The effect of confinement on the flow and turbulent heat transfer in a mist impinging jet

doi:10.1016/j.ijheatmasstransfer.2011.05.019

International Journal of Heat and Mass Transfer

Volume 54, Issues 19–20, September 2011, Pages 4266-4274

https://doi.org/10.1016/j.ijheatmasstransfer.2011.05.019 Get rights and content

Abstract

Numerical study of the effect of confinement on a flow structure and heat transfer in an impinging mist jets with low mass fraction of droplets (M_L₁ ⩽ 1%) were presented. The turbulent mist jet is issued from a pipe and strikes into the center of the flat heated plate. Mathematical model is based on the steady-state RANS equations for the two-phase flow in Euler/Euler approach. Predictions were performed for the distances between the nozzle and the target plate x/(2R) = 0.5–10 and the initial droplets size (d₁ = 5–100 μm) at the varied Reynolds number based on the nozzle diameter, Re = (1.3–8) × 10⁴. Addition of droplets causes significant increase of heat transfer intensity in the vicinity of the jet stagnation point compared with the one-phase air impinging jet. The presence of the confinement upper surface decreases the wall friction and heat transfer rate, but the change of friction and heat transfer coefficients in the stagnation point is insignificant. The effect of confinement on the heat transfer is observed only in very small nozzle-to-plate distances (H/(2R) < 0.5) both in single-phase and mist impinging jets.

Introduction

Turbulent impinging jet widely used in many industrial engineering and applications (e.g. cooling of electronic devices or gas turbines blades, spray painting, mine ventilation and drying of paper and steel). This has been due to the high heat transfer rate of jet impingement. There are numerous experimental and numerical investigations focused on characteristics of flow and heat transfer produced by unconfined (submerged) impinging jet (see for example a number of reviews [1], [2], [3], [4], [5], [6], [7]). The impinging jet flow exhibits extremely complex flow behavior. In the area of free jet (1) all correlations specific for free jet remain relevant. The flow in stagnation region (2) has a large total strain and substantial curvature along the streamlines. Away from this region, the flow forms wall jet boundary layer (3) along the plate (see Fig. 1a). Impinging jets are of great interest at the validation of turbulence models. Most existing two-equations LEVM were tested for the flows parallel to the walls. Therefore, they can not provide for the acceptable accuracy at modeling of these complex flows, where streamlines are not parallel to the wall surfaces.

Industrial applications, such as electronic cooling and GT blades cooling, often use the jet impingement to be confined by a solid surface at the level of a jet nozzle exit or pipe exit (see Fig. 1b). The flow produced by the confined impinging jet differs drastically from the flow created by unconfined jet. The presence of the upper boundary stopped the air entrainment from quiescent ambient space into the impinging jet region. Several computational papers and measurements have been carried out to study the effect of confinement on the flow, wall friction and heat transfer in round impinging jets [8], [9], [10], [11], [12], [13], [14], [15].

Obot et al. [8] concluded that there was between a 5% and 10% reduction in the heat transfer rate with addition of upper confinement wall for jets with nozzle-to-plate distance H/(2R) = 2–12.

The comparison analysis of the “standard” and five LRN versions of k–ε turbulence models were performed in the paper [9]. They also applied the Yap correction (described in detail by Craft et al. [16]) to improve the prediction of heat transfer of impinging jets. The heat transfer significantly enhanced for smaller nozzle-to-plate spacing and a higher jet Reynolds number. The locations and widths of the spent fluid exit do not influence heat transfer at either the stagnation point or downstream of the second impinging jet at a constant mass flow rate exhausting condition. Spent fluid suction can enhance downstream heat transfer because of the reduction of the upstream cross-flow effect.

In the papers [10], [12], [14] were experimentally examined the effect of the confinement on flow and heat transfer in the liquid jet impingement with H/(2R) = 2–4 and for Re = (0.85–2.3) × 10⁴. The velocity and turbulence measurements were obtained with LDA method. It was observed a appearance of toroidal recirculating flow region that moved toward the jet stagnation point as the nozzle-to-plate distance decreased. The position of the center of the recirculation zone moved to the upper boundary with increase of Reynolds number and with growth in nozzle-to-plate spacing. The location of the center of toroid moved along the impinging plate with increase of Reynolds number.

RANS approach in connection with elliptic relaxation turbulence model (v2f model) has been used by Behnia et al. [13] to predict the flow and heat transfer in circular confined and unconfined impinging jet configurations. The model has been validated against available experimental data sets. Results have been obtained for a range of jet Reynolds numbers and jet-to-target distances. The effect of confinement on the wall friction and local heat transfer behavior has been determined. It has been shown that confinement leads to a decrease in the friction coefficient and average heat transfer rate, but the local stagnation heat transfer coefficient is unchanged. The effect of confinement is only significant in very low nozzle-to-plate distance (H/(2R) < 0.25).

More recently, Gao and Ewing [15] performed experimental study of confined impinging jet exiting a long pipe with Reynolds number Re = (1.7–2.8) × 10⁴. The presence of the upper confinement surface did not have large effect on the heat transfer by H/(2R) > 1. The mean velocity profiles measured at the pipe exit cross-section for the case of free jet were in good agreement with distributions for a fully developed pipe flow. Local temperature distributions of heated impinging surface were obtained with the use of infrared camera. For small nozzle-to-plate distance H/(2R) < 0.5 was observed the reduction of heat transfer rate in the zone r/(2R) > 1.5 by up to 50%. It was correlated with results of [8], [9], [10], [11], [12], [13], [14], [15]. The locus of the heat transfer decrease in the confined impinging jet shifted toward outward as nozzle-to-plate spacing increased. Authors think that it was coupled with the flow reattachment to the upper confined plate.

All the previous papers have been performed for single-phase gas or liquid impinging jets. The using of a gas-droplets mist jet impingement is one of the efficient methods of surface cooling augmentation. An accurate prediction of flow and heat transfer rate in the mist jet impingement poses a significant problem. For the development and optimization of two-phase jet impingement cooling systems, it is essential that the affects of these important parameters are identified and understood. Two-phase mist heat carriers increase heat transfer several times (see, for instance, works [17], [18], [19], [20], [21], [22]. Modeling of heat transfer in the plane confined vapor-droplets impinging jet was performed in the work [17], [19], [21].

Li et al. [17]presented an experimental study for 1.1 bar steam invested with water mist in a confined slot jet. A slot of width B = 7.5 mm located in a flat injection plate. The jet impacted a target wall of length 250 mm spaced H = 22.5 mm from the injection plate (H/B = 3). The droplet velocity and size distribution was obtained by a phase Doppler particle analyzer PDPA. It was obtained up to 200% heat transfer enhancement at the stagnation point was achieved by injecting of water droplets only M_L₁ = 1.5% by mass of mist. Direct observation through the wall showed a dry heated surface in the experiment conditions.

Numerical simulations [18] were provided with the use of CFD code FLUENT. The CFD models used k–ε model [18]. In papers were used the Euler/Lagrange approach for mist jet. Water droplets, less than 15 μm diameter and at concentrations below 10 percent of mass, are considered. The heat transfer is assumed to be the superposition of three components: heat flow to the steam, heat flow to the dispersed mist, and heat flow to the impinging droplets. The latter is modeled as heat flow to a spherical cap for a time dependent on the droplet size, surface tension, impact velocity and surface temperature. The model is used to interpret experimental results for steam invested with water mist in a confined slot jet. The enhancement mechanisms include effects of mixing of mist with the gas phase and effects of evaporation of the droplets.

In the work [20] was carried numerical study of the round unconfined gas-droplets jet impingement out with the use of CFD FLUENT package. It was used the Euler/Lagrange approach for gas-droplets jet. For the description of droplets dynamics Lagrange approach was applied. In the calculations the realizable k– model was used as the one that describes the jet dynamics more accurately. In the work [20] the case of the same temperature of the plate surface and the particles was investigated; and only heat transfer between gas and wall was considered (difference between gas and droplets/wall temperatures equaled 20°). Effect of main thermogasdynamic parameters such as droplets mass fraction, their size, two-phase flow velocities, nozzle diameter and distance from the nozzle to the plate on heat transfer between flat surface and two-phase flow has been investigated. For the case of small concentrations of dispersed phase the results are reasonable only at consideration of heat transfer intensification at droplets evaporation in the gas flow.

A CFD model [21] has been calibrated against the available experimental results of injecting 2 fine-droplet mist into steam impinging jets of a 2D slot jet and 3D three rows of jets. The calibration process reveals that the RSM turbulence model with standard wall function gives better results on this application than well known k– model. The calibrated CFD model can predict the wall temperature of the 2D mist/steam slot impinging jet flow within 5% and the 3D multiple rows of impinging jets within 8%. The prediction of mist/steam cooling at gas turbine operating condition with 1.5% mist showed 20% enhancement. This value was much higher as 80% in the low operating condition. Increasing the mist ratio to 5% at GT operating condition increased the mist enhancement to about 100%.

The work [22] presents the results of numerical investigation of the flow structure and heat transfer of unconfined impinging mist jet with low concentration of droplets (M_L₁ = 1%). Mathematical model is based in the solution to RANS equations for the two-phase flow in Euler/Euler approach. For the prediction of the fluctuation characteristics of the dispersed phase equations of Zaichik model [23] were applied. Predictions were performed for the distances between the nozzle and target plate H/(2R) = 1–10 and the initial droplets size (d₁ = 5–100 μm) at the fixed Reynolds number based on the nozzle diameter, Re = 26600. Addition of droplets causes significant increase of heat transfer intensity in the vicinity of the jet stagnation point compared with the one-phase air impact jet.

From the analysis of the papers [17], [18], [19], [20], [21], [22] note the following. It is shown that in the gas-droplets flow the Nusselt number increases several times compared to the single-phase flow. In the literature there are almost no data on the structure of turbulent gas-droplets confined impinging jets. All abovementioned works were dealt with the unconfined gas-droplets impinging jets. The studies of slot confined impinging jets were carried out for large nozzle-to-plate distance H/(2R) = 3 and for one-component vapor-droplets mist. As it was previously shown in one-phase impinging jets [13], [15], the effect of the upper confined surface on flow patterns and heat transfer is not observed at such a distance. Perhaps, similar effects will be also observed for the two-phase mist jets.

The main aims of this paper were provided numerical study of effect of varying of nozzle-to-plate distance on the flow and heat transfer in the impinging mist jet in cases of unconfined and confined geometry and comparison of obtained results.

Section snippets

Gas phase

The Euler/Euler model developed in [22] is used in this study. For the gas phase we used the set of steady-state, axisymmetric Reynolds averaged Navier–Stokes (RANS) equations for two-phase flow $\begin{matrix} ρ \frac{\partial U_{j}}{\partial x_{j}} = \frac{6 J}{d} Φ \\ ρ \frac{\partial (U_{i} U_{j})}{\partial x_{i}} = - \frac{\partial (P + 2 k / 3)}{\partial x_{i}} + \frac{\partial}{\partial x_{j}} [(μ + μ_{T}) (\frac{\partial U_{i}}{\partial x_{j}} + \frac{\partial U_{j}}{\partial x_{i}})] \\ - (U_{i} - U_{Li}) \frac{Φ}{d} \times [\frac{1}{8} C_{D} ρ | \vec{U} - {\vec{U}}_{L} | + J] + ρ_{L} g_{u} 〈 u_{i} u_{j} 〉 \frac{\partial Φ}{\partial x_{j}} \\ ρ \frac{\partial (U_{i} T)}{\partial x_{i}} = \frac{\partial}{\partial x_{i}} (\frac{μ}{\Pr} + \frac{μ_{T}}{\Pr_{T}}) \frac{\partial T}{\partial x_{i}} - \frac{6 Φ}{C_{P} d} [α (T - T_{L}) + JL] \\ + \frac{ρ D_{T}}{C_{P}} (C_{PV} - C_{PA}) (\frac{\partial K_{V}}{\partial x_{i}} \frac{\partial T}{\partial x_{i}}) + \frac{C_{PL} ρ_{L} τ g_{ut}}{C_{P}} 〈 u_{j} t 〉 \frac{\partial Φ}{\partial x_{j}} \\ ρ \frac{\partial (U_{i} K_{V})}{\partial x_{i}} = \frac{\partial}{\partial x_{i}} (\frac{μ}{Sc} + \frac{μ_{T}}{{Sc}_{T}}) \frac{\partial K_{V}}{\partial x_{i}} + \frac{6 J Φ}{d} \\ ρ = P / (\bar{R} T) \end{matrix}$ Value of turbulent Prandtl and Schmidt numbers were equal to

Boundary conditions

All boundary conditions correspond to those in [22]. The main difference is the presence of upper confined adiabatic plate $(\partial T / \partial x)_{UW} = 0$ at the tube exiting cross-section. The inlet profile corresponding to fully developed pipe flow is generated with separate RANS simulations of the one-phase air flow using the LRN turbulence model [24]. On the jet axis conditions of symmetry for the gas and dispersed phases were set. On the wall the condition of impermeability was set for the gas phase and wall

Validation of the model for the single-phase impinging confined jet

The detailed testing of numerical model for the case of unconfined impinging jets was carried out in [22]. In the paper [22] are shown possibilities and limitations of turbulence LEVM of [24] with Durbin’s corrections [29] used by the authors. It was demonstrated that despite the well-known problems by use of isotropic models of turbulence, model [24] with corrections [28] gives satisfactory accuracy for predictions of one-phase and gas-droplet impinging jets with evaporating droplets at

Computational results and discussions

Computations were executed for the monodisperse mixture of air and water droplets under the atmospheric pressure. The nozzle diameter is 2R = 20 mm. The profiles of gas phase parameters were set in the inlet cross-section (nozzle edge) on the basis of preliminary simulations of single-phase air flow in a round tube with length 150R. The mean velocity of gas at the nozzle edge was U_m₁ = 10–60 m/s, Reynolds number for the gas phase was Re = 2RU_m₁/ = (1.3–8) × 10⁴. The disperse phase was set as uniform

Comparison with experimental results

The Fig. 11 gives a comparison between our predictions and data for steam-droplets impinging confined jet of [19]. Here B is the slot (nozzle) width. Predictions have been made at the following conditions: B = 7.5 mm; nozzle-to-plate distance H/B = 3; Reynolds number Re = 22500; heat flux density on the impinging surface q_W = 20.9 kW/m²; mass concentration of water droplets M_L₁ = 0.015; temperature of saturated vapor t_Sat = 105 °C and initial diameter of droplets d₁ = 7 μm.

In the Fig. 11a is shown the

Conclusions

Mathematical model using Euler/Euler approach for both phases was developed for prediction of the flow and heat and mass transfer processes in the impinging two-phase mist jet.

The effect of confinement on the flow and local heat transfer behavior in the mist flow has been studied. The profiles of velocity, mass fraction of droplets and gas temperature in confined and unconfined jets are qualitatively similar. Recirculation zones within small nozzle-to-plate distances are shown for the confined

Acknowledgments

This work was partially supported by the President’s Fund for Young PhD Scientists (Grant MK-504.2010.8) and by the Russian Foundation for Basic Research (Projects No. 09-08-00197).

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The effect of confinement on the flow and turbulent heat transfer in a mist impinging jet

Abstract

Introduction

Section snippets

Gas phase

Boundary conditions

Validation of the model for the single-phase impinging confined jet

Computational results and discussions

Comparison with experimental results

Conclusions

Acknowledgments

Int. J. Heat Fluid Flow

Int. J. Exp. Thermal Fluid Sci.

Adv. Heat Transfer

Int. J. Exp. Thermal Fluid Sci.

Int. J. Heat Mass Transfer

Int. J. Heat Fluid Flow

Int. J. Heat Mass Transfer

Int. J. Heat Fluid Flow

Int. J. Heat Mass Transfer.

Int. J. Heat Mass Transfer

Int. J. Heat Fluid Flow

Int. J. Heat Mass Transfer

Int. J. Heat Fluid Flow

Heat and mass transfer between impinging gas jets and solid surfaces

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