CN110427661A - A kind of high efficient heat exchanging structure adaptive optimum design method based on variational method - Google Patents
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Abstract
The high efficient heat exchanging structure adaptive optimum design method based on variational method that the embodiment of the invention discloses a kind of, include the steps of determining that boundary condition, geometry and the heat flow density of heat exchange structure, wherein boundary condition includes geometrical boundary condition and thermal boundary condition；Adaptive optimization model of the heat exchange structure based on calculus of variations method is established, and profile-followed grid is first formed based on geometrical boundary condition, then generates adaptive mesh according to according to thermal boundary condition on the basis of profile-followed grid；The geometric dimension, shape and distribution of cooling duct are determined based on adaptive mesh, and calculate the Temperature Distribution of heat exchange structure；Establish objective function and judge objective function whether meet demand, heat exchange structure parameter, otherwise return step 300 are exported when meet demand；The present invention can accordingly be adjusted according to the difference or variation of boundary condition, and either for cooling down or heating, which can be improved heat exchange amount compared with traditional heat exchange structure, and heat transfer effect is more preferable.
Description
Technical Field
The embodiment of the invention relates to the technical field of efficient heat exchange, in particular to a variational method-based efficient heat exchange structure self-adaptive optimization design method.
Background
In rocket engines, the wall surface of the engine can be subjected to the combined action of convection radiation of high-temperature fuel gas (more than 3000K) and the like, and the test of a severe thermal environment is carried out, so that the quality of an internal cooling structure can directly influence whether the engine can normally work. Similarly, in an aircraft gas turbine engine, turbine blades need to operate normally at high temperatures for improved performance, and likewise, turbine blades need efficient internal cooling structures. In addition, in electronic equipment devices, the heat dissipation structure is also very important for the design of the electronic equipment structure, and especially when facing complex conditions such as high energy consumption density, uneven distribution, high thermal design requirements and the like, the optimal design is difficult to realize depending on engineering experience.
For a liquid rocket engine, the working pressure of a thrust chamber of the engine which seeks high performance is higher, so that the heat flux density on the wall surface of the thrust chamber is high, and the temperature of fuel gas is very high and can reach thousands of degrees centigrade, which exceeds the temperature which can be borne by common engine materials. If necessary protection measures are not taken, the temperature of the wall surface of the thrust chamber is overhigh under the severe condition, and the wall surface of the thrust chamber is even burnt, so that the prevention of overheating of the wall surface of the engine is one of the core problems of the thermal protection of the engine. Liquid rocket engines have long operating times and require a large amount of propellant coolant, and generally use fuel as the coolant. Since the flow rate of the fuel is relatively small in the application, it is important to sufficiently cool the wall surface of the thrust chamber by using the fuel reasonably.
The traditional cooling channel design mostly depends on engineering experience, and due to the lack of necessary theoretical basis, the optimal design is difficult to realize. With the development of 3D printing technology, efficient cooling channels can be manufactured without the limitations of previous processing techniques. However, the new technology is still limited in popularization and application due to the lack of effective guidance of an adaptive optimization design method.
Disclosure of Invention
Therefore, the embodiment of the invention provides a high-efficiency heat exchange structure self-adaptive optimization design method based on a variational method, so as to solve the problems in the prior art.
In order to achieve the above object, the embodiments of the present invention provide the following technical solutions:
a high-efficiency heat exchange structure self-adaptive optimization design method based on a variational method comprises the following steps:
step 100, determining boundary conditions, geometric shapes and heat flow densities of a heat exchange structure;
step 200, establishing a self-adaptive optimization model of the heat exchange structure, forming a conformal grid, and establishing the self-adaptive grid based on the conformal grid according to boundary conditions;
step 300, determining the shape of a cooling channel based on the self-adaptive grid, and calculating the temperature distribution of the heat exchange structure;
step 400, establishing a target function and judging whether the target function meets the requirements, outputting heat exchange structure parameters when the requirements are met, and otherwise, returning to the step 300.
The embodiment of the invention is further characterized in that the temperature distribution of the heat exchange structure is calculated through fluid-solid coupling and is iterated for multiple times.
The embodiment of the invention is further characterized in that the heat exchange structure comprises a wall surface of the thrust chamber, a cooling channel is arranged in the wall surface of the thrust chamber, an outlet and an inlet of the cooling channel are respectively arranged on two side surfaces of the wall surface of the thrust chamber, wherein the thermal boundary condition and the geometric boundary condition of the heat exchange structure are specifically the heat flow density and the overall dimension of the wall surface of the thrust chamber.
The embodiment of the invention is further characterized in that the specific steps of generating the conformal grid are as follows:
establishing a potential flow function of the coolant fluid in the cooling channel: f ═ ξ + i η, where ξ is the potential function, η is the flow function, and ξ and η satisfy the laplace equation, i.e.
Exchange variables and independent variables give:
αxξξ+2βxξη+γxηη＝0
αyξξ+2βyξη+γyηη＝0；
wherein,β＝-(xξxη+yξyη)，
and generating conformal grids of the wall surface of the thrust chamber according to the formula.
The embodiment of the invention is also characterized in that the method for producing the self-adaptive grid based on the variational method comprises the following steps:
the functional of the weighting function is:
the functional of mesh smoothness is:
the functional of grid orthogonality is:
wherein J ═ xξyη-xηyξQ is the heat flux density of the wall surface of the thrust chamber;
substituting the three functional functions into I ═ lambdavIv+λsIs+λoIoAnd minimizes functional I.
An embodiment of the present invention is also characterized in that,
setting xix＝yη/J,ξy＝-xη/J,ηx＝-yξ/J,ηy＝xξAfter exchanging variables and arguments,/J, we get:
wherein the coefficients are:
ai＝λvavi+λsasi+λoaoi，
bi＝λvbvi+λsbsi+λoboi，
ci＝λvcvi+λscsi+λocoi，
and obtaining a generation control equation of the self-adaptive grid according to the transformation.
The embodiment of the present invention is also characterized in that finite differences are used for iterative solution of partial differential equations, and Δ ξ ═ 1 and Δ η ═ 1 are set in a calculation domain:
the following difference format is used for the derivative of x in the equation:
the following difference format is used for the derivative of y in the equation:
an embodiment of the invention is further characterized in that the geometric dimension of the cooling channel is proportional to the local density of the conformal grid, wherein line η is a centerline of the cooling channel, and the width d of the cooling channel is perpendicular to the line η and is expressed as:
the embodiment of the present invention is further characterized in that the temperature distribution of the wall surface of the thrust chamber is obtained under the distribution of the cooling channels, and an objective function is determined, wherein the minimum average temperature and temperature unevenness is selected as the objective function, and specifically:
F0＝w1A+w2B+…+wnD，
wherein A represents the temperature unevenness, B represents the average temperature, D is other factors of the temperature, w1、w2、wnRespectively representing the proportion of different terms in the objective function, T is temperature,is the average temperature, VsIs the volume of solid, NsThe number of solid nodes, specifically,
the embodiment of the invention is further characterized in that the optimized mathematical model is established according to the objective function:
wherein Y is a shape design variable, F0Is an objective function, gi(Y)、Rj(Y) Are constraints.
The embodiment of the invention has the following advantages:
in the self-adaptive optimization design, the size, the shape and the distribution of the heat exchange channels can be correspondingly adjusted according to different or changed boundary conditions, and the heat exchange structure can improve the heat exchange amount and has better heat exchange effect compared with the traditional heat exchange structure no matter used for cooling or heating.
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In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below. It should be apparent that the drawings in the following description are merely exemplary, and that other embodiments can be derived from the drawings provided by those of ordinary skill in the art without inventive effort.
The structures, ratios, sizes, and the like shown in the present specification are only used for matching with the contents disclosed in the specification, so as to be understood and read by those skilled in the art, and are not used to limit the conditions that the present invention can be implemented, so that the present invention has no technical significance, and any structural modifications, changes in the ratio relationship, or adjustments of the sizes, without affecting the effects and the achievable by the present invention, should still fall within the range that the technical contents disclosed in the present invention can cover.
FIG. 1 is a schematic overall flow diagram of the present invention;
FIG. 2 is a schematic diagram of the physical and computational fields of the cooling structure of the present invention;
FIG. 3 is a schematic diagram of an adaptive mesh for a cooling structure of the present invention;
FIG. 4 is a schematic diagram of a grid generated according to an adaptive grid generation control equation in accordance with the present invention;
FIG. 5 is a schematic diagram of an optimized heat exchange structure of the present invention;
FIG. 6 is a schematic diagram of an optimization process according to the present invention.
Detailed Description
The present invention is described in terms of particular embodiments, other advantages and features of the invention will become apparent to those skilled in the art from the following disclosure, and it is to be understood that the described embodiments are merely exemplary of the invention and that it is not intended to limit the invention to the particular embodiments disclosed. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
As shown in fig. 1, the invention provides a high-efficiency heat exchange structure adaptive optimization design method based on a variational method, which comprises the following steps:
step 100, determining boundary conditions, geometric shapes and heat flow densities of a heat exchange structure;
step 200, establishing a self-adaptive optimization model of the heat exchange structure, forming a conformal grid, and establishing the self-adaptive grid based on the conformal grid according to boundary conditions;
step 300, determining the shape of a cooling channel based on the self-adaptive grid, and calculating the temperature distribution of the heat exchange structure;
step 400, establishing a target function and judging whether the target function meets the requirements, outputting heat exchange structure parameters when the requirements are met, and otherwise, returning to the step 300.
As shown in fig. 2, the heat exchange structure includes a thrust chamber wall surface, a cooling channel is disposed in the thrust chamber wall surface, an outlet and an inlet of the cooling channel are respectively disposed on two side surfaces of the thrust chamber wall surface, wherein a thermal boundary condition and a geometric boundary condition of the heat exchange structure are specifically a heat flux density and an external dimension of the thrust chamber wall surface, the heat flux density of the thrust chamber wall surface is set to q, and independent parameters of the cooling channel inlet, such as an inlet flow m and a pressure p, are determined according to an actual situation0Temperature T0Etc. and the coolant thermal property parameter, thermal conductivity kfAnd a constant specific heat capacity Cp and a density rho. And establishing a self-adaptive optimization design model according to the target requirement to be achieved, the boundary condition of the wall surface of the thrust chamber, the geometric parameters of the wall surface of the thrust chamber and the independent parameters of the inlet of the cooling channel, and carrying out analysis and solution according to the model to obtain the self-adaptive design cooling structure of the wall surface of the thrust chamber.
As shown in fig. 3, a one-to-one mapping is established between the physical field and the computational field of the thrust chamber wall surface, and then a conformal mesh is generated based on the shape of the thrust chamber wall surface.
In the present embodiment, since the fluid flows in the flow passage of the cooling passage without swirling and without pressure, the potential flow function is:
f ═ ξ + i η, where ξ is the potential function, η is the flow function, and ξ and η satisfy the laplace equation, i.e.
Wherein, for computational convenience, the exchange variables and the independent variables are obtained:
αxξξ+2βxξη+γxηη＝0
αyξξ+2βyξη+γyηη＝0；
the coefficients are:β＝-(xξxη+yξyη)，and accordingly, a corresponding conformal grid can be generated in the wall surface of the thrust chamber with the observation hole.
And generating a self-adaptive grid of the wall surface of the thrust chamber based on a variational method, and comprehensively considering a weighting function and the orthogonality and smoothness of the grid to make the orthogonality and smoothness of the grid to be minimum.
Among these, functional considerations for three relevant factors are specifically as follows:
the functional of the weighting function is:
the functional of mesh smoothness is:
the functional of grid orthogonality is:
wherein J is jacobi formula of mapping physical domain with any shape to right-angle quadrilateral calculation domain: j ═ xξyη-xηyξAnd q is the heat flux density of the wall surface of the thrust chamber.
Substituting the three functional functions into I ═ lambdavIv+λsIs+λoIoAnd minimizing the functional I, an adaptive grid equation can be generated.
In order to calculate the functional, it is necessary to exchange variables and arguments, and use the following relation:
setting xix＝yη/J,ξy＝-xη/J,ηx＝-yξ/J,ηy＝xξAfter exchanging variables and arguments,/J, we get:
wherein the coefficients are:
ai＝λvavi+λsasi+λoaoi，
bi＝λvbvi+λsbsi+λoboi，
ci＝λvcvi+λscsi+λocoi，
thus, a self-adaptive structural grid generation control equation is obtained, and the weighting coefficients need to be selected according to the requirements of specific problems.
Finite differences are used to iteratively solve the partial differential equations. Within the domain of computation, Δ ξ ═ 1 and Δ η ═ 1, the following difference format is used for the derivatives of x in the equation:
the same is true for y.
As shown in fig. 4, which is a mesh generated according to the adaptive mesh generation control equation. The cooling channels are generated based on an adaptive grid, the cooling channels are narrow where the grid is dense and wide where the grid is loose. Where η is the centerline of the cooling channel, the width of the cooling channel is perpendicular to η, expressed as:
determining an objective function under the condition that the temperature distribution of the wall surface is obtained under the current distribution of the cooling channels, wherein various methods can be adopted for the objective function, and the objective function with the minimum average temperature and the minimum temperature unevenness is selected as follows:
F0＝w1A+w2B+…+wnD，
wherein A represents the temperature unevenness, B represents the average temperature, D is other factors of the temperature, w1、w2、wnRespectively representing the proportion of different terms in the objective function, T is temperature,is the average temperature, VsIs the volume of solid, NsThe number of solid nodes, specifically,
in addition, an optimized mathematical model is established according to the established objective function:
wherein Y is a shape design variable, F0Is an objective function, gi(Y)、Rj(Y) is a constraint. The constraint here is that the thickness between the cooling channels is not less than a certain size, etc. According to the final target to be achieved, the value of n and the number of cooling channels are adjusted, and then the optimal heat exchange structure is obtained, as shown in fig. 5.
The above specific flow is shown in fig. 6.
In addition, the method related in the invention, the shape of the cooling channel is determined by boundary conditions, the conformal grid is obtained according to the geometric shape of the heat exchange structure, on the basis, the density degree, the smoothness and the orthogonality of the grid are controlled by adopting a variable component formula according to the heat flux density on the heat exchange structure, so that the grid is dense at a place with large heat flux and the grid is sparse at a place with small heat flux, the width of the cooling channel is in direct proportion to the density of the local grid, the temperature distribution of the structure is obtained through fluid-solid coupling calculation, and the optimized heat exchange structure meeting the target requirement is obtained through multiple iterations.
The cooling channel is designed according to the cooling structure optimization method based on the variation method, and the following advantages can be obtained:
(1) the calculation model adopted here can accurately calculate the values of the various parameters, so the model can be applied to the optimal design of the cooling structure;
(2) the cooling channel designed according to the method can take away more heat in places with large heat flow compared with the conventional cooling channel, and the optimized cooling channel changes along with the local heat flow, so that the average temperature and the temperature unevenness of the cooling structure can be reduced;
(3) according to the method, the optimized design of the cooling channel is obtained, and a plurality of groups of designs with better objective functions can be selected from the optimized design to be better than the conventional artificial design.
Although the invention has been described in detail above with reference to a general description and specific examples, it will be apparent to one skilled in the art that modifications or improvements may be made thereto based on the invention. Accordingly, such modifications and improvements are intended to be within the scope of the invention as claimed.
Claims (10)
1. A high-efficiency heat exchange structure self-adaptive optimization design method based on a variational method is characterized by comprising the following steps:
step 100, determining boundary conditions, geometric shapes and heat flow densities of a heat exchange structure, wherein the boundary conditions comprise geometric boundary conditions and thermal boundary conditions;
200, establishing a self-adaptive optimization model of the heat exchange structure based on a variational method, forming a conformal grid based on a geometric boundary condition, and generating a self-adaptive grid based on the conformal grid according to a thermal boundary condition;
step 300, determining the geometric size, shape and distribution of the cooling channel based on the self-adaptive grid, and calculating the temperature distribution of the heat exchange structure;
step 400, establishing a target function and judging whether the target function meets the requirements, outputting heat exchange structure parameters when the requirements are met, and otherwise, returning to the step 300.
2. The efficient heat exchange structure self-adaptive optimization design method based on the variational method according to claim 1, characterized in that the temperature distribution of the heat exchange structure is calculated through fluid-solid coupling and is subjected to multiple iterations.
3. The adaptive optimization design method for the efficient heat exchange structure based on the variational method is characterized in that the heat exchange structure comprises a thrust chamber wall surface, a cooling channel is arranged in the thrust chamber wall surface, an outlet and an inlet of the cooling channel are respectively arranged on two side surfaces of the thrust chamber wall surface, and the thermal boundary condition and the geometric boundary condition of the heat exchange structure are specifically the heat flow density and the external dimension of the thrust chamber wall surface.
4. The efficient heat exchange structure self-adaptive optimization design method based on the variational method according to claim 3, characterized in that the specific steps of generating the conformal grid are as follows:
establishing a potential flow function of the coolant fluid in the cooling channel: f ═ ξ + i η, where ξ is the potential function, η is the flow function, and ξ and η satisfy the laplace equation, i.e.
Exchange variables and independent variables give:
αxξξ+2βxξη+γxηη＝0
αyξξ+2βyξη+γyηη＝0；
wherein ,β＝-(xξxη+yξyη)， for Hamiltonian, x and y are the physical field abscissa and ordinate, xi and eta are the calculated field abscissa and xηIs the first partial derivative of x with respect to η, xξIs the first partial derivative of x with respect to xi, xξξIs the second partial derivative of x with respect to xi, xηηIs the second partial derivative of x with respect to η, xξηX calculates the first partial derivative of xi and eta; y isηIs one order of y to ηPartial derivative, yξIs the first partial derivative of y with respect to xi, yξξIs the second partial derivative of y to xi, yηηIs the second partial derivative of y with respect to η, yξηRespectively solving a first-order partial derivative of y to xi and eta;
and generating conformal grids of the wall surface of the thrust chamber according to the formula.
5. The efficient heat exchange structure self-adaptive optimization design method based on the variational method according to claim 4, characterized in that the method for producing the self-adaptive grid based on the variational method comprises the following steps:
the functional of the weighting function is:
the functional of mesh smoothness is:
the functional of grid orthogonality is:
wherein ,J＝xξyη-xηyξQ is the heat flux density of the wall surface of the thrust chamber;
substituting the three functional functions into I ═ lambdavIv+λsIs+λoIoAnd minimizing functional I, where λv，λsλ, is a weighting coefficient, and the value of the weighting coefficient is selected according to the requirement of a specific problem.
6. The efficient heat exchange structure self-adaptive optimization design method based on the variational method according to claim 5, characterized in that a grid smoothness functional and a relation after a grid orthogonality functional is changed are obtained according to coordinate transformation between a physical field and a calculation field after variables and independent variables are exchanged, and a generation control equation of a self-adaptive grid is obtained according to the transformation.
7. The method for adaptively and optimally designing the efficient heat exchange structure based on the variational method as claimed in claim 6, wherein finite differences are adopted to iteratively solve the partial differential equation, and Δ ξ ═ 1 and Δ η ═ 1 are set in the calculation domain, Δ ξ is the distance between two adjacent grid points in the x direction in the calculation field, Δ η is the distance between two adjacent grid points in the y direction in the calculation field, i is the coordinate of the grid point in the x direction, and j is the coordinate of the grid point in the y direction:
the following difference format is used for the derivative of x in the equation:
the following difference format is used for the derivative of y in the equation:
8. the adaptive optimization design method for the efficient heat exchange structure based on the variational method as claimed in claim 7, wherein the geometric dimension of the cooling channel is positively correlated with the local density of the adaptive grid, wherein the η line is the central line of the cooling channel, and the width of the cooling channel is perpendicular to the η line, and is expressed as:
d is the width of the cooling channel.
9. The self-adaptive optimization design method of the efficient heat exchange structure based on the variational method according to claim 8, is characterized in that the temperature distribution of the wall surface of the thrust chamber is obtained under the distribution of the cooling channels, and an objective function is determined, wherein the objective function is selected as the minimum average temperature and the minimum temperature unevenness, and specifically comprises the following steps:
F0＝w1A+w2B+…+wnD，
wherein A represents the temperature unevenness, B represents the average temperature, D is other factors of the temperature, w1、w2、wnRespectively representing the proportion of different terms in the objective function, T is temperature,is the average temperature, VsIs the volume of solid, NsThe number of solid nodes, specifically,
10. the efficient heat exchange structure self-adaptive optimization design method based on the variational method according to claim 9 is characterized in that an optimization mathematical model is established according to an objective function:
wherein Y is a shape design variable, F0Is an objective function, ynIs the physical field ordinate, gi(Y)、Rj(Y) is a constraint.
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Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN113420392A (en) * | 2021-07-02 | 2021-09-21 | 中国船舶重工集团公司第七二四研究所 | Conjugate heat transfer radiator design method based on flow channel track optimization |
| WO2024045089A1 (en) * | 2022-08-31 | 2024-03-07 | 西门子股份公司 | Method for generating cooling flow channels, and device |
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| CN110427661B (en) | 2023-06-02 |
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