MODELLING OF TWO PHASE ROCKET EXHAUST PLUMES AND
OTHER PLUME PREDICTION DEVELOPMENTS
A.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 <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
• mf = (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 -p = mf / (Mfi / i) (2)
• Particulate volume fraction Vf
= (mf/p) / [(1-mf)/g + mf/p] (3)
where g is the gas mixture density
• Overall mean density = Vf.p + (1-Vf).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 = Kh.As.(Tmp-T) (5)
where Kh is a heat transfer coefficient and As is the
surface area.T is temperature
• Kh = Nu/Dp (6)
where 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 /(Dp3/6) (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*/p (10)
• where Cl 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 - Ci) (11)
• Co = Kh.6/Dp/Hfs.|Tmp-T|*smw*/p (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). (13)
• where Km is a mass transfer coefficient, As is the surface area. Cg is the gas species concentration in kmol/kg, 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).. 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.2/p (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
Phase change results
Two phase - validation• Particle velocities measured
• Full range of velocities observed
• Particle sizes measuredAccelerationPeriod
SteadyVelocityPeriod
DecelerationPeriod
Run Est02 - D10 Size Distribution 275 Samples
0
4
8
12
16
0 20 40 60 80 100 120
Diameter [um]
Occ
urr
en
ce [
%]
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