On the three families of instability waves of high-speed jets

Tam, Christopher K. W.; Hu, Fang Q.

doi:10.1017/s002211208900100x

Cited by 298 publications

(274 citation statements)

References 20 publications

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“…There has been ample evidence that instability waves are major sources of noise in supersonic jets. [1][2][3][4][5][6] The noise generation is most efficient when the phase speed of an instability wave is supersonic relative to the ambient fluid and intense Mach waves are emitted. [7][8][9] Therefore, determination of stability characteristics of supersonic jets is a vital step for the prediction of jet noise, where compressibility often plays an important role.…”

Section: Introductionmentioning

confidence: 99%

“…At the beginning of the core region, the shear layer is very thin and often modeled by a vortex sheet, as in the theoretical studies of Gill, 10 Zaninetti 11,12 and Tam and Hu. 4 The ''tophat'' profile also belongs to the potential core region with a thin but finite shear layer. This region can be represented by hyperbolic-tangent functions.…”

Section: Introductionmentioning

confidence: 99%

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Instability of vortical and acoustic modes in supersonic round jets

Luo

Sandham

1997

Physics of Fluids

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The stability of ''top-hat'' and fully developed jet profiles is investigated by an inviscid linear stability theory for compressible flow. The study covers a wide range of the Mach number and the temperature ratio. Two types of instabilities are found: vortical and acoustic, each of which can be subdivided into non-radiating ͑subsonic͒ and radiating ͑supersonic͒ modes. The vortical mode is the continuation of the Kelvin-Helmholtz instability from incompressible flow. The acoustic mode is a compressible flow phenomenon, which becomes important at large Mach numbers. Temperature-ratio effects can be destabilizing or stabilizing, depending on the Mach number and mode of instability. A spectrum of unstable acoustic modes, including axisymmetric ones, are found to exist in the fully developed jet. For this jet, acoustic axisymmetric waves become more unstable than both vortical and acoustic helical waves at Mach numbers over about 3. Strong evidence of a resonance mechanism for acoustic modes is seen in the growth rate curves at high Mach numbers, where a spectrum of local peaks and valleys appears at regularly distributed frequencies. © 1997 American Institute of Physics.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Instability of vortical and acoustic modes in supersonic round jets

Luo

Sandham

1997

Physics of Fluids

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“…The instabilities originate from the nozzle lip and are the growing eigenmodes of the shear layer. Indeed, Tam and Hu [14] showed that an appropriate modelling of the instability initial growth is by considering small shear layer perturbations, based on hydrodynamic instability theory. Tam and Hu's result indicates that the excitation of these Kelvin-Helmholtz type instabilities is essentially an inviscid process that can equally be modelled by a time-dependent numerical solution of the flow governing equations.…”

Section: Numerical Methods 31 Governing Equationsmentioning

confidence: 99%

Time accurate numerical study of turbulent supersonic jets

Rona

Zhang

2004

Journal of Sound and Vibration

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A time accurate numerical study is presented of an over-expanded Mach 2 circular turbulent jet in which the flow is assumed axisymmetric. The focus of this investigation is on the jet screech phenomenon resulting from the interaction between the large scale turbulent mixing region instabilities and the regular spacing of the shock wave-expansion system, (shock cells), in the over-expanded jet. The solution is obtained of the 'short' Time Dependent Reynolds Averaged Navier-Stokes equations (TRANS), using a two-equation, k − ω, turbulence model. The time accurate method was first calibrated for the given model geometry when the flow was fully expanded, and the resulting mean flow characteristics were compared with experimental data. The results were in broad agreement for the first ten diameters of the jet downstream of the exit. Further downstream the time averaged axial velocity decayed at a slightly faster rate than in the experiments. In an ideal inviscid fully expanded jet no shock cells would be present but in the turbulent jet calculations weak shock cells appeared which gradually died out beyond about ten diameters from the nozzle exit. The calculated non-dimensional time averaged transverse velocity profiles showed self-similarity, when allowance was made for the false origin of the shear layer, in agreement with the measured results. In the calculations for the over-expanded jet it was found, in agreement with experimental data, that the interaction between shock cell modulated instability waves and the shock-expansion system generated jet screech. It was found, as part of the screech phenomenon, that the shocks and the shock cells oscillated over a small distance which increased from the axis to a maximum within the shear layer. This shock unsteadiness resulted in the shocks being smeared when viewed in the equivalent steady flow calculations.

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“…Experimental studies of jets issuing from convergent-divergent nozzles have identified three families of instability waves; see Oertel [12,13,14]. Theoretical analyses [15,16] show that high-speed jets with thin mixing layers support families of subsonic, supersonic, and Kelvin-Helmholtz instability waves. Tam and Hu [15] note that Kelvin-Helmholtz instability waves are key to the formation of large scale turbulence structures in jets and the associated turbulent mixing noise.…”

Section: Jet Instabilitymentioning

confidence: 99%

“…Theoretical analyses [15,16] show that high-speed jets with thin mixing layers support families of subsonic, supersonic, and Kelvin-Helmholtz instability waves. Tam and Hu [15] note that Kelvin-Helmholtz instability waves are key to the formation of large scale turbulence structures in jets and the associated turbulent mixing noise. Moreover, for imperfectly expanded jets, the quasi-periodic shock cell structure causes the radiation of additional noise: broadband shock-associated noise and screech tones.…”

Section: Jet Instabilitymentioning

confidence: 99%

Subsonic to Supersonic Nozzle Flows

Kryeziu¹,

Johnson²

2013

SIAM J. Appl. Math.

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Abstract. Steady, irrotational flow of a compressible fluid through a two-dimensional planar and axisymmetric nozzle is formulated and solved numerically in the hodograph or velocity plane. The Legendre potential is used to express the governing equation which for planar flow is linear and for axisymmetric flow nonlinear. The hodograph transformation method is extended to solve the nozzle problem for supersonic flow. A rectangular numerical domain for the supersonic case results from the way the information travels in the region that is the image of the flow that occurs around the lip of the nozzle surface. Knowledge of the characteristic's exact location in the supercritical region of the domain is not required, but only the general direction in which information propagates. 1. Introduction. The study of air flow through a convergent nozzle is well established and has important practical applications such as in rocketry, the converging propulsive nozzle of a subsonic turbojet engine, and jet engines. This paper discusses two forms of compressible flow: two-dimensional planar and axisymmetric flow. The geometry of the nozzle for planar flow consists of two convergent nozzle walls which extend to upstream infinity, while the axisymmetric nozzle surface is conical. For both cases, the angle δ which the nozzle surface makes with the nozzle center-line is assumed to be within the range −π/2 ≤ δ < 0. Only the upper half of the physical plane is considered due to symmetry about the center-line.The hodograph transformation was first applied by Chaplygin [1] to obtain analytical solutions for the nozzle problem in the form of a series of hypergeometric functions. Chaplygin's method is limited to planar subcritical and critical flow, in general. Frankl [2] obtained the value of the discharge coefficient analytically for supersonic choked flow. Norwood [3] solved the two-dimensional supercritical problem numerically in the hodograph plane. He considered the subsonic and supersonic regions separately by modifying iteratively the solution along the sonic line to achieve a continuous solution from one region to the other. The method relies on the linearity of the planar equations in that characteristics are fixed and easily determined in the hodograph plane. Alder [4] developed a numerical method for planar and axisymmetric flow in which the subsonic region is treated in the hodograph plane and the supersonic region in the physical plane by applying the method of characteristics. A matching technique is used to obtain smooth transition of streamlines from one region to the other.The approach here follows Cook et al. [5], who express the governing equation in terms of the Legendre potential and solve the two-dimensional and axisymmetric nozzle problems for subsonic and sonic flows. Introducing the Legendre potential has

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On the three families of instability waves of high-speed jets

Cited by 298 publications

References 20 publications

Instability of vortical and acoustic modes in supersonic round jets

Instability of vortical and acoustic modes in supersonic round jets

Time accurate numerical study of turbulent supersonic jets

Subsonic to Supersonic Nozzle Flows

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