Session: 34-09 High-fidelity CFD – General

Submission Number: 176112

Compressible Coriolis and Centrifugal Effects in Aeroengine-Like Rotating Boundary Layer Flows 

Rotating supersonic boundary layers (BLs) are fundamental to understanding compressible wall-bounded turbulence in turbomachinery, particularly within aeroengine and propulsion applications. However, most studies have focused on Coriolis and centrifugal effects in incompressible or subsonic regimes, or in complex geometries, leaving a gap in the analysis of rotating, compressible, supersonic canonical boundary layers. This work addresses that gap through direct numerical simulations (DNS) of a spatially developing supersonic turbulent BL over a flat plate in a rotating reference frame, providing the first systematic quantification of how rotation reorganizes the structure and energetics of compressible wall turbulence.

Simulations are performed using URANOS (Unsteady Robust All-around Navier–Stokes Solver), a high-order DNS/LES solver developed at the University of Padua. The code integrates the Navier–Stokes equations in conservative form, including Coriolis and centrifugal source terms. Convective fluxes are discretized using a sixth-order, fully split, nominally energy-preserving scheme, while viscous fluxes employ a semi-conservative sixth-order finite-difference method. Time integration uses a low-storage TVD Runge–Kutta algorithm.

The spatially developing rotating supersonic turbulent boundary layer is simulated at a inlet freestream Mach number Ma_∞ = 1.1, and the inflow friction Reynolds number to Re_τ = 250. The computational domain is defined in a Cartesian coordinate system, where x is the streamwise, y is wall-normal, and z is the spanwise direction. The computational domain spans L_x × L_y × L_z = 100δ₀ × 10δ₀ × 8δ₀, where δ₀ is the inlet boundary-layer thickness. The flow is solved in Cartesian coordinates with an adiabatic no-slip wall and periodic spanwise boundaries. Rotation is applied by solving the governing equations in a rotating frame with angular velocity Ω = (0, Ω, 0), corresponding to an axis located at (−200δ₀, 0, 0) (r = 200δ₀, δ₀/r = 5×10^-3), representative of turbomachinery conditions. Four cases are examined for rotational Mach numbers Ma_rot = {0.0, 0.2, 0.4, 0.6}, keeping all other parameters constant. Flow statistics are extracted at a streamwise station where Re_τ = 450.

Rotation induces a progressive acceleration of the mean velocity across the boundary layer while preserving the self-similar near-wall scaling when normalized by the friction velocity u_T​. The outer region undergoes a mild thinning, reflected by a decrease in momentum thickness and a corresponding increase in shape factor with increasing rotation rate. Using the van Driest II transformation, the skin friction coefficient collapses cleanly at all 𝑀𝑎_𝑟𝑜𝑡 and follows the expected incompressible law.

Reynolds stresses reveal a consistent damping effect: the streamwise component retains its inner peak location but exhibits reduced energy in the outer layer, while wall-normal and spanwise components—as well as the primary Reynolds shear stress—decrease monotonically with rotation. In contrast, the turbulent transport in the y-w plane and u-w plane, negligible in non-rotating flows, acquire measurable magnitude for higher 𝑀𝑎_𝑟𝑜𝑡, highlighting enhanced three-dimensional coupling between fluctuating velocity components.

The analysis of two-point velocity correlations reveals that the position of the first zero crossing shifts to smaller spanwise separations, indicating reduced spanwise coherence of near-wall fluctuations. This suggests that rotation leads to more compact, localized turbulent structures.

The turbulent kinetic-energy budget confirms that rotation predominantly suppresses the production term, while viscous dissipation remains nearly unchanged. Thermodynamic fluctuations—quantified through the r.m.s. of pressure, density, and temperature—are progressively attenuated by rotation. Notably, the inner layer peak of the density fluctuations decreses more rapidly than the one in the outer layer peak for higher 𝑀𝑎_𝑟𝑜𝑡.

Overall, the simulations provide a first DNS dataset for spatially developing rotating supersonic boundary layers, revealing how rotation modifies anisotropy, inter-component coupling, and the exchange of mechanical and thermal energy. These results deliver new physical understanding of rotation–compressibility interaction and supply high-fidelity reference data for the development and calibration of turbulence models in rotating, compressible regimes relevant to turbomachinery flows.

Presenting Author: Stefano Regazzo University of Padua

Presenting Author Biography: Stefano Regazzo is a Ph.D. student in Industrial Engineering at the University of Padua, Italy, under the supervision of Prof. Ernesto Benini and co-supervision of PhD Francesco De Vanna. His research focuses on high-fidelity DNS-LES and RANS-based Computational Fluid Dynamics for turbomachinery and aerodynamic applications. He contributes to the development of the in-house solver URANOS, developed by PhD Francesco De Vanna, and has experience in DNS and LES of compressible/supersonic and rotating flows for turbomachinery applications.

Authors:

Stefano Regazzo University of Padua
Francesco De Vanna University of Padua
Ernesto Benini University of Padua