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the walls are near and nearly parallel is computed from the solution of the LTLS equation this will be explained later in the lecture The distributions of these two quantities are shown by Fig 14 for the former and by Fig 15 for the latter next back or contents It will be seen that WGAP has a uniform value in the region of between the top of the duct and the tops of the upper metal slabs between which the actual distance is 0 008 meters Further it has approximately twice this value near the convex corners and it becomes zero in the concave corners next back or contents Contours of auxiliary quantities used in the fluid flow calculation The flow field was calculated by means of the LVEL turbulence model which makes use of the wall distance WDIS field This like WGAP is also derived from the LTLS distribution The contours of WDIS are displayed in Fig 16 which exhibits the expected maximum of 0 004 between the parallel horizontal walls and a somewhat greater value near the cavity where the true distance from the wall depends on the direction in which it is measured next back or contents LVEL like IMMERSOL is a heuristic model by which is meant that it is incapable of rigorous justification but is nonetheless useful WDIS is calculated once for all at the start of the computation From it and from the developing velocity distribution the evolving distribution of ENUT the effective turbulent viscosity is derived The resulting contours of ENUT are shown in Fig 17 Since the laminar viscosity is of the order of 1 e 5 m 2 s it is evident that turbulence raises the effective value far from the walls by an order of magnitude next back or contents c How the stresses were calculated As will be shown below the equations governing the displacements are very similar to those governing the velocities The CFD code PHOENICS like many others can calculate velocities in fluids but this ability is not needed in the solid region so such codes are usually idle there However PHOENICS can be tricked into calculating what it thinks are velocities everywhere whereas what it actually calculates in the solid regions are displacements The details of the trickery now follow next back or contents 3 The mathematics of the method a Similarities between the equations for displacement and velocity The similarities already referred to are here described for only one cartesian direction x but they prevail for all three directions next back or contents The x direction displacement U obeys the equation del 2 U d dx D C1 Te C3 Fx C2 0 where Te local temperature measured above that of the un stressed solid in the zero displacement condition multiplied by the thermal expansion coefficient D d dx U d dy V d dz W which is called the dilatation Fx external force per unit volume in x direction V and W displacements in y and z directions C1 C2 and C3 are functions of Young s modulus and Poisson s ratio next back or contents When the viscosity is uniform and the Reynolds number is low so that convection effects are negligible the x direction velocity u obeys the equation del 2 u d dx p c1 fx c2 0 where p pressure fx external force per unit volume in x direction c1 c2 the reciprocal of the viscosity next back or contents Notes The two equations are now set one below the other so that they can be easily compared del 2 U d dx D C1 Te C3 Fx C2 0 del 2 u d dx p c1 fx c2 0 The equations can thus be seen to become identical if p c1 D C1 Te C3 which implies D p c1 Te C3 C1 and fx c2 Fx C2 next back or contents The expressions for C1 C2 and C3 are C1 1 1 2 PR C2 2 1 PR YM where PR Poisson s Ratio and YM Young s Modulus and C3 2 1 PR 1 2 PR next back or contents A solution procedure designed for computing velocities will therefore in fact compute the displacements if the convection terms are set to zero within the solid region and the linear relation between D ie d dx U and p is introduced by inclusion of a pressure and temperature dependent mass source term next back or contents b Deduction of the associated stresses and strains The strains ie extensions ex ey and ez are obtained from differentiation of the computed displacements Thus ex d dx U ey d dx V ez d dx W next back or contents Then the corresponding normal stresses sx sy sz and shear stresses tauxy tauyz tauzx are obtained from the strains by way of equations such as sx YM 1 PR 2 ex PR ey and tauxy YM 1 PR 2 0 5 1 PR gamxy where gamxy d dy U d dx V next back or contents c The SIMPLE algorithm for the computation of displacements PHOENICS employs a variant of the SIMPLE algorithm of Patankar Spalding 1972 for computing velocities from pressures under a mass conservation constraint Its essential features are All the velocity equations are solved first with the current values of p The consequent errors in the mass balance equations are computed These errors are used as sources in equations for corrections to p The corresponding corrections are applied and the process is repeated next back or contents All that it is necessary to do in order to solve for displacements simultaneously is in solid regions to treat the dilatation B as the mass source error and to ensure that p obeys the above linear relation to it Therefore a CFD code based on SIMPLE can be made to solve the displacement equations by eliminating the convection terms ie setting Re low and making D linearly dependent on p

Original URL path: http://www.cham.co.uk/phoenics/d_polis/d_lecs/solstr/solstr.htm (2016-02-15)

Open archived version from archive - Turbulence models for CFD in the 21st century

mean temperature or concentration next16 back or contents In the saline layer example the vertical velocity of the fluid fragments is negative for the heavier and positive for the lighter members of the population Kolmogorov type models compute only population mean values although they are sometimes supplemented by guesses about the PDFs This is why they simulate combustion processes for example inadequately next17 back or contents 5 How multi fluid models MFMs work The working concepts of a multi fluid model are few and simple They are as follows The fluid mixture is regarded as composed of an intermingling population of individual fluids each distinguished by the interval it occupies on the discretised PDF abscissa A differential equation of the standard conservation type is solved for the mass fraction i e PDF ordinate of each member of the population The solutions of these equations provides the PDF for every location and time next18 back or contents The source terms in these equations express the postulated micro mixing hypothesis which defines the frequency with which the different fluids collide and the re distribution of material between population members which ensues and the speed of movement of material in population space as when a heat source shifts material from low temperature intervals into higher temperature ones next19 back or contents Additional equations either differential or algebraic are also solved for non discretised dependent variables for example the velocity components of the distinct fluids each of which will ordinarily have a different density and so be subject to different body forces Such operations of course increase computer times as compared with those required for Kolmogorov type models but the increases are not exorbitant See below for an example next20 back or contents One dimensional PDFs discretized look like this or this or this Left hand diagram only In these pictures the left hand half gives the PDF the right hand half is merely a reminder of the inter mingling fluid concept next21 back or contents Populations of fluids may be multi dimensional Examples of two dimensional populations would be the use of temperature and salinity for simulating the turbulent mixing and un mixing processes described in section 3 above and the use of fuel air ratio and completeness of reaction for simulating the flow and combustion of turbulent gases in a combustion chamber next22 back or contents A discretised two dimensional PDF looks like this or this Examples of three dimensional populations would be the discretization of all three velocity components for the detailed simulation of turbulent hydrodynamics and the use of fragment size as a third population dimension when temperature and salinity are the other two next23 back or contents It is important to recognise that the modeller can choose freely which dependent variables to discretise and which to allow to vary continuously for each fluid and how finely to discretise These choices can be made with the aid of physical insight into what variables are of dominant importance and population refinement studies of essentially the same nature as are used to determine how finely it is necessary to sub divide space and time next24 back or contents Example 3 how many fluids are needed for accuracy when predicting smoke generation These choices may differ from place to place and from time to time MFM allows the possibility of using un structured and adaptive population grids next25 back or contents It should also be understood that MFM models can be combined with enlarged viscosity models Thus it is common to use the k epsilon model for the hydrodynamics when the phenomena of greater interest involve chemical reaction or radiation During the oral presentation of the present lecture examples will be shown of the applications of multi fluid modelling to Example 4 Smoke generation in gas turbine combustors and Example 5 Chemical reaction in a paddle stirred reactor next26 back or contents 6 Calibrating MFMs Multi fluid models like those of Kolmogorov type have a priori unknown constants and functions in their equations the values and forms of which must be deduced from experimental data It is possible to use the same measurements as have been used for calibrating the EV type models for example the rates of spread of and the profiles of velocity and temperature in turbulent jets wakes and plumes However these provide only indirect evidence of the crucial quantities next27 back or contents More direct evidence is provided by difficult to make measurements of the PDFs themselves At present there are too few such data in the literature and these pertain almost entirely to one dimensional populations It is therefore important to devise new experiments which are easy to perform and rather directly indicative of the micro mixing process next28 back or contents The so called puff jet experiment which possesses these qualities will now be described A jet of fluid containing a small proportion of chemically reactive species A is injected steadily into a reservoir containing the same fluid Then for a short period of time a small amount of a second species B is injected at the jet orifice at a rate which is too small to affect the flow field A and B react as swiftly as they are allowed by the micro mixing process to form a third species C which species emits or reflects light with the result that a visible perhaps coloured cloud of material is seen to move downstream as indicated below next29 back or contents stream of reactant A visible cloud of C nozzle where B was briefly injected followed by A again next30 back or contents Since if there were no micro mixing there would be no coloured light emission and if micromixing were intense there would be maximum emission measurement of the amount of the actual emission allows the micro mixing rate to be determined The shape and speed of motion of the cloud will also provide hypothesis testing information Such experiments will be undertaken at South Bank University

Original URL path: http://www.cham.co.uk/phoenics/d_polis/d_lecs/turb2000/t2000lec.htm (2016-02-15)

Open archived version from archive - Introductory Lectures on PHOENICS

Flash Version of Latest News Letter Introductory Lectures on PHOENICS Introduction to PHOENICS to the VR Interface to PIL Mathematics Mathematical basis Boundary conditions Solution techniques Convergence monitoring and control Higher order Convection Schemes Physics Turbulence models Two phase flow

Original URL path: http://www.cham.co.uk/ChmSupport/intrlecs.php (2016-02-15)

Open archived version from archive - PHOENICS User Meeting: Sydney Feb 2008 (AIRAH) Proceedings

CFD in the Air Conditioning and Fire Protection Industry John Ludwig CHAM Ltd The Use of CFD in Alternative Solutions Jamie Vistnes Stephen Grubits Associates Pty Ltd Case Studies on Displacement Ventilation Richard Palmer Advanced Environmental Pty Ltd Using PHOENICS

Original URL path: http://www.cham.co.uk/PUC/PUM_Sydney/Contents.htm (2016-02-15)

Open archived version from archive - PHOENICS European User Meeting 2006 - Presentation CD

Greenwich University PowerPoint Experience using a CFD Code for Estimating the Noise generated by Gusts along the Sun roof of a Car Mr K Lai Greenwich University UK Vortex de Mexico PowerPoint Hydraulic Analogy for Compressible Flow Dr A Palacio Vortex de Mexico Mexico DSTL PowerPoint DSTL PDF Some Underwater Applications of PHOENICS at the DSTL Dr R Hornby DSTL UK TU Vilnius 1 PowerPoint TU Vilnius 1 PDF Simulation of Convective Conductive Radiative Heat Transfer in a Cooling Basin Prof P Vaitiekunas TU Vilnius Lithuania Brighton University PowerPoint A Mathematical Model of Steady State Cavitation in Diesel Injectors Dr S Martynov Brighton University UK ENIT 2 PDF Predicting the Appearance of Cavitation in Pumps with a Numerical Approach Prof R Zgolli ENI Tunisia Corsica University PowerPoint Corsica University PDF Set up of Radiative Cooled Dew Condensers by Computational Fluid Dynamics CFD Mr O Clus Corsica University France Liverpool University PowerPoint PHOENICS based Arc Models as a Test Tool for New Design Ideas in Switching Devices Dr J Yan Liverpool University UK PHOENICS Focus PHOENICS Today 1 PowerPoint Overview of PHOENICS 3 6 2 2006 Dr J Ludwig CHAM UK PHOENICS Focus PHOENICS Today 2 PowerPoint INFORM Prof B Spalding CHAM UK Flowsolve 1 A CFD Study of Ventilation in the Blizard Building Queen Mary London Dr D Glynn Flowsolve UK Heriot Watt University PowerPoint Modelling Sheltering Effects of Windbreaks in Open Spaces Dr F Wang Heriot Watt Glasgow Universities UK Alpha PI PowerPoint Alpha PI Description Doc Optimisation of Air Distribution for the Théâtre National de Belgique Mr A DeWindt Alpha PI Belgium Novenco PowerPoint Modelling Smoke and Temperature Spread from Car Park Fires Mr J Agema Novenco BV The Netherlands TU Vilnius 2 Doc Not Presented Abstract Only Numerical Modelling of Heavy Metal Sorption Isotherms Calculation Prof D

Original URL path: http://www.cham.co.uk/PUC/PUM_London/Contents.htm (2016-02-15)

Open archived version from archive - PUM Eindhoven

Uffelen Adviesburo Peutz BV 3 G Janssen A2TE PPS Designing Equipment by using CFD Benefits and Pitfalls G Janssen A2TE 4 P Phelps Flowsolve PPS Modelling Discharges from Rooftop Stacks in Confined Environments P Phelps Flowsolve Ltd 5 H Mindt a CFD PDF H Mindt a CFD PPS From GIS to CFD a CAD Solution for Data Transfer between GIS and CFD H W Mindt a CFD GmbH 6 J

Original URL path: http://www.cham.co.uk/PUC/PUM_Eindhoven/Contents.htm (2016-02-15)

Open archived version from archive - PHOENICS 10th International User Conference

Environment and Fire Safety Design Q Wang K Ma and M Lundqvist Ove Arup Pty Ltd Sydney Australia Jal Sports Stadia PDF Jal Sports Stadia Presentation Using CFD for Sports Arena and Stadia Design EN Jal Connell Wagner Pty Ltd Victoria Australia Palacio PDF Palacio Presentation Application of the ASAP Technique in the Geophysical and Industrial Scales a Comparison with BFC A Palacio A Rodriguez E Lombard M Salinasand and W Vicente Engineering Institute of the UNAM Mexico Suzuki PDF Suzuki Presentation High Viscous Flow in Silk Spinneret T Asakura and A Ino Tokyo University of Agriculture and Technology T Suzuki CHAM Japan Phelps PDF Phelps Presentation Predicting the Dispersion Consequences of Gaseous Releases from a Research Facility in an Urban Environment PJ Phelps and J Gibson Flowsolve UK Komarov PDF Komarov Presentation Simulation of Sintering of Iron Ore Bed with Variable Porosity SV Komarov and E Kasai Institute of Multidisciplinary Research for Advanced Materials Tohoku University Japan Guimaraes Tundish PDF Guimaraes Tundish Presentation Understanding the Steel Solidification in Tundish Nozzles C Fontes and F Guimaraes CHEMTECH Brazil H Furtado and S Santos CST Brazil Smith PDF Smith Presentataion Prediction of Flow and Mass Transfer in Canister Filters AG Smith and K Taylor S C Thermofluids UK MW Smith DSTL Porton Down UK Toften PDF Toften Presentation PHOENICS in Safety Analyses of Offshore and Underground Constructions T Toften and B Venås LM Flow Consult Norway Partha Sarathy PDF Partha Sarathy Presentation Thermal Hydraulic Studies for Prototype Fast Breeder Reactor using PHOENICS U Partha Sarathy K Velusamy P Selvaraj P Chellapandi S C Chetal and SB Bhoje Indira Ghandi Centre for Atomic Research India Kumar PDF Kumar Presentation CFD Analysis of Cross Flow Air to Air Tube Type Heat Exchangers V Kumar Centre for Development of Advanced Computing Pune University India

Original URL path: http://www.cham.co.uk/PUC/PUC_Melbourne/Contents.htm (2016-02-15)

Open archived version from archive - 2002 Moscow PHOENICS User Conference - Proceedings Contents

in a Test Facility for Industrial Chillers P Phelps Flowsolve Glacialtech Glacialtech ppt Geometry Parameters Analysis of CPU Heat Sink Y Wang Glacialtech Glasgow Caledonian Uni Glasgow Caledonian Uni ppt Numerical Prediction of Dispersion Characteristcs of Air Pollutants in Idealised Urban Street Canyons D Mumovic J Crowther Glasgow Caledonian University Hertfordshire Uni Hertfordshire Uni ppt Two phase Flow Modelling for Industrial Applications A Holdo R Calay Hertfordshire University Kazan State TU 1 Kazan State TU 1 ppt Three Dimensional Computations of Gravitational Separation of Two Phase Systems R Takhaviutdinov M Farakhov A Altapov Kazan State Technological University LITEC 1 Hydrodynamic and Chemical Modelling of a Flue Gas Desulpherisation Plant N Fueyo LITEC LITEC 2 pdf Inverse Problem Solving using Genetic Algorithms N Fueyo LITEC Liverpool Uni Computer Simulation of High Pressure Plasmas M Fang J Yan J Zhang V Liu C Dixon University of Liverpool MBSTU 2D Shell side Flow Modelling in a Spiral Flow Heat exchanger K Olesevich M Osipov MBSTU n a Bauman MEFOS Computational Fluid Dynamic Simulation of Raceway Behaviour in a Blast Furnace D Sheng J Wikstrom MEFOS MFRDC pdf New Features of MIGAL Solver M Ferry MFRDC MPEI Local Parameters of Longditudinal Fins Heat Sink Heating from below Surface E Sergievsky E Krinitsky V Travkin MPEI MSISA Simulation of Atmospheric Turbulent Airflow within and above Roughness Layer B Mastryukov A Ivanov MSISA Nippon Inst of Tech CFD Simulation of Flow around a Square Prism Controlled by a Rod Set Upstream M Fujino Nippon Institute of Technology Nis Uni Numerical Simulation of Tube Bundle Friction and Heat Transfer in a Shell and Tube Heat Exchanger G Ilic M Vukic University of Nis NNC NNC ppt A CFD Model of the AGR HOTBOX G Hulme NNC North Carolina State Uni Modelling of Drinking Water UV Disinfection Reactors using PHOENICS Comparison between Eulerian and Lagrangian Approach J Ducoste North Carolina State University NRC NRC pdf NRC ppt Numerical Studies of the Thermo Electrochemical Performance of Fuel Cells S Beale NRC S Zhubrin CHAM W Dong Global Thermoelectric Oulu Uni Oulu Uni ppt Different Methods obtained by PHOENICS Simulation to improve the Performance of Pusher Type Steel Slab Reheating Furnace Y Tang J Laine T Fabritus J Harkki Oulu University S C Thermofluids 1 S C Thermofluids 1 ppt The Problem of Exhaust Plume Radiation during the Launch Phase of a Spacecraft A Smith S C Thermofluids A Cretella Fiat Avio S C Thermofluids 2 S C Thermofluids 2 ppt An Automated Optimisation Technique for Rocket Motor Nozzle Design based on PHOENICS Flowfield Solution A Smith S C Thermofluids Scetaroute Scetaroute ppt Numerical Simulation of Fire in the Underground Parking of Annecy City Hall using the PHOENICS Code H Biollay E Casale SCETAROUTE J Ouazzani ARCOFLUID SSC 1 Temperature Distribution into Room of Bearing wall Building in Russian Winter A Ginevsky V Konuhov SSC SSC 2 Parameters of Heat Exchange in Monodisperse Droplet Stream A Ginevsky V Konuhov SSC Southwest Petroleum Inst Computer Simulation of Bottom Hole Fluid Field

Original URL path: http://www.cham.co.uk/PUC/PUC_Moscow/Contents.HTM (2016-02-15)

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