CN113420392B - Conjugate heat transfer radiator design method based on flow channel track optimization - Google Patents
Conjugate heat transfer radiator design method based on flow channel track optimization Download PDFInfo
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Abstract
The invention discloses a conjugate heat transfer radiator design method based on flow channel track optimization, which comprises the steps of determining the inlet and outlet positions and the geometric dimensions of a conjugate heat transfer radiator and the boundary parameters of a system; fitting a flow channel track by adopting a Bernstein function as a mathematical tool by combining a spline curve function and a least square method; determining the normal direction of the curve by using a Bernstein function to further define a flow channel track function; taking a circle as the cross section shape of the flow channel; taking a coefficient embedded with a Bernstein function as a design variable, taking the minimum average temperature of an important plane as a target function, and establishing a shape optimization model by space size constraint; and optimizing the flow channel distribution by adopting a linear approximate constraint optimization algorithm COBYLA (chip on Board analysis) and simultaneously normalizing the design variables to improve the optimization stability. The invention can reasonably consider the defects of the traditional radiator design method and the application of the conventional optimization technology, further release the influence of the geometric dimension on the heat dissipation performance of the conjugated heat transfer radiator and improve the temperature distribution of an important plane.
Description
Technical Field
The invention belongs to the field of electronic equipment.
Background
In electronic equipment systems, heat sinks are indispensable or even central components. Most electronic devices must be designed with sufficient consideration of the effects of heat generating components, thermal environments, random thermal runaway, etc. on system efficiency, stability, and lifetime. Statistically, more than 55% of electronic products fail due to poor heat dissipation. In order to ensure the reliability and stability of the electronic equipment and prolong the service life of the electronic equipment, the development of a novel efficient heat dissipation technology is an urgent need at present. The traditional design method is based on experience, geometric dimensions of a given radiator are usually simply compared through an enumeration method, and the traditional design method is flexible in advantageous design and relatively intuitive. However, the design method inevitably has the defects of randomness, indefinite design period, indefinite design structure, and the like. With continuous development and development of computer technology and numerical methods, optimization methods are well applied in the design process of the geometric structure of the heat sink as novel technologies. The most representative methods are shape optimization and topology optimization. In general, topology optimization is in a conceptual design stage in the whole design flow, the mathematical demonstration and engineering application thereof are not mature, and a lot of improvement work needs to be carried out after that. Shape optimization has been widely used in structural design as a sophisticated method, although there is a limitation that the optimization result depends on initial design guessing. However, most designs simply optimize the geometry using simple, clear-to-the-eye dimensions as design variables, which greatly limits the potential for further heat dissipation. The invention further improves the temperature distribution of the important plane by digitizing the flow channel track and combining the shape optimization method by taking the minimum average temperature as the target. The potential of improving the heat dissipation performance of the geometric dimension is further mined under the constraint of limited space, and the result can be qualitatively understood and quantitatively analyzed. The method provides a theoretical basis for engineering practice.
Disclosure of Invention
The invention provides a design method of a conjugate heat transfer radiator based on flow channel track optimization. Liquid is used as a transport working medium of the conjugated heat transfer radiator, a Bernstein function is used for parameterizing a flow channel track, and the method further excavates the potential of improving the heat dissipation performance by changing parameters defining the geometric dimension.
The invention is realized by the following technical scheme:
step 1, determining the surface heat flux density of a power device, the external dimension of a radiator and the inlet and outlet positions of a flow channel according to the configuration condition of on-site electronic equipment; according to the determined heat flow density and the determined overall dimension, determining an inlet and outlet geometric dimension parameter, a heat transfer attribute parameter, a flow attribute parameter and a heat dissipation system material attribute of the heat radiator; wherein the radiator inlet diameter R in Outlet diameter R out (ii) a The heat transfer property parameter comprises an inlet fluid temperature T in The heat convection coefficient h with the outside world and the heat source Q are dispersed; the flow property parameter comprises an inlet pressure P in Outlet pressure P out (ii) a The material properties of the heat dissipation system comprise solid aluminum and fluid water, and the heat dissipation system has solid thermal conductivity k s Thermal conductivity of fluid k f Fluid constant pressure specific heat capacity C p Fluid density ρ;
(2a) According to the distribution of power devices, preliminarily determining the track of a flow channel by using a spline interpolation curve function, wherein the curve function of the ith section is
(2b) Roughly determining a flow channel track defined by a Bernstein function according to the spline interpolation curve function determined in the step (2 a), wherein the parameter equation of the ith section of curve function is as follows:
wherein the content of the first and second substances,
respectively representing Bernstein parameter equations with respect to the parameter t in a Cartesian coordinate system; ξ is the highest power of the Bernstein function;
coefficients corresponding to the bernstein function;
(2c) According to the spline interpolation curve function determined in (2 a) and the Bernstein curve function determined roughly in (2 b), when the condition is
Accurately determining the coefficients defined in (2 b) by a least squares method
The numerical model is as follows:
Subject to 0≤t λ ≤1；
wherein, the process divides the ith curve into K sections, and λ (λ =0, …, K) is one of the nodes;
(3a) And (3) further determining a function defined by the Bernstein function in the curve normal direction according to the Bernstein function accurately defined in the step (2 c), wherein the parameter equation is as follows:
wherein, the first and the second end of the pipe are connected with each other,
respectively representing parametric equations defined in terms of bernstein normal directions of the parameter t in a cartesian coordinate system; ψ is respectively the highest power of the corresponding bernstein function,
for coefficients corresponding to the Bernstein function, the initial value is determined as
The normal direction is located by cos theta and sin theta, d i (t) defines the distance from the initial curve in the normal direction. cos θ and sin θ are determined as:
(3b) A function defined by the normal direction of the Bernstein deterministic curve determined in accordance with (3 a), the value d of the distance from the initial curve in the normal direction i (t) is defined as:
wherein the content of the first and second substances,
is the maximum value of the distance moving in the normal direction; sin [ b ] i (t)]Is the distance and maximum value of the movement
The ratio of (a) to (b).
Is defined as:
where Δ t represents the step size; a is a coefficient matrix determined by a Lagrangian interpolation method; t is t k Is composed of
The highest order variable of (2); (3c) According to the function from the initial curve in the normal direction determined in (3 b), the flexible degree of freedom is formed by the embedded function b i (t) determining, defined as:
wherein
Is b is i (t) the highest power;
as a function b i (t) coefficient;
step 4, determining the cross section shape of the trajectory of the flow channel according to the further determined Bernstein function of the trajectory, and further determining the configuration of the whole flow channel;
step 5, according to engineering requirements, establishing optimization criteria including a coefficient embedded into a Bernstein function as a design variable, a minimum average temperature of a contact surface of the heat radiator and the power device as a target function, space size constraint and the like, and establishing a shape optimization model of the conjugated heat transfer heat radiator as follows:
Subject toφ min ≤φ≤φ max ；
where φ is a vector of design variables whose elements include coefficients defined by (4 a) and (4 c); phi is a min And phi max Respectively representing the minimum value and the maximum value of the design variable constraint; n is the number of curves for constructing the flow channel track;
to determine the average temperature of the surface; t (phi) is a temperature value at a certain point of a determined surface, which is implicitly expressed by a design variable phi; Ω is a defined surface;
step 6, applying boundary conditions according to the shape optimization model, and establishing a finite element model of the radiator;
step 7, optimizing an objective function by adopting a linear approximate constraint optimization algorithm COBYLA according to a finite element model of the radiator, and improving the temperature distribution of the contact surface of the radiator and the power device; setting corresponding optimization tolerance sigma, and meanwhile, unitizing design variables into:
wherein the content of the first and second substances,
for optimizing design variables formed during the process
The unitized values for the initial design variable φ, corresponding to the design variable constraints in step 6, become:
wherein the content of the first and second substances,
and
each represents the minimum and maximum values of the unitized design variable.
Preferably, the cross section determined in step (4) may be circular, and the finite element model may be established in step (6) by using a non-structural tetrahedral mesh.
Compared with the prior art, the invention has the following characteristics:
1. the method is combined with the advantage that the curve formed by the Bernstein function only needs a few control points to determine the approximate trend of the curve, and the least square method is used for gradually approaching an auxiliary spline curve function which can be more accurately represented in the initial stage. This process avoids solving solutions that are quadratic and power-above.
2. A fitting function for the normal direction is defined. The process defines that the moving range of the initial flow path track is limited to the normal direction, and the quality of the optimized important plane temperature distribution depends on the moving distance of the initial track in the normal direction. This process mathematically defines the maximum distance traveled in order to avoid numerical instability due to "boundary collisions" that occur during the optimization process. Meanwhile, the moving range is strongly restricted through the trigonometric function, so that the problem that the optimization system is too rigid due to too much restriction is solved.
3. The whole process further releases the constraint of the geometric dimension on the heat dissipation performance, further improves the temperature distribution of the concerned surface, is easy to understand and operate, and provides a theoretical basis for engineering practice.
Drawings
FIG. 1 is a flow chart of the present invention;
FIG. 2 is a three-dimensional conjugate heat transfer heat sink model; wherein: 1. a flow channel inlet 2, a flow channel outlet 3 and a heat source.
FIG. 3 is a three-dimensional conjugate heat transfer radiator flow path model; wherein: 4. a flow path trajectory.
FIG. 4 is an optimized front heat sink flow path trajectory;
fig. 5 is an optimized rear heat sink flow path footprint.
Detailed Description
The invention is described in further detail below with reference to the drawings and embodiments, but the invention is not limited thereto.
Referring to fig. 1, the invention relates to a method for designing a heat sink based on channel trajectory optimization, which comprises the following steps:
step 1, determining boundary parameters such as surface heat flux density of power device, outline dimension of radiator, and inlet and outlet positions of flow channel
Determining the surface heat flux Q of the power device according to the configuration condition of the field electronic equipment real (ii) a The overall dimension parameters of the radiator are as follows: length L, width W, height H; the position of the gate is shown in fig. 2.
Determining the diameter R of the inlet of the radiator according to the determined heat flow density and the external dimension in Outlet diameter R out (ii) a The heat transfer property parameter comprises an inlet fluid temperature T in The heat convection coefficient h with the outside world and the heat source Q are dispersed; the flow property parameter comprises an inlet pressure P in Outlet pressure P out (ii) a The material properties of the heat dissipation system comprise solid aluminum and fluid water, and the heat dissipation system has solid thermal conductivity k s Thermal conductivity of fluid k f Fluid constant pressure specific heat capacity C p Fluid density ρ.
substep 2a, preliminary determination by spline interpolationFlow path trajectory defined by the value curve function: the determined i-th segment of the spline curve function is
Substep 2b, roughly determining the flow path trajectory defined by the bernstein function: the parameter equation of the curve function of the ith section is determined as follows:
wherein the content of the first and second substances,
respectively representing Bernstein parameter equations with respect to the parameter t in a Cartesian coordinate system; ξ is the highest power of the Bernstein function;
are coefficients corresponding to the bernstein function.
Substep 2c, precisely determining the flow path trajectory defined by the bernstein function:
when the conditions are
By means of a least-squares method, the coefficients defined in step 3 are determined accurately
And
the numerical model is as follows:
Subject to 0≤t λ ≤1
wherein, this process divides the ith curve into K segments, λ (λ =0, …, K) is one of the nodes.
substep 3a, determining the i-th curve function parameter equation as:
wherein the content of the first and second substances,
respectively representing parameter equations defined in terms of Bernstein normal directions of the parameters t in a Cartesian coordinate system; ψ is respectively the highest power of the corresponding bernstein function,
for coefficients corresponding to the Bernstein function, the initial value is determined as
The normal direction is located by cos theta and sin theta, d i (t) defines the distance from the initial curve in the normal direction. cos θ and sin θ are determined as
Substep 3b, value d from the initial curve in the direction of the function normal i (t) is defined as
Wherein the content of the first and second substances,
is the maximum value of the distance moving in the normal direction; sin [ b ] i (t)]Distance to move and maximum value
The ratio of (a) to (b).
Is defined as
Where Δ t represents the step size; a is a coefficient matrix determined by a Lagrangian interpolation method; t is t k Is composed of
The highest order variable of (c).
Substep 3c, function of the initial curve, the flexible degrees of freedom of which are defined by the embedded function b i (t) determination, defined as
Wherein
Is b is i (t) the highest power;
as a function b i Coefficient of (t).
Step 4, determining the shape of the cross-section of the flow channel
The shape of the cross section is determined to be circular.
Step 5, determining the shape optimization criterion
Establishing a shape optimization criterion:
Subject toφ min ≤φ≤φ max
where φ is a vector of design variables whose elements include the coefficients defined by steps (6 a) and (6 c); phi is a min And phi max Respectively representing the minimum value and the maximum value of the design variable constraint; n is the number of curves for constructing the flow channel track;
to determine the average temperature of the surface; t (phi) is a temperature value at a certain point of a determined surface, which is implicitly expressed by a design variable phi; Ω is a defined surface.
Step 6, building a finite element model
And establishing a finite element model by adopting a non-structural tetrahedral mesh.
Step 7, set optimization algorithm parameters and finite element analysis
And setting a corresponding optimization tolerance sigma by adopting a linear approximate constraint optimization algorithm COBYLA, and unitizing the design variables. Finite element analysis was implemented in COMSOL software.
The advantages of the present invention are further illustrated by the following simulation cases:
1. simulation parameters
Referring to fig. 2 and 3, the three-dimensional external dimension of the conjugated heat transfer radiator is 80mm 60mm 12mm, and the size of each discrete heat source is Q =0.5W/mm 2 The diameter of the inlet and outlet is R in ＝R out =6mm, inlet temperature T in =20 ℃, and the convective heat transfer coefficient is h = 5W/(m) 2 K) inlet pressure P in =50Pa, outlet pressure P out =0Pa. The solid material is aluminum, and the liquid working medium is water. The case only focuses on the flow path distribution of the z = constant plane.
2. Simulation content and results
Table 1 shows the data of the corresponding average temperature and maximum temperature. Fig. 4 and 5 give pre-optimized and post-optimized heat sink flow path trajectories.
Table 1 comparison of surface properties on heat sink before and after optimization
| Scheme(s) | Average temperature (. Degree. C.) | Maximum temperature (. Degree. C.) |
| A | 73.595 | 108 |
| II | 72.042 | 91 |
| Δ | 1.548 | 17 |
Wherein, the first scheme is the result of the shape optimization pretreatment, the second scheme is the result of the shape optimization posttreatment, and delta represents the data difference value between the first scheme and the second scheme. From data and temperature distribution, the optimized temperature distribution becomes better, and the heat dissipation performance is further improved.
Claims (1)
1. A design method of a conjugate heat transfer radiator based on flow channel track optimization is characterized by comprising the following steps:
step 1, determining the surface heat flux density of a power device and the outline ruler of a radiator according to the configuration condition of field electronic equipmentThe position of the inlet and the outlet of the runner; according to the determined heat flow density and the determined overall dimension, determining an inlet and outlet geometric dimension parameter, a heat transfer attribute parameter, a flow attribute parameter and a heat dissipation system material attribute of the heat radiator; wherein the radiator inlet diameter R in Outlet diameter R out (ii) a The heat transfer property parameter comprises an inlet fluid temperature T in The heat convection coefficient h with the outside world and the heat source Q are dispersed; the flow property parameter comprises an inlet pressure P in Outlet pressure P out (ii) a The material properties of the heat dissipation system comprise solid aluminum and fluid water, and the heat dissipation system has solid thermal conductivity k s Thermal conductivity of fluid k f Fluid constant pressure specific heat capacity C p Fluid density ρ;
step 2, fitting and parameterizing a flow channel track by using a Bernstein function according to the distribution of field power devices; appointing the fitting coordinate system to be carried out in the xoy plane, wherein z is the height direction, and the method comprises the following substeps:
(2a) According to the distribution of power devices, preliminarily determining the track of a flow channel by using a spline interpolation curve function, wherein the curve function of the ith section is
(2b) Roughly determining a flow channel track defined by a Bernstein function according to the spline interpolation curve function determined in the step (2 a), wherein the parameter equation of the ith section of curve function is as follows:
wherein, the first and the second end of the pipe are connected with each other,
respectively representing Bernstein parameter equations with respect to the parameter t in a Cartesian coordinate system; ξ is the highest power of the Bernstein function;
coefficients corresponding to the bernstein function;
(2c) According to the spline interpolation curve function determined in (2 a) and the Bernstein curve function determined roughly in (2 b), when the condition is
Accurately determining the coefficients defined in (2 b) by a least squares method
The numerical model is as follows:
Subject to 0≤t λ ≤1；
wherein, the process divides the ith curve into K sections, and λ (λ =0, …, K) is one of the nodes;
step 3, further determining a function defined by the Bernstein function in the direction of the curve normal according to the determined Bernstein function of the flow channel track, and comprising the following substeps:
(3a) And (3) further determining a function defined by the Bernstein function in the curve normal direction according to the Bernstein function accurately defined in the step (2 c), wherein the parameter equation is as follows:
wherein, the first and the second end of the pipe are connected with each other,
individual watchA parametric equation defined in terms of bernstein normal directions for a parameter t in a cartesian coordinate system; ψ is respectively the highest power of the corresponding bernstein function,
for coefficients corresponding to the Bernstein function, the initial value is determined as
The normal direction is located by cos theta and sin theta, d i (t) defining the distance from the initial curve in the normal direction, cos θ and sin θ being determined as:
(3b) A function defined by the normal direction of the Bernstein deterministic curve determined in accordance with (3 a), the value d of the distance from the initial curve in the normal direction i (t) is defined as:
wherein the content of the first and second substances,
is the maximum value of the distance moving in the normal direction; sin [ b ] i (t)]Distance to move and maximum value
The ratio of (a);
is defined as:
where Δ t represents the step size; a is a coefficient matrix determined by a Lagrangian interpolation method; t is t k Is composed of
The highest order variable of (2);
(3c) According to the function from the initial curve in the normal direction determined in (3 b), the flexible degree of freedom is formed by the embedded function b i (t) determining, defined as:
wherein
Is b is i (t) the highest power;
as a function b i (t) coefficient;
step 4, determining the cross section shape of the track of the flow channel according to the further determined Bernstein function of the track, and further determining the configuration of the whole flow channel;
step 5, according to engineering requirements, establishing optimization criteria including a coefficient embedded into a Bernstein function as a design variable, a minimum average temperature of a contact surface of the heat radiator and the power device as a target function, space size constraint and the like, and establishing a shape optimization model of the conjugated heat transfer heat radiator as follows:
Subject toφ min ≤φ≤φ max ；
where φ is a vector of design variables whose elements include coefficients defined by (4 a) and (4 c); phi is a min And phi max Respectively representing the minimum value and the maximum value of the design variable constraint; n is the number of curves for constructing the flow channel track;
to determine the average temperature of the surface; t (phi) is a temperature value at a certain point of a determined surface, which is implicitly expressed by a design variable phi; Ω is a defined surface;
step 6, applying boundary conditions according to the shape optimization model, and establishing a finite element model of the radiator;
step 7, optimizing an objective function by adopting a linear approximate constraint optimization algorithm COBYLA according to a finite element model of the radiator, and improving the temperature distribution of the contact surface of the radiator and the power device; setting corresponding optimization tolerance sigma, and meanwhile, unitizing design variables into:
wherein the content of the first and second substances,
for optimizing design variables formed during the process
With the unitized values of the initial design variable φ, the design variable constraints corresponding to step 6 become:
wherein, the first and the second end of the pipe are connected with each other,
and
each represents the minimum and maximum values of the unitized design variable.
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