Showing papers by "Parviz Moin published in 2020"

Shock-induced heating and transition to turbulence in a hypersonic boundary layer

Abstract: The interaction between an incident shock wave and a Mach-6 undisturbed hypersonic laminar boundary layer over a cold wall is addressed using direct numerical simulations (DNS) and wall-modeled large-eddy simulations (WMLES) at different angles of incidence. At sufficiently high shock-incidence angles, the boundary layer transitions to turbulence via breakdown of near-wall streaks shortly downstream of the shock impingement, without the need of any inflow free-stream disturbances. The transition causes a localized significant increase in the Stanton number and skin-friction coefficient, with high incidence angles augmenting the peak thermomechanical loads in an approximately linear way. Statistical analyses of the boundary layer downstream of the interaction for each case are provided that quantify streamwise spatial variations of the Reynolds analogy factors and indicate a breakdown of the Morkovin's hypothesis near the wall, where velocity and temperature become correlated. A modified strong Reynolds analogy with a fixed turbulent Prandtl number is observed to perform best. Conventional transformations fail at collapsing the mean velocity profiles on the incompressible log law. The WMLES prompts transition and peak heating, delays separation, and advances reattachment, thereby shortening the separation bubble. When the shock leads to transition, WMLES provides predictions of DNS peak thermomechanical loads within $\pm 10\%$ at a computational cost lower than DNS by two orders of magnitude. Downstream of the interaction, in the turbulent boundary layer, WMLES agrees well with DNS results for the Reynolds analogy factor, the mean profiles of velocity and temperature, including the temperature peak, and the temperature/velocity correlation.

Non-equilibrium three-dimensional boundary layers at moderate Reynolds numbers

Abstract: Non-equilibrium wall turbulence with mean-flow three-dimensionality is ubiquitous in geophysical and engineering flows. Under these conditions, turbulence may experience a counter-intuitive depletion of the turbulent stresses, which has important implications for modelling and control. Yet, current turbulence theories have been established mainly for statistically two-dimensional equilibrium flows and are unable to predict the reduction in the Reynolds stress magnitude. In the present work, we propose a multiscale model that captures the response of non-equilibrium wall-bounded turbulence under the imposition of three-dimensional strain. The analysis is performed via direct numerical simulation of transient three-dimensional turbulent channels subjected to a sudden lateral pressure gradient at friction Reynolds numbers up to 1000. We show that the flow regimes and scaling properties of the Reynolds stress are consistent with a model comprising momentum-carrying eddies with sizes and time scales proportional to their distance to the wall. We further demonstrate that the reduction in Reynolds stress follows a spatially and temporally self-similar evolution caused by the relative horizontal displacement between the core of the momentum-carrying eddies and the flow layer underneath. Inspection of the flow energetics reveals that this mechanism is associated with lower levels of pressure–strain correlation, which ultimately inhibits the generation of Reynolds stress, consistent with previous works. Finally, we assess the ability of the state-of-the-art wall-modelled large-eddy simulation to predict non-equilibrium three-dimensional flows.

Turbophoresis of small inertial particles: theoretical considerations and application to wall-modelled large-eddy simulations

Abstract: In wall-bounded turbulent flows, the wall-normal gradient in turbulence intensity causes inertial particles to move preferentially toward the wall, leading to elevated concentration levels in the viscous sublayer. At first glance, wall-modelled large-eddy simulations may seem ill suited for accurately simulating this behaviour, given that the sharp gradients and coherent structures in the viscous sublayer and buffer region are unresolved in this approach. In this paper, a detailed inspection of conservation equations describing the influence of turbophoresis and near-wall structures on particle concentration profiles reveals a more nuanced view depending on the friction Stokes number. The dynamics of low and moderate Stokes number particles indeed depends strongly on the complex spatio-temporal details of streaks, ejections, and sweeps in the near-wall region. This significantly impacts the near-wall particle concentration through a biased sampling effect which provides a net force away from the wall on the particle ensemble caused by the tendency of inertial particles to accumulate in low-speed ejection regions. At higher Stokes numbers, however, this biased sampling is of minimal importance, and the particle concentration becomes inversely proportional to the wall-normal particle velocity variance at a given distance from the wall. As a result, wall-modelled large-eddy simulations can predict concentration profiles with more accuracy in the high Stokes number regime than low Stokes numbers simply by modifying the interpolation scheme for particles between the first grid point and the boundary. However, accurate representation of low and moderate Stokes number particles depends critically on information not present in standard wall-modelled large-eddy simulations.

The turbulent bubble break-up cascade. Part 2. Numerical simulations of breaking waves

Abstract: Breaking waves generate a distribution of bubble sizes that evolves over time. Knowledge of how this distribution evolves is of practical importance for maritime and climate studies. The analytical framework developed in Part 1 examined how this evolution is governed by the bubble-mass flux from large to small bubble sizes, which depends on the rate of break-up events and the distribution of child bubble sizes. These statistics are measured in Part 2 as ensemble-averaged functions of time by simulating ensembles of breaking waves, and identifying and tracking individual bubbles and their break-up events. The break-up dynamics are seen to be statistically unsteady, and two intervals with distinct characteristics were identified. In the first interval, the dissipation rate and bubble-mass flux are quasi-steady, and the theoretical analysis of Part 1 is supported by all observed statistics, including the expected -10/3 power-law exponent for the super-Hinze-scale size distribution. Strong locality is observed in the corresponding bubble-mass flux, supporting the presence of a super-Hinze-scale break-up cascade. In the second interval, the dissipation rate decays, and the bubble-mass flux increases as small- and intermediate-sized bubbles become more populous. This flux remains strongly local with cascade-like behaviour, but the dominant power-law exponent for the size distribution increases to -8/3 as small bubbles are also depleted more quickly. This suggests the emergence of different physical mechanisms during different phases of the breaking-wave evolution, although size-local break-up remains a dominant theme. Parts 1 and 2 present an analytical toolkit for population balance analysis in two-phase flows.

The turbulent bubble break-up cascade. Part 1. Theoretical developments

Abstract: Breaking waves entrain gas beneath the surface. The wave-breaking process energizes turbulent fluctuations that break bubbles in quick succession to generate a wide range of bubble sizes. Understanding this generation mechanism paves the way towards the development of predictive models for large-scale maritime and climate simulations. Garrett et al. (2000) suggested that super-Hinze-scale turbulent breakup transfers entrained gas from large to small bubble sizes in the manner of a cascade. We provide a theoretical basis for this bubble-mass cascade by appealing to how energy is transferred from large to small scales in the energy cascade central to single-phase turbulence theories. A bubble break-up cascade requires that break-up events predominantly transfer bubble mass from a certain bubble size to a slightly smaller size on average. This property is called locality. In this paper, we analytically quantify locality by extending the population balance equation in conservative form to derive the bubble-mass transfer rate from large to small sizes. Using our proposed measures of locality, we show that scalings relevant to turbulent bubbly flows, including those postulated by Garrett et al. (2000) and observed in breaking-wave experiments and simulations, are consistent with a strongly local transfer rate, where the influence of non-local contributions decays in a power-law fashion. These theoretical predictions are confirmed using numerical simulations in Part 2, revealing key physical aspects of the bubble break-up cascade phenomenology. Locality supports the universality of turbulent small-bubble break-up, which simplifies the development of subgrid-scale models to predict oceanic small-bubble statistics of practical importance.

Subgrid-scale Capillary Breakup Model for Liquid Jet Atomization

Abstract: A subgrid-scale capillary breakup model has been developed by coupling a Eulerian interface-capturing approach to a Lagrangian point particle method. At the fully resolved scale, the evolution of p...

Laminar to fully turbulent flow in a pipe: Scalar patches, structural duality of turbulent spots and transitional overshoot

Abstract: We present findings on scalar flashes, turbulent spots and transition statistics in a direct numerical simulation of a 500 radius-long pipe flow with a radial-mode inlet disturbance. Transitional spots are found to contain two different types of eddies. The wall region consists primarily of ‘reverse hairpin vortices’. This unusual structure is related to the high-speed streaks arising from the prescribed inlet perturbation. The core region is populated by the normally observed ‘forward’ hairpin vortices. Number density of the reverse hairpins is quantified indirectly and conservatively by measuring the number density of negative skin-friction patches. During the late stages of transition, second-order statistics such as Reynolds stresses and the rate of dissipation of turbulent kinetic energy exhibit substantial overshoot. This is associated with mid-to-high frequency content in the energy spectra that exceeds the corresponding levels in fully developed turbulence. Flow visualizations reveal bursts of small-scale vortex motions, including the reverse hairpins, that probably account for the enhanced mid-to-high frequency spectral content. A passive scalar is injected at the centreline of the inlet plane, mimicking laboratory injection of dye through a needle, to investigate the mysterious phenomenon of turbulent scalar patches residing in fully developed turbulent pipe flow. At several hundred radii downstream of transition where the velocity field is genuine fully developed turbulence, the scalar patches retain persistent memory of events far upstream. Comparing the present flow with a similar pipe flow disturbed by a significantly different inlet condition suggests that the foregoing observations are insensitive to the form of the disturbances.

Heat transfer in three-dimensional intersecting shock-wave/turbulent boundary-layer interactions with wall-modeled large-eddy simulations

Abstract: The accurate prediction of aerothermal surface loading is of paramount importance for the design of high speed flight vehicles. In this work, we consider the numerical solution of hypersonic flow over a double-finned geometry, representative of the inlet of an air-breathing flight vehicle, characterized by three-dimensional intersecting shock-wave/turbulent boundary-layer interaction at Mach 8.3. High Reynolds numbers ($Re_L \approx 11.6 \times 10^6$ based on free-stream conditions) and the presence of cold walls ($T_w/T_o \approx 0.27$) leading to large near-wall temperature gradients necessitate the use of wall-modeled large-eddy simulation (WMLES) in order to make calculations computationally tractable. The comparison of the WMLES results with experimental measurements shows good agreement in the time-averaged surface heat flux and wall pressure distributions, and the WMLES predictions show reduced errors with respect to the experimental measurements than prior RANS calculations. The favorable comparisons are obtained using an LES wall model based on equilibrium boundary layer approximations despite the presence of numerous non-equilibrium conditions including three dimensionality, shock-boundary layer interactions, and flow separation. Lastly, it is also demonstrated that the use of semi-local eddy viscosity scaling (in lieu of the commonly used van Driest scaling) in the LES wall model is necessary to accurately predict the surface pressure loading and heat fluxes.

On the evolution of the velocity gradient tensor in transitional boundary layers

Abstract: We study the transition to turbulence from the perspective of the velocity gradient tensor dynamics. Our work is motivated by the observation of nonlinear structures emerging during transition, as revealed by vortex identifiers such as the Q-criterion. To that end, we have derived transport equations based on several invariants of the velocity gradient tensor to obtain integral budgets spanning the different stages of transition from laminar to turbulent flow. We have also discussed which quantity would be the most appropriate in our study, while keeping in mind the potential for future modeling applications.

Wall-modeled large-eddy simulation of non-equilibrium turbulent boundary layers

Abstract: We conducted WMLES to examine the performance of a simple and widely used ODE-based equilibrium wall model in a spatially-developing 3D TBL inside a bent square duct (Schwarz and Bradshaw 1994) and 3D separated flows behind a skewed bump (Ching et al. 2018a,b; Ching and Eaton 2019). From the square duct simulation, the mean velocity profiles and crossflow angles in the outer region were predicted with high accuracy for all the considered mesh resolutions. Some disagreement was observed in the crossflow angles in the bend region where the non-equilibrium effect is most significant. Also, the simulation for the wall-mounted skewed bump showed that this simple ODE-based equilibrium wall model along with an adequate grid resolution around the 3D separation point resulted in reasonable predictions of 3D separating and reattaching flows, including mean velocity distributions, separation bubbles, and vortex structures in the bump wake.

General method for determining the boundary layer thickness in nonequilibrium flows

Abstract: While the computation of the boundary-layer thickness is straightforward for canonical equilibrium flows, there are no established definitions for general non-equilibrium flows. In this work, a method is developed based on a local reconstruction of the "inviscid" velocity profile $U_I[y]$ resulting from the application of the Bernoulli equation in the wall-normal direction. The boundary-layer thickness $\delta_{99}$ is then defined as the location where $U/U_I = 0.99$, which is consistent with its classical definition for the zero-pressure-gradient boundary layers (ZPGBLs). The proposed local-reconstruction method is parameter free and can be deployed for both internal and external flows without resorting to an iterative procedure, numerical integration, or numerical differentiation. The superior performance of the local-reconstruction method over various existing methods is demonstrated by applying the methods to laminar and turbulent boundary layers and two flows over airfoils. Numerical experiments reveal that the local-reconstruction method is more accurate and more robust than existing methods, and it is applicable for flows over a wide range of Reynolds numbers.

Requirements and sensitivity analysis of RANS-free wall-modeled LES.

Abstract: We study the sensitivity of wall model input variables to the modeling choices of the outer LES. This work is motivated by sensitivities observed in dynamic slip wall models. These dynamic wall models use variables from the near-wall LES solution as inputs to predict the wall stress without relying on a priori coefficients or equilibrium assumption. Mitigating the sensitivities in the wall model inputs allows development of robust dynamic wall models. The effects of SGS model, boundary condition type, numerics, and mesh topology are assessed through a series of WMLES calculations of turbulent channels. Probability density functions are computed from planes of the WMLES solutions at a wall-normal sampling height and are used as a metric for sensitivity. Sensitivity to SGS model is alleviated when the fraction of total wall stress carried by the SGS model is held constant. Use of hexagonal close-packed grids mitigated numerical sensitivities.

Wall-modeled large-eddy simulation of turbulent boundary layers with mean-flow three-dimensionality

Abstract: We examine the performance of wall-modeled large-eddy simulation (WMLES) to predict turbulent boundary layers (TBLs) with mean-flow three-dimensionality. The analysis is performed for an ordinary-d...