Number Flow Research Articles

Secondary Flow in a Strong Curved Converging Channel

A three-dimensional model is developed to evaluate the effect of secondary flow generated from strongly bent duct profiles and turbulent flow of high Reynolds number on fibre movement in a bent channel. The fibre configuration is more complex in a three-dimensional model with the introduction of secondary flow. The strategies of mesh generation for threedimensional problems are discussed. The flow characteristic in the transfer-channel of a rotor spinning machine is predicted.

On the minimum of extended dissipation in viscous nematodynamics

This paper develops the variational principle of minimum “extended” dissipation for slow (low Reynolds number) flows of nematic liquids as described by the five parametric Leslie–Ericksen–Parodi (LEP) constitutive equations. It is shown that the Euler’s equations for minimizer of the extended dissipative functional are the Stokes equations for the LEP fluid. When the molecular (including magnetic) field is absent, the extended dissipative functional coincides with the true dissipative functional, whose Euler equations are the Stokes equations for the Ericksen fluid.

격자 볼츠만 방법을 이용한 미소 채널에서의 혼합효율 증가를 위한 수동형 믹서의 최적화

In this work, Scalar Passive code in Lattice Boltzmann Method is employed to simulate two-phase flow of low Reynolds number in a micro-channel. The mixing characteristics in a micro-channel is a function of Peclet number. The mixing length increases with the Peclet number. It is found that with the inclusion of static elements at the channel, rapid mixing of two liquids can be achieved, as shown by the results of computer simulations. The enhancement in mixing performance is thought to be caused by the generation of eddies and by lateral velocity component when the mixture flows past static elements. The results indicate that the size of static element has more effect on the mixing than the number of static element.

Reduced-basis modeling of turbulent plane channel flow

Very-large-eddy simulations of turbulent plane channel flow of various Reynolds numbers have been performed. The simulations are based on relatively small sets of modes from a proper orthogonal decomposition (POD) of a direct numerical simulation or large-eddy simulation of the same flow. The intention is to investigate how these reduced basis simulations respond to change in Reynolds number and geometry. We find that the dynamical systems are able to reproduce the mean velocity and Reynolds stress profiles as long as the aspect ratio of the channel or the Reynolds number does not increase or decrease from the original setting with more than 50% or 30%, respectively. When the objective is a coarse description of the flow dynamics, significant savings in terms of computational cost are achieved by deriving the dynamical systems from the POD-basis. One possible application of such reduced basis simulations can be to efficiently generate turbulent inlet boundary conditions for direct numerical simulations.

Dissipative soft modes in viscous nematodynamics

The paper analyses a possible occurrence of soft and semi-soft viscous modes in slow (low Reynolds number) flows of uniaxially anisotropic nematic liquids as described by the five parametric Leslie-Ericksen-Parodi (LEP) constitutive equations (CEs). As in the similar elastic case, the soft viscous modes theoretically cause no resistance to flow, nullifying the corresponding components of the viscous part of the total stress tensor, and do not contribute to the dissipation. That is why these modes can also be called dissipative soft modes. In some flows, these dissipative soft modes may cause the effect of “nematic superfluidity”. As in the theories of nematic elastic solids, this effect is caused by a marginal thermodynamic stability. The analysis is simplified in a specific local, rotating orthogonal coordinate system whose one axis is directed along the director. We demonstrate that depending on closeness of material parameters to the marginal stability conditions, LEP CEs describe the entire variety of soft, semi-soft and harder behaviors of nematic viscous liquids. When the only shearing dissipative modes are soft, the viscous part of stress tensor is symmetric, and LEP CE for stress, scaled with isotropic viscosity is reduced to a one-parametric, stress-strain rate anisotropic relation. When additionally the elongation dissipative mode is also soft, this scaled relation has no additional parameters and shows that the dissipation is always less than that in isotropic phase. Simple shearing and simple elongation flows illustrate these possible effects.

Insight into the flow‐condition‐based interpolation finite element approach: solution of steady‐state advection–diffusion problems

AbstractThe flow‐condition‐based interpolation (FCBI) finite element approach is studied in the solution of advection–diffusion problems. Two FCBI procedures are developed and tested with the original FCBI method: in the first scheme, a general solution of the advection–diffusion equation is embedded into the interpolation, and in the second scheme, the link‐cutting bubbles approach is used in the interpolation. In both procedures, as in the original FCBI method, no artificial parameters are included to reach stability for high Péclet number flows. The procedures have been implemented for two‐dimensional analysis and the results of some test problems are presented. These results indicate good stability and accuracy characteristics and the potential of the FCBI solution approach. Copyright © 2005 John Wiley & Sons, Ltd.

Estimating Results of a Proposed Simple Performance Test for Hot-Mix Asphalt from Superpave Gyratory Compactor Results

This study intended to use the Superpave® gyratory compactor (SGC) as a basis for estimating the stability of asphalt mixtures as a surrogate for proposed method for the simple performance test. Several asphalt mixtures were produced with varying aggregate sources, asphalt contents, and gradations. Every mixture was compacted with the SGC and evaluated with the repeated compression test procedure for rutting measurements recommended by NCHRP Project 9–19 and the AASHTO 2002 pavement design manual to evaluate whether the results from the SGC can be related to the rutting of mixtures. Densification curves produced by the SGC were used to determine the volumetric properties besides the calculation of the traffic densification index (TDI), which represents the densification experienced by traffic loading during pavement service life. The traffic force index (TFI) was also calculated with a special accessory added to the SGC during compaction (the pressure distributor analyzer). The TFI represents the work done by the traffic to densify the mixture. Results from the mixture rutting tests were used to estimate the flow number (FN). The FN, an important mixture property, is shown to have a strong correlation to the TFI. The TFI was also found to be strongly correlated with the TDI and gives an opportunity to estimate the mixture resistance to compaction forces with the use of its volumetric behavior. The main finding of the study is that the SGC appears to give information that can be used to characterize the stability of the mixtures. Such information could be used as an initial screening criterion to select mixtures for various traffic levels.

Estimating Results of a Proposed Simple Performance Test for Hot-Mix Asphalt from Superpave Gyratory Compactor Results

This study intended to use the Superpave® gyratory compactor (SGC) as a basis for estimating the stability of asphalt mixtures as a surrogate for proposed method for the simple performance test. Several asphalt mixtures were produced with varying aggregate sources, asphalt contents, and gradations. Every mixture was compacted with the SGC and evaluated with the repeated compression test procedure for rutting measurements recommended by NCHRP Project 9–19 and the AASHTO 2002 pavement design manual to evaluate whether the results from the SGC can be related to the rutting of mixtures. Densification curves produced by the SGC were used to determine the volumetric properties besides the calculation of the traffic densification index (TDI), which represents the densification experienced by traffic loading during pavement service life. The traffic force index (TFI) was also calculated with a special accessory added to the SGC during compaction (the pressure distributor analyzer). The TFI represents the work done by the traffic to densify the mixture. Results from the mixture rutting tests were used to estimate the flow number (FN). The FN, an important mixture property, is shown to have a strong correlation to the TFI. The TFI was also found to be strongly correlated with the TDI and gives an opportunity to estimate the mixture resistance to compaction forces with the use of its volumetric behavior. The main finding of the study is that the SGC appears to give information that can be used to characterize the stability of the mixtures. Such information could be used as an initial screening criterion to select mixtures for various traffic levels.

Modeling of Gravity Effects on the Collision Frequency of Monodisperse Particles in Turbulent Flows

Collisions of monodisperse particles in turbulent flows are important phenomena appearing in both the mechanical engineering and cloud microphysics. Although many researchers investigated the phenomena, they neglected the gravity effects in order to use a simple assumption of isotropic particle motions. In this study, we therefore investigated the gravity effects on the collision frequency and proposed a model that can predict the effects. We confirmed the reliability of the proposed model with the data obtained by direct numerical simulations (DNS). Furthermore, we clarified that, although the gravity effects are significant for moderately small Re number flows, they are negligibly small in typical convective clouds.

ASSESSING THE PROBABILISTIC FUZZY NET PRESENT VALUE FOR A CAPITAL INVESTMENT CHOICE USING FUZZY ARITHMETIC

ABSTRACT This work applies fuzzy theory to capital budgeting and combines with a probability method in developing the fuzzy net present value algorithms for evaluating the investment projects. The estimation of cash flows in fuzzy numbers catches the vague characteristics of estimation, and the forecast of probabilities of economic prospects describes the randomness of outcomes. Using α-cuts and the interval of confidence of fuzzy numbers, this study defines the fuzzy net present value (FNPV), expected FNPV, and deviation, and derives their membership functions. The fuzzy performance index (FPI), the fuzzy expected value to standard deviation, is then proposed to be the decision indicator. After a ranking procedure, the higher-FPI project is a better choice. The situations of unequal durations and unequal costs of capital for mutually exclusive projects, which are seldom discussed in previous studies, are considered by estimating the fuzzy equivalent annuity (FEA) and fuzzy equivalent annuity to infinity (FEAI). The ranking of their FPIs is also derived. The proposed step-by-step operational algorithms of the membership functions hopefully conduce to more convenient practical implementation. Finally, a numerical example demonstrates the feasibility of the proposed algorithms.

Stochastic coherent adaptive large eddy simulation method

In this paper we propose a novel approach called the stochastic coherent adaptive large eddy simulation (SCALES) method which takes advantage of both the coherent vortex simulation (CVS) and large eddy simulation (LES) methods. With the SCALES method a wavelet filter is applied to a turbulent field such that the maximum number of modes are resolved in the simulation, given the balance between computing resources and user defined acceptable simulation error. As with CVS, the wavelet thresholding filter will allow a SCALES simulation to resolve and “track” the coherent energetic structures in a turbulent flow field. The wavelet filter compression in SCALES will be substantially greater than the “ideal” wavelet compression used in CVS, making it cost effective for simulating high Re number flows. The SCALES methodology will simulate the most important modes given the resources available. Because of the higher wavelet compression the subgrid scales (SGS) in a SCALES simulation will contain both coherent and incoherent modes like with LES. In this work the SCALES method is presented for both velocity and vorticity space wavelet filtering. A novel coherency diagram of a turbulent field is introduced to present the physical relationships between direct numerical simulation and different large eddy capturing methods. In this work we show that with both LES filtering and SCALES filtering the residual SGS field contains both coherent and incoherent parts and that with both methodologies the total SGS dissipation is dominated by the coherent part of the SGS field. A possible implementation of the SCALES methodology for incompressible turbulent flows is also discussed.

Approximate Analytic Estimate of Axial Fluid Conduction in Laminar Forced Convection Tube Flows with Zero-to-Uniform Step Wall Heat Fluxes

The influence of axial fluid conduction on low Péclet number flows in the thermal entrance region of long circular tubes is investigated in this theoretical study. The convective heat transport of viscous fluids relates to a specific condition under which the first part of the tube ( x h 0) is insulated and the second part of the tube ( x > 0) receives a heat flux of uniform intensity. A conjugate one-dimensional lumped model produces a solution of compressed algebraic form that is able to deliver dependable mean bulk temperatures that are in perfect agreement with those obtained numerically by the formal conjugate two-dimensional distributed model. As a by-product of the succession of algebraic calculations within the platform of the lumped model, the critical Péclet number Pe cr has been easily quantified. This number is a figure-of-merit of remarkable importance in the modeling of forced heat convection in tubes because it establishes the threshold between two contrasting situations: one embracing axial fluid conduction (finite Pe) and the other implicating negligible axial fluid conduction (Pe M X ). In addition, the local wall temperatures were calculated with an approximate engineering procedure, showing good agreement with those determined numerically by the formal conjugate two-dimensional distributed model.

The steady/pulsatile flow and macromolecular transport in T-bifurcation blood vessels

A numerical analysis of the steady and pulsatile, macromolecular (such as low density lipopotein (LDL), Albumin) transport in T-bifurcation was proposed. The influence of Reynolds number and mass flow ratio etc. parameters on the velocity field and mass transport were calculated. The computational results predict that the blood flow factors affect the macromolecular distribution and the transport across the wall, it shows that hemodynamic play an important role in the process of atherosclerosis. The LDL and Albumin concentration on the wall varies most greatly in flow bifurcation area where the wall shear stress varies greatly at the branching vessel and the atherosclerosis often appears there.

Numerical Simulation of Developing Pulsating Flow (Low Re Number Flow) in a U-shaped Pipe

This paper concerns the secondary flow due to pulsating flows with various frequencies in a U-shaped pipe, solved by a finite difference method with CIP and fractional step methods in a general coordinate system. The streamwise velocity distributions obtained are confirmed with experimental results. The resultant secondary flow is complicatedly changed by the induced secondary and third vortex cores. The intensity of the secondary flow does change throughout the curved pipe, indicating the flow is still developing even at the exit. The overall intensity of the secondary flow within the pipe increases with an increase in the pulsating frequency.

The Impact of Linear Deformations on Stationary Hydrostatic Thrust Bearings

In this work, the operating sensitivity of the hydrostatic thrust bearing with respect to pressure-induced deformations will be studied in a stationary setting. Using the classical lubrication equations for low Reynold’s number flow, closed-form expressions are generated for describing the pressure distribution, the flow rate, and the load carrying capacity of the bearing. These expressions are developed to consider deformations of the bearing that result in either concave or convex shapes relative to a flat thrust surface. The impact of both shapes is compared, and the sensitivity of the flow rate and the load carrying capacity of the bearing with respect to the magnitude of the deformation is discussed. In summary, it is shown that all deformations increase the flow rate of the bearing and that concave deformations increase the load carrying capacity while convex deformations decrease this same quantity relative to a non-deformed bearing condition.

A flow-condition-based interpolation finite element procedure for incompressible fluid flows

A new finite element procedure for the solution of the incompressible Navier–Stokes equations is presented. In the Petrov–Galerkin formulation employed, the velocities are interpolated using the flow conditions over the elements and the pressure is interpolated to satisfy the inf–sup condition for incompressible analysis. Element control volumes are employed to satisfy local mass and momentum conservation (as in finite volume methods), which corresponds to using step functions as weight functions in the finite element method. An important achievement of the discretization scheme is that no artificial parameters are set in the scheme to reach stability for low and high Reynolds (and Péclet) number flows. The solutions of nontrivial test problems are presented to demonstrate the capability and potential of the scheme.

Design of an oscillating flow apparatus for the study of low Reynolds number particle dynamics

An apparatus was designed and built to explore the effects of transient flow fluctuations on the dynamic behavior of particles in low Reynolds number (LRN) flows. While many experiments have been performed on LRN particle flows, relatively few have investigated periodic oscillations on the flow dynamics. The apparatus was oscillated at a frequency of 10 Hz with peak-to-peak displacements on the order of 10 mm. Particles of varying densities and diameters were placed into the oscillating flow. Video images of the particle dynamics were captured with both a personal video camcorder and high-speed digital camera. In parallel, computations were performed for the particle system in order to validate the experimental method and apparatus.

Effect of Reynolds number, turbulence level and periodic wake flow on heat transfer on low pressure turbine blades.

The development of effective cooling methods is of major importance for the design of new gas turbines blades. The conception of optimal cooling schemes requires a detailed knowledge of the heat transfer processes on the blade's surfaces. The thermal load of turbine blades is predominantly determined by convective heat transfer which is described by the local heat transfer coefficient. Heat transfer is closely related to the boundary layer development along the blade surface and hence depends on various flow conditions and geometrical parameters. Particularly Reynolds number, pressures gradient and turbulence level have great impact on the boundary layer development and the according heat transfer. Therefore, in the present study, the influence of Reynolds number, turbulence intensity, and periodic unsteady inflow on the local heat transfer of a typical low pressure turbine airfoil is experimentally examined in a plane cascade.

502 LBMにCIP法を適用した多孔質内高レイノルズ数流動の数値シミュレーション(OS22-1 粒子法(格子気体法,格子ボルツマン法など)による熱流動解析(1))(OS22 粒子法(格子気体法,格子ボルツマン法など)による熱流動解析)

502 LBMにCIP法を適用した多孔質内高レイノルズ数流動の数値シミュレーション(OS22-1 粒子法(格子気体法,格子ボルツマン法など)による熱流動解析(1))(OS22 粒子法(格子気体法,格子ボルツマン法など)による熱流動解析)

Numerical analysis of a symmetrically heated vertical channel with obstruction

In this paper, a numerical investigation of laminar natural convection flows in a vertical channel with obstructions is carried out. The main purpose was to analyze the effects of the locations of symmetric obstructions. The computations were performed in a two-dimensional domain and a symmetric uniform wall temperature has been taken as thermal boundary condition. The governing equations were solved using a control volume method and the SIMPLER algorithm for the velocity–pressure coupling was employed. The profiles of the local Nusselt number were given for three different locations of the obstructions. The variation of the average Nusselt number and inlet flow rate versus the modified Rayleigh number were investigated. The results demonstrated that the average Nusselt number decreases as the distance of the obstructions from the inlet increases.