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Heat transfer distribution of swirling flame jet impinging on a flat plate using twisted tapes
International Journal of Heat and Mass Transfer 91 (2015) 1128–1139
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Heat transfer distribution of swirling flame jet impinging on a flat plate using twisted tapes Vijaykumar Hindasageri, Rajendra P. Vedula, Siddini V. Prabhu ⇑ Department of Mechanical Engineering, Indian Institute of Technology, Bombay, India
a r t i c l e
i n f o
Article history: Received 14 October 2014 Received in revised form 24 July 2015 Accepted 14 August 2015
Keywords: Swirling flame jet Tube burner Twisted tape Infrared thermography Heat flux distribution
a b s t r a c t Impinging flame jets have wide applications in industrial and domestic heating purpose. The aim of the present study is to study the effect of swirl on flame jet impingement heat transfer characteristics. Four twisted tapes of twist ratios 2, 3.2, 4.5 and 7.5 (corresponding swirl numbers of 0.79, 0.49, 0.35 and 0.21) are used to experimentally obtain the swirling flame jet. The effect of twist ratio at Reynolds number varying from 500 to 2500 and equivalence ratio varying from 0.7 to 1.5 for burner tip to impingement plate distances of 2 and 4 is studied. The effect of swirl is compared with that of no tape in the tube burner by estimating the average heat flux distribution and coefficient of variation of heat flux for two impingement regions – within two times the burner diameter from the stagnation point and four times diameter from the stagnation point. From the experimental study, it is found that swirl enhances the heat flux distribution by 40–140% at low Reynolds number. At higher Reynolds number the effect of swirl is negative and is found to decrease the average heat flux distribution by 10–40%. Ó 2015 Elsevier Ltd. All rights reserved.
1. Introduction Heat transfer by flame jet impingement is extensively used in several industrial and domestic applications like melting of metal billets in a closed heating furnace, glass processing, domestic gas geysers and others. Reviews by Viskanta [1], Baukal and Gebhart [2,3] and Chander and Ray [4] give substantial information of the flame jet impingement studies. Extensive studies are reported in the literature on impinging flame jets. Chander and Ray [5] have experimentally studied the heat transfer distribution for impingement with tube burner, orifice and nozzle. They have further carried out numerical simulation using CFD software to explain the shift in peak heat flux from the stagnation point for low Reynolds number [6]. They attributed the influence of axial velocity to the shift in peak heat flux away from stagnation point. Zhao et al. [7] have studied the effect of impingement plate material on the heat transfer characteristics of impinging flame jet. Dong et al. [8] have studied the heat transfer distribution for impingement with a pair of rectangular burners. Chander and Ray [9] have studied the heat transfer distribution of three interacting flames impinging on a flat
⇑ Corresponding author at: Department of Mechanical Engineering, Indian Institute of Technology, Bombay, Powai, Mumbai 400 076, India. Tel.: +91 22 25767515; fax: +91 22 2572 6875, 2572 3480. E-mail addresses: [email protected] (V. Hindasageri), rpv@me. iitb.ac.in (R.P. Vedula), [email protected] (S.V. Prabhu). http://dx.doi.org/10.1016/j.ijheatmasstransfer.2015.08.038 0017-9310/Ó 2015 Elsevier Ltd. All rights reserved.
plate. Remie et al. [10,11] have arrived at analytical expressions for heat flux distribution from methane–oxygen flame impinging on a flat plate. Little information is available on heat transfer by swirling flame jets in literature [12–15]. Swirl is found to improve the heat transfer distribution at small distances of the burner tip from the impingement plate [12–15]. However, the uniformity of heat transfer distribution is not reported properly and the test cases reported are very limited. The heat flux distribution for swirling jets would have high spatial variation and hence the technique of measurement of heat flux should have high resolution. The heat flux sensor and calorimetric method used in most of the work reported in literature does not provide sufficient resolution. While the resolution of the heat flux sensor is limited by their diameters which are of the order of 5 mm, the calorimetric technique gives average of heat flux data of the entire heated surface. Inverse heat conduction (IHCP) technique using numerical method of estimating the heat flux also lacks sufficient resolution due to the requirement of high computational memory and time [16,17]. IHCP solution using appropriate analytical solution requires less computational time. The known analytical solution is directly applied to find the unknown parameter (usually boundary condition) of the problem with simple iterative methods as presented in our previous work [18]. Swirl is generated by the following methods: (i) Tangential entry of fluid, (ii) Vaned rotor or stator, (iii) Rotating the burner and (iv) Twisted tape.
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Nomenclature Symbol d k r Lf M Nu q00 Re t T TR u X p w x, y z Z
l q
Meaning tube diameter (mm) thermal conductivity (W/m K) arbitrary radius (m) flame height (m) molecular weight (g/mol) Nusselt number heat flux (W/m2) Reynolds number time (sec) temperature (K) twist ratio average velocity of fuel–air mixture (m/s) mole fraction twisted tape pitch (mm) twisted tape width (mm) coordinate axis burner tip to target plate distance (mm) quartz plate thickness (mm)
/
absolute viscosity (Pa-s) density (kg/m3) equivalence ratio
Subscripts/Superscripts m mixture adf adiabatic flame aw adiabatic wall i initial – average value 1 ambient condition Abbreviations CFD computational fluid dynamics COV coefficient of variance IHCP inverse heat conduction problem FOV field of view MC methane cylinder MFC mass flow controller MT mixing tube RSS root sum of squares TC thermal camera FCRI fluid control research of India
Greek symbols a thermal diffusivity (m/s2) rstd standard deviation g effectiveness
In the present work, twisted tapes are used to obtain swirl. Twisted tapes are very easy to fabricate and can be twisted to different twist ratios to obtain the desired swirl [19]. Swirling air jets using twisted tape are found to enhance heat transfer by 20–30% [20,21] at low z/d and high Re. Swirling air jets with twisted tapes are also found to give more uniform distribution of heat flux as compared to non-swirling air jets [20,21]. The structure of the non-impinging swirling flame jets is presented in detail by Syred and Beer [22]. However, limited information of flame structure for impinging condition of swirling flame jets is also available in literature [23].
In the present work, the heat flux is estimated by the assumption of semi-infinite medium concept for the impingement plate [18]. The heat flux distribution is presented for Reynolds number (Re) = 500–2500, impingement plate to burner tip distance (z/d) = 2 and 4 and equivalence ratio (/) = 0.6–1.5. Following are the objectives of the present work: (i) To obtain high resolution heat flux distribution of swirling flame jets by using twisted tapes of different twist ratios.
Desktop Computer TC Compressed Air Tank
Air MFC
z MT
y x Quartz Plate
Burner MC
Methane MFC
MC - Methane Cylinder
MFC - Mass flow controller
MT - Mixing Tube
TC - Thermal infrared camera
x, y - Coordinates parallel to the quartz plate
z - Coordinate perpendicular to the quartz plate
Fig. 1. Schematic of the experimental setup.
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Table 1 Specifications of the thermal camera used in the present study.
Table 2 Flame heights (Lf) for varying Re, TR and /.
Model
VisIRÒ Ti 200
Detector Spectral range Pixel resolution FOV (field of view) Minimum focus distance Temperature range Accuracy Frames per second
Microbolometer Uncooled FPA 7.5–13 lm 320 240 25 19 0.3 m 20–1200 °C ±2% of reading 25
(ii) To compare the average heat flux and uniformity (through coefficient of variance (COV)) distribution over a certain area on the impingement plate of swirling flame jets with that of non-swirling (no tape in the tube burner) flame jets. (iii) To obtain the Nusselt number and effectiveness distribution by the proper estimation of adiabatic wall temperature using analytical–numerical method [18]. 2. Experimental technique 2.1. Flow control and instrumentation Fig. 1 is the schematic of the experimental set-up used in the present study. Mass Flow controllers (MFC) of accuracy 1.5% of full
Re
TR
/
Lf (mm)
500 1000 1000 1000 1000 1500 1500 1500 1500 2500
4.5 2 2 2 2 2 3.2 4.5 7.5 4.5
1 0.8 1.1 1.3 1.5 1 1 1 1 1
9.5 15.2 15.4 32.3 41.6 17.5 18.5 20.5 22.3 33
scale are used to meter the flow of methane gas (99.5% purity) and air from compressed air storage tank. The mass flow controllers used are of Aalborg make, USA. The air mass flow controller is calibrated with DryCal (DCLITE H) calibrator, BIOS International make whose accuracy is 1% of the reading traceable to NIST standards. The methane mass flow controller is calibrated by Soap bubble meter of PCI Analytics make, India whose accuracy is 2% of reading traceable to FCRI standards, India. Methane and air are mixed in a mixing tube. The accuracy of the flow metering is further validated by the measurement of the burning velocity [24].
y x
z w=d
p
Fig. 2. Photographs of the twisted tapes used in present study along with the schematic diagram of twisted tape of one full twist.
TR = 2
TR = 3.2
TR = 4.5
Fig. 3. Flame shapes for varying TR at z/d = 4 and Re = 1500.
TR = 7.5
V. Hindasageri et al. / International Journal of Heat and Mass Transfer 91 (2015) 1128–1139
No tape
Twist ratio = 4.5
Re = 500
Re = 1500
Re = 2500
Fig. 4. Flame shapes for varying Re at z/d = 4 and TR = 4.5.
No tape
Twist ratio = 2 = 0.8
= 1.1
= 1.3
Fig. 5. Flame shapes for varying / at z/d = 4 and Re = 1000.
= 1.5
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2.2. Impingement plate and temperature recording The impingement plate is made of quartz whose size is 150 150 mm. The quartz plate thickness is 3 mm. The emissivity of the quartz plate reported in the literature is 0.93 [25]. The temperature distribution of the quartz plate is measured by the use of thermal infrared camera (Thermoteknix make VisIRÒ Ti 200). Specifications of this camera are given in Table 1. This camera is calibrated with a black body calibrator of TEMPSENS Make, CALsys 1500BB model. The accuracy of curve fit expression from calibration is 2% of reading. 2.3. Details of the twisted tape In the present work, 4 twisted tapes of twist ratio (TR) = 2, 3.2, 4.5 and 7.5 (corresponding swirl numbers of 0.79, 0.49, 0.35 and 0.21) are used to obtain the swirling flame jet. The photographs
of the twisted tapes used in the present study are shown in Fig. 2 along with the schematic diagram of the twisted tape of one full twist. The width of the tapes is 11 mm while the tube burner inside diameter is 11.5 mm and length is 60 mm. These twisted tapes are made from brass tape of 1 mm thickness by the procedure mentioned by Saha et al. [19]. The advantage of brass material is that it does not untwist after removing from the holding device used to twist the tape. Brass material has further advantage of being more ductile as compared to Stainless steel and hence the twisting is more uniform. The swirl number is defined by Gupta et al. [26] as the ratio of axial flux of angular momentum to the axial flux of axial momentum. The twist ratio (TR) is defined as the ratio of pitch (p) of the twisted tape to its width (w). Pitch (p) for a twisted tape is defined as the axial distance between two points on the twisted tape corresponding to the 180° rotation of the twisted tape. The swirl number is related to the twist ratio by the Eq. (1).
Fig. 6. Contours of heat flux (kW/m2) distribution for different TR at Re = 1500, / = 1 and z/d = 4.
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S
p
ð1Þ
2ðTRÞ
2.4. Data reduction The viscosity is calculated from Eq. (2) and the mixture Reynolds number (Re) is calculated from Eq. (3).
P
pffiffiffiffiffiffi
lj X j M j
lm ¼ P pffiffiffiffiffiffi
ð2Þ
qm um d lm
ð3Þ
Xj
Re ¼
Mj
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The heat flux distribution for flame jet (q00 ) is estimated by knowing the transient temperature at a given depth (Z) in a semi-infinite medium [18]. The temperature distribution, T (Z, t) with time (t) at a given depth in a semi-infinite medium for a constant heat flux (q00 ) is given by Eq. (4).
TðZ; tÞ T i ¼
2q00
! pffiffiffiffiffiffiffiffiffiffiffi at=p Z 2 q00 Z Z exp erfc pffiffiffiffiffi k k 4at 2 at
ð4Þ
The temperature distribution on the back side of the quartz plate is recorded using the infrared thermal camera. This recorded temperature T (Z, t) is then matched with that of Eq. (4) at different time intervals, for short time, by varying the heat flux value (q00 ) such that the square root of the sum of squares, qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Pn 2 RSS ¼ i¼1 ðT analytical T experimental Þ is minimum.
Fig. 7. Contours of heat flux (kW/m2) distribution for different Re at TR = 4.5, / = 1 and z/d = 4.
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The evaluation of heat transfer coefficient requires the data of adiabatic wall temperature (Taw) as given by Eq. (5) and therefore Taw has to be determined separately.
q00 ¼ hðT aw T w Þ
ð5Þ
An analytical–numerical method proposed in our previous work is used to estimate Taw [18]. Nusselt number is calculated using Eq. (6) with the thermal conductivity of the flame taken at adiabatic wall temperatures using CEA software developed by NASA [27].
Nu ¼
hd k
ð6Þ 3. Results and discussion
Effectiveness for the flame impingement process is given by Eq. (7).
T T1 g ¼ aw T adf T 1
The adiabatic flame temperature (Tadf) for stoichiometric mixture of methane air premixed flame is taken as 2200 K and the ambient temperature is taken as 300 K. The uncertainties in the measured parameters are estimated by the method of Moffat [28]. The uncertainties in equivalence ratio and Reynolds number is 10% while that in the temperature measured from thermal camera and estimated heat flux are 2% and 12% respectively. The uncertainties in the Nusselt number and effectiveness are 15% and 5% respectively.
ð7Þ
The heat flux distribution is presented for Re = 500–2500, z/d = 2 and 4 for / = 0.8–1.5. A comparison of burners with tapes of different twist ratios is made with the burner without tape.
Fig. 8. Contours of heat flux (kW/m2) distribution for different / for TR = 2 and no tape at z/d = 4 and Re = 1000.
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Fig. 9. Enhancement in averaged heat flux with different twist ratios of twisted tape in tube burner as compared with no tape in tube burner for varying Re at / = 1.
Fig. 10. Enhancement in COV with different twist ratios of twisted tape in tube burner as compared with no tape in tube burner for varying Re at / = 1.
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3.1. Flame shape study The photographs of the flame shapes at Re = 1500 and / = 1 at z/ d = 4 for varying twist ratios (TR) is shown in Fig. 3. The maximum flame length for different Re, TR and / as shown in photographs of Figs. 3–5 is given in Table 2. The effect of swirl is clearly visible in Fig. 3, the unburnt flame height is longer for higher TR (lower swirl) as compared to that with lesser TR (higher swirl). The presence of twisted tape results in splitting of the inner premixed cone into multiple distinct segments. The photographs of the flame shapes at Re = 500, 1500 and 2500 for / = 1 at z/d = 4 are shown in Fig. 4. With the increase in Re, the size of unburnt (premixed) part of the flame along the tube axis increases as shown in Fig. 4. The photographs of the flame shapes at Re = 1000 and varying / at z/d = 4 for no tape and TR = 2 are shown in Fig. 5. The flame tip is closer to the impingement plate for higher / for no tape and with a twisted tape of TR = 2. The presence of the twisted tape results in shortening of the flame height and results in spreading in radial direction for all the cases presented in the present study.
The contour plots for varying Re, / = 1, z/d = 4 and TR = 4.5 is shown in Fig. 7. With the increase in Re, the unburnt (premixed) part of the flame approaches closer to the impingement plate and hence the flame temperature near the impingement plate is also higher. Therefore, the heat fluxes are higher for higher Re. The contour plots for varying /, Re = 1000, z/d = 4 and TR = 2 and no tape is shown in Fig. 8. With the increase or decrease of fuel fraction from the stoichiometric condition the length of the inner premixed cone of the flame increases. Hence, the reaction zone of the flame where temperature is highest is closer to the impingement plate and will result in higher heat transfer rate if the premixed (unburnt) part of the flame does not touch the impingement plate. For no tape case, the inner premixed cone of the flame has touched the impingement plate for / = 1.3 and 1.5. Hence, the heat flux is lower at the stagnation point for / = 1.3 and 1.5. For TR = 2, the unburnt (premixed) part does not touch the impingement plate for all /. This is because swirl results in splitting of the inner premixed part of the flame into segments. Two distinct lobes are produced on the impingement plate at / = 1.5. This is not observed for / = 0.8 and 1.1 because the reaction zone is relatively far away from the impingement plate.
3.2. Heat flux contour maps The contour plots of heat flux for varying TR at Re = 1500, / = 1 and z/d = 4 is shown in Fig. 6. Two distinct lobes are observed which are formed due to the splitting of the unburnt (premixed) part of the flame into two segments. For higher TR (lower swirl), the unburnt (premixed) part of the flame is closer to the impingement plate and hence the temperature of the flame near the impingement plate is also higher. Lower swirl also means that the axial component of velocity is relatively higher as compared to higher swirl. These two factors are responsible for higher heat flux distribution on the impingement plate for lower swirl.
3.3. Comparison of average heat flux and uniformity (COV) distribution of burner with twisted tape inserted and twisted tape removed The performance of the swirling flame jet impingement is compared with that of no swirl (no twisted tape in tube burner). The 00 ) and the coefficomparison is made for the average heat flux (q cient of variation defined by Eqs. (8)–(10).
00 ¼ q
PN
00 i¼1 qi
N
ð8Þ
Fig. 11. Enhancement in averaged heat flux and COV with different twist ratios of twisted tape in tube burner as compared with no tape in tube burner for Re = 1000 and varying /.
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COV ¼
rstd ¼
rstd
ð9Þ
00 q
PN
00 Þ2 q N1
00 i¼1 ðqi
ð10Þ
N is the total number of data points. The average heat flux and the coefficient of variation (COV) are compared for two regions: (i) 0 < r/ d < 2 and (ii) 0 < r/d < 4. The enhancement factor, E for average heat flux and COV are defined in Eqs. (11) and (12).
q00 with twisted tape Eq00 ¼ 00 q no twisted tape ECOV ¼
COV with twisted tape COV no twisted tape
ð11Þ
ð12Þ
Eq00 > 1 means higher (preferable) heat flux distribution with tape and ECOV < 1 means more uniform heat flux distribution with twisted tape as compared to that of tube without tape. Figs. 9 and 10 are the comparison of enhancement in average heat flux and COV, respectively, of burners with twisted tapes as compared to no twisted tape in the burner. 3.3.1. Effect of Reynolds number 3.3.1.1. Average heat flux distribution. There is an enhancement of 20–50% in average heat flux for 0 < r/d < 2 and 40–130% for 0 < r/ d < 4 at z/d = 2 for Re = 500 as shown in Fig. 9 (a) and (b).
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It is further observed from Fig. 9 (a) and (b) that higher twist ratio (TR) results in higher heat flux at z/d = 2 for Re = 500. The reason for this the location of the reaction zone of the premixed part of the flame. Higher twist ratio have flame whose reaction zone is relatively closer to the impingement plate and hence higher heat flux. At other Reynolds numbers for z/d = 2, there is reduction in the average heat flux distribution by 0–40% as shown in Fig. 9 (a) and (b). The reason for lesser enhancement in heat flux at higher Re is again the location of the reaction zone of the premixed part of the flame. For Re = 1000–2500 at z/d = 2, the reaction zone of the premixed part of the flame without twisted tape is much closer to the impingement plate as compared to with twisted tape. Also, there is a considerable loss of axial momentum of the jet in case of tubes with twisted tapes due to swirling component that is partly obtained from the axial momentum. At z/d = 4, the enhancement in heat flux is 40–60% at Re = 1000 for 0 < r/d < 2 as shown in Fig. 9c. At Re = 500 and z/d = 4 there is an increase in Eq00 for TR = 2 and 3.2 but a reduction in Eq00 for TR = 4.5 as shown in Fig. 9c. For higher Re, the enhancement in heat flux decreases which is again because of the influence of the reaction zone of the premixed part of the flame. At z/d = 4 and the region 0 < r/d < 4, lower twist ratios of 2 and 3.2 result in an enhancement of 0–40% for Re = 500–1500 and a reduction of 0–20% for Re = 2000 and 2500 as shown in Fig. 9 (c) and (d). At z/d = 4 and the region 0 < r/d < 4, higher twist ratios of 4.5 and 7.5 result in lesser enhancement in average heat flux by 0–30% for Re = 500 and 2500. With the increase in z/d from 2 to 4 it is observed that there is enhancement in heat flux for much wider range of Reynolds
Fig. 12. Nusselt number and effectiveness for varying TR, different Re at z/d = 2.
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Fig. 13. Nusselt number and effectiveness for varying TR, different Re at z/d = 4.
number (Re = 500–1500). For z/d = 2, the enhancement is observed for Re = 500 only. 3.3.1.2. Coefficient of variance. The coefficient of variance (COV) is found to correlate the enhancement in heat flux in an opposite way as shown in Fig 10 (a)–(d). For the cases of higher enhancement in heat flux there is a corresponding lesser enhancement in COV as shown in Figs. 9 and 10. However, it should be noted that lesser enhancement means more uniformity of heat flux distribution. Therefore, higher enhancement of heat flux also means more uniformity of heat flux distribution. 3.3.2. Effect of equivalence ratio The effect of equivalence ratio is studied at z/d = 4, Re = 1000 and / = 0.8–1.5. There is a enhancement of heat flux by 10–35% for / = 1.5 and a reduction of heat flux by 0–30% for / = 0.8–1.3 for 0 < r/d < 2 as shown in Fig. 11a. This is again because of the influence of the location of the reaction zone of the premixed flame from the impingement plate. For 0 < r/d < 4 and TR = 4.5 and 7.5, there is an increase in enhancement in average heat flux by 0– 25% and decrease in heat flux by 0–35% for TR = 2 and 3.2. The enhancement of COV is again found to correlate enhancement of heat flux in an opposite fashion as shown in Fig. 11. As the enhancement in heat flux increases, the corresponding enhancement in COV decreases.
3.4. Nusselt number and effectiveness distribution The local distribution of Nusselt number and effectiveness normal to the tape thickness (along y direction shown in Fig. 2), for Re = 500–2500 at z/d = 2 and 4 is shown in Figs. 12 and 13. Two peaks of Nusselt number and effectiveness are noticed for Re = 1500 and 2500 for all twist ratios. Furthermore, one of the two peaks is always higher than the other. This observation is inline with the heat flux contour maps shown in Figs. 6 and 7. It is observed that for Re = 500, the peak Nusselt number and effectiveness for impingement without tape is lower than that with impingement with twisted tapes of different twist ratios. For Re = 1500 and 2500 (except Re = 2500 at z/d = 2) the peak Nusselt number and effectiveness for impingement without tape is comparable with that of impingement with twisted tapes of different twist ratios. For Re = 2500 at z/d = 2, most part of the inner premixed cone touches the impingement plate and hence results in lesser heat transfer to the plate. It is further observed that the peak Nusselt number and effectiveness are higher for most cases of impingement with the twisted tape of highest ratio (TR = 7.5). The reason attributed to this is the inner premixed cone height which decreases with the decrease in twist ratio thereby increasing the distance of the inner premixed cone from the impingement plate.
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4. Conclusions An experimental study is carried out to study the effect of swirl on flame jet impinging on a flat plate. Four twisted tapes of twist ratios 2, 3.2, 4.5 and 7.5 are used to obtain the swirling flame jet. The average heat flux distribution and coefficient of variation distribution of swirling flame jet is compared with flame jet without swirl. Following are the outcomes of the present study. (i) Swirling effect increases the average heat flux distribution on the impingement plate by 40–140% at low Reynolds number. (ii) At higher Reynolds number, the use of swirl decreases the average heat flux distribution on the impingement plate by 10–40%. (iii) The coefficient of variation of heat flux distribution is minimum when the corresponding average heat flux distribution is higher. Conflict of interest None declared. Acknowledgments The first author would like to acknowledge the support of MHRD, Govt. of India and NITK Surathkal, Mangalore for sponsoring him to pursue Ph.D at Indian Institute of Technology, Bombay. The authors are also thankful to Aeronautical Research and Development Board, Govt. of India for partial funding of this work (the project sanction number is: DARO/08/1041685/M/I). References [1] R. Viskanta, Heat transfer to impinging isothermal gas and flame jets, Exp. Thermal Fluid Sci. 6 (1993) 111–134. [2] C.E. Baukal, B. Gebhart, A review of empirical flame impingement heat transfer correlations, Int. J. Heat Fluid Flow 17 (1996) 386–396. [3] C.E. Baukal, B. Gebhart, A review of semi-analytical solutions for flame impingement heat transfer, Int. J. Heat Mass Transfer 39 (1996) 2989–3002. [4] S. Chander, A. Ray, Flame impingement heat transfer: a review, Energy Convers. Manage. 46 (2005) 2803–2837. [5] S. Chander, A. Ray, Influence of burner geometry on heat transfer characteristics of methane/air flame impinging on a flat surface, Exp. Heat Transfer 19 (2006) 15–38. [6] S. Chander, A. Ray, Experimental and numerical study on the occurrence of offstagnation peak in heat flux for laminar methane/air flame impinging on a flat surface, Int. J. Heat Mass Transfer 54 (2011) 1179–1186.
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[7] Z. Zhao, T.T. Wong, C.W. Leung, S.D. Probert, Wok design: thermalperformance influencing parameters, Appl. Energy 83 (2006) 387–400. [8] L. Dong, C.W. Leung, C.S. Cheung, Heat transfer characteristics of a pair of impinging rectangular flame jets, J. Heat Transfer 125 (2003) 1140–1146. [9] S. Chander, A. Ray, Heat transfer characteristics of three interacting methane/ air flame jets impinging on a flat surface, Int. J. Heat Mass Transfer 50 (2007) 640–653. [10] M.G. Remie, M.F.G. Cremers, K.R.A.M. Schreel, L.P.H. De Goey, Analysis of the heat transfer of an impinging laminar flame jet, Int. J. Heat Mass Transfer 50 (2007) 2816–2827. [11] M.G. Remie, G. Sarner, M.F.G. Cremers, A. Omrane, K.R.A.M. Schreel, L.E.M. Alden, L.P.H. De Goey, Heat-transfer distribution for an impinging laminar flame jet to a flat plate, Int. J. Heat Mass Transfer 51 (2008) 3144–3152. [12] Z. Zhao, D.W. Yuen, C.W. Leung, T.T. Wong, Thermal performance of a premixed impinging circular flame jet array with induced-swirl, Appl. Therm. Eng. 29 (2009) 159–166. [13] X.Q. Huang, C.W. Leung, C.K. Chan, S.D. Probert, Thermal characteristics of a premixed impinging circular laminar-flame jet with induced swirl, Appl. Energy 83 (2006) 401–411. [14] H.S. Zhen, C.W. Leung, C.S. Cheung, Emission of impinging swirling and nonswirling inverse diffusion flames, Appl. Energy 88 (2011) 1629–1634. [15] G. Singh, S. Chander, A. Ray, Heat transfer characteristics of natural gas/air swirling flame impinging on a flat surface, Exp. Thermal Fluid Sci. 41 (2012) 165–176. [16] D. Nortershauser, P. Millan, Resolution of a three-dimensional unsteady inverse problem by sequential method using parameter reduction and infrared thermography measurements, Numer. Heat Transfer, Part A 37 (2000) 587– 611. [17] R. Loubat, P. Reulet, B. Estebe, P. Milan, Heat flux characterisation in hot jet and flame/wall interaction by IHCP resolution coupled with infrared measurements, Quant. InfraRed Thermography J. 1 (2) (2004) 205–228. [18] V. Hindasageri, R.P. Vedula, S.V. Prabhu, A novel method of estimation of adiabatic wall temperature for impinging premixed flame jets, Int. J. Heat Mass Transfer 77 (2014) 185–193. [19] S.K. Saha, U.N. Gaitonde, A.W. Date, Heat transfer and pressure drop characteristics of turbulent flow in a circular tube fitted with regularly spaced twisted-tape elements, Exp. Thermal Fluid Sci. 3 (1990) 632–640. [20] K. Nanan, K. Wongcharee, C. Nuntadusit, S. Eiamsa-ard, Forced convective heat transfer by swirling impinging jets issuing from nozzles equipped with twisted tapes, Int. Commun. Heat Mass Transfer 39 (2012) 844–852. [21] C. Nuntadusit, M. Wae-haye, A. Bunyajitradulya, S. Eiamsa-ard, Heat transfer enhancement by multiple swirling impinging jets with twisted-tape swirl generators, Int. Commun. Heat Mass Transfer 39 (2012) 102–107. [22] N. Syred, J.M. Beer, Combustion in swirling flows: a review, Combust. Flame 23 (1974) 143–201. [23] C. Nuntadusit, M. Wae-haye, A. Bunyajitradulya, S. Eiamsa-ard, Visualization of flow and heat transfer characteristics for swirling impinging jet, Int. Commun. Heat Mass Transfer 39 (2012) 640–648. [24] V. Hindasageri, R.P. Vedula, S.V. Prabhu, Blowoff stability of methane-air premixed flame stabilized on tube burner, Int. J. Emerging Multidiscip. Fluid Sci. 3 (4) (2012) 209–225. [25] A.E. Wald, J.W. Salisbury, Thermal infrared directional emissivity of powdered quartz, J. Geophys. Res. 100 (B12) (1995) 665–675. [26] A.K. Gupta, D.G. Lilley, N. Syred, Swirl Flow, Abacus Press, Great Britain, 1984. [27]
Contents lists available at ScienceDirect
International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt
Heat transfer distribution of swirling flame jet impinging on a flat plate using twisted tapes Vijaykumar Hindasageri, Rajendra P. Vedula, Siddini V. Prabhu ⇑ Department of Mechanical Engineering, Indian Institute of Technology, Bombay, India
a r t i c l e
i n f o
Article history: Received 14 October 2014 Received in revised form 24 July 2015 Accepted 14 August 2015
Keywords: Swirling flame jet Tube burner Twisted tape Infrared thermography Heat flux distribution
a b s t r a c t Impinging flame jets have wide applications in industrial and domestic heating purpose. The aim of the present study is to study the effect of swirl on flame jet impingement heat transfer characteristics. Four twisted tapes of twist ratios 2, 3.2, 4.5 and 7.5 (corresponding swirl numbers of 0.79, 0.49, 0.35 and 0.21) are used to experimentally obtain the swirling flame jet. The effect of twist ratio at Reynolds number varying from 500 to 2500 and equivalence ratio varying from 0.7 to 1.5 for burner tip to impingement plate distances of 2 and 4 is studied. The effect of swirl is compared with that of no tape in the tube burner by estimating the average heat flux distribution and coefficient of variation of heat flux for two impingement regions – within two times the burner diameter from the stagnation point and four times diameter from the stagnation point. From the experimental study, it is found that swirl enhances the heat flux distribution by 40–140% at low Reynolds number. At higher Reynolds number the effect of swirl is negative and is found to decrease the average heat flux distribution by 10–40%. Ó 2015 Elsevier Ltd. All rights reserved.
1. Introduction Heat transfer by flame jet impingement is extensively used in several industrial and domestic applications like melting of metal billets in a closed heating furnace, glass processing, domestic gas geysers and others. Reviews by Viskanta [1], Baukal and Gebhart [2,3] and Chander and Ray [4] give substantial information of the flame jet impingement studies. Extensive studies are reported in the literature on impinging flame jets. Chander and Ray [5] have experimentally studied the heat transfer distribution for impingement with tube burner, orifice and nozzle. They have further carried out numerical simulation using CFD software to explain the shift in peak heat flux from the stagnation point for low Reynolds number [6]. They attributed the influence of axial velocity to the shift in peak heat flux away from stagnation point. Zhao et al. [7] have studied the effect of impingement plate material on the heat transfer characteristics of impinging flame jet. Dong et al. [8] have studied the heat transfer distribution for impingement with a pair of rectangular burners. Chander and Ray [9] have studied the heat transfer distribution of three interacting flames impinging on a flat
⇑ Corresponding author at: Department of Mechanical Engineering, Indian Institute of Technology, Bombay, Powai, Mumbai 400 076, India. Tel.: +91 22 25767515; fax: +91 22 2572 6875, 2572 3480. E-mail addresses: [email protected] (V. Hindasageri), rpv@me. iitb.ac.in (R.P. Vedula), [email protected] (S.V. Prabhu). http://dx.doi.org/10.1016/j.ijheatmasstransfer.2015.08.038 0017-9310/Ó 2015 Elsevier Ltd. All rights reserved.
plate. Remie et al. [10,11] have arrived at analytical expressions for heat flux distribution from methane–oxygen flame impinging on a flat plate. Little information is available on heat transfer by swirling flame jets in literature [12–15]. Swirl is found to improve the heat transfer distribution at small distances of the burner tip from the impingement plate [12–15]. However, the uniformity of heat transfer distribution is not reported properly and the test cases reported are very limited. The heat flux distribution for swirling jets would have high spatial variation and hence the technique of measurement of heat flux should have high resolution. The heat flux sensor and calorimetric method used in most of the work reported in literature does not provide sufficient resolution. While the resolution of the heat flux sensor is limited by their diameters which are of the order of 5 mm, the calorimetric technique gives average of heat flux data of the entire heated surface. Inverse heat conduction (IHCP) technique using numerical method of estimating the heat flux also lacks sufficient resolution due to the requirement of high computational memory and time [16,17]. IHCP solution using appropriate analytical solution requires less computational time. The known analytical solution is directly applied to find the unknown parameter (usually boundary condition) of the problem with simple iterative methods as presented in our previous work [18]. Swirl is generated by the following methods: (i) Tangential entry of fluid, (ii) Vaned rotor or stator, (iii) Rotating the burner and (iv) Twisted tape.
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Nomenclature Symbol d k r Lf M Nu q00 Re t T TR u X p w x, y z Z
l q
Meaning tube diameter (mm) thermal conductivity (W/m K) arbitrary radius (m) flame height (m) molecular weight (g/mol) Nusselt number heat flux (W/m2) Reynolds number time (sec) temperature (K) twist ratio average velocity of fuel–air mixture (m/s) mole fraction twisted tape pitch (mm) twisted tape width (mm) coordinate axis burner tip to target plate distance (mm) quartz plate thickness (mm)
/
absolute viscosity (Pa-s) density (kg/m3) equivalence ratio
Subscripts/Superscripts m mixture adf adiabatic flame aw adiabatic wall i initial – average value 1 ambient condition Abbreviations CFD computational fluid dynamics COV coefficient of variance IHCP inverse heat conduction problem FOV field of view MC methane cylinder MFC mass flow controller MT mixing tube RSS root sum of squares TC thermal camera FCRI fluid control research of India
Greek symbols a thermal diffusivity (m/s2) rstd standard deviation g effectiveness
In the present work, twisted tapes are used to obtain swirl. Twisted tapes are very easy to fabricate and can be twisted to different twist ratios to obtain the desired swirl [19]. Swirling air jets using twisted tape are found to enhance heat transfer by 20–30% [20,21] at low z/d and high Re. Swirling air jets with twisted tapes are also found to give more uniform distribution of heat flux as compared to non-swirling air jets [20,21]. The structure of the non-impinging swirling flame jets is presented in detail by Syred and Beer [22]. However, limited information of flame structure for impinging condition of swirling flame jets is also available in literature [23].
In the present work, the heat flux is estimated by the assumption of semi-infinite medium concept for the impingement plate [18]. The heat flux distribution is presented for Reynolds number (Re) = 500–2500, impingement plate to burner tip distance (z/d) = 2 and 4 and equivalence ratio (/) = 0.6–1.5. Following are the objectives of the present work: (i) To obtain high resolution heat flux distribution of swirling flame jets by using twisted tapes of different twist ratios.
Desktop Computer TC Compressed Air Tank
Air MFC
z MT
y x Quartz Plate
Burner MC
Methane MFC
MC - Methane Cylinder
MFC - Mass flow controller
MT - Mixing Tube
TC - Thermal infrared camera
x, y - Coordinates parallel to the quartz plate
z - Coordinate perpendicular to the quartz plate
Fig. 1. Schematic of the experimental setup.
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Table 1 Specifications of the thermal camera used in the present study.
Table 2 Flame heights (Lf) for varying Re, TR and /.
Model
VisIRÒ Ti 200
Detector Spectral range Pixel resolution FOV (field of view) Minimum focus distance Temperature range Accuracy Frames per second
Microbolometer Uncooled FPA 7.5–13 lm 320 240 25 19 0.3 m 20–1200 °C ±2% of reading 25
(ii) To compare the average heat flux and uniformity (through coefficient of variance (COV)) distribution over a certain area on the impingement plate of swirling flame jets with that of non-swirling (no tape in the tube burner) flame jets. (iii) To obtain the Nusselt number and effectiveness distribution by the proper estimation of adiabatic wall temperature using analytical–numerical method [18]. 2. Experimental technique 2.1. Flow control and instrumentation Fig. 1 is the schematic of the experimental set-up used in the present study. Mass Flow controllers (MFC) of accuracy 1.5% of full
Re
TR
/
Lf (mm)
500 1000 1000 1000 1000 1500 1500 1500 1500 2500
4.5 2 2 2 2 2 3.2 4.5 7.5 4.5
1 0.8 1.1 1.3 1.5 1 1 1 1 1
9.5 15.2 15.4 32.3 41.6 17.5 18.5 20.5 22.3 33
scale are used to meter the flow of methane gas (99.5% purity) and air from compressed air storage tank. The mass flow controllers used are of Aalborg make, USA. The air mass flow controller is calibrated with DryCal (DCLITE H) calibrator, BIOS International make whose accuracy is 1% of the reading traceable to NIST standards. The methane mass flow controller is calibrated by Soap bubble meter of PCI Analytics make, India whose accuracy is 2% of reading traceable to FCRI standards, India. Methane and air are mixed in a mixing tube. The accuracy of the flow metering is further validated by the measurement of the burning velocity [24].
y x
z w=d
p
Fig. 2. Photographs of the twisted tapes used in present study along with the schematic diagram of twisted tape of one full twist.
TR = 2
TR = 3.2
TR = 4.5
Fig. 3. Flame shapes for varying TR at z/d = 4 and Re = 1500.
TR = 7.5
V. Hindasageri et al. / International Journal of Heat and Mass Transfer 91 (2015) 1128–1139
No tape
Twist ratio = 4.5
Re = 500
Re = 1500
Re = 2500
Fig. 4. Flame shapes for varying Re at z/d = 4 and TR = 4.5.
No tape
Twist ratio = 2 = 0.8
= 1.1
= 1.3
Fig. 5. Flame shapes for varying / at z/d = 4 and Re = 1000.
= 1.5
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2.2. Impingement plate and temperature recording The impingement plate is made of quartz whose size is 150 150 mm. The quartz plate thickness is 3 mm. The emissivity of the quartz plate reported in the literature is 0.93 [25]. The temperature distribution of the quartz plate is measured by the use of thermal infrared camera (Thermoteknix make VisIRÒ Ti 200). Specifications of this camera are given in Table 1. This camera is calibrated with a black body calibrator of TEMPSENS Make, CALsys 1500BB model. The accuracy of curve fit expression from calibration is 2% of reading. 2.3. Details of the twisted tape In the present work, 4 twisted tapes of twist ratio (TR) = 2, 3.2, 4.5 and 7.5 (corresponding swirl numbers of 0.79, 0.49, 0.35 and 0.21) are used to obtain the swirling flame jet. The photographs
of the twisted tapes used in the present study are shown in Fig. 2 along with the schematic diagram of the twisted tape of one full twist. The width of the tapes is 11 mm while the tube burner inside diameter is 11.5 mm and length is 60 mm. These twisted tapes are made from brass tape of 1 mm thickness by the procedure mentioned by Saha et al. [19]. The advantage of brass material is that it does not untwist after removing from the holding device used to twist the tape. Brass material has further advantage of being more ductile as compared to Stainless steel and hence the twisting is more uniform. The swirl number is defined by Gupta et al. [26] as the ratio of axial flux of angular momentum to the axial flux of axial momentum. The twist ratio (TR) is defined as the ratio of pitch (p) of the twisted tape to its width (w). Pitch (p) for a twisted tape is defined as the axial distance between two points on the twisted tape corresponding to the 180° rotation of the twisted tape. The swirl number is related to the twist ratio by the Eq. (1).
Fig. 6. Contours of heat flux (kW/m2) distribution for different TR at Re = 1500, / = 1 and z/d = 4.
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S
p
ð1Þ
2ðTRÞ
2.4. Data reduction The viscosity is calculated from Eq. (2) and the mixture Reynolds number (Re) is calculated from Eq. (3).
P
pffiffiffiffiffiffi
lj X j M j
lm ¼ P pffiffiffiffiffiffi
ð2Þ
qm um d lm
ð3Þ
Xj
Re ¼
Mj
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The heat flux distribution for flame jet (q00 ) is estimated by knowing the transient temperature at a given depth (Z) in a semi-infinite medium [18]. The temperature distribution, T (Z, t) with time (t) at a given depth in a semi-infinite medium for a constant heat flux (q00 ) is given by Eq. (4).
TðZ; tÞ T i ¼
2q00
! pffiffiffiffiffiffiffiffiffiffiffi at=p Z 2 q00 Z Z exp erfc pffiffiffiffiffi k k 4at 2 at
ð4Þ
The temperature distribution on the back side of the quartz plate is recorded using the infrared thermal camera. This recorded temperature T (Z, t) is then matched with that of Eq. (4) at different time intervals, for short time, by varying the heat flux value (q00 ) such that the square root of the sum of squares, qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Pn 2 RSS ¼ i¼1 ðT analytical T experimental Þ is minimum.
Fig. 7. Contours of heat flux (kW/m2) distribution for different Re at TR = 4.5, / = 1 and z/d = 4.
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The evaluation of heat transfer coefficient requires the data of adiabatic wall temperature (Taw) as given by Eq. (5) and therefore Taw has to be determined separately.
q00 ¼ hðT aw T w Þ
ð5Þ
An analytical–numerical method proposed in our previous work is used to estimate Taw [18]. Nusselt number is calculated using Eq. (6) with the thermal conductivity of the flame taken at adiabatic wall temperatures using CEA software developed by NASA [27].
Nu ¼
hd k
ð6Þ 3. Results and discussion
Effectiveness for the flame impingement process is given by Eq. (7).
T T1 g ¼ aw T adf T 1
The adiabatic flame temperature (Tadf) for stoichiometric mixture of methane air premixed flame is taken as 2200 K and the ambient temperature is taken as 300 K. The uncertainties in the measured parameters are estimated by the method of Moffat [28]. The uncertainties in equivalence ratio and Reynolds number is 10% while that in the temperature measured from thermal camera and estimated heat flux are 2% and 12% respectively. The uncertainties in the Nusselt number and effectiveness are 15% and 5% respectively.
ð7Þ
The heat flux distribution is presented for Re = 500–2500, z/d = 2 and 4 for / = 0.8–1.5. A comparison of burners with tapes of different twist ratios is made with the burner without tape.
Fig. 8. Contours of heat flux (kW/m2) distribution for different / for TR = 2 and no tape at z/d = 4 and Re = 1000.
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Fig. 9. Enhancement in averaged heat flux with different twist ratios of twisted tape in tube burner as compared with no tape in tube burner for varying Re at / = 1.
Fig. 10. Enhancement in COV with different twist ratios of twisted tape in tube burner as compared with no tape in tube burner for varying Re at / = 1.
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3.1. Flame shape study The photographs of the flame shapes at Re = 1500 and / = 1 at z/ d = 4 for varying twist ratios (TR) is shown in Fig. 3. The maximum flame length for different Re, TR and / as shown in photographs of Figs. 3–5 is given in Table 2. The effect of swirl is clearly visible in Fig. 3, the unburnt flame height is longer for higher TR (lower swirl) as compared to that with lesser TR (higher swirl). The presence of twisted tape results in splitting of the inner premixed cone into multiple distinct segments. The photographs of the flame shapes at Re = 500, 1500 and 2500 for / = 1 at z/d = 4 are shown in Fig. 4. With the increase in Re, the size of unburnt (premixed) part of the flame along the tube axis increases as shown in Fig. 4. The photographs of the flame shapes at Re = 1000 and varying / at z/d = 4 for no tape and TR = 2 are shown in Fig. 5. The flame tip is closer to the impingement plate for higher / for no tape and with a twisted tape of TR = 2. The presence of the twisted tape results in shortening of the flame height and results in spreading in radial direction for all the cases presented in the present study.
The contour plots for varying Re, / = 1, z/d = 4 and TR = 4.5 is shown in Fig. 7. With the increase in Re, the unburnt (premixed) part of the flame approaches closer to the impingement plate and hence the flame temperature near the impingement plate is also higher. Therefore, the heat fluxes are higher for higher Re. The contour plots for varying /, Re = 1000, z/d = 4 and TR = 2 and no tape is shown in Fig. 8. With the increase or decrease of fuel fraction from the stoichiometric condition the length of the inner premixed cone of the flame increases. Hence, the reaction zone of the flame where temperature is highest is closer to the impingement plate and will result in higher heat transfer rate if the premixed (unburnt) part of the flame does not touch the impingement plate. For no tape case, the inner premixed cone of the flame has touched the impingement plate for / = 1.3 and 1.5. Hence, the heat flux is lower at the stagnation point for / = 1.3 and 1.5. For TR = 2, the unburnt (premixed) part does not touch the impingement plate for all /. This is because swirl results in splitting of the inner premixed part of the flame into segments. Two distinct lobes are produced on the impingement plate at / = 1.5. This is not observed for / = 0.8 and 1.1 because the reaction zone is relatively far away from the impingement plate.
3.2. Heat flux contour maps The contour plots of heat flux for varying TR at Re = 1500, / = 1 and z/d = 4 is shown in Fig. 6. Two distinct lobes are observed which are formed due to the splitting of the unburnt (premixed) part of the flame into two segments. For higher TR (lower swirl), the unburnt (premixed) part of the flame is closer to the impingement plate and hence the temperature of the flame near the impingement plate is also higher. Lower swirl also means that the axial component of velocity is relatively higher as compared to higher swirl. These two factors are responsible for higher heat flux distribution on the impingement plate for lower swirl.
3.3. Comparison of average heat flux and uniformity (COV) distribution of burner with twisted tape inserted and twisted tape removed The performance of the swirling flame jet impingement is compared with that of no swirl (no twisted tape in tube burner). The 00 ) and the coefficomparison is made for the average heat flux (q cient of variation defined by Eqs. (8)–(10).
00 ¼ q
PN
00 i¼1 qi
N
ð8Þ
Fig. 11. Enhancement in averaged heat flux and COV with different twist ratios of twisted tape in tube burner as compared with no tape in tube burner for Re = 1000 and varying /.
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COV ¼
rstd ¼
rstd
ð9Þ
00 q
PN
00 Þ2 q N1
00 i¼1 ðqi
ð10Þ
N is the total number of data points. The average heat flux and the coefficient of variation (COV) are compared for two regions: (i) 0 < r/ d < 2 and (ii) 0 < r/d < 4. The enhancement factor, E for average heat flux and COV are defined in Eqs. (11) and (12).
q00 with twisted tape Eq00 ¼ 00 q no twisted tape ECOV ¼
COV with twisted tape COV no twisted tape
ð11Þ
ð12Þ
Eq00 > 1 means higher (preferable) heat flux distribution with tape and ECOV < 1 means more uniform heat flux distribution with twisted tape as compared to that of tube without tape. Figs. 9 and 10 are the comparison of enhancement in average heat flux and COV, respectively, of burners with twisted tapes as compared to no twisted tape in the burner. 3.3.1. Effect of Reynolds number 3.3.1.1. Average heat flux distribution. There is an enhancement of 20–50% in average heat flux for 0 < r/d < 2 and 40–130% for 0 < r/ d < 4 at z/d = 2 for Re = 500 as shown in Fig. 9 (a) and (b).
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It is further observed from Fig. 9 (a) and (b) that higher twist ratio (TR) results in higher heat flux at z/d = 2 for Re = 500. The reason for this the location of the reaction zone of the premixed part of the flame. Higher twist ratio have flame whose reaction zone is relatively closer to the impingement plate and hence higher heat flux. At other Reynolds numbers for z/d = 2, there is reduction in the average heat flux distribution by 0–40% as shown in Fig. 9 (a) and (b). The reason for lesser enhancement in heat flux at higher Re is again the location of the reaction zone of the premixed part of the flame. For Re = 1000–2500 at z/d = 2, the reaction zone of the premixed part of the flame without twisted tape is much closer to the impingement plate as compared to with twisted tape. Also, there is a considerable loss of axial momentum of the jet in case of tubes with twisted tapes due to swirling component that is partly obtained from the axial momentum. At z/d = 4, the enhancement in heat flux is 40–60% at Re = 1000 for 0 < r/d < 2 as shown in Fig. 9c. At Re = 500 and z/d = 4 there is an increase in Eq00 for TR = 2 and 3.2 but a reduction in Eq00 for TR = 4.5 as shown in Fig. 9c. For higher Re, the enhancement in heat flux decreases which is again because of the influence of the reaction zone of the premixed part of the flame. At z/d = 4 and the region 0 < r/d < 4, lower twist ratios of 2 and 3.2 result in an enhancement of 0–40% for Re = 500–1500 and a reduction of 0–20% for Re = 2000 and 2500 as shown in Fig. 9 (c) and (d). At z/d = 4 and the region 0 < r/d < 4, higher twist ratios of 4.5 and 7.5 result in lesser enhancement in average heat flux by 0–30% for Re = 500 and 2500. With the increase in z/d from 2 to 4 it is observed that there is enhancement in heat flux for much wider range of Reynolds
Fig. 12. Nusselt number and effectiveness for varying TR, different Re at z/d = 2.
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Fig. 13. Nusselt number and effectiveness for varying TR, different Re at z/d = 4.
number (Re = 500–1500). For z/d = 2, the enhancement is observed for Re = 500 only. 3.3.1.2. Coefficient of variance. The coefficient of variance (COV) is found to correlate the enhancement in heat flux in an opposite way as shown in Fig 10 (a)–(d). For the cases of higher enhancement in heat flux there is a corresponding lesser enhancement in COV as shown in Figs. 9 and 10. However, it should be noted that lesser enhancement means more uniformity of heat flux distribution. Therefore, higher enhancement of heat flux also means more uniformity of heat flux distribution. 3.3.2. Effect of equivalence ratio The effect of equivalence ratio is studied at z/d = 4, Re = 1000 and / = 0.8–1.5. There is a enhancement of heat flux by 10–35% for / = 1.5 and a reduction of heat flux by 0–30% for / = 0.8–1.3 for 0 < r/d < 2 as shown in Fig. 11a. This is again because of the influence of the location of the reaction zone of the premixed flame from the impingement plate. For 0 < r/d < 4 and TR = 4.5 and 7.5, there is an increase in enhancement in average heat flux by 0– 25% and decrease in heat flux by 0–35% for TR = 2 and 3.2. The enhancement of COV is again found to correlate enhancement of heat flux in an opposite fashion as shown in Fig. 11. As the enhancement in heat flux increases, the corresponding enhancement in COV decreases.
3.4. Nusselt number and effectiveness distribution The local distribution of Nusselt number and effectiveness normal to the tape thickness (along y direction shown in Fig. 2), for Re = 500–2500 at z/d = 2 and 4 is shown in Figs. 12 and 13. Two peaks of Nusselt number and effectiveness are noticed for Re = 1500 and 2500 for all twist ratios. Furthermore, one of the two peaks is always higher than the other. This observation is inline with the heat flux contour maps shown in Figs. 6 and 7. It is observed that for Re = 500, the peak Nusselt number and effectiveness for impingement without tape is lower than that with impingement with twisted tapes of different twist ratios. For Re = 1500 and 2500 (except Re = 2500 at z/d = 2) the peak Nusselt number and effectiveness for impingement without tape is comparable with that of impingement with twisted tapes of different twist ratios. For Re = 2500 at z/d = 2, most part of the inner premixed cone touches the impingement plate and hence results in lesser heat transfer to the plate. It is further observed that the peak Nusselt number and effectiveness are higher for most cases of impingement with the twisted tape of highest ratio (TR = 7.5). The reason attributed to this is the inner premixed cone height which decreases with the decrease in twist ratio thereby increasing the distance of the inner premixed cone from the impingement plate.
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4. Conclusions An experimental study is carried out to study the effect of swirl on flame jet impinging on a flat plate. Four twisted tapes of twist ratios 2, 3.2, 4.5 and 7.5 are used to obtain the swirling flame jet. The average heat flux distribution and coefficient of variation distribution of swirling flame jet is compared with flame jet without swirl. Following are the outcomes of the present study. (i) Swirling effect increases the average heat flux distribution on the impingement plate by 40–140% at low Reynolds number. (ii) At higher Reynolds number, the use of swirl decreases the average heat flux distribution on the impingement plate by 10–40%. (iii) The coefficient of variation of heat flux distribution is minimum when the corresponding average heat flux distribution is higher. Conflict of interest None declared. Acknowledgments The first author would like to acknowledge the support of MHRD, Govt. of India and NITK Surathkal, Mangalore for sponsoring him to pursue Ph.D at Indian Institute of Technology, Bombay. The authors are also thankful to Aeronautical Research and Development Board, Govt. of India for partial funding of this work (the project sanction number is: DARO/08/1041685/M/I). References [1] R. Viskanta, Heat transfer to impinging isothermal gas and flame jets, Exp. Thermal Fluid Sci. 6 (1993) 111–134. [2] C.E. Baukal, B. Gebhart, A review of empirical flame impingement heat transfer correlations, Int. J. Heat Fluid Flow 17 (1996) 386–396. [3] C.E. Baukal, B. Gebhart, A review of semi-analytical solutions for flame impingement heat transfer, Int. J. Heat Mass Transfer 39 (1996) 2989–3002. [4] S. Chander, A. Ray, Flame impingement heat transfer: a review, Energy Convers. Manage. 46 (2005) 2803–2837. [5] S. Chander, A. Ray, Influence of burner geometry on heat transfer characteristics of methane/air flame impinging on a flat surface, Exp. Heat Transfer 19 (2006) 15–38. [6] S. Chander, A. Ray, Experimental and numerical study on the occurrence of offstagnation peak in heat flux for laminar methane/air flame impinging on a flat surface, Int. J. Heat Mass Transfer 54 (2011) 1179–1186.
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