7 results
Reynolds number effects in shock-wave/turbulent boundary-layer interactions
- L. Laguarda, S. Hickel, F.F.J. Schrijer, B.W. van Oudheusden
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- Journal:
- Journal of Fluid Mechanics / Volume 989 / 25 June 2024
- Published online by Cambridge University Press:
- 29 July 2024, A20
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We investigate Reynolds number effects in strong shock-wave/turbulent boundary-layer interactions (STBLI) by leveraging a new database of wall-resolved and long-integrated large-eddy simulations. The database encompasses STBLI with massive boundary-layer separation at Mach $2.0$, impinging-shock angle $40^{\circ }$ and friction Reynolds numbers ${\textit {Re}}_\tau$ $355$, $1226$ and $5118$. Our analysis shows that the shape of the reverse-flow bubble is notably different at low and high Reynolds number, while the mean-flow separation length, separation-shock angle and incipient plateau pressure are rather insensitive to Reynolds number variations. Velocity statistics reveal a shift in the peak location of the streamwise Reynolds stress from the separation-shock foot to the core of the detached shear layer at high Reynolds number, which we attribute to increased pressure transport in the separation-shock excursion domain. Additionally, in the high Reynolds case, the separation shock originates deep within the turbulent boundary, resulting in intensified wall-pressure fluctuations and spanwise variations associated with the passage of coherent velocity structures. Temporal spectra of various signals show energetic low-frequency content in all cases, along with a distinct peak in the bubble-volume spectra at a separation-length-based Strouhal number $St_{L_{sep}}\approx 0.1$. The separation shock is also found to lag behind bubble-volume variations, consistent with the acoustic propagation time from reattachment to separation and a downstream mechanism driving the shock motion. Finally, dynamic mode decomposition of three-dimensional fields suggests a Reynolds-independent statistical link among separation-shock excursions, velocity streaks and large-scale vortices at low frequencies.
Direct numerical simulation of interaction between a stationary crossflow instability and forward-facing steps
- J. Casacuberta, S. Hickel, S. Westerbeek, M. Kotsonis
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- Journal:
- Journal of Fluid Mechanics / Volume 943 / 25 July 2022
- Published online by Cambridge University Press:
- 20 June 2022, A46
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The interaction between forward-facing steps of several heights and a pre-existing critical stationary crossflow instability of a swept-wing boundary layer is analysed. Direct numerical simulations (DNS) are performed of the incompressible three-dimensional laminar base flow and the stationary distorted flow that arise from the interaction between an imposed primary stationary crossflow perturbation and the steps. These DNS are complemented with solutions of the linear and the nonlinear parabolised stability equations, used towards identifying the influence of linearity and non-parallelism near the step. A fully stationary solution of the Navier–Stokes equations is enforced numerically, in order to isolate the mechanisms pertaining to the interaction of the stationary disturbance with the step. Results provide insight into the salient modifications of the base laminar boundary layer due to the step, and the response of the incoming crossflow instability to these changes. The fundamental spanwise Fourier mode of the disturbance field gradually lifts up as it approaches the step and passes over it. The flow environment around the step is characterised by a sudden spanwise modulation of the base-flow streamlines. Additional stationary perturbation structures are induced at the step, which manifest in the form of spanwise-aligned velocity streaks near the wall. Shortly downstream of the step, the fundamental component of the crossflow perturbation maintains a rather constant amplification for the smallest steps studied. For the largest step, however, the fundamental crossflow perturbation is stabilised significantly shortly downstream of the largest step. This surprising result is ascribed to a modulation of the kinetic energy transfer between the base flow and the fundamental perturbation field, which is brought forward as a new step interaction mechanism. Possible non-modal growth effects at the step are discussed. Furthermore, the results from DNS indicate significant amplification of the high-order harmonic crossflow components downstream of the step.
Dynamics of unsteady asymmetric shock interactions
- L. Laguarda, S. Hickel, F. F. J. Schrijer, B. W. van Oudheusden
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- Journal:
- Journal of Fluid Mechanics / Volume 888 / 10 April 2020
- Published online by Cambridge University Press:
- 10 February 2020, A18
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The response of asymmetric and planar shock interactions to a continuous excitation of the lower incident shock is investigated numerically. Incident shock waves and centred expansion fans are generated by two wedges asymmetrically deflecting the inviscid free stream flow at Mach 3. The excitations mechanisms considered are (i) pitching of the lower wedge traversing the steady-state dual-solution domain (DSD) of regular interaction (RI) and Mach interaction (MI), (ii) a periodic (sinusoidal) oscillation of the lower wedge deflection with a mean value both within and outside of the steady-state DSD and (iii) a periodic (sinusoidal) streamwise oscillation of the lower wedge location with fixed wedge deflection. A detailed analysis of characteristic unsteady flow features, including the Mach stem growth, pressure evolution across the shock system and corresponding flow deflections and entropy rise, is presented with a focus on the bi-directional RI$\rightleftarrows$MI transition process. For fast pitching conditions, the MI pattern is maintained far inside the steady-state RI domain. The observed $\text{MI}\rightarrow \text{RI}$ transition limit as the rotational velocity decreases does not fully match steady-state theory, however. This is attributed to geometry-related effects. In the opposite case, $\text{RI}\rightarrow \text{MI}$ transition, good agreement with steady-state theoretical predictions is obtained for slow rotations, and a shock polar analysis applied in the (moving) frame of reference of the shock interaction location improves the agreement with fast pitching numerical data significantly. Furthermore, the MI pattern is found to be more robust against periodic perturbations than the corresponding RI configuration for mean flow conditions inside the steady-state DSD, which appears to be a consequence of the dynamics of the Mach stem during a period of excitation. This is not the case for mean flow conditions outside the steady-state DSD in the RI domain for which a periodic $\text{RI}\rightarrow \text{MI}\rightarrow \text{RI}$ alternation occurs instead.
Rossby-number effects on columnar eddy formation and the energy dissipation law in homogeneous rotating turbulence
- T. Pestana, S. Hickel
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- Journal:
- Journal of Fluid Mechanics / Volume 885 / 25 February 2020
- Published online by Cambridge University Press:
- 18 December 2019, A7
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Two aspects of homogeneous rotating turbulence are quantified through forced direct numerical simulations in an elongated domain, which, in the direction of rotation, is approximately 340 times larger than the typical initial eddy size. First, by following the time evolution of the integral length scale along the axis of rotation $\ell _{\Vert }$, the growth rate of the columnar eddies and its dependence on the Rossby number $Ro_{\unicode[STIX]{x1D700}}$ is determined as $\unicode[STIX]{x1D6FE}=3.90\exp (-16.72\,Ro_{\unicode[STIX]{x1D700}})$ for $0.06\leqslant Ro_{\unicode[STIX]{x1D700}}\leqslant 0.31$, where $\unicode[STIX]{x1D6FE}$ is the non-dimensional growth rate. Second, a scaling law for the energy dissipation rate $\unicode[STIX]{x1D700}_{\unicode[STIX]{x1D708}}$ is sought. Comparison with current available scaling laws shows that the relation proposed by Baqui & Davidson (Phys. Fluids, vol. 27(2), 2015, 025107), i.e. $\unicode[STIX]{x1D700}_{\unicode[STIX]{x1D708}}\sim {u^{\prime }}^{3}/\ell _{\Vert }$, where $u^{\prime }$ is the root-mean-square velocity, approximates well part of our data, more specifically the range $0.39\leqslant Ro_{\unicode[STIX]{x1D700}}\leqslant 1.54$. However, relations proposed in the literature fail to model the data for the second and most interesting range, i.e. $0.06\leqslant Ro_{\unicode[STIX]{x1D700}}\leqslant 0.31$, which is marked by the formation of columnar eddies. To find a similarity relation for the latter, we exploit the concept of a spectral transfer time introduced by Kraichnan (Phys. Fluids, vol. 8(7), 1965, p. 1385). Within this framework, the energy dissipation rate is considered to depend on both the nonlinear time scale and the relaxation time scale. Thus, by analysing our data, expressions for these different time scales are obtained that result in $\unicode[STIX]{x1D700}_{\unicode[STIX]{x1D708}}\sim (u^{\prime 4}Ro_{\unicode[STIX]{x1D700}}^{0.62}\unicode[STIX]{x1D70F}_{nl}^{iso})/\ell _{\bot }^{2}$, where $\ell _{\bot }$ is the integral length scale in the direction normal to the axis of rotation and $\unicode[STIX]{x1D70F}_{nl}^{iso}$ is the nonlinear time scale of the initial homogeneous isotropic field.
On the Richtmyer–Meshkov instability evolving from a deterministic multimode planar interface
- V. K. Tritschler, B. J. Olson, S. K. Lele, S. Hickel, X. Y. Hu, N. A. Adams
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- Journal:
- Journal of Fluid Mechanics / Volume 755 / 25 September 2014
- Published online by Cambridge University Press:
- 19 August 2014, pp. 429-462
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We investigate the shock-induced turbulent mixing between a light and a heavy gas, where a Richtmyer–Meshkov instability (RMI) is initiated by a shock wave with Mach number $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}\mathit{Ma}= 1.5$. The prescribed initial conditions define a deterministic multimode interface perturbation between the gases, which can be imposed exactly for different simulation codes and resolutions to allow for quantitative comparison. Well-resolved large-eddy simulations are performed using two different and independently developed numerical methods with the objective of assessing turbulence structures, prediction uncertainties and convergence behaviour. The two numerical methods differ fundamentally with respect to the employed subgrid-scale regularisation, each representing state-of-the-art approaches to RMI. Unlike previous studies, the focus of the present investigation is to quantify the uncertainties introduced by the numerical method, as there is strong evidence that subgrid-scale regularisation and truncation errors may have a significant effect on the linear and nonlinear stages of the RMI evolution. Fourier diagnostics reveal that the larger energy-containing scales converge rapidly with increasing mesh resolution and thus are in excellent agreement for the two numerical methods. Spectra of gradient-dependent quantities, such as enstrophy and scalar dissipation rate, show stronger dependences on the small-scale flow field structures as a consequence of truncation error effects, which for one numerical method are dominantly dissipative and for the other dominantly dispersive. Additionally, the study reveals details of various stages of RMI, as the flow transitions from large-scale nonlinear entrainment to fully developed turbulent mixing. The growth rates of the mixing zone widths as obtained by the two numerical methods are ${\sim } t^{7/12}$ before re-shock and ${\sim } (t-t_0)^{2/7}$ long after re-shock. The decay rate of turbulence kinetic energy is consistently ${\sim } (t-t_0)^{-10/7}$ at late times, where the molecular mixing fraction approaches an asymptotic limit $\varTheta \approx 0.85$. The anisotropy measure $\langle a \rangle _{xyz}$ approaches an asymptotic limit of ${\approx }0.04$, implying that no full recovery of isotropy within the mixing zone is obtained, even after re-shock. Spectra of density, turbulence kinetic energy, scalar dissipation rate and enstrophy are presented and show excellent agreement for the resolved scales. The probability density function of the heavy-gas mass fraction and vorticity reveal that the light–heavy gas composition within the mixing zone is accurately predicted, whereas it is more difficult to capture the long-term behaviour of the vorticity.
Direct numerical simulation of a breaking inertia–gravity wave
- S. Remmler, M. D. Fruman, S. Hickel
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- Journal:
- Journal of Fluid Mechanics / Volume 722 / 10 May 2013
- Published online by Cambridge University Press:
- 28 March 2013, pp. 424-436
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We have performed fully resolved three-dimensional numerical simulations of a statically unstable monochromatic inertia–gravity wave using the Boussinesq equations on an $f$-plane with constant stratification. The chosen parameters represent a gravity wave with almost vertical direction of propagation and a wavelength of 3 km breaking in the middle atmosphere. We initialized the simulation with a statically unstable gravity wave perturbed by its leading transverse normal mode and the leading instability modes of the time-dependent wave breaking in a two-dimensional space. The wave was simulated for approximately 16 h, which is twice the wave period. After the first breaking triggered by the imposed perturbation, two secondary breaking events are observed. Similarities and differences between the three-dimensional and previous two-dimensional solutions of the problem and effects of domain size and initial perturbations are discussed.
6 - Approximate Deconvolution
- from SECTION B - CAPTURING PHYSICS WITH NUMERICS
- Edited by Fernando F. Grinstein, Len G. Margolin, Los Alamos National Laboratory, William J. Rider, Los Alamos National Laboratory
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- Book:
- Implicit Large Eddy Simulation
- Published online:
- 08 January 2010
- Print publication:
- 30 July 2007, pp 222-242
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Summary
Introduction
In this chapter we make a connection between the filtering approach (Leonard 1974) and the averaged-equation approach (Schumann 1975) to large eddy simulation (LES). With the averaged-equation approach, the discrete system for evolving a grid-function approximation of the continuous solution is considered directly as a truncated representation of the continuous system. With the filtering approach, a continuous filtered system is considered as an approximation; the numerical error in solving this continuous system is considered to be negligibly small. The filtering approach provides an analytic framework for deriving LES equations and commonly is employed as a basis for the development of functional and structural models (Sagaut 2005) and Chapter 3 of this book. In practice, models derived on the basis of the filtering approach were plagued by the problem that the numerical error in most cases was nonnegligible. The effect of discretizing the filtered continuous equations on the subgrid-scale (SGS) force was analyzed in detail for the first time by Ghosal (1996). It was revealed that, over a large wave-number range, the truncation error of commonly employed nonspectral discretizations can be as large as the SGS stress, if not larger.
During the attempt of improving eddy-viscosity-based models, it was revealed that the correlation of predicted SGS stresses with the exact SGS stresses is much less than unity. This fact is reviewed by Meneveau and Katz (2000) on the basis of experimental data. A much larger correlation is achieved by the scale-similarity model (Bardina, Ferziger, and Reynolds 1983), which does, however, underpredict SGS dissipation.