Upward Buoyancy Force Research Articles

Why does tropical cyclone intensify faster under weaker parameterized horizontal diffusion in three-dimensional numerical simulations?

The mechanisms by which the parameterized horizontal diffusion impacts the tropical cyclone (TC) intensification are investigated via a series of numerical simulations of Supertyphoon Lekima (2019) with different horizontal mixing lengths (Lh). Consistent with previous studies, the TC intensifies faster and attains a higher peak intensity as Lh decreases, which is attributed to a more compact wind structure and the stronger eyewall convective heating. The azimuthal-mean tangential wind and vertical momentum budgets are conducted to explain the differences in TC size and convective strength between the simulations. It is found that when horizontal diffusion weakens, the eddy mixing of tangential momentum becomes larger inside the radius of maximum wind, therefore promoting size contraction. The stronger eddy mixing is attributed to the more active eyewall mesovortices whose growth is suppressed when horizontal diffusion strengthens. The vertical momentum budget results indicate that the air parcels in the simulation with smaller Lh experience stronger upward buoyancy force in the lower-to-mid troposphere (3–7 km) than those in the larger-Lh simulation, leading to more vigorous eyewall convection. It is further revealed that the reduced horizontal diffusion helps maintain the strength of virtual potential temperature perturbations and therefore the buoyancy in the eyewall updrafts. The findings from this study imply that the horizontal diffusion plays an important role in regulating the mesoscale and convective-scale processes in the inner-core region and improvements in its parameterization are urged for improving TC intensity forecast.

Flow control using hot splitter plates in the wake of a circular cylinder: A hybrid strategy

A novel and effective hybrid technique, which involves active surface heating strategies in conjunction with the use of passive splitter plates in the wake of the cylinder, is proposed. In this report, we present the results of a numerical investigation on the two-dimensional, laminar mixed convection flow over a circular cylinder with a hot rigid splitter plate attached to it on the wake side. A projection algorithm-based finite volume method is employed to obtain the solution of the coupled, nonlinear governing partial differential equations subjected to Courant–Friedrichs–Lewy conditions. The isothermal heating of the splitter plate under the influence of the gravity field generates an upward buoyancy force in the wake of the cylinder. For different length-to-diameter (L/D) ratios, the effect of heating on aerodynamic, wake, and heat transfer characteristics has been studied for a wide range of parameters; 75 ≤Re≤ 150, 0 ≤Ri≤ 1, and 0.5 ≤L/D≤ 1 at Pr = 0.7. It is observed that the hot splitter plate would bring about conspicuous changes such as asymmetry in the vortex shedding behind the cylinder at low Reynolds numbers. The outcomes demonstrate a notable improvement in convective heat transfer and drag, with gains of up to 7% and 15%, respectively. It is found that the rate of heat transfer and vortex shedding frequency decrease with an increase in L/D ratio. Correlations for the estimation of Strouhal number and Nusselt number have also been proposed which helps provide a more thorough understanding of thermal and aerodynamic features of the hybrid approach.

Self-oscillation of 3D trapped bubbles

In this study, we focus on the trapping and self-oscillation of microbubbles in ethanol using a low-power continuous-wave laser. The microbubble formation is achieved by heating of ethanol by light absorption (λ = 658 nm) at silver nanoparticles deposited on the distal end of a multi-mode optical fiber. Subsequently, a second low-power continuous-wave laser (λ = 1,550 nm) coupled to a single-mode optical fiber is used to trap the microbubble. To trap the microbubble, the red laser is turned off after its generation, and immediately the trapping laser is activated. The bulk light absorption at λ = 1,550 nm in ethanol modulates the surface tension of the bubble wall, creating a 3D potential well that effectively traps the bubble. Once the bubble is trapped, random variations in the bubble's radius led to instabilities in the trap, triggering the microbubble oscillation. The trapped bubble tends to oscillate along the light propagation between two points of quasi-steady-state equilibrium. These bubble oscillations result from the opposing competing forces: a changing-direction Marangoni force and drag forces and the upward buoyancy force. To explain the self-oscillation, we present a simple model that qualitatively describes the main features observed in the experimental data.

The Buoyancy of the Tunnel Segmental Lining in the Surrounding Filling Material and its Effects on the Concrete Stress State

Segmental lining is subject to significant upward buoyancy forces when a grouting material (slurry), initially fluid, is adopted to fill the gap between its external profile and the wall of a tunnel excavated with a TBM machine. The analysis of the effects of these forces is important in order to correctly dimension the segmental lining and avoid damage to the lining and subsequent costly maintenance and restoration actions. Given the complexity of the behavior of a segmental lining consisting of segmental rings and circular joints that alternate in the longitudinal direction of the tunnel, a specific numerical model has been implemented, adopting the Finite Element Method (FEM). This model is able to obtain the development of the vertical displacements of the segmental lining starting from the TBM tail, together with the bending moments and the shear forces induced inside it. The developed model is able to assess the risks of breaking and damaging the concrete and steel bolts that are used to connect the segmental rings at the circular joints; therefore, it represents a useful design tool for being able to correctly dimension the segmental lining also in relation to the risks produced by the appearance of considerable buoyancy forces around it, due to the presence of the initially fluid filling material. The proposed numerical model was applied to a real case (Ningbo metro tunnel) and allowed to obtain satisfactory results from the comparison of the calculated displacements with in situ measurements. Some sensitivity analyzes developed on the studied case have made it possible to detect which are the influencing parameters that have the greatest impact on the behavior of segmental lining in the presence of the studied buoyancy forces.

A pseudopotential lattice Boltzmann model for simulating mass transfer around a rising bubble under real buoyancy effect

A pseudopotential multicomponent lattice Boltzmann (LB) model that can account for the real buoyancy effect is proposed to simulate the mass transfer process around a rising bubble. The density profiles at the equilibrium state are determined based on the hydrostatic condition and the zero diffusion flux condition (the balance of chemical potential). Compared with the LB models using effective buoyancy force, the proposed model has three advantages: (1) avoiding the unrealistic distribution of gas components within the bubble due to the upward effective buoyancy force, (2) removing the undesirable diffusion process due to the application of effective buoyancy force, and (3) considering the effect of the pressure gradient on the change of bubble size. In addition, Henry's law, which can be automatically recovered from the multicomponent LB equation, is re-interpreted from the perspective of the balance of chemical potential. Simulation results showed that the diffusion flux non-uniformly distributes over the surface of a rising bubble. The diffusion zone primarily occurs at the top and the lateral side of a rising bubble, whereas the diffusion transport just below the rising bubble is much less significant than its counterpart above the rising bubble. Various bubble shapes and their corresponding diffusion zones have been obtained. Moreover, the correlation between the Sherwood number and the Peclet number derived from the simulation results is consistent with those from previous numerical results. Thus, the proposed LB model is capable of conducting a quantitative analysis of the mass transfer around a rising bubble.

Experimental study of flame morphology and size model of a horizontal jet flame impinging a wall

The production and transportation processes of gas fuel may be faced with a safety challenge in the form of a jet fire from pipeline leakage. In actual accidents, sometimes some obstacles may appear in the path of the horizontal jet fire development leading to impingement. The spread mechanism of such a flame is complex due to the coupling relation of the wall resistance force, buoyancy force and initial momentum. Experiments were conducted to study a horizontal jet flame impinging a wall as a function of fuel initial velocity and nozzle-wall spacing. Results show the transient development of flame morphology and spread mechanism of the steady flame. The upward buoyancy force of the horizontal jet flame gradually increases with the fuel as it moves further away until flame impinges the wall. From the side view, flame morphologies include the flame impinging the wall (up-down spread and up spread stages) and flame not impinging the wall (free spread stage). A counterclockwise flame vortex occurs due to the competition between the upward buoyancy force and downward momentum below the nozzle projection point. From the front view, the flame morphology changes from "U" morphology to "O" morphology. By combining the knowledge of the jet fluid, momentum conservation principle and Newton's second law, a flame size model of the horizontal jet flame impinging the wall is proposed.

Numerical investigations of Re-independence and influence of wall heating on flow characteristics and ventilation in full-scale 2D street canyons

Validated by wind tunnel data, this study numerically investigates the integrated impacts of wind and thermal buoyancy on urban turbulence, ventilation and pollutant dispersion in full-scale 2D deep street canyons (aspect ratio AR = H/W = 3 and 5, W = 24 m). Isothermal urban airflows for such deep street canyons can be Reynolds-number-independent when reference Reynolds number (Re) exceeds the critical Re (Rec~106,107 when AR = 3, 5), i.e. AR = 5 experiences two main vortices and one-order smaller NEV* (~10−3, the normalized net escape velocity) than AR = 3 with a single main vortex (NEV*~10−2).With sufficiently large Re (Re > Rec) and the same air-wall temperature difference (Ri = 2.62, 4.36 when AR = 3, 5), four uniform wall heating patterns were considered, including leeward-wall heating (L-H), windward-wall heating (W–H), ground heating (G-H), and all-wall heating (A-H). Various indicators were adopted to evaluate street ventilation and pollutant dilution capacity (e.g. age of air (τ,s), NEV*, pollutant transport rates (PTR)). Full-scale wall heating produces a strong upward near-wall buoyancy force, which significantly influences flow patterns and improves street ventilation for most cases. When AR = 3, L-H strengthens the single-vortex airflow. When AR = 5, L-H converts the isothermal double vortices into a single-clockwise vortex. For both ARs, W–H reverses the main clockwise vortex to an enhanced counterclockwise one, moreover G-H and A-H cause a more complicated multi-vortex pattern than isothermal cases. Overall, when AR = 3, L-H and W–H increase NEV* by 68% and 40% than the isothermal case. When AR = 5, four wall heating patterns all raise NEV* considerably (by 150%–556%). For both ARs, the L-H, W–H and A-H amplify the contribution of mean flows on removing pollutants but reduce that by turbulent diffusion compared with isothermal cases.

Lithospheric Structure of the Central Andes Forearc from Gravity Data Modeling: Implication for Plate Coupling

Abstract Geodetic and seismological data indicates that the Central Andes subduction zone is highly coupled. To understand the plate locking mechanism within the Central Andes, we developed 2.5-D gravity models of the lithosphere and assessed the region’s isostatic state. The densities within the gravity models are based on satellite and surface gravity data and constrained by previous tomographic studies. The gravity models indicate a high-density (~2940 kg m-3) forearc structure in the overriding South American continental lithosphere, which is higher than the average density of the continental crust. This structure produces an anomalous pressure (20-40 MPa) on the subducting Nazca plate, contributing to intraplate coupling within the Central Andes. The anomalous lithostatic pressure and buoyancy force may be controlling plate coupling and asperity generation in the Central Andes. The high-density forearc structure could be a batholith or ophiolite emplaced onto the continental crust. The isostatic state of the Central Andes and Nazca plate is assessed based on residual topography (difference between observed and isostatic topography). The West-Central Andes and Nazca ridge have ~0.78 km of residual topography, indicating undercompensation. The crustal thickness beneath the West-Central Andes may not be sufficient to isostatically support the observed topography. This residual topography may be partially supported by small-scale convective cells in the mantle wedge. The residual topography in the Nazca ridge may be attributed to density differences between the subducting Nazca slab and the Nazca ridge. The high density of the subducted Nazca slab has a downward buoyancy force, while the less dense Nazca ridge provides an upward buoyancy force. These two forces may effectively raise the Nazca ridge to its current-day elevation.

Realistic Buoyancy Model for Real‐Time Applications

AbstractFollowing Archimedes' Principle, any object immersed in a fluid is subject to an upward buoyancy force equal to the weight of the fluid displaced by the object. This simple description is the origin of a set of effects that are ubiquitous in nature, and are becoming commonplace in games, simulators and interactive animations. Although there are solutions to the fluid‐to‐solid coupling problem in some particular cases, to the best of our knowledge, comprehensive and accurate computational buoyancy models adequate in general contexts are still lacking. We propose a real‐time Graphics Processing Unit (GPU) based algorithm for realistic computation of the fluid‐to‐solid coupling problem, which is adequate for a wide generality of cases (solid or hollow objects, with permeable or leak‐proof surfaces, and with variable masses). The method incorporates the behaviour of the fluid into which the object is immersed, and decouples the computation of the physical parameters involved in the buoyancy force of the empty object from the mass of contained liquid. The dynamics of this mass of liquid are also computed, in a way such that the relation between the centre of mass of the object and the buoyancy force may vary, leading to complex, realistic beha viours such as the ones arising for instance with a sinking boat.

Ice Particles Sink below the Water Surface Due to a Balance of Salt, van der Waals, and Buoyancy Forces

According to the classical Archimedes’ principle, ice floats in water and has a fraction of its volume above the water surface. However, for very small ice particles, other competing forces such as van der Waals forces due to fluctuating charge distributions and ionic forces due to salt ions and charge on the ice surface also contribute to the force balance. The latter crucially depends on both the pH of the water and the salt concentration. We show that a bulge in the air–water interface due to interaction of surface tension with the rising ice particle becomes significant when the particle radius is greater than 50–100 μm. The role of these forces in governing the initial stages of ice condensation has never been considered. Here, we show that small ice particles can only form below an exclusion zone, from 2 nm (in high salt concentrations) up to 1 μm (in pure water at pH 7) thick, under the water surface. This distance is defined by an equilibrium of upward buoyancy forces and repulsive van der Waals forces. Ionic forces due to salt and ice surface charge push this zone further down. Only after growing to a radius larger than 10 μm, will the ice particles eventually float toward the water surface in agreement with the simple intuition based on Archimedes’ principle. Our result is the first prediction of observable repulsive van der Waals forces between ice particles and the water surface outside a laboratory setting. We posit that it has consequences on the biology of ice water as we predict an exclusion zone free of ice particles near the water surface which is sufficient to support the presence of bacteria.

Archimedes\u2019 principle for characterisation of recombinant whole cell biocatalysts

The ability of whole cells to catalyse multistep reactions, often yielding synthetically demanding compounds later used by industrial biotech or pharma, makes them an indispensable tool of synthetic chemistry. The complex reaction network employed by cellular catalysts and the still only moderate predictive power of modelling approaches leaves this tool challenging to engineer. Frequently, large libraries of semi-rationally generated variants are sampled in high-throughput mode in order to then identify improved catalysts. We present a method for space- and time-efficient processing of very large libraries (107) of recombinant cellular catalysts, in which the phenotypic characterisation and the isolation of positive variants for the entire library is done within one minute in a single, highly parallelized operation. Specifically, product formation in nanolitre-sized cultivation vessels is sensed and translated into the formation of catalase as a reporter protein. Exposure to hydrogen peroxide leads to oxygen gas formation and thus to a density shift of the cultivation vessel. Exploiting Archimedes’ principle, this density shift and the resulting upward buoyancy force can be used for batch-wise library sampling. We demonstrate the potential of the method for both, screening and selection protocols, and envision a wide applicability of the system for biosensor-based assays.

A parametric simulation of solar chimney power plant

The strong solar radiation, continuous supplies of sunlight and environmental friendly factors have made the solar chimney power plant becoming highly feasible to build in Malaysia. Solar chimney power plant produces upward buoyancy force through the greenhouse effect. Numerical simulation was performed on the model of a solar chimney power plant using the ANSYS Fluent software by applying standard k-epsilon turbulence model and discrete ordinates (DO) radiation model to solve the relevant equations. A parametric study was carried out to evaluate the performance of solar chimney power plant, which focused on the temperature rise in the collector, air velocity at the chimney base, and pressure drop inside the chimney were based on the results of temperature, velocity, and static pressure distributions. The results demonstrate reliability by comparing a model with the experimental data of Manzanares Spanish prototype. Based on the numerical results, power capacity and efficiency were analysed theoretically. Results indicate that a stronger solar radiation and larger prototype will improve the performance of solar chimney power plant.

Flow field investigation in a rotating disk chemical vapor deposition chamber with a perforated showerhead

A flow field in a simulated rotating disk chemical vapor deposition chamber in which the inflow gases entered through a showerhead inlet was experimentally investigated using particle image velocimetry. The deposition uniformity was highly related to the flow pattern, which was influenced by the buoyancy, centrifugal, and flow inertia forces. This study investigated flow patterns for different processing parameters, namely chamber heights (20 and 40mm), jet-to-disk temperature differences (0–500°C), and disk rotational speeds (0–500rpm). The time-averaged axial and radial velocity profiles were determined for examining the effects of rotation and heating on flow uniformity above the rotating disk. The Reynolds stress and turbulence intensity was found to be influenced by the buoyancy and rotation induced flow. At a high jet-to-disk temperature difference, the upward buoyancy force lifted the flow and prevented the inlet flow from reaching the disk surface. The buoyancy-induced flow can be suppressed through disk rotation or chamber height reduction. Moreover, the nondimensional parameters (Grashof number and rotational Reynolds number) can be used to construct flow regime maps and quantify the effects of rotation and heating even with the contribution from different chamber heights, disk temperatures, and rotational speeds.

Settling of heated particles in homogeneous turbulence

We study the case of inertial particles heated by thermal radiation while settling by gravity through a turbulent transparent gas. We consider dilute and optically thin regimes in which each particle receives the same heat flux. Numerical simulations of forced homogeneous turbulence are performed taking into account the two-way coupling of both momentum and temperature between the dispersed and continuous phases. Particles much smaller than the smallest flow scales are considered and the point-particle approximation is adopted. The particle Stokes number (based on the Kolmogorov time scale) is of order unity, while the nominal settling velocity is up to an order of magnitude larger than the Kolmogorov velocity, marking a critical difference with previous two-way coupled simulations. It is found that non-heated particles enhance turbulence when their settling velocity is sufficiently high compared to the Kolmogorov velocity. Energy spectra show that the non-heated particle settling impacts both the very small and very large flow scales, while the intermediate scales are weakly affected. When heated, particles shed plumes of buoyant gas, further modifying the turbulence structure. At the considered radiation intensities, clustering is strong but the classic mechanism of preferential concentration is modified, while preferential sweeping is eliminated or even reversed. Particle heating also causes a significant reduction of the mean settling velocity, which is caused by rising buoyant plumes in the vicinity of particle clusters. The turbulent kinetic energy is affected non-monotonically as the radiation intensity is increased due to the competing effects of the downward gravitational force and the upward buoyancy force. The thermal radiation influences all scales of the turbulence. The effects of settling and buoyancy on the turbulence anisotropy are also discussed.

Integrated Effects of Street Layouts and Wall Heating on Vehicular Pollutant Dispersion and their Reentry Toward Downstream Canyons

ABSTRACTVehicle emission is becoming one of the major sources of gaseous pollutants and aerosol particles in urban air environments. Apart from pollutant source control, sustainable street design is another significant technique to reduce street air pollution. Under the validation by wind tunnel data, this paper conducts computational fluid dynamic (CFD) simulations by RNG k-e model to investigate the impacts of typical street layouts and wall heating on the dispersion of gaseous pollutants and particles (diameter d = 1 µm, 5 µm, 20 µm) in the target street canyons and their reentry toward downstream streets. The dispersion processes of gaseous pollutants and fine particles (d = 1 µm) are found similar. For uniform street layouts (aspect ratio H/W = 1) with small Froude number (Fr = 0.19–0.38), leeward-wall heating, ground heating and all-wall heating significantly enhance the primary clock-wise vortex and improve pollutant dispersion, but windward-wall heating does not. Taller upstream buildings (H1/W = 2–3) produce a clockwise vortex over the target canyon and a much weaker counter-clockwise vortex within it, seriously weakening the capacity of pollutant dispersion. For large particles (d = 20 µm), the major fraction deposits onto street ground because the gravity force dominates particle transportation. For particles of d = 5 µm, the dispersion dynamics are more complicated: In the isothermal case less particles of d = 5 µm suspend in the target canyon than d = 1 µm because the gravity force and particle deposition are more important, however, with all-wall heating more particles of d = 5 µm float in the target canyon because the upward thermal buoyancy force reduces particle deposition onto the ground. Finally for both gaseous pollutants and particles, their bulk concentrations in downstream streets decrease exponentially with increasing distance from the target canyon, whose decreasing rates are quantified. Although further investigations are still required to propose a practical framework, this paper is one of the first attempts to quantify the capacity of street particle dispersion for street design purpose.

Reducing response of offshore platforms to wave loads using hydrodynamic buoyant mass dampers

In this paper, an innovative concept is introduced for reducing the displacement response of tower type fixed offshore platforms to wave loads. The idea is based on utilizing a Hydrodynamic Buoyant Mass Damper (HBMD), which employs damper’s buoyancy and inertia forces, along with hydrodynamic damping effects, to reduce the displacement response of the platform. A four-legged platform is investigated in which the HBMD is added at the appropriate elevation. Because of the high volume of the damper, the associated added mass and consequently the generated inertia force is significant. On the other hand, as a result of the damper’s eccentricity with respect to the platform’s position in its deformed configuration, the upward buoyancy force causes reversal moment that can potentially counteract those generated by wave loads. Our results indicate that, if positioned and attached appropriately, the damper interacts with the platform in a way that could result in reducing the response of the platform to wave loads. Response reduction factors are proposed to evaluate the performance of the hydrodynamic buoyant mass damper and seek the optimal stiffness in damper’s attachment to the platform.

Three-dimensional CFD analysis for simulating the greenhouse effect in solar chimney power plants using a two-band radiation model

The greenhouse effect in the solar collector has a fundamental role to produce the upward buoyancy force in solar chimney power plant systems. This study underlines the importance of the greenhouse effect on the buoyancy-driven flow and heat transfer characteristics through the system. For this purpose, a three-dimensional unsteady model with the RNG k–ε turbulence closure was developed, using computational fluid dynamics techniques. In this model, to solve the radiative transfer equation the discrete ordinates (DO) radiation model was implemented, using a two-band radiation model. To simulate radiation effects from the sun's rays, the solar ray tracing algorithm was coupled to the calculation via a source term in the energy equation. Simulations were carried out for a system with the geometry parameters of the Manzanares power plant. The effects of the solar insolation and pressure drop across the turbine on the flow and heat transfer of the system were considered. Based on the numerical results, temperature profile of the ground surface, thermal collector efficiency and power output were calculated and the results were validated by comparing with experimental data of this prototype power plant. Furthermore, enthalpy rise through the collector and energy loss from the chimney outlet between 1-band and two-band radiation model were compared. The analysis showed that simulating the greenhouse effect has an important role to accurately predict the characteristics of the flow and heat transfer in solar chimney power plant systems.

Design and Building of a Fast-acting and Intelligent Lifting System of Submerged Objects

In this paper, a new lifting system for rising of the seabed submerged objects is proposed. The processes of design and building are also presented in detail. Fast-acting, intelligent, easy-performing and portability are most important characteristics of the new system. The required force for most of the existing lift systems is usually provided by creating a hollow-water volume, or a gas-filled bag, under the water. Based on the Archimedes' law, an upward buoyancy force produces at these conditions. A compressed air capsule is usually used for filling the bag in most of the existing methods. Big and heavy components of those systems cause some operating difficulties. Also, the presence of a frogman is a necessity for those systems. It is obvious that the depth of the presence for a frogman is limited. It is very harmful for a frogman to be present at the water depth of more than about 40 meters without using of the pressure chambers and more safety equipments. In order to deduce the above matters, a new design for a lifting system is proposed in this research. In this system, instated of using a compressed air system, combustion of a solid-fuel substance with a controlled condition and cooling of the gaseous products, provides the required gas for filling the bag. The most important applications of this new system can be where shortening of the operation time is vital, such as at naval, safety and emergency subjects of the marine engineering applications.

Particle image velocimetry measurement of jet impingement in a cylindrical chamber with a heated rotating disk

We studied the flow field of a jet impingement on a rotating heated disk to simulate the flow field surrounding the rotating disk of a chemical vapor deposition (CVD) reactor, which is widely used for large-scale production of thin-films and semiconductor materials. The flow field influences the growth rate and deposition uniformity, and is subject to the combined effects of buoyancy, centrifugal, and flow inertia forces that occur during the deposition process. The study investigated various flow-cell sizes and locations, such as the inlet flow-rate (1–10slpm), jet-to-disk temperature difference (40–80°C), and disk rotational speeds (0–500rpm). Particle image velocimetry (PIV) was used to measure the flow-velocity field and flow-streamlines in the test chamber. The time-averaged axial and radial velocity profiles near the disk were used to determine the variations in flow velocity resulting from rotation and heating. Upward buoyancy forces, caused by the heated disk, produce flow cells and break the flow uniformity above the disk. When the rotational Reynolds number increases, the rotational effect eventually dominates the flow field that increases the flow velocity and generates flow cells near the chamber wall. Flow regime maps of these flow patterns were constructed, based on the Grashof number and rotational Reynolds number.

Numerical study of eccentric core-annular flow

A numerical study (taking into account inertial -, viscous - and pressure forces) has been made of eccentric core-annular flow through a horizontal pipe, special attention being paid to the vertical force on the core. The viscosity of the core is assumed to be so large that it behaves as a rigid solid. A wave is present at its surface. The shape of the wave is based on experimental results published earlier in the open literature. Due to the eccentricity the centre line of the core is shifted in the upward vertical direction with respect to the centre line of the tube. The vertical force on the core was found to be dependent on the Reynolds number: at small values of the Reynolds number the force is in the upward vertical direction, at large values the force is downward. This means that at large values of the Reynolds number an upward buoyancy force on the core due to a density difference between core and annulus can be counterbalanced. So a stationary core-annular flow is then possible.