Effect of pressure-dependent slip on flow curve multiplicity

Various microstructural pictures for slip at polymer/solid interfaces lead to relations which have a region where multiple values of slip velocity are predicted for the same shear stress. This leads to the expectation of multivalued flow curves, which has been verified in specific cases by numerous researchers. We study the effect of pressure dependence on flow curve multiplicity using a simple multivalued slip relation to model the phenomena of hysteresis and spurt flow in polymer extrusion. A continuation technique is used to trace out the boundaries of the region of flow curve multiplicity as pressure drop and die length to diameter (L/D) ratio are changed. Results for Newtonian, shear thinning and viscoelastic constitutive equations show that, despite the multivalued nature of the slip model, multiplicity (and thus hysteresis) is absent at high L/D.  For the sake of completeness, we also carry out time-dependent simulations at constant piston speed taking fluid compressibility into account. These simulations show that oscillations in the pressure drop and exit volumetric flow rate result only if the system is operated in the multiplicity region of the steady state flow curve, in agreement with the results of similar simulations by researchers using various multivalued slip models without pressure dependence. The results demonstrate that a multivalued slip model does not guarantee multiplicity in the flow curve for the constant pressure drop operation, nor oscillations for constant piston speed operation. Received: 18 August 1997 Accepted: 30 March 1998     

Multi-dimensional simulation of thermal non-equilibrium channel flow

The Homogenous Relaxation Model (HRM) is used to study thermal non-equilibrium, two-phase flows with flash-boiling and condensation. Typically, such non-equilibrium phase-change models have been studied in one-dimensional flow, but the goal of the present work is to create and utilize a multi-dimensional CFD implementation. The simulations are able to handle general polyhedral meshes, an important convenience for irregular channel or nozzle shapes. The model is applied to flash-boiling flow in short channels and validated against experimental measurements. The simulations predict the multi-dimensional features that have been observed in the past in experiments. Nozzle choking is also observed in the calculations.     

Calculation of the natural frequencies and the principal modes of helicopter blades

Summary A procedure for calculating the natural frequencies and the principal modes of rotating helicopter blades based on the transfer matrix method is described. The blade is divided into a finite number of elements considered as continuous. A solution involving less laborious calculation, in which the masses are assumed to be concentrated, is also supplied.The advantage of the method developed is that it takes due account of the effective rotor-shaft constraints.Some numeric applications are given.

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Sommario Nel presente lavoro si espone un metodo di calcolo delle frequenze proprie e delle deformate di pale d'elicottero rotanti basato sul metodo delle matrici di trasferimento. Con tale metodo la pala viene suddivisa in un numero finito di tronchi considerati come continui. Si espone pure a scopo di confronto una soluzione meno gravosa per il calcolo in cui si assumono concentrate le masse.Il metodo esposto permette di tener conto con particolare cura delle effettive condizioni di vincolo del rotore con l'albero.Si riportano infine alcune applicazioni numeriche.

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跨音速湿空气非平衡凝结流动的数值研究

跨音速流动条件下湿空气中的水蒸气由于快速膨胀而发生非平衡凝结,凝结潜热对跨音速气流进行加热,会显著改变气流的流动特性。通过对商用计算流体动力学软件FLUENT进行二次开发,建立了湿空气非平衡凝结流动的数值求解方法。该方法可用于二维或三维、粘性或无粘、内流或外流的求解中。采用该方法分剐对缩放喷管、透平叶栅以及绕CA-0.1圆弧翼型的湿空气非平衡凝结流动进行了数值分析。计算结果表明：湿空气凝结手l起缩放喷管中的凝结激波、导致叶橱流动中总压降低;对于翼型周围的流动,在相对湿度分别为50％、57．1％、64.1％时,依次计算得到了单激波、五激波、双激波。     

非结构混合网格化学非平衡粘性绕流数值模拟

在非结构混合网格上对化学非平衡粘性绕流进行了数值模拟。控制方程为考虑了化学非平衡效应的二维Navier-Stokes方程,化学动力学模型为7组元、7反应模型。控制方程中的对流项采用VanLeer逆风分裂格式处理,并应用MUSCL方法及Minmod限制器扩展到二阶精度,粘性项用中心差分格式处理。时间推进采用显式5步龙格-库塔方法。为了适应高超声速流场计算,对VanLeer通量分裂方法进行了改进,并引入了化学反应时间步长。对RAMC-II模型的飞行试验流场进行了数值模拟,计算结果与试验测量数据符合较好,并与参考文献中的数值模拟结果吻合。     

Measurement of the relaxation time in Darcy flow

The inertia of a liquid flowing through a porous medium is normally ignored, but if the acceleration is great, it may be important. The relaxation time, defined so that it alone accounts for the inertia, has been determined experimentally with a simple oscillator. A U-Tube is provided with a porous plug and filled with a liquid. During pendulation of the liquid, the frequency and the damping define the relaxation time. The measured value of the relaxation time is about 10 times the theoretical estimate derived from Navier-Stokes equation.Symbols E modulus of elasticity - E _D dissipated energy - E _k kinetic energy - g acceleration of gravity - G pressure gradient - h height - K ₀ permeability - L length of porous plug - n porosity - P dissipated power - pressure - R half the tube length - R _c radius of the tube bend - r radial coordinate - r _o radius of the tube - s coordinate along a streamline in the tube - t time - v flux per unit area - it relaxation time - , auxiliary variables - , v dynamic and kinematic viscosity - , velocity potential for inviscid flow and gravity potential - dissipation function - displacement of the liquid - , _o frequency of damped and undamped oscillations     

Consequences of the second law for a turbulent fluid flow

Second Law statements in thermomechanics applicable to turbulent fluid flow, in which the internal energy in a macroscopic field theory includes contributions both from molecular vibrations and from turbulent fluctuations, are discussed. In the absence of turbulence, these statements naturally reduce to the known and accepted Second Law statements for a nonturbulent medium. The usual version of the Second Law statements — which deny the existence of perpetual motion and place restrictions on the constitutive equations —is extended here in the presence of turbulence; and an additional statement is introduced associated with the tendency of turbulent fluctuations to decay in the absence of external work or the addition of thermal heat. The mathematical representations of various Second Law statements are then used to derive several restrictions on the response variables of the macroscopic turbulence theory. Examples of such variables include the rates of production and dissipation of turbulent fluctuations, the rate of thermal entropy production, internal energy (involving constitutive coefficients which may be taken to be the thermal and turbulent specific heats), turbulent viscosity coefficients and other response functions which control the degree of flow anisotropy in the medium. These Second Law restrictions are then applied to a recent theory of macroscopic turbulent flow by the present authors in which fairly general constitutive equations are presented for the dependent variables of the theory. It is found that not only is the range of values of several constitutive coefficients limited by these Second Law restrictions, but the presence of a number of terms in the constitutive equations is entirely denied.     

Couette flow of a binary mixture of rigid-sphere gases described by the linearized Boltzmann equation

A concise and accurate solution to the problem of plane Couette flow for a binary mixture of rigid-sphere gases described by the linearized Boltzmann equation and general (specular-diffuse) Maxwell boundary conditions for each of the two species of gas particles is developed. An analytical version of the discrete-ordinates method is used to establish the velocity, heat-flow, and shear-stress profiles for both types of particles, as well as the particle-flow and heat-flow rates associated with each of the two species. Accurate numerical results are given for the case of a mixture of helium and argon confined between molybdenum and tantalum plates.     

Effect of flow on the magnetization relaxation process in a magnetic fluid

The effect of shear flow (flow in a circular tube) on the process of relaxation of the magnetization of a magnetic fluid is investigated theoretically and experimentally. The experiments reveal a jump in the high-frequency susceptibility when the flow stops. This jump depends on the measurement frequency on the interval from 2 to 40 kHz, on the flow rate and on the structure of the magnetic fluid. A theory describing the dependence of the jump in high-frequency susceptibility on the frequency and the structure and flow rate of the fluid is proposed. The theory is found to be consistent with the experimental data.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 94–98, November–December, 1988.     

On transition of type V interaction in double-wedge flow with non-equilibrium effects

The transition between regular reflection(RR) and Mach reflection(MR) of type V shock–shock interaction on a double-wedge geometry with high temperature non-equilibrium effects is investigated by extended shock-polar method and numerical simulation. First, the critical angles of transition from detachment criterion and von Neumann criterion are determined by the extended shock-polar method considering the non-equilibrium effects. Then wave patterns and the transition process are numerically obtained. Results of the critical transition angles from shock-polar calculation and numerical simulation show evident disagreement, indicating transition mechanism between RR and MR of type V interaction is changed. By comparing with the frozen counterpart, it is also found that non-equilibrium effects lead to a larger critical wedge angle and a larger hysteresis interval.     

Multiple-relaxation-time lattice Boltzmann method for study of two-lid-driven cavity flow solution multiplicity

As a fundamental subject in fluid mechanics, sophisticated cavity flow patterns due to the movement of multi-lids have been routinely analyzed by the computational fluid dynamics community. Unlike those reported computational studies that were conducted using more conventional numerical methods, this paper features employing the multiple-relaxation-time (MRT) lattice Boltzmann method (LBM) to numerically investigate the two-dimensional cavity flows generated by the movements of two adjacent lids. The obtained MRT-LBM results reveal a number of important bifurcation flow features, such as the symmetry and steadiness of cavity flows at low Reynolds numbers, the multiplicity of stable cavity flow patterns when the Reynolds number exceeds its first critical value, as well as the periodicity of the cavity flow after the second critical Reynolds number is reached. Detailed flow characteristics are reported that include the critical Reynolds numbers, the locations of the vortex centers, and the values of stream function at the vortex centers. Through systematic comparison against the simulation results obtained elsewhere by using the lattice Bhatnagar–Gross–Krook model and other numerical schemes, not only does the MRT-LBM approach exhibit fairly satisfactory accuracy, but also demonstrates its remarkable flexibility that renders the adjustment of its multiple relaxation factors fully manageable and, thus, particularly accommodates the need of effectively investigating the multiplicity of flow patterns with complex behaviors.     

Effects of under‐relaxation factors on turbulent flow simulations

Under‐relaxation factors are significant parameters affecting the convergence of a numerical scheme. Some earlier work has been done to optimize these parameters, but this was restricted to special flow domains, and the range of changes for under‐relaxation factors and convective algorithms are limited. In this paper, the effects of changing under‐relaxation factors for different variables, different convective schemes and grid sizes on the convergence of the numerical solution of three 2D turbulent flow situations are studied. These three flows are duct flow, trench flow and inclined free falling jet flow. Copyright © 2003 John Wiley & Sons, Ltd.     

PML absorbing boundary conditions for the linearized and nonlinear Euler equations in the case of oblique mean flow

For the case of uniform mean flow in an arbitrary direction, perfectly matched layer (PML) absorbing boundary conditions are presented for both the linearized and nonlinear Euler equations. Although linear perfectly matched side layers with an oblique mean flow have been studied in previous works, we propose in the present paper a construction of corner layer equations that are dynamically stable. Stability issues are investigated by examining the dispersion relations of linear waves supported by the corner layer equations. For increased efficiency, a pseudo mean flow is included in the derivation of the PML equations for the nonlinear case. Numerical examples are given to support the validity of the proposed equations. Specifically, the linear PML formulation is tested for the case of acoustic, vorticity, and entropy waves traveling with an oblique mean flow. The nonlinear formulation is tested with an isentropic vortex moving diagonally with a constant velocity. Copyright © 2008 John Wiley & Sons, Ltd.     

Radar imaging of water surface flow fields

 We describe the capabilities of coherent high resolution radar to observe remotely the effects of an upwelling subsurface flow on the water surface. This observation is possible because the radar radiation backscatters very strongly from surface features with dimensions similar to its wavelength, in this case X-band at 0.03 m. This technique provides imaging capability with relatively high spatial resolution (∼0.3 m) and fast time sampling (∼0.006 s) over a large surface area. The processed data reveal both the line-of-sight velocity spectrum of moving water surface features, and their water surface radar backscatter cross-section. We believe that the surface features are generated by subsurface vortices oriented normal to the surface. The vortices are advected with the bulk flow of the jet. Our radar observations of the down-stream flow from a submerged waterjet that is directed parallel to the surface are consistent with those previously measured by laser velocimetry. Received: 25 February 1994/Accepted: 16 May 1996     

Stress relaxation of a polymer melt after extensional flow

The relaxation behaviour of a stretched polymer melt is described with the aid of the semi-empirical constitutive equation of Wagner. The theoretical predictions based on this model, are in fair agreement with the experimental results, as far as the period of stress decay following the stress build-up is not too long.