MODELLING OF TWO PHASE ROCKET EXHAUST PLUMES AND OTHER PLUME PREDICTION DEVELOPMENTSA.G.SMITH and K.TAYLORS & C Thermofluids Ltd
Overview • Background to the PLUMES software • Two phase rocket exhaust modelling • Use of parabolic solver • Assessment of parallel PHOENICS • Transient plume modelling • Conclusions
Plumes modelling • Combustion processes result in waste products - exhaust • When the exhaust is released the resultant flow is known as the plume • Although exhaust is waste - there are implications - impingement, infra-red, pollution - and a need to study
PLUMES Developed for general plume flowfield prediction - Rocket exhausts - DERA Fort Halstead Air breathing engine exhausts - DERA Farnborough Land system exhausts - DERA Chertsey Ships - DERA Portsdown West Based on PHOENICS CFD code
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
Particle modelling • Most particles are small <10m • Follow gas velocity (small lag) • Follow gas temperature • Extra set of momentum equations too much overhead - still only one diameter • Use of particle tracking - cannot really study bulk effects
Two phase treatment - momentum • Single set of momentum equations (accept velocity lag) • Calculate a bulk density to modify overall momentum of exhaust • mf = S (Mfi*smw/mmw) (1) • mf is the overall mass fraction of any particulate species • Mfi … mole fraction of any particulate species • smw is the species molecular weight • mmw is the overall mixture molecular weight.
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 density • Overall mean density r = Vf.rp + (1-Vf).rg(4)
Two phase temperature • Small particles close to gas temperature • Second energy equation not solved • Cp calculated for particulates in the same way as for gaseous species - via ninth order polynomial
Phase changes in plumes • Chamber is high temperature and contains gaseous species as well as particulates • Acceleration through convergent/divergent nozzle causes static temperature to fall • Reactions slow and condensation/solidification • Mixing of oxygen into plume • Shock waves raise static temperature • Secondary combustion • Melting and evaporation
Phase change modelling • Solid, liquid and gas species all solved within single phase • Source terms added for heat and mass transfer to allow changes between each phase to take place
Phase change (liquid/solid) • Q = Kh.As.(Tmp-T) (5) where Kh is a heat transfer coefficient and As is the surface area.T is temperature • Kh = Nul/Dp (6) where l is the gas thermal conductivity and Dp the particle diameter. Nu is 2 for low Re - low slip velocity
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 and phase per unit volume is given by; • np = rp /(pDp3/6) (8)
Phase change (liquid/solid) The liquid-to-solid transfer rate per unit volume (in kmol/s/m3) is then • Svol = Sp * np • = Kh.6/Dp.(Tmp-T) rp/Hfs (9) • and • rp = (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.
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 = 0 for the solid phase Val = Cl +Cs • This 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.
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.
Phase change (gas/liquid) • The vapour pressure is a function of temperature and can be estimated as • psat = 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.
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 therefore • Svol = Sp * np • = Km.6/Dp.(Csat-Cg).r. rp (17) • where rp is defined in equation (10)
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) • and • for the gas phase Val = Csat • for the liquid phase Val = Cg-Csat+Cl
Phase change results Plume reacting - no phase change Plume reacting + condensation and solidification
Two phase - validation • Particle velocities measured • Full range of velocities observed • Particle sizes measured
Application of Parabolic extensions • IPARAB=5 for underexpanded free jets • Significant increases in solution speed for 2D and 3D plumes • Increased resolution of plume without large storage requirements • Need to combine elliptic and parabolic solvers has become apparent
PARALLEL PHOENICS • Domain decomposition is slabwise • Plume flowfield predominantly slabwise • PLUME software linked with PARALLEL PHOENICS (v3.1) on SGI Origin 200(MPI) • Approximately 3x speed up for 4 processor • Increase in performance good but hardware and software costs high
Transient plumes - method • Lack of initial fields makes convergence difficult • Use of small time steps (100microseconds) to resolve phenomena and stabilise the convergence of the solution
Conclusions • PHOENICS based PLUME software development continued • Limited two phase rocket exhaust prediction capability created • Enhanced parabolic solver incorporated • Parallel PHOENICS - potential speed increases • Transient plumes now being modelled