Search

Turbulent concentric coaxial pipe flows are numerically investigated as canonical problem addressing spanwise curvature effects on heat and momentum transfer that are encountered in various engineering applications. It is demonstrated that the wall-adapting local eddy-viscosity (WALE) model within a large-eddy simulation (LES) framework, without model parameter recalibration, has limited predictive capabilities as signalized by poor representation of wall curvature effects and notable grid dependence. The identified lack in the modeling of radial transport processes is therefore addressed here by utilizing a stochastic one-dimensional turbulence (ODT) model. A standalone ODT formulation for cylindrical geometry is used in order to asses to which extent the predictability can be expected to improve by utilizing an advanced wall-modeling modeling strategy. It is shown that ODT is capable of capturing spanwise curvature and finite Reynolds number effects for fixed adjustable ODT model parameters. Based on the analogy of heat and mass transfer, present results yield new opportunities for modeling turbulent transfer process in chemical, process, and thermal engineering., Comment: In: New Results in Numerical and Experimental Fluid Mechanics XIV -- Contributions to the 23rd STAB/DGLR Symposium Berlin, Germany, 2022, edited by Andreas Dillmann, Gerd Heller, Ewald Kr\"amer, Claus Wagner, and Julien Weiss

Accurate and economical modeling of near-surface transport processes is a standing challenge for various engineering and atmospheric boundary-layer flows. In this paper, we address this challenge by utilizing a stochastic one-dimensional turbulence (ODT) model. ODT aims to resolve all relevant scales of a turbulent flow for a one-dimensional domain. Here ODT is applied to turbulent channel flow as stand-alone tool. The ODT domain is a wall-normal line that is aligned with the mean shear. The free model parameters are calibrated once for the turbulent velocity boundary layer at a fixed Reynolds number. After that, we use ODT to investigate the Schmidt ($Sc$), Reynolds ($Re$), and Peclet ($Pe$) number dependence of the scalar boundary-layer structure, turbulent fluctuations, transient surface fluxes, mixing, and transfer to a wall. We demonstrate that the model is able to resolve relevant wall-normal transport processes across the turbulent boundary layer and that it captures state-space statistics of the surface scalar-flux fluctuations. In addition, we show that the predicted mean scalar transfer, which is quantified by the Sherwood ($Sh$) number, self-consistently reproduces established scaling regimes and asymptotic relations. For high asymptotic $Sc$ and $Re$, ODT results fall between the Dittus--Boelter, $Sh\sim Re^{4/5}\,Sc^{2/5}$, and Colburn, $Sh\sim Re^{4/5}\,Sc^{1/3}$, scalings but they are closer to the former. For finite $Sc$ and $Re$, the model prediction reproduces the relation proposed by Schwertfirm and Manhart (Int. J. Heat Fluid Flow, vol. 28, pp. 1204-1214, 2007) that yields locally steeper effective scalings than any of the established asymptotic relations. The model extrapolates the scalar transfer to small asymptotic $Sc\ll Re_\tau^{-1}$ (diffusive limit) with a functional form that has not been previously described., Comment: Accepted manuscript. 30 pages, 13 figures. Version-of-record available online 11/30/2021 at URL: https://www.sciencedirect.com/science/article/pii/S0142727X21001193

Passive scalars in turbulent channel flows are investigated as canonical problem for heat and mass transfer in turbulent boundary-layer flows. The one-dimensional turbulence model is used to numerically investigate the Schmidt and Reynolds number dependence of the scalar transfer to a wall due to fluctuating wall-normal transport. First, the model is calibrated for low-order velocity statistics. After that, we keep the model parameters fixed and investigate low-order passive scalar statistics for a relevant Schmidt and Reynolds number range. We show that the model consistently predicts the boundary layer structure and the scaling regimes, for which it is close to asymptotic one-dimensional theory., Comment: 8 pages, 5 figures, preprint

Noise prediction requires the resolution of relevant acoustic sources on all scales of a turbulent flow. High-resolution direct numerical and large-eddy simulation would be ideal but both are usually too costly despite developments in high performance computing. Lower-order modeling approaches are therefore of general interest. A crucial but standing problem for accurate predictive modeling is the estimation of missing noise from the modeled scales. In this paper we address this problem by presenting a novel lower-order framework that couples the one-dimensional turbulence model to the Ffowcs-Williams and Hawkings approach for prediction of the far-field noise of a subsonic turbulent round jet., Comment: 4 pages, 3 figures

The Rayleigh number $Ra$ dependence of the Nusselt number $Nu$ in turbulent Rayleigh--B\'enard convection is numerically investigated for a moderate and low Prandtl number, $Pr=0.7$ and $0.021$, respectively. Here we specifically address the case of a Boussinesq fluid in a planar configuration with smooth horizontal walls and notionally infinite aspect ratio. Numerical simulations up to $Ra=10^{16}$ for $Pr=0.7$ and up to $Ra=8\times10^{13}$ for $Pr=0.021$ are made feasible on state-of-the-art workstations by utilising the stochastic one-dimensional turbulence (ODT) model. The ODT model parameters were estimated once for two combinations $(Pr,Ra)$ in the classical regime and kept fixed afterwards in order to address the predictive capabilities of the model. The ODT results presented exhibit various effective Nusselt number scalings $Nu\propto Ra^b$. The exponent changes from $b\approx1/3$ to $b\approx1/2$ when the $Ra$ number increases beyond the critical value $Ra_*\simeq6\times10^{14}$ ($Pr=0.7$) and $Ra_*\simeq6\times10^{11}$ ($Pr=0.021$), respectively. This is consistent with the literature. Furthermore, our results suggest that the transition to the ultimate regime is correlated with a relative enhancement of the temperature-velocity cross-correlations in the bulk of the fluid as hypothesised by Kraichnan, R. H., Phys. Fluids, 5, 1374 (1962)., Comment: Preprint

Small-scale effects of turbulent mixing are numerically investigated by applying the map-based, stochastic, one-dimensional turbulence (ODT) model to confined planar jets. The model validation is carried out for the momentum transport by comparing ODT results to available reference data for the bulk Reynolds numbers $Re=20\,000$ and $40\,000$. Various pointwise statistical quantities are computed and compared to the available reference data. We show that these quantities can be captured well, or at least to a reasonable extent, by the stand-alone model formulation and for fixed model parameters. Only the root-mean-square velocity fluctuations remain systematically underestimated in the ODT results (by an approximate factor of $1.5$). Afterwards, the turbulent transport of a passive scalar is addressed for the Schmidt numbers $Sc=1$ and $1250$. For the high Schmidt number and in contrast to the velocity fluctuations, it is shown that the scalar fluctuation variance is up to ten times larger in the ODT simulations resolving the Batchelor scale. The fluctuation variance is notably smaller for the lower Schmidt number, but exhibits better agreement with the references at a nominally higher Schmidt number. We suggest that this is due to implicit filtering in the references, which barely resolve the Kolmogorov scale. ODT turbulence spectra support this interpretation since a Batchelor-like scalar turbulence spectrum is only observed for the higher Schmidt number. With the aid of these spectra and the fluctuation statistics we conclude that implicit filtering has a similar effect as a reduction of the Schmidt number., Comment: Accepted by Chemical Engineering Science

In this paper we overcome a key problem in an otherwise highly potential approach to study turbulent flows, ODTLES (One-Dimensional Turbulence Large Eddy Simulation). From a methodological point of view, ODTLES is an approach in between Direct Numerical Simulations (DNS) and averaged/filtered approaches like RANS (Reynolds Averaged Navier-Stokes) or LES (Large Eddy Simulations). In ODTLES, a set of 1D ODT models is embedded in a coarse grained 3D LES. On the ODT scale, the turbulent advection is modeled as a sequence of stochastic eddy events, also known as triplet maps, while the other (deterministic) terms are fully resolved in space (along the ODT- line) and time. Schmidt et al. first (2008) introduced ODTLES and Gonzalez et al. (2011) applied the model for a variety of wall-bounded flow problems. Although the results were notable for a first proof of concept, the numerical methods used are subject to debate. First of all, an unstable discretization for the large scale 3D advective terms was used as shown by Glawe (2013). The scheme can be stabilized by reducing the CFL number for the explicitly discretized LES terms to the order of the small scale ODT time step, but this of course reduces the advantage of the ODTLES multi-scale approach. The stochastic ODT eddies were also allowed to overlap two LES cells introducing an artificial smoothing (stabilizing) effect. Glawe (2013) limited the overlap consistently to one LES cell and used a stable Runge Kutta (RK) discretization, however maintaining the low CFL number problem. In this paper we adapt a new implicit/explicit (IMEX) time scheme to ODTLES in order to remedy the small CFL number issue.

In turbulence research and flow applications, turbulence models like RaNS (Reynolds averaged Navier-Stokes) models and LES (Large Eddy Simulation) are used. Both models filter the governing flow equations. Thus a scale separation approach is introduced for modeling purposes with the large scales simulated using a numerical scheme while smaller scales are assumed to be less important and might be modeled more or less easily. Unfortunately small scales are frequently of big importance, e.g. in reactive flows, wall bounded flows, or flows with significant Prandtl or Schmidt number effects. Recent alternatives to these standard models are the class of models based on the one-dimensional turbulence (ODT) idea, like ODTLES. The ability of ODT to capture highly turbulent flows (recently up to $Re_\tau = 6\times 10^5$) allows ODTLES to realize 3D resolutions basically independent of the turbulent intensity. In two papers we provide a formal theory and application of an innovative modeling strategy for highly turbulent flows in domains of moderate complexity: In part I (see Glawe et al. (2015)) a new general filtering approach, called XLES (extended LES), is introduced. Contrary to LES, XLES is based on 2D filtering of the governing equations, whereby additional small scale terms are interpreted numerically. In this work a new ansatz for the ODTLES model is introduced as one special approach in the XLES family of models by incorporating the ODT model into XLES. The ODT model introduces microstructures not captured by the XLES filtered equations. To illustrate the ODTLES model capabilities, turbulent channel and duct flows up to friction Reynolds number $Re_\tau = 10000$ are studied.

Direct numerical simulation (DNS), mostly used in fundamental turbulence research, is limited to low turbulent intensities due the current and future computer resources. Standard turbulence models, like RaNS (Reynolds averaged Navier-Stokes) and LES (Large Eddy Simulation), are applied to flows in engineering, but they miss small scale effects, which are frequently of importance, see e.g. the whole area of reactive flows, flows with apparent Prandtl or Schmidt number effects, or even wall bounded flows. A recent alternative to these standard approaches is the one-dimensional turbulence (ODT) model, which is limited to 1D sub-domains. In two papers we will provide a generalized filter strategy, called XLES (extended LES), including a formal theory (part I) and one special approach in the XLES family of models, called ODTLES (in part II (see Glawe et al. (2015))). ODTLES uses an ODT sub-grid model to describe all turbulent scales not represented by XLES, which leaves the larger scales to be simulated in 3D. This allows a turbulence modeling approach with a 3D resolution mainly independent of the turbulent intensity. Thus ODTLES is able to compute highly turbulent flows in domains of moderate complexity affordably and including the full range of turbulent and diffusive scales. The convergence of XLES to DNS is shown and the unconventional XLES advection approach is investigated in basic numerical tests. In part II, highly turbulent channel and duct flow results are discussed and show the future potential of XLES and ODTLES.