Low Reynolds number k—ε modelling with the aid of direct simulation data

1993 ◽  
Vol 250 ◽  
pp. 509-529 ◽  
Author(s):  
W. Rodi ◽  
N. N. Mansour
Keyword(s):  
Reynolds Number ◽  
Channel Flow ◽  
Eddy Viscosity ◽  
Reynolds Numbers ◽  
Relative Magnitude ◽  
Direct Simulation ◽  
Simulation Data ◽  
Layer Flow ◽  
High Reynolds ◽  
Improved Model

The constant Cμ and the near-wall damping function fμ in the eddy-viscosity relation of the k–ε model are evaluated from direct numerical simulation (DNS) data for developed channel and boundary-layer flow, each at two Reynolds numbers. Various existing fμ model functions are compared with the DNS data, and a new function is fitted to the high-Reynolds-number channel flow data. The ε-budget is computed for the fully developed channel flow. The relative magnitude of the terms in the ε-equation is analysed with the aid of scaling arguments, and the parameter governing this magnitude is established. Models for the sum of all source and sink terms in the ε-equation are tested against the DNS data, and an improved model is proposed.

Turbulent boundary layer statistics at very high Reynolds number

2015 ◽  
Vol 779 ◽  
pp. 371-389 ◽  
Author(s):  
M. Vallikivi ◽  
M. Hultmark ◽  
A. J. Smits
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
High Reynolds Number ◽  
Reynolds Numbers ◽  
Working Fluid ◽  
Mean Velocity ◽  
High Reynolds Numbers ◽  
Layer Flow ◽  
High Reynolds ◽  
Very High

Measurements are presented in zero-pressure-gradient, flat-plate, turbulent boundary layers for Reynolds numbers ranging from $\mathit{Re}_{{\it\tau}}=2600$ to $\mathit{Re}_{{\it\tau}}=72\,500$ ($\mathit{Re}_{{\it\theta}}=8400{-}235\,000$). The wind tunnel facility uses pressurized air as the working fluid, and in combination with MEMS-based sensors to resolve the small scales of motion allows for a unique investigation of boundary layer flow at very high Reynolds numbers. The data include mean velocities, streamwise turbulence variances, and moments up to 10th order. The results are compared to previously reported high Reynolds number pipe flow data. For $\mathit{Re}_{{\it\tau}}\geqslant 20\,000$, both flows display a logarithmic region in the profiles of the mean velocity and all even moments, suggesting the emergence of a universal behaviour in the statistics at these high Reynolds numbers.

scholarly journals Numerical investigations of flow around subsea covers at high Reynolds numbers

2021 ◽  
Vol 1201 (1) ◽  
pp. 012013
Author(s):  
G Yin ◽  
Y Zhang ◽  
M C Ong
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Numerical Simulations ◽  
Layer Thickness ◽  
Boundary Layer Thickness ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
Stream Velocity ◽  
Layer Flow ◽  
High Reynolds

Abstract Two-dimensional (2D) numerical simulations of flow over wall-mounted rectangular and trapezoidal ribs subjected to a turbulent boundary layer flow with the normalized boundary layer thickness of δ/D = 0.73,1.96,2.52 (D is the height of the ribs) have been carried out by using the Reynolds-averaged Navier-Stokes (RANS) equations combined with the k – ω SST (Shear Stress Transport) turbulence model. The angles of the two side slopes of trapezoidal rib varies from 0° to 60°. The Reynolds number based on the free-stream velocity U ∞ and D are 1 × 106 and 2 × 106. The results obtained from the present numerical simulations are in good agreement with the published experimental data. Furthermore, the effects of the angle of the two side slopes of the trapezoidal ribs, the Reynolds number and the boundary layer thickness on the hydrodynamic quantities are discussed.

scholarly journals Comparison of turbulence profiles in high-Reynolds-number turbulent boundary layers and validation of a predictive model

2017 ◽  
Vol 814 ◽  
Author(s):  
J.-P. Laval ◽  
J. C. Vassilicos ◽  
J.-M. Foucaut ◽  
M. Stanislas
Keyword(s):  
Reynolds Number ◽  
High Reynolds Number ◽  
Salt Lake ◽  
Reynolds Numbers ◽  
Turbulent Pipe Flow ◽  
Test Facility ◽  
Flow Data ◽  
Wide Range ◽  
Layer Flow ◽  
High Reynolds

The modified Townsend–Perry attached-eddy model of Vassilicos et al. (J. Fluid Mech., vol. 774, 2015, pp. 324–341) combines the outer peak/plateau behaviour of root-mean-square streamwise turbulence velocity profiles and the Townsend–Perry log decay of these profiles at higher distances from the wall. This model was validated by these authors for high-Reynolds-number turbulent pipe flow data and is shown here to describe equally well, and with approximately the same parameter values, turbulent boundary layer flow data from four different facilities and a wide range of Reynolds numbers. The model has predictive value as, when extrapolated to the extremely high Reynolds numbers of the SLTEST data obtained at the Great Salt Lake Desert atmospheric test facility, it matches these data quite well.

Spectral and hyper eddy viscosity in high-Reynolds-number turbulence

2000 ◽  
Vol 421 ◽  
pp. 307-338 ◽  
Author(s):  
STEFANO CERUTTI ◽  
CHARLES MENEVEAU ◽  
OMAR M. KNIO
Keyword(s):  
Reynolds Number ◽  
Energy Transfer ◽  
Strain Rate ◽  
High Reynolds Number ◽  
Eddy Viscosity ◽  
Isotropic Turbulence ◽  
Reynolds Numbers ◽  
Local Isotropy ◽  
Viscous Term ◽  
High Reynolds

For the purpose of studying the spectral properties of energy transfer between large and small scales in high-Reynolds-number turbulence, we measure the longitudinal subgrid-scale (SGS) dissipation spectrum, defined as the co-spectrum of the SGS stress and filtered strain-rate tensors. An array of four closely spaced X-wire probes enables us to approximate a two-dimensional box filter by averaging over different probe locations (cross-stream filtering) and in time (streamwise filtering using Taylor's hypothesis). We analyse data taken at the centreline of a cylinder wake at Reynolds numbers up to Rλ ∼ 450. Using the assumption of local isotropy, the longitudinal SGS stress and filtered strain-rate co-spectrum is transformed into a radial co-spectrum, which allows us to evaluate the spectral eddy viscosity, v(k, kΔ). In agreement with classical two-point closure predictions, for graded filters, the spectral eddy viscosity deduced from the box-filtered data decreases near the filter wavenumber kΔ. When using a spectral cutoff filter in the streamwise direction (with a box-filter in the cross-stream direction) a cusp behaviour near the filter scale is observed. In physical space, certain features of a wavenumber-dependent eddy viscosity can be approximated by a combination of a regular and a hyper-viscosity term. A hyper-viscous term is also suggested from considering equilibrium between production and SGS dissipation of resolved enstrophy. Assuming local isotropy, the dimensionless coefficient of the hyper-viscous term can be related to the skewness coefficient of filtered velocity gradients. The skewness is measured from the X-wire array and from direct numerical simulation of isotropic turbulence. The results show that the hyper-viscosity coefficient is negative for graded filters and positive for spectral filters. These trends are in agreement with the spectral eddy viscosity measured directly from the SGS stress–strain rate co-spectrum. The results provide significant support, now at high Reynolds numbers, for the ability of classical two-point closures to predict general trends of mean energy transfer in locally isotropic turbulence.

Instabilities in channel flow with system rotation

1989 ◽  
Vol 202 ◽  
pp. 543-557 ◽  
Author(s):  
P. Henrik Alfredsson ◽  
Håkan Persson
Keyword(s):  
Reynolds Number ◽  
Channel Flow ◽  
Large Scale ◽  
Critical Reynolds Number ◽  
Flow Direction ◽  
Reynolds Numbers ◽  
Tollmien Schlichting ◽  
Scale Turbulence ◽  
High Reynolds ◽  
Primary Instability

A flow visualization study of instabilities caused by Coriolis effects in plane rotating Poiseuille flow has been carried out. The primary instability takes the form of regularly spaced roll cells aligned in the flow direction. They may occur at Reynolds numbers as low as 100, i.e. almost two orders of magnitude lower than the critical Reynolds number for Tollmien-Schlichting waves in channel flow without rotation. The development of such roll cells was studied as a function of both the Reynolds number and the rotation rate and their properties compared with results from linear spatial stability theory. The theoretically obtained most unstable wavenumber agrees fairly well with the experimentally observed value. At high Reynolds number a secondary instability sets in, which is seen as a twisting of the roll cells. A wavytype disturbance is also seen at this stage which, if the rotational speed is increased, develops into large-scale ‘turbulence’ containing imbedded roll cells.

scholarly journals Movement of a finite body in channel flow

2016 ◽  
Vol 472 (2191) ◽  
pp. 20160164 ◽  
Author(s):  
Frank T. Smith ◽  
Edward R. Johnson
Keyword(s):  
Reynolds Number ◽  
Channel Flow ◽  
Flow Instability ◽  
Flow Direction ◽  
Finite Size ◽  
The Body ◽  
Thin Body ◽  
Shear Stresses ◽  
Unsteady Interaction ◽  
High Reynolds

A body of finite size is moving freely inside, and interacting with, a channel flow. The description of this unsteady interaction for a comparatively dense thin body moving slowly relative to flow at medium-to-high Reynolds number shows that an inviscid core problem with vorticity determines much, but not all, of the dominant response. It is found that the lift induced on a body of length comparable to the channel width leads to differences in flow direction upstream and downstream on the body scale which are smoothed out axially over a longer viscous length scale; the latter directly affects the change in flow directions. The change is such that in any symmetric incident flow the ratio of slopes is found to be cos ⁡ ( π / 7 ) , i.e. approximately 0.900969, independently of Reynolds number, wall shear stresses and velocity profile. The two axial scales determine the evolution of the body and the flow, always yielding instability. This unusual evolution and linear or nonlinear instability mechanism arise outside the conventional range of flow instability and are influenced substantially by the lateral positioning, length and axial velocity of the body.

scholarly journals Aerodynamics of smooth and rough square-section prisms at incidence in very high Reynolds-number cross-flows

2021 ◽  
Vol 62 (3) ◽  
Author(s):  
Nils Paul van Hinsberg
Keyword(s):  
Reynolds Number ◽  
Cross Sections ◽  
Reynolds Numbers ◽  
Circular Cylinders ◽  
Surface Boundary ◽  
Experimental Proof ◽  
Surface Boundary Layer ◽  
Pitch Moment ◽  
The Mean ◽  
High Reynolds

Abstract The aerodynamics of smooth and slightly rough prisms with square cross-sections and sharp edges is investigated through wind tunnel experiments. Mean and fluctuating forces, the mean pitch moment, Strouhal numbers, the mean surface pressures and the mean wake profiles in the mid-span cross-section of the prism are recorded simultaneously for Reynolds numbers between 1$$\times$$ × 10$$^{5}$$ 5 $$\le$$ ≤ Re$$_{D}$$ D $$\le$$ ≤ 1$$\times$$ × 10$$^{7}$$ 7 . For the smooth prism with $$k_s$$ k s /D = 4$$\times$$ × 10$$^{-5}$$ - 5 , tests were performed at three angles of incidence, i.e. $$\alpha$$ α = 0$$^{\circ }$$ ∘ , −22.5$$^{\circ }$$ ∘ and −45$$^{\circ }$$ ∘ , whereas only both “symmetric” angles were studied for its slightly rough counterpart with $$k_s$$ k s /D = 1$$\times$$ × 10$$^{-3}$$ - 3 . First-time experimental proof is given that, within the accuracy of the data, no significant variation with Reynolds number occurs for all mean and fluctuating aerodynamic coefficients of smooth square prisms up to Reynolds numbers as high as $$\mathcal {O}$$ O (10$$^{7}$$ 7 ). This Reynolds-number independent behaviour applies to the Strouhal number and the wake profile as well. In contrast to what is known from square prisms with rounded edges and circular cylinders, an increase in surface roughness height by a factor 25 on the current sharp-edged square prism does not lead to any notable effects on the surface boundary layer and thus on the prism’s aerodynamics. For both prisms, distinct changes in the aerostatics between the various angles of incidence are seen to take place though. Graphic abstract

scholarly journals High-Reynolds-number effects on turbulent scalings in compressible channel flow

PAMM ◽  
2015 ◽  
Vol 15 (1) ◽  
pp. 489-490
Author(s):  
Davide Modesti ◽  
Matteo Bernardini ◽  
Sergio Pirozzoli
Keyword(s):  
Reynolds Number ◽  
Channel Flow ◽  
High Reynolds Number ◽  
Reynolds Number Effects ◽  
High Reynolds

Direct numerical simulation of turbulent channel flow up to

2015 ◽  
Vol 774 ◽  
pp. 395-415 ◽  
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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