5 results
Transient growth analysis of hypersonic flow over an elliptic cone
- Helio Quintanilha, Jr., Pedro Paredes, Ardeshir Hanifi, Vassilis Theofilis
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- Journal:
- Journal of Fluid Mechanics / Volume 935 / 25 March 2022
- Published online by Cambridge University Press:
- 03 February 2022, A40
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Non-modal linear stability analysis results are presented for hypersonic flow over an elliptic cone with an aspect ratio of two at zero angle of attack, completing earlier modal instability analysis of flow around the same geometry. The theoretical framework to perform transient growth analysis of compressible flows on a generalized two-dimensional frame of reference is developed for the first time and is then applied to solve the initial-value problem governing non-modal linear instability on planes perpendicular to the cone axis, taken at successive streamwise locations along the elliptic cone. Parameter ranges examined here are chosen so as to model flight of the Hypersonic International Flight Research Experimentation 5 (HIFiRE-5) test geometry at altitudes of 21 km and 33 km, corresponding to Mach numbers 7.45 and 8.05 and unit Reynolds numbers $Re' = 1.07\times 10^7$ and $1.89\times 10^6$, respectively. Results obtained indicate that the significance of the non-modal growth for laminar–turbulent transition increases with increasing flight altitude (decreasing Reynolds number). At a given set of flow parameters, transient growth is stronger in the vicinity of the tip of the cone and in azimuthal locations away from both of the minor (centreline) and major (attachment line) axes of the cone. Linear optimal disturbances calculated at conditions of maximal transient growth are found to peak in the crossflow region of the elliptic cone. These structures are elongated along the streamwise spatial direction, while being periodic along the spanwise direction with periodicity lengths of the same order of magnitude as the well-known structures identified as crossflow vortices in both experiments and simulations.
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.
Linear modal instabilities of hypersonic flow over an elliptic cone
- Pedro Paredes, Ryan Gosse, Vassilis Theofilis, Roger Kimmel
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- Journal:
- Journal of Fluid Mechanics / Volume 804 / 10 October 2016
- Published online by Cambridge University Press:
- 09 September 2016, pp. 442-466
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Steady laminar flow over a rounded-tip $2\,:\,1$ elliptic cone of 0.86 m length at zero angle of attack and yaw has been computed at Mach number $7.45$ and unit Reynolds number $Re^{\prime }=1.015\times 10^{7}~\text{m}^{-1}$. The flow conditions are selected to match the planned flight of the Hypersonic Flight Research Experimentation HIFiRE-5 test geometry at an altitude of 21.8 km. Spatial linear BiGlobal modal instability analysis of this flow has been performed at selected streamwise locations on planes normal to the cone symmetry axis, resolving the entire flow domain in a coupled manner while exploiting flow symmetries. Four amplified classes of linear eigenmodes have been unravelled. The shear layer formed near the cone minor-axis centreline gives rise to amplified symmetric and antisymmetric centreline instability modes, classified as shear-layer instabilities. At the attachment line formed along the major axis of the cone, both symmetric and antisymmetric instabilities are also discovered and identified as boundary-layer second Mack modes. In both cases of centreline and attachment-line modes, symmetric instabilities are found to be more unstable than their antisymmetric counterparts. Furthermore, spatial BiGlobal analysis is used for the first time to resolve oblique second modes and cross-flow instabilities in the boundary layer between the major- and minor-axis meridians. Contrary to predictions for the incompressible regime for swept infinite wing flow, the cross-flow instabilities are not found to be linked to the attachment-line instabilities. In fact, cross-flow modes peak along most of the surface of the cone, but vanish towards the attachment line. On the other hand, the leading oblique second modes peak near the leading edge and their associated frequencies are in the range of the attachment-line instability frequencies. Consequently, the attachment-line instabilities are observed to be related to oblique second modes at the major-axis meridian. The linear amplification of centreline and attachment-line instability modes is found to be strong enough to lead to laminar–turbulent flow transition within the length of the test object. The predictions of global linear theory are compared with those of local instability analysis, also performed here under the assumption of locally parallel flow, where use of this assumption is permissible. Fair agreement is obtained for symmetric centreline and symmetric attachment-line modes, while for all other classes of linear disturbances use of the proposed global analysis methodology is warranted for accurate linear instability predictions.
Linear global instability of non-orthogonal incompressible swept attachment-line boundary-layer flow
- José Miguel Pérez, Daniel Rodríguez, Vassilis Theofilis
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- Journal:
- Journal of Fluid Mechanics / Volume 710 / 10 November 2012
- Published online by Cambridge University Press:
- 23 August 2012, pp. 131-153
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Flow instability in the non-orthogonal swept attachment-line boundary layer is addressed in a linear analysis framework via solution of the pertinent global (BiGlobal) partial differential equation (PDE)-based eigenvalue problem. Subsequently, a simple extension of the extended Görtler–Hämmerlin ordinary differential equation (ODE)-based polynomial model proposed by Theofilis et al. (2003) for orthogonal flow, which includes previous models as special cases and recovers global instability analysis results, is presented for non-orthogonal flow. Direct numerical simulations have been used to verify the analysis results and unravel the limits of validity of the basic flow model analysed. The effect of the angle of attack, , on the critical conditions of the non-orthogonal problem has been documented; an increase of the angle of attack, from (orthogonal flow) up to values close to which make the assumptions under which the basic flow is derived questionable, is found to systematically destabilize the flow. The critical conditions of non-orthogonal flows at are shown to be recoverable from those of orthogonal flow, via a simple algebraic transformation involving .