Three-dimensional, unsteady, acoustic-shear flow dynamics in a cylinder with sidewall mass addition

Staab, Peter; Kassoy, D. R.

doi:10.1063/1.869513

Cited by 11 publications

(7 citation statements)

References 8 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This was later used at the foundation of many studies seeking to determine (a) the ensuing unsteady wave motion or (b) the flow instability (e.g. Beddini & Roberts 1988Staab & Kassoy 1996;Casalis, †Author to whom correspondence should be addressed: maji@utsi.edu. Avalon & Pineau 1998).…”

Section: Introductionmentioning

confidence: 99%

On the rotational compressible Taylor flow in injection-driven porous chambers

Maicke

Majdalani

2008

J. Fluid Mech.

View full text Add to dashboard Cite

This work considers the compressible flow field established in a rectangular porous channel. Our treatment is based on a Rayleigh–Janzen perturbation applied to the inviscid steady two-dimensional isentropic flow equations. Closed-form expressions are then derived for the main properties of interest. Our analytical results are verified via numerical simulation, with laminar and turbulent models, and with available experimental data. They are also compared to existing one-dimensional theory and to a previous numerical pseudo-one-dimensional approach. Our analysis captures the steepening of the velocity profiles that has been reported in several studies using either computational or experimental approaches. Finally, explicit criteria are presented to quantify the effects of compressibility in two-dimensional injection-driven chambers such as those used to model slab rocket motors.

show abstract

Section: Introductionmentioning

confidence: 99%

On the rotational compressible Taylor flow in injection-driven porous chambers

Maicke

Majdalani

2008

J. Fluid Mech.

View full text Add to dashboard Cite

show abstract

“…The isothermal boundary condition in (11) represents the temperature of the hot gaseous products, typically 2500K-3000K in dimensional value. The axial variation of the combustion zone flame temperature is likely to be small compared to the flame temperature because it is controlled primarily by gas phase exothermic chemical kinetics.…”

Section: Summary Of Results and Conclusionmentioning

confidence: 99%

Acoustic-Rotational Internal Flow Caused by Transient Sidewall Mass Addition

Staab¹,

Rempe²,

Kassoy³

2004

SIAM J. Appl. Math.

Self Cite

View full text Add to dashboard Cite

Asymptotic and numerical methods are used to describe thermal transients in an internal flow caused by time-dependent, spatially distributed sidewall mass addition. Solutions are obtained for the temperature distribution and wall heat transfer, as well as the vorticity, in a high Reynolds number (Re), low Mach number (M ), compressible flow in a cylinder. A multiple-scale analysis, valid in the limit of M → 0 and Re → ∞, is used to derive an equation for O(M ) acoustic disturbances arising from transient injection. The limit process is also used to obtain reduced equations for the rotational axial velocity field and the nonacoustic temperature variation arising from a balance of convection and transverse diffusion. The convection-diffusion equations are characterized by viscous and conductive transport on an O(M ) radial scale relative to the O(1) nondimensional cylinder radius. These small-scale diffusive effects are pervasive throughout the entire cylinder in this large Re, injected flow. The thermal analysis presented here shows that the transient temperature disturbance consists of an O(M ) acoustic component and an O(M ) radially dependent "rotational" component arising from the convection and diffusion of large radial gradients. The latter are generated on the injection surface and then gradually fill the cylinder as time elapses. The radial gradient of temperature is O(1), although the temperature disturbance is only O(M ). Results for the radial and axial variations of the instantaneous temperature distribution imply that the O(M ) acoustic and "rotational" temperature components make the largest contributions to the total energy transient. Smaller kinetic energy effects appear only at O(M 2 ). These results emphasize the importance of modeling intense thermal transients, including the sidewall heat transfer, in addition to the more familiar vorticity distributions.

show abstract

“…This choice provides the necessary freedom to achieve a balance in the governing ODE between diffusive, convective, and inertial terms. A similar choice of a nonlinear transformation was determined to be necessary and thus employed recently by Zhao et al, 35 Staab and Kassoy, 36 Majdalani, 33 and Majdalani and Van Moorhem. 7 The current study will obviate the need for conjecture because the correct nonlinear scaling transformation will be derived directly from the problem's solvability condition.…”

Section: Two-variable Multiple-scales Expansionmentioning

confidence: 99%

Two Forms of the Rotational Solution for Wave Propagation Inside Porous Channels

Majdalani

Rienstra

2002

3rd Theoretical Fluid Mechanics Meeting

View full text Add to dashboard Cite

In this article, a long rectangular channel is considered with two transpiring walls that are a small distance apart. The channel's head end is hermetically closed while the aft end is either open (isobaric) or acoustically closed (choked). A mean flow enters uniformly across the permeable walls, turns, and exits from the downstream end. The slightest unsteadiness in flow velocity is inevitable and occurs at random frequencies. Small pressure disturbances are thus produced. Those waves whose oscillations match the enclosure's natural frequencies are promoted. Inception of small pressure perturbations alters the flow character and leads to a temporal field that we wish to analyze. The mean flow is of the Berman type and can be obtained from the Navier-Stokes equations over different ranges of the cross-flow Reynolds number. The unsteady component can be formulated from the linearized momentum equation. This has been carried out in numerous studies and has routinely given rise to a singular, boundary-value, double-perturbation problem in the cross-flow direction. The current study focuses on the resulting second-order differential equation that prescribes the rotational wave motion in the transverse direction. This equation exhibits unique features that define a general class of ODEs. Due to the problem's oscillatory behavior, two general asymptotic formulations are derived, for an arbitrary mean-flow profile, using WKB and multiple-scales expansions. The fundamental asymptotic solutions reveal the same similarity parameter that controls the rotational wave character. The multiple-scales solution unravels the problem's characteristic length scale following a unique, nonlinear variable transformation. The latter is derived rigorously from the problem's solvability condition. The advantage of using a multiple-scales procedure lies in the ease of construction, accuracy, and added physical insight stemming from its leading-order term. For verification purposes, a specific mean-flow solution is used for which an exact solution can be derived. Comparisons between asymptotic and exact predictions are gratifying, showing an excellent agreement over a wide range of physical parameters.

show abstract

Three-dimensional, unsteady, acoustic-shear flow dynamics in a cylinder with sidewall mass addition

Cited by 11 publications

References 8 publications

On the rotational compressible Taylor flow in injection-driven porous chambers

On the rotational compressible Taylor flow in injection-driven porous chambers

Acoustic-Rotational Internal Flow Caused by Transient Sidewall Mass Addition

Two Forms of the Rotational Solution for Wave Propagation Inside Porous Channels

Contact Info

Product

Resources

About