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- Concentration fluctuations in confined jet: multi-fluid approach

only take place between those parent fluids which would produce the appropriate offsprings inheriting the attributes of either parent in equal proportion The frequency in population is calculated for each fluid by solving its fluid mass fraction equation with the source sink terms are first fluid mass fraction first fluid mass fraction 5 0 the energy dissipation rate turbulence energy 17 conservation equations for fluid mass fractions are solved for all calculations reported here and statistical properties of the fluid population are then deduced The above number of fluids was found sufficient for concentration fluctuations to be fluid population grid independent 2 More details of MFM can be found elsewhere 6 5 Implementation All the results to be displayed below have been created by use of the PLANT feature of PHOENICS 3 1 7 The necessary formulae for calculations of source sinks physical properties statistical operations auxilliary computations and post processing preparations have been set by way of appropriate statements in Q1 file Running SATELLITE then results in the generation of all relevant GROUND codings compilation and re linking Running private EARTH initiates the calculations and produces the field distributions of all relevant variables The basic Q1 file is supplied in Appendix Further related Q1 s can be found in PLANT data input library 6 Comparison with experiment It will be shown that neglect of the incompletness of the micro mixing leads to predictions of heat and mass transfer properties of the flame which can differ significantly from those predicted by the multi fluid model Fig 1 and observed in the experiments Fig 2 The center line variation of mean temperature is shown in Fig 2 along with the experimental results from Razdan and Stevens There are significant differences both in the magnitude of SCRS results and experimental data The instant reaction model fails to fit the data reasonable both in location and magnitude of the maximum temperature In contrast the calculations of Multi Fluid Model and instant reaction with presumed scalar fluctuations are in acceptable agreement with measurements The former appears to be marginally better than the latter In what follows the results will be presented in a sequence which allows the reader to asses the performance of combustion models employed in more details The distribution of the averaged gas composition along the centre line is plotted in Fig 3 together with experimental data of Razdan and Stevens Fig 4 illustrates a comparison between calculations of the radial profiles for the temperature and experimental data The radial distance is normalized by the diameter of the nozzle It can be seen that both SCRS and SCRS plus presumed PDF models overpredict the temperatures in the outer half of the chamber The Multi Fluid Model gives a more accurate predictions in that region and seems to be better in the inner zone as well The shapes of the distribution predicted by the models are also different The location of the minimum temperature is predicted by SCRS and SCRS plus PDF models

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

Open archived version from archive - cmbstr5.htm

as to find out everything elsew hich was necessary This notion led to the eddy break up model EBU Spalding 1971 the concentration fluctuations model CFM Spalding 1971 the eddy dissipation concept EDC Magnussen 1976 the two fluid model 2FM Spalding 1981 and innumerable variants on the same theme All of these involved the supposition that any turbulent mixture could be treated as the inter mingling of two fluids the states and mixture fractions of which required to be computed from easy to formulate differential equations This represented an advance on Kolmogorov s ignore the PDFs approach but it was not good enough Somebody might have thought at the time If two is not enough what about four or eight or sixteen etc Refine the grid dummy But that did not happen for another 24 years So the next invention by Bray 1980 was the flamelet model which involves the presumption that the turbulent mixture consist of fully burned gas at the local time average fuel air ratio fully un burned gas at the local time average fuel air ratio and a small amount of intermediate state gas with a PDF which is the same as that prevailing in laminar steadily propagating one dimensional flames This enables CFD chemistry specialists to perform expensive calculations but in the present author s view has no other merit if that is the right word whatever 3 The direct route to the goal Presumed PDF methods are what are mainly used by high tech engineering companies at the present time Nevertheless direct methods of calculating PDFs have been available for many years The how to do it idea was provided by Dopazo and O Brien in 1974 however those authors were not numerical analysts at the time so provided no solutions In 1982 Pope started to solve the relevant equations but he used a Monte Carlo method which proved to be expensive in terms of computer time This may have given the compute the PDF approach a bad name It is indeed little used in engineering practice More recently the present author made the even more direct approach of discretising the PDF and solving for its ordinates This so called Multi Fluid Model MFM approach has proved to be simple in concept economical in implementation and realistic in its predictions This is what dummy should and could have done many years before Turbulence modelling history is a catalogue of missed opportunities and false starts MFM can be regarded as what EBU should swiftly have developed into in the 1970s having as many fluids and as many PDF dimensions 2 will be quite enough for the time being as the situation requires MFM is too new five years old to have been adopted in engineering practice At some time in the next millennium it will be the author believes perhaps even in Year 2000 4 Relation to flamelet and other models Since the laminar flamelet model LFM is the most advanced which is currently used

Original URL path: http://www.cham.co.uk/phoenics/d_polis/d_lecs/cmbstr5/cmbstr5.htm (2016-02-15)

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which is being developed by CHAM during 1996 for the prediction of gas dispersion phenomena which may give rise to explosions within partly ventilated enclosures containing solid objects the pressure velocity and temperature fields in an enclosure after ignition of the gas air mixture the consequent damage to solid objects which leads to the projection of missiles and the spread of fire which may result from subsequent oil spillages EXPLOITS is an acronym for EXPLOsIon and blasT Simulator EXPLOITS differs from other ostensibly similar software packages by way of its ability to employ the full scientific model and computer methods capabilities of a powerful and well validated general purpose computer code namely PHOENICS so taking account of multi phase effects water sprays or missiles gas liquid interfaces simultaneous modelling of stresses in solids automatic selection of numerical settings parallel computing capabilites its possession of a Virtual Reality user interface for setting up problems and displaying results its availability for purchase and direct use by sufficiently confident users and for assisted and metered use at remote sites with resident human experts by other users possessing personal computers equipped with modems EXPLOITS is also supplied with novel and unique turbulence and combustion

Original URL path: http://www.cham.co.uk/phoenics/d_polis/d_lecs/exploits/exploit0.htm (2016-02-15)

Open archived version from archive- END.HTM

are taken as 1 0E 3 Information on how the linear equation solver is performing can be elicited by adding the line SPEDAT SET SELREF PRNSOL L T to Group 19 of Q1 For each variable on each sweep the solver will write a line to RESULT stating how many iterations were performed and giving an indication of why iteration stopped A typical extract of the printout is shown here Done LU CR solver for P1 isweep 73 IZ 20 iter 12 2 8 168808E 08 1 364782E 00 6 493849E 04 Done STONE solver for U1 isweep 73 IZ 20 iter 1 2 1 028983E 12 1 673497E 01 1 673497E 04 Done STONE solver for V1 isweep 73 IZ 20 iter 1 2 1 391361E 12 2 119821E 01 2 119821E 04 Done STONE solver for W1 isweep 73 IZ 20 iter 1 2 2 556446E 12 3 189903E 01 3 189903E 04 The first line states that the conjugate gradient solver is in use for the pressure variable P1 On sweep 72 12 iterations were performed For the velocity variables U1 V1 and W1 the default Stone solver is in use This terminated after 1 iteration for each velocity If the slabwise solver is in use the line will be repeated for each IZ plane The next number in this case 2 is an exit code The exit codes for the various solvers are as follows 1 Stone Solver 0 all LITER iterations were performed 1 solver terminated because the sum of corrections second REAL number is less than ENDIT the sum of corrections on the first iteration third REAL number 2 solver terminated because the sum of normalised residuals first REAL number is below ENDIT RESFAC 3 solver terminated because the sum of residuals is greater than 10 the sum of residuals on the previous iteration This indicates divergence rather than convergence 2 Conjugate Gradient LU CR Solver 0 all LITER iterations were performed 1 solver terminated because the sum of corrections second REAL number is less than ENDIT the sum of corrections on the first iteration third REAL number 2 solver terminated because the sum of normalised residuals first REAL number is below ENDIT RESFAC 3 solver terminated because sum of corrections greater than sum of corrections on previous iteration and less than 0 1 sum of corrections on first iteration 3 Sequential GCV Solver 0 all LITER iterations were performed 1 not used 2 solver terminated because the sum of normalised residuals first REAL number is below ENDIT RES1 2 solver terminated because the sum of normalised residuals first REAL number is below ENDIT RESFAC 3 for LSG1 F default solver terminated because sum of residuals second REAL number is greater than the sum of residuals on previous iteration and is less than 0 1 the sum of residuals on the first iteration 3 for LSG1 T and P1 solver terminated because sum of normalised residuals first REAL number less than 0 1 sum

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

Open archived version from archive - VIRT.HTM

GX2PHS FOR which is located in the directory d earth d opt d twophs Subroutine GXVMCF is called from Group 1 Section 1 and Group 10 Section 5 of GREX3 FOR 2 Activation in PHOENICS The virtual mass sources for the momentum equations are activated by assigning a non zero value to the PIL variable CVM The value ascribed to CVM determines how the virtual mass coefficient is to be calculated as follows CVM 0 0 the default cuts out the virtual mass terms entirely CVM positive constant K say sets the virtual mass coefficient to Cvm K CVM GRND1 selects Cvm CVMA rc where CVMA is a positive constant 0 5 by default and rc is the volume fraction of the continuous phase CVM GRND2 selects Cvm CVMA 1 2 78 min 0 2 rd where CVMA is a positive constant 0 5 by default and rd is the volume fraction of the dispersed phase The virtual mass coding presumes phase 1 to be the continuous phase and phase 2 the dispersed phase However if CVM is set to a negative value other than GRND the reverse is presumed so that phase 2 is taken as the continuous phase and phase 1 as dispersed CVM GRND permits the user to supply his own formula for Cvm in Group 10 Section 5 of GROUND For example CALL SUB2 L0CVM L0F LD12 L0R2 L0F R2 DO 1052 I 1 NXNY F L0CVM I CVMA 1 2 78 AMIN1 0 2 F L0R2 I 1052 CONTINUE computes Cvm from equation 4 above When STORE VMSU VMSV VMSW appears in the Q1 file the virtual mass forces for each cell of the continuous phase as given by equations 1 and 2 and integrated over the control volume are placed in the 3D stores VMSU etc and may be printed in the RESULT file or viewed via PHOTON and AUTOPLOT in the ususal way 3 Implementation The virtual mass momentum source term to be introduced is T Cvm integral rd rhoc D Ud i dt D Uc i dt dVol 5 where the integral is over the cell volume The term T which must be subtracted from the dispersed phase momentum equation and added to the continuous phase momentum equation is expressed approximately as T Cvm rhoc rhod sum Md n Ud n Ud rd rc sum Mc n Uc n Uc 6 where Md n and Mc n are the phase specific coefficients of the finite volume equations representing the effects of spatial and temporal convection The subscript n stands for neighbour in space and time The word approximately is appropriate because the volume fractions and densities used in formulating the Md s and Mc s are neighbour cell rather than in cell values This approximation is insignificant in comparison with the uncertainty regarding the proper value of the virtual mass coefficient Cvm The finite volume form of the indivicual phase momentum equations can be expressed in correction form as Ud sd f

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

Open archived version from archive - EARDAT.HTM

formatted sequential data file which specifies the following input data all default values of logical character integer and real variables in the SATELLITE common block all solved variables and terms all initial values specified in SATELLITE all values calculated for non bfc geometry and stored in the SATELLITE F array all boundary conditions specified by PATCH all flow conditions specified in Q1 and debug information required all information supplied by

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

Open archived version from archive - EARTH.HTM

to elements of material distributed in space and time EARTH reads the EARDAT file provided by SATELLITE and executes the corresponding computations it then produces a human readable output file called RESULT and also a second file usuall called PHI which can be read by the display modules PHOTON and AUTOPLOT by the file handling utility PINTO or by EARTH itself when a new run is started The relationships of

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

Open archived version from archive - EDIT.HTM

By contrast editing the stack permits modification to the ORDER of the instructions For example typing NX 10 will change NX only but NX 10 edited into the stack above any other uses of NX but below the current setting of NX on line 15 say by use of i 15 RETURN NX 20 for example RETURN RETURN will once the stack is re interpreted cause all NX dependencies to be modified Re interpretation of the stack is activated by the command LOAD STACK The edit commands available are LD displays 15 lines of the stack from current line LC displays 15 lines about current line LU displays 15 lines above current line L n moves to line n and displays it L n m moves to line m and displays n to m LT moves to first line and displays it LB moves to bottom line and displays it I n inserts entry following after line n the entry being terminated by the user entering RETURN twice R m n replaces lines m to n with entry following D m n deletes lines m to n The SATELLITE editor is primitive in comparisons with those which are available on

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

Open archived version from archive

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