- Email: [email protected]
Effect of compressibility and nozzle configuration on heat transfer by impinging air jet over a smooth plate
Accepted Manuscript Title: Effect of compressibility and nozzle configuration on heat transfer by impinging air jet over a smooth plate Author: Ravish Vinze, S. Chandel, M.D. Limaye, S.V. Prabhu PII: DOI: Reference:
S1359-4311(16)30212-5 http://dx.doi.org/doi: 10.1016/j.applthermaleng.2016.02.069 ATE 7798
To appear in:
Applied Thermal Engineering
Received date: Accepted date:
5-11-2015 13-2-2016
Please cite this article as: Ravish Vinze, S. Chandel, M.D. Limaye, S.V. Prabhu, Effect of compressibility and nozzle configuration on heat transfer by impinging air jet over a smooth plate, Applied Thermal Engineering (2016), http://dx.doi.org/doi: 10.1016/j.applthermaleng.2016.02.069. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Effect of compressibility and nozzle configuration on heat transfer by impinging air jet over a smooth plate Ravish Vinze1, S. Chandel2, M.D. Limaye3 and S.V. Prabhu4, a 1, 2
Department of Mechanical Engineering, D.I.A.T. Pune, India 3
4
R & D E (E), DRDO, Pune, India
Department of Mechanical Engineering, I.I.T., Bombay, Mumbai, India 1
[email protected], [email protected]
Address for correspondence a
Dr. S.V.Prabhu,
Professor, Department of Mechanical Engineering, Indian Institute of Technology, Bombay, Powai, Mumbai India Pin: 400 076 Telephone: 91-22-25767515 Fax: 91-22-25726875 E-mail: [email protected]
1 Page 1 of 37
Highlights
Effect of nozzle profile and Mach number on the heat transfer is studied
Correlations for the Nusselt number distribution are suggested
Recovery factor is independent of Re for a given jet to plate distance
Abstract: Jet impingement experiments are conducted to study influence of nozzle profile on heat transfer for compressible subsonic jets. Three different circular profiles namely contoured nozzle, orifice and pipe are selected for the present experimental study. For each nozzle profile, Mach numbers covered are 0.3, 0.5 and 0.7 and the corresponding Reynolds numbers are around 48000, 82000 and 120000. Appropriate diameters for these nozzles are chosen to maintain nearly same Reynolds number. Thin metal foil technique with Infrared red camera is used to measure the heat transfer coefficient and adiabatic wall temperature. Pressure distribution in the stagnation regions is measured for all the cases. Correlations for local heat transfer distribution over the surface are presented in this study. Pipe nozzle provides higher heat transfer coefficient compared to contoured nozzle and orifice. The Mach number affects the heat transfer in the stagnation region. The recovery factor distribution is insensitive to change in Reynolds number. Keywords: Nusselt number, Pressure loss coefficient, Recovery factor, Thermal Imaging, Mach number and Reynolds number Nomenclature A
Exit area of the nozzle, m2
Cp
Specific heat of air at constant pressure, kJ/kg K
c
Velocity of sound, m/sec
d
Hydraulic diameter of the nozzle, m
2 Page 2 of 37
D
Diameter of the supply pipe, m
h
Heat transfer coefficient, W/m2K
I
Current, A
k
Thermal conductivity of the air, W/mK
K
Loss coefficient
l
Length of pipe, m
Nu
Nusselt number,
Nuₒ
Nusselt Number at the stagnation point
Nucomp
Nusselt number for compressible jets
Nuincomp
Nusselt number for incompressible jets
M
Mach number, Mass flow rate, (gm/sec)
p
Perimeter, m
ΔP
Pressure difference, N/m2
Pr
Prandtl number , (Cp/k)
q
Heat transfer rate, W/m2 Heat carried out by convection through impinging jet, W/m2 Heat carried out by convection from back side of plate, W/m2 Total heat supplied, W/m2 Heat loss by radiation and convection from the plate, W/m2 Heat loss by radiation from the back side, W/m2 Heat loss by radiation from the front side, W/m2
R
Recovery Factor, Characteristic gas constant of jet fluid, kJ/kg K
r
Radial distance from the stagnation point, m
3 Page 3 of 37
Re
Reynolds Number,
t
Thickness of orifice plate, m
Tj
Jet static temperature, K
Taw
Adiabatic wall temperature, K
Td
Jet dynamic temperature, K
Tw
Wall temperature, K
T0
Jet total temperature, K
ve
Average velocity of the jet at the nozzle exit, m/sec
V
Voltage, V
z
Nozzle to plate distance, m
Greek Symbols γ
Specific heat ratio
µ
Viscosity of fluid, Pa.s
ρ
Density of fluid, kg/m3
4 Page 4 of 37
1.
Introduction:
Jet impingement is a very extensively used method for efficient heat transfer. This technique is used extensively for various applications like cooling of gas turbine engine components and blades, pre-heating and cooling of metal parts in mills, drying, heating in fabric and paper mills and cooling of electronic components, etc. The jet can be generated from a straight pipe, a profiled nozzle or an orifice depending on the application. The flow structure generated by each of the nozzle configuration is different. This difference in the flow structure causes different local heat transfer distribution on a flat plate impinged by different nozzle configurations. Present study is more intended to bring out the influence of nozzle configuration on the heat transfer so that an engineer can choose an appropriate nozzle for a given application. Studies on impinging air jets are conducted by various authors. In these studies, parameters like nozzle diameter, nozzle shape, Nusselt number, Reynolds number, nozzle to plate spacing (z/d) and turbulence are studied. Majority of this work is concentrated on the study of influence of Reynolds number and jet to plate distance on the local Nusselt number distribution. Jambunathan et al. [1] and Viskanta [2] provide comprehensive review on jet impingement heat transfer. They reported results for Reynolds numbers ranging from 5000124000. The influence of jet diameter, profile of flow device and nozzle to plate distance (z/d) is reported. It is reported that the variation in the turbulence level due to different nozzle shapes affects the shear layer of the jet which in turn affects heat transfer. Colucci and Viskanta [3], Kanamori et al. [4], Garimella and Nenaydykh [5], Lee and Lee [6, 7] reported results on the influence of nozzle geometry on local heat transfer coefficient using various experimental techniques. Experiments are conducted for jets generating from different nozzle configurations (Sharp/standard/square edge orifices, hyperbolic nozzle and pipes) and Reynolds number ranging from 10000 to 50000. From all these studies, it can be concluded 5 Page 5 of 37
heat transfer in influenced more by sharp edge orifice in comparison with a convergent nozzle. The sharp edge orifice greatly influences the velocity profile at the nozzle exit inducing higher rate of turbulence intensities in the jet. This greater rate of turbulence intensity results in higher heat transfer coefficient. Brignoni and Garimella [8], Attalla and Salem [9], Gao et al. [10] studied the effect of nozzle chamfering and triangular tabs on heat transfer (local and average) and axial pressure drop for Reynolds number from 5000 to 40000. Average heat transfer for square edged nozzle is higher compared to chamfered nozzle because chamfered nozzles provide greater pressure drop compared to other nozzle configurations. Triangular tabs increase turbulence in the jet and facilitate entrainment in the jet resulting in increase in heat transfer. Gordon and Akfirat [11], Knowles and Myszko [12] and Mi et al. [13] studied influence of turbulence on the heat transfer for Reynolds number ranging from 4000 to 90000. They carried out measurements for velocity and turbulence in submerged jets and reported that the distribution in turbulence levels caused by jets spreading and centerline velocity decay and mixing plays important role in governing heat transfer rates over the surface. Mi et al. [14] studied mixing characteristics of circular free jet issuing from contoured nozzle, an orifice and a pipe. They measured centerline passive temperature by cold wire probe and visualized flow. The jet velocity measurements are performed by hot wire anemometer. They reported that sharp edged orifice enables greatest amount of mixing with surrounding air, decay rate and widest spreading angle. O’Donovan and Murray [15, 16] reported heat transfer distribution, mean velocity distribution and local velocity distribution in flow field for Reynolds number ranging from 10000 to 30000. In these studies, they demonstrated association of high fluid velocity and turbulence intensity with the rate of heat transfer.
6 Page 6 of 37
Kim et al. [17], Li et al. [18] and Goldstein et al. [19] conducted experimental (thermal imaging and laser-Doppler- velocimetry) and numerical studies for measurement of recovery factor and surface pressure distribution on the flat plate for compressible jets for Reynolds number ranging from 61000 to 124000 (Mach number 0.23-0.47). The interface of shock waves exists in the jet with a stand-off shock before of the impingement surface which relies strongly on the nozzle to plate distance. Consequently, the distribution of pressure and recovery factor over the surface change drastically with nozzle to plate distance (z/d). They reported that the recovery factor does not depend on Reynolds number, but it depends on nozzle to plate distances. Brevet et al. [20], Goodro et al. [21] and Limaye et al. [22] studied the influence of Mach number (compressibility) on the heat transfer distribution of a flata plate impinged by compressible jets. Brevet et al. [20] reported that the influence of Mach number is to be considered in addition to Reynolds number for compressible jets. The Reynolds numbers covered in their study are ranging from 7200 to 71500, Mach number from 0.02 to 0.69. A correlation is proposed for average Nusselt number in terms of Mach number, Reynolds number and the area over which the averaging is carried out. It is concluded that Mach number has negligible influence on heat transfer for M < 0.2. Goodro et al. [21] investigated the effect of jet array on heat transfer for Reynolds number (5600 to 60 000) and Mach number varying from 0.1 to 0.74 respectively. Similar studies are carried out by Limaye et al. [22] for Mach number and Reynolds number ranging from 0.2-1.0 and 41000 -221000 respectively. Review of the literature suggests that there is no correlation reported to predict the Nusselt number and recovery factor distributions for subsonic compressible jets in terms of Reynolds number and Mach number. Further, there is no information available on the influence of nozzle shapes on heat transfer distribution. Hence, the present study focuses on the influence 7 Page 7 of 37
of nozzle profile (countered nozzle, orifice and pipe) on heat transfer of a flat plate impinged by compressible jets. Hence proposed objectives of this study are as follows
To measure the Nusselt number and
recovery factor distribution for countered
nozzle, orifice and pipe for a given Reynolds number and Mach number.
To examine influence of compressibility on the heat transfer in subsonic compressible jets, Mach number is maintained in the range of 0.3 to 0.7 and Reynolds number in the range of 48000 to 120000.
To measure the pressure loss coefficient for different nozzle profiles at various Reynolds numbers and Mach numbers.
To suggest a correlation for Nusselt number as a function of Mach number, Reynolds number, nozzle to plate distance and radial location.
2.
Experimental Setup and Procedure:
The arrangement of the experimental set up used in this study is shown in Fig.1. Centrifugal air compressor (capacity 10bar at 50gm/sec) supplies compressed air, which is then passed through a calibrated venturi flow meter. Upstream to the venturi, air filter and pressure regulator are installed to filter the air and to maintain the downstream pressure as desired. Two needle valves control the mass flow rate. One of the needle valves is on the upstream side and another on the downstream side of the venturi-meter. The temperature of air is measured upstream to the nozzle by calibrated K-type thermocouples. The output of the thermocouples is measured by a ‘Meco’ mill voltmeter. The venturi is calibrated using catch and time method using water as the working fluid. Calibration curve comprising coefficient of discharge variation with Reynolds number is generated and used for air subsequently. Thermocouples are calibrated using constant temperature bath using resistance temperature detector as the reference sensor whose accuracy is of the order of 0.05 C.
8 Page 8 of 37
Figure 2 and Table 1 show the nozzle configurations covered in this study. The diameter of these profiles is selected such that the diameter remains same and hence mass flow rate remains almost same. The shape of contoured nozzle (d = 8.37 mm) with a contraction ratio of 3 is shown in Fig. 2 based on the details of nozzle profile are reported by Gibbings [23] and similar nozzle was used by Rahimi et al. [24]. This profile of the nozzle enables smooth pressure drop across nozzle contraction and uniform velocity profile at the nozzle exit plane. Square edged orifice of 8.4 mm is used in the present study which is fixed at the end of pipe with an orifice plate thickness to pipe diameter ratio (t/D) is 0.2 as used by Lee and Lee [6]. In the experimental setup, the supply pipe length is around 35 times the pipe diameter. The supply pipe length (l/D >10) is sufficient for fully developed turbulent flow as suggested by Rohsenow and Choi [25]. The diameter of pipe is about 8.0 mm for which length to diameter ratio is chosen 75 (l/d) which ensures fully developed flow at nozzle exit. The target made of thin foil of steel (150 mm 130 mm, and 0.06 mm) which is clamped between copper bus bars. 5mm of foil on either side which ensures firm grip. To measure the wall temperature, thermal images are recorded by infrared camera which is positioned at the opposite side of impinging pipe (Fig. 1 and 2). Lesser thickness of the steel foil ensures negligible lateral heat conduction [26]. Hence, the local wall temperature recorded on the surface is considered to be same as that on impinging plane. The surface on which thermal images are captured is painted black using a thick coat of Tempil Pyromark ‘Matt finish’ of high emissivity (0.99). This helps us to achieve higher spatial resolution of temperature compared to thermocouples. The local temperature distribution is recorded by Ti200 infrared camera ‘Thermoteknix’ with a resolution of about 0.5 mm per pixel. A set of step down transformer (220V to 16V) and a variac is used to supply AC Power to the test plate. The voltage and current supplied to the heater are measured by ‘Meco’ digital meters of 0 to 20 ± 0.5% V and 0 to 400 ± 0.5% A, respectively. At suitable position, voltage taps are fixed in 9 Page 9 of 37
each the bus bars. A traverse system is used to set different jet-to-plate distances. Power losses from the exposed surface of the target plate due to natural convection and radiation are measured experimentally and deducted from the supplied power. Pressure drop is measured using three different digital differential pressure transducer (DPT) Rosemont’ make as shown in Fig 1b which are positioned at different r/d locations according to their range. Table 1 shows experimental parameters for different nozzles used to study influence of nozzle shape on heat transfer distribution. For the ease of explanation, the Reynolds number is taken as 48000, 82000 and 120000, although there is 3% variation among the nozzles configurations studied. 3.
Data Reduction:
The Reynolds number and Nusselt number are calculated based on hydraulic diameter (
) as given by Eq. 1 and 6. The nozzle diameter for all the cases is chosen such that
the mass flow rate is maintained almost identical for all the Reynolds numbers as shown Table 1. In order to evaluate the adiabatic wall temperature and the heat transfer coefficient simultaneously, thermal images are captured for six different (including zero flux condition) heat fluxes supplied to the target plate. At each heat flux, five images are captured. Average of these images gives temperature measurement for a heat flux. The resolution of temperature measurement depends upon number of pixel captured by infrared camera (0.5mm/pixel). The captured data is digitised by MATLAB code which gives values of the adiabatic wall temperature and Nusselt number simultaneously. The radiation and convective heat losses are accounted in the heat transfer calculations as given in Eq. (2 - 4). The convective heat transfer rate between the impinging jet and the target plate, qconv, is estimated using Eq. 5. (1)
10 Page 10 of 37
(2) (3) = V×I
(4)
(5)
(6)
The adiabatic wall temperature is in non-dimensional form represented by the recovery factor. The recovery factor is influenced by the dynamic temperature which shows kinetic energy conversion into thermal energy due to the viscous heating as reported by Kim et al. [17].
(7) The dynamic temperature is defined as.
(8)
The loss coefficient (K) is calculated as (9) The typical uncertainties the measurement of heat transfer coefficient, Nusselt number, recovery factor and static pressure drop measurements are around 6.5 % , 8.8%, 3.5% and 2.3%, as evaluated by a method suggested by Moffat [27].
11 Page 11 of 37
4.
Results and discussions:
The influence of nozzle shape, Reynolds number and Mach number on the Nusselt number and recovery factor is investigated for jets issuing from circular nozzles having three different profiles. For compressible subsonic jets Mach number in the range of 0.3 to 0.7 and Reynolds number from 48000 to 120000 are maintained during the experimental study. Figure 3 shows the variation of average Nusselt number with respect to nozzle to plate distances (z/d) for different Reynolds numbers. The average Nusselt number is calculated over an area corresponding to 6d of the test plate. The Nusselt number of contoured nozzle and orifice is lower than that of circular pipe configuration by 3.5 % and 20% for z/d ≤ 4 for a Reynolds number of 48000. However, for z/d ≥ 6, the Nusselt number of contoured nozzle and orifice is lower than that of circular pipe configuration by 9 % and 27% for z/d ≤ 4 for a Reynolds number of 48000. This suggests that the influence of the shape is greater for larger to nozzle to plate distances. Similar observations are seen for Reynolds number of 82000 and 120000. Hence, it may be concluded that the average Nusselt number is higher for pipe nozzle compared to contoured nozzle for all Reynolds number covered in this study. Further, Nusselt number of contoured nozzle is higher than that of orifice for all Reynolds number covered in this study. Figure 4 shows the stagnation point Nusselt number distribution at different z/d for a given Reynolds number for all configurations. The Nusselt distribution is similar to that for average Nusselt number as shown in Fig. 3. Jambunathan et al. [1] reported that orifice jet decays faster than the jet originated from the pipe. Mi et al. [14] reported that the exit turbulence intensity of pipe is greater than that of contoured nozzle and orifice. This explains the higher stagnation point Nusselt number for circular pipe compared to contoured nozzle and orifice. It is also observed that with the increase in the Reynolds number, the nozzle profile becomes
12 Page 12 of 37
insignificant and there is marginal difference in the Nusselt number at the stagnation point among different nozzle shapes. Figure 5 – 8 show the comparison of local Nusselt number and recovery factor distribution over a flat plate for circular pipe, contoured nozzle and orifice at a nozzle to plate distance of 1, 2, 6 and 10 for different Mach numbers. In general, circular pipe results in higher Nusselt number compared to contoured nozzle and orifice. Lower nozzle to plate distances (z/d 2) At z/d = 1, at stagnation point, the difference between Nusselt numbers for pipe nozzle is around 12-15% greater than other two nozzle configurations. Nusselt number distribution has shown that there is marginal difference among different nozzle profiles up to r/d ≤ 2.5. For r/d ≥ 2.5, the Nusselt number distribution is almost same for all nozzle profiles and Reynolds number. At Reynolds number 48000, for lower nozzle to plate distances at z/d =1 (Fig. 5), the local Nusselt number distribution shows that in the stagnation region (r/d ± 1), the Nusselt number remains almost uniform and after that it decreases monotonously for greater radial distances (r/d ≥ 1). No secondary peak is observed for lower z/d unlike incompressible jet as observed by Katti et al. [28]. For Reynolds number 82000 and 120000, the Nusselt number distributions are similar to that of 48000. But, for lower nozzle to plate distance (z/d = 1), the Nusselt number increases in the radial direction up to r/d ~ 2.5 starting from the stagnation point. At around r/d = 2.5 - 3.0, maximum Nusselt number is observed. Similar distribution of Nusselt number is observed for nozzle to plate distance (z/d) of 2. Kim et al. [17] and Goldstein et al. [19] reported that local maxima in heat transfer for z/d ≤ 5 is attributed to the enhancement of heat transfer from entrainment caused by vortex rings in the shear layer. Mi et al. [14], Kim et al. [17] and Goldstein et al. [19] reported that, for
13 Page 13 of 37
compressible jets, vortex rings are formed in the shear layer at the nozzle exit. These vortex rings move along the jet axis and promote entrainment of surrounding air. For smaller nozzle to plate distances (z/d ≤ 2), vortex ring causes sudden acceleration and entrainment in the flow over the plate, and causes increase in the local increase in Nusselt number. This sudden expansion of fluid also can be explained by local pressure distribution over the plate for different nozzle to plate distances as shown in Fig. 9. There is favorable pressure gradient up to radial distance of r/d = 1 – 1.5. The pressure distribution shows that for lower nozzle to plate distance (z/d < 2), the static pressure drops sharply up to around r/d ≈ 1. This coincides with the start of expansion region where acceleration of the fluid results in higher heat transfer rates. Recovery factor distribution (Fig 5 and 6) is identical for all nozzle profiles at a given Reynolds number cases. For low nozzle to plate distances (z/d ≤ 2), recovery factor remains lower than unity (R ≈ 0.9) in the stagnation region (r/d ± 1). From the stagnation point, the recovery factor increases to unity up to 2.5-3 nozzle diameters from stagnation point. In the wall jet region (r/d > 2.5), the recovery factor remains almost uniform. Goldstein et al. [19] reported that the local minima in recovery factor distribution near the stagnation point (r/d ≈ 2) for small z/d is be attributed to energy separation in the presence of the curvature in the streamlines. At small nozzle to plate distances where flow in within the potential core length of the jet, the jet is surrounded by a vortex ring in the shear layer. Due to these vortex rings, energy separation takes place and minimum energy occurs at the center of vortex. This observation coincides with the lowest value of recovery factor measured (for r/d ≈ 1.5 and z/d ≤ 2) in the present results. This is line with the results reported in previous studies [17, 19]. As the radial distance from stagnation point increases, the vortex breaks down and mixing of the surrounding air takes place due to which recovery factor increases.
14 Page 14 of 37
Higher nozzle to plate distances (z/d ≥ 4) Figures 7 and 8 show the Nusselt number and recovery factor distribution for nozzle to plate distances of 6 and 10 respectively. The Nusselt number decreases with the increase in radial distance from the stagnation point at a given nozzle to plate distance and Reynolds number. Maximum Nusselt is observed at the stagnation point and no secondary peak in Nusselt number is observed unlike lower nozzle to plate distances (z/d 2). Nusselt number distribution at z/d = 6 and 10 shows that there is marginal difference (within 10%) among Nusselt number distributions for different nozzle profiles except at z/d = 10 and Re = 48000. The recovery factor is uniform for a given nozzle to plate distance and it is independent of nozzle profile.
The recovery factor is almost independent of Reynolds number. For all
practical purposes, the recovery factor can be taken as unity for all the nozzle profiles, the range of Reynolds number and Mach number covered in this study. This recovery factor being unity can be attributed to viscous heating and adiabatic compression of air. The fluid is brought to rest at stagnation point which leads to adiabatic compression and frictional heating gives rise to temperature. 5.
Correlation for local Nusselt number for compressible air jets:
From the experimental results of heat transfer for impinging compressible jets for three different nozzle profiles, it may be concluded that the nozzle profile has not much influence on the heat transfer distribution for a given z/d (Fig. 5 to 8). Hence, it may be concluded that the Nusselt number for all the nozzle profiles depends on the same parameters like Reynolds number, Mach number, nozzle to plate distance and radial location. The three regions considered are stagnation region (r/d = 0 -1), transition region (r/d = 1- 3.5) and wall jet region (> 3.5). Katti et al. [28] suggested correlation for Nusselt number in all three regions for incompressible jets. The present study focuses on compressible jets i.e., takes into account the effect of Mach number. Hence, the correlations for present compressible jets are 15 Page 15 of 37
suggested as a modification of the correlations suggested by Katti et al. [28] by incorporating the influence of Mach number. (a)
Nusselt number in the stagnation region (r/d = 0 -1)
From the local Nusselt number distribution, it may be concluded that the Nusselt number is uniform in the stagnation region (r/d = 0 - 1) remain same as that at stagnation point. The correlation suggested by Katti et al. [28] for Nusselt number at the stagnation point for incompressible jets is given by (10) The values of a1 are given in Table 2. For compressible jets, Nusselt number can be obtained by modifying the incompressible jet correlation as given by Eq.11. This correlation is obtained by performing curve fitting operation using MATALAB. R2 value for the curve fit is around 0.95.The Nusselt number in the stagnation region for compressible jets is given by Eq.11.
(11) This equation predicts the Nusselt number in the stagnation region within 10% in comparison with the present experimental results as shown in Fig. 10. (b)
Heat transfer in the transition region (1 ≤ r/d ≤ 3.5)
In the transition region, the boundary layer is transiting from laminar to turbulent. For incompressible jets, this region exists from r/d = 1 to r/d = 2.5. But, for compressible jets, this region is observed to extend up to 3.5 nozzle diameters as shown in Figs. 6 - 9. In the transition region, the correlations suggested by Katti et al. [28] for incompressible jets predict the Nusselt number for present compressible jets within 12% as shown in Fig. 11. The correlations proposed by Katti et al. [28] are given by
16 Page 16 of 37
(c)
for z/d ≤ 3
(12)
for z/d ≥ 4
(13)
Heat transfer in the wall jet region (r/d ≥ 3.5)
In the wall jet region, heat transfer decreases with the radial distance from the stagnation point for all nozzle to plate distances. Katti et al. [28] suggested a correlation for heat transfer in the wall jet region as given in Eq. 14, where ‘E’ is the enhancement factor which varies with z/d. This correlation shows good agreement with the present experimental results with minor modifications in the enhancement factor for compressible jets as given in Table 3. Enhancement factor values provided by Katti et al. [28] and values for enhancement factor for compressible jets obtained for present results are shown in Table 3. The heat transfer estimated by Eq. 14 shows good concurrence with the experimental results within 15% as presented in Fig. 12. (14)
Conclusions: Experiments are conducted to investigate the influence of nozzle profile (circular pipe, contoured nozzle and orifice), compressibility (Mach number), Reynolds number and nozzle to plate distance.
The Nusselt number and recovery factor distribution is studied for
Reynolds number ranging from 48000 to 120000, Mach number varying from 0.3 – 0.7 and nozzle to plate distances varying from 1 to 10 with air as the working fluid. The local temperature is measured using thin metal foil technique by employing thermal camera. Following are the conclusions that may be drawn from the present study
17 Page 17 of 37
Average Nusselt number of circular pipe provides slightly higher values for low Reynolds number (Re = 48000). However, average Nusselt number for higher Reynolds number shows marginal difference for different nozzle profiles.
Local Nusselt number distribution is almost insensitive to the nozzle profiles covered in this study for a given nozzle to plate distance, Reynolds number and Mach number.
Recovery factor is as unity for all the configurations covered in this study.
It is concluded that the correlations for local Nusselt number for incompressible jets suggested by Katti and Prabhu [28] are applicable for compressible jets as well except with some modifications involving Mach number as an additional parameter.
The correlations in the transition and wall jet region suggested for incompressible jets by Katti and Prabhu [28] are valid for compressible jets also. This infers that the compressibility has negligible influence on the Nusselt number distribution in the transition and wall jet region. The Nusselt number in the stagnation region for compressible jets is lower compared to the corresponding values for incompressible jets. The decrease is given by 0.97M0.13. Hence, the compressibility is affecting only the stagnation region. In the transition region, correlation for incompressible jets predicts the local heat transfer for compressible jets reasonably well.
Acknowledgements: Authors acknowledge the efforts put in by Mr. Rahul Shirsat in building the experimental setup and fixing the mechanical problems during the course of the experiments.
The first author is thankful to Fluid Power lab, Mechanical Engineering
department, IITB, for allowing him to do experimental work. 18 Page 18 of 37
References: 1. Jambunathan K., Lai E., Moss M.A. and Button B.L., A review of heat transfer data for single circular jet impingement, International Journal of Heat and Fluid Flow (1992), Vol.13, 106–115. 2. Viskanta R., Heat transfer to impinging isothermal gas and flame jets, Experimental Thermal and Fluid Science (1993), Vol.6, 111–134. 3. Colucci D. W. and Viskanta R., Effect of nozzle geometry on local convective heat transfer to a confined impinging air jet, Experimental Thermal and Fluid Science (1996), Vol.13, 71-80. 4. Kanamori A., Hiwada M., Oyakawa K. and Senaha I., Effect of orifice shape on flow behavior and impingement heat transfer, The Open Transport Phenomena Journal (2011), Vol.3, 9-16. 5. Garimella S.V., Nenaydykh B., Nozzle-geometry effects in liquid jet impingement heat transfer, International Journal of Heat and Mass Transfer (1995), Vol.39, 2915 – 2923. 6. Lee J. And Lee S. J., Stagnation region heat transfer of a turbulent axisymmetric jet impingement, Experimental heat transfer (1999), Vol.12, 137 – 156. 7. Lee J., Lee S.J., The effect of nozzle configuration on stagnation region heat transfer enhancement of axisymmetric jet impingement, International Journal of Heat and Mass Transfer (2000), Vol. 43, 3497–3509. 8. Brignoni Luis A. and Garimella Suresh V., Effects of nozzle-inlet chamfering on pressure drop and heat transfer in confined air jet impingement, International Journal of Heat and Mass Transfer (2000), Vol.43, 1133-1139. 9. Attalla M. and Salem M., Effect of nozzle geometry on heat transfer characteristics from a single circular air jet, Applied Thermal Engineering (2013), Vol.51, 723-733.
19 Page 19 of 37
10. Gao N., Sun H. and Ewing D., Heat transfer to impinging round jets with triangular tabs, International Journal of Heat Mass Transfer (2003), Vol.46, 2557–2569. 11. Gardon Robert and Akfirat J. Cahit, The role of turbulence in determining the heattransfer characteristics of impinging jets, International Journal of Heat and Mass Transfer (1965), Vol.8, 1261-1272. 12. Knowles K. and Myszko M., Turbulence measurements in radial wall-jets, Experimental Thermal and Fluid Science (1998), Vol.17, 71-78. 13. Mi J., Xu M., and Zhou T., Reynolds number influence on statistical behaviors of turbulence in a circular free jet, Physics of fluids (2013), Vol.25, 1-30. 14. Mi J., Nathan G. J. and Nobes D. S., Mixing characteristics of axisymmetric free jets from a contoured nozzle, an orifice plate and a pipe, ASME Journal of Fluids Engineering (2001),Vol.123, 878-883. 15. O’Donovan T.S. and Murray D.B., Jet impingement heat transfer—Part I: Mean and rootmean-square heat transfer and velocity distributions, International Journal of Heat and Mass Transfer (2007), Vol.50, 3291–3301. 16. O’Donovan T.S. and D.B. Murray, Jet impingement heat transfer—Part II: A temporal investigation of heat transfer and local fluid velocities, International Journal of Heat and Mass Transfer (2007), Vol.50, 3302–3314. 17. Kim Byung Gi, Yu Man Sun, and Cho Hyung Hee, Recovery temperature measurement of under-expanded sonic jets impinging on a flat plate, Journal of Thermo-physics and Heat Transfer (2003), Vol.17, 313-319. 18. Li De-Yu, Guo Zeng-Yuan and Ma Chong-Fang, Relationship between the recovery factor and the viscous dissipation in a confined, impinging, circular jet of high-Prandtl number liquid, International Journal for Heat and Fluid Flow (1997), Vol.18, 585-590.
20 Page 20 of 37
19. Goldstein R. J., Behbahani A. I. and Kieger Heppelmann K, Stream-wise distribution of the recovery factor and the local heat transfer coefficient to an impinging circular air jet, International Journal for. Heat and Mass Transfer (1986), Vol.29, 1227-1235. 20. Brevet P., Dorignac E. and Vullierme J.J., Mach number effect on jet impingement heat transfer, Annals of the New York Academy of Sciences -Heat Transfer in Gas Turbine Systems (2001), Vol.934, 409–416. 21. Goodro Matt, Park Jongmyung, Ligrani Phil, Fox Mike and Moon Hee-Koo, Effects of Mach number and Reynolds number on jet array impingement heat transfer, International Journal of Heat and Mass Transfer (2007), Vol.50, 367-380. 22. Limaye M.D., Vedula R.P. and Prabhu S.V., Local heat transfer distribution on a flat plate impinged by a compressible round air jet, International Journal of Thermal Sciences (2010), Vol.49, 2157-2168. 23. Gibbings J.C., The combination of a contraction with a supersonic nozzle for a wind tunnel, Ingenieur-Archiv Archive of Applied Mechanics (1966), Vol.35, 269–275. 24. Rahimi M, Owen I, Mistry J., Impingement heat transfer in an under-expanded axisymmetric air jet, International Journal of Heat and Mass Transfer (2003), Vol.46, 263–272. 25. Rohsenow, Warren M., and Harry Y. Choi, Heat, mass, and momentum transfer. Prentice Hall, 1961. 26. Lytle D. and Webb B.W, Air jet impingement heat transfer at low nozzle spacing, International Journal of Heat and Mass Transfer (1994), Vol.37, 1687– 1697. 27. Moffat Robert J., Describing the Uncertainties in Experimental Results, Experimental Thermal and Fluid Science (1988), Vol.1, 3-17. 28. Katti Vadiraj and Prabhu S.V., Experimental study and theoretical analysis of local heat transfer distribution between smooth flat surface and impinging air jet from a circular
21 Page 21 of 37
straight pipe nozzle, International Journal of Thermal Sciences (2008), Vol.51, 44804495. 35.
22 Page 22 of 37
Figure captions: Fig. 1 Schematic of the experimental set-up a.
(1) Air filter (2) Air compressor (3) Air reservoir
(4) Needle valves (5) Air filter
(6) Pressure regulator (7) Venturi (8) U-tube water manometer to measure differential pressure (9) U-tube manometer to measure gage pressure (10) Pipe nozzle (11) Contoured nozzle (12) Orifice (13) Impingement assembly (14) Traverse system (15) Infrared camera (16) Computer b.
(1) Traverse system (2) Pipe (3) Test plate (4) Pressure tap (5) Differential pressure
transducer Fig. 2 Nozzle Configurations a. Contoured nozzle profile b. Orifice c.
Pipe Nozzle
Fig. 3 Comparison of average Nusselt number for different nozzle profiles at various Reynolds number and nozzle to plate distance Fig. 4 Comparison of stagnation point Nusselt number for different nozzle profiles at various Reynolds number and nozzle to plate distance Fig.5 Local Nusselt number and recovery factor distribution for different nozzle profile and Reynolds number at z/d = 1 Fig.6 Local Nusselt number and recovery factor distribution for different nozzle profile and Reynolds number at z/d = 2 Fig. 7 Local Nusselt number and recovery factor distribution for different nozzle profile and Reynolds number at z/d = 6
23 Page 23 of 37
Fig. 8 Local Nusselt number and recovery factor distribution for different nozzle profile and Reynolds number at z/d = 10 Fig. 9 Static pressure distribution over the plate at different nozzle to plate distances Fig. 10 Comparison of local Nusselt number between present experimental results and correlations, a. At stagnation point r/d = 0, b. stagnation region at z/d =1, c. stagnation region at z/d = 8 Fig. 11 Comparison between the present experimental Nusselt number distribution and correlations in the transition region Fig. 12 Comparison between the present experimental Nusselt number distribution and correlations in the wall jet region
Table 1 Details of the pipe nozzles Hydraulic Mach Number Type of nozzle
Shape
diameter (d)
Reynolds number (M)
(mm) 0.29
47900
0.48
81000
0.71
120000
0.29
48500
0.49
83000
0.70
119000
0.30
49600
0.49
82400
Contoured 8.37 nozzle
Orifice
Pipe
8.4
8.0
24 Page 24 of 37
0.70
118000
Table 2 Values of constants a1 for different z/d used in Eq. 10 z/d
1
2
4
6
8
10
a1
1.2
1.32
1.42
1.6
1.63
1.63
Table 3 Enhancement factor for different z/d used in Eq.14 z/d
1
2
4
6
8
10
2.8
2.6
2.4
2.35
2.3
2.3
2.6
2.6
2.4
2.35
2
2
‘E’ From Katti et al. [28] ‘E’ from Present study
25 Page 25 of 37
a.
b. Figure 1
26 Page 26 of 37
Y(mm)
8.37mm
8.4mm
25.4 mm
0
12
25.4 mm
24 36 X(mm)
48
60
a.
b.
8.0mm
25.4mm
l/d = 75
c. Figure 2
27 Page 27 of 37
Figure 3
28 Page 28 of 37
Figure 4
29 Page 29 of 37
Figure 5
30 Page 30 of 37
Figure 6
31 Page 31 of 37
Figure 7
32 Page 32 of 37
Figure 8
33 Page 33 of 37
Contoured Nozzle Re = 82000
Orifice Re = 82000
Pipe Nozzle, Re = 82000 Figure 9
34 Page 34 of 37
Figure 10
35 Page 35 of 37
Figure 11
36 Page 36 of 37
Figure 12
37 Page 37 of 37
S1359-4311(16)30212-5 http://dx.doi.org/doi: 10.1016/j.applthermaleng.2016.02.069 ATE 7798
To appear in:
Applied Thermal Engineering
Received date: Accepted date:
5-11-2015 13-2-2016
Please cite this article as: Ravish Vinze, S. Chandel, M.D. Limaye, S.V. Prabhu, Effect of compressibility and nozzle configuration on heat transfer by impinging air jet over a smooth plate, Applied Thermal Engineering (2016), http://dx.doi.org/doi: 10.1016/j.applthermaleng.2016.02.069. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Effect of compressibility and nozzle configuration on heat transfer by impinging air jet over a smooth plate Ravish Vinze1, S. Chandel2, M.D. Limaye3 and S.V. Prabhu4, a 1, 2
Department of Mechanical Engineering, D.I.A.T. Pune, India 3
4
R & D E (E), DRDO, Pune, India
Department of Mechanical Engineering, I.I.T., Bombay, Mumbai, India 1
[email protected], [email protected]
Address for correspondence a
Dr. S.V.Prabhu,
Professor, Department of Mechanical Engineering, Indian Institute of Technology, Bombay, Powai, Mumbai India Pin: 400 076 Telephone: 91-22-25767515 Fax: 91-22-25726875 E-mail: [email protected]
1 Page 1 of 37
Highlights
Effect of nozzle profile and Mach number on the heat transfer is studied
Correlations for the Nusselt number distribution are suggested
Recovery factor is independent of Re for a given jet to plate distance
Abstract: Jet impingement experiments are conducted to study influence of nozzle profile on heat transfer for compressible subsonic jets. Three different circular profiles namely contoured nozzle, orifice and pipe are selected for the present experimental study. For each nozzle profile, Mach numbers covered are 0.3, 0.5 and 0.7 and the corresponding Reynolds numbers are around 48000, 82000 and 120000. Appropriate diameters for these nozzles are chosen to maintain nearly same Reynolds number. Thin metal foil technique with Infrared red camera is used to measure the heat transfer coefficient and adiabatic wall temperature. Pressure distribution in the stagnation regions is measured for all the cases. Correlations for local heat transfer distribution over the surface are presented in this study. Pipe nozzle provides higher heat transfer coefficient compared to contoured nozzle and orifice. The Mach number affects the heat transfer in the stagnation region. The recovery factor distribution is insensitive to change in Reynolds number. Keywords: Nusselt number, Pressure loss coefficient, Recovery factor, Thermal Imaging, Mach number and Reynolds number Nomenclature A
Exit area of the nozzle, m2
Cp
Specific heat of air at constant pressure, kJ/kg K
c
Velocity of sound, m/sec
d
Hydraulic diameter of the nozzle, m
2 Page 2 of 37
D
Diameter of the supply pipe, m
h
Heat transfer coefficient, W/m2K
I
Current, A
k
Thermal conductivity of the air, W/mK
K
Loss coefficient
l
Length of pipe, m
Nu
Nusselt number,
Nuₒ
Nusselt Number at the stagnation point
Nucomp
Nusselt number for compressible jets
Nuincomp
Nusselt number for incompressible jets
M
Mach number, Mass flow rate, (gm/sec)
p
Perimeter, m
ΔP
Pressure difference, N/m2
Pr
Prandtl number , (Cp/k)
q
Heat transfer rate, W/m2 Heat carried out by convection through impinging jet, W/m2 Heat carried out by convection from back side of plate, W/m2 Total heat supplied, W/m2 Heat loss by radiation and convection from the plate, W/m2 Heat loss by radiation from the back side, W/m2 Heat loss by radiation from the front side, W/m2
R
Recovery Factor, Characteristic gas constant of jet fluid, kJ/kg K
r
Radial distance from the stagnation point, m
3 Page 3 of 37
Re
Reynolds Number,
t
Thickness of orifice plate, m
Tj
Jet static temperature, K
Taw
Adiabatic wall temperature, K
Td
Jet dynamic temperature, K
Tw
Wall temperature, K
T0
Jet total temperature, K
ve
Average velocity of the jet at the nozzle exit, m/sec
V
Voltage, V
z
Nozzle to plate distance, m
Greek Symbols γ
Specific heat ratio
µ
Viscosity of fluid, Pa.s
ρ
Density of fluid, kg/m3
4 Page 4 of 37
1.
Introduction:
Jet impingement is a very extensively used method for efficient heat transfer. This technique is used extensively for various applications like cooling of gas turbine engine components and blades, pre-heating and cooling of metal parts in mills, drying, heating in fabric and paper mills and cooling of electronic components, etc. The jet can be generated from a straight pipe, a profiled nozzle or an orifice depending on the application. The flow structure generated by each of the nozzle configuration is different. This difference in the flow structure causes different local heat transfer distribution on a flat plate impinged by different nozzle configurations. Present study is more intended to bring out the influence of nozzle configuration on the heat transfer so that an engineer can choose an appropriate nozzle for a given application. Studies on impinging air jets are conducted by various authors. In these studies, parameters like nozzle diameter, nozzle shape, Nusselt number, Reynolds number, nozzle to plate spacing (z/d) and turbulence are studied. Majority of this work is concentrated on the study of influence of Reynolds number and jet to plate distance on the local Nusselt number distribution. Jambunathan et al. [1] and Viskanta [2] provide comprehensive review on jet impingement heat transfer. They reported results for Reynolds numbers ranging from 5000124000. The influence of jet diameter, profile of flow device and nozzle to plate distance (z/d) is reported. It is reported that the variation in the turbulence level due to different nozzle shapes affects the shear layer of the jet which in turn affects heat transfer. Colucci and Viskanta [3], Kanamori et al. [4], Garimella and Nenaydykh [5], Lee and Lee [6, 7] reported results on the influence of nozzle geometry on local heat transfer coefficient using various experimental techniques. Experiments are conducted for jets generating from different nozzle configurations (Sharp/standard/square edge orifices, hyperbolic nozzle and pipes) and Reynolds number ranging from 10000 to 50000. From all these studies, it can be concluded 5 Page 5 of 37
heat transfer in influenced more by sharp edge orifice in comparison with a convergent nozzle. The sharp edge orifice greatly influences the velocity profile at the nozzle exit inducing higher rate of turbulence intensities in the jet. This greater rate of turbulence intensity results in higher heat transfer coefficient. Brignoni and Garimella [8], Attalla and Salem [9], Gao et al. [10] studied the effect of nozzle chamfering and triangular tabs on heat transfer (local and average) and axial pressure drop for Reynolds number from 5000 to 40000. Average heat transfer for square edged nozzle is higher compared to chamfered nozzle because chamfered nozzles provide greater pressure drop compared to other nozzle configurations. Triangular tabs increase turbulence in the jet and facilitate entrainment in the jet resulting in increase in heat transfer. Gordon and Akfirat [11], Knowles and Myszko [12] and Mi et al. [13] studied influence of turbulence on the heat transfer for Reynolds number ranging from 4000 to 90000. They carried out measurements for velocity and turbulence in submerged jets and reported that the distribution in turbulence levels caused by jets spreading and centerline velocity decay and mixing plays important role in governing heat transfer rates over the surface. Mi et al. [14] studied mixing characteristics of circular free jet issuing from contoured nozzle, an orifice and a pipe. They measured centerline passive temperature by cold wire probe and visualized flow. The jet velocity measurements are performed by hot wire anemometer. They reported that sharp edged orifice enables greatest amount of mixing with surrounding air, decay rate and widest spreading angle. O’Donovan and Murray [15, 16] reported heat transfer distribution, mean velocity distribution and local velocity distribution in flow field for Reynolds number ranging from 10000 to 30000. In these studies, they demonstrated association of high fluid velocity and turbulence intensity with the rate of heat transfer.
6 Page 6 of 37
Kim et al. [17], Li et al. [18] and Goldstein et al. [19] conducted experimental (thermal imaging and laser-Doppler- velocimetry) and numerical studies for measurement of recovery factor and surface pressure distribution on the flat plate for compressible jets for Reynolds number ranging from 61000 to 124000 (Mach number 0.23-0.47). The interface of shock waves exists in the jet with a stand-off shock before of the impingement surface which relies strongly on the nozzle to plate distance. Consequently, the distribution of pressure and recovery factor over the surface change drastically with nozzle to plate distance (z/d). They reported that the recovery factor does not depend on Reynolds number, but it depends on nozzle to plate distances. Brevet et al. [20], Goodro et al. [21] and Limaye et al. [22] studied the influence of Mach number (compressibility) on the heat transfer distribution of a flata plate impinged by compressible jets. Brevet et al. [20] reported that the influence of Mach number is to be considered in addition to Reynolds number for compressible jets. The Reynolds numbers covered in their study are ranging from 7200 to 71500, Mach number from 0.02 to 0.69. A correlation is proposed for average Nusselt number in terms of Mach number, Reynolds number and the area over which the averaging is carried out. It is concluded that Mach number has negligible influence on heat transfer for M < 0.2. Goodro et al. [21] investigated the effect of jet array on heat transfer for Reynolds number (5600 to 60 000) and Mach number varying from 0.1 to 0.74 respectively. Similar studies are carried out by Limaye et al. [22] for Mach number and Reynolds number ranging from 0.2-1.0 and 41000 -221000 respectively. Review of the literature suggests that there is no correlation reported to predict the Nusselt number and recovery factor distributions for subsonic compressible jets in terms of Reynolds number and Mach number. Further, there is no information available on the influence of nozzle shapes on heat transfer distribution. Hence, the present study focuses on the influence 7 Page 7 of 37
of nozzle profile (countered nozzle, orifice and pipe) on heat transfer of a flat plate impinged by compressible jets. Hence proposed objectives of this study are as follows
To measure the Nusselt number and
recovery factor distribution for countered
nozzle, orifice and pipe for a given Reynolds number and Mach number.
To examine influence of compressibility on the heat transfer in subsonic compressible jets, Mach number is maintained in the range of 0.3 to 0.7 and Reynolds number in the range of 48000 to 120000.
To measure the pressure loss coefficient for different nozzle profiles at various Reynolds numbers and Mach numbers.
To suggest a correlation for Nusselt number as a function of Mach number, Reynolds number, nozzle to plate distance and radial location.
2.
Experimental Setup and Procedure:
The arrangement of the experimental set up used in this study is shown in Fig.1. Centrifugal air compressor (capacity 10bar at 50gm/sec) supplies compressed air, which is then passed through a calibrated venturi flow meter. Upstream to the venturi, air filter and pressure regulator are installed to filter the air and to maintain the downstream pressure as desired. Two needle valves control the mass flow rate. One of the needle valves is on the upstream side and another on the downstream side of the venturi-meter. The temperature of air is measured upstream to the nozzle by calibrated K-type thermocouples. The output of the thermocouples is measured by a ‘Meco’ mill voltmeter. The venturi is calibrated using catch and time method using water as the working fluid. Calibration curve comprising coefficient of discharge variation with Reynolds number is generated and used for air subsequently. Thermocouples are calibrated using constant temperature bath using resistance temperature detector as the reference sensor whose accuracy is of the order of 0.05 C.
8 Page 8 of 37
Figure 2 and Table 1 show the nozzle configurations covered in this study. The diameter of these profiles is selected such that the diameter remains same and hence mass flow rate remains almost same. The shape of contoured nozzle (d = 8.37 mm) with a contraction ratio of 3 is shown in Fig. 2 based on the details of nozzle profile are reported by Gibbings [23] and similar nozzle was used by Rahimi et al. [24]. This profile of the nozzle enables smooth pressure drop across nozzle contraction and uniform velocity profile at the nozzle exit plane. Square edged orifice of 8.4 mm is used in the present study which is fixed at the end of pipe with an orifice plate thickness to pipe diameter ratio (t/D) is 0.2 as used by Lee and Lee [6]. In the experimental setup, the supply pipe length is around 35 times the pipe diameter. The supply pipe length (l/D >10) is sufficient for fully developed turbulent flow as suggested by Rohsenow and Choi [25]. The diameter of pipe is about 8.0 mm for which length to diameter ratio is chosen 75 (l/d) which ensures fully developed flow at nozzle exit. The target made of thin foil of steel (150 mm 130 mm, and 0.06 mm) which is clamped between copper bus bars. 5mm of foil on either side which ensures firm grip. To measure the wall temperature, thermal images are recorded by infrared camera which is positioned at the opposite side of impinging pipe (Fig. 1 and 2). Lesser thickness of the steel foil ensures negligible lateral heat conduction [26]. Hence, the local wall temperature recorded on the surface is considered to be same as that on impinging plane. The surface on which thermal images are captured is painted black using a thick coat of Tempil Pyromark ‘Matt finish’ of high emissivity (0.99). This helps us to achieve higher spatial resolution of temperature compared to thermocouples. The local temperature distribution is recorded by Ti200 infrared camera ‘Thermoteknix’ with a resolution of about 0.5 mm per pixel. A set of step down transformer (220V to 16V) and a variac is used to supply AC Power to the test plate. The voltage and current supplied to the heater are measured by ‘Meco’ digital meters of 0 to 20 ± 0.5% V and 0 to 400 ± 0.5% A, respectively. At suitable position, voltage taps are fixed in 9 Page 9 of 37
each the bus bars. A traverse system is used to set different jet-to-plate distances. Power losses from the exposed surface of the target plate due to natural convection and radiation are measured experimentally and deducted from the supplied power. Pressure drop is measured using three different digital differential pressure transducer (DPT) Rosemont’ make as shown in Fig 1b which are positioned at different r/d locations according to their range. Table 1 shows experimental parameters for different nozzles used to study influence of nozzle shape on heat transfer distribution. For the ease of explanation, the Reynolds number is taken as 48000, 82000 and 120000, although there is 3% variation among the nozzles configurations studied. 3.
Data Reduction:
The Reynolds number and Nusselt number are calculated based on hydraulic diameter (
) as given by Eq. 1 and 6. The nozzle diameter for all the cases is chosen such that
the mass flow rate is maintained almost identical for all the Reynolds numbers as shown Table 1. In order to evaluate the adiabatic wall temperature and the heat transfer coefficient simultaneously, thermal images are captured for six different (including zero flux condition) heat fluxes supplied to the target plate. At each heat flux, five images are captured. Average of these images gives temperature measurement for a heat flux. The resolution of temperature measurement depends upon number of pixel captured by infrared camera (0.5mm/pixel). The captured data is digitised by MATLAB code which gives values of the adiabatic wall temperature and Nusselt number simultaneously. The radiation and convective heat losses are accounted in the heat transfer calculations as given in Eq. (2 - 4). The convective heat transfer rate between the impinging jet and the target plate, qconv, is estimated using Eq. 5. (1)
10 Page 10 of 37
(2) (3) = V×I
(4)
(5)
(6)
The adiabatic wall temperature is in non-dimensional form represented by the recovery factor. The recovery factor is influenced by the dynamic temperature which shows kinetic energy conversion into thermal energy due to the viscous heating as reported by Kim et al. [17].
(7) The dynamic temperature is defined as.
(8)
The loss coefficient (K) is calculated as (9) The typical uncertainties the measurement of heat transfer coefficient, Nusselt number, recovery factor and static pressure drop measurements are around 6.5 % , 8.8%, 3.5% and 2.3%, as evaluated by a method suggested by Moffat [27].
11 Page 11 of 37
4.
Results and discussions:
The influence of nozzle shape, Reynolds number and Mach number on the Nusselt number and recovery factor is investigated for jets issuing from circular nozzles having three different profiles. For compressible subsonic jets Mach number in the range of 0.3 to 0.7 and Reynolds number from 48000 to 120000 are maintained during the experimental study. Figure 3 shows the variation of average Nusselt number with respect to nozzle to plate distances (z/d) for different Reynolds numbers. The average Nusselt number is calculated over an area corresponding to 6d of the test plate. The Nusselt number of contoured nozzle and orifice is lower than that of circular pipe configuration by 3.5 % and 20% for z/d ≤ 4 for a Reynolds number of 48000. However, for z/d ≥ 6, the Nusselt number of contoured nozzle and orifice is lower than that of circular pipe configuration by 9 % and 27% for z/d ≤ 4 for a Reynolds number of 48000. This suggests that the influence of the shape is greater for larger to nozzle to plate distances. Similar observations are seen for Reynolds number of 82000 and 120000. Hence, it may be concluded that the average Nusselt number is higher for pipe nozzle compared to contoured nozzle for all Reynolds number covered in this study. Further, Nusselt number of contoured nozzle is higher than that of orifice for all Reynolds number covered in this study. Figure 4 shows the stagnation point Nusselt number distribution at different z/d for a given Reynolds number for all configurations. The Nusselt distribution is similar to that for average Nusselt number as shown in Fig. 3. Jambunathan et al. [1] reported that orifice jet decays faster than the jet originated from the pipe. Mi et al. [14] reported that the exit turbulence intensity of pipe is greater than that of contoured nozzle and orifice. This explains the higher stagnation point Nusselt number for circular pipe compared to contoured nozzle and orifice. It is also observed that with the increase in the Reynolds number, the nozzle profile becomes
12 Page 12 of 37
insignificant and there is marginal difference in the Nusselt number at the stagnation point among different nozzle shapes. Figure 5 – 8 show the comparison of local Nusselt number and recovery factor distribution over a flat plate for circular pipe, contoured nozzle and orifice at a nozzle to plate distance of 1, 2, 6 and 10 for different Mach numbers. In general, circular pipe results in higher Nusselt number compared to contoured nozzle and orifice. Lower nozzle to plate distances (z/d 2) At z/d = 1, at stagnation point, the difference between Nusselt numbers for pipe nozzle is around 12-15% greater than other two nozzle configurations. Nusselt number distribution has shown that there is marginal difference among different nozzle profiles up to r/d ≤ 2.5. For r/d ≥ 2.5, the Nusselt number distribution is almost same for all nozzle profiles and Reynolds number. At Reynolds number 48000, for lower nozzle to plate distances at z/d =1 (Fig. 5), the local Nusselt number distribution shows that in the stagnation region (r/d ± 1), the Nusselt number remains almost uniform and after that it decreases monotonously for greater radial distances (r/d ≥ 1). No secondary peak is observed for lower z/d unlike incompressible jet as observed by Katti et al. [28]. For Reynolds number 82000 and 120000, the Nusselt number distributions are similar to that of 48000. But, for lower nozzle to plate distance (z/d = 1), the Nusselt number increases in the radial direction up to r/d ~ 2.5 starting from the stagnation point. At around r/d = 2.5 - 3.0, maximum Nusselt number is observed. Similar distribution of Nusselt number is observed for nozzle to plate distance (z/d) of 2. Kim et al. [17] and Goldstein et al. [19] reported that local maxima in heat transfer for z/d ≤ 5 is attributed to the enhancement of heat transfer from entrainment caused by vortex rings in the shear layer. Mi et al. [14], Kim et al. [17] and Goldstein et al. [19] reported that, for
13 Page 13 of 37
compressible jets, vortex rings are formed in the shear layer at the nozzle exit. These vortex rings move along the jet axis and promote entrainment of surrounding air. For smaller nozzle to plate distances (z/d ≤ 2), vortex ring causes sudden acceleration and entrainment in the flow over the plate, and causes increase in the local increase in Nusselt number. This sudden expansion of fluid also can be explained by local pressure distribution over the plate for different nozzle to plate distances as shown in Fig. 9. There is favorable pressure gradient up to radial distance of r/d = 1 – 1.5. The pressure distribution shows that for lower nozzle to plate distance (z/d < 2), the static pressure drops sharply up to around r/d ≈ 1. This coincides with the start of expansion region where acceleration of the fluid results in higher heat transfer rates. Recovery factor distribution (Fig 5 and 6) is identical for all nozzle profiles at a given Reynolds number cases. For low nozzle to plate distances (z/d ≤ 2), recovery factor remains lower than unity (R ≈ 0.9) in the stagnation region (r/d ± 1). From the stagnation point, the recovery factor increases to unity up to 2.5-3 nozzle diameters from stagnation point. In the wall jet region (r/d > 2.5), the recovery factor remains almost uniform. Goldstein et al. [19] reported that the local minima in recovery factor distribution near the stagnation point (r/d ≈ 2) for small z/d is be attributed to energy separation in the presence of the curvature in the streamlines. At small nozzle to plate distances where flow in within the potential core length of the jet, the jet is surrounded by a vortex ring in the shear layer. Due to these vortex rings, energy separation takes place and minimum energy occurs at the center of vortex. This observation coincides with the lowest value of recovery factor measured (for r/d ≈ 1.5 and z/d ≤ 2) in the present results. This is line with the results reported in previous studies [17, 19]. As the radial distance from stagnation point increases, the vortex breaks down and mixing of the surrounding air takes place due to which recovery factor increases.
14 Page 14 of 37
Higher nozzle to plate distances (z/d ≥ 4) Figures 7 and 8 show the Nusselt number and recovery factor distribution for nozzle to plate distances of 6 and 10 respectively. The Nusselt number decreases with the increase in radial distance from the stagnation point at a given nozzle to plate distance and Reynolds number. Maximum Nusselt is observed at the stagnation point and no secondary peak in Nusselt number is observed unlike lower nozzle to plate distances (z/d 2). Nusselt number distribution at z/d = 6 and 10 shows that there is marginal difference (within 10%) among Nusselt number distributions for different nozzle profiles except at z/d = 10 and Re = 48000. The recovery factor is uniform for a given nozzle to plate distance and it is independent of nozzle profile.
The recovery factor is almost independent of Reynolds number. For all
practical purposes, the recovery factor can be taken as unity for all the nozzle profiles, the range of Reynolds number and Mach number covered in this study. This recovery factor being unity can be attributed to viscous heating and adiabatic compression of air. The fluid is brought to rest at stagnation point which leads to adiabatic compression and frictional heating gives rise to temperature. 5.
Correlation for local Nusselt number for compressible air jets:
From the experimental results of heat transfer for impinging compressible jets for three different nozzle profiles, it may be concluded that the nozzle profile has not much influence on the heat transfer distribution for a given z/d (Fig. 5 to 8). Hence, it may be concluded that the Nusselt number for all the nozzle profiles depends on the same parameters like Reynolds number, Mach number, nozzle to plate distance and radial location. The three regions considered are stagnation region (r/d = 0 -1), transition region (r/d = 1- 3.5) and wall jet region (> 3.5). Katti et al. [28] suggested correlation for Nusselt number in all three regions for incompressible jets. The present study focuses on compressible jets i.e., takes into account the effect of Mach number. Hence, the correlations for present compressible jets are 15 Page 15 of 37
suggested as a modification of the correlations suggested by Katti et al. [28] by incorporating the influence of Mach number. (a)
Nusselt number in the stagnation region (r/d = 0 -1)
From the local Nusselt number distribution, it may be concluded that the Nusselt number is uniform in the stagnation region (r/d = 0 - 1) remain same as that at stagnation point. The correlation suggested by Katti et al. [28] for Nusselt number at the stagnation point for incompressible jets is given by (10) The values of a1 are given in Table 2. For compressible jets, Nusselt number can be obtained by modifying the incompressible jet correlation as given by Eq.11. This correlation is obtained by performing curve fitting operation using MATALAB. R2 value for the curve fit is around 0.95.The Nusselt number in the stagnation region for compressible jets is given by Eq.11.
(11) This equation predicts the Nusselt number in the stagnation region within 10% in comparison with the present experimental results as shown in Fig. 10. (b)
Heat transfer in the transition region (1 ≤ r/d ≤ 3.5)
In the transition region, the boundary layer is transiting from laminar to turbulent. For incompressible jets, this region exists from r/d = 1 to r/d = 2.5. But, for compressible jets, this region is observed to extend up to 3.5 nozzle diameters as shown in Figs. 6 - 9. In the transition region, the correlations suggested by Katti et al. [28] for incompressible jets predict the Nusselt number for present compressible jets within 12% as shown in Fig. 11. The correlations proposed by Katti et al. [28] are given by
16 Page 16 of 37
(c)
for z/d ≤ 3
(12)
for z/d ≥ 4
(13)
Heat transfer in the wall jet region (r/d ≥ 3.5)
In the wall jet region, heat transfer decreases with the radial distance from the stagnation point for all nozzle to plate distances. Katti et al. [28] suggested a correlation for heat transfer in the wall jet region as given in Eq. 14, where ‘E’ is the enhancement factor which varies with z/d. This correlation shows good agreement with the present experimental results with minor modifications in the enhancement factor for compressible jets as given in Table 3. Enhancement factor values provided by Katti et al. [28] and values for enhancement factor for compressible jets obtained for present results are shown in Table 3. The heat transfer estimated by Eq. 14 shows good concurrence with the experimental results within 15% as presented in Fig. 12. (14)
Conclusions: Experiments are conducted to investigate the influence of nozzle profile (circular pipe, contoured nozzle and orifice), compressibility (Mach number), Reynolds number and nozzle to plate distance.
The Nusselt number and recovery factor distribution is studied for
Reynolds number ranging from 48000 to 120000, Mach number varying from 0.3 – 0.7 and nozzle to plate distances varying from 1 to 10 with air as the working fluid. The local temperature is measured using thin metal foil technique by employing thermal camera. Following are the conclusions that may be drawn from the present study
17 Page 17 of 37
Average Nusselt number of circular pipe provides slightly higher values for low Reynolds number (Re = 48000). However, average Nusselt number for higher Reynolds number shows marginal difference for different nozzle profiles.
Local Nusselt number distribution is almost insensitive to the nozzle profiles covered in this study for a given nozzle to plate distance, Reynolds number and Mach number.
Recovery factor is as unity for all the configurations covered in this study.
It is concluded that the correlations for local Nusselt number for incompressible jets suggested by Katti and Prabhu [28] are applicable for compressible jets as well except with some modifications involving Mach number as an additional parameter.
The correlations in the transition and wall jet region suggested for incompressible jets by Katti and Prabhu [28] are valid for compressible jets also. This infers that the compressibility has negligible influence on the Nusselt number distribution in the transition and wall jet region. The Nusselt number in the stagnation region for compressible jets is lower compared to the corresponding values for incompressible jets. The decrease is given by 0.97M0.13. Hence, the compressibility is affecting only the stagnation region. In the transition region, correlation for incompressible jets predicts the local heat transfer for compressible jets reasonably well.
Acknowledgements: Authors acknowledge the efforts put in by Mr. Rahul Shirsat in building the experimental setup and fixing the mechanical problems during the course of the experiments.
The first author is thankful to Fluid Power lab, Mechanical Engineering
department, IITB, for allowing him to do experimental work. 18 Page 18 of 37
References: 1. Jambunathan K., Lai E., Moss M.A. and Button B.L., A review of heat transfer data for single circular jet impingement, International Journal of Heat and Fluid Flow (1992), Vol.13, 106–115. 2. Viskanta R., Heat transfer to impinging isothermal gas and flame jets, Experimental Thermal and Fluid Science (1993), Vol.6, 111–134. 3. Colucci D. W. and Viskanta R., Effect of nozzle geometry on local convective heat transfer to a confined impinging air jet, Experimental Thermal and Fluid Science (1996), Vol.13, 71-80. 4. Kanamori A., Hiwada M., Oyakawa K. and Senaha I., Effect of orifice shape on flow behavior and impingement heat transfer, The Open Transport Phenomena Journal (2011), Vol.3, 9-16. 5. Garimella S.V., Nenaydykh B., Nozzle-geometry effects in liquid jet impingement heat transfer, International Journal of Heat and Mass Transfer (1995), Vol.39, 2915 – 2923. 6. Lee J. And Lee S. J., Stagnation region heat transfer of a turbulent axisymmetric jet impingement, Experimental heat transfer (1999), Vol.12, 137 – 156. 7. Lee J., Lee S.J., The effect of nozzle configuration on stagnation region heat transfer enhancement of axisymmetric jet impingement, International Journal of Heat and Mass Transfer (2000), Vol. 43, 3497–3509. 8. Brignoni Luis A. and Garimella Suresh V., Effects of nozzle-inlet chamfering on pressure drop and heat transfer in confined air jet impingement, International Journal of Heat and Mass Transfer (2000), Vol.43, 1133-1139. 9. Attalla M. and Salem M., Effect of nozzle geometry on heat transfer characteristics from a single circular air jet, Applied Thermal Engineering (2013), Vol.51, 723-733.
19 Page 19 of 37
10. Gao N., Sun H. and Ewing D., Heat transfer to impinging round jets with triangular tabs, International Journal of Heat Mass Transfer (2003), Vol.46, 2557–2569. 11. Gardon Robert and Akfirat J. Cahit, The role of turbulence in determining the heattransfer characteristics of impinging jets, International Journal of Heat and Mass Transfer (1965), Vol.8, 1261-1272. 12. Knowles K. and Myszko M., Turbulence measurements in radial wall-jets, Experimental Thermal and Fluid Science (1998), Vol.17, 71-78. 13. Mi J., Xu M., and Zhou T., Reynolds number influence on statistical behaviors of turbulence in a circular free jet, Physics of fluids (2013), Vol.25, 1-30. 14. Mi J., Nathan G. J. and Nobes D. S., Mixing characteristics of axisymmetric free jets from a contoured nozzle, an orifice plate and a pipe, ASME Journal of Fluids Engineering (2001),Vol.123, 878-883. 15. O’Donovan T.S. and Murray D.B., Jet impingement heat transfer—Part I: Mean and rootmean-square heat transfer and velocity distributions, International Journal of Heat and Mass Transfer (2007), Vol.50, 3291–3301. 16. O’Donovan T.S. and D.B. Murray, Jet impingement heat transfer—Part II: A temporal investigation of heat transfer and local fluid velocities, International Journal of Heat and Mass Transfer (2007), Vol.50, 3302–3314. 17. Kim Byung Gi, Yu Man Sun, and Cho Hyung Hee, Recovery temperature measurement of under-expanded sonic jets impinging on a flat plate, Journal of Thermo-physics and Heat Transfer (2003), Vol.17, 313-319. 18. Li De-Yu, Guo Zeng-Yuan and Ma Chong-Fang, Relationship between the recovery factor and the viscous dissipation in a confined, impinging, circular jet of high-Prandtl number liquid, International Journal for Heat and Fluid Flow (1997), Vol.18, 585-590.
20 Page 20 of 37
19. Goldstein R. J., Behbahani A. I. and Kieger Heppelmann K, Stream-wise distribution of the recovery factor and the local heat transfer coefficient to an impinging circular air jet, International Journal for. Heat and Mass Transfer (1986), Vol.29, 1227-1235. 20. Brevet P., Dorignac E. and Vullierme J.J., Mach number effect on jet impingement heat transfer, Annals of the New York Academy of Sciences -Heat Transfer in Gas Turbine Systems (2001), Vol.934, 409–416. 21. Goodro Matt, Park Jongmyung, Ligrani Phil, Fox Mike and Moon Hee-Koo, Effects of Mach number and Reynolds number on jet array impingement heat transfer, International Journal of Heat and Mass Transfer (2007), Vol.50, 367-380. 22. Limaye M.D., Vedula R.P. and Prabhu S.V., Local heat transfer distribution on a flat plate impinged by a compressible round air jet, International Journal of Thermal Sciences (2010), Vol.49, 2157-2168. 23. Gibbings J.C., The combination of a contraction with a supersonic nozzle for a wind tunnel, Ingenieur-Archiv Archive of Applied Mechanics (1966), Vol.35, 269–275. 24. Rahimi M, Owen I, Mistry J., Impingement heat transfer in an under-expanded axisymmetric air jet, International Journal of Heat and Mass Transfer (2003), Vol.46, 263–272. 25. Rohsenow, Warren M., and Harry Y. Choi, Heat, mass, and momentum transfer. Prentice Hall, 1961. 26. Lytle D. and Webb B.W, Air jet impingement heat transfer at low nozzle spacing, International Journal of Heat and Mass Transfer (1994), Vol.37, 1687– 1697. 27. Moffat Robert J., Describing the Uncertainties in Experimental Results, Experimental Thermal and Fluid Science (1988), Vol.1, 3-17. 28. Katti Vadiraj and Prabhu S.V., Experimental study and theoretical analysis of local heat transfer distribution between smooth flat surface and impinging air jet from a circular
21 Page 21 of 37
straight pipe nozzle, International Journal of Thermal Sciences (2008), Vol.51, 44804495. 35.
22 Page 22 of 37
Figure captions: Fig. 1 Schematic of the experimental set-up a.
(1) Air filter (2) Air compressor (3) Air reservoir
(4) Needle valves (5) Air filter
(6) Pressure regulator (7) Venturi (8) U-tube water manometer to measure differential pressure (9) U-tube manometer to measure gage pressure (10) Pipe nozzle (11) Contoured nozzle (12) Orifice (13) Impingement assembly (14) Traverse system (15) Infrared camera (16) Computer b.
(1) Traverse system (2) Pipe (3) Test plate (4) Pressure tap (5) Differential pressure
transducer Fig. 2 Nozzle Configurations a. Contoured nozzle profile b. Orifice c.
Pipe Nozzle
Fig. 3 Comparison of average Nusselt number for different nozzle profiles at various Reynolds number and nozzle to plate distance Fig. 4 Comparison of stagnation point Nusselt number for different nozzle profiles at various Reynolds number and nozzle to plate distance Fig.5 Local Nusselt number and recovery factor distribution for different nozzle profile and Reynolds number at z/d = 1 Fig.6 Local Nusselt number and recovery factor distribution for different nozzle profile and Reynolds number at z/d = 2 Fig. 7 Local Nusselt number and recovery factor distribution for different nozzle profile and Reynolds number at z/d = 6
23 Page 23 of 37
Fig. 8 Local Nusselt number and recovery factor distribution for different nozzle profile and Reynolds number at z/d = 10 Fig. 9 Static pressure distribution over the plate at different nozzle to plate distances Fig. 10 Comparison of local Nusselt number between present experimental results and correlations, a. At stagnation point r/d = 0, b. stagnation region at z/d =1, c. stagnation region at z/d = 8 Fig. 11 Comparison between the present experimental Nusselt number distribution and correlations in the transition region Fig. 12 Comparison between the present experimental Nusselt number distribution and correlations in the wall jet region
Table 1 Details of the pipe nozzles Hydraulic Mach Number Type of nozzle
Shape
diameter (d)
Reynolds number (M)
(mm) 0.29
47900
0.48
81000
0.71
120000
0.29
48500
0.49
83000
0.70
119000
0.30
49600
0.49
82400
Contoured 8.37 nozzle
Orifice
Pipe
8.4
8.0
24 Page 24 of 37
0.70
118000
Table 2 Values of constants a1 for different z/d used in Eq. 10 z/d
1
2
4
6
8
10
a1
1.2
1.32
1.42
1.6
1.63
1.63
Table 3 Enhancement factor for different z/d used in Eq.14 z/d
1
2
4
6
8
10
2.8
2.6
2.4
2.35
2.3
2.3
2.6
2.6
2.4
2.35
2
2
‘E’ From Katti et al. [28] ‘E’ from Present study
25 Page 25 of 37
a.
b. Figure 1
26 Page 26 of 37
Y(mm)
8.37mm
8.4mm
25.4 mm
0
12
25.4 mm
24 36 X(mm)
48
60
a.
b.
8.0mm
25.4mm
l/d = 75
c. Figure 2
27 Page 27 of 37
Figure 3
28 Page 28 of 37
Figure 4
29 Page 29 of 37
Figure 5
30 Page 30 of 37
Figure 6
31 Page 31 of 37
Figure 7
32 Page 32 of 37
Figure 8
33 Page 33 of 37
Contoured Nozzle Re = 82000
Orifice Re = 82000
Pipe Nozzle, Re = 82000 Figure 9
34 Page 34 of 37
Figure 10
35 Page 35 of 37
Figure 11
36 Page 36 of 37
Figure 12
37 Page 37 of 37