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CHAPTER 8

Experimental and Numerical Study on Heat Transfer Enhancement of Impingement Jet Cooling by Adding Ribs on Target Surface

K. Takeishi & Y. OdaDepartment of Mechanical Engineering, Osaka University, Japan.

Abstract

Impingement jet cooling heat transfer with a two-dimensional and a circular nozzle

enhanced by a rib was studied experimentally and numerically. The effect of a rib

on heat transfer enhancement in the wall jet region of an impinging jet has been

studied via mass transfer experiments conducted using a naphthalene sublimation

technique and numerical simulations using the Reynolds-averaged Navier–Stokes

(RANS) model and large eddy simulation (LES). The averaged Nusselt number

was at its highest value when the rib was as tall as the corresponding boundary

layer thickness of a no-rib case at the rib position. With respect to the effect of

rib location, the best enhancement in the heat transfer rate was seen when the rib

was installed closest to the boundary between the stagnation region and the wall

jet region. From the results of the numerical simulation, it was evident that the

Abe–Kondoh–Nagano (AKN) model yielded the best prediction of reattachment

length from among the three RANS models; this predicted value agreed well with

the experimentally obtained local heat transfer coeffi cient distribution; however, in

the stagnation and reattachment regions, over- and under-estimation, respectively,

occurred. In addition, LES was found to be effective for predicting the decay of

Nusselt number downstream of the reattachment point and the effect of rib height

on the peak Nusslet number.

Keywords: Naphthalene sublimation method, turbulence promoter, RANS, LES.

1 Introduction

Heat transfer using an impinging jet heat transfer can be used for achieving high convective heat transfer rates in the stagnation region. Hence, the technique has

www.witpress.com, ISSN 1755-8336 (on-line) WIT Transactions on State of the Art in Science and Engineering, Vol 76, © 2014 WIT Press

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204 IMPINGEMENT JET COOLING IN GAS TURBINES

been used widely in a number of industrial areas such as thermal heating, cooling and drying target surfaces, and electronic device cooling. One of the advantages of the jet impingement cooling is that the stagnation heat transfer can be adjusted easily depending on the required heat fl uxes by optimizing the jet velocity, nozzle spacing, etc. Thus, the jet impingement cooling plays an important role in the internal surface cooling of gas turbine vanes using a minimal volume of cool-ing air. For realizing higher turbine inlet temperatures, which results in a higher thermal effi ciency, than those in the current 1500°C-class gas turbines, further enhancement of impinging jet heat transfer must be pursued.

Currently, there exist many sets of data on fundamental jet impingement fl ow and heat transfer for a single-jet impingement on a smooth fl at surface [1–3]. Multiple jets on a fl at and concave surface are also useful for internal surface cool-ing of gas turbine vanes and there exist many data [4, 5].

Recently, investigations of heat transfer and pressure loss across jets impinging on roughened surfaces such as dimpled and pin fi nned surfaces and surfaces with turbulence promoters have been conducted to improve the overall heat transfer on target plates [6–13]. Although the stagnation heat transfer of impinging jets is very high, one of the defects of single-jet impingement heat transfer is the rapid decay of the heat transfer rate in the wall jet region. Thus, installing turbulence promoters in the wall jet region can be one of the promising solutions for main-taining a high heat transfer rate across a wider area because doing so induces fl ow separation and reattachment, which results in redevelopment of the thermal boundary layer [14].

In this chapter, the enhancement of jet impingement heat transfer using turbu-lence promoters is studied experimentally and numerically for a two-dimensional (2D) slot jet and an axisymmetric round jet. Detailed measurement of the local convective heat transfer distribution was obtained using the naphthalene sublima-tion method for clarifying the enhancing effect of the turbulence promoter on the heat transfer rate and for optimizing rib geometry and location. In addition, numerical simulation using the Reynolds-averaged Navier–Stokes (RANS) model and large eddy simulation (LES) was performed for evaluating their prediction capability and for examining the detailed mechanism of heat transfer enhancement resulting from the addition of a rib on a target plate.

2 Experimental Study

2.1 Heat transfer test with two-dimensional impinging jet nozzle

Figure 1 shows a schematic layout of the experimental setup for the 2D jet impinge-ment heat transfer test using the naphthalene sublimation method. Dry air was supplied from an air compressor to a 4 × 100 mm slit nozzle (Dh = 8 mm) through a pressure regulator. The slit nozzle generates a 2D jet on a fl at surface covered with a naphthalene layer. Upstream of the nozzle exit, there is a fl ow-settling cham-ber equipped with a honeycomb having a 200/inch mesh for reducing the turbu-lence intensity and shaping uniform airfl ow at the exit. Therefore, the airfl ow has


EXPERIMENTAL AND NUMERICAL STUDY ON HEAT TRANSFER 205

low turbulence intensity and a uniform velocity profi le before entering the nozzle section. Furthermore, as shown in Fig. 1, as the nozzle converges smoothly toward the exit, it allows for the rapid acceleration of air without fl ow separation and tur-bulence generation. Consequently, the slit nozzle generates a 2D jet that impinges on the target surface mounted below the nozzle. The volume fl ow rate of air was carefully measured using a rotameter for maintaining the nozzle exit velocity at 20 m/s, i.e. ReDh = 10,000.

The 100 × 100 × 20 mm target plate is made of aluminum. The surface of the target plate is covered with a 3-mm-thick layer of molded naphthalene. Figure 2a shows the schematic layout of the 2D nozzle and the target plate with a continuous rib. The nozzle-to-plate distance is 40 mm (H/Dh = 5). The continuous rib was located at Lr = 20 mm (Lr/Dh = 2.5) in the wall jet region. The height and width of the square rib, e, were varied from 0.5 to 2.0 mm. Figure 2b shows a schematic

Figure 1: Schematic layout of experimental apparatus.

Figure 2: Continuous rib and broken rib on target plate with 2D impingement nozzle.



layout of a 2D nozzle and a target plate with a broken rib, the length of which is half the continuous rib’s span-wise length. The location and height of the broken square rib are the same as that of the continuous square rib.

2.2 Heat transfer test with circular impinging jet nozzle

Figure 3 shows the schematic diagram of the experimental setup for the single circular impinging jet cooling test using the naphthalene sublimation method. Dry air from an air compressor is supplied to an air chamber, which has a fl ow strainer, through a pressure regulator and a heat exchanger for maintaining constant air jet temperature. The air jet is spouted from a round nozzle (D = 32 mm), the exit of which is orifi ce-shaped. The round nozzle generates an axisymmetric round jet on the naphthalene-covered fl at surface. The naphthalene layer is a part of the impinged surface because the time-mean fl ow and heat transfer fi eld is expected to be axisymmetric under the current fl ow confi guration. Upstream of the nozzle exit, there is a fl ow-settling chamber equipped with a honeycomb having a 200/inch mesh for reducing the turbulence intensity and for shaping uniform air fl ow at the exit. Therefore, the airfl ow has low turbulence intensity and uniform veloc-ity profi le before entering the nozzle section. The volume fl ow rate of air was carefully measured using a mass fl ow controller for maintaining the nozzle exit velocity at 4.9 m/s (ReD= 10,000). A circular aluminum rib of radius r or a square aluminum rib of height e is set on the target surface as the turbulence promoter. Thermocouples were installed for measuring the temperature of the naphthalene surface, which signifi cantly infl uences the extent of naphthalene sublimation. The 400 × 400 × 10 mm target plate is made of acrylic. Molded naphthalene having

Figure 3: Schematic layout of experimental apparatus for circular impinging jet nozzle.



dimensions of 210 × 50 × 3 mm is set in a hollow on the acrylic target plate, as shown in Fig. 3.

2.3 Naphthalene sublimation method

To ensure that the surface of the solidifi ed naphthalene is fl at and smooth, the following steps were executed. First, reagent grade (98% pure) naphthalene crys-tals were heated on a pan using an induction heater until they melted and boiled vigorously. Secondly, after the molten naphthalene attained a temperature of about 380K, it was poured into a mold preheated to 330K. Thirdly, after the mold was cooled to room temperature and the naphthalene solidifi ed, the mold cover plate was removed by striking it on the side with a hammer.

The molded naphthalene surface profi le before and after experiments was scanned at an interval of 0.2–0.9 mm using a two-axis auto-traverse equipment with a resolution of 1 μm and a laser displacement sensor, which has a measure-ment depth of ±1 mm with a resolution of 0.1 μm and a linearity error of 0.3%. The local mass transfer coeffi cient was calculated using the following relationship:

(1)

where R denotes the gas constant, Tw denotes the naphthalene surface temperature, pw denotes the saturated vapor pressure of naphthalene in air, rs denotes the den-sity of solid naphthalene, d denotes the depth of naphthalene sublimation, and te denotes the fl ow exposure time.

In this experiment, the exposure time was set to 60 min. The sublimation depth was 50–200 μm. The thermo-physical properties of naphthalene were obtained from Goldstein and Cho [15]. The local mass transfer coeffi cient can be converted to the local heat transfer coeffi cient using the following analogy between heat and mass transfer:

(2)

where r denotes air density, Cp denotes specifi c heat under constant pressure, Sc denotes the Schmidt number, and Pr denotes the Prandtl number. An index n gives the empirical constant for the naphthalene sublimation method. The value n is set to be 0.4, which is the typical value for turbulent fl ow, following guidelines from the JSME Heat Transfer Handbook (1993).

Nusselt number is defi ned as follows:

(3)

where k denotes the thermal conductivity of air and Dh denotes the hydraulic diameter.

Using the partial derivative method described by Moffat [16], uncertainty analysis was performed on the measured values of local heat transfer coeffi cient, h, based on uncertainties associated with the measured depth of naphthalene sublimation, naphthalene temperatures, fl ow rate, and operation time. The preci-sion uncertainties of the naphthalene sublimation depth measured by the laser



displacement sensing system, temperature measured by K-type thermocouples, fl ow rate measured by a mass fl ow controller, and total operation time were ±0.3%, ±0.1°C, ±0.8%, and ±5 s, respectively. Combining these uncertainties, the total uncertainty of the local heat transfer coeffi cient, dh, was found to be 5.5%–8.3% over a ReD range of 10,000–70,000.

2.4 Results and discussion

2.4.1 Two-dimensional impinging jet nozzle2.4.1.1 Heat transfer of continuous rib on target plate Figure 4 shows a com-parison of the local Nusselt number distributions for the cases with and without a continuous rib under Lr/Dh = 2.5 and Re = 10,000. As shown in this fi gure, the local Nusselt number behind the rib is enhanced owing to the fl ow separation and reattachment induced by the rib. As Gau and Lee [6] reported, a low-pressure area exists behind the rib owing to rib protrusion, and this region sucks the separated fl ow and causes the shear layer to reattach to the wall. In the separated shear layer, turbulent transport of momentum and heat (mass) are known to be enhanced, and thus, the turbulent shear layer has large turbulence kinetic energy. This results in heat transfer enhancement behind the rib owing to impingement of the turbulent-free shear layer onto the reattachment point and redevelopment of the boundary layer in the wall jet region. Consequently, it is clear that installing a continuous rib in the wall jet region is effective for interrupting the rapid decay of convective heat transfer in the wall jet region and for enhancing the total heat transfer rate from the target wall. The effect of rib height on the local Nusselt number distributions for e = 0.5–2.0 mm is shown in the same fi gure. This fi gure indicates the follow-ing. First, as the rib height increases, the reattachment length increases and the enhanced heat transfer region behind the rib, where Nusselt number is increased, becomes larger. This is because the low-pressure area behind the rib becomes

Figure 4: Effect of continuous rib height on local Nusselt number distribution.



larger and the force sucking the separation fl ow toward the wall weakens as the rib height increases. In addition, the physical distance between the wall and the separation point at the upper corner of the rib increases as the rib height increases. Secondly, the secondary peak of the local Nusselt number, which exists around the reattachment point, shows the maximum value for e = 0.65 mm, and decreases as the rib height increases. This is mainly because the decay of turbulence in the turbulent shear layer, which impinges onto the wall, proceeds as the traveling dis-tance of the free shear layer increases with the reattachment length. Preceding results and discussions indicate that installing a rib in the wall jet region of a 2D impinging jet is effective for enhancing the total convective heat transfer rate on the target surface. In addition, there seems to exist an optimal rib height that yields the maximum increase in the total heat transfer from the wall, that is, the maxi-mum average Nusselt number on the target surface. Seeking the optimal rib height is particularly important when designing a cooling structure for gas turbine vanes. Figure 5 shows the average Nusselt number for e = 0.5–2.0 mm. The streamwise-averaged Nusselt number was obtained through numerical integration of the local Nusselt number for 2 ≤ x/Dh ≤ 5.5, where the installed rib infl uences local heat transfer. Although the local heat transfer at x/Dh > 5.5 is infl uenced by the installed rib for e = 1.5 and 2.0 mm, the area for averaging is limited by the available traversal distance range. However, the present averaging area range seems to be adequate for determining the optimal rib height in this experiment. It was found that the most effective rib height is e = 0.65 mm from among the tested ribs and that the averaged Nusselt number decreases as the rib height increases beyond 0.65 mm. The boundary layer thickness at the rib-location of x = Lr = 20 mm was about 0.5 mm, as measured using a hot wire anemometer, for the same jet impinging onto a fl at surface with no rib, as shown in Fig. 6. As Oda et al. [17] suggested, it seems that the Nusselt number augmentation mechanism can be closely related to the time-averaged velocity profi les before the rib location.

Figure 5: Effect of continuous rib height on averaged Nusselt number.



2.4.1.2 Heat transfer of broken rib on target plate Figures 7–9 show contour drawings of the local Nusselt number distributions and detailed distributions of the local Nusselt number in the stream-wise direction on the target plate surface on which a broken rib of e = 0.5–2.0 mm was installed at Lr/Dh= 2.5 for Re = 10,000. These fi gures show the same tendency as a continuous rib. As the rib height increases, the enhanced Nusselt number region behind the rib becomes larger. For ribs taller than 0.65 mm, the Nusselt number of the enhanced region decreases as the rib height increases. These results, which are similar to the continuous rib case, indicate that three-dimensional fl ows induced by the broken ribs do not affect the entire region downstream of the ribs and sustain the basic fl ow and heat trans-fer characteristics of a statistically 2D turbulent fl ow in the continuous rib cases. However, the effect of three-dimensional fl ows induced by the edges of the broken ribs, i.e. secondary fl ows such as a longitudinal vortex, on the wall heat transfer becomes signifi cant as the rib height increases. This is confi rmed by the enhanced heat transfer region behind the rib, which loses its two-dimensionality near the downstream region of the rib edge at y/Dh = 0 as the rib height increases. In par-ticular, for e = 2.0 mm, the enhanced heat transfer region clearly exists around the rib edge, and its area extends continuously toward the downstream generation of a longitudinal vortex motion at the rib edge, which interrupts the development of a boundary layer in the wall jet and introduces fresh air near the region of the edge until it merges with the reattachment region. This indicates the wall due to the vortex’s sweeping motion. The curved area toward the rib center indicates that the low-pressure region downstream the rib attracts a secondary fl ow toward the region downstream of the rib center.

Figure 9b shows the local Nusselt number distributions for the broken rib hav-ing e = 2.0 mm. The distributions are greatly different from those for the continu-ous rib having e = 2.0 mm. For y/Dh ≤ 0, the secondary Nusselt number peak at each span-wise location approaches the rib as y/Dh increases. This is because the

Figure 6: Velocity distribution of wall jet at x = 20 mm.



rib-edge-induced vortex is drawn into the low-pressure recirculating fl ow region. Thus, these secondary peaks are ascribed not to fl ow separation and reattachment but to the rib-edge-induced vortex motion. Additionally, this vortex has the effect of enhancing wall heat transfer in the upstream region, 3 < x/Dh <4, of the second-ary peak compared with the continuous rib. Figure 9c shows that the enhanced heat transfer region exists even outside the edge of the broken rib at y/Dh = 0.125 and 0.25. This is because the vortex generated from the broken rib edge having e = 2.0 mm has a larger scale than that of the broken rib edge having e = 0.65 mm and it spreads widely in the span-wise direction. As shown in Fig. 9d, the broken rib does not enhance heat transfer in the area corresponding to y/Dh ≥ 0.375. In the case of the broken rib having e = 2.0 mm, it is considered that the vortex generated by the edge of broken rib is dominant over fl ow separation and reattachment in enhancing heat transfer in the wall jet region.

Figure 10 shows the average Nusselt number for e = 0.5–2.0 mm. The area-averaged Nusselt number was obtained by numerical integration in the area

Figure 7: Nusselt number distribution with installed broken rib having e = 0.5 mm.



corresponding to 2 ≤ x/Dh ≤ 5.5 and –0.625 ≤ y/Dh ≤ 0.625. For rib heights <0.65 mm, the area-averaged Nusselt number increases as the broken rib height increases. This tendency is similar to that for a continuous rib. However, interestingly, for rib heights >1.5 mm, the area-averaged Nusselt number increases as the height of the broken rib increases. This tendency is opposite to the continuous rib cases. It seems that the vortex generated from the broken rib edge has a stronger infl uence on enhancing the total heat transfer from the target surface than do fl ow separation and reattachment, which seem to dominate wall heat transfer for e = 0.5 and 0.65 mm. In addition, it is considered that a larger scale vortex is generated as the height of the broken rib increases, and thus, the vortex leads to an increase in the local Nusselt number over a wider area for e = 2.0 mm.

These two representative cases, i.e. e = 0.65 and 2.0 mm, indicate the following. When a short broken rib is installed, the peak value of the local Nusselt number has a high value, whereas the enhanced heat transfer region is limited to a small area. In contrast, when a tall broken rib is installed, the increase in the peak Nus-selt number is less than that with a short rib, whereas the enhanced heat transfer

Figure 8: Nusselt number distribution with installed broken rib having e = 0.65 mm.



region becomes large. As a result, the most effective rib height for increasing the average Nusselt number is e = 2.0 mm for the broken rib case in this experiment.

2.4.2 Circular impingement jet nozzleFigure 11a shows the effect of rib height on the local Nusselt number distribution for e/d = 0, 0.58, 0.98, and 1.42 with circular ribs at rrib/D = 3.5 and Re = 10,000. Note that d is the boundary layer thickness of the wall jet, which is known to be

Figure 9: Nusselt number distribution installed broken rib with e = 2.0 mm.

Figure 10: Effect of broken rib height on averaged Nusselt number.



proportional to the distance from the virtual origin of the wall jet. In this study, d was estimated to be 0.02r based on literature [18]. As is clear from this fi gure, the same mechanism as that for the continuous rib on the wall jet region of a 2D impinging jet, as mentioned in Section 2.4.1.1 occurred for the case of circular ribs on the wall jet region of a circular nozzle impinging jet.

Figure 11b shows the average Nusselt number on the target surface with a cir-cular rib normalized to that of e/d = 0.0, 0.58, 0.98, and 1.42; Nu0 is the average Nusselt number on the target surface without a circular rib. The averaged Nusselt number was obtained through numerical integration of the local Nusselt number over 2.0 ≤ r/D ≤ 5.6. The averaging region was determined based on a common defi nition of the wall jet region (r/D ≥ 2.0). In addition, because Fig. 11a indicates that the major effect of rib installation is limited to the area corresponding to 2.0 ≤ r/D ≤ 5.6, we can evaluate rib performance by comparing the Nu averaged over this area. It is clear that the most effective rib height is e/d = 0.98 and that the

Figure 11: Effect of rib height on local and averaged Nusselt number distribution with a circular jet nozzle.



average Nusselt number ratio decreases at e/d = 1.42. In short, for the rib height equal to the corresponding boundary layer thickness d of the no rib case at the rib position, the average Nusselt number showed the highest improvement.

Figure 12a shows the effect of rib location on the local Nusselt number distribu-tion for rrib/D = 1.6–4.5. In this case, the ratio of rib height to boundary layer thick-ness, e/d, is fi xed at 1. Thus, rib height is changed depending on the rib location to maintain e/d = 1. As the distance between the rib location and the stagnation point decreases, the peak of the local Nusselt number becomes higher. This is because turbulent energy is higher at locations closer to the stagnation point. In addition, because the radial velocity of the wall jet decreases rapidly downstream for the round impinging jet case, a higher approach velocity to the rib is expected when the rib is closer to the stagnation point. As in the case of rib height shown in Fig. 6, there seems to be an optimal rib location at which the average Nusselt number is at its maximum value on the target plate. Figure 12b shows the average Nusselt number

Figure 12: Effect of rib location on increase in local Nusselt number with a cir-cular jet nozzle.



on the target surface with a circular rib normalized against that without a rib for 2.0 ≤ r/D ≤ 5.6 under rrib/D = 1.6–4.5. It is clear that the most effective rib location is rrib/D = 2.2 and that the averaged Nusselt number decreases as the rib is located beyond rrib/D = 2.2. However, the average Nusselt number improves for rrib/D = 4.5. This is because the ratio of the enhanced heat transfer area due to the rib to the total area increases when the rib location is shifted downstream. Nevertheless, a circular rib installed at rrib/D = 2.2 yields the best enhancement of the heat transfer rate in the wall jet region. Regarding the effect of the rib location, the best enhancement in the heat transfer rate was obtained when the rib was installed at a location closest to the boundary between the stagnation region and the wall jet region.

3 Numerical Study

In this section, numerical studies corresponding to a series of mass transfer experi-ments described in the previous section are shown. A 2D impinging slot jet and a three-dimensional round jet are discussed in Sections 3.1 and 3.2, respectively. First, in each section, our numerical methods for RANS simulation and LES are described with their computational domains and boundary conditions. Secondly, the prediction capabilities of the RANS and LES methods as well as the heat trans-fer augmentation mechanism are discussed in comparison with the corresponding experimental data obtained using the naphthalene sublimation method.

3.1 Rib-enhanced two-dimensional jet impingement heat transfer

3.1.1 Numerical method for RANSRANS simulations were conducted using FLUENT 6.2 to compare the pre-dicted results with the data obtained using the naphthalene sublimation tech-nique. Figure 13 shows a computational domain corresponding to the experiment described in Section 2.1. For simple and stable computation, only the right side of the test section was considered assuming symmetry at x = 0. In addition, the outer walls of the 2D nozzle were regarded as being straight, and the upper boundaries of the entire domain were treated as impermeable walls. Furthermore, fl ow inside the nozzle was not solved. Physical quantities such as u, n, k, and e at the nozzle

Figure 13: Computational domains for comparison with experimental results; domain on left is only for obtaining nozzle exit profi le.



exit were calculated in advance using the left domain of Fig. 13. For this prelimi-nary computation, a uniform air velocity of 2 m/s and turbulence intensity of 0.5% based on measurements using a hotwire anemometer were input as the nozzle inlet conditions for obtaining a nozzle-exit fl ow with an average velocity of 20 m/s and a reasonable turbulent intensity. The obtained physical quantities were used as boundary conditions for computations using the right domain of Fig. 13.

The multi-block method was employed for minimizing the grid size and for maintaining an adequate spatial resolution where necessary. As shown in Fig. 13, the entire domain was divided into three blocks (A), (B), and (C) of grid sizes 360 × 200, 100 × 50, and 100 × 80, respectively. The total number of grid points was 72,000. The minimum grid spacing in the x and y directions was e/50, which satisfi es y+ < 1 at grid points adjacent to the walls.

Three different RANS models built in FLUENT 6.2 were employed, that is, the low-Re k–e model (AKN model) by Abe et al. [19], k–w model by Wilcox [20], and v2-f model by Durbin [21]. In each model, the default model constants were employed, e.g. Cm = 0.09, Cε1 = 1.44, Cε2 = 1.92, sk = 1.0, and se = 1.3 for the AKN model, given that this conventional set of turbulence model constants has been widely tested and validated in the turbulent core region. For the k–w model, a transitional fl ows option, which enables a low-Re number correction to turbulent viscosity, was employed. For predicting turbulent heat fl uxes, a constant turbulent Prandtl number, Prt = 0.85, was used assuming direct analogy between the turbu-lent heat transport and momentum transport.

The QUICK scheme and the second-order upwind differential scheme were employed for discretizing the convection terms of the momentum and energy equations, respectively. The fi rst-order upwind differential scheme was used for the convection terms of the k and e equations.

For boundary conditions, symmetry and pressure-outlet conditions were employed at x = 0 and 17.5H, respectively. Non-slip conditions were employed at all wall boundaries. Temperatures at the nozzle exit and the target surface, except rib surfaces, were assumed to be uniform at 300K and 350K, respectively. Considering the experimental conditions, we applied adiabatic conditions to the rib surfaces on which no sublimation occurs. The geometric conditions of rib shape and rib location were the same as those in the corresponding experiments.

3.1.2 Numerical method for LESLES using our in-house multi-block CFD code was performed for simulating 2D jet impingement fl ows and heat transfer with a square rib on the wall jet region of the target plate. Figure 14 shows the computational domain for LES corresponding to the mass transfer experiment. The shape of the nozzle outer wall was slightly modifi ed from that in the RANS simulations for adapting it to the body-fi tted structured grid system in our CFD code. In addition, a contraction area was added to the outfl ow region of the domain for stabilizing the computation. To reduce computational cost, we considered only the right side of the test section assuming symmetry at x = 0. The width of the domain in the span-wise direction was set to 10 mm considering the maximum rib height of 0.5 mm in the LES. The outer walls



of the 2D nozzle were regarded as being straight, and the upper boundaries of the entire domain were treated as impermeable walls. Flow inside the nozzle was also solved considering a uniform air velocity of 2.0 m/s with no fl uctuations for obtaining a nozzle-exit fl ow with an average velocity of 20 m/s. In the numerical procedure, the following fi ltered conservation equations of mass, momentum, and energy were solved in the general coordinate system.

(4)

(5)

(6)

Sub-grid scale (SGS) stress was based on the eddy viscosity concept, and the SGS eddy viscosity ne was determined using the following mixed-time-scale (MTS) model proposed by Inagaki et al. [22]:

(7)

(8)

(9)

Figure 14: Computational domain of large eddy simulations for the comparison with mass transfer experiments in Section 2.1.



Model parameters CMTS and CT were set to 0.05 and 10, respectively. The nota-tion (ˆ) denotes the fi ltering operator, for which the Simpson rule was adopted. D denotes grid fi lter width. For temperature fi elds, the SGS heat fl ux was modeled using a constant SGS Prandtl number value of 0.5. Note that the kinematic pres-sure P in eqn (5) is defi ned as P/r + tii/3, including the diagonal components of residual stress.

The governing equations were solved with a fi nite difference method on a col-located grid system in each of the multi-block structured grids. The spatial deriva-tives were approximated using a conservative skew-symmetric form of second-order central differences, with the exception of the convective terms in eqn (6), to which Roe’s superbee fl ux limiter [23] was applied. For time integration, a fractional step method coupled with a fully implicit scheme for the molecular diffusive terms was used, and the second-order Adams–Bashforth method was used for the remaining terms.

To reduce the computational cost of LES, in this study, the fl ow and thermal fi elds were solved over the entire domain only for the case of a fl at target wall without a rib. For the cases with a rib on the target surface, the fl ow and thermal fi elds were solved only in the regions of interest, where the installed rib affects fl ow and heat transfer. The dimensions of the rib-affected regions were determined to be 10 < x < 50, 0 < y < 5, and 0 < z < 5 mm based on our experimental observa-tions [17]. An orthogonal structured grid was employed in the region of interest, and there were 330 × 80 (50 on the rib) × 50 grid points in the x, y and z directions, respectively. The time step was set to Dt = 1.25 × 10–7 s. For ensuring fl uctuating velocities and temperature at the infl ow plane of the domain, a basic (or back-ground) fl ow and temperature fi elds with no rib installed were solved simultane-ously over the entire domain shown in Fig. 14. At the infl ow plane (x = 10 mm) in the region of interest around the rib, tri-linear interpolation was used for calculat-ing velocities and temperature from the background fl ows.

For other boundaries, a periodic condition was employed in the span-wise direc-tion. The no-slip condition was applied to the wall at y = 0 along with the Neumann condition for pressure. The symmetry condition was applied at y = 5. On the out-fl ow plane at x = 50, the convective outfl ow condition was applied to all variables including P

(10)

Temperatures at the nozzle exit and target surface, with the exception of rib surfaces, were assumed to be uniform at 300 K and 330 K, respectively. Consider-ing the experimental conditions, we applied adiabatic conditions to the rib surfaces on which no sublimation occurs. In the LES, the geometric conditions of the rib shape were identical to those in the corresponding experiments.

3.1.3 Results and discussion3.1.3.1 Effect of rib installation Figure 15 shows the time-mean local Nusselt number distribution measured using the naphthalene sublimation technique for a no-rib case; additionally, the numerical results obtained using the RANS model [17]



and LES [24] are shown for comparison. It can be confi rmed that the numerical prediction by both the RANS (AKN model) and LES (MTS model) agree well with the experimental data; however, both RANS and LES overestimate the Nusselt number around the jet impingement region. For LES, this overestimation seems to stem from the assumption of fl ow symmetry at the x = 0 plane, which forces zero velocity in the x-direction even for instantaneous velocity fi elds. However, in the wall jet region, there is good agreement between experimental and numerical results; however, the current LES slightly underestimates the Nusselt number than the AKN model in the downstream region. Thus, it can be said that the current numerical simulation enables us to examine the effect of rib installation on heat transfer augmentation in the wall jet region of 2D impingement-jet heat transfer.

Figure 16 shows a representative result of LES at L = 20 mm and e = 0.5 mm; additionally, the numerical results [17] of three RANS models, i.e. AKN [19], k–w [20], and v2-f [21], are shown with the current LES result. As shown in the fi gure, heat transfer behind the rib is enhanced because the rib induces fl ow separation and reattachment, which interrupt boundary layer development in the wall jet region. The reattachment point and the relatively low heat/mass transfer region right behind the rib, generated because of the recirculation fl ow, can be identifi ed clearly given the high resolution of the naphthalene sublimation technique. Comparing the results predicted using LES with those predicted using the three RANS models, we found that LES and the AKN model can more accurately predict the location of the maximum heat transfer coeffi cient, which implies the fl ow reattachment point, than the other two models. However, all numerical prediction methods underesti-mate the peak Nusselt number in the fl ow reattachment region behind the rib. Although the v2-f model can accurately predict stagnation heat transfer at x = 0, it overestimates the reattachment length and underestimates heat transfer in the wall jet region before the rib. In addition, the AKN model overestimates the heat transfer coeffi cient at the stagnation point (x = 0) owing to the stagnation point anomaly,

Figure 15: Nusselt number distribution in no-rib case.



which is known to be an intrinsic problem for k–e models. Comparing the results obtained using LES and the AKN model, we found that LES can predict Nusselt number decay downstream of the fl ow reattachment point better than the AKN model considering the overall underestimation behind the rib location.

3.1.3.2 Effect of rib height Figure 17 shows the effect of rib height on heat transfer at e = 0.2 and 0.5 mm, respectively, as predicted by the AKN model and LES. As the rib height increases, the reattachment length increases, and the enhanced heat transfer region behind the rib becomes larger. In addition, it is con-fi rmed that the current LES can reasonably predict the reattachment point even when the rib height is changed; however, the local Nusselt number at the reat-tachment points continues to be underestimated. Although similar results were obtained using the AKN model, the reattachment length for e = 0.2 mm predicted by the AKN model is shorter. If the mechanism of heat transfer enhancement at the reattachment point can be considered as a type of impingement heat transfer, underestimation around the reattachment points has an opposite tendency to our expectation based on the above-mentioned stagnation anomaly of k–e models. One possible explanation of this problem is as follows. The empirical constant in eqn (2), which is used for converting mass transfer coeffi cients to heat transfer coeffi -cients, should be changed locally depending on the fl ow confi guration. Therefore, a uniform value of n = 0.4 may be inadequate in the present fl ow confi guration, where impinging jet fl ow and separation, and reattachment fl ow coexist. However, because a clear explanation of this problem cannot be given here, the problem would be addressed in future studies.

Figure 18 shows the Nu distributions for e = 0.2–0.5 mm obtained from LES. It is clear that the enhanced heat transfer regions become large as the rib height increases. However, the maximum heat transfer coeffi cients do not increase con-siderably between e = 0.4 and 0.5 mm. Figure 19 shows the experimental results

Figure 16: Comparison between LES and three RANS models.



related to the rate of increase of Nu from the value for the no-rib case at the reat-tachment point, that is, Nurib/Nuno-rib at the reattachment point. Additionally, the numerical results obtained using the AKN model and LES are shown for compari-son. For rib heights <0.5 mm, Nurib/Nuno-rib obtained using experiments and LES shows the same tendency of increasing as the rib height increases. In contrast, the AKN model failed to predict the increasing tendency observed in the experiments and LES. However, both the AKN model and LES underestimate Nurib/Nuno-rib for the reason suggested in the previous paragraph. Because the boundary layer thick-ness at the rib location of x = L is estimated to be 0.55 mm in the simulation for the no-rib case and that this value is comparable to the rib height, the mechanism of heat transfer augmentation can be closely related to the profi les of time-averaged velocity u and turbulence kinetic energy k before the rib location.

Figure 17: Effect of rib height on Nusselt number.



Figure 20 shows the effect of rib height on (a) mean stream-wise velocity, (b) turbulence kinetic energy, and (c) Reynolds shear stress at e = 0.2 and 0.5 mm, and L = 20 mm, obtained using LES. Additionally, the fi gure shows the velocity vector at x/e from −5 to 12. As shown in Fig. 20a, the u profi le approaching the top-left edge of rib has a smaller ∂u/∂y at e = 0.5 mm than that at e = 0.2 mm. This smaller ∂u/∂y affects a drastic change in ∂u/∂y at the top-left edges because u abruptly decreases to zero on the top surface of the rib. This leads to the generation of strong Reynolds shear stress and turbulent kinetic energy in the free-shear-layer separating from the rib, as shown in Fig. 20b and c. Because the stronger free-shear-layer eddies impinging on the wall lead to a larger Nu at the fl ow reattach-ment point as suggested by Vogel and Eaton [25] for back-ward facing step fl ow, Nurib/Nuno-rib increases slightly as the rib height increases.

Figure 18: Effect of rib height on Nu distribution.

Figure 19: Effect of rib-height on Nurib/Nuno-rib.



Figure 20: Effect of rib height on (a) mean stream-wise velocity, (b) turbulence kinetic energy, and (c) Reynolds shear stress.



3.2 Round jet impingement heat transfer enhanced by circular rib

3.2.1 Numerical setupFor round jet impingement heat transfer, only LES was conducted with the same in-house CFD code and SGS model used for the 2D jet.

Figure 21 shows a computational domain consisting of the impinging jet section with a circular rib on the target plate and an air chamber with a jet nozzle. The jet nozzle is orifi ce-shaped for satisfying the above-mentioned experimental condi-tion. To reduce the computational cost with a suffi cient mesh resolution, we con-ducted LES over a quarter of the entire three-dimensional domain. The radius of the domain in the impinging jet section was limited to 12.5D. This is adequate because the downstream edge of the domain is far from the fl ow reattachment point behind the rib, which is typically in the 2–5D range. Figure 22 denotes a computational mesh of the impinging jet surface. Around the r/D < 0.56 region of the impinging jet section, the computational domains are composed of a square structured grid. In contrast, the computational grids are divided into sub-blocks of structured grids in the r/D > 0.56 region. Meshes near the targeted plate and the circular rib are suffi ciently small to restrict the wall unit normal to the surface to less than unity (z+ < 1) for catching turbulent eddies precisely; this infl uences the heat transfer coeffi cient of the targeted plate.

At the top of the air chamber, a uniform velocity was imparted for realizing a Reynolds number of 10,000. At the exit plane of the impinging section, a convec-tive outfl ow condition was applied to all variables including pressure. On the impinged surface, an isothermal condition was applied for simulating the equiva-lent boundary condition on the naphthalene layer in the mass transfer experiments. However, the rib surface was treated as thermally adiabatic because the circular rib was not covered with a naphthalene layer in the experiments. The total number of grid points was 2.42 million. The time step was Δt = 1.0 × 10−6 s. In addition, we applied circumferential periodic conditions at the sides of the computational domain. The case showing the highest Nusselt number in the experiments was calculated as a representative of all experimental conditions. Other major condi-tions are summarized in Table 1.

Figure 21: Numerical domain for round jet.



3.2.2 Results and discussionFigure 23 shows the time-mean Nusselt number on the target plate obtained by averaging instantaneous local Nusselt numbers in LES. The white area in the fi gure denotes the rib, which is a quarter of the circular rib located at rrib/D = 2.2. As observed in the mass transfer experiments, the Nusselt number decreases from any stagnation point toward the rib location, but increases behind the circular rib owing to fl ow separation and reattachment. Figure 24 shows a comparison between a cir-cumferentially averaged time-mean Nusselt number obtained from Fig. 23 and the experimental data. The average Nusselt number predicted with LES is obtained by averaging circumferentially from q = 40° to 50°, where less infl uence of the peri-odic boundary is expected. In comparison with the above experimental result of the corresponding conditions, the Nusselt number distribution has a similar profi le.

Figure 22: Computational mesh: (a) an overview; (b) near stagnation point; and (c) near circular rib.

Table 1: Numerical conditions for LES.

Rib height, e/d 1Rib location, rrib/D 2.2Infl ow velocity (m/s) 0.39Infl ow temperature (K) 300Impinged plate temperature (K) 330



However, the magnitude of the Nusselt number is underestimated slightly down-stream of the rib. This tendency is similar to the case of 2D jet impingement heat transfer. However, in the round jet case, the peak Nusselt number near the fl ow reattachment point agrees well with the experimental data, whereas the predicted reattachment length is shorter. This displacement of the Nusselt number peak for a

Figure 23: Time-mean Nusselt number distribution.

Figure 24: Circumferentially averaged time-mean Nusselt number.



similar confi guration has been reported by Ashforth-Frost and Jambunathan [26], and Lee and Lee [27].

Figure 25 shows snapshots of the instantaneous Nusselt number at two different times. Relatively large-scale spots of locally high Nusselt number regions are observed around the jet impingement region. The structure of the high Nusselt number spots becomes fi ner as the distance from the stagnation point increases. In addition, it is observed that the Nusselt number is recovered in a wide area down-stream of the circular rib owing to the fl ow separation and reattachment. This gener-ates fi ne spots of local high Nusselt number regions downstream of the circular rib.

Figure 25: Two snapshots of instantaneous Nusselt number.



4 Summary

The heat transfer enhancement due to a continuous rib, broken rib, and circular rib mounted in the wall jet region of a 2D impinging jet and a round jet were studied experimentally and numerically. The following conclusions were arrived:

(1) Installing a rib in the wall jet region of an impinging jet is very useful for increasing the averaged heat transfer of a target plate. There is an optimum rib height for attaining the maximum averaged heat transfer, and the aver-aged heat transfer improves the most when the ratio of rib height e and boundary layer thickness d, e/d, at the rib location on the target plate is 1.0 or slightly >1.0.

(2) With respect to the effect of rib location on the target plate, the best enhance-ment in the heat transfer rate is attained when the rib is installed at the position closest to the boundary between the stagnation region and the wall jet region.

(3) Installing a broken rib in the wall jet region induces a vortex from the rib edge. When a broken rib of e/d = 1.0 is installed, the vortex barely enhances wall heat transfer. In contrast, when a broken rib of e/d = 4.0 is installed, the vortex is dominant and increases the heat transfer over the entire target plate.

(4) LES was found to be effective for predicting the fl ow reattachment length and the Nusselt number decay downstream of the reattachment point, and its results were better than those of the three tested RANS models. This resulted in good agreement between the predicted local Nusselt number distributions and the experimentally obtained distributions, except in the stagnation and reattachment regions, where over- and underestimation occur.

References

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