CN115358014A - Power device air-cooled radiator model, optimization method and performance calculation method - Google Patents

Power device air-cooled radiator model, optimization method and performance calculation method Download PDF

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CN115358014A
CN115358014A CN202210856028.XA CN202210856028A CN115358014A CN 115358014 A CN115358014 A CN 115358014A CN 202210856028 A CN202210856028 A CN 202210856028A CN 115358014 A CN115358014 A CN 115358014A
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贾倩
刘小栋
徐登
白金池
许姣姣
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Shaanxi Aero Electric Co Ltd
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Abstract

The invention belongs to the technical field of power device heat dissipation design, and discloses a power device air-cooled radiator model, an optimization method and a performance calculation method. The method comprises the following steps: determining structural parameters of the radiator; establishing a radiator model; step two: determining the optimized variables of the radiator as a radiator fin gap b and a radiator fin thickness d; step three: selecting an optimization target; step four: taking the weight m of the radiator as an optimization target, taking the highest temperature Tmax on the radiator as a constraint function, carrying out optimization calculation on the mathematical model of the radiator by an optimization design program based on Matlab programming, and obtaining a radiator structure with the lightest weight and the temperature not exceeding the constraint value; step five: and (3) taking the highest temperature Tmax on the radiator as an optimization target, taking the weight m of the radiator as a constraint function, carrying out an optimization design program based on Matlab programming on the mathematical model of the radiator, and carrying out optimization calculation to obtain a radiator structure with the lowest temperature and weight not exceeding a constraint value.

Description

Model, optimization method and performance calculation method for air-cooled radiator of power device
Technical Field
The invention belongs to the technical field of power device heat dissipation design, and particularly relates to a power device air-cooled radiator model, an optimization method and a performance calculation method.
Background
With the gradual increase of the power of the airplane power supply system and the light weight development of the power electronic conversion device, the heat dissipation technology of the power device becomes one of the key technologies to be solved urgently. Forced air cooling is one of the main forms of the heat dissipation design of the power module of the motor controller at present, and compared with a liquid cooling heat dissipation technology, the forced air cooling heat dissipation structure is simple, convenient to process and manufacture and low in installation requirement, so that the forced air cooling heat dissipation structure is widely applied to heat dissipation of power devices of equipment such as controllers. The existing air-cooled radiator of the IGBT power module mainly comprises a substrate and fins, and factors influencing the radiating effect of the radiator comprise the substrate, the radiator structure, the fin size, the fin gaps and the like. Usually, the model selection of the radiator mainly adopts engineering experience and thermal design software such as Icepak or Flotherm and the like to perform early-stage simulation analysis so as to obtain structural parameters of the radiator meeting the requirements, and sometimes, multiple times of iterative simulation are required to obtain a satisfactory result. The method not only has high requirements on the thermal design engineering experience of designers, but also has the advantages of high design cost and poor operability because the use of heat dissipation design software is skilled and thorough enough to obtain the final result.
Disclosure of Invention
The invention aims to provide a power device air-cooled radiator model, an optimization method and a performance calculation method, which can improve the reliability of air-cooled heat dissipation of a power device, simplify the flow and steps of air-cooled heat dissipation design and realize rapid research and development and design.
Technical scheme one
A model of an air-cooled radiator of a power device comprises: a radiator pressure drop calculation mathematical model and a thermal resistance calculation mathematical model;
the pressure drop calculation mathematical model comprises:
radiator pressure drop
Figure BDA0003755321660000011
Where ρ is air Is air density, constant, V ch Is the flow rate of the inlet of the fin gap,
Figure BDA0003755321660000021
f app in order to obtain an apparent coefficient of friction,
Figure BDA0003755321660000022
d h the diameter of the flow channel is the hydraulic diameter,
Figure BDA0003755321660000023
Re f the reynolds number is used for the pressure drop calculation,
Figure BDA0003755321660000024
wherein q is the fan air volume, k yn For kinematic air viscosity, the ambient temperature k is specified yn Is a constant;
kc1 is the inlet drag loss coefficient
Figure BDA0003755321660000025
Kc2 is the coefficient of loss of outlet drag
Figure BDA0003755321660000026
Wherein L is the length of the heat sink, W is the width of the heat sink, t is the thickness of the base plate, H is the height of the fins, and b is the ribsThe piece clearance, d is the thickness of the fins, n is the equivalent number of the fins, ls is the length of the power module, ws is the width of the power module, and x is the distance between the power modules; wherein
Figure BDA0003755321660000027
Slot ratio of radiator
Figure BDA0003755321660000028
The mathematical model for calculating the thermal resistance comprises the following steps: the heat radiator thermal resistance Rh is the sum of the heat radiator substrate diffusion thermal resistance Rsp and the fin air side convection heat transfer thermal resistance Rcov;
diffusion thermal resistance of heat sink substrate
Figure BDA0003755321660000029
Air side heat convection heat transfer thermal resistance
Figure BDA00037553216600000210
In which there is no dimensional number
Figure BDA00037553216600000211
Dimensionless number
Figure BDA0003755321660000031
Calculating the pilow number
Figure BDA0003755321660000032
Empirical parameters
Figure BDA0003755321660000033
Equivalent convective heat transfer coefficient
Figure BDA0003755321660000034
Efficiency of fins
Figure BDA0003755321660000035
Wherein
Figure BDA0003755321660000036
λ h Heat conductivity of fins of a heat sink;
heat transfer coefficient by convection of air
Figure BDA0003755321660000037
Wherein λ is air The heat conductivity of air is constant, pr is a Plantt number and can be calculated from the specific heat capacity, the dynamic viscosity and the heat conductivity of air;
equivalent radius of heat sink substrate
Figure BDA0003755321660000038
Equivalent radius of heat source
Figure BDA0003755321660000039
Dimensionless characteristic radius
Figure BDA00037553216600000310
Thickness of dimensionless substrate
Figure BDA00037553216600000311
Re L The reynolds number was used for the calculation of the thermal resistance,
Figure BDA00037553216600000312
further, the equivalent radius r of the heat source in the diffusion thermal resistance model of the radiator substrate s In relation to the distance x between the power modules, the following is expressed by a quadratic polynomial:
Figure BDA00037553216600000313
taking a plurality of different x values according to the powderEstablishing a thermal simulation model for finite element simulation according to the structural parameters of the heat radiator, and obtaining a correction coefficient a by adopting a least square method according to the temperature simulation result of the air-cooled radiator 2 、a 1 、a 0 So as to minimize the error between the calculation result and the simulation result of the mathematical model, and determine the equivalent radius r of the heat source according to the correction coefficient s 。
Further, when the structural parameters of the radiator are determined, the calculated model of the pressure drop of the radiator is delta P h ＝f h (q) wherein f h As a function of radiator pressure drop with respect to q;
for the selected fan, its P-Q curve P = f fan (q) wherein P is fan pressure, f fan Simultaneous fan P-Q curve P = f as a function of fan pressure with respect to Q fan (q) and radiator pressure drop calculation mathematical model such that P = Δ P h Then f is h (q)＝f fan And (q), solving the air quantity q of the working point of the fan and the pressure P.
Further, the maximum temperature T on the radiator max Is T max ＝Q*R h +T a Where Q is the heat source power consumption, T a Is ambient temperature;
when the structural parameters of the radiator are determined, the heat resistance calculation mathematical model of the radiator is R h ＝f R (q) wherein f R Calculating the heat resistance of the radiator according to the air quantity q of the working point of the fan as a function of the heat resistance of the radiator on q, and further obtaining the highest temperature T of the radiator max 。
Technical scheme two
A method for optimizing an air-cooled radiator of a power device comprises the following steps:
the method comprises the following steps: determining the structural parameters of the radiator: the structure comprises a radiator length L, a radiator width W, a base plate thickness t, fin heights H, fin gaps b, fin thicknesses d and the equivalent number n of fins; determining the structural parameters of the heat source: power module length Ls, power module width Ws, and power module distance x; establishing a model of the heat sink of claim 1 or 2;
step two: determining the optimized variables of the radiator as the clearance b and the thickness d of the radiator fins;
step three: selecting an optimization target, if the optimization target is the weight of the radiator, entering the fourth step, and if the optimization target is the highest temperature of the radiator, entering the fifth step;
step four: taking the weight m of the radiator as an optimization target, taking the highest temperature Tmax on the radiator as a constraint function, carrying out optimization calculation on the mathematical model of the radiator by an optimization design program based on Matlab programming to obtain a radiator structure with the lightest weight and the temperature not exceeding the constraint value;
step five: and (3) taking the highest temperature Tmax on the radiator as an optimization target, taking the weight m of the radiator as a constraint function, carrying out an optimization design program based on Matlab programming on the mathematical model of the radiator, and carrying out optimization calculation to obtain a radiator structure with the lowest temperature and weight not exceeding a constraint value.
Further, in the second step, after the structural parameters of the radiator are determined, the calculated model of the pressure drop of the radiator is delta P h ＝f h (q,b,d)，f h As a function of radiator pressure drop with respect to q, b, d;
simultaneous fan P-Q curve P = f fan (q) and radiator pressure drop calculation mathematical model such that P = Δ P h The solved air quantity q of the fan working point is a function of the fin gap b and the fin thickness d, and q = f r (b,d)，f r Is a function of the air volume related to b and d;
when the structural parameters of the radiator are determined, the heat resistance calculation mathematical model of the radiator is R h ＝f R (q,b,d)，f R As a function of the heat sink thermal resistance with respect to q, b, d; the maximum temperature Tmax on the radiator is T max ＝Q*R h +T a Where Q is the heat source power consumption, T a Is ambient temperature; q = f r (b, d) are substituted to obtain T max ＝f T (b,d)，f T As a function of the maximum temperature on the heat sink with respect to b, d.
Further, in the fourth step, a nonlinear programming function fmincon in Matlab is used as an optimization function, and constraint conditions for constraining variables are determined by the structural parameters of the heat radiator and the heat radiation performance parameters, wherein the constraint conditions are as follows:
Figure BDA0003755321660000051
in the formula, x i To optimize the variables; x is the number of min To optimize the lower bound of the variable values, x max In order to optimize the upper limit of variable values, x is the fin gap b and the fin thickness d of the radiator; f. of m As a function of weight with respect to b and d, T 1 Is a temperature constraint value.
Further, in the fifth step, a nonlinear programming function fmincon in Matlab is used as an optimization function, and constraint conditions for constraining variables are determined by both the structural parameters and the heat dissipation performance parameters of the heat sink, wherein the constraint conditions are as follows:
Figure BDA0003755321660000052
in the formula, x i To optimize the variables; x is a radical of a fluorine atom min For optimizing the lower limit of the value of the variable, x max In order to optimize the upper limit of variable values, x is the fin gap b and the fin thickness d of the radiator; f. of T As a function of temperature, b and d, m 1 Is a weight constraint value.
Technical scheme three
A method for calculating the heat exchange performance of an air-cooled radiator of a power device is characterized in that the corrected mathematical model of claim 2 is adopted for the radiator with known structural parameters, fan curves and environmental conditions to calculate the maximum temperature of the radiator, the pressure drop of the radiator and the thermal resistance parameter of the radiator.
The invention provides a model, an optimization method and a performance calculation method of an air-cooled radiator of a power device, which realize two functions, namely, the heat exchange performance of the radiator can be quickly obtained by correcting a mathematical model under the condition of giving the structural parameters of the radiator, and whether the designed radiator meets the requirements or not is evaluated; and secondly, obtaining the structural parameters of the radiator by calling an optimization algorithm under the condition of limiting the constraint conditions, and realizing the optimization design of the radiator. According to the invention, the calculation precision of the heat exchange performance of the radiator is improved by constructing a mathematical model, the calculation check and the optimized design of the heat dispersion performance of the radiator can be rapidly realized, the engineering experience requirements on designers are reduced, the heat dispersion design cost and the design difficulty of a power device are reduced, and the method has practical engineering application value.
Drawings
FIG. 1 is a schematic diagram of a design flow for optimizing structural parameters of a heat sink;
FIG. 2 is a view showing the structure of a heat sink and a heat source;
FIG. 3 is a schematic diagram of a mathematical model construction process.
Detailed Description
According to one aspect of the invention, a power device air-cooled radiator model is shown in fig. 1, the structural parameters of a radiator are determined, and a radiator mathematical model is constructed, wherein the model comprises a radiator pressure drop calculation mathematical model and a thermal resistance calculation mathematical model;
as shown in fig. 2, the structural parameters of the heat sink include a length L of the heat sink, a width W of the heat sink, a thickness t of the substrate, a height H of the fins, a gap b of the fins, a thickness d of the fins, and an equivalent number n of the fins, and the structural parameters of the heat source include a length Ls of the power module, a width Ws of the power module, and a distance x of the power module. Wherein
Figure BDA0003755321660000061
Radiator slot ratio
Figure BDA0003755321660000062
(1) Pressure drop calculation model
Hydraulic diameter of flow channel
Figure BDA0003755321660000071
Reynolds number
Figure BDA0003755321660000072
In the calculation of the pressure drop, the characteristic length is taken as the hydraulic diameter d of the flow passage h When the temperature of the water is higher than the set temperature,
reynolds number for pressure drop calculation
Figure BDA0003755321660000073
Wherein q is the fan air volume, k yn For kinematic air viscosity, the ambient temperature k is specified yn Is a constant;
coefficient of inlet drag loss
Figure BDA0003755321660000074
Coefficient of exit drag loss
Figure BDA0003755321660000075
Apparent coefficient of friction
Figure BDA0003755321660000076
Radiator pressure drop
Figure BDA0003755321660000077
Where ρ is air Is air density, constant, V ch Is the flow rate of the inlet of the fin gap,
Figure BDA0003755321660000078
therefore, from the above calculation, when the structural parameters of the radiator are determined, the calculated model of the radiator pressure drop is Δ P h ＝f h (q) wherein f h Is a function of radiator pressure drop with respect to q;
for the selected fan, its P-Q curve P = f fan (q) wherein P is fan pressure, f fan The P-Q curve of the simultaneous fan P = f as a function of the fan pressure with respect to Q fan (q) and radiator pressure drop calculation mathematical model such that P = Δ P h I.e. f h (q)＝f fan And (q), solving the air quantity q of the working point of the fan and the pressure P.
(2) Thermal resistance calculation model
The heat radiator thermal resistance Rh is the sum of the heat radiator substrate diffusion thermal resistance Rsp and the fin air side convection heat transfer thermal resistance Rcov. And analyzing the relationship between the structural parameters of the radiator, the fluid motion parameters and the thermal resistance of the radiator to construct a thermal resistance calculation mathematical model of the radiator.
Equivalent radius of heat sink substrate
Figure BDA0003755321660000081
Equivalent radius of heat source
Figure BDA0003755321660000082
Dimensionless characteristic radius
Figure BDA0003755321660000083
Dimensionless thickness of substrate
Figure BDA0003755321660000084
In the calculation of thermal resistance, the characteristic length is the length L of the fin, and Reynolds number is used for calculating the thermal resistance
Figure BDA0003755321660000085
Convective heat transfer coefficient of air
Figure BDA0003755321660000086
Wherein λ is air The heat conductivity of air is constant, pr is a Plantt number and can be calculated from the specific heat capacity, the dynamic viscosity and the heat conductivity of air;
efficiency of fins
Figure BDA0003755321660000087
Wherein
Figure BDA0003755321660000088
λ h Thermal conductivity of fins of a heat sink;
equivalent convective heat transfer coefficient
Figure BDA0003755321660000089
Calculating the pilow number
Figure BDA00037553216600000810
Empirical parameters
Figure BDA00037553216600000811
Dimensionless number
Figure BDA00037553216600000812
Dimensionless number
Figure BDA00037553216600000813
Diffusion thermal resistance of heat sink substrate
Figure BDA0003755321660000091
Air side convective heat transfer thermal resistance
Figure BDA0003755321660000092
Heat radiator thermal resistance R h ＝R sp +R cov ；
Maximum temperature T on radiator max Is T max ＝Q*R h +T a Where Q is the heat source power consumption, T a Is ambient temperature;
therefore, from the above calculation, when the structural parameters of the radiator are determined, the heat resistance calculation mathematical model of the radiator is R h ＝f R (q) wherein f R Calculating the heat resistance of the radiator according to the air quantity q of the working point of the fan as a function of the heat resistance of the radiator on q, and further calculating the highest temperature T of the radiator max 。
Preferably, the mathematical model of the radiator is corrected;
substrate diffusion thermal resistance R sp In the calculation of (2), a non-circular substrate is requiredAnd the heat source are converted into a circle with equivalent area,
and the equivalent radius r of the heat source is practical s Is related to the distance x between the power modules and cannot be calculated accurately, so a quadratic polynomial a related to x is used 2 x 2 +a 1 x+a 0 To express its influence, i.e.
Figure BDA0003755321660000093
The maximum temperature of the heat sink is a function of x. Taking a plurality of different x values, establishing a thermal simulation model according to the structural parameters of the radiator to perform finite element simulation, and obtaining a correction coefficient a by adopting a least square method according to the temperature simulation result of the air-cooled radiator 2 、a 1 、a 0 And the error between the calculation result of the mathematical model and the simulation result is minimized.
According to another aspect of the present invention, a method for optimizing an air-cooled heat sink of a power device, as shown in fig. 3, includes the following steps:
the method comprises the following steps: determining the structural parameters of the radiator: the method comprises the following steps of (1) enabling the length L of a radiator, the width W of the radiator, the thickness t of a base plate, the height H of fins, the gaps b of the fins, the thickness d of the fins and the equivalent number n of the fins to be equal; determining the structural parameters of the heat source: power module length Ls, power module width Ws and power module distance x; establishing a mathematical model of the air-cooled radiator of the power device;
step two: determining the optimized variables of the radiator as the clearance b and the thickness d of the radiator fins; when other structural parameters of the radiator are known, the pressure drop calculation model of the radiator is delta P h ＝f h (q,b,d)，f h As a function of radiator pressure drop with respect to q, b, d;
simultaneous fan P-Q curve P = f fan (q) and radiator pressure drop calculation mathematical model such that P = Δ P h I.e. f h (q,b,d)＝f fan (q) solving for the fan operating point's air volume as a function of fin gap b and fin thickness d, i.e. q = f r (b,d)，f r Is a function of the air volume related to b and d;
the heat resistance calculation mathematical model of the radiator is R h ＝f R (q, b, d) powderThe maximum temperature on the heater Tmax is T max ＝Q*R h +T a Let q = f r (b, d) are substituted to obtain T max ＝f T (b,d)，f T As a function of the maximum temperature on the radiator with respect to b, d;
step three: selecting an optimization target, if the optimization target is the weight of the radiator, entering the fourth step, and if the optimization target is the highest temperature of the radiator, entering the fifth step;
step four: taking the weight m of the radiator as an optimization target, taking the highest temperature Tmax on the radiator as a constraint function, carrying out optimization calculation on the mathematical model of the radiator by an optimization design program based on Matlab programming, and obtaining a radiator structure with the lightest weight and the temperature not exceeding the constraint value; the method comprises the following specific steps:
the adopted optimization function is a nonlinear programming function fmincon in Matlab, and the constraint condition for constraining the variables is determined by the structural parameters and the heat dissipation performance parameters of the radiator, namely:
Figure BDA0003755321660000101
in the formula, x i To optimize variables; x is the number of min For optimizing the lower limit of the value of the variable, x max In order to optimize the upper limit of variable values, x is the fin gap b and the fin thickness d of the radiator; f. of m As a function of weight with respect to b and d, T 1 Is a temperature constraint value.
Step five: and (3) taking the maximum temperature Tmax on the radiator as an optimization target, taking the weight m of the radiator as a constraint function, carrying out an optimization design program based on Matlab programming on the mathematical model of the radiator, and carrying out optimization calculation to obtain a radiator structure with the weight not exceeding the constraint value and the lowest temperature. In particular to
The adopted optimization function is a nonlinear programming function fmincon in Matlab, and the constraint condition for constraining the variables is determined by the structural parameters and the heat dissipation performance parameters of the radiator, namely:
Figure BDA0003755321660000111
in the formula, x i To optimize variables; x is the number of min For optimizing the lower limit of the value of the variable, x max In order to optimize the upper limit of the variable value, x is the fin gap b and the fin thickness d of the radiator; f. of T As a function of temperature, b and d, m 1 Is a weight constraint value.
According to another aspect of the invention, the method for calculating the heat exchange performance of the air-cooled radiator of the power device can accurately calculate the performance parameters such as the highest temperature of the radiator, the pressure drop of the radiator, the thermal resistance of the radiator and the like by adopting the corrected mathematical model of the radiator under the condition that all structural parameters, fan curves and environmental conditions of a given radiator are known.
Example 1: optimization of structural parameters of heat radiator
For a heat sink, the structural parameters are: the width W =200mm of the radiator, the length L =300mm of the radiator, the thickness t =7mm of the base plate, the height H =30mm of the fin. The structural parameters of the heat source are as follows: length Ls =50mm, width Ws =50mm, and heat source distance x =15mm. The total power consumption of the heat source is 345 watts, and the ambient temperature is 20 ℃.
Determining the optimized variables of the radiator as the clearance b and the thickness d of the radiator fins;
and taking the minimum weight m of the radiator as an optimization target, taking the maximum temperature Tmax on the radiator not exceeding 55 ℃ as a constraint function, carrying out an optimization design program based on Matlab programming on the mathematical model of the radiator, and carrying out optimization calculation to obtain the radiator fin gap b meeting the requirement of 5.86mm and the radiator fin thickness d of 1mm.
Example 1: optimization of structural parameters of heat radiator
For a heat sink, the structural parameters are as follows: the width W =200mm of the radiator, the length L =300mm of the radiator, the thickness t =7mm of the base plate, the height H =30mm of the fin. The structural parameters of the heat source are as follows: length Ls =50mm, width Ws =50mm, and heat source distance x =15mm. The total power consumption of the heat source is 345 watts, and the ambient temperature is 20 ℃.
Determining the optimized variables of the radiator as the clearance b and the thickness d of the radiator fins;
and taking the minimum Tmax of the highest temperature on the radiator as an optimization target, taking the weight m of the radiator not more than 3kg as a constraint function, carrying out an optimization design program based on Matlab programming on the mathematical model of the radiator, and carrying out optimization calculation to obtain the radiator fin gap b meeting the requirement of 2mm and the radiator fin thickness d of 1.07mm.
Example 3: heat exchange performance calculation of heat sink
For a heat sink, the structural parameters are as follows: the radiator width W =200mm, the radiator length L =300mm, the base plate thickness t =6mm, the fin height H =31mm, the fin gap b =1.5mm, the fin thickness d =1mm. The structural parameters of the heat source are as follows: length Ls =50mm, width Ws =50mm, and heat source distance x =15mm. The total power consumption of the heat source is 345 watts, and the ambient temperature is 20 ℃.
The maximum temperature of the radiator calculated by adopting the corrected calculation model is 49.26 ℃, the maximum temperature of the radiator simulated by adopting software is 50.38 ℃, and the error is 2.23%.
Example 4: heat exchange performance calculation of heat sink
For a heat sink, the structural parameters are as follows: the radiator width W =200mm, the radiator length L =300mm, the base plate thickness t =8mm, the fin height H =29mm, the fin gap b =2mm, the fin thickness d =2mm. The structural parameters of the heat source are as follows: length Ls =50mm, width Ws =50mm, and heat source distance x =15mm. The total power consumption of the heat source is 345 watts, and the ambient temperature is 20 ℃.
The maximum temperature of the radiator calculated by adopting the corrected calculation model is 52.67 ℃, the maximum temperature of the radiator simulated by adopting software is 51.52 ℃, and the error is 2.24%.
Example 5: heat transfer performance calculation of heat sink
For a heat sink, the structural parameters are as follows: the radiator width W =200mm, the radiator length L =290mm, the base plate thickness t =10mm, the fin height H =27mm, the fin gap b =3mm, the fin thickness d =1mm. The structural parameters of the heat source are as follows: length Ls =50mm, width Ws =50mm, and heat source distance x =15mm. The total power consumption of the heat source is 345 watts, and the ambient temperature is 20 ℃.
The highest temperature of the radiator calculated by adopting the corrected calculation model is 47.895 ℃, the highest temperature of the radiator simulated by adopting software is 48.41 ℃, and the error is 1.07%.
The technical solutions of the present invention or similar technical solutions designed by those skilled in the art based on the teachings of the technical solutions of the present invention are all within the scope of the present invention to achieve the above technical effects.

Claims (9)

1. A power device air-cooled radiator model is characterized in that: the model comprises the following components: a radiator pressure drop calculation mathematical model and a thermal resistance calculation mathematical model;
the pressure drop calculation mathematical model comprises:
radiator pressure drop
Figure FDA0003755321650000011
Where ρ is air Is air density, constant, V ch Is the flow rate of the inlet of the fin gap,
Figure FDA0003755321650000012
f app in order to obtain an apparent coefficient of friction,
Figure FDA0003755321650000013
d h the diameter of the flow channel is the hydraulic diameter,
Figure FDA0003755321650000014
Re f the reynolds number is used for the pressure drop calculation,
Figure FDA0003755321650000015
wherein q is the fan air volume, k yn For kinematic air viscosity, the ambient temperature k is specified yn Is a constant;
kc1 is inlet drag lossCoefficient of loss
Figure FDA0003755321650000016
Kc2 is the outlet drag loss coefficient
Figure FDA0003755321650000017
Wherein L is the length of the radiator, W is the width of the radiator, t is the thickness of the base plate, H is the height of the fins, b is the gap between the fins, d is the thickness of the fins and n is the equivalent number of the fins, ls is the length of the power module, ws is the width of the power module, and x is the distance between the power modules; wherein
Figure FDA0003755321650000018
Radiator slot ratio
Figure FDA0003755321650000019
The thermal resistance calculation mathematical model comprises: the heat radiator thermal resistance Rh is the sum of the heat radiator substrate diffusion thermal resistance Rsp and the fin air side convection heat transfer thermal resistance Rcov;
diffusion thermal resistance of heat sink substrate
Figure FDA0003755321650000021
Air side heat convection heat transfer thermal resistance
Figure FDA0003755321650000022
In which there is no dimensional number
Figure FDA0003755321650000023
Dimensionless number
Figure FDA0003755321650000024
Calculating the pilow number
Figure FDA0003755321650000025
Empirical parameters
Figure FDA0003755321650000026
Equivalent convective heat transfer coefficient
Figure FDA0003755321650000027
Efficiency of fins
Figure FDA0003755321650000028
Wherein
Figure FDA0003755321650000029
λ h Heat conductivity of fins of a heat sink;
heat transfer coefficient by convection of air
Figure FDA00037553216500000210
Wherein λ is air The heat conductivity of air is constant, pr is a prandtl number and can be calculated from the specific heat capacity, the dynamic viscosity and the heat conductivity of the air;
equivalent radius of heat sink substrate
Figure FDA00037553216500000211
Equivalent radius of heat source
Figure FDA00037553216500000212
Dimensionless characteristic radius
Figure FDA00037553216500000213
Thickness of dimensionless substrate
Figure FDA00037553216500000214
Re L The reynolds number was used for the calculation of the thermal resistance,
Figure FDA00037553216500000215
2. the model of the power device air-cooled heat sink of claim 1, wherein: the equivalent radius r of the heat source in the diffusion thermal resistance model of the radiator substrate s In relation to the distance x between the power modules, the following is expressed by a quadratic polynomial:
Figure FDA0003755321650000031
taking a plurality of different x values, establishing a thermal simulation model according to the structural parameters of the radiator to perform finite element simulation, and obtaining a correction coefficient a by adopting a least square method according to the temperature simulation result of the air-cooled radiator 2 、a 1 、a 0 So as to minimize the error between the calculation result of the mathematical model and the simulation result, and determine the equivalent radius r of the heat source according to the correction coefficient s 。
3. The model of the power device air-cooled heat sink of claim 2, wherein: when the structural parameters of the radiator are determined, the pressure drop calculation model of the radiator is delta P h ＝f h (q) wherein f h As a function of radiator pressure drop with respect to q;
for the selected fan, its P-Q curve P = f fan (q) wherein P is fan pressure, f fan The P-Q curve of the simultaneous fan P = f as a function of the fan pressure with respect to Q fan (q) and radiator pressure drop calculation mathematical model such that P = Δ P h Then f is h (q)＝f fan And (q), solving the air quantity q of the working point of the fan and the pressure P.
4. The model of power device air-cooled heat sink of claim 3, wherein: maximum temperature T on radiator max Is T max ＝Q*R h +T a Where Q is the heat source power consumption, T a Is ambient temperature;
when the structural parameters of the radiator are determined, the heat resistance calculation mathematical model of the radiator is R h ＝f R (q) wherein f R Calculating the heat resistance of the radiator according to the air quantity q of the working point of the fan as a function of the heat resistance of the radiator on q, and further obtaining the highest temperature T of the radiator max 。
5. A power device air-cooled radiator optimization method is characterized in that: the method comprises the following steps:
the method comprises the following steps: determining the structural parameters of the radiator: the structure comprises a radiator length L, a radiator width W, a base plate thickness t, fin heights H, fin gaps b, fin thicknesses d and the equivalent number n of fins; determining the structural parameters of the heat source: power module length Ls, power module width Ws, and power module distance x; establishing a model of the heat sink of claim 1 or 2;
step two: determining the optimized variables of the radiator as a radiator fin gap b and a radiator fin thickness d;
step three: selecting an optimization target, if the optimization target is the weight of the radiator, entering the fourth step, and if the optimization target is the highest temperature of the radiator, entering the fifth step;
step four: taking the weight m of the radiator as an optimization target, taking the highest temperature Tmax on the radiator as a constraint function, carrying out optimization calculation on the mathematical model of the radiator by an optimization design program based on Matlab programming, and obtaining a radiator structure with the lightest weight and the temperature not exceeding the constraint value;
step five: and (3) taking the highest temperature Tmax on the radiator as an optimization target, taking the weight m of the radiator as a constraint function, carrying out an optimization design program based on Matlab programming on the mathematical model of the radiator, and carrying out optimization calculation to obtain a radiator structure with the lowest temperature and weight not exceeding a constraint value.
6. The method of claim 5, wherein: in the second step, heat dissipation is performedAfter the structural parameters are determined, the pressure drop calculation model of the radiator is delta P h ＝f h (q,b,d)，f h As a function of radiator pressure drop with respect to q, b, d;
simultaneous fan P-Q curve P = f fan (q) and radiator pressure drop calculation mathematical model such that P = Δ P h The solved air quantity q of the fan working point is a function of the fin gap b and the fin thickness d, and q = f r (b,d)，f r Is a function of the air volume related to b and d;
when the structural parameters of the radiator are determined, the heat resistance calculation mathematical model of the radiator is R h ＝f R (q,b,d)，f R As a function of the heat sink thermal resistance with respect to q, b, d; the maximum temperature Tmax on the radiator is T max ＝Q*R h +T a Where Q is the heat source power consumption, T a Is ambient temperature; q = f r (b, d) are substituted to obtain T max ＝f T (b,d)，f T As a function of the maximum temperature on the heat sink with respect to b, d.
7. The method of claim 6, wherein: in the fourth step, a nonlinear programming function fmincon in Matlab is used as an optimization function, and constraint conditions for constraining variables are determined by the structural parameters of the radiator and the heat dissipation performance parameters, wherein the constraint conditions are as follows:
Figure FDA0003755321650000041
in the formula, x i To optimize variables; x is the number of min For optimizing the lower limit of the value of the variable, x max In order to optimize the upper limit of variable values, x is the fin gap b and the fin thickness d of the radiator; f. of m As a function of weight with respect to b and d, T 1 Is a temperature constraint value.
8. The method of claim 6, wherein: in the fifth step, a nonlinear programming function fmincon in Matlab is used as an optimization function, and constraint conditions for constraining variables are determined by the structural parameters of the radiator and the heat dissipation performance parameters together, wherein the constraint conditions are as follows:
Figure FDA0003755321650000051
in the formula, x i To optimize variables; x is the number of min To optimize the lower bound of the variable values, x max In order to optimize the upper limit of variable values, x is the fin gap b and the fin thickness d of the radiator; f. of T M as a function of temperature with respect to b and d 1 Is a weight constraint value.
9. A method for calculating heat exchange performance of an air-cooled radiator of a power device is characterized by comprising the following steps: for a heat sink with known structural parameters, fan curves and environmental conditions, the modified mathematical model of claim 2 is used to calculate the heat sink maximum temperature, heat sink pressure drop and heat sink thermal resistance parameters.
CN202210856028.XA 2022-07-20 2022-07-20 Power device air-cooled radiator model, optimization method and performance calculation method Pending CN115358014A (en)

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Cited By (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN116738639A (en) * 2023-07-24 2023-09-12 哈尔滨工程大学 Loop heat pipe radiation radiating fin structure optimization design method and device
CN117172033A (en) * 2023-11-02 2023-12-05 北京蓝威技术有限公司 Fin radiator optimization method based on inverse distance weighted mean predictive thermal resistance
CN117320362A (en) * 2023-11-29 2023-12-29 四川赛狄信息技术股份公司 Heat dissipation case, determination method of heat dissipation part and signal processing equipment
CN117434110A (en) * 2023-12-19 2024-01-23 北京蓝威技术有限公司 Testing method for thermal resistance of serial liquid cooling radiator under forced convection

Cited By (7)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN116738639A (en) * 2023-07-24 2023-09-12 哈尔滨工程大学 Loop heat pipe radiation radiating fin structure optimization design method and device
CN117172033A (en) * 2023-11-02 2023-12-05 北京蓝威技术有限公司 Fin radiator optimization method based on inverse distance weighted mean predictive thermal resistance
CN117172033B (en) * 2023-11-02 2024-01-26 北京蓝威技术有限公司 Fin radiator optimization method based on inverse distance weighted mean predictive thermal resistance
CN117320362A (en) * 2023-11-29 2023-12-29 四川赛狄信息技术股份公司 Heat dissipation case, determination method of heat dissipation part and signal processing equipment
CN117320362B (en) * 2023-11-29 2024-02-13 四川赛狄信息技术股份公司 Heat dissipation case, determination method of heat dissipation part and signal processing equipment
CN117434110A (en) * 2023-12-19 2024-01-23 北京蓝威技术有限公司 Testing method for thermal resistance of serial liquid cooling radiator under forced convection
CN117434110B (en) * 2023-12-19 2024-03-08 北京蓝威技术有限公司 Testing method for thermal resistance of serial liquid cooling radiator under forced convection

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