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DarcyForchheimer law for specifying Porous Zones 

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July 30, 2010, 07:53 
DarcyForchheimer law for specifying Porous Zones

#1 
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usn
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Hi all,
I would like to use DarcyForchheimer law for specifying Porous Zones in Exhaust System application. But I am confused with coordinate system specification. Can anyone please explain what is e1 and e2? and I have the values a = 9.367 b = 1.029E7 alpha = 0.5 * a * density [kg/m^4] beta = viscocity * b [kg/m^3s] How can I calculate d and f parameters from the above data? My guess: d= beta/viscocity [1/m^2] f=alpha/density [1/m] Am I correct? if not, please tell me how to calculate d and f parameters. thank you in advance 

July 30, 2010, 09:35 

#2 
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Vincent de Graaf
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e1 and e2 are the vectors that are used to specify the porosity. In the porousZones file, you have to specify three components of f and d. The first component is in the direction of e1, the second in the direction of e2 and the third in the direction perpendicular to e1 and e2. An example can be found in tutorials/incompressible/porousSimpleFoam/angledDuctImplicit.
Furthermore, d= beta/viscocity [1/m^2] f=2*alpha/density [1/m] 

August 3, 2010, 05:30 

#3  
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Mark Olesen
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Quote:


August 3, 2010, 06:34 

#4 
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usn
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Hi,
thank you very much for your replies...here I am giving my data...can anyone please tell me e1 and e2 vectors are correct...I attached my porous part file (I gave not fully because it is confidential) coordinateSystem { e1 (1 0 0); e2 (0 0 1); } Darcy { d d [0 2 0 0 0 0 0] (1.029e7 1 1); f f [0 1 0 0 0 0 0] (0 0 0); } Thanks 

August 3, 2010, 06:42 

#5 
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Vincent de Graaf
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Hi Ger_US,
you have specified a Darcy resistance in xdirection, and virtually no resistance in y and zdirection. If your intention is to model an anisotropic medium, this might be correct. Note that for isotropic media, all three components of d (and f) should have the same value. 

August 3, 2010, 07:44 

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Mark Olesen
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Quote:
http://foam.sourceforge.net/doc/Doxy....html#_details You may also wish to specify the 'origin' of your local coordinate system. BTW: in you Darcy term, you have close to no resistance in the local y/z directions, but a fairly large one in the xdirection  what type of porous media should this be? 

August 3, 2010, 10:47 

#7 
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usn
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Hi,
I think I am wrong...that is ceramic porous media... this is information which I have a = 9.367 b = 1.029E7 alphax = 0.5 * a * density [kg/m^4] betax = viscocity * b [kg/m^3s] d= beta/viscocity [1/m^2] f=2*alpha/density [1/m] alphay=1e6 betay=1e6 alphaz=1e6 betaz=1e6 viscocity=1.663e5 kg/ms density=0.61935 at Inlet coordinateSystem { e1 (1 0 0); e2 (0 0 1); } Darcy { d d [0 2 0 0 0 0 0] (1.029e7 (6.01e10??) (6.01e10??)); f f [0 1 0 0 0 0 0] (18.367 (?) (?)); } please tell me if anything wrong because I am new to OpenFoam and CFD I forgot to mention that it is anisotropic medium Thanks 

August 3, 2010, 11:02 

#8 
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Vincent de Graaf
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Hi,
from the description I assume that the medium has a certain resistance in the xdirection (d = 1.029e7, f = 18.367) and is impermeable in the other directions. My usual approach to this situation is to set the y and zresistance to a finite but much larger value than the xresistance. Typically, I choose to set the y and zcomponents of f to 1000 times the xvalue. In your case, this would become: f f [0 1 0 0 0 0 0] (18.367 18e3 18e3 ); 

August 6, 2010, 05:33 

#9 
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usn
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Hi,
as you suggested I tried without success. I don't why rho is not stable and bounding p. Time = 92 smoothSolver: Solving for Ux, Initial residual = 0.00292406, Final residual = 2.10951e05, No Iterations 2 smoothSolver: Solving for Uy, Initial residual = 0.00583214, Final residual = 0.000111279, No Iterations 2 smoothSolver: Solving for Uz, Initial residual = 0.013854, Final residual = 0.000225707, No Iterations 2 DILUPBiCG: Solving for h, Initial residual = 0.0369572, Final residual = 0.000357835, No Iterations 1 GAMG: Solving for p, Initial residual = 0.165261, Final residual = 0.00597301, No Iterations 2 time step continuity errors : sum local = 2.06879, global = 0.061706, cumulative = 16.778 bounding p, min: 24708.8 max: 824884 average: 145678 rho max/min : 12.1778 0.0591955 smoothSolver: Solving for epsilon, Initial residual = 0.00295326, Final residual = 9.7231e07, No Iterations 2 smoothSolver: Solving for k, Initial residual = 0.00285544, Final residual = 1.06368e06, No Iterations 2 ExecutionTime = 354.46 s ClockTime = 355 s Time = 93 smoothSolver: Solving for Ux, Initial residual = 0.00298496, Final residual = 2.15188e05, No Iterations 2 smoothSolver: Solving for Uy, Initial residual = 0.0047816, Final residual = 9.21071e05, No Iterations 2 smoothSolver: Solving for Uz, Initial residual = 0.0134613, Final residual = 0.000221754, No Iterations 2 DILUPBiCG: Solving for h, Initial residual = 0.0368796, Final residual = 0.00035114, No Iterations 1 GAMG: Solving for p, Initial residual = 0.171999, Final residual = 0.00616598, No Iterations 2 time step continuity errors : sum local = 2.14248, global = 0.0565349, cumulative = 16.8345 bounding p, min: 28114.3 max: 848170 average: 145624 rho max/min : 12.769 0.0610522 smoothSolver: Solving for epsilon, Initial residual = 0.00294399, Final residual = 9.54477e07, No Iterations 2 smoothSolver: Solving for k, Initial residual = 0.00287104, Final residual = 1.05367e06, No Iterations 2 ExecutionTime = 358.29 s ClockTime = 359 s Time = 94 smoothSolver: Solving for Ux, Initial residual = 0.00304401, Final residual = 2.19977e05, No Iterations 2 smoothSolver: Solving for Uy, Initial residual = 0.00406858, Final residual = 7.70121e05, No Iterations 2 smoothSolver: Solving for Uz, Initial residual = 0.00943227, Final residual = 0.000157461, No Iterations 2 DILUPBiCG: Solving for h, Initial residual = 0.0366639, Final residual = 0.000342336, No Iterations 1 GAMG: Solving for p, Initial residual = 0.179248, Final residual = 0.00637306, No Iterations 2 time step continuity errors : sum local = 2.22181, global = 0.0517805, cumulative = 16.8863 bounding p, min: 29897.8 max: 870334 average: 145566 rho max/min : 14.1506 0.0643263 smoothSolver: Solving for epsilon, Initial residual = 0.00293563, Final residual = 9.37558e07, No Iterations 2 smoothSolver: Solving for k, Initial residual = 0.00288938, Final residual = 1.04439e06, No Iterations 2 ExecutionTime = 362.13 s ClockTime = 363 s Time = 95 smoothSolver: Solving for Ux, Initial residual = 0.0030967, Final residual = 2.26804e05, No Iterations 2 smoothSolver: Solving for Uy, Initial residual = 0.0035207, Final residual = 6.69516e05, No Iterations 2 smoothSolver: Solving for Uz, Initial residual = 0.00715987, Final residual = 0.000122852, No Iterations 2 DILUPBiCG: Solving for h, Initial residual = 0.0362804, Final residual = 0.000331438, No Iterations 1 GAMG: Solving for p, Initial residual = 0.186293, Final residual = 0.00661338, No Iterations 2 time step continuity errors : sum local = 2.31546, global = 0.0470522, cumulative = 16.9333 bounding p, min: 32319.1 max: 893740 average: 145497 rho max/min : 15.0995 0.0689234 smoothSolver: Solving for epsilon, Initial residual = 0.00293385, Final residual = 9.21299e07, No Iterations 2 smoothSolver: Solving for k, Initial residual = 0.00290919, Final residual = 1.03662e06, No Iterations 2 ExecutionTime = 365.96 s ClockTime = 367 s Time = 96 smoothSolver: Solving for Ux, Initial residual = 0.00314822, Final residual = 2.34295e05, No Iterations 2 smoothSolver: Solving for Uy, Initial residual = 0.00319378, Final residual = 6.15854e05, No Iterations 2 smoothSolver: Solving for Uz, Initial residual = 0.00594322, Final residual = 0.00010551, No Iterations 2 DILUPBiCG: Solving for h, Initial residual = 0.0360695, Final residual = 0.000327196, No Iterations 1 GAMG: Solving for p, Initial residual = 0.194211, Final residual = 0.00690557, No Iterations 2 time step continuity errors : sum local = 2.42775, global = 0.0442164, cumulative = 16.9776 bounding p, min: 33417.8 max: 915435 average: 145415 rho max/min : 15.7051 0.0746939 smoothSolver: Solving for epsilon, Initial residual = 0.00293065, Final residual = 9.05813e07, No Iterations 2 smoothSolver: Solving for k, Initial residual = 0.00293521, Final residual = 1.03033e06, No Iterations 2 ExecutionTime = 369.81 s ClockTime = 370 s Time = 97 smoothSolver: Solving for Ux, Initial residual = 0.00320052, Final residual = 2.42225e05, No Iterations 2 smoothSolver: Solving for Uy, Initial residual = 0.00296225, Final residual = 5.77766e05, No Iterations 2 smoothSolver: Solving for Uz, Initial residual = 0.00504761, Final residual = 8.91875e05, No Iterations 2 DILUPBiCG: Solving for h, Initial residual = 0.0357983, Final residual = 0.000325011, No Iterations 1 GAMG: Solving for p, Initial residual = 0.203505, Final residual = 0.00724398, No Iterations 2 time step continuity errors : sum local = 2.56053, global = 0.045573, cumulative = 17.0231 bounding p, min: 34279 max: 933095 average: 145318 rho max/min : 16.0785 0.0807459 smoothSolver: Solving for epsilon, Initial residual = 0.00291039, Final residual = 8.86735e07, No Iterations 2 smoothSolver: Solving for k, Initial residual = 0.00298268, Final residual = 1.0239e06, No Iterations 2 ExecutionTime = 373.66 s ClockTime = 374 s Time = 98 smoothSolver: Solving for Ux, Initial residual = 0.00326285, Final residual = 2.48943e05, No Iterations 2 smoothSolver: Solving for Uy, Initial residual = 0.00276879, Final residual = 5.35671e05, No Iterations 2 smoothSolver: Solving for Uz, Initial residual = 0.00437289, Final residual = 7.91479e05, No Iterations 2 DILUPBiCG: Solving for h, Initial residual = 0.0351593, Final residual = 0.000313212, No Iterations 1 [0] #0 Foam::error:rintStack(Foam::Ostream&) in "/server/appl/Programme/OpenFOAM/OpenFOAM1.6/lib/linux64GccDPOpt/libOpenFOAM.so" [0] #1 Foam::sigFpe::sigFpeHandler(int) in "/server/appl/Programme/OpenFOAM/OpenFOAM1.6/lib/linux64GccDPOpt/libOpenFOAM.so" [0] #2 __restore_rt in "/lib64/tls/libc.so.6" [0] #3 Foam::hPsiThermo<Foam:ureMixture<Foam::sutherlan dTransport<Foam::specieThermo<Foam::hConstThermo<F oam:erfectGas> > > > >::calculate() in "/server/appl/Programme/OpenFOAM/OpenFOAM1.6/lib/linux64GccDPOpt/libbasicThermophysicalModels.so" [0] #4 Foam::hPsiThermo<Foam:ureMixture<Foam::sutherlan dTransport<Foam::specieThermo<Foam::hConstThermo<F oam:erfectGas> > > > >::correct() in "/server/appl/Programme/OpenFOAM/OpenFOAM1.6/lib/linux64GccDPOpt/libbasicThermophysicalModels.so" [0] #5 main in "/server/appl/Programme/OpenFOAM/OpenFOAM1.6/applications/bin/linux64GccDPOpt/rhoPorousSimpleFoam" [0] #6 __libc_start_main in "/lib64/tls/libc.so.6" [0] #7 _start at ../sysdeps/x86_64/elf/start.S:116 [cn12:16978] *** Process received signal *** [cn12:16978] Signal: Floating point exception (8) [cn12:16978] Signal code: (6) [cn12:16978] Failing at address: 0x26c00004252 [cn12:16978] [ 0] /lib64/tls/libc.so.6 [0x3e2842e2f0] [cn12:16978] [ 1] /lib64/tls/libc.so.6(gsignal+0x3d) [0x3e2842e25d] [cn12:16978] [ 2] /lib64/tls/libc.so.6 [0x3e2842e2f0] [cn12:16978] [ 3] /server/appl/Programme/OpenFOAM/OpenFOAM1.6/lib/linux64GccDPOpt/libbasicThermophysicalModels.so(_ZN4Foam10hPsiTher moINS_11pureMixtureINS_19sutherlandTransportINS_12 specieThermoINS_12hConstThermoINS_10perfectGasEEEE EEEEEE9calculateEv+0x4b7) [0x2a95597f77] [cn12:16978] [ 4] /server/appl/Programme/OpenFOAM/OpenFOAM1.6/lib/linux64GccDPOpt/libbasicThermophysicalModels.so(_ZN4Foam10hPsiTher moINS_11pureMixtureINS_19sutherlandTransportINS_12 specieThermoINS_12hConstThermoINS_10perfectGasEEEE EEEEEE7correctEv+0x33) [0x2a955a1303] [cn12:16978] [ 5] rhoPorousSimpleFoam [0x41cd9d] [cn12:16978] [ 6] /lib64/tls/libc.so.6(__libc_start_main+0xdb) [0x3e2841c3fb] [cn12:16978] [ 7] rhoPorousSimpleFoam [0x41ab29] [cn12:16978] *** End of error message ***  mpirun noticed that process rank 0 with PID 16978 on node cn12 exited on signal 8 (Floating point exception).  Boundary conditions: U: In: type flowRateInletVelocity; flowRate 0.16448; value uniform (0 0 0); Out: type zeroGradient; wall: type fixedValue; value uniform (0 0 0); P: internalField uniform 134980; In: type fixedValue; value uniform 152697; Out: type fixedValue; value $internalField; wall: type zeroGradient; T: internalField uniform 882.8; In: type fixedValue; value uniform 879.23; Out: type fixedValue; value uniform 882.86; wall: type zeroGradient; K: internalField uniform 64.3817; In: type fixedValue; value uniform 64.3817; Out:type zeroGradient; wall: type kqRWallFunction; value uniform 64.3817; Epsilon: internalField uniform 16975.07; In: type fixedValue; value uniform 16975.07; Out:type zeroGradient; wall: type kqRWallFunction; value uniform 16975.07; Porous Zones: Table_2 { coordinateSystem { e1 (1 0 0); e2 (0 0 1); } Darcy { d d [0 2 0 0 0 0 0] (3.029e7 5.8275e10 5.8275e10); f f [0 1 0 0 0 0 0] (20.367 20367 20367); } } Table_3 { coordinateSystem { e1 (1 0 0); e2 (0 0 1); } Darcy { d d [0 2 0 0 0 0 0] (8.808e7 5.8275e10 5.8275e10); f f [0 1 0 0 0 0 0] (509.12 509120 509120); } } But rho is stable when I used y and z coordinates of porouszones as 1 or 1000 I don't know why rho is not stable for the above Porous Zones parameters. Can anyone please tell me where I am doing mistake Thanks 

August 6, 2010, 10:04 

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Hi,
check your discretization in fvSchemes and play a bit with the underrelaxation factors of p. I realized that they should be really low (about 0.05) in exhaust systems. And for a first calculation you should take a first order disrectization for the divSchemes (Gauss upwind). Best regards Chrisi 

August 7, 2010, 01:09 

#11 
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Robert
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Hi Ger_US
I am wondering how do you get the a & b values? what are they? I think your f value should be 9.367 instead of 18.367 ? Kind Regards, Robert 

October 20, 2010, 06:11 

#12  
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MarcFlorian Uth
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Quote:
I have the same question. What are the a & b values. How can I calculate alpha and beta from a certain Permeability K? 

March 11, 2013, 05:09 

#13 
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hesam
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hi
can anyone explain to me what are a,b which are use in equ.? excuse me if i have mistake in my writing . 

May 3, 2013, 09:20 
references

#14 
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maddalena
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a and b are the two coefficients in Deltap = a*v^2 + b*v, which defines the relation between pressure drop and velocity on the porous medium.
see here: https://www.sharcnet.ca/Software/Flu...e233.htm#36964 just as further reference for everybody interested on the subject: Last edited by maddalena; May 3, 2013 at 10:49. 

May 12, 2013, 04:56 

#15  
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hesam
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thanks a lot maddalena for your answer...
where can i get these coefficient (a,b) for porous medium? i have an example that have alpha ,beta which have different value in 3 aspects would you please explain me where can i get them? a = 9.367 b = 1.029E7 alphax = 0.5 * a * density [kg/m^4] betax = viscocity * b [kg/m^3s] d= beta/viscocity [1/m^2] f=2*alpha/density [1/m] alphay=1e6 betay=1e6 alphaz=1e6 betaz=1e6 Quote:


May 13, 2013, 03:30 

#16 
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maddalena
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Hi,
I really cannot understand what you miss on your example. Anyway: a and b can be calculated with different techniques depending on your input. Simply scroll down the cited post and look for the one which best fit your need. mad 

May 19, 2013, 12:08 

#17 
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hesam
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thanks again for your help maddalena
would you mind please tell me one of the way that i can reach to these 2 parameters (a,b)? i have the velocity inlet and the pressure(zero gradient in of) ,are these values enough to calculate a,b? i have confused for 2 months to calculate d & f coeff. in open foam ... 

August 30, 2013, 10:30 
same problem

#18  
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Reza
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did you solve your problem about how to get a and b ? If yes, please help me about that
Quote:


November 11, 2014, 05:50 

#19  
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gaetan Hamel
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Hello,
I reopen the post because the answers are bugging me. if we have Quote:
Quote:
I have read a few topics about this question but the definition of D and F remains unclear. Thanks in advance. 

November 11, 2014, 12:54 

#20 
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Marco
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