Prediction of heat transfer to supercritical CO₂ flowing upward in a uniformly heated vertical tube

Prediction of heat transfer to supercritical CO₂ flowing upward in a uniformly heated vertical tube: Master thesis

Krijgsman, Floris (TU Delft Mechanical Engineering; TU Delft Cognitive Robotics)

Pecnik, Rene (mentor)
Peeters, J.W.R. (mentor)
Caesar, Holger (mentor)
Pourquie, M.J.B.M. (graduation committee)

Delft University of Technology

Mechanical Engineering | Vehicle Engineering | Cognitive Robotics

2024-05-01

Supercritical CO₂ (SCO₂) is a promising alternative to traditional working fluids in heat pumps and power cycles due to its high density, thermal efficiency, and stability. These properties allow for the design of more compact and efficient equipment. However, accurately modeling supercritical heat transfer, especially near its pseudocritical point, is challenging, because of extreme variations in its thermophysical properties. As a result of these inaccuracies in modeling, large fault margins must be taken into account, leading to overdesign of equipment.

Current methods for estimating heat transfer in such systems include empirical measurements, computational fluid dynamics (CFD), and Nusselt correlations. Although measurements provide accurate data, it is not a scalable solution. CFD methods offer this scalability. However, CFD cannot be applied in complex scenarios such as modeling of SCO₂ due to the trade-off between computational cost and accuracy. Nusselt correlations have low computational demand and are a scalable solution but come with low accuracy. Therefore, Nusselt correlations are not suitable for the design of equipment.

To overcome these limitations, this research applies a new model to predict heat transfer to SCO₂ flowing upward in a heated vertical tube. Current prediction methods use artificial neural networks (ANN). This research applies a convolutional neural network (CNN) for its ability to capture spatial context from the heat transfer trajectory. This property enables CNN to capture global and local patterns important for accurate prediction in SCO₂ heat transfer. In addition, the multiple kernels per layer enables the model to extract a large range of features from the heat transfer trajectory allowing for higher accuracy. The developed CNN model has shown superior performance, achieving an R² score of 0.970 and an MSE of 1477, outperforming existing ANNs and Nusselt correlations.

Furthermore, a feature importance study is done, to identify the nondimensional parameters that are important for heat transfer prediction The feature importance study highlighted the importance of parameters such as the Reynolds number and the Froude number in improving the model predictions. In addition, the feature importance study led to the development and identification of a new nondimensional parameter, (q_wk)/(T d), as one of the most important features influencing heat transfer. Furthermore, the experiments show that normalization is vital to enhance model stability and performance, countering issues such as exploding or vanishing gradients.

The findings in this research suggest great potential for using machine learning models to design more effective and compact heat transfer equipment. Future work will focus on a feature importance study for normalized, dimensional and nondimensional parameters for improved predictions. In addition, more synthetic data should be generated in the heat transfer detoriation and heat transfer enhancement areas for better prediction of those parts. Finally, a study into the application of machine learning models for designing heat transfer equipment should be done to show the benefits of such models.

prediction of heat transfer
Supercritical CO2
Convolutional Neural Networks (CNNs)
upward heated tube

http://resolver.tudelft.nl/uuid:8e05e3a7-5aba-4ccc-9d98-97d562d92300

Student theses

master thesis

© 2024 Floris Krijgsman