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August 7, 2023

Calculation of water-cooling thermal resistance of high-power IGBT radiator

Abstract: In order to optimize the heat dissipation capacity of the water-cooled radiator and ensure its reliable operation, the basic principles and formulas in heat transfer are cited, and the mechanical dimensions of the radiator shape, the forced convection heat transfer coefficient of water and the thermal conductivity of water are used as parameters and Variables derive the formula for calculating the heat sink's water-cooling thermal resistance. At the same time, in order to meet the practical application, a special water-cooled radiator thermal resistance calculation and curve drawing software has been developed, which can display various curves of thermal resistance changing with parameter changes, and can also directly calculate and display thermal resistance values. It provides an intuitive and convenient reference for the optimal selection of parameters in the design of the radiator.

Key words: water-cooled radiator; thermal resistance calculation; software; high-power IGBT radiator

Harmony electric locomotive is an AC-DC-AC inverter electric locomotive using high-power semiconductor technology. Because of its technical features such as advanced AC frequency conversion speed regulation, regenerative braking, high-power AC motor control and high degree of automation, it is widely used in high-speed and high-power locomotives in railway trunk line transportation. The converter of each locomotive uses three kinds of IGBT modules, namely: four-quadrant chopper (4QC) module, motor side inverter module (Inv) and auxiliary inverter module. Investigated the faults of 305 HXD1B electric locomotive converters in a certain locomotive depot from July 2009 to May 4, 2011, and found that a total of 4,880 modules were in use, with 255 faults, and the number of faults The IGBT module shows that at least one IGBT chip has failed. So far, there has been no module failure caused by reasons other than power semiconductor devices. This kind of failure increases with the increase of seasonal ambient temperature. It can be inferred that the failure of IGBT is closely related to its heat dissipation, so the cooling and digital heat of electronic devices have become one of the focuses of later research. By studying the cooling and heat dissipation problems of the device, the heat dissipation conditions are optimized and transformed, so that it can work as long as possible in an environment with a suitable temperature and reduce the incidence of accidents, which plays an important role in maintaining the safe operation of railway locomotives.

In this paper, through the analysis of the heat dissipation process of the high-power IGBT radiator, the basic principles and formulas in heat transfer are cited first, and the calculation of thermal resistance is divided into the heat conduction thermal resistance generated by the solid heat transfer process in the radiator and the radiator and cooling system. The convective heat transfer thermal resistance produced by the heat transfer process between the liquids is two parts, and the calculation of the radiator water cooling thermal resistance is deduced by taking the mechanical size of the radiator shape, the forced convective heat transfer coefficient of water and the thermal conductivity coefficient of water as parameters and variables formula. To simplify the analysis, software for thermal resistance calculations was compiled. The software has a simple and clear operation interface, which can display various curves of thermal resistance changing with parameters, and can also directly calculate and display thermal resistance values. It provides an intuitive and convenient reference for the design analysis of the radiator.

1 Basic formulas and principles of heat transfer

1.1 The principle and basic way of heat transfer

The basic formula for heat conduction is:

Q=KA△T／△L (1)

In the formula, Q represents the heat, that is, the heat generated or conducted by heat conduction; K is the thermal conductivity coefficient of the material. △T represents the temperature difference between the two ends; △L is the distance between the two ends. Convection refers to heat transfer in which a fluid (gas or liquid) comes into contact with a solid surface, causing the fluid to remove heat from the solid surface.

The formula for heat convection is:

Q=hA△T (2)

In the formula: Q still represents heat, that is, the heat taken away by heat convection; h is the value of heat convection coefficient; A is the effective contact area of heat convection; △T represents the temperature difference between the solid surface and the regional fluid.

1.2 Calculation of thermal resistance

Thermal resistance represents the resistance in the heat conduction process, and it is a comprehensive parameter that reflects the ability to prevent heat transfer. In order to simplify the analysis, after simplifying the radiator model, it is considered that there are two forms of convective heat transfer thermal resistance and thermal conduction thermal resistance. There is a heat conduction thermal resistance in the planar plate of the heat sink. The calculation formula is:

Rnd=L／KA (3)

In the formula: L represents the thickness of the radiator plate; K represents the thermal conductivity of the plate aluminum; A represents the cross-sectional area perpendicular to the direction of heat flow, that is, the area of the plate.

The thermal resistance between the water in the radiator and the heat sink is the convective heat transfer thermal resistance. The calculation formula is:

Rnv=1/hAs (4)

In the formula: As represents the total effective convective heat transfer area; h represents the convective heat transfer coefficient, which is related to the Nusselt number. According to the calculation formula of Nusselt number, the calculation formula of h can be inversely deduced as follows:

In the formula: Nu represents the Nusselt number; λf represents the thermal conductivity of the fluid; h here should be the thermal conductivity of water forced convection; Dh is the geometric characteristic length representing the heat transfer surface, here represents the hydraulic diameter of the pipe.

The total thermal resistance defining the heat sink is calculated as follows:

Rtd=RnvλfB+RndKB (6)

In the formula: B represents the width of the radiator, and other values are introduced earlier. When the outer dimensions of the radiator are fixed, it can be seen from formula (3) that Rnd is a certain value, and both K and B are fixed values. If λf is constant, the total thermal resistance of the radiator is directly related to Rnv. Let's look at the convective heat transfer thermal resistance of the radiator. From formula (5), formula (6) can get:

It can be seen from formula (7) that the thermal resistance of convective heat transfer is directly proportional to Dh and inversely proportional to As. It can be seen that the hydraulic diameter of the pipeline cannot be increased blindly in order to increase the amount of circulating water, so that a good cooling effect cannot be achieved. Reducing Rnv will correspondingly reduce the total thermal resistance of the radiator and enhance the heat dissipation effect. Substituting formula (3) and formula (7) into formula (6), the total thermal resistance calculation formula is:

Where: le represents the length of the radiator; λf is the thermal conductivity of water, and h is the forced convection heat transfer coefficient of water.

1.3 Calculation example

Generally, when the radiator of electronic equipment adopts the water-cooling heat dissipation method, the liquid circulation inside the radiator is divided into two types: series channel and parallel channel. As shown in Figure 1, the channel cross-sections of the two models are shown respectively. Among them, model A is a series water channel distribution, and the model is to add several cooling fins to each series water channel. The B model is that the parallel water channels only have straight channels, and the liquid flows through the parallel water channels from the water inlet to the water outlet.

The thermal conductivity of λf water is selected as 0.5W/mK, and the forced convection heat transfer coefficient of h water is 1 000 W/m2K. For the convenience of calculation, the small dimensions such as the thickness of the heat sink are ignored. The overall dimensions of the heat sink of the IGBT four-quadrant module for locomotives are L=0.005 m, L=0.55 m, and B=0.45 m. Since the external dimensions are the same, the difference in the thermal resistance between the series A model and the parallel B model lies in the difference in As. Set the area of the upper and lower panels of the inner wall of the radiator, the area of the front and rear panels, the area of the left and right panels, and the total area of the heat sink as As1, As2, As3, and As4, respectively. The series A model has 19 internal heat sinks. As1=0.495m2, As2=0.0432m2, As3=0.0528m2, As4=0.8208m2. The total effective cooling area becomes: As=As1+As2+As3+As4=1.4118 m2. Substituting each parameter into formula (9), the thermal resistance of the series A model is obtained as:

Model B, as can be seen from the screenshot of the velocity distribution, the water enters from the water inlet, and only flows through the middle 1/3 of the radiator, and the flow velocity of the other parts on the left and right sides is almost 0, which is negligible. In this way, the effective heat dissipation area of the upper and lower panels can be defined as 1/3 of the overall area, and the effective heat dissipation area of the front and rear panels is also 1/3 of the overall area. No water flow through the left and right panels does not count as the effective heat dissipation area. The effective number of water flow through the middle heat sink is 6 pieces. Then there are:

2 Software for solving heat sink thermal resistance and drawing thermal resistance curve

2.1 Interface form

The form of the main interface is shown in Figure 3. According to needs, this software mainly designs two functional modules. One is a module for calculating specific water-cooling thermal resistance values, and the other is a module for drawing water-cooling thermal resistance curves.

The interface of the radiator water-cooling thermal resistance calculation module is shown in Figure 4.

Among them, l is the length of the radiator, the unit is m; B is the width of the radiator, the unit is meter; L is the thickness of the radiator, the unit is meter; A is the total effective cooling area of the radiator, the unit is square meter; h is the water Forced convection heat transfer coefficient, unit W/m2K; λ is the thermal conductivity of water, unit is W/mK. The calculation result is the thermal resistance value of the water-cooled radiator, and the unit is cm2K/W. The function of this module has the nature of calculation, which can realize the calculation of the corresponding thermal resistance value of the radiator under the conditions of the geometrical size of the radiator, the forced convection heat transfer coefficient of water, and the thermal conductivity of water. The drawing module of the thermal resistance curve of the water-cooled radiator is shown in Figure 5 and Figure 6. The meaning of its parameters is the same as that in Figure 4. The water-cooled radiator curve gives the quantitative relationship between the total area of the radiator, the forced convection heat transfer coefficient of water, and the thermal resistance. Two problems are solved; for a radiator with a given effective heat dissipation area, in order to achieve a specific thermal resistance, how much water's forced convection heat transfer coefficient needs to be achieved, that is, how much pipe diameter is needed. For a specific forced convection heat transfer coefficient of water, how to control the thermal resistance through the heat dissipation area of the radiator.

2.2 Thermal Resistance Calculation Instructions

The drawing process of the thermal resistance curves in Fig. 5 and Fig. 6 is illustrated below with examples. In "1.3 Examples", the total thermal resistance of the series A model and the B model has been calculated. First, we fill in the corresponding blanks with the thermal conductivity of water λ=0.5 W/mk, L=0.005 m, ls=0.55 m, B=0.45 m. Then choose the curve type. Under different forced convection heat transfer coefficients of water, the relationship between the effective heat dissipation area of the radiator and the thermal resistance is shown in Figure 5. Under different effective heat dissipation areas, the relationship between the forced convection heat transfer coefficient of water and the thermal resistance is shown in Figure 6. There is also "Calculate Water Cooling Thermal Resistance" at the bottom left of the interface, click to enter the thermal resistance calculation interface, as shown in the figure. Fill in each parameter value as required: λ=0.5 W/mK, L=0.005 m, ls=0.55 m, B=0.45 m, h=1 000W/m2K when the input area is 1.4118 The calculated thermal resistance value is 92.502 801 066 337 cm2K/W, which is consistent with the calculation model A result of the above formula 92.503 cm2K/W.