Viscous Flow Analysis Research Articles

Second Law Analysis of Unsteady MHD Viscous Flow over a Horizontal Stretching Sheet Heated Non-Uniformly in the Presence of Ohmic Heating: Utilization of Gear-Generalized Differential Quadrature Method.

In this article, the entropy generation characteristics of a laminar unsteady MHD boundary layer flow are analysed numerically for an incompressible, electrically conducting and dissipative fluid. The Ohmic heating and energy dissipation effects are added to the energy equation. The modelled dimensional transport equations are altered into dimensionless self-similar partial differential equations (PDEs) through suitable transformations. The reduced momentum and energy equations are then worked out numerically by employing a new hybrid method called the Gear-Generalized Differential Quadrature Method (GGDQM). The obtained numerical results are incorporated in the calculation of the Bejan number and dimensionless entropy generation. Quantities of physical interest, like velocity, temperature, shear stress and heat transfer rate, are illustrated graphically as well as in tabular form. Impacts of involved parameters are examined and discussed thoroughly in this investigation. Exact and GGDQM solutions are compared for special cases of initial unsteady flow and final steady state flow. Furthermore, a good harmony is observed between the results of GGDQM and those given previously by the Spectral Relaxation Method (SRM), Spectral Quasilinearization Method (SQLM) and Spectral Perturbation Method (SPM).

Analysis of unsteady viscous dissipative poiseuille fluid flow of two-step exothermic chemical reaction through a porous channel with convective cooling

Abstract In this study, the viscous dissipation of heat transfer of poiseuille fluid flow of two-step exothermic chemical reaction through a porous channel is investigated under different chemical kinetics. The flow is pressure-driven past fixed plates with heat generation. The upper wall surface is exposed to heat exchange with the temperature of the ambient aligning with the Newton’s law of cooling. The modeled coupled partial differential equations are non-dimensional and solved using stable and unconditional semi-implicit convergent finite difference method. The results are represented graphical and discussed accordingly for the velocity and temperature profiles showing the effect of some embodiment parameters entrenched in the system. From the results it was noticed that an increase in Frank-Kamenetskii parameters produces significant rises in the temperature distribution.

Interfacial wave analysis of low viscous oil-water flow in upwardly inclined pipes

The interfacial wave phenomenon in oil-water flow systems is an important area of research, due to its importance in real world applications, especially in oil-water transportation in petroleum industry. The influence of interfacial wavy flow and transition of flow regimes on pressure drop, hold-up and heat transfer has motivated the research on this topic to enhance the understanding, to ensure the process safety and to improve the process economy.This paper investigates the interfacial oil-water wavy flow in upwardly inclined pipes. The test fluids are mineral oil (viscosity-1.6 mPa s, density-788 kg/m3) and water. The scope of the study covers the upward pipe inclination angles of +3°, +5°, +6°, mixture velocities of 0.2–0.5 m/s, and input water cut (input water volume ratio) 0.1–0.9. Two different flow patterns were observed in wavy flow in upwardly inclined pipes, namely stratified wavy (SW) and stratified wavy and mixed interface (SW&MI). The flow images were recorded using a high-speed video camera through a transparent test section. The image analysis was performed using several Matlab programs to extract wave properties such as wavelength and wave amplitude, as well as the wave speed.It is observed that the interfacial instabilities increase with the increasing mixture velocity and with increasing inclinations. Increased instabilities cause interfacial waves to generate and release droplets, while the turbulent intensity in the oil phase also influence droplet formation. An approximately linear relation between wave velocity and mixture velocity was obtained for the wavy flow and a correlation is presented accordingly. Wave energy manifests itself in the combined potential and kinetic energy. The potential energy via the wave amplitude and kinetic energy via the wave speed and wavelength. The overall energy for nonlinear breaking waves is a major source for generation of interfacial droplets. When the flow velocities are increased at a constant input water cut and at a given pipe inclination, the flow regime transition from SW to SW&MI occurs. Meanwhile, the prevailing wavelength decreases and the wave amplitude increases towards the point of transition from SW to SW&MI. The wavelength and the amplitude reach a critical value and remain constant until droplets start to form and release. Once the onset of drop formation occurs at the SW&MI flow regime, the wavelength starts to increase and the wave amplitude decreases with respect to their magnitudes at the point of transition. For a given velocity range, the mean amplitude increases with increasing inclination and decreases with increasing water cut. There is an inverse relation between wavelength and wave amplitude, which means higher amplitude always results in lower wavelength and vice versa.The wave velocity was calculated independently by two different analysis techniques applied to high-speed video images. One was carried out in space domain and one in time domain from high-speed image sequences. All data points were within the 7% error margin with respect to 1:1 reference correlation line, assuring the accuracy of analysis techniques and the validity of the correlation derived for relating the wave velocity to the mixture velocity.

Linear stability analysis of a liquid jet in a weak crossflow

In an effort to better understand the primary breakup mechanism of liquid jets in crossflow, a theoretical model for three-dimensional spatial linear stability of a viscous liquid jet injected in a weak gaseous crossflow is developed. The results are presented for the behavior of jet instabilities in the range of crossflow-to-jet momentum flux ratio of less than 0.01. In this range, the deformation of the liquid column allows a parallel base flow which is described by a modified viscous potential flow analysis. Focusing on the early stages of the jet evolution, a characteristic equation accounting for the growth of columnar waves is obtained and the most dominant wavelength and the corresponding growth rates are calculated. The predicted results for the asymptotic case of free jet flow are examined against the results available in the literature. Symmetric and asymmetric modes of liquid jet disturbance are investigated for a wide range of viscous, surface tension, and aerodynamic force ratios.

Isogeometric Boundary Element Analysis of steady incompressible viscous flow, Part 2: 3-D problems

This is a sequel to a previous paper (Beer et al., 2017) [1] where a novel approach was presented to the 2-D Boundary Element analysis of steady incompressible viscous flow. Here the method is extended to three dimensions. NURBS basis functions are used for describing the geometry of the problem and for approximating the unknowns. In addition, the arising volume integrals are treated differently to published work and volumes are described by bounding NURBS surfaces instead of cells and only one mapping is used. The advantage of the present approach is that complex boundary shapes can be described with very few parameters and that no generation of cells is required. For the solution of the non-linear equations full and modified Newton–Raphson methods are used. A comparison of the two methods is made on the classical example of a forced cavity flow, where accurate two-dimensional solutions are available in the literature. Finally, it is shown on a practical example of an airfoil how more complex boundary shapes can be approximated with few parameters and a solution obtained with a small number of unknowns.

Grid-converged solution and analysis of the unsteady viscous flow in a two-dimensional shock tube

The flow in a shock tube is extremely complex with dynamic multi-scale structures of sharp fronts, flow separation, and vortices due to the interaction of the shock wave, the contact surface, and the boundary layer over the side wall of the tube. Prediction and understanding of the complex fluid dynamics are of theoretical and practical importance. It is also an extremely challenging problem for numerical simulation, especially at relatively high Reynolds numbers. Daru and Tenaud [“Evaluation of TVD high resolution schemes for unsteady viscous shocked flows,” Comput. Fluids 30, 89–113 (2001)] proposed a two-dimensional model problem as a numerical test case for high-resolution schemes to simulate the flow field in a square closed shock tube. Though many researchers attempted this problem using a variety of computational methods, there is not yet an agreed-upon grid-converged solution of the problem at the Reynolds number of 1000. This paper presents a rigorous grid-convergence study and the resulting grid-converged solutions for this problem by using a newly developed, efficient, and high-order gas-kinetic scheme. Critical data extracted from the converged solutions are documented as benchmark data. The complex fluid dynamics of the flow at Re = 1000 are discussed and analyzed in detail. Major phenomena revealed by the numerical computations include the downward concentration of the fluid through the curved shock, the formation of the vortices, the mechanism of the shock wave bifurcation, the structure of the jet along the bottom wall, and the Kelvin-Helmholtz instability near the contact surface. Presentation and analysis of those flow processes provide important physical insight into the complex flow physics occurring in a shock tube.

Model of Stress Generation in Anodic Aluminum Oxide Films: Part II. Surface Stress Accumulation Preceding Formation of Self-Organized Pore Arrays

Growth of self-organized porous anodic alumina films initiates after growth of the initial compact barrier oxide becomes unstable. The process of self-ordering is characterized by evolution of an irregular distribution of incipient pores into the characteristic steady-state pore array. We explore the roles of mechanical stress and oxide flow in self-ordering, through a modeling analysis of stress-driven viscous flow of oxide. To account for oxide topography evolution, the model domain is chosen to be a spherical shell of oxide representative of the film during the transition to the steady-state porous layer. The model is based on coupled viscous flow of oxide and stress- and electric field-driven migration of Al+3 and O−2 ions. The calculation results successfully depict the buildup of compressive stress within a layer of a few nanometers thickness at the oxide surface, as inferred previously from in situ stress measurements. Additionally, the model predictions are consistent with observations of tensile bulk stress in the oxide accompanying inward oxide flow during the transition to the steady-state pore array. This transition is due to competitive growth of the initially nonuniform distribution of incipient pores until a monodisperse steady-state distribution is attained.

Coupled Viscous Fluid Flow and Joint Deformation Analysis for Grout Injection in a Rock Joint

Fluid flow modeling is a major area of interest within the field of rock mechanics. The main objective of this study is to gain insight into the performance of grout injection inside jointed rock masses by numerical modeling of grout flow through a single rock joint. Grout flow has been widely simulated using non-Newtonian Bingham fluid characterized by two main parameters of dynamic viscosity and shear yield strength both of which are time dependent. The increasing value of these properties with injection time will apparently affect the parameters representing the grouting performance including grout penetration length and volumetric injection rate. In addition, through hydromechanical coupling a mutual influence between the injection pressure from the one side and the joint opening/closing behavior and the aperture profile variation on the other side is anticipated. This is capable of producing a considerable impact on grout spread within the rock joints. In this study based on the Bingham fluid model, a series of numerical analysis has been conducted using UDEC to simulate the flow of viscous grout in a single rock joint with smooth parallel surfaces. In these analyses, the time-dependent evolution of the grout fluid properties and the hydromechanical coupling have been considered to investigate their impact on grouting performance. In order to verify the validity of these simulations, the results of analyses including the grout penetration length and the injection flow rate were compared with a well-known analytical solution which is available for the simple case of constant grout properties and non-coupled hydraulic analysis. The comparison demonstrated that the grout penetration length can be overestimated when the time-dependent hardening of grout material is not considered. Moreover, due to the HM coupling, it was shown that the joint opening induced by injection pressure may have a considerable increasing impression on the values of penetration length and injected grout volume.

Analysis of Three-dimension Viscous Flow in the Model Axial Compressor Stage K1002L

The main investigation subject considered in this paper is axial compressor model stage K1002L. Three simulation models were designed: Scheme 1 – inlet stage model consisting of IGV (Inlet Guide Vane), rotor and diffuser; Scheme 2 – two-stage model: IGV, first-stage rotor, first-stage diffuser, second-stage rotor, EGV (Exit Guide Vane); Scheme 3 – full-round model: IGV, rotor, diffuser.Numerical investigation of the model stage was held for four circumferential velocities at the outer diameter (Uout=125,160,180,210 m/s) within the range of flow coefficient: ϕ = 0.4 – 0.6. The computational domain was created with ANSYS CFX Workbench.According to simulation results, there were constructed aerodynamic characteristic curves of adiabatic efficiency and the adiabatic head coefficient calculated for total parameters were compared with data from the full-scale test received at the Central Boiler and Turbine Institution (CBTI), thus, verification of the calculated data was carried out. Moreover, there were conducted the following studies: comparison of aerodynamic characteristics of the schemes 1, 2; comparison of the sector and full-round models.The analysis and conclusions are supplemented by gas-dynamic method calculation for axial compressor stages.

Magnetohydrodynamic two-phase dusty fluid flow and heat model over deforming isothermal surfaces

This paper is devoted to the mathematical analysis of a magnetohydrodynamic viscous two-phase dusty fluid flow and heat transfer over permeable stretching or shrinking bodies. The wall boundary is subjected to a linear deformation as well as to a quadratic surface temperature. Such a highly nonlinear phenomenon, for the first time in the literature, is attacked to search for occurrence of exact solutions, whose numerical correspondences are already available for limited wall transpiration velocities. The obtained analytical solutions are found be in perfect line with the numerical computations. Besides this, exact solutions point to the existence of dual solutions for both permeable stretching and shrinking cases, which were not detected from the numerical studies up to date. The existence of such exact solutions and their parameter domain particularly depending on the wall suction or injection are successfully analyzed. The physical outcomes concerning the effects of suspended particles on the momentum and thermal boundary layers well-documented in the open literature can be best understood from the presented exact solutions.

Aerodynamic Design of Half-Ducted Propeller Fan with Meridional Viscous Flow Analysis Using the Lattice Boltzmann Method

Aerodynamic Design of Half-Ducted Propeller Fan with Meridional Viscous Flow Analysis Using the Lattice Boltzmann Method

Initial stage densification during spark plasma sintering of Fe-based amorphous alloy powder: Analysis of viscous flow

Understanding the mechanism of densification of amorphous alloy powders is important for determining the parameters during sintering of these materials. In this paper, we report on the analysis of densification of Fe48Cr15Mo14Y2C15B6 amorphous alloy powder during spark plasma sintering. Sintering up to 1000 °C resulted in two clearly distinguishable stages of densification: stage I from 320 °C to 740 °C and stage II from 830 °C to 1000 °C. The maximum densification rate during stage I was attained at 585 °C up to which the sample remained fully amorphous. During the entire stage II, the sample was fully crystalline, and the maximum densification rate attained at 935 °C was much lower than that observed during stage I. Viscous flow during stage I was analyzed, yielding an estimate of the activation energy to be 94.0 ± 0.2 kJ mol−1 in the temperature range from 525 °C to 580 °C.

Study of fluid resonance between two side-by-side floating barges

The hydrodynamic interaction between two vessels in a side-by-side configuration attracted research attentions in recent years. However, because the conventional potential flow theory does not consider the fluid viscosity, in the hydrodynamic results, the wave elevations were overestimated in the narrow gap under resonance conditions. To overcome this limitation and investigate the complex fluid flow around multiple bodies in detail, this study examines the fluid resonance between two identical floating barges using a viscous flow analysis program FLOW-3D. The volume of fluid method is implemented for tracking the free surface, and a porous media model is used near the outflow boundary to enhance the wave absorption. A three-dimensional numerical wave basin is established and validated by comparison with the waves generated using theoretical values. On this basis, a computational fluid dynamics (CFD) simulation of the two barges in a resonance wave period is performed, and the wave elevations, the fluid flow around the barges, and the motions of the barges are discussed. The numerical simulation is verified by comparison with results of corresponding experimental data.

Preliminary Study on Factor Technology of Selective Catalytic Reduction System in Marine Diesel Engine

2016년부터 배출통제지역(ECA : Emission Control Atea)을 운항하는 선박에 대하여 배출되는 NOx(질소산화물) 및 SOx(황산화물)의 배기량 감소규제가 강화되었다. 상기의 규제 물질 중 NOx를 제거하는 탈질장비 중 선택적 촉매 환원(SCR : Selectivity Catalytic Reduction) 시스템은 효율이 높고 상업적으로 많이 활용되고 있으나, 높은 온도에서 요소수가 활성화되는 단점이 있다. 이에 초미세기포를 이용하여 낮은 온도에서도 반응할 수 있는 요소수 및 요소수 활성화 기기를 개발하여 상기의 문제점들을 최소화 할 수 있도록 하였다. 또한 SCR 시스템의 효율성을 향상시키는 방안을 마련하기 위하여, ANSYS-CFX package를 이용한 전산유체역학(CFD : Computational fluid dynamics)기법을 사용하였다. Navier-Stokes 방정식을 해석의 지배방정식으로 적용하여 SCR 시스템의 점성유동해석 시뮬레이션을 수행하였다. SCR 시스템의 형상은 CATIA V5를 사용하여 3D 모델링을 하였고, SCR 시스템의 효율성을 비교하기 위해 요소수 분사 노즐의 위치를 요소수 분사 노즐은 배기관의 입구로부터 1/3, 1/2, 2/3로 변경하며 확인하였다. 또한, 노즐의 분사구 수가 SCR 시스템의 효율에 미치는 영향을 확인하기 위하여 분사구 수가 4, 6, 8개일 경우를 시뮬레이션 하여 비교 분석하였다. 시뮬레이션 결과 배기관 입구에 가까울수록, 분사구 수가 많을수록 효율이 향상됨을 확인하였다. From 2016, controls on reduction of NOx and SOx emissions from the vessels that are operated in the emission control area were tightened. The selectivity catalytic reduction system of the denitrification equipment which NOx among the above controlled materials is very effective and used commercially very much. But it has the disadvantage that CSR is activated at high temperatures. Therefore, the SCR and SCR activation instrument that can react even at low temperatures by using micro-nano bubbles so that the above problems can be minimized were developed. And the computational fluid dynamics technique was used by ANSYS-CFX package to prepare the plan that improves the SCR system's efficiency. Simulation for the viscous flow analysis of the SCR system was executed by applying the Navier-Stokes equation to it as a governing equation. For the SCR system's shape, 3D modeling was done by using CATIA V5. SCR jet nozzle's position was checked by changing it to the intervals of 1/3, 1/2, and 2/3 from the inlet of the vent pipe to compare the SCR system's efficiency. And the number of nozzles was compared and analyzed by simulating 4, 6, and 8 holes to check an effect of the number on the SCR system's efficiency. The simulation result has found that the closer nozzles are to the inlet of the vent pipe and the more nozzles are, the more efficiency is improved.

INSTABILITY OF THE RAYLEIGH-BENARD CONVECTION FOR INCLINED LOWER WALL WITH TEMPERATURE VARIATION

This paper deals with an analysis of a two-dimensional viscous fluid flow between the two parallel plates inclined with respect to the horizontal plane, where the lower plate is heated and the upper one is cooled. The temperature difference between the plates is gradually increased during a certain time period after which it is temporarily constant. The temperature distribution on the lower plate is not constant in x-direction, there is a longitudinal sinusoidal temperature variation imposed on the mean temperature. We have investigated the wave number and amplitude influence of this variation on the subcritical stability and the onset of the Rayleigh-Bénard convective cells, by direct numerical simulation of 2D Navier-Stokes and energy equation.

A biharmonic approach for the global stability analysis of 2D incompressible viscous flows

This manuscript embodies an investigation of stabilities in flows governed by the incompressible Navier–Stokes equations with the recently developed compact scheme by Kalita and Gupta (2010) which was derived by using the biharmonic formulation of the 2-D incompressible Navier–Stokes equations. In the current work, we globally analyze the flow stability utilizing this transient ψ–v approach. Critical parameters are found by constructing a generalized eigenvalue problem resulting from the discretization of the stability equations through the above mentioned scheme. This approach is seen to drastically reduce the CPU time for finding the critical eigenvalues. Three fluid flow problems, namely, the square lid-driven cavity, the two sided cross lid-driven cavity and the flow past an inclined square cylinder have been chosen as test cases. For the square cavity and the flow past an inclined square cylinder, critical parameters found by us are in excellent agreement with the established results while for the two-sided cross cavity, its global stability analysis has been carried out for the first time and new results are obtained. The critical parameters are also reconfirmed by phase plane and spectral density analysis.

Mathematical Analysis of a Reactive Viscous Flow through a Channel Filled with a Porous Medium

An investigation has been carried out to study entropy generation in a viscous, incompressible, and reactive fluid flowing steadily through a channel with porous materials. Approximate solutions for both velocity and temperature fields are obtained by using a rapidly convergent Adomian decomposition method (ADM). These solutions are then used to determine the heat irreversibility and Bejan number of the problem. Variations of other important fluid parameters are conducted, presented graphically, and discussed.

子午面粘性流れ解析に基づく空力設計法による遠心圧縮機の空力性能向上

This paper presents an aerodynamic design method for centrifugal compressor using meridional viscous flow analysis and one-dimensional inverse method. The meridional viscous flow analysis can estimate the flow distribution around the blade and extract design blade loading distribution for the original blade. The blade shape has been designed by the present design method with improved blade loading distribution. The improved blade loading distribution is generated based on the original design blade loading distribution which was extracted from the meridional viscous flow analysis result and the improved blade loading near the leading edge is lower than the original one. The designed and original blades have been investigated by three-dimensional Reynolds Averaged Navier Stokes (3D-RANS) analyses and experiments. The numerical result shows the flow separation near the leading edge is successfully suppressed as intended in the design concept. As a result, the aerodynamic performances obtained both from the 3D-RANS analyses and the experiments in the designed blade are improved.

半開放形軸流ファンの空力性能に及ぼす翼負荷分布およびスタッキングの影響

This paper presents the effects of blade loading distribution and blade stacking on aerodynamic performance of a semi-open type axial flow fan. A semi-open type axial flow fan is connected to open area on upstream side and downstream side. In the fan, a complicated flow field, in which internal flow and external flow are mixed, is produced. The blade loading and blade stacking are factors which decide the flow field in the blade area. This study incorporated the blade loading into the design condition. We designed the blade using meridional viscous flow analysis and one-dimensional inverse method. The meridional viscous flow analysis can take into account the mixing loss related to the vortices in the meridional flow field. Also, this study assessed the detailed flow field and aerodynamic performance using Open FOAM. As a result, the blade loading distribution modified was able to successfully suppress the flow separation. In addition, the aerodynamic performance in the designed blade was improved.

Efficient method to compute full eigenspectrum of incompressible viscous flows: Application on two-layer rectinear flow

An efficient algorithm based on the matrix transformation method (Valerio et al., 2007) is presented for solving the generalized eigenvalue problem (GEVP) derived from linear stability analysis of incompressible viscous flow. The proposed method uses the formulation based on primitive variables, i.e. velocity and pressure, instead of streamfunction used by typical Orr-Sommerfeld equation. A series of matrix operations removes non-physical eigenvalues at infinity and leads to a non-singular smaller size eigenvalue problem (EVP), which contains full eigenspectrum, than the original GEVP. Two different solution strategies for the transformed EVP are proposed, and their accuracies are discussed. The proposed procedure is used to solve the stability of two layer rectilinear flow. The computed eigenspectrum are compared to previously reported values.