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CFD Modelling of the Acoustic Response of Sprays

Dr Jialin Su Nick Treleaven

Dr Andrew Garmory

Rolls-Royce University Technology Centre in Combustion System Aerothermal Processes

Summary

• Role of fuel injector in thermoacoustics • Experimental setup for acoustically forced sprays • Simulation setup • Results

• Flow field (impedance) • Spray statistics using quasi-steady breakup • Spray statistics with breakup delay model

• Conclusions and future work


Thermoacoustics in gas turbine combustors

• Thermoacoustic oscillations present a major challenge in design of GT combustors

• Particularly in ‘lean-burn’ designs

• Feedback loop between unsteady heat release and reactant delivery

• Has been the subject of much previous work for premixed, gaseous flames


Pressure

Mass Flow

Fuel Spray Mixture

Heat Release

FTF Spray Transfer Function (STF)

Acoustic Impedance

The response of the reactant delivery to an incident acoustic wave is crucial. This is a two-phase process for aero engines.

Lean-burn fuel injectors

• ‘Fuel injector’ or ‘fuel spray nozzle’ (FSN) has multiple jobs

• Delivers ~70% of air • Provides swirl to stabilise flame • Atomizes fuel using ‘air-blast’ method

• Previous work (GT2015-43248, GT2017-64527) has looked at simulating the response of the air to acoustic forcing

• Here we attempt to include the spray response

• The fuel injector is a representative lean-burn injector provided by Rolls-Royce

• Pilot – central (purple) passage • Mains – outer (yellow, red) passages


Mains fuel delivered onto prefilmer surface – then atomized by high momentum swirling flow either side.

Aims

• The work presented here is part of an EPSRC grant. The specific aims of the work carried out using ARCHER are as follows: • Extend acoustically forced CFD methodology to include

time varying spray size distribution

• Compare simulations using quasi-steady breakup models with experimental data

• Extend breakup models beyond quasi-steady


Experimental setup


• Acoustically forced spray rig at Loughborough UTC used • Three sectors, central injector is fuelled • Spray statistics measured downstream using PDA at several points • Atmospheric rig forced at Strouhal numbers relevant to ‘rumble’

• Low frequency (<500Hz) so plane wave approximation is valid

Simulation setup


Computational Domain Unsteady RANS simulations using open source code OpenFOAM

Setup for Continuous Phase: • Solver algorithm: Mean flow: compressible PIMPLE Excited flow: compressible PISO • Turbulence model: k-ω SST • Time step: Mean flow: 1 × 10−4 s Excited flow: 1 × 10−6 s

Mesh size: ≈ 9.2 million cells

Simulation setup – spray injection


Injection Parameters: • Injection location: randomly selected on a ring located axially 2mm (approximate length of ligaments) downstream of splitter • Thickness of ring: 1mm • Injection direction: swirl angle fixed, polar angle randomly selected between θin and θout,. • Fuel injection velocity: 6.8m/s

Simulation setup – spray injection


Injection Setup Using Quasi-steady Assumption: • Time step: 1 × 10−6 s • Simulation duration: 0.2 sec • Rosin-Rammler size distribution: • dmin=1μm, dmax=150μm, n=3.5

(chosen to match experiment) • Correlation for d0 with air velocity and

air flow rate: Jasula 1979, Lefebvre 1980 • These are found using instantaneous

velocity field from simulation.

Correlation


• Jasuja:

• Lefebvre:

�̇�𝒎𝑨𝑨 𝑼𝑼𝑨𝑨

Jasuja 1 air flow rate through main passages air velocity averaged over annulus of main passage flow

Jasuja 2 air flow rate through main passages air velocity averaged over injection ring

Jasuja 3 air flow rate through injection ring air velocity averaged over injection ring

Lefebvre 1 air flow rate through main passages air velocity averaged over annulus of main passage flow

Lefebvre 2 air flow rate through main passages air velocity averaged over injection ring

Lefebvre 3 air flow rate through injection ring air velocity averaged over injection ring

• Constants calibrated using steady state experimental data

Results – gas phase


Reflection Coefficient

Impedance

Axial Velocity in Centre Plane


Results – example flow field with droplets

Variation of SMD range with forcing frequency

• Using velocity local to prefilmer gives better agreement for SMD range – however the range is not as large as seen in experiment


• Phase averaged particle statistics were collected downstream of the injector – at the same position as in experiment

• Shown here are the maximum and minimum SMD found during cycle from PDA and CFD

• Results shown are from Lefebvre correlation – those from Jasuja are very similar

Results – SMD comparison with experiment


Phase Portrait of SMD and Local Air Velocity at 150Hz

Lefebvre Jasuja




Jasuja Lefebvre




Lefebvre Jasuja



• SMD variation lags behind air velocity fluctuation because droplets are accelerated by the local air.

• Phase portrait changes direction when phase lag exceeds 180 degrees.

• Both correlations for SMD and instantaneous flow field produce similar results when calibrated.

• Correlations using air velocity averaged over injection ring produce better fits with the PDA results.

• Quasi-steady correlation fails to produce reverse of phase portrait direction at high frequencies.

Adding time delay to breakup model

• At higher frequencies the phase shift between SMD and velocity is bigger than can be explained by transit time

• This suggests there is a time delay in the breakup response • Following Chaussonnet 2016, it is argued that velocity field

controlling breakup process should be averaged over a time scale τ

• Running averaging requires storage of the large amount of results from past time steps

• Running averaging is approximated with a second order low pass filter by matching Fourier transforms at low frequencies:

1−𝑒𝑒−𝜏𝜏𝜏𝜏

𝜏𝜏𝑠𝑠 (running averaging) ≈ 1

1+12𝜏𝜏𝑠𝑠+112𝜏𝜏

2𝑠𝑠2 (𝜏𝜏𝑠𝑠 → 0)


Results – breakup delay model (300Hz)


• Implementation on Jasuja correlation • τ = 0.3ms, 0.8ms and 1.2ms • Collapse of phase portrait at 300Hz is

produced with τ = 0.8ms • More simulations are required for both

lower and higher frequencies Setup1

Setup3 Setup2

Conclusions and Future Work

• Suitably calibrated quasi-steady breakup correlations can give reasonable agreement with experiment for variation of SMD magnitude

• Variation of SMD seen to be smaller at low frequency than experiment

• At high frequencies the phase shift between local air velocity and SMD cannot be predicted by the quasi-steady assumption • This can be corrected for to some extent by including a time delay

• Results show large changes in spray size distribution through the acoustic

forcing cycle • This is without considering fluctuations in fuel flow rate

• The changing size population will affect the flame response. The relative

effects of unsteady air-flow and droplet size on a forced flame simulation are now being investigated. Rolls-Royce University Technology Centre in Combustion System Aerothermal Processes

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