Some numerical schemes using curvilinear coordinate grids for incompressible and compressible Navier-Stokes equations

In this review paper some numerical schemes recently developed by the authors and their coworkers for analysing the cascade flows of turbomachinery are described. These schemes use the curvilinear coordinate grid and solve the momentum equations of contravariant velocities (volume flux). The compressible flow schemes are based on the delta-form approximate-factorization finite-difference scheme, and are improved by using the diagonalization, the flux difference splitting and thetvd schemes to save computational effort and to increase stability and resolvability. Furthermore, using higher-order compacttvd muscl schemes, we can capture not only shock waves but also contact surfaces very sharply. On the other hand, the incompressible flow schemes are based on the well-knownSMAC scheme, and are extended to the curvilinear coordinate grid and further to the implicit scheme to reduce computations. These schemes, like thesmac scheme, satisfy the continuity condition identically, and suppress the occurrence of spurious errors. In both the compressible and incompressible schemes, for the turbulent flow thek-ɛ turbulence model with the law of the wall or considering the low Reynolds number effects is employed, and for the unsteady flow the Crank-Nicholson method is employed and the solution at each time step is obtained by the Newton iteration. Use of the volume flux instead of the physical velocity is inevitable for theMAC type schemes, and makes it easy to impose boundary conditions. Finally, some calculated results using the present schemes are shown.     

Analysis of high temperature gasdynamics in a rectangular channel using a coupled core-boundary layer model

In this paper two-dimensional steady state compressible, turbulent boundary layer equations along with the core are solved for a channel of rectangular cross-section. The behaviour of core velocity, core temperature, pressure profile, friction coefficient and heat flow for different mass flow rates and inlet pressures are analysed for combustion gases. The results are compared with experimental results obtained onzinc (zero induction channel) during the commissioning of themhd plant at Tiruchirapalli. The results match the theoretical predictions quite well.     

Velocity and turbulence at a wing-wall abutment

Experimental investigation of the 3D turbulent flow field around a 45‡ wing-wall abutment, resting on a rough rigid bed, is reported. The experiment was conducted in a laboratory flume using the Acoustic Doppler Velocimeter (ADV). Profiles of time-averaged velocity components, turbulent intensity components, turbulent kinetic energy and Reynolds stresses at different azimuthal planes are presented. Vector plots of flow fields at azimuthal and horizontal planes show the presence of a primary vortex associated with the downflow in the upstream side of the abutment and a wake vortex on the downstream side. The shear stresses acting on the bed around the abutment are estimated from the Reynolds stresses and velocity gradients. The data presented in this study would be useful to researchers for future development and comparison of theoretical models of flow fields around bridge abutments.     

The Effect of Hydrodynamic Unsteadiness on the Flow Structure and on the Coefficients of Heat Transfer and Skin Friction under Conditions of Turbulent Pipe Flow of Heat-Transfer Agent

Critical analysis is made of the current status of investigations of heat transfer and skin friction under conditions of unsteady-state turbulent pipe flow. This analysis is based on the experimental data on the structure of turbulent flows and heat transfer. Comparison is made of experimental and theoretical results.     

基于蜂群算法的等压灌装阀阀口流道结构优化

目的为了改善等压灌装阀的灌装性能,分析阀口流道结构参数对液料流场的影响,求解流道内最大压力损失、最大液料流速和最大湍动能均最小化的约束多目标优化问题。方法基于正交试验设计和Fluent流场仿真软件对灌装阀阀口流道流场进行数值模拟,并通过回归分析建立以阀口流道结构参数为自变量的最大压力损失、最大液料流速和最大湍动能的经验方程,进而建立阀口流道结构参数约束多目标优化模型,采用约束多目标人工蜂群算法对优化模型进行求解。结果流道内最大压力损失最小化、最大液料流速最小化和最大湍动能最小化这3个目标之间存在冲突,无法同时达到最优,基于多目标人工蜂群算法获得了阀口流道结构参数的最优Pareto解集。结论约束多目标人工蜂群算法能有效用于等压灌装阀阀口流道结构参数的优化。     

Direct Numerical Simulation of Turbulence at Lower Costs

Direct Numerical Simulation (DNS) is the most accurate, but also the most expensive, way of computing turbulent flow. To cut the costs of DNS we consider a family of second-order, explicit one-leg time-integration methods and look for the method with the best linear stability properties. It turns out that this method requires about two times less computational effort than Adams–Bashforth. Next, we discuss a fourth-order finite-volume method that is constructed as the Richardson extrapolate of a classical second-order method. We compare the results of this fourth-order method and the underlying second-order method for a DNS of the flow in a cubical driven cavity at Re= 10⁴. Experimental results are available for comparison. For this example, the fourth-order results are clearly superior to the second-order results, whereas their computational effort is about twenty times less. With the improved simulation method, a DNS of a turbulent flow in a cubical lid-driven flow at Re = 50,000 and a DNS of a turbulent flow past a square cylinder at Re = 22,000 are performed.     

Analysis and control of dynamic stall phenomenon using Navier-Stokes formulation involving vorticity,stream function and circulation

An unsteady Navier-Stokes (ns) analysis is developed for studying flow past a maneuvering body. The present inclusion ofcirculation in the earlierns analysis of the authors makes it feasible,for the first time, to accurately simulate the asymptotic far-field boundary condition. In the overall analysis, a clustered conformal mesh withC-grid topology is used, with the governing differential equations being solved using the implicitadi-bge technique. The effects of grid size and clustering on the flow solution, and the effect of grid stretching on the far-field solution, are studied using the flow configuration with Re=45,000 and constantrate pitch-up motion, with . The results obtained for this case compare very satisfactorily with available experimental data. Other numerical results are also used for carefully validating the analysis developed here. Anactive control strategy, consisting of modulated suction/injection at the airfoil surface, is studied, and provides satisfactory control of the unsteady separation process and, hence, of the dynamic stall vortex. This research is supported, in part, byafosr Grant Nos. 90-0249 and F49620-92-J-0292, and Ohio Supercomputer Center Grant No.pes080.     

Direct numerical simulation of flow and surface reaction in de-NOx catalyst

Selective catalytic reaction is a very efficient method to reduce NO_x emissions from thermal power plants and is widely used in Japan. To develop a higher performance de-NO_x system and optimize its maintenance schedule, it is important to understand the NO_x reduction mechanism in the honeycomb channel which supports the de-NO_x catalysts. In this study, the effects of duct channel flow behavior on the de-NO_x reaction at the catalyst surface were investigated using a direct numerical simulation (DNS). The DNS computations were performed for three inflow conditions, one laminar and two turbulent. The results show that although the flow transitions from turbulent to laminar flow as the flow moves downstream for the turbulent inflow conditions, de-NO_x reaction rates for the turbulent inflow conditions are higher than that for the laminar inflow condition even in the downstream region. This is because of the remaining cross-sectional fluid motions caused by the inflow turbulence. As a result, de-NO_x efficiencies for the turbulent conditions are higher than that for the laminar case. For both laminar and turbulent inflow conditions, de-NO_x reaction is suppressed in the corner regions due to the flow stagnation.     

Vorticity field structure associated with the 3D Tollmien-Schlichting waves

Details of the vorticity field structure associated with the 3D Tollmien-Schlichting waves have been examined based upon the recent numerical studies of the subject. First, a single obliquet-s wave has been found to have the velocity component parallel to the wave front playing an overall dominant role, in particular, to create the longitudinal vorticity. The so-called Benney-Lin longitudinal vortices are then demonstrated to be, in fact, a minor consequence compared with the localized longitudinal vorticity field and its periodic pumping. Finally, the formation of the longitudinal vorticity field in the fundamental- and subharmonic-mode interactions is explained. The research reported in this paper has been supported in part by Bundesministerium für Forschung und Technologie and by Deutsche Forschungsgemeinschaft. The major part of the paper has been presented at the Third Asian Congress of Fluid Mechanics, 1–5 September 1986, in Tokyo, as a General Lecture by the senior author, FRH.     

X-ray spectroscopy and local structures in glasses

X-ray spectroscopy which is a combination of two techniques, namely x-ray absorption near edge structure (xanes) and extended x-ray absorption fine structure (EXAFS) analyses, is a unique technique for the study of local structures in glasses. Availability of synchrotron radiation sources has made the technique quite attractive and useful because the photon flux from synchrotrons is very intense and polarized. In this article, a brief summary ofxanes andEXAFS techniques is given along with a few applications to the study of local structures in glasses. Communication No. 323 from Solid State and Structural Chemistry Unit.     

A review of computerized tomography with application to two-phase flows

The technique of computerized tomography (Ct) has established itself as a leading tool in diagnostic radiology over the past twenty years and is catching on fast in the non-destructive evaluation area in a variety of situations. Ct instrumentation involves a source and a detector system to scan the object of interest. The source can be acoustic, microwave, X-ray, gamma-ray, etc. depending upon the type of material being investigated. For fluid-flows, gamma-rays are quite suitable. There are basically two types of data collection geometries — fan-beam and parallel beam. Fan-beam requires less number of sources as one source feeds several detectors arranged in a fan-beam. The use ofCt in multi-phase flow studies has been limited presently to only a few laboratory experiments and the results indicate thatCt does hold a lot of promise as an effective investigative methodology to understand some of the complex phenomena encountered in multi-phase flows. Some newCt algorithms developed specifically for pipe-flows have shown good results on some air-water flow data for a 15 cm dia pipe.     

Characteristics of a typical lifting symmetric supercritical airfoil

The theoretical aerodynamic characteristics of a typical lifting symmetric supercritical airfoil demonstrating its superiority over thenaca 0012 airfoil from which it was derived are presented in this paper. Further, limited experimental results confirming the theoretical inference are also presented. Invited Lecture given at the 3rd Asian Congress on Fluid Mechanics, held in Tokyo during 1–5 September, 1986     

Metallic glasses

Metallic glasses are a new class of materials produced by rapidly quenching the melts at rates often exceeding a million deg/sec. These have been found to display an optimum combination of properties such as high strength, good bend ductility, improved corrosion resistance and excellent soft magnetic properties. Thus, metallic glasses are emerging as economically viable competitors to conventional engineering materials. A clear understanding of the atomic structure of metallic glasses and its change during annealing are of prime importance. Although techniques such as field-ion microscopy (fim) x-ray diffraction and small angle x-ray scattering have been employed for this purpose, high resolution electron microscopic (hrem) investigations conducted during the last few years aided greatly in deriving information on the atomic scale. Availability of high-voltage high-resolution electron microscopes has been mainly responsible for this happy situation. Studies on several metallic glasses have revealed thathrem images contain well-defined pattern of fringes over local regions, even though the diffraction pattern is that of a typical amorphous structure. The details of structure in the early stages of crystallization derived throughhrem, fim and analytical microscopic techniques are presented and discussed.     

Turbulence/shock wave interactions in chemically reacting flows

Physical interactions between turbulence and shock waves are very complex phenomena. If these interactions take place in chemically reacting flows, the degree of complexity increases dramatically. Examples of applications may be cited in the area of supersonic combustion, in which the controlled generation of turbulence and/or large scale vortices in the mixing and flame-holding zones is crucial for efficient combustion. Equally important, shock waves interacting with turbulence and chemical reactions affect the combustor flowfield resulting in enhanced relaxation and chemical reaction rates. Chemical reactions in turn contribute to dispersion of shock waves and reduction of turbulent kinetic energies. Computational schemes to address these physical phenomena must be capable of resolving various length and time scales. These scales are widely disparate and the most optimum approach is found in explicit/implicit adjustable schemes for the Navier-Stokes solver. This is accomplished by means of the generalized Taylor-Galerkin (gtg) finite element formulations. Adaptive meshes are used in order to assure efficiency and accuracy of solutions. Various benchmark problems are presented for illustration of the theory and applications. Geometries of ducted rockets, supersonic diffusers, flame holders, and hypersonic inlets are included. Merits of proposed schemes are demonstrated through these example problems. This research was supported by the US Army Missile Command (daah01-91-D-R002) and National Science Foundation (asc-8918081) and contributions were made by a number of graduate students, notably by W S Yoon.     

Preparation and characterization of <Emphasis Type="SmallCaps">l-</Emphasis>cystine and <Emphasis Type="SmallCaps">l-</Emphasis>cysteine intercalated layered double hydroxides

l-cystine and l-cysteine have been intercalated into magnesium–aluminum layered double hydroxide by the methods of coprecipitation and ion-exchange. The structure and composition of the intercalated materials have been characterized by X-ray diffraction (XRD), Fourier transform infrared (FT-IR) spectroscopy and elemental analysis. For l-cysteine intercalated composites, two kinds of well-crystallized materials with different basal spacing were obtained, as a result of the different charge on an ion and orientation of the gallery anions. The schematic models of the intercalation structures were proposed. In addition, the thermal decomposition of l-cystine and l-cysteine intercalated LDHs has been investigated by means of thermogravimetry and differential thermal analysis (TG-DTA).     

Rotating-disk-type flow over loose boundaries

Rotating-disk-type flow of a liquid over a loose boundary, such as a layer of sand, is investigated. For this flow the formation of a new large-scale spiral pattern has been discovered. The new pattern is reminiscent of the Type-I spiral-vortex structures which characterize the laminar–turbulent transition region of boundary layers over rigid rotating disks. Flow visualizations reveal that the new pattern and the Type-I spiral vortices co-exist in the loose-boundary flow. The research investigating the origin of the new large-scale pattern is reviewed. Then photographs from flow visualizations are analysed to obtain estimates for the critical Reynolds number for which Type-I spiral vortices first appear for the loose-boundary flow and for the critical Reynolds numbers for the laminar–turbulent transition of the boundary layer. The results suggest that Type-I vortices appear at much lower Reynolds numbers over loose boundaries in comparison with flow over rigid rotating disks and that transition also appears to be advanced to much lower Reynolds numbers. The discussion of the results suggests that advanced transition arises from disturbances introduced into the flow after the loose boundary has been mobilized and not from disturbances associated with the roughness that the surfaces of the granular layer represents to the flow while grains are at rest.     

Computational techniques and validation of 3-dimensional viscous/turbulent codes for internal flows

Computational techniques and codes developed for the prediction of three-dimensional turbulent flows in internal configurations and rotor passages are described. Detailed calibration and validation of the flow fields in 90° curved ducts, cascades, end-wall flows and turbomachinery rotors are presented. Interpretation and comments on accuracy, level of agreement with various turbulence models and limitations of the codes are described. The single pass space-marching code is found to be efficient for curved duct and two-dimensional cascade flows. Multipass space-marching, time-marching and zonal methods are found to be accurate for complex situations. The efficiency and accuracy of a zonal technique, with considerable saving in computational time, is demonstrated. Paper presented atagard Symposium “Validation of Computational Fluid Dynamics,” May 2–5, 1988, Lisbon, Portugal The research work on computation was sponsored by the David Taylor Naval Ship Research and Development Center with Dr D Fuhs as the technical monitor, and NASA Lewis Research Center with Dr P Sockol as the technical monitor.     

Typical flow between enclosed corotating disks and its dependence on Reynolds number

Abstract

The flow in an enclosed co‐rotating disk pair is investigated by Laser Doppler Velocimetry (LDV) measurements and flow visualizations. First, the typical flow structure at Re = 5.25 × 10⁵ and S = 0.09 is clarified. The flow fields in the r – θ and the r – z planes are both investigated and then divided into several flow regions based on the distinct flow types observed. The flow regions found in the two different planes are also compared and integrated. Second, with S fixed, the dependence of the flow field structure upon the Reynolds number is discussed. Three regimes of the r – θ plane flow with different Reynolds numbers are identified based on the measured mean velocity and spectral intensity. When Re < 1.6 × 10⁵, no solid body region is found and the flow is in a laminar regime. In the range 1.6 × 10⁵ ≤ Re ≤ 2.0 × 10⁶, the solid body region and the outer region vortices coexist, and an empirical equation is developed to estimate the number of vortices. When Re > 2.0 × 10⁶, the flow becomes turbulent. As Re increases from 9.3 × 104 to 5.25 × 10⁵, the spectral intensity initially increases and then decreases before increasing again to an even higher level, resulting in an increasing sawtooth pattern.     

Serrated plastic flow

This paper attempts an assessment of the current understanding of the phenomenon of “serrated plastic flow”, which manifests itself as serrations, load drops, jerkiness or other discontinuities in the stress-strain curves obtained in constant extension rate tensile tests, and as sudden bursts of strain in constant loading rate tests and in constant load (stress) creep tests (the so called staircase creep). Though one can identify at least seven physical processes that can cause serrations, the discussion here is restricted mainly to serrated yielding in tension tests originating from dynamic strain ageing (dsa). The characteristics of the five types of serrations that have been identified so far and the experimental conditions under which they occur are discussed. The various models of serrated flow that have been put forward are reviewed critically. Some recent results on 316 stainless steel are presented to illustrate the effects of grain size, temperature and strain rate on serrated flow. Manifestations ofdsa other than serrations such as a negative strain rate sensitivity, positive temperature dependence for flow stress and work hardening, and the ductility minimum are also discussed. Finally the various issues to be resolved are enumerated.     

Carbonization behavior of <Emphasis Type="SmallCaps">l</Emphasis>-tryptophan and gluten

Carbonization behavior of l-tryptophan and gluten has been investigated in comparison with that of acenaphthylene using CHN elemental analysis, wide angle X-ray diffractometry, laser Raman spectroscopy and polarizing light microscopy. The carbon derived from l-tryptophan by the heat-treatment at 3,000 °C showed almost the same degree of graphitization as that from acenaphthylene and the average interlayer spacings of both these carbons approached to 0.3354 nm. The average interlayer spacing of the carbon from gluten, on the other hand, did not approach to this value at 3,000 °C. The crystallites in the carbon from l-tryptophan were smaller than those in the carbon from acenaphthylene but larger than those in the carbon from gluten. The ratio, R, of the intensity of the Raman band at 1,360 cm⁻¹ against that at 1,580 cm⁻¹ and the half width, Δλ, of the Raman band at 1,580 cm⁻¹ were measured. The R and Δλ are the measures for the degree of graphitization. Those values for the carbon from l-tryptophan were nearly equal to those for the carbon from acenaphthylene and smaller than those for the carbon from gluten. The thin film of l-tryptophan heat-treated at 500 °C for 2 h showed a texture consisting of a fine mosaic mesophase structure and an anisotropic flow-type texture of mesophase.