双螺杆挤出机流场数值模拟中流道进出口边界条件的探讨

在对双螺杆挤出机流场的数值模拟中,流道进出口边界条件的设置一直是一个颇具争议的问题。由于事先无法获得计算域进出口平面上的真实边界条件,研究人员在进行双螺杆挤出机的流场分析时,大都采用放松边界条件。为了考察放松边界条件对双螺杆挤出机流场数值模拟结果的影响,本文采用聚合物流动分析软件POLYFLOW,在流量恒定的前提下对双螺杆挤出机流道进出口给定三种不同分布形式的速度边界条件,对其流场进行了数值模拟。数值计算结果表明,在体积流量恒定的条件下,流道进出口不同分布形式的速度边界条件对流场的影响主要集中在进出口附近区域,但对离进出口边界较远的流场影响很小。一般而言,当计算域所对应的螺杆较长时,可以忽略流道进出口的放松边界条件所引起的误差;当计算域较短时,不宜直接采用放松边界条件,而应根据螺杆的实际构型．在计算域的进出口增加适当长度的发展段。     

Optimal control for quasi-Newtonian flows with defective boundary conditions

We consider a generalized-Newtonian fluid with defective boundary conditions where only flow rates or mean pressures are prescribed on parts of boundary. The defect boundary condition problem is formulated as an optimal control problem in which a Neumann or Dirichlet boundary control is used for matching given flow rates or mean pressures. For the constrained optimization problem an optimality system is derived from which a solution of the problem is obtained. Computational algorithms are discussed and numerical results are also presented.     

Finite element approximation to buoyancy-driven flows with cyclic boundary conditions

The calculation of the total normal forces and the dynamic pressure on a rectangular wing at different rocket velocities is presented. Two programs for computer-aided design of rocket wings were developed. Variations of velocity and air temperature modify the expected performance curves.     

Cores of swirling particle motion in unsteady flows

In nature and in flow experiments particles form patterns of swirling motion in certain locations. Existing approaches identify these structures by considering the behavior of stream lines. However, in unsteady flows particle motion is described by path lines which generally gives different swirling patterns than stream lines. We introduce a novel mathematical characterization of swirling motion cores in unsteady flows by generalizing the approach of Sujudi/Haimes to path lines. The cores of swirling particle motion are lines sweeping over time, i.e., surfaces in the space-time domain. They occur at locations where three derived 4D vectors become coplanar. To extract them, we show how to re-formulate the problem using the Parallel Vectors operator. We apply our method to a number of unsteady flow fields.     

Molecular dynamics simulations of oscillatory Couette flows with slip boundary conditions

The effect of interfacial slip on steady-state and time-periodic flows of monatomic liquids is investigated using non-equilibrium molecular dynamics simulations. The fluid phase is confined between atomically smooth rigid walls, and the fluid flows are induced by moving one of the walls. In steady shear flows, the slip length increases almost linearly with shear rate. We found that the velocity profiles in oscillatory flows are well described by the Stokes flow solution with the slip length that depends on the local shear rate. Interestingly, the rate dependence of the slip length obtained in steady shear flows is recovered when the slip length in oscillatory flows is plotted as a function of the local shear rate magnitude. For both types of flows, the friction coefficient at the liquid–solid interface correlates well with the structure of the first fluid layer near the solid wall.     

Investigation of wall bounded flows using SPH and the unified semi-analytical wall boundary conditions

Semi-analytical wall boundary conditions present a mathematically rigorous framework to prescribe the influence of solid walls in smoothed particle hydrodynamics (SPH) for fluid flows. In this paper they are investigated with respect to the skew-adjoint property which implies exact energy conservation. It will be shown that this property holds only in the limit of the continuous SPH approximation, whereas in the discrete SPH formulation it is only approximately true, leading to numerical noise. This noise, interpreted as a form of “turbulence”, is treated using an additional volume diffusion term in the continuity equation which we show is equivalent to an approximate Riemann solver. Subsequently two extensions to the boundary conditions are presented. The first dealing with a variable driving force when imposing a volume flux in a periodic flow and the second showing a generalization of the wall boundary condition to Robin type and arbitrary-order interpolation. Two modifications for free-surface flows are presented for the volume diffusion term as well as the wall boundary condition. In order to validate the theoretical constructs numerical experiments are performed showing that the present volume flux term yields results with an error 5 orders of magnitude smaller then previous methods while the Robin boundary conditions are imposed correctly with an error depending on the order of the approximation. Furthermore, the proposed modifications for free-surface flows improve the behavior at the intersection of free surface and wall as well as prevent free-surface detachment when using the volume diffusion term. Finally, this paper is concluded by a simulation of a dam break over a wedge demonstrating the improvements proposed in this paper.     

Isogeometric variational multiscale modeling of wall-bounded turbulent flows with weakly enforced boundary conditions on unstretched meshes

In this work, we combine (i) NURBS-based isogeometric analysis, (ii) residual-driven turbulence modeling and iii) weak imposition of no-slip and no-penetration Dirichlet boundary conditions on unstretched meshes to compute wall-bounded turbulent flows. While the first two ingredients were shown to be successful for turbulence computations at medium-to-high Reynolds number [I. Akkerman, Y. Bazilevs, V. M. Calo, T. J. R. Hughes, S. Hulshoff, The role of continuity in residual-based variational multiscale modeling of turbulence, Comput. Mech. 41 (2008) 371–378; Y. Bazilevs, V.M. Calo, J.A. Cottrell, T.J.R. Hughes, A. Reali, G. Scovazzi, Variational multiscale residual-based turbulence modeling for large eddy simulation of incompressible flows, Comput. Methods Appl. Mech. Engrg., 197 (2007) 173–201], it is the weak imposition of no-slip boundary conditions on coarse uniform meshes that maintains the good performance of the proposed methodology at higher Reynolds number [Y. Bazilevs, T.J.R. Hughes. Weak imposition of Dirichlet boundary conditions in fluid mechanics, Comput. Fluids 36 (2007) 12–26; Y. Bazilevs, C. Michler, V.M. Calo, T.J.R. Hughes, Weak Dirichlet boundary conditions for wall-bounded turbulent flows. Comput. Methods Appl. Mech. Engrg. 196 (2007) 4853–4862]. These three ingredients form a basis of a possible practical strategy for computing engineering flows, somewhere between RANS and LES in complexity. We demonstrate this by solving two challenging incompressible turbulent benchmark problems: channel flow at friction-velocity Reynolds number 2003 and flow in a planar asymmetric diffuser. We observe good agreement between our calculations of mean flow quantities and both reference computations and experimental data. This lends some credence to the proposed approach, which we believe may become a viable engineering tool.     

On the application of boundary conditions to time dependent computations for quasi one-dimensional fluid flows

A study is made of the influence of boundary and initial conditions on time-dependent finite-difference solutions of quasi-one-dimensional duct flows. Several questions are addressed: (1) Under what conditions will a time-dependent solution converge to a steady-state supersonic flow, (2) Under what conditions will it converge to subsonic flow and (3) What conditions are necessary to insure a particular unique solution for subsonic flows. The results provide an orientation, or way of thinking, about the role of such conditions in time-dependent solutions of steady-state flows. The results also show that supersonic solutions are readily obtained by holding only pressure and temperature fixed at the duct inlet, and allowing velocity to float. However, subsonic solutions require pressure, temperature and velocity to be fixed at both the duct inlet and exit. If no conditions are held fixed at the exit, the results always converge to the supersonic solution, even if the fixed inlet mass flow is less than critical. In such a case, the program appears to generate additional mass flow between the inlet and throat, sufficient to choke the flow. These results also have some impact on two- and three-dimensional time-dependent solutions where subsonic flow is present on some or all portions of the flow boundaries.     

Effect of sidewall boundary conditions on unsteady high speed cavity flow and acoustics

The effect of sidewall boundary conditions on the computed unsteady flow and sound pressure level is investigated in a transonic open cavity. The hybrid approach used for modeling turbulence combines a Reynolds averaged mode in the boundary layer, and a large eddy simulation mode in the massively separated flow region within the cavity to resolve the wide dynamic range involved. Computational results are presented for the instantaneous vorticity and for the sound pressure level spectra. Comparison of the results obtained using inviscid and periodic sidewall boundary conditions show the sensitivity of the computed SPL spectra and autocorrelation to the conditions enforced at the sidewalls. The computed SPL spectra are also compared with available experimental results, with LES computational results, and with prior investigations based on the same hybrid turbulence model without the wall function used in the current investigation. The comparisons show that the current results obtained using inviscid sidewall boundary conditions are closest to the experimental sound pressure level spectra and that agreement is achieved at considerable saving in required computational resources.     

Numerical solutions of unsteady flows with low inlet Mach numbers

This study deals with a numerical solution of a 2D unsteady flow of a compressible viscous fluid in a channel for low inlet airflow velocity. The unsteadiness of the flow is caused by a prescribed periodic motion of a part of the channel wall with large amplitudes, nearly closing the channel during oscillations. The channel is a simplified model of the glottal space in the human vocal tract and the flow can represent a model of airflow coming from the trachea, through the glottal region with periodically vibrating vocal folds, and to the human vocal tract.     

Calculations of axisymmetric swirling flows by the use of parabolic type equations

Numerical solutions of boundary layer like equations are presented for steady, axisymmetric swirling flows in a pipe; the fluid is incompressible. Calculations were performed for combinations of two parameters; Wa and Ω are the velocity on the axis and the swirl strength at the upstream boundary, respectively. One of the solutions was in qualitative agreement, over some axial distance, with earlier Navier-Stokes calculations obtained by the authors.     

Numerical approximation of incompressible flows with net flux defective boundary conditions by means of penalty techniques

We consider incompressible flow problems with defective boundary conditions prescribing only the net flux on some inflow and outflow sections of the boundary. As a paradigm for such problems, we simply refer to Stokes flow. After a brief review of the problem and of its well posedness, we discretize the corresponding variational formulation by means of finite elements and looking at the boundary conditions as constraints, we exploit a penalty method to account for them. We perform the analysis of the method in terms of consistency, boundedness and stability of the discrete bilinear form and we show that the application of the penalty method does not affect the optimal convergence properties of the finite element discretization. Since the additional terms introduced to account for the defective boundary conditions are non-local, we also analyze the spectral properties of the equivalent algebraic formulation and we exploit the analysis to set up an efficient solution strategy. In contrast to alternative discretization methods based on Lagrange multipliers accounting for the constraints on the boundary, the present scheme is particularly effective because it only mildly affects the structure and the computational cost of the numerical approximation. Indeed, it does not require neither multipliers nor sub-iterations or additional adjoint problems with respect to the reference problem at hand.     

Accurate numerical simulations of vortex flows II: Interaction of swirling vortex rings

An accurate numerical method is applied to the investigation of the flow generated by two co-rotating vortex rings with axial flow in opposite direction at the Reynolds number Re = 2000. The rings are shown to generate a strong wake with significant axial vorticity due to the stretching induced by the rings. The rings merge and form a single ring with complex internal structure.     

Effects of various inlet/outlet positions and header forms on flow distribution and thermal performance in microchannel heat sink

Microsystem Technologies - Three-dimensional simulations are performed numerically to investigate the influence of inlet/outlet positions (Z-, I-, and C-type) and header forms (rectangular,...     

Purely analytic solutions of magnetohydrodynamic swirling boundary layer flow over a porous rotating disk

The prime objective of the present study is to derive analytical expressions for the solution of steady, laminar, incompressible, viscous and electrically conducting fluid of the boundary layer flow due to a rotating disk subjected to a uniform suction and injection through the wall in the presence of a uniform transverse magnetic field. To serve this purpose, the recently popular homotopy analysis method is employed to obtain the exact solutions, in contrast to the numerically evaluated ones in the literature. It is shown here that such a technique is extremely powerful in gaining magnetohydrodynamic solutions in terms of the purely exponential and decaying functions if a special care is taken into account. This makes it possible to obtain explicitly analytic solutions particularly in coincident with the Ackroyd’s solutions in (Ackroyd, 1978) [1] and with the solutions in (Ariel, 2001) [2]. The method is further shown to be capable of overcoming the difficulties existed in calculating Ackroyd’s solutions for high values of injection. Using the homotopy analysis method, electrically conducting mean velocity profiles corresponding to a wide range of suction and injection velocities can be readily computed non-iteratively and analytically. Explicit formulas are also derived for some parameters of physical significance.     

Effects of planar inlet plenums on the hydrodynamically developing flows in rectangular microchannels of complementary aspect ratios

The effects of planar inlet plenum geometry on the developing flow fields in two rectangular microchannels of reciprocal aspect ratios (H/W ∼2.75 and ∼0.40) were investigated for Re _D =  1–100 using micro particle image velocimetry (μPIV). These two microchannels were made by a precision sawing and silicon microfabrication techniques. Both the velocity profiles and centerline velocity developments were clearly resolved and extracted along the axial distance from μPIV results. The entrance lengths were found from the centerline velocities using a decaying exponential fitting function where the centerline velocity reaches 99% of the fully developed centerline velocity. The proposed fitting function showed excellent agreement with the experimental results. The planar plenum was shown to cause an upstream predevelopment resulting in the significant reductions in the entrance lengths. Two entrance length correlations were proposed in the forms of Atkinson et al.’s (AIChE J 15:548–553, 1969) and Chen’s (J Fluids Eng 95:153–158, 1973) correlations. The proposed entrance length correlations showed that acquired constant portion and slope of the entrance lengths showed 23–27 and 70–81% reductions for H/W =  2.75 while the entrance length correlation for H/W =  0.40 showed 69–73% increase and 41–63% decrease in the constant portion and slope, respectively.     

On the stability of almost parallel boundary layer flows

The spatial stability of a two-dimensional boundary-layer flow along a flat plate, including its non-parallel character, is determined by means of a multiple scale approximation. This leads to inhomogeneous Orr-Sommerfeld equations for the corrections due to the non-parallel effect. These equations have been solved by the method of order reduction. A neutral curves of total amplifications have been calculated based on the kinetic energy of the disturbance. The non-parallel effect decreasesthe stability.     

Numerical simulation of turbulent spots in channel and boundary layer flows

The initiation and early growth of spots in channel and boundary layer flows is simulated using a three-dimensional spectral code. The simulated spots show significant agreement with available experimental data for such quantities as growth rates and spreading angles. Disturbances are introduced into the center and edge of the developing channel spots to investigate the relative sensitivity of spots.     

Creases and boundary conditions for subdivision curves

Our goal is to find subdivision rules at creases in arbitrary degree subdivision for piece-wise polynomial curves, but without introducing new control points e.g. by knot insertion. Crease rules are well understood for low degree (cubic and lower) curves. We compare three main approaches: knot insertion, ghost points, and modifying subdivision rules. While knot insertion and ghost points work for arbitrary degrees for B-splines, these methods introduce unnecessary (ghost) control points.The situation is not so simple in modifying subdivision rules. Based on subdivision and subspace selection matrices, a novel approach to finding boundary and sharp subdivision rules that generalises to any degree is presented. Our approach leads to new higher-degree polynomial subdivision schemes with crease control without introducing new control points.