A transient thermal management method and system for integrated chip microchannel fluid-structure interaction based on FDTD

Abstract

This invention discloses a transient thermal management method and system for integrated chip microchannel fluid-structure interaction based on FDTD. The method includes the following steps: constructing a three-dimensional microchannel cooling model, including solid and liquid regions; discretizing the three-dimensional microchannel cooling model and determining the time step required for simulation based on CFL stability conditions; deriving explicit finite-difference time-domain update formulas for both the solid and liquid regions to establish a solid-liquid transient coupling heat conduction numerical model; and obtaining the transient temperature distribution results of the cooling model based on the solid-liquid transient coupling heat conduction numerical model and the time step. This invention significantly improves the efficiency and accuracy of transient thermal analysis of microchannel cooling systems, greatly reducing memory usage and computation time while ensuring the accuracy of temperature distribution calculation results. It effectively supports the thermal management design and optimization of highly integrated electronic devices, while also possessing good numerical stability and convergence.

Description

Technical Field

[0001] This invention relates to the field of thermal management technology for electronic devices, and in particular to a transient thermal management method and system for integrated chip microchannel fluid-structure interaction based on FDTD. Background Technology

[0002] With the rapid development of information technology and integrated circuit technology, modern electronic devices are showing a trend towards high integration and miniaturization. This not only improves the functionality and performance of electronic devices but also brings unprecedented challenges to their thermal management. In particular, the multi-chip stacking in system-in-package (SiP) technology often leads to localized heat accumulation, causing problems such as overheating, thermal stress concentration, and solder joint fatigue. These problems not only affect the performance of the equipment but may also impact its reliability.

[0003] Traditional heat dissipation methods, such as air cooling and passive heat dissipation designs, are no longer sufficient to meet the heat dissipation efficiency requirements of modern electronic devices. In contrast, microchannel cooling technology offers a highly efficient solution based on heat conduction and convection, significantly improving heat dissipation capacity per unit area. In high-power integrated circuits and system-on-a-chip (SoC) packaging technologies, microchannel cooling utilizes the flow of microscale fluids within tiny channels to enhance heat exchange efficiency, making it an important thermal management technology.

[0004] However, the design and optimization of microchannel cooling systems rely on accurate simulation of complex heat-fluid couplings. Traditional thermal analysis methods typically refer to numerical computation techniques such as the finite element method (FEM) or finite difference method (FDM). However, these methods exhibit drawbacks when dealing with complex microchannel cooling systems, including high computational complexity, large memory consumption, and insufficient simulation accuracy. For example, commercial software COMSOL, based on implicit finite element methods, usually saves the entire system matrix during calculation, leading to significant memory consumption for large-scale complex models, especially when high simulation accuracy is required, significantly impacting simulation speed. The finite-difference time-domain method (FDTD) has become a better choice in the field of thermal analysis due to its explicit computation and efficient simulation capabilities. In microchannel cooling systems, the temperature distribution changes of fluids and solids are complex. The explicit computational characteristics of FDTD enable it to accurately calculate the instantaneous heat transfer process. During the calculation, the FDTD method uses an explicit algorithm, eliminating the need to solve the global matrix, greatly reducing memory requirements, and accurately simulating the transient response of the system, avoiding potential heat propagation lag issues. Summary of the Invention

[0005] The purpose of this invention is to provide an efficient thermal analysis method for microchannel cooling systems. By combining the finite-difference time-domain (FDTD) method and the Courant-Friedrichs-Lewy (CFL) stability condition, the transient heat conduction problem in the microchannel cooling model is accurately simulated, the thermal management design is optimized, and the problems of high memory consumption and low computational efficiency in traditional calculation methods are effectively solved.

[0006] To achieve the above objectives, this invention provides an integrated chip microchannel fluid-structure interaction transient thermal management method based on FDTD, comprising the following steps: A three-dimensional microchannel cooling model is constructed, which includes a solid region and a liquid region; The three-dimensional microchannel cooling model is discretized, and the time step required for simulation is determined by combining the CFL stability condition; Explicit time-domain finite-difference update formulas are derived for both the solid and liquid regions, and a numerical model of solid-liquid transient coupled heat conduction is established. Based on the solid-liquid transient coupled heat conduction numerical model and the time step, the transient temperature distribution results of the cooling model are obtained.

[0007] Preferably, the step of discretizing the three-dimensional microchannel cooling model includes: The transverse grid size is set to 1×10 based on the scale of heat conduction change. -5 m, vertical grid size is 1×10 -4 m; The three-dimensional microchannel cooling model was discretized according to the grid size, generating a total of 36,800 spatial grids.

[0008] Preferably, the steps for determining the time step required for the simulation include: in, Δt Indicates the unit time step; ρ Indicates the density of the material; Cp Indicates specific heat capacity; k Indicates thermal conductivity; Δx express x Orientation grid size; Δy express y Orientation grid size; Δz express z Orientation grid size 。

[0009] Preferably, the solid-liquid transient coupled heat conduction numerical model includes: In the formula, n Indicates the direction of the outward normal to the boundary;T Indicates temperature; g Indicates heat power density; i express x Number of grid cells in the direction; j express y Number of grid cells in the direction; u Indicates flow rate; , , They represent about x , y , z The second-order finite difference operator; in, px , py , pz As an intermediate value, the following calculation formula applies: w express x , y , z Three directions; Represents about variables w The second-order finite difference operator.

[0010] Preferably, the boundary conditions for the solid-liquid transient coupled heat conduction numerical model include: in, h This represents the heat transfer coefficient between a solid medium and a fluid flow. T solid Indicates the temperature of the solid medium; T fluid Indicates the temperature of the fluid.

[0011] The present invention also provides an integrated chip microchannel fluid-structure interaction transient thermal management system based on FDTD, the system being used to implement the above method, comprising: a construction module, a determination module, a derivation module, and an acquisition module; The building module is used to construct a three-dimensional microchannel cooling model, which includes solid and liquid regions. The determining module is used to discretize the three-dimensional microchannel cooling model and determine the time step required for simulation in combination with the CFL stability condition. The derivation module is used to derive explicit time-domain finite difference update formulas for the solid region and the liquid region respectively, and to establish a solid-liquid transient coupled heat conduction numerical model. The acquisition module is used to acquire the transient temperature distribution results of the cooling model based on the solid-liquid transient coupled heat conduction numerical model and the time step.

[0012] Compared with the prior art, the beneficial effects of the present invention are as follows: This invention significantly improves the efficiency and accuracy of transient thermal analysis of microchannel cooling systems. It can greatly reduce memory usage and computation time while ensuring the accuracy of temperature distribution calculation results, effectively supporting the thermal management design and optimization of highly integrated electronic devices. At the same time, it has good numerical stability and convergence, and is suitable for rapid simulation and analysis of complex solid-liquid coupled heat conduction scenarios. Attached Figure Description

[0013] To more clearly illustrate the technical solution of the present invention, the drawings used in the embodiments are briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0014] Figure 1 This is a schematic diagram of a microchannel cooling model according to an embodiment of the present invention; Figure 2 The transient temperature distribution results at the observation points of silicon, coolant and glass cover in this embodiment of the invention are shown; where (a) represents observation point T1; (b) represents observation point T2; (c) represents observation point T3; and (d) represents observation point T4. Detailed Implementation

[0015] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0016] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0017] Example 1 This embodiment provides a transient thermal management method for integrated chip microchannel fluid-structure interaction based on FDTD, the steps of which include: S1. Construct a three-dimensional microchannel cooling model, which includes a solid region and a liquid region.

[0018] A three-dimensional microchannel cooling model was established. The corresponding material parameters for the silicon substrate, coolant channels, and glass cover were set as shown in Table 1.

[0019] Table 1 .

[0020] S2. Discretize the three-dimensional microchannel cooling model and determine the time step required for simulation based on the CFL stability condition.

[0021] (1) Spatial dimensions Considering that the change in heat conduction is very small, the model requires a fine mesh, resulting in a transverse mesh size of 1×10⁻⁶. -5 m, vertical grid size 1×10 -4 m, with a total of 36,800 grid cells.

[0022] (2) Time step The time step obtained based on the modified CFL conditions is as follows: (1) Where, Δ t Indicates the unit time step; ρ Indicates the density of the material; Cp Indicates specific heat capacity; k Indicates thermal conductivity; Δ x express x Orientation grid size; Δ y express y Orientation grid size; Δ z Indicates the grid size in the z-direction 。

[0023] S3. Derive explicit time-domain finite difference update formulas for both the solid and liquid regions, and establish a numerical model for solid-liquid transient coupled heat conduction.

[0024] For integrated circuits and packaging structures that integrate microchannel cooling systems, the transient heat conduction control equation in solids can be expressed as: (2) in, T It's temperature. g It is the heat power density. i yes x Number of grids in the direction, j yes y Number of grids in the direction, t It's time.

[0025] The formula for the explicit finite-difference time-domain (FDTD) algorithm for solids is obtained by performing central differences in time and space on the heat conduction equation as follows: (3) In the formula, , , They represent about x , y , zThe second-order finite difference operator.

[0026] and px , py , pz As an intermediate value, the following calculation formula applies: (4) w express x , y , z Three directions; Represents about variables w The second-order finite difference operator.

[0027] (5) Where n is the direction of the outward normal to the boundary.

[0028] Assuming the fluid within the microchannel is incompressible, the corresponding transient conjugate heat conduction equation can be expressed as: (6) in, Represents the direction vector. c Indicates specific heat capacity. u The velocity represents the flow rate. If the ratio of the cross-sectional dimension to the length of the microchannel is very small, it can be assumed that the fluid flows longitudinally within the microchannel. The explicit FDTD formula obtained by performing central difference in time and space on the above solid-liquid coupling heat conduction equation is as follows: (7) S4. Based on the solid-liquid transient coupled heat conduction numerical model and the time step, obtain the transient temperature distribution results of the cooling model.

[0029] (1) Solid domain Apply heat flux density boundary to the bottom of the solid: heat flux density Q s = 50000 watts / rice 2 ; Top / bottom set as natural convection boundary: convection coefficient h = 10 watts / rice 2 Kelvin.

[0030] The heat flux density boundary condition, also known as the Neumann boundary condition, is expressed by the following formula: (8) in, Represents the direction vector; Represents the normal phase vector; Qs Γ1 represents the heat flux density; Γ1 represents the heat flux density boundary.

[0031] Assuming the heat flux density boundary is planar z = k Then the above equation simplifies to: (9) When an object comes into contact with a gas, and a temperature difference is formed between the object's boundary surface and the fluid surface, the convection boundary condition can be used for convective heat transfer analysis at the object's contact surface. The following formula expresses the relationship between heat flux density and temperature difference at the convective boundary surface: (10) Assuming a plane z = k As a convective boundary, T a Representing the ambient temperature at the convective boundary, the above equation can be simplified to: (11) (2) Fluid domain The coolant inlet is a constant temperature boundary surface with a temperature of 293.15 Kelvin.

[0032] An isothermal interface, also known as a Dirichlet boundary condition, indicates that the temperature of an object remains constant at the isothermal boundary. (12) in, T 0 Γ2 represents the constant temperature value on the boundary; Γ2 represents the isothermal interface.

[0033] Assuming the isothermal section is a plane z = k Then it can be simplified to: (13) (3) Solid-liquid coupling interface The solid-liquid interface is set as a convective boundary condition. For heat exchange between the solid medium and the fluid flow on the wall of the microchannel, it can be described using the convective boundary, and the equation of the convective boundary is as follows: MERGEFORMAT (14) in, h It is the heat transfer coefficient between the solid medium and the fluid flow. T solid It is the temperature of the solid medium. T fluid It is the temperature of the fluid.

[0034] Assume the convective boundary between the solid and the liquid is z = k Then the above equation simplifies to: (15) in h The average heat transfer coefficient is defined as: (16) in k f It is the thermal conductivity of the fluid in the microchannel.

[0035] For a fully developed, steady-state laminar fluid in a rectangular microchannel, the Nusselt number... Nu It is given by the following formula: (17) in α The aspect ratio (height) of the rectangular microchannel H With width W Hydraulic diameter of microchannels D h Defined as: (18) Considering that the fluid within the microchannel is incompressible and exhibits unidirectional laminar flow, the model assumes an average flow velocity of 0.1. m / s The dynamic viscosity of the coolant at 25°C is 8.9 × 10⁻⁶. -4 Pa・s From the above formula, we can see that the diameter in the water is 133. μm According to the Reynolds number calculation formula: (19) in, μ Indicates dynamic viscosity.

[0036] Calculations show that the Reynolds number in this study is 15, which is much less than 2300. The flow state of the liquid can be determined based on the Reynolds number. Only when Re > 4300 is it turbulent. For the low-speed laminar flow in this paper, the turbulence effect and compressibility effect can be ignored.

[0037] Experimental analysis showed that the simulation results obtained by the FDTD algorithm and the COMSOL method were highly consistent, which verified the accuracy of the FDTD method. In terms of efficiency, the FDTD method is more efficient than COMSOL and consumes less memory.

[0038] Example 2 To verify the effectiveness of the present invention, this embodiment is set up as a comparative experiment.

[0039] The simulation model selected in this embodiment is a bulk silicon with an embedded single microchannel structure, the structure of which is as follows: Figure 1 As shown in the figure. The structure includes a glass cover, silicon, and coolant material. The glass cover, placed above the microchannel, has a thickness of 0.175 mm. The coolant microchannel below the glass cover has a cross-sectional dimension of 0.1 mm × 0.2 mm and a length of 20 mm. The silicon thickness is 0.4 mm. The relevant thermal parameters of the structure are shown in Table 1.

[0040] Natural convection boundaries with a convection coefficient of 10 W / m²·K and an ambient temperature of 293.15 K were applied to the top and bottom of the model; the remaining surfaces were set as thermally insulating boundary conditions. Considering the small cross-sectional size of the microchannels, it was assumed that the coolant flow direction in the microchannels was along the y-axis with an average velocity of 0.1 m / s, and the inflow boundary of the microchannels was set as an isothermal boundary condition with a temperature of 293.15 K. A heat flux boundary surface with a heat flux density of 50000 W / m² was applied to the bottom surface of the model.

[0041] While maintaining computational accuracy, the FDTD method and COMSOL were compared in terms of memory usage and computation time, and the results are shown in Table 2. The results show that, with a simulation time of 0.05 s, the FDTD method significantly reduces memory usage and computation time compared to COMSOL while maintaining computational accuracy. Therefore, from an efficiency perspective, the FDTD method is more practically valuable than the finite element method used by COMSOL.

[0042] Table 2 .

[0043] To verify the numerical stability and convergence of the FDTD method, the CFL condition was strictly adhered to. This condition rigorously defines the maximum allowable time step size for the FDTD method; in this microchannel model, the time step should be less than 1e-7 s, otherwise, the error will grow exponentially. For an explicit FDTD method with first-order temporal accuracy and second-order spatial accuracy, truncation errors inevitably occur during discretization. To mitigate these errors, this paper systematically studies mesh refinement and adjusts the time step accordingly to satisfy the CFL condition. The results show that at the same observation point, when the spatial resolution is halved (from Δz = 12.5 μm to 6.25 μm), as shown in Table 3.

[0044] Table 3 .

[0045] By comparing the transient simulation results of the COMSOL and FDTD methods, samples were taken at 0mm, 10mm, and 20mm along the positive y-axis of the model, and the corresponding cross-sectional temperature distribution maps at 1s were obtained. The results show that the temperature distribution maps obtained by the two methods are basically consistent, indicating that the two algorithms have similar results in terms of temperature change trends.

[0046] Observation points (T1, T2, T3, T4) were sampled in the microchannel model, with coordinates of (0.1mm, 10mm, 0.125mm), (0.1mm, 10mm, 0.25mm), (0.1mm, 10mm, 0.375mm), and (0.1mm, 10mm, 0.5mm), respectively. T1 and T4 were located within a solid, while T2 and T3 were located within a liquid. After 1 second of simulation, all sampling points reached a steady state. The explicit FDTD simulation results for the sampling points were compared with the COMSOL results. Figure 2 The results show that the temperature change curves of the sample points in both methods are consistent, where (a) represents observation point T1; (b) represents observation point T2; (c) represents observation point T3; and (d) represents observation point T4. This indicates that the accuracy difference between the two methods is very small. Therefore, FDTD can be considered a reliable and general algorithm for accurately calculating transient temperature changes.

[0047] Example 3 This invention also provides an integrated chip microchannel fluid-structure interaction transient thermal management system based on FDTD, comprising: a construction module, a determination module, a derivation module, and an acquisition module; the construction module is used to construct a three-dimensional microchannel cooling model, the model including a solid region and a liquid region; the determination module is used to discretize the three-dimensional microchannel cooling model and determine the time step required for simulation in combination with CFL stability conditions; the derivation module is used to derive explicit time-domain finite difference update formulas for the solid region and the liquid region respectively, and establish a solid-liquid transient coupling heat conduction numerical model; the acquisition module is used to acquire the transient temperature distribution results of the cooling model based on the solid-liquid transient coupling heat conduction numerical model and the time step.

[0048] The embodiments described above are merely preferred embodiments of the present invention and are not intended to limit the scope of the present invention. Various modifications and improvements made to the technical solutions of the present invention by those skilled in the art without departing from the spirit of the present invention should fall within the protection scope defined by the claims of the present invention.

Claims

1. A transient thermal management method for integrated chip microchannel fluid-structure interaction based on FDTD, characterized in that, Includes the following steps: A three-dimensional microchannel cooling model is constructed, which includes a solid region and a liquid region; The three-dimensional microchannel cooling model is discretized, and the time step required for simulation is determined by combining the CFL stability condition; Explicit time-domain finite-difference update formulas are derived for both the solid and liquid regions, and a numerical model of solid-liquid transient coupled heat conduction is established. Based on the solid-liquid transient coupled heat conduction numerical model and the time step, the transient temperature distribution results of the cooling model are obtained.

2. The transient thermal management method for integrated chip microchannel fluid-structure interaction based on FDTD according to claim 1, characterized in that, The steps for discretizing the three-dimensional microchannel cooling model include: The transverse grid size is set to 1×10 based on the scale of heat conduction change. -5 m, vertical grid size is 1×10 -4 m; The three-dimensional microchannel cooling model was discretized according to the grid size, generating a total of 36,800 spatial grids.

3. The transient thermal management method for integrated chip microchannel fluid-structure interaction based on FDTD according to claim 1, characterized in that, The steps to determine the required time step for the simulation include: Where Δt represents the unit time step; ρ represents the density of the material; C p Δx represents specific heat capacity; k represents thermal conductivity; Δx represents the grid size in the x-direction; Δy represents the grid size in the y-direction; Δz represents the grid size in the z-direction.

4. The FDTD-based integrated chip microchannel fluid-structure interaction transient thermal management method according to claim 3, characterized in that, The solid-liquid transient coupled heat conduction numerical model includes: In the formula, n represents the outward normal direction of the boundary; T represents the temperature; g represents the thermal power density; i represents the number of grids in the x-direction; j represents the number of grids in the y-direction; and u represents the flow velocity. , , Let x, y, and z represent second-order finite difference operators, respectively. Where, p x p y p z As an intermediate value, the following calculation formula applies: w represents the three directions: x, y, and z; Let w represent a second-order finite difference operator with respect to the variable w.

5. The FDTD-based integrated chip microchannel fluid-structure interaction transient thermal management method according to claim 4, characterized in that, The boundary conditions for setting the solid-liquid transient coupled heat conduction numerical model include: Where h represents the heat transfer coefficient between the solid medium and the fluid flow; T solid T represents the temperature of a solid medium. fluid Indicates the temperature of the fluid.

6. An integrated chip microchannel fluid-structure interaction transient thermal management system based on FDTD, the system being used to implement the method according to any one of claims 1-5, characterized in that, include: Modules for building, determining, deriving, and obtaining; The building module is used to construct a three-dimensional microchannel cooling model, which includes solid and liquid regions. The determining module is used to discretize the three-dimensional microchannel cooling model and determine the time step required for simulation in combination with the CFL stability condition. The derivation module is used to derive explicit time-domain finite difference update formulas for the solid region and the liquid region respectively, and to establish a solid-liquid transient coupled heat conduction numerical model. The acquisition module is used to acquire the transient temperature distribution results of the cooling model based on the solid-liquid transient coupled heat conduction numerical model and the time step.

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