An official website of the United States government
A novel numerical method is proposed for the solution of transient multi-physics problems involving heat conduction, electrical current sharing and Joule heating. The innovation consists of a mesh-free Monte Carlo approach that eliminates or drastically reduces the particle scattering requirements typical of conventional Monte-Carlo methods. The proposed algorithm encapsulates a volume around each point that affects the solution at a given point in the domain; the volume includes other points that represent small perturbations along the path of energy transfer. The proposed method is highly parallelizable and amenable for GPU computing, and its computational performance was substantially increased by the elimination of scattered interpolation. The accuracy and simulation time of the proposed method are compared against a finite element solution and also against experimental results from existing literature. The proposed method provides accuracy comparable to that of finite element methods, achieving an order of magnitude reduction in simulation time.
more »
« less
Development of complex-modeling with Fourier transform (CFT) for ultrafast simulation of transient energy transport
Solving transient energy transport is crucial for accurately predicting the behavior of materials and devices during thermal cycling, pulsed heating, and transient operational states where heat generation and dissipation rates vary over time. Traditional methods, like the finite difference and element methods, discretize space and time and update temperature values at each grid point iteratively over time steps. Its straightforward implementation makes it popular for solving heat transfer problems. However, when high temporal and spatial resolutions or prolonged heating durations are required, the computational demand rises significantly, leading to significantly greater resource consumption. To address this, in this work we develop a new method termed Complex-modeling with Fourier Transform (CFT) that enables rapid and efficient simulations of transient energy transport problems. The CFT method decomposes the periodical heating problem into a complex-temperature energy transport problem with a single harmonic heat source. 1D and 3D transient heat conduction problems (conjugated with hot carrier transfer) are solved using the CFT method to demonstrate its effectiveness. The CFT method produces similar or higher accuracy results compared with the finite difference method, while the computational speed is increased by more than two orders of magnitude. We also developed a new method termed Complex-modeling with Fourier and Heaviside Transforms (CFHT) that can solve any transient energy transport problems with orders of magnitude speed increase. The CFT and CFHT methods developed in this work are applicable to linear problems that could involve mechanical, thermal, optical, and electrical responses.
more »
« less
- PAR ID:
- 10635737
- Publisher / Repository:
- AIP
- Date Published:
- Journal Name:
- Journal of Applied Physics
- Volume:
- 138
- Issue:
- 1
- ISSN:
- 0021-8979
- Page Range / eLocation ID:
- 015104
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
null (Ed.)Modern digital manufacturing processes, such as additive manufacturing, are cyber-physical in nature and utilize complex, process-specific simulations for both design and manufacturing. Although computational simulations can be used to optimize these complex processes, they can take hours or days--an unreasonable cost for engineering teams leveraging iterative design processes. Hence, more rapid computational methods are necessary in areas where computation time presents a limiting factor. When existing data from historical examples is plentiful and reliable, supervised machine learning can be used to create surrogate models that can be evaluated orders of magnitude more rapidly than comparable finite element approaches. However, for applications that necessitate computationally- intensive simulations, even generating the training data necessary to train a supervised machine learning model can pose a significant barrier. Unsupervised methods, such as physics- informed neural networks, offer a shortcut in cases where training data is scarce or prohibitive. These novel neural networks are trained without the use of potentially expensive labels. Instead, physical principles are encoded directly into the loss function. This method substantially reduces the time required to develop a training dataset, while still achieving the evaluation speed that is typical of supervised machine learning surrogate models. We propose a new method for stochastically training and testing a convolutional physics-informed neural network using the transient 3D heat equation- to model temperature throughout a solid object over time. We demonstrate this approach by applying it to a transient thermal analysis model of the powder bed fusion manufacturing process.more » « less
-
Induction heating is one of the cleanest and most efficient methods for heating materials, utilizing electromagnetic fields induced through AC electric current. This article reports an analytical solution for transient heat transfer in a three‐dimensional (3D) cylindrical object under induction heating. A simplified form of Maxwell's equations is solved to determine the heat generation inside the cylinder by calculating the current density distribution within the body. The temperature within the solid is found from the solution of the unsteady heat equation based on Green's function. Owing to multiple spatial dimensions and time, a separation of variables technique is used to find Green's function. In addition, an innovative algorithm is proposed to take care of the variable material properties in analytical treatment. The analytical solution for temperature is verified with the data obtained from experiments for identical operating conditions. The analytical solution is used to study the impact of heat transfer coefficient and input AC current frequency and amplitude during transient heat diffusion. Our analytical solution suggests that the temperature‐dependent material properties significantly affect the thermal response within the solid. Unlike many other conventional heating methods, the thermal boundary condition changes with time in induction heating, which makes our solution much more challenging.more » « less
-
We present a spacetime DG method for 1D spatial domains and three linear hyperbolic, damped hyperbolic, and parabolic PDEs. The latter two correspond to Maxwell-Cattaneo-Vernotte (MCV) and Fourier heat conduction problems. The method is called the tent-pitcher spacetime DG method (tpSDG) due to its resemblance to the causal spacetime DG method (cSDG) wherein the solution advances in time by pitching spacetime patches. The tpSDG method extends the applicability of such methods from hyperbolic to parabolic and hyperbolic PDEs. For problems with a spatially uniform mesh, a transfer matrix approach is derived wherein the inflow, boundary, and source term values are mapped to the solution coefficient and output values. This resembles a finite difference scheme, but with grid points at the Gauss points of the spatial elements and arbitrarily tunable order of accuracy in spacetime. The spectral stability analysis of the method provides stability correction factors for the parabolic case. Numerical examples demonstrate the applicability of the method to problems with heterogeneous material properties.more » « less
-
Microstructured materials that can selectively control the optical properties are crucial for the development of thermal management systems in aerospace and space applications. However, due to the vast design space available for microstructures with varying material, wavelength, and temperature conditions relevant to thermal radiation, the microstructure design optimization becomes a very time-intensive process and with results for specific and limited conditions. Here, we develop a deep neural network to emulate the outputs of finite-difference time-domain simulations (FDTD). The network we show is the foundation of a machine learning based approach to microstructure design optimization for thermal radiation control. Our neural network differentiates materials using discrete inputs derived from the materials’ complex refractive index, enabling the model to build relationships between the microtexture’s geometry, wavelength, and material. Thus, material selection does not constrain our network and it is capable of accurately extrapolating optical properties for microstructures of materials not included in the training process. Our surrogate deep neural network can synthetically simulate over 1,000,000 distinct combinations of geometry, wavelength, temperature, and material in less than a minute, representing a speed increase of over 8 orders of magnitude compared to typical FDTD simulations. This speed enables us to perform sweeping thermal-optical optimizations rapidly to design advanced passive cooling or heating systems. The deep learning-based approach enables complex thermal and optical studies that would be impossible with conventional simulations and our network design can be used to effectively replace optical simulations for other microstructures.more » « less
- Free Publicly Accessible Full Text
-
Accepted Manuscript
- Journal Article:
- https://doi.org/10.1063/5.0275419
