Unsteady Evolution Research Articles

A model based on Hirano-Exner equations for two-dimensional transient flows over heterogeneous erodible beds

In order to study the morphological evolution of river beds composed of heterogeneous material, the interaction among the different grain sizes must be taken into account. In this paper, these equations are combined with the two-dimensional shallow water equations to describe the flow field. The resulting system of equations can be solved in two ways: (i) in a coupled way, solving flow and sediment equations simultaneously at a given time-step or (ii) in an uncoupled manner by first solving the flow field and using the magnitudes obtained at each time-step to update the channel morphology (bed and surface composition). The coupled strategy is preferable when dealing with strong and quick interactions between the flow field, the bed evolution and the different particle sizes present on the bed surface. A number of numerical difficulties arise from solving the fully coupled system of equations. These problems are reduced by means of a weakly-coupled strategy to numerically estimate the wave celerities containing the information of the bed and the grain sizes present on the bed. Hence, a two-dimensional numerical scheme able to simulate in a self-stable way the unsteady morphological evolution of channels formed by cohesionless grain size mixtures is presented. The coupling technique is simplified without decreasing the number of waves involved in the numerical scheme but by simplifying their definitions. The numerical results are satisfactorily tested with synthetic cases and against experimental data.

Interactions of vortices, thermal effects and cavitation in liquid hydrogen cavitating flows

Abstract The cavitating flow of liquid hydrogen over an ogive is numerically investigated in a compressible mathematic framework for both gas and liquid phase, based on the homogeneous mixture model coupled with Schnerr–Sauer cavitation model and large eddy simulation. The model for simulating the complex flow is firstly validated by comparing the calculations with the experiments by Hord. Then, the calculated unsteady evolutions of vapor content, temperature and pressure field within the cavity are presented. A special cavitation shedding mechanism, named the partially shedding mode, is revealed for the first time, in which, the primary cavity keeps quasi-steady, while, the much smaller cavity cloud is found to intermittently form near the leading edge inside the primary cavity, then convects downstream along the wall surface and flow out of the closure with a frequency of about 2500 Hz. As the separation of the small cloud from the primary cavity, the volume of the latter diminishes until it is totally swept away with a frequency of about 275 Hz, forming the so called cavitation cloud. The vorticity transport equation in a variable density flow is used to illustrate the complex phenomena of the partially shedding mode. The results reveal that the generation of vorticity mainly happens near the solid surface inside the cavity in non-isothermal cases while it mainly happens at the interface and closure part in isothermal cases. The dynamic interactions between vortices, cavitation and thermal effects are the fundamental cause of the generation of the small bubble clouds, and the three are indispensable. This research helps to understand the complex dynamic mechanism of the cavitation cloud in liquid hydrogen with strong thermal effects.

Numerical analysis of the unsteady behavior of cloud cavitation around a hydrofoil based on an improved filter-based model

The unsteady cavitation evolution around the Clark-Y hydrofoil is investigated in this paper, by using an improved filter-base model (FBM) with the density correction method (DCM). To improve the prediction accuracy, the filter scale is adjusted based on the grid size. The numerical results show that a small filter scale is crucial for the unsteady simulations of the cavity shedding flow. The hybrid method that combines the FBM and the DCM could help to limit the overprediction of the turbulent viscosity in the cavitation region on the wall of the hydrofoil and in the wake. The large value of the maximum density ratio ρl/ρv,clip promotes the mass transfer rate between the liquid phase and the vapor phase, which results in a large sheet cavity length and the vapor fraction rise inside the cavity. The cavity patterns predicted by the improved method are verified by the experimental visualizations. The time-average lift, the drag coefficient and the primary oscillating frequency St for the cavitation number σ = 0.8, the angle of attack, α = 8°, at a Reynolds number Re = 7 × 105 are 0.735, 0.115 and 0.183, respectively, and the predicted errors are 3.29%, 3.36% and 8.93%. The typical three stages in one revolution are well-captured, including the initiation of the sheet/attached cavity, the growth toward the trailing edge (TE) with the development of the re-entrant jet flow, and the large scale cloud cavity shedding. It is observed that the cloud cavity shedding flow induces the vortex pairs of the TE vortices in the wake and the shedding vortices. The positive vorticity vortex of the re-entrant jet and the TE vortices interacts and merges with the negative vorticity vortex of the leading edge (LE) cavity to produce the shedding flow.

An Experimental Study of the Aerodynamics and Performance of a Vertical Axis Wind Turbine in a Confined and Unconfined Environment

This paper presents the results of a wide experimental study on an H-type vertical axis wind turbine (VAWT) carried out at the Politecnico di Milano. The experiments were carried out in a large-scale wind tunnel, where wind turbines for microgeneration can be tested in real-scale conditions. Integral torque and thrust measurements were performed, as well as detailed aerodynamic measurements to characterize the flow field generated by the turbine downstream of the rotor. The machine was tested in both a confined (closed chamber) and unconfined (open chamber) environment, to highlight the effect of wind tunnel blockage on the aerodynamics and performance of the VAWT under investigation. The experimental results, compared with the blockage correlations presently available, suggest that specific correction models should be developed for VAWTs. The experimental thrust and power curves of the turbine, derived from integral measurements, exhibit the expected trends with a peak power coefficient of about 0.28 at tip-speed ratio equal to 2.5. Flow measurements, performed in three conditions for tip speed ratio equal to 1.5, 2.5, and 3.5, show the fully three-dimensional character of the wake, especially in the tip region where a nonsymmetrical wake and tip vortex are found. The unsteady evolution of the velocity and turbulence fields further highlights the effect of aerodynamic loading on the wake unsteadiness, showing the time-dependent nature of the tip vortex and the onset of dynamic stall for tip speed ratio lower than 2.

Simultaneous O and Al diffusion in the combustion of sub-micron aluminium drops

We examine the problem of sub-micron aluminium drop combustion when both O diffusion and Al diffusion occur. During the unsteady evolution of the combustion field the oxide that is generated has the form of a shell whose inner surface encloses an aluminium bath and whose outer surface is exposed to an air bath. The diffusing atoms can react at these surface baths and also, in principle, between themselves in the interior of the oxide. However, the mass concentrations of the atoms are small so that the interior collisions necessary for this reaction are negligible.With this important simplification we are able to define a model that leads to an analytical discussion. For small Damköhler numbers (of which there are two, one defined by the O atoms the other by the Al atoms) the relative values of the bath reaction rates determine the proportion of oxide accretion on the outer surface to accretion on the inner surface. For large Damköhler numbers the relative values of the diffusion coefficients play the same role.

Unsteady evolution of localized unidirectional deep-water wave groups.

We study the evolution of localized wave groups in unidirectional water wave envelope equations [the nonlinear Schrödinger (NLSE) and the modified NLSE (MNLSE)]. These localizations of energy can lead to disastrous extreme responses (rogue waves). We analytically quantify the role of such spatial localization, introducing a technique to reduce the underlying partial differential equation dynamics to a simple ordinary differential equation for the wave packet amplitude. We use this reduced model to show how the scale-invariant symmetries of the NLSE break down when the additional terms in the MNLSE are included, inducing a critical scale for the occurrence of extreme waves.

Evolution of flux ropes in the magnetotail: A three-dimensional global hybrid simulation

Flux ropes in the Earth's magnetotail are widely believed to play a crucial role in energy transport during substorms and the generation of energetic particles. Previous kinetic simulations are limited to the local-scale regime, and thus cannot be used to study the structure associated with the geomagnetic field and the global-scale evolution of the flux ropes. Here, the evolution of flux ropes in the magnetotail under a steady southward interplanetary magnetic field are studied with a newly developed three-dimensional global hybrid simulation model for dynamics ranging from the ion Larmor radius to the global convection time scales. Magnetic reconnection with multiple X-lines is found to take place in the near-tail current sheet at geocentric solar magnetospheric distances x=−30RE∼−15RE around the equatorial plane ( z=0). The magnetotail reconnection layer is turbulent, with a nonuniform structure and unsteady evolution, and exhibits properties of typical collisionless fast reconnection with the Hall effect. A number of small-scale flux ropes are generated through the multiple X-line reconnection. The diameter of the flux ropes is several RE, and the spatial scale of the flux ropes in the dawn-dusk direction is on the order of several RE and does not extend across the entire section of the magnetotail, contrary to previous models and MHD simulation results and showing the importance of the three-dimensional effects. The nonuniform and unsteady multiple X-line reconnection with particle kinetic effects leads to various kinds of flux rope evolution: The small-scale flux ropes propagate earthward or tailward after formation, and eventually merge into the near-Earth region or the mid-/distant-tail plasmoid, respectively. During the propagation, some of the flux ropes can be tilted in the geocentric solar magnetospheric (x,y) plane with respect to the y (dawn-dusk) axis. Coalescence between flux ropes is also observed. At the same time, the evolution of the flux ropes in the multiple X-line reconnection layer can also lead to the acceleration and heating of ions.

Visualisation on supersonic flow over backward-facing step with or without roughness

At Mach number 3.4, visualisation experiments of flow over backward-facing step (BFS) with or without roughness band attached on upstream wall are carried out via traditional schlieren and newly developed nano-tracer-based planar laser scattering (NPLS). The time-averaged flow characteristic of the reattachment region and the instantaneous rich structures of the redeveloping boundary layer in the steamwise-normal plane are both revealed. Additionally, top views in the different planes (y/h = 0.67, 1.00, 1.33, 1.67, 2.00) are imaged with a resolution of 0.064 mm/pixel. By contrasting the NPLS images at different times, the unsteady evolution characteristic of the coherent vortices in the redeveloping boundary layer was discussed. Static wall pressure is measured by a micro-pressure scanning system. The incipient formation positions are pointed out statistically. Without roughness, the longitudinal structures with scales of 1.0h and 1.2h form later and distribute in a longer region compared to that with roughness. Fractal analysis is applied and the averaged fractal dimensions of the overall and sectional flow structures are calculated. If roughness is adopted, the fractal dimension will be larger and the turning point in the sectional fractal dimensions is earlier. However, the dimension tends to be one coincided value in the farther downstream.

Experiment and simulation on air layer drag reduction of high-speed underwater axisymmetric projectile

Injection of air could lead to creation of a bubbly mixture or air layer near the surface that can significantly adjust the flow within the turbulent boundary layer. In this paper, stress wave propagation techniques and Split Hopkinson Pressure Bar (SHPB) are used in underwater launching experiment. Simulation with volume of fluid (VOF) method and modified renormalization group (RNG) k-ε model is also performed to study the physical process of drag reduction of axisymmetric body. Comparison between numerical and experimental air layer length shows good correlation. Results indicate that air layer has good effect on drag reduction. Friction drag reduction mechanism is analyzed from two aspects due to different air volume fraction α. At area with high α, fluid is heterogeneous and layered. Drag reduction is from decrease of velocity gradient and dynamic viscosity at the wall. At area with small α, the mixture is homogeneous. Empirical equation of turbulent boundary layer shear stress is applied to describe drag reduction mechanism. The unsteady evolution of drag with injection of air is also studied at last.

Three-dimensional large eddy simulation of round liquid jet primary breakup in coaxial gas flow using the VOF method

Large eddy simulation (LES) was performed on a liquid primary breakup process of twin-fluid atomizers with various dimensions. Volume of fluid (VOF) method was applied to track the unsteady evolution and breakup of the liquid jet. It was observed that the liquid primary breakup morphology of the thin central tube nozzle was more sensitive to the liquid inlet velocity distribution than that of the thick central tube nozzle, and the possible reasons were analyzed. The effect of liquid inlet velocity distributions on the primary breakup morphology was explored in detail. A criterion parameter was defined to assess the relative importance of liquid inlet velocity distributions on the liquid breakup shape of a selected atomizer. The combination of the present numerical scheme and the proper liquid inlet velocity distribution, which was determined by the dimensions of atomizers, was reliable and efficient for the numerical investigation of coaxial atomizer with various dimensions.

An Adaptive Support Vector Regression Machine for the State Prognosis of Mechanical Systems

Due to the unsteady state evolution of mechanical systems, the time series of state indicators exhibits volatile behavior and staged characteristics. To model hidden trends and predict deterioration failure utilizing volatile state indicators, an adaptive support vector regression (ASVR) machine is proposed. In ASVR, the width of an error-insensitive tube, which is a constant in the traditional support vector regression, is set as a variable determined by the transient distribution boundary of local regions in the training time series. Thus, the localized regions are obtained using a sliding time window, and their boundaries are defined by a robust measure known as the truncated range. Utilizing an adaptive error-insensitive tube, a stabilized tolerance level for noise is achieved, whether the time series occurs in low-volatility regions or in high-volatility regions. The proposed method is evaluated by vibrational data measured on descaling pumps. The results show that ASVR is capable of capturing the local trends of the volatile time series of state indicators and is superior to the standard support vector regression for state prediction.

Loads and pressure evaluation of the flow around a flapping wing from instantaneous 3D velocity measurements

The flow around a flapping wing is characterized by an unsteady evolution of three-dimensional vortices, which are one of the main sources of loads. The difficulty in directly measuring such low forces by means of sensors and the need of the characterization of the evolution of the flow have lead to the evaluation of loads using the integral form of the momentum equation. This paper describes methods for evaluating instantaneous loads and three-dimensional pressure fields using 3D3C velocity fields only. An evaluation of the accuracy of these methods using DNS velocity fields is presented. Loads and pressure fields are then calculated using scanning tomography PIV velocity fields, around a NACA 0012 airfoil for a flapping motion in a water tank at a Reynolds number of 1,000. The results suggest a sufficient accuracy of calculated pressure fields for a global analysis of the topology of the flow and for the evaluation of loads by integrating the calculated pressure field over the surface of the wing.

Hydro-thermo-viscoelastic Based Finite Element Modelingof Apple Convective Drying Process

In the present work we aim to simulate unsteady two-dimensional evolution of the moisture content, temperature and mechanical stress in a parallelepiped apple sample during convective drying. The model is based on the heat and mass transfer equations and the mechanical equilibrium equation under the assumptions of plane deformation, viscoelasticity and isotropic hydric shrinkage. The Finite Elements COMSOL Multiphysics solver is used to solve the developed model. The hydro-thermal model was validated on experimental data drawn in our laboratory for moisture and temperature internal profiles of the product. Excellent agreement has been obtained between numerical and measured data for different drying temperatures. The hydrothermal model was, then, implemented in a Finite Element Hydro-thermo-viscoelastic developed model. Results for mechanical stresses are found to be in good agreement with former observations. It was found, also, that the maximum stress arises at the beginning of drying and holds at the top external surface of the sample which is the surface facing the airflow. The phenomenon is augmented by temperature.

Shape of Slender Axisymmetric Ventilated Supercavities

The integral-differential equation was obtained to simulate unsteady evolutions of the slender axisymmetric ventilated supercavity with the use of one-dimensional inviscid flow of the incompressible gas in the channel between the cavity surface and the body of revolution. For small ventilation rates, the solution of this equation was expressed as asymptotic series. In the steady case the nonlinear differential equation and its solutions were obtained. It was shown that the ventilation can increase and diminish the supercavity dimensions. Examples of calculations for different hull shapes are presented. At some critical values of the gas injection rate the cavity dimensions can become unbounded. Stability of steady and pulsating gas cavities was investigated in the case of the low gas injection rate.

THE NUMERICAL SIMULATION OF UNSTEADY CAVITATION EVOLUTION INDUCED BY PRESSURE WAVE

The present study is focused on the numerical simulation of pressure wave propagation through the cavitating compressible liquid flow, its interaction with cavitation bubble and the resulting unsteady cavitation evolution. The compressibility effects of liquid water are taken into account and the cavitating flow is governed by one-fluid cavitation model which is based on the compressible Euler equations with the assumption that the cavitation is the homogeneous mixture of liquid and vapour which are locally under both kinetic and thermodynamic equilibrium. Several aspects of the method employed to solve the governing equations are outlined. The unsteady features of cavitating flow due to the external perturbation, such as the cavitation deformation and collapse and consequent pressure increase are resolved numerically and discussed in detail. It is observed that the cavitation bubble collapse is accompanied by the huge pressure surge of order of 100 bar, which is thought to be responsible for the material erosion, noise, vibration and loss of efficiency of operating underwater devices.

The influence of the cellular instability on lead shock evolution in weakly unstable detonation

The evolution of the normal detonation shock velocity (Dn) with local shock curvature (κ) is experimentally and numerically examined along entire evolving fronts of a weakly unstable cellular detonation cycle with the intention of extending the understanding of cellular evolution dynamics. As expected, a single velocity–curvature relation is not recovered due to the unsteady evolution of the cell. However, geometric features of the Dn–κ evolution during a cell cycle reveal some new details of the mechanisms driving cellular detonation. On the cell centerline, the local shock velocity and curvature monotonically decrease throughout the cellular cycle. Off centerline, a larger range of wavefront curvature was exhibited in expanding cells as compared to shrinking ones, indicating that most curvature variation in a detonation cell occurs near the Mach stem. In normal shock velocity–curvature space, the cell dynamics can be mapped to three features that are characteristic of (feature 1) a detonation with a spatially short reaction zone, (feature 2) a transitional regime of shock and reaction zone decoupling, and (feature 3) a diffracting inert blast wave. New, growing cells predominately exhibited features 1 and 2, while decaying cells only exhibited feature 3. The portions of all profiles with normal velocities below the Chapman–Jouguet velocity were characteristic of inert blast propagation, indicating the possibility that exceeding this velocity may be a necessary condition for the existence of shock and reaction zone coupling. In this inert blast regime, Dn and κ vary spatially across the wave front so each segment is not geometrically cylindrical, but when accumulated, the Dn–κ data map out a straight line, indicating elements of self-similar flow for each stage in the cell cycle.

A laterally averaged two-dimensional simulation of unsteady supersaturated total dissolved gas in deep reservoir

Elevated levels of the Total Dissolved Gas (TDG) may be reached downstream of dams, leading to increased incidences of gas bubble diseases in fish. The supersaturated TDG dissipates and transports more slowly in reservoirs than in natural rivers because of the greater depth and the lower turbulence, which endangers the fish more seriously. With consideration of the topographical characteristics of a deep reservoir, a laterally averaged two-dimensional unsteady TDG model for deep reservoir is proposed. The dissipation process of the TDG inside the waterbody and the mass transfer through the free surface are separately modeled with different functions in the model. Hydrodynamics equations are solved coupling with those of water temperature and density. The TDG concentration is calculated based on the density current field. A good agreement is found in the simulation of the Dachaoshan Reservoir between the simulation results and the field data of the hydrodynamics parameters and the TDG distribution in the vertical direction and their unsteady evolution with time. The hydrodynamics parameters, the temperature and the TDG concentration are analyzed based on the simulation results. This study demonstrates that the model can be used to predict the evolutions of hydrodynamics parameters, the temperature and the TDG distribution in a deep reservoir with unsteady inflow and outflow. The results can be used in the study of the mitigation measures of the supersaturated TDG.

Aerodynamic characterization of the wake of an isolated rolling wheel

The flow around the wheels of road vehicles exhibits complex unsteady 3D phenomena, including massive boundary layer separations, recirculation areas and 3D vortical structures. Although the mechanisms generating the wake main vortices have been identified, their exact topology is still indeterminate and a description of their unsteady evolution has not yet been proposed.The aim of this paper is to characterize the structure and unsteady motion of an isolated wheel wake. For this purpose, wind tunnel investigations have been carried out with a smooth rotating wheel in contact with a moving belt and compared to URANS simulations based on the geometry used for experiments.CFD calculations appeared to have successfully predicted the main features of the flow. Particle Image Velocimetry and hot-wire anemometry measurements coupled with numerical simulation results enabled the origin and the nature of the main vortical structures in the near-wake to be confirmed and their unsteady behaviour to be investigated. The results show good agreement with previous knowledge and provide new insight into the unsteady features of the wake.

Study on the Wake Shape behind a Wing in Ground Effect Using an Unsteady Discrete Vortex Panel Method

The unsteady evolution of trailing vortex sheets behind a wing in ground effect is simulated using an unsteady discrete vortex panel method. The ground effect is included by image method. The present method is validated by comparing the simulated wake roll-up shapes to published numerical results. When a wing is flying in a very close proximity to the ground, the optimal wing loading is parabolic rather than elliptic. Thus, a theoretical model of wing load distributions is suggested, and unsteady vortex evolutions behind lifting lines with both elliptic and parabolic load distributions are simulated for several ground heights. For a lifting line with elliptic and parabolic loading, the ground has the effect of moving the wingtip vortices laterally outward and suppressing the development of the vortex. When the wing is in a very close proximity to the ground, the types of wing load distributions does not affect much on the overall wake shapes, but parabolic load distributions make the wingtip vortices move more laterally outward than the elliptic load distributions.

Mit N‐Methylpiperidin stabilisierte Halogenalane

AbstractAlanes of the formula HxAlX3–x (x = 0, 1, 2, 3; X = Cl, Br, I) and the mixed halogen species HAlClBr were synthesized as N‐methyl‐piperidin (nmp) adducts HxAlX3–x·znmp (z = 1, 2) and HAlClBr·2nmp by different routes. The crystal and molecular structures of (H3Al·nmp)2, H2AlBr·2nmp, H2AlI·2nmp, the isotypic and isomorphous HAlBr2·2nmp, HAlI2·2nmp, as well as ACl3·nmp, ABr3·nmp, AI3·nmp, and HAlClBr·2nmp are described. The aluminum atoms in these molecular structures either form a pentagonal bipyramid as coordination sphere with the amine bases in apical positions or are in the center of a distorted tetrahedron (AlCl3·nmp, ABr3·nmp, AI3·nmp). In the nmp adduct of alane, a central Al2H2 ring is formed by dimerisation of AlH3, each aluminum atom displaying a further nmp ligand together with two terminal hydrogen atoms. The influence of the halogen atoms on the hydrogen bonds in the iso‐structural compounds were studied by IR spectroscopy, showing in both series H2AlX·2nmp and HAlX2·2nmp (X = Cl, Br, I) a dependence of ν(Al–H) on the substitution pattern: 1770.2–1775.2–(not measured) cm–1 (H2AlX) and 1785.0–1788.0–1791.0 cm–1 (HAlX2). The δ values of the 27Al‐NMR spectra in solution show dependences on the halide numbers bonded to aluminum and display a regular growth with heavier element in the H2AlX·2nmp series δ (27Al): 121.2 (Cl), 126.0 (Br), 131.5 (I)], whereas they have an unsteady evolution in the HAlX2·2nmp series [δ (27Al): 118.0 (Cl), 122.0 (Br), 108.0 (I)] and the AlX3·nmp series [δ (27Al): 102.1 (Cl), 104.8 (Br), 61.9 (I)].