A low reynolds number k-ϵ modelling of turbulent pipe flow: Flow pattern and energy balance

2001 ◽  
Vol 79 (2) ◽  
pp. 214-226 ◽  
Author(s):  
Shirish S. Thakre ◽  
Jyeshtharaj B. Joshi
1996 ◽  
Vol 118 (1) ◽  
pp. 189-194 ◽  
Author(s):  
J. O. Ismael ◽  
M. A. Cotton

The low-Reynolds-number k-ε turbulence model of Launder and Sharma is applied to the calculation of wall shear stress in spatially fully-developed turbulent pipe flow oscillated at small amplitudes. It is believed that the present study represents the first systematic evaluation of the turbulence closure under consideration over a wide range of frequency. Model results are well correlated in terms of the parameter ω+ = ωv/Uτ2 at high frequencies, whereas at low frequencies there is an additional Reynolds number dependence. Comparison is made with the experimental data of Finnicum and Hanratty.


Author(s):  
Andrew Duggleby ◽  
Kenneth S Ball ◽  
Markus Schwaenen

Using large-scale numerical calculations, we explore the proper orthogonal decomposition of low Reynolds number turbulent pipe flow, using both the translational invariant (Fourier) method and the method of snapshots. Each method has benefits and drawbacks, making the ‘best’ choice dependent on the purpose of the analysis. Owing to its construction, the Fourier method includes all the flow fields that are translational invariants of the simulated flow fields. Thus, the Fourier method converges to an estimate of the dimension of the chaotic attractor in less total simulation time than the method of snapshots. The converse is that for a given simulation, the method of snapshots yields a basis set that is more optimal because it does not include all of the translational invariants that were not a part of the simulation. Using the Fourier method yields smooth structures with definable subclasses based upon Fourier wavenumber pairs, and results in a new dynamical systems insight into turbulent pipe flow. These subclasses include a set of modes that propagate with a nearly constant phase speed, act together as a wave packet and transfer energy from streamwise rolls. It is these interactions that are responsible for bursting events and Reynolds stress generation. These structures and dynamics are similar to those found in turbulent channel flow. A comparison of structures and dynamics in turbulent pipe and channel flows is reported to emphasize the similarities and differences.


Author(s):  
Huihe Qiu ◽  
Peng Zhang

The development of MEMS requires deliberate designs for controlling fluids in the low Reynolds number regime. Arranging surface charges in rectangular channels to obtain in-plane or out-of-plane vortices have been studied by previous researchers. However, previous surface modification techniques require different signs of zeta potentials from the other wall surfaces which made it difficult in selecting and coating microchannels. Previously, the opposite polarities are usually adjusted by changing the pH value of the solution with acid chemicals in other researches which made the solution complicated and difficult to simulate a real application. Meanwhile the acid chemicals may also destroy the coating. It is convenient to use same polarity patches if a vortex flow can also be generated. However, it is not clear if the patterned surface charges have the same polarity of zeta potentials as the other walls, what kind flow pattern will be generated and what mechanism behind the flow pattern. Furthermore, the cross-section of previously studied microchannels is usually limited to a rectangular shape. Therefore, the surface charge patterns are usually in 2D since the sidewalls of the rectangular microchannels are difficult to be patterned. However, a channel with round cross-section has better leak-proof performance of the membrane valve. Furthermore, a round channel is also advantageous in mimicking the human vein when a vascular structure is needed in tissue scaffolding, the round microfluidic channel is considered as a good candidate for an artificial capillary vessel. It is anticipated that there will be no stagnation occurs at the corner edges, which occurs at the corners of a rectangular channel, for a round microchannel owing to the perfectly symmetrical velocity profile. This is important when the microfluidic chip is subjected to a separation process such as liquid chromatography. In this paper, effects of patterned surface modification on 3D vortex flows generation in a micro capillary tube under very low Reynolds number have been investigated. Microfabrication technology was successfully employed to pattern surface charges on inner surfaces of round capillary tubes, which form non-uniform zeta-potentials. This technique extends the heterogeneous surfaces from flat surface to curved surface. 3D vortices are visualized and measured at the vicinity of tube walls when an electric field is applied across the surfaces utilizing micro resolution PIV. It demonstrated that 3D vortices can also be generated by the patterned surface charges with a same polarity. Experimental results have been compared with the numerical simulations using CFD-ACE+.


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