scholarly journals Turbulence and secondary motions in square duct flow

2018 ◽  
Vol 840 ◽  
pp. 631-655 ◽  
Author(s):  
Sergio Pirozzoli ◽  
Davide Modesti ◽  
Paolo Orlandi ◽  
Francesco Grasso
Keyword(s):  
Reynolds Number ◽  
Turbulent Flows ◽  
Good Accuracy ◽  
Streamwise Velocity ◽  
Secondary Flows ◽  
Duct Flow ◽  
Streamwise Vorticity ◽  
Square Duct ◽  
Developed Turbulence ◽  
Number Variation

We study turbulent flows in pressure-driven ducts with square cross-section through direct numerical simulation in a wide enough range of Reynolds number to reach flow conditions which are representative of fully developed turbulence ($Re_{\unicode[STIX]{x1D70F}}\approx 1000$). Numerical simulations are carried out over very long integration times to get adequate convergence of the flow statistics, and specifically to achieve high-fidelity representation of the secondary motions which arise. The intensity of the latter is found to be on the order of 1 %–2 % of the bulk velocity, and approximately unaffected by Reynolds number variation, at least in the range under scrutiny. The smallness of the mean convection terms in the streamwise vorticity equation points to a simple characterization of the secondary flows, which in the asymptotic high-$Re$ regime are approximated with good accuracy by eigenfunctions of the Laplace operator, in the core part of the duct. Despite their effect of redistributing the wall shear stress along the duct perimeter, we find that secondary motions do not have a large influence on the bulk flow properties, and the streamwise velocity field can be characterized with good accuracy as resulting from the superposition of four flat walls in isolation. As a consequence, we find that parametrizations based on the hydraulic diameter concept, and modifications thereof, are successful in predicting the duct friction coefficient.

scholarly journals Reynolds number dependence of mean flow structure in square duct turbulence

2010 ◽  
Vol 644 ◽  
pp. 107-122 ◽  
Author(s):  
ALFREDO PINELLI ◽  
MARKUS UHLMANN ◽  
ATSUSHI SEKIMOTO ◽  
GENTA KAWAHARA
Keyword(s):  
Reynolds Number ◽  
Secondary Flow ◽  
Buffer Layer ◽  
Turbulent Flows ◽  
Reynolds Numbers ◽  
The Other ◽  
Streamwise Vorticity ◽  
Square Duct ◽  
Layer Structures ◽  
The Mean

We have performed direct numerical simulations of turbulent flows in a square duct considering a range of Reynolds numbers spanning from a marginal state up to fully developed turbulent states at low Reynolds numbers. The main motivation stems from the relatively poor knowledge about the basic physical mechanisms that are responsible for one of the most outstanding features of this class of turbulent flows: Prandtl's secondary motion of the second kind. In particular, the focus is upon the role of flow structures in its generation and characterization when increasing the Reynolds number. We present a two-fold scenario. On the one hand, buffer layer structures determine the distribution of mean streamwise vorticity. On the other hand, the shape and the quantitative character of the mean secondary flow, defined through the mean cross-stream function, are influenced by motions taking place at larger scales. It is shown that high velocity streaks are preferentially located in the corner region (e.g. less than 50 wall units apart from a sidewall), flanked by low velocity ones. These locations are determined by the positioning of quasi-streamwise vortices with a preferential sign of rotation in agreement with the above described velocity streaks' positions. This preferential arrangement of the classical buffer layer structures determines the pattern of the mean streamwise vorticity that approaches the corners with increasing Reynolds number. On the other hand, the centre of the mean secondary flow, defined as the position of the extrema of the mean cross-stream function (computed using the mean streamwise vorticity), remains at a constant location departing from the mean streamwise vorticity field for larger Reynolds numbers, i.e. it scales in outer units. This paper also presents a detailed validation of the numerical technique including a comparison of the numerical results with data obtained from a companion experiment.

scholarly journals Suspensions of finite-size neutrally buoyant spheres in turbulent duct flow

2018 ◽  
Vol 851 ◽  
pp. 148-186 ◽  
Author(s):  
Walter Fornari ◽  
Hamid Tabaei Kazerooni ◽  
Jeanette Hussong ◽  
Luca Brandt
Keyword(s):  
Reynolds Number ◽  
Slip Velocity ◽  
Volume Fraction ◽  
Secondary Flows ◽  
Duct Flow ◽  
Turbulent Kinetic Energy Budget ◽  
Square Duct ◽  
The Core ◽  
The Mean ◽  
Neutrally Buoyant

We study the turbulent square duct flow of dense suspensions of neutrally buoyant spherical particles. Direct numerical simulations (DNS) are performed in the range of volume fractions $\unicode[STIX]{x1D719}=0{-}0.2$, using the immersed boundary method (IBM) to account for the dispersed phase. Based on the hydraulic diameter a Reynolds number of 5600 is considered. We observe that for $\unicode[STIX]{x1D719}=0.05$ and 0.1, particles preferentially accumulate on the corner bisectors, close to the corners, as also observed for laminar square duct flows of the same duct-to-particle size ratio. At the highest volume fraction, particles preferentially accumulate in the core region. For plane channel flows, in the absence of lateral confinement, particles are found instead to be uniformly distributed across the channel. The intensity of the cross-stream secondary flows increases (with respect to the unladen case) with the volume fraction up to $\unicode[STIX]{x1D719}=0.1$, as a consequence of the high concentration of particles along the corner bisector. For $\unicode[STIX]{x1D719}=0.2$ the turbulence activity is reduced and the intensity of the secondary flows reduces to below that of the unladen case. The friction Reynolds number increases with $\unicode[STIX]{x1D719}$ in dilute conditions, as observed for channel flows. However, for $\unicode[STIX]{x1D719}=0.2$ the mean friction Reynolds number is similar to that for $\unicode[STIX]{x1D719}=0.1$. By performing the turbulent kinetic energy budget, we see that the turbulence production is enhanced up to $\unicode[STIX]{x1D719}=0.1$, while for $\unicode[STIX]{x1D719}=0.2$ the production decreases below the values for $\unicode[STIX]{x1D719}=0.05$. On the other hand, the dissipation and the transport monotonically increase with $\unicode[STIX]{x1D719}$. The interphase interaction term also contributes positively to the turbulent kinetic energy budget and increases monotonically with $\unicode[STIX]{x1D719}$, in a similar way as the mean transport. Finally, we show that particles move on average faster than the fluid. However, there are regions close to the walls and at the corners where they lag behind it. In particular, for $\unicode[STIX]{x1D719}=0.05,0.1$, the slip velocity distribution at the corner bisectors seems correlated to the locations of maximum concentration: the concentration is higher where the slip velocity vanishes. The wall-normal hydrodynamic and collision forces acting on the particles push them away from the corners. The combination of these forces vanishes around the locations of maximum concentration. The total mean forces are generally low along the corner bisectors and at the core, also explaining the concentration distribution for $\unicode[STIX]{x1D719}=0.2$.

The production and diffusion of vorticity in duct flow

1964 ◽  
Vol 19 (3) ◽  
pp. 375-394 ◽  
Author(s):  
E. Brundrett ◽  
W. D. Baines
Keyword(s):  
Reynolds Number ◽  
Turbulent Flow ◽  
Secondary Flow ◽  
Longitudinal Component ◽  
Secondary Flows ◽  
Duct Flow ◽  
Square Duct ◽  
Circular Pipes ◽  
Flow Circulation ◽  
Diffusion And Convection

Secondary flows in non-circular ducts are accompanied by a longitudinal component of vorticity. The equation of motion defining this component in a turbulent flow is composed of three terms giving the rates of production, diffusion and convection. Since the expression for production is the second derivative of Reynolds strees components, longitudinal vorticity cannot exist in laminar flow. For turbulent flow in a square duct the Reynolds stress tensor is examined in detail. Symmetry requirements alone provide relationships showing that the production is zero along all lines of symmetry. General characteristics of flow in circular pipes are sufficient to indicate where the production must be greatest. Experimental measurements verify this result and define the point density of production, diffusion and convection of vorticity. Data also indicate that the basic pattern of secondary flow is independent of Reynolds number, but that with increasing values of Reynolds number the flows penetrate the corners and approach the walls. A similar experimental investigation of a rectangular duct shows that the corner bisectors separate independent secondary flow circulation zones. Production of vorticity is again associated with the region near the bisector. However, there is some evidence that the secondary flow pattern is not so complex as inferred from the distortion of the main longitudinal flow.

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.

Laminarization of Internal Flows Under the Combined Effect of Strong Curvature and Rotation

2008 ◽  
Vol 130 (9) ◽  
Author(s):  
K. M. Guleren ◽  
I. Afgan ◽  
A. Turan
Keyword(s):  
Secondary Flows ◽  
Combined Effect ◽  
Navier Stokes ◽  
Duct Flow ◽  
Internal Flows ◽  
Square Duct ◽  
Eddy Simulation ◽  
Numerical Predictions ◽  
Wide Range ◽  
Strong Curvature

The laminarization phenomenon for the flow under the combined effect of strong curvature and rotation is discussed based on numerical predictions of large-eddy simulation (LES). Initially, the laminarization process is presented for the fully developed flow inside a spanwise rotating straight square duct. LES predictions over a wide range of rotation numbers (Ro=0–5) show that the turbulent kinetic energy decreases monotonically apart from 0.2<Ro<0.5. Subsequently, a spanwise rotating U-duct flow is considered with Ro=±0.2. The interaction of curvature and Coriolis induced secondary flows enhances the turbulence for the negative rotating case, whereas this interaction ensues strong laminarization for the positive rotating case. Finally, the laminarization is presented in the impeller of a typical centrifugal compressor, rotating at a speed of Ω=1862rpm(Ro=0.6). The resulting LES predictions are observed to be better than those of Reynolds-averaged Navier-Stokes (RANS) in the regions where turbulence is significant. However, for the regions dominated by strong laminarization, RANS results are seen to approach those of LES and experiments.

203 Vortical structures in low-Reynolds-number turbulent square duct flow(2)

2007 ◽  
Vol 2007 (0) ◽  
pp. _203-1_-_203-4_
Author(s):  
Atsushi SEKIMOTO ◽  
Genta KAWAHARA ◽  
Markus UHLMANN ◽  
Alfredo PINELLI
Keyword(s):  
Reynolds Number ◽  
Low Reynolds Number ◽  
Duct Flow ◽  
Square Duct ◽  
Vortical Structures ◽  
Low Reynolds

scholarly journals Turbulent fluctuations above the buffer layer of wall-bounded flows

2008 ◽  
Vol 611 ◽  
pp. 215-236 ◽  
Author(s):  
JAVIER JIMÉNEZ ◽  
SERGIO HOYAS
Keyword(s):  
Reynolds Number ◽  
Buffer Layer ◽  
Turbulent Flows ◽  
Large Scale ◽  
Pressure Fluctuations ◽  
Strong Support ◽  
Reynolds Numbers ◽  
Streamwise Velocity ◽  
Normal Velocity ◽  
Channel Statistics

The behaviour of the velocity and pressure fluctuations in the logarithmic and outer layers of turbulent flows is analysed using spectral information and probability density functions from channel simulations at Reτ≤2000. Comparisons are made with experimental data at higher Reynolds numbers. It is found, in agreement with previous investigations, that the intensity profiles of the streamwise and spanwise velocity components have logarithmic ranges that are traced to the widening spectral range of scales as the wall is approached. The same is true for the pressure, both theoretically and observationally, but not for the normal velocity or for the tangential stress cospectrum, although even those two quantities have structures with lengths of the order of several hundred times the wall distance. Because the logarithmic range grows longer as the Reynolds number increases, variables which are ‘attached’ in this sense scale in the buffer layer in mixed units. These results give strong support to the attached-eddy scenario proposed by Townsend (1976), but they are not linked to any particular eddy model. The scaling of the outer modes is also examined. The intensity of the streamwise velocity at fixed y/h increases with the Reynolds number. This is traced to the large-scale modes, and to an increased intensity of the ejections but not of the sweeps. Several differences are found between the outer structures of different flows. The outer modes of the spanwise and wall-normal velocities in boundary layers are stronger than in internal flows, and their streamwise velocities penetrate closer to the wall. As a consequence, their logarithmic layers are thinner, and some of their logarithmic slopes are different. The channel statistics are available electronically at http://torroja.dmt.upm.es/ftp/channels/.

Laminarization of turbulent pipe flow by fluid injection

1972 ◽  
Vol 52 (3) ◽  
pp. 451-464 ◽  
Author(s):  
W. T. Pennell ◽  
E. R. G. Eckert ◽  
E. M. Sparrow
Keyword(s):  
Reynolds Number ◽  
Turbulence Intensity ◽  
Pipe Flow ◽  
Streamwise Velocity ◽  
Turbulent Pipe Flow ◽  
Buffer Layers ◽  
Fluid Injection ◽  
Axial Component ◽  
Developed Turbulence ◽  
Porous Pipe

The effects of fluid injection on the structure of an initially fully developed, low Reynolds number, turbulent pipe flow have been studied by means of a hot-film anemometer. Measurements were made of the axial turbulence intensity field and of the time-mean streamwise velocity distribution, both in the porous-walled pipe and in the solid-walled hydrodynamic development section. Oscilloscope traces showing the timewise pattern of the local velocity fluctuations were also monitored. The Reynolds number of the air flow at the inlet of the porous pipe was varied from 3090 to 6350, and the Reynolds number of the injected air ranged from 60 to 160.Near the tube wall, the initial effect of injection is a significant reduction of the axial turbulence level and an increase in the thickness of the viscous and buffer layers. The degree by which turbulence is reduced in this region is more or less proportional to the ratio of the injection to entrance Reynolds numbers. In the core region of the flow, which is centred about the tube axis, there is also an initial reduction in the magnitude of the axial component of turbulence which is thought to be due to injection-induced acceleration of the flow. There is also an annular region, which separates the wall and core regions, in which the turbulence intensity initially increases. In the downstream portion of the porous tube the entire flow undergoes a re-transition to fully developed turbulence.

scholarly journals A priori tests of eddy viscosity models in square duct flow

2020 ◽  
Vol 34 (5-6) ◽  
pp. 713-734
Author(s):  
Davide Modesti
Keyword(s):  
Shear Stress ◽  
Normal Stress ◽  
Eddy Viscosity ◽  
Constitutive Relations ◽  
A Priori ◽  
Secondary Flows ◽  
Duct Flow ◽  
Square Duct ◽  
Viscosity Models ◽  
Similar Accuracy

Abstract We carry out a priori tests of linear and nonlinear eddy viscosity models using direct numerical simulation (DNS) data of square duct flow up to friction Reynolds number $${\text {Re}}_\tau =1055$$ Re τ = 1055 . We focus on the ability of eddy viscosity models to reproduce the anisotropic Reynolds stress tensor components $$a_{ij}$$ a ij responsible for turbulent secondary flows, namely the normal stress $$a_{22}$$ a 22 and the secondary shear stress $$a_{23}$$ a 23 . A priori tests on constitutive relations for $$a_{ij}$$ a ij are performed using the tensor polynomial expansion of Pope (J Fluid Mech 72:331–340, 1975), whereby one tensor base corresponds to the linear eddy viscosity hypothesis and five bases return exact representation of $$a_{ij}$$ a ij . We show that the bases subset has an important effect on the accuracy of the stresses and the best results are obtained when using tensor bases which contain both the strain rate and the rotation rate. Models performance is quantified using the mean correlation coefficient with respect to DNS data $${\widetilde{C}}_{ij}$$ C ~ ij , which shows that the linear eddy viscosity hypothesis always returns very accurate values of the primary shear stress $$a_{12}$$ a 12 ($${\widetilde{C}}_{12}>0.99$$ C ~ 12 > 0.99 ), whereas two bases are sufficient to achieve good accuracy of the normal stress and secondary shear stress ($${\widetilde{C}}_{22}=0.911$$ C ~ 22 = 0.911 , $${\widetilde{C}}_{23}=0.743$$ C ~ 23 = 0.743 ). Unfortunately, RANS models rely on additional assumptions and a priori analysis carried out on popular models, including k–$$\varepsilon $$ ε and $$v^2$$ v 2 –f, reveals that none of them achieves ideal accuracy. The only model based on Pope’s expansion which approaches ideal performance is the quadratic correction of Spalart (Int J Heat Fluid Flow 21:252–263, 2000), which has similar accuracy to models using four or more tensor bases. Nevertheless, the best results are obtained when using the linear correction to the $$v^2$$ v 2 –f model developed by Pecnik and Iaccarino (AIAA Paper 2008-3852, 2008), although this is not built on the canonical tensor polynomial as the other models.

Experimental and Numerical Investigation Into Turbulent High Reynolds Number Flows Through a Square Duct With 90-Degree Streamwise Curvature: II — Numerical Methods

2014 ◽  
Author(s):  
Faustin Ondore
Keyword(s):  
Reynolds Number ◽  
Turbulent Flows ◽  
High Reynolds Number ◽  
Pressure Ratio ◽  
Pressure Rise ◽  
Stress Model ◽  
Complex Flow ◽  
Square Duct ◽  
Recirculating Flow ◽  
High Reynolds

A square duct with a 90-degree streamwise curvature is representative of complex flow domains. Such flow domains are encountered in the designs of fluids engineering systems, especially in the aerospace turbo-machinery components. Examples include the gas turbine engine axial compressor interstage spaces, where the rise in air pressure (and hence compressor efficiency) is dependent on suppression of turbulence. In the case of the centrifugal compressor, pressure rise in the U-shaped diffuser assembly where the suppression of turbulence is critical to the attainable pressure ratio. The results obtained from numerical calculations are analysed and discussed along with the corresponding hot-wire measurements and flow visualization result from a wind-tunnel of identical configuration. Calculations are implemented in four turbulent models, i.e. Standard k-e Module, Algebraic Stress Model (ASM), Non-linear Renormalization Group (RNG) - k-e Model and Differential Stress Model (DSM). The discretization up-winding scheme is the Quadratic Up-winding with Interpolation Kinematics (QUICK). Two high Reynolds number turbulent flows are investigated, with mainstream velocities of 12.3 m/s and 20.4 m/s, representing Re=3.56×105 and Re=6.43×105 respectively. Generally strong correlation between theory and experimental data are recorded. Further, as reported in similar studies, the turbulence modules that are formulated to account for turbulence anisotropy return results that more closely match experimental measurements. Uniquely for this configuration, a massive flow detachment is predicted along the convex wall at about the 90° position. Also, the core of the fluid flow is observed to shift from the outer to the inner areas of the bend in proportion to the secondary (recirculating) flow generated by the bend.

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