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.

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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.@en

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.

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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.

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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.

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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.@en

There was an omission in the original publication [1]. The authors showed SOTR values in a figure but did not mention how these values were calculated. As a consequence, the calculations based upon the SOTR also need to be more specific, which is why “the twisted regime of” has been added in front of “the hyperbolic funnel”. An addition has been made to the paper as Supplementary Information where this information has been added, Section 3, Paragraph 5: Figure 4 shows K_La and SOTR values (see Supplementary Information for details) dependent also as a function of flow rate. Average K_La values (for 20 °C) for air jet, impellers and paddle aerators [12] are shown for comparison. The plot shows that the K_La values obtained with the free surface vortex in a hyperbolically shaped funnel are considerably higher than those of the three commercial systems used for comparison, especially in the twisted regime. These high oxygen transfer rates are a consequence of the aforementioned combination of high area-to-volume ratios and possibly enhanced turbulence close to the interface. On the other hand, the SOTR values (up to 0.5 kg/h) [12] are comparable to air jet system and lower than those reported for impeller and paddle systems (between 1.0 and 2.5 kg/h) [12]. This is due to the short hydraulic retention times in the hyperbolic funnel (typically less than a minute). A possibility to increase the SOTR value is the application of a cascade of funnels which would multiply the HRT with a factor representing the number of funnels, whilst maintaining the desired flow regime and thus the K_La value. For practical applications the specific energy demand of such a cascade can be estimated as follows: The twisted regime of the hyperbolic funnel tested in this work has a specific energy demand of 0.01 kWh/kg O₂ (see Appendix A for calculation details). In comparison, the specific energy demands of mechanical aerators range from 0.42 to 0.83 kWh/kg O₂ [13] and the specific energy demands of air jets range from 0.74 to 1.0 kWh/kg O₂ [12]. However, the industrial applicability of this system depends on its scalability to higher flow rates in larger funnels on the one hand, and on the possibility to achieve the described regimes with liquids of different viscosities as found in wastewater streams on the other. Thus, while the potential improvements in the energy efficiency of the aeration process seem promising, further work is required for confirmation and to exclude negative impacts on the sludge characteristics and WWTP performances. The authors state that the scientific conclusions are unaffected. This correction was approved by the Academic Editor. The original publication has also been updated. Supplementary Materials: The following supporting information can be downloaded at: https://www.mdpi.com/article/10.3390/w14050771/s1, The calculation method of SOTR values.

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Isentropic processes in thermodynamics are fundamental to our understanding of numerous physical phenomena across different scientific and engineering fields. They provide a theoretical reference case for the evaluation of real thermodynamic processes and observations. Yet, as analytical relations for isentropic transformations in gas dynamics are limited to ideal gases, the inability to analytically describe isentropic processes for non-ideal gases is a fundamental shortcoming. This work presents generalised isentropic relations in thermodynamics based on the work by Kouremenos et al., where three isentropic exponents γPv, γTv and γPT are introduced to replace the ideal gas isentropic exponent γ to incorporate the departure from the non-ideal gas behaviour. The general applicability of the generalised isentropic relations is presented by exploring its connections to existing isentropic models for ideal gases and incompressible liquids. Generalised formulations for the speed of sound, the Bernoulli equation, compressible isentropic flow transformations, and isentropic work are presented thereafter, connecting previously disjoint theories for gases and liquids. Lastly, the generalised expressions are demonstrated for practical engineering examples, and their accuracy is discussed.@en

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. 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. Additionally, we introduce L2 regularization to mitigate over-fitting and to reduce the importance of non-essential features. In order to analyze the results of our deep learning system, we utilize 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. In the most successful case, the L-infinity modeling error on the velocity profile was reduced from 23.4% to 4.0%. 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.

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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 ^◦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.

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A transformation that relates a compressible wall-bounded turbulent flow with nonuniform 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.

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Aeration is one of the most cost intensive steps in water and wastewater treatment due to the large energy requirement for the creation of large surfaces for sufficient gas exchange as well as for providing efficient liquid transport in order to exchange saturated liquid elements at the surface with unsaturated ones from the bulk. In this work we show that geometrically constrained vortices in a hyperbolic funnel are a promising aeration technique as they meet these criteria and allow oxygen transfer coefficients up to 50 h⁻¹, a number significantly higher than that of comparable methods like air jets or impellers (<10 h⁻¹).

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Ren et al. (2019) recently studied the stability of the boundary layer flow over a flat plate for supercritical CO2. While only one unstable mode usually exists for boundary layer flows, the authors found an additional unstable mode, whose origin has so far not been identified. In the present work, we carry out a stability analysis in the general case of a fluid following the Van der Waals equation of state and flowing over a heated flat plate in the limit of zero Eckert number. In this framework, the second unstable mode is also recovered, ruling out an acoustic origin. From the Rayleigh equation derived in the presence of density gradients, a generalised inflection point (GIP) criterion of instability exists, similar to that of fully compressible flows. Inviscid stability calculations confirm the existence of an unstable mode in the presence of a GIP, which is linked to the additional second mode found at finite Reynolds numbers. A theoretical analysis is then carried out by approximating the momentum equation for a base flow exhibiting strong gradients of dynamic viscosity. It is shown that the origin of the GIP, and hence the additional unstable mode, is associated with a minimum of kinematic viscosity at the Widom line. The universality of this result beyond supercritical fluids is eventually discussed.

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In supersonic turbulent boundary layers over isothermal walls, we investigate how the wall heat flux affects turbulent statistics and velocity scaling laws. To distinguish local Reynolds number and compressibility effects, we consider a conventional ideal gas with Sutherland's law and a fluid for which the dynamic viscosity is proportional to the square root of density, such that the semi-local Reynolds number is constant in the wall-normal direction. The results clearly indicate that the changes of the semi-local Reynolds number within the boundary layer affect the coherent turbulent structures, which induces the deviation of the viscous stress, Reynolds stress, and semi-local transformed mean velocity between different wall temperature conditions. For the cases with constant semi-local Reynolds number, we observe that the wall heat flux does not affect the turbulent structures and that the velocity profiles perfectly collapse among each other, indicating the importance of the semi-local Reynolds number, rather than the temperature or density themselves, on turbulent statistics and structures. Also, the conditional averaged analysis for the near-wall turbulent phenomena indicates a clear relationship between the turbulent structures and the mean velocity gradients. Additionally, an existing analytical temperature-velocity relation is verified based on the examinations of the applied equilibrium flow assumptions, and the results explain the disagreement between the present data and the analytical solutions in the outer boundary layer region, especially for isothermal wall cases.

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Organic Rankine cycle (ORC) systems are a readily available technology to convert thermal energy from renewable- and waste heat sources into electricity. However, their thermal performance is relatively low due to the low temperature of the available heat sources, but more importantly, due to the low efficiency of the employed expander. Designing the turboexpander is exceptionally challenging, because the flow field is highly supersonic and unsteady, and since the expansion takes place in the highly non-ideal dense-vapor region. In this work, we perform unprecedented three-dimensional unsteady simulations of several high-expansion cantilever ORC turbines to highlight distinctive loss mechanisms. The simulations indicate strong unsteady effects in the rotor blade passage, as a result of unsteady propagating shock waves interacting with viscous wakes and boundary layers. Moreover, the flow field in the rotor blade passage is strongly affected by three-dimensional secondary flow features and a sharp expansion in the shroud region at the inlet of the rotor blade. These span-wise mechanisms and unsteady flow interactions introduce irreversible losses which must be taken into account for designing highly efficient ORC expanders.

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New technologies are being developed to produce electricity cleaner and more efficient. Promising technologies among these are the solid oxide fuel cell and the supercritical carbon dioxide Brayton cycle. This study investigates the potential of integrating both technologies. The solid oxide fuel cell is known as a potentially clean and highly efficient technology to convert chemical energy to electricity. The high operating temperatures (600–1000 °C) allow the possibility of a bottoming cycle to utilize the high quality excess heat and also facilitate reforming processes, making it possible to use higher hydrocarbons as fuel. The supercritical carbon dioxide Brayton cycle has received attention as a promising power cycle. It has already been identified as a suitable cycle for relatively low temperature, compared to traditional gas turbines, heat sources for several reasons. Firstly because of the high efficiency, around 40%–45% for the common simple recuperative cycle. Secondly, because the turbine inlet temperature of a supercritical carbon dioxide is around 700 °C is low, compared to well over 1000 °C for a common air Brayton cycle. This is especially of interest because solid oxide fuel cell developers are targeting lower operating temperatures to avoid the use of exotic and expensive materials. And thirdly, the cycle can operate entirely above the critical point. Therefore the temperature increases gradually with the energy added to the cycle. This is more suitable for waste heat because the exergy loss decreases and more low temperature heat can be utilized compared to a steam Rankine cycle where most of the heat is added above the relatively high boiling point of pressurized water. A thermodynamic model of the solid oxide fuel cell- supercritical carbon dioxide Brayton cycle hybrid system is developed to explore and analyze different concepts of integration. Several conclusions are drawn. Firstly it is found that recirculating cathodic air increases the efficiency of the system and decreases the size of the heat exchangers. Secondly, applying a pinch point optimization decreases the size of the heat exchangers but increases the complexity of the system while the efficiency is not much affected. Thirdly, applying the recompression cycle in stead of a simple recuperative supercritical carbon dioxide cycle increases the efficiency of the system but not as significantly when operating the supercritical carbon dioxide as a stand-alone system while the complexity of the system increases even more. And finally, compared to a directly coupled solid oxide fuel cell-gas turbine system the solid oxide fuel cell- supercritical carbon dioxide Brayton cycle hybrid system is more efficient but significantly more complex.

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