International Communications in Heat and Mass Transfer

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1 International Communications in Heat and Mass Transfer 39 (2012) Contents lists available at SciVerse ScienceDirect International Communications in Heat and Mass Transfer journal homepage: Numerical simulation of heat transfer to separation air flow in an annular pipe C.S. Oon, Hussein Togun, S.N. Kazi, A. Badarudin, M.N.M. Zubir, E. Sadeghinezhad Department of Mechanical Engineering, University of Malaya, Kuala Lumpur, Malaysia article info abstract Available online 23 June 2012 Keywords: Backward facing steps Annular pipe flow Heat exchanger Numerical simulation Separation and reattachment of air flow through a sudden expansion in an annular passage are considered in this study. Backward facing steps play a vital role in the design of many heat related applications where heat transfer is concerned. In the present work, numerical simulation is performed using computer fluid dynamics package (Fluent) to study the effect of step flow in an annular passage. The results are compared with the preliminary experimental findings. In the study, the flowing fluid was considered heated uniformly from the beginning of the expansion. Constant heat flux approach was also considered for the heat transfer investigation. Annular pipe flow system having a step ratio of D/d=1.8 was considered where d and D are representing the diameter of the pipe before and after expansion. Numerical simulation review shows that the reattachment point extends further with the increase of velocity for different occasions. Finally, the local Nusselt number (Nu) in separation flow increases with the increase of Reynolds number (Re) Elsevier Ltd. All rights reserved. 1. Introduction Turbulent flow separation occurs in many flow situations in nature. Variable pressure gradients are generated due to changes in the geometry of the flow boundaries by introducing flow separation. The recirculation flow with separation causes high pressure loss, enhancement of turbulence and increase mass and heat transfer rate. Separation fluid flows are extensively used in industrial applications even though there is still a lack of knowledge about information of the flow around the recirculation zone [1]. Flow separation at a boundary surface happens when the flow stream lines (the closest stream line to the boundary surface) break or separate away from the boundary surface and then the flow reattached. If the boundary surface is a finite dimension, then flow separation is expected due to the flow divergence over the downstream edge and the fluid flows away from the surface whereas air flows across an airfoil. The separation of fluid flow is represented by viscous flow. It has got scientific and practical importance as well. From the classical concept, viscosity induces flow separation, it is recognized as boundary layer separation [2]. Backward facing step flow plays a vital role in the design of many equipment and engineering applications where heat transfer is concerned. The noted heat transfer applications are combustion engines, heat exchangers, environmental temperature control systems, cooling systems for electronic devices and cooling channels in turbine blades [3]. Mixing of low and high thermal fluid happens in the reattachment flow region of the considered equipment which affects the heat transfer characteristic. Due to this phenomena, convection over forward and Communicated by W.J. Minkowycz Corresponding author. Tel.: address: salimnewaz@um.edu.my (S.N. Kazi). backward step geometries have been investigated by researches [4,5]. Fig. 1 illustrates the backward facing step in a sudden expanded pipe. In industries, rotating cylindrical surface in annular passage is commonly used. Thus, the knowledge of this type of flow passage has got special attention. The simplest representation of this geometry is an annulus space between two concentric-shaped surfaces [6]. Study of separation and reattachment flow was conducted first in the late 1950s. With the development of advanced instrumentations and numerical codes, the investigations are more facilitated to study complex three dimensional flows in the recirculation area. The works were further extended to vertical, horizontal, inclined etc. cases for different fluids, geometrical shapes and boundary conditions [7,8]. Recently, there are a lot of researches conducted by using nanofluids to investigate the heat transfer characteristics of various geometries [9 12]. Large portion of the research on separation flow is performed on duct and circular pipe flow on the other hand, little is published about heat transfer and flow phenomena in annular passage. Such knowledge is critical for optimizing the performance of physical heat exchanging systems in parallel and counter flow heat exchangers. The objective of the present research is to compute the heat transfer rate to turbulent air flow in concentric pipe, and also to investigate the effect of flow separation due to sudden enlargement in the flow passage. Heat transfer rate along the walls expected to differ for the long and short stall condition in any given flow situation as shown in Fig. 2 [13]. 2. Methodology 2.1. Design description The numerical simulations are conducted to verify the accuracy and reliability of experimental results. The schematic drawing of the annular /$ see front matter 2012 Elsevier Ltd. All rights reserved. doi: /j.icheatmasstransfer

2 C.S. Oon et al. / International Communications in Heat and Mass Transfer 39 (2012) Nomenclature ρ Density of air (kg/m 3 ) u Velocity components in the x direction (m/s) v Velocity components in the y direction (m/s) Re d Reynolds number based on hydraulic diameter ρ f Density of fluid (kg/m 3 ) U Velocity of the fluid (m/s) D h Hydraulic diameter of the annular pipe (m) μ f Dynamic viscosity of the fluid at film temperature (kg/ ms) h x Local heat transfer coefficient (W/m 2 K) q c Convection heat flux (W/m 2 ) T sx Local surface temperature (K) T bx Local bulk air temperature (K) d Diameter of the pipe (m) K f Thermal conductivity (W/m K) Nu d Nusselt numbers evaluated from Dittus Boelter correlation Pr Prandtl number sudden expansion pipe flow is presented graphically in Fig. 3 [14]. The inner or outer surface temperature of the annular pipe with sudden expansion can be influenced by many parameters, such as flow velocity, surface heat flux, and the step heights. The fluid utilized to conduct heat transfer in this experiment is air. The inlet and outlet diameters of the pipe are 46 and 83 mm respectively and the inner tube diameter of the annular pipe is 22 mm. In the simulations, 4 different cases were considered over an annular passage. The surface heat flux of the annular pipe is selected at 2098 W/m 2 with the variable Reynolds number between 17,050 to 44,545 and D/d=1.8 which is corresponding to 18.5 mm of step height. The numerical simulation parameters are summarized in Table 1. Only Reynolds number of 17,050 and heat flux equal to 2098 W/m 2 is considered experimentally to verify the numerical results Computational fluid dynamic (CFD) Fluid flow in a physical domain is governed by the laws of conservation of mass and momentum. These conservation laws, for steady flows in a two-dimensional domain can be stated by Eqs. (1) (3). Continuity equation: x ðρuþþ y ðρvþ ¼ 0 ð1þ Momentum conservation equations: x ðρuvþþ y ðρuvþ ¼ p x þ μ x ðρvuþþ y ðρuvþ ¼ p y þ μ! 2 u x þ 2 u 2 y 2! 2 v x þ 2 v 2 y 2 where u and v are the velocity components in the x and y directions. These equations are discretized using the finite volume scheme. On the basis of two dimensional Navier Stokes equations, the flow-solver formulates the principle of momentum, energy and mass conservation in partial differential equation forms. Navier Stokes equations are discretized along with cells from the division of computational domain by finite volume method CFD simulations Numerical simulation in this paper was aimed to investigate the heat transfer, typically Nusselt number and understand the flow phenomena of the sudden expansion in annular pipe. The diagram of the concentric pipe is drawn and meshed using Gambit software. The mesh of the simulation domain consisted of 920 cells. As the geometry of the annular pipe is symmetrical, only the lower half is drawn and simulated. A finite volume based flow solver of computational fluid dynamics software (FLUENT) 6.3 was selected in the investigation. The iteration of the standard K-epsilon viscous model is based on energy and Reynolds averaged Navier Stokes equations. The viscous model also provides good solutions for steady, axisymmetric, incompressible and turbulent flow. The second order upwind is used to solve the field variables at the finite volume cell faces for computing the solution. A SIMPLE algorithm is used to establish coupling between velocity and pressure [15,16]. According to Patankar and Spalding [17], the SIMPLE algorithm links the momentum and mass conservation equations using pressure corrections. The algorithm was selected over others due to the computational robustness and efficiency in calculating higher order differencing schemes and coupled parameters. A balance between computing cost as well as accuracy is achieved by this method in numerical differentiation of the convective terms, with the linear upwind differencing scheme. Table 2 shows the computational conditions of the numerical simulation. The properties of air were set to the standard atmosphere values at sea level, with a constant temperature. The flow solver used was steady state and pressure based which associates both the momentum and mass conservation equation. Unsteady assumption is used for most cases where convergence could be obtained. Simulations were performed until the residual values were less than ð2þ ð3þ Inlet Outlet Step Height Recirculation zone Fig. 1. Backward facing step in sudden expansion pipe.

3 1178 C.S. Oon et al. / International Communications in Heat and Mass Transfer 39 (2012) Short Stall Reattachment Point Table 1 Experiment parameters. Parameter Value Inlet dimension m Outlet dimension m Reynolds number 1, Re 1 17,050 Reynolds number 2, Re 2 30,720 Reynolds number 3, Re 3 39,993 Reynolds number 4, Re 4 45,545 Long Stall Fig. 2. Flow geometry. Table 2 Computational conditions. Computational conditions The Reynolds number (Re d ) can be obtained by the following Eq. (4): Re d ¼ ρ f U D h μ f where ρ f is the density of the fluid, U is the velocity of the fluid, D h is the hydraulic diameter of the annular pipe and μ f is the dynamic viscosity of the fluid at film temperature. The local heat transfer coefficients are calculated using convection heat flux as shown by Eq. (5): h x q c ¼ ðt sx T bx Þ where q c is the convection heat flux, T sx is the local surface temperature and T bx is the local bulk air temperature. The local Nusselt number (Nu) can be evaluated by Eq. (6): Nu ¼ h x d K f where d is the diameter of the pipe and K f is the thermal conductivity. Using Eqs. (4) (6), the experimental of data were reduced for the case of expansion ratio D/d=1.8, Heat flux q=2098 and Reynolds number Re=17,050 to 44,545. By using Eq. (5), the local heat transfer coefficient was calculated and subsequently local Nusselt number was evaluated from Eq. (6). Nusselt number for turbulent fully develop flow was then calculated from Dittus Boelter's correlation (7). The previously calculated local Nusselt numbers were divided by Nusselt d Recirculation flow 50cm Flow Flow S Di = constant 60cm Reattachment point q = constant Inner pipe D ð4þ ð5þ ð6þ Density 1.23 kg/m 3 Interpolating scheme (turbulence) Second order upwind Viscosity kg/m s Interpolating scheme (momentum) Second order upwind Pressure 101,325 Pa Inlet boundary type Velocity inlet Residual error Reference frame Absolute CFD algorithm Simple Reynolds number See Table 1 Viscous model k and ε Outlet boundary type Pressure outlet Space/time Two dimensional, second order implicit, unsteady numbers evaluated from Dittus Boelter correlation (Nu d ) to obtain the ratio Nu/Nu d [18]. Nu d ¼ 0:023 Re d 0:8 Pr 0:4 ð7þ Where Re d is Reynolds number based on hydraulic diameter and Pr is Prandtl number. 3. Result and discussion The present backward facing step in the pipe flow shows reduction of temperature on the inner surface of the pipe. Due to turbulent flow, the heat transfer is augmented in some areas. The lowest temperature is obtained at the end of flow recirculation zone where the flow reattachment occurred after the flow separation at the beginning of the step. Then, the fully developed turbulent flow will carries the heat though the rest of the pipe up to the exhaust to discharge hot air. Fig. 4 shows the temperature distributions along the pipe where the colors ranging from blue to red indicate low temperature to high temperature. In the simulations, 4 different cases were considered over an annular passage. The surface heat fluxes from the annular pipe is selected at 2098 W/m 2 with a variable Reynolds number between 17,050 to 44,545 in a given geometry. The average temperature for Re=17,505 for both numerical and experimental results are K and K respectively, where the percentage of error is less than 1. The temperature versus x/d graph is shown in Fig. 5. The evaluated Nusselt numbers for the specific Reynolds numbers are plotted in Fig. 6. The noticeable trend of the results is the sudden increase in the local Nusselt number when the fluid flows to the end Unheated pipe Test pipe Fig. 3. Schematic diagram of the annular sudden expansion in annular pipe flow [8]. Fig. 4. Temperature distribution along the pipe.

4 C.S. Oon et al. / International Communications in Heat and Mass Transfer 39 (2012) Fig. 5. The graph of surface temperature versus x/d. Fig. 6. The graph of Nusselt number versus x/d. of the recirculation zone. In a study conducted by Charwat et al. [19], this result is identical to an intervallic vortex shedding followed by the reattachment at the corner area of the recirculation zone. Also, the process of fresh fluid intervallic filling and emptying the recirculation zone may contribute to the dramatic increase in local Nusselt number. Lastly, the numerically simulated Nusselt number distributions at Reynolds number 17,505 are in reasonable agreement with experimental results concerning location and magnitude of the highest Nusselt number. Both average differences in Nusselt numbers are less than 10%. The variation of local Nusselt number (Nu/Nu d ) with x/d for heat flux q=2098 W/m 2 and expansion ratio D/d=1.8 are plotted in Fig. 7. The local Nusselt number ratio increases to maximum magnitude then decreases towards the end of the test pipe. The maximum value of local Nusselt number appears between the distance x/d of 1 and 2 for all the four Reynolds numbers and the experiment data. The highest peak of local Nusselt number falls in the range 34.8 to The highest local Nusselt number at Re=44,545 is 4.9% times higher than those obtained from turbulent fully developed flow occurred at Reynolds number Re=17,050. The augmentation of Fig. 7. The graph of Nusselt number/nusselt number (Dittus Boelter) versus x/d.

5 1180 C.S. Oon et al. / International Communications in Heat and Mass Transfer 39 (2012) heat transfer is observed with increase of Reynolds number where the value of local Nusselt number enhances due to induced eddies. 4. Conclusion From the numerical simulation at different Reynolds numbers, it can be concluded that the increase of flow reduces the surface temperature along the pipe to a minimum point then continues increasing throughout the rest of the pipe. The minimum surface temperature is obtained at flow reattachment point. The position of the minimum temperature point depends on the flow velocity over sudden expansion. The local Nusselt number (Nu) increases with the increase of Reynolds number which is valid for all the four cases. Augmented Nusselt number is obtained in backward facing steps. Nusselt and Reynolds number correlation shows similar trend as in case of concentric annular flow. The advent of computational fluid dynamic software (Fluent) could provide fair and agreeable result with experimental data in the present research. Acknowledgement The authors gratefully acknowledge High Impact Research Grant UM.C/625/1/HIR/C3/026 and the UMRG Fund RG084/10AET, University of Malaya, Malaysia for support to conduct this research work. References [1] W.T. Ashurst, F. Durst, C. Tropea, Two-dimensional separated flow: experiment and discrete vortex dynamics simulation, In: Symposium on Computation of Viscous Inviscid Interactions. Colorado Springs, CO, USA, [2] P.K. Chang, Control of Flow Separation: Energy Conservation, Operational Efficiency and Safety, McGraw-Hill Book Co., New York, [3] P.D.L. Calzada, M. Valdes, M.A. Burgos, Heat transfer in separated flows on the pressure side of turbine blades, Numerical Heat Transfer Part A: Applications 60 (8) (2011) [4] H.I. Abu-Mulaweh, A review of research on laminar mixed convection flow over backward- and forward-facing steps, International Journal of Thermal Sciences 42 (9) (2003) [5] B. Wang, H.Q. Zhang, X.L. Wang, A time-series stochastic separated flow (TSSSF) model for turbulent two-phase flows, Numerical Heat Transfer Part B: Fundamentals 55 (1) (2009) [6] A. Murata, K. Iwamoto, Heat and fluid flow in cylindrical and conical annular flow-passages with through flow and inner-wall rotation, International Journal of Heat and Fluid Flow 32 (2) (2011) [7] A.A. Al-aswadi, H.A. Mohammed, N.H. Shuaib, Laminar forced convection flow over a backward facing step using nanofluids, International Communications in Heat and Mass Transfer 37 (8) (2010) [8] D. Khoeini, M.A. Akhavan-Behabadi, A. Saboonchi, Experimental study of condensation heat transfer of R-134a flow in corrugated tubes with different inclinations, International Communications in Heat and Mass Transfer 39 (1) (2012) [9] R. Roslan, H. Saleh, I. Hashim, Buoyancy-driven heat transfer in nanofluid-filled trapezoidal enclosure with variable thermal conductivity and viscosity, Numerical Heat Transfer Part A: Applications 60 (10) (2011) [10] A. Raisi, B. Ghasemi, S.M. Aminossadati, A numerical study on the forced convection of laminar nanofluid in a microchannel with both slip and no-slip conditions, Numerical Heat Transfer Part A: Applications 59 (2) (2011) [11] B. Ghasemi, S.M. Aminossadati, Natural convection heat transfer in an inclined enclosure filled with a water-cuo nanofluid, Numerical Heat Transfer Part A: Applications 55 (8) (2009) [12] Y. Zhang, L. Li, H.B. Ma, M. Yang, Effect of Brownian and thermophoretic diffusions of nanoparticles on nonequilibrium heat conduction in a nanofluid layer with periodic heat flux, Numerical Heat Transfer Part A: Applications 56 (4) (2009) [13] E.G. Filetti, W.M. Kays, Heat transfer in separated, reattached, and redevelopment regions behind a double step at entrance to a flat duct, Journal of Heat Transfer 89 (2) (1967) [14] Hussein Togun, Y.K. Salman, H.S. Sultan Aljibori, S.N. Kazi, An experimental study of heat transfer to turbulent separation fluid flow in an annular passage, International Journal of Heat and Mass Transfer 54 (4) (2011) [15] M. Rahgoshay, A.A. Ranjbar, A. Ramiar, Laminar pulsating flow of nanofluids in a circular tube with isothermal wall, International Communications in Heat and Mass Transfer 39 (3) (2012) [16] A.H. Mahmoudi, M. Shahi, F. Talebi, Entropy generation due to natural convection in a partially open cavity with a thin heat source subjected to a nanofluid, Numerical Heat Transfer Part A: Applications 61 (4) (2012) [17] S.V. Patankar, D.B. Spalding, A calculation procedure for heat, mass and momentum transfer in three-dimensional parabolic flows, International Journal of Heat and Mass Transfer 15 (10) (1972) [18] F. Kreith, M.S. Bohn, Principles of Heat Transfer, sixth ed., Brooks/Cole, CA, USA, [19] A.E. Charwat, C.E. Dewey, J.N. Roos, J.A. Hitz, An investigation of separated flows-part II: flow in the cavity and heat transfer, Journal of Aerospace Sciences 28 (7) (1961)