1,363 research outputs found
Stagnation–saddle points and flow patterns in Stokes flow between contra-rotating cylinders
The steady flow is considered of a Newtonian fluid, of viscosity mu, between contra-rotating cylinders with peripheral speeds U-1 and U-2 The two-dimensional velocity field is determined correct to O(H-0/2R)(1/2), where 2H(0) is the minimum separation of the cylinders and R an 'averaged' cylinder radius. For flooded/moderately starved inlets there are two stagnation-saddle points, located symmetrically about the nip, and separated by quasi-unidirectional flow. These stagnation-saddle points are shown to divide the gap in the ratio U-1 : U-2 and arise at \X\ = A where the semi-gap thickness is H(A) and the streamwise pressure gradient is given by dP/dX = mu(Ulf U-2)/H-2(A). Several additional results then follow.
(i) The effect of non-dimensional flow rate, lambda: A(2) = 2RH(0)(3 lambda - 1) and so the stagnation-saddle points are absent for lambda 1/3.
(ii) The effect of speed ratio, S = U-1/U-2: stagnation-saddle points are located on the boundary of recirculating flow and are coincident with its leading edge only for symmetric flows (S = i). The effect of unequal cylinder speeds is to introduce a displacement that increases to a maximum of O(RH0)(1/2) as S --> 0.
Five distinct flow patterns are identified between the nip and the downstream meniscus. Three are asymmetric flows with a transfer jet conveying fluid across the recirculation region and arising due to unequal cylinder speeds, unequal cylinder radii, gravity or a combination of these. Two others exhibit no transfer jet and correspond to symmetric (S = 1) or asymmetric (S not equal 1) flow with two asymmetric effects in balance. Film splitting at the downstream stagnation-saddle point produces uniform films, attached to the cylinders, of thickness H-1 and H-2, where
H-1/H-2 = S(S + 3)/3S + 1,
provided the flux in the transfer jet is assumed to be negligible.
(iii) The effect of capillary number, Ca: as Ca is increased the downstream meniscus advances towards the nip and the stagnation-saddle point either attaches itself to the meniscus or disappears via a saddle-node annihilation according to the flow topology.
Theoretical predictions are supported by experimental data and finite element computations
Efficient and accurate time adaptive multigrid simulations of droplet spreading
An efficient full approximation storage (FAS) Multigrid algorithm is used to solve a range of droplet spreading flows modelled as a coupled set of non-linear lubrication equations. The algorithm is fully implicit and has embedded within it an adaptive time-stepping scheme that enables the same to be optimized in a controlled manner subject to a specific error tolerance.
The method is first validated against a range of analytical and existing numerical predictions commensurate with droplet spreading and then used to simulate a series of new, three-dimensional flows consisting of droplet motion on substrates containing topographic and wetting heterogeneities. The latter are of particular interest and reveal how droplets can be made to spread preferentially on substrates owing to an interplay between different topographic and surface wetting characteristics
Droplet migration: quantitative comparisons with experiment
An important practical feature of simulating droplet migration computationally,
using the lubrication approach coupled to a disjoining pressure term, is
the need to specify the thickness, H, of a thin energetically stable wetting layer,
or precursor lm, over the entire substrate. The necessity that H be small in
order to improve the accuracy of predicted droplet migration speeds, allied to the
need for mesh resolution of the same order as H near wetting lines, increases the
computational demands signicantly. To date no systematic investigation of these
requirements on the quantitative agreement between prediction and experimental
observation has been reported. Accordingly, this paper combines highly ecient
Multigrid methods for solving the associated lubrication equations with a parallel
computing framework, to explore the eect of H and mesh resolution. The solutions
generated are compared with recent experimentally determined migration
speeds for droplet
ows down an inclined plane
Gravity-driven flow of continuous thin liquid films on non-porous substrates with topography
A range of two- and three-dimensional problems is explored featuring the gravity-driven flow of a continuous thin liquid film over a non-porous inclined flat surface containing well-defined topography. These are analysed principally within the framework of the lubrication approximation, where accurate numerical solution of the governing nonlinear equations is achieved using an efficient multigrid solver.
Results for flow over one-dimensional steep-sided topographies are shown to be in very good agreement with previously reported data. The accuracy of the lubrication approximation in the context of such topographies is assessed and quantified by comparison with finite element solutions of the full Navier–Stokes equations, and results support the consensus that lubrication theory provides an accurate description of these flows even when its inherent assumptions are not strictly satisfied. The Navier–Stokes solutions also illustrate the effect of inertia on the capillary ridge/trough and the two-dimensional flow structures caused by steep topography.
Solutions obtained for flow over localized topography are shown to be in excellent agreement with the recent experimental results of Decré & Baret (2003) for the motion of thin water films over finite trenches. The spread of the ‘bow wave’, as measured by the positions of spanwise local extrema in free-surface height, is shown to be well-represented both upstream and downstream of the topography by an inverse hyperbolic cosine function.
An explanation, in terms of local flow rate, is given for the presence of the ‘downstream surge’ following square trenches, and its evolution as trench aspect ratio is increased is discussed. Unlike the upstream capillary ridge, this feature cannot be completely suppressed by increasing the normal component of gravity. The linearity of free-surface response to topographies is explored by superposition of the free surfaces corresponding to two ‘equal-but-opposite’ topographies. Results confirm the findings of Decré & Baret (2003) that, under the conditions considered, the responses behave in a near-linear fashion
Aerodynamic shape optimization of a low drag fairing for small livestock trailers
Small livestock trailers are commonly used to transport animals from farms to market
within the United Kingdom. Due to the bluff nature of these vehicles there is great potential
for reducing drag with a simple add-on fairing. This paper explores the feasibility of
combining high-fidelity aerodynamic analysis, accurate metamodeling, and efficient
optimization techniques to find an optimum fairing geometry which reduces drag, without
significantly impairing internal ventilation. Airflow simulations were carried out using
Computational Fluid Dynamics (CFD) to assess the performance of each fairing based on
three design variables. A Moving Least Squares (MLS) metamodel was built on a fifty-point
Optimal Latin Hypercube (OLH) Design of Experiments (DoE), where each point
represented a different geometry configuration. Traditional optimization techniques were
employed on the metamodel until an optimum geometrical configuration was found. This
optimum design was tested using CFD and it matched closely to the metamodel prediction.
Further, the drag reduction was measured at 14.4% on the trailer and 6.6% for the
combined truck and trailer
Polo like kinase 2 tumour suppressor and cancer biomarker: new perspectives on drug sensitivity/resistance in ovarian cancer
The polo-like kinase PLK2 has recently been identified as a potential theranostic marker in the management of chemotherapy sensitive cancers. The methylation status of the PLK2 CpG island varies with sensitivity to paclitaxel and platinum in ovarian cancer cell lines. Importantly, extrapolation of these in vitro data to the clinical setting confirms that the methylation status of the PLK2 CpG island predicts outcomes in patients treated with carboplatin and paclitaxel chemotherapy. A second cell cycle regulator, p57Kip2, is also subject to epigenetic silencing in carboplatin resistance in vitro and in vivo, emphasising that cell cycle regulators are important determinants of sensitivity to chemotherapeutic agents and providing insights into the phenomenon of collateral drug sensitivity in oncology. Understanding the mechanistic basis and identification of robust biomarkers to predict collateral sensitivity may inform optimal use of chemotherapy in patients receiving multiple lines of treatment
Ventilation of small livestock trailers
A large number of livestock is transported to market in small box trailers. The welfare
of animals transported in this way is now assuming greater importance with the onset
of tougher EU legislation. This paper presents the first study into the ventilation of
small livestock trailers using experimental and computational methods. Wind tunnel
studies, using a 1/7th scale model, highlight the important influence of the towing
vehicle and trailer design on the airflow within the trailer. Detailed CFD analysis
agrees well with the wind tunnel data and offers the ability to assess the impact of
design changes
Free-surface film flow over topography: full three-dimensional finite element solutions
An efficient Bubnov-Galerkin finite element formulation is employed to solve the Navier-Stokes and continuity equations in three-dimensions for the case of surface-tension dominated film flow over substrate topography, with the free-surface location obtained using the method of spines. The computational challenges encountered are overcome by employing a direct parallel multi-frontal method in conjunction with memory-efficient out-of-core storage of matrix co-factors. Comparison is drawn with complementary computational and experimental results for low Reynolds number flow where they exist, and a range of new benchmark solutions provided. These, in turn, are compared with corresponding solutions, for non-zero Reynolds number, from a simplified model based on the long-wave approximation; the latter is shown to produce comparatively acceptable results for the free-surface disturbance experienced, when the underpinning formal restrictions on geometry and capillary number are not exceeded
Drying air-induced disturbances in multi-layer coating systems
A range of new experimental techniques is developed to quantify drying-air induced disturbances on low viscosity
single and multi-layer coating systems. Experiments on prototype slide-bead coating systems show that the surface
disturbances take the form of a wavelike pattern and quantify precisely how its amplitude increases rapidly with wet
thickness and decreases with viscosity. Heat transfer measurements show that the redistribution of water to form an
additional lower viscosity carrier layer while increasing the solids concentration of the upper layer or layers enables
the maximum drying rate, for which drying-air induced surface disturbances are acceptably small, to be increased
with significant commercial benefits
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