Fluids

Viscous linear surface waves are studied at arbitrary wavelength, layer thickness, viscosity, and surface tension. We find that in shallow enough fluids no surface waves can propagate. This layer thickness is determined for some fluids, water, glycerin, and mercury. Even in any thicker fluid layers, propagation of very short and very long waves is forbidden. When wave propagation is possible, only a single propagating mode exists for a given horizontal wave number. In contrast, there are two types of non-propagating modes. One kind of them exists at all wavelength and material parameters, and there are infinitely many such modes for a given wave number, distinguished by their decay rates. The other kind of non-propagating mode that is less attenuated may appear in zero, one, or two specimens. We notice the presence of two length scales as material parameters, one related to viscosity and the other to surface tension. We consider possible modes for a given material on the parameter plane layer thickness versus wave number and discuss bifurcations among different mode types. Motion of surface particles and time evolution of surface elevation is also studied at various parameters in glycerin, and a great variety of behaviour is found, including counterclockwise surface particle motion and negative group velocity in wave propagation. Full article

Cavitation, as a unique technology for influencing liquid substances, has attracted much attention in the oil refining industry. The unique capabilities of cavitation impact can initiate the destruction of molecular compounds in the liquid. At the same time with a large number of successful experimental studies on the treatment of liquid hydrocarbon raw materials, cavitation has not been introduced in the oil refining industry. Often the impossibility of implementation is based on the lack of a unified methodology for assessing the intensity and threshold of cavitation creation. The lack of a unified methodology does not allow for predicting the intensity and threshold of cavitation generation in different fluids and cavitation-generating devices. In this review, the effect of cavitation on various rheological properties and fractional composition of liquid hydrocarbons is investigated in detail. The possibility of using the cavitation number as a single parameter for evaluating the intensity and threshold of cavitation generation is analyzed, and the limitations of its application are evaluated. The prospects of introducing the technology into the industry are discussed and a new vision of calculating the analog of cavitation numbers based on the analysis of the mutual influence of feedstock parameters and geometry of cavitators on each other is presented. Full article

We have developed and tested a numerical model for turbulence resolving simulations of dense mud–water mixtures in oscillatory bottom boundary layers, based on a low Stokes number formulation of the two-phase equations. The resulting non-Boussinesq equation for the fluid momentum is coupled to a transport equation for the mud volumetric concentration, giving rise to a volume-averaged fluid velocity that is non-solenoidal, and the model was implemented as a new compressible flow solver. An oscillating pressure gradient force was implemented in the correction step of the standard semi-implicit method for pressure linked equations (SIMPLE), for consistency with the treatment of other volume forces (e.g., gravity). The flow solver was further coupled to a new library for Bingham plastic materials, in order to model the rheological properties of dense mud mixtures using empirically determined concentration-dependent yield stress and viscosity. We present three direct numerical simulation tests to validate the new MudMixtureFoam solver against previous numerical solutions and experimental data. The first considered steady flow of Bingham plastic fluid with uniform concentration around a sphere, with Bingham numbers ranging from 1 to 100 and Reynolds numbers ranging from 0.1 to 100. The second considered the development of turbulence in oscillatory bottom boundary layer flow, and showed the formation of an intermittently turbulent layer with peak velocity perturbations exceeding 10 percent of the freestream flow velocity and occurring at a distance from the bottom comparable to the Stokes boundary layer thickness. The third considered the effects of density stratification due to resuspended sediment on turbulence in oscillatory bottom boundary layer flow with a bulk Richardson number of $1\times {10}^{-4}$ and a Stokes–Reynolds number of 1000, and showed the formation of a lutocline between 20 and 40 Stokes boundary layer depths. In all cases, the new solver produced excellent agreement with the previous results. Full article

In this study, a numerical simulation of fluid flow through railway ballast in the time domain is presented, providing a model for unsteady-state flow. It is demonstrated that the position of the free surface with respect to time can also be used to solve the steady flow case. The effect of ballast fouling is included in the model to capture the realistic behavior of railway ballast, which is critical to understanding the impact of flooding. A thorough comparison with a range of previous studies, including theoretical and experimental approaches, is made, and very close agreement is obtained. The significant impact of ballast fouling on fluid flow and its potential consequences for railway infrastructure are highlighted by the simulation. Valuable insights into the behavior of water flow through porous media and its relevance to railway ballast management are offered by this study. Full article

Reduction of energy expenditures required for various technological processes is a pressing issue in today’s economy. One of the ways to solve this issue in regard to liquefied natural gas (LNG) storage is the recovery of its vapours from LNG tanks using an ejector system. In that respect, studies on the outflow of the real gas through the nozzle, the main element of the ejector, and identifying differences from the ideal gas outflow, are of high relevance. Particularly, this concerns the determination of the discharge coefficient µ as the ratio of the actual flowrate to the ideal one, taking into account the energy losses at gas outflow through the nozzle. The discharge coefficient values determined to date for various nozzle geometries are, as a rule, evaluated empirically and contradictory in some cases. The authors suggest determining the discharge coefficient by means of an experiment. This paper includes µ values determined using this method for the critical outflow of air to atmosphere through constrictor nozzles with different outlet diameters (0.003 m; 0.004 m; 0.005 m) in the pressure range at the nozzle inlet of 0.5–0.9 MPa. The obtained results may be used for the design of an ejector system for the recovery of the boil-off gas from LNG tanks, as well as in other fields of industry, for the design of technical and experimental devices with nozzles for various applications. Full article

The acoustic cavitation of fluids, as well as related physical and chemical phenomena, causes a variety of effects that are highly important in technological processes and medicine. Therefore, it is important to be able to control the conditions that allow cavitation to begin and progress. However, the accurate prediction of acoustic cavitation is dependent on a complex relationship between external influence parameters and fluid characteristics. The multiparameter problem restricts the development of successful theoretical models. As a result, it is critical to identify the most important parameters influencing the onset of the cavitation process. In this paper, the ultrasonic frequency, hydrostatic pressure, temperature, degassing, density, viscosity, volume, and surface tension of a fluid were investigated using machine learning to determine their significance in predicting acoustic cavitation strength. Three machine learning models based on support vector regression (SVR), ridge regression (RR), and random forest (RF) algorithms with different input parameters were trained. The results showed that the SVM algorithm performed better than the other two algorithms. The parameters affecting the active cavitation nuclei, namely hydrostatic pressure, ultrasound frequency, and outgassing degree, were found to be the most important input parameters influencing the prediction of the cavitation threshold. Other parameters have a minor impact when compared to the first three, and their role can be compensated for by alternative variables. The further development of the obtained results provides a new way to optimize and improve existing theoretical models. Full article

Studying transport processes in the brain’s extracellular space is a complicated problem when considering the brain’s tissue. Tests of corresponding physical and mathematical problems, as well as the need for materials with cheap but realistic properties to allow for testing of drug delivery systems, lead to the development of artificial phantom media, one kind of which is explored in this work. We report results from quantifying the spread of a standard contrast agent used in clinical computed tomography, Iopromide, in samples of collagen-based hydrogels. Its pure variant as well as samples supplied with lipid and surfactant additives were explored. By comparing to solutions of the diffusion equation which reproduce these data, the respective diffusion coefficients were determined. It was shown that they are relevant to the range typical for living tissue, grow with elevation in the lipid content and diminish with growth in surfactant concentration. Full article

The impingement of a short-duration water jet on a pool of molten Rose’s metal is studied experimentally herein. Short-duration water jet impacting on the free surface of a molten metal pool with a temperature of 300 °C are generated with a pneumatic water delivery system, with two-camera high-speed video registration. A total of 14 experimental series, each containing 5 repeated tests, are performed for a water volume of 0.2–1 mL and a jet impact velocity of 4.1–9.0 m/s. The cavity development in the melt layer is studied, with the main stages described herein. Despite the significantly higher density of melt in comparison with water, the cavity can reach the melt pool bottom; furthermore, its further collapse results in the formation of a central jet rising to the height of a few centimeters. The maximum height of the central jet is shown to depend linearly on the total momentum of the water jet, and a semi-logarithmic correlation is found for the maximum diameter of the cavity. Repeatability analysis is performed within each experimental series, and the relative standard deviation for the melt splash height is shown to be from 8.8% to 26.8%. The effects of the pool depth, the vessel shape, and the water temperature are weaker in the range of the experimental parameters used here. Full article

We present the theoretical description of plane Couette flow based on the previously proposed equations of vortex fluid, which take into account both the longitudinal flow and the vortex tubes rotation. It is shown that the considered equations have several stationary solutions describing different types of laminar flow. We also discuss the simple model of turbulent flow consisting of vortex tubes, which are moving chaotically and simultaneously rotating with different phases. Using the Boussinesq approximation, we obtain an analytical expression for the stationary profile of mean velocity in turbulent Couette flow, which is in good agreement with experimental data and results of direct numerical simulations. Our model demonstrates that near-wall turbulence can be described by a coordinates-independent coefficient of eddy viscosity. In contrast to the viscosity of the fluid itself, this parameter characterizes the turbulent flow and depends on Reynolds number and roughness of the channel walls. Potentially, the proposed model can be considered as a theoretical basis for the experimental measurement of the eddy viscosity coefficient. Full article

We investigate the effect of horizontal quasi-periodic oscillation on the stability of two superimposed immiscible fluid layers confined in a horizontal Hele-Shaw cell. To approximate real oscillations, a quasi-periodic oscillation with two incommensurate frequencies is considered. Thus, the linear stability analysis leads to a quasi-periodic oscillator, with damping, which describes the evolution of the amplitude of the interface. Two types of quasi-periodic instabilities occur: the low-wavenumber Kelvin-Helmholtz instability and the large-wavenumber resonances. We mainly show that, for equal amplitudes of the superimposed accelerations, and for a low irrational frequency ratio, there is competition between several resonance modes allowing a very large selection of the wavenumber from lower to higher values. This is a way to control the sizes of the waves. Furthermore, increasing the frequency ratio has a stabilizing effect for both types of instability whose thresholds are found to correspond to quasi-periodic solutions using the frequency spectrum. For a ratio of the two superimposed displacement amplitudes equal to unity and less than unity, the number of resonances and competition between their modes also become significant for the intermediate values of the ratio of frequencies. The effects of other physical and geometrical parameters, such as the damping coefficient, density ratio, and heights of the two fluid layers, are also examined. Full article

This article focuses on the prediction of the small bubble holdups (assuming the existence of two major bubble classes) in two bubble columns (0.289 m in ID and 0.102 m in ID), operated with organic liquids under various conditions (including high temperature and pressure). A new correction factor has been established in the existing model for the prediction of the gas holdups in the homogeneous regime. The correction parameter is a single function of the Eötvös number (gravitational forces to surface tension forces), which characterizes the bubble shape. In addition, the behavior of small bubble holdups in 1-butanol (selected as a frequently researched alcohol) aerated with nitrogen, in a smaller BC (0.102 m in ID), at various operating pressures, is presented and discussed. The ratio of small bubble holdup to overall gas holdup, as a function of superficial gas velocity and operating pressure, has been investigated. All small bubble holdups in this work have been measured by means of the dynamic gas disengagement technique. Full article

In this work, we experimentally investigated the cavitation effects on the hydrodynamic behavior of a circular cylinder at different cavitating flows. We analyzed the cavitation dynamics behind the circular cylinder using a high-speed camera and also measured the associated hydrodynamic forces on the circular cylinder using a load cell. We studied the cavitation dynamics around the cylinder at various types of the cavitating regimes such as cloud cavitation, partial cavitation and cavitation inception. In addition, we analyzed the cavitation dynamics at three different Reynolds numbers: 1 × 10${}^5$, 1.25 × 10${}^5$ and 1.5 × 10${}^5$. The results showed that the hydrodynamics force on the circular cylinder can be increased with the formation of the cavitation behind the cylinder compared with the cylinder at cavitation inception regime. The three-dimensional flow caused complex cavitation behavior behind the cylinder and a strong interaction between vortex structures and cavity shedding mechanism. In addition, the results revealed that the effects of the Reynolds number on the cavitation dynamics and amplitude of the shedding frequency is significant. However the effects of the cavitation number on the enhancement of the amplitude of the shedding frequency in the cavitating flow with a constant velocity is slightly higher than the effects of Reynolds number on the enhancement of the amplitude of the shedding frequency at a constant cavitation number. Full article

Erythrocyte enrichment is needed for blood disease diagnosis and research. DLD arrays with an I-shaped pillar (I-pillar) sort erythrocytes in a unique, accurate, and low-reagent method. However, the existing I-shaped pillar DLD arrays for erythrocyte sorting have the drawbacks of higher flow resistance and more challenging fabrication. A two-dimensional erythrocyte simulation model and the arbitrary Lagrangian–Euler equations at the cell–fluid boundary were built based on the fluid–solid coupling method to investigate the influencing factors of the erythrocyte flow path in an I-pillar DLD array and find its optimization method. Three different sizes of I-pillars were built and multiple sets of corresponding arrays were constructed, followed by finite element simulations to separately investigate the effects of these arrays on the induction of erythrocyte motion paths. This work demonstrates the motion paths of erythrocyte models in a series of I-pillar arrays with different design parameters, aiming to summarize the variation modes of erythrocyte motion paths, which in turn provides some reference for designing and optimizing the pillar size and array arrangement methods for I-pillar array DLD chips. Full article

Gaussian solutions of the diffusion equation can be applied to visualize the flow paths in subsurface reservoirs due to the spatial advance of the pressure gradient caused by engineering interventions (vertical wells, horizontal wells) in subsurface reservoirs for the extraction of natural resources (e.g., water, oil, gas, and geothermal fluids). Having solved the temporal and spatial changes in the pressure field caused by the lowered pressure of a well’s production system, the Gaussian method is extended and applied to compute and visualize velocity magnitude contours, streamlines, and other relevant flow attributes in the vicinity of well systems that are depleting the pressure in a reservoir. We derive stream function and potential function solutions that allow instantaneous modeling of flow paths and pressure contour solutions for transient flows. Such analytical solutions for transient flows have not been derived before without time-stepping. The new closed-form solutions avoid the computational complexity of time-stepping, required when time-dependent flows are modeled by superposing steady-state solutions using complex analysis methods. Full article

Acting upon clinical patient data, acquired in the pathway of percutaneous intervention, we deploy hierarchical, multi-stage, data-handling protocols and interacting low- and high-order mathematical models (chamber elastance, state-space system and CFD models), to establish and then validate a framework to quantify the burden of ischaemia. Our core tool is a compartmental, zero-dimensional model of the coupled circulation with four heart chambers, systemic and pulmonary circulations and an optimally adapted windkessel model of the coronary arteries that reflects the diastolic dominance of coronary flow. We guide the parallel development of protocols and models by appealing to foundational physiological principles of cardiac energetics and a parameterisation (stenotic Bernoulli resistance and micro-vascular resistance) of patients’ coronary flow. We validate our process first with results which substantiate our protocols and, second, we demonstrate good correspondence between model operation and patient data. We conclude that our core model is capable of representing (patho)physiological states and discuss how it can potentially be deployed, on clinical data, to provide a quantitative assessment of the impact, on the individual, of coronary artery disease. Full article

Evaluating the hydrodynamic force fluctuations acting on each structure in a group of subsea objects of different cross-section shapes, sizes and relative positions represents a challenge due to the sensitivity of the vortex shedding process, especially for a variety of sheared flows. The present study uses the numerical 2D computational fluid dynamics model to estimate the flow-induced forces on a group of small circular and D-shaped cylinders in the linear and parabolic sheared flow, which are placed in proximity to a larger structure of the squared cross-section. This allows us to evaluate loads, which are affected by the presence of subsea equipment located on the seabed. The average Reynolds number of the considered linear flow profile is 3900, while the parabolic flow profile has the maximum Reynolds number of 3900. The k-ω SST turbulence model is used for simulations. The work demonstrates the effect of the cross-sectional shape of smaller cylinders on hydrodynamic coefficients, explores the effect from the spacing in between the structures and highlights differences between loads in the linearly sheared and parabolic flow. The results obtained show that the presence of the squared cylinder notably influences the mean drag coefficient on the first cylinder, for both circular and D-shaped cylinders. The parabolic sheared flow profile in this series leads to the highest mean drag and the highest amplitudes of the fluctuating drag and lift coefficients. Full article

Racecar aerodynamic development requires well-correlated simulation data for rapid and incremental development cycles. Computational Fluid Dynamics (CFD) simulations and wind tunnel testing are industry-wide tools to perform such development, and the best use of these tools can define a race team’s ability to compete. With CFD usage being limited by the sanctioning bodies, large-scale mesh and large-time-step CFD simulations based on Reynolds-Averaged Navier–Stokes (RANS) approaches are popular. In order to provide the necessary aerodynamic performance advantages sought by CFD development, increasing confidence in the validity of CFD simulations is required. A previous study on a Scale-Averaged Simulation (SAS) approach using RANS simulations of a Gen-6 NASCAR, validated against moving-ground, open-jet wind tunnel data at multiple configurations, produced a framework with good wind tunnel correlation (within 2%) in aerodynamic coefficients of lift and drag predictions, but significant error in front-to-rear downforce balance (negative lift) predictions. A subsequent author’s publication on a Scale-Resolved Simulation (SRS) approach using Improved Delayed Detached Eddy Simulation (IDDES) for the same geometry showed a good correlation in front-to-rear downforce balance, but lift and drag were overpredicted relative to wind tunnel data. The current study compares the surface pressure distribution collected from a full-scale wind tunnel test on a Gen-6 NASCAR to the SAS and SRS predictions (both utilizing SST $k-\omega$ turbulence models). CFD simulations were performed with a finite-volume commercial CFD code, Star-CCM+ by Siemens, utilizing a high-resolution CAD model of the same vehicle. A direct comparison of the surface pressure distributions from the wind tunnel and CFD data clearly showed regions of high and low correlations. The associated flow features were studied to further explore the strengths and areas of improvement needed in the CFD predictions. While RANS was seen to be more accurate in terms of lift and drag, it was a result of the cancellation of positive and negative errors. Whereas IDDES overpredicted lift and drag and requires an order of magnitude more computational resources, it was able to capture the trend of surface pressure seen in the wind tunnel measurements. Full article

The present article addresses the topic of grid motion computation in Arbitrary Lagrange–Euler (ALE) simulations, where a fluid mesh must be updated to follow the displacements of Lagrangian boundaries. A widespread practice is to deduce the motion for the internal mesh nodes from a parabolic equation, such as the harmonic equation, introducing an extra computational cost to the fluid solver. An alternative strategy is proposed to minimize that cost by changing from the parabolic equation to a hyperbolic equation, implementing an additional time derivative term allowing an explicit solution of the grid motion problem. A fictitious dynamic problem is thus obtained for the grid, with dedicated material parameters to be carefully chosen to enhance the computational efficiency and preserve the mesh quality and the accuracy of the physical problem solution. After reminding the basics of the ALE expression of the Navier–Stokes equations and describing the proposed hyperbolic equation for the grid motion problem, the paper provides the necessary characterization of the influence of the fictitious grid parameters and the analysis of the robustness of the new approach compared to the harmonic reference equation on a significant 2D test case. A 3D test case is finally extensively studied in terms of computational performance to highlight and discuss the benefits of the hyperbolic equation for ALE grid motion. Full article

Among the most relevant fields of research recently investigated for improving the performance of gasoline direct injection (GDI) engines, there are ultrahigh injection pressures and the flash-boiling phenomenon. Both perform relevant roles in improving the air/fuel mixing process, reducing tailpipe emissions and implementing new combustion methods. When a high-temperature fuel is released into an environment with a pressure lower than the fuel’s saturation pressure, flash boiling occurs. Due to complex two-phase flow dynamics and quick droplet vaporization, flash boiling can significantly modify spray formation. Specifically, if properly controlled, flash boiling produces important benefits for the fuel–air mixture formation, the combustion quality and, in general, for overall engine operation. Flash boiling was broadly investigated for classical injection pressure, but few works concern ultrahigh injection pressure. Here, the investigation of the spray produced by a multihole injector was performed using both experimental imaging techniques and CFD simulations aiming to highlight the combined impact of the injection pressure and the flash boiling occurrence on the spray morphology. The shadowgraph method was employed to observe the spray experimentally. The information gathered allows for assessing the performances of an Eulerian–Lagrangian algorithm purposely developed. Breakup and evaporation models, appropriate for flashing sprays, were implemented in a CFD (Computational Fluid Dynamics) code. The experimental results and the CFD simulations demonstrate a good agreement, demonstrating that through adoption of a flash-boiling breakup model, it is possible to reproduce non-evaporating and superheated sprays while changing few simulation parameters. Finally, the results also show the significance of injection pressure in preventing spray collapse. Full article