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    has been a less popular subject for research As a consequence inability to model radiation properly is often the main cause of inaccuracy in CFD predictions This is understandably true of high temperature processes such as those in the combustion chambers of engines and furnaces but it is no less true of lower temperature ones such as in electronic equipment or in the living accommodation of human beings where convective conductive and radiative modes of heat transfer may have similar orders of magnitude 2 A common misconception Radiative heat transfer can be described mathematically with exactness Perhaps for this reason it is commonly supposed that enabling a CFD code to add radiation to its predictive capabilities is simply a matter of selecting and attaching to it one or other of the available equation solving methods such as those which go under the names of Monte Carlo discrete transfer discrete ordinates zone etc This is a misconception for unfortunately consideration of how these methods will perform when applied to problems of more than modest size makes plain that they must all require very much more computer time and elapsed time than anyone can afford and this is so even with neglect of the influences of wave length on absorption and emission angle on the reflectivity of surfaces temperature on the radiative properties of materials the chemical composition and surface finish of those materials and the complicating presence of turbulent fluctuations of temperature and of multi phase flow It is true that such are the desires of CFD code vendors to sell their products and of purchasers to believe that they have spent their money wisely that many publications can be found which purport to validate the radiation simulating capabilities of the codes Rarely however do these publications contain the results of

    Original URL path: http://www.cham.co.uk/phoenics/d_polis/d_enc/enc_rad0.htm (2016-02-15)
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  • list of early lectures on MFM the main contents of which were conflated in 2010 into one document More recent power point presentations are PTA PTB 2009 Benjamin Franklin and CFD 2010 Population Models of Turbulence 2010 Populational CFD 2011 5 3 Multi fluid models of turbulence MFM Section 5 3 of Encyclopaedia article Turbulence models in PHOENICS Contents How MFMs differ from conventional turbulence models The essential ideas of

    Original URL path: http://www.cham.co.uk/phoenics/d_polis/d_enc/turmod/enc_tu53.htm (2016-02-15)
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  • MFM and flamelet models
    may have any number of continuously varying attributes CVAs the values of which are also computed from transport equations The turbulent micro mixing process is a consequence of brief encounters of the kind described in section 1 1 c above and results in the production of interface material at a rate per unit volume equal to CONMIX epsilon k where CONMIX is a constant The rate of production of interface material from such encounters between fluid i and fluid j is Mi Mj CONMIX epsilon k where Mi and Mj are the mass fractions of the two fluids The intermediate fluid layer material called offspring in MFM parlance which is produced as a consequence of the encounter called coupling and splitting goes to increase the concentration of the appropriate population member If two PDAs are chosen eg reactedness and fuel air ratio with N1 allowable values of the first and N2 allowable values of the second the population would contain N1 N2 distinct fluids the model would be called a N1 N2 fluid model and the number of diagrams illustrating their coupling and splitting referred to in 1 above would be N1 N2 2 back to highlights b Connexions with conventional turbulence modelling concepts The well known epsilon and k quantities have already been referred to It will be useful also to connect MFM concepts with three others namely the effective kinematic viscosity nuturb the mixing length Lmix and the local Reynolds Number of turbulence Re These quantities are inter related by equally well known relationships namely nuturb CMU k 2 0 epsilon with CMU 0 09 Lmix CD k 1 5 epsilon with CD 0 164 Re nuturb nulam where nulam laminar kinematic viscosity Since sigma has the dimensions of 1 length being a measure of the average thickness of the gas fragments engaging in the coupling and splitting process it can be expected to be proportional to the reciprocal of Lmix Therefore to avoid having to introduce another constant let it be taken as equal to this reciprocal so that sigma Lmix 1 0 Important note It is necessary to distinguish between the sigma employed in the FLM from that which is employed in MFM for FLM pays attention only to interfaces between fully burned and fully unburned gases whereas MFM recognises that the coupling and splitting process is a consequence of the turbulence which disregards the chemical compositions of the materials which are brought into contact Thus FLM s sigma has to be zero when there is no more unburned combustible whereas MFM s sigma can reasonably be taken as inversely proportional to Lmix regardless of the extent of the reaction It is now interesting to ask two questions namely how is the average time of the brief encounters Tcont related to the typical micro mixing time namely k epsilon and how can one determine the ratio of the average thickness of the inter block layer Llay say to the block size Lmix First however it is necessary to justify the linkage of the rate of offspring production to epsilon k by a more detailed discussion of the energy dissipation process than has been provided anywhere in the MFM literature until now c The mechanism of energy dissipation If as MFM supposes the dominant behaviour pattern of the multi fluid population is coupling and splitting it must be possible to use this description to explain how turbulent kinetic energy is dissipated Such a use of the concept now follows The two blocks of fluid which engage in the brief encounter illustrated in Figure 1 will in general have different velocities Let the average difference for all encounters be veld Obviously this velocity difference is related to the turbulent kinetic energy by k constant veld 2 The effect of viscosity in the interfacial layer is to reduce the differences of velocity as is shown by the following contour plot Figure 4 with the consequence that there is a reduction in the turbulent kinetic energy of the mixture which is proportional to the amount of interfacial material which is created and veld 2 ie to k It is noteworthy that the velocity difference contours unlike the reactedness ones of Figure 3 which were calculated for the same conditions are fully symmetrical The rate of reduction of kinetic energy per unit mass is of course epsilon and if the rate of production of interface material ie of offspring is given the symbol Roff the foregoing argument leads to epsilon k constant Roff Comparison with the equation above which introduced CONMIX shows that constant is nothing but 1 0 CONMIX and it leads to the conclusion that CONMIX is greater than 1 0 because constant is certainly less than 1 0 since the interfacial material does retain some kinetic energy It is interesting to observe that such comparisons of MFM predictions with experiment as have been made so far have favoured a value of between 5 0 and 10 0 for CONMIX The value most favoured by users of the Eddy Break Up model is much lower namely around 0 5 but this is easily explained by the fact that EBU is a mere two fluid model i e one with a very coarse population grid d The average contact time Since the interfacial layer grows as a result of molecular action it is certain that its maximum thickness Llay i e that which exists at the end of the brief encounter when coupling gives way to splitting is of the order of nulam Tcont 0 5 Also the same analysis would show that the rate of production of interface material per unit volume is equal to sigma Llay Tcont ie to sigma nulam Tcont 0 5 It follows that CONMIX epsilon k sigma nulam Tcont 0 5 and so that Tcont nulam k sigma CONMIX epsilon 2 Let now this contact time be compared with the micro mixing time Tmix defined by Tmix 1 0 Roff If sigma is taken as the reciprocal of Lmix and use is made of the above definitions of nuturb Re etcetera it can be shown by algebraic substitution that Tcont Tmix constant Re where constant CMU CONMIX CD 2 which is of the order of unity It follows that since Re is usually much greater than unity in a turbulent flame the contact time is much smaller than the mixing time One implication is that the interfacial layer does not have enough time to grow so as to have a dimension comparable with those of the blocks of fluid which are enjoying their brief encounter Indeed it can be algebraically deduced from the above equations that Llay Lmix constant Re also 1 3 Connexions between FLM and MFM a An important question It has been remarked above in connexion with Figure 4 that conditions in the interfacial layer governing momentum exchange are symmetrical throughout the encounter whereas those for the reactedness Figure 3 are symmetrical only at the start Obviously the relevance of the epsilon k quantity to the creation of interface material is greater if the encounter is broken off before the reactedness profile has become very unsymmetrical i e before the laminar flame propagation process has had time to dominate so it is interesting to estimate whether this condition is likely to be satisfied The following argument allows this question to answered The maximum amount of extra interface material which could be created by laminar flame propagation during the contact time is Ulam Tcont This is to be compared with Llay the layer thickness calculated by the above formulae The result is that the ratio of the two quantities is Ulam CONMIX CD k 0 5 wherein as already stated CONMIX CD is of the order of unity Since the laminar flame speed is only rarely of the same order as the typical turbulent fluctuation velocity which k 0 5 represents it can be concluded that the contact time will usually be short enough for the velocity and reactedness layers to be of the same order of magnitude The following summarising remarks about the connexions between FLM and MFM therefore appear to be appropriate FLM and MFM both pay attention to the interfacial material which results from turbulence occasioned encounters between fluid fragments of unlike composition FLM considers only encounters between fully burned and fully unburned fragments both having the same fuel air ratio wheareas MFM allows the fragments to have any pairs of values of reactedness and fuel air ratio FLM practitioners tend to think of the interfacial layers as being similar to steadily propagating laminar flames admittedly modified in some way by stretching whereas the MFM presumptions suggest that they are mainly of the transient inter diffusion kind Since a major aim of many users of FLM is to compute the production rates of secondary reaction products such as NOX by postulating that profiles in the inter facial layers are those of propagating flames it must be suspected that those rates will be wrongly calculated MFM also has a presumption about the profiles in the layer as part of its coupling and splitting hypotheses The only presumption which has been seriously explored so far namely the promiscuous Mendelian one implies symmetry within the inter diffusion layer but this can easily be remedied 2 MFM applied to circumstances for which FLM may be valid 2 1 The well stirred reactor description FLM requires for validity uniformity of fuel air ratio high Reynolds number and a highly reactive combustible mixture These requirements are satisfied by PHOENICS Input Library Case L103 of which the descriptive part runs as follows Stirred reactor with a 1D population distribution and reactedness ranging from zero to 1 as the population distinguishing attribute It is supposed that two streams of fluid enter a reactor which is sufficiently A well stirred for space wise differences stirred of conditions to be negligible but not C sufficiently for micro mixing to be reactor complete B The two streams have the same elemental composition but one may be more reacted than the other The flow is steady and the total mass flow rate per unit volume is 1 kg s m 3 The flow is zero dimensional in the geometrical sense but to give it significance for a three dimensional combustor simulation it might be regarded as representing a single computational cell in the 3D grid Then the conditions in the inlet streams might represent those in the neighbouring cells from which material enters by way of diffusion and convection The calculations to be reported have been conducted with a 25 fluid model and with reactedness as the population defining attribute The reaction rate versus reactedness formula is of the well known kind rate CONREA1 1 R R CONREA2 where R stands for reactedness The exponent CONREA2 has been given the value 5 0 which represents sufficiently well for the present illustrative purposes the temperature dependence of combustion reactions Stream A has been chosen as being completely unburned R 0 0 and stream B as fully reacted R 1 0 Various values have been chosen for the micro mixing constant CONMIX and the pre exponential factor of the reactivity CONREA2 2 2 The PDFs predicted by MFM In the following table the second third and fourth columns disclose the input parameters Clicking on the number in the first column will display the computed PDFs on the left hand side and the average and root mean square deviations of the reactedness together with a pictorial representation of the intermingling fluids on the right hand side The PDFs appear as histograms with frequency of appearance in the population as ordinate and reactedness as abscissa The references to spikes should be noted Comparison of the values ascribed to the height of these spikes with the also printed maximum ordinates shows that they are often much larger This is the justification for the two fluids mainly idea which underlies FLM The average reactedness and RMS deviations appear in the fifth and sixth columns Figure CONMIX CONREA RB ave R rms R 6 10 0 100 0 0 0 0 577 0 448 7 10 0 50 0 0 0 0 472 0 427 8 100 0 100 0 0 0 0 937 0 197 9 100 0 50 0 0 0 0 922 0 202 10 100 0 25 0 0 0 0 897 0 206 11 100 0 10 0 0 0 0 815 0 199 12 10 0 10 0 1 0 0 739 0 354 13 100 0 50 0 1 0 0 963 0 145 14 100 0 10 0 1 0 0 927 0 151 15 100 0 5 0 1 0 0 884 0 148 16 100 0 1 0 1 0 0 541 0 114 Some trends revealed by these figures will now be discussed as follows Comparison of Figures 6 with 8 or 7 with 9 reveals what a large influence is exerted on the shape of the PDF by the micro mixing constant for fixed reactivity constant In particular increasing CONMIX increase the height of the right hand spikes which measure the concentration of fully reacted fluid In all four cases however at least one of the spikes is large Inspection of the sequence of figures 8 9 10 and 11 all for the same CONMIX value but for steadily decreasing CONREA show a further dramatic change of PDF shape The last one shows that the spikes have totally disappeared Any further reduction of CONREA leads it should be mentioned to extinction of the chemical reaction For figures 12 onwards RB equals unity it was zero before This means that the reactor is fed equally with fully burned and fully unburned gas Understandably the average reactednesses for the same CONMIX and CONREA are greater than for the RB 0 flames The sequence of figures 13 14 15 and 16 shows that a steady reduction of the reactivity constant with CONMIX remaining unchanged transforms the PDF from a mainly two spike one albeit with one spike much shorter than the other to one of Gaussian appearance This last is evidently influenced predominantly by mixing for it is nearly symmetrical whereas the effect of chemical reaction must be to shift the centre of gravity to the right 2 3 Comparison with the presumptions of FLM It is now possible to consider to what extent MFM confirms or contradicts the presumptions of the flamelet model of turbulent combustion The best confirmation of FLM presumptions is afforded by Figures 6 and 7 for both of these exhibit the large spikes of zero and unity reactedness gas with low concentrations of gases of intermediate reactedness Whether the distributions of concentration of the intermediate gases is the same for MFM and LFM is another matter As has already been indicated LFM practitioners are inclined to believe albeit without any closely reasoned argument that the distributions correspond to those of a steadily propagating flame whereas the foregoing analysis suggests that the transient interdiffusion model is more appropriate When the sequence of Figures 8 9 10 and 11 is considered support for the FLM concept becomes weaker the last of these figure revealing a PDF which is quite unlike that which LFM presumes Even less supportive are Figures 15 and 16 for these again show distributions which are different from those to which FLM applies It must indeed be concluded that FLM can be expected to represent turbulent combustion in pre mixed gases only when the chemical reaction rate measured here by CONREA is large compared with the micro mixing rate measured by CONMIX This condition is perhaps satisfied for a gasoline engine where the fuel air ratio may be close to stoichiometric throughout but it is unlikely to prevail for combustors into which the fuel and air enter separately Separate introduction of fuel and air is the subject of the next section 3 MFM in more general circumstances 3 1 Non uniform fuel ratio a The cases considered A further series of calculations has been performed for the conditions in which the two streams of fluids entering the stirred reactor have differing fuel air ratios Such conditions lie beyond the capabilities of the flamelet model at the present time Specifically stream A has been taken as pure air and stream B has been taken as having a fuel air ratio of twice the stoichiometric value and a reactedness of 50 The two streams are equal in flow rate A 100 fluid model has been employed for this study with a two dimensional population grid of which the PDAs ie population defining attributes are The so called mixture fraction fmx which represents the mass of material in the time average local mixture which has emanated from the fuel bearing stream namely stream B in the present case and the burned fuel fraction fbu which represents the mass fraction of material emanating from the fuel bearing stream which has been oxidised This equals fmx fub where fub the mass fraction of unburned fuel The last named PDA is related to but not precisely equal to the reactedness for this is not as fbu is strictly speaking a conserved property of the gas because mixing a 50 reacted mixture with a 100 reacted mixture results in a 75 reacted mixture only when 5veer the fuel air ratios are the same The input conditions have been selected from the multiply infinite range of possibilities because they sufficiently illustrate what the multi fluid model of turbulence has to say about chemical reactions in gases in which both fuel air mixing and finite rate chemistry are influential Further information about the definition of the model will be provided during the discussion of the results and of their displays which may be inspected by clicking on the relevant number in the left hand column of the following table Figure CONMIX CONREA average F average R 17 10 0 10 0 0

    Original URL path: http://www.cham.co.uk/phoenics/d_polis/d_lecs/mfm/flamelet.htm (2016-02-15)
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  • using the PHOENICS VR geometry convertor PHOENICS VR Editor then used the geometry file to construct the VR world and to attach CFD attributes Then the VR to CFD convertor generated CFD settings and saved the geometry in the form of facets for the PHOENICS solver EARTH to use The burner geometry in the VR editor Burner geometry viewed in outline mode Grid cells which are within the burner geometry

    Original URL path: http://www.cham.co.uk/phoenics/d_polis/d_info/cadi/cadburnr.htm (2016-02-15)
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  • Geometry creation for VR
    the usability of the file as follows 8 point Y 0 0000E 00 1 0000E 00 0 0000E 00 1 4 3 1 0000E 00 1 0000E 00 0 0000E 00 2 1 0000E 00 1 0000E 00 1 0000E 00 3 Z 8 7 0 0000E 00 1 0000E 00 1 0000E 00 4 1 0000E 00 0 0000E 00 0 0000E 00 5 1 2 0 0000E 00 0 0000E 00 0 0000E 00 6 1 0000E 00 0 0000E 00 1 0000E 00 7 6 5 0 0000E 00 0 0000E 00 1 0000E 00 8 O X 6 2 1 4 3 48 5 2 3 7 49 6 5 7 8 48 1 6 8 4 49 8 7 3 4 50 1 2 5 6 50 Two examples of files created by editing cube dat are cencube1 dat and cencube2 dat The first reduces the size of the cube by making the lower and upper limits of the vertex coordinates 0 4 rather that 0 0 and 0 6 rather than 1 0 and this also has the effect of placing the reduced size cube centrally within its bounding box The second enlarges the size of the box ten fold so that when it is brought by the VR Editor into the 1m by 1m by 1m default domain the shrinkage which the editor imposes by default is cancelled The two objects therefore have the appearance shown here when first brought in Click here for access to other dat files 3 The use of Fortran To create by hand editing a file which would describe a complex many faceted object would be very tedious therefore the use of a Fortran program has much to recommend it 4 An example the incomplete cone frustrum How to do so is best seen by inspection of the following example which can be used to create a sector of the cone frustrum illustrated here 4 1 The Fortran file frustrum for The Fortran program which creates objects such as can be seen by clicking here Comment lines within the listing may explain sufficiently to those who are familiar with Fortran how it does what is needed 4 2 The parameter input file frustrum The parameters which describe precisely which member of the class of thick walled cone frustra is to be produced are supplied by editing the file frustrum which is also to be found in the directory phoenics d utils d vrgeom It is as follows frustrum variable meaning 0 8 boufr bottom outer radius 0 6 binfr bottom inner radius 0 6 toufr top outer radius 0 2 tinfr top inner radius 24 nsides number of facets 0 45 angfac proportion of 2PI 0 25 angf starting angle 0 0 zpf z location of bottom of frustrum 1 0 zpl z location of top of frustrum 1 isign 1 for opaque 1 for transparent It is only the left hand column entries which are read by

    Original URL path: http://www.cham.co.uk/phoenics/d_polis/d_enc/geomvr.htm (2016-02-15)
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  • is the one which he wants to solve all that should be necessary is to click on the EXIT button then the data should be exported to the equation solver and after the requisite number crunching time the results should be returned to the VR Interface The should be implies the condition if the user is not a specialist in computational fluid dynamics but simply wants to get the results of the computations as quickly as possible in a form which he can understand This condition is frequently satisfied and it will be almost universally so in the future as the CAD to CFD traffic increases Fig 2 1 2 shows some of the results of the flow simulation corresponding to the data input specification of Fig 2 1 1 The VR viewer is capable of showing vectors streamlines contours and iso surfaces Fig 2 1 2 The same object in the VR viewer 2 2 An aeronautical example the 3 part airfoil Description of the problem Handling the obliquely cut cells via PARSOL a Description of the problem Creating computational grids to fit bodies with curved surfaces is one of the tedious tasks of conventional CFD and it wastes the time of highly paid specialists In order to show that it is often unnecessary a two dimensional example will be shown in which a three part airfoil is represented in a cartesian grid possessing three levels of fineness The grid refinement is easily effected by way of mouse clicks and keyboard entered refinement ratios in the VR editor operation The first of the following two pictures shows the airfoil itself and the second shows a close up of part of it and of the associated grid back to here Fig 2 2 1 The three part airfoil Fig 2 2 2 The three part airfoil close up Description of the problem Handling the obliquely cut cells via PARSOL b Handling the obliquely cut cells via PARSOL There was a time at which inaccuracies of solution were generated in those cells of the cartesian grid which were cut obliquely by the surface of immersed solids Taking extra care about the formulation of the equations relating to such cells has however removed the inaccuracies Relevant references are Yang et al 1997 a b c and PHOENICS has its own version of the technique called PARSOL standing for PARtial SOLid When appropriately implemented computer codes which employ such techniques can provide solutions of the fluid flow equations of a quality which is equal to those which employ body fitted grids Because of their superior ease of use such codes make travel along the CAD to CFD road especially smooth back to here The next four pictures show results for the three part airfoil Fig 2 2 3a Contours of velocity Fig 2 2 3b a closer look Fig 2 2 3c and another Fig 2 2 4 Contours of pressure 2 3 A test of PARSOL As a further demonstration of the

    Original URL path: http://www.cham.co.uk/phoenics/d_polis/d_lecs/cad2sft/chap2.htm (2016-02-15)
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    well as computations 2 The objective of MICA MICA is intended to create test and publicise for the practical use of CFD by industry a New Model which exploits Virtual Reality at the user interface parallel computing at remote computing centres user to centre to user communication via Internet intelligent software supplemented by human expertise 3 How the objective is to be attained 10 industrial sectors have been identified 5 in the furnace and 5 in the built environment areas 10 sector specific interfaces are to be designed created and tested with the aid of associates with special knowledge of each Where necessary sector specific physical model attachments will be added to the core software Enhancements will be provided to the core software to enable it better to provide the needed simulations these enhancements comprising optimal physical model selection optimal numerical settings 4 The special sectors currently attended to by MICA The ten sectors which have been selected for attention are Environmental group Oil platform explosions Smoke movement and fire spread in buildings Heating and ventilating of buildings Air and pollutant flow around assemblies of buildings Flow around marine structures Heat transfer equipment group Coal fired industrial furnaces Glass melting and refining furnaces Annealing furnaces Industrial ovens Steam condensers for power stations 5 Diagrammatic representation 10 front ends Internet connexion 3 computer centres with parallel software 6 What is meant by a front end Definition of user requirements in respect of input data options Corresponding creation of VR world editor and VR to CFD linker Definition of user requirements in respect of results display and assessment Corresponding creation of VR world viewer All this to be done for each of the ten sectors listed above 6 1 What is meant by the Internet connexion User s requirements are encoded and

    Original URL path: http://www.cham.co.uk/phoenics/d_polis/d_enc/enc_mica.htm (2016-02-15)
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  • НАУКА-СЕРВИС-ЦЕНТР: официальный представитель компании CHAM в России
    в России оказывает услуги по продаже и техническому сопровождению программы Phoenics Наши координаты Россия 111250 Москва Красноказарменная 14 Тел 495 362 7360 495 918 1080 Тел факс 495 918 1469

    Original URL path: http://www.cham.co.uk/ssc/ssc_main.htm (2016-02-15)
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