Two-phase co-current flow simulations using periodic boundary conditions in horizontal, 4, 10 and 90° inclined eccentric annulus,flow prediction using a modified interFoam solver and comparison with experimental results

Two-phase oil and gas flow were simulated in an entirely eccentric annulus and compared with experimental data at horizontal, 4, 10, and 90° inclination. The gas-phase was sulphur hexafluoride and the liquid phase a mixture of Exxsol D60 and Marcol 82 for the inclined cases (5–16), and pure Exxsol D60 for the horizontal cases (1–4). The diameter of the outer and inner cylinders was 0.1 and 0.04 m, respectively, for the inclined domains and 0.1 and 0.05 m for the horizontal domain. The cases studied consist of liquid phase fractions between 0.3 and 0.65 and mixture velocities from 1.2 to 4.25 m/s. The mean pressure gradient is within 33% of the expected experimental behavior for all inclined cases. In contrast, the low-velocity horizontal domains exhibit significant deviation, with a drastic over-prediction of the mean pressure gradient by as much as 200–335% for cases 1 and 2. The two remaining horizontal cases (3 and 4) are within 22% of the expected mean pressure gradient. Cases 13–16 are a replication of cases 5–8 at an increased inclination; the mean pressure gradient is within 6.5% of the expected increase due to the increase in hydrostatic pressure. By comparing cases 1–4 to previous published simulations at a lower eccentricity, we found a decrease of the mean pressure gradient by 30–40%, which is in line with existing literature, although for single-phase flows. The simulated and experimental liquid holdup profiles are in good agreement when comparing the fractional data; wave and slug frequencies match to within 0.5 Hz; however, at closer inspection, it is apparent that there is a decrease in the amount of phase-mixing of the simulations compared to the experiments. When increasing the mesh density from 115 k cells/m to 2 million cells/m, the simulations exhibit significantly more phase mixing, but are still unable to produce conventional slugs. In a simplified case, conventional slugs are observed at grid sizing of 1 × 1 × 1 mm, whereas the cells of the 2 million cells/m mesh are roughly 1.5 × 1.5 × 1.5 mm.     

Two-phase flow phenomena along an adiabatic riser – An experimental study at the test-facility GENEVA

Long adiabatic riser geometries with low system pressures are present in a lot of energy and petrochemical processes. Natural-circulation systems are an appropriate solution to save operating and maintenance costs. Under certain circumstances natural-circulation systems tend to unstable mass flow, especially in the riser section. The pressure gradients can stress the construction materials and affect the heat transfer. This paper focuses on GENEVA test-facility and its natural-circulation circuit with heat input by steam condensation. The GENEVA test-facility is explained in detail with focus on the local void fraction measurement system in the adiabatic riser section. The differences to former natural circulation test-facilities are particular emphasized. Therefore a transient experiment is presented and analysed. Moreover the influence of flow restrictions at the downcomer outlet is explained and an experimental method is presented, to determine the maximum natural circulation mass flow of the natural-circulation circuit. Besides, a comparison between the two different riser inner diameters, which were used during the experiments, is presented. The convective heat transfer is analysed by taking into account different dimensionless numbers. A variety of experiments were performed up to 100 kW_el input power from the evaporators. Flashing and geysering as two types of occurred instabilities are stated and discussed in comparison to former test-facilities. Further phenomena like water hammer and counter current liquid flow are investigated. Based on these analyses constructive solutions can be derived, to stabilize the presented natural-circulation two-phase flow system.     

Two phase mixed convection Al2O3–water nanofluid flow in an annulus

Heat transfer enhancement of a mixed convection laminar Al₂O₃–water nanofluid flow in an annulus with constant heat flux boundary condition has been studied employing two phase mixture model and effective expressions of nanofluid properties. The fluid flow properties are assumed constant except for the density in the body force, which varies linearly with the temperature (Boussinesq’s hypothesis), thus the fluid flow characteristics are affected by the buoyancy force. The Brownian motions of nanoparticles have been considered to determine the effective thermal conductivity and the effective dynamic viscosity of Al₂O₃–water nanofluid, which depend on temperature. Three-dimensional Navier–Stokes, energy and volume fraction equations have been discretized using the finite volume method while the SIMPELC algorithm has been introduced to couple the velocity–pressure. Numerical simulations have been presented for the nanoparticles volume fraction (?) between 0 and 0.05 and different values of the Grashof and Reynolds numbers. The calculated results show that at a given Re and Gr, increasing nanoparticles volume fraction increases the Nusselt number at the inner and outer walls while it does not have any significant effect on the friction factor. Both the Nusselt number and the friction coefficient at the inner wall are more than their corresponding values at the outer wall.     

Effects of heat and mass transfer peristaltic flow of?Williamson fluid in a vertical annulus

In the present investigation, we have studied the effects of mixed convection heat and mass transfer on peristaltic flow of Williamson fluid model in a vertical annulus. The governing equations of Williamson fluid model are simplified using the assumptions of long wavelength and low Reynold’s number. An approximated analytical and numerical solutions are found for the velocity field using (i) Perturbation method (ii) Shooting method. The comparisons of analytical and numerical solutions have been presented. The expressions for pressure rise, velocity against various physical parameter are discussed through graphs.     

Experimental investigation of the fluid–structure interaction in an elastic 180° curved vessel at laminar oscillating flow

Fluid–structure interaction phenomena are extremely important when laminar flows through elastic vessels such as in biomedical flow problems are considered. In general, such elastic vessels are curved which is why an elastic 180° bend at a curvature ratio \(\delta = D/D_{\rm C} = 0.\bar{2}\) defines the reference geometry in this study. It is the purpose of this study to compare the results with the steady flow through a 180° rigid pipe bend and to quantify the impact of the fluid–structure interaction on the overall flow pattern and the vessel deformation at oscillating fully developed entrance flow. The findings comprise velocity, pressure, and structure deformation measurements. The vessel dilatation amplitude was varied between 3.75 % and 7 % of the vessel diameter at Dean De and Womersley number Wo ranges of \(327\,\le\,De\,\le\,350\) and \(7\,\le\,Wo\,\le\,8.\) The flow is investigated by time-resolved stereoscopic particle-image velocimetry in five radial cross sections located in the elastic 180° bend and in the inlet pipes. The unsteady static vessel pressure is measured synchronously at these cross sections. The comparison of the steady with the unsteady flow field shows a strong change in the axial and secondary velocity distributions at periods of transition between the centrifugal forces and the unsteady inertia forces dominated regimes. These changes are characterized by asymmetric fluctuations of the centers of the counter-rotating vortex pair. The investigation of the impact of the structure deformation amplitude on these fluctuations reveals a significant attenuation at high deformation amplitudes. The spatial motion of the elastic vessel due to the forces applied by the flow exhibits amplitudes up to 15 % of the vessel diameter. Considering the fluid–structure interaction, an amplification of the volume flux amplitude by a factor of 2.1 at the vessel outlet and phase lags up to 30° occur. The static pressure distribution is characterized by a pronounced asymmetry between forward and backward flow with a 40 % higher peak magnitude at backward flow and phase lags of 35°. The results evidence that a strong distortion of the velocity distribution in the bend, which is caused by the oscillating nature of the flow, is reduced as a result of the fluid–structure interaction.     

Wave–mean flow interaction in an MHD wake behind bluff body

Experimental studies of the effect of constant magnetic field on the process of mean velocity profile stabilization in a wake behind a bluff body are described. To interpret the obtained results, a theoretical model is proposed explaining the scheme of wave-mean flow interaction. We assume that the stabilization process is based on the injection of energy of respective turbulent modes into vortical structures through non-attenuating inertial waves generated in these vortical structures. We also take into account helical character of turbulence in the conditions under study, with weak energy dissipation and its accumulation in large scales.     

High-order resolution Eulerian–Lagrangian simulations of particle dispersion in the accelerated flow behind a moving shock

This paper presents a computational study of the two-dimensional particle-laden flow developments of bronze particle clouds in the accelerated flow behind a moving normal shock. Particle clouds with a particle volume concentration of 4% are arranged initially in a rectangular, triangular and circular shape. Simulations are performed with a recently developed high-order resolution Eulerian–Lagrangian method that approximates the Euler equations governing the gas dynamics with the improved high order weighted essentially non-oscillatory (WENO-Z) scheme, while individual particles are traced in the Lagrangian frame using high-order time integration schemes. Reflected shocks form ahead of all the cloud shapes. The detached shock in front of the triangular cloud is weakest. At later times, the wake behind the cloud becomes unstable, and a two-dimensional vortex-dominated wake forms. Separated shear layers at the edges of the clouds pull particles initially out of the clouds that are consequently transported along the shear layers. Since flows separated trivially at sharp corners, particles are mostly transported out of the cloud into the flow at the sharp front corner of the rectangular cloud and at the trailing corner of the triangular cloud. Particles are transported smoothly out of the circular cloud, since it lacks sharp corners. At late times, the accelerated flow behind the running shock disperses the particles in cross-stream direction the most for the circular cloud, followed by the rectangular cloud and the triangular cloud.     

Surface/interface effects on elastic behavior of a screw dislocation in an eccentric core–shell nanowire

The elastic behavior of a screw dislocation which is positioned inside the shell domain of an eccentric core–shell nanowire is addressed with taking into account the surface/interface stress effect. The complex potential function method in combination with the conformal mapping function is applied to solve the governing non-classical equations. The dislocation stress field and the image force acting on the dislocation are studied in detail and compared with those obtained within the classical theory of elasticity. It is shown that near the free outer surface and the inner core–shell interface, the non-classical solution for the stress field considerably differs from the classical one, while this difference practically vanishes in the bulk regions of the nanowire. It is also demonstrated that the surface with positive (negative) shear modulus applies an extra non-classical repelling (attracting) image force to the dislocation, which can change the nature of the equilibrium positions depending on the system parameters. At the same time, the non-classical solution fails when the dislocation approaches very close to the surface/interface with negative shear modulus. The effects of the core–shell eccentricity and nanowire diameter on dislocation behavior are discussed. It is shown that the non-classical surface/interface effect has a short-range character and becomes more pronounced when the nanowire diameter is smaller than 20 nm.     

Phragmén-Lindel(o)f and continuous dependence type results in a Stokes flow

This paper investigates the asymptotic behavior of end effects for a Stokes flow defined on a three-dimensional semi-infinite cylinder.With homogeneous Dirichlet conditions of the velocity on the lateral surface of the cylinder,solutions either grow or decay exponentially in the distance from the finite end of the cylinder.In the case of decay,the effect of perturbing the equation parameters is also investigated.     

Nonlinear resonances in an axially excited beam carrying a top mass: simulations and experiments

In this paper, nonlinear resonances in a coupled shaker-beam-top mass system are investigated both numerically and experimentally. The imperfect, vertical beam carries the top mass and is axially excited by the shaker at its base. The weight of the top mass is below the beam’s static buckling load. A semi-analytical model is derived for the coupled system. In this model, Taylor-series approximations are used for the inextensibility constraint and the curvature of the beam. The steady-state behavior of the model is studied using numerical tools. In the model with a single beam mode, parametric and direct resonances are found, which affect the dynamic stability of the structure. The model with two beam modes not only shows an additional second harmonic resonance, but also reveals some extra small resonances in the low-frequency range, some of which can be identified as combination resonances. The experimental steady-state response is obtained by performing a (stepped) frequency sweep-up and sweep-down with respect to the harmonic input voltage of the amplifier-shaker combination. A good correspondence between the numerical and experimental steady-state responses is obtained.     

Vortical patterns in turbulent flow downstream a 90° curved pipe at high Womersley numbers

The present experimental work focuses on highly pulsatile, i.e. inertia dominated, turbulent flow downstream a curved pipe and aims at investigating the vortical characteristics of such a flow. The flow parameters (Dean and Womersley number) investigated are of the same order as those met in the internal combustion engine environment. The technique employed is time-resolved stereoscopic particle image velocimetry at different cross-sections downstream the pipe bend. These measurements allow the large-scale structures that are formed to be analyzed by means of proper orthogonal decomposition. The flow field changes drastically during a pulsatile cycle, varying from a uniform flow direction across the pipe section from the inside to the outside of the bend to vortical patterns consisting of two counter-rotating cells. This study characterizes and describes pulsatile curved pipe flow at Womersley numbers much higher than previously reported in the literature. Furthermore, the oscillatory behaviour of the Dean cells for the steady flow – the so-called ‘swirl switching’ – is investigated for different downstream stations from the bend exit and it is shown that this motion does not appear in the immediate vicinity of the bend, but only further downstream.     

One-way coupled fluid–structure interaction of gas–liquid slug flow in a horizontal pipe: Experiments and simulations

Pipelines conveying a multiphase mixture must withstand the cyclic induced stresses that occur due to the alternating motion of gas pockets and liquid slugs. Few previous studies have considered gas–liquid slug flow and the associated fluid–structure interaction problems. In this study, experimental and numerical techniques were adopted to simulate and analyze the two-phase slug flow and the associated stresses in the pipe structure. In the numerical simulation, a one-way coupled fluid–structure framework was developed to explore the slug flow interaction with a horizontal pipe assembly under various superficial gas and liquid velocities. A modified Volume of Fluid and finite element methods were utilized to model the fluid and structure domains. The file-based coupling technique was adopted to execute the coupling mechanism. By contrast, slug characteristics were measured experimentally, while Bi-axial strain gauges were used to capture time-varying strain signals. Excellent agreements between the predicted and measured stress results were achieved with a maximum error of 10.2 %. It was found that at constant superficial liquid velocity, the maximum induced stresses on the pipe wall increased with increasing the slug length and slug velocity. While for the slug frequency, the maximum principal stresses decreased with increasing the slug frequency.     

Effect of thermal radiation on heat transfer in an unsteady copper–water nanofluid flow over an exponentially shrinking porous sheet

The effect of thermal radiation on an unsteady boundary layer flow and heat transfer in a copper–water nanofluid over an exponentially shrinking porous sheet is investigated. With the use of suitable transformations, the governing equations are transformed into ordinary differential equations. Dual non-similarity solutions are obtained for certain values of some parameters. Owing to the presence of thermal radiation, the heat transfer rate is greatly enhanced, and the thermal boundary layer thickness decreases.     

Uniqueness of positive solutions of Δu−u+up=0 in Rn

We establish the uniqueness of the positive, radially symmetric solution to the differential equation u–u+u^p=0 (with p>1) in a bounded or unbounded annular region in R ⁿ for all n1, with the Neumann boundary condition on the inner ball and the Dirichlet boundary condition on the outer ball (to be interpreted as decaying to zero in the case of an unbounded region). The regions we are interested in include, in particular, the cases of a ball, the exterior of a ball, and the whole space. For p=3 and n=3, this a well-known result of Coffman, which was later extended by McLeod & Serrin to general n and all values of p below a certain bound depending on n. Our result shows that such a bound on p is not needed. The basic approach used in this work is that of Coffman, but several of the principal steps in the proof are carried out with the help of Sturm's oscillation theory for linear second-order differential equations. Elementary topological arguments are widely used in the study.     

Mitigation of flow-induced pressure fluctuations in a Francis turbine operating at the design and partial load regimes—LES simulations

High-fidelity large eddy simulations (LES) were conducted to characterize the spatial and temporal structure of turbulent flows in an industrial-sized Francis turbine while the unit operated at the design point and partial load. A pressure surge with an amplitude of 8% of the turbine head was observed at partial load while the amplitude was <1% at the design point. The vortex rope precession observed in the draft tube correlated to the amplitude and frequency of the pressure surge. Central and peripheral water injections at various volumetric rates were considered to control the flow-induced pressure fluctuations. Central injection at the 4% and 6% flow rates attenuated high amplitude pressure fluctuations by 40% and 75% respectively at partial load. At the same operating conditions, peripheral injections did not have the same desired effect. Although power generation was not changed with water injection at the design point, it was reduced by about 2.5% by central injection and 0.5% by peripheral injection at partial load, showing a water injection mitigation strategy could be applied without any penalty.     

Large-eddy simulation of flow separation on an airfoil at a high angle of attack and Re = 105 using Cartesian grids

Incompressible flow separating from the upper surface of an airfoil at an 18° angle of attack and a Reynolds number of Re = 10⁵, based on the freestream velocity and chord length c, is studied by the means of large-eddy simulation (LES). The numerical method is based on second-order central spatial discretization on a Cartesian grid using an immersed boundary technique. The results are compared with an LES using body-fitted nonorthogonal grids and with experimental data.