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
Rolls-Royce University Technology Centre in Combustion System Aerothermal Processes
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
Rolls-Royce University Technology Centre in Combustion System Aerothermal Processes
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
Rolls-Royce University Technology Centre in Combustion System Aerothermal Processes
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
Rolls-Royce University Technology Centre in Combustion System Aerothermal Processes
Experimental setup
Rolls-Royce University Technology Centre in Combustion System Aerothermal Processes
• 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
Rolls-Royce University Technology Centre in Combustion System Aerothermal Processes
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
Rolls-Royce University Technology Centre in Combustion System Aerothermal Processes
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
Rolls-Royce University Technology Centre in Combustion System Aerothermal Processes
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
Rolls-Royce University Technology Centre in Combustion System Aerothermal Processes
• 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
Rolls-Royce University Technology Centre in Combustion System Aerothermal Processes
Reflection Coefficient
Impedance
Axial Velocity in Centre Plane
Rolls-Royce University Technology Centre in Combustion System Aerothermal Processes
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
Rolls-Royce University Technology Centre in Combustion System Aerothermal Processes
• 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
Rolls-Royce University Technology Centre in Combustion System Aerothermal Processes
Phase Portrait of SMD and Local Air Velocity at 150Hz
Lefebvre Jasuja
Results – SMD comparison with experiment
Rolls-Royce University Technology Centre in Combustion System Aerothermal Processes
Phase Portrait of SMD and Local Air Velocity at 200Hz
Jasuja Lefebvre
Results – SMD comparison with experiment
Rolls-Royce University Technology Centre in Combustion System Aerothermal Processes
Phase Portrait of SMD and Local Air Velocity at 300Hz
Lefebvre Jasuja
Results – SMD comparison with experiment
Rolls-Royce University Technology Centre in Combustion System Aerothermal Processes
Phase Portrait of SMD and Local Air Velocity at 350Hz
Lefebvre Jasuja
Results – SMD comparison with experiment
Rolls-Royce University Technology Centre in Combustion System Aerothermal Processes
Phase Portrait of SMD and Local Air Velocity at 400Hz
Lefebvre Jasuja
Results – SMD comparison with experiment
Rolls-Royce University Technology Centre in Combustion System Aerothermal Processes
• 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)
Rolls-Royce University Technology Centre in Combustion System Aerothermal Processes
Results – breakup delay model (300Hz)
Rolls-Royce University Technology Centre in Combustion System Aerothermal Processes
• 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