Advancing Turbomachinery Meanline Modeling and Optimization with Automatic Differentiation

Srinivas Prakash Diwanji*, Lasse Borg Anderson , Roberto Agromayor, Fredrik Haglind

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingArticle in proceedingsResearchpeer-review

Abstract

Meanline modelling is vital in turbomachinery design process, enabling accurate and computationally efficient performance analysis and design optimization. In gradient-based optimization, accurate derivatives are crucial for finding optimal
solutions as inaccurate gradients, especially in high-dimensional simulations, can compromise optimization reliability, causing convergence issues. Obtaining exact derivatives analytically is often infeasible due to complexity of meanline models and equations of state, while numerical differentiation techniques like finite difference methods introduce inaccuracies due to truncation and round-off errors. To address these challenges, this paper introduces the first application of automatic differentiation in turbomachinery meanline optimization. Exact gradients were computed by differentiating an existing meanline model using the JAX library, and the performance of various gradient-based optimization solvers was compared by evaluating convergence with exact derivatives from automatic differentiation versus approximate derivatives from finite differences. Results for turbines involving 1-, 2-, and 3-stage configurations indicate that using exact gradients obtained using automatic differentiation significantly improves computational efficiency by reducing model evaluations by 25–50 % with respect to finite difference approximations, depending on turbine configuration and finite difference step size. additionally, the computational cost of gradient evaluations with automatic differentiation is significantly lower, as JAX optimizes code execution using Accelerated Linear Algebra. These findings demonstrate that the meanline model using automatic differentiation for gradient calculations leads to faster and more reliable convergence, paving the way for its use in complex flow problems like reversible and two-phase turbomachinery.
Original languageEnglish
Title of host publicationProceedings of the ASME Turbo Expo 2025
Number of pages12
PublisherThe American Society of Mechanical Engineers (ASME)
Publication statusAccepted/In press - 2025
EventASME Turbo Expo 2025: Turbomachinery Technical Conference and Exposition - Memphis, United States
Duration: 16 Jun 202520 Jun 2025

Conference

ConferenceASME Turbo Expo 2025
Country/TerritoryUnited States
CityMemphis
Period16/06/202520/06/2025

Keywords

  • Design optimization
  • Gradient-based
  • JAX
  • Jacobian
  • Axial turbine
  • Equation-oriented

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