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