用插值DMD模型快速预测纳米流体在未知参数下的温度场。
Parametric Dynamic Mode Decomposition with multi-linear interpolation for prediction of thermal fields of Al2O3-water nanofluid flows at unseen parameters
- 结合多线性插值与动态模态分解，构建参数化预测模型。
- 在未见工况下，温度预测误差最高仅0.21%，努塞尔数误差6.08%。
- 适用于高精度热场预测，适合工程仿真加速场景。
本文提出一种数据驱动模型，将动态模态分解与多线性插值结合，用于预测阿尔法氧化铝-水纳米流体在未知雷诺数（Re）和颗粒体积浓度（ε）下的热场分布。研究对象为二维矩形通道内层流、不可压流动，底部壁面受均匀热通量。采用自研Fortran求解器进行模拟。对比了一维与二维参数空间下的两种模型性能。首先，基于线性插值的DMD-LI模型可在Re > 100条件下预测温度，与CFD求解器相比，在Re=960、ε=1.0%时最大温度差仅为0.0273%，平均努塞尔数误差仅0.39%。随后，引入双线性插值的DMD-BLI模型，支持Re > 100且ε > 0.5%的参数范围。在Re=800、ε=1.35%下，温度预测最大误差为0.21%，平均努塞尔数误差为6.08%。不同数据堆叠方式的影响也被评估，所有结果均详细报告，研究还提出了未来方向。
原文摘要 · Abstract (English)
The study proposes a data-driven model which combines the Dynamic Mode Decomposition with multi-linear interpolation to predict the thermal fields of nanofluid flows at unseen Reynolds numbers (Re) and particle volume concentrations ($ε$). The flow, considered for the study, is laminar and incompressible. The study employs an in-house Fortran-based solver to predict the thermal fields of Al$_2$O$_3$-water nanofluid flow through a two-dimensional rectangular channel, with the bottom wall subjected to a uniform heat flux. The performance of two models operating in one- and two-dimensional parametric spaces are investigated. Initially, a DMD with linear interpolation (DMD-LI) based solver is used for prediction of temperature of the nanofluid at any Re $>$ 100. The DMD-LI based model, predicts temperature fields with a maximum percentage difference of just 0.0273\%, in comparison with the CFD-based solver at Re =960, and $ε$ = 1.0\%. The corresponding difference in the average Nusselt numbers is only 0.39\%. Following that a DMD with bi-linear interpolation (DMD-BLI) based solver is used for prediction of temperature of the nanofluid at any Re $>$ 100 and $ε$ $>$ 0.5\%. The performance of two different ways of stacking the data are also examined. When compared to the CFD-based model, the DMD-BLI-based model predicts the temperature fields with a maximum percentage difference of 0.21 \%, at Re = 800 and $ε$ = 1.35\%. And the corresponding percentage difference in the average Nusselt number prediction is only 6.08\%. All the results are reported in detail. Along side the important conclusions, the future scope of the study is also listed.
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