Publications

January 2026

Tertiary, quaternary and higher order states in the sequence of bifurcations approach (SBA) to turbulence for laterally heated shear flows within a rectangular tube

We consider a vertical rectangular tube of large aspect ratio with side-wall heating in order to mimic realistic experimental conditions. We therefore impose the condition that across any lateral cross-section of the rectangular tube the fluid flow vanishes. We find through our numerical analysis that oscillatory modes yield critical conditions and offer therefore sequential bifurcations that lead to the turbulent regime. Although the linear stability analysis is the same as the case where the imposed constant flux condition is absent, the corresponding nonlinear regime displays fundamentally different characteristics to the open narrow channel case. Here we focus on the sequence of bifurcations approach of a fluid enclosed in a rectangular tube, aligning with engineering applications. We additionally assume the limit of small Prandtl number and thus the effects caused by temperature perturbations are negligible. Finally we identify the oscillatory states that lead to turbulence as the Grashof number increases up to the value 1000. Our fully nonlinear numerical analysis shows that all bifurcations are supercritical and here we concentrate on the critical axial wavenumber of the linear stability analysis of the laminar flow and its pairing with a specific azimuthal wavenumber.

May 2024

Continuum Modeling of Slightly Wet Fluidization with Electrical Capacitance Tomograph Validation

Gas–solid fluidized bed reactors are widely used in the power generation industry. The critical effect of the presence of liquid phase, either as a result of heat, chemical reaction or physical interaction, on the hydrodynamics of the reactor is well recognized by academic researchers and industrial operators. However, theory and simulation frameworks to predict such a condition using the continuum modeling approach are not yet available. This study first shows the significant changes in the flow pattern and distinguishable flow regimes in a slightly wet fluidized bed recorded by an advanced imaging technique. The study then describes the development and implementation of new mathematical formulations for wet particle-particle interactions in a continuum model based on the classic kinetic theory of granular flow (KTGF). Quantitative validation, carried out by comparing the predicted and measured fluidization index (FI) expressed in terms of pressure drop, has shown a good match. The prediction also demonstrates increased bubble splitting, gas channeling, slugging fluidization, and energy dissipation induced by liquid bridges developing from wet particle interactions. These characteristics are similar to those commonly observed in the fluidization of cohesive powders. This model constitutes an important step in extending the continuum theories of dry flow to wet particle-particle interactions. This will allow accurate description and simulation of the fluidized bed in its widest application including power generation systems that involve wet particle fluidization.

February 2024

A falling fluid droplet in an oscillating flow field

We examine the flow in and around a falling fluid droplet in a vertically oscillating flow. We assume axisymmetric Stokes flow, and for small deformations to the droplet, the governing equations can be linearized leading to an infinite system of linear ordinary differential equations. In this study, we have analytically solved the problem in the small-capillary limit. We note that the solution locally breaks down at the poles of the droplet. The drag and center of the mass were also obtained. In the case when only odd modes are present, the droplet shows three-dimensional axisymmetric heart-shaped solutions oscillating vertically in time. When only even modes are present, the droplet exhibits axisymmetric stretching and squeezing.

July 2023

Transient Dynamics in Counter-Rotating Stratified Taylor–Couette Flow

This study focuses on the investigation of stratified Taylor–Couette flow (STCF) using non-modal analysis, which has received relatively limited attention compared to other shear flows. The dynamics of perturbations under different temperature conditions are explored, and their patterns of amplification are analyzed. The study highlights the correlation between flow configurations, emphasizing the similarity in transient dynamics despite different speed ratios. The subcritical effects of thermal stratification on disturbance dynamics are examined, considering the interplay between viscous and buoyancy effects counteracted by strong centrifugal forces. It is found that increasing the wall temperature beyond a critical value leads to buoyancy forces dominating, resulting in a linear increase in the amplification factor. The research reveals significant deviations from previous results, indicating the significant role of temperature stratification.

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May 2023

Pattern competition for the sequential bifurcations approach (SBA) to turbulence in the co-rotating Taylor–Couette system: Quinary states

In this study systematic numerical analyses are outlined searching for additional instabilities in the co-rotating Taylor–Couette system within the fully deterministic sequential approach of bifurcations (SBA) to turbulence. The main idea of the search strategy is the application of a forcing function, rotation, which has a direct physical interpretation, and that was realized in prior experimental work. The forcing induces disturbances that lead to bifurcations of new states. Thus, turbulence can be generated and observed in a rotating fluid without the imposing additional forcing sources. The imposition of thermoconvective forcing in the Taylor–Couette system will be discussed separately. Important findings include the discovery of the interplay of new and already known states, the transition of steady states to oscillatory ones and higher order states in the SBA via vortex merger/separation and re- allocation of symmetries for a more intensified mass transport. The results of the present work enhance the results of [1]. They will be revisited within an internal length gradient (ILG) framework accounting for weekly nonlocal effects as suggested in the concluding section of the paper.

April 2023

Pattern competition in the sequential bifurcation approach to turbulence in homogeneously heated inclined fluid and solid layers

Non-linear solutions and their stability are presented for homogeneously heated channel flows with a simple geometry under the influence of a constant pressure gradient or when the vanishing of the mass flux across any lateral cross-section of the channel is imposed. The critical Grashof number is determined by linear stability analysis for various values of the Prandtl number. In our numerical study the angle of inclination of the channel is taken into account. We found that in each case studied, with the exception of a horizontal layer of fluid and when the applied constant pressure gradient is zero, the basic flow looses stability through a Hopf bifurcation. Following the linear stability analysis our numerical studies are focused on the emerging secondary flows and their stability, in order to identify possible bifurcation points for tertiary flows. We conclude with a few comments on revisiting the present results within an internal length gradient (ILG) framework accounting for higher order velocity and temperature gradients.

March 2023

Numerical reproduction of the spiral wave visualized experimentally in a wide-gap spherical Couette flow

Spherical Couette flow experiments were conducted according to the work of Egbers and Rath [Acta Mech. 111, 125–140 (1995)]. While the value of the critical Reynolds number obtained by the previous experiments was in good agreement with the numerical prediction, it has remained a question why a spiral wave bifurcating over the critical Reynolds number can be visualized even by a classical flow visualization technique like the mixing of a small amount of aluminum flakes to the working fluid. In the present study, through visualization using aluminum flakes drifting on a horizontal plane illuminated by a laser sheet, the flow was identified as a spiral wave with azimuthal wavenumber m=3, using the experimentally obtained and numerically deduced comparison between phase velocities. By solving the equation of motion for the infinitesimal planar particles advecting in the flow field of the spiral wave, a visual distribution of reflected light was virtually reproduced, which is in good agreement with the experimentally obtained picture.

December 2022

The interfacial layer breaker: a violation of Stokes' law in high-speed Atomic Force Microscope flows

Structured water near surfaces is important in non-classical crystallization, biomineralization, and restructuring of cellular membranes. In addition to equilibrium structures, studied by atomic force microscopy (AFM), high-speed AFM (H-S AFM) can now detect piconewton forces in microseconds. With increasing speeds and decreasing tip diameters, there is a danger that continuum water models will not hold, and molecular dynamics (MD) simulations would be needed for accurate predictions. MD simulations, however, can only evolve over tens of nanoseconds due to memory and computational efficiency/speed limitations, so new methods are needed to bridge the gap. Here we report a hybrid, multi-scale simulation method, which can bridge the size and timescale gaps to existing experiments. Structured water is studied between a moving silica AFM colloidal tip and a cleaved mica surface. The computational domain includes 1472766 atoms. To mimic the effect of long-range hydrodynamic forces occurring in water, when moving the AFM tip at speeds from to 30 m/s, a 5 × 10-7 2 hybrid multiscale method with local atomistic resolution is used, which serves as an effective open-domain boundary condition. The multiscale simulation is thus equivalent to using a macroscopically large computational domain with equilibrium boundary conditions. Quantification of the drag force shows breaking of continuum behaviour. Non-monotonic dependence on both tip speed and distance from the surface imply breaking of the hydration layer around the moving tip at timescales smaller than water cluster formation and strong water compressibility effects at the highest speeds.

November 2022

On the Convective Stability and Pattern Formation of Volumetrically Heated Flows with Asymmetric Boundaries

Non-linear solutions and their stability are presented for homogeneously heated fluids bounded by rigid conducting and insulating plates. In particular, we sought roll-type solutions emerging from the neutral stability curve for fluids with Prandtl numbers of 0.025, 0.25, 0.705, and 7. We determined the stability boundaries for the roll states in order to identify possible bifurcation points for the secondary flow in the form of regions that are equivalent to the Busse balloon. We also compared the stability exchange between ‘‘up’’ and ‘‘down’’ hexagons for a Prandtl number of $$0.25$$ obtained from weakly non-linear analysis in relation to the fully non-linear analysis, consistent with earlier studies. Our numerical analysis showed that there are potential bistable regions for both hexagons and rolls, a result that requires further investigations with a fully non-linear analysis.

June 2022

Application of Genetic Programming and Artificial Neural Network Approaches for Reconstruction of Turbulent Jet Flow Fields

Two Machine Learning (ML) methods are considered for reconstruction of turbulet signals corresponding to the Large Eddy Simulation database obtained by application of the high-resolution CABARET method accelerated on GPU cards for flow solutions of NASA Small Hot Jet Acoustic Rig (SHJAR) jets. The first method is the Feedforward Neural Networks technique, which was successfully implemented for a turbulent flow over a plunging aerofoil in (Lui and Wolf, 2019). The second method is based on the application of Genetic Programming, which is well-known in optimisation research, but has not been applied for turbulent flow reconstruction before. The reconstruction of local flow velocity and pressure signals as well as time-dependent principle coefficients of the Spectral Proper Orthogonal Decomposition of turbulent pressure fluctuations are considered. Stability and dependency of the ML algorithms on the smoothness property and the sampling rate of the underlying turbulent flow signals are discussed.

June 2022

A thermal convection limit of spiral state in wide-gap spherical Couette flow

Symmetries of flow structures are often prescribed by their mechanical instability and geometry. In this study, as an example, we present the homotopy of a rotating threefold spiral state that is robust in a spherical Couette flow toward a hybrid system with thermal stratification effects. The rotating wave state has not yet been confirmed to smoothly connect to the thermal stratification system. Through continuation, the most dangerous mode at a purely spherical Couette flow of m=4 modes of spherical harmonics is replaced by l=4 and m=3 in a purely thermal convective system. For the state obtained at the limit under only the thermal effect, the residual quantities of both the torque to the outer sphere and meridional circulation are discussed in detail.

May 2022

Statistical Analysis of High-Speed Jet Flows

The spatiotemporal dynamics of pressure fluctuations of a turbulent jet flow is examined from the viewpoints of symbolic permutations theory and Kolmogorov-Smirnov statistics. The methods are applied to unveil hidden structures in the near-field of the two jets corresponding to the NASA SHJAR SP3 and SP7 experiments. Large Eddy Simulations (LES) are performed using the high-resolution Compact Accurately Boundary-Adjusting high-REsolution Technique (CABARET) accelerated on Graphics Processing Units (GPUs). It is demonstrated that the decomposition of the LES pressure solutions into symbolic patterns of simpler temporal structure reveals the existence of some orderly structures in the jet flows. To separate the non-linear dynamics of the revealed structures from the linear part, the results based on the pressure signals obtained from LES are compared with the surrogate dataset constructed from the original data.

November 2021

Bifurcation aspect of polygonal coherence over transitional Reynolds numbers in wide-gap spherical Couette flow

This study numerically investigates the bifurcation aspect of the wide-gap spherical Couette flow (SCF), with an emphasis on the competition among polygonal coherence with different wave numbers observed over transitional Reynolds numbers. Focusing on a representative case, the half-radius ratio η=1/2, we confirm that the axisymmetric state becomes unstable over the first transitional Reynolds number at which the fourfold spiral state bifurcates, using the continuation method based on the Newton–Raphson algorithm. The Galerkin-spectral method was employed to numerically solve the governing equations. It is found that the threefold spiral state bifurcates from the axisymmetric state at a slightly higher Reynolds number than the first transitional Reynolds number. The attraction of the threefold spiral state expands rapidly with an increase in the Reynolds number, which is determined by verifying the distance of the unstable periodiclike state to both spiral states in the state space. This aspect of the state space explains the experimentally bistable realization of different equilibrium states over the first transitional Reynolds number. This study also found that the periodiclike state is composed of the three- and fourfold spiral states, similar to a beat with two different frequencies.

October 2021

A Thermostat‐Consistent Fully Coupled Molecular Dynamics–Generalized Fluctuating Hydrodynamics Model for Non‐Equilibrium Flows

The thermostat-consistent fully coupled molecular dynamics-generalised fluctuating hydrodynamics method is developed for non-equilibrium water flow simulations. The model allows for strong coupling between the atomistic and the continuum hydrodynamics representations of water and shows an improved stability in comparison with the previous formulations of similar multiscale methods. Numerical results are demonstrated for a periodic nano-scale Poiseuille flow problem with SPC/E water. The computed time-averaged velocity profiles are compared with the analytical solution, and the thermal velocity fluctuations are well reproduced in comparison with the Equilibrium Molecular Dynamics (EMD) simulation. Several options to account for the long-range electrostatics interactions available in GROMACS are incorporated in the model and compared. It is demonstrated that the suggested non-equilibrium multiscale model is a factor of 4 to 18 faster in comparison with the standard all-atom equilibrium molecular dynamics model for the same computational domain size.

September 2021

On the Problem of Resonant Incompressible Flow in Ventilated Double Glazing

We employ a homotopy method, rather than conventional stability theory, in order to resolve the degeneracy due to resonance, which exists in fluid motion associated with a channel of infinite extent in ventilated double glazing. The introduction of a symmetry breaking perturbation, in the form of a Poiseuille flow component, alters substantially the resonant bifurcation tree of the original flow. Previously unknown resonant higher order nonlinear solutions, i.e. after the removal of the perturbative Poiseuille flow component, are discovered. A possible extension of the methodology to consider non-Newtonian gradient enhanced incompressible viscous fluids is also briefly discussed.

October 2021

Lateral migration of proteins in transversely sheared flows in water: a scale-resolved simulation

For atomistic scale-resolving simulations of protein diffusion, which are representative of molecular sorting in micro-fluidic device, a hybrid Fluctuating Hydrodynamics-Molecular Dynamics model is implemented. In comparison with existing simulations in the literature, the suggested model captures inter-atomic forces between proteins and water atoms at atomistic resolution while concurrently taking into account the non-uniform flow effect. Multiscale models of one and two proteins solvated in water with a Poiseuille flow applied are implemented with dynamically resolving each diffusing protein and surrounding water shell. The models are validated in comparison with the pure all-atom molecular dynamics simulations for the no flow case and then used to investigate how the flow rate and the starting location of proteins in the parabolic flow profile affect their lateral migration at flow Reynolds numbers typical of the experiment.