Fluids

We present novel analytic solutions of the axial-symmetric boundary value problem of the Stokes equation for incompressible liquids with rapidly varying viscosity, which cover the hydrodynamics of collapsing glass tubes with moving torch. We meet requirements to optimize the contactless measuring of dynamical viscosities and surface tensions of molten glasses through collapsing for tools working with sharply peaked axial temperature courses. We study model solutions for axial courses of the reciprocal viscosity specified as Gaussians extended on small distances compared to the outer tube radius, and we neglect the boundary inclination, corresponding to measuring conditions for large torch velocities. The surface tension is assumed to be constant across the collapsing zone. The boundary value problem becomes disentangled, changing to a gradually independent hierarchy of streaming function, vorticity, and pressure. Axial Fourier transforms are introduced to focus on solutions for infinitely extended tubes. Beyond the predictions of the asymptotic collapsing theory, a successively increasing steepness of the reciprocal viscosity induces an increasing radial pressure gradient that acts against the surface tension and diminishes the collapsing efficiency. The arising systematic error in evaluating the viscosity from experimental data in virtue of the asymptotic collapsing theory is corrected. Error estimations regarding deviations from the specified viscosity course, the neglected boundary inclination, and heat conduction within the tube wall are outlined, and preconditions to simplify the measuring of surface tensions through collapsing are discussed. Full article

Phosphate ore slurry is a suspension of insoluble particles of phosphate rock, the primary raw material for fertilizer and phosphoric acid, in a continuous phase of water. This suspension has a non-Newtonian flow behavior and exhibits yield stress as the shear rate tends toward zero. The suspended particles in the present study were assumed to be noncolloidal. Various grades and phosphate ore concentrations were chosen for this rheological investigation. We created some experimental protocols to determine the main characteristics of these complex fluids and established relevant rheological models with a view to simulate the numerical flow in a cylindrical pipeline. Rheograms of these slurries were obtained using a rotational rheometer and were accurately modeled with commonly used yield-pseudoplastic models. The results show that the concentration of solids in a solid–liquid mixture could be increased while maintaining a desired apparent viscosity. Finally, the design equations for the laminar pipe flow of yield pseudoplastics were investigated to highlight the role of rheological studies in this context. Full article

Mixing of carbon dioxide dissolved in a multicomponent gas mixture at different pressures was researched. It was found that the mechanical equilibrium of the ternary gas mixture 0.4163H₂ (1) + 0.5837CO₂ (2) − N₂ (3) is violated at a pressure of p = 0.7 MPa and structured flows appear in the system. The pressure area (from 0.7 to 1.5 MPa) at which the conditions of priority transfer of components with the highest molecular weight in the mixture are realised in the system is fixed. To analyse the effect of pressure on the process of changing “diffusion–convection” modes, a mathematical model, which takes into account the kinetic features of multicomponent mixing, was applied. It was shown that the change in the modes of mass transfer is associated with a significant difference in the diffusion ability of the components. It is noted that the difference in the diffusion coefficients of components results in the nonlinearity of the concentration distribution, which leads to the inversion of the density gradient of the gas mixture, which is the cause of convective flows. Full article

The marginal ice zone is a highly dynamical region where sea ice and ocean waves interact. Large-scale sea ice models only compute domain-averaged responses. As the majority of the marginal ice zone consists of mobile ice floes surrounded by grease ice, finer-scale modelling is needed to resolve variations of its mechanical properties, wave-induced pressure gradients and drag forces acting on the ice floes. A novel computational fluid dynamics approach is presented that considers the heterogeneous sea ice material composition and accounts for the wave-ice interaction dynamics. Results show, after comparing three realistic sea ice layouts with similar concentration and floe diameter, that the discrepancy between the domain-averaged temporal stress and strain rate evolutions increases for decreasing wave period. Furthermore, strain rate and viscosity are mostly affected by the variability of ice floe shape and diameter. Full article

This work presents the simulation of a steam generator or water-tube boiler through the implementation in MATLAB^® for a proposed mathematical model. Mass and energy balances for the three main components of the boiler - the drum, the riser and down-comer tubes - are presented. Three alternative solutions to the ordinary differential equation (ODE) were studied, based on Runge–Kutta 4th order method, Heun’s method, and MATLAB function Ode45. The best results were obtained using MATLAB^® function Ode45 based on the Runge–Kutta 4th Order Method. The error was less than 5% for the simulation of the steam pressure in the drum, the total volume of water in the boiler, and the mixture quality in relation to what was reported. Full article

Air-ventilated cavities formed under or around the hulls of marine vehicles can reduce water drag. Hull configurations with partial air ventilation where air cavities reattach to body surfaces are of special practical interest, since the required air supply rates to achieve significant drag reduction can be made rather low. However, formation and stability of such air cavities are sensitive to the hull geometry and operational conditions. In this study, an attempt is made to numerically simulate one setup with a partial air cavity that was previously tested experimentally at high Reynolds numbers, above 50 million. A computational fluid dynamics software Star-CCM+ has been employed for numerical modeling. Stable and unstable states of the air-cavity setup, characterized by long and collapsing air cavities, respectively, were modeled at two air supply rates near the stability boundary. Numerical results were similar to experimental data at the optimal water speed for the tested geometry, when a long air cavity was sustained at a minimal air supply rate. For water speeds that were substantially higher or lower than the optimal case, a stable cavity could not be maintained with small air supply rates for the given hull geometry. Numerical simulations demonstrated how alterations of the body surface could help sustain long air cavities across a broader speed range using air supply rates that were similar to the optimal case. These findings suggest that morphing hull surfaces can potentially be used for control of drag-reducing air cavities and expand the viable operating range for their application to marine vehicles. Full article

This article considers the principle of constructing mathematical models of functionally complex multidimensional multiloop continuous–discrete UAV stabilization systems. This is based on the proposal for constructing a mathematical model based on the class of the considered complexity of the stabilization system-multidimensionality, multi-rating, and elasticity. Multiloop (multidimensional) UAV stabilization systems are often characterized by the control of several interconnected state elements and the existence of several channels for the propagation of signals and mutual connections between individual objects. This is due to the need not only to take into account the numerous disturbing factors (for example, wind) acting on the control object as well as the need to use several points of application of control actions. Additionally, an important point is the possible separation of the mutual influence of the roll and yaw channels of the UAV on its synthesis and analysis. For this purpose, a mathematical model has been constructed using a description in the form of transfer functions, and therefore, in the form of structural diagrams. The principle of obtaining transfer functions is shown to demonstrate additional dynamic constraints introduced by elastic deformations into the stabilization loop through gyroscopic devices and accelerometers. This will make it possible to formulate a methodology for analyzing the influence of aeroelastic constraints on the stabilization loop, which will allow developing approaches to formulate requirements for the effective placement of gyroscopes and accelerometers on the UAV. The proposed approach allows creating a complete system of analysis and synthesis tools for complex multidimensional continuous–discrete UAV stabilization systems. Full article

Air-coupled ultrasonic testing is widely used in the industry for the non-destructive testing of compound materials. It provides a fast and efficient way to inspect large concrete civil infrastructures for damage that might lead to catastrophic failure. Due to the large penetration depths required for concrete structures, the use of traditional piezoelectric transducer requires high power electric systems. In this study, a novel fluidic transducer based on a bistable fluidic amplifier is investigated. Previous experiments have shown that the switching action of the device produces a high-power broadband ultrasonic signal. This study will provide further insight into the switching behaviour of the fluidic switch. Therefore, parametric CFD simulations based on compressible supersonic RANS simulations were performed, varying the inlet pressure and velocity profiles for the control flow. Switching times are analyzed with different methods, and it was found that these are mostly independent of the slope of the velocity profile at the control port. Furthermore, it was found that an inversely proportional relationship exists between flow velocity in the throat and the switching time. The results agree with the theoretical background established by experimental studies that can be found in the literature. Full article

Transient fluid flows through tubes are critical in such topics as water hammer, ram pumps and pipeline dynamics. While analytical solutions exist in the literature for simple geometries such as tapered and non-tapered tube diameters, one area that is lacking is the case where the wave speed changes along the length. An example of this is a flexible pipe with a tapered wall thickness. In order to calculate the transient pressure response of such a system, this previously required a computationally expensive gridded method of characteristics (MOC) solution. This paper describes an analytical solution to the dynamic laminar flow of liquid in a tube where the wave speed varies along its length. This frequency-domain solution includes frequency-dependent friction effects. A comparison to a method of characteristics (MOC) solution is used to verify the solution. The paper also discusses some numerical issues and provides an approximate method that can be used for high-frequency calculations where limited numerical precision can cause errors. Finally, a preliminary comparison of the computational performance is presented, in which the new method is an order of magnitude faster to calculate than an MOC solution. Full article

This paper addresses the challenges of pressure-based sensing using axisymmetric probes whose axes are at small angles to the mean flow. Mean pressure measurements around three yawed circular cylinders with aspect ratios of 28, 64, and 100 were made to determine the effect of changes in the yaw angle, γ, and freestream velocity on the average pressure coefficient, ${\overline{C}}_{pN}$, and drag coefficient, $C_{DN}$. The existence of four distinct types of circumferential pressure distributions—subcritical, transitional, supercritical, and asymmetric—were confirmed, along with the appropriateness of scaling ${\overline{C}}_{pN}$ and $C_{DN}$ on a streamwise Reynolds number, $R{e}_{sw}$, based on the freestream velocity and the fluid path length along the cylinder in the streamwise direction. It was found that there was a distinct difference in the values of $C_{DN}$ and ${\overline{C}}_{pN}$ at identical $R{e}_{sw}$ values for cylinders yawed between 5° and 30°, and for cylinders at greater than a 30° yaw. For γ < 5°, there did not appear to be any large-scale vortices in the near wake, and $C_{DN}$ and $\overline{C}$_pN appeared to become independent of $R{e}_{sw}$. Over the range of 5° ≤ γ ≤ 30°, there was a complex interplay of freestream speed, yaw angle, and aspect ratio that affected the formation and shedding of Kármán-like vortices. Full article

The momentum flux in a canonical turbulent boundary layer is known to have a time-series signature that is characterised by a highly intermittent variation, which includes very short periods of intense flux activity. Here, we study the variation in these flux signal characteristics across almost a decade of flow Reynolds number ($R{e}_{\tau }$) by analysing datasets acquired using miniature cross-wire probes with matched spatial resolution. The analysis is facilitated by conditionally sampling the signal based on the quadrant (Qi; i = 1–4) and magnitude of the flux, revealing fractional cumulative contribution from Q4 to increase at a much faster rate than from Q2 with $R{e}_{\tau }$. An episodic description of the flux signal is subsequently undertaken, which associates this rapid increase in Q4 contributions with the emergence of extreme and rare flux events with $R{e}_{\tau }$. The same dataset is also used to test Townsend’s hypothesis on the active and inactive components of the momentum flux, which are obtained for the first time by implementing a spectral linear stochastic estimation-based decomposition methodology. While the active component is found to be the dominant contributor to the mean momentum flux consistent with Townsend’s hypothesis, the inactive component is found to be small but non-zero, owing to the non-linear interactions associated with the modulation phenomenon. Finally, an episodic description of the active and inactive momentum flux signal is undertaken to highlight the starkly different time series characteristics of the two flux components. The inactive flux signal is found to comprise individual statistically significant events associated with all four quadrants, leading to a small net contribution to the total flux. Full article

In this paper, we use a fluid–structure interaction (FSI) approach to simulate a Coriolis mass flowmeter (CMF). The fluid dynamics is calculated by the open-source framework OpenLB, based on the lattice Boltzmann method (LBM). For the structural dynamics we employ the open-source software Elmer, an implementation of the finite element method (FEM). A staggered coupling approach between the two software packages is presented. The finite element mesh is created by the mesh generator Gmsh to ensure a complete open source workflow. The Eigenmodes of the CMF, which are calculated by modal analysis, are compared with measurement data. Using the estimated excitation frequency, a fully coupled, partitioned, FSI simulation is applied to simulate the phase shift of the investigated CMF design. The calculated phase shift values are in good agreement to the measurement data and verify the suitability of the model to numerically describe the working principle of a CMF. Full article

The control of flow separation on aerodynamic surfaces remains a fundamental goal for future air transportation. On airplane wings and control surfaces, the effects of flow separation include decreased lift, increased drag, and enhanced flow unsteadiness and noise, all of which are detrimental to flight performance, fuel consumption, and environmental emissions. Many types of actuators have been designed in the past to counter the negative effects of flow separation, from passive vortex generators to active methods like synthetic jets, plasma actuators, or sweeping jets. At the Chair of Aerodynamics at TU Berlin, significant success has been achieved through the use of pulsed jet actuators (PJA) which operate by ejecting a given amount of fluid at a specified frequency through a slit-shape slot on the test surface, thereby increasing entrainment and momentum in a separating boundary layer and thus delaying flow separation. Earlier PJAs were implemented using fast-switching solenoid valves to regulate the jet amplitude and frequency. In recent years, the mechanical valves have been replaced by fluidic oscillators (FO) in an attempt to generate the desired control authority without any moving parts, thus paving the way for future industrial applications. In the present article, we present in-depth flow and design analysis which affect the operation of such FO-based PJAs. We start by reviewing current knowledge on the mechanism of flow separation control with PJAs before embarking on a detailed analysis of single-stage FO-based PJAs. In particular, we show that there is a fundamental regime where the oscillation frequency is mainly driven by the feedback loop length. Additionally, there are higher-order regimes where the oscillation frequency is significantly increased. The parameters that influence the oscillation in the different regimes are discussed and a strategy to incorporate this new knowledge into the design of future actuators is proposed. Full article

Cardiovascular disease is one of the world’s leading causes of morbidity and mortality. Fractional flow reserve (FFR) was proposed in the 1990s to more accurately evaluate the functional severity of intermediate coronary stenosis, and it is currently the gold standard in cardiac catheterization laboratories where coronary pressure and flow are routinely obtained. The clinical measurement of FFR relies on a pressure wire for the recording of pressures; however, in computational fluid dynamics studies, an FFR is frequently predicted using a wire-absent model. We aim to investigate the influence of the physical presence of a 0.014-inch (≈0.36 mm) pressure wire in the calculation of virtual FFR. Ideal and patient-specific models were simulated with the absence and presence of a pressure wire. The computed FFR reduced from 0.96 to 0.93 after inserting a wire in a 3-mm non-stenosed (pipe) ideal model. In mild stenotic cases, the difference in FFR between the wire-absent and wire-included models was slight. The overestimation in severe case was large but is of less clinical significance because, in practice, this tight lesion does not require sophisticated measurement to be considered critical. However, an absence of the pressure wire in simulations could contribute to an over-evaluation for an intermediate coronary stenosis. Full article

This study evaluates the stiffness and damping characteristics of low-profile magnetorheological (MR) fluid mounts (MRFM) to provide a better understanding of the vibration improvements offered by such mounts, as compared with conventional elastomeric mounts. It also aims at assessing how much of the mount’s performance is due to the MR fluid and how much is due to the elastomer and steel insert that is used in MRFM. The study includes the design, analysis, fabrication, and testing of a unique class of MRFM that is suitable for the isolation of sensitive machinery and sensors. The MR fluid is compressed (squeezed) in response to dynamic force applied to the mount. The test results are compared with conventional elastomeric (rubber) mounts of the same configuration as MRFM, to highlight the changes in stiffness and damping characteristics for frequencies ranging from 1 to 35 Hz. With no current supplied, the MRFM has a slightly higher stiffness and nearly the same damping as a conventional rubber mount. The slight increase in MRFM stiffness is attributed to the MR fluid’s compressive stiffness, which is higher than the rubber. When current is supplied to the MRFM, the stiffness and damping increase significantly at lower frequencies and taper off to nearly the same level as the rubber mount at higher frequencies. Both the stiffness and damping are directly proportional to the supplied current. At the maximum current of 2 A, the MRFM has 200% higher stiffness and 700% higher damping than the rubber mount. The significantly higher damping and stiffness and the tapering off to nearly the same level as the rubber mount is quite interesting and intriguing. It indicates that MRFM delivers high damping and stiffness when needed, while significantly tapering them off when high damping and stiffness are not desirable. Full article

We present the results of direct numerical simulations of power spectral densities for kinetic energy, convective entropy, and heat flux for unsteady Rayleigh–Bénard magnetoconvection in the frequency space. For larger values of frequency, the power spectral densities for all the global quantities vary with frequency (f) as $f^{-2}$. The scaling exponent is independent of Rayleigh number, Chandrasekhar’s number, and thermal Prandtl number. Full article

Professor N.E. Zhukovsky was a famous Russian mechanic and engineer. In 1876 he defended his master’s thesis at Moscow University. At a careful reading of N.E. Zhukovsky’s master’s thesis in 1997, V.A. Bubnov—a professor at the Moscow City Pedagogical University—discovered terms of the second order of smallness in the continuity equation for an incompressible fluid. Zhukovsky calculated them, but did not use the amount of substance in the balance. Ten years later, the author found high-order terms in Euler’s derivation of the 1752 continuity equation for an incompressible fluid. The physical meaning of the additional terms became clear after the derivation in 2006 of the continuity equation with terms of high order of smallness for a compressible gas. The higher order terms of the smallness of the continuity equation penetrate into the inhomogeneous part of the wave equation and lead to the generation of self-oscillations, vibrations, sound, and the initial stage of turbulent pulsations. The stochastic approach ensured success in modeling turbulent flows. The use of high-order terms of smallness of the Euler continuity equation makes it possible to transfer the description of some part of the motions from the stochastic part of the equation to the deterministic part. The article contains a review of works with the derivation of the inhomogeneous wave equation. These works use additional terms of a high order of smallness in the continuity equation. Full article

Numerical simulations are subject to uncertainties due to the imprecise knowledge of physical properties, model parameters, as well as initial and boundary conditions. The assessment of these uncertainties is required for some applications. In the field of Computational Fluid Dynamics (CFD), the reliable prediction of hydrogen distribution and pressure build-up in nuclear reactor containment after a severe reactor accident is a representative application where the assessment of these uncertainties is of essential importance. The inital and boundary conditions that significantly influence the present buoyancy-driven flow are subject to uncertainties. Therefore, the aim is to investigate the propagation of uncertainties in input parameters to the results variables. As a basis for the examination of a representative reactor test containment, the investigations are initially carried out using the Differentially Heated Cavity (DHC) of aspect ratio 4 with $Ra=2\times {10}^9$ as a test case from the literature. This allows for gradual method development for guidelines to quantify the uncertainty of natural convection flows in large-scale industrial applications. A dual approach is applied, in which Large Eddy Simulation (LES) is used as reference for the Unsteady Reynolds-Averaged Navier–Stokes (URANS) computations. A methodology for the uncertainty quantification in engineering applications with a preceding mesh convergence study and sensitivity analysis is presented. By taking the LES as a reference, the results indicate that URANS is able to predict the underlying mixing process at $Ra=2\times {10}^9$ and the variability of the result variables due to parameter uncertainties. Full article