CN116541910A - Heat transfer module for biological cryopreservation and design and manufacturing method thereof - Google Patents
Heat transfer module for biological cryopreservation and design and manufacturing method thereof Download PDFInfo
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- 238000012546 transfer Methods 0.000 title claims abstract description 151
- 238000005138 cryopreservation Methods 0.000 title claims abstract description 22
- 238000013461 design Methods 0.000 title abstract description 11
- 238000004519 manufacturing process Methods 0.000 title abstract description 10
- 238000005457 optimization Methods 0.000 claims abstract description 61
- 239000004065 semiconductor Substances 0.000 claims abstract description 59
- 239000010949 copper Substances 0.000 claims abstract description 58
- RYGMFSIKBFXOCR-UHFFFAOYSA-N Copper Chemical compound [Cu] RYGMFSIKBFXOCR-UHFFFAOYSA-N 0.000 claims abstract description 54
- 229910052802 copper Inorganic materials 0.000 claims abstract description 53
- 238000000034 method Methods 0.000 claims abstract description 47
- 238000007710 freezing Methods 0.000 claims abstract description 39
- 230000008014 freezing Effects 0.000 claims abstract description 39
- 238000005057 refrigeration Methods 0.000 claims abstract description 21
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- 125000004122 cyclic group Chemical group 0.000 claims description 3
- 238000000265 homogenisation Methods 0.000 claims description 3
- 239000000203 mixture Substances 0.000 claims description 3
- -1 polypropylene Polymers 0.000 claims description 3
- 229910052797 bismuth Inorganic materials 0.000 claims 1
- JCXGWMGPZLAOME-UHFFFAOYSA-N bismuth atom Chemical compound [Bi] JCXGWMGPZLAOME-UHFFFAOYSA-N 0.000 claims 1
- XSOKHXFFCGXDJZ-UHFFFAOYSA-N telluride(2-) Chemical compound [Te-2] XSOKHXFFCGXDJZ-UHFFFAOYSA-N 0.000 claims 1
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- Y02B—CLIMATE CHANGE MITIGATION TECHNOLOGIES RELATED TO BUILDINGS, e.g. HOUSING, HOUSE APPLIANCES OR RELATED END-USER APPLICATIONS
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Abstract
The invention provides a heat transfer module for biological cryopreservation and a design and manufacturing method thereof, wherein the design of the heat transfer module for biological cryopreservation is completed by assuming the initial shape of a red copper heat transfer end, calculating the number of slots and the positioning of circle centers, setting boundary conditions of topological optimization of heat transfer science, setting a limited network of two-dimensional heat transfer surfaces of components, iterating a homogenized SIMP method, and judging topological optimization results so as to adapt and optimize biological cryopreservation equipment based on semiconductor refrigeration. The heat transfer module obtained by the design method can meet the requirements of the normal pressure slow freezing process on the cooling rate and the temperature uniformity of the biological material, realizes the accurate control of the cooling rate, and reduces the risks of damage, inactivation and the like of frozen matters.
Description
Technical Field
The invention relates to the technical field of heat transfer structure design optimization, in particular to a heat transfer module for biological freezing and a design and manufacturing method thereof.
Background
In recent years, the biobanking industry (Bio-banking), which is a mechanism for collecting, processing, storing and dispensing biological materials of different dimensions (e.g., blood, DNA, cells, tissues, etc.), has been rapidly developed to use the stored materials for scientific research, diagnosis or treatment in the future; biological Cryopreservation (cryoconservation) technology is one of the most commonly used sample preservation and processing technologies in biological banks. According to the Arrhenius equation (Arrhenius equation) proposed in 1889, the chemical reaction rate is proportional to temperature; i.e., when the temperature is lowered, collision energy between molecules is reduced, and collision frequency is lowered, thereby lowering the chemical reaction rate. In biological materials, many adverse chemical reactions, such as lipid oxidation, protein denaturation, etc., are accelerated at high temperatures; by lowering the temperature, the rate of these chemical reactions can be effectively slowed down, thereby reducing the risk of damaging and spoiling the biological sample. It can be seen that it is very necessary to cool and freeze the biological material in order to ensure the integrity of the biological material after long-term storage.
Currently, the mainstream biological cryopreservation methods include: quick freezing storage and extremely quick freezing storage; the slow freezing technology is used for reducing the formation of ice nuclei by controlling the cooling rate at an optimal constant value; the temperature reduction rate of the quick freezing storage is different according to the type, the scale and the like of the biological materials, and is generally between-0.5K/min and-10K/min. In the liquid-solid phase change process, intracellular liquid gradually forms ice nuclei, and extracellular buffer gradually nucleates and crystallizes; in retarded freezing, improper cooling rates can affect the processes of Ice nucleation (Ice nucleation) and Ice crystallization (Ice crystallization), thereby creating damage to tissues, cells and proteins. Ice nucleation, the initial stage of ice crystallization, involves structural rearrangement of water molecules to form a stable ice core; if the cooling rate is too high, excessive ice crystals and ice nuclei are formed outside the cells; too slow a cooling rate may result in excessive ice nuclei being formed in the cell. In both cases, the non-uniform distribution of ice nuclei may cause irreversible damage to the cell structure. Therefore, the rate of cooling is a physical quantity that must be precisely controlled.
The use of domestic refrigerators, or ultra-low temperature refrigerators (-80 ℃) and low temperature refrigerators (-20 ℃) used by laboratories, medical institutions, is not suitable for the rapid freezing of biological materials, because the air temperature inside their refrigerators is approaching constant without excessive consumption of heat capacity; under the condition of constant ambient temperature, the temperature change of the biological material in the refrigerator which conducts heat in a heat convection mode is nonlinear, namely the temperature reduction rate of the refrigerator is always changed, and the refrigerator is not a certain value which is most suitable for the biological material. At present, the prior art lacks a heat transfer module capable of rapidly adjusting/compensating the cooling rate aiming at different types and scales of biological materials, thereby effectively weakening the problem that the ice nucleation causes irreversible damage to the structures of tissues, cells and proteins.
Disclosure of Invention
To the problem that prior art exists above, the aim at of this application provides a heat transfer module for biological cryopreservation, this module is through the mode of adjusting the output of semiconductor refrigerating system (Thermoelectric Cooler, TEC), can the accurate control self-defined cooling rate, and then the biological material of cryopreservation is at the irreversible harm that ice nucleation, the ice crystallization brought during liquid solid phase transformation, avoid the thermal resistance of tissue to produce the cooling temperature gradient that can influence crystallization homogeneity, avoid irregular ice crystal to cause inelastic deformation to the cell membrane simultaneously, and thereby cause the cell dehydration because local ion concentration that local icing leads to is too high, still avoid the cold deactivation of protein (specifically the expansion of protein third layer structure).
It is another object of the present application to provide a method of designing the above heat transfer module, combining topological optimization of the SIMP method (Solid Isotropic Material with Penalization) of heat transfer chemistry, optimization of the uniformity heat transfer chemistry, and micromachining of the SIMP method adaptations, to obtain the heat transfer module.
A third object of the present application is to provide a method for manufacturing the heat transfer module.
The aim of the invention is achieved by the following technical scheme:
a heat transfer module for biological cryopreservation, characterized in that: the cold face of the semiconductor refrigeration piece is stuck to the red copper heat transfer end; the freezing pipe is a hollow cylinder with an inner circle bottom (namely, the longitudinal section of the freezing pipe is a hollow disc), the red copper heat transfer end is uniformly provided with slots corresponding to the structure of the freezing pipe and used for installing the freezing pipe, and the number of the slots is even and symmetrically arranged about the central line of the two semiconductor refrigerating sheets.
As a preferable scheme of the application, the semiconductor refrigerating sheet has the size of S multiplied by D, and the material is N and P type bismuth telluride (Bi 2 Te 3 ) The method comprises the steps of carrying out a first treatment on the surface of the The freezing tube adopts polypropylene, and the inner diameter of the freezing tube is R 1 The external diameter is R 2 (R 1 ＜R 2 ) The height is H.
As a preferred scheme of the application, the freezing tube can also adopt zirconia ceramics, titanium alloy and other materials, and the material can meet the requirements of biocompatible, biological inertia and sterilizable materials; at the same time, in order to meet the requirement of lightening the heat transfer module, the cylindrical wall thickness of the freezing tube (i.e.) As small as possible.
The design method of the heat transfer module for biological cryopreservation is characterized by comprising the following steps of: comprising the following steps:
step S1: combining the basic and fixed characteristics of the red copper heat transfer end, before performing topology optimization, assuming that the red copper heat transfer end is a cuboid, the length and width dimensions of the red copper heat transfer end are limited by the dimensions of the semiconductor refrigerating sheet, wherein the length of the red copper heat transfer end is as follows:
wherein: l (L) j Indicating the length of the hypothetical red copper heat transfer end;represents the outer diameter of the freezing tube;
initial length L 0 The method comprises the following steps:
wherein:representing the diameter of the slot; />Representing the transverse heat transfer length, which is reduced to a reasonable value in an iterative loop manner following the following steps;
step S2: in a heat transfer module, the number of slots n c Coordinates (x) of the center of the circle with the cylindrical slot c ,y c ) Depending on the size of the semiconductor refrigeration sheet and the outside diameter of the freezer pipeThe method comprises the following steps:
wherein L is TEC The length of the long side of the cold surface of the semiconductor refrigeration piece is represented (the side length is the side length if the semiconductor refrigeration piece is square); y is Y c Representing each center coordinate y of the slot on the symmetry axis of the heat transfer module structure c,i Is a set of points; x is x c-l 、x c-r Respectively representing left and right center coordinates of the slot in the transverse heat transfer direction; l represents the length of the red copper heat transfer end (at this stage, l=l j Thereafter, as L decreases, x c-r The value of (2) will vary with the change);
step S3: the dimension of two finite element analysis problems including topological optimization and subsequent transient homogeneity heat transfer simulation is reduced from three dimensions to two dimensions, and two-dimensional heat transfer study is carried out on a long-wide plane of a heat transfer end;
for topological optimization boundary condition setting, based on the basic assumption of continuous medium mechanics, two widths of a heat transfer end closely attached to a cold surface of a semiconductor refrigeration piece can be regarded as Dirichlet boundary conditions (Dirichlet Boundary Condition); the round boundary of the slot which is tightly attached to the refrigerating tube is set as a Neumann boundary condition (Neumann Boundary Condition), which is also called a second type boundary condition;
the boundary condition setting assumption of the topological optimization of the heat transfer is different from the boundary condition of the transient homogeneity heat transfer simulation simulating the temperature reduction process of the biological material solution: in the topology optimization boundary condition setting, the temperature of the semiconductor refrigerating piece is assumed to be a certain fixed value (Dirichlet boundary condition) different from the ambient temperature, and the semiconductor refrigerating piece exists as a heat source with stable temperature, because the purpose of topology optimization is to reduce the overall quality of the heat transfer end on the premise that the heat flux at each part of the heat transfer end is as uniform as possible, thereby improving the response capability of the heat transfer end to the power output change of the semiconductor refrigerating piece; namely: the topology optimization is performed by space optimization, so that the increment of time in the transient heat transfer problem is not needed to be considered, two widths in contact with the cold surfaces of two semiconductor refrigerating sheets can be set as Dirichlet boundary conditions, simple heat transfer simulation which only considers an initial state-an equilibrium state is performed, and the solving process is further stabilized to ensure the solvability and uniqueness of the problem;
step S4: constructing a finite element network of a two-dimensional heat transfer surface based on heat transfer science simulation software;
step S5: the shape of a two-dimensional heat transfer surface is denoted by Ω, and its boundaries consist of three disjoint parts, specifically:
from the above, it can be seen that the two-dimensional heat transfer surfaceThe variation of the shape Ω of (a) can be regarded as two widths Γ in contact with the semiconductor cooling plate (heat source) D Circular boundary Γ of the socket against which the freezer pipe is in close contact N And the union of the remaining free optimized portions Γ;
temperature field T (x) in the thermal conduction study of the continuum: omega-R N Obtained by:
it means that the topologically optimized heat transfer equation holds over the entire two-dimensional heat transfer surface Ω;
which is represented at dirichlet boundary Γ D The temperature of the semiconductor refrigerating sheet heat source is fixed;
which is represented at the Neumann boundary Γ N On the heat flow q n Normal vector to the circular boundary of the socket
It means that by adjusting the material density ρ (x) of the free optimizing part Γ in the two-dimensional heat transfer surface, a reasonable material distribution is obtained, thereby finally homogenizing and minimizing the heat flux of the heat transfer end;
wherein, the liquid crystal display device comprises a liquid crystal display device,is a Nabla operator, also known as a vector differential operator, represented here asPartial derivative operation of two space vectors of a row two-dimensional space; />The method is a full-scale word of space coordinates in mathematical sense, and under the two-dimensional space background, all two-dimensional space coordinates meeting the subsequent definition conditions are selected;
in the topology optimization process, the material of the heat transfer end is regarded as the mixture of red copper and air; based on the premise that the heat conductivity coefficient of red copper is far higher than that of air, the effective heat conductivity coefficient of the material of the free optimization part is as follows:
κ Γ (x)＝κ air ·(1-ρ(x) p )+κ Cu ·ρ(x) p ；
wherein: p represents a penalty factor for controlling the effect of material density on thermal conductivity; kappa (kappa) Cu 390W/(m.K), κ air 0.025W/(m.K);
since the scheme of the application is at the boundary Γ N Upper minimization T (x) 2 I.e. minimizing the transfer of heat, the objective function of the topology optimization is therefore in particular:
Obj(T,q n )＝∫T(x) 2 dΓ N +λ N ∫(q n (x)-q avg ) 2 dΓ N ；
wherein: lambda (lambda) N Representing a Lagrangian multiplier for homogenization, as an empirical constant; q avg Representing boundary Γ N Average heat flux on;
wherein: ds represents a minute boundary length element;
the weak form of the heat conduction problem is specifically:
wherein: v (x) represents an auxiliary function for solving a weak form of Partial Differential Equation (PDE); in the finite element method, the weak form is a method of converting the PDE problem into a linear algebraic problem for numerical solution;
the concomitant problem, in combination with the problem of thermal conduction, contributes to the calculation of the sensitivity of the objective function during the topological optimization, the weak form of which is in particular:
wherein, the solution of the concomitant function pp (x) and the solution of the original heat conduction problem act together on the topology optimization process, thereby obtaining the sensitivity of the objective function Obj (x);
gradient of energy densityThe method comprises the following steps:
the iterative equation is:
wherein: τ represents a step size, which is used for controlling the amplitude of parameter update during each iteration of the optimization algorithm; j represents the number of iterations;
step S6: judging the topology optimization result, and if the red copper materials around the slots on two sides of the symmetry axis are intersected, performing the following step S7; if the red copper materials around the slots on the two sides of the symmetry axis are not intersected, the length L of the red copper heat transfer end is shortened by 0.2mm, and the step S2 is returned to for cyclic iteration;
step S7: and storing the optimization result, and storing the combination of the final topological optimization in a picture form.
As a preferred embodiment of the present application, the lagrangian multiplier λ N 0.3.
As a preferred embodiment of the present application, the step size τ is 0.1; the iteration number j is 1-200.
As a preferred embodiment of the present application, the penalty factor p is specifically:
a method of manufacturing a heat transfer module for biological cryopreservation, characterized by: firstly, carrying out equal proportion drawing on a final two-dimensional topological optimization result in CAD software, stretching the final two-dimensional topological optimization result into a three-dimensional structure, and adjusting the three-dimensional structure; then, adopting a triaxial numerical control milling machine to perform material reduction processing on the red copper square block, adopting a deep groove milling cutter with the diameter less than or equal to 1mm as a processing cutter, wherein the effective length (namely the length of a cutting edge and the clearance length) of the processing cutter is greater than 1/2 of the height of a heat transfer end; in the processing process, the cylindricity of the slot is +/-0.01 mm, the actual processing diameter of the slot is 0.03mm larger than the diameter of the freezing pipe, and the tolerance of +/-0.01 mm is ensured; two heat transfer surfaces in contact with the cold surface of the semiconductor refrigeration piece ensure flatness of +/-0.02 mm; and after the processing is finished, obtaining the heat transfer module.
The invention has the following technical effects:
the application provides a heat transfer module for biological freezing and storage, and a design and manufacturing method thereof, so as to adapt to a semiconductor biological freezing and storage refrigerating system with an extremely high application scene in the future, thereby precisely controlling the self-defined cooling speed in a mode of adjusting the output power of a semiconductor refrigerating sheet and finally greatly reducing irreversible damage caused by ice nucleation and ice crystallization of frozen biological materials in a solid-liquid phase change period; the heat transfer module obtained through the design and the manufacture of the application has the advantages of higher heat conduction capacity, more uniform temperature distribution, high response capacity, processing convenience, economy and the like, so that the biological slow freezing storage based on the semiconductor refrigeration system (TEC) is realized. The method combines the SIMP topology optimization method, the homogeneity heat transfer optimization method and the numerical control machine micromachining, and integrates the steps, so that the heat transfer module for the biological material quick freezing storage matched with the semiconductor refrigeration system (TEC) is obtained, and the heat transfer module has the advantages of reliability, high robustness, high adaptability and the like.
Drawings
Fig. 1 is a schematic view of an overall three-dimensional structure of a heat transfer module according to an embodiment of the present application.
Fig. 2 is a schematic two-dimensional structure of a heat transfer module according to an embodiment of the present application.
FIG. 3 is a schematic diagram of a boundary condition setup and two-dimensional finite element network for thermal topology optimization in an embodiment of the present application.
Fig. 4 is a partial schematic diagram of a topology optimization 200 iteration process in an embodiment of the present application.
Fig. 5 is a schematic diagram of convergence of an objective function of topology optimization iteration according to an embodiment of the present application with an increase in iteration number.
FIG. 6 is a flow chart of design and manufacture in an embodiment of the present application.
Wherein, 10, semiconductor refrigerating sheets; 20. red copper heat transfer end; 30. a freezing tube; 100 dirichlet boundary conditions of the first class; 200. a second type of neumann boundary condition.
Detailed Description
The following description of the embodiments of the present invention will be made clearly and completely with reference to the accompanying drawings, in which it is apparent that the embodiments described are only some embodiments of the present invention, but not all embodiments.
Example 1:
as shown in fig. 1-2, a heat transfer module for biological cryopreservation is characterized in that: comprises a semiconductor refrigerating sheet 10, a red copper heat-transfer end 20 and a freezing tube 30, wherein the semiconductor refrigerating sheet 10 is two square thin plates which are symmetrically arranged, the size of the semiconductor refrigerating sheet is S multiplied by D (for example, 40 multiplied by 1.9mm, the model is TECu1-12708, and the semiconductor refrigerating sheet can also be 62 multiplied by 3.2mm with larger area), and the semiconductor refrigerating sheet 10 is made of N and P-type bismuth telluride (Bi 2 Te 3 ) The red copper heat transfer end 20 is arranged between the two square thin plates, and the cold face of the semiconductor refrigeration piece 10 is attached to the red copper heat transfer end 20; the freezing tube 30 is a hollow cylinder with an inner circular bottom (i.e. its longitudinal section is a hollow disc), the freezing tube 30 adopts Polypropylene (PP) with an inner diameter R 1 The external diameter is R 2 (R 1 ＜R 2 ) Height H (e.g., using the manufacturer sammer Thermo Fisher; model: 1.8ml of internally corrugated freezer pipe 30 with a cross section having an inner diameter of 10.4mm, an outer diameter of 12.4mm and a height of 49mm matching the dimensions of the semiconductor cooling fin 10); the freezing tube 30 can also be made of zirconia ceramics, titanium alloy and other materials, and the materials can meet the requirements of biocompatible, biological inertia and sterilizable materials; meanwhile, in order to meet the demand for lightening the heat transfer module, the cylindrical wall thickness of the freezing pipe 30 (i.e.) As small as possible. The red copper heat transfer end 20 is provided with slots corresponding to the structure of the freezing pipe 30 and is used for installing the freezing pipe 30, the number of the slots is even and is symmetrically arranged about the central line of the two semiconductor refrigerating sheets 10, the structure of the slots is cylindrical, the diameter of the slots is consistent with the outer diameter of the freezing pipe 30, namely, the diameter of the slots is 12.4mm, the slots are tightly attached, the height of the heat transfer end is the height of the heat transfer end, and the side length of the semiconductor refrigerating sheet 10 is 40mm.
Example 2:
as shown in fig. 3 to 6, a method for designing a heat transfer module for biological cryopreservation as shown in example 1 is characterized by: comprising the following steps:
step S1: combining the basic and fixed characteristics of the red copper heat transfer end, before performing topology optimization, assuming that the red copper heat transfer end is a cuboid, the length and width dimensions of the red copper heat transfer end are limited by the dimensions of the semiconductor refrigerating sheet, wherein the length of the red copper heat transfer end is as follows:
wherein: l (L) j Indicating the length of the hypothetical red copper heat transfer end;represents the outer diameter of the freezing tube;
initial length L 0 The method comprises the following steps:
wherein:representing the diameter of the slot; />Representing the transverse heat transfer length, which is reduced to a reasonable value in an iterative loop manner following the following steps;
step S2: in a heat transfer module, the number of slots n c Coordinates (x) of the center of the circle with the cylindrical slot c ,y c ) Depending on the size of the semiconductor refrigeration sheet and the outside diameter of the freezer pipeThe method comprises the following steps:
wherein L is TEC The length of the long side of the cold surface of the semiconductor refrigeration piece is represented (the side length is the side length if the semiconductor refrigeration piece is square); y is Y c Representing each center coordinate y of the slot on the symmetry axis of the heat transfer module structure c,i Is a set of points; x is x c-l 、x c-r Respectively representing left and right center coordinates of the slot in the transverse heat transfer direction; l represents the length of the red copper heat transfer end (at this stage, l=l j Thereafter, as L decreases, x c-r The value of (2) will vary with the change);
for example, as described in example 1: the semiconductor refrigerating sheet has the dimensions of 40×40×1.9mm, the inner diameter of the refrigerating tube is 10.4mm, and the outer diameter is 12.4mm, then:
thus, the coordinates of the four slots are respectively: (9, 10), (9, 30), (36.8,10), (36.8,30);
step S3: because the whole heat transfer module is of a symmetrical structure similar to a sandwich (as shown in fig. 1 and 2), the dimension of two finite element analysis problems including topological optimization and subsequent transient homogeneity heat transfer simulation is reduced from three-dimension to two-dimension, and two-dimension heat transfer study is carried out on a long-wide plane of a heat transfer end;
as shown in fig. 3: for topological optimization boundary condition setting, based on the basic assumption of continuous medium mechanics, two widths of a heat transfer end closely attached to a cold surface of a semiconductor refrigeration piece can be regarded as Dirichlet boundary conditions (Dirichlet Boundary Condition); the round boundary of the slot which is tightly attached to the refrigerating tube is set as a Neumann boundary condition (Neumann Boundary Condition), which is also called a second type boundary condition;
the boundary condition setting assumption of the topological optimization of the heat transfer is different from the boundary condition of the transient homogeneity heat transfer simulation simulating the temperature reduction process of the biological material solution: in the topology optimization boundary condition setting, the temperature of the semiconductor refrigerating piece is assumed to be a certain fixed value (Dirichlet boundary condition) different from the ambient temperature, and the semiconductor refrigerating piece exists as a heat source with stable temperature, because the purpose of topology optimization is to reduce the overall quality of the heat transfer end on the premise that the heat flux at each part of the heat transfer end is as uniform as possible, thereby improving the response capability of the heat transfer end to the power output change of the semiconductor refrigerating piece; namely: the topology optimization is performed by space optimization, so that the increment of time in the transient heat transfer problem is not needed to be considered, two widths in contact with the cold surfaces of two semiconductor refrigerating sheets can be set as Dirichlet boundary conditions, simple heat transfer simulation which only considers an initial state-an equilibrium state is performed, and the solving process is further stabilized to ensure the solvability and uniqueness of the problem;
step S4: constructing a finite element network of a two-dimensional heat transfer surface based on heat transfer science simulation software; for example: the software named FreeFEM4.61 based on the C++ environment is adopted, and has the advantages of being capable of customizing grid size distribution, customizing heat transfer equation and the like;
step S5: the shape of a two-dimensional heat transfer surface is denoted by Ω, and its boundaries consist of three disjoint parts, specifically:
from the above equation, the change in the shape Ω of the two-dimensional heat transfer surface can be regarded as two widths Γ in contact with the semiconductor refrigeration sheet (heat source) D Circular boundary Γ of the socket against which the freezer pipe is in close contact N And the union of the remaining free optimized portions Γ;
temperature field T (x) in the thermal conduction study of the continuum: omega-R N Obtained by:
it means that the topologically optimized heat transfer equation holds over the entire two-dimensional heat transfer surface Ω;
which is represented at dirichlet boundary Γ D The temperature of the semiconductor refrigerating sheet heat source is fixed;
which is represented at the Neumann boundary Γ N On the heat flow q n Normal vector to the circular boundary of the socket
It means that by adjusting the material density ρ (x) of the free optimizing part Γ in the two-dimensional heat transfer surface, a reasonable material distribution is obtained, thereby finally homogenizing and minimizing the heat flux of the heat transfer end;
wherein, the liquid crystal display device comprises a liquid crystal display device,is a Nabla operator, also known as a vector differential operator, here representing the partial derivative operation of two spatial vectors in two dimensions; />The method is a full-scale word of space coordinates in mathematical sense, and under the two-dimensional space background, all two-dimensional space coordinates meeting the subsequent definition conditions are selected;
in the topology optimization process, the material of the heat transfer end is regarded as the mixture of red copper and air; based on the premise that the heat conductivity coefficient of red copper is far higher than that of air, the effective heat conductivity coefficient of the material of the free optimization part is as follows:
κ Γ (x)＝κ air ·(1-ρ(x) p )+κ Cu ·ρ(x) p ；
wherein: p represents a penalty factor for controlling the effect of material density on thermal conductivity; kappa (kappa) Cu 390W/(m.K), κ air 0.025W/(m.K);
since the scheme of the application is at the boundary Γ N Upper minimization T (x) 2 I.e. minimizing the transfer of heat, and therefore, in order to achieve at the same time: from Γ D To Γ N Minimizing energy loss while at the same time, the gamma surrounded by the slot of the red copper heat transfer end N Tend to be uniform in heat fluxA uniform target; the objective function of topology optimization is specifically:
Obj(T,q n )＝∫T(x) 2 dΓ N +λ N ∫(q n (x)-q avg ) 2 dΓ N ；
wherein: lambda (lambda) N A lagrangian multiplier for homogenization is shown, which is an empirical constant, 0.3 in this example, and if convergence is difficult, the value can be properly reduced, but cannot be negative; q avg Representing boundary Γ N Average heat flux on;
wherein: ds represents a minute boundary length element;
the weak form of the heat conduction problem is specifically:
wherein: v (x) represents an auxiliary function for solving a weak form of Partial Differential Equation (PDE); in the finite element method, the weak form is a method of converting the PDE problem into a linear algebraic problem for numerical solution;
the concomitant problem, in combination with the problem of thermal conduction, contributes to the calculation of the sensitivity of the objective function during the topological optimization, the weak form of which is in particular:
wherein, the solution of the concomitant function pp (x) and the solution of the original heat conduction problem act together on the topology optimization process, thereby obtaining the sensitivity of the objective function Obj (x);
gradient of energy densityThe method comprises the following steps:
the iterative equation is:
wherein: τ represents a step size, which is used to control the parameter update amplitude during each iteration of the optimization algorithm, and in this embodiment, the step size is 0.1; j represents the iteration number, and in this embodiment, the total iteration number is 200 times;
the penalty factor p is specifically:
step S6: judging the topology optimization result, and if the red copper materials around the slots on two sides of the symmetry axis are intersected, performing the following step S7; if the red copper materials around the slots on the two sides of the symmetry axis are not intersected, the length L of the red copper heat transfer end is shortened by 0.2mm, and the step S2 is returned to for cyclic iteration;
step S7: and storing the optimization result, and storing the combination of the final topological optimization in a picture form.
Example 3:
a method of manufacturing a heat transfer module for biological cryopreservation, characterized by: firstly, carrying out equal proportion drawing on a final two-dimensional topological optimization result in CAD software, and stretching the final two-dimensional topological optimization result into a three-dimensional structure by adopting a boss; then, red copper thin plates with the thickness of 1.5mm are respectively added on two sides of the heat transfer end, so that the red copper thin plates can be attached to the cold surface of the semiconductor refrigerating sheet; then, carrying out fuzzification filling treatment on each dendritic red copper structure in the middle of the red copper thin plate of the cold face of the slot and the attached semiconductor refrigeration piece; then, all sides parallel to the axes of the slots except the sides which are in contact with the cold surface of the semiconductor refrigerating sheet are subjected to rounding treatment with the radius of 0.5 mm; and finally, the drawn CAD three-dimensional graph is saved as a step or step format.
Then, adopting a triaxial numerical control milling machine to perform material reduction processing on the red copper square block, adopting a deep groove milling cutter with the diameter less than or equal to 1mm as a processing cutter, wherein the effective length (namely the length of a cutting edge and the clearance length) of the processing cutter is greater than 1/2 of the height of a heat transfer end so as to facilitate forward and reverse cutting processing; for example: the size of the semiconductor refrigerating sheet is 40X 40mm, the height of the red copper heat transfer end is 40mm, the length of the blade of the 1mm deep groove milling cutter and the clearance length should be more than 20mm, such as a 1mm tungsten steel alloy deep groove milling cutter with the effective length of 25 mm.
In the processing process, the cylindricity of the slot is +/-0.01 mm, the actual processing diameter of the slot is 0.03mm larger than the diameter of the freezing pipe, and the tolerance of +/-0.01 mm is ensured; two heat transfer surfaces in contact with the cold surface of the semiconductor refrigeration piece ensure flatness of +/-0.02 mm; and after the processing is finished, obtaining the heat transfer module.
Claims (6)
1. A heat transfer module for biological cryopreservation, characterized in that: the cold-face type red copper refrigerating device comprises a semiconductor refrigerating sheet (10), red copper heat-transfer ends (20) and refrigerating pipes (30), wherein the semiconductor refrigerating sheet (10) is two square thin plates which are symmetrically arranged, the red copper heat-transfer ends (20) are arranged between the two square thin plates, and the cold faces of the semiconductor refrigerating sheet (10) are attached to the red copper heat-transfer ends (20); the freezing pipes (30) are hollow cylinders with inner bottoms, the red copper heat-transfer ends (20) are uniformly provided with slots corresponding to the structures of the freezing pipes (30), and the number of the slots is even and symmetrically arranged about the central line of the two semiconductor refrigerating sheets (10).
2. Root of Chinese characterA heat transfer module for biological cryopreservation according to claim 1, wherein: the semiconductor refrigerating sheet has the size of S x D and is made of N and P type bismuth telluride (Bi) 2 Te 3 ) The method comprises the steps of carrying out a first treatment on the surface of the The freezing tube adopts polypropylene, and the inner diameter of the freezing tube is R 1 The external diameter is R 2 The height is H.
3. A method of designing a heat transfer module for biological cryopreservation according to claim 1 or 2, characterized in that: comprising the following steps:
step S1: combining the basic and fixed characteristics of the red copper heat transfer end, before performing topology optimization, assuming that the red copper heat transfer end is a cuboid, the length and width dimensions of the red copper heat transfer end are limited by the dimensions of the semiconductor refrigerating sheet, wherein the length of the red copper heat transfer end is as follows:
wherein: l (L) j Indicating the length of the hypothetical red copper heat transfer end;represents the outer diameter of the freezing tube;
initial length L 0 The method comprises the following steps:
wherein:representing the diameter of the slot; />Representing the transverse heat transfer length, which is reduced to a reasonable value in an iterative loop manner following the following steps;
step S2: in a heat transfer module, the number of slots n c Coordinates (x) of the center of the circle with the cylindrical slot c ,y c ) Depending on the size of the semiconductor refrigeration sheet and the outside diameter of the freezer pipeThe method comprises the following steps:
wherein L is TEC The length of the long side of the cold surface of the semiconductor refrigeration piece is shown; y is Y c Representing each center coordinate y of the slot on the symmetry axis of the heat transfer module structure c,i Is a set of points; x is x c-l 、x c-r Respectively representing left and right center coordinates of the slot in the transverse heat transfer direction; l represents the length of the red copper heat transfer end;
step S3: the dimension of two finite element analysis problems including topological optimization and subsequent transient homogeneity heat transfer simulation is reduced from three dimensions to two dimensions, and two-dimensional heat transfer study is carried out on a long-wide plane of a heat transfer end;
for the boundary condition setting of topological optimization, based on the basic assumption of continuous medium mechanics, two widths of a heat transfer end closely attached to a cold surface of a semiconductor refrigeration piece are regarded as Dirichlet boundary conditions; the round boundary of the slot which is tightly attached to the freezing tube is set as a Neumann boundary condition, which is also called a second class boundary condition;
step S4: constructing a finite element network of a two-dimensional heat transfer surface based on heat transfer science simulation software;
step S5: the shape of a two-dimensional heat transfer surface is denoted by Ω, and its boundaries consist of three disjoint parts, specifically:
from the above equation, the change in the shape Ω of the two-dimensional heat transfer surface can be regarded as two widths Γ in contact with the semiconductor refrigeration sheet D Circular boundary Γ of the socket against which the freezer pipe is in close contact N And remainA union of the free optimization portions Γ;
temperature field T (x) in the thermal conduction study of the continuum: omega-R N Obtained by:
it means that the topologically optimized heat transfer equation holds over the entire two-dimensional heat transfer surface Ω;
which is represented at dirichlet boundary Γ D The temperature of the semiconductor refrigerating sheet heat source is fixed;
which is represented at the Neumann boundary Γ N On the heat flow q n Normal vector to the circular boundary of the socket
It means that by adjusting the material density ρ (x) of the free optimizing part Γ in the two-dimensional heat transfer surface, a reasonable material distribution is obtained, thereby finally homogenizing and minimizing the heat flux of the heat transfer end;
in the topology optimization process, the material of the heat transfer end is regarded as the mixture of red copper and air; based on the premise that the heat conductivity coefficient of red copper is far higher than that of air, the effective heat conductivity coefficient of the material of the free optimization part is as follows:
κ Γ (x)＝κ air ·(1-ρ(x) p )+κ Cu ·ρ(x) p ；
wherein: p represents a penalty factor for controlling the effect of material density on thermal conductivity;
since the scheme of the application is at the boundary Γ N Upper minimization T (x) 2 I.e. minimizing the transfer of heat, the objective function of the topology optimization is therefore in particular:
Obj(T,q n )＝∫T(x) 2 dΓ N +λ N ∫(q n (x)-q avg ) 2 dΓ N ；
wherein: lambda (lambda) N Representing a Lagrangian multiplier for homogenization, as an empirical constant; q avg Representing boundary Γ N Average heat flux on;
wherein: ds represents a minute boundary length element;
the weak form of the heat conduction problem is specifically:
wherein: v (x) represents an auxiliary function for solving the weak form of the partial differential equation;
the concomitant problem, in combination with the problem of thermal conduction, contributes to the calculation of the sensitivity of the objective function during the topological optimization, the weak form of which is in particular:
wherein, the solution of the concomitant function pp (x) and the solution of the original heat conduction problem act together on the topology optimization process, thereby obtaining the sensitivity of the objective function Obj (x);
gradient of energy densityThe method comprises the following steps:
the iterative equation is:
wherein: τ represents a step size, which is used for controlling the amplitude of parameter update during each iteration of the optimization algorithm; j represents the number of iterations;
step S6: judging the topology optimization result, and if the red copper materials around the slots on two sides of the symmetry axis are intersected, performing the following step S7; if the red copper materials around the slots on the two sides of the symmetry axis are not intersected, the length L of the red copper heat transfer end is shortened by 0.2mm, and the step S2 is returned to for cyclic iteration;
step S7: and storing the optimization result, and storing the combination of the final topological optimization in a picture form.
4. A method of designing a heat transfer module for biological cryopreservation according to claim 1 or 3, characterized in that: the Lagrangian multiplier lambda N 0.3.
5. A method of designing a heat transfer module for biological cryopreservation according to claim 1 or 3, characterized in that: the step size tau is 0.1; the iteration number j is 1-200.
6. A method of designing a heat transfer module for biological cryopreservation according to claim 1 or 5, characterized in that: the penalty factor p is specifically:
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