Advancing Turbomachinery Meanline Modeling and Optimization With Automatic Differentiation

Abstract

Abstract. Meanline modeling 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 article 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.