Kinetic Simulations of Compressible Non-Ideal Fluids: From Supercritical Flows to Phase-Change and Exotic Behavior

We investigate a kinetic model for compressible non-ideal fluids. The model imposes the local thermodynamic pressure through a rescaling of the particle’s velocities, which accounts for both long- and short-range effects and hence full thermodynamic consistency. The model is fully Galilean invariant and treats mass, momentum, and energy as local conservation laws. The analysis and derivation of the hydrodynamic limit is followed by the assessment of accuracy and robustness through benchmark simulations ranging from the Joule–Thompson effect to a phase-change and high-speed flows. In particular, we show the direct simulation of the inversion line of a van der Waals gas followed by simulations of phase-change such as the one-dimensional evaporation of a saturated liquid, nucleate, and film boiling and eventually, we investigate the stability of a perturbed strong shock front in two different fluid mediums. In all of the cases, we find excellent agreement with the corresponding theoretical analysis and experimental correlations. We show that our model can operate in the entire phase diagram, including super- as well as sub-critical regimes and inherently captures phase-change phenomena.

3D anatomy and flow dynamics of net-depositional cyclic steps on the world’s largest submarine fan: a joint 3D seismic and numerical approach

Supercritical flows are ubiquitous in natural environments; however, there is rare 3D anatomy of their deposits. This study uses high-quality 3D seismic datasets from the world’s largest submarine fan, Bengal Fan, to interpret 3D architectures and flow processes of Pliocene undulating bedforms that were related to supercritical flows. Bengal undulating bedforms as documented in this study were developed in unconfined settings, and are seismically imaged as strike-elongated, crescentic bedforms in plan view and as rhythmically undulating, upstream migrating, erosive, discontinuous reflections in section view. Their lee sides are overall 3 to 4 times steeper (0.28° to 1.19° in slope) and 3 to 4 times shorter (117 to 419 m in length) than their stoss flanks and were ascribed to faster (high flow velocities of 2.70 to 3.98 m/s) supercritical flows (Froude numbers of 1.53 to 2.27). Their stoss sides, in contrast, are overall 3 to 4 times gentler (0.12° to 0.27° in slope) and 3 to 4 times longer (410 to 1139 m in length) than their lee flanks and were related to slower (low velocities of 2.35 to 3.05 m/s) subcritical flows (Froude numbers of 0.58 to 0.97). Bengal wave-like features were, thus, created by supercritical-to-subcritical flow transformations through internal hydraulic jumps (i.e., cyclic steps). They have crests that are positive relative to the surrounding region of the seafloor, suggesting the predominant deposition of draping sediments associated with net-depositional cyclic steps. Turbidity currents forming Bengal wave-like features were, thus, dominated by deposition, resulting in net-depositional cyclic steps. Sandy deposits associated with Bengal net-depositional cyclic steps are imaged themselves as closely spaced, strike-elongated high RMS-attribute patches, thereby showing closely spaced, long and linear, strike-elongated distribution patterns.

Eulerian and Lagrangian Comparison of Wind Jets in the Tokar Gap Region

The Lagrangian and Eulerian structure and dynamics of a strong wind event in the Tokar Gap region are described using a Weather Research and Forecasting (WRF) model hindcast for 2008. Winds in the Tokar Gap reach 25 m s−1 and remain coherent as a jet far out over the Red Sea, whereas equally strong wind jets occurring in neighboring gaps are attenuated abruptly by jump-like hydraulic transitions that occur just offshore of the Sudan coast. The transition is made possible by the supercritical nature of the jets, which are fed by air that spills down from passes at relatively high elevation. By contrast, the spilling flow in the ravine-like Tokar Gap does not become substantially supercritical and therefore does not undergo a jump, and also carries more total horizontal momentum. The Tokar Wind Jet carries some air parcels across the Red Sea and into Saudi Arabia, whereas air parcel trajectories in the neighboring jets ascend as they cross through the jumps, then veer sharply to the southeast and do not cross the Red Sea. The mountain parameter Nh/U is estimated to lie in the range of 1.0–4.0 for the general region, a result roughly consistent with a gap jet having a long extension, and supercritical flows spilling down from higher elevation passes. The strong event is marked by the formation of a feature with a vertical cellular structure in the upstream entrance region of the Tokar Gap, a feature absent from the more moderate events that occur throughout the summer. The cell contains descending air parcels that are fed into the Tokar Gap and one of the neighboring gaps. An analysis of the Bernoulli function along air parcel trajectories reveals an approximate balance between the loss of potential energy and gain of internal energy and pressure, with surprisingly little contribution from kinetic energy, along the path of the descending flow. The winds in all gaps attain the critical wind speed nominally required to loft dust into the atmosphere, though only the Tokar Gap has a broad, silty delta region capable of supplying particulate matter for dust storms.

Heat Transfer for Supercritical Flow With TRACE

Flow regimes at water pressures above the critical pressure are characterized as supercritical flow. Supercritical flows have no phase change. The heat transfer from the wall to the fluid is single phase (there is no boiling or condensation). Experimental data indicate that for conditions that involve supercritical single-phase heat transfer, the Dittus-Boelter heat transfer correlation can be in significant error. A pseudo-critical temperature can be defined as a function of pressure for pressures that exceed the supercritical pressure. The pseudo-critical temperature is defined for heat transfer purposes as the temperature at which the specific heat peaks as the pressure is held constant. There is significant variation in fluid properties across the heat transfer boundary layer at temperatures near the pseudo-critical temperature. The large variation in properties is the reason for the failure of the Dittus-Boelter heat transfer correlation. Comparisons to experimental data indicate that the Mokry heat transfer correlation is a significant improvement over the Dittus-Boelter heat transfer correlation for single phase supercritical heat transfer. The Mokry correlation was chosen to be included into TRACE.

The particularities of near-critical flows formation in open channels

This article considers the current problems of near-critical flows. It provides short characteristics of each phenomenon and describes the cases of near-critical flow formation during the operation of the different hydraulic structures. Each of the considered phenomena has a number of characteristic features which distinguish them from the usual subcritical and supercritical flows with smooth or slowly varied movement. Such properties include the wave-like or roller nature of free-surface curves, the presence of a streamline inclination and curvature, and also a non-hydrostatic pressure distribution in depth mainly in the vertical cross-section of these phenomena. Therefore, during mathematical and numerical simulations at the designing stage of hydraulic structures it is necessary to take into account the additional parameters which characterise the particularities of near-critical flows. In cases in which these moments are neglected, there are many cases of accidents and damage being caused to structures which are operated in conditions of near-critical flow formation. An objective of this work is to provide a detailed analysis of the particularities of near-critical flows and show their negative consequences on hydraulic structures. The article presents the results of the mathematical and hydraulic simulation of wavelike near-critical flows and a comparison of the full-scale measurement and a mathematical model of translation waves.

Scour at Bridge Foundations in Supercritical Flows: An Analysis of Knowledge Gaps

The scour at bridge foundations caused by supercritical flows is reviewed and knowledge gaps are analyzed focusing on the flow and scour patterns, available measuring techniques for the laboratory and field, and physical and advanced numerical modeling techniques. Evidence suggests that the scour depth caused by supercritical flows is much smaller than expected, by an order of magnitude compared to that found in subcritical flows, although the reasons for this behavior remain still unclear. Important questions on the interaction of the horseshoe vortex with the detached hydraulic-jump and the wall-jet flow observed in supercritical flows arise, e.g., does the interaction between the flow structures enhance or debilitate the bed shear stresses caused by the horseshoe vortex? What is the effect of the Froude number of the incoming flow on the flow structures around the foundation and on the scour process? Recommendations are provided to develop and adapt research methods used in the subcritical flow regime for the study of more challenging supercritical flow cases.

Experimental studies on scour of supercritical flow jets in upstream of screens and modelling scouring dimensions using artificial intelligence to combine multiple models (AIMM)

Performances of screens in watercourses are investigated for dissipating energy of supercritical flows, capable of inducing scour or stabilising hydraulic jumps. Subsequent scouring pits are characterised by pit depth and pit length. Inherent processes are studied through laboratory tests by producing a set of empirical data to formulate a model of the scour for explaining subsequent processes. The experimental set-up comprises: (i) Froude number of supercritical flows (range: 3.5–8.0); (ii) particle densimetric Froude number (range: 2–10) using five granular samples; and (iii) two screen porosities (40% and 50%). Trained and tested artificial intelligence models explain the data by expressing depth and length of the pit through the following levels: Level 1: use the experimental data and test the models of: Sugeno fuzzy logic (SFL) and neuro-fuzzy (NF); and Level 2: use outputs of Level 1 models as inputs to support vector machine (SVM). The results reveal that the Level 2 model improves model performances compared with the single models with respect to R2, root mean square error (RMSE), Nash–Sutcliffe coefficient (NSC) and residual errors. While Level 1 models remain fit-for-purpose, the comparative improvement from Level 1 to Level 2 can be as high as 58% in terms of NSC for the testing phase.