arXiv subjects

Rene Pecnik

Publications and source records attributed to Rene Pecnik.

At least 19 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↗

arXiv2026

Generalized Tadmor Conditions and Structure-Preserving Numerical Fluxes for the Compressible Flow of Real Gases

We generalize Tadmor's algebraic numerical flux condition for entropy-conservative discretizations of conservation laws to a broader class of secondary structures, i.e. possibly non-convex secondary quantities whose evolution can consist of both conservative and non-conservative contributions. The resulting generalized Tadmor condition yields a discrete local balance law for secondary structures alongside the discrete conservation law that is solved. In contrast to the convex entropy setting, non-convex secondary quantities can have singular Hessians and non-injective gradients; this introduces an additional necessary structural requirement, which we term (discrete) null-consistency. Null-consistency constrains admissible numerical work terms and is required for the existence and well-posedness of fluxes satisfying the generalized Tadmor condition. To construct such fluxes in practice, we show how discrete gradient operators provide systematic construction methods even when some of the functions entering the secondary structure are arbitrary, as in compressible flow closed by an arbitrary equation of state. As an application, we derive an entropy-conserving and kinetic-energy-consistent numerical flux for the Euler equations with an arbitrary (non-ideal) equation of state. We demonstrate the performance of the resulting scheme on a set of supercritical/transcritical compressible-flow test cases using several non-ideal equations of state, including a fully turbulent transcritical flow with a state-of-the-art equation of state and models for viscosity and heat conductivity. Computations are performed with our new open-source, flexible, JAX-based, multi-GPU compressible flow solver for Helmholtz-based equations of state available at github.com/rbklein/HelmEOS2.

math.NA↗

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

Mean velocity profile in stably stratified turbulent channel flow

The Monin-Obukhov Similarity Theory (MOST) is a cornerstone of atmospheric science for describing turbulence in stable boundary layers. Extending MOST to stably stratified turbulent channel flows, however, is non-trivial due to confinement by solid walls and the much smaller turbulent length scales involved. In this study, we investigate the applicability of MOST in closed channels and identify where and to what extent the theory remains valid. A key finding is that the ratio of the half-channel height to the Obukhov length serves as a governing parameter for identifying distinct flow regions and determining the scaling of the mean velocity within them. Hence, we propose a closure relation to estimate this ratio directly from the governing input parameters: friction Reynolds and friction Richardson numbers ($Re_{\tau}$ and $Ri_{\tau}$). The framework is tested against a series of direct numerical simulations (DNS) across a range of $Re_{\tau}$ and $Ri_{\tau}$. The reconstructed velocity profiles enable accurate prediction of the skin friction coefficient crucial for quantifying pressure losses in stratified flows in engineering applications.

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 $\Lambda$-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↗

arXiv2025

Scaling of wall pressure and the peak of streamwise turbulence intensity in compressible wall flows

This paper develops scaling laws for wall-pressure root-mean-square (r.m.s.) and the peak of streamwise turbulence intensity, accounting for both variable-property and intrinsic compressibility effects -- those associated with changes in fluid volume due to pressure variations. To develop such scaling laws, we express the target quantities as an expansion series in powers of an appropriately defined Mach number. The leading-order term is represented using the scaling relations developed for incompressible flows, but with an effective Reynolds number. Higher-order terms capture intrinsic compressibility effects and are modeled as constant coefficients, calibrated using flow cases specifically designed to isolate these effects. The resulting scaling relations are shown to be accurate for a wide range of turbulent channel flows and boundary layers.

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 $\Lambda$-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 $\Lambda$-vortices. Nonetheless, transition to turbulence is not violent and is significantly delayed compared to the subcritical regime.

physics.flu-dyn↗

arXiv2024

Variable-property and intrinsic compressibility corrections for turbulence models using near-wall scaling theories

We introduce a novel approach to derive compressibility corrections for Reynolds-averaged Navier-Stokes (RANS) models. Using this approach, we derive variable-property corrections for wall-bounded flows that take into account the distinct scaling characteristics of the inner and outer layers, extending the earlier work of Otero Rodriguez et al. [Int. J. Heat Fluid Flow, 73, 2018]. We also propose modifying the eddy viscosity to account for changes in the near-wall damping of turbulence due to intrinsic compressibility effects. The resulting corrections are consistent with our recently proposed velocity transformation [Hasan et al., Phys. Rev. Fluids, 8, L112601, 2023] in the inner layer and the Van Driest velocity transformation in the outer layer. Furthermore, we address some important aspects related to the modeling of the energy equation, primarily focusing on the turbulent Prandtl number and the modeling of the source terms. Compared to the existing state-of-the-art compressibility corrections, the present corrections, combined with accurate modeling of the energy equation, lead to a significant improvement in the results for a wide range of turbulent boundary layers and channel flows. The proposed corrections have the potential to enhance modeling across a range of applications, involving low-speed flows with strong heat transfer, fluids at supercritical pressures, and supersonic and hypersonic flows.

physics.flu-dyn↗

arXiv2024

The stability of stratified horizontal flows of carbon dioxide at supercritical pressures

Fluids at supercritical pressures exhibit large variations in density near the pseudo critical line, such that buoyancy plays a crucial role in their fluid dynamics. Here, we experimentally investigate heat transfer and turbulence in horizontal hydrodynamically developed channel flows of carbon dioxide at 88.5 bar and 32.6{\deg}C, heated at either the top or bottom surface to induce a strong vertical density gradient. In order to visualise the flow and evaluate its heat transfer, shadowgraphy is used concurrently with surface temperature measurements. With moderate heating, the flow is found to strongly stratify for both heating configurations, with bulk Richardson numbers Ri reaching up to 100. When the carbon dioxide is heated from the bottom upwards, the resulting unstably stratified flow is found to be dominated by the increasingly prevalent secondary motion of thermal plumes, enhancing vertical mixing and progressively improving heat transfer compared to a neutrally buoyant setting. Conversely, stable stratification, induced by heating from the top, suppresses the vertical motion leading to deteriorated heat transfer that becomes invariant to the Reynolds number. The optical results provide novel insights into the complex dynamics of the directionally dependent heat transfer in the near-pseudo-critical region. These insights contribute to the reliable design of heat exchangers with highly property-variant fluids, which are critical for the decarbonisation of power and industrial heat. However, the results also highlight the need for further progress in the development of experimental techniques to generate reliable reference data for a broader range of non-ideal supercritical conditions.

physics.flu-dyn↗

arXiv2024

Entropy-Stable Model Reduction of One-Dimensional Hyperbolic Systems using Rational Quadratic Manifolds

In this work we propose a novel method to ensure important entropy inequalities are satisfied semi-discretely when constructing reduced order models (ROMs) on nonlinear reduced manifolds. We are in particular interested in ROMs of systems of nonlinear hyperbolic conservation laws. The so-called entropy stability property endows the semi-discrete ROMs with physically admissible behaviour. The method generalizes earlier results on entropy-stable ROMs constructed on linear spaces. The ROM works by evaluating the projected system on a well-chosen approximation of the state that ensures entropy stability. To ensure accuracy of the ROM after this approximation we locally enrich the tangent space of the reduced manifold with important quantities. Using numerical experiments on some well-known equations (the inviscid Burgers equation, shallow water equations and compressible Euler equations) we show the improved structure-preserving properties of our ROM compared to standard approaches and that our approximations have minimal impact on the accuracy of the ROM. We additionally generalize the recently proposed polynomial reduced manifolds to rational polynomial manifolds and show that this leads to an increase in accuracy for our experiments.

math.NA↗

arXiv2024

Intrinsic compressibility effects in near-wall turbulence

The impact of intrinsic compressibility effects -- changes in fluid volume due to pressure variations -- on high-speed wall-bounded turbulence has often been overlooked or incorrectly attributed to mean property variations. To unambiguously quantify these intrinsic compressibility effects, we perform direct numerical simulations of compressible turbulent channel flows with nearly uniform mean properties. Our simulations reveal that intrinsic compressibility effects yield a significant upward shift in the logarithmic mean velocity profile that can be attributed to the reduction in the turbulent shear stress. This reduction stems from the weakening of the near-wall quasi-streamwise vortices. We in turn attribute this weakening to the spontaneous opposition of sweeps and ejections from the near-wall expansions and contractions of the fluid, and provide a theoretical explanation for this mechanism. Our results also demonstrate that intrinsic compressibility effects are responsible for the increase in the inner-scaled streamwise turbulence intensity in compressible flows compared to incompressible flows, previously regarded to be an effect of mean property variations.

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↗

arXiv2023

Estimating mean profiles and fluxes in high-speed turbulent boundary layers using inner/outer-layer transformations

Accurately predicting drag and heat transfer for compressible high-speed flows is of utmost importance for a range of engineering applications. This requires the precise knowledge of the entire velocity and temperature profiles. A common approach is to use compressible velocity scaling laws (transformation), that inverse transform the velocity profile of an incompressible flow, together with a temperature-velocity relation. In this Note, we use distinct velocity transformations for the inner and outer layers. In the inner layer, we utilize a recently proposed scaling law that appropriately incorporates variable property and intrinsic compressibility effects, while the outer layer profile is inverse-transformed with the well-known Van Driest transformation. The result is an analytical expression for the mean shear valid in the entire boundary layer, which combined with a temperature-velocity relationship, provides predictions of mean velocity and temperature profiles at unprecedented accuracy. Using these profiles, drag and heat transfer is evaluated with an accuracy of +/-4% and +/-8%, respectively, for a wide range of compressible turbulent boundary layers up to Mach numbers of 14.

physics.flu-dyn↗

arXiv2023

Incorporating intrinsic compressibility effects in velocity transformations for wall-bounded turbulent flows

A transformation that relates a compressible wall-bounded turbulent flow with non-uniform fluid properties to an equivalent incompressible flow with uniform fluid properties is derived and validated. The transformation accounts for both variable-property and intrinsic compressibility effects, the latter being the key improvement over the current state-of-the-art. The importance of intrinsic compressibility effects contradicts the renowned Morkovin's hypothesis.

physics.flu-dyn↗

arXiv2023

The steady behavior of the supercritical carbon dioxide natural circulation loop

The steady state behavior of thermodynamically supercritical natural circulation loops (NCLs) is investigated in this work. Experimental steady state results with supercritical carbon dioxide are presented for reduced pressures in the range of 1.1-1.5, and temperatures in the range of 20-65 {\deg}C. Distinct thermodynamic states are reached by traversing a set of isochors. A generalized equation for the prediction of the steady state is presented, and its performance is assessed using empirical data. Changes of mass flow rate as a result of changes of thermodynamic state, heating- and driving height are shown to be accurately captured by the proposed predictive equation. However, the enhanced viscous losses in the instrumentation of the loop and in the proximity of heat transfer equipment are shown to significantly limit the steady state flow rate. Subsequently, the findings are put forward in aid of the development of safe, novel supercritical natural circulation facilities.

physics.flu-dyn↗

arXiv2022

Machine Learning for RANS Turbulence Modelling of Variable Property Flows

This paper presents a machine learning methodology to improve the predictions of traditional RANS turbulence models in channel flows subject to strong variations in their thermophysical properties. The developed formulation contains several improvements over the existing Field Inversion Machine Learning (FIML) frameworks described in the literature, as well as the derivation of a new modelling technique. We first showcase the use of efficient optimization routines to automatize the process of field inversion in the context of CFD, combined with the use of symbolic algebra solvers to generate sparse-efficient algebraic formulas to comply with the discrete adjoint method. The proposed neural network architecture is characterized by the use of an initial layer of logarithmic neurons followed by hyperbolic tangent neurons, which proves numerically stable. The machine learning predictions are then corrected using a novel weighted relaxation factor methodology, that recovers valuable information from otherwise spurious predictions. The study uses the K-fold cross-validation technique, which is beneficial for small datasets. The results show that the machine learning model acts as an excellent non-linear interpolator for DNS cases well-represented in the training set, and that moderate improvement margins are obtained for sparser DNS cases. It is concluded that the developed machine learning methodology corresponds to a valid alternative to improve RANS turbulence models in flows with strong variations in their thermophysical properties without introducing prior modeling assumptions into the system.

physics.flu-dyn↗

arXiv2018

A fast GPU Monte Carlo Radiative Heat Transfer Implementation for Coupling with Direct Numerical Simulation

We implemented a fast Reciprocal Monte Carlo algorithm, to accurately solve radiative heat transfer in turbulent flows of non-grey participating media that can be coupled to fully resolved turbulent flows, namely to Direct Numerical Simulation (DNS). The spectrally varying absorption coefficient is treated in a narrow-band fashion with a correlated-k distribution. The implementation is verified with analytical solutions and validated with results from literature and line-by-line Monte Carlo computations. The method is implemented on GPU with a thorough attention to memory transfer and computational efficiency. The bottlenecks that dominate the computational expenses are addressed and several techniques are proposed to optimize the GPU execution. By implementing the proposed algorithmic accelerations, a speed-up of up to 3 orders of magnitude can be achieved, while maintaining the same accuracy.

cs.CE↗

arXiv2018

Linear instability of Poiseuille flows with highly non-ideal fluids

The objective of this work is to investigate linear modal and algebraic instability in Poiseuille flows with fluids close to their vapour-liquid critical point. Close to this critical point, the ideal gas assumption does not hold and large non-ideal fluid behaviours occur. As a representative non-ideal fluid, we consider supercritical carbon dioxide (CO$_2$) at pressure of 80 bar, which is above its critical pressure of 73.9 bar. The Poiseuille flow is characterized by the Reynolds number ($Re=\rho_{w}^{*}u_{r}^{*}h^{*}/\mu_{w}^{*}$), the product of Prandtl ($Pr=\mu_{w}^{*}C_{pw}^{*}/\kappa_{w}^{*}$) and Eckert number ($Ec=u_{r}^{*2}/C_{pw}^{*}T_{w}^{*}$), and the wall temperature that in addition to pressure determines the thermodynamic reference condition. For low Eckert numbers, the flow is essentially isothermal and no difference with the well-known stability behaviour of incompressible flows is observed. However, if the Eckert number increases, the viscous heating causes gradients of thermodynamic and transport properties, and non-ideal gas effects become significant. Three regimes of the laminar base flow can be considered, subcritical (temperature in the channel is entirely below its pseudo-critical value), transcritical, and supercritical temperature regime. If compared to the linear stability of an ideal gas Poiseuille flow, we show that the base flow is more unstable in the subcritical regime, inviscid unstable in the transcritical regime, while significantly more stable in the supercritical regime. Following the corresponding states principle, we expect that qualitatively similar results will be obtained for other fluids at equivalent thermodynamic states.

physics.flu-dyn↗