Computational investigation of the velocity and temperature fields in corrugated heat exchanger channels using RANS based turbulence models with experimental validation

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Computational investigation of the velocity and

temperature fields in corrugated heat exchanger

channels using RANS based turbulence models with

experimental validation

Erman Aslan

Mechanical Engineering Department, Istanbul University,

TR-34320, Istanbul, Turkey Email: erman.aslan@istanbul.edu.tr

Imdat Taymaz* and Yasar Islamoglu

Mechanical Engineering Department,

Sakarya University, TR-54187, Sakarya, Turkey Email: taymaz@sakarya.edu.tr Email: yasari@sakarya.edu.tr *Corresponding author

Mardiros Engin and Ilkay Colpan

Mechanical Engineering Department,

Istanbul University,

TR-34320, Istanbul, Turkey

Email: mardirosengin@hotmail.com Email: ilkaycolpan@windowslive.com

Gokhan Karabas

Kevser Isı Sanayii ve Ticaret Limited Sirketi, TR-34040, Istanbul, Turkey

Email: gokhan@kevserisi.com.tr

Guven Ozcelik

Mechanical Engineering Department, Istanbul Arel University,

TR-34537, Istanbul, Turkey Email: guvenozcelik@arel.edu.tr

Abstract: The characteristics of convective heat transfer and friction factor for periodic

corrugated channels are investigated numerically. In the numerical study, the finite volume method (FVM) is used. Three different Reynolds averaged numerical simulation (RANS) based turbulent models, namely the k-ω, the shear stress transport (SST) model and the transition SST model are employed and compared with each other. Experimental results obtained from a previous study are used for the assessment of the numerical results. Investigations are performed for air flowing through corrugated channels with an inclination angle of 30°. The Reynolds number is varied within the range 2,000 to 11,000, while keeping the Prandtl number constant at 0.70. Variations of the Nusselt number, Colburn factor, friction factor and goodness factor with the Reynolds number are studied. Effects of the corrugation geometry and channel height are discussed. The overall performances of the considered turbulence model are observed to be quite similar. The SST model is observed to show a slightly better overall performance.

Keywords: corrugated channel; convective heat transfer; friction factor; finite volume method;

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Reference to this paper should be made as follows: Aslan, E., Taymaz, I., Islamoglu, Y.,

Engin, M., Colpan,, I., Karabas, G. and Ozcelik, G. (2018) ‘Computational investigation of the velocity and temperature fields in corrugated heat exchanger channels using RANS based turbulence models with experimental validation’, Progress in Computational Fluid Dynamics, Vol. 18, No. 1, pp.33–45.

Biographical notes: Erman Aslan received his BSc, MSc and PhD in Mechanical Engineering

from the University of Sakarya, Turkey. He was a Visiting Researcher to prepare his PhD thesis at the Düsseldorf University of Applied Sciences, Germany. He is an Assistant Professor of Mechanical Engineering Department at the University of Istanbul, Turkey.

Imdat Taymaz received his BSc and MSc in Mechanical Engineering from the Technical University of Istanbul, Turkey and his PhD from the University of Sakarya, Turkey. He is a Professor at the Mechanical Engineering Department at University of Sakarya. He teaches undergraduate and graduate courses in automotive division. His research areas of interest include advanced technologies in engines for automotive industry.

Yasar Islamoglu received his BSc and MSc in Mechanical Engineering from the Technical University of Istanbul, Turkey and his PhD from the University of Sakarya, Turkey. He is a Professor at the Mechanical Engineering Department at University of Sakarya. He teaches undergraduate and graduate courses in heat transfer.

Mardiros Engin received his BSc in Mechanical Engineering from the University of Istanbul, Turkey. He is an MSc student at the University of Istanbul, Turkey. His research area is forced convection and turbulence modelling.

Ilkay Colpan received her BSc in Mechanical Engineering from the University of Istanbul, Turkey. She is an MSc student at the University of Istanbul, Turkey. She is currently employed as a Research Assistant at University of Kirklareli, Turkey.

Gokhan Karabas received his BSc in Mechanical Engineering from the University of Istanbul, Turkey. He is an MSc student at the University of Istanbul, Turkey. He is currently employed at Kevser Isı Sanayi Ltd. Şti as a Project Engineer.

Guven Ozcelik received his BSc in Mechanical Engineering from the University of Istanbul, Turkey. He is an MSc student at the Technical University of Yildiz, Turkey. He is currently employed as a Research Assistant at the University of Istanbul Arel.

1 Introduction

Recently, because of the increasing demand by industries for more efficient and compact heat exchangers, heat transfer enhancements have gained great momentum. For this purpose, two techniques can generally be identified, namely, active and passive techniques (Webb, 1994). Active techniques contain surface vibration, fluid vibration, electrostatic fields, boundary layer injection, boundary layer suction and electro-hydrodynamics, etc. for increasing heat transfer. Therefore, active techniques need more costs and, thus have attracted relatively little attention in research and practice (Kuppan, 2000).

In passive techniques, besides using fluid additives, the applied approaches generally involve a modification of the channel geometry in a way to increase the heat transfer rate. A specific category of heat transfer enhancement is the use of bluff bodies, prisms in ducts that increase the heat transfer coefficient by turbulence generation and vortex shedding in their wake (Benim et al., 2011, Taymaz et al., 2015). A further category is the insertion of structures such as twisted tapes (Bhattacharyya et al., 2017) that induce a swirling motion, where the swirl component increases the near-wall velocity in magnitude, along with the wall shear

stress and, thus, enhances the convective transport ability of the fluid.

The presently investigated passive heat transfer enhancement technique belongs to the category of the direct augmentation of the heat transfer surface, where structures such as pins, fins or channel corrugations are introduced that increase the heat transfer surface, on the one hand, but also increase the convective heat transfer coefficient by the introduced recirculation zones that interrupt the thermal boundary layer and lead to higher transfer rates by increased turbulence levels. In the present study, surface corrugations are investigated without additionally introduced artificial roughnesses such as ribs and pins.

Experimental investigations of the forced convection in corrugated channels were performed by Sparrow and Hossfeld (1984), Snyder et al. (1993), Bilen et al. (2009) and Nilpueng and Wongwises (2006), who investigated the velocity and temperature fields experimentally and suggested empirical expressions for the calculation of the Nusselt number. An optimal design method for plate heat exchangers with and without pressure drop specification was presented by Wang and Sundén (2003).

As far as the computational investigations are concerned, like in the other areas of the convective heat

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transfer research (Benim et al., 2007, Chattopadhyay and Benim, 2011), the main concern has been the turbulence modelling. Currently, the most sophisticated turbulence modelling approach for practical applications is the so-called large eddy simulations (LES), whereas some authors also attempt direct numerical simulations (DNS) for low Reynolds numbers. Ciofalo et al. (1993) studied the flow and heat transfer characteristics in corrugated passages using LES and DNS within a range of Reynolds numbers from 103_{to 10}4_{. They also compared the numerical results}

with the experimental ones and found a quite satisfactory agreement. LES of convective heat transfer over a half-corrugated channel with various wave amplitudes (wave amplitudes present the ratio of wave height to wave length) was performed by Mirzaei et al. (2014) for Re = 10,000 and Pr = 0.71.

LES requires a three-dimensional and unsteady analysis, by definition, along with a quite fine computational grid and, thus, represents, in general, a computationally expensive method (Benim et al., 2005). In the Reynolds averaged numerical simulation (RANS) approach, the Reynolds-averaged equations are solved and since an unsteady or three-dimensional simulation is not necessarily needed in this framework, the associated computational costs are much lower and this approach is most widely applied in practical applications. Unsteady phenomena caused by a deterministic unsteadiness such as time-dependent boundary conditions can be treated within an unsteady solution procedure, using a turbulence model for the unsteadiness caused by turbulence (unsteady RANS). Within this framework, Benim et al. (2004) investigated the unsteady convective heat transfer in turbulent pipe flow, computationally, for step-like, puls-like and sinusoidal perturbations of the flow, using different turbulence models. An investigation of time-dependent channel flow was presented by by Zafer and Delale (2014), where the emphasis was placed upon the formulation of non-reflecting boundary conditions in the considered transonic flow. Hossain and Sadrul Islam (2007) applied an unsteady numerical analysis to three different geometries of the wavy passages, which are sine-shaped, triangular and arc-shaped, to investigate flow and heat transfer behaviours, numerically. However, the study was limited to low Reynolds numbers, where the flow is still laminar and, consequently, no turbulence model was employed.

In the present work, the considered flow problem is statistically steady and a RANS framework has been adopted for modelling turbulence. A recent RANS analysis of forced convection in compact heat exchangers was presented by Oclon et al. (2015), where the prediction of fouling was staying in foreground and no surface corrugations were considered.

Zhang and Tian (2006) performed a numerical simulation of flow and heat transfer in cross-corrugated plate heat exchangers, using a RANS based turbulence model, namely the renormalisation group (RNG) k-ε turbulence model. The effect of corrugation inclination angle on heat transfer and pressure drop was investigated.

They observed that, numerical results agreed well with the previous experimental results. A numerical investigation of turbulent forced convection in a two-dimensional channel with periodic transverse grooves on the lower channel was performed by Eimsa-ard and Promvonge (2008). In their numerical studies, four turbulence models, namely k-ε, RNG k-ε, k-ω and the shear stress transport (SST) models were used. The RNG k-ε and the k-ε turbulence models generally provided a better agreement with the available experimental results. It was observed that grooved channels provide a considerable increase in heat transfer about 158% over the smooth channel.

Kanaris et al. (2009) suggested a general method for the optimal design of plate heat exchangers with undulated surfaces. The computational model was a three-dimensional narrow channel with angled triangular undulations in a herringbone pattern, whose blockage ratio; channel aspect ratio, corrugation aspect ratio, angle of attack and Reynolds number were used as design variables. For the optimisation procedure, response surface methodology was used. New correlations were provided for predicting Nusselt number and friction factors in such plate heat exchangers. Zhang and Chen (2011) performed experimental and numerical studies in cross-corrugated triangular ducts under uniform heat flux boundary condition. A low Reynolds number k-ω turbulence model was employed. Correlations were provided for the estimation of the Nusselt number and friction factor. Thermohydraulic characteristics of periodic corrugated channels for Reynolds numbers in the range of 200-3000 were investigated under different geometrical parameters by Liu and Niu (2015). The effect of apex angle and aspect ratio was investigated. Seven RANS based turbulence models, namely the k-ε, RNG k-ε, realisable k-ε, SST, transition SST, k-kl-ω and Reynolds stress model were applied. The Reynolds stress model was found to show the best agreement with the experimental data. Artemov et al. (2015) investigated liquid-nitrogen flow in an annular channel with outer transversally corrugated wall, experimentally and numerically. As turbulence models, two-equation low Reynolds number turbulence models (k-ε and k-ω) and the algebraic LVEL model were used. Both approaches were observed to deliver sufficiently accurate results.

The present investigation applies a RANS based turbulence modelling strategy to predict the turbulent forced convection in corrugated channels for three different geometries. A major focus of the work is an assessment of three turbulence models by comparing them against each other and with measurements. A special emphasis is placed upon the numerical accuracy, especially with regard to grid independence.

In the present study, heat transfer and pressure drop characteristics in a periodic corrugated channel are investigated numerically using the finite volume method (FVM). Three different RANS based turbulence models, namely the k-ω model, the SST.

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2 Problem definition

Symmetric corrugated channels are considered in this investigation. Two types of corrugation peaks are considered,

a rounded corrugation peak b sharp corrugation peak.

The channel types are sketched in Figure 1, with indication of the parameters controlling their geometry. For the parameters, the list of the considered values is provided in Table 1. The effect of the channel geometry on the flow development and temperature distributions is investigated, while keeping the contact angle θ constant at 30° (Table 1). In this numerical study, Reynolds number (Re) is varied from 2,000 to 11,000 and Prandtl number (Pr) is taken to be 0.7.

Figure 1 The corrugated channel with the representative

parameters, (a) The wall with rounded corrugation peak (b) The wall with sharp corrugation peak

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Table 1 Geometric configurations of corrugated walls (unit-mm) Channel no. θ(°) S a b Hmin = (b – a ) × 2 r 1 30 17.32 3.91 6.41 5 7 2 30 17.32 5 7.5 5 - 3 30 17.32 5 10 10 -

Maximum channel height is defined as

max 2

H = b (1a)

while the minimum channel height is given by

min 2( )

H = b a− (1b)

3 Modelling

Incompressible flow of a Newtonian fluid with constant material properties is considered, where the buoyancy forces and natural convection are neglected. Obviously, the radiative heat transfer (Benim, 1988) does either not play a significant role in the present problem with rather low temperatures. Turbulence is modelled within a RANS approach (Durbin and Reif, 2011). The modelled

differential equations for mass, momentum and energy conservation, along with the transport equations of the turbulence model, are solved numerically in two-dimensions and steady-state. For the computational analysis, the multi-purpose, FVM based computational fluid dynamics code, ANSYS Fluent is employed (ANSYS-Fluent, 2012).

For turbulence modelling, three models, namely the k-ω model (Wilcox, 1998), the SST model (Menter, 1994) and the transition SST model (Menter et al., 2006) are employed. For modelling the near-wall turbulence, no wall-functions approach (Durbin and Reif, 2011) is used. The applied turbulence equations are capable of representing the near-wall turbulence, provided that the grid resolution is sufficiently fine.

The semi-implicit method for pressure-linked equations (SIMPLE) is used for pressure velocity coupling (ANSYS-Fluent, 2012). The second order upwind procedure is used for discretising the convective terms (ANSYS Fluent, 2012). The default under-relaxation factors are used (pressure: 0.3, momentum: 0.7, turbulence quantities: 0.8, energy: 1.0). As the converge criteria, a residual value of 10–6_{is required for all equations except the}

energy equation. For the latter, a residual of 10–8_{is required}

for convergence.

3.1 The solution domain and boundary conditions

Figure 2 shows a schematic of a typical solution domain with boundary types. At the inlet, a constant velocity and constant temperature profile are used as boundary conditions for the momentum and energy equations. For deriving the inlet boundary conditions at the inlet, a turbulence intensity of 4% and a macro-mixing length equal to 30% of the hydraulic diameter is assumed. The assumed inlet turbulent intensity of 4% is in accordance with the measured value in the experiments (Aslan et al., 2016). At the outlet, a constant pressure and a zero-gradient condition for the remaining variables is applied. At the walls, the no-slip boundary condition applies for the momentum equations. For the energy equation, a constant heat flux is applied as boundary condition.

Figure 2 A schematic of typical solution domain with boundary

types

3.2 Computational grids

A structured meshing strategy based on quadrilateral finite volumes is used. A grid independence study is performed for finding an adequate grid resolution here; the Nusselt number and the friction factor are taken as the quantities to be monitored. The grid independence study is performed only for the highest Reynolds number for each geometry. The resulting grid is, then, used also for the lower Reynolds numbers, assuming that a sufficient resolution will be

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guaranteed also for these cases. In order to cope with the requirements of the turbulence models for modelling the near-wall turbulence, without using wall-functions, in all grids, it is ensured that the distance of the first near-wall cell fulfils the condition of y+_{< 1 and at least three cells are}

contained in the region for y+_{< 5. The grid independence}

study, in this sense, is performed for all three geometries and using all three turbulence models.

The results of the grid independence study, performed using the SST turbulence model, for channel-1, channel-2 and channel-3 are displayed in Figures 3, 4 and 5, respectively. One can see that the different geometries show different grid convergence characteristics and, in all geometries a sufficient grid independence is ensured.

Figure 3 Grid independence study using the SST turbulence

model for channel-1, (a) Nusselt number, (b) friction factor

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The total number or grid nodes of the resulting grids ensuring sufficient independence for different channel geometries and different turbulence models are presented in Table 2.

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(b)

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model for channel-3, (a) Nusselt number, (b) friction factor (continued)

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Table 2 Number of nodes of grids ensuring sufficient grid independence

Channel no. k-ω SST Transition SST

1 471,040 264,960 317,952 2 256,000 192,000 172,800 3 268,800 259,200 264,000

Detail views of the grids for channel-1 and chanel-2 used for the SST turbulence model are shown in Figure 6.

Figure 6 Detail views of the grids used in combination with the

SST turbulence model, (a) channel-1, (b) channel-2 (see online version for colours)

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3.3 Dimensionless numbers

For the present study, the four integral parameters of interest are;

1 the Nusselt number 2 the friction factor 3 the Colburn factor 4 the goodness factor.

The calculated parameters are compared with the measured values of Aslan et al. (2016). Please note that these parameters are calculated for the previous three cycles before the last cycle of the corrugated channel, where the flow reaches a rather periodic pattern and where the wall and fluid temperatures were measured in the experiments (Aslan et al., 2016).

The definition of the Nusselt number is h

hD Nu

k

= (2)

where Dh is hydraulic diameter, h is the cycle-average heat transfer coefficient and k is the thermal conductivity.

The hydraulic diameter is defined as a twice the average channel height. The average channel height is average of minimum channel height and maximum channel height. Therefore, the hydraulic diameter is defined as (Nicĕno and Nobile, 2001)

(

min max

)

h

D = H +H (3)

The cycle averaged heat transfer coefficient (h) is obtained by integrating the local heat transfer coefficient for the previous three cycles before the last cycle, as indicated below 0 1 3 S x h h dx S =

∫

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In order to calculate the average Nusselt number, cycle-average heat transfer coefficient is used.

For predicting the friction factor, again, the previous three cycles before the last cycle are used. The friction factor is calculated as 2 1 2 h dP_D dX f ρV − = (5)

where ρ is density and V is mean velocity.

The Colburn factor is defined as (Kuppan, 2000)

1/3

Re Pr Nu

j= (6)

where Re is Reynolds number and Pr is Prandtl number. Reynolds number is based on the inlet velocity and hydraulic diameter. The goodness factor is the ratio of

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Colburn factor j to the friction factor f (London, 1964; Shah and London, 1978; Kuppan, 2000)

4 Results and discussions

Figure 7 shows the axial velocity distribution predicted by the SST turbulence model, for three channels, for an inlet velocity of 6.79 m/s. This result in a Reynolds number of 6,576 for channel-1, 7,380 for channel-2 and 11,071 for channel-3, which represent, each, the highest Reynolds number considered for each category of the channel geometry. The flow develops through the channel and the flow characteristics are observed to reach a certain periodicity for the last cycles of corrugated channel for all three geometries. Thus, one can say that the flow is rather fully developed, in this sense, for the last cycles of the channel. The results of the other turbulence models (k-ω and transition SST) predict quite similar flow patterns that are not shown here. At the lower Reynolds numbers, the flow is observed to reach the fully-developed state earlier.

Figure 7 Axial velocity contours obtained by SST turbulence

model, (a) channel-1, (b) channel-2, (c) channel-3 (see online version for colours)

(a)

(b)

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Figure 8 displays the SST turbulence model prediction of the streamlines for three corrugated channels and for the cases considered in Figure 7, for the two cycles before the last cycle. The displayed streamline patterns confirm the periodicity reached by the flow. One can observe that the recirculation zones of channel-2 [Figure 8(b)] are more intense compared to the other configurations, which implies comparably better heat transfer characteristics for channel-2 (Figure 8).

The computed temperature distribution by the SST turbulence model for three different channels and the maximum Reynolds numbers (the same cases as in Figure 7) are presented in Figure 9. The flow is gradually and continuously heated up through the channel by the

applied constant heat flux at the wall. It is clearly seen in Figure 9, that the onset and the growth of the recirculation zones promote the mixing of cold fluid from the core with the hot fluid near the boundary layer. This induces higher temperature gradients near the corrugated walls. Therefore, the net heat transfer rate from the corrugated wall to the fluid gets enhanced.

Figure 8 Streamlines obtained by SST turbulence model,

(a) channel-1, (b) channel-2, (c) for channel-3 (see online version for colours)

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(b)

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Figure 9 Temperature contours obtained by SST turbulence

model, (a) channel-1, (b) channel-2, (c) channel-3 (see online version for colours)

(a)

(b)

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Figure 10 Nusselt number as function of Reynolds number,

(a) experimental (Aslan et al., 2016), (b) channel-1, (c) channel-2, (d) channel-3

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(b)

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Figure 10 Nusselt number as function of Reynolds number,

(a) experimental (Aslan et al., 2016), (b) channel-1, (c) channel-2, (d) channel-3 (continued)

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Figure 10(a) shows the Nusselt number as a function Reynolds number as obtained by the experimental study (Aslan et al., 2016) for three channels. Figure 10(b), Figure 10(c) and Figure 10(d) display the relationship between the Nusselt and Reynolds number as predicted by the three turbulence models in comparison with the measurements, respectively. Nusselt number is a function of the Reynolds number and the channel geometry. Nusselt number increases with the Reynolds number for three channels. The channel-1 which is the one with rounded corrugations shows the steepest increase with Reynolds number and reaches the maximum Nusselt number value at Re = 6,270. With decreasing minimum channel height, the convective heat transfer increases. Nusselt numbers of channel-2 are higher than the Nusselt numbers of channel-3, since the recirculation zones near the walls increase for the smaller channel height of channel-2. Since the channel with rounded corrugations produce less intense recirculation zones compared to the sharp corrugations, Nusselt numbers of the channel with sharp corrugation ae generally larger than those of the channel with rounded corrugations with the same minimum channel height.

For channel-1, SST and k-ω turbulence models predict reasonable overall results within the Reynolds number range of 4,434–6,576, where the k-ω model shows a better agreement in the mean. For low Reynolds numbers, the predictions of SST and k-ω turbulence models deviate from the experimental results. The transition SST turbulence model over-predicts the Nusselt number throughout for channel-1. Still, it is interesting to observe that the slope of the predicted curve is very close to that of the experiments. For channel-2, the best prediction is obtained by the SST turbulence model for Reynolds numbers beyond Re = 5,887. The k-ω turbulence model under-predicts the Nusselt number. The transition SST is generally over-predicting. For channel-3, the SST turbulence model performs comparably well for high Reynolds numbers. The transition SST turbulence model predictions of the Nusselt number are

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also quite good for Reynolds numbers higher than Re = 6,676. However, at low Reynolds numbers, the results of the models are not that close to the experiments. The Nusselt number is under-predicted by the k-ω turbulence model for channel-3.

Figure 11 Friction factor as function of Reynolds number,

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(b)

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Figure 11 Friction factor as function of Reynolds number,

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The friction factor comparison as a function of Reynolds number is shown in Figure 11. The friction factor increases with increasing channel height. The minimum and maximum friction factors are observed at the channel-1 and channel-3, respectively. For the same minimum channel height (Hmin = 5 mm), sharp corrugated peak channel

(channel-2) produces larger friction factors than the rounded corrugated peak channel (channel-1). For channel-1, friction factor predictions of the SST turbulence model are close to the experimental results especially after Re = 4,434. The k-ω and transition SST models also produce reasonable results for channel-1. For channel-2, an under-prediction and an over-prediction are observed for the k-ω and transition SST models, respectively. The SST turbulence model produce the closest result to experimental results. For channel-3, the SST and k-ω turbulence models show a similar overall agreement, where the former is over-predicting and the latter under-predicting. Transition SST model predictions at high Reynolds numbers are quite close to the experimental results, but, at lower Reynolds numbers there are larger discrepancies.

Figure 12 shows the Colburn factor as function Reynolds number. As it can be clearly seen in the figure, the Colburn factor decreases with the Reynolds number. It can also be seen that the Colburn factor increases with decreasing channel height. For the same minimum channel height (Hmin = 5 mm), the Colburn factor of the channel

with rounded corrugation peak is smaller than the channel with sharp corrugation peak at Re < 5,000. For channel-1, the SST and k-ω turbulence models produce similar results. These results are close to the experimental results especially at high Reynolds numbers. Also, a reasonable agreement with the measurements is predicted by the transition SST turbulence model. The Colburn factor predictions of the SST turbulence models are close to the experimental results at high Reynolds numbers for channel-2 and channel-3. The k-ω turbulence model under-predicts the Colburn factor for

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channel-2 and channel-3. At high Reynolds numbers, an over-prediction is observed for the transition SST turbulence model for channel-2. For channel-3, the transition SST turbulence model produces close results to measurements after Re = 7,464. At lower Reynolds numbers, Colburn factor predictions generally deviate from the experimental results.

Figure 12 Colburn factor as function of Reynolds number,

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(b)

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Figure 12 Colburn factor as function of Reynolds number,

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Figure 13 Performance comparison as a function of Reynolds

number, (a) experimental (Aslan et al., 2016), (b) channel-1, (c) channel-2, (d) channel-3

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Figure 13 Performance comparison as a function of Reynolds

number, (a) experimental (Aslan et al., 2016), (b) channel-1, (c) channel-2, (d) channel-3 (continued)

(c)

(d)

For optimal design, both the convective heat transfer rate and the pressure drop must be considered simultaneously. For this reason, an additional parameter is introduced, namely the area goodness factor, which is defined as the ratio of the Colburn factor j, to the friction factor f. The corresponding curves are presented in Figure 13. The performance decreases with Reynolds number for all channels. It is observed that the performance for the channel with rounded corrugated peak is greater than for the sharp corrugated peak about 100% for the same minimum channel height (Hmin = 5 mm). In the sharp corrugated peak

channels, the performance of the (Hmin = 10 mm) is lower

than the performance of the (Hmin = 5 mm). The SST, k-ω

and transition SST turbulence models predict close results to experiments especially at high Reynolds numbers (4,857 ≤ Re ≤ 6,576) for channel-1. For lower Reynolds number, SST, k-ω and transition SST turbulence models produce also reasonable results. The characteristics observed for channel-2 are similar to those of channel-1. For channel-3,

all turbulence models produce close results to experiments at high Reynolds numbers. The SST and k-ω turbulence models produce very similar results throughout and deviate from the measurements at low Reynolds numbers.

5 Conclusions

The present paper presents a computational study of forced convection in corrugated channels, where the predictions are assessed by comparisons with experiments. Three channel geometries are considered that vary in the minimum and maximum channel heights and corrugation shapes. Three turbulence models are used, namely the k-ω model, the SST model and the transitional SST model. The major conclusions to be drawn are:

• Nusselt number depends strongly on the minimum channel height. With increasing minimum channel height, the Nusselt numbers decreases.

• With the same minimum channel height, Nusselt number of the channel with sharp corrugated peak is large than channel with the same minimum channel height.

• The friction factor decreases with increasing minimum channel height. The minimum friction factor occurs for the channel with rounded corrugated peak.

• The Colburn factor decreases with an increasing minimum channel height. Colburn factor of the channel with sharp corrugated peak is greater than channel with rounded corrugated peak for Re < 5,000.

• The performance increases with decreasing minimum channel height. The flow area goodness factor of the channel with rounded corrugated peak is larger than that of the channel with sharp corrugated peak. • For the overall performance of turbulence models; the

overall performance of the models are observed to be quite similar. The SST model is observed to show a slightly better overall performance.

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Nomenclature

Dh Hydraulic diameter

f Friction factor

H Channel height

h Cycle average heat transfer coefficient

hx Axially local heat transfer coefficient

j Colburn factor

k Thermal conductivity, turbulence kinetic energy

L Length

Nu Nusselt number

P Pressure Pr Prandtl number Re Reynolds number