Nonlinear Liquid Rocket Combustion Instability Behavior Using UCDS Process

Jacob, Eric J.; Flandro, Gary A.; Gloyer, Paul; French, Jonathan

doi:10.2514/6.2010-6800

Cited by 9 publications

(10 citation statements)

References 6 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Culick and coworkers used an eigenfunction expansion together with a two-time variable technique that had some of the same advantages (see Awad & Culick 1986;Yang, Kim & Culick 1990;Culick 1994Culick , 2006. More recently, a Galerkin approach (also known as reduced-basis modelling) has been employed by Flandro, Fischbach & Majdalani (2007) and Jacob et al (2010).…”

Section: Review Of Lpre Combustion Instability Literaturementioning

confidence: 99%

Stochastic modelling of transverse wave instability in a liquid-propellant rocket engine

2014

View full text Add to dashboard Cite

The combustion stability of a liquid-propellant rocket engine experiencing a random, finite perturbation from steady-state conditions is examined. The probability is estimated for a nonlinear resonant limit-cycle oscillation to be triggered by a random disturbance. Transverse pressure waves are considered by using a previously published two-dimensional nonlinear pressure wave equation coupled with Euler equations governing the velocity components. The cylindrical combustion chamber is a complex system containing multiple co-axial methane-oxygen injectors; each co-axial jet is analysed for mixing and burning on its own local grid scheme, with the energy release rate coupled to the wave oscillation on the more global grid. Two types of stochastic forcing for the random disturbance are explored: a travelling Gaussian pressure pulse and an oscillating pressure dipole source. The random variables describing the pulse are magnitude, location, duration and orientation of the disturbances. The polynomial chaos expansion (PCE) method is used to determine the long-time behaviour and infer the asymptote of the solution to the governing partial differential equations. Depending on the random disturbance, the asymptote could be the steady-state solution or a limit-cycle oscillation, e.g. a first tangential travelling wave mode. The asymptotic outcome is cast as a stochastic variable which is determined as a function of input random variables. The accuracy of the PCE application is compared with a Monte Carlo calculation and is shown to be significantly less costly for similar accuracy.

show abstract

Section: Review Of Lpre Combustion Instability Literaturementioning

confidence: 99%

Stochastic modelling of transverse wave instability in a liquid-propellant rocket engine

2014

View full text Add to dashboard Cite

show abstract

“…To do so requires consideration of nonlinear energy transfer pathways between the fundamental mode and its harmonics. 62,63 However, quantifying linear energy transfer in this way facilitates the distinct advantage of correlating driving and damping of periodic, unsteady flowfields with specific flow phenomena. This leads to identifying the influence of geometric features on the mean flow and ultimately the emergence of acoustic waves.…”

Section: Quantifying Unsteady Energy Transfermentioning

confidence: 99%

Transverse Vortico-Acoustic Waves in the Presence of Strong Mean Flow Shear Layers

Kovacic¹,

Batterson²,

Majdalani³

2015

51st AIAA/SAE/ASEE Joint Propulsion Conference

View full text Add to dashboard Cite

Several analytical models describing the formation of resonant waves in simple geometric configurations are available in the open literature. Their solutions are predicated on several limiting assumptions, namely, that the mean flow velocity is uniform and that the wall injection Mach number is sufficiently small to justify asymptotic reductions to the governing equations. When considering acoustic waves in a convecting medium where 1 M  , the effect of mean flow motion appears at 2 ( ) M which, from an asymptotic standpoint, represents a higher-order correction that is traditionally dismissed with no afterthought. Naturally, the ensuing truncation leads to a simple Helmholtz-type wave equation. In practice though, the influence of the mean flow appears at leading order when accounting for acoustic boundary layers. Acoustic boundary layers, when strongly coupled with the mean flow, give rise to the so-called vorticity (or vortical) waves. When combined with the acoustic wave motion, the resulting pair constitutes what is typically referred to as a vortico-acoustic wave. By strictly enforcing the 1 M  condition, analytical solutions can be recovered for vortico-acoustic waves in simple planar and axisymmetric chambers. The present study focuses on a numerical approach that resolves the unsteady field equations computationally for the threefold purpose of verifying existing analytical solutions, providing practical bounds for their applicability, and extending their predictive capabilities to more complex configurations. In particular, the interaction between acoustic waves and a strong mean flow shear layer is investigated by computationally resolving the vortico-acoustic field developing behind a backward facing step. In this context, deviations from the analytical solutions are reported both at high injection Mach numbers and when considering the emergence of acoustically-synchronized vortex cells around a shear layer. These vortex cells exhibit a spatial instability that continues to grow as the flow is further accelerated. Lastly, the temporal stability of the flow is quantified by computing the rate of energy transfer into the unsteady field. Similarly to the spatial instability, the increased vorticity at higher injection velocities tends to drive temporal instability as well. Nomenclature a = chamber radius or half-height [m] s a = speed of sound [m/s] j = mode number M = injection Mach number, / inj s U a p = pressure [Pa] R = specific gas constant [J/kg-K] j R = pressure amplitude for mode j [Pa] r = spatial coordinate, , , r z  T = temperature [K] inj U = injection velocity [m/s] u = velocity vector [m/s] j u = velocity associated with mode j [m/s] Symbols  = acoustic velocity potential [m 2 /s]  = dynamic viscosity [N-m/s]  = density [kg/m 3 ] Ω = steady vorticity [1/s] ω = unsteady vorticity [1/s] j  = circular frequency of mode j [rad/s] Superscripts and Subscripts 0 = denotes a mean flow variable 1= denotes an unsteady flow variable , , m n l = denotes the tangential, radial, and axial acoust...

show abstract

“…In 2010 3 it was predicted that if the first two modes in a system were both unstable it was possible (given a strong enough second mode instability) for the second mode to stabilize the first mode. This is due to nonlinear coupling between the modes.…”

Section: Introductionmentioning

confidence: 99%

Forced Nonlinear Acoustic Damping in a Rijke Tube and its Application to Combustion Instability Control

Jacob¹,

Brooks²

2014

50th AIAA/ASME/SAE/ASEE Joint Propulsion Conference

View full text Add to dashboard Cite

Nonlinear unsteady energy transport theory predicts that when multiple coupled oscillatory acoustic modes are unstable, only one of these modes may dominate. This phenomenon produces unusual experimental results in propulsion systems as small changes may alter the stability of many modes, thereby altering their interactions as well. These nonlinear interactions create instances where unstable modes appear to switch, where, in fact, multiple modes are unstable. Understanding this phenomenon is critical in diagnosing combustion instability and in developing damping techniques in unstable systems. In order to verify this predicted phenomenon a forced Rijke tube experiment was performed. This experiment shows that the first mode instability caused by the Rijke tube is eliminated when higher modes are driven. This effect only occurs near the natural frequencies of the Rijke tube and is likely not the result of changes in the Rijke tube operation itself. The positive results of this experiment have applications in the development of new innovative combustion instability damping techniques in propulsion systems as well as validating the analytical methods applied. With this process, a fundamentally new way of damping is presented as it is possible to eliminate low frequency oscillations by either destabilizing higher frequency modes or by directly driving those higher modes. I. Nomenclature Rm= amplitude of oscillation for mode, m αm = normalized linear energy transfer rate for mode, m A = nonlinear energy transfer factor Emnl = nonlinear coupling matrix ω1 = first longitudinal frequency ζm = driven energy transfer rate p1 = unsteady pressure P0 = mean flow pressure ηm = time dependent function km = mode number II. IntroductionNERGY transferred from the bulk fluid flow into the unsteady field manifests as a growing acoustic pressure amplitude. This is the fundamental source of instability in all systems. Once in the unsteady field, nonlinear unsteady energy transport theory 1, 2 defines the flow of energy between unsteady modes. This results in a nonlinear energy cascade and limit cycle behavior. It is this behavior that is responsible for the appearance of harmonic modes and wave steepening 1 .In 2010 3 it was predicted that if the first two modes in a system were both unstable it was possible (given a strong enough second mode instability) for the second mode to stabilize the first mode. This is due to nonlinear coupling between the modes. These observations were explored experimentally by driving higher mode harmonics in a selfexcited Rijke tube in 2012 and presented in 2013 7 . Initial results were promising and the a-priori theoretical prediction 1 Engineer, 112 Mitchell Blvd, Tullahoma, TN, AIAA Member 2 Engineer, 112 Mitchell Blvd, Tullahoma, TN, AIAA Member E Downloaded by UNIVERSITY OF NEW SOUTH WALES on August 2, 2015 | http://arc.aiaa.org |

show abstract

Nonlinear Liquid Rocket Combustion Instability Behavior Using UCDS Process

Cited by 9 publications

References 6 publications

Stochastic modelling of transverse wave instability in a liquid-propellant rocket engine

Stochastic modelling of transverse wave instability in a liquid-propellant rocket engine

Transverse Vortico-Acoustic Waves in the Presence of Strong Mean Flow Shear Layers

Forced Nonlinear Acoustic Damping in a Rijke Tube and its Application to Combustion Instability Control

Contact Info

Product

Resources

About