The depth-averaged numerical simulation of laminar thin-film flows with capillary waves

Thin-film flows encountered in engineering systems such as aero-engine bearing chambers often exhibit capillary waves and occur within a moderate to high Weber number range. Although the depth-averaged simulation of these thin-film flows is computationally efficient relative to traditional volume-of-fluid (VOF) methods, numerical challenges remain particularly for solutions involving capillary waves and in the higher Weber number, low surface tension range. A depth-averaged approximation of the Navier–Stokes equations has been used to explore the effect of surface tension, grid resolution, and inertia on thin-film rimming solution accuracy and numerical stability. In shock and pooling solutions where capillary ripples are present, solution stability, and accuracy are shown to be highly sensitive to surface tension. The common practice in analytical studies of enforcing unphysical low Weber number stability constraints is shown to stabilize the solution by artificially damping capillary oscillations. This approach, however, although providing stable solutions is shown to adversely affect solution accuracy. An alternative grid resolution-based stability criterion is demonstrated and used to obtain numerically stable shock and pooling solutions without recourse to unphysical surface tension values. This allows for the accurate simulation of thin-film flows with capillary waves within the constrained parameter space corresponding to physical material and flow properties. Results obtained using the proposed formulation and solution strategy show good agreement with available experimental data from literature for low Re coating flows and moderate to high Re falling wavy film flows

On the dynamics of a high-speed coned fluid-lubricated bearing

An incompressible air-flow model for a fluid film bearing is derived using a modified Reynolds equation for the thin-film dynamics of a rapidly rotating rotor and stator. Mathematical and numerical modelling is applied to the coupled processes of the fluid flow through the bearing and the axial motion of the rotor and stator. This work focuses on extending previous studies to incorporate the dynamics of a coned rotor operating at high speeds and an incompressible lubrication approximation. The dynamics of fully coupled, unsteady bearing motion and associated forcing of the rotor with axial periodic oscillations are studied. The axial motion of the stator is modelled as a spring–mass–damper system that responds to the rotor displacement through the film dynamics. In order to solve the modified Reynolds equation and stator equation simultaneously, a new variable is introduced, namely the time-dependent face clearance. This leads to explicit analytical expressions for the pressure and force in terms of the face clearance and the stator equation is transformed to a non-linear, second-order, non-autonomous, ordinary differential equation for the face clearance. Applying a transient solver gives solutions settling down to a stable periodic behaviour which motivates seeking a solver for periodic solutions. A Fourier spectral collocation scheme is derived to compute the periodic time-dependent face clearance. Both solvers have matching periodic solutions of O(1) with an absolute error of order of magnitude 10−5. The dynamics of the unsteady bearing are examined for a range of pressure gradients and configurations including an asymptotic investigation of small face clearance associated with a start-up transient. Results are provided relating to changes in the width of the bearing, strength of the spring holding stator to its housing, damping of the stator and strength of the force coupling and rotor mass. The dynamics of the bearing are also investigated relative to values of key system parameters including the coning of the rotor, rotation speed and value of the bearing squeeze number. A parameter investigation is undertaken to highlight ideal bearing configurations to maximize the load-carrying capacity, fluid stiffness and damping

Effect of possible rotor deformation on the probability of face contact for a liquid film bearing

The possibility of face contact is examined for a coaxial rotor-stator bearing in dynamic motion constrained by a highly rotating very thin liquid film. A modified Reynolds equation for pressurised flow is coupled to the bearing structure leading to determination of the bearing gap from solving a nonlinear second-order non-autonomous ordinary differential equation. Periodic solutions are found via a mapping solver. Rotor deformation is parametrised by a coning angle and considered a random variable. The method of derived distributions is used to quantify variation in coning angle and examine the probability of rotor-stator contact. Additionally, effects of possible destabilising random aspects on the axial rotor oscillations are investigated. Exact solutions for probability of contact are obtained for various bearing configurations

On the dynamics of a high-speed coned fluid-lubricated bearing

An incompressible air-flow model for a fluid film bearing is derived using a modified Reynolds equation for the thin-film dynamics of a rapidly rotating rotor and stator. Mathematical and numerical modelling is applied to the coupled processes of the fluid flow through the bearing and the axial motion of the rotor and stator. This work focuses on extending previous studies to incorporate the dynamics of a coned rotor operating at high speeds and an incompressible lubrication approximation. The dynamics of fully coupled, unsteady bearing motion and associated forcing of the rotor with axial periodic oscillations are studied. The axial motion of the stator is modelled as a spring–mass–damper system that responds to the rotor displacement through the film dynamics. In order to solve the modified Reynolds equation and stator equation simultaneously, a new variable is introduced, namely the time-dependent face clearance. This leads to explicit analytical expressions for the pressure and force in terms of the face clearance and the stator equation is transformed to a non-linear, second-order, non-autonomous, ordinary differential equation for the face clearance. Applying a transient solver gives solutions settling down to a stable periodic behaviour which motivates seeking a solver for periodic solutions. A Fourier spectral collocation scheme is derived to compute the periodic time-dependent face clearance. Both solvers have matching periodic solutions of O(1) with an absolute error of order of magnitude 10−5. The dynamics of the unsteady bearing are examined for a range of pressure gradients and configurations including an asymptotic investigation of small face clearance associated with a start-up transient. Results are provided relating to changes in the width of the bearing, strength of the spring holding stator to its housing, damping of the stator and strength of the force coupling and rotor mass. The dynamics of the bearing are also investigated relative to values of key system parameters including the coning of the rotor, rotation speed and value of the bearing squeeze number. A parameter investigation is undertaken to highlight ideal bearing configurations to maximize the load-carrying capacity, fluid stiffness and damping

Identification of new members of the Escherichia coli K-12 MG1655 SlyA regulon.

SlyA is a member of the MarR family of bacterial transcriptional regulators. Previously, SlyA has been shown to directly regulate only two operons in Escherichia coli K-12 MG1655, fimB and hlyE (clyA). In both cases SlyA activates gene expression by antagonizing repression by the nucleoid associated protein H-NS. Here the transcript profiles of aerobic glucose-limited steady-state chemostat cultures of E. coli K-12 MG1655, slyA mutant and slyA over-expression strains are reported. The transcript profile of the slyA mutant was not significantly different to that of the parent; however, that of the slyA expression strain was significantly different from that of the vector control. Transcripts representing 27 operons were increased in abundance, whereas 3 were decreased. Of the 30 differentially regulated operons, 24 have been previously associated with sites of H-NS binding, suggesting that antagonism of H-NS repression is a common feature of SlyA-mediated transcription regulation. Direct binding of SlyA to DNA located upstream of a selection of these targets permitted the identification of new operons likely to be directly regulated by SlyA. Transcripts of four operons coding for cryptic adhesins exhibited enhanced expression and this was consistent with enhanced biofilm formation associated with the SlyA over-producing strain

Where next for mathematics education in higher education? A one-day meeting in honour of Professor John Blake

On the 10 June 2016 Professor John Blake, known to many readers of MSOR Connections for his leadership of the Maths, Stats OR Network and his passionate support for mathematics education, passed away peacefully following a short illness. He was 69. In recognition of Johns work, a number of his friends and colleagues came together to organise a one-day education meeting in his honour that comprised part of a larger event celebrating his many achievements in applied mathematics. The meeting was held in July 2017 at the University of Birmingham, a place where John spent many years of his career and established a legacy for teaching and learning from which many now benefit today. John was a man for action and the purpose of this one-day meeting was to explore the current needs and priorities of the mathematical sciences community and identify mechanisms by which we can continue to work together in a changed, and changing, higher education landscape: this article comprises a record of the thoughts and ideas of those who presented in honour of Johns legacy

Mixed ice accretion on aircraft wings

Ice accretion is a problematic natural phenomenon that an effects a wide range of engineering applications including power cables, radio masts and wind turbines. Accretion on aircraft wings occurs when supercooled water droplets freeze instantaneously on impact to form rime ice or runback as water along the wing to form glaze ice. Most models to date have ignored the accretion of mixed ice, which is a combination of rime and glaze. A parameter we term the `freezing fraction', is defined as the fraction of a supercooled droplet that freezes on impact with the top surface of the accretion ice to explore the concept of mixed ice accretion. Additionally we consider different `packing densities' of rime ice, mimicking the different bulk rime densities observed in nature. Ice accretion is considered in four stages: rime, primary mixed, secondary mixed and glaze ice. Predictions match with existing models and experimental data in the limiting rime and glaze cases. The mixed ice formulation consequently however provides additional insight into the composition of the overall ice structure, which ultimately influences adhesion and ice thickness; and shows that for similar atmospheric parameter ranges, this simple mixed ice description leads to very different accretion rates. A simple one-dimensional energy balance was solved to show how this freezing fraction parameter increases with decrease in atmospheric temperature, with lower freezing fraction promoting glaze ice accretion

Mixed ice accretion on aircraft wings

Ice accretion is a problematic natural phenomenon that an effects a wide range of engineering applications including power cables, radio masts and wind turbines. Accretion on aircraft wings occurs when supercooled water droplets freeze instantaneously on impact to form rime ice or runback as water along the wing to form glaze ice. Most models to date have ignored the accretion of mixed ice, which is a combination of rime and glaze. A parameter we term the `freezing fraction', is defined as the fraction of a supercooled droplet that freezes on impact with the top surface of the accretion ice to explore the concept of mixed ice accretion. Additionally we consider different `packing densities' of rime ice, mimicking the different bulk rime densities observed in nature. Ice accretion is considered in four stages: rime, primary mixed, secondary mixed and glaze ice. Predictions match with existing models and experimental data in the limiting rime and glaze cases. The mixed ice formulation consequently however provides additional insight into the composition of the overall ice structure, which ultimately influences adhesion and ice thickness; and shows that for similar atmospheric parameter ranges, this simple mixed ice description leads to very different accretion rates. A simple one-dimensional energy balance was solved to show how this freezing fraction parameter increases with decrease in atmospheric temperature, with lower freezing fraction promoting glaze ice accretion

BAsE-Seq: a method for obtaining long viral haplotypes from short sequence reads.

We present a method for obtaining long haplotypes, of over 3 kb in length, using a short-read sequencer, Barcode-directed Assembly for Extra-long Sequences (BAsE-Seq). BAsE-Seq relies on transposing a template-specific barcode onto random segments of the template molecule and assembling the barcoded short reads into complete haplotypes. We applied BAsE-Seq on mixed clones of hepatitis B virus and accurately identified haplotypes occurring at frequencies greater than or equal to 0.4%, with >99.9% specificity. Applying BAsE-Seq to a clinical sample, we obtained over 9,000 viral haplotypes, which provided an unprecedented view of hepatitis B virus population structure during chronic infection. BAsE-Seq is readily applicable for monitoring quasispecies evolution in viral diseases