Design method of directional solidification furnace heater

Abstract

The invention belongs to the field of heaters, and discloses a design method of a directional solidification furnace heater, which comprises the following steps of: 1, calculating the total power of the heater; 2, modular design is carried out on the heater; step 3, performing preliminary simulation and verification; step 4, power distribution of the heating element is carried out; 5, selecting the material of the heating element; step 6, designing the shape of the heating element; and step 7, performing simulation and verification again. The heater designed by the invention can effectively realize the uniformity and consistency of the contour temperature of the outer surface of a heated object and the control of the position of a cold point, and effectively reduce the temperature gradient of a radial section. And particularly, the method shows obvious advantages when heating special-shaped materials, and is suitable for directional solidification of materials with complex shapes.

Description

Technical Field

[0001] The invention relates to the field of heaters, in particular to a design method for a directional solidification furnace heater. Background Art

[0002] Directional solidification (HDS) is an advanced crystal growth technology that controls the temperature gradient of the thermal field to achieve the melting of the raw materials and then directionally solidify and grow crystals at a specific rate. Compared with other crystal growth methods, directional solidification is more flexible in controlling the temperature gradient and the direction of crystal growth, and it is easy to achieve a uniform solidification process, which greatly reduces the thermal stress and strain generated during the solidification process of the material. At the same time, it is more suitable for complex crucibles and molds, and is widely used in the preparation of materials such as turbine blades, high-purity crystals, and high-strength alloys. The core of directional solidification is the temperature distribution of the thermal field, among which the heater is the key. It provides enough heat to ensure the melting of the raw materials, and it creates a suitable temperature gradient to achieve directional growth of crystals.

[0003] So far, a large number of heater optimization schemes have been applied to achieve precise control of the temperature of multiple independent zones. CN108253780A discloses a vacuum sintering furnace that realizes four-zone temperature control. The temperature distribution uniformity of the thermal field is improved by arranging multiple radial heaters. CN111457715A discloses a heater and a vacuum furnace with multi-zone temperature control. A heater is formed by connecting multiple heating elements in series and parallel. The segmented independent control of the heater realizes temperature control of multiple zones. CN117737826A discloses a temperature field structure and a melting zone control method for growing crystals by a horizontal directional crystallization method. The control of the melting zone length is realized by two independent sets of heaters. CN118516741A discloses a heating lattice to realize local precise and flexible temperature control in directional solidification heating.

[0004] There are still many deficiencies in the radial temperature control of the heated object in the heater of the directional solidification furnace: the temperature gradient of the surface contour of the heated object is large, and the growth interface is difficult to be stable and controllable; the radial temperature gradient is large, resulting in a concave or convex solid-liquid interface; the cold spot of the radial section of the heated object is difficult to control at the geometric center of the cross section. At present, the design of the heater of the directional solidification furnace still mainly relies on the empirical design of its shape, quantity and arrangement. A single rectangular or spiral structure is generally adopted, which is arranged on both sides or the bottom of the furnace. This design lacks scientificity and is not accurate enough. The temperature distribution of the radial section of the heated object is uneven, and it is difficult to adapt to the heating requirements of heated objects of different shapes. It leads to excessive temperature gradient at the front of the crystal growth interface, causing instability of the growth interface. Specifically, the solid-liquid interface may become rough and irregular, forming undesirable structures such as dendrites. This unstable interface morphology will cause significant changes in grain size and orientation, resulting in uneven grain growth. In addition, excessive temperature gradient will also aggravate component segregation, resulting in uneven distribution of different elements in the alloy, affecting the macroscopic properties of the material, such as mechanical strength and toughness. Ultimately, these factors will reduce the overall quality and application performance of the material. Therefore, reasonable heater design is the key to controlling the appropriate radial temperature gradient and achieving high-quality crystal growth. Summary of the invention

[0005] The object of the present invention is to provide a design method for a directional solidification furnace heater to solve the problems raised in the above background technology.

[0006] To achieve the above object, the present invention provides the following technical solutions:

[0007] A design method for a directional solidification furnace heater, comprising:

[0008] Step 1, calculating the total power of the heater;

[0009] Step 2, modular design of the heater;

[0010] Step 3, conduct preliminary simulation and verification;

[0011] Step 4, distributing the power of the heating element;

[0012] Step 5, selecting the material of the heating element;

[0013] Step 6, designing the shape of the heating element;

[0014] Step 7, performing simulation and verification again, includes: after completing the overall design of the heater, simulating the heating effect through computer simulation to verify whether the design of the heater meets the target requirements.

[0015] Furthermore, the step 1 specifically includes:

[0016] i. Calculate the power demand during the heating phase

[0017] During the heating stage, the heater needs to provide enough heat to raise the temperature inside the furnace, calculated using the following formula:

[0018] Q 总 =∑Q 蓄热 +∑Q 损耗

[0019] Among them, Q 总 Indicates the total heat that the heater needs to provide during the heating phase, ∑Q 蓄热 Indicates the heat storage of all materials in the furnace during the heating stage, ∑Q 拐耗 Indicates the heat energy lost by the furnace shell system during the heating stage;

[0020] a. The total heat Q that the heater needs to provide during the heating phase 总 :

[0021]

[0022] Among them, P1(t) represents the output power of the heater changing with time t during the heating stage, and T represents the total heating time during the heating stage;

[0023] b. Heat storage of all materials in the furnace during the heating stage ∑Q 蓄热 :

[0024]

[0025] Where μ represents the proportional factor, which is 1 to 1.3 according to the complexity of the internal structure of the furnace shell; assuming that there are m kinds of materials in the furnace shell, where ρ k represents the density of the kth material, c k represents the specific heat capacity of the kth material, ΔT′ k represents the average temperature of the entire k-th material, represents the initial temperature of the kth material, V k represents the volume of the kth material;

[0026] c. Heat loss of furnace shell system during heating stage∑Q 拐耗 :

[0027] ∑Q 损耗 =α(Q 传导 +Q 辐射 +Q 对流 )

[0028] Among them, α represents the proportional factor, Q 传导 Indicates the heat conduction loss of the furnace shell during the heating stage, Q 辐射 Indicates the heat radiation loss of the furnace shell during the heating stage, Q对流 It represents the heat loss caused by the airflow exchange inside and outside the furnace during the heating stage;

[0029] Heat conduction loss of furnace shell during heating stage Q 传导 Involving the heat transfer process from the high temperature center to the outside of the low temperature furnace shell, the following conditions are set:

[0030] Condition 1: The average temperature of the high temperature area in the center of the furnace is T heater ;

[0031] Condition 2: The average temperature of the furnace shell is T RT ;

[0032] Condition 3: Heat conduction passes through n layers of different materials, each layer has a different thermal conductivity λ i and thickness d i , the conduction area is A;

[0033] Then we have:

[0034]

[0035] Among them, d i represents the thickness of the i-th layer, λ i represents the thermal conductivity of the i-th layer, A represents the conductive surface area of ​​each layer, T heater (t) represents the average temperature of the high temperature area in the center of the furnace changing with time, T RT (t) represents the furnace shell temperature changing with time;

[0036] Heat radiation loss of furnace shell during heating stage Q 辐射 , set the following conditions:

[0037] Condition 4: The insulation layer forms a closed space. The heat radiation inside the insulation layer is equivalent to circulating inside the system, which does not cause net heat loss. Therefore, the difference between the temperature outside the insulation layer and the temperature of the furnace shell is the key factor in determining the heat radiation loss.

[0038] Condition 5: The temperature of the furnace shell is T RT ;

[0039] Then we have:

[0040]

[0041] Where ε is the emissivity of the outer surface of the thermal insulation layer, σ is the Stefan-Boltzmann constant, and A sur represents the radiation surface area of ​​the outer surface of the insulation layer, T sur (t) represents the average temperature of the outer surface of the insulation layer changing with time, T RT (t) represents the average temperature of the furnace shell changing with time, and T represents the total heating time;

[0042] Heat loss Q caused by the flowing atmosphere in the furnace during the heating stage 对流 :

[0043]

[0044] in, represents the mass flow rate of gas, c p represents the specific heat capacity of the gas, A sur represents the radiation surface area of ​​the outer surface of the insulation layer, T outlet (t) represents the average temperature of the gas flowing out of the furnace that changes with time, T inlet (t) represents the average temperature of the gas flowing into the furnace body changing with time, and T represents the total heating time;

[0045] ii. Calculate the power demand during the thermal balance phase

[0046] The target temperature is reached and maintained in a thermal equilibrium state. The temperature of each area in the furnace remains stable. At this time, the main task of the heater is to compensate for the heat loss of the directional solidification furnace system. The output power of the heater corresponding to the thermal equilibrium stage is expressed as:

[0047]

[0048] Where P2 represents the heater output power in the thermal equilibrium stage, T heater represents the temperature of the heater at thermal equilibrium, T RT Indicates the temperature of the furnace shell when in thermal equilibrium, T sur Indicates the temperature outside the insulation layer when in thermal equilibrium, T outlet Indicates the temperature of the gas flowing out of the furnace when thermal equilibrium occurs, T inlet represents the temperature of the gas flowing into the furnace when thermal equilibrium occurs, and α represents the proportional factor;

[0049] iii. Calculation of the theoretical maximum output power requirement of the heater:

[0050] P 理论 =max(P1,P2)

[0051] Among them, P 理论 It indicates the theoretical maximum output power of the heater during the heating process of the entire directional solidification furnace system. max(*) indicates the maximum value.

[0052] iv. Redundant design

[0053] After considering power redundancy, the total design power of the heater is P 设计 Expressed as the actual required power P 理论 A multiple of , expressed as the redundancy coefficient β:

[0054] P 设计=(1+β)·P 理论

[0055] Among them, P 设计 It represents the total design output power of the directional solidification furnace heater.

[0056] Furthermore, the step 2 specifically includes:

[0057] i. Heater outline design:

[0058] The outer contour of the heater is generated by offsetting a fixed distance d in the normal direction of the outer contour of the irregular object, so as to ensure that the closest distance between the heater and the surface of the heated object is always kept at d;

[0059] ii. Construction of two-dimensional geometric model of directional solidification furnace system:

[0060] A two-dimensional geometric simulation model corresponding to the radial cross section of the raw material of the directional solidification furnace system is constructed by simulation software. The geometric simulation model includes raw materials, crucibles, heaters, insulation layers, gas domains and furnace shells. The temperature field distribution and stress field distribution of the geometric simulation model are simulated and calculated.

[0061] iii. Modular division of heaters:

[0062] According to the simulation results of ii, the temperature concentration area of ​​the heated object corresponding to the heater position is divided into module areas to form multiple independent heating elements, or the heater stress concentration area is divided into module areas according to the heater stress to form multiple independent heating elements.

[0063] Furthermore, the step 3 specifically includes:

[0064] Based on the heating elements divided in step 2, a simulation experiment is carried out on the geometric simulation model built in step 2. By analyzing the temperature distribution on the surface of the heated object, the power of the heating elements at each position is adjusted, and finally the optimal power distribution ratio η of each heating element i in a single heater is determined. i .

[0065] Furthermore, the step 4 specifically includes:

[0066] Assume that the furnace has n heaters in total, then the design power of a single heater is The design power of the heating element i in the heater is P 元件i =P 加热器 ×η i .

[0067] Among them, P 加热器 Represents the design output power of a single heater, P 设计 represents the total design output power of the directional solidification furnace heater, n represents the number of heaters in the furnace, P元件i represents the design output power of heating element i in a single heater, η i It represents the optimal power distribution ratio of heating element i to the entire heater.

[0068] Furthermore, the step 5 specifically includes:

[0069] Select the appropriate material according to the working environment's temperature, atmosphere, heating element's operating power and the requirements of the heated object.

[0070] Furthermore, the step 6 specifically includes:

[0071] The shape of the heating element is designed according to the design power of the heating element and the allowable surface load, including:

[0072] i. Design of heating element length and cross-sectional shape:

[0073]

[0074] P 元件i =W 许用 *A

[0075]

[0076] A=S*L″ i

[0077] L i =(L′ imin , L″ imax )

[0078] Among them, P 元件i represents the design output power of heating element i in a single heater, w 许用 Indicates the allowable surface load of the heating element, R t represents the resistance of the heating element at temperature t, ρ t represents the resistivity of the heating element at temperature t, U represents the terminal voltage of the heating element, A represents the surface area of ​​the heating element, S represents the cross-sectional circumference of the heating element, f represents the cross-sectional area of ​​the heating element, and L' i Indicates that R t Calculated length of the i-th heating element, L″ i represents the length of the i-th heating element calculated by A, L i represents the absolute length of the i-th heating element;

[0079] ii. Heating element structure and shape design:

[0080] According to the relative length L of the i-th heating element ri and the absolute length L of the i-th heating element iDesign heating elements in curved, wrap-around or multi-segment shapes.

[0081] Furthermore, the step 7 specifically includes:

[0082] Design the heater's wiring terminals, support structure, insulation, and thermocouple layout.

[0083] Compared with the prior art, the present invention has the following beneficial effects:

[0084] 1) The design method provided by the present invention provides a scientific basis for the design of the heater of the directional solidification furnace through a series of steps. By calculating the power of the heater and modularizing the heater according to the two-dimensional simulation model, the position, quantity, power and shape of the heating elements with different temperature field requirements can be designed;

[0085] 2) The heater designed by the present invention can effectively achieve uniform temperature of the outer surface contour of the heated object, control the position of the cold spot, and effectively reduce the temperature gradient of the radial section. It has significant advantages in heating special-shaped materials and is suitable for directional solidification of complex-shaped materials. BRIEF DESCRIPTION OF THE DRAWINGS

[0086] Figure 1 The present invention is a flow chart of a method for designing a heater for a directional solidification furnace.

[0087] Figure 2 It is a schematic diagram of the structure of a directional solidification furnace heater according to Example 1 of the present invention.

[0088] Figure 3 It is a schematic diagram of a supporting structure of a directional solidification furnace heater according to Example 1 of the present invention.

[0089] Figure 4 It is an isometric view of a horizontal directional solidification furnace according to Example 2 of the present invention.

[0090] Figure 5 It is a schematic diagram of a left-view reference plane cross-sectional view of a horizontal directional solidification furnace according to Example 2 of the present invention.

[0091] Figure 6 It is a schematic diagram of the outer contour design of the heater of the horizontal directional solidification furnace according to Example 2 of the present invention.

[0092] Figure 7 It is a schematic diagram of the modular heater design of the horizontal directional solidification furnace according to Example 2 of the present invention.

[0093] Figure 8 This is a diagram of the temperature field simulation results of the modular heating element of the horizontal directional solidification furnace according to Example 2 of the present invention.

[0094] Fig. 9 It is a schematic diagram of the shape design of the heating element of the horizontal directional solidification furnace according to Example 2 of the present invention.

[0095] Fig.10 This is one of the schematic diagrams of the simulation results of the thermal field temperature distribution of the horizontal directional solidification furnace according to Example 2 of the present invention.

[0096] Fig.11 This is the second schematic diagram of the simulation results of the thermal field temperature distribution of the horizontal directional solidification furnace according to Example 2 of the present invention.

[0097] In the figure: 1 is a heating element, 2 is a terminal, 2-1 is a terminal body 1, 2-2 is a terminal body 2, 2-3 is a fixing clip, 3 is a supporting structure, 3-1 is a supporting rod, 3-2 is a fixing ring, 4 is an insulating member, 5 is a thermocouple, 6 is a furnace shell, 7 is an insulation layer, 8 is a crucible, 9 is a silicon material, and 10 is a heater. DETAILED DESCRIPTION

[0098] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0099] See also Figure 1 , a directional solidification furnace heater design method, comprising the following steps:

[0100] Step 1: Calculate the total power of the heater

[0101] The total power calculation of the heater needs to be based on the material properties, size, shape and required heating temperature of the heated object, taking into account the heat loss in the system and the expected heating speed. The total power demand of the heater will be determined comprehensively through the power demand in the heating stage and the power demand in the thermal balance stage. The specific calculation steps are as follows:

[0102] i. Calculate the power demand during the heating phase

[0103] In the heating stage, the heater needs to provide enough heat to raise the temperature in the furnace. The directional solidification furnace referred to in the present invention needs to consider a series of workpieces such as raw materials, crucibles, and insulation materials, which can be calculated using the following formula:

[0104] Q 总 =∑Q 蓄热 +∑Q 损耗

[0105] Among them, Q 总Indicates the total heat that the heater needs to provide during the heating phase, ∑Q 蓄热 Indicates the heat storage of all materials in the furnace during the heating stage, ∑Q 拐耗 Represents the heat energy lost in the furnace shell system during the heating stage.

[0106] a. The total heat that the heater needs to provide during the heating phase (Q 总 ).

[0107]

[0108] Among them, P1(t) represents the output power of the heater changing with time t during the heating stage, and T represents the total heating time during the heating stage.

[0109] b. Heat storage of all materials in the furnace during the heating stage (∑Q 蓄热 ).

[0110]

[0111] Where μ represents the proportional factor, which is 1 to 1.3 according to the complexity of the internal structure of the furnace shell. Assume that there are m kinds of materials in the furnace shell, which can be: heater, raw material, crucible, insulation layer, furnace shell, etc., where ρ k represents the density of the kth material, c k represents the specific heat capacity of the kth material, ΔT′ k represents the average temperature of the kth material as a whole, T 0k represents the initial temperature of the kth material, V k represents the volume of the kth material.

[0112] c. Heat loss of the furnace shell system during the heating stage (∑Q 拐耗 ):

[0113] ∑Q 损耗 =α(Q 传导 +Q 辐射 +Q 对流 )

[0114] Where α is the proportional factor, which is 1.05 to 1.15 in a system with good sealing and low operating frequency. It is 1.15 to 1.30 in a system with frequent door opening, poor sealing or complex structure. A larger value can be used in actual calculations. Q 传导 Indicates the heat conduction loss of the furnace shell during the heating stage, Q 辐射 Indicates the heat radiation loss of the furnace shell during the heating stage, Q 对流 It represents the heat loss caused by the air flow exchange inside and outside the furnace during the heating stage.

[0115] Heat conduction loss of furnace shell during heating stage (Q 传导 ) involves the heat transfer process from the high temperature center to the outside of the low temperature furnace shell, setting the following conditions:

[0116] Condition 1: The average temperature of the high temperature area in the center of the furnace is T heater (K).

[0117] Condition 2: The average temperature of the furnace shell is T RT (K).

[0118] Condition 3: Heat conduction passes through n layers of different materials, each layer has a different thermal conductivity λ i and thickness d i , the conduction area is A.

[0119] Then we have:

[0120]

[0121] d i : Thickness of the i-th layer (m).

[0122] λ i : Thermal conductivity of the ith layer (W / m·℃).

[0123] A: Conductive surface area of ​​each layer (m 2 ).

[0124] T heater (t): Average temperature of the high temperature area in the center of the furnace changing with time (K)

[0125] T RT (t): furnace shell temperature changing with time (K).

[0126] Heat radiation loss of furnace shell during heating stage (Q 辐射 ), set the following conditions:

[0127] Condition 4: The insulation layer forms a closed space, and the heat radiation inside the insulation layer mainly circulates inside the system. The heat radiation inside the insulation layer is equivalent to circulating inside the system, which does not cause net heat loss. Therefore, the difference between the temperature outside the insulation layer and the temperature of the furnace shell is the key factor in determining the heat radiation loss.

[0128] Condition 5: The temperature of the furnace shell is T RT (K).

[0129] Then we have:

[0130]

[0131] ε: emissivity of the outer surface of the insulation layer.

[0132] σ: Stefan-Boltzmann constant (5.67×10 -8 W / m 2 ·K 4 ).

[0133] A sur : Radiant surface area of ​​the outer surface of the insulation layer (m 2 )

[0134] T sur (t): Average temperature of the outer surface of the insulation layer changing with time (K)

[0135] T RT (t): Average temperature of furnace shell changing with time (K).

[0136] T: total heating time (s).

[0137] Heat loss caused by the flowing atmosphere in the furnace during the heating stage (Q 对流 ):

[0138]

[0139] Mass flow rate of gas (kg / s).

[0140] c p : Specific heat capacity of gas (J / kg·K).

[0141] A sur : Radiant surface area of ​​the outer surface of the insulation layer (m 2 )

[0142] T outlet (t): Average temperature of the gas flowing out of the furnace changing with time (K).

[0143] T inlet (t): Average temperature of the gas flowing into the furnace changing with time (K).

[0144] T: total heating time (s).

[0145] ii. Calculate the power demand during the thermal balance phase

[0146] The target temperature is reached and maintained in a thermal equilibrium state, and the temperature of each area in the furnace remains stable. At this time, the main task of the heater is to compensate for heat loss. The output power of the heater corresponding to the thermal equilibrium stage is expressed as:

[0147]

[0148] Where P2 represents the heater output power in the thermal equilibrium stage, T heater represents the temperature of the heater at thermal equilibrium, T RT Indicates the temperature of the furnace shell when in thermal equilibrium, T sur Indicates the temperature outside the insulation layer when in thermal equilibrium, T outletIndicates the temperature of the gas flowing out of the furnace when thermal equilibrium occurs, T inlet It indicates the temperature of the gas flowing into the furnace body when the heat is balanced. α indicates the proportional factor, which is 1.05 to 1.15 in a system with good sealing and low operating frequency; and 1.15 to 1.30 in a system with frequent door opening, poor sealing or complex structure. A larger value can be used in actual calculations.

[0149] iii. Calculation of the theoretical maximum output power requirement of the heater:

[0150] P 理论 =max(P1,P2)

[0151] Among them, P 理论 It indicates the theoretical maximum output power of the heater during the heating process of the entire directional solidification furnace system. max(*) indicates the maximum value.

[0152] iv. Redundant design

[0153] After considering power redundancy, the total design power of the heater is P 设计 Expressed as the actual required power P 理论 A multiple of , expressed as the redundancy coefficient β:

[0154] P 设计 =(1+β)·P 总

[0155] P 设计 : Total design power of directional solidification furnace heater (W).

[0156] β: Redundancy coefficient, generally between 0.1 and 0.3.

[0157] Step 2: Heater modular design

[0158] i. Heater outline design

[0159] The outer contour of the heater is generated by offsetting a fixed distance d along the normal direction of the outer contour of the irregular object, ensuring that the closest distance between the heater and the surface of the heated object is always maintained at d.

[0160] ii. Construction of two-dimensional geometric model of directional solidification furnace system:

[0161] A two-dimensional geometric simulation model corresponding to the radial cross section of the raw material of the directional solidification furnace system is built by simulation software. The geometric simulation model includes raw materials, crucibles, heaters, insulation layers, gas domains, furnace shells, etc., and the temperature field distribution and stress field distribution of the geometric simulation model are simulated and calculated;

[0162] iii. Modular division of heaters:

[0163] According to the simulation results of ii, the temperature concentration area of ​​the heated object corresponding to the heater position is divided into module areas to form multiple independent heating elements, or the heater stress concentration area is divided into module areas according to the heater stress to form multiple independent heating elements.

[0164] Step 3: Simulation and verification

[0165] Based on the heating elements divided in step 2, a simulation experiment is carried out on the geometric simulation model built in step 2. By analyzing the temperature distribution on the surface of the heated object, the power of the heating elements at each position is adjusted, and finally the optimal power distribution ratio η of each heating element i in a single heater is determined. i .

[0166] Step 4: Power distribution of heating elements

[0167] Assume that the furnace has n heaters in total, then the design power of a single heater is The design power of the heating element i in the heater is P 元件i =P 加热器 ×η i .

[0168] Among them, P 加热器 Represents the design output power of a single heater, P 设计 represents the total design output power of the directional solidification furnace heater, n represents the number of heaters in the furnace, P 元件i represents the design output power of heating element i in a single heater, η i It represents the optimal power distribution ratio of heating element i to the entire heater.

[0169] Step 5: Material selection of heating element

[0170] Choose the appropriate material according to the working environment temperature, atmosphere, heating element working power and the requirements of the heated object. Heating element materials include but are not limited to: tungsten, molybdenum, nickel-chromium alloy, silicon-molybdenum alloy, carbon-silicon alloy or graphite, etc.

[0171] Step 6: Shape design of heating element

[0172] The shape of the heating element is designed according to the design power of the heating element and the allowable surface load.

[0173] i. Design of heating element length and cross-sectional shape.

[0174]

[0175] P 元件i =W 许用 *A

[0176]

[0177] A=S*L″ i

[0178] L i =(L′ imin , L″ imax )

[0179] P 元件i : Design power of heating element i (W).

[0180] w 许用 :Allowable surface load of heating element (W / m 2 ).

[0181] R t : Resistance of the heating element at temperature t (Ω).

[0182] ρ t : Resistivity of the heating element at temperature t (Ω·m)

[0183] U: Terminal voltage of heating element (V).

[0184] A: Surface area of ​​heating element (m 2 ).

[0185] S: cross-sectional circumference of the heating element (m).

[0186] f: Cross-sectional area of ​​heating element (m 2 ).

[0187] L′ i : By R t The calculated length of the i-th heating element (m 2 ).

[0188] L″ i : The length of the i-th heating element calculated by A (m 2 ).

[0189] L i : The absolute length of the ith heating element (m 2 ).

[0190] ii. Design of heating element structure and shape.

[0191] According to the relative length L of the heating element i ri (straight line distance between the two ends of the heating element) and the absolute length L of the heating element i i Design the heating element to be curved, wrapped or multi-sectioned. The shapes include but are not limited to S-shaped, arched, spiral, and corrugated.

[0192] Step 7: Optimize the overall structure of the heater

[0193] It includes the design of the heater's wiring terminals, the design of the heater's supporting structure, the design of the heater's insulation parts, and the design of the heater's thermocouple layout.

[0194] Step 8: Simulation and verification

[0195] After the overall design of the heater is completed, the heating effect is simulated through computer simulation to verify whether the design of the heater meets the target requirements. The simulation content includes heat conduction, temperature distribution, thermal stress analysis, etc., to ensure that the designed heater can operate efficiently under actual engineering conditions and that the designed heater layout can achieve the ideal temperature distribution of the heated object.

[0196] Example 1

[0197] See also Figure 2 and Figure 3 , this embodiment provides a directional solidification furnace heater designed using the above-mentioned design method, the heater comprising a heating element 1, two left and right terminals 2, a support structure 3, an insulating member 4 and a thermocouple 5. The terminal 2 is used to ensure that the electrical connection between the cable and the heating element 1 is safe and reliable. The support structure 3 is arranged on the terminal 2 to support and fix the heating element. The heating element is arranged between the left and right terminals 2 to provide thermal energy. The insulating member 4 is arranged between the terminals 2 to isolate the electrical connections between different heating elements. The thermocouple is used to monitor the temperature of the heating element 1 in real time, and is fixedly installed at one end of the heating element through the insulating member 4.

[0198] Furthermore, the terminal 2 includes a terminal body 1 2-1, a terminal body 2-2 and a fixing clip 2-3. The terminal body 1 2-1 and the terminal body 2 2-2 are connected and separated by an insulating member 4, and both the terminal body 1 2-1 and the terminal body 2 2-2 have a fixing clip 2-3. The terminal body 1 2-1 and the terminal body 2 2-2 are used to carry the electrical connection of the cable and the heating element. The terminal body 1 2-1 and the terminal body 2 2-2 are made of high temperature resistant and oxidation resistant materials, preferably copper, silver, silver-plated copper, nickel-copper alloy or stainless steel, to ensure good electrical conductivity and the ability to withstand the working temperature of the heating element. The fixing clip 2-3 is used to fix the terminal body and the heating element, and has good insulation performance, low thermal expansion coefficient and high temperature resistance. It is preferably made of ceramic materials such as aluminum oxide, zirconium oxide, silicon nitride, silicon carbide or magnesium oxide.

[0199] Furthermore, the support structure 3 includes a support rod 3-1 and a fixing ring 3-2, wherein the support rod 3-1 is used to support the heater, ensure the position stability of the heater in the directional solidification furnace, provide sufficient mechanical strength and rigidity, and is preferably made of ceramic material, graphite or silicon carbide. The fixing ring 3-2 is used to fix and constrain the position of the heater, ensure that the heating element does not shift or loosen during high-temperature operation, and is preferably made of ceramic material, graphite or silicon carbide. Through the synergistic effect of the support rod 3-1 and the fixing ring 3-2, the support structure 3 can provide reliable support and fixation for the heater in the horizontal and vertical directions under high temperature conditions, ensuring the stable operation of the heater in the directional solidification furnace.

[0200] Furthermore, the insulating member 4 is used to isolate the electrical connections between different heating elements to prevent current leakage and short circuit, ensuring the independent operation of each heating element and the safety of the overall system. The insulating member 4 is made of high temperature resistant and corrosion resistant materials, such as high purity aluminum oxide, magnesium oxide or silicon nitride, which can provide electrical insulation and thermal isolation in a high temperature environment to prevent leakage and local overheating. Each terminal 2 includes an insulating member 4, which is used to connect and separate the terminal body 1 2-1 and the terminal body 2 2-2.

[0201] Furthermore, the thermocouple 5 is used to monitor the temperature of the heater 1 in real time to achieve precise control. It is installed at one end of each heating element constituting the heater through the support structure 3. The thermocouple 5 transmits the real-time temperature signal to the temperature control system to automatically adjust the power output of the heating element, optimize the temperature control, ensure the stability and safety of the heating process, improve the energy efficiency of the equipment and prevent overheating or temperature runaway.

[0202] Furthermore, the heating element is a heating resistor, and the heating resistor is made of a material suitable for a high temperature environment, including but not limited to: nickel-chromium alloy (NiCr), iron-chromium-aluminum alloy (FeCrAl), molybdenum disilicide (MoSi2), tungsten (W), graphite, silicon carbide (SiC) materials. The heating resistor can be designed to be spiral, straight or corrugated. According to the thermal field structure and process requirements, the geometric shape of the heating resistor can be custom designed to meet the service life of the heating element while achieving uniform heating and efficient energy transmission. Among them, the heating element includes a heating element 1-1 and a heating element 2-2, the heating element 1-1 is arranged between the fixing clips 2-3 of the left and right terminal bodies 1-1, and the heating element 2-2 is arranged between the fixing clips 2-3 of the left and right terminal bodies 2-2.

[0203] Furthermore, the heating element, the connecting terminal 2, the supporting structure 3, the insulating member 4 and the thermocouple are all designed as a modular structure to facilitate the assembly, maintenance and replacement of the heater.

[0204] It should be noted that the main structure of the above-mentioned heater is a well-known technology and will not be described in detail.

[0205] Example 2

[0206] This embodiment provides a method for designing a heater having a trapezoidal crucible in a horizontal directional solidification furnace, comprising the following steps:

[0207] Step 1: Calculate the total power of the heater

[0208] The horizontal directional solidification growth crystal silicon is 500mm long, and the left side is an isosceles trapezoid with upper and lower sides of 200mm and 100mm respectively, and a height of . The corresponding crucible, insulation layer, and furnace shell are designed accordingly, such as Figure 4 and Figure 5 shown.

[0209] In this embodiment, the power demand in the thermal equilibrium stage is directly calculated. The horizontal directional solidification furnace is set to reach the thermal equilibrium stage. The average temperature of the heating body, crucible, and raw materials is 1480°C, the temperature inside the insulation layer is 1500°C, the temperature outside is 500°C, the temperature inside the furnace shell is 100°C, and the temperature outside is 30°C. Use the formula:

[0210]

[0211] d i : Thickness of the i-th layer (m).

[0212] λ i : Thermal conductivity of the ith layer (W / m·℃).

[0213] A: Conductive surface area of ​​each layer (m 2 ).

[0214] Mass flow rate of gas (kg / s).

[0215] c p : Specific heat capacity of gas (J / kg·K).

[0216] T heater : Temperature of the heater at thermal equilibrium (K).

[0217] T RT : Temperature of the furnace shell at thermal equilibrium (K).

[0218] T sur : Temperature outside the insulation layer at thermal equilibrium (K).

[0219] T outlet : The temperature of the gas flowing out of the furnace at thermal equilibrium (K).

[0220] T inlet : Temperature of gas flowing into the furnace at thermal equilibrium (K).

[0221] α: Proportional factor. In a system with good sealing and low operating frequency, it is 1.05 to 1.15; in a system with frequent door opening, poor sealing or complex structure, it is 1.15 to 1.30. In actual calculation, a larger value can be used.

[0222] We get P2≈21kW. After considering power redundancy, we get P 设计 =25kW.

[0223] Step 2: Heater modular design

[0224] i. Heater outline design

[0225] The outer contour of the heater is generated by offsetting a fixed distance of 30 mm in the normal direction of the outer contour of the irregular object, such as Figure 6 As shown, ensure that the closest distance between the heater and the surface of the heated object is always maintained at 30mm.

[0226] ii. Modular division of heaters

[0227] Build a two-dimensional simulation model, and divide the temperature concentration area of ​​the heated object corresponding to the heater position as a module to form multiple independent heating elements, such as Figure 7 shown.

[0228] Step 3: Simulation and verification

[0229] Based on the modular heating element in step 2, a corresponding two-dimensional simulation model is constructed and a simulation experiment is carried out. By analyzing the temperature distribution on the surface of the heated object, such as Figure 8 As shown, the power of the heating elements at various positions is adjusted, and finally it is determined that the optimal power distribution ratio of the heating element 1 in a single heater is η1=0.3, and the optimal power distribution ratio of the heating element 2 in a single heater is η1=0.7.

[0230] Step 4: Power distribution of heating elements

[0231] Assume that the furnace has 10 heaters in total, then the design power of a single heater is P 加热器 =2.5kW. The design power of the heating element 1 in the heater is P 元件1 =P 加热器 ×η1=0.75kW, the design power of the second heating element in the heater is P 元件2 =1.75kW.

[0232] Step 5: Material selection of heating element

[0233] The material of the heating element is tungsten.

[0234] Step 6: Shape design of heating element

[0235] i. Design of heating element length and cross-sectional shape.

[0236]

[0237] P 元件i =W 许用 *A

[0238]

[0239] A=S*L″1

[0240] L1=(L″ 1min , L′ 1max )

[0241] Among them, P 元件i represents the design output power of heating element i in a single heater, w 许用 Indicates the allowable surface load of the heating element, R t represents the resistance of the heating element at temperature t, ρ t represents the resistivity of the heating element at temperature t, U represents the terminal voltage of the heating element, A represents the surface area of ​​the heating element, S represents the cross-sectional circumference of the heating element, f represents the cross-sectional area of ​​the heating element, and L' i Indicates that R t Calculated length of the i-th heating element, L″ i represents the length of the i-th heating element calculated by A, L i represents the absolute length of the i-th heating element;

[0242] The shape of the heating element is designed according to the design power of the heating element and the allowable surface load. The cross section of the heating element is set to be a tungsten wire with a radius of 2mm, U≤220V, w 许用 ≤250000W / m 2 Furthermore, the absolute length of the heating element one is obtained as 0.24≤L1≤64.53m, and the absolute length of the heating element two is obtained as 0.56≤L2≤28.95m.

[0243] ii. Design of heating element structure and shape.

[0244] Relative length L of heating element 1 r1 is 0.2m, the relative length L of the heating element 2 r2 It is 0.39m.

[0245] According to the relative length L of the heating element r (straight line distance between the two ends of the heating element) and the absolute length L of the heating element i Design the heating element to bend, wrap around or combine multiple sections. Design shapes such as Fig. 9As shown, the absolute length of the corresponding heating element 1 is L1 = 0.45m, and the absolute length of the corresponding heating element 2 is L2 = 0.85m.

[0246] Step 7: Optimize the overall structure of the heater

[0247] It includes the design of the heater's wiring terminals, the design of the heater's supporting structure, the design of the heater's insulation parts, and the design of the heater's thermocouple layout.

[0248] Step 8: Simulation and verification

[0249] The temperature field of the horizontal directional solidification furnace of this example is simulated by computer simulation to verify that the design of the heater meets the requirements, such as Fig.10 and Fig.11 As shown, the uniformity of the temperature of the outer contour of the raw material can be achieved, the temperature gradient of the cross section perpendicular to the horizontal direction is less than 0.03℃ / mm, and the cold spot is centrally controlled.

[0250] Although embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that various changes, modifications, substitutions and variations may be made to the embodiments without departing from the principles and spirit of the present invention, and that the scope of the present invention is defined by the appended claims and their equivalents.

Claims

1. A method for designing a heater for a directional solidification furnace, characterized in that: include: Step 1, calculating the total power of the heater; Step 2, modular design of the heater; Step 3, conduct preliminary simulation and verification; Step 4, distributing the power of the heating element; Step 5, selecting the material of the heating element; Step 6, designing the shape of the heating element; Step 7, performing simulation and verification again, includes: after completing the overall design of the heater, simulating the heating effect through computer simulation to verify whether the design of the heater meets the target requirements.

2. The design method of a directional solidification furnace heater according to claim 1, characterized in that: The step 1 specifically includes: i. Calculate the power demand during the heating phase During the heating stage, the heater needs to provide enough heat to raise the temperature inside the furnace, calculated using the following formula: Q 总 =∑Q 蓄热 +∑Q 损耗 Among them, Q 总 Indicates the total heat that the heater needs to provide during the heating phase, ∑Q 蓄热 Indicates the heat storage of all materials in the furnace during the heating stage, ∑Q 损耗 Indicates the heat energy lost by the furnace shell system during the heating stage; a. The total heat Q that the heater needs to provide during the heating phase 总 : Among them, P1(t) represents the output power of the heater changing with time t during the heating stage, and T represents the total heating time during the heating stage; b. Heat storage of all materials in the furnace during the heating stageΣQ 蓄热 : Where μ represents the proportional factor, which is 1 to 1.3 according to the complexity of the internal structure of the furnace shell; assuming that there are m kinds of materials in the furnace shell, where ρ k represents the density of the kth material, c k represents the specific heat capacity of the kth material, ΔT' k represents the average temperature of the entire k-th material, represents the initial temperature of the kth material, V k represents the volume of the kth material; c. Heat loss of furnace shell system during heating stage∑Q 损耗 : ∑Q 损耗 =α(Q 传导 +Q 辐射 +Q 对流 ) Among them, α represents the proportional factor, Q 传导 Indicates the heat conduction loss of the furnace shell during the heating stage, Q 辐射 Indicates the heat radiation loss of the furnace shell during the heating stage, Q 对流 It represents the heat loss caused by the airflow exchange inside and outside the furnace during the heating stage; Heat conduction loss of furnace shell during heating stage Q 传导 Involving the heat transfer process from the high temperature center to the outside of the low temperature furnace shell, the following conditions are set: Condition 1: The average temperature of the high temperature area in the center of the furnace is T heater ; Condition 2: The average temperature of the furnace shell is T RT ; Condition 3: Heat conduction passes through n layers of different materials, each layer has a different thermal conductivity λ i and thickness d i , the conduction area is A; Then we have: Among them, d i represents the thickness of the i-th layer, λ i represents the thermal conductivity of the i-th layer, A represents the conductive surface area of ​​each layer, T heater (t) represents the average temperature of the high temperature area in the center of the furnace changing with time, T RT (t) represents the furnace shell temperature changing with time; Heat radiation loss of furnace shell during heating stage Q 辐射 , set the following conditions: Condition 4: The insulation layer forms a closed space. The heat radiation inside the insulation layer is equivalent to circulating inside the system, which does not cause net heat loss. Therefore, the difference between the temperature outside the insulation layer and the temperature of the furnace shell is the key factor in determining the heat radiation loss. Condition 5: The temperature of the furnace shell is T RT ; Then we have: Where ε is the emissivity of the outer surface of the thermal insulation layer, σ is the Stefan-Boltzmann constant, and A sur represents the radiation surface area of ​​the outer surface of the insulation layer, T sur (t) represents the average temperature of the outer surface of the insulation layer changing with time, T RT (t) represents the average temperature of the furnace shell changing with time, and T represents the total heating time; Heat loss Q caused by the flowing atmosphere in the furnace during the heating stage 对流 : in, represents the mass flow rate of gas, c p represents the specific heat capacity of the gas, A sur represents the radiation surface area of ​​the outer surface of the insulation layer, T outlet (t) represents the average temperature of the gas flowing out of the furnace that changes with time, T inlet (t) represents the average temperature of the gas flowing into the furnace body changing with time, and T represents the total heating time; ii. Calculate the power demand during the thermal balance phase The target temperature is reached and maintained in a thermal equilibrium state. The temperature of each area in the furnace remains stable. At this time, the main task of the heater is to compensate for the heat loss of the directional solidification furnace system. The output power of the heater corresponding to the thermal equilibrium stage is expressed as: Where P2 represents the heater output power in the thermal equilibrium stage, T heater represents the temperature of the heater at thermal equilibrium, T RT Indicates the temperature of the furnace shell when in thermal equilibrium, T sur Indicates the temperature outside the insulation layer when in thermal equilibrium, T outlet Indicates the temperature of the gas flowing out of the furnace when thermal equilibrium occurs, T inlet represents the temperature of the gas flowing into the furnace when thermal equilibrium occurs, and α represents the proportional factor; iii. Calculation of the theoretical maximum output power requirement of the heater: P 理论 =max(P1,P2) Among them, P 理论 It indicates the theoretical maximum output power of the heater during the heating process of the entire directional solidification furnace system. max(*) indicates the maximum value. iv. Redundant design After considering power redundancy, the total design power of the heater is P 设计 Expressed as the actual required power P 理论 A multiple of , expressed as the redundancy coefficient β: P 设计 =(1+β)P 理论 Among them, P 设计 It represents the total design output power of the directional solidification furnace heater.

3. The design method of a directional solidification furnace heater according to claim 1, characterized in that: The step 2 specifically includes: i. Heater outline design: The outer contour of the heater is generated by offsetting a fixed distance d in the normal direction of the outer contour of the irregular object, so as to ensure that the closest distance between the heater and the surface of the heated object is always kept at d; ii. Construction of two-dimensional geometric model of directional solidification furnace system: A two-dimensional geometric simulation model corresponding to the radial cross section of the raw material of the directional solidification furnace system is constructed by simulation software. The geometric simulation model includes raw materials, crucibles, heaters, insulation layers, gas domains and furnace shells. The temperature field distribution and stress field distribution of the geometric simulation model are simulated and calculated. iii. Modular division of heaters: According to the simulation results of ii, the temperature concentration area of ​​the heated object corresponding to the heater position is divided into module areas to form multiple independent heating elements, or the heater stress concentration area is divided into module areas according to the heater stress to form multiple independent heating elements.

4. The method for designing a heater for a directional solidification furnace according to claim 3, characterized in that: The step 3 specifically includes: Based on the heating elements divided in step 2, a simulation experiment is carried out on the geometric simulation model built in step 2. By analyzing the temperature distribution on the surface of the heated object, the power of the heating elements at each position is adjusted, and finally the optimal power distribution ratio η of each heating element i in a single heater is determined. i .

5. The method for designing a heater for a directional solidification furnace according to claim 1, characterized in that: The step 4 specifically includes: Assume that the furnace has n heaters in total, then the design power of a single heater is The design power of the heating element i in the heater is P 元件i =P 加热器 ×η i . Among them, P 加热器 Represents the design output power of a single heater, P 设计 represents the total design output power of the directional solidification furnace heater, n represents the number of heaters in the furnace, P 元件i represents the design output power of heating element i in a single heater, η i It represents the optimal power distribution ratio of heating element i to the entire heater.

6. The method for designing a heater for a directional solidification furnace according to claim 1, characterized in that: The step 5 specifically includes: Select the appropriate material according to the working environment's temperature, atmosphere, heating element's operating power and the requirements of the heated object.

7. The method for designing a heater for a directional solidification furnace according to claim 1, characterized in that: The step 6 specifically includes: The shape of the heating element is designed according to the design power of the heating element and the allowable surface load, including: i. Design of heating element length and cross-sectional shape: P 元件i =W 许用 *A A=S*L″ i L i =(L′ i min ,L ″i max ) Among them, P 元件i Represents the design output power of heating element i in a single heater, W 许用 Indicates the allowable surface load of the heating element, R t represents the resistance of the heating element at temperature t, ρ t represents the resistivity of the heating element at temperature t, U represents the terminal voltage of the heating element, A represents the surface area of ​​the heating element, S represents the cross-sectional circumference of the heating element, f represents the cross-sectional area of ​​the heating element, and L' i Indicates that R t Calculated length of the i-th heating element, L″ i represents the length of the i-th heating element calculated by A, L i represents the absolute length of the i-th heating element; ii. Heating element structure and shape design: According to the relative length L of the i-th heating element ri and the absolute length L of the i-th heating element i Design heating elements in curved, wrap-around or multi-segment shapes.

8. The method for designing a heater for a directional solidification furnace according to claim 1, characterized in that: The step 7 specifically includes: Design the heater's wiring terminals, support structure, insulation, and thermocouple layout.

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