Direct numerical simulation of a puff and a slug in transitional cylindrical pipe flow

1999 ◽  
Vol 387 ◽  
pp. 39-60 ◽  
Author(s):  
H. SHAN ◽  
B. MA ◽  
Z. ZHANG ◽  
F. T. M. NIEUWSTADT
Keyword(s):  
Numerical Simulation ◽  
Reynolds Number ◽  
Direct Numerical Simulation ◽  
Pipe Flow ◽  
Leading Edge ◽  
Transition Process ◽  
Axial Position ◽  
Trailing Edge ◽  
Mean Velocity ◽  
The Mean

A direct numerical simulation of transitional pipe flow is carried out with the help of a spectral element method and used to investigate the localized regions of ‘turbulent’ flow that are observed in experiments. Two types of such regions can be distinguished: the puff and the slug. The puff, which is generally found at low values of the Reynolds numbers, is simulated for Re = 2200 where the Reynolds number Re is based on the mean velocity UB and pipe diameter D. The slug occurs at a higher Reynolds number and it is simulated for Re = 5000. The computations start with a laminar pipe flow to which is added a prescribed velocity disturbance at a given axial position and for a finite time. The disturbance then evolves further into a puff or slug structure.The simulations confirm the experimentally observed fact that for a puff the velocity near the leading edge changes more gradually than for a slug where an almost discontinuous change is observed. The positions of the leading and trailing edges of the puff and slug are computed from the simulations as a function of time. The propagation velocity of the leading edge is found to be constant and equal to 1.56UB and 1.69UB for the puff and slug, respectively. For the trailing edge the velocity is found to be 0.73UB and 0.52UB, respectively. By rescaling the simulation results obtained at various times to a fixed length, we define an ensemble average. This method is used to compute the average characteristics of the puff and slug such as the spatial distribution of the mean velocity, the turbulent velocity fluctuations and also the wall shear stress. By computing particle trajectories we have investigated the entrainment and detrainment of fluid by a puff and slug. We find that the puff detrains through its trailing edge and entrains through its leading edge. The slug entrains fluid through its leading and through most of its trailing edge. As a consequence the fluid inside the puff is constantly exchanged with fluid outside whereas the fluid inside a slug remains there. These entrainment/detrainment properties which are in agreement with the measurements of Wygnanski & Champagne (1973) imply that the puff has the characteristics of a wave phenomenon while the slug can be characterized more as a material property which travels with the flow.Finally, we have investigated in more detail the velocity field within the puff. In a coordinate system that travels with the mean velocity we find recirculation regions both near the trailing and leading edges which agrees at least qualitatively with experimental data. We also find streamwise vortices, predominantly in the trailing-edge region which have been also observed in experiments and which are believed to play an important role in the dynamics of the transition process.

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.

Numerical Simulations of Particle-Laden Flow Based on Given Friction Reynolds Number and Mean Reynolds Number Respectively

2014 ◽  
Author(s):  
Zhenzhong Li ◽  
Jinjia Wei ◽  
Bo Yu
Keyword(s):  
Numerical Simulation ◽  
Reynolds Number ◽  
Direct Numerical Simulation ◽  
Wide Spectrum ◽  
Natural World ◽  
Industrial Applications ◽  
Particle Parameters ◽  
The Mean ◽  
The Difference ◽  
Particle Laden Flow

Multiphase flow with particles covers a wide spectrum of flow conditions in natural world and industrial applications. The experiments and the direct numerical simulation have become the most popular means to study the dilute particle-laden flow in the last two decades. In the experimental study, the mean Reynolds number is often adjusted to the value of single-phase flow for each set of particle conditions. However, the friction Reynolds number usually keeps invariable in the direct numerical simulation of the particle-laden flows for convenience. In this study the effect of the difference between given mean Reynolds number and friction Reynolds number was investigated. Two simulations were performed for each set of particle parameters, and the mean Reynolds number and friction Reynolds number were kept invariant respectively. From the results it can be found that the turbulence intensity and the dimensionless velocities are larger when keeping the friction Reynolds constant. And the results calculated from the cases of keeping the mean Reynolds number invariable agree with the experiment results better. In addition, the particle distribution along the wall-normal coordinate was found to be unchanged between two simulation conditions. As a suggestion, keeping the same mean Reynolds number in the direct numerical simulation of particle-laden flow is more appropriate.

Direct Numerical Simulation of Turbulent Channel Flow With Streamwise System-Rotation

2015 ◽  
Author(s):  
Masayoshi Okamoto
Keyword(s):  
Numerical Simulation ◽  
Reynolds Number ◽  
Direct Numerical Simulation ◽  
High Reynolds Number ◽  
Turbulent Channel Flow ◽  
Quadrant Analysis ◽  
Mean Velocity ◽  
Reynolds Number Flow ◽  
High Reynolds ◽  
Low Speed Streaks

The direct numerical simulation (DNS) of the fully developed turbulent channel flows rotating along the streamwise direction with several rotation parameters and two Reynolds numbers is performed. The bulk mean velocity decreases with increasing the rotation parameter, but the decrement is weakened in the high Reynolds number case. Applying the second-kind Chebyshev polynomial expansion into the mean spanwise velocity, the second mode coefficient, which becomes large in the strong rotation, is greatly influenced by the Reynolds number effect. Due to the streamwise rotation, the derivative and integral length scales obtained from the streamwise two-point correlation are extended. From viewpoints of the quadrant analysis, spectral one and instantaneous visualization, the high correlation among three fluctuating velocity components appears and the low-speed streaks are accumulated in the strong rotation and high Reynolds number flow.

scholarly journals Nonlinear waves with a threefold rotational symmetry in pipe flow: influence of a strongly shear-thinning rheology

2017 ◽  
Vol 818 ◽  
pp. 595-622
Author(s):  
Emmanuel Plaut ◽  
Nicolas Roland ◽  
Chérif Nouar
Keyword(s):  
Reynolds Number ◽  
Laminar Flow ◽  
Nonlinear Waves ◽  
Pipe Flow ◽  
Rotational Symmetry ◽  
Shear Thinning ◽  
Transition To Turbulence ◽  
Mean Velocity ◽  
The Mean ◽  
The One

In order to model the transition to turbulence in pipe flow of non-Newtonian fluids, the influence of a strongly shear-thinning rheology on the travelling waves with a threefold rotational symmetry of Faisst & Eckhardt (Phys. Rev. Lett., vol. 91, 2003, 224502) and Wedin & Kerswell (J. Fluid Mech., vol. 508, 2004, pp. 333–371) is analysed. The rheological model is Carreau’s law. Besides the shear-thinning index $n_{C}$, the dimensionless characteristic time $\unicode[STIX]{x1D706}$ of the fluid is considered as the main non-Newtonian control parameter. If $\unicode[STIX]{x1D706}=0$, the fluid is Newtonian. In the relevant limit $\unicode[STIX]{x1D706}\rightarrow +\infty$, the fluid approaches a power-law behaviour. The laminar base flows are first characterized. To compute the nonlinear waves, a Petrov–Galerkin code is used, with continuation methods, starting from the Newtonian case. The axial wavenumber is optimized and the critical waves appearing at minimal values of the Reynolds number $\mathit{Re}_{w}$ based on the mean velocity and wall viscosity are characterized. As $\unicode[STIX]{x1D706}$ increases, these correspond to a constant value of the Reynolds number based on the mean velocity and viscosity. This viscosity, close to the one of the laminar flow, can be estimated analytically. Therefore the experimentally relevant critical Reynolds number $\mathit{Re}_{wc}$ can also be estimated analytically. This Reynolds number may be viewed as a lower estimate of the Reynolds number for the transition to developed turbulence. This demonstrates a quantified stabilizing effect of the shear-thinning rheology. Finally, the increase of the pressure gradient in waves, as compared to the one in the laminar flow with the same mass flux, is calculated, and a kind of ‘drag reduction effect’ is found.

Nonasymptotic behavior of developing turbulent pipe flow

1976 ◽  
Vol 54 (3) ◽  
pp. 268-278 ◽  
Author(s):  
J. K. Reichert ◽  
R. S. Azad
Keyword(s):  
Reynolds Number ◽  
Pipe Flow ◽  
Reynolds Numbers ◽  
Peak Position ◽  
Turbulent Pipe Flow ◽  
Shear Stresses ◽  
Mean Velocity ◽  
Inlet Region ◽  
The Mean ◽  
Hot Film

Detailed measurements of mean velocity U profiles, in the inlet 70 diameters of a pipe, show that the development of turbulent pipe flow is nonasymptotic. Experiments were done at seven Reynolds numbers in the range 56 000–15 3000. Contours of U and V fields are presented for two representative Reynolds numbers. A U component peak exceeding the fully developed values has been found to occur along the pipe centerline. The Reynolds number behavior of the peak position has been determined. Hot film measurements of the mean wall shear stresses in the inlet region also show a nonasymptotic development consistent with the mean velocity results.

scholarly journals Experimental study on the mean velocity profile in the high Reynolds number turbulent pipe flow

2015 ◽  
Vol 81 (826) ◽  
pp. 15-00091-15-00091 ◽  
Author(s):  
Yuki WADA ◽  
Noriyuki FURUICHII ◽  
Yoshiya TERAO ◽  
Yoshiyuki TSUJI
Keyword(s):  
Experimental Study ◽  
Reynolds Number ◽  
Velocity Profile ◽  
Pipe Flow ◽  
High Reynolds Number ◽  
Turbulent Pipe Flow ◽  
Mean Velocity ◽  
The Mean ◽  
High Reynolds

Direct Numerical Simulation of Forced Convective Heat Transfer From a Heated Rotating Sphere in Laminar Flows

2014 ◽  
Vol 136 (4) ◽  
Author(s):  
Zhi-Gang Feng
Keyword(s):  
Numerical Simulation ◽  
Reynolds Number ◽  
Direct Numerical Simulation ◽  
Density Function ◽  
Heat Diffusion ◽  
Rotating Sphere ◽  
Nusselt Numbers ◽  
Flow Reynolds Number ◽  
The Mean ◽  
Simulation Results

The laminar forced convection of a heated rotating sphere in air has been studied using a three-dimensional immersed boundary based direct numerical simulation method. A regular Eulerian grid is used to solve the modified momentum and energy equations for the entire flow region simultaneously. In the region that is occupied by the rotating sphere, a moving Lagrangian grid is used, which tracks the rotational motion of the particle. A force density function or an energy density function is introduced to represent the momentum interaction or thermal interaction between the sphere and fluid. This numerical method is validated by comparing simulation results with analytical solutions of heat diffusion problem and other published experimental data. The flow structures and the mean Nusselt numbers for flow Reynolds number ranging from 0 to 1000 are obtained. We compared our simulation results of the mean Nusselt numbers with the correlations from the literature and found a good agreement for flow Reynolds number greater than 500; however, a significant discrepancy arises at flow Reynolds number below 500. This leads us to develop a new equation that correlates the mean Nusselt number of a heated rotating sphere for flows of 0≤Re≤500.

Behavior of Separation Bubble and Reattached Boundary Layer Around a Circular Leading Edge

1994 ◽  
Author(s):  
B. K. Hazarika ◽  
C. Hirsch
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Separation Bubble ◽  
Low Frequency ◽  
Leading Edge ◽  
Reynolds Numbers ◽  
Mean Velocity ◽  
Low Frequency Oscillations ◽  
Lower Reynolds Number ◽  
The Mean

The flow around a circular leading edge airfoil is investigated in an incompressible, low turbulence freestream. Hot-wire measurements are performed through the separation bubble, the reattachment and the recovery region till development of the fully turbulent boundary layer. The results of the experiments in the range of Reynolds numbers 1.7×103 to 11.8×103 are analysed and presented in this paper. A separation bubble is present near the leading edge at all Reynolds numbers. At the lowest Reynolds number investigated, the transition is preceded by strong low frequency oscillations. The correlation given by Mayle for prediction of transition of short separation bubbles is successful at the lower Reynolds number cases. The length of the separation bubble reduces considerably with increasing Reynolds number in the range investigated. The turbulence in the reattached flow persists even when the Reynolds number based on momentum thickness of the reattached boundary layer is small. The recovery length of the reattached layer is relatively short and the mean velocity profile follows logarithmic law within a short distance downstream of the reattachment point and the friction coefficient conforms to Prandtl-Schlichting skin-friction formula for a smooth flat plate at zero incidence.

scholarly journals Direct numerical simulation of a self-similar adverse pressure gradient turbulent boundary layer at the verge of separation

2017 ◽  
Vol 829 ◽  
pp. 392-419 ◽  
Author(s):  
V. Kitsios ◽  
A. Sekimoto ◽  
C. Atkinson ◽  
J. A. Sillero ◽  
G. Borrell ◽  
...  
Keyword(s):  
Numerical Simulation ◽  
Boundary Layer ◽  
Reynolds Number ◽  
Direct Numerical Simulation ◽  
Pressure Gradient ◽  
Adverse Pressure Gradient ◽  
Streamwise Velocity ◽  
Far Field ◽  
Self Similar ◽  
The Mean

The statistical properties are presented for the direct numerical simulation of a self-similar adverse pressure gradient (APG) turbulent boundary layer (TBL) at the verge of separation. The APG TBL has a momentum thickness-based Reynolds number range from $Re_{\unicode[STIX]{x1D6FF}_{2}}=570$ to 13 800, with a self-similar region from $Re_{\unicode[STIX]{x1D6FF}_{2}}=10\,000$ to 12 300. Within this domain the average non-dimensional pressure gradient parameter $\unicode[STIX]{x1D6FD}=39$, where for a unit density $\unicode[STIX]{x1D6FD}=\unicode[STIX]{x1D6FF}_{1}P_{\!e}^{\prime }/\unicode[STIX]{x1D70F}_{w}$, with $\unicode[STIX]{x1D6FF}_{1}$ the displacement thickness, $\unicode[STIX]{x1D70F}_{w}$ the mean shear stress at the wall and $P_{\!e}^{\prime }$ the far-field pressure gradient. This flow is compared with previous zero pressure gradient and mild APG TBL ($\unicode[STIX]{x1D6FD}=1$) results of similar Reynolds number. All flows are generated via the direct numerical simulation of a TBL on a flat surface with far-field boundary conditions tailored to apply the desired pressure gradient. The conditions for self-similarity, and the appropriate length and velocity scales, are derived. The mean and Reynolds stress profiles are shown to collapse when non-dimensionalised on the basis of these length and velocity scales. As the pressure gradient increases, the extent of the wake region in the mean streamwise velocity profiles increases, whilst the extent of the log-layer and viscous sublayer decreases. The Reynolds stress, production and dissipation profiles of the APG TBL cases exhibit a second outer peak, which becomes more pronounced and more spatially localised with increasing pressure gradient. This outer peak is located at the point of inflection of the mean velocity profiles, and is suggestive of the presence of a shear flow instability. The maximum streamwise velocity variance is located at a wall normal position of $\unicode[STIX]{x1D6FF}_{1}$ of spanwise wavelength of $2\unicode[STIX]{x1D6FF}_{1}$. In summary as the pressure gradient increases the flow has properties less like a zero pressure gradient TBL and more akin to a free shear layer.

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