Three dimensional flow structures in journal bearings

This paper was presented at the 2nd Micro and Nano Flows Conference (MNF2009), which was held at Brunel University, West London, UK. The conference was organised by Brunel University and supported by the Institution of Mechanical Engineers, IPEM, the Italian Union of Thermofluid dynamics, the Process Intensification Network, HEXAG - the Heat Exchange Action Group and the Institute of Mathematics and its Applications.In general, the fluid flow in journal bearings can be described by the Navier-Stokes Equations and the conservation of mass. The application of the small gap criterion allows a simplification of these equations yielding the Reynolds Equation, which links the local gap size with the pressure gradient resulting in a powerful tool for the designing process of journal bearings. Typically, the Reynolds Equation is used in EHD-design software based on FE-methods, which is used to compute pressure distributions, forces, deformations and many more parameters needed for the selection of the right bearing geometry. However, there are regions in the journal bearing where the Reynolds Equation must fail, because either the small gap criterion or the Couette flow assumption is violated. There are pockets, grooves and holes, which are necessary to distribute the oil supply across the gap. Moreover, the oil feed represents a cross flow perpendicular to the circumferential main flow. In these regions three dimensional flow structures replace the undisturbed Couette flow, which are strongly affected by vortices, but are non-turbulent due to the Re-scale. This work presents experimental data obtained from a cylinder apparatus with moderate gap sizes, which features independently rotating cylinders and a cross flow through a hole in the sidewall. LDV-measurements of velocity profiles and visualization methods to animate the three dimensional nature of the flow are presented. The experimental data are used to validate 3D-CFD calculations, which are expanded towards smaller gap sizes in the range of typical journal bearings in automotive applications

Numerical meshing issues for three-dimensional flow simulation in journal bearings

This paper was presented at the 3rd Micro and Nano Flows Conference (MNF2011), which was held at the Makedonia Palace Hotel, Thessaloniki in Greece. The conference was organised by Brunel University and supported by the Italian Union of Thermofluiddynamics, Aristotle University of Thessaloniki, University of Thessaly, IPEM, the Process Intensification Network, the Institution of Mechanical Engineers, the Heat Transfer Society, HEXAG - the Heat Exchange Action Group, and the Energy Institute.Hydrodynamic journal bearings are widely used in technical and industrial applications due to their favourable wearing quality and operating characteristics. In the recent years, various experimental and numerical analyses were carried out on the design layout, the load capacity and the durability of the bearing. For typical applications the two-dimensional Reynolds differential equation is solved numerically to calculate the pressure distribution in the oil film, which is essential to simulate the dynamic behavior of the bearing. This approach however, does not allow any detailed predictions of the local three-dimensional flow structures. To understand the mechanisms, which are driven by local flow phenomena, it is necessary to solve the full Navier-Stokes-Equations in 3D together with the conservation of mass. An accurate computation of a three-dimensional flow field requires a careful discretisation of the model. Moreover, only a deliberately chosen meshing based on the optimum number of cells across the gap achieves a sufficient numerical accuracy with acceptable computational effort. This work presents variations of the mesh generation of small gaps in journal bearing models and the computed flow fields, respectively. The threedimensional calculations are validated with measured experimental data done by Laser-Doppler-Velocimetry (LDV). In conclusion of this process the comparison of the velocity profiles of the flow field across the gap yield the necessary numerical discretisation limit applicable to the computation of the flow in journal bearings

Three-dimensional simulation of cavitating flow in real journal bearing geometry

This paper was presented at the 4th Micro and Nano Flows Conference (MNF2014), which was held at University College, London, UK. The conference was organised by Brunel University and supported by the Italian Union of Thermofluiddynamics, IPEM, the Process Intensification Network, the Institution of Mechanical Engineers, the Heat Transfer Society, HEXAG - the Heat Exchange Action Group, and the Energy Institute, ASME Press, LCN London Centre for Nanotechnology, UCL University College London, UCL Engineering, the International NanoScience Community, www.nanopaprika.eu.Hydrodynamic journal bearings are commonly used in many technical applications because they provide low friction and minimal wear. In general, flow simulation during the engineering design process is carried out by means of the Reynolds equation. The Reynolds equation is a non-linear two-dimensional differential equation, which is based on the pressure and the gap between shaft and bushing in relation to bearing clearance, eccentricity, bushing deformation and load. However, due its two-dimensional nature it is inaccurate where the lubricant flow inside the bearing becomes three-dimensional e.g., in the vicinity of feed holes or grooves. The work on hand presents the numerical approach and the cavitation model based on the Rayleigh-Plesset equation. Moreover, a bearing flow experiment was designed and constructed with the goal to validate numerical results. Finally, the validated 3D simulation model is applied on a real bearing, which was subject to an experimental investigation targeting cavitation. The numerical results include images of complex three-dimensional flow structures, vortices and vapor distributions. In comparison of 2D and 3D simulation, the two-dimensional approach gives wrong information in 2 out of 6 critical regions pertaining cavitation failing in both, over- and under-prediction of cavitation. In summary, a new numerical model expands the scope for the numerical simulation of the lubricant flow in hydrodynamic journal bearings and improves the prediction of cavitation

Quantifier-Free Interpolation of a Theory of Arrays

The use of interpolants in model checking is becoming an enabling technology to allow fast and robust verification of hardware and software. The application of encodings based on the theory of arrays, however, is limited by the impossibility of deriving quantifier- free interpolants in general. In this paper, we show that it is possible to obtain quantifier-free interpolants for a Skolemized version of the extensional theory of arrays. We prove this in two ways: (1) non-constructively, by using the model theoretic notion of amalgamation, which is known to be equivalent to admit quantifier-free interpolation for universal theories; and (2) constructively, by designing an interpolating procedure, based on solving equations between array updates. (Interestingly, rewriting techniques are used in the key steps of the solver and its proof of correctness.) To the best of our knowledge, this is the first successful attempt of computing quantifier- free interpolants for a variant of the theory of arrays with extensionality

Automated Synthesis of Tableau Calculi

This paper presents a method for synthesising sound and complete tableau calculi. Given a specification of the formal semantics of a logic, the method generates a set of tableau inference rules that can then be used to reason within the logic. The method guarantees that the generated rules form a calculus which is sound and constructively complete. If the logic can be shown to admit finite filtration with respect to a well-defined first-order semantics then adding a general blocking mechanism provides a terminating tableau calculus. The process of generating tableau rules can be completely automated and produces, together with the blocking mechanism, an automated procedure for generating tableau decision procedures. For illustration we show the workability of the approach for a description logic with transitive roles and propositional intuitionistic logic.Comment: 32 page

Search for WW and WZ production in lepton plus jets final state at CDF

We present a search for WW and WZ production in final states that contain a charged lepton (electron or muon) and at least two jets, produced in sqrt(s) = 1.96 TeV ppbar collisions at the Fermilab Tevatron, using data corresponding to 1.2 fb-1 of integrated luminosity collected with the CDF II detector. Diboson production in this decay channel has yet to be observed at hadron colliders due to the large single W plus jets background. An artificial neural network has been developed to increase signal sensitivity, as compared with an event selection based on conventional cuts. We set a 95% confidence level upper limit of sigma_{WW}* BR(W->lnu,W->jets)+ sigma_{WZ}*BR(W->lnu,Z->jets)We present a search for WW and WZ production in final states that contain a charged lepton (electron or muon) and at least two jets, produced in √s=1.96  TeV pp̅ collisions at the Fermilab Tevatron, using data corresponding to 1.2  fb-1 of integrated luminosity collected with the CDF II detector. Diboson production in this decay channel has yet to be observed at hadron colliders due to the large single W plus jets background. An artificial neural network has been developed to increase signal sensitivity, as compared with an event selection based on conventional cuts. We set a 95% confidence level upper limit of σWW×BR(W→ℓνℓ,W→jets)+σWZ×BR(W→ℓνℓ,Z→jets)<2.88  pb, which is consistent with the standard model next-to-leading-order cross section calculation for this decay channel of 2.09±0.12  pb.Peer reviewe

A five year longitudinal study investigating the prevalence of childhood obesity: comparison of BMI and waist circumference.

Objective: The purpose of this study was to examine the prevalence of obesity over time in the same individuals comparing body mass index (BMI), waist circumference (WC) and waist to height ratio (WHtR). Study design: Five year longitudinal repeated measures study (2005–2010). Children were aged 11–12 (Y7) years at baseline and measurements were repeated at age 13–14 (Y9) years and 15–16 (Y11) years. Methods: WC and BMI measurements were carried out by the same person over the five years and raw values were expressed as standard deviation scores (sBMI and sWC) against the growth reference used for British children. Results: Mean sWC measurements were higher than mean sBMI measurements for both sexes and at all assessment occasions and sWC measurements were consistently high in girls compared to boys. Y7 sWC = 0.792 [95% confidence interval (CI) 0.675–0.908], Y9 sWC = 0.818 (95%CI 0.709–0.928), Y11 sWC = 0.943 (95%CI 0.827–1.06) for boys; Y7 sWC = 0.843 (0.697–0.989), Y9 sWC = 1.52 (95%CI 1.38–0.67), Y11 sWC = 1.89 (95%CI 1.79–2.04) for girls. Y7 sBMI = 0.445 (95%CI 0.315–0.575), Y9 sBMI = 0.314 (95%CI 0.189–0.438), Y11 sBMI = 0.196 (95%CI 0.054–0.337) for boys; Y7 sBMI = 0.353 (0.227–0.479), Y9 sBMI = 0.343 (95%CI 0.208–0.478), Y11 sBMI = 0.256 (95%CI 0.102–0.409) for girls. The estimated prevalence of obesity defined by BMI decreased in boys (18%, 12% and 10% in Y 7, 9 and 11 respectively) and girls (14%, 15% and 11% in Y 7, 9 and 11). In contrast, the prevalence estimated by WC increased sharply (boys; 13%, 19% and 23%; girls, 20%, 46% and 60%). Conclusion: Central adiposity, measured by WC is increasing alongside a stabilization in BMI. Children appear to be getting fatter and the additional adiposity is being stored centrally which is not detected by BMI. These substantial increases in WC are a serious concern, especially in girls

Curricular orientations to real-world contexts in mathematics

A common claim about mathematics education is that it should equip students to use mathematics in the ‘real world’. In this paper, we examine how relationships between mathematics education and the real world are materialised in the curriculum across a sample of eleven jurisdictions. In particular, we address the orientation of the curriculum towards application of mathematics, the ways that real-world contexts are positioned within the curriculum content, the ways in which different groups of students are expected to engage with real-world contexts, and the extent to which high-stakes assessments include real-world problem solving. The analysis reveals variation across jurisdictions and some lack of coherence between official orientations towards use of mathematics in the real world and the ways that this is materialised in the organisation of the content for students

Determinants of response to a parent questionnaire about development and behaviour in 3 year olds: European multicentre study of congenital toxoplasmosis.

Background: We aimed to determine how response to a parent-completed postal questionnaire measuring development, behaviour, impairment, and parental concerns and anxiety, varies in different European centres. Methods: Prospective cohort study of 3 year old children, with and without congenital toxoplasmosis, who were identified by prenatal or neonatal screening for toxoplasmosis in 11 centres in 7 countries. Parents were mailed a questionnaire that comprised all or part of existing validated tools. We determined the effect of characteristics of the centre and child on response, age at questionnaire completion, and response to child drawing tasks. Results: The questionnaire took 21 minutes to complete on average. 67% (714/1058) of parents responded. Few parents (60/1058) refused to participate. The strongest determinants of response were the score for organisational attributes of the study centre (such as direct involvement in follow up and access to an address register), and infection with congenital toxoplasmosis. Age at completion was associated with study centre, presence of neurological abnormalities in early infancy, and duration of prenatal treatment. Completion rates for individual questions exceeded 92% except for child completed drawings of a man (70%), which were completed more by girls, older children, and in certain centres. Conclusion: Differences in response across European centres were predominantly related to the organisation of follow up and access to correct addresses. The questionnaire was acceptable in all six countries and offers a low cost tool for assessing development, behaviour, and parental concerns and anxiety, in multinational studies

Effect of transport-induced charge inhomogeneity on point-contact Andreev reflection spectra at ferromagnet-superconductor interfaces

We investigate the transport properties of a ferromagnet-superconductor interface within the framework of a modified three-dimensional Blonder-Tinkham-Klapwijk formalism. In particular, we propose that charge inhomogeneity forms via two unique transport mechanisms, namely, evanescent Andreev reflection and evanescent quasiparticle transmission. Furthermore, we take into account the influence of charge inhomogeneity on the interfacial barrier potential and calculate the conductance as a function of bias voltage. Point-contact Andreev reflection (PCAR) spectra often show dip structures, large zero-bias conductance enhancement, and additional zero-bias conductance peak. Our results indicate that transport-induced charge inhomogeneity could be a source of all these anomalous characteristics of the PCAR spectra.Comment: 9 pages, 6 figure