Presentation on theme: "MODELLING OF TWO PHASE ROCKET EXHAUST PLUMES AND OTHER PLUME PREDICTION DEVELOPMENTS A.G.SMITH and K.TAYLOR S & C Thermofluids Ltd."— Presentation transcript:
MODELLING OF TWO PHASE ROCKET EXHAUST PLUMES AND OTHER PLUME PREDICTION DEVELOPMENTS A.G.SMITH and K.TAYLOR S & 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 <10 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 m f = (M fi *smw/mmw) (1) m f is the overall mass fraction of any particulate species M fi … mole fraction of any particulate species smw is the species molecular weight mmw is the overall mixture molecular weight.
Two phase momentum Particulate density - p = m f / (M fi / i ) (2) Particulate volume fraction V f = (m f / p ) / [(1-m f )/ g + m f / p ] (3) where g is the gas mixture density Overall mean density = V f. p + (1-V f ). g (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
Results of initial 2 phase work
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 = K h.A s.(T mp -T) (5) where K h is a heat transfer coefficient and A s is the surface area.T is temperature K h = Nu /D p (6) where is the gas thermal conductivity and D p the particle diameter. Nu is 2 for low Re - low slip velocity
Phase change (liquid/solid) If T < T mp, the liquid-to-solid transfer (Sp) rate for each particle is then: S p = Q/H fs = K h.A s.(T mp -T)/H fs (7) where H fs is the latent heat of fusion in J/kmol. Number of particles of a particular species and phase per unit volume is given by; n p = r p /( D p 3 /6) (8)
Phase change (liquid/solid) The liquid-to-solid transfer rate per unit volume (in kmol/s/m 3 ) is then S vol = S p * n p = K h.6/D p.(T mp -T) r p /H fs (9) and r p = (C l )*smw* / p (10) where C l is the species concentration (in kmol/kg) of the liquid species, is the bulk mean density and p is the particle density.
Phase change (liquid/solid) The source term for each phase i, S = cell vol.Co.(Val - C i ) (11) Co = K h.6/D p /H fs.|T mp -T|*smw* / p (12) If T < T mp, for the liquid phase Val = 0 for the solid phaseVal = C l +C s This source term will also function as a melting rate if T>T mp, but with Val = C l +C s for the liquid, and Val = 0 for the solid.
Phase change (gas/liquid) S p = K m.A s.(C sat -C g ). (13) where K m is a mass transfer coefficient, A s is the surface area. C g is the gas species concentration in kmol/kg, the bulk mean density and C g > C sat if condensation is taking place. C sat is proportional to the saturation vapour pressure p sat of the species: C sat *gmw = p sat /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 p sat = 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) K m = Sh* D /D p (16) where D is the diffusivity of the species in the mixture and D p 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/m 3 ) is therefore S vol = S p * n p = K m.6/D p.(C sat -C g ).. r p (17) where r p 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 - C i ) (11) where Co = K m.6/D p.*smw*C l. 2 / p (18) and for the gas phase Val = C sat for the liquid phaseVal = C g -C sat +C l
Phase change results Plume reacting - no phase change Plume reacting + condensation and solidification
Phase change results
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 - the need
Transient plumes - the model
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