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Dynamical Study of Pulsed Impinging Jet with Time Varying Heat Flux Boundary Condition

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Pulsed jets in different configuration are potentially considered for enhancing transport phenomenon generally. Flow and temperature field in a pulsed impinging jet are simulated numerically by solving the governing equations using the control volume method. Ensemble Averaging Method as well as Phase Averaging has been employed for reporting the results in this study. In order to simulate a pulsating jet, inlet velocity profile was exerted as a time dependent sinusoidal and step signals. The results of this simulation showed an oscillatory jet could lead to an increase in jet development and its cross section with the wall and also a more uniform Nusselt profile would be obtained compared to the steady jet. For parametric investigations and extracting flow and thermal characteristics of a pulsed impinging jet, the effects of various parameters including flow frequency and amplitude and heat flux frequency were considered. It has been seen that Nusselt number varies by the changes in frequency, amplitude and the type of the excitation. It has been shown that the oscillating impinging jet has a better performance rather than the steady case when the excitation amplitude and frequency increase. Finally, it is also observed how a thermal field is going to respond with two pulsating inputs.
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   Heat Transfer—Asian Research ,  00  (0), 2014 Dynamical Study of Pulsed Impinging Jet with Time Varying HeatFlux Boundary Condition Sina Ghadi, Kazem Esmailpour, Mostafa Hosseinalipour, and Mehrdad KalantarCFD&CAE laboratory, Department of Mechanical Engineering, Iran University of Science andTechnology, Tehran, IranPulsed jets in different con󿬁guration are potentially considered for enhancingtransport phenomenon generally. Flow and temperature 󿬁eld in a pulsed impinging jet are simulated numerically by solving the governing equations using the controlvolume method. Ensemble Averaging Method as well as Phase Averaging has beenemployed for reporting the results in this study. In order to simulate a pulsating jet,inlet velocity pro󿬁le was exerted as a time dependent sinusoidal and step signals.The results of this simulation showed an oscillatory jet could lead to an increase in jet development and its cross section with the wall and also a more uniform Nus-selt pro󿬁le would be obtained compared to the steady jet. For parametric investi-gations and extracting 󿬂ow and thermal characteristics of a pulsed impinging jet,the effects of various parameters including 󿬂ow frequency and amplitude and heat󿬂ux frequency were considered. It has been seen that Nusselt number varies by thechanges in frequency, amplitude and the type of the excitation. It has been shownthat the oscillating impinging jet has a better performance rather than the steadycase when the excitation amplitude and frequency increase. Finally, it is also obser-ved how a thermal 󿬁eld is going to respond with two pulsating inputs.  C     ⃝  2014 WileyPeriodicals, Inc. Heat Trans Asian Res, 00(0): 1–16, 2014; Published online in WileyOnline Library (wileyonlinelibrary.com/journal/htj). DOI 10.1002/htj.21154 Key words:  pulsed impinging jet, heat transfer, oscillating, parametric study 1. Introduction An impinging jet is a 󿬂uid jet that is used for cooling or heating a surface which may bearranged in a perpendicular or inclined con󿬁guration. Due to the high rate of heat transfer, thismethod is involved in many industrial drying processes like the drying of tissues, photographic neg-atives, cloth, and so on, or for making some foods like corn, chips, pizza, and so on and also for seedproducing like coffee, cocoa, and nuts. In industrial food, depending on the kind of product, and inordertoreachthedesiredpointwatervaporwasalsousedinsteadofhotair.Duringthepast30years,many experimental and computational investigations on 󿬂ow and heat transfer characteristics of single and multiple impinging jets were one of researcher’s favorite 󿬁elds of study in 󿬂uid dynamicsextent.Effectsofjet’snozzlegeometry,distancefromsurface,andboundaryconditionswerestudiedexperimentally [1–3]. Polat has done a thorough review on the effects of the above parameterson the transform phenomenon of an imping jet [4]. A thorough comprehensive review was done C     ⃝  2014 Wiley Periodicals, Inc.1  experimentally and computationally on heat transfer of impinging jets by Huang and colleagues [5].They also showed that the  k  –   standard model with various wall functions has some errors in antic-ipating Nusselt number and temperature 󿬁eld near the wall. A comparative evaluation on differenthigh-Reynolds and low-Reynolds RANS model was done by Hosseinalipour and Mujumdar [6]that shows low-Reynolds models are much more successful in predicting the Nusselt number.In general, there are two methods for improving a system’s 󿬂ow and thermal characteristics:passive and active. In the passive method geometry characteristics of the system have to be changedthat is expensive and in some situations impossible. In the active method the system is controlled dy-namically by designing different mechanisms to control transport phenomenon. Researchers of 󿬂uiddynamics attribute transport phenomenon in a system to a series of coherent and organized struc-tures that are named according to their appearance shape (e.g., tube vortex, sheet vortex, horse shoevortex, and hair pin vortex). These structures have the ability to produce, dissipation of turbulenceenergy, and energy exchange. This hypothesis that turbulent 󿬂ow is strongly affected by formationand interaction between big coherent structures is approved by all researchers. In order to controlthe production rate and strength of vortexes, inlet mass 󿬂ow rate can be adjusted. Dynamical controlof the mass 󿬂ow rate or time dependency is included in active methods of improving engineeringsystems. This method is divided into two main categories: ● Synthetic jet injection:  inlet 󿬂ow exerted as a time dependent function such that net entering󿬂ow rate is zero. ● Pulsed jet injection:  inlet 󿬂ow exerted as a time dependent function such that a mean none-zero󿬂ow rate entered into the system.By discovering the crucial role of big coherent structures in the growth and mixing of a jet,studies on them have increased impressively. Researchers thought about how we can make thesestructures more organized with a pulsating jet and also with increasing mixing and growth rate.Crow and Champagne [7] showed that in a round jet these structures would be formed in shear layer.The Strouhal Number of those structures was between 0.3 and 0.4. They also showed that thesestructures can get more coherent and larger at a Strouhal number around 0.3. Most initial researchwhich was done in the 󿬁eld of oscillating impinging jet is attributed to Nevins and Ball [8]. Theyconsidered heat transfer between a 󿬂at surface and an oscillating jet and reported that there are nosigni󿬁cant differences between and an oscillating jet and a steady one. The tests were done for 1,200 <  Re  <  120,000 and 10-4 <  St  < 10-2 and the distance between the nozzle and 󿬂at surface was 8 to32. Nevins and Ball presented nothing about formation of second 󿬂ow structures and their exper-iments were limited to low St. Due to the research of Nevins and Ball, oscillating impinging jetswere not considered and were not researched for about 25 years. In the late 1980s and early 1990s,several research groups started to work on oscillating streams again. Azevedo and colleagues con-sidered impinging heat transfer for a wide range of frequencies [9]. They made the 󿬂ow oscillatingby means of a valve which was like a ball valve and rotates at speci󿬁c frequencies. The instant andaverageheattransferweremeasuredbyhot-wireandinfraredphotographytechniquesandcomparedto those of the steady one where the 4,000  <  Re  <  40,000 and the frequency was between zero and200 Hz. Their studies showed that the value of Nu for an oscillating one is less than steady. Therate of heat transfer in an oscillating jet is about 0% to 20% less than a steady one. Mladin andZumbrunnen theoretically and by means of a boundary layer model considered the effects of 2  different kinds of inlet oscillating function, frequency, and amplitude on the instant and averageconvectional heat transfer of a 󿬂at plate [10]. They presented that there is a critical St at which nosigni󿬁cant increase in heat transfer, compared to a steady one, will be observed in values less thanthat. They reported the critical St is equal to 0.26. Mujumdar and colleagues simulated the 󿬂owand thermal 󿬁eld of a laminar oscillating 󿬂ow numerically [11]. Considered parameters include:average Reynolds number (100  ≤  Re  ≤  1,000), oscillating frequency (1  ≤  f   ≤  20Hz), and distancebetween nozzle and 󿬂at plate (4 ≤ H/D ≤ 9). Their results show that increasing Re causes no signif-icant changes in Nu, but as the distance from impingement area increases the harmonic oscillationof Nu will increase. Mujumdar and colleagues simulated heat transfer of an impinging jet under astep kind of oscillation numerically [12]. The effects of reave, the temperature difference betweenthe entering stream and impingement plate, the distance of nozzle to plate, and frequency on heattransfer were investigated. They showed that Nu values will increase as Re increases due to thefact that turbulence intensity and turbulence eddy viscosity will increase by raising the Re values.The Nu o  value for steady state is larger than for the oscillating one. By tracing Nu downstreamand near the wall region, the ratio of Nu for the oscillating to the steady one will increase. Sailorand colleagues considered an oscillating impinging jet experimentally and introduce an extra 󿬂owparameter as the duty cycle which is de󿬁ned as the percentage of one period in which a signal isactive [13]. While Zumbrunnen focused on boundary layer differentiation and oscillating effects onits average thickness, Eibek claimed that 󿬂ow secondary structures have the critical role in transportphenomenon [14]. Liewkongsataporn and colleagues [15] studied pulsating slot impinging jet heattransfer numerically. They showed that periodic formation of a recirculation zone in pulsating jetcan improve heat transfer from a hot surface. Their parametric study reveals that higher frequencieshave more effect on cooling performance at low pulsation amplitudes. Jiang and colleagues issuedimpinging jets from the tailpipe of pulse combustors which have been evaluated in their studies forpossible applications in the rapid drying of continuous sheets [16]. Their examination of the velocityand thermal 󿬁elds showed that the instantaneous heat transfer rate on the target surface was highlydependent on development of the hydrodynamic boundary layer with time. An investigation wasperformed on a pulsating impinging jet array under large temperature differences between jet 󿬂owsand impingement wall [17]. Their results show that pulsating an impinging jet without phase an-gle difference has a marginal effect on heat transfer, while introducing a phase angle difference canstrongly enhance heat transfer. In other studies, phase difference between the nozzle exit velocitypro󿬁lesanditspotentialtomakethestagnationpointoscillatebetweenthetwojetswereinvestigated.This is so important in mixing behavior and drying [18–20]. Kurnia and colleagues investigate theperformance of impinging jet drying under various con󿬁gurations [21]. They noted that lower en-ergy consumption of impinging jet with pulsating and/or intermittent 󿬂ow offers comparable dryingkinetics as compared with that of a steady jet, which shows potential for energy saving. As a keyparameter, the distance between the nozzle exit and impinging surface (H/W) has a crucial role onthe physics of a pulsating impinging jet. It was investigated numerically that for various H/W thefrequency would affect rate of heat transfer in completely different ways. Thus, an increase in heattransfer, as a result of increasing frequency, could not be expected under every condition [22].Because of the periodic formation of structures in the shear layer and the non-linear dynam-ics and chaotic behavior in the boundary layer induced by pulsation, prediction of 󿬂ow and heattransfer characteristics of pulsating jet impingement has been a complex and challenging problem.Moreover, most of the previous studies have focused on steady heat 󿬂ux [23–27]. While, consider-ing that unsteady heat 󿬂ux does not have less importance than steady heat 󿬂ux due to their physical3  applications in a computer’s CPU, air-cooled reciprocating engines, and in metal forming process. Itshould also be mentioned that very few practical events are going to experience speci󿬁cally shapedperiodic heat 󿬂uxes like a sinusoidal or square type. As an example, in CPUs or reciprocating en-gines we have heat 󿬂uxes which are not exactly sinusoidal or square shaped but they are periodic. Inanother way, in a metal stretching process unsteady heat 󿬂ux which is not periodic can be observed.Further studies are therefore needed to examine the effect of the intermittent pulsations onheat transfer of an impinging jet with a variable heat 󿬂ux input. In this study a parametric investi-gation is thus performed on a two-dimensional pulsating turbulent impinging jet with variable heat󿬂ux input by the computational 󿬂uid dynamic approach. The local and instantaneous heat transferrate and 󿬂ow dynamics of pulsating impinging jet is compared with the steady case. To have a goodparametric study, the effect of amplitude, frequency and shape of the pulsation signal on the localand instantaneous Nusselt number distribution on the target surface is investigated. Nomenclature C  p  speci󿬁c heat capacity (J/kg.K)  D  inlet diameter (m)  H   height of the channel (m) k   heat conduction coef󿬁cient (W/m.K)  L  length of the channel (m)  p  time averaged pressure (Pa) t   time (s) T   temperature (k) T  p  period of pulsation  x  ,  y  system coordinate (m) ̄ u  velocity vector (m/s) u  jet  jet inlet velocity (m/s) u i  time averaged velocity (m/s) u ′ i u ′  j  Reynolds stress (m 2  /s 2 ) u ′ i T  ′ turbulent heat 󿬂ux (mK/s)  f   frequency (Hz)  A  amplitude (m) Dimensionless Number Nu Nusselt number ( hD ∕ k   )Nu o  Stagnation Nusselt numberRe Reynolds number ( 󽠵 u  jet   D 󰀯 􍠵  )St Strouhal number (  f D 󰀯 u  jet  ) Greek Symbols 􍠵  dynamic viscosity (Pa s) 󽠵  density (kg/m 3 )4
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