Features of the supercritical transition in the wake of a circular cylinder

The features of the wake behind a uniform circular cylinder atRe=200, which is just beyond the critical Reynolds number of 3-D transition, are investigated in detail by direct numerical simulations by solving 3-D incompressible Navier-Stokes equations using mixed spectral-spectral-element method. The high-order splitting algorithm based on the mixed stiffly stable scheme is employed in the time discretization. Due to the nonlinear evolution of the secondary instability of the wake, the spanwise modes with different wavelengths emerge. The spanwise characteristic length determines the transition features and global properties of the wake. The existence of the spanwise phase difference of the primary vortices shedding is confirmed by Fourier analysis of the time series of the spanwise vorticity and attributed to the dominant spanwise mode. The spatial energy distributions of various modes and the velocity profiles in the near wake are obtained. The numerical results indicate that the near wake is in 3-D quasi-periodic laminar state with transitional behaviors at this supercritical Reynolds number. The project supported by the State Key Fundamental Research Project of “Large Scale Scientific Computation Research” (G199903281)     

Control of a submerged jet in a thin rectangular cavity

An innovative method is presented for control of an oscillatory turbulent jet in a thin rectangular cavity with a thickness to width ratio of 0.16. Jet flow control is achieved by mass injection of a secondary jet into the region above the submerged primary jet nozzle exit and perpendicular to the primary nozzle axis. An experimental model, a 2-D and a 3-D computational fluid dynamics (CFD) model are used to investigate the flow characteristics under various secondary injection mass flow rates and injection positions. Two-dimensional laser Doppler anemometry (LDA) measurements are compared with results from the CFD models, which incorporate a standard k–ε turbulence model or a 2-D and 3-D realisable k–ε model. Experimental results show deflection angles up to 23.3° for 24.6% of relative secondary mass flow are possible. The key to high jet control sensitivity is found to be lateral jet momentum with the optimum injection position at 12% of cavity width (31.6% of the primary nozzle length) above the primary nozzle exit. CFD results also show that a standard k–ε turbulence closure with nonequilibrium wall functions provides the best predictions of the flow.     

Experimental study of flow patterns and regimes of condensation in horizontal three-dimensional micro-fin tubes

During condensation of R134a the flow patterns inside two three-dimensional (3-D) micro-fin tubes with different fin geometries were investigated. The flow patterns and their transitions were visibly observed and recorded. The experimental findings revealed the following results: a comparison of the condensation flow patterns in the 3-D micro-fin tubes with those in smooth tubes revealed no qualitative differences. The mist flow and the mist-annular flow that appeared in the smooth tube entrance region were not observed in 3-D micro-fin tubes. In the maps of the Mandhane flow regime and the Soliman flow regime, the area of annular flow region of the 3-D micro-fin tube extends towards lower Fr number range in the Soliman map and smaller vapor velocity range in the Mandhane map when compared with that of a smooth tube. The criterion of the flow regime transition between the annular flow and the wavy flow decreases from Fr=7 to Fr=2 in the Soliman flow regime map. However, no significant effect on the criterion for the plug flow transition was observed. The experimental data points of plug flow in the 3-D micro-fin tubes were also obtained in the same regime of smooth tube in Mandhane flow regime map. The Soliman flow regime map indicates the criterion for plug flow transition to be Fr=0.4.     

Investigation of flow mechanism of a robotic fish swimming by using flow visualization synchronized with hydrodynamic force measurement

When swimming in water by flapping its tail, a fish can overcome the drag from uniform flow and propel its body. The involved flow mechanism concerns 3-D and unsteady effects. This paper presents the investigation of the flow mechanism on the basis of a 3-D robotic fish model which has the typical geometry of body and tail with periodic flapping 2-freedom kinematical motion testing in the case of St = 0.78, Re = 6,600 and phase delay mode (φ = −75°), in which may have a greater or maximum propulsion (without consideration of the optimal efficiency). Using a special technique of dye visualization which can clearly show vortex sheet and vortices in detail and using the inner 3-component force balance and cable supporting system with the phase-lock technique, the 3-D flow structure visualized in the wake of fish and the hydrodynamic force measurement were synchronized and obtained. Under the mentioned flapping parameters, we found the key flow structure and its evolution, a pair of complex 3-D chain-shape vortex (S–H vortex-rings, S₁–H₁ and S₂–H₂, and their legs L₁ and L₂) flow structures, which attach the leading edge and the trailing edge, then shed, move downstream and outwards and distribute two anti-symmetric staggering arrays along with the wake of the fish model in different phase stages during the flapping period. It is different with in the case of St = 0.25–0.35. Its typical flow structure and evolution are described and the results prove that they are different from the viewpoints based on the investigation of 2-D cases. For precision of the dynamic force measurement, in this paper it was provided with the method and techniques by subtracting the inertial forces and the forces induced by buoyancy and gravity effect in water, etc. from original data measured. The evolution of the synchronized measuring forces directly matching with the flow structure was also described in this paper.     

Three-dimensional steady supersonic duct flow using Lagrangian formulation

In this paper, numerical simulation of three-dimensional supersonic flow in a duct is presented. The flow field in the duct is complex and can find its applications in the inlet of air-breathing engines. A unique streamwise marching Lagrangian method is employed for solving the steady Euler equations. The method was first initiated by Loh and Hui (1990) for 2-D steady supersonic flow computations and then extended to 3-D computation by the present authors Loh and Liou (1992). The new scheme is shown to be capable of accurately resolving complicated shock or contact discontinuities and their interactions. In all the computations, a free stream of Mach numberM=4 is considered.This article was processed using Springer-Verlag T_EX Shock Waves macro package 1.0 and the AMS fonts, developed by the American Mathematical Society.     

Sensitivity analysis for 3-D elastoplastic structural reliability

By taking the elastoplastic effect of structural material into account and based on 3-D elastoplastic stochastic finite element method, methods for sensitivity analysis with respect to both the distribution parameters of random variables and parameters in the limit state function are suggested. In the incremental iterative calculation, the sub-increment changingK, method and the corresponding formulas for accelerating convergence are used. The sensitivity of 3-D structural system reliability with respect to random variables is also studied.     

Simulation of cross-flow-induced vibration of cylinder arrays by surface vorticity method

The surface vorticity method (SVM), which is a fast and practical grid-free two-dimensional (2-D) method, and a fluid–structure interaction model incorporating the effects of cylinder motions and displacements is used to simulate the vortex-induced vibration of cylinder arrays at sub-critical Reynolds number Re=2.67×10⁴. The SVM is found to be most suitable for simulating a 2-D cylinder row with large-amplitude vibrations where the vorticity field and the fluid forces of the cylinder row change drastically, and the effect of the stream on the transverse direction vibration is very significant. The fluidelastic instability of a flexible cylinder row at small pitch ratio is also investigated, and the critical reduced velocity of the cylinder row at a reduced damping parameter S_G=1.29 is calculated, which is in good agreement with experimental and analytical results of the unsteady model. Vortex-induced vibration of a staggered cylinder array is simulated using different structural parameters. When the cylinders are relatively more flexible, the flow pattern changes dramatically and the fluid–structure interaction has a dominant impact on the flow field. Compared with grid-based methods, the grid-free SVM is a fast and practical method for the simulation of the FIV of cylinder arrays due to vortex shedding at sub-critical Reynolds numbers.     

Comparison of slamming and whipping loads by fully coupled hydroelastic analysis and experimental measurement

This paper proposes a numerical method for analyzing whipping using a fully coupled hydroelastic model. The numerical analysis method utilizes a 3-D Rankine panel method, 1-D/3-D finite element methods, and a 2-D generalized Wagner model, which are strongly coupled in the time domain. The computational results were compared with those of a model test of an 18 000-TEU containership. The slamming pressures and whipping responses to regular waves for bow flare and stern slamming were compared. Furthermore, the slamming pressure was decomposed into its dynamic and static components. The numerical and experimental models produced similar results. In addition, the effects of the discretization and geometric approximation of the 2-D slamming sections were investigated.     

A, φ-Ω METHOD FOR 3-D EDDY CURRENT ANALYSIS

After the field equations and the snonumuoo conditions between the interfaces for 3D eddy current problems Under various gauges were discussed, it was pointed cut in this paper that using the magnetic vector potential A. the electric scalar potential φ and Coulomb gauge ∇·A = 0 in eddy current regions and using the magntetic scalar potential Ω in the non-conducting regions are more suitable. All field equations, the boundary conditions, the interface continuity conditions and the corresponding variational principle of this method are also given.     

Numerical simulation of cross-flow around four cylinders in an in-line square configuration

Successful numerical simulations can reveal important flow characteristics and information which are extremely difficult to obtain experimentally. Two- and three-dimensional (3-D) numerical simulations of cross-flow around four cylinders in an in-line square configuration are performed using a finite-volume method. For 2-D studies, the Reynolds numbers (Re) are chosen to be Re=100 and 200 and the spacing ratio L/D is set at 1.6, 2.5, 3.5, 4.0 and 5.0. For the 3-D investigation, the simulation is only performed at a Re=200, a spacing ratio L/D=4.0 and an aspect ratio H/D=16. The 2-D studies reveal three distinct flow patterns: (I) a stable shielding flow; (II) a wiggling shielding flow and (III) a vortex shedding flow. A transformation of the flow pattern from (I) to (II) at Re=100 will increase the amplitude of the maximum fluctuating pressure on the downstream cylinder surface by 4–12 times, while a transformation of the flow pattern from (II) to (III) will enhance the maximum fluctuating pressure amplitude by 2–3 times. There is a large discrepancy between 2-D simulation and flow visualization results at L/D=4.0 and Re=200. A probable cause could be the strong 3-D effect at the ends of the cylinder at low H/D. It was found that, for an in-line square configuration at critical L/D and when H/D is lower than a certain value, 3-D effects are very significant at the ends of the cylinders. In such cases, a time-consuming 3-D numerical simulation will have to be performed if full replication of the flow phenomenon were to be achieved.     

Numerical simulation of 3-D turbulent flows over dredged trenches

A 3-D free surface flow in open channels based on the Reynolds equations with thek-ε turbulence closure model is presented in this paper. Insted of the “rigid lid” approximation, the solution of the free surface equation is implemented in the velocity—pressure iterative procedure on the basis of the conventional SIMPLE method. This model was used to compute the flow in rectangular channels with trenches dredged across the bottom. The velocity, eddy viscosity coefficient, turbulent shear stress, turbulent kinetic energy and elevation of the free surface can be obtained. The computed results are in good agreement with previous experimental data.     

A closed form solution for stress intensity factors of shear modes for 3-D finite bodies with cracks by energy release rate method

In this paper, a new analytical-engineering method of closed form solution for stress intensity factors of shear modes for 3-D finite bodies with cracks is derived by the time saving energy release rate method. Hence a complete series of useful results of stress intensity factorsK _II andK _III can be obtained. And the results provided by this method are in good agreement with some obtained by other methods.     

APPLICATION OF A MODIFIED k–ε MODEL TO THE PREDICTION OF AERODYNAMIC CHARACTERISTICS OF RECTANGULAR CROSS-SECTION CYLINDERS

Aerodynamic characteristics of rectangular cylinders of infinite length and various breadth-to-depth ratios ranging from B/D=0·6 to 8·0 were investigated numerically by a two-layerk –ε model with a modified k -production term. Although the numerical method is two-dimensional (2-D), a physically reasonable smooth, periodic vortex shedding was obtained, even in the range of high Reynolds number. This kind of behaviour cannot normally be simulated by ordinary 2-D analyses which do not incorporate a turbulence model. Various typical aerodynamic features were successfully obtained, particularly including the discontinuity in Strouhal number at the critical section of B/D=2·8 and 6·0. Also, drag coefficients and distributions of mean surface pressure were in good agreement with results of experiments and 3-D analyses for the range of B/D ratios. However, as regards the prediction of pressure and force fluctuations, since the currently available Reynolds-Averaged Navier–Stokes models are able to analyse only periodic components and not stochastic components, the total fluctuations in surface pressure and aerodynamic lift force were considerably underestimated in some cases, compared with those measured in experiments and calculated from 3-D analyses.     

Linear stability analysis of coupled parallel flexible plates in an axial flow

We study here the linear stability of N identical flexible plates with clamped–free boundary conditions forced by a uniform parallel flow. Flow viscosity and elastic damping are neglected, and the flow around the plates is assumed potential. The shedding of vorticity from the plates’ trailing edges is accounted for by introducing a force-free wake behind each plate. A Galerkin method is used to compute the eigenmodes of the system. We are interested in the effects of the number of plates and their relative distance on the stability property of the state of rest, as well as in the nature and structure of the coupled states. Detailed results are presented for the cases N=2, N=3 and N1.     

Post-necking behaviour modelled by a gradient dependent plasticity theory

The delay of the onset of localization and the post-necking behaviour for stretched thin sheets are determined by three-dimensional effects. Thus, a 2-D finite element analysis based on a local plasticity theory will give a physically unrealistic mesh dependent solution. This, in spite of the fact that the stress state, is essentially two-dimensional. By incorporating a length scale with relation to the thickness of the sheet, it is demonstrated how a 2-D finite element analysis based on a gradient dependent plasticity theory can give a good approximation of the post-necking behaviour. This is illustrated by numerical comparison of results from a full 3-D finite element analysis, with results from a 2-D finite element model based on a finite strain version of a gradient dependent J₂-flow theory. Some numerical problems in the modeling will be discussed briefly.     

THREE-DIMENSIONAL MODELING FOR THIN PLATE-LIKE STRUCTURES INCLUDING SURFACE EFFECTS BY USING STATE SPACE METHOD

<正>A three-dimensional(3-D)approach based on the state space method is proposed to study size-dependent mechanical properties of ultra-thin plate-like elastic structures considering surface effects.The structure is modeled as a laminate composed of a bulk bounded with upper and bottom surface layers,which are allowed to have different material properties from the bulk layer.State equations,including the surface properties of the structure,can be established on the basis of 3-D fundamental elasticity to analyze the size-dependent static characteristics of the thin plate-like structure.Compared with two-dimensional plate theories based size-dependent models for thin film structures in literature,the present 3-D approach is exact,which can provide benchmark results to assess the accuracy of 2-D plate theories and various numerical approaches. To show the feasibility of the proposed approach,a 3-D analytical solution for a simply supported plate-like thin structure including surface layers is derived.An algorithm is proposed for the calculation of the state equations obtained to ensure that the numerical results can reveal the surface effects clearly even for extremely thin surface layers.Numerical examples are carried out to exhibit the surface effects and some discussions are provided based on the results obtained.     

Equivalent Fracture Network Permeability of Multilayer-Complex Naturally Fractured Reservoirs

Modeling naturally fractured reservoirs (NFRs) requires an accurate representation of fracture network permeability (FNP). Conventionally, logs, cores, seismic, and pressure transient tests are used as a data base for this. Our previous attempts showed that a strong correlation exists between the fractal parameters of 2-D fracture networks and their permeability (Jafari and Babadagli, SPE 113618, Western Regional and Pacific Section AAPG joint meeting, 2008; Jafari and Babadagli, SPE Reserv Eval Eng 12(3):455–469, 2009a). We also showed that 1-D well (cores-logs) and 3-D reservoir data (well test) may not be sufficient in FNP mapping and that 2-D (outcrop) characteristics are needed (Jafari and Babadagli, SPE 124077, SPE/EAGE reservoir characterization and simulation conference, 2009b). This paper is an extension of those studies, where only 2-D (single-layer, uniform fracture characteristics in z direction) representations were used. In this paper, we considered a more complex and realistic 3-D network system. Two-dimensional random fractures with known fractal and statistical characteristics were distributed in the x- and y directions. A variation of fracture network characteristics in the z direction was presented by a multilayer system representing three different facieses with different fracture properties. Wells were placed in different locations of the model to collect 1-D fracture density and pressure transient data. In addition, five different fractal and statistical properties of the network of each layer were measured. The equivalent FNP was calculated using a commercial software package as the base case. Using available 1-D, 2-D, and 3-D data, multivariable regression analyses were performed to obtain equivalent FNP correlations for many different fracture network realizations. The derived equations were validated against a new set of synthetic fracture networks, and the conditions at which 1-D, 2-D and 3-D data are sufficient to map FNP were determined. The importance of the inclusion of each data type, i.e., 1-D, 2-D and 3-D, in the correlations was discussed. It was shown that using only 3-D data are insufficient to predict the FNP due to wide spatial heterogeneity of the fracture properties in the reservoir, which cannot be captured from single-well tests. Incorporating all types of data (1-D, 2-D, and 3-D) would result in better prediction. Also, it is recommended that the 2-D data of the most conductive layer in reservoir, which has longer fractures with a higher density, should be incorporated in the correlations.     

Reduction of dimensions in random,elastic soil medium

The paper deals with an application of the plane strain analysis in a stochastic three-dimensional soil medium. In a framework of random elasticity theory, the geostatical state of stresses and the problem of a unit force acting in a statistically homogeneous half-space are considered. Only the modulus of elasticity is considered to be random and is modelled as a three-dimensional (3-D) homogeneous random field. As the result of imposed constrains due to the plane strain assumption the additional body and surface forces are induced. In order to determine them, additional equations must be introduced. The equations in a form of constrain relations are proposed in this paper. These equations are also valid for a case of uniformly distributed external loading.First, the two-dimensional (2-D) problem and its reduction to the uni-axial strain state, for the gravity forces and uniform, unlimited surface loading is considered. Then, it is generalised into a 2-D schematization of the 3-D state. Next, the problem of a unit force acting in a statistically homogeneous half-space is considered. For a 3-D state of stress and strain the resulting stresses are compared with those for a 2-D state. These stresses for the multidimensional state of strain and stress are presented as a sum of two components. The first one reflects plane strain state stresses and is given in a form of a 3-D random field. This term allows for incorporating a spatial, 3-D soil variability into a two-dimensional analysis. The second component can be treated as a correction term and it represents the longitudinal influence of a 3-D analysis.Some numerical results are presented in this paper. The proposed method can be regarded as a framework for further research aiming at application to a variety of geotechnical problems, for which the plane strain state is assumed.     

Some Reynolds number effects on two- and three-dimensional turbulent boundary layers

Experimental data for a two-dimensional (2-D) turbulent boundary layer (TBL) flow and a three-dimensional (3-D) pressure-driven TBL flow outside of a wing/body junction were obtained for an approach Reynolds number based on momentum thickness of Re _θ =23,200. The wing shape had a 3:2 elliptical nose, NACA 0020 profiled tail, and was mounted on a flat wall. Some Reynolds number effects are examined using fine spatial resolution (Δy ⁺=1.8) three-velocity-component laser-Doppler velocimeter measurements of mean velocities and Reynolds stresses at nine stations for Re _θ =23,200 and previously reported data for a much thinner boundary layer at Re _θ =5,940 for the same wing shape. In the 3-D boundary layers, while the stress profiles vary considerably along the flow due to deceleration, acceleration, and skewing, profiles of the parameter correlate well and over available Reynolds numbers. The measured static pressure variations on the flat wall are similar for the two Reynolds numbers, so the vorticity flux and the measured mean velocities scaled on wall variables agree closely near the wall. The stresses vary similarly for both cases, but with higher values in the outer region of the higher Re _θ case. The outer layer turbulence in the thicker high Reynolds number case behaves similarly to a rapid distortion of the flow, since stream-wise vortical effects from the wall have not diffused completely through the boundary layer at all measurement stations. Received: 9 June 2000/Accepted: 26 January 2001