4 Plumes modellingCombustion processes result in waste products - exhaustWhen the exhaust is released the resultant flow is known as the plumeAlthough exhaust is waste - there are implications - impingement, infra-red, pollution - and a need to study
5 Based on PHOENICS CFD code PLUMESDeveloped for general plume flowfield prediction -Rocket exhausts - DERA Fort HalsteadAir breathing engine exhausts - DERA FarnboroughLand system exhausts - DERA ChertseyShips - DERA Portsdown WestBased on PHOENICS CFD code
6 Particles within exhaust plume Momentum (changes in bulk density and interphase friction)Temperature (Cp of particles, solidification, evaporation, further reaction)Increased radiative heat transfer (grey bodies as opposed to selective emissions)Further pollution issues
7 Particle modelling Most particles are small <10m Follow gas velocity (small lag)Follow gas temperatureExtra set of momentum equations too much overhead - still only one diameterUse of particle tracking - cannot really study bulk effects
8 Two phase treatment - momentum Single set of momentum equations (accept velocity lag)Calculate a bulk density to modify overall momentum of exhaustmf = S (Mfi*smw/mmw) (1)mf is the overall mass fraction of any particulate speciesMfi … mole fraction of any particulate speciessmw is the species molecular weightmmw is the overall mixture molecular weight.
9 Two phase momentum Particulate density - rp = mf / S (Mfi / ri) (2) Particulate volume fraction Vf= (mf/rp) / [(1-mf)/rg + mf/rp] (3)where rg is the gas mixture densityOverall mean density r = Vf.rp + (1-Vf).rg (4)
10 Two phase temperature Small particles close to gas temperature Second energy equation not solvedCp calculated for particulates in the same way as for gaseous species - via ninth order polynomial
12 Phase changes in plumes Chamber is high temperature and contains gaseous species as well as particulatesAcceleration through convergent/divergent nozzle causes static temperature to fallReactions slow and condensation/solidificationMixing of oxygen into plumeShock waves raise static temperatureSecondary combustionMelting and evaporation
13 Phase change modelling Solid, liquid and gas species all solved within single phaseSource terms added for heat and mass transfer to allow changes between each phase to take place
14 Phase change (liquid/solid) Q = Kh.As.(Tmp-T) (5)where Kh is a heat transfer coefficient and As is thesurface area.T is temperatureKh = Nul/Dp (6)where l is the gas thermal conductivity and Dp theparticle diameter.Nu is 2 for low Re - low slip velocity
15 Phase change (liquid/solid) If T < Tmp, the liquid-to-solid transfer (Sp) rate for each particle is then:Sp = Q/Hfs = Kh.As.(Tmp-T)/Hfs (7)where Hfs is the latent heat of fusion in J/kmol.Number of particles of a particular species andphase per unit volume is given by;np = rp /(pDp3/6) (8)
16 Phase change (liquid/solid) The liquid-to-solid transfer rate per unit volume (inkmol/s/m3) is thenSvol = Sp * np= Kh.6/Dp.(Tmp-T) rp/Hfs (9)andrp = (Cl)*smw*r/rp (10)where Cl is the species concentration (in kmol/kg) of the liquid species, r is the bulk mean density and rp is the particle density.
17 Phase change (liquid/solid) The source term for each phase i,S = cell vol.Co.(Val - Ci) (11)Co = Kh.6/Dp/Hfs.|Tmp-T|*smw*r/rp (12)If T < Tmp,for the liquid phase Val = 0for the solid phase Val = Cl +CsThis source term will also function as a melting rate if T>Tmp, but with Val = Cl+Cs for the liquid, and Val = 0 for the solid.
18 Phase change (gas/liquid) Sp = Km.As.(Csat-Cg).r (13)where Km is a mass transfer coefficient, As is the surface area. Cg is the gas species concentration in kmol/kg, r the bulk mean density and Cg > Csat if condensation is taking place.Csat is proportional to the saturation vapour pressure psat of the species:Csat*gmw = psat/p (14)Where p is the local static pressure and gmw the mean molecular weight of all the gaseous species.
19 Phase change (gas/liquid) The vapour pressure is a function of temperature and can be estimated aspsat = e(a-b/T) (15)where a and b are constant for a particular species and can be determined if two points on the saturation line are known.
20 Phase change (gas/liquid) Km = Sh*D/Dp (16)where D is the diffusivity of the species in the mixture and Dp the particle diameter.The number of droplets of a particular species and phase per unit volume is given by equation 8.The gas-to-liquid transfer rate per unit volume (in kmol/s/m3) is thereforeSvol = Sp * np= Km.6/Dp.(Csat-Cg).r. rp (17)where rp is defined in equation (10)
21 Phase change (gas/liquid) This transfer rate can be linearised for inclusion as a PHOENICS source term in the following way:The source term for each phase i,S = cell vol.Co.(Val - Ci) (11)where Co = Km.6/Dp.*smw*Cl.r2/rp (18)andfor the gas phase Val = Csatfor the liquid phase Val = Cg-Csat+Cl
22 Phase change results Plume reacting - no phase change Plume reacting + condensation and solidification
24 Two phase - validation Particle velocities measured Full range of velocities observedParticle sizes measured
25 Application of Parabolic extensions IPARAB=5 for underexpanded free jetsSignificant increases in solution speed for 2D and 3D plumesIncreased resolution of plume without large storage requirementsNeed to combine elliptic and parabolic solvers has become apparent
26 PARALLEL PHOENICS Domain decomposition is slabwise Plume flowfield predominantly slabwisePLUME software linked with PARALLEL PHOENICS (v3.1) on SGI Origin 200(MPI)Approximately 3x speed up for 4 processorIncrease in performance good but hardware and software costs high
29 Transient plumes - method Lack of initial fields makes convergence difficultUse of small time steps (100microseconds) to resolve phenomena and stabilise the convergence of the solution
30 Conclusions PHOENICS based PLUME software development continued Limited two phase rocket exhaust prediction capability createdEnhanced parabolic solver incorporatedParallel PHOENICS - potential speed increasesTransient plumes now being modelled