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Deep learning based hybrid POD-LSTM framework for laminar natural convection flow in a rectangular enclosure

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Published/Copyright: November 11, 2024
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Chemical Product and Process Modeling
From the journal Chemical Product and Process Modeling Volume 20 Issue 2

Abstract

Laminar natural convection in side-heated enclosures is characterized by transient phenomena of the working fluid till it reaches steady state. The side heating can done in several ways the most common way being heating one end at constant temperature and cooling the other end. One of the other ways is heating both sides of the enclosure at a constant heat flux. Mathematical modeling of such problems using Computational Fluid Dynamics (CFD) essentially involves considerable amount of computational time and power to predict the flow phenomena observed in actual experimentation. In the last few years, data driven model frameworks have proven to be anefficient way in saving both time and computational cost in several applications. In the present study, a data driven model framework using a combination of unsupervised machine learning (using Proper Orthogonal Decomposition [POD]) and supervised deep learning models (using Long Short Term Memory [LSTM]) has been developed and referred to as POD-LSTM framework. The selection of a few dominant spatial bases and accompanying temporal modes provides us with a reduced order model of the system. The flow is then reconstructed and compared with results of CFD simulations. The Rayleigh number (Ra) chosen for the study is 3.27 × 1010. The estimated time to reach stedy state for this Ra number is 15,000 s. The POD-LSTM framework is trained using data obtained from a validated CFD model for the first 1,000 s. The trained model was then tested to predict temporal dynamics for the entire 15,000 s. The predictions provided by POD-LSTM framework were found upto 98 % accurate compared to the ones predicted by CFD. The computational time and power was however an order of magnitude lower for the POD-LSTM framework than that required for the CFD model.

Keywords: CFD; laminar natural convection; deep learning; long short term memory (LSTM); proper orthogonal decomposition (POD); side heated enclosures
Corresponding author: Arijit A. Ganguli, Institute of Chemical Technology, Matunga, Mumbai 400 019, India; and School of Engineering and Applied Sciences, Ahmedabad University, Ahmedabad, Gujarat, India, E-mail:

Acknowledgments

The authors acknowledge the resources provided by their respective organizations for carrying out this work.

  1. Research ethics: Not applicable.

  2. Informed consent: Not applicable.

  3. Author contributions: All authors have accepted responsibility for the entire content of this manuscript and approved its submission.

  4. Use of Large Language Models, AI and Machine Learning Tools: None declared.

  5. Conflict of interest: The authors state no conflict of interest.

  6. Research funding: None declared.

  7. Data availability: The datasets generated and/or analyzed during the current study are available from the corresponding author on reasonable request.

Notations

A

Snapshot data matrix

a 1k

Kth Modal coefficient for velocity

a k ( σ + 1 )

Kth Modal coefficient for lookback time window

y k ( n + 1 ) ˆ

LSTM prediction

b

Bias vectors for each gates

F

Output gate

I

Input gate

O

Output gate

c

Cell activation vector

h

Cell output

‘h’

Heat transfer coefficient, W m−2 K−1

k

Thermal conductivity, W m−1 K−1

M

Trained model

m k ( n )

Gate function

N

Number of snapshots or components

n

nth component

n λ

the total number of node points

R

Largest number of energy containing eddies

Y

Output sequential data matrix

T

Temperature K

t

Time (s)

V

Vector matrix

W

Weight matrices for each gates

Subscripts

k

Denotes the kth component for a coefficient e.g. modal coefficient

c

Subscript which denotes cell state

j

Denotes row component in a matrix

i

iteration variable having values from 1 to n λ for equation (20)

Greek symbols

Ϛ

Logistic sigmoid function

ξ

Tan-hyperbolic function used in cell state definition

σ

Lookback time-window

χ k ( n )

Input sequential data matrix

∅2k

Orthogonal POD basis function for temperature

∅1k

Orthogonal POD basis function for velocity

λ k

Scaling factor to guarantee the orthogonality of PODmodes

⨀

Element-wise product of vectors

Abbreviations

ANN

Artificial Neural Network

CFD

Computational Fluid Dynamics

LSTM

Long Short Term Memory

NIROM

Nonintrusive Reduced Order Model

RMSE

Root Mean Square Error

ROM

Reduced Order Model

POD

Proper Orthogonal Decomposition

SSIM

Structural Similarity Index

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Received: 2023-12-30
Accepted: 2024-10-15
Published Online: 2024-11-11

© 2024 Walter de Gruyter GmbH, Berlin/Boston

Articles in the same Issue

  1. Frontmatter
  2. Editorial
  3. CPPM special issue in honor of Professor Eugeny Kenig
  4. Review
  5. Capture and catalytic conversion of CO2 from marine and offshore applications – A review
  6. Research Articles
  7. Deep learning based hybrid POD-LSTM framework for laminar natural convection flow in a rectangular enclosure
  8. Application of CFD simulation to predict the fluid dynamics of tube columns with stacked packings for gas-liquid systems
  9. High order moment conserving method of classes in CFD code
  10. A framework for validating efficiency models of thermal separation columns with tray internals
  11. A systematic selection and decision matrix for energy-efficient intensified distillation technologies
  12. Capillary flow in corners slowed down by gravity and evaporation
https://doi.org/10.1515/cppm-2023-0102
Keywords for this article
CFD; laminar natural convection; deep learning; long short term memory (LSTM); proper orthogonal decomposition (POD); side heated enclosures

Articles in the same Issue

  1. Frontmatter
  2. Editorial
  3. CPPM special issue in honor of Professor Eugeny Kenig
  4. Review
  5. Capture and catalytic conversion of CO2 from marine and offshore applications – A review
  6. Research Articles
  7. Deep learning based hybrid POD-LSTM framework for laminar natural convection flow in a rectangular enclosure
  8. Application of CFD simulation to predict the fluid dynamics of tube columns with stacked packings for gas-liquid systems
  9. High order moment conserving method of classes in CFD code
  10. A framework for validating efficiency models of thermal separation columns with tray internals
  11. A systematic selection and decision matrix for energy-efficient intensified distillation technologies
  12. Capillary flow in corners slowed down by gravity and evaporation
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