9 results
A data-driven approach to guide supersonic impinging jet control
- Spencer L. Stahl, Datta V. Gaitonde
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- Journal:
- Journal of Fluid Mechanics / Volume 978 / 10 January 2024
- Published online by Cambridge University Press:
- 27 December 2023, R2
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A data-driven framework using snapshots of an uncontrolled flow is proposed to identify, and subsequently demonstrate, effective control strategies for different objectives in supersonic impinging jets. The open-loop, feed-forward control approach, based on a dynamic mode decomposition reduced-order model (DMD-ROM), computes forcing receptivity in an economical manner by projecting flow and actuator-specific forcing snapshots onto a reduced subspace and then evolving the dynamics forwards in time. Since it effectively determines a linear response around the unsteady flow in the time domain, the method differs materially from typical techniques that use steady basic states, such as stability or input–output approaches that employ linearized Navier–Stokes operators in the frequency domain. The method presented naturally accounts for factors inherent to the snapshot basis, including configuration complexity and flow parameters such as Reynolds number. Furthermore, gain metrics calculated in the reduced subspace facilitate rapid assessments of flow sensitivities to a wide range of forcing parameters, from which optimal actuator inputs may be selected and results confirmed in scale-resolved simulations or experiments. The DMD-ROM approach is demonstrated from two different perspectives. The first concerns asymptotic feedback resonance, where the effects of harmonic pressure forcing are estimated and verified with nonlinear simulations using a blowing–suction actuator. The second examines time-local behaviour within critical feedback events, where the phase of actuation becomes important. For this, a conditional space–time mode is used to identify the optimal forcing phase that minimizes convective instability growth within the resonance cycle.
A robust physics-based method to filter coherent wavepackets from high-speed schlieren images
- Chitrarth Prasad, Datta V. Gaitonde
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- Journal:
- Journal of Fluid Mechanics / Volume 940 / 10 June 2022
- Published online by Cambridge University Press:
- 05 April 2022, R1
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A complete understanding of jet dynamics is greatly enabled by the accurate separation of acoustically efficient wavepackets from their higher-energy convecting turbulent counterparts. Momentum potential theory (MPT) has proven highly effective in filtering the desired acoustic component irrespective of operating conditions or nozzle complexity. However, MPT is a data-intensive method predicated on the knowledge of fluctuation quantities in the entire flow field; as such, it has to date been applied only to numerically obtained data. This work develops an approach to extend its application to extract coherent wavepacket data from high-speed schlieren images. Pixel intensities from the schlieren image are mapped to a scaled surrogate for the line-of-sight integrated density gradient. The linear relation between the irrotational scalar MPT potential and time derivatives of density fluctuations is then exploited to perform the filtering. The effectiveness of the procedure is demonstrated using experimental as well as numerical schlieren images representing a wide range of imperfectly expanded free and impinging jet configurations. When combined with spectral proper orthogonal decomposition (SPOD), the method yields modes that accurately capture (i) the Mach wave radiation from a military-style jet, (ii) the mode shapes of the feedback tones in an impinging jet and (iii) the screech signature in twin rectangular jets, without recourse to user adjusted parameters. This technique can greatly enhance the use of high-speed diagnostics for real-time monitoring of the near-field acoustic content for potential feedback control. Additionally, the general nature of the approach allows a straightforward application to other flows, such as cavity and airfoil flow-acoustic interactions.
Lagrangian approach for modal analysis of fluid flows
- Vilas J. Shinde, Datta V. Gaitonde
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- Journal:
- Journal of Fluid Mechanics / Volume 928 / 10 December 2021
- Published online by Cambridge University Press:
- 15 October 2021, A35
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Common modal decomposition techniques for flow-field analysis, data-driven modelling and flow control, such as proper orthogonal decomposition and dynamic mode decomposition, are usually performed in an Eulerian (fixed) frame of reference with snapshots from measurements or evolution equations. The Eulerian description poses some difficulties, however, when the domain or the mesh deforms with time as, for example, in fluid–structure interactions. For such cases, we first formulate a Lagrangian modal analysis (LMA) ansatz by a posteriori transforming the Eulerian flow fields into Lagrangian flow maps through an orientation and measure-preserving domain diffeomorphism. The development is then verified for Lagrangian variants of proper orthogonal decomposition and dynamic mode decomposition using direct numerical simulations of two canonical flow configurations at Mach 0.5, i.e. the lid-driven cavity and flow past a cylinder, representing internal and external flows, respectively, at pre- and post-bifurcation Reynolds numbers. The LMA is demonstrated for several situations encompassing unsteady flow without and with boundary and mesh deformation as well as non-uniform base flows that are steady in Eulerian but not in Lagrangian frames. We show that application of LMA to steady non-uniform base flow yields insights into flow stability and post-bifurcation dynamics. LMA naturally leads to Lagrangian coherent flow structures and connections with finite-time Lyapunov exponents. We examine the mathematical link between finite-time Lyapunov exponents and LMA by considering a double-gyre flow pattern. Dynamically important flow features in the Lagrangian sense are recovered by performing LMA with forward and backward (adjoint) time procedures.
Instabilities and transition in cooled wall hypersonic boundary layers
- S. Unnikrishnan, Datta V. Gaitonde
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- Journal:
- Journal of Fluid Mechanics / Volume 915 / 25 May 2021
- Published online by Cambridge University Press:
- 11 March 2021, A26
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Wall cooling has substantial qualitative and quantitative effects on the development of instabilities and subsequent transition processes in hypersonic boundary layers (HBLs). A sequence of linear stability theory, nonlinear two-dimensional and three-dimensional direct numerical simulations is used to analyse Mach 6 boundary layers, with wall temperatures ranging from near-adiabatic to highly cooled conditions, where the second-mode instability is accompanied by radiation of energy. Decomposition of linear stability modes into their fluid-thermodynamic (acoustic, vortical and thermal) components shows that this radiation comprises both acoustic as well as vortical waves. Furthermore, in these cases, two-dimensional simulations show that the conventional ‘trapped’ nature of second-mode instability is ruptured. A quantitative analysis indicates that although the energy efflux of both acoustic and vortical components increases with wall cooling, the destabilization effect is much stronger and no significant abatement of pressure perturbations is realized. The direct impact of these mechanisms on the transition process itself is examined with high-fidelity simulations of three-dimensional second-mode wavepacket propagation. In the near-adiabatic HBL, the wavepacket remains trapped within the boundary layer and attenuates outside the region of linear instability. However, wavepackets in the cooled wall HBLs amplify and display nonlinear distortion, and transition more rapidly. The structure of the wavepacket also displays different behaviour; moderately cooled walls show bifurcation into a leading turbulent head region and a trailing harmonic region, while highly cooled wall cases display lower convection speeds and significant wavepacket elongation, with intermittent spurts of turbulence in the wake of the head region. This elongation effect is associated with a weakening of the lateral jet mechanism due to the breakdown of spanwise coherent structures. These features have a direct impact on wall loading, including skin friction and heat transfer. In moderately cooled walls, the spatially localized wall loading is similar to those in near-adiabatic walls, with dominant impact due to coherent structures in the leading turbulent head region. In highly cooled walls, the elongated near-wall streaks in the wake region of the wavepacket result in more than twice as large levels of skin friction and heat transfer over a sustained period of time.
Linear, nonlinear and transitional regimes of second-mode instability
- S. Unnikrishnan, Datta V. Gaitonde
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- Journal:
- Journal of Fluid Mechanics / Volume 905 / 25 December 2020
- Published online by Cambridge University Press:
- 28 October 2020, A25
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The evolution of the potent second-mode instability in hypersonic boundary layers (HBLs) is examined holistically, by tracking its linear and nonlinear evolution, followed by its role in initiating transition and eventual breakdown of the HBL into a fully turbulent state. Linear stability theory is utilized to first identify the features of the second-mode wave after $FS$-synchronization. These are then employed in separate linearly and nonlinearly forced two-dimensional (2-D) and three-dimensional (3-D) direct numerical simulations (DNS). The nonlinear 2-D DNS shows saturation of the fundamental frequency, and the resulting superharmonics induce tightly braided ‘rope-like’ patterns near the generalized inflection point (GIP). The instability exhibits a second region of growth constituted by the fundamental frequency downstream of the primary envelope, which is absent in the linear scenario. Subsequent fully 3-D DNS identify this region as crucial in amplifying oblique instabilities riding on the 2-D second-mode ‘rollers’. This results in lambda vortices below the GIP, which are detached from the rollers in the inner boundary layer. Streamwise vortex-stretching results in a localized peak in length scales inside the HBL, eventually forming hairpin vortices. Spectral analyses track the transformation of harmonic peaks into a turbulent spectrum. The appearance of oblique modes at the fundamental frequency suggests that fundamental resonance is the most dominant mechanism of transition. The bispectrum reveals coupled nonlinear interactions between the fundamental and its superharmonics leading to spectral broadening, as well as traces of subharmonic resonance. The global forms of the fundamental and subharmonic modes show that the former disintegrate at the location of spanwise breakdown, beyond which the latter amplify. Statistical analyses of the near-wall flow field indicate an increase in large-scale ‘splatting’ motions immediately following transition, resulting in extreme skin-friction events, which equilibrate as turbulence sets in. Fundamental resonance results in complete breakdown of streamwise streaks in the lower log-layer, ultimately resulting in a fully turbulent HBL.
Dynamics of strong swept-shock/turbulent-boundary-layer interactions
- Michael C. Adler, Datta V. Gaitonde
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- Journal:
- Journal of Fluid Mechanics / Volume 896 / 10 August 2020
- Published online by Cambridge University Press:
- 08 June 2020, A29
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The mechanisms of unsteadiness in nominally two-dimensional (2-D) shock/turbulent-boundary-layer interactions (STBLIs) cannot be directly extended to three-dimensional (3-D) STBLIs, because of differences in interaction structure; swept 3-D interactions, including the sharp-fin and swept-compression-ramp configurations, are of particular interest in this work. Complications arise from the observation that the separation length employed to scale low-frequency unsteadiness in 2-D (spanwise homogeneous) interactions is not a global property of 3-D (swept) interactions, due to the quasi-conical symmetry of the latter. Also, flow separation in 3-D interactions is topologically different, in that closure of the primary separation cannot occur without breaking the quasi-conical symmetry of the interaction – consequently, the unsteady properties of the separation are different. To address these points, large-eddy simulations are performed to assess unsteadiness in 3-D interactions, with the aim of understanding key differences relative to analogous 2-D interactions, the former of which have received less attention in the literature. The mechanism underlying the prominent band of low-frequency unsteadiness (two decades below the characteristic boundary-layer frequency) is shown to be significantly muted in swept interactions. An interesting scaling for the band of mid-frequency unsteadiness is uncovered (at least one decade below the characteristic boundary-layer frequency). This is a consequence of the observed connection between coherent fluctuations in the separated shear layer and local mean-flow gradients, indicating a mix between competing 2-D and 3-D free-interaction scaling laws. In contrast, high-frequency fluctuations largely retain the 2-D scaling introduced by the incoming turbulent boundary layer. The spatial structure of the mid-frequency coherence in 3-D STBLIs is isolated, revealing the significant influence of these convective coherent structures on shock rippling/corrugation, as well as a spanwise dependence of coherence size consistent with the 3-D mean-flow similarity scaling. Finally, the dynamic linear response of a representative 3-D interaction is compared to that of a representative 2-D interaction; the absolute instability present in the 2-D interaction is not present in the 3-D interaction. The coincident absence of both the absolute instability and associated band of low-frequency unsteadiness in 3-D STBLIs underscores the significance of this absolute instability in facilitating low-frequency unsteadiness in 2-D interactions.
Interactions between vortical, acoustic and thermal components during hypersonic transition
- S. Unnikrishnan, Datta V. Gaitonde
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- Journal:
- Journal of Fluid Mechanics / Volume 868 / 10 June 2019
- Published online by Cambridge University Press:
- 16 April 2019, pp. 611-647
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Discrete unstable modes of hypersonic laminar boundary layers, obtained from an eigenvalue analysis, provide insight into key transition scenarios. The character of such modes near the leading edge is often identified with the corresponding asymptotic free-stream behaviour of acoustic, vortical or entropic (thermal) content, which we designate fluid-thermodynamic (FT) components. In downstream regions, however, this direct one-to-one correspondence between discrete modes and FT components does not hold, since FT components interact in well-defined ways with the basic state and with each other (even under linear scenarios). In the present work, we perform an FT decomposition of discrete modes using momentum potential theory, to yield a physics-based analysis that complements linear stability theory in the linear regime, and seamlessly extends to the nonlinear domain where direct numerical simulations are appropriate. Linear and nonlinear saturated disturbance effects, different forcing types and wall thermal conditions are considered, with emphasis on phenomena occurring near stability-mode synchronization locations. The results show that, in the linear regime, each discrete mode contains all FT components, whose relative amplitudes vary with streamwise distance. Vortical components are always the largest, followed by thermal and acoustic components. These latter two show distinct fore and aft signatures near mode synchronization. The vortical component displays a series of rope-shaped recirculation-cell patterns across the generalized inflection point. However, both acoustic and thermal components display ‘trapped’ structures. The former contains an alternating monopole array between the wall and the critical layer, while the latter is confined to an undulating region between the wall and a wavy locus straddling the generalized inflection point. Nonlinear saturation in the region of Mack-mode growth further strengthens the rope-shaped structures in the vortical component and higher harmonics appear, whose form and location depend on the specific component. Wall cooling modifies the eigenfunctions such that the acoustic component accounts for more of its composition, consistent with its destabilization. Analysis of energy interactions among the FT components indicates that, even though the vorticity component is the largest, the thermal component induces the most significant source term for the growth of acoustic perturbations, possibly due to the trapped nature of both.
Dynamic linear response of a shock/turbulent-boundary-layer interaction using constrained perturbations
- Michael C. Adler, Datta V. Gaitonde
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- Journal:
- Journal of Fluid Mechanics / Volume 840 / 10 April 2018
- Published online by Cambridge University Press:
- 12 February 2018, pp. 291-341
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Comprehensive experimental and computational investigations have revealed possible mechanisms underlying low-frequency unsteadiness observed in spanwise homogeneous shock-wave/turbulent-boundary-layer interactions (STBLI). In the present work, we extend this understanding by examining the dynamic linear response of a moderately separated Mach 2.3 STBLI to small perturbations. The statistically stationary linear response is analysed to identify potential time-local and time-mean linear tendencies present in the unsteady base flow: these provide insight into the selective amplification properties of the flow at various points in the limit cycle, as well as asymmetry and restoring mechanisms in the dynamics of the separation bubble. The numerical technique uses the synchronized large-eddy simulation method, previously developed for free shear flows, significantly extended to include a linear constraint necessary for wall-bounded flows. The results demonstrate that the STBLI fosters a global absolute linear instability corresponding to a time-mean linear tendency for upstream shock motion. The absolute instability is maintained through constructive feedback of perturbations through the recirculation: it is self-sustaining and insensitive to external forcing. The dynamics are characterized for key frequency bands corresponding to high–mid-frequency Kelvin–Helmholtz shedding along the separated shear layer $(St_{L}\sim 0.5)$, low–mid-frequency oscillations of the separation bubble $(St_{L}\sim 0.1)$ and low-frequency large-scale bubble breathing and shock motion $(St_{L}\sim 0.03)$, where the Strouhal number is based on the nominal length of the separation bubble, $L$: $St_{L}=fL/U_{\infty }$. A band-pass filtering decomposition isolates the dynamic flow features and linear responses associated with these mechanisms. For example, in the low-frequency band, extreme shock displacements are shown to correlate with time-local linear tendencies toward more moderate displacements, indicating a restoring mechanism in the linear dynamics. However, a disparity between the linearly stable shock position and the mean shock position leads to an observed asymmetry in the low-frequency shock motion cycle, in which upstream motion occurs more rapidly than downstream motion. This is explained through competing linear and nonlinear (mass depletion through shedding) mechanisms and discussed in the context of an oscillator model. The analysis successfully illustrates how time-local linear dynamics sustain several key unsteady broadband flow features in a causal manner.
Acoustic, hydrodynamic and thermal modes in a supersonic cold jet
- S. Unnikrishnan, Datta V. Gaitonde
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- Journal:
- Journal of Fluid Mechanics / Volume 800 / 10 August 2016
- Published online by Cambridge University Press:
- 07 July 2016, pp. 387-432
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Large-eddy simulation data for a Mach 1.3 round jet are decomposed into acoustic, hydrodynamic and thermal components using Doak’s momentum potential theory. The decomposed fields are then analysed to examine the properties of each mode and their dynamics based on the transport equation for the total fluctuating enthalpy. The solenoidal fluctuations highlight hydrodynamic components of the jet and capture the shear layer growth and breakdown process. The acoustic mode exhibits a jittering coherent wavepacket structure in the turbulent region and consequent highly directional downstream radiation. The expected radial decay rates, $r^{-6}$ for hydrodynamic and $r^{-2}$ for acoustic, are recovered and closely follow the universal radiation spectra in the sideline and downstream directions. The scalogram of the acoustic mode in the near-acoustic-field region is consistent with that of the pressure perturbation signal in the acoustic-frequency range, but effectively removes the hydrodynamic and thermal content. The time-resolved and mean behaviour of terms in the total fluctuating enthalpy equation is analysed in detail. A large-scale intermittent event in the near-acoustic field is shown to be associated with an intrusion of vortices from the shear layer into the core of the jet. Acoustic sources are created when the resulting negative fluctuations in the solenoidal component interact with positive fluctuations in the Coriolis acceleration term. The latter are associated with regions of high vorticity on the inner side of the shear layer. In contrast, sinks result from the interaction of solenoidal momentum fluctuations with positive entropy gradients along entrainment streaks.