arXiv subjects

Pietro Carlo Boldini

Publications and source records attributed to Pietro Carlo Boldini.

5 recordsLinked to original sources

arXiv2026

A global mass-preserving numerical method for low-Mach-number real-gas flows in closed systems

A mass-preserving low-Mach-number framework is proposed for closed-system real-fluid flows governed by general nonlinear equations of state. The formulation enforces consistency between the spatially uniform thermodynamic pressure, the equation of state, and global mass conservation. Moreover, the numerical algorithm employs a segregated strategy in which the thermodynamic state is updated before the momentum equations, and the velocity field is advanced using a pressure-correction method. This approach enables an efficient solution procedure by decoupling the thermodynamic and momentum updates and retaining the use of FFT-based solvers for the pressure correction. The resulting formulation is implemented with second-order spatial accuracy. The implementation is first verified using the method of manufactured solutions, in which the thermodynamic state is prescribed through analytical density and thermodynamic-pressure fields, enabling verification of the nonlinear equation of state, thermodynamic-pressure evolution, and the low-Mach-number divergence constraint. The framework is subsequently validated against benchmark laminar and turbulent flows for both ideal and real fluids, particularly transcritical CO$_2$ channel flow, demonstrating its accuracy and robustness in the presence of strong thermodynamic nonlinearities.

physics.flu-dyn↗

arXiv2025

First-order buoyancy correction of modal instabilities in stratified boundary layers

We present a perturbation-based framework that captures buoyancy effects on modal instabilities in stratified boundary-layer flows within the fully compressible, non-Oberbeck-Boussinesq formulation. Treating the Richardson number as a small parameter and recasting the stability problem into an adjoint-residual form, we derive a first-order correction for the eigenvalues using only the neutrally buoyant eigenvalue problem. This eliminates the need to re-solve the eigenvalue problem at each stratification level. For ideal-gas boundary layers, the framework accurately predicts how stable and unstable stratification modifies Tollmien-Schlichting waves, from growth rates and eigenfunctions to $N$-factors, holding across a wide range of Prandtl numbers, temperature ratios, and Mach numbers. Notably, the buoyancy sensitivity varies strongly with Prandtl number, revealing that for a given Richardson number, buoyancy can switch from destabilising to stabilising depending on the fluid. Beyond ideal-gas conditions, we apply the first-order buoyancy correction to strongly stratified boundary layers with supercritical fluids, where the phase relationship between density and velocity perturbations determines whether buoyancy stabilises or destabilises the underlying instability. The resulting $N$-factors demonstrate, for the first time, that buoyancy significantly affects transition predictions under pseudo-boiling conditions.

physics.flu-dyn↗

arXiv2025

Direct numerical simulation of complete transition to turbulence with a fluid at supercritical pressure

The objective of this work is to investigate the unexplored laminar-to-turbulent transition of a heated flat-plate boundary layer with a fluid at supercritical pressure. Two temperature ranges are considered: a subcritical case, where the fluid remains entirely in the liquid-like regime, and a transcritical case, where the pseudo-critical (Widom) line is crossed and pseudo-boiling occurs. Fully compressible direct numerical simulations are used to study (i) the linear and nonlinear instabilities, (ii) the breakdown to turbulence, and (iii) the fully developed turbulent boundary layer. In the transcritical regime, two-dimensional forcing generates not only a train of billow-like structures around the Widom line, resembling Kelvin-Helmholtz instability, but also near-wall travelling regions of flow reversal. These spanwise-oriented billows dominate the early nonlinear stage. When high subharmonic three-dimensional forcing is applied, staggered $Λ$-vortices emerge more abruptly than in the subcritical case. However, unlike the classic H-type breakdown under zero pressure gradient observed in ideal-gas and subcritical regimes, the H-type breakdown is triggered by strong shear layers caused by flow reversals -- similar to that observed in adverse-pressure-gradient boundary layers. Without oblique wave forcing, transition is only slightly delayed and follows a naturally selected fundamental breakdown (K-type) scenario. Hence, in the transcritical regime, it is possible to trigger nonlinearities and achieve transition to turbulence relatively early using only a single two-dimensional wave that strongly amplifies background noise. In the fully turbulent region, we demonstrate that variable-property scaling accurately predicts turbulent skin-friction and heat-transfer coefficients.

physics.flu-dyn↗

arXiv2024

Direct Numerical Simulations of K-type transition in a flat-plate boundary layer with supercritical fluids

We investigate the controlled K-type breakdown of a flat-plate boundary-layer with highly non-ideal supercritical fluid at a reduced pressure of $p_{r,\infty}=1.10$. Direct numerical simulations are performed at a Mach number of $M_\infty=0.2$ for one subcritical (liquid-like regime) temperature profile and one strongly-stratified transcritical (pseudo-boiling) temperature profile with slightly heated wall. In the subcritical case, the formation of aligned $Λ$-vortices is delayed compared to the reference ideal-gas case of Sayadi et al. (J. Fluid Mech., vol. 724, 2013, pp. 480-509), with steady longitudinal modes dominating the late-transitional stage. When the wall temperature exceeds the pseudo-boiling temperature, streak secondary instabilities lead to the simultaneous development of additional hairpin vortices and near-wall streaky structures near the legs of the primary aligned $Λ$-vortices. Nonetheless, transition to turbulence is not violent and is significantly delayed compared to the subcritical regime.

physics.flu-dyn↗

arXiv2024

Transient growth in diabatic boundary layers with fluids at supercritical pressure

In the region close to the thermodynamic critical point and in the proximity of the pseudo-boiling (Widom) line, strong property variations substantially alter the growth of modal instabilities, as revealed in Ren et al. (J. Fluid Mech., vol. 871, 2019, pp. 831-864). Here, we study non-modal disturbances in the spatial framework using an eigenvector decomposition of the linearized Navier-Stokes equations under the assumption of locally parallel flow. The boundary layers with the fluid at supercritical pressure are heated or cooled by prescribing the wall and free-stream temperatures so that the temperature profile is either entirely subcritical (liquid-like), supercritical (gas-like), or transcritical (across the Widom line). The free-stream Mach number is set to $10^{-3}$. In the non-transcritical regimes, the resulting streamwise-independent streaks originate from the lift-up effect. Wall cooling enhances the energy amplification for both subcritical and supercritical regimes. When the temperature profile is increased beyond the Widom line, a strong sub-optimal growth is observed over very short streamwise distances due to the Orr mechanism. The non-modal growth is put in perspective with modal growth by means of an $N$-factor comparison. In the non-transcritical regimes, modal stability dominates regardless of a wall-temperature variation. In contrast, in the transcritical regime, non-modal $N$-factors are found to resemble the imposition of an adverse pressure gradient in the ideal-gas regime. When cooling beyond the Widom line, optimal growth is greatly enhanced, yet strong inviscid instability prevails. When heating beyond the Widom line, optimal growth could be sufficiently large to favor transition, particularly with a high free-stream turbulence level.

physics.flu-dyn↗