- Email: [email protected]
Impinging Air Jets on Flat Surfaces at Low Reynolds Numbers
Available online at www.sciencedirect.com
ScienceDirect Energy Procedia 112 (2017) 194 – 203
Sustainable Solutions for Energy and Environment, EENVIRO 2016, 26-28 October 2016, Bucharest, Romania
Impinging Air Jets on Flat Surfaces at Low Reynolds Numbers Ştefan-Mugur Simionescua*, Nicoleta-Octavia Tănasea, Diana Broboanăa, Corneliu Bălana a
REOROM Group, Hydraulics Department, University "Politehnica" of Bucharest, 313 Splaiul Independentei sector 6, 060042 Bucharest, Romania
Abstract Many practical applications and developing devices assume impinging jets to be spreading on smooth surfaces or in narrow gaps with controlled wall roughness. This work presents results of an experimental investigation and a CFD numerical modeling regarding the impact of a laminar circular air jet on a wall with smooth surface. First, the tests are directed to the experimental study of a jet impinging on a perpendicular wall, then a CFD study in the same flow conditions is performed. Both cases study the evolution of the flow in the area where the jet is deflected from axial to radial direction. The non-stationary jet dynamics is characterized by small time scales, while in the stagnation region small length scales occur in the same time, so direct visualizations using high speed/resolution camera are performed. Because not all the flow parameters can be inferred from experiments, the visualizations are correlated with corresponding numerical simulations. The present work brings the opportunity for new numerical simulations on jets impinging on walls with more complex geometries, where the right choosing of numerical test cases and parameters is of great importance. © 2017The TheAuthors. Authors.Published Published Elsevier © 2017 by by Elsevier Ltd.Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the organizing committee of the international conference on Sustainable Solutions for Energy Peer-review under responsibility of the organizing committee of the international conference on Sustainable Solutions for Energy Environment 2016. and and Environment 2016 Keywords: Structured surface, impinging jet, circular nozzle, wall shear stress;
*
Corresponding author. Tel.: +4-074.390.5552; Fax: +4-021.318.1015. E-mail address:[email protected]
1876-6102 © 2017 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the organizing committee of the international conference on Sustainable Solutions for Energy and Environment 2016 doi:10.1016/j.egypro.2017.03.1083
Ştefan-Mugur Simionescu et al. / Energy Procedia 112 (2017) 194 – 203
1. Introduction Due to their industrial importance, impinging jet flows have received considerable attention, with particular interest in modifying the heat transfer at the wall. In practical applications, impinging jets are efficient tools in Nomenclature ݀ ݂ ݐ ݖ כݐ ݒ
nozzle diameter ሺ݉ሻ frequency ሺݖܪሻ radius, radial distance ሺ݉ሻ time ሺݏሻ axial distance between nozzle and target wall ሺ݉ሻ characteristic time of flow כ ݐൌ ݀ Τ ݒሺݏሻ mean velocity ሺ݉Τݏሻ
ݔǡ ݕ ܴ݁ ܴ݁ ܵݐ ߩ
Cartesian coordinates Reynolds number, ܴ݁ ൌ ߩ݀ݒȀߟ ሺെሻ critical Reynolds number ሺെሻ Strouhal number, ݂݈ Τ ݒሺെሻ fluid density ሺ Τଷ ሻ
߬௪ ߟ
wall shear stress ሺሻ fluid viscosity ሺሻ
cooling or heating systems through their ability to enhance heat transfer between the fluid and the impinged solid target. The aim of this work is to study the time evolution of an air jet impinging on a smooth solid wall, from both experimental and numerical point of view. The experiments will provide a validation mean for the CFD results, which could thus be extended to other similar cases. The near-wall behavior of impinging jet flows has been extensively investigated experimentally. Some of the first studies are summarized in the review of Gauntner, Livingood & Hrycak [1], focused mainly on basic flow statistics. A comprehensive study was performed by Fitzgerald and Garimella [2] using laser-Doppler velocimetry. A classification of the different parameters that characterize impinging slot jets is provided by Tahsini et al. [3]. The effect of the jet Reynolds number, nozzle to plate distance, jet confinement and turbulent intensity are discussed. Later studies involved the phenomenon of heat transfer from a solid surface in the presence of impinging jets, as the work of Jambunathan et al. [4] on single circular jet impingement. Geers et al. [5] studied turbulent structures and heat transfer from an array of impinging jets. Benmouhoub and Mataoui [6] and Jaramillo [7] show results on turbulent heat transfer from a slot jet. More recently, it has been recognized that impinging jets, despite geometric simplicity, contain interesting physics. This makes them attractive for studying various features of jet dynamics, its interaction with the impinged wall and resulting effects on heat and mass transfer – Hadziabdic and Hanjalic [8]. Despite significant progress in understanding various phenomena in different configurations of impinging jets, many issues remain open because of limitations in the available measuring techniques. CFD numerical simulations (RANS, LES and DNS), with their potential to provide the flow dynamics in both space and time, have thus been considered as a valuable instrument to providing comprehensive information and to complementing the experimental results. 2. Theoretical aspects The flow structure of unconfined impinging jets is commonly divided into three main regions: free jet region, stagnation region and wall jet region. After the air jet exits from the nozzle’s inlet, it is released into the surrounding ambient and the free jet begins to develop by entrainment of surrounding fluid. The second region is the stagnation region, where the jet hits the solid wall and is deflected to radial direction. After impinging, the jet develops as a wall jet over the target
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plate. Theoretical and experimental studies show that no surface effect exists beyond a distance of about two jet diameters from the impinging plate. Consequently, an impinging jet can be considered to behave like a free jet, except in the immediate vicinity of the impingement surface [1]. The physical shape and characteristics of impinging jets is not unique since it depends upon a number of parameters, such as the Reynolds number, nozzle-to-wall distance, surface geometry and roughness, jet configuration and orifice shape and profile. A fundamental importance in the study of impinging jets presents the distinction between laminar and turbulent jets. There are many studies on this subject, but some show different results, so it is not possible to have a general rule about this. A first but not general classification for circular jets, based on a critical Reynolds number ܴ݁ is given by Gardon and Akfirat [9], which distinguishes laminar from turbulent jets at ܴ݁ ؆ ͳͲͲͲ. Four characteristic jet patterns for free jets were reported, namely: x Dissipated laminar jets, ܴ݁ ൏ ͵ͲͲ. The viscous forces are larger compared with the inertial forces. The jet diffuses rapidly in the surrounding fluid; x Fully laminar jets, ͵ͲͲ ൏ ܴ݁ ൏ ͳͲͲͲ. There is no noticeable diffusion of the jet into the surrounding fluid; x Transition or semi-turbulent jets, ͳͲͲͲ ൏ ܴ݁ ൏ ͵ͲͲͲ; x Fully turbulent jets, ܴ݁ ͵ͲͲͲ. 3. Methodology 3.1. Experimental study The experimental facility used to perform the visualizations is presented in Fig. 1a. The impingement plate used for the tests is a ͵݉݉ thick smooth plexiglas plate whose vertical position can be modified to allow the change of the nozzle-to-plate distance. The air jet is formed by the submerged injection of air through a circular nozzle (Fig. 1b). Four jet nozzles with different inner diameters ( ͶǤͺǡ ͳͲǡ ͳʹǤͶǡ ͳͻǤʹ݉݉ ) are used. They are obtained from PLA thermoplastic material, by using a 3D printer. The jet settling chamber has a volume of ͳͲ݀݉ଷ . The air is seeded with particles using a smoke machine Showtec Atmos ͳͲͲͲ and is sent inside the settling chamber and then through the jet nozzle by a fan with adjustable speed. A continuous wave laser with ͷ͵ʹ݊݉ wavelength, equipped with a cylindrical lens to convert the beam in a planar sheet, is then lighting the impinging jet through its axis in order to make it visible. The laser beam is reflected by a mirror to increase the lighting power in the area where the jet hits the wall. The dynamics of the impinging jet is recorded with a Nikon 1 J5 camera at ͶͲͲ݂ ݏand a resolution of ͺͲͲ ൈ ʹͻ pixels. The camera is placed perpendicular to the plane lighted by the laser sheet, so that the focus is made on the zone between the nozzle mouth and the impingement plate. The mean jet velocity was measured as the distance traveled by the fluid in a known time period. The distance between the nozzle mouth and the solid wall is rigorously set and is taken as reference, as for the time, it is inferred from the camera framerate. 3.2. Numerical domain and boundary conditions
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The objective of the CFD study is to provide a closer touch with the numerical approach by analyzing the flow configuration of a laminar flow impinging over a plate, in similar cases to the ones experimentally analyzed. Hence, a comparison with experimental results will be presented. The numerical simulations are carried out by using the commercial software Fluent, developed by ANSYS, in the context of Reynolds-averaged Navier-Stokes (RANS) modeling. The Fluent solver is based on a finite-volume solution of the mean momentum, energy and turbulent a)
Plane laser + electronics
Mirror
b)
݀
Impingement plate Interchangeable ʹͲ݀ jet nozzle
Fan with adjustable speed
Settling chamber Smoke machine
transport equations. The scheme selected to perform all the computations is second order upwind. Fig. 1. Sketch of experimental set-up (a) and sketch of typical jet nozzle used in experiments (b).
ͳʹ݀
a)
b)
Solid wall
ݖ FLUID - AIR
͵݀
ʹͲ݀
Mesh details: 63405 cells 127864 faces 64460 nodes
x Axis Inlet
Outlet
y
݀ Τʹ Fig. 2. Numerical flow domain with boundary conditions (a) and detail of mesh in the impingement zone (b).
This case was modeled using the axis symmetry condition. In Fluent, axis-symmetric indicates that the flow domain is symmetric around the ݔaxis, like described in reference [10]. The domain was built according to this condition. When axis-symmetry condition is enabled, the 2D axis-symmetrical form of the governing equations is solved instead of the 2D cartesian form. The geometrical dimensions of the domain defined for computations are dependent on the nozzle diameter and the nozzle-to-plate distance. The outlet border should be placed at a sufficiently large radial distance, so that error arising from the application of outlet-pressure condition will not significantly affect the region of interest. According to the references [11] and [12], the radial expansion of the flow domain was chosen at 12d.
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In order to achieve a fully developed flow at the nozzle exit, a pipe section with a length of 20d was added to the domain. Another consideration is about the vertical distance from the nozzle mouth to the lower boundary of the domain, as from the latter some flow entrainment can occur. Then, a sufficient large distance between the two is necessary in order to limit boundary influences. A three nozzle diameters distance from the nozzle mouth to the lower boundary was selected. A schematic view of the computational domain characteristics is presented in Fig. 2a. A detail of the mesh used and the mesh characteristics are shown in Fig. 2b. Table 1 shows the test cases that are simulated numerically. The three parameters: jet standoff distance ݖΤ݀ , Reynolds number ܴ݁ and jet diameter ݀ are considered. Table 1. Numerical test matrix for the case in study.
ݖΤ݀ ൌ ͳ
ݖΤ݀ ൌ ʹ
ݖΤ݀ ൌ Ͷ
ݖΤ݀ ൌ
݀ଵ
݀ଵ
െ
െ
݀ଵ
݀ଵ
݀ଵ
݀ଵ
݀ଵ
݀ଵ
െ
െ
െ
െ
ܴ݁ ൌ ͵ͲͲ ܴ݁ ൌ ͶʹͲ ܴ݁ ൌ ͲͲ ܴ݁ ൌ ͳͲͲͲ
݀ଵ
݀ଵ ǡ ݀ଶ ǡ ݀ଷ ǡ ݀
݀ଵ ൌ ͶǤͺ݉݉ ݀ଶ ൌ ͳͲ݉݉ ݀ଷ ൌ ͳʹǤͶ݉݉ ݀ସ ൌ ͳͻǤʹ݉݉
4. Results 4.1. Experimental results
327 220 110
Time from jet emergence ݐሺ݉ݏሻ
The growth of the Kelvin–Helmholtz instabilities in the shear layer leads to the formation of roll-up vortices (Fig. 3a) with a natural frequency characterized by the Strouhal number ܵݐ defined in terms of mean jet velocity ݒand nozzle diameter ݀ . Periodic formation and breakdown of the side vortices lead to pressure pulsation in the jet irrespective of whether it is laminar or partially turbulent. In the jet developing zone, the axial velocity decreases as a result of radial spreading due to a strong shear at the jet boundary and the entrainment of surrounding fluid.
b) a)
4.8
10
19.2
12.4
Nozzle diameter ݀ሺ݉݉ሻ Fig. 3. Side vortices in the free jet region for z/d >> 1 (a); Time evolution of impinging jet for different nozzle diameters, z/d=2. Scale bars represent 10 mm (b).
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As the jet approaches the wall, its presence begins to affect the velocity and stress fields. A stagnation region is formed in the center of the impingement zone. Due to the presence of the solid impermeable wall, the axial velocity diminishes fast, followed by an increase of the static pressure [1]. After hitting the wall, the jet deflects to radial direction and a wall-jet is formed further downstream. Around the jet deflection region, corresponding to the maximum streamline curvature, the accelerating boundary layer becomes thinner – see the streamlines distribution in Fig. 5, in the interval ݎΤ݀ ൌ ͳ ǥ ͵. Eventually, it evolves into a radial wall-jet where the fluid is decelerated because of the radial spreading. The wall-jet is characterized by a strong shear with the turbulence level much higher than in an ordinary boundary layer [8]. After hitting the wall, as the direction of the jet changes to radial, a vortex ring begins to form. The ejected fluid enters the ambient fluid. The vortex core and the detachment point from the wall (Fig. 4a) are qualitatively inferred from the experimental pictures. As the vortex rolls up and develops, the different layers of air with seeding, as well as entrained air without seeding (Fig. 4a), are visible in the plane of the laser light. r/d (-)
10
Stagnation region
Vortex core
6 5
8
Detachment point
8 7
4 6
4
3
8
2 Air with seeding
7
3
4 Air without seeding
1 2
2
6
a) 5
1
b) 0 0
150
300
450
600
t/t* (-)
Fig. 4. Specific points and regions of the vortex ring and typical fluid layers in the vortex (a); Time evolution of vortex radial development for Re=420, d=4.8 mm, z/d=1 (b). r/d (-)
4 u [m/s]
2
0
4 u [m/s]
Re=1000
0
0,1
0,1
0,1
0,1
0,2
0,2
0,2
0,2
0,3
0,3
0,3
0,3
0,4
0,4
0,4
0,4
0,5
0,5
0,5
0,5
z/d [-]
Re=600
4 u [m/s]
0
Re=300 Re=420
2
0
z/d [-]
0 0
z/d [-]
Re=420 Streamlines
2
z/d [-]
0 0
2
4 u [m/s]
750
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Fig. 5. Flow field for ܴ݁ ൌ ͶʹͲ at steady state and radial velocity profiles in the near-wall region for various Reynolds numbers.
The vortex evolution is presented in Fig. 4b. Pictures taken at different time instants can be seen, together with a graph showing the progress in time of the vortex core radial position. The time axis is normalized with כ ݐ, defined as the ratio between the jet diameter ݀ and the mean flow velocity ݒ. This evolution has a quasi-linear trend for ݎΤ݀ ൏ ͺ, then an oscillatory character around the mean value of ݎΤ݀ ؆ ͺǤͷ is observed. As a consequence of the increase in standoff distance ݖΤ݀ , the jet starts to flap and the stagnation point changes in time around the geometrical center. 4.2. Numerical results Fig. 5 illustrates the flow field for ܴ݁ ൌ ͶʹͲ. The insets show the radial velocity distribution at different radial positions (0.5d; 1.5d; 3d; 6d) for the four Reynolds numbers considered. The results show that the peak velocity of the wall jet is located closer to the wall at higher Reynolds numbers. This trend agrees with the DNS numerical results from Rohlfs et al. [12], although different Reynolds numbers (392; 1177; 1804) were examined there. A comparison in terms of wall shear stress and wall static pressure distributions for the four Reynolds numbers tested at ݀ ൌ ͶǤͺ݉݉ and ݖΤ݀ ൌ ͳ is presented in Fig. 6. The shape of the profiles is similar, but the magnitude increases with the Reynolds number. The maximum value of wall shear stress occurs at the radial position of 0.5 diameters. As expected, the wall shear stress in the impact point takes the value of zero, and the pressure distribution reaches its maximum.
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Re=300 Re=420 Re=600 Re=1000
τw (Pa)
1 0,8 0,6 0,4 0,2 0 2
4
6
p (Pa)
0
r/d (-)
8
Re=300 Re=420 Re=600 Re=1000
16 12 8 4 0
0
2
4
6
r/d (-)
8
Fig. 6. Wall shear stress and wall static pressure distributions on impingement plate for different Reynolds numbers, d=4.8 mm, z/d=1. 0,4
τw (Pa)
z/d=1 z/d=2 z/d=4 z/d=6
0,3
0,2
0,1
0 0
2
4
6
4
r/d (-)
8
p (Pa)
z/d=1 z/d=2 z/d=4 z/d=6
3
2
1
0 0
2
4
6
r/d (-)
8
Fig. 7. Wall shear stress and wall static pressure distributions on impingement plate for different z/d distances, d=4.8 mm, Re=420.
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Wall shear stress and wall static pressure distributions are also computed by keeping constant the jet diameter and Reynolds number and modifying the nozzle-to-wall distance ݖΤ݀ (Fig. 7). From this graphs one can deduce that the ݖΤ݀ has a lower influence than the jet Reynolds number on wall shear stress and static pressure at the wall, both in absolute value and relative to a reference amount. 4.3. Comparison and validation of numerical results The direct flow visualizations obtained from experiments are compared with the numerical results in terms of contours of velocity magnitude and velocity pathlines. A good agreement is found towards the radial development of the vortex, axial and radial position of the vortex core. Another parameter considered is the detachment position of the vortex from the wall. Experimentally, it is qualitatively inferred from the visualizations. In the numerical simulations the detachment is identified as the point where the wall shear stress is zero. By analysing the detachment of the vortex from the wall, one can notice its tendency to occur sooner in the numerical case. This issue may be caused by an insufficient mesh size in the numerical domain and can be solved by a further refinement of the mesh close to the wall. The present results show that the procedure applied returns good results. However, while computing the Reynolds number for the experimental case errors can occur, namely from the way the velocity is calculated or from a slight change in air density and viscosity when seeded with particles.
65
135
265
535
1065 Time from jet emergence ݐሺ݉ݏሻ
Fig. 8. Comparison between experimental and numerical results at different time steps for Re=420, d=4.8 mm, z/d=1.
5. Conclusion A set of flow visualizations on the behavior of a laminar air jet impinging on a flat surface was conducted to reveal the non-stationary jet dynamics of the flow. In parallel a CFD study in the same flow conditions was performed in ANSYS Fluent. The evolution of the vortex rings observed in the numerical simulations, emerging after the jet hits the impermeable wall, agrees well with the one found experimentally. The analysis of the three main zones through which the fluid passes (free jet, stagnation region and radial wall jet) show a distinct dynamics with specific features. The dominant event that characterizes the flow in the free jet region at high ݖΤ݀ values are the small roll-up vortices generated by instabilities in the shear layer. The stagnation region is the one with the highest
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gradients for velocity, pressure and shear stress distributions, as the jet is constrained by the wall to take radial direction. The wall shear stress decreases from its maximum to zero in the stagnation point, while the pressure reaches here the maximum value. In the wall jet region a vortex ring begins to develop and evolves as soon as the flow exceeds the stagnation region. As it travels downstream, this vortex ring stretches and finally brakes up into smaller coherent turbulent structures. After performing this work, the opportunity arises for new numerical simulations on the dynamics of jets impinging on walls with more complex geometries, from plates with pillars or grooves to micropatterned surfaces where results from experimental visualizations are more difficult to achieve. Acknowledgements The work has been funded by the Sectorial Operational Programme Human Resources Development 2007-2013 of the Ministry of European Funds through the Financial Agreement POSDRU/159/1.5/S/132395. The authors acknowledge the financial support received from the grant UEFISCDI project PNII-ID-PCE-2012-4-0245/2013 and PN-II-PT-PCCA-2011-3.1-0052. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12]
Gauntner J, Livingood JNB, Hrycak P, N.A.S.A.T.N. D-, J.W. Guzlntner, P. Hrycuk, Survey of literature on flow characteristics of a single turbulent jet impinging on a flat plate, Washington, DC, 1970, 43. Fitzgerald JA, Garimella SV, A study of the flow field of a confined and submerged impinging jet, Int. J. Heat Mass Transf. 41, 1998, 1025–1034. Tahsini AM, Mousavi ST, Parametric Study of Confined Turbulent Impinging Slot Jets upon a Flat Plate, 6, 2012, 1220–1224. Jambunathan K, Lai E, Moss MA, Button BL, A review of heat transfer data for single circular jet impingement, Int. J. Heat Fluid Flow. 13, 1992, 106–115. Geers LFG, Hanjalic K, Tummers MJ, Wall imprint of turbulent structures and heat transfer in multiple impinging jet arrays, J. Fluid Mech. 546, 2006, 255–284. Benmouhoub D, Mataoui A, Turbulent Heat Transfer From a Slot Jet Impinging on a Flat Plate, J. Heat Transfer. 135, 2013, 102201. Jaramillo JE, Trias FX, Gorobets A, Pérez-Segarra CD, Oliva A, DNS and RANS modelling of a turbulent plane impinging jet, Int. J. Heat Mass Transf. 55, 2012, 789–801. Hadžiabdić M, Hanjalić K, Vortical structures and heat transfer in a round impinging jet, J. Fluid Mech. 596, 2008, 221–260. Gardon R, Akfirat JC, The role of turbulence in determining the heat-transfer characteristics of impinging jets, Int. J. Heat Mass Transf. 8, 1965, 1261–1272. ANSYS, ANSYS FLUENT User’s Guide, 15317 (2011) 2498. http://cdlab2.fluid.tuwien.ac.at/LEHRE/TURB/Fluent.Inc/v140/ flu_ug.pdf. Dairay T, Fortuné V, Lamballais E, Brizzi LE, Direct numerical simulation of a turbulent jet impinging on a heated wall, Int. J. Heat Fluid Flow. 764, 2015, 362–394. Rohlfs W, Haustein HD, Garbrecht O, Kneer R, Insights into the local heat transfer of a submerged impinging jet: Influence of local flow acceleration and vortex-wall interaction, Int. J. Heat Mass Transf. 55, 2012, 7728–7736.
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ScienceDirect Energy Procedia 112 (2017) 194 – 203
Sustainable Solutions for Energy and Environment, EENVIRO 2016, 26-28 October 2016, Bucharest, Romania
Impinging Air Jets on Flat Surfaces at Low Reynolds Numbers Ştefan-Mugur Simionescua*, Nicoleta-Octavia Tănasea, Diana Broboanăa, Corneliu Bălana a
REOROM Group, Hydraulics Department, University "Politehnica" of Bucharest, 313 Splaiul Independentei sector 6, 060042 Bucharest, Romania
Abstract Many practical applications and developing devices assume impinging jets to be spreading on smooth surfaces or in narrow gaps with controlled wall roughness. This work presents results of an experimental investigation and a CFD numerical modeling regarding the impact of a laminar circular air jet on a wall with smooth surface. First, the tests are directed to the experimental study of a jet impinging on a perpendicular wall, then a CFD study in the same flow conditions is performed. Both cases study the evolution of the flow in the area where the jet is deflected from axial to radial direction. The non-stationary jet dynamics is characterized by small time scales, while in the stagnation region small length scales occur in the same time, so direct visualizations using high speed/resolution camera are performed. Because not all the flow parameters can be inferred from experiments, the visualizations are correlated with corresponding numerical simulations. The present work brings the opportunity for new numerical simulations on jets impinging on walls with more complex geometries, where the right choosing of numerical test cases and parameters is of great importance. © 2017The TheAuthors. Authors.Published Published Elsevier © 2017 by by Elsevier Ltd.Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the organizing committee of the international conference on Sustainable Solutions for Energy Peer-review under responsibility of the organizing committee of the international conference on Sustainable Solutions for Energy Environment 2016. and and Environment 2016 Keywords: Structured surface, impinging jet, circular nozzle, wall shear stress;
*
Corresponding author. Tel.: +4-074.390.5552; Fax: +4-021.318.1015. E-mail address:[email protected]
1876-6102 © 2017 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the organizing committee of the international conference on Sustainable Solutions for Energy and Environment 2016 doi:10.1016/j.egypro.2017.03.1083
Ştefan-Mugur Simionescu et al. / Energy Procedia 112 (2017) 194 – 203
1. Introduction Due to their industrial importance, impinging jet flows have received considerable attention, with particular interest in modifying the heat transfer at the wall. In practical applications, impinging jets are efficient tools in Nomenclature ݀ ݂ ݐ ݖ כݐ ݒ
nozzle diameter ሺ݉ሻ frequency ሺݖܪሻ radius, radial distance ሺ݉ሻ time ሺݏሻ axial distance between nozzle and target wall ሺ݉ሻ characteristic time of flow כ ݐൌ ݀ Τ ݒሺݏሻ mean velocity ሺ݉Τݏሻ
ݔǡ ݕ ܴ݁ ܴ݁ ܵݐ ߩ
Cartesian coordinates Reynolds number, ܴ݁ ൌ ߩ݀ݒȀߟ ሺെሻ critical Reynolds number ሺെሻ Strouhal number, ݂݈ Τ ݒሺെሻ fluid density ሺ Τଷ ሻ
߬௪ ߟ
wall shear stress ሺሻ fluid viscosity ሺሻ
cooling or heating systems through their ability to enhance heat transfer between the fluid and the impinged solid target. The aim of this work is to study the time evolution of an air jet impinging on a smooth solid wall, from both experimental and numerical point of view. The experiments will provide a validation mean for the CFD results, which could thus be extended to other similar cases. The near-wall behavior of impinging jet flows has been extensively investigated experimentally. Some of the first studies are summarized in the review of Gauntner, Livingood & Hrycak [1], focused mainly on basic flow statistics. A comprehensive study was performed by Fitzgerald and Garimella [2] using laser-Doppler velocimetry. A classification of the different parameters that characterize impinging slot jets is provided by Tahsini et al. [3]. The effect of the jet Reynolds number, nozzle to plate distance, jet confinement and turbulent intensity are discussed. Later studies involved the phenomenon of heat transfer from a solid surface in the presence of impinging jets, as the work of Jambunathan et al. [4] on single circular jet impingement. Geers et al. [5] studied turbulent structures and heat transfer from an array of impinging jets. Benmouhoub and Mataoui [6] and Jaramillo [7] show results on turbulent heat transfer from a slot jet. More recently, it has been recognized that impinging jets, despite geometric simplicity, contain interesting physics. This makes them attractive for studying various features of jet dynamics, its interaction with the impinged wall and resulting effects on heat and mass transfer – Hadziabdic and Hanjalic [8]. Despite significant progress in understanding various phenomena in different configurations of impinging jets, many issues remain open because of limitations in the available measuring techniques. CFD numerical simulations (RANS, LES and DNS), with their potential to provide the flow dynamics in both space and time, have thus been considered as a valuable instrument to providing comprehensive information and to complementing the experimental results. 2. Theoretical aspects The flow structure of unconfined impinging jets is commonly divided into three main regions: free jet region, stagnation region and wall jet region. After the air jet exits from the nozzle’s inlet, it is released into the surrounding ambient and the free jet begins to develop by entrainment of surrounding fluid. The second region is the stagnation region, where the jet hits the solid wall and is deflected to radial direction. After impinging, the jet develops as a wall jet over the target
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plate. Theoretical and experimental studies show that no surface effect exists beyond a distance of about two jet diameters from the impinging plate. Consequently, an impinging jet can be considered to behave like a free jet, except in the immediate vicinity of the impingement surface [1]. The physical shape and characteristics of impinging jets is not unique since it depends upon a number of parameters, such as the Reynolds number, nozzle-to-wall distance, surface geometry and roughness, jet configuration and orifice shape and profile. A fundamental importance in the study of impinging jets presents the distinction between laminar and turbulent jets. There are many studies on this subject, but some show different results, so it is not possible to have a general rule about this. A first but not general classification for circular jets, based on a critical Reynolds number ܴ݁ is given by Gardon and Akfirat [9], which distinguishes laminar from turbulent jets at ܴ݁ ؆ ͳͲͲͲ. Four characteristic jet patterns for free jets were reported, namely: x Dissipated laminar jets, ܴ݁ ൏ ͵ͲͲ. The viscous forces are larger compared with the inertial forces. The jet diffuses rapidly in the surrounding fluid; x Fully laminar jets, ͵ͲͲ ൏ ܴ݁ ൏ ͳͲͲͲ. There is no noticeable diffusion of the jet into the surrounding fluid; x Transition or semi-turbulent jets, ͳͲͲͲ ൏ ܴ݁ ൏ ͵ͲͲͲ; x Fully turbulent jets, ܴ݁ ͵ͲͲͲ. 3. Methodology 3.1. Experimental study The experimental facility used to perform the visualizations is presented in Fig. 1a. The impingement plate used for the tests is a ͵݉݉ thick smooth plexiglas plate whose vertical position can be modified to allow the change of the nozzle-to-plate distance. The air jet is formed by the submerged injection of air through a circular nozzle (Fig. 1b). Four jet nozzles with different inner diameters ( ͶǤͺǡ ͳͲǡ ͳʹǤͶǡ ͳͻǤʹ݉݉ ) are used. They are obtained from PLA thermoplastic material, by using a 3D printer. The jet settling chamber has a volume of ͳͲ݀݉ଷ . The air is seeded with particles using a smoke machine Showtec Atmos ͳͲͲͲ and is sent inside the settling chamber and then through the jet nozzle by a fan with adjustable speed. A continuous wave laser with ͷ͵ʹ݊݉ wavelength, equipped with a cylindrical lens to convert the beam in a planar sheet, is then lighting the impinging jet through its axis in order to make it visible. The laser beam is reflected by a mirror to increase the lighting power in the area where the jet hits the wall. The dynamics of the impinging jet is recorded with a Nikon 1 J5 camera at ͶͲͲ݂ ݏand a resolution of ͺͲͲ ൈ ʹͻ pixels. The camera is placed perpendicular to the plane lighted by the laser sheet, so that the focus is made on the zone between the nozzle mouth and the impingement plate. The mean jet velocity was measured as the distance traveled by the fluid in a known time period. The distance between the nozzle mouth and the solid wall is rigorously set and is taken as reference, as for the time, it is inferred from the camera framerate. 3.2. Numerical domain and boundary conditions
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The objective of the CFD study is to provide a closer touch with the numerical approach by analyzing the flow configuration of a laminar flow impinging over a plate, in similar cases to the ones experimentally analyzed. Hence, a comparison with experimental results will be presented. The numerical simulations are carried out by using the commercial software Fluent, developed by ANSYS, in the context of Reynolds-averaged Navier-Stokes (RANS) modeling. The Fluent solver is based on a finite-volume solution of the mean momentum, energy and turbulent a)
Plane laser + electronics
Mirror
b)
݀
Impingement plate Interchangeable ʹͲ݀ jet nozzle
Fan with adjustable speed
Settling chamber Smoke machine
transport equations. The scheme selected to perform all the computations is second order upwind. Fig. 1. Sketch of experimental set-up (a) and sketch of typical jet nozzle used in experiments (b).
ͳʹ݀
a)
b)
Solid wall
ݖ FLUID - AIR
͵݀
ʹͲ݀
Mesh details: 63405 cells 127864 faces 64460 nodes
x Axis Inlet
Outlet
y
݀ Τʹ Fig. 2. Numerical flow domain with boundary conditions (a) and detail of mesh in the impingement zone (b).
This case was modeled using the axis symmetry condition. In Fluent, axis-symmetric indicates that the flow domain is symmetric around the ݔaxis, like described in reference [10]. The domain was built according to this condition. When axis-symmetry condition is enabled, the 2D axis-symmetrical form of the governing equations is solved instead of the 2D cartesian form. The geometrical dimensions of the domain defined for computations are dependent on the nozzle diameter and the nozzle-to-plate distance. The outlet border should be placed at a sufficiently large radial distance, so that error arising from the application of outlet-pressure condition will not significantly affect the region of interest. According to the references [11] and [12], the radial expansion of the flow domain was chosen at 12d.
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In order to achieve a fully developed flow at the nozzle exit, a pipe section with a length of 20d was added to the domain. Another consideration is about the vertical distance from the nozzle mouth to the lower boundary of the domain, as from the latter some flow entrainment can occur. Then, a sufficient large distance between the two is necessary in order to limit boundary influences. A three nozzle diameters distance from the nozzle mouth to the lower boundary was selected. A schematic view of the computational domain characteristics is presented in Fig. 2a. A detail of the mesh used and the mesh characteristics are shown in Fig. 2b. Table 1 shows the test cases that are simulated numerically. The three parameters: jet standoff distance ݖΤ݀ , Reynolds number ܴ݁ and jet diameter ݀ are considered. Table 1. Numerical test matrix for the case in study.
ݖΤ݀ ൌ ͳ
ݖΤ݀ ൌ ʹ
ݖΤ݀ ൌ Ͷ
ݖΤ݀ ൌ
݀ଵ
݀ଵ
െ
െ
݀ଵ
݀ଵ
݀ଵ
݀ଵ
݀ଵ
݀ଵ
െ
െ
െ
െ
ܴ݁ ൌ ͵ͲͲ ܴ݁ ൌ ͶʹͲ ܴ݁ ൌ ͲͲ ܴ݁ ൌ ͳͲͲͲ
݀ଵ
݀ଵ ǡ ݀ଶ ǡ ݀ଷ ǡ ݀
݀ଵ ൌ ͶǤͺ݉݉ ݀ଶ ൌ ͳͲ݉݉ ݀ଷ ൌ ͳʹǤͶ݉݉ ݀ସ ൌ ͳͻǤʹ݉݉
4. Results 4.1. Experimental results
327 220 110
Time from jet emergence ݐሺ݉ݏሻ
The growth of the Kelvin–Helmholtz instabilities in the shear layer leads to the formation of roll-up vortices (Fig. 3a) with a natural frequency characterized by the Strouhal number ܵݐ defined in terms of mean jet velocity ݒand nozzle diameter ݀ . Periodic formation and breakdown of the side vortices lead to pressure pulsation in the jet irrespective of whether it is laminar or partially turbulent. In the jet developing zone, the axial velocity decreases as a result of radial spreading due to a strong shear at the jet boundary and the entrainment of surrounding fluid.
b) a)
4.8
10
19.2
12.4
Nozzle diameter ݀ሺ݉݉ሻ Fig. 3. Side vortices in the free jet region for z/d >> 1 (a); Time evolution of impinging jet for different nozzle diameters, z/d=2. Scale bars represent 10 mm (b).
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As the jet approaches the wall, its presence begins to affect the velocity and stress fields. A stagnation region is formed in the center of the impingement zone. Due to the presence of the solid impermeable wall, the axial velocity diminishes fast, followed by an increase of the static pressure [1]. After hitting the wall, the jet deflects to radial direction and a wall-jet is formed further downstream. Around the jet deflection region, corresponding to the maximum streamline curvature, the accelerating boundary layer becomes thinner – see the streamlines distribution in Fig. 5, in the interval ݎΤ݀ ൌ ͳ ǥ ͵. Eventually, it evolves into a radial wall-jet where the fluid is decelerated because of the radial spreading. The wall-jet is characterized by a strong shear with the turbulence level much higher than in an ordinary boundary layer [8]. After hitting the wall, as the direction of the jet changes to radial, a vortex ring begins to form. The ejected fluid enters the ambient fluid. The vortex core and the detachment point from the wall (Fig. 4a) are qualitatively inferred from the experimental pictures. As the vortex rolls up and develops, the different layers of air with seeding, as well as entrained air without seeding (Fig. 4a), are visible in the plane of the laser light. r/d (-)
10
Stagnation region
Vortex core
6 5
8
Detachment point
8 7
4 6
4
3
8
2 Air with seeding
7
3
4 Air without seeding
1 2
2
6
a) 5
1
b) 0 0
150
300
450
600
t/t* (-)
Fig. 4. Specific points and regions of the vortex ring and typical fluid layers in the vortex (a); Time evolution of vortex radial development for Re=420, d=4.8 mm, z/d=1 (b). r/d (-)
4 u [m/s]
2
0
4 u [m/s]
Re=1000
0
0,1
0,1
0,1
0,1
0,2
0,2
0,2
0,2
0,3
0,3
0,3
0,3
0,4
0,4
0,4
0,4
0,5
0,5
0,5
0,5
z/d [-]
Re=600
4 u [m/s]
0
Re=300 Re=420
2
0
z/d [-]
0 0
z/d [-]
Re=420 Streamlines
2
z/d [-]
0 0
2
4 u [m/s]
750
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Fig. 5. Flow field for ܴ݁ ൌ ͶʹͲ at steady state and radial velocity profiles in the near-wall region for various Reynolds numbers.
The vortex evolution is presented in Fig. 4b. Pictures taken at different time instants can be seen, together with a graph showing the progress in time of the vortex core radial position. The time axis is normalized with כ ݐ, defined as the ratio between the jet diameter ݀ and the mean flow velocity ݒ. This evolution has a quasi-linear trend for ݎΤ݀ ൏ ͺ, then an oscillatory character around the mean value of ݎΤ݀ ؆ ͺǤͷ is observed. As a consequence of the increase in standoff distance ݖΤ݀ , the jet starts to flap and the stagnation point changes in time around the geometrical center. 4.2. Numerical results Fig. 5 illustrates the flow field for ܴ݁ ൌ ͶʹͲ. The insets show the radial velocity distribution at different radial positions (0.5d; 1.5d; 3d; 6d) for the four Reynolds numbers considered. The results show that the peak velocity of the wall jet is located closer to the wall at higher Reynolds numbers. This trend agrees with the DNS numerical results from Rohlfs et al. [12], although different Reynolds numbers (392; 1177; 1804) were examined there. A comparison in terms of wall shear stress and wall static pressure distributions for the four Reynolds numbers tested at ݀ ൌ ͶǤͺ݉݉ and ݖΤ݀ ൌ ͳ is presented in Fig. 6. The shape of the profiles is similar, but the magnitude increases with the Reynolds number. The maximum value of wall shear stress occurs at the radial position of 0.5 diameters. As expected, the wall shear stress in the impact point takes the value of zero, and the pressure distribution reaches its maximum.
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Re=300 Re=420 Re=600 Re=1000
τw (Pa)
1 0,8 0,6 0,4 0,2 0 2
4
6
p (Pa)
0
r/d (-)
8
Re=300 Re=420 Re=600 Re=1000
16 12 8 4 0
0
2
4
6
r/d (-)
8
Fig. 6. Wall shear stress and wall static pressure distributions on impingement plate for different Reynolds numbers, d=4.8 mm, z/d=1. 0,4
τw (Pa)
z/d=1 z/d=2 z/d=4 z/d=6
0,3
0,2
0,1
0 0
2
4
6
4
r/d (-)
8
p (Pa)
z/d=1 z/d=2 z/d=4 z/d=6
3
2
1
0 0
2
4
6
r/d (-)
8
Fig. 7. Wall shear stress and wall static pressure distributions on impingement plate for different z/d distances, d=4.8 mm, Re=420.
201
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Wall shear stress and wall static pressure distributions are also computed by keeping constant the jet diameter and Reynolds number and modifying the nozzle-to-wall distance ݖΤ݀ (Fig. 7). From this graphs one can deduce that the ݖΤ݀ has a lower influence than the jet Reynolds number on wall shear stress and static pressure at the wall, both in absolute value and relative to a reference amount. 4.3. Comparison and validation of numerical results The direct flow visualizations obtained from experiments are compared with the numerical results in terms of contours of velocity magnitude and velocity pathlines. A good agreement is found towards the radial development of the vortex, axial and radial position of the vortex core. Another parameter considered is the detachment position of the vortex from the wall. Experimentally, it is qualitatively inferred from the visualizations. In the numerical simulations the detachment is identified as the point where the wall shear stress is zero. By analysing the detachment of the vortex from the wall, one can notice its tendency to occur sooner in the numerical case. This issue may be caused by an insufficient mesh size in the numerical domain and can be solved by a further refinement of the mesh close to the wall. The present results show that the procedure applied returns good results. However, while computing the Reynolds number for the experimental case errors can occur, namely from the way the velocity is calculated or from a slight change in air density and viscosity when seeded with particles.
65
135
265
535
1065 Time from jet emergence ݐሺ݉ݏሻ
Fig. 8. Comparison between experimental and numerical results at different time steps for Re=420, d=4.8 mm, z/d=1.
5. Conclusion A set of flow visualizations on the behavior of a laminar air jet impinging on a flat surface was conducted to reveal the non-stationary jet dynamics of the flow. In parallel a CFD study in the same flow conditions was performed in ANSYS Fluent. The evolution of the vortex rings observed in the numerical simulations, emerging after the jet hits the impermeable wall, agrees well with the one found experimentally. The analysis of the three main zones through which the fluid passes (free jet, stagnation region and radial wall jet) show a distinct dynamics with specific features. The dominant event that characterizes the flow in the free jet region at high ݖΤ݀ values are the small roll-up vortices generated by instabilities in the shear layer. The stagnation region is the one with the highest
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gradients for velocity, pressure and shear stress distributions, as the jet is constrained by the wall to take radial direction. The wall shear stress decreases from its maximum to zero in the stagnation point, while the pressure reaches here the maximum value. In the wall jet region a vortex ring begins to develop and evolves as soon as the flow exceeds the stagnation region. As it travels downstream, this vortex ring stretches and finally brakes up into smaller coherent turbulent structures. After performing this work, the opportunity arises for new numerical simulations on the dynamics of jets impinging on walls with more complex geometries, from plates with pillars or grooves to micropatterned surfaces where results from experimental visualizations are more difficult to achieve. Acknowledgements The work has been funded by the Sectorial Operational Programme Human Resources Development 2007-2013 of the Ministry of European Funds through the Financial Agreement POSDRU/159/1.5/S/132395. The authors acknowledge the financial support received from the grant UEFISCDI project PNII-ID-PCE-2012-4-0245/2013 and PN-II-PT-PCCA-2011-3.1-0052. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12]
Gauntner J, Livingood JNB, Hrycak P, N.A.S.A.T.N. D-, J.W. Guzlntner, P. Hrycuk, Survey of literature on flow characteristics of a single turbulent jet impinging on a flat plate, Washington, DC, 1970, 43. Fitzgerald JA, Garimella SV, A study of the flow field of a confined and submerged impinging jet, Int. J. Heat Mass Transf. 41, 1998, 1025–1034. Tahsini AM, Mousavi ST, Parametric Study of Confined Turbulent Impinging Slot Jets upon a Flat Plate, 6, 2012, 1220–1224. Jambunathan K, Lai E, Moss MA, Button BL, A review of heat transfer data for single circular jet impingement, Int. J. Heat Fluid Flow. 13, 1992, 106–115. Geers LFG, Hanjalic K, Tummers MJ, Wall imprint of turbulent structures and heat transfer in multiple impinging jet arrays, J. Fluid Mech. 546, 2006, 255–284. Benmouhoub D, Mataoui A, Turbulent Heat Transfer From a Slot Jet Impinging on a Flat Plate, J. Heat Transfer. 135, 2013, 102201. Jaramillo JE, Trias FX, Gorobets A, Pérez-Segarra CD, Oliva A, DNS and RANS modelling of a turbulent plane impinging jet, Int. J. Heat Mass Transf. 55, 2012, 789–801. Hadžiabdić M, Hanjalić K, Vortical structures and heat transfer in a round impinging jet, J. Fluid Mech. 596, 2008, 221–260. Gardon R, Akfirat JC, The role of turbulence in determining the heat-transfer characteristics of impinging jets, Int. J. Heat Mass Transf. 8, 1965, 1261–1272. ANSYS, ANSYS FLUENT User’s Guide, 15317 (2011) 2498. http://cdlab2.fluid.tuwien.ac.at/LEHRE/TURB/Fluent.Inc/v140/ flu_ug.pdf. Dairay T, Fortuné V, Lamballais E, Brizzi LE, Direct numerical simulation of a turbulent jet impinging on a heated wall, Int. J. Heat Fluid Flow. 764, 2015, 362–394. Rohlfs W, Haustein HD, Garbrecht O, Kneer R, Insights into the local heat transfer of a submerged impinging jet: Influence of local flow acceleration and vortex-wall interaction, Int. J. Heat Mass Transf. 55, 2012, 7728–7736.
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