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991.
The velocity field and the associated shear stress corresponding to the longitudinal oscillatory flow of a generalized second grade fluid, between two infinite coaxial circular cylinders, are determined by means of the Laplace and Hankel transforms. Initially, the fluid and cylinders are at rest and at t = 0+ both cylinders suddenly begin to oscillate along their common axis with simple harmonic motions having angular frequencies Ω1 and Ω2. The solutions that have been obtained are presented under integral and series forms in terms of the generalized G and R functions and satisfy the governing differential equation and all imposed initial and boundary conditions. The respective solutions for the motion between the cylinders, when one of them is at rest, can be obtained from our general solutions. Furthermore, the corresponding solutions for the similar flow of ordinary second grade fluid and Newtonian fluid are also obtained as limiting cases of our general solutions. At the end, the effect of different parameters on the flow of ordinary second grade and generalized second grade fluid are investigated graphically by plotting velocity profiles. 相似文献
992.
Stefan Langer 《国际流体数值方法杂志》2012,69(2):332-352
We derive and investigate point implicit Runge–Kutta methods to significantly improve the convergence rate to approximate steady‐state solutions of inviscid flows. It turns out that the point implicit Runge–Kutta can be interpreted as a preconditioned explicit Runge–Kutta method, where the preconditioner arises naturally as local derivative of the residual function. Moreover, many preconditioners suggested in the literature so far are identified as special case of our general ansatz. Conditions will be formulated such that explicit Runge–Kutta methods with local time stepping are equivalent to point implicit methods. In numerical examples, we will demonstrate the improved convergence rates. Copyright © 2011 John Wiley & Sons, Ltd. 相似文献
993.
Since the (original) ghost fluid method (OGFM) was proposed by Fedkiw et al. in 1999 [5], a series of other GFM-based methods such as the gas–water version GFM (GWGFM), the modified GFM (MGFM) and the real GFM (RGFM) have been developed subsequently. Systematic analysis, however, has yet to be carried out for the various GFMs on their accuracies and conservation errors. In this paper, we develop a technique to rigorously analyze the accuracies and conservation errors of these different GFMs when applied to the multi-medium Riemann problem with a general equation of state (EOS). By analyzing and comparing the interfacial state provided by each GFM to the exact one of the original multi-medium Riemann problem, we show that the accuracy of interfacial treatment can achieve “third-order accuracy” in the sense of comparing to the exact solution of the original mutli-medium Riemann problem for the MGFM and the RGFM, while it is of at most “first-order accuracy” for the OGFM and the GWGFM when the interface approach is actually near in balance. Similar conclusions are also obtained in association with the local conservation errors. A special test method is exploited to validate these theoretical conclusions from the numerical viewpoint. 相似文献
994.
Gravity‐driven Stokes flow down an inclined plane over and around multiple obstacles is considered. The flow problem is formulated in terms of a boundary integral equation and solved using the boundary element method. A Hermitian radial basis function (RBF) is used for the interpolation of the free surface, generation of the unit normal and curvature, and to prescribe the far‐field conditions. For flow over an obstacle, hemispheres are taken. For flow around an obstacle, circular cylinders are modelled and the contact angle condition on the obstacle/free surface intersection specified using the RBF formulation. Explicit profiles are produced for flow over and around two obstacles placed in various locations relative to one another. Interaction due to two obstacles is given by comparisons made with the profiles for flow over and around individual obstacles. In general, when the obstacles are separated by a sufficiently large distance the flow profiles are identical to a single obstacle analysis. For flow over and around two obstacles in‐line with the incident flow, effects of the governing parameters are examined, with variations in plane inclination angle, Bond number, obstacle size, and in the case of obstacles intersecting the free surface, static contact angle is considered. Finally flows over and around three obstacles are modelled. Copyright © 2009 John Wiley & Sons, Ltd. 相似文献
995.
In this article we have studied the peristaltic motion of an incompressible Williamson fluid with constant and radially varying magnetohydrodynamics (MHD) in an endoscope. Using the low Reynolds and long wavelength assumptions, the equations of Williamson fluid model in simplified form are solved using (i) the HAM method and (ii) the Shooting method. The comparisons of both solutions have been found a very good agreement. Graphical results have been presented for various emerging parameters. © British Crown Copyright 2010/MOD. Reproduced with permission. Published by John Wiley & Sons, Ltd. 相似文献
996.
Himanshu Joshi Arpit Agarwal Bhalchandra Puranik Chang Shu Amit Agrawal 《国际流体数值方法杂志》2010,62(4):403-427
The lattice Boltzmann method (LBM) has established itself as an alternative approach to solve the fluid flow equations. In this work we combine LBM with the conventional finite volume method (FVM), and propose a non‐iterative hybrid method for the simulation of compressible flows. LBM is used to calculate the inter‐cell face fluxes and FVM is used to calculate the node parameters. The hybrid method is benchmarked for several one‐dimensional and two‐dimensional test cases. The results obtained by the hybrid method show a steeper and more accurate shock profile as compared with the results obtained by the widely used Godunov scheme or by a representative flux vector splitting scheme. Additional features of the proposed scheme are that it can be implemented on a non‐uniform grid, study of multi‐fluid problems is possible, and it is easily extendable to multi‐dimensions. These features have been demonstrated in this work. The proposed method is therefore robust and can possibly be applied to a variety of compressible flow situations. Copyright © 2009 John Wiley & Sons, Ltd. 相似文献
997.
M. Digruber W. Schneider K. Mörwald S. Haas 《Archive of Applied Mechanics (Ingenieur Archiv)》2000,70(1-3):17-29
Summary The paper is concerned with a one-dimensional analysis of plane open-channel flow with continuous solidification. The process
is of relevance for recent developments in the casting of steel and other metals. The bottom of the channel consists of a
rotating casting roll and a horizontal cooling table, where the solidified material is withdrawn with given velocity. The
study is restricted to the region downstream of the top of the casting roll. Surface tension is neglected.
In the main part of the analysis inviscid fluid flow is considered since the Reynolds number is very large in the applications.
It is found that the steady-state solutions are nonunique in a certain parameter range. In addition to a continuous solution,
there are two solutions including hydraulic jumps, with one hydraulic jump being located on the casting roll, the other one
on the cooling table. Regarding the stability of the non unique solutions, the evolution of disturbances is investigated numerically
as an initial-value problem. It is concluded that the hydraulic jump on the cooling table is unstable, while the other discontinuous
solution as well as the continuous solution are stable for sufficiently small disturbances. Which stable solution is attained
in the steady state, depends on the history of the process.
Friction at the liquid/solid interface is taken into account in the last part of the analysis. A constant friction coefficient
is assumed. It is found that the history of the process determines the steady-state solution if, and only if, the friction
coefficient is sufficiently small. For larger values of the friction coefficient, the steady-state solution is unique and
independent of the history of the transient process. Furthermore, for sufficiently large friction coefficients, stable hydraulic
jumps are found, in contrast to the inviscid case, also on the cooling table.
Received 19 March 1999; accepted for publication 3 May 1999 相似文献
998.
Over the past 15 years direct numerical simulations (DNS) of turbulent flow and particle image velocimetry (PIV) have provided
the opportunity to obtain information about a turbulent velocity field simultaneously at a large number of locations. This
paper gives a personal viewpoint of how these techniques are providing new insights about the Reynolds stress producing structures
in turbulence generated by flow over a smooth boundary.
This revised version was published online in August 2006 with corrections to the Cover Date. 相似文献
999.
Reza Farzad Stefan Puttinger Stefan Pirker Simon Schneiderbauer 《Journal of Dispersion Science and Technology》2018,39(2):250-258
In this paper, we investigate oil-in-water emulsions in a Taylor-Couette flow. A high-speed camera was employed to record the formation of those emulsions, and image processing was used to obtain the diameter of the droplets. No surfactants were added in order to study the pure effect of the fluid dynamical forces on the droplets. The results for three different oil-in-water emulsions show that the Sauter mean diameter considerably depends on the local shear rate and the material properties and that the droplet size distribution follows a log-normal distribution. We, therefore, propose to express the Sauter mean diameter normalized by Prandtl mixing length in terms of a correlation, which is based on the Kolmogorov turbulence theory. This correlation subsequently depends on the local shear rate and the material properties such as viscosity, density, and interfacial tension. The predictions of the correlation show fairly good agreement with the experimental measurement the Sauter mean diameter. Finally, comparing the predictions of the correlation to the data presented by Eskin et al. [Chem. Eng. Sci. 161 36–47; 2017] shows excellent agreement in the case, where the droplets are larger than the Kolmogorov length scale. 相似文献
1000.