4 results
Influence of nozzle external geometry on wavepackets in under-expanded supersonic impinging jets
- Shahram Karami, Julio Soria
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- Journal:
- Journal of Fluid Mechanics / Volume 929 / 25 December 2021
- Published online by Cambridge University Press:
- 27 October 2021, A20
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In this study, large-eddy simulations are utilised to unravel the influence of the nozzle's external geometry on upstream-travelling waves in under-expanded supersonic impinging jets. Three configurations, a thin-lipped, a thin-lipped with a sponge and an infinite-lipped nozzle are considered with the other non-dimensionalised geometrical and flow variables identical for the three cases. Spectral proper orthogonal decomposition is applied to the Mack norm, i.e. the energy norm based on the stagnation energy, to obtain the spatial modes at their corresponding frequency. The spectral decomposition of the spatial modes at optimal and suboptimal frequencies is used to isolate the wavepackets into upstream- and downstream-propagating waves based on their phase velocity. It is found that the external geometry of the nozzle has a significant influence on the first-order statistics even though the governing non-dimensional parameters are the same for all three cases. Multiple peaks emerge in the energy spectra at distinct frequencies corresponding to axisymmetric azimuthal modes for each case. The downstream-propagating wavepackets have a high amplitude at the shear layer of the three jets with the mode shapes resembling Kelvin–Helmholtz instability waves, while the upstream-travelling wavepackets exist in the three regions of the near field, shear layer and inside of the jet. The barrel shock at the nozzle exit appears as a flexible shield, which prevents upstream-travelling waves from reaching the internal region of the nozzle, where the upstream-travelling waves travel obliquely with one side of the wavefront is crawling on the reflected shock while the other side is guided by the shear layer. These latter waves can reach the nozzle lip via inside of the jet. The spectral decomposition of the spatial modes at optimal and suboptimal frequencies show that all three forms of the near field, shear layer and inside jet upstream-travelling wavepackets contribute to the receptivity process while their contributions and strength are altered by the change of the external geometry of the nozzle.
Characteristics of acoustic and hydrodynamic waves in under-expanded supersonic impinging jets
- Shahram Karami, Daniel Edgington-Mitchell, Vassilis Theofilis, Julio Soria
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- Journal:
- Journal of Fluid Mechanics / Volume 905 / 25 December 2020
- Published online by Cambridge University Press:
- 04 November 2020, A34
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In this study large-eddy simulations of under-expanded supersonic impinging jets are performed to develop a better understanding of the characteristics of the acoustic and hydrodynamic waves. Time history, dispersion relation and autocorrelation of the velocity and pressure fluctuations are used to investigate the propagation velocity, time and length scales of the dominant flow structures in the shear layer and near field. The mechanism by which the initial high-frequency instabilities change to low-frequency coherent structures within a short distance is investigated utilising Mach energy norm and linear spatial instability analysis with streamwise varying mean flow profiles. It is shown that the hydrodynamic and acoustic wavepackets have different propagation velocities and length scales while having a similar dominant frequency. It is also observed that the hydrodynamic wavepackets form approximately one jet diameter downstream of the nozzle lip. No evidence has been found to support the ‘collective interactive’ mechanism proposed by Ho & Nosseir (J. Fluid Mech., vol. 105, 1981, pp. 119–142). The ‘vortex pairing’ proposed by Winant & Browand (J. Fluid Mech., vol. 63, 1974, pp. 237–255) is observed near the nozzle; however, it has an insignificant role in the sharp reduction of the most unstable frequency of disturbances. Nonetheless, both Mach energy norm and linear spatial instability analyses show that the most unstable frequency of disturbances decreases rapidly in a very short distance from the nozzle lip in the near-nozzle region through the spatial growth of instabilities where the linear instability analysis overpredicts the frequency of the most unstable instabilities downstream of the nozzle.
Receptivity characteristics of under-expanded supersonic impinging jets
- Shahram Karami, Paul C. Stegeman, Andrew Ooi, Vassilis Theofilis, Julio Soria
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- Journal:
- Journal of Fluid Mechanics / Volume 889 / 25 April 2020
- Published online by Cambridge University Press:
- 26 February 2020, A27
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The receptivity of an under-expanded supersonic impinging jet flow at a sharp nozzle lip to acoustic impulse disturbances is investigated as a function of geometric and flow parameters. The under-expanded supersonic jets emanate from an infinite-lipped nozzle, i.e. the nozzle exit is a circular hole in a flat plate. Two specific cases have been investigated corresponding to nozzle-to-wall distances of $h=2d$ and $5d$, where $d$ is the jet diameter, at a nozzle pressure ratio of 3.4 and a Reynolds number of 50 000. Receptivity in this study is defined as originally coined by Morkovin (Tech. Rep. AFFDL TR, 1969, pp. 68–149; see also Reshotko, AGARD Special Course on Stability and Transition of Laminar Flow, N84-33757 23-34) as the internalisation of an external disturbance into the initial condition that either initiates or sustains a vortical fluid dynamic instability. Notionally, receptivity can be considered as a transfer function between the external disturbance and the initial conditions of the vortical instability. In the case of under-expanded supersonic impinging jet flow subjected to an acoustic disturbance, this transfer function is located at the nozzle lip and, thus, is amenable to an impulse response analysis using the linearised compressible three-dimensional Navier–Stokes equations. In this study, the transfer function at the nozzle lip is defined as the ratio of the output flow energy to the input acoustic energy of the acoustic disturbance. The sensitivity of this transfer function to the angular acoustic disturbance location, its azimuthal mode number and Strouhal number has been investigated for the two under-expanded supersonic impinging jet flow cases. It is found that for both the $h=2d$ and $5d$ cases, acoustic disturbances located at angles greater than $80^{\circ }$ from the jet centreline, with Strouhal numbers in the range between 0.7 and 6.5, have the highest receptivity for all azimuthal mode numbers investigated, except the azimuthal mode number 2 in the case of $h=5d$. The case with $h=5d$ is found to also have high receptivity to acoustic disturbances located at angles between $15^{\circ }$ and $50^{\circ }$ from the jet centreline for acoustic disturbances of all azimuthal mode numbers.
Mechanisms of flame stabilisation at low lifted height in a turbulent lifted slot-jet flame
- Shahram Karami, Evatt R. Hawkes, Mohsen Talei, Jacqueline H. Chen
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- Journal:
- Journal of Fluid Mechanics / Volume 777 / 25 August 2015
- Published online by Cambridge University Press:
- 23 July 2015, pp. 633-689
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A turbulent lifted slot-jet flame is studied using direct numerical simulation (DNS). A one-step chemistry model is employed with a mixture-fraction-dependent activation energy which can reproduce qualitatively the dependence of the laminar burning rate on the equivalence ratio that is typical of hydrocarbon fuels. The basic structure of the flame base is first examined and discussed in the context of earlier experimental studies of lifted flames. Several features previously observed in experiments are noted and clarified. Some other unobserved features are also noted. Comparison with previous DNS modelling of hydrogen flames reveals significant structural differences. The statistics of flow and relative edge-flame propagation velocity components conditioned on the leading edge locations are then examined. The results show that, on average, the streamwise flame propagation and streamwise flow balance, thus demonstrating that edge-flame propagation is the basic stabilisation mechanism. Fluctuations of the edge locations and net edge velocities are, however, significant. It is demonstrated that the edges tend to move in an essentially two-dimensional (2D) elliptical pattern (laterally outwards towards the oxidiser, then upstream, then inwards towards the fuel, then downstream again). It is proposed that this is due to the passage of large eddies, as outlined in Su et al. (Combust. Flame, vol. 144 (3), 2006, pp. 494–512). However, the mechanism is not entirely 2D, and out-of-plane motion is needed to explain how flames escape the high-velocity inner region of the jet. Finally, the time-averaged structure is examined. A budget of terms in the transport equation for the product mass fraction is used to understand the stabilisation from a time-averaged perspective. The result of this analysis is found to be consistent with the instantaneous perspective. The budget reveals a fundamentally 2D structure, involving transport in both the streamwise and transverse directions, as opposed to possible mechanisms involving a dominance of either one direction of transport. It features upstream transport balanced by entrainment into richer conditions, while on the rich side, upstream turbulent transport and entrainment from leaner conditions balance the streamwise convection.