Turbomachinery & Aero-Acoustics Group Chalmers University of Technology Analysis of thermo-acoustic properties of combustors including liner wall modeling Guillaume Jourdain & Lars-Erik Eriksson Division of Fluid Dynamics Department of Applied Mechanics

Turbomachinery & Aero-Acoustics Group Chalmers University of Technology Industrial relevance Current low-NOx combustor designs often based on lean premixed flames. Usually works well in ‘open flame’ configurations. For practical confined flames, pressure oscillations are often encountered in the desirable operating range. Flexi-fuel designs (eg syngas burners) introduce additional risk of instability. Alleviation of problem is difficult due to a lack of knowledge of mode structure and heat release feedback mechanism.

Turbomachinery & Aero-Acoustics Group Chalmers University of Technology Outline Project goals Methodology Test cases Current status Plans for next 6 months

Turbomachinery & Aero-Acoustics Group Chalmers University of Technology Project goals To investigate three different linearization concepts in combination with the spectral transformation and Arnoldi eigenmode extraction technique: –Linearized Euler Equations (LEE). –Linearized Navier-Stokes Equations (LNSE). –(Numerically) Linearized Unsteady RANS approach (L-URANS). To further improve and develop knowledge and modeling capabilities (both flow and acoustics) in the field of combustor liner walls, i.e. porous walls of various types. To evaluate out-of-loop flame transfer modeling (LEE, LNSE) or in- the-loop flame transfer modeling (L-URANS).

Turbomachinery & Aero-Acoustics Group Chalmers University of Technology Methodology Standard RANS CFD solution provides mean flow field. Unsteady flow expressed in terms of perturbations field. Assumption of small amplitude perturbations leads to LEE, LNSE or L-URANS solution for the aero-acoustic perturbations field. Application of Arnoldi’s method and spectrum transformation (= time stepping scheme) provides desired a number of least damped eigenmodes.

Turbomachinery & Aero-Acoustics Group Chalmers University of Technology Test cases Validation Rig I –”Cold” case (T in =288 K,  =0.72, massflow=0.6 kg/s) –”Hot” case (T in =600 K,  =0.61, massflow=0.6 kg/s)

Turbomachinery & Aero-Acoustics Group Chalmers University of Technology Current status ( ) RANS solutions –Hot case: Coarse grid used Flame development validated against experimental data (gas analysis) Velocity profiles agree reasonably well with experimental data (LDA) –Cold case: Refined grid used Flame development validated against experimental data Arnoldi eigenmode extraction –Hot case: LEE solver used (coarse grid) L-URANS solver used (coarse grid) Several modes obtained: hydrodynamic type (low freq), mixed type (med freq), acoustic type (high freq) –Cold case: LEE solver used (refined grid) L-URANS solver used (work in progress) Analysis work on-going, several modes obtained (low, med, high freq)

Turbomachinery & Aero-Acoustics Group Chalmers University of Technology Validation Rig I, RANS solution, Realizable k-eps turb model, EDC type comb model Static temperature (T)

Turbomachinery & Aero-Acoustics Group Chalmers University of Technology Validation Rig I, RANS solution, Realizable k-eps turb model, EDC type comb model Axial velocity component (u)

Turbomachinery & Aero-Acoustics Group Chalmers University of Technology Validation Rig I, RANS solution for cold case Fit T lim of our combustion model with the data from Validation Rig I for the “cold case” i.e the upstream temperature = 288 K, mass flow = 0.6 kg/s, F/A=0.72. => T lim = 440K.

Turbomachinery & Aero-Acoustics Group Chalmers University of Technology Validation Rig I, RANS solution for cold case T lim = 440K, m=1.1kg/s, F/A=0.72, Time-averaged URANS

Turbomachinery & Aero-Acoustics Group Chalmers University of Technology Exp: Power spectrum of p’, with buzz mode

Turbomachinery & Aero-Acoustics Group Chalmers University of Technology Exp: Power spectrum of p’, with screech mode

Turbomachinery & Aero-Acoustics Group Chalmers University of Technology No pressure oscillation Buzz mode Screech mode High speed Schlieren visualization of flame downstream of flameholder

Turbomachinery & Aero-Acoustics Group Chalmers University of Technology Initial interpretation of exp data No oscillations: –Modes excited by turbulence –Primarily low frequencies: ~50 Hz, ~100 Hz, ~110 Hz, ~150 Hz, ~200 Hz, ~275 Hz, ~300 Hz, ~375 Hz, Low order buzz modes or pure flow modes? Oscillations present: –”Buzz” mode at low frequency: ~120 Hz (+weak harmonics) Longitudinal mixed type mode or hydrodynamic type mode? –Screech mode at intermediate frequency: ~1250 Hz (+harmonics due to interaction with 120 Hz mode) Transversal or longitudinal mixed type mode? Questions to be answered by analysis

Turbomachinery & Aero-Acoustics Group Chalmers University of Technology Val Rig I, hot case, candidate screech mode: f= Hz (5 th buzz mode, longitudinal mixed mode) p’ contours ro’ contours Validation Rig I –”Hot” case (T in =600 K,  =0.61, massflow=0.6 kg/s) –Linearized Euler Equation (LEE) solver

Turbomachinery & Aero-Acoustics Group Chalmers University of Technology Summary of results for hot case, LEE solver: Several modes seen in non-oscillating case are captured by eigenmode extraction method, eg. –~50 Hz, ~100 Hz, ~150 Hz, ~380 Hz 120 Hz ”buzz” mode is not clearly identified: –Hydrodynamic mode ~117 Hz that couples with combustion? –Heat release and flame front dynamics may modify mode structure –Clearly not an acoustic mode since 1st buzz mode has f~150 Hz 1200 Hz screech mode probably identified: –5th buzz mode (longitudinal mixed mode) –Not tranverse mode as previously thought!

Turbomachinery & Aero-Acoustics Group Chalmers University of Technology Val Rig I, cold case: Eigenmode analysis results F = Hz, Longitudinal mixed mode (1st buzz mode) Pressure fluctuations (Real and imaginary parts) Density fluctuations (Real and imaginary parts) Validation Rig I –”Cold” case (T in =288 K,  =0.72, massflow=1.1 kg/s, oscillating) –Linearized Euler Equation (LEE) solver

Turbomachinery & Aero-Acoustics Group Chalmers University of Technology Val Rig I, cold case: Eigenmode analysis results F = Hz, Transverse acoustic mode Pressure fluctuations (Real and imaginary parts) LEE solver Density fluctuations (Real and imaginary parts)

Turbomachinery & Aero-Acoustics Group Chalmers University of Technology Comparison with the Test Rig (cold case)

Turbomachinery & Aero-Acoustics Group Chalmers University of Technology Summary of results for cold case, LEE solver: Some calculated frequencies are seen in exp data (eg Hz, Hz, Hz). Some calculated frequencies are not seen in exp results (eg. 275 Hz, Hz). Some modes seen in exp data are not (yet) found in the calculations (eg. the buzz mode (~ 120 Hz) and the screech mode (~ 1200 Hz).

Turbomachinery & Aero-Acoustics Group Chalmers University of Technology Linearized Unsteady RANS URANS solver T=NSTEP x  t Q1+XQ1+XQ2+YQ2+Y URANS solver T=NSTEP x  t Q1-XQ1-XQ2-YQ2-Y Input field X + - 1/(2  ) Linear response Y For sufficiently small , we have: Output field Y is the linearized response of the URANS solver to a perturbation field X added to the initial solution

Turbomachinery & Aero-Acoustics Group Chalmers University of Technology f=125 Hz (Low frequency flame flapping mode) Arnoldi spectral analysis of linearized URANS solver Validation rig 1, Tin=600 K, F/A=0.61, mass flow = 0.6 kg/s

Turbomachinery & Aero-Acoustics Group Chalmers University of Technology Summary of results for hot case, L-URANS solver: 120 Hz ”buzz” mode probably identified: –Hydrodynamic mode with flame/wake flapping (125 Hz) –Differs from LEE solver result, where this mode was not found (closest was ~117 Hz), involving wake only –No acoustics involved since 1st buzz mode has f~150 Hz 1200 Hz screech mode not yet identified: –2nd, 3rd, 4th, 6th and higher buzz modes found so far –1st and 5th buzz modes will probably be found (takes time to analyze all computed modes) –All buzz modes found are similar to those found for LEE solver in terms of frequency and overall structure, but differ in terms of damping and detailed structure (more ”smooth” modes)

Turbomachinery & Aero-Acoustics Group Chalmers University of Technology Plans for next 6 months Complete Val Rig I cold case analysis (L- URANS) Perform corresponding analysis with LNSE solver Draw conclusions concerning the optimal methodology in terms of captured physics, efficiency, maintenance effort (1 st milestone). Submit conference paper(s)