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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., Energy Technology

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., Energy Technology

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 KLa and SOTR values (see Supplementary Information for details) dependent also as a function of flow rate. Average KLa values (for 20 °C) for air jet, impellers and paddle aerators [12] are shown for comparison. The plot shows that the KLa 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 KLa 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

Editorial, Green Open Access added to TU Delft Institutional Repository 'You share, we take care!' - Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public., Energy Technology

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 KLa and SOTR values (see Supplementary Information for details) dependent also as a function of flow rate. Average KLa values (for 20 °C) for air jet, impellers and paddle aerators [12] are shown for comparison. The plot shows that the KLa 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 KLa 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., Energy Technology

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., Energy Technology

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., Energy Technology

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)., Energy Technology

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., Energy Technology

The present work investigates the modeling of turbulent heat transfer in flows where radiative and convective heat transfer are coupled. In high temperature radiatively participating flows, radiation is the most relevant heat transfer mechanism and, due to its non-locality, it causes counter intuitive interactions with the turbulent temperature field. These so-called Turbulence-Radiation Interactions (TRI) largely affect the temperature field, modifying substantially the turbulent heat transfer. Therefore, in the context of modeling (RANS/LES), these interactions require a closure model. This work provides the inclusion of TRI in the modeling of the turbulent heat transfer by adopting a unique approach which consists in approximating the fluctuations of the radiative field with temperature fluctuations only. Based on this approximation, coefficients of proportionality are employed in order to close the unknown terms in the relevant model equations. A closed form of all radiation-temperature-velocity correlation is explicitly derived depending on the chosen turbulent heat transfer model. This model is applied to a standard two-equation turbulent heat transfer closure and used to reproduce results obtained with high-fidelity DNS simulations. While a standard approach (i.e., neglecting TRI) is not able to correctly predict the DNS data, the new model's results shows exceptional agreement with the high-fidelity data. This clearly proves the validity (and the necessity) of the proposed model in non-reactive, radiative turbulent flows., Energy Technology, Fluid Mechanics

A horizontal electrohydrodynamic (EHD) liquid bridge (also known as a “floating water bridge”) is a phenomenon that forms when high voltage DC (kV·cm-1) is applied to pure water in two separate beakers. The bridge, a free-floating connection between the beakers, acts as a cylindrical lens and refracts light. Using an interferometric set-up with a line pattern placed in the background of the bridge, the light passing through is split into a horizontally and a vertically polarized component which are both projected into the image space in front of the bridge with a small vertical offset (shear). Apart from a 100 Hz waviness due to a resonance effect between the power supply and vortical structures at the onset of the bridge, spikes with an increased refractive index moving through the bridge were observed. These spikes can be explained by an electrically induced liquid-liquid phase transition in which the vibrational modes of the water molecules couple coherently., Energy Technology

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 ef, Energy Technology

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., Energy Technology