Session: 15-07 Numerical Studies of Internal Cooling

Paper Number: 122883

122883 - Direct Numerical Simulation of Air-Cooled and Air-Heated Channels 

Air-cooling and air-heating by forced thermal convection are common in several engineering applications, and they are the primary method for internal cooling of turbine blades. Preliminary design of cooling ducts is based on predictive formulas for the Nusselt number and the pressure drop, which are used for sizing the cooling passages. Among the most classical engineering formulas, we can certainly mention Dittus--Boelter and Gnielinski for the Nusselt number, and Prandtl friction formula for the pressure drop. Despite their widespread use, these formulas are based on the passive scalar hypothesis, which assumes constant fluid and thermodynamic properties, which are not valid conditions in turbine blade cooling. The effect of variable fluid properties is usually accounted for using empirical corrections to the passive scalar formulas; however, their accuracy is often questionable.

In this study, we use a combination of theory and high-fidelity data from compressible direct numerical simulation (DNS) to derive accurate predictive formulas for the Nusselt number and the skin-friction coefficient of cooling channels with variable thermodynamic and fluid properties. Unlike classical formulas which are based on the fitting of experimental or numerical data, we derive a solid theoretical framework for estimating the friction and heat transfer coefficients for any bulk-to-wall-temperature ratio. Moreover, the theory also returns the mean temperature and velocity profiles, which can be used for tabulated wall-functions in RANS simulations.

The new predictions are validated with DNS data of plane channel flow at friction Reynolds number 500 and 1000, for bulk-to-wall temperature ratios ranging between 0.3 and 3, showing deviations of the order of 1-2% compared to the DNS.

The robust theoretical foundation of the new predictive formulas ensures their accuracy, making them ideal for use with optimization tools. This allows for exploration of a vast parameter space without being limited by the confines of the original training dataset, which is often a concern with traditional formulas based on data fitting.

 

Presenting Author: Davide Modesti TU Delft

Presenting Author Biography: Davide Modesti is a tenured Assistant Professor in the Faculty of Aerospace Engineering at Delft University of Technology. He received his PhD in Theoretical and Applied Mechanics from La Sapienza Università di Roma in
2017, where he carried out direct numerical simulations of compressible wall-bounded flows at high Reynolds number. After completing his PhD, he has been a Research Fellow at DynFluid laboratory in Paris and at the University of Melbourne, before joining TU Delft in 2020. His research focuses on high-fidelity simulations of wall bounded turbulence, and on the development of numerical methods for computation fluid mechanics.

Authors:

Davide Modesti TU Delft
Sergio Pirozzoli Sapienza Universit`a di Roma