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International Journal of Mechanical Engineering and Technology (IJMET) Volume 10, Issue 03, March 2019, pp. 421-433. Article ID: IJMET_10_03_043 Available online at http://www.iaeme.com/ijmet/issues.asp?JType=IJMET&VType=10&IType=3 ISSN Print: 0976-6340 and ISSN Online: 0976-6359 © IAEME Publication Scopus Indexed UNSTEADY THREE-DIMENSIONAL NUMERICAL STUDY OF LAMINAR FLOW IN SUDDEN EXPANSION CHANNEL (EFFECT OF ASPECT RATIO) Ahmed N. Naeyyf Post Graduate Student, Engineering CollegeMechanical Engineering Department, Basra Iraq Qais A. Rishack Lecture Engineering CollegeMechanical Engineering Department, Basra Iraq ABSTRACT Three-Dimensional, Unsteady Laminar Flow through Sudden Expansion Channel has been studied numerically. Used rectangular and symmetric sudden expansions (ER=H/h) with different aspect ratio (AR=Wch/h). CFD software ANSYS FLUENT 15.0 was developed to solve the Naviar-Stokes equation by used the finite volume method to transfer these equations from differential form to algebraic form which can be solved by SIMPLE algorithm procedure. The results obtained were represented on graphs and discussed the suitable parameters like: pressure drop, velocity recirculation region and skin fraction coefficient. From the results founded the time steady state increase with the increasing of the aspect ratio and this effects become more clearly at the high of Reynolds numbers and the aspect ratio, so founded high effect of the time on the hydrodynamic parameters, behavior of the flow, recirculation region and the velocity profile, and this effect was clearly at high of Reynolds numbers. Also observed the increasing both the Reynolds numbers and aspect ratio leaded to increase the recirculation zone and streamwise velocity, the pressure drop increase with Reynolds number increase but reduce with increasing the aspect ratio, the results of the numerical study were compared with the other research and obtained acceptable convergence. Keywords: Unsteady, Laminar Flow, Sudden Expansion Channel, expansion ratio, aspect ratio. Cite this Article: Ahmed N. Naeyyf, and Qais A. Rishack, Unsteady ThreeDimensional Numerical Study of Laminar Flow in Sudden Expansion Channel (Effect of Aspect Ratio), International Journal of Mechanical Engineering and Technology, 10(3), 2019, pp. 421-433. http://www.iaeme.com/IJMET/issues.asp?JType=IJMET&VType=10&IType=3 http://www.iaeme.com/IJMET/index.asp 421 [email protected] Unsteady Three-Dimensional Numerical Study of Laminar Flow in Sudden Expansion Channel (Effect of Aspect Ratio) 1. INTRODUCTION In many systems the flow separation and its subsequent reattachment to a solid surface are occurred. The flow through duct with sudden expansion can be also occurred in different industrial application such as environmental control system, combustion chamber, electronic cooling equipment and many other devices. The characterization of flow could be done by increasing the losses of pressure which is caused by the flow separation near the expansion area, [1]. Based on the variation of the pressure losses, erosion rates are increased as well as the heat and mass transfer rates in the area where flows are occurring, [2]. In order to focus our studying on flow with separation region experimental and theoretical techniques have been developed based on many conducted attempts and this is due to stress such flow in many engineering equipment. Therefore, numerical and experimental methods for characterizing these flow features are still far from perfect due to the complexity of the flow’s behavior associated with the flow separation [2], [3]. An overview of the relevant available literature. Ali J. Chamkha, [4], unsteady laminar flow and heat transfer in channel and circular pipe has been studied numerically. It is used the hydro-magnetic fluid with particle suspension flow. The finite difference method used to solve the non-linear equations. The graphical results discussed the volumetric flow rate and the friction coefficient for the both fluid and particle phases to show the influences of the Hartmann magnetic number, the viscosity ratio and the particle loading on the solutions. The finite difference computation showed the effect of temperature inverse stock number on the heat transfer and the temperature profile of both phases. Radhi [5], numerical study has been conducted on the viscous incompressible laminar and turbulent flow in two geometries through step channel, with time depended and two dimensions. The Navier-Stokes equation is used to solve each laminar and turbulent flow while the finite difference method is used to solve the equations using two models to study the turbulent flow. The first one called zero-equation and the second called one-equation model. At Re=100000, it is observed stable and convergent results with acceptable accuracy. Rathish Kumar.et al., [6], in this paper, the unsteady laminar flow through three dimensional doubly constricted has been studied numerically, the flow with pulsatile condition. Time accurate finite volume method is used to solve the non-linear partial differential equation. The computational showed the effect of Reynolds number and the spase between the two constrictions on the pressure drop through the constrictions. At the pressure drops near the constriction increased with increasing of Reynolds number. For a small distance between the constrictions, they observed the drop of the total pressure was large in the first section of the flow acceleration and the second section of the flow deceleration phases. But for the large distance between the constrictions, they observed in the second section of the flow acceleration and the first section of the flow deceleration phases, the drop of the total pressure was large. Hassan AL-Abode .et al [7], the laminar and turbulent flow through expansion channel have been studied numerically with three-dimensional flow and different aspect ratio, used the finite volume to solve the continuity and momentum equations. The results illustrated the maximum reattachment length is located in the laminar flow and it's observed in the upper stepped wall, and in the turbulent flow observed the kinetic energy, friction factor and streamwise velocity inside the reverse flow increase with increasing Reynolds number. The result also showed the critical Reynolds numbers increase as the aspect ratio decrease and the revers flow region increase with aspect ratio increase. Finally, in the laminar flow the recirculation flow region is increased but it is approximately constant in the turbulent flow. Vijayalakshmi R. et al., (2017) [8], unsteady flow, heat and mass transfer of a casson fluid in vertical expansion and contraction channel has been studied numerically. They used the Runge-Kutta method to solve the reduced ordinary differential equations that is derived from the governing partial differential equations. The pivotal velocity, temperature http://www.iaeme.com/IJMET/index.asp 422 [email protected] Ahmed N. Naeyyf, and Qais A. Rishack and the concentration distribution are showed in different graphs and discussed their behavior for variable parameters casson parameter, magnetic field parameter, Reynolds number, expansion ratio, heat source parameter, Prandtl number, Groshoff number, Chemical reaction parameter, Schmidt s number. The obtained results showed multi case, firstly for the expansion region ( ) lead to high axial velocity in the center and low velocity vicinity the walls, secondly for the contracting region ( ) increasing the lead to low axial velocity in the center even invert the direction near the walls, thirdly for ( ) the axial velocity in the center increases with increasing the casson parameter even it reduces vicinity the walls. Also, the result showed the heat source parameter for ( ) lead to increase the Nusselt-number at the left wall, and at the right wall the Sherwood number increase with the high value of chemical reaction. Khudheyer S. et al., (2015) [9], in this paper research, the laminar flow through an obstacle sudden expansion channel has been studied numerically. The obstacles position is behind the expansion region for the geometry on the upper and lower wall of the used channel. In this research, they showed that the influence of the length, thickness and the number of obstacles on the flow and the thermal fields for different parameters such as expansion ratio and Reynolds number. The results illustrated the obstacles have important effect on the dynamic flow and edification on the heat rate. In other word the heat transfer rate increases with increasing the thickness and the number of the obstacles while its decreases with increasing of the obstacles length. 2. MODELING AND THEORETICAL The present section introduces the physical model of laminar flow through sudden expansion channel configurations and its mathematical analysis; includes the, governing equations that describe flow, boundary conditions and assumptions. Also, this chapter contains the procedure of simulation; the employed method in this work for numerical attaining of hydraulic behaviors of the present problems. ANSYS 15 was used in simulations and computations of problems that included in this thesis. 2.1 Description of Model The physicals model that was study is shows in the figure (1). This exhibits the threedimension horizontal channel have symmetric sudden expansions. The heights of channel downstream, upstream of the expansion are (H) and (h) consecutively. The height of step is preserved as (s). The geometry prepare an arrangement within expansions ratio (ER=2), and "aspect ratio" (AR=W/h) are different, the location of the coordinates axes at the center of the inlet channel; the direction of the stream wise (x), transverse (y), and span wise (z) coordinates are showed in figure (3.1), the inlet duct length (Li) selected to make sure that inlet flow through the channel is fully developed [10], [11]. http://www.iaeme.com/IJMET/index.asp 423 [email protected] Unsteady Three-Dimensional Numerical Study of Laminar Flow in Sudden Expansion Channel (Effect of Aspect Ratio) Figure 1 explain the schematic sudden expansion with the boundary condition [12] 2.3 Assumption For carrying out the numerical simulations of the present work, the bellow assumptions are considered for the flow: 1. The fluid of work is air. 2. Three dimension, laminar and unsteady state flow. 3. The flow is Incompressible. 4. Neglected the effect of gravity. 5. The flow assumed is Non-slip. 2.4 Governing Equations The motion equations of the laminar flow are used in Cartesian coordinates as the follows [11], [13], [14]: Equation of continuity: Equation of momentum: x-direction ( ) ( ) y-direction ( ) ( ) z-direction ( ) ( ) 2.5 Boundary Condition When looking at figure (1) which explain the boundary condition for the presented model (sudden expansions channel), and based on the last presumptions the boundary conditions of the laminar flow can be summed as ahead: The velocity in the walls of channel equal zero (no slipping). i.e u, v, w=0 with the x, y, and z directions. The velocity in the inlet of channel is known (u= uin, v=0, w=0). The Pressure at the outlet equal zero. 3. VERIFICATION To check the validity of the present numerical model, verification was made by comparing the results of the present model with numerical results reported in the literature. The verification was made by comparison the present results and Abdu Latif et al. [8]. The model is presented http://www.iaeme.com/IJMET/index.asp 424 [email protected] Ahmed N. Naeyyf, and Qais A. Rishack in [14] is Finite element model for unsteady open channel flows with sudden contraction/expansion, the used two unsymmetrical channels of different lengths with contraction and expansion to study the flow behavior. The numerical results found using the present model and that found by [14] are shown in Figure (1) which shows the velocity profile with Re=60 and different position, before contraction(X/B=1) and during contraction (X/B=1.2), from this figure, the agreement is acceptable, and the error is 13.11 %. From the past verification, we deduction that, the present numerical model is dependable and can be used accurately to simulate the flow in the expansion channel and study the variable parameters affecting. 4. MESH INDEPENDENCY It is very important to specify the elements number that obtains the accurate results. So, the grid refinement was tested for every studied case through dividing the domain into many different grids and comparing their results of x-velocity (U) and friction coefficient (Cƒ). As shown in figure (2), the deviation between results that obtained from each two consequent grids is decreased at finer grids due to the convergence in these results. For all studied cases in present work, the deviation less than 1 % in both x-velocity (u) and friction coefficient (Cƒ) is considered for selecting the grid at which the results will be stable and grid independent. 5. RESULTS AND DISCUSSED (EFFECT OF ASPECT RATIO) This thesis will explain the aspect ratio on varicose of hydrodynamic parameters (velocity, the zones of recirculation flow, pressure and the fraction coefficient) for presented flow (laminar type).There is important conditions must be insured prior discussion the last parameters or the influence, which is the required condition for the entry and the exit of the sudden expansion. The inlet condition for the sudden expansion channel included known velocity, and the out let condition included the static pressure equal zero. A study was performed to verify the influence of aspect ratio on the time steady state and the flow state after the stepped walls. Figure (3) shows the effect of the aspect ratio on the time steady state at constant Reynolds numbers, observed at AR=2 the effect of the time was little so the period to approach to the steady state its short, by increase the aspect ratio (AR=4) the time become longer, so at AR=6 The effect has become clearer and the time to approach to steady state become more, all the last study at constant Reynolds number (Re=500). The reason for this behavior; increase the AR mean increase the area of the fluid motion and this will take more freedom for the partial fluid motion and this will cause more random for the fluid, and the increase the random need more time for the stability and a approach to the steady state Figure (4) shows the influence of the aspect ratio on the distribution of the velocity profile at the center of channel and at position x=3, from this figure observed same recirculation zone in the upper and lower wall for same the aspect ratio, also the value of velocity in the center of channel increase with the AR increasing. Figure (5) shows the effect of the aspect ratio on the distribution of the velocity profile with the z axis, the center of channel and at position x=2, observed the value of velocity decrease with the increasing of aspect ratio this for 30% of the first width after this the velocity will increase with aspect ratio increasing, that’s mean the flow will become twodimensional velocities due the large of aspect ratio. Figure (6) explain the boundary for the reattachment line on the lower of channel for different aspect ratio, by observed the figure will find the increasing of the aspect ratio lead to reattachment line increasing by decreases the pressure, so the result show the reattachment http://www.iaeme.com/IJMET/index.asp 425 [email protected] Unsteady Three-Dimensional Numerical Study of Laminar Flow in Sudden Expansion Channel (Effect of Aspect Ratio) line it be symmetric through the center of channel then has gradually increasing as a head to the wall. Figure (7) show the reattachment length with the Reynolds numbers for the upper and lower step wall with different aspect ratio, the figure explains the effect of the aspect ratio and Reynolds numbers on the flow reattachment length. The results show the symmetric flow increase with the decreasing of aspect ratio (at AR=2 the symmetric observed clearly), so the flow behavior after the bifurcation point increase in the upper step wall and decrease in the lower, the last observed point seen the zone of reverse flow increase with the aspect ratio increasing. Figure (8) explain the distribution for the static pressure along the length of channel at different of aspect ratio at constant Reynolds number, observed at high aspect ratio (AR=6) the drop pressure was lowest from the other cases (AR=2, AR=4), so for AR=4 and AR=6 the value of the pressure ware closely but for low aspect ratio AR=2 the pressure value far from the others. The pressure still dropping at arrived to zero at the out let of channel and this dropping increase with decreasing of aspect ratio. 60 present study [40] Abdul Latif et al., 50 40 y(m) 30 20 10 0 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 u (m/s) Velocity profile at X/B=1 http://www.iaeme.com/IJMET/index.asp 426 [email protected] Ahmed N. Naeyyf, and Qais A. Rishack 50 present study 45 [40] Abdul Latif et al., 40 35 y(m) 30 25 20 15 10 u(m/s) 0 0.5 1 1.5 2 2.5 Velocity profile X/B=1.2 Figure 2 Verification of the present numerical model using the numerical results of [8] Averag e velocity (m/s) No. of elements (a) http://www.iaeme.com/IJMET/index.asp 427 [email protected] Unsteady Three-Dimensional Numerical Study of Laminar Flow in Sudden Expansion Channel (Effect of Aspect Ratio) Cƒ (b) No. of elements Figure (3) computing results for the expansion channel at different grids at Re=2000 (a) Average velocity. (b) Friction coefficient Average velocity (m/s) AR=2 4.007 4.0065 4.006 4.0055 4.005 4.0045 4.004 4.0035 4.003 4.0025 t(s) 4.002 0 5 10 15 20 http://www.iaeme.com/IJMET/index.asp 25 428 30 35 40 45 50 55 [email protected] Ahmed N. Naeyyf, and Qais A. Rishack Figure (4) variation of the average velocity with the time at different aspect ratio and Re=500 http://www.iaeme.com/IJMET/index.asp 429 [email protected] Unsteady Three-Dimensional Numerical Study of Laminar Flow in Sudden Expansion Channel (Effect of Aspect Ratio) 1 # 10 -3 AR=2 AR=4 AR=6 0.8 0.6 0.4 y (m) 0.2 0 -0.2 -0.4 Re=250 X=3 t=120 s -0.6 -0.8 -1 0 0.5 1 1.5 2 2.5 3 U (m/s) Figure (5) velocity profile with the high of channel at different aspect ratio Figure (6) velocity profile with the width of channel at different aspect ratio http://www.iaeme.com/IJMET/index.asp 430 [email protected] Ahmed N. Naeyyf, and Qais A. Rishack 0.0045 AR=6 0.004 AR=4 0.0035 AR=2 𝑋𝑢 0.003 0.0025 0.002 0.0015 0.001 0.0005 0 0 0.2 0.4 0.6 0.8 1 1.2 z(mm) Figure (7) Diagram of the upper reattachment length at different Aspect ratio, Re=250, z=0 and t=120s AR=4 lower wall AR=6 lower wall AR=2 lower wall 0.008 AR=4 upper wall AR=6 upper wall AR=2 upper wall 0.007 𝑋𝑢 0.006 0.005 0.004 0.003 0.002 0.001 0 0 250 500 750 1000 Z (mm) 1250 1500 1750 2000 Figure (8) Diagram of the lower and upper reattachment length at different Aspect ratio, z=0 and t=120s http://www.iaeme.com/IJMET/index.asp 431 [email protected] Unsteady Three-Dimensional Numerical Study of Laminar Flow in Sudden Expansion Channel (Effect of Aspect Ratio) 80 AR=2 AR=4 AR=6 70 Re=250 t=120 s 60 y (m) 50 40 30 20 10 0 -0.08 -0.06 -0.04 -0.02 0 0.02 0.04 0.06 U (m/s) Figure (9) variation of the static pressure along the channel with different aspect ratio 5. CONCLUSIONS A numerical study has been conducted to investigate the three-dimensional, unsteady state, laminar flow through sudden expansion channel; CFD software ANSYS FLUENT 15.0 was developed to solve the Naviar-Stokes equation by used the finite volume method. Had been Investigated the influence for many parameters on the fluid in present model, The conclusions presented below have been obtained by the results obtained: Increase the time of the steady state as the aspect ratio increasing with fixed the Reynolds numbers. Founded high effect of the time on the hydrodynamic parameters, behavior of the flow, recirculation region and the velocity profile. The reverse flow region increases with the aspect ratio increasing. The drop of the pressure increases with Reynolds number increasing but its decrease with the aspect ratio increase REFERENCES [1] [2] [3] [4] [5] [6] R. P. Chhabra And J. F. Richardson, Non-Newtonian Flow and Applied Rheology, Oxford: Butterworth-Heinemann, 2008. T. 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