Effects of undulated wall on the hydrodynamic and thermal transport characteristics of turbulent jet

doi:10.1016/j.ijthermalsci.2020.106297

International Journal of Thermal Sciences

Volume 152, June 2020, 106297

https://doi.org/10.1016/j.ijthermalsci.2020.106297 Get rights and content

Highlights

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Effect of wall undulation on thermo-hydraulic transport characteristics of turbulent jet.
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Strong influence of undulation of wall on the transport characteristics.
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Intricate interplay between undulation height and offset ratio for offset jet.

Abstract

The present study investigates numerically the effect of wall undulation on the thermo-hydraulic transport characteristics of turbulent jet. In order to explore the influence of position of the nozzle exit from the wall, both wall jet and offset jet are considered. The theoretical model is numerically solved using shear stress transport (SST) model to predict the effects of height of undulation of the wall and the offset jet ratio on the re-attachment length, the velocity profile at different downstream locations, the coefficient of friction and the Nusselt number. The results indicate that the undulation of wall has a strong influence in altering the friction coefficient, Nusselt number and re-attachment length for offset jet. It further reveals that there is an intricate interplay between undulation height and offset ratio in dictating the flow and heat transfer characteristics.

Introduction

Turbulent wall jet is frequently used in various practical applications such as solid smoothing, flow deflection devices, cooling of gas turbine blades, inlet devices of ventilation, to name a few. The widespread engineering applications of turbulent jet have motivated various researchers to execute extensive research investigations on the thermo-hydraulic characteristics of turbulent jet. Turbulent plane wall jet is obtained by injecting the fluid at high velocity tangentially to a solid wall parallel to the axis of the nozzle. A plane wall jet here refers to the jet with the nozzle exit at the wall; while in the same context, the offset jet refers to jet with nozzle exit at some distance away from the wall parallel to the flow. The schematic diagram of the offset jet with various regions is shown in Fig. 1. The parameter exclusively used to characterize the offset jet is offset ratio, defined as the ratio of jet width (h) and the jet height (H) from the wall. An offset jet is characterized differently from wall jet by the formation of recirculation region, and impingement region, after which the characteristics of offset jet and wall jet appear to be same for any offset ratio [1]. The difference in entrainment of fluid in the surroundings and in the lower wall region causes Coanda effect [2] which results in impingement of offset jet on the lower wall.

A plethora of investigations [[3], [4], [5], [6], [7], [8], [9], [10], [11], [12], [13], [14], [15], [16]] have been carried out by the researchers to study the hydrodynamic transport characteristics of turbulent jet. Most of the studies have been focused on the effect of parameters like reattachment distance, velocity profiles at various downstream distances and variation of coefficient of friction in flow direction. Earlier work in this area was reported by Bourque and Newman [6] who studied the reattachment for 2D incompressible jet flow and concluded that for large values of Reynolds number and length of attaching surface, the re-attachment phenomenon becomes independent of these parameters. Villafruella et al. [7] experimentally studied the flow characteristics for parallel and inclined turbulent wall jets and reported that the stream wise location where the jet becomes self-similar are farther from the exit in case of inclined jet as compared to parallel wall jet. Mohammadaliha et al. [8] numerically studied the effect of nozzle geometry on turbulent 3-D water offset jet flows and observed that the reattachment length decreases for square shaped nozzle due to entrainment and the presence of same fluid in the recirculation region. They also reported the upstream shift of point of maximum shear stress along with the increase in magnitude of shear stress. Kechiche et al. [9] studied numerically the effect of various inlet conditions on a turbulent wall jet and found that the flow characteristics do not depend anymore on jet exit conditions after certain distance from the nozzle exit. Miozzi et al. [10] studied the Coanda effect on free surface offset turbulent jet and reported that Coanda effect is dependent on lateral wall distance. Mondal et al. [11] analyzed periodically unsteady interaction between wall and offset jet for various velocity ratio. Further, Mondal et al. [12] developed a model to study the effect of bottom wall proximity on the unsteady flow structures for combined turbulent wall jet and offset jet flow. Zhiwei et al. [13] studied the interaction between wall jet and offset jet with different velocity and offset ratio and they concluded that the flow pattern shifts from offset jet to wall jet and the decay of maximum velocity becomes gradually slower. The effect of wall inclination on the mean flow and turbulence characteristics in a two-dimensional wall jet were experimentally studied by Lai and Lu [14] using hot wire anemometry. Pramanik and Das [15] developed a model to make a comparison of the characteristics of a planar turbulent offset jet to that of oblique wall. They showed the velocity distribution of oblique offset jet in inner coordinates and reported differences with that of the boundary layer as well as plane wall jet. Bouda et al. [16] used a combination of experimental and numerical methods to study the characteristics of turbulent wall jet over a backward facing step.

Pioneering work in this context of thermal characteristics of wall jet turbulent flow was carried out by Holland and Liburdy [17]. They considered adiabatic as well as heated wall and reported the development of local similarity of temperature profiles at the downstream of impingement. Kim and Yoon [18] performed experiments using msplit film probe and thermo-chromic liquid crystal and the key conclusions drawn from the study include the co-incidence of time averaged reattachment point with the point of maximum Nusselt number. They also found that the initially dividing streamline of the jet reattaches the wall in the re-attachment region. Gao et al. [19] experimentally studied the flow and heat transfer characteristics of a planar offset attaching jet with a co-flowing wall jet. They concluded that the higher velocity wall jets remain attached to walls in all geometric configurations considered and results in the formation of a recirculation region between the two jets which induces periodic motion and hence significantly increases the turbulent fluctuations normal to the wall. They further observed that there is a significant increase in the pressure fluctuations on the wall below the near field flow for the flows with smaller wall jets resulting in enhanced heat transfer in that region. Further, Gao et al. [20] performed experiments to explore the dependency of the heat transfer coefficient on the Reynolds number and established an empirical co-relation for maximum Nusselt number. Nebuchinov et al. [21] experimentally investigated the heat transfer in near-wall area of an axisymmetric turbulent jet, impinging onto the heated surface by using combined particle image velocimetry and planar laser induced fluorescence methods and found that the mechanism of turbulence adds up to 25% of heat intensity. Xu et al. [22] carried out an investigation on a jet impinging on a rough surface and observed that the effect of roughness is not significant in the impingement zone although it has prominent effect in the wall jet region.

All the foregoing investigations are concerned with plane walls. However, the surface of the walls in many applications may not be plane, rather it becomes undulated and accordingly influence of the geometry of impingement wall may be one of the important issues to be considered. It is important to mention in this context that in spite of the large volume of work carried out on turbulent jet flow as delineated above, the influence of undulation on wall surface on the fluid flow and heat transfer characteristics remains largely overlooked and needs to be explored in greater detail due to its relevance in several applications. Accordingly, the aim of the present work is to analyze the effect of undulated wall on the hydrodynamic and thermal transport characteristics of turbulent jet flow both for wall jet and offset jet. The theoretical model is numerically solved to predict the effects of height of undulation of the wall and the offset jet ratio on the re-attachment length, the velocity profile at different downstream locations, the coefficient of friction and the Nusselt number.

Section snippets

Theoretical formulations

We consider a steady, two-dimensional, incompressible turbulent jet is issued into a quiescent ambient as shown in Fig. 1. The surface profile of the undulated wall is given by the following equation: $y = y_{\max} \sin (\frac{π}{5} x)$ where y_max is the amplitude of the wall undulation. The fluid is considered as Newtonian with constant thermo-physical properties. The body forces and the heat transfer due to radiation are neglected. In order to predict the turbulent mean flow, the steady-state Reynolds averaged

Numerical solution methodology and model validation

The governing transport equations delineated in the previous section have been solved using a present in-house code. The governing differential equations are discretized using the finite volume method. The diffusive terms are discretized by using central difference scheme and second-order upwind scheme is employed to discretize the convective terms. Non-uniform grid with higher grid density both near the wall and in the jet entrance region is used in order to capture the steep gradient of the

Results and discussion

The main focus of the present investigation is to portray the effect of undulation of the wall on the thermo-hydraulic transport characteristics for turbulent jet flow. Both wall jet and offset jet are considered in the analysis. In order to assess the implication of undulation of wall on the transport characteristics, the results obtained for undulated wall have been compared with that for plane wall. Results are presented in terms of contours of streamlines showing re-attachment length, axial

Conclusions

Numerical investigations have been carried out to study the effect of undulated wall on the thermo-fluidic transport characteristics of turbulent jet. Both wall jet and offset jet are considered. The important findings from the present study are as follows:

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For offset jet, the re-attachment length is altered significantly with undulation for smaller values of undulation height and the change is more prominent for lower values of offset ratio.
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There is a significant alteration in the variation of

Acknowledgment

SS gratefully acknowledges the help and cooperation received from Mr. Debayan Bhowmick.

References (29)

T. Mondal et al.
Computational study of periodically unsteady interaction between a wall jet and an offset jet for various velocity ratios
Comput. Fluids
(2015)
T. Mondal et al.
Effect of bottom wall proximity on the unsteady flow structures of a combined turbulent wall jet and offset jet flow
Euro. J. Mechanics B/Fluids
(2016)
L. Zhiwei et al.
Interaction between wall jet and offset jet with different velocity and offset ratio
Procedia Eng.
(2012)
J. Lai et al.
Effect of wall inclination on the mean flow and turbulence characteristics in a two dimensional wall jet
Int. J. Heat Fluid Flow
(1996)
S. Pramanik et al.
Numerical characterization of a planar turbulent offset jet over an oblique wall
Comput. Fluids
(2013)
J.T. Holland et al.
Measurements of the thermal characteristics of heated offset jets
Int. J. Heat Mass Tran.
(1990)
D. Kim et al.
Flow and heat transfer measurements of a wall attaching offset jet
Int. J. Heat Mass Tran.
(1996)
N. Gao et al.
Flow and heat transfer measurements in a planar offset attaching jet with a co-flowing wall jet
Int. J. Heat Mass Tran.
(2014)
N. Gao et al.
Heat transfer in turbulent planar offset attaching jets with small initial offset distances
Int. J. Heat Mass Tran.
(2015)
A.S. Nebuchinov et al.
Flow and heat transfer measurements in a planar offset attaching jet with a co-flowing wall jet
Exp. Therm. Fluid Sci.
(2017)

S.K. Rathore et al.

A comparative study of heat transfer characteristics of wall-bounded jets using different turbulence models

Int. J. Heat Mass Tran.

(2015)

S. Pati et al.

Numerical investigation of thermo-hydraulic transport characteristics in wavy channels: comparison between raccoon and serpentine channels

Int. Commun. Heat Mass Tran.

(2017)

N. Rajaratnam et al.

Plane turbulent reattached wall jets

ASCE J. Hydraul.

(1968)

D.J. Tritton

Physical Fluid Dynamics

(1977)

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Enhancement of heat transfer by flowing turbulent jet on a linearly decaying (LD) wavy wall
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The influence of a partial linearly decaying (LD) wavy wall on different fluid flow and thermal parameters has been investigated for the turbulent jet. For the present study, a segment of wall from the leading edge is made with a constant amplitude 0.8a (a = nozzle height), followed by a segment of LD wavy wall. In the region of LD wavy wall, the amp (amplitude) of wavy wall is linearly reduced from 0.8a amplitude to 0a in the downstream direction. The LD wavy wall segment varies from 100% to 0%. For 100% LD wavy wall, the whole wall is made of linearly decaying amplitude, whereas for, 0% LD wavy wall, the whole wall is made wavy with a constant amplitude. The Reynolds number at the inlet is same for all the cases, i.e. 15,000 to maintain the fully turbulent condition at the exit of nozzle. The problem is solved numerically using $k - ε$ RNG model. The results obtained from this study show that for 100% LD wavy wall the velocity decay is minimum and as the % of LD wavy wall decreases, the velocity decay increases. Whereas the thermal decay of jet is maximum in the case of 100% LD wavy wall. Similarly, Y_max, Y_Tmax, and the velocity and thermal jet spread are found to be minimum for the 100% LD wavy wall and all these parameters increase as the % of LD wavy wall decreases. The maximum increment in the heat transfer rate is 27.9% for 100% LD wavy wall in regards to the baseline case (plane wall). However, the maximum increment in thermal hydraulic performance (THP) is noticed for the wavy wall with 50% LD wavy wall, which is equal to 6.7%. In a previous study (ArchanaKumari, 2021 [1]), the increment of 19.0% and 5.3% is observed for the heat transfer and THP respectively. In the present study by introducing LD wavy wall, the increment in the heat transfer and THP are quite significant.
Effect of frequency of the wavy wall on turbulent wall jet heat transfer characteristics
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The thermal and hydraulic characteristics of a sinusoidal wavy wall are studied numerically to increase the heat transfer rate of the turbulent wall jet. To do so, the sinusoidal profile $(y = A * s i n (ω_{N} x))$ is used for the wavy wall, where $ω_{N} = 2 π N / L$ is the frequency with suffix N denoting the number of cycles for the given length L and $A$ is the amplitude. The amplitude “A” is varied from 0 to 0.8 $a$ and $ω_{N}$ is changed from $ω_{4}$ to $ω_{12}$ , to find out the optimum amplitude and frequency for which the heat transfer rate is maximum. The low Reynolds number two equations RNG $k - ϵ$ model is used for the detailed study and to understand the impact of a re-circulation zone on the heat transfer rate. The inlet velocity is uniform and equals to 10.95 m/s for all the cases to achieve the inlet Reynolds number 15000 for a 20 mm nozzle height. At the inlet, jet is heated to a temperature of 330 K and the wavy wall on which the jet flows is provided an isothermal condition with 300 K temperature. With these conditions, the results for streamwise maximum velocity decay, skin friction coefficient, re-circulation area and local Nusselt number have been compared for different amplitudes and frequencies of the wavy wall. From the results, it has been observed that with the increasing amplitude and frequency the $U_{m a x}$ increases, the area of re-circulation zone increases and the thermal potential core decreases. For the wavy wall amplitude A = 0.8 and frequency $ω_{12}$ , the peak of $U_{m a x}$ is 170% more than the plane wall jet, the area covered by re-circulation zone is 58.2% of the total area and the thermal potential core reduces to $X = 3.7$ which is about 50% of the plane wall jet. The local Nusselt number also increases with the increasing amplitude and frequency in the near field, but in the far field it starts decreasing as the re-circulation effect dominates there. For the wavy wall, the maximum increase in heat transfer rate is 23.23% with respect to the plane wall case.
Transient flow and thermal transport characteristics of wall-bounded turbulent dual jet with heated undulated wall
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Citation Excerpt :
They considered turbulent offset jet for two offset ratios 3 and 5 and compared it with a turbulent wall jet for a constant heat flux boundary condition with Re = 15,000 and amplitude from 0.1 to 0.8 [13-14]. The normalised URANS equations in the indicial notations for the SST k-ω turbulence model equations are expressed as [29-30]. The correlations (Eqs. 18 and 19) predict 99.54% and 98.01% of goodness fits with the present computational results.
The present computational study aims to investigate and improve the turbulent dual jet cooling performance on an undulated surface with varying profiles. This study also aims to highlight the flow and thermal features arising owing to an undulated surface having amplitude (UA) between 0.0 and 0.7. The transient RANS equations are considered to simulate the complex behaviour of turbulent dual jet. Four Reynolds-Averaged Navier-Stokes (RANS) turbulence models, namely, standard k-ω, shear-stress transport (SST) k-ω, renormalization group (RNG) k-ϵ, and realizable k-ϵ models, are used to predict the thermal performance and flow field of a turbulent dual jet for a fixed Reynolds number (Re) of 10,000 and offset ratio of 2. A constant wall temperature and constant wall heat flux boundary conditions are used. For the amplitude between 0.0 and 0.1, a periodic vortex shedding phenomenon near the jet exit is observed. However, two stable counter-rotating vortices are observed with no periodic vortex shedding for higher values of UA ≥ 0.3. The axial position of the merge point reduces with a rise in the amplitude. It is also observed that the velocity profile becomes self-similar and the inflection point in the velocity profile rises near the wall region with amplitude. The time series of U and V velocity signals unveil sinusoidal oscillations and display almost the same peak to peak amplitude for UA ≤ 0.1 at various times. The FFT of U velocity signals displays a solo peak dominant frequency which is the same as shown by V velocity in the FFT plot corresponding to the Strouhal number of the vortex shedding phenomenon. The average Nusselt number is increased up to 63.89% and 65.03% for higher amplitude for the constant heat flux and constant temperature boundary conditions. Correlations have been also proposed for the average Nusselt number, the average heat flux and the merge point. The outcomes of the present research can be implemented for better design in automobile industries and utilization of cooling or heating jets in electronics, metal, and material processing.
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In this study, with the help of with and without sidewall configurations, experimental and numerical approaches are utilised to investigate the sidewall influence on a three-dimensional turbulent wall jet. The mean flow profile of the three-dimensional turbulent wall jet is measured through experimental method and compared with the numerical results. In addition, the numerical method is used to characterise the turbulence characteristics of the wall jet for both the configurations. A 200 mm square nozzle (height h=20 $\pm$ 0.5 mm) is used to generate the developing jet exit profile for the experimental results. The Reynolds number based on the jet exit velocity and nozzle height is 25,000. The numerical results are obtained by solving the Reynolds Average Navier stokes (RANS) equations with low Reynolds number $k - ε$ turbulence models proposed by Yang and Shih and Launder and Sharma. The experimental results are obtained by a single probe hotwire anemometer and a K-type thermocouple. It is observed that the sidewall affects the temperature distribution just after the potential core region $(x / h = 5)$ whereas the velocity distribution is affected in the fully developed region after the downstream location $x / h = 22.5$ . Sidewalls drastically influenced the thermal and velocity decay in wall-normal and lateral directions. It is found from the numerical simulation that the decay of maximum streamwise velocity is increased by 9%, whereas centerline temperature decay is decreased by 25% in sidewall configuration as compared to without sidewall configuration. The contour plots of temperature and velocity also exhibit the sidewall effect on the whole domain. The Reynolds shear stress $< u^{'} v^{'} >$ dominates in the vertical jet centerline plane $(at z = 0)$ , whereas $< u^{'} w^{'} >$ dominates in the lateral direction at $y_{m a x}$ plane in both the configurations. On the vertical jet centerline plane $(at z = 0)$ , Reynolds shear stress $< u^{'} v^{'} >$ is nearly increased by 10% in the presence of sidewall compared to without sidewall configuration. The entrainment of the ambient fluid initially decreases, but after the downstream location $x / h = 22.4$ , it increases for the case of the sidewall compared to the corresponding case without the sidewall. This happens owing to an increase in maximum turbulent kinetic energy generation inside the flow domain by 10%. The turbulent heat flux $< T^{'} V^{'} >$ dominates in lateral and wall-normal shear layers in both the configurations. The correlations of decay of temperature and velocity are also suggested through numerical techniques.
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Citation Excerpt :
A schematic diagram of the three dimensional turbulent wall jet is shown in Fig. 1. The heat transfer characteristics for the three dimensional unheated turbulent wall jet are studied by different authors [2–7] at different bottom wall boundary conditions like adiabatic, isothermal, and isoflux, without considering the effect of sidewall. To the authors’ best knowledge, there is scarcity of literature on three dimensional heated turbulent wall jet with sidewall effect.
Effect of sidewall on the thermal characteristics of a three dimensional turbulent wall jet with a square nozzle is explored experimentally. The mean and fluctuating quantities are presented through temperature decay, thermal half widths and temperature fluctuation. It is observed that the decay rate of centerline bottom wall temperature of without sidewall is almost half than the corresponding case with the sidewall. The sidewall influences the temperature variation drastically. As a result, the asymptotic nature of temperature is lost. Also, the thermal half width in wall normal direction varies non-linearly as compared to the linear variation for the case without sidewall. The side infiltration is more dominant than the top infiltration in the near field region for both the cases. But, the sidewall plays an important role in suppressing the fluctuation at the far downstream locations. In addition, several correlations are proposed for the mean thermal parameters of the three dimensional turbulent jet.

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Effects of undulated wall on the hydrodynamic and thermal transport characteristics of turbulent jet

Highlights

Abstract

Introduction

Section snippets

Theoretical formulations

Numerical solution methodology and model validation

Results and discussion

Conclusions

Acknowledgment

Comput. Fluids

Euro. J. Mechanics B/Fluids

Procedia Eng.

Int. J. Heat Fluid Flow

Comput. Fluids

Int. J. Heat Mass Tran.

Int. J. Heat Mass Tran.

Int. J. Heat Mass Tran.

Int. J. Heat Mass Tran.

Exp. Therm. Fluid Sci.

Int. J. Heat Mass Tran.

Int. Commun. Heat Mass Tran.

Plane turbulent reattached wall jets

ASCE J. Hydraul.

Physical Fluid Dynamics