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    given of the physical concepts and mathematical formulations of a multi fluid model MFM of turbulence Similarities to and differences from earlier turbulence models are described References to recent works on MFM are provided but with only brief summaries of their contents the aim of the present paper being to collect and explain all the relevant ideas without distraction by particular examples Consideration is given to the advantages likely to

    Original URL path: http://www.cham.co.uk/phoenics/d_polis/d_lecs/mfm/mfmbas1.htm (2016-02-15)
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  • 1. An introduction to the multi-fluid-model concept
    the fuel rich entry mixture fraction f stream The vertical dimension f mfu ie the mass proportion of fuel stream derived material in the local mixture less the mass proportion of unburned fuel measures the extent of the reactedness of the gas being at its maximum namely f when no unburned fuel remains and at its minimum namely 0 when all the fuel is unburned Other examples of two dimensional populations might involve the attributes temperature and salinity ie salt content for use in simulations of sea water flows in estuaries along wall velocity and normal to wall velocity in a boundary layer and temperature and upward direction velocity in a buoyancy driven flow simulation For example a 2 dimensional concentration space concerned with two mixture components A and B might focus attention on 10 distinct values of the concentrations of each component The whole set of relevant mixture composition possibilities would then be represented by the 100 pairs of A and B concentration values Once again real mixtures possessing intermediate compositions would be represented by interpolation between the nearest 4 of the 100 allowed possibilities Three four and more dimensional models can of course be envisaged There is no limit 1 7 Processes affecting the fluid population distribution a The atmosphere as a suggestive example Clouds in the sky may be regarded as easily recognisable manifestations of the multi fluid character of the Earth s atmosphere with water vapour content as the distinguishing attribute Observation of such clouds reveals that they are convected across the sky by the wind more or less at a uniform velocity they move upwards and downwards at what may sometimes be differing velocities and they may come into existence grow in size then diminish and ultimately disappear Similar remarks can be made about smoke plumes from chimneys and about the much larger plumes which are created by forest fires The processes so revealed must be expected to take place in all multi fluid populations b Convection and diffusion About the first mentioned uniform convection process there is little to be said for it takes place whether the atmosphere is turbulent or not As to the second two modes of relative motion between members of the fluid population can be distinguished namely turbulent diffusion as a consequence of the gradients of concentration and sifting convection which is the relative motion according to which by reason of gravity lighter fluids move upwards more rapidly or downwards more slowly than heavier ones The speed of relative motion can be reasonably supposed to be the outcome of the balance between the buoyancy force difference which increases the speed and friction between the different velocity fluids which decreases it Thus friction between fluids in relative motion is one of the interactions to be accounted for Heat transfer and mass transfer between the fluids by reason of their differences in temperature and composition are also certain to take place to some extent c Sources and sinks of individual fluids Finally the creation growth diminution and disappearance of clouds is a reminder that a multi fluid model of turbulence must make provision since mass energy and concentration must obey their relevant conservation laws for the transfer of mass from one element of the population into another Just as a human population which is decribed by its age distribution eg 50 under 30 and 25 over 60 or political allegiances eg 40 left 35 right 20 centre and the rest don t know will change as its members grow older or change their opinions so will a fluid population distribution change Heating will effect this if temperature is one of the distinguishing attributes momentum sources will do so if the attributes are velocities and chemical reaction will bring it about if one attribute is the mass concentration of one of the reactants Sources and sinks of the above kind can take place in a single fluid on its own However multi fluid turbulence modelling involves consideration also of sources and sinks which result from the interactions BETWEEN fluids These are of such central importance as to need a section to themselves which now follows 1 8 Coupling and splitting a The general idea The present author Spalding 1995a has used the somewhat anthropomorphic term coupling and splitting to describe the interactions between fluids This term suggests that two fluid fragments making contact act as parents and that after the contact there exist what is left of the parents and a collection of offspring The coupling process is conceived as the approach of two fragments of unlike fluids followed by their partial coalescence and mixing The splitting process is their subsequent break up into new fragments which possess concentrations or temperatures velocities etc which are intermediate in value between those of the parent fluids Although more sophisticated hypotheses may prove to be more in accord with reality it is the simplest which will be described here namely that which has been called promiscuous and Mendelian Promiscuity implies that any fluid will couple with any other ie indiscriminately at a rate depending only on its availability Mendelian implies that the offspring may possess the character istics of either parent in any proportion The following diagram may serve to convey this idea frequency in population father mother promiscuous coupling Mendelian splitting v v fluid attribute b The underlying mechanisms envisaged The way in which this redistribution of material between fluids is effected is imagined to be as follows Two fragments of fluid are brought into temporary contact by the random turbulent motion thus xxxxxxxxxxxxxxx xxxxxxxxxxxxxxx xxxxxxxxxxxxxxx xxxxxxxxxxxxxxx xxxxxxxxxxxxxxx xxxxxxxxxxxxxxx Molecular and smaller scale turbulent mixing proceses cause intermingling to occur with the result that after some time the distribution of x father and mother material within the coupling fragments appears as xxxxx xxxxx x x x x x xxxxxxxx x x x x x x xxxxxx xx x x x x x x x xxxx xx xxxx x x x x x xxxxxxxxx xxx x

    Original URL path: http://www.cham.co.uk/phoenics/d_polis/d_lecs/mfm/mfmbas2.htm (2016-02-15)
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  • Multi-fluid Combustion Model
    from the base and a single radial line Specifically FPDs will be shown for six radial locations starting near the axis and moving outward to about one third of the radius Near the axis most of the fluid is still alkaline Farther from the axis more acidic fluids are found This tendency increases with increase of radius Also the shape of the PDF changes The shape change continues This is the last PDF to be shown f The salt distribution after 10 paddle rotations The acid and the alkali are supposed to react chemically in accordance with the classic prescription acid base salt water Of course no chemical reaction can occur in the unmixed fluids which to use the parent offspring analogy are the Adam and Eve of the whole population It is only their descendants with both acid and alkali in their blood who can produce any salt This is why the prediction of the yield of salt necessitates knowledge of the concentrations of the offspring fluids The next picture shows the salt concentrations after 10 paddle rotations which the multi fluid model has predicted These concentrations are the averages for all eleven fluids The salt concentrations predicted by the multi fluid model They are greatest in the region which has been most vigorously stirred by the paddle which tends to thrust fluid downwards and outwards g The salt concentrations predicted by a single fluid model If no account is taken of the existence of the fluctuations as is perforce the usual case only the mean value of the acid base ratio is available If the salt concentration distribution is calculated from this as the next picture will show the values will be different from before Indeed it can be expected that they will be larger because the implication of using a single fluid model which is what neglect of fluctuations amounts to is that micro mixing is perfect This is indeed what is revealed by the calculations The salt concentrations predicted by the single fluid model They are larger than the multi fluid values because micro mixing is presumed wrongly to be perfect h Discussion of the results The following conclusions appear to be justified by the studies conducted so far It is possible and not very expensive to compute the probability density functions describing the extent of micro mixing of initially separated materials in a stirred tank The 11 fluids used in the calculations were probably too few but any number can be used 100 is common so that fluid grid independence can be tested When a chemical reaction can take place between the materials the yield can be computed accurately only by way of a multi fluid model Even without further refinement MFM is probably more reliable than any presumed pdf method because it predicts instead of presuming 7 2 Smoke generation in a gas turbine combustor a The problem and its solution In order to compute the rate of smoke production in a 3D combustor

    Original URL path: http://www.cham.co.uk/phoenics/d_polis/d_lecs/mfm/mfm7.htm (2016-02-15)
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    on surface elements STR ream information on streamline elements TE xt information on text elements BL ocks information on blocked regions GE ometry information on user geometry For grids vectors and contours the display shows the plane and region over which the element is plotted the colour and line type and whether that element is currently switched on or off For grids the type of grid HATCH GRID or OUTLINE is also given For geometry the element number the element name and the status are shown Show Photon Help Show is used to view the plotted GEOMETRY element in the graphic window including the name of the segment depth and the current status SHOWELEM Autoplot Help SHO W E ELEMENTS Gives a list of current data elements in memory entered using the DATA command See also HELP on SHOW SHOW FILES SHOW KEYS SHOW TEXT SHOW GROUPS SHOWFILE Autoplot Help SHO W F ILES Gives list of attached files and their types Grid file also listed for RESTART files that need BFC grid files See also HELP on SHOW SHOW ELEMENTS SHOW KEYS SHOW TEXT SHOW GROUPS SHOWGROU Autoplot Help SHO W GRO UPS Gives a list of the contents

    Original URL path: http://www.cham.co.uk/phoenics/d_polis/d_enc/show.htm (2016-02-15)
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    co uk Code expiry date is the end oct 2012 Running with 64 bit Single Precision executable Initial estimated storage requirement is 10000000 Information about material properties Total number of SPEDATs is 13 number of materials specified by SPEDATs is 1 solprp 100 porprp 198 vacprp 199 The properties file is PROPS Properties being read from PROPS Properties have been read from PROPS Formula used for setting RHO1 Formula used

    Original URL path: http://www.cham.co.uk/phoenics/d_polis/d_enc/492res.htm (2016-02-15)
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  • Nett Source Printout
    each solved for variable the summation of all the positive sources the summations of all the negative sources and the difference between them which is to say the whole domain nett source for the variable For mass sources at fixed pressure boundaries additional information is provided As well as the nett mass flow through the boundary the individual positive In flow and negative out flow flows are reported as shown in this example Nett source of R1 at patch named OB5 INLET 5 945001E 00 Nett source of R1 at patch named OB6 OUTLET 5 944975E 00 Mass Out 6 226088E 00 In 2 811145E 01 pos sum 5 945001 neg sum 5 944975 nett sum 2 574921E 05 For the energy equation in temperature form the average temperature of the inflow and outflow is reported as here Nett source of TEM1 at patch named OB5 INLET 1 775355E 04 Average 1 999991E 01 Nett source of TEM1 at patch named OB6 OUTLET 1 820721E 04 Ave Out 2 729029E 01 In 2 000000E 01 Nett source of TEM1 at patch named OC1 FENCE 5 000002E 02 pos sum 1 825355E 04 neg sum 1 820721E 04 nett sum 46 341797 For other scalars the average value of the scalar in the in and out flow stream is reported When EGWF Earth Generated Wall Functions is active the nett friction force on each blockage is also reported There are three exceptions namely nett sources which are equal to zero perhaps because CO has been set to zero are not printed sources are also not printed for those patches for which CO has been set to FIXVAL when CO has been set to a sufficiently large value that VAL VAR becomes so small in comparison with VAL and or VAR themselves

    Original URL path: http://www.cham.co.uk/phoenics/d_polis/d_enc/nettsour.htm (2016-02-15)
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    e EMUL divided by density which is specified rather than the dynamic viscosity EMUL The empirical functions employed to calculate ENUL in PHOENICS for Bingham and Power law fluids are given below 2 Power law model For a power law fluid the non Newtonian scalar kinematic viscosity ENUL is given by ENUL ENULA LGEN1 0 5 ENULB 1 RHO1 equation 2 1 where RHO is the local fluid density ENULA is the fluid consistency index at a reference temperature ENULB is the power law or flow behaviour index and LGEN1 is the magnitude of the total rate of strain given by LGEN1 0 5 Dij Dij equation 2 2 where denotes the double dot scalar product of two tensors In PHOENICS LGEN1 is simply the generation function which is stored in the F array location identified by the integer variable LGEN1 For ENULB 1 0 the power law model reduces to a Newtonian fluid model For ENULB 1 the fluid behaves as a Pseudoplastic so that ENUL decreases with increasing rate of shear For ENULB 1 the fluid behaves as a dilitant so that ENUL increases with increasing rate of shear The power law model may be activated in PHOENICS by introducing the following PIL commands in the Q1 file ENUL GRND4 ENULA consistency index ENULB flow behaviour index STORE VISL The calculation of strain rate squared LGEN1 is activated automatically via GREX3 where GENK T but can also be controlled by DUDX DUDY etc In addition printout LGEN1 may be effected when a variable named GENK is stored in the Q1 file This option is a general one which is available for use with both Newtonian and non Newtonian simulations see the Encyclopaedia entry entitled TURBULENCE ENERGY GENERATION The model may also be activated for use in conjugate heat transfer applications by setting ENUL GRND10 and using GRND4 in the props file to select the power law option for ENUL Alternatively the option may be selected via the Q1 file rather than the props file e g the following commands would be equivalent to using ENUL GRND4 with ENULA 0 02 and ENULB 0 25 ENUL GRND10 STORE VISL STORE PRPS FIINIT PRPS 33 mat no rho enul cp kond expan CSG10 Q1 MATFLG T NAMAT 1 33 1 GRND4 1 1 0 0 02 0 25 In the foregoing example the settings made for the tabulated entries rho cp kond and expan are merely dummies 3 Bingham model For the Bingham model ENUL is given by ENUL ENULA TAUO SQRT LGEN1 RHO equation 3 1 when TAU TAUO and by ENUL infinity equation 3 2 when TAU TAUO ENULA is the rigidity coefficient or plastic viscosity TAUO is the yield stress and TAU is the magnitude of stress tensor given by TAU 0 5 TAUij TAUij equation 3 3 which here is also given by TAU TAUO ENULA SQRT LGEN1 equation 3 4 Note that LGEN1 is given by equation 2 2 above The Bingham model may be

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  • Read prompts for the name of a file that contains your geometry for display on the plot The file name screen as default activates the geometry input menu which allows

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