temperature, so that the melt does not solidify prematurely.

[0117] Therefore, the present application utilizes the heat loss at the bottom of the crucible 10 generated by the directional solidification to drive the auxiliary liquid storage tank 60 and the inflatable diaphragm capsule 61. When the heat-conducting liquid in the main liquid storage tank 40 expands after being heated, it enters the auxiliary liquid storage tank 60 through the heat-compensating horizontal pipe, the inflatable diaphragm capsule 61 senses the temperature change around the bottom of the crucible 10, actuates the gate valve type piston 62 in the auxiliary liquid storage tank 60, controls the liquid level in the heat-compensating vertical pipe 30, and makes the heat at the bottom of the crucible 10 be conducted to the side wall of the crucible 10 by the liquid.

[0118] The present application not only realizes side heat preservation, but also adjusts the shape of the phase transition interface by the change of the liquid level in the heat-compensating vertical pipe 30 at the side wall of the crucible 10, so as to achieve the process purpose of changing the heat preservation and heat dissipation intensity of the melt. Compared with the traditional heat preservation and heat dissipation scheme, the present application has the ability to dynamically adjust the heat preservation and heat dissipation intensity during the directional solidification process and automatically correct the shape of the phase transition interface, and has the characteristics of simple and reliable control equipment and low cost.

[0119] In the present embodiment, when the heat loss at the side wall of the crucible 10 increases, the phase transition interface appears concave, the inflatable diaphragm capsule 61 becomes smaller, the gate valve type piston 62 is driven to rise, the liquid level in the heat-compensating vertical pipe 30 is raised to strengthen the heat preservation and inhibit the concave of the phase transition interface.

[0120] When the heat at the side wall of the crucible 10 is excessive, the phase transition interface appears convex, the inflatable diaphragm capsule 61 becomes larger, the gate valve type piston 62 is driven to lower, the liquid level in the heat-compensating vertical pipe 30 is lowered to reduce the heat preservation and inhibit the convex of the phase transition interface.

[0121] When the heat loss of the sidewall of the crucible 10 increases or heat is excessive, the device can automatically adjust the liquid level height in the thermally compensated standpipe 30 to strengthen or reduce the heat preservation, so as to realize the automatic control of the solidification process and improve the automation level of the process.

[0122] In the embodiment, the first formula is obtained based on a temperature field formula and a boundary condition formula in a calculation region, and at least includes the following steps:

[0123] The temperature field formula and the boundary condition formula are transformed to obtain a first temperature field formula, a second temperature field formula, a third temperature field formula, a first boundary condition formula, a second boundary condition formula and a third boundary condition formula.

[0124] Since the solidification temperature of the directional solidification is certain, the thermal characteristics in the region are consistent at any height of Δ during the whole solidification process. The directional solidification process also continuously releases the latent heat of solidification, and the temperature field satisfies the Poisson equation with internal heat source (i.e. the temperature field formula), which is specifically:

[0125] The boundary condition formula is: ; wherein, is a temperature distribution function at the lower edge of the calculation region, is a temperature distribution function at the upper edge of the calculation region.

[0126] Based on the first temperature field formula and the first boundary condition formula, the second temperature field formula and the second boundary condition formula, and the third temperature field formula and the third boundary condition formula, the first formula is solved respectively.

[0127] For the temperature field formula, the left edge x=0 of the calculation region is located at the center of the crucible 10, and because of the central symmetry, this place can be regarded as adiabatic, i.e. x=W / 2 is located at the right edge of the calculation region, and there may be heat exchange with the outside, i.e. there is heat flux density q, which can be obtained as:

[0128] When q>0, the direction of the heat flux density is along the positive direction of the x-axis, i.e. the heat is lost at the right edge of the calculation region;

[0129] When q<0, the direction of the heat flux density is along the negative direction of the x-axis, i.e. the heat is obtained at the right edge of the calculation region;

[0130] When q=0, there is no heat exchange, and the edge of the calculation region is ideally adiabatic.

[0131] ​The most core parameter of the directional solidification process is the net heat exchange amount of the side wall of the crucible 10, which determines the shape of the phase change interface, and the horizontal phase change interface is the key to the success of directional solidification. Therefore, it is necessary to establish a mathematical model to explore the mathematical relationship between the side wall heat exchange, the bottom heat dissipation intensity and the phase change interface shape, to provide a theoretical basis for the present application, and also facilitate quantitative phase change interface shape control. The first formula of the present application is obtained based on the temperature field formula and the boundary condition formula in the calculation region, which provides accurate theoretical support for heat compensation, making the heat compensation more scientific and accurate.

[0132] Since the temperature field formula contains non-homogeneous boundary conditions, it is difficult to solve directly, therefore, in this embodiment, based on the first formula of the temperature field and the first formula of the boundary condition, the second formula of the temperature field and the second formula of the boundary condition, the third formula of the temperature field and the third formula of the boundary condition, are solved respectively to obtain the first formula, which at least includes the following steps:

[0133] Based on the first formula of the temperature field and the first formula of the boundary condition, the second formula is solved;

[0134] The first formula of the temperature field is: ;

[0135] The first formula of the boundary condition is: ;

[0136] Based on the second formula of the temperature field and the second formula of the boundary condition, the third formula is solved;

[0137] The second formula of the temperature field is: ;

[0138] The second formula of the boundary condition is: ;

[0139] Based on the third formula of the temperature field and the third formula of the boundary condition, the fourth formula is solved;

[0140] The third formula of the temperature field is: ;

[0141] The third formula of the boundary condition is: ;

[0142] Based on the second formula, the third formula, the fourth formula, the boundary condition formula, and the sum of the first formula of the temperature field, the second formula of the temperature field and the third formula of the temperature field, the first formula is solved.

[0143] The present application obtains the first formula through a multi-step accurate solving process, further improving the accuracy and reliability of heat compensation.

[0144] In the embodiment, based on the temperature field first formula and the boundary condition first formula, a second formula is solved, including the following steps:

[0145] Let , then u satisfies a fifth formula: ;

[0146] And the boundary condition satisfies a sixth formula: ;

[0147] By Fourier expansion, the analytical solution of u is solved as:

[0148] .

[0149] The analytical solution solved by Fourier expansion of the present application provides accurate control parameters for heat compensation, so that the morphology of the phase change interface can be more accurately controlled.

[0150] In the embodiment, based on the temperature field second formula and the boundary condition second formula, a third formula is solved by using the separation of variables method as follows:

[0151] ;

[0152] Wherein, m is a positive integer greater than or equal to 2.

[0153] In the embodiment, based on the temperature field third formula and the boundary condition third formula, a fourth formula is solved by using the separation of variables method as follows:

[0154] .

[0155] In the embodiment, based on the second formula, the third formula, the fourth formula, the boundary condition formula, and the sum of the temperature field first formula, the temperature field second formula and the temperature field third formula, a first formula is solved, including the following steps:

[0156] Based on the sum of the temperature field first formula, the temperature field second formula and the temperature field third formula, the following formula is obtained:

[0157] ;

[0158] Based on the second formula, the third formula and the fourth formula, let t Δ(x) (representing and ) be a constant value, the boundary condition formula is transformed to obtain a fifth formula as follows:

[0159] ;

[0160] Based on the second formula, the third formula, the fourth formula, the fifth formula, and the sum of the temperature field first formula, the temperature field second formula and the temperature field third formula, the first formula is obtained by using the separation of variables method.

[0161] .

[0162] The first formula is obtained based on the second formula, the third formula, the fourth formula, the boundary condition formula, and the sum of the temperature field first formula, the temperature field second formula and the temperature field third formula, and the influence of multiple factors is comprehensively considered, thereby improving the precision of the phase change interface shape control.

[0163] By drawing the image of the first formula (refer to Figure 4 It can be seen that the influence of the heat flux density q of the crucible 10 edge on the phase change interface: the greater the heat loss value of the crucible 10 side wall (q is positive), the greater the concave degree of the phase change interface; the greater the heat value obtained by the crucible 10 side wall (q is negative), the greater the convex degree of the phase change interface; the ideal adiabatic of the crucible 10 side wall (q is 0), the phase change interface remains horizontal.

[0164] Therefore, it is theoretically proved that the heat compensation stand pipe 30 of the present scheme changes the heat preservation characteristics of the crucible 10 side wall, and then adjusts the heat exchange strength, so as to realize the control of the phase change interface shape. When directional solidification is used for precision casting or crystal growth purification, if the side wall loses heat, the phase change interface is concave, the solidification thermal stress is concentrated, the purity of the ingot is reduced, and even there is a risk of cracking the ingot; when the side wall obtains heat, the phase change interface presents a convex shape, the crystal (grain) growth direction is inclined during solidification, and the crystal branch arrangement is out of control; when the side wall has no heat exchange, the phase change interface is a horizontal plane, and at this time, the solidification quality is best. Since the solidification process is a comprehensive result of heat conduction, heat convection mass transfer and heat radiation, therefore, in each stage of solidification, it is the key to the success of solidification to keep the phase change interface horizontal, and it is also the difficulty and emphasis in the process.

[0165] According to the first formula, the most core parameter of the directional solidification process is the heat exchange condition of the side wall of the crucible 10 and the heat dissipation intensity of the bottom, which determines the phase change interface form and the solidification quality. The traditional directional solidification equipment more relies on passive heat insulation materials, even if the active mechanical structure (such as the lifting type heat insulation cover directional solidification method) is used, the heat preservation capacity has no adjustment margin and flexibility when the working condition changes, and the form of the phase change interface in the solidification process cannot be monitored and corrected in real time. The present application adds a heat compensation vertical pipe 30, designs an automatic control structure of an inflatable diaphragm box 61 linkage liquid storage tank, only uses the simple control logic of liquid expansion under heating and the thermal expansion and contraction of the gas in the inflatable diaphragm box 61 to drive the flow of the liquid working medium in the pipe, so as to adjust the liquid level height in the heat compensation vertical pipe 30 in real time, and then realize the process requirements of dynamic heat preservation of the crucible 10 side wall and control of the phase change interface form following the solidification process. Moreover, the present application does not need to bury multiple sensors and does not need to use complex circuits and control chips for closed-loop control, further reducing the comprehensive cost.

[0166] It should be noted that in the present application, one auxiliary liquid storage tank 60 corresponds to control one heat compensation vertical pipe group, but the number of heat compensation vertical pipes 30 included in each heat compensation vertical pipe group has no special requirement, and the number of heat compensation vertical pipes 30 included in different heat compensation vertical pipe groups can be the same or different. However, the number of auxiliary liquid storage tanks 60 is determined according to the temperature field control accuracy in the directional solidification process.

[0167] For example: if the phase change interface form needs to be controlled more finely, then more number of auxiliary liquid storage tanks 60 are needed, and the number of heat compensation vertical pipes 30 included in the heat compensation vertical pipe group corresponding to each auxiliary liquid storage tank 60 is less.

[0168] As for the thickness and number of the heat compensation vertical pipes 30, it is mainly limited by three aspects: one is the processing difficulty; two is the processing cost; three is the liquid flow resistance. In theory, the thinner and the more the heat compensation vertical pipes 30 are, the better the temperature field control accuracy is. But in practical application, with the increase of processing difficulty, cost and liquid flow resistance, it is not necessarily that the expected effect can be achieved in the case of thinner and more heat compensation vertical pipes 30 (such as too slow liquid flow, poor control effect).

[0169] Therefore, the number of auxiliary liquid storage tanks 60 is generally 8-16, and the number of heat compensation vertical pipes 30 included in one heat compensation vertical pipe group corresponding to one auxiliary liquid storage tank 60 is 4-8. It can be understood that the position of the auxiliary liquid storage tank 60 is set near the position of the heat compensation vertical pipe group corresponding to it.

[0170] It should be noted that the above is only an exemplary description and does not constitute an improper limitation on the present application.

[0171] Further, the principle of the heat supplement method of the present application is described in combination with the drawings so as to facilitate the understanding of the present application.

[0172] After the interior of the main liquid storage tank 40, the auxiliary liquid storage tank 60, the heat compensation horizontal pipe and the heat compensation vertical pipe 30 are vacuumized, the main liquid storage tank 40 is filled with the heat-conductive liquid (working medium).

[0173] In the initial stage of solidification, the heat-conductive liquid is stored in the main liquid storage tank 40 (for reference Figure 5 ), because the main liquid storage tank 40 and the heat compensation horizontal pipe are close to the heat-conductive pad 20 at the bottom of the crucible 10, the heat-conductive liquid in the main liquid storage tank 40 expands under the heat, enters the heat compensation vertical pipe 30 via the auxiliary liquid storage tank 60. Therefore, part of the heat dissipated from the bottom of the crucible 10 is transferred to the heat compensation vertical pipe 30 by the heat-conductive liquid, which is equivalent to that the heat dissipated from the bottom of the crucible 10 is "guided" to the sidewall of the crucible 10 which needs to be heat-insulated and heat-preserved, thereby realizing the active auxiliary heat-preservation of the sidewall. Meanwhile, the heat compensation vertical pipe 30 in the vacuum section also plays a passive heat-insulation and heat-preservation role.

[0174] After the solidification starts, with the heat dissipation from the bottom of the crucible 10, the heat-conductive liquid in the main liquid storage tank 40 expands under the heat, and the bottom buffer air chamber 50 starts to expand and press the main liquid storage tank 40, the heat-conductive liquid in the main liquid storage tank 40 gradually enters the auxiliary liquid storage tank 60 through the heat compensation horizontal pipe. The temperature of the heat dissipation from the bottom is higher in the initial solidification, because the inflatable diaphragm 61 is close to the bottom of the crucible 10, the initial temperature is higher than that of the bottom buffer air chamber 50 of the main liquid storage tank 40. Therefore, the internal air pressure of the inflatable diaphragm 61 is larger. When the pressure difference is enough to open the one-way air valve 71 between them, the inflatable diaphragm 61 will be slightly smaller, the sluice valve type piston 62 in the auxiliary liquid storage tank 60 rises, causing the volume of the auxiliary liquid storage tank 60 to slightly increase, which can accommodate more liquid, thereby delaying the rapid rise of the liquid level in the heat compensation vertical pipe 30. Therefore, in the initial stage of solidification, this design well controls the imbalance of the phase change interface caused by the too fast directional solidification rate. With the progress of the solidification, the liquid level in the heat compensation vertical pipe 30 rises with the phase change interface, thereby heat-preservation and annealing the solidified part (solid phase), reducing the thermal stress and preventing cracking. Until the end of the solidification process, the heat compensation vertical pipe 30 is filled with the heat-conductive liquid (for reference Figure 6 ), thereby heat-preservation of the whole ingot.

[0175] In the directional solidification, if the phase change interface is imbalanced (such as overall or local concave and convex), the present application can automatically adjust and correct the phase change interface. As shown in Figure 7 , 8 groups of mutually independent heat compensation pipes can be controlled by the respective inflatable diaphragm 61 and auxiliary liquid storage tank 60, for example, taking the heat compensation pipes at the corners as an example, the specific control principle and steps of the phase change interface correction are as follows:

[0176] When the phase interface is concave, according to the first formula analysis, the heat loss of the crucible 10 side wall, especially the heat loss at the corner of the crucible 10 side wall, is considerable, so the heat dissipation intensity at the bottom corner of the crucible 10 is reduced, the volume of the inflatable membrane box 61 is reduced (thinned), the auxiliary liquid storage tank 60 is driven to rise (reference Figure 8 ), the flow resistance is reduced, the liquid level in the side wall heat compensation stand pipe 30 is raised, and the heat compensation at this place is strengthened. At this time, the air pressure in the inflatable membrane box 61 is lower than that in the buffer air chamber 50, but the buffer air chamber 50 is connected to the air pipe 70 between the inflatable membrane boxes 61, and the one-way air valve 71 is installed in the air pipe 70, so the buffer air chamber 50 cannot enter the inflatable membrane box 61, and the position of the gate valve type piston 62 in the main liquid storage tank 40 is basically unchanged, so the liquid level in the other heat compensation stand pipes 30 is lower than the liquid level in the stand pipe at the corner of the crucible 10, and then a height difference is generated in the entire heat compensation stand pipe 30, forming a concave side wall heat preservation mode similar to the concave phase interface (reference Figure 9 ), which compensates for the heat loss of the crucible 10 side wall and restores the phase interface from concave to horizontal.

[0177] When the crucible 10 side wall is heated, the phase interface is convex. To correct the convex interface shape, the heat preservation intensity of the crucible 10 side wall at the interface height position needs to be reduced. Due to the thermal expansion of the inflatable membrane box 61, the gate valve type piston 62 in the auxiliary liquid storage tank 60 is lowered, the flow resistance is increased, the liquid level height in the corresponding heat compensation stand pipe 30 is lowered, the side wall heat compensation is reduced (reference Figure 10 ), and the solidification of the melt at the side wall is accelerated, so that the phase interface returns to horizontal. In this process, because the air pressure in the inflatable membrane box 61 is higher than that in the buffer air chamber 50, the air pressure difference pushes open the spring of the one-way air valve 71 between them, the air valve is opened, the inflatable membrane box 61 performs gas compensation to the buffer air chamber 50, the volume of the buffer air chamber 50 is further increased, the bottom of the main liquid storage tank 40 is squeezed, the liquid level in the other heat compensation stand pipes 30 is slightly raised, forming a heat preservation mode with a convex liquid level (reference Figure 11 ), which can effectively correct the phase interface.

[0178] When there is no heat exchange in the crucible 10 side wall, the phase interface is horizontal, and the directional solidification effect is best. At this time, the air pressures in the buffer air chamber 50 and each inflatable membrane box 61 are basically equal, the inflatable membrane box 61 and the gate valve type piston 62 are slowly actuated synchronously with the solidification process (reference Figure 12 ), and the liquid level in all heat compensation stand pipes 30 rises slowly with the phase interface, realizing the process effect of dynamic heat preservation (reference Figure 13 ).

[0179] According to the first formula of the present application, the thickness, density and grouping of the sidewall heat compensation riser 30 can be designed for different directional solidification materials, which improves the application flexibility of the method of the present application. The above parameter changes for different solidification conditions are summarized in Table 1.

[0180] Table 1: Summary of parameter changes for different solidification conditions

[0181]

[0182] It should be noted that in actual application, the heat compensation riser is thinner and denser than the one shown in the figure, and the heat compensation riser shown in the drawings of the present application is appropriately enlarged and simplified for the convenience of illustration and drawing, which is only an example for illustration and does not constitute an improper limitation on the present application.

[0183] It should be noted that in this paper, the term "including", "containing" or any other variant thereof is intended to cover non-exclusive inclusion, so that the process, method, article or device including a series of elements not only includes those elements, but also includes other elements not explicitly listed, or includes elements inherent to such process, method, article or device. Without more limitations, the element defined by the statement "including a" does not exclude the presence of other identical elements in the process, method, article or device including the element.

[0184] The above description shows and describes the preferred embodiments of the present application, it should be understood that the present application is not limited to the forms disclosed herein, should not be regarded as excluding other embodiments, but can be used in various other combinations, modifications and environments, and can be modified within the scope of the present application concept by the above teaching or related art or knowledge. The modifications and changes made by those skilled in the art without departing from the spirit and scope of the present application shall be within the protection scope of the claims of the present application.

Claims

1. A directional solidification device, characterized in that, include: crucible; A heat-conducting pad is placed at the bottom of the crucible; Multiple thermal compensation riser groups, each thermal compensation riser group including multiple thermal compensation risers arranged parallel to the side wall of the crucible; The main liquid storage tank is in contact with the thermal pad, and a buffer gas chamber is provided below it; Multiple auxiliary liquid storage tanks, equal in number to the heat compensation riser group, are located on the side of the main liquid storage tank. The top of each auxiliary liquid storage tank is connected to multiple heat compensation risers of a heat compensation riser group. Each auxiliary reservoir is equipped with a gate valve piston inside, and an inflatable diaphragm is located above the gate valve piston. The inflatable membrane box is connected to the buffer air chamber via an air pipe equipped with a one-way air valve; Each auxiliary storage tank is connected to the main storage tank via a thermally compensated horizontal pipe; The top of the main liquid storage tank is connected to all the heat compensation risers.

2. The directional solidification equipment according to claim 1, characterized in that, Also includes: An insulating cover that covers the top and sides of the crucible; The heat insulation layer covering the heat compensation riser is placed between the crucible and the heat insulation cover.

3. A heat compensation method for the directional solidification equipment according to claim 1 or 2, characterized in that, Includes the following steps: Vacuum the inside of the main liquid storage tank, auxiliary liquid storage tank, thermal compensation horizontal pipe and thermal compensation vertical pipe; The main storage tank is filled with a thermally conductive liquid. During the directional solidification process, the heat emitted from the bottom of the crucible drives the thermally conductive liquid in the main storage tank to expand. By sensing the temperature change at the bottom of the crucible through an inflatable diaphragm, and combining the linkage mechanism between the inflatable diaphragm and the gate valve piston, the thermally conductive liquid in the main storage tank flows into the auxiliary storage tank through the thermal compensation horizontal pipe. During directional solidification, the morphological changes of the phase transition interface are monitored in real time; Based on the first formula of phase change interface morphology and crucible sidewall heat exchange, temperature change and morphological change, the liquid level in the heat compensation riser is dynamically adjusted to make the net heat exchange on the sidewall approach zero and maintain the phase change interface level. The first formula is as follows: ； In this calculation, the vertical axis of symmetry of the melt is taken as the y-axis, the width of the melt is set as W, the lower boundary of the region with height Δ where the phase transformation interface is located is set as the x-axis, and the height Δ is taken as the calculation region. q is the heat flux density of the crucible sidewall, and t is the temperature of the calculation region. To calculate the temperature at the lower edge of the region, The temperature at the upper edge of the calculation region is given by s, where s is the latent heat of solidification continuously released during solidification, and λ is the thermal conductivity of the melt. n is an odd number.

4. The heat compensation method for directional solidification equipment according to claim 3, characterized in that, When the heat loss from the crucible sidewall increases, the phase change interface becomes concave, the volume of the gas-filled membrane box decreases, and the gate valve piston rises, causing the liquid level in the heat compensation riser to enhance heat preservation and suppress the concavity of the phase change interface. When there is excess heat on the side wall of the crucible, the phase change interface bulges upward, the volume of the gas-filled membrane box increases, and the gate valve piston is driven to descend, which lowers the liquid level in the heat compensation riser to reduce heat preservation and suppress the upward bulge of the phase change interface.

5. The heat compensation method for directional solidification equipment according to claim 3, characterized in that, The first formula is derived from the temperature field formula and boundary condition formula within the computational domain, and includes at least the following steps: By transforming the temperature field formula and the boundary condition formula, we obtain the first temperature field formula, the second temperature field formula, the third temperature field formula, the first boundary condition formula, the second boundary condition formula, and the third boundary condition formula. The temperature field formula is: ; The boundary condition formula is: ;in, To calculate the temperature distribution function along the lower edge of the region, This is the temperature distribution function along the upper edge of the computational region; Based on the first formula for temperature field and the first formula for boundary conditions, the second formula for temperature field and the second formula for boundary conditions, and the third formula for temperature field and the third formula for boundary conditions, the first formula is obtained by solving them respectively.

6. The heat compensation method for directional solidification equipment according to claim 5, characterized in that, Based on the first formula for the temperature field and the first formula for boundary conditions, the second formula for the temperature field and the second formula for boundary conditions, and the third formula for the temperature field and the third formula for boundary conditions, the solutions are performed respectively to obtain the first formula, which includes at least the following steps: Based on the first formula for temperature field and the first formula for boundary conditions, the second formula is obtained by solving. The first formula for the temperature field is: ; The first formula for boundary conditions is: Where t1 is the temperature variable in the first formula of the temperature field; Based on the second formula for temperature field and the second formula for boundary conditions, the third formula is obtained by solving. The second formula for the temperature field is: ; The second formula for boundary conditions is: Where t2 is the temperature variable in the second formula of the temperature field; Based on the third formula for temperature field and the third formula for boundary conditions, the fourth formula is obtained by solving. The third formula for the temperature field is: ; The third formula for boundary conditions is: Where t3 is the temperature variable in the third formula of the temperature field, and the temperature of the calculation area is t = t1 + t2 + t3; Based on the second, third, and fourth formulas, the boundary condition formula, and the sum of the first, second, and third temperature field formulas, the first formula is obtained.

7. The heat compensation method for directional solidification equipment according to claim 6, characterized in that, Based on the first formula for temperature field and the first formula for boundary conditions, the second formula is obtained by solving the problem, including the following steps: make Then u satisfies the fifth formula: Where u is the transformation variable used to transform a non-homogeneous differential equation into a homogeneous differential equation; And the boundary conditions satisfy the sixth formula: ; By using Fourier expansion, the analytical solution for u is obtained as follows: ； Based on u and the analytical solution, the second formula is obtained as follows: 。 8. The heat compensation method for directional solidification equipment according to claim 7, characterized in that, Based on the second formula for the temperature field and the second formula for the boundary conditions, the third formula is obtained by using the method of separation of variables as follows: ； in, is a periodic constant factor, where m is a positive integer greater than or equal to 2.

9. The heat compensation method for directional solidification equipment according to claim 8, characterized in that, Based on the third formula for the temperature field and the third formula for the boundary conditions, the fourth formula is obtained by using the method of separation of variables as follows: 。 10. The heat compensation method for directional solidification equipment according to claim 9, characterized in that, Based on the second, third, and fourth formulas, the boundary condition formula, and the sum of the first, second, and third temperature field formulas, the first formula is obtained by solving the problem, including the following steps: Based on the sum of the first, second, and third formulas for the temperature field, we obtain the following formula: ； Based on the second, third, and fourth formulas, the boundary condition formulas are transformed to obtain the fifth formula as follows: ； Based on the second, third, fourth, and fifth formulas, as well as the sum of the first, second, and third temperature field formulas, the method of separation of variables is used to solve the problem and obtain the first formula.

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