Models of Galaxy Clusters with Thermal Conduction

We present a simple model of hot gas in galaxy clusters, assuming hydrostatic equilibrium and energy balance between radiative cooling and thermal conduction. For five clusters, A1795, A1835, A2199, A2390 and RXJ1347.5-1145, the model gives a good description of the observed radial profiles of electron density and temperature, provided we take the thermal conductivity $\kappa$ to be about 30% of the Spitzer conductivity. Since the required $\kappa$ is consistent with the recent theoretical estimate of Narayan & Medvedev (2001) for a turbulent magnetized plasma, we consider a conduction-based equilibrium model to be viable for these clusters. We further show that the hot gas is thermally stable because of the presence of conduction. For five other clusters, A2052, A2597, Hydra A, Ser 159-03 and 3C295, the model requires unphysically large values of $\kappa$ to fit the data. These clusters must have some additional source of heat, most likely an active galactic nucleus since all the clusters have strong radio galaxies at their centers. We suggest that thermal conduction, though not dominant in these clusters, may nevertheless play a significant role by preventing the gas from becoming thermally unstable.Comment: Published in ApJ; 22 pages, including 2 tables, 4 figures; typos corrected to match the published versio

CFD simulation of an industrial spiral refrigeration system

This is the final version. Available on open access from MDPI via the DOI in this recordIn the food industry, heating and cooling are key processes where CFD can play an important role in improving quality, productivity and reducing energy costs. Cooling products after baking is crucial for storage and transportation; the product has to be cooled efficiently to a specified temperature (often to fulfill regulatory requirements) whilst preserving its quality. This study involves the analysis of spiral cooling refrigerators used in cooling food products, in this case, Cornish Pasties. Three separate sets of CFD models were developed and validated against experimental data taken in the laboratory and measurements taken in use in industry. In the first set of models a full CFD model was developed of a refrigeration spiral including the pasties, and used to study the heat transfer from the products to the air. Further simulations were carried out on individual pasties to explore the pasty cooling and heat transfer to the air in more detail, with the pasty geometry being determined from MRI scans. In the final set of simulations, Image Based Meshing (IBM) was used to determine the interior structure of the pasty and develop a full heat conduction model of the interior, which was compared with separate laboratory experiments using jets of cold air to cool the pasty. In all cases, good agreement was obtained between the CFD results and experimental data, whilst the CFD simulations provide valuable information about the air flows and cooling in the industrial system.Innovate U

On vacuum gravitational collapse in nine dimensions

We consider the vacuum gravitational collapse for cohomogeneity-two solutions of the nine dimensional Einstein equations. Using combined numerical and analytical methods we give evidence that within this model the Schwarzschild-Tangherlini black hole is asymptotically stable. In addition, we briefly discuss the critical behavior at the threshold of black hole formation.Comment: 4 pages, 4 figure

CFD characterization of flow regimes inside open cell foam substrates

This is the author accepted manuscript. The final version is available from the publisher via the DOI in this record.In this work a combination of micro-CT, image-based modeling and CFD has been applied to investigate the pressure drop in open-cell foams. The analysis covers a range of flow regimes and is aimed at determining the effects of important morphological parameters on the pressure drop. The adoption of micro-CT technology along with detailed CFD modeling allows the investigation of phenomena occurring in real foam micro-structures. Moreover, by means of image processing tools, the geometry can be artificially modified in order to investigate the effects of mathematical transformation of the geometrical parameters of a real foam, one parameter at a time, e.g. varying pore size without affecting the porosity. Non-dimensional coefficients have been defined for the analysis of the results, with the purpose of describing the pressure drop as a function of the Reynolds number. The proposed formulation allows us to relate the permeability properties of an open-cell foam to its morphology alone, without any dependence on the properties of the fluid adopted or on the effective characteristic dimension of the foam micro-structure (pore or cell size). Comparison with experimental results available in the literature is also provided for one of the cases studied

Thermal conduction and particle transport in strong MHD turbulence, with application to galaxy-cluster plasmas

We investigate field-line separation in strong MHD turbulence analytically and with direct numerical simulations. We find that in the static-magnetic-field approximation the thermal conductivity in galaxy clusters is reduced by a factor of about 5-10 relative to the Spitzer thermal conductivity of a non-magnetized plasma. We also estimate how the thermal conductivity would be affected by efficient turbulent resistivity.Comment: Major revision: higher resolution simulations lead to significantly different conclusions. 26 pages, 10 figure

Shape optimisation using Computational Fluid Dynamics and Evolutionary Algorithms

This is the author accepted manuscript.Optimisation of designs using Computational Fluid Dynamics (CFD) are frequently performed across many fields of research, such as the optimisation of an aircraft wing to reduce drag, or to increase the efficiency of a heat exchanger. General optimisation strategies involves altering design variables with a view to improve appropriate objective function(s). Often the objective function(s) are non-linear and multi-modal, and thus polynomial time algorithms for solving such problems may not be available. In such cases, applying Evolutionary Algorithms (EAs - a class of stochastic global optimisation techniques inspired from natural evolution) may locate good solutions within a practical time frame. The traditional CFD design optimisation process is often based on a ‘trial-and-error type approach. Starting from an initial geometry, Computational Aided Design changes are introduced manually based on results from a limited number of design iterations and CFD analyses. The process is usually complex, time-consuming and relies heavily on engineering experience, thus making the overall design procedure inconsistent, i.e. different ‘best’ solutions are obtained from different designers. [...]This work was supported by the UK Engineering and Physical Sciences Research Council (EPSRC) grant (reference number: EP/M017915/1) for the University of Exeter’s College of Engineering, Mathematics, and Physical Sciences

Automatic shape optimisation of the turbine-99 draft tube

This is the author accepted manuscript.INTRODUCTION The performance of a hydraulic reaction turbine is significantly affected by the efficiency of its draft tube. Factors which impede the tube’s performance include the geometrical shape (profile), and velocity distribution at the inflow. So far, the design of draft tubes has been improved through experimental observations resulting in empirical formulae or ‘rules of thumb’. The use of Computational Fluid Dynamics (CFD) in this design process has only been a recent addition due to its robustness and cost-effectivenesses with increasing availability to computational power. The flexibility of CFD, allowing for comprehensive analysis of complex profiles, is especially appealing for optimising the design. Hence, there is a need for developing an accurate and reliable CFD approach together with an efficient optimisation strategy. Flows through a turbine draft tube are characterised as turbulent with a range of flow phenomena, e.g. unsteadiness, flow separation, and swirling flow. With the aim of improving the techniques for analysing such flows, the turbomachinery community have proposed a standard test case in the form of the Turbine-99 draft tube [1]. Along with this standard geometry, with the aim of simulating the swirling inflow, an additional runner proposed by Cervantes [2] is included in the present work. The draft tube geometry is shown in Fig.1. The purpose of this abstract is to outline the framework developed to achieve the automated shape optimisation of this draft tube.This work was supported by the UK Engineering and Physical Sciences Research Council (EPSRC) grant (reference number: EP/M017915/1) for the University of Exeters College of Engineering, Mathematics, and Physical Sciences

Equilibrium Models of Galaxy Clusters with Cooling, Heating and Conduction

It is generally argued that most clusters of galaxies host cooling flows in which radiative cooling in the centre causes a slow inflow. However, recent observations by Chandra and XMM conflict with the predicted cooling flow rates. Amongst other mechanisms, heating by a central active galactic nucleus and thermal conduction have been invoked in order to account for the small mass deposition rates. Here, we present a family of hydrostatic models for the intra-cluster medium where radiative losses are exactly balanced by thermal conduction and heating by a central source. We describe the features of this simple model and fit its parameters to the density and temperature profiles of Hydra A.Comment: 16 pages, submitted to Ap