Effects of the Reynolds number on a scale-similarity model of Lagrangian velocity correlations in isotropic turbulent flows

This paper provides a discussion of several aspects of the construction of approaches that combine statistical (Reynolds-averaged Navier–Stokes, RANS) models with large eddy simulation (LES), with the objective of making LES an economically viable method for predicting complex, high Reynolds number turbulent flows. The first part provides a review of alternative approaches, highlighting their rationale and major elements. Next, two particular methods are introduced in greater detail: one based on coupling near-wall RANS models to the outer LES domain on a single contiguous mesh, and the other involving the application of the RANS and LES procedures on separate zones, the former confined to a thin near-wall layer. Examples for their performance are included for channel flow and, in the case of the zonal strategy, for three separated flows. Finally, a discussion of prospects is given, as viewed from the writer's perspective.

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A note on von Kármán's constant in low Reynolds number turbulent flows

Journal of Fluid Mechanics ◽

10.1017/s0022112072000035 ◽

1972 ◽

Vol 53 (01) ◽

pp. 45 ◽

Cited By ~ 79

Author(s):

G. David Huffman ◽

Peter Bradshaw

Keyword(s):

Reynolds Number ◽

Turbulent Flows ◽

Low Reynolds Number ◽

Low Reynolds

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Parameter Extension Simulation of Turbulent Flows in a Compressor Cascade With a High Reynolds Number

Volume 2C: Turbomachinery ◽

10.1115/gt2020-14809 ◽

2020 ◽

Author(s):

Yan Jin

Keyword(s):

Reynolds Number ◽

Turbulent Flow ◽

Turbulent Flows ◽

Stokes Equations ◽

Simulation Method ◽

Potential Method ◽

Navier Stokes ◽

Reference Solution ◽

Compressor Cascade ◽

High Reynolds

Abstract The turbulent flow in a compressor cascade is calculated by using a new simulation method, i.e., parameter extension simulation (PES). It is defined as the calculation of a turbulent flow with the help of a reference solution. A special large-eddy simulation (LES) method is developed to calculate the reference solution for PES. Then, the reference solution is extended to approximate the exact solution for the Navier-Stokes equations. The Richardson extrapolation is used to estimate the model error. The compressor cascade is made of NACA0065-009 airfoils. The Reynolds number 3.82 × 105 and the attack angles −2° to 7° are accounted for in the study. The effects of the end-walls, attack angle, and tripping bands on the flow are analyzed. The PES results are compared with the experimental data as well as the LES results using the Smagorinsky, k-equation and WALE subgrid models. The numerical results show that the PES requires a lower mesh resolution than the other LES methods. The details of the flow field including the laminar-turbulence transition can be directly captured from the PES results without introducing any additional model. These characteristics make the PES a potential method for simulating flows in turbomachinery with high Reynolds numbers.

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The structure of internal intermittency in turbulent flows at large Reynolds number: experiments on scale similarity

Journal of Fluid Mechanics ◽

10.1017/s0022112073001692 ◽

1973 ◽

Vol 59 (3) ◽

pp. 537-559 ◽

Cited By ~ 7

Author(s):

C. W. Van Atta ◽

T. T. Yeh

Keyword(s):

Reynolds Number ◽

Probability Density ◽

Streamwise Velocity ◽

Statistical Characteristics ◽

Large Reynolds Number ◽

Higher Moments ◽

Scale Similarity ◽

Probability Densities ◽

Scale Ratio ◽

Velocity Derivative

Some of the statistical characteristics of the breakdown coefficient, defined as the ratio of averages over different spatial regions of positive variables characterizing the fine structure and internal intermittency in high Reynolds number turbulence, have been investigated using experimental data for the streamwise velocity derivative ∂u/∂tmeasured in an atmospheric boundary layer. The assumptions and predictions of the hypothesis of scale similarity developed by Novikov and by Gurvich & Yaglom do not adequately describe or predict the statistical characteristics of the breakdown coefficientqr,lof the square of the streamwise velocity derivative. Systematic variations in the measured probability densities and consistent variations in the measured moments show that the assumption that the probability density of the breakdown coefficient is a function only of the scale ratio is not satisfied. The small positive correlation between adjoint values ofqr,land measurements of higher moments indicate that the assumption that the probability densities for adjoint values ofqr,lare statistically independent is also not satisfied. The moments ofqr,ldo not have the simple power-law character that is a consequence of scale similarity.As the scale ratiol/rchanges, the probability density ofqr,levolves from a sharply peaked, highly negatively skewed density for large values of the scale ratio to a very symmetrical distribution when the scale ratio is equal to two, and then to a highly positively skewed density as the scale ratio approaches one. There is a considerable effect of heterogeneity on the values of the higher moments, and a small but measurable effect on the mean value. The moments are roughly symmetrical functions of the displacement of the shorter segment from the centre of the larger one, with a minimum value when the shorter segment is centrally located within the larger one.

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Direct numerical simulation of turbulent channel flow up to

Journal of Fluid Mechanics ◽

10.1017/jfm.2015.268 ◽

2015 ◽

Vol 774 ◽

pp. 395-415 ◽

Cited By ~ 420

Author(s):

Myoungkyu Lee ◽

Robert D. Moser

Keyword(s):

Numerical Simulation ◽

Reynolds Number ◽

Direct Numerical Simulation ◽

Turbulent Flows ◽

Channel Flow ◽

Turbulent Channel Flow ◽

Streamwise Velocity ◽

Mean Velocity ◽

Layer Structures ◽

High Reynolds

A direct numerical simulation of incompressible channel flow at a friction Reynolds number ($\mathit{Re}_{{\it\tau}}$) of 5186 has been performed, and the flow exhibits a number of the characteristics of high-Reynolds-number wall-bounded turbulent flows. For example, a region where the mean velocity has a logarithmic variation is observed, with von Kármán constant ${\it\kappa}=0.384\pm 0.004$. There is also a logarithmic dependence of the variance of the spanwise velocity component, though not the streamwise component. A distinct separation of scales exists between the large outer-layer structures and small inner-layer structures. At intermediate distances from the wall, the one-dimensional spectrum of the streamwise velocity fluctuation in both the streamwise and spanwise directions exhibits $k^{-1}$ dependence over a short range in wavenumber $(k)$. Further, consistent with previous experimental observations, when these spectra are multiplied by $k$ (premultiplied spectra), they have a bimodal structure with local peaks located at wavenumbers on either side of the $k^{-1}$ range.

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Turbulent kinetic energy production and flow structures in flows past smooth and rough walls

Journal of Fluid Mechanics ◽

10.1017/jfm.2019.96 ◽

2019 ◽

Vol 866 ◽

pp. 897-928 ◽

Cited By ~ 2

Author(s):

P. Orlandi

Keyword(s):

Reynolds Number ◽

Kinetic Energy ◽

Turbulent Kinetic Energy ◽

Turbulent Flows ◽

Energy Production ◽

Compressive Strain ◽

Turnover Time ◽

Flow Structures ◽

Wall Region ◽

Rate Of Dissipation

Data available in the literature from direct numerical simulations of two-dimensional turbulent channels by Lee & Moser (J. Fluid Mech., vol. 774, 2015, pp. 395–415), Bernardini et al. (J. Fluid Mech., 742, 2014, pp. 171–191), Yamamoto & Tsuji (Phys. Rev. Fluids, vol. 3, 2018, 012062) and Orlandi et al. (J. Fluid Mech., 770, 2015, pp. 424–441) in a large range of Reynolds number have been used to find that $S^{\ast }$ the ratio between the eddy turnover time ($q^{2}/\unicode[STIX]{x1D716}$, with $q^{2}$ being twice the turbulent kinetic energy and $\unicode[STIX]{x1D716}$ the isotropic rate of dissipation) and the time scale of the mean deformation ($1/S$), scales very well with the Reynolds number in the wall region. The good scaling is due to the eddy turnover time, although the turbulent kinetic energy and the rate of isotropic dissipation show a Reynolds dependence near the wall; $S^{\ast }$, as well as $-\langle Q\rangle =\langle s_{ij}s_{ji}\rangle -\langle \unicode[STIX]{x1D714}_{i}\unicode[STIX]{x1D714}_{i}/2\rangle$ are linked to the flow structures, and also the latter quantity presents a good scaling near the wall. It has been found that the maximum of turbulent kinetic energy production $P_{k}$ occurs in the layer with $-\langle Q\rangle \approx 0$, that is, where the unstable sheet-like structures roll-up to become rods. The decomposition of $P_{k}$ in the contribution of elongational and compressive strain demonstrates that the two contributions present a good scaling. However, the good scaling holds when the wall and the outer structures are separated. The same statistics have been evaluated by direct simulations of turbulent flows in the presence of different types of corrugations on both walls. The flow physics in the layer near the plane of the crests is strongly linked to the shape of the surface and it has been demonstrated that the $u_{2}$ (normal to the wall) fluctuations are responsible for the modification of the flow structures, for the increase of the resistance and of the turbulent kinetic energy production.

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