6th TANGO Project Meeting (Ansaldo Energia, Genoa) 14 September 2015 Aswathy Surendran (ESR) Advisor: Prof. Maria A. Heckl Keele University, UK

Contents Research Task Recap Work done On-going & Future work Outlook

Research Task Task 3.3 : Analytical study of idealised combustion system with heat exchanger

Recap Tube row modelling Cavity backed tube row : No flow T and R coefficients Parametric study Cavity backed tube row : No flow No Structural Loss Structural Loss

Recap Slit-plate backed by cavity : With flow Increasing Mach number First mode Surendran and Heckl (ICSV22)

Work done Tube row backed by cavity : With flow Ongoing

Work done Complete system Open end

Work done Complete system n – τ law

Work done Complete system Assuming that ∆𝑥→0 Transfer Function

Work done Secondment at Bekaert Gain – Phase plots Uin 340 K 1500 K 𝐻𝑇𝐹= 𝑄 ′ / 𝑄 𝑜 𝑢 / 𝑈 𝑖𝑛

Work done Transfer Function Approximations Constrained Least Squares Piecewise Continuous Gain Phase Ongoing

Work done Complete system TF Approx.

Work done Complete system Assuming that ∆𝑥→0 Quasi-Steady

Work done Quasi-Steady Analysis Compressible Quasi-Steady M1 and Point of separation 1+ 𝑀 2 𝑝 2 + 1− 𝑀 1 𝑝 1 − = 𝑇 + 𝑅 − 𝑅 + 𝑇 − 1+ 𝑀 1 𝑝 1 + 1− 𝑀 2 𝑝 2 −

Analytical estimation Work done Quasi-Steady Analysis Compressible Quasi-Steady M1 and Point of separation 1+ 𝑀 2 𝑝 2 + 1− 𝑀 1 𝑝 1 − = 𝑇 + 𝑅 − 𝑅 + 𝑇 − 1+ 𝑀 1 𝑝 1 + 1− 𝑀 2 𝑝 2 − Ongoing Analytical estimation

Work done Secondment at Bekaert Centreline velocity Separation Location

Work done Complete system Quasi-Steady

Work done Complete system Closed end

Increasing Mach number Work done Complete system Stability maps First mode Increasing Mach number

On-going & Future work On-going Future Work Flow separation point Approximations to TF Gain and Phase Complete system Validity of assumptions Future Work Secondment at KTH Experiments for T± and R±

Thank You ! Outlook Experimental/Numerical study on the same Including the effects of other loss mechanism Structural loss Thank You !

Tube row: Structural loss lc Reff σs = 0.5 ωres of Rijke tube ~ [700 1700] s-1

Tube row: Structural loss Coinciding frequencies Appropriate tube row (radius) Appropriate damping

Slit-plate with bias flow Slit-plate with flow Slit-plate with bias flow 𝑇= 𝜌 𝑜 𝜔 𝑉 / 𝑘𝑑 𝑅=1− 𝜌 𝑜 𝜔 𝑉 / 𝑘𝑑 𝜌 𝑜 𝜔 𝑉 𝑘𝑑 = 𝑓(𝜔,𝑑,𝑠, 𝑐 𝑜 ,𝑈)† Perturbation volume flux through the slit Accounts for influence of vortex shedding Sound energy Unsteady vortices † Dowling, A. P. and Hughes, I. J. (1992), Sound absorption by a screen with a regular array of slits, Journal of Sound and Vibration, Vol. 156 (3), 387–405.

Quasi-Steady Analysis Hofmans (1998)† 𝑆𝑟= 𝑓 ℎ 𝑑 𝑢 𝑑 , 𝐻𝑒= 𝑓 ℎ 𝑝 𝑐 𝑜 Incompressible model Sr ≪ 1, He ≪ 1, M1 ≪ 1 Compressible model Sr ≪ 1, He ≪ 1, M1 – finite, Mj ~ 𝒪(1) † Hofmans, G. C. J., Vortex Sound in Confined Flows, Technische Universiteit Eindhoven, PhD Thesis, (1998).

Quasi-Steady Analysis Our Model Incompressible Quasi-Steady 𝑝 2 + 𝑝 1 − = 𝑇 + 𝑅 − 𝑅 + 𝑇 − 𝑝 1 + 𝑝 2 −

Work done Secondment at Bekaert ANSYS Fluent Geometry – , , Inlet velocity – 0.1 , 0.2 , 0.5 m/s Tube diameter – 3 , 5 mm Open-area ratio – 0.1 , 0.2

Source & Sink COMSOL