RANSE modeling of the oscillatory flow over two‐dimensional rigid ripples

Author(s):  
B. Sishah ◽  
G. Vittori
1978 ◽  
Vol 1 (16) ◽  
pp. 87 ◽  
Author(s):  
P. Nielsen ◽  
I.A. Svensen ◽  
C. Staub

A theoretical model is developed for the movement of loose sediments in oscillatory flow with or without a net current. In the present formulation the model is two-dimensional, but may readily be extended to three dimensions. It is assumed that all movement of sediments occurs in suspension, and exact analytical solutions are given for the time variation of the concentration profile, the instantaneous sediment flux and the net flux of sediment over a wave period. The model requires as empirical input a diffusion coefficient e and pick-up function p(t), for which experimental data are presented. Two examples are discussed in detail, illustrating important aspects of the onshore-offshore sediment motion.


2014 ◽  
Vol 751 ◽  
pp. 1-37 ◽  
Author(s):  
Ming Zhao ◽  
Liang Cheng

AbstractOscillatory flow past two circular cylinders in side-by-side and tandem arrangements at low Reynolds numbers is simulated numerically by solving the two-dimensional Navier–Stokes (NS) equations using a finite-element method (FEM). The aim of this study is to identify the flow regimes of the two-cylinder system at different gap arrangements and Keulegan–Carpenter numbers (KC). Simulations are conducted at seven gap ratios $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}G$ ($G=L/D$ where $L$ is the cylinder-to-cylinder gap and $D$ the diameter of a cylinder) of 0.5, 1, 1.5, 2, 3, 4 and 5 and KC ranging from 1 to 12 with an interval of 0.25. The flow regimes that have been identified for oscillatory flow around a single cylinder are also observed in the two-cylinder system but with different flow patterns due to the interactions between the two cylinders. In the side-by-side arrangement, the vortex shedding from the gap between the two cylinders dominates when the gap ratio is small, resulting in the gap vortex shedding (GVS) regime, which is different from any of the flow regimes identified for a single cylinder. For intermediate gap ratios of 1.5 and 2 in the side-by-side arrangement, the vortex shedding mode from one side of each cylinder is not necessarily the same as that from the other side, forming a so-called combined flow regime. When the gap ratio between the two cylinders is sufficiently large, the vortex shedding from each cylinder is similar to that of a single cylinder. In the tandem arrangement, when the gap between the two cylinders is very small, the flow regimes are similar to that of a single cylinder. For large gap ratios in the tandem arrangement, the vortex shedding flows from the gap side of the two cylinders interact and those from the outer sides of the cylinders are less affected by the existence of the other cylinder and similar to that of a single cylinder. Strong interaction between the vortex shedding flows from the two cylinders makes the flow very irregular at large KC values for both side-by-side and tandem arrangements.


1971 ◽  
Vol 93 (4) ◽  
pp. 543-549
Author(s):  
B. A. Gastrock ◽  
J. A. Miller

The development of a numerical technique for the treatment of two-dimensional non-similar, unsteady, laminar boundary layers is presented. The method is an extension to nonsteady flows of the integral matrix procedure of Kendall. Solutions of example problems are presented demonstrating good agreement with known classical results. Core storage requirements of 130K bytes allow consideration of as many as 1250 field points and 50 time increments per oscillation cycle. Solution of oscillating Blasius flow for 8 nodal points and 16 time increments in 13.49 seconds demonstrates the practicality of the computational time required, while agreement with both the analysis and experiment of Nickerson for this flow is excellent.


Author(s):  
M. H. Saidi ◽  
M. Taheri ◽  
R. Jahanbakhshi ◽  
A. Jafarian ◽  
S. K. Hannani

Recently a great attention has been given to the oscillatory flow modeling in the pulse tube cryocoolers. In this paper multi dimensioning effects of the fluid flow in the pulse tube are investigated. A complete system of governing equations is solved to report the flow field, friction coefficient and Nusselt number in the pulse tube. Harmonic approximation technique is employed to derive an analytical solution. In this respect, mass, momentum and energy balance equations as well as the equation of state for ideal gas are transformed by implementing the harmonic approximation technique. The present model is able to predict the behavior of the two dimensional compressible oscillatory flow in the tube section of the regenerative cryocoolers. Based on the proposed analytical model, friction coefficient and complex Nusselt number is reported.


2017 ◽  
Vol 813 ◽  
pp. 85-109 ◽  
Author(s):  
Feifei Tong ◽  
Liang Cheng ◽  
Chengwang Xiong ◽  
Scott Draper ◽  
Hongwei An ◽  
...  

Two-dimensional direct numerical simulation and Floquet stability analysis have been performed at moderate Keulegan–Carpenter number ($KC$) and low Reynolds number ($Re$) for a square cross-section cylinder with its face normal to the oscillatory flow. Based on the numerical simulations a map of flow regimes is formed and compared to the map of flow around an oscillating circular cylinder by Tatsuno & Bearman (J. Fluid Mech., vol. 211, 1990, pp. 157–182). Two new flow regimes have been observed, namely A$^{\prime }$ and F$^{\prime }$. The regime A$^{\prime }$ found at low $KC$ is characterised by the transverse convection of fluid particles perpendicular to the motion; and the regime F$^{\prime }$ found at high $KC$ shows a quasi-periodic feature with a well-defined secondary period, which is larger than the oscillation period. The Floquet analysis demonstrates that when the two-dimensional flow breaks the reflection symmetry about the axis of oscillation, the quasi-periodic instability and the synchronous instability with the imposed oscillation occur alternately for the square cylinder along the curve of marginal stability. This alternate pattern in instabilities leads to four distinct flow regimes. When compared to the vortex shedding in otherwise unidirectional flow, the two quasi-periodic flow regimes are observed when the oscillation frequency is close to the Strouhal frequency (or to half of it). Both the flow regimes and marginal stability curve shift in the $(Re,KC)$-space compared to the oscillatory flow around a circular cylinder and this shift appears to be consistent with the change in vortex formation time associated with the lower Strouhal frequency of the square cylinder.


1993 ◽  
Vol 247 ◽  
pp. 179-204 ◽  
Author(s):  
O. R. Tutty ◽  
T. J. Pedley

Two-dimensional, unsteady flow of a viscous, incompressible fluid in a stepped channel has been studied by the numerical solution of the Navier–Stokes equation using an accurate finite-difference method.With a sinusoidal mass flow rate, the problem has three governing parameters: the Reynolds number, the Strouhal number, and the step height. The effects on the flow of varying all three parameters has been investigated systematically. In appropriate parameter regimes, a strong ‘vortex wave’ is generated during the forward phase when the flow is over the step into the expansion. Secondary effects on the wave can result in a complex flow pattern with each major structure of the flow consisting of an eddy with more than one core. No such wave is found during the reverse phase of the flow. The generation and development of the wave is examined in some detail, and our results are compared and contrasted with those of previous studies, both experimental and theoretical, of flow in non-uniform vessels.


2000 ◽  
Vol 412 ◽  
pp. 355-378 ◽  
Author(s):  
P. SCANDURA ◽  
G. VITTORI ◽  
P. BLONDEAUX

The process which leads to the appearance of three-dimensional vortex structures in the oscillatory flow over two-dimensional ripples is investigated by means of direct numerical simulations of Navier–Stokes and continuity equations. The results by Hara & Mei (1990a), who considered ripples of small amplitude or weak fluid oscillations, are extended by considering ripples of larger amplitude and stronger flows respectively. Nonlinear effects, which were ignored in the analysis carried out by Hara & Mei (1990a), are found either to have a destabilizing effect or to delay the appearance of three-dimensional flow patterns, depending on the values of the parameters. An attempt to simulate the flow over actual ripples is made for moderate values of the Reynolds number. In this case the instability of the basic two-dimensional flow with respect to transverse perturbations makes the free shear layer generated by boundary layer separation become wavy as it leaves the ripple crest. Then the amplitude of the waviness increases and eventually complex three-dimensional vortex structures appear which are ejected in the irrotational region. Sometimes the formation of mushroom vortices is observed.


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