A semi-Lagrangian finite volume method for Newtonian contraction flows

A new finite volume method for solving the incompressible Navier--Stokes equations is presented. The main features of this method are the location of the velocity components and pressure on different staggered grids and a semi-Lagrangian method for the treatment of convection. An interpolation procedure based on area-weighting is used for the convection part of the computation. The method is applied to flow through a constricted channel, and results are obtained for Reynolds numbers, based on half the flow rate, up to 1000. The behavior of the vortex in the salient corner is investigated qualitatively and quantitatively, and excellent agreement is found with the numerical results of Dennis and Smith [Proc. Roy. Soc. London A, 372 (1980), pp. 393-414] and the asymptotic theory of Smith [J. Fluid Mech., 90 (1979), pp. 725-754].

Details of an integrated approach to three-dimensional dynamic fluid structure interaction

Fluid structure interaction, as applied to flexible structures, has wide application in diverse areas such as flutter in aircraft, wind response of buildings, flows in elastic pipes and blood vessels. Numerical modelling of dynamic fluid-structure interaction (DFSI) involves the coupling of fluid flow and structural mechanics, two fields that are conventionally modelled using two dissimilar methods, thus a single comprehensive computational model of both phenomena is a considerable challenge and until recently work in this area focused on one phenomenon and represented the behaviour of the other more simply. A single, finite volume unstructured mesh (FV-UM) spatial discretisation method has been employed on a single mesh for the entire domain. The Navier Stokes equations for fluid flow are solved using a SIMPLE type procedure and the Newmark b algorithm is employed for solving the dynamic equilibrium equations for linear elastic solid mechanics and mesh movement is achieved using a spring based mesh procedure for dynamic mesh movement. In the paper we describe a number of additional computation issues for the efficient and accurate modelling of three-dimensional, dynamic fluid-structure interaction problems.

Dynamic fluid-structure interaction using finite volume unstructured mesh procedures

A three dimensional finite volume, unstructured mesh method for dynamic fluid-structure interation is described. The broad approach is conventional in that the fluid and structure are solved sequentially. The pressure and viscous stresses from the flow algorithm provide load conditions for the solid algorithm, whilst at the fluid structure interface the deformed structure provides boundary condition from the structure to the fluid. The structure algorithm also provides the necessary mesh adaptation for the flow field, the effect of which is accounted for in the flow algorithm. The procedures described in this work have several novel features, namely: * a single mesh covering the entire domain. * a Navier Stokes flow. * a single FV-UM discretisation approach for both the flow and solid mechanics procedures. * an implicit predictor-corrector version of the Newmark algorithm. * a single code embedding the whole strategy. The procedure is illustrated for a three dimensional loaded cantilever in fluid flow.

An acoustic correction method for extracting sound signals

Sound waves are propagating pressure fluctuations and are typically several orders of magnitude smaller than the pressure variations in the flow field that account for flow acceleration. On the other hand, these fluctuations travel at the speed of sound in the medium, not as a transported fluid quantity. Due to the above two properties, the Reynolds averaged Navier-Stokes (RANS) equations do not resolve the acoustic fluctuations. Direct numerical simulation of turbulent flow is still a prohibitively expensive tool to perform noise analysis. This paper proposes the acousticcorrectionmethod, an alternative and affordable tool based on a modified defect correction concept, which leads to an efficient algorithm for computational aeroacoustics and noise analysis.

Maximising heat transfer efficiency in the cold crucible induction melting process

Induction heating is an efficient method used to melt electrically conductive materials, particularly if melting takes place in a ceramic crucible. This form of melting is particularly good for alloys, as electromagnetic forces set up by the induction coil lead to vigorous stirring of the melt ensuring homogeneity and uniformity in temperature. However, for certain reactive alloys, or where high purity is required, ceramic crucibles cannot be used, but a water-cooled segmented copper crucible is employed instead. Water cooling prevents meltdown or distortion of the metal wall, but much of the energy goes into the coolant. To reduce this loss, the electromagnetic force generated by the coil is used to push the melt away from the walls and so minimise contact with water-cooled surfaces. Even then, heat is lost through the crucible base where contact is inevitable. In a collaborative programme between Greenwich and Birmingham Universities, computer modelling has been used in conjunction with experiments to improve the superheat attainable in the melt for a,number of alloys, especially for y-TiAl intermetallics to cast aeroengine turbine blades. The model solves the discretised form of the turbulent Navier-Stokes, thermal energy conservation and Maxwell equations using a Spectral Collocation technique. The time-varying melt envelope is followed explicitly during the computation using an adaptive mesh. This paper briefly describes the mathematical model used to represent the interaction between the magnetic field, fluid flow, heat transfer and change of phase in the crucible and identifies the proportions of energy used in the melt, lost in the crucible base and in the crucible walls. The role of turbulence is highlighted as important in controlling heat losses and turbulence damping is introduced as a means of improving superheat. Model validation is against experimental results and shows good agreement with measured temperatures and energy losses in the cooling fluid throughout the melting cycle.

Experience of using a CFD code for estimating the noise generated by gusts along the sun-roof of a car

The problem to be examined here is the fluctuating pressure distribution along the open cavity of the sun-roof at the top of a car compartment due to gusts passing over the sun-roof. The aim of this test is to investigate the capability of a typical commercial CFD package, PHOENICS, in recognising pressure fluctuations occurring in an important automotive industrial problem. In particular to examine the accuracy of transporting pulsatory gusts traveling along the main flow through the use of finite volume methods with higher order schemes in the numercial solutins of the unsteady compressible Navier-Stokes equations. The Helmholtz equation is used to solve the sound distribution inside the car compartment, resulting from the externally induced fluctuations.

Three-dimensional simulation of the influence of convection on dendritic solidification

Bulk and interdendritic flow during solidification alters the microstructure development, potentially leading to the formation of defects. In this paper, a 3D numerical model is presented for the simulation of dendritic growth in the presence of fluid flow in both liquid and semi-solid zones during solidification. The dendritic growth was solved by the combination of a stochastic nucleation approach with a finite difference solution of the solute diffusion equation and. a projection method solution of the Navier-Stokes equations. The technique was applied first to simulate the growth of a single dendrite in 2D and 3D in an isothermal environment with forced fluid flow. Significant differences were found in the evolution of dendritic morphology when comparing the 2D and 3D results. In 3D the upstream arm has a faster growth velocity due to easier flow around the perpendicular arms. This also promotes secondary arm formation on the upstream arm. The effect of fluid flow on columnar dendritic growth and micro-segregation in constrained solidification conditions is then simulated. For constrained growth, 2D simulations lead to even greater inaccuracies as compared to 3D.

Determining surface tension using DC magnetic levitation

The values of material physical properties are vital for the successful use of numerical simulations for electromagnetic processing of materials. The surface tension of materials can be determined from the experimental measurement of the surface oscillation frequency of liquid droplets. In order for this technique to be used, a positioning field is required that results in a modification to the oscillation frequency. A number of previous analytical models have been developed that mainly focus on electrically conducting droplets positioned using an A.C. electromagnetic field, but due to the turbulent flow resulting from the high electromagnetic fields required to balance gravity, reliable measurements have largely been limited to microgravity. In this work axisymmetric analytical and numerical models are developed, which allow the surface tension of a diamagnetic droplet positioned in a high DC magnetic field to be determined from the surface oscillations. In the case of D.C. levitation there is no internal electric currents with resulting Joule heating, Marangoni flow and other effects that introduce additional physics that complicates the measurement process. The analytical solution uses the linearised Navier-Stokes equations in the inviscid case. The body force from a DC field is potential, in contrast to the AC case, and it can be derived from Maxwell equations giving a solution for the magnetic field in the form of a series expansion of Legendre polynomials. The first few terms in this expansion represent a constant and gradient magnetic field valid close to the origin, which can be used to position the droplet. Initially the mathematical model is verified in microgravity conditions using a numerical model developed to solve the transient electromagnetics, fluid flow and thermodynamic equations. In the numerical model (as in experiment) the magnetic field is obtained using electrical current carrying coils, which provides the confinement force for a liquid droplet. The model incorporates free surface deformation to accurately model the oscillations that result from the interaction between the droplet and the non-uniform external magnetic field. A comparison is made between the analytical perturbation theory and the numerical pseudo spectral approximation solutions for small amplitude oscillations.

Thermoelectric MHD in dendritic solidification

The effects of a constant uniform magnetic field on dendritic solidification were investigated using an enthalpy based numerical model. The interaction between thermoelectric currents on a growing crystal and the magnetic field generates a Lorentz force that creates flow. The need for very high resolution at the liquid-solid boundary where the thermoelectric source originates plus the need to accommodate multiple grains for a realistic simulation, make this a very demanding computational problem. For practical simulations, a quasi 3-dimensional approximation is proposed which nevertheless retains essential elements of transport in the third dimension. A magnetic field normal to the plane of growth leads to general flow circulation around an equiaxed dendrite, with secondary recirculations between the arms. The heat/solute advection by the flow is shown to cause a change in the morphology of the dendrite; secondary growth is promoted preferentially on one side of the dendrite arm and the tip velocity of the primary arm is increased. The degree of approximation introduced is quantified by extending the model into 3-dimensions, where the full Navier-Stokes equation is solved, and compared against the 2-dimensional solution.

Survival in 176 patients with inoperable non small cell lung cancer treated initially with chemotherapy in a district general hospital

In advanced non-small cell lung cancer (NSCLC) platinum based chemotherapy with second generation drugs improves median survival (MS) to 8 months and 29% and 10% at 1 and 2 years. Platinum with a third generation drug can improve survival further (BMJ 1995;311: 899) (Spiro et al. Thorax 2004;59:828 Big Lung Trial; N Engl J Med 2003;346:92 ECOG study). NICE now recommends chemotherapy with platinum and a third generation drug for inoperable NSCLC as the first treatment modality. Methods: We audited survival of 176/461 consecutive patients referred for at least 3 courses of platinum and either gemcitabine or vinorelbine from July 2001 to December 2005. Minimal follow up 17 months. Chemotherapy was given on site. Radical radiotherapy for stage IIIA, palliative radiotherapy and second line drugs were given as felt appropriate. Results: 64% were male. 30 (17%) were <55 years ; 66 (37.5%) age 55–65 years; 63 (35.8%) aged 66–75 and 16 (9.1%) >75 years. 5 (2.8%) were stage II; 46 (26%) stage IIIA; 68 (38%) stage IIIB and 55 (30.8%) stage IV. 68 (38%) had 0– 2 courses; 63 (36%) 3 courses and 44 (25%) had 4 or more.

A Note On Tidal Asymmetry In The Severn Estuary

A one-dimensional, non-linear numerical model is used to investigate the tidally averaged frictional stress and set-up of water level due to tidal asymmetry in the Severn Estuary; these quantities depend on the overtides in the region. A linearized model of the overtides is applied to calculations of the M4 currents in order to delineate the mechanisms responsible for their generation. The relative importance of individual non-linear mechanisms to the tidally averaged stress and set-up is determined; these mechanisms are interactions between tidal flow and changes in depth or breadth over a cross-section, frictional interaction between the tidal flow and Stokes drift, interaction between the tidal fluctuations in water depth and frictional retardation and non-linear advection.

Passive Control of Plume Interference on Slender Axisymmetric Bodies

The physics of the plume-induced shock and separation, particularly at high plume to exit pressure ratios with and without shock-turbulent boundary-layer control methods, were studied using computational techniques. Mass-averaged Navier-Stokes equations with a two-equation turbulence model were solved by using a fully implicit finite volume scheme and time.marching algorithm. The control methodologies for shock interactions included a porous tail and a porous extension attached at the nozzle exit or trailing edge. The porous tail produced a weaker shock and fixed the shock position on the control surface. The effect of the porous extension on shock interactions was mainly to restrain the plume from strongly underexpanding during a change in flight conditions. These techniques could give an additional dimension to the design and control of supersonic missiles.

Co-melt fluidised bed granulation of pharmaceutical powders: Improvements in drug bioavailability

This study investigates the use of co-melt fluidised bed granulation for the agglomeration of model pharmaceutical powders, namely, lactose mono-hydrate, PEG 10000, poly-vinyl pyrolidone and ibuprofen as a model drug. Granulation within the co-melt system was found to follow a nucleationâ??steady growthâ??coating regime profile. Using high molecular weight PEG binder, the granulation mechanism and thus the extent of granulation was found to be significantly influenced by binder viscosity. The compression properties of the granulate within the hot fluidised bed were correlated using a novel high temperature experimental procedure. It was found that the fracture stress and fractural modulus of the materials under hot processing conditions were orders of magnitude lower than those measured under ambient conditions. A range of particle velocities within the granulator were considered based on theoretical models. After an initial period of nucleation, the Stokes deformation number analysis indicated that only velocities within the high shear region of the fluidised bed were sufficient to promote significant granule deformation and therefore, coalescence. The data also indicated that larger granules de-fluidised preventing agglomeration by coalescence. Furthermore, experimental data indicated that dissipation of the viscous molten binder to the surface was the most important factor in the latter stages of the granulation process. From a pharmaceutical perspective the inclusion of the model drug, ibuprofen, combined with PVP in the co-melt process proved to be highly significant. It was found that using DSC analysis on the formulations that the decrease in the heat of fusion associated with the melting of ibuprofen within the FHMG systems may be attributed to interaction between PVP and ibuprofen through inter-molecular hydrogen bonding. This interaction decreases the crystallinity of ibuprofen and facilitates solubilisation and bioavailability within the solid matrix.

Wavelet phase coherence analysis: Application to a quiet-sun magnetic element

A new application of wavelet analysis is presented that utilizes the inherent phase information residing within the complex Morlet transform. The technique is applied to a weak solar magnetic network region, and the temporal variation of phase difference between TRACE 1700 Angstrom and SOHO/SUMER C II 1037 Angstrom intensities is shown. We present, for the first time in an astrophysical setting, the application of wavelet phase coherence, including a comparison between two methods of testing real wavelet phase coherence against that of noise. The example highlights the advantage of wavelet analysis over more classical techniques, such as Fourier analysis, and the effectiveness of the former to identify wave packets of similar frequencies but with differing phase relations is emphasized. Using cotemporal, ground-based Advanced Stokes Polarimeter measurements, changes in the observed phase differences are shown to result from alterations in the magnetic topology.