This paper develops scaling laws for wall-pressure root mean square and the streamwise turbulence intensity peak, 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 modelled 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.

We investigate the controlled K-type breakdown of a flat-plate boundary-layer with highly non-ideal supercritical fluid. Direct numerical simulations are performed at a Mach number of M_∞=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-critical 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.

FluidsDraskic, M.Westerweel, J.Pecnik, R. display sharp, non-linear variations of thermodynamic properties when they are heated at a supercritical pressure. As such, near-pseudo-critical heat transfer is often characterized by large variations in density, leading to sharp near-wall accelerations or strong stratifications when buoyancy becomes dominant. We study the modulation of heat transfer and turbulence by non-negligible buoyancy in such property-variant flows, for the development of near-pseudo-critical heat exchangers for supercritical energy conversion systems. In particular, a liquid-like, horizontal base flow of carbon dioxide at 88.5 bar and 32.6 ^∘C is considered, which is subjected to a vertical heat flux of up to 12.0 kW/m² at Reynolds numbers of up to Re_Dh≤10.000. Here, optical- and surface temperature measurements are used concurrently to evaluate the flow. Integratced visualizations of the flow field show the onset of strong stratifications with limited heating rates in the near-pseudo-critical region. During unstable stratification, the channel flow is dominated by the upward motion of thermal plumes. When the stratification is stable, any vertical motion and turbulence present in an equivalent neutrally buoyant flow is suppressed. As a result, wall heat is removed more effectively in the unstably stratified configuration than in a forced convective flow, whereas the opposite is true for a stably stratified flow. The difference in the perceived heat transfer between the considered configurations increases as buoyancy becomes more dominant.

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. (Intl J. Heat Fluid Flow, 73, 2018, 114–123). 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, 2023, L112601) in the inner layer and the Van Driest velocity transformation in the outer layer. Furthermore, we address some important aspects related to the modelling of the energy equation, primarily focusing on the turbulent Prandtl number and the modelling of the source terms. Compared with the existing state-of-the-art compressibility corrections, the present corrections, combined with accurate modelling 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 modelling across a range of applications, involving low-speed flows with strong heat transfer, fluids at supercritical pressures, and supersonic and hypersonic flows.

Supercritical natural circulation loops (NCLs) promise passive cooling for critical systems like nuclear reactors and solar collectors, eliminating the need for mechanical pumps. However, instabilities similar to those seen in two-phase systems can emerge in supercritical NCLs, leading to undesirable oscillatory behaviour, marked by system-wide fluctuations in density, temperature, pressure, and flow rate. This study investigates the stability of NCLs at supercritical pressures (73.7≤p≤110.0bar) using CO₂ in an experimental setup with vertical cooling and vertically adjustable heaters to control convective flow rates and to oppose flow reversal. Oscillations were found to originate in the heater of the NCL, and demonstrated a high sensitivity to the thermodynamic state and proximity to the pseudo-critical line of the system. Increased mass flow rates and added resistance upstream of the heater suppressed the oscillations, while increased pressures and reduced heating rates dampened them. A static model which takes into account the non-ideality of the heat exchangers is introduced to assess the presence of multiple steady states. The system is concluded to be statically stable, and the oscillations are considered to be dynamically induced. In particular, the modulation of the NCL velocity by the traversal of the current oscillations in density is assumed to periodically re-incite non-ideality in the heater. These findings intend to refine our understanding of the stability boundaries in NCLs, to ensure a safer operation of prospective passive cooling and circulation systems employing fluids at supercritical pressure.

We present a massively parallel GPU-accelerated solver for direct numerical simulations of transitional and turbulent flat-plate boundary layers and channel flows involving fluids in non-ideal thermodynamic states. While several high-fidelity solvers are currently available as open source, all of them are restricted to the ideal-gas region. In contrast, the CUBic Equation of state Navier-Stokes solver (CUBENS) can accurately model and simulate the non-ideal thermodynamics of single-phase compressible fluids in the vicinity of the vapor-liquid saturation line or the thermodynamic critical point. By employing high-order finite-difference schemes and convective terms in split, kinetic-energy-, and entropy-preserving form, the solver is numerically stable, and robust with minimal numerical dissipation, enabling it to capture the steep variations of non-ideal thermodynamic properties. For cost-effective high-fidelity simulations, in addition to MPI parallelization, CUBENS is GPU-accelerated using OpenACC directives for computation offloading, and asynchronous GPU-aware MPI for efficient GPU-GPU communication. Moreover, CUBENS is compatible with both NVIDIA and AMD GPU architectures, achieving significant performance results while ensuring energy-efficient simulations. For instance, using 64 NVIDIA A100 GPUs compared to 8192 CPUs at the same computational cost results in a speedup of approximately 130×. In multi-node and multi-GPU configurations ranging from 2 to 128 compute nodes (8 to 512 GPUs), a strong scaling efficiency of around 52% and a weak scaling efficiency of 0.88 with 1024³ points per GPU, corresponding to approximately 5 billion degrees of freedom, are achieved. The CUBENS solver is validated against selected cases from the literature, covering transitional to turbulent ideal and non-ideal flows up to the transonic regime. In particular, we demonstrate the solver's suitability and applicability for direct numerical simulations of transitional boundary layers with fluids at supercritical pressure and with buoyancy effects. The development of this high-fidelity solver offers the potential for future fundamental research in non-ideal compressible fluid dynamics. Program summary: Program Title: CUBic Equation of state Navier-Stokes (CUBENS) CPC Library link to program files: https://doi.org/10.17632/6jfy758gyv.1 Developer's repository link: https://github.com/pcboldini/CUBENS Licensing provisions: MIT Programming language: Fortran 90, OpenACC, MPI, Python, MATLAB Nature of problem: This code solves the three-dimensional Navier-Stokes equations for non-ideal gas flows in a Cartesian domain, applicable to boundary layers and channels. Solution method: This code uses high-order central finite-differences with split-convective form, preserving kinetic energy and entropy (KEEP) and pressure-equilibrium-preserving (PEP) property, for spatial discretization. The time advancement is performed with a third-order Total Variation Diminishing low-storage Runge-Kutta scheme. Flow non-ideality is accounted for by cubic equations of state and complex transport-properties models. Alongside MPI parallelization, the solver is GPU-accelerated using OpenACC for computation offloading and CPU-GPU data transfer, along with GPU-aware MPI for GPU-GPU communication.

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∘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 with 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.

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.

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-amplitude 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.

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 quantify these intrinsic compressibility effects unambiguously, 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. In turn, we 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 play a crucial role in the increase in inner-scaled streamwise turbulence intensity in compressible flows, as compared with incompressible flows, which was previously regarded to be an effect of mean property variations alone.

This chapter focuses on modeling compressible wall-bounded turbulent flows. We first make the distinction between variable-property effects and intrinsic compressibility effects. Variable-property effects are associated with changes in density, viscosity, etc., primarily due to heat transfer, while intrinsic compressibility effects are associated with volume changes induced by pressure fluctuations. Both phenomena significantly impact turbulence and thus complicate turbulence modeling. The focus is on adapting Reynolds-averaged Navier-Stokes (RANS) models to account for these effects, which can also be applied to wall-modeled large eddy simulations (WMLES). Canonical flows are examined to illustrate the necessary modifications needed to incorporate compressibility effects into general RANS models. These improvements are applicable to many turbulence models and for complex flow geometries.

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. 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 their corresponding mean velocity scaling. Hence, we propose a relation to estimate this ratio directly from the governing input parameters: the friction Reynolds and friction Richardson numbers (Re_τ and Ri_τ). The framework is tested against a series of direct numerical simulations across a range of Re_τ and Ri_τ. The reconstructed velocity profiles enable accurate prediction of the skin-friction coefficient crucial for quantifying pressure losses in stratified flows in engineering applications.

Heating in industrial processes is responsible for approximately 13% of greenhouse gas emissions in Europe. Switching from fossil-fuel based boilers to heat pumps can help mitigate the effect of global warming. The present work proposes novel high-temperature transcritical heat pump cycles targeted at heating air with a mass flow rate of 10 kg/s up to 200 °C for spray drying processes. Four low-GWP refrigerants, R1233zd(E), R1336mzz(Z), n-Butane, and Ammonia are considered as the candidate working fluids. The pressure ratio of the compressor is optimized to achieve a maximum coefficient of performance (COP) for the four working fluids. A shell & tube heat exchanger is considered as the gas cooler. Using a generalized version of the ϵ-NTU method, the gas cooler is sized and a second law analysis is conducted. Striking a balance between the first- and second-law performance and size of the gas cooler, the R1233zd(E) transcritical heat pump cycle with a COP of 3.6 is judged to be the most promising option.

Experimental investigations into the characterization of vortices in hyperbolic funnels have shown efficient aeration properties. Certain regimes of vortices have been observed to exhibit high gas dissolution rates. This phenomenon has prompted inquiries into the underlying physical mechanisms at both micro and macroscopic scales. The present study employs computational fluid dynamics to numerically analyze the flow field organization inside these vortices, aiming to elucidate the observed high gas transfer rates. Transient simulations are performed on a three-dimensional radially structured hexahedral mesh, utilizing a multiphase Euler-Euler approach-based volume of fluid method for modeling, along with shear stress transport turbulence modeling based on k − ω equations with curvature correction. The evaluation of the two vortex regimes was conducted in terms of hydraulic retention time, water volume in the reactor, air-water interfacial area, and bulk mixing. Instabilities resembling Taylor vortices observed in Taylor-Couette flow systems emerge in the secondary flow field of these vortical structures, facilitating turbulent mixing. A qualitative analysis of the strength of these instabilities in terms of average vorticity per unit mass of water explains the high gas transfer efficiency. Despite high gas transfer rates, water exiting the funnel remains undersaturated under given operating conditions due to the short hydraulic retention time.

In the region close to the thermodynamic critical point and in the proximity of the pseudoboiling (Widom) line, strong property variations substantially alter the growth of modal instabilities, as revealed in Ren et al. [J. Fluid Mech. 871, 831 (2019)0022-112010.1017/jfm.2019.348]. Here, we study nonmodal disturbances in the spatial framework using an eigenvector decomposition of the linearized Navier-Stokes equations under the assumption of locally parallel flow. To account for nonideality, a new energy norm is derived. Several heat transfer scenarios at supercritical pressure are investigated, which are of practical relevance in technical applications. 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 (liquidlike), supercritical (gaslike), or transcritical (across the Widom line). The free-stream Mach number is set to 10-3. In the nontranscritical 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 suboptimal growth is observed over very short streamwise distances due to the Orr mechanism. Due to the additional presence of transcritical Mode II, the optimal energy growth at large distances is found to arise from an interplay between lift-up and Orr mechanism. As a result, optimal disturbances are streamwise-modulated streaks with strong thermal components and with a propagation angle inversely proportional to the local Reynolds number. The nonmodal growth is put in perspective with modal growth by means of an N-factor comparison. In the nontranscritical regimes, modal stability dominates regardless of a wall-temperature variation. In contrast, in the transcritical regime, nonmodal 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.

This paper presents numerical predictions of the flow field in the swirl-stabilized OP16 DLE combustor using hydrogen as a fuel. Computational Fluid Dynamics (CFD) simulations employing unsteady Reynolds-Averaged Navier-Stokes (URANS) and Wall Modelled Large Eddy Simulations (WMLES) are performed without including reaction mechanisms. The objective is to gain insights into scalar mixing predictions of the two approaches when hydrogen and air undergo shear-driven turbulent mixing. Accurate scalar mixing predictions are crucial in the combustors’ design process to assess the uniformity of fuel-air mixing as localized regions of high fuel concentrations can lead to increased NOx emissions and to identify locations with a propensity for Boundary Layer Flashback (BLF). Results are compared and analyzed in terms of time-averaged equivalence ratio, unmixedness and Turbulent Kinetic Energy (TKE) profiles. TKE predictions are lower in URANS, leading to significantly lower fuel-air mixing levels than WMLES, indicating differences in their predictions of shear-layer interactions in the mixing region and the swirl section of the combustor.

The competitiveness of hydrogen as a sustainable energy carrier depends greatly on its transportation and storage costs. Liquefying hydrogen offers advantages such as enhanced purity, versatility, and higher density, yet current industrial liquefaction processes face efficiency and cost challenges. Although various large-scale and efficient liquefaction concepts exist in the literature, they often overlook the economic and technical viability of such plants. Here, we addresses this issue by establishing a framework for modeling a large-scale hydrogen liquefaction concept and conducting both technical and economic assessments, with a specific focus on 125 tonnes per day (TPD) high-pressure hydrogen Claude-cycle concept. The technical analysis involves preliminary designs of key process components, while the economic assessment utilizes Aspen Process Economic Analyzer. Our findings indicate that at an electricity price of €0.1/kWh, the Claude-cycle liquefier concept yields a specific liquefaction cost (SLC) of €1.55/kg_LH2. A sensitivity analysis was performed, which shows that electricity price has a significant influence on the economics. Further investigation on the compressors design shows that incorporating high-speed centrifugal compressors could reduce the SLC by 5.42% and potentially more. Scaling up to 250 and 500 TPD reveals further cost improvements, while cost projections indicate substantial declines as the technology matures. Ultimately, this paper presents novel cost-scaling and experience curves of hydrogen liquefaction technology, demonstrating the compelling economic viability of integrating large-scale hydrogen liquefaction into sustainable energy infrastructure.

This paper addresses the stability of plane Couette flow in the presence of strong density and viscosity stratifications. It demonstrates the existence of a generalised inflection point that satisfies the generalised Fjørtoft criterion of instability when a minimum of kinematic viscosity is present in the base flow. The characteristic scales associated with this minimum are identified as the primary controlling parameters of the associated instability, regardless of the type of stratification. To support this finding, analytical stability models are derived in the long-wave approximation using piecewise linear base flows. Numerical stability calculations are carried out to validate these models and to provide further information on the production of disturbance vorticity. All instabilities are interpreted as arising from the interaction between two vorticity waves. Depending on the type of stratification, these two waves are produced by different physical mechanisms. When both strong density and viscosity stratifications are present, we show that they result from the concurrent action of shear and inertial baroclinic effects. The stability models developed for simple fluid models ultimately shed light on a recently observed unstable mode in supercritical fluids (Ren et al., J. Fluid Mech., vol. 871, 2019, pp. 831–864), providing a quantitative prediction of the stability diagram and identifying the dominant mechanisms at play. Furthermore, our study suggests that the minimum of kinematic viscosity reached at the Widom line in these fluids is the leading cause of their instability. The existence of similar instabilities in different fluids and flows (e.g. miscible fluids) is finally discussed.