Transverse Waves in Simulated Liquid Rocket Engines

Haddad, Charles T.; Majdalani, Joseph

doi:10.2514/6.2011-6029

Cited by 3 publications

(8 citation statements)

References 24 publications

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“…In comparison to the acoustic pressure distribution displayed in Fig. 2, the nodal lines of the vorticoacoustic waves are shifted by a phase angle of / (2 ). m …”

Section: A Acoustic Formulationmentioning

confidence: 89%

“…The uniform injection case was first investigated by Fischbach, Flandro and Majdalani 1 and then reaffirmed by Haddad and Majdalani. 2 In both studies, the vorticoacoustic waves can be written as ), three conclusions may be drawn. Firstly, the total vorticoacoustic pressure will coincide with the acoustic pressure, which is common to all cases considered.…”

Section: A Validation Of Generalized Solutionmentioning

confidence: 95%

“…A more in-depth formulation that focuses on wave characterization is later furnished wherein detailed solutions for the uniform and bell-shaped injection profiles are carefully constructed. 2 The present approach will therefore apply a regular perturbation expansion to a well-established variant of the conservation equations. For the case of an arbitrary mean flow, Eqs.…”

Section: Arbitrary Injection Profilementioning

confidence: 99%

“…The rotational gaseous motion that arises in such an environment may be described by a set of four coupled partial differential equations (PDEs) representing continuity and momentum conservation in the context of a fluid oscillating in a relatively short cylindrical chamber with a permeable headwall. 1,2 The formulation to be developed here will therefore seek to accommodate a multitude of axisymmetric mean flow velocities that may be envisioned along conventional injector faceplates. These will be seen to influence the chamber's vorticoacoustic wave oscillations.…”

Section: Introductionmentioning

confidence: 99%

“…However, their chief objective remains focused on understanding the mechanism of acoustic streaming rather than the vorticoacoustic wave character itself. In a follow-up study, Haddad and Majdalani 2 introduce a higher-order solution of the rotationally traveling wave in a similarly configured LRE. At the outset, formulations are produced for both uniform and bell-shaped injection profiles, with the latter constituting a more realistic representation of the mean flow.…”

Section: Introductionmentioning

confidence: 99%

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Transverse Waves in Simulated Liquid Rocket Engines with Variable Headwall injection

Haddad

Majdalani

2012

50th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition

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In this study, the transverse vorticoacoustic wave in a circular cylinder is characterized for a variable velocity profile at the injector faceplate. This particular configuration mimics the conditions leading to the onset of traveling radial and tangential waves in a simple liquid rocket engine (LRE). To capture the unsteady behavior in this physical setting, we consider a short thrust chamber with an injecting headwall and combine the benefits of three techniques: regular perturbations, Helmholtz decomposition, and boundary layer theory. First, regular perturbations are leveraged to linearize the equations of motion and, in the process, help to identify the unsteady interaction equations. Second, a Helmholtz decomposition of the first-order disturbance equations gives rise to a compressible, inviscid, and acoustic set that is responsible for driving the unsteady motion. This is accomplished in conjunction with an essentially incompressible, viscous, and vortical set that materializes by virtue of coupling with the acoustic wave at the boundaries. After recovering the acoustic mode from the resulting wave equation, the last step is to solve for the vortical mode by applying boundary layer theory and a judicious expansion of the rotational set with respect to a small viscous parameter, . After some effort, an explicit formulation for variable headwall injection is obtained and validated by means of a limiting process verification that is based on two previously investigated cases, the uniform and bell-shaped injection profiles. The solution is then illustrated using two new configurations corresponding to laminar and turbulent profiles. In the process of comparing the four representative cases, the characteristics of the vorticoacoustic wave, including its penetration depth, spatial wavelength, and overshoot factor, are systematically explored and discussed. Most characteristics are found to depend on the penetration and Strouhal numbers along with the distance from the centerline. Along the axis of the chamber, the waves attributed to different injection profiles behave similarly to the extent that behavioral deviations among them increase as the sidewall is approached. This work also accounts for the presence of a downstream boundary that stands to produce left-traveling reflections whose pairing with the right-traveling waves promotes the establishment of a standing wave environment. The combined waves are formulated analytically and shown to be appreciable in view of their amplitudes that twice exceed those associated with traveling waves.

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“…In comparison to the acoustic pressure distribution displayed in Fig. 2, the nodal lines of the vorticoacoustic waves are shifted by a phase angle of / (2 ). m …”

Section: A Acoustic Formulationmentioning

confidence: 89%

Section: A Validation Of Generalized Solutionmentioning

confidence: 95%

Section: Arbitrary Injection Profilementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations