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Journal ArticleDOI

The influence of near-wall density and viscosity gradients on turbulence in channel flows

TL;DR: In this paper, the influence of nearwall density and viscosity gradients on near-wall turbulence in a channel is studied by means of Direct Numerical Simulation (DNS) of the low-Mach number approximation of the Navier-Stokes equations.
Abstract: The influence of near-wall density and viscosity gradients on near-wall turbulence in a channel are studied by means of Direct Numerical Simulation (DNS) of the low-Mach number approximation of the Navier--Stokes equations. Different constitutive relations for density and viscosity as a function of temperature are used in order to mimic a wide range of fluid behaviours and to develop a generalised framework for studying turbulence modulations in variable property flows. Instead of scaling the velocity solely based on local density, as done for the van Driest transformation, we derive an extension of the scaling that is based on gradients of the semi-local Reynolds number $Re_\tau^*$. This extension of the van Driest transformation is able to collapse velocity profiles for flows with near-wall property gradients as a function of the semi-local wall coordinate. However, flow quantities like mixing length, turbulence anisotropy and turbulent vorticity fluctuations do not show a universal scaling very close to the wall. This is attributed to turbulence modulations, which play a crucial role on the evolution of turbulent structures and turbulence energy transfer. We therefore investigate the characteristics of streamwise velocity streaks and quasi-streamwise vortices and found that, similar to turbulent statistics, the turbulent structures are also strongly governed by $Re_\tau^*$ profiles and that their dependence on individual density and viscosity profiles is minor. Flows with near-wall gradients in $Re_\tau^*$ ($d {Re_\tau^*}/dy eq 0$) showed significant changes in the inclination and tilting angles of quasi-streamwise vortices. These structural changes are responsible for the observed modulation of the Reynolds stress generation mechanism and the inter-component energy transfer in flows with strong near-wall $Re_\tau^*$ gradients.
Citations
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Journal Article
TL;DR: In this paper, a series of Mach-number invariant scalings for compressible turbulent boundary layers (CTBLs) is derived, leading to a viscosity weighted transformation for the mean-velocity profile.
Abstract: A series of Mach-number- (M) invariant scalings is derived for compressible turbulent boundary layers (CTBLs), leading to a viscosity weighted transformation for the mean-velocity profile that is superior to van Driest transformation. The theory is validated by direct numerical simulation of spatially developing CTBLs with M up to 6. A boundary layer edge is introduced to compare different M flows and is shown to better present the M-invariant multilayer structure of CTBLs. The new scalings derived from the kinetic energy balance substantiate Morkovin's hypothesis and promise accurate prediction of the mean profiles of CTBLs.

35 citations

Journal ArticleDOI
TL;DR: In this article , the effects of Mach number and wall temperature on the statistics of wall shear stress, pressure, and heat flux fluctuations in compressible wall-bounded turbulence were investigated.
Abstract: This two-part study investigates the effects of Mach number and wall temperature on the statistics of wall shear stress, pressure, and heat flux fluctuations in compressible wall-bounded turbulence. In the first part, we focus on their one-point statistics, including the root mean square (r.m.s.), skewness factor (third-order moment), flatness factor (fourth-order moment), and their correlations. By exploiting the direct numerical simulation databases, we found that the r.m.s. of the streamwise wall shear stress and pressure, the skewness factor of all the flow quantities considered, and the flatness factor of streamwise wall shear stress monotonically vary with the friction Mach number ([Formula: see text]), while for the rest, the wall heat flux and global temperature parameters should be taken into account as well for a monotonic trend of variation. The correlation coefficients between wall shear stress, pressure, and heat flux fluctuations increase with the Mach number [Formula: see text], suggesting the underlying interactions between dynamic and thermodynamic processes. The distributions of spectra and probability density functions indicate that the increased correlation is induced by the highly intermittent traveling wave packets among the streaky structures, as reflected by the “double-peak” feature of the spectra that gradually emerges with the increasing compressibility effects. The probability density distribution also manifests the alteration of the occurrence of extreme events caused by these structures. By accordingly decomposing the fluctuations with cutoff filtering, it is found that the root mean squares of streamwise wall shear stress and heat flux fluctuations related to the streaky structures are Mach number-independent, while those related to the traveling wave packets monotonically increase with the friction Mach number.

7 citations

DOI
TL;DR: In this paper , the authors assess several popular velocity transformations for non-canonical compressible wall-bounded turbulent boundary layers through their application to several types of boundary layers, including high-enthalpy boundary layers with dissociation and vibrational excitation.
Abstract: While several velocity transformations for compressible zero-pressure-gradient (ZPG) boundary layers have been proposed in the past decades, their performance for non-canonical compressible wall-bounded turbulent flows has not been systematically investigated. This work assesses several popular transformationsfor the velocity profile through their application to several types of non-canonical compressible wall-bounded turbulent flows. Specifically, this work explores DNS databases of high-enthalpy boundary layers with dissociation and vibrational excitation, supercritical channel and boundary-layer flows, and adiabatic boundary layers with pressure gradients. The transformationsconsidered include the van Driest [Van Driest, J. Aero-naut. Sci., 18(1951):145-216], Zhang et al. [Zhang et al., Phys. Rev. Lett., 109(2012):054502], Trettel-Larsson [Trettel and Larsson, Phys. Fluids, 28(2016):026102], data-driven [Volpiani et al., Phys. Rev. Fluids, 5(2020):052602], and total-stress-based [Griffin et al., Proc. Natl. Acad. Sci. U.S.A., 118(2021):e2111144118] transformations. The Trettel-Larsson transformation collapses velocity profiles of high-enthalpy temporal boundary layers but not the spatial boundary layers considered. For supercritical channel flows, the Trettel-Larsson transformation also performs well over Nevertheless, the present assessment provides a useful guideline on the deployment of these transformations on various non-canonical flows.

6 citations

Journal ArticleDOI
TL;DR: In this article , a span-wise wall motion is induced to reduce turbulence intensity and hence friction drag in compressible supersonic flow by means of direct numerical simulation, and the results show that the higher Mach number cases show a larger net power saving compared to the incompressible ones.
Abstract: Active turbulence control has been pursued continuously for the last decades, striving for an altered, energetically more favorable flow. In this article, our focus is on a promising method inducing a spanwise wall movement in order to reduce turbulence intensity and hence friction drag, investigated by means of direct numerical simulation. This approach transforms a previously time dependent oscillatory wall motion into a static spatial modulation with prescribed wavelength in the streamwise direction [48]. Most procedures related to turbulence control including the present one have been overwhelmingly applied to incompressible flow. This work is different and novel to the effect, that this control method is applied to compressible, supersonic channel flow up to a bulk Mach number of Ma=3 . Due to substantial variations of viscosity, density, and temperature within the near‐wall region in supersonic flow, the impact of the control method is altered compared to solenoidal flow conditions. By creating a data set of different Mach‐/Reynolds numbers and control parameters, knowledge is gained in which way the effectiveness of oscillatory techniques and physical mechanisms change under the influence of compressibility. It is shown that the control method is able to effectively reduce turbulence levels and lead to large drag reduction levels in compressible supersonic flow. Variable property effects even enhance this behavior for the whole set of investigated parameters. Overall, the higher Mach number cases show a larger net power saving compared to the incompressible ones. Furthermore, we observe an increase of the optimum wavelength with increasing Mach number, which helps in guiding optimal implementations of such a control method.

3 citations

Journal ArticleDOI
27 Oct 2022
TL;DR: In this article , a machine learning methodology was proposed to improve the predictions of traditional RANS turbulence models in channel flows subject to strong variations in their thermophysical properties, and the proposed neural network architecture is characterized by the use of an initial layer of logarithmic neurons followed by hyperbolic tangent neurons.
Abstract: This paper presents a machine learning methodology to improve the predictions of traditional RANS turbulence models in channel flows subject to strong variations in their thermophysical properties. The developed formulation contains several improvements over the existing Field Inversion Machine Learning (FIML) frameworks described in the literature. We first showcase the use of efficient optimization routines to automatize the process of field inversion in the context of CFD, combined with the use of symbolic algebra solvers to generate sparse-efficient algebraic formulas to comply with the discrete adjoint method. The proposed neural network architecture is characterized by the use of an initial layer of logarithmic neurons followed by hyperbolic tangent neurons, which proves numerically stable. The machine learning predictions are then corrected using a novel weighted relaxation factor methodology, that recovers valuable information from otherwise spurious predictions. Additionally, we introduce L2 regularization to mitigate over-fitting and to reduce the importance of non-essential features. In order to analyze the results of our deep learning system, we utilize the K-fold cross-validation technique, which is beneficial for small datasets. The results show that the machine learning model acts as an excellent non-linear interpolator for DNS cases well-represented in the training set. In the most successful case, the L-infinity modeling error on the velocity profile was reduced from 23.4% to 4.0%. It is concluded that the developed machine learning methodology corresponds to a valid alternative to improve RANS turbulence models in flows with strong variations in their thermophysical properties without introducing prior modeling assumptions into the system.

3 citations

References
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Journal ArticleDOI
TL;DR: In this article, the authors present finite-difference schemes for the evaluation of first-order, second-order and higher-order derivatives yield improved representation of a range of scales and may be used on nonuniform meshes.

5,832 citations

Journal ArticleDOI
TL;DR: In this article, the authors describe the formation of low-speed streaks in the region very near the wall, which interact with the outer portions of the flow through a process of gradual lift-up, then sudden oscillation, bursting, and ejection.
Abstract: Extensive visual and quantitative studies of turbulent boundary layers are described. Visual studies reveal the presence of surprisingly well-organized spatially and temporally dependent motions within the so-called ‘laminar sublayer’. These motions lead to the formation of low-speed streaks in the region very near the wall. The streaks interact with the outer portions of the flow through a process of gradual ‘lift-up’, then sudden oscillation, bursting, and ejection. It is felt that these processes play a dominant role in the production of new turbulence and the transport of turbulence within the boundary layer on smooth walls.Quantitative data are presented providing an association of the observed structure features with the accepted ‘regions’ of the boundary layer in non-dimensional co-ordinates; these data include zero, negative and positive pressure gradients on smooth walls. Instantaneous spanwise velocity profiles for the inner layers are given, and dimensionless correlations for mean streak-spacing and break-up frequency are presented.Tentative mechanisms for formation and break-up of the low-speed streaks are proposed, and other evidence regarding the implications and importance of the streak structure in turbulent boundary layers is reviewed.

2,753 citations

Journal ArticleDOI
TL;DR: In this paper, numerical simulations of fully developed turbulent channel flow at three Reynolds numbers up to Reτ=590 were reported, and it was noted that the higher Reynolds number simulations exhibit fewer low Reynolds number effects than previous simulations at Reτ = 180.
Abstract: Numerical simulations of fully developed turbulent channel flow at three Reynolds numbers up to Reτ=590 are reported. It is noted that the higher Reynolds number simulations exhibit fewer low Reynolds number effects than previous simulations at Reτ=180. A comprehensive set of statistics gathered from the simulations is available on the web at http://www.tam.uiuc.edu/Faculty/Moser/channel.

2,618 citations

Journal ArticleDOI
TL;DR: In this paper, the role of coherent structures in the production and dissipation of turbulence in a boundary layer is characterized, summarizing the results of recent investigations, and diagrams and graphs are provided.
Abstract: The role of coherent structures in the production and dissipation of turbulence in a boundary layer is characterized, summarizing the results of recent investigations. Coherent motion is defined as a three-dimensional region of flow where at least one fundamental variable exhibits significant correlation with itself or with another variable over a space or time range significantly larger than the smallest local scales of the flow. Sections are then devoted to flow-visualization experiments, statistical analyses, numerical simulation techniques, the history of coherent-structure studies, vortices and vortical structures, conceptual models, and predictive models. Diagrams and graphs are provided.

2,518 citations

Journal ArticleDOI
TL;DR: In this article, the evolution of a single hairpin vortex-like structure in the mean turbulent field of a low-Reynolds-number channel flow is studied by direct numerical simulation, and the detailed mechanisms for this upstream process are determined, and they are generally similar to the mechanisms proposed by Smith et al. (1991), with some notable differences in the details.
Abstract: The evolution of a single hairpin vortex-like structure in the mean turbulent field of a low-Reynolds-number channel flow is studied by direct numerical simulation. The structure of the initial three-dimensional vortex is extracted from the two-point spatial correlation of the velocity field by linear stochastic estimation given a second-quadrant ejection event vector. Initial vortices having vorticity that is weak relative to the mean vorticity evolve gradually into omega-shaped vortices that persist for long times and decay slowly. As reported in Zhou, Adrian & Balachandar (1996), initial vortices that exceed a threshold strength relative to the mean flow generate new hairpin vortices upstream of the primary vortex. The detailed mechanisms for this upstream process are determined, and they are generally similar to the mechanisms proposed by Smith et al. (1991), with some notable differences in the details. It has also been found that new hairpins generate downstream of the primary hairpin, thereby forming, together with the upstream hairpins, a coherent packet of hairpins that propagate coherently. This is consistent with the experimental observations of Meinhart & Adrian (1995). The possibility of autogeneration above a critical threshold implies that hairpin vortices in fully turbulent fields may occur singly, but they more often occur in packets. The hairpins also generate quasi-streamwise vortices to the side of the primary hairpin legs. This mechanism bears many similarities to the mechanisms found by Brooke & Hanratty (1993) and Bernard, Thomas & Handler (1993). It provides a means by which new quasi-streamwise vortices, and, subsequently, new hairpin vortices can populate the near-wall layer.

1,994 citations