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Isothermal air jet and premixed flame jet impingement: Heat transfer characterisation and comparison
International Journal of Thermal Sciences 100 (2016) 401e415
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International Journal of Thermal Sciences journal homepage: www.elsevier.com/locate/ijts
Isothermal air jet and premixed flame jet impingement: Heat transfer characterisation and comparison Pramod Kuntikana, S.V. Prabhu* Department of Mechanical Engineering, Indian Institute of Technology Bombay, Powai, Mumbai 400 076 India
a r t i c l e i n f o
a b s t r a c t
Article history: Received 15 June 2015 Received in revised form 2 October 2015 Accepted 13 October 2015 Available online xxx
The jet impingement heat transfer is a well-established technique for obtaining high heat transfer rates for many cooling and heating applications. Impingement heat transfer methods are widely used in domestic and industrial appliances. The impinging isothermal gas jets are used for both heating and cooling. However, premixed flame jets are used for heating the target surface. Present study is an attempt to compare the heat transfer characteristics of the isothermal air jets and premixed flame jets. The isothermal air jet having jet temperature of 30 C (cold jet or ambient temperature jet), 100 C (hot jet), and premixed methaneeair flame jet (stoichiometric mixture) with Reynolds numbers of 500, 750, 1000, 1250 and 1500 and nozzle or burner to plate spacings of 2d, 4d and 6d are experimentally investigated for heat transfer characterisation. Thin metal foil technique is used for characterising isothermal air jets. For a fixed jet Reynolds number, the Nusselt number of isothermal air jet is found independent of the temperature difference between jet and surrounding fluid. A steady state technique is proposed for characterisation of premixed flame jets. The outcome of the present study reveals that the heat transfer characteristics of isothermal air jet and the premixed flame jet are almost same. The higher thermal entrainment in premixed flame jet in comparison with isothermal air jet results in a lower effectiveness. The present heat transfer data can be directly utilised for many practical applications. © 2015 Elsevier Masson SAS. All rights reserved.
Keywords: Jet impingement Heat transfer analogy Entrainment Flame jet Air jet
1. Introduction Impinging jets find a variety of applications ranging from electronic cooling to industrial heating due to their peculiarity of having higher heat transfer coefficients. Common applications of gas jets include synthetic jet cooling, gas turbine blade cooling, combustion chamber cooling, glass manufacturing, textile industries, paper drying, preheating of metal billets, etc. Hydrocarboneair flame jets are widely used in industries for direct heating processes such as glass processing, boiler furnace wall heating, ladle preheating, melting of scrap metal parts, steam generation plants, etc.
Abbreviations: CFD, computational fluid dynamics; FJ, flame jet; HFM, heat flux micro-sensor; HJ, hot jet; IR, infrared; IS, impingement surface; MFC, mass flow controller; RS, rear surface; SLPM, standard litres per minute; UDF, user defined function. * Corresponding author. Tel.: þ91 22 25767515; fax: þ91 22 25726875. E-mail addresses: [email protected] (P. Kuntikana), svprabhu@iitb. ac.in (S.V. Prabhu). http://dx.doi.org/10.1016/j.ijthermalsci.2015.10.018 1290-0729/© 2015 Elsevier Masson SAS. All rights reserved.
The jet impingement heat transfer is a well-established research area with practical relevance, with good amount of contributions by several researchers in the field for last four decades. Numerous studies with ambient temperature air jet impingement are reported in literature. Jambunathan et al. [1] reported extensive review listing various parameters (such as Reynolds number, nozzle to plate distance, radial distance and the Prandtl number) affecting the impinging turbulent jet heat transfer. It reveals that the turbulent intensity at the nozzle exit, jet confinement and the nozzle geometries also play a very significant role in heat transfer characteristics. Viskanta [2] reported the studies on single and multiple impinging isothermal jets and flame jets. The separation distance between the jets is observed to be an important parameter in multiple jet arrays. Lytle and Webb [3] investigated the heat transfer characteristics of the impinging air jets for lower nozzle to plate spacing. The studies on effect of the nozzle geometry on impingement heat transfer are reported in literature [4e11]. The geometries other than circular found to induce secondary flow influencing the flow field of the jet. It is reported that axial velocity decay in noncircular jet is faster than the circular jets. Hofmann et al. [12], O'Donovan and Murray [13,14], Katti and Prabhu [15]
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Nomenclature A d h I k L l M m_ Nu Q_ q00 r Re T V v X Z z
surface area (m2) burner diameter (m) heat transfer coefficient (W/m2 K) current (A) thermal conductivity (W/m K) height (m) length of burner (m) molecular weight (kg/kmol) mass flow rate (kg/s) Nusselt number volume flow rate (m3/s) heat flux (W/m2) radial distance (m) Reynolds number temperature (K) voltage (V) velocity (m/s) mole fraction spacing between burner or nozzle and target plate (m) axial distance (m)
studied the ambient temperature jets and proposed correlations for radial distributions of heat transfer coefficient in terms of jet Reynolds number, jet to plate spacing, turbulent intensity. There are certain studies reporting the effect of jet temperature and surrounding temperature on the heat transfer characteristics of the impinging air jets. Bouchez and Goldstein [16] reported the local heat transfer coefficient and effectiveness for impinging circular jet interacting with the cross flow. It is reported that the impinging jet effectiveness decreases with the increase in the cross flow blowing rate. Striegel and Diller [17,18] reported the experimental and analytical studies on the effect of the entraining fluid temperature on the local heat transfer characteristics of multiple impinging turbulent air jets by varying the surrounding temperature. Hollworth and Wilson [19] and Hollworth and Gero [20] investigated the effect of the jet temperature on the heat transfer characteristics of a square edged nozzle. They found that the local heat transfer coefficient is independent of the temperature difference between the jet and surroundings. Goldstein et al. [21] presented the heat transfer characteristics of the impinging turbulent circular jets heated 20 C above the ambient. The effectiveness and the recovery factor are found to be independent of the temperature difference (jet temperature and ambient temperature) and flow Reynolds number. However, nozzle to plate spacing of impinging hot jets showed a strong dependency on both effectiveness and recovery factor. Baughn et al. [22] reported the effectiveness and Nusselt number profiles for heated jet at high Reynolds number (Re > 25,000). The effectiveness is found to be varying with the not et al. [23] invesradial location and nozzle to plate spacing. Fe tigated the local Nusselt number and effectiveness profiles of impinging jets of temperature varying from ambient to 141 C. The radial distributions of Nusselt number and effectiveness are found to be independent of jet temperatures. For a fixed nozzle to plate spacing, it is observed that the jet effectiveness is independent of jet Reynolds number. Impinging flame jet heat transfer investigations studying the effect of jet Reynolds number, mixture equivalence ratio, inter jet
Greek symbols 3 emissivity h effectiveness m absolute viscosity (Pa s) r density (kg/m3) s StefaneBoltzmann constant (5.67 108 W/m4 K) f equivalence ratio Subscripts/superscripts ∞ ambient aw adiabatic wall b bottom conv convection elec electrical f flame i looping variable, component number j jet m mean film mix mixture nc natural convection rad radiation ref reference t top w wall
spacing, burner to plate spacing, burner geometries, surface characteristics of impingement plate, incident angle and oxygen enhancement are reported in the literature. Baukal and Gebhart [24,25] reported the some analytical and semi-analytical solution for flame jet impingement heat transfer. Remie et al. [26,27] reported the analytical and experimental investigations on twodimensional axisymmetric cases for flame jet impingement. Van der Meer [28] presented the comparison between the heat transfer characteristics of the non-reacting jets and the flame jets. Chander and Ray [29] presented a review on flame jet impingement heat transfer. It is reported that the rate of heat transfer from the flame jet to a target solid surface depends on the structure of the flame, convective and radiative properties of the constituent gas species of the flame and the temperature of the gas within the boundary layer in vicinity of the plate. Chander and Ray [30] reported the heat transfer characteristics of premixed methaneeair flame jets. The convective flame heat flux and wall temperature data is reported for various impinging jet parameters. Chander and Ray [31] also presented the effect of inter jet spacing in interacting methane-air premixed flame jets. Hou and Ko [32], Agrawal et al. [33] and Dong et al. [34] investigated the effect of the oblique premixed flame jet impingement. The oblique flame jet impingement results in asymmetric heat flux over the impingement surface. The premixed butaneeair premixed flame jet impingement heat transfer characteristics are reported by Zhao et al. [35]. Researchers have used direct measurement with heat flux sensor [30,33e35] and inverse heat transfer technique [36] to determine the flame heat flux on to the target plate. Generally copper [30], bronze, stainless steel [35] and quartz [36] plates of various thickness are used as target surfaces for the for impingement studies. In the literature, heat flux and wall temperature of the plate is reported for premixed impinging flame jets [30,35]. These results would be specific to the material of the plate, the magnitude of wall temperatures of the plate (convection dominant or convection and radiation dominant) and the fuel (methane or butane) being used. However, Nusselt number and effectiveness
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distributions reported for isothermal air jets [15] are highly generic in nature. There is a need to generalise the premixed flame jet analogous to isothermal jet in order to enhance the practical applicability of reported results. Hence, the present study focuses on. i. Heat transfer characterisation of impinging cold (Tj ¼ T∞) and hot (Tj ¼ 100 C) air jets for Re ¼ 500, 750, 1000, 1250 and 1500 with nozzle to plate spacing, Z of 2d, 4d and 6d. ii. Steady state technique is proposed to find the heat transfer coefficient and the reference temperature for impinging premixed flame jets. iii. Heat transfer characterisation of impinging premixed flame jets for Re ¼ 500, 750, 1000, 1250 and 1500 with nozzle to plate spacing, Z of 2d, 4d and 6d for stoichiometric mixture (f ¼ 1.0). iv Comparison of heat transfer characteristics of impinging isothermal air jets and premixed flame jets. v Practical significance/usefulness of the results.
2. Experimental details 2.1. Description of experimental setup for isothermal air jet impingement heat transfer studies Fig. 1 shows the layout of the experimental setup used for the isothermal air jet impingement heat transfer studies. The compressed air is supplied from an air compressor (ELGI make) through air filter and pressure regulator maintaining the supply pressure of 2 bar. Air flow is metered through a mass flow controller (MFC) of
403
Aalborg make having range of 0e66.67 SLPM with an accuracy of 1.5% of full scale. The MFC is calibrated using DryCal (BIOS Defender 530H, Range: 300e30 000 cm3) primary gas flow calibrator. Metered air is passed through the plate heater having a heating capacity of 2 kW. The power supply to the heater is regulated with a variable auto-transformer to get different jet temperatures. The heated air is then carried to the pipe nozzle through a flexible high temperature stainless steel hose pipe. The heater, hose pipe and the pipe nozzle are insulated with ceramic blanket to avoid the heat loss from the heated air to the surrounding. The pipe nozzle is held firmly by a nozzle holder with a threaded clamp. The nozzle tip to the impingement surface distance is varied by moving the nozzle with respect to the impingement surface and then clamping. The stainless steel pipe nozzle has an inner diameter of 10 mm (measured with inside micrometre) and length to diameter ratio (l/ d) of 50 to ensure fully developed flow at the exit of the nozzle. The air jet issuing from the nozzle exit is made to impinge over a target surface. The target surface is a thin (thickness ¼ 0.05 mm) stainless steel foil having dimensions of 150 mm 220 mm is clamped firmly and stretched between the two copper bus bars. Firm grip is assured by sandwiching 5 mm of the foil from either side in between the pieces of the flat bus bars bolted together to a thick bakelite sheet for support. This prevents the target surface from ripple formation. The impingement plate assembly is mounted over a mild steel frame for support. For an experimental condition resulting in highest temperature gradient in the plate (for Re ¼ 1000 and Z/d ¼ 2), the numerical simulations with two dimensional axisymmetric modelling of the impingement surface revealed a maximum of 4% of the imposed heat flux is laterally conducted in the plate. Therefore, the lateral conduction in the plate is neglected. The plate is heated electrically (by resistance
Fig. 1. Schematic of experimental set up for isothermal air jet impingement heat transfer studies.
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heating) using a variable autotransformer and a step down transformer. The copper power cables from the transformer are connected across the copper bus bars. The copper bus bars have very low electrical resistance and hence the heating is uniform. The electric heating is varied by varying the voltage across the transformer. The local temperature of the plate on the impingement plane and the rear side is assumed to be the same as the one dimensional energy balance across the heated plate showed negligible temperature difference across two surfaces. The impingement plate is painted with Pyromark having an emissivity of 0.99 (painted with brush, spray paint and then cured by electrical heating) [37], on the impingement surface of the thin metal foil for thermal imaging purpose. Infrared thermal camera (Thermoteknix make VisIR® 640S) mounted on the rear side of the impingement surface is used to capture the steady state thermal images of the impinging surface. The camera captures the intensity of the incident radiation and during post processing of thermal images; the user must input the surface emissivity and temperature of the surroundings between the camera and the emitting surface to get the surface temperature values. The thermal camera is calibrated with a black body calibrator of TEMPSENS Make, CALsys 1500BB model. A linear curve is fit with an accuracy of 2% for the actual temperature of the surface based on the measured temperature over the entire operating range. The cold jet experiments are performed by switching off the power supply to the inline heater. Power is supplied to both the heater and the plate from an AC power source through a voltage stabilizer. The voltage and current across the heater and the plate are measured with digital meters (‘Meco’ make) having an accuracy of 20 ± 0.5% V and 400 ± 0.5% A, respectively. The jet temperature is measured with four ChromeleAlumel (Ktype) thermocouples mounted peripherally inside a tube of 13.5 mm inner diameter, 20 mm length at an axial spacing of 3 mm between the consecutive thermocouples. This assembly can be easily mounted on the tip of pipe nozzle for steady state jet temperature measurement. The output of the thermocouple is measured with milli-voltmeter (‘Meco’ make). The average of four thermocouple readings is taken for calculating the jet temperature. The thermocouples are calibrated with a constant temperature oil bath (‘Julabo’ make) over a temperature range of 25 C to 200 C. After the desired temperature is achieved, the thermocouple assembly is dismounted, suitable jet to plate distance is set with the clamped holder traverse mechanism and the jet is allowed to impinge over the plate. The jet impingement assembly is kept inside a transparent acrylic sheet box with MS Frame for support. This isolates the jet from the atmospheric fluctuations due to local wind movements. The power loss from the heated plate by radiation and natural convection are accounted in the calculation of the local heat transfer coefficient. In the present study, the pipe nozzle is mounted vertical and the impingement surface is held parallel to the ground unlike other cold jet studies where the nozzle is mounted parallel and the impingement surface is held normal to the ground. These two configurations do not differ much for cold jet and high Reynolds number heated jet studies, but for low Reynolds number heated jets the flow velocity induced by the buoyancy effect becomes comparable with the jet flow velocity. The flow momentum and the buoyancy force in the present configuration are in the same direction. This produces a symmetric temperature distribution over the impingement surface. In the latter configuration, the flow momentum is in the horizontal direction with the buoyancy force acting vertically upwards creating a resultant flow hitting the impingement plate in an oblique direction. This produces an eccentric temperature distribution over the impingement surface, which is not desirable.
2.2. Description of experimental setup for premixed flame jet impingement heat transfer studies Fig. 2 shows the experimental setup used for premixed flame jet impingement heat transfer study. The methane gas (99.5% purity) and the air from compressed air storage tank are metered through mass flow controllers (MFCs) having accuracy of 1.5% of full scale. The MFCs used are Aalborg make, USA. The air MFC has a range of 0e10 SLPM and that of methane MFC is 0e1 SLPM. The air and methane lines are maintained at 2 bar pressure. The air MFC is calibrated with DryCal (BIOS Defender 530H, Range: 300e30,000 cm3) calibrator and methane mass flow controller is calibrated by DryCal (BIOS Defender 530M, Range: 50e5000 cm3) calibrator, BIOS International make with an accuracy of 1% of the reading traceable to NIST standards. Metered methane and air are mixed thoroughly in a mixing cup. The mixing cup consists of steel balls to ensure the proper mixing of the fuel and air, and to reduce the flow fluctuations. The mixture is fed to a 10 mm diameter burner having length to diameter (l/d) ratio of approximately 50 to ensure fully developed flow. The target plate upon which the flame jet is impinged is made of quartz is having dimension of 150 mm 150 mm with thickness of 1 mm. The quartz has surface emissivity of 0.93 [38]. The burner is mounted on a holder which provides various burner to plate spacings by moving the burner with respect to the plate. The plate is mounted on a platform which holds the plate firmly. The steady state thermal images of the plate are captured from both the flame impingement surface and the rear surface. The premixed flame (blue flame) has very low emissivity (3 f z 0.02) [39]. So the premixed flame can be treated as transparent to the thermal radiation making the temperature measurements with the thermal camera valid on the flame jet impingement surface also. The one dimensional local energy balance across the thin quartz plate results in negligible lateral conduction. This can be assured with the impingement surface temperature and the rear surface temperature of the quartz plate captured by the thermal camera showing less than 2% deviation at steady state. The uncertainties in the measured and predicted quantities are obtained using the method reported by Moffat [40]. The uncertainty in Reynolds number and equivalence ratio is 5%, for temperature recorded with IR thermal camera is 2%, Nusselt number and reference temperature is around 12%. 3. Data reduction 3.1. Isothermal air jets The Reynolds number of the jet is given by
Re ¼
rvj d 4rQ_ ¼ pdm m
(1)
where, r is the density of the fluid in kg/m3, vj is the jet velocity in m/s, d is the pipe nozzle diameter in m and m is the dynamic viscosity of the fluid in Pa s. All the fluid properties are evaluated at the jet temperature, Tj. Average of ten thermal images is considered for analysis. For each Re, Z/d and jet temperature, the impingement plate is subjected to five different electrical heat fluxes by varying the power input to the plate. The plate loses heat to the surrounding by natural convection and the radiation depending on its surface temperature. There is only forced convection heat transfer due to the impingement of the jet. Thus, the energy balance across the plate surfaces assuming one dimensional heat conduction would be
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405
Fig. 2. Schematic of experimental setup for premixed flame jet impingement heat transfer studies.
00
00
00
00
00
qelec ¼ qconv þ qncðtÞ þ qradðtÞ þ qradðbÞ 00
(2)
9 VI 00 00 > = ; qconv ¼ h Tref Tw ; qncðtÞ ¼ hnc ðTw T∞ Þ; > A > 00 > 4 4 4 4 ; and qradðbÞ ¼ s3 ðbÞ Tw ¼ s3 ðtÞ Tw T∞ T∞
qelec ¼ 00
qradðtÞ
(3) where, V is the voltage across the target plate, I is the current flow, A is the surface area of the target plate, T∞ is the ambient temperature, 3 (t) ¼ 0.99 and 3 (b) ¼ 0.25 are respectively emissivities of top and bottom surfaces of target plate and hnc is the natural convection heat transfer coefficient equal to 10 W/m2 K. The top and the bottom surface temperature of the plate are taken equal to Tw. For a known electrical power input to the plate with the measured wall temperature, the convection heat flux of the impinging jet is given by
00 00 00 00 00 qconv ¼ h Tref Tw ¼ qelec qncðtÞ þ qradðtÞ þ qradðbÞ |fflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflffl} |fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl} Unknown
(4)
Known
By varying the electrical power input to the plate, the wall temperature of the plate changes. Let the five different convection heat fluxes and the corresponding wall temperatures obtained by 00 00 00 00 00 varying the electrical heat input to the plate be, q1 ; q2 ; q3 ; q4 ; q5 and Tw1, Tw2, Tw3, Tw4, Tw5 respectively. Now by rearranging Eq. (4) a 00 linear fit between qðiÞ and Tw(i) is obtained. 00
TwðiÞ ¼
qðiÞ h
þ Tref
(5)
Thus, for a linear curve fit with the convective heat flux along the abscissa and the wall temperature along the ordinate axes, the slope of the line will be negative of inverse of the heat transfer coefficient and the intercept along the ordinate axis will be the reference temperature. The reference temperature for the room temperature jet is nearly ambient temperature. The heat transfer coefficient and the reference temperature are non-dimensionalised to get Nusselt number and effectiveness.
Nu ¼
h¼
hd k
(6)
Tref T∞ Tj T∞
(7)
where, h is the convective heat transfer coefficient in W/m2 K, d is the nozzle diameter in m, k is the thermal conductivity (W/m K) of the fluid at mean film temperature, Tm ¼ ðTw þ Tref Þ=2. 3.2. Flame jets 3.2.1. Mixture parameters The mixture density, viscosity and the Reynolds number at burner exit are given by Eqs. (8)e(10) respectively.
rmix ¼
X
ri
(8)
pffiffiffiffiffiffi mi Xi Mi ¼ P pffiffiffiffiffiffi Xi Mi
(9)
i
P
mmix
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Re ¼
rmix vmix d mmix
(10)
3.2.2. Steady state technique for the measurement of heat transfer coefficient and reference temperature In this technique, the steady state surface temperature of the plate is measured for two different situations for the same flame jet impingement parameters (Re and Z/d) namely. The bottom side of the plate exposed to the impinging flame jet and the top side exposed to the ambient as shown in Fig. 3. The energy balance for this situation is given by 00
00
00
00
qconvð1Þ ¼ qncðtÞ þ qradðtÞ þ qradðbÞ |fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl} Known
4 4 ¼ hnc Twð1Þ T∞ þ 2s3 Twð1Þ T∞ |fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl} ¼ h Tref Twð1Þ
Known
(11) Fig. 4. Local energy balance for top insulated quartz plate impinged by flame jet.
The bottom surface of the plate is exposed to the flame jet and the top surface is insulated with a thick ceramic blanket as shown in Fig. 4. The energy balance for this situation is given by
00 00 4 4 qconvð2Þ ¼ qradðbÞ ¼ s3 Twð2Þ T∞ ¼ h Tref Twð2Þ |fflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflffl} Known Known
the plate for the two situations. Due to the low emissivity of the premixed flame jet, the radiation from the flame to plate is neglected [39]. The heat transfer coefficient for both the cases is assumed to be same as the radial temperature distribution is observed to be parallel resulting same temperature gradient within the plate.
(12) 00
00
where, ðqconvð1Þ ; Twð1Þ Þ and ðqconvð2Þ ; Twð2Þ Þ are respectively convective flame heat flux and corresponding wall temperature of
Eqs. (11) and (12) have two unknowns h and Tref which can be solved simultaneously to get,
00
00
qconvð1Þ qconvð2Þ h¼ Twð2Þ Twð1Þ
!
00
Tref ¼
qconvð1Þ h
(13)
þ Twð1Þ
!
00
¼
qconvð2Þ h
þ Twð2Þ
(14)
The reference temperature can be non-dimensionalised as effectiveness given by
h¼
Tref T∞ Tf T∞
(15)
For premixed flame, the thermo-physical properties of the combustion products at different temperatures are obtained from CEARUN (Chemical Equilibrium Applications), an online program developed by NASA. The thermo-physical properties of the combustion products are to be taken at the mean film temperature. The flame temperature for the methaneeair premixed (stoichiometric mixture) jet varies from 1800 K to 1950 K [41] for the range flame Reynolds numbers studied in the present work. In the present study, the flame temperature is taken an average of 1875 K all Reynolds numbers. 4. Results and discussions 4.1. Comparison of heat transfer distribution for cold jet and hot jet
Fig. 3. Local energy balance for uncovered quartz plate impinged by flame jet.
The Nusselt number and effectiveness distributions for isothermal air jets are obtained from the analysis of the steady
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state surface temperature by performing the local energy balance. The Reynolds number of the jet is varied from 500 to 1500 in steps of 250 for nozzle tip to the impingement surface distances of 2d, 4d and 6d. The cold jet represents the jet at room temperature. The hot jet has a temperature of 100 C at the exit of the nozzle. Fig. 5(aee) shows the comparison between cold and hot jet Nusselt number distributions for Z/d ¼ 2 for various Reynolds number of the jet flow. The Nusselt number distributions for the hot and cold jets follow a Gaussian profile with a maximum value at the stagnation point. The cold and hot jet Nusselt number distributions match reasonably well for a fixed Reynolds number. This suggests that the heat transfer characteristics of the impinging air jet are independent of the jet temperature provided an appropriate reference temperature is chosen for hot jet. Maximum deviation in Nu of 7% is observed for cold and hot jet for Re ¼ 1500 at the
407
stagnation region. This deviation is within the uncertainty limits. With the increase in the jet Reynolds number, the Nusselt number increases. Fig. 5(f) shows the radial effectiveness distribution for Z ¼ 2d for various jet Reynolds numbers. The effectiveness represents the thermal dilution of the impinging air jet due to the mass entrainment of the surrounding fluid into the main stream. For a fixed nozzle tip to plate distance, it is observed that the effectiveness at the stagnation point is independent of Reynolds number up to an r/d of 4 [23]. For radial distances greater than 4d, the effectiveness is dependent on Reynolds numbers. The effectiveness is lower for higher Reynolds number of 1500. This may be because of the thermal dilution of hot air caused by the entrainment of the ambient air into the hot air. This entrainment increases with the increase in the Reynolds number. Ricou and Spalding's relation [42] between the mass flow rate entrained to
(a) Re = 500
(b) Re = 750
(c) Re = 1000
(d) Re = 1250
(e) Re = 1500
(f) Effectiveness (hot jet)
Fig. 5. Heat transfer characteristics of clod and hot impinging air jets for various Reynolds numbers with Z/d ¼ 2.
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the mass flow rate at the exit of the nozzle suggests this increase in the entrainment.
0:5 r z m_ z ¼ 0:32 1 d r0 m_ 0
(16)
where, m0 is the mass flow rate of the jet fluid at the nozzle exit in kg/s, mz is the mass flow rate of the jet fluid at a distance of z from the nozzle exit due to entrainment in kg/s, r0 is the density of the jet fluid in kg/m3, r1 is the density of the surrounding fluid entraining into the jet in kg/m3 and d is the diameter of the nozzle in m. Fig. 6(aec) gives the comparison of Nusselt number distributions for cold and hot jets for nozzle tip to plate distances of 2d, 4d and 6d for a Reynolds number of 1000. Fig. 6(d) shows the radial distribution of effectiveness for nozzle to plate spacing of 2d, 4d and 6d for a jet Reynolds number of 1000. With the increase in the nozzle tip to impingement plate, the cold or hot jet stagnation point Nusselt number remains almost constant (from Z ¼ 2d to 6d) for Re ¼ 1000. This is due to the fact that the potential core region with in the free jet extends till certain length which depends on the jet Reynolds number [43]. The effectiveness of the jet decreases with the increase in the nozzle to the plate distance. This is because of increased surrounding air entrainment that thermally dilutes the jet as understood from Eq. (16). For a nozzle to plate distance of 2d, the effectiveness at the impingement point is around 0.9 (closer to unity). For smaller jet to plate spacings, the thermal entrainment is less and the effectiveness is closer to unity.
4.2. Comparison of heat transfer distribution of premixed flame jets with heated air jets The hot jet heat transfer characteristics (Nu and effectiveness) are independent of the jet temperature as both the potential core length and the entrainment characteristics are not functions of jet temperature [21]. Thus, for flame jets, the gas temperature is taken equal to temperature of flame along the centreline proximity to the flame tip as reported by Hindasageri et al. [41]. The flame temperature is averaged over the Reynolds number range of the study and a constant flame temperature of 1875 K is assumed for all the Reynolds numbers. Fig. 7(aee) shows the comparison of the premixed flame jet Nusselt number with cold and hot jet for various Reynolds numbers for burner to plate spacing of 6d. The Nusselt number distribution of premixed flame jet matches reasonably well with cold and hot jets. This suggests that the reference temperature (shown in the form of effectiveness) measured is quantified appropriately. The deviation between the Nusselt number for flame jet with that of hot jet is less than 8% for all Reynolds number except lower Reynolds number of 500 (deviation is around 18%). With the increase in the mixture Reynolds number, for a fixed burner to plate distance, the premixed flame cone height increases as shown in Table 1. This increases the Nusselt number as the flame tip approaches the plate. The premixed flame cone height plays an important role in heat transfer characteristics of impinging premixed flame jets similar to the potential core length of isothermal air jets. The premixed flame jet effectiveness is compared with that of hot jet in Fig. 8(aee) for various Reynolds numbers for burner to
(a) Z/d = 2
(b) Z/d = 4
(c) Z/d = 6
(d) Effectiveness (hot jet)
Fig. 6. Heat transfer characteristics of cold and hot impinging air jets for various nozzle to plate spacing at a Reynolds number of 1000.
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(a) Re = 500
(b) Re = 750
(c) Re =1000
(d) Re = 1250
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(e) Re = 1500 Fig. 7. Comparison of Nusselt number for cold, hot and premixed flame jet for Z/d ¼ 6 at different Reynolds numbers.
Table 1 Premixed flame cone height for various Reynolds numbers. Reynolds number, Re
Premixed flame cone height, Lf in mm
500 750 1000 1250 1500
9.2 13.8 18.6 22.8 28.0
plate spacing of 6d. It is observed that the effectiveness of premixed flame jet is lower in comparison with the hot jet for same Re and Z/ d. In reacting flows, the heat release and velocity field have strong interaction. This interaction substantially affects the combustion process. In flame jets due to instantaneous heat release, the combustion
products undergo a substantial stretching, causing higher entrainment (recirculation bubbles are formed between inflow and the outgoing products of combustion) of the ambient fluid into the flame jet in comparison with non-reacting hot jet [44]. This results in dilution of the combustion products and reduction in the reference temperature. The density of the products of combustion is less than the density of the hot air at the same temperature. Thus, from Eq. (16), it can be observed that the mass entrainment is more for the premixed flame jets resulting in a lower effectiveness. The effect of the burner to plate spacing on the jet Nusselt number and effectiveness for Re ¼ 1500 are shown in Figs. 9(aec) and 10(aec) respectively. For Re ¼ 1500 and Z/d ¼ 2, the premixed flame cone touches the impingement plate resulting in cool central core flame. Thus, the stagnation point of the plate in contact with cold unburnt mixture results a decrease in Nusselt number and effectiveness distribution in the stagnation region. This
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(a) Re = 500
(b) Re = 750
(c) Re =1000
(d) Re = 1250
(e) Re = 1500 Fig. 8. Comparison of effectiveness for hot and premixed flame jet for Z/d ¼ 6 at different Reynolds numbers.
phenomenon is observed for all Reynolds numbers having the flame heights higher than the burner to plate spacing. For Z/d ¼ 4, the premixed flame cone is located very closer to the impingement surface. Due to the reaction taking just on the surface of the plate, the effectiveness is higher than that of the hot jet. For Z/d ¼ 6, the flame tip is located at a farther distance with respect to the plate causing a decrement in the Nusselt number. This may be attributed to the increase in the entrainment causing thermal dilution which is more effective at higher Z/d. 4.3. Generalisation of the heat flux and wall temperature reported in the literature by calculating Nusselt number The radial distributions of steady state convective flame heat flux and wall temperature (measured with micro-heat flux sensor HFM) for premixed methane (CH4)eair flame jets impinging over copper plate are reported by Chander and Ray [30]. Zhao et al. [35]
reported the wall temperature and the steady state convective for heat fluxes (measured with heat flux transducer) for butane (C4H10)eair premixed flame jets impinging over brass and stainless steel plates. It may be observed that the heat flux and the wall temperatures reported by Zhao et al. [35] for stainless steel plate and brass plate are very different. Thus, the data reported in the literature is too specific and applicable to a particular plate material, thickness and the heat transfer condition on the rear side of the plate. The generalisation of the heat flux and the wall temperature data reported in the literature is carried out by using the reference temperatures from the present study and thereby calculating the heat transfer coefficient. The heat transfer coefficient is nondimensionalised in terms of Nusselt number with the properties of combustion products evaluated at mean film temperature. Fig. 11(aed) shows the comparison of the methaneeair flame jet Nusselt number from the present study with the Nusselt number
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(a) Z/d = 2
(b) Z/d = 4
(c) Z/d = 6 Fig. 9. Comparison of cold, hot and premixed flame jet Nusselt numbers for different burner to plate spacing at a Reynolds number of 1500.
(a) Z/d = 2
(b) Z/d = 4
(c) Z/d = 6 Fig. 10. Comparison of hot air jet and premixed flame jet effectiveness for different burner to plate spacing at a Reynolds number of 1500.
411
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(a) Re = 500
(b) Re = 1000
(c) Re = 1250
(d) Re = 1500
Fig. 11. Comparison of present study with Chander and Ray [30] e impinging premixed methane (CH4)eair flame jets.
calculated with the heat flux and wall temperatures of Chander and Ray [30] for burner to plate spacing of 4d for various Reynolds numbers (Re ¼ 600, 1000, 1200 and 1600). It may be observed that the Nusselt number distribution obtained from data of Chander and Ray [30] is reasonably matching with the present flame and hot jet results. However, data of Chander and Ray [30] underpredicts the stagnation region Nusselt number and overpredicts Nusselt number in the wall jet region. This may be due to the higher thermal conductivity of the plate material (copper) and higher heat transfer coefficient of water in the rear side resulting in radial diffusion of the heat imparted by the flame to the plate. Hence, the Nusselt number profile is more uniform. The flame temperature for butane (C4H10)eair flame is taken as 2150 K [45] for calculating the reference temperature from the effectiveness distribution (independent of fuel) for premixed methaneeair flame jet. Fig. 12(aee) shows the comparison of the Nusselt number calculated from heat flux and wall temperature data of Zhao et al. [35] for premixed butaneeair flame jets (using the effectiveness data of the current study to calculate the reference temperature) with the hot jet of the present study for various Reynolds numbers for a fixed burner to plate distance of 5d. The Nusselt number and the effectiveness of present study for Z ¼ 4d and 6d are averaged for Z ¼ 5d. In the wall jet region, Nusselt numbers of the flame jet and the hot jet match reasonably well. However, in the stagnation region, Nusselt number for flame jets is lower than that of hot jet. This is similar to that as observed in methaneeair flame jets of present study. It may be emphasized that, in general, the Nusselt number and effectiveness distribution for premixed flame jet is independent of the fuel provided an appropriate flame temperature is taken.
4.4. Practical significance/usefulness of present results Nusselt number and effectiveness distributions of the present study can be utilised for determining the steady state convective heat flux and wall temperatures for impinging cold jets, hot jets and premixed-flame jets. The data is valid for Reynolds number ranging from 500 to 1500 and nozzle or burner to plate distance of 2d to 6d. The strength of this generalisation is that, the present results can be used for any wall material, any surface heat transfer conditions (heat transfer coefficient and emissivity) of the plate on the front and rear surfaces and for any plate thickness, given the proper boundary conditions based on the practical application. This is demonstrated through a case study carried out using CFD package (FLUENT). The gas or flame temperature is appropriately taken and with the radial distribution of the effectiveness, the reference temperature distribution is obtained. Similarly, the heat transfer coefficient distribution is obtained from the Nusselt number distribution with the thermo-physical properties of gas or combustion products evaluated at the reference temperature. A user defined function (UDF) is written for the radial profiles of reference temperature and heat transfer coefficient on the jet impingement side of the plate. Suitable boundary conditions with the material and thermal properties are specified on all the surfaces. With the proper numerical model, the energy equation is solved for steady state by setting proper convergence criterion. When the solution is converged, the wall temperature on the impingement side is taken and the heat transfer coefficient profile in the UDF is modified with the thermo-physical properties of the gas or combustion products evaluated at mean film temperature. Then, the energy equation is solved with the modified UDF to get the wall temperature. The
P. Kuntikana, S.V. Prabhu / International Journal of Thermal Sciences 100 (2016) 401e415
(a) Re = 500
(b) Re = 750
(c) Re = 1000
(d) Re = 1250
413
(e) Re = 1500 Fig. 12. Comparison of present study with Zhao et al. [35] e impinging premixed butane (C4H10)eair flame jets.
process of modifying the UDF for heat transfer coefficient based on corrected mean film temperature and solving the energy equation is repeated until the wall temperatures of two successive iterations are within 2%. By using the steady state wall temperature, reference temperature and the heat transfer coefficient, the local steady state flame heat flux can be estimated. A quartz plate (1 mm thick, 150 mm 150 mm) is modelled. Tetrahedron body mesh was generated with minimum element size of 0.0002 m. Mixed boundary condition (h and Tref from UDF, 3 ¼ 0.93, T∞ ¼ 300 K) is specified on the impingement surface (IS) of the plate. Side surface is subjected to convection (hnc ¼ 10 W/m2 K, T∞ ¼ 300 K) boundary condition. Rear surface (RS) is subjected to mixed boundary condition (hnc ¼ 10 W/m2 K, T∞ ¼ 300 K and 3 ¼ 0.93). The energy equation is solved with second order upwind scheme. The residual for energy equation is set to 1010. For Chander and Ray's [30] case, the material of the plate is copper with the rear surface boundary condition of constant temperature of
310 K (assuming flowing water maintains constant temperature of the plate). Impingement surface is subjected to mixed boundary condition (hnc ¼ 10 W/m2 K, T∞ ¼ 300 K) and 3 ¼ 0.99 (for black paint coated over the sensor). Side surface is subjected to convection (hnc ¼ 10 W/m2 K, T∞ ¼ 300 K) boundary condition. Fig. 13(a) shows the steady state wall temperature for 10 mm diameter burner with impinging methaneeair premixed flame jet having Re ¼ 1000 and Z/d ¼ 4 impinging over a quartz plate (present study) and copper plate (Chander and Ray [30]). The wall temperatures from the numerical simulation match reasonably well with the experimentally measured wall temperatures. The wall temperatures measured by Chander and Ray [30] is very low compared with the present study due to cooling of the plate. Fig. 13(b) shows the comparison of the steady state convective flame heat flux obtained from the numerically computed steady state wall temperature, heat transfer coefficient and reference temperature with that obtained by the one-dimensional energy
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(a)
(b)
Fig. 13. Comparison of numerically computed steady state wall temperature and convective flame heat flux with the experimentally measured values for methaneeair premixed flame jet (Re ¼ 1000 and Z/d ¼ 4).
balance of the plate with the experimentally obtained wall temperature. Chander and Ray [30] measured the steady state flame heat flux with the heat flux sensor. The numerically predicted flame heat flux matches well with the experimental flame heat flux of the present study. Numerically predicted values for Chander and Ray [30] deviate from the experimental flame heat flux. This is due to the constant temperature boundary condition assumed during the numerical simulation, which may not be actually constant. The wall temperature profile on the top surface measured with thermocouples is not reported by Chander and Ray [30]. Thus, an approximate constant profile is assumed. It may be observed that the flame heat flux mainly depends on the wall temperature which is a function of thermal properties of plate material and thermal conditions. 5. Conclusions The present study compares the heat transfer characteristics of impinging isothermal air jets and premixed flame jets. The heat transfer characteristics of isothermal air jets are investigated with thin foil technique. The jet Reynolds numbers of 500, 750, 1000, 1250 and 1500 with nozzle to plate spacing's of 2d, 4d and 6d are considered for both impinging isothermal air jet and premixed flame jet studies. A steady state method is proposed to determine the heat transfer coefficient and the reference temperature of the impinging premixed flame jet (cone flame). The major findings of the present study are: i. For a fixed Reynolds number of the isothermal air jet, the local Nusselt number and effectiveness (for hot jet) distributions are independent of the difference in the jet and surrounding fluid temperature. ii The Nusselt number distributions for isothermal air jets and premixed flame jets match reasonably well for a fixed jet Reynolds number. Thus, the heat transfer characteristics of impinging premixed flame jet are analogous to that of isothermal air jet. The potential core length of isothermal air jets and the premixed flame cone height of premixed flame jets play a significant role in jet impingement heat transfer.
iii For a fixed jet Reynolds number, as the reacting flame jets entrain much surrounding fluid into them compared with the isothermal air jets, the impinging isothermal air jets have higher effectiveness than impinging premixed flame jets. iv For a fixed nozzle or burner to plate spacing, the effectiveness distributions for various jet Reynolds numbers overlap. As the spacing is increased, the thermal entrainment dilutes the jet temperature and the effectiveness decreases. 6. Contributions of the present work The present work suggests that the premixed flame can be visualized as an isothermal jet. This is because the Nusselt number distribution and the effectiveness of isothermal jet compares reasonably well with the premixed flame jet. The outcome of present study can be utilised for various industrial and domestic heating applications as benchmark data. The steady state wall temperature and the convective heat flux can be predicted numerically for any target surface material of any thickness for a circular isothermal air jet or premixed flame jet (of any fuel) impingement by appropriately taking gas or flame temperature. A steady state technique is proposed for determining the premixed flame jet heat transfer coefficient and reference temperature simultaneously. By using this reference temperature, the flame jet impingement data available in the literature is generalised in terms of Nusselt number. Acknowledgements The authors are thankful to Aeronautical Research and Development Board, India for partial funding of this work. The ARDB project sanction number is DARO/08/1041685/M/I. Authors are grateful to Mr. Rahul Shirsat for his assistance in building the experimental setup. References [1] K. Jambunathan, E. Lai, M.A. Moss, B.L. Button, A review of heat transfer data for single circular jet impingement, Int. J. Heat Fluid Flow 13 (1992) 106e115.
P. Kuntikana, S.V. Prabhu / International Journal of Thermal Sciences 100 (2016) 401e415 [2] R. Viskanta, Heat transfer to impinging isothermal gas and flame jets, Exp. Therm. Fluid Sci. 6 (1993) 111e134. [3] D. Lytle, B.W. Webb, Air jet impingement heat transfer at low nozzle spacing, Int. J. Heat Mass Transf. 37 (1994) 1687e1697. [4] J. Lee, S.J. Lee, The effect of nozzle configuration on stagnation region heat transfer enhancement of axisymmetric jet impingement, Int. J. Heat Mass Transf. 43 (2000) 3497e3509. [5] N. Gao, H. Sun, D. Ewing, Heat transfer to impinging round jets with triangular tabs, Int. J. Heat Mass Transf. 46 (2003) 2557e2569. [6] D.H. Lee, J. Song, C.J. Myeong, The effect of nozzle diameter on impinging jet heat transfer and fluid flow, J. Heat Transf. 126 (2004) 554e557. [7] W. Zhao, K. Kumar, A.S. Mujumdar, Flow and heat transfer characteristics of confined noncircular turbulent impinging jets, Dry. Technol. 22 (2004) 2027e2049. [8] P. Gulati, V. Katti, S.V. Prabhu, Influence of the shape of the nozzle on local heat transfer distribution between smooth flat surface and impinging air jet, Int. J. Therm. Sci. 48 (3) (2009) 602e617. [9] G. Singh, T. Sundarajan, K.A. Bhaskaran, Mixing and entrainment characteristics of circular and noncircular confined jets, J. Fluid Eng. 125 (5) (2003) 835e842. [10] D.W. Colucci, R. Viskanta, Effect of nozzle geometry on local convective heat transfer to a confined impinging air jet, Exp. Therm. Fluid Sci. 13 (1) (1996) 71e80. [11] S.V. Garimella, B. Nenaydykh, Nozzle-geometry effects in liquid jet impingement heat transfer, Int. J. Heat Mass Transf. 39 (1996) 2915e2923. [12] H.M. Hofmann, M. Kind, H. Martin, Measurements on steady state heat transfer and flow structure and new correlations for heat and mass transfer in submerged impinging jets, Int. J. Heat Mass Transf. 50 (2007) 3957e3965. [13] T.S. O'Donovan, D.B. Murray, Jet impingement heat transferdpart I: mean and root-mean-square heat transfer and velocity distributions, Int. J. Heat Mass Transf. 50 (2007) 3291e3301. [14] T.S. O'Donovan, D.B. Murray, Jet impingement heat transferdpart II: a temporal investigation of heat transfer and local fluid velocities, Int. J. Heat Mass Transf. 50 (2007) 3302e3314. [15] V. Katti, S.V. Prabhu, Experimental study and theoretical analysis of local heat transfer distribution between smooth flat surface and impinging air jet from a circular straight pipe nozzle, Int. J. Heat Mass Transf. 51 (2008) 4480e4495. [16] J.P. Bouchez, R.J. Goldstein, Impingement cooling from circular jet in cross flow, Int. J. Heat Mass Transf. 18 (1975) 719e730. [17] S.A. Striegel, T.E. Diller, An analysis of the effect of entrainment temperature on jet impingement heat transfers, ASME J. Heat Transf. 106 (1984) 804e810. [18] S.A. Striegel, T.E. Diller, The effect of entrainment temperature on jet impingement heat transfer, ASME J. Heat Transf. 106 (1984) 27e33. [19] B.R. Hollworth, S.I. Wilson, Entrainment effects on impingement heat transfer: part I e measurements of heated jet velocity and temperature distributions and recovery temperatures on target surface, J. Heat Transf. 106 (1984) 797e803. [20] B.R. Hollworth, L.R. Gero, Entrainment effects on impingement heat transfer: part II e local heat transfer measurements, J. Heat Transf. 107 (1985) 910e915. [21] R.J. Goldstein, K.A. Sobolik, W.S. Seol, Effect of entrainment on the heat transfer to a heated circular air jet impinging on a flat surface, Trans. ASME 112 (1990) 608e611. [22] J.W. Baughn, A.E. Hechanova, Y. Xiaojun, An experimental study of entrainment effects on the heat transfer from a flat surface to a heated circular impinging jet, J. Heat Transf. 113 (1991) 1023e1025. not, J.J. Vullierme, D. Eva, Heat transfer measurement of jet impingement [23] M. Fe with high injection temperature, C.R. Mec. 333 (2005) 778e782. [24] C.E. Baukal Jr., B. Gebhart, A review of empirical flame impingement heat transfer correlations, Int. J. Heat Fluid Flow 17 (14) (1996) 386e396.
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[25] C.E. Baukal, B. Gebhart, A review of semi-analytical solutions for flame impingement heat transfer, Int. J. Heat Mass Transf. 39 (1996) 2989e3002. [26] M.J. 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 Transf. 50 (13e14) (2007) 2816e2827. [27] M.J. Remie, G. S€ arnerb, M.F.G. Cremers, A. Omrane, K.R.A.M. Schreel, n, L.P.H. de Goey, Heat-transfer distribution for an impinging L.E.M. Alde laminar flame jet to a flat plate, Int. J. Heat Mass Transf. 51 (11e12) (2008) 3144e3152. [28] T.H. Van der Meer, Stagnation point heat transfer from turbulent low Reynolds number jets and flame jets, Exp. Therm. Fluid Sci. (1991) 115e126. [29] S. Chander, A. Ray, Flame impingement heat transfer: a review, Energy Convers. Manag. 46 (18e19) (2005) 2803e2837. [30] S. Chander, A. Ray, Influence of burner geometry on heat transfer characteristics of methane/air flame impinging on a flat surface, Exp. Heat Transf. 19 (2006) 15e38. [31] S. Chander, A. Ray, Heat transfer characteristics of three interacting methane/ air flame jets impinging on a flat surface, Int. J. Heat Mass Transf. 50 (3e4) (2007) 640e653. [32] S.S. Hou, Y.C. Ko, Influence of oblique angle and heating height on flame structure, temperature field and efficiency of an impinging laminar jet flame, Energy Convers. Manag. 46 (6) (2005) 941e958. [33] G.K. Agrawal, S. Chakraborty, S.K. Som, Heat transfer characteristics of premixed flame impinging upwards to plane surfaces inclined with the flame jet axis, Int. J. Heat Mass Transf. 53 (9e10) (2010) 1899e1907. [34] L. Dong, C.W. Leung, C.S. Cheung, Heat transfer characteristics of premixed butane/air flame jet impinging on an inclined flat surface, Heat Mass Transf. 39 (2002) 19e26. [35] Z. Zhao, T.T. Wong, C.W. Leung, Impinging premixed butane/air circular laminar flame jeteeinfluence of impingement plate on heat transfer characteristics, Int. J. Heat Mass Transf. 47 (2004) 5021e5031. [36] V. Hindasageri, R.P. Vedula, S.V. Prabhu, Heat transfer distribution for impinging methaneeair premixed flame jets, Appl. Therm. Eng. 73 (1) (2014) 459e471. [37] S. Clausen, Spectral emissivity of surface blackbody calibrators, Int. J. Thermophys. 28 (2007) 2145e2154. [38] A.E. Wald, J.W. Salisbury, Thermal infrared directional emissivity of powdered quartz, J. Geophys. Res. 100 (B12) (1995) 665e675. [39] V. Hindasageri, Heat Transfer Characteristics of Impinging MethaneeAir Flame Jets, Ph.D thesis, Indian Institute of Technology, Bombay, Mumbai, 2014. [40] R.J. Moffat, Using uncertainty analysis in the planning of an experiment, J. Fluids Eng. Trans. ASME 107 (2) (1986) 173e178. [41] V. Hindasageri, R.P. Vedula, S.V. Prabhu, Thermocouple error correction for measuring the flame temperature with determination of emissivity and heat transfer coefficient, Rev. Sci. Instrum. 84 (2013) 024902. [42] F.P. Ricou, D.B. Spalding, Measurements of entrainment by axisymmetrical turbulent jets, J. Fluid Mech. 11 (1961) 21e32. [43] T.L. Labus, E.P. Symons, Experimental Investigations of an Axisymmetric Free Jet with an Initially Uniform Velocity Profile, NASA Technical Note, NASA TN D-6783, Lewis Research Center, National Aeronautics and Space Administration, Cleveland, Ohio, May 1972. [44] G. Priya, Effects of the Reacting Flow Field on Combustion Processes in a Stagnation Point Reverse Flow Combustor, Ph.D thesis, Georgia Institute of Technology, North Avenue, Atlanta, 2008. [45] R.J. Reed, North American Combustion Handbook: A Basic Reference on the Art and Science of Industrial Heating with Gaseous and Liquid Fuels, third ed., vol. 1, North American Manufacturing Co., Ohio, 1985, pp. 11e12.
Contents lists available at ScienceDirect
International Journal of Thermal Sciences journal homepage: www.elsevier.com/locate/ijts
Isothermal air jet and premixed flame jet impingement: Heat transfer characterisation and comparison Pramod Kuntikana, S.V. Prabhu* Department of Mechanical Engineering, Indian Institute of Technology Bombay, Powai, Mumbai 400 076 India
a r t i c l e i n f o
a b s t r a c t
Article history: Received 15 June 2015 Received in revised form 2 October 2015 Accepted 13 October 2015 Available online xxx
The jet impingement heat transfer is a well-established technique for obtaining high heat transfer rates for many cooling and heating applications. Impingement heat transfer methods are widely used in domestic and industrial appliances. The impinging isothermal gas jets are used for both heating and cooling. However, premixed flame jets are used for heating the target surface. Present study is an attempt to compare the heat transfer characteristics of the isothermal air jets and premixed flame jets. The isothermal air jet having jet temperature of 30 C (cold jet or ambient temperature jet), 100 C (hot jet), and premixed methaneeair flame jet (stoichiometric mixture) with Reynolds numbers of 500, 750, 1000, 1250 and 1500 and nozzle or burner to plate spacings of 2d, 4d and 6d are experimentally investigated for heat transfer characterisation. Thin metal foil technique is used for characterising isothermal air jets. For a fixed jet Reynolds number, the Nusselt number of isothermal air jet is found independent of the temperature difference between jet and surrounding fluid. A steady state technique is proposed for characterisation of premixed flame jets. The outcome of the present study reveals that the heat transfer characteristics of isothermal air jet and the premixed flame jet are almost same. The higher thermal entrainment in premixed flame jet in comparison with isothermal air jet results in a lower effectiveness. The present heat transfer data can be directly utilised for many practical applications. © 2015 Elsevier Masson SAS. All rights reserved.
Keywords: Jet impingement Heat transfer analogy Entrainment Flame jet Air jet
1. Introduction Impinging jets find a variety of applications ranging from electronic cooling to industrial heating due to their peculiarity of having higher heat transfer coefficients. Common applications of gas jets include synthetic jet cooling, gas turbine blade cooling, combustion chamber cooling, glass manufacturing, textile industries, paper drying, preheating of metal billets, etc. Hydrocarboneair flame jets are widely used in industries for direct heating processes such as glass processing, boiler furnace wall heating, ladle preheating, melting of scrap metal parts, steam generation plants, etc.
Abbreviations: CFD, computational fluid dynamics; FJ, flame jet; HFM, heat flux micro-sensor; HJ, hot jet; IR, infrared; IS, impingement surface; MFC, mass flow controller; RS, rear surface; SLPM, standard litres per minute; UDF, user defined function. * Corresponding author. Tel.: þ91 22 25767515; fax: þ91 22 25726875. E-mail addresses: [email protected] (P. Kuntikana), svprabhu@iitb. ac.in (S.V. Prabhu). http://dx.doi.org/10.1016/j.ijthermalsci.2015.10.018 1290-0729/© 2015 Elsevier Masson SAS. All rights reserved.
The jet impingement heat transfer is a well-established research area with practical relevance, with good amount of contributions by several researchers in the field for last four decades. Numerous studies with ambient temperature air jet impingement are reported in literature. Jambunathan et al. [1] reported extensive review listing various parameters (such as Reynolds number, nozzle to plate distance, radial distance and the Prandtl number) affecting the impinging turbulent jet heat transfer. It reveals that the turbulent intensity at the nozzle exit, jet confinement and the nozzle geometries also play a very significant role in heat transfer characteristics. Viskanta [2] reported the studies on single and multiple impinging isothermal jets and flame jets. The separation distance between the jets is observed to be an important parameter in multiple jet arrays. Lytle and Webb [3] investigated the heat transfer characteristics of the impinging air jets for lower nozzle to plate spacing. The studies on effect of the nozzle geometry on impingement heat transfer are reported in literature [4e11]. The geometries other than circular found to induce secondary flow influencing the flow field of the jet. It is reported that axial velocity decay in noncircular jet is faster than the circular jets. Hofmann et al. [12], O'Donovan and Murray [13,14], Katti and Prabhu [15]
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Nomenclature A d h I k L l M m_ Nu Q_ q00 r Re T V v X Z z
surface area (m2) burner diameter (m) heat transfer coefficient (W/m2 K) current (A) thermal conductivity (W/m K) height (m) length of burner (m) molecular weight (kg/kmol) mass flow rate (kg/s) Nusselt number volume flow rate (m3/s) heat flux (W/m2) radial distance (m) Reynolds number temperature (K) voltage (V) velocity (m/s) mole fraction spacing between burner or nozzle and target plate (m) axial distance (m)
studied the ambient temperature jets and proposed correlations for radial distributions of heat transfer coefficient in terms of jet Reynolds number, jet to plate spacing, turbulent intensity. There are certain studies reporting the effect of jet temperature and surrounding temperature on the heat transfer characteristics of the impinging air jets. Bouchez and Goldstein [16] reported the local heat transfer coefficient and effectiveness for impinging circular jet interacting with the cross flow. It is reported that the impinging jet effectiveness decreases with the increase in the cross flow blowing rate. Striegel and Diller [17,18] reported the experimental and analytical studies on the effect of the entraining fluid temperature on the local heat transfer characteristics of multiple impinging turbulent air jets by varying the surrounding temperature. Hollworth and Wilson [19] and Hollworth and Gero [20] investigated the effect of the jet temperature on the heat transfer characteristics of a square edged nozzle. They found that the local heat transfer coefficient is independent of the temperature difference between the jet and surroundings. Goldstein et al. [21] presented the heat transfer characteristics of the impinging turbulent circular jets heated 20 C above the ambient. The effectiveness and the recovery factor are found to be independent of the temperature difference (jet temperature and ambient temperature) and flow Reynolds number. However, nozzle to plate spacing of impinging hot jets showed a strong dependency on both effectiveness and recovery factor. Baughn et al. [22] reported the effectiveness and Nusselt number profiles for heated jet at high Reynolds number (Re > 25,000). The effectiveness is found to be varying with the not et al. [23] invesradial location and nozzle to plate spacing. Fe tigated the local Nusselt number and effectiveness profiles of impinging jets of temperature varying from ambient to 141 C. The radial distributions of Nusselt number and effectiveness are found to be independent of jet temperatures. For a fixed nozzle to plate spacing, it is observed that the jet effectiveness is independent of jet Reynolds number. Impinging flame jet heat transfer investigations studying the effect of jet Reynolds number, mixture equivalence ratio, inter jet
Greek symbols 3 emissivity h effectiveness m absolute viscosity (Pa s) r density (kg/m3) s StefaneBoltzmann constant (5.67 108 W/m4 K) f equivalence ratio Subscripts/superscripts ∞ ambient aw adiabatic wall b bottom conv convection elec electrical f flame i looping variable, component number j jet m mean film mix mixture nc natural convection rad radiation ref reference t top w wall
spacing, burner to plate spacing, burner geometries, surface characteristics of impingement plate, incident angle and oxygen enhancement are reported in the literature. Baukal and Gebhart [24,25] reported the some analytical and semi-analytical solution for flame jet impingement heat transfer. Remie et al. [26,27] reported the analytical and experimental investigations on twodimensional axisymmetric cases for flame jet impingement. Van der Meer [28] presented the comparison between the heat transfer characteristics of the non-reacting jets and the flame jets. Chander and Ray [29] presented a review on flame jet impingement heat transfer. It is reported that the rate of heat transfer from the flame jet to a target solid surface depends on the structure of the flame, convective and radiative properties of the constituent gas species of the flame and the temperature of the gas within the boundary layer in vicinity of the plate. Chander and Ray [30] reported the heat transfer characteristics of premixed methaneeair flame jets. The convective flame heat flux and wall temperature data is reported for various impinging jet parameters. Chander and Ray [31] also presented the effect of inter jet spacing in interacting methane-air premixed flame jets. Hou and Ko [32], Agrawal et al. [33] and Dong et al. [34] investigated the effect of the oblique premixed flame jet impingement. The oblique flame jet impingement results in asymmetric heat flux over the impingement surface. The premixed butaneeair premixed flame jet impingement heat transfer characteristics are reported by Zhao et al. [35]. Researchers have used direct measurement with heat flux sensor [30,33e35] and inverse heat transfer technique [36] to determine the flame heat flux on to the target plate. Generally copper [30], bronze, stainless steel [35] and quartz [36] plates of various thickness are used as target surfaces for the for impingement studies. In the literature, heat flux and wall temperature of the plate is reported for premixed impinging flame jets [30,35]. These results would be specific to the material of the plate, the magnitude of wall temperatures of the plate (convection dominant or convection and radiation dominant) and the fuel (methane or butane) being used. However, Nusselt number and effectiveness
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distributions reported for isothermal air jets [15] are highly generic in nature. There is a need to generalise the premixed flame jet analogous to isothermal jet in order to enhance the practical applicability of reported results. Hence, the present study focuses on. i. Heat transfer characterisation of impinging cold (Tj ¼ T∞) and hot (Tj ¼ 100 C) air jets for Re ¼ 500, 750, 1000, 1250 and 1500 with nozzle to plate spacing, Z of 2d, 4d and 6d. ii. Steady state technique is proposed to find the heat transfer coefficient and the reference temperature for impinging premixed flame jets. iii. Heat transfer characterisation of impinging premixed flame jets for Re ¼ 500, 750, 1000, 1250 and 1500 with nozzle to plate spacing, Z of 2d, 4d and 6d for stoichiometric mixture (f ¼ 1.0). iv Comparison of heat transfer characteristics of impinging isothermal air jets and premixed flame jets. v Practical significance/usefulness of the results.
2. Experimental details 2.1. Description of experimental setup for isothermal air jet impingement heat transfer studies Fig. 1 shows the layout of the experimental setup used for the isothermal air jet impingement heat transfer studies. The compressed air is supplied from an air compressor (ELGI make) through air filter and pressure regulator maintaining the supply pressure of 2 bar. Air flow is metered through a mass flow controller (MFC) of
403
Aalborg make having range of 0e66.67 SLPM with an accuracy of 1.5% of full scale. The MFC is calibrated using DryCal (BIOS Defender 530H, Range: 300e30 000 cm3) primary gas flow calibrator. Metered air is passed through the plate heater having a heating capacity of 2 kW. The power supply to the heater is regulated with a variable auto-transformer to get different jet temperatures. The heated air is then carried to the pipe nozzle through a flexible high temperature stainless steel hose pipe. The heater, hose pipe and the pipe nozzle are insulated with ceramic blanket to avoid the heat loss from the heated air to the surrounding. The pipe nozzle is held firmly by a nozzle holder with a threaded clamp. The nozzle tip to the impingement surface distance is varied by moving the nozzle with respect to the impingement surface and then clamping. The stainless steel pipe nozzle has an inner diameter of 10 mm (measured with inside micrometre) and length to diameter ratio (l/ d) of 50 to ensure fully developed flow at the exit of the nozzle. The air jet issuing from the nozzle exit is made to impinge over a target surface. The target surface is a thin (thickness ¼ 0.05 mm) stainless steel foil having dimensions of 150 mm 220 mm is clamped firmly and stretched between the two copper bus bars. Firm grip is assured by sandwiching 5 mm of the foil from either side in between the pieces of the flat bus bars bolted together to a thick bakelite sheet for support. This prevents the target surface from ripple formation. The impingement plate assembly is mounted over a mild steel frame for support. For an experimental condition resulting in highest temperature gradient in the plate (for Re ¼ 1000 and Z/d ¼ 2), the numerical simulations with two dimensional axisymmetric modelling of the impingement surface revealed a maximum of 4% of the imposed heat flux is laterally conducted in the plate. Therefore, the lateral conduction in the plate is neglected. The plate is heated electrically (by resistance
Fig. 1. Schematic of experimental set up for isothermal air jet impingement heat transfer studies.
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heating) using a variable autotransformer and a step down transformer. The copper power cables from the transformer are connected across the copper bus bars. The copper bus bars have very low electrical resistance and hence the heating is uniform. The electric heating is varied by varying the voltage across the transformer. The local temperature of the plate on the impingement plane and the rear side is assumed to be the same as the one dimensional energy balance across the heated plate showed negligible temperature difference across two surfaces. The impingement plate is painted with Pyromark having an emissivity of 0.99 (painted with brush, spray paint and then cured by electrical heating) [37], on the impingement surface of the thin metal foil for thermal imaging purpose. Infrared thermal camera (Thermoteknix make VisIR® 640S) mounted on the rear side of the impingement surface is used to capture the steady state thermal images of the impinging surface. The camera captures the intensity of the incident radiation and during post processing of thermal images; the user must input the surface emissivity and temperature of the surroundings between the camera and the emitting surface to get the surface temperature values. The thermal camera is calibrated with a black body calibrator of TEMPSENS Make, CALsys 1500BB model. A linear curve is fit with an accuracy of 2% for the actual temperature of the surface based on the measured temperature over the entire operating range. The cold jet experiments are performed by switching off the power supply to the inline heater. Power is supplied to both the heater and the plate from an AC power source through a voltage stabilizer. The voltage and current across the heater and the plate are measured with digital meters (‘Meco’ make) having an accuracy of 20 ± 0.5% V and 400 ± 0.5% A, respectively. The jet temperature is measured with four ChromeleAlumel (Ktype) thermocouples mounted peripherally inside a tube of 13.5 mm inner diameter, 20 mm length at an axial spacing of 3 mm between the consecutive thermocouples. This assembly can be easily mounted on the tip of pipe nozzle for steady state jet temperature measurement. The output of the thermocouple is measured with milli-voltmeter (‘Meco’ make). The average of four thermocouple readings is taken for calculating the jet temperature. The thermocouples are calibrated with a constant temperature oil bath (‘Julabo’ make) over a temperature range of 25 C to 200 C. After the desired temperature is achieved, the thermocouple assembly is dismounted, suitable jet to plate distance is set with the clamped holder traverse mechanism and the jet is allowed to impinge over the plate. The jet impingement assembly is kept inside a transparent acrylic sheet box with MS Frame for support. This isolates the jet from the atmospheric fluctuations due to local wind movements. The power loss from the heated plate by radiation and natural convection are accounted in the calculation of the local heat transfer coefficient. In the present study, the pipe nozzle is mounted vertical and the impingement surface is held parallel to the ground unlike other cold jet studies where the nozzle is mounted parallel and the impingement surface is held normal to the ground. These two configurations do not differ much for cold jet and high Reynolds number heated jet studies, but for low Reynolds number heated jets the flow velocity induced by the buoyancy effect becomes comparable with the jet flow velocity. The flow momentum and the buoyancy force in the present configuration are in the same direction. This produces a symmetric temperature distribution over the impingement surface. In the latter configuration, the flow momentum is in the horizontal direction with the buoyancy force acting vertically upwards creating a resultant flow hitting the impingement plate in an oblique direction. This produces an eccentric temperature distribution over the impingement surface, which is not desirable.
2.2. Description of experimental setup for premixed flame jet impingement heat transfer studies Fig. 2 shows the experimental setup used for premixed flame jet impingement heat transfer study. The methane gas (99.5% purity) and the air from compressed air storage tank are metered through mass flow controllers (MFCs) having accuracy of 1.5% of full scale. The MFCs used are Aalborg make, USA. The air MFC has a range of 0e10 SLPM and that of methane MFC is 0e1 SLPM. The air and methane lines are maintained at 2 bar pressure. The air MFC is calibrated with DryCal (BIOS Defender 530H, Range: 300e30,000 cm3) calibrator and methane mass flow controller is calibrated by DryCal (BIOS Defender 530M, Range: 50e5000 cm3) calibrator, BIOS International make with an accuracy of 1% of the reading traceable to NIST standards. Metered methane and air are mixed thoroughly in a mixing cup. The mixing cup consists of steel balls to ensure the proper mixing of the fuel and air, and to reduce the flow fluctuations. The mixture is fed to a 10 mm diameter burner having length to diameter (l/d) ratio of approximately 50 to ensure fully developed flow. The target plate upon which the flame jet is impinged is made of quartz is having dimension of 150 mm 150 mm with thickness of 1 mm. The quartz has surface emissivity of 0.93 [38]. The burner is mounted on a holder which provides various burner to plate spacings by moving the burner with respect to the plate. The plate is mounted on a platform which holds the plate firmly. The steady state thermal images of the plate are captured from both the flame impingement surface and the rear surface. The premixed flame (blue flame) has very low emissivity (3 f z 0.02) [39]. So the premixed flame can be treated as transparent to the thermal radiation making the temperature measurements with the thermal camera valid on the flame jet impingement surface also. The one dimensional local energy balance across the thin quartz plate results in negligible lateral conduction. This can be assured with the impingement surface temperature and the rear surface temperature of the quartz plate captured by the thermal camera showing less than 2% deviation at steady state. The uncertainties in the measured and predicted quantities are obtained using the method reported by Moffat [40]. The uncertainty in Reynolds number and equivalence ratio is 5%, for temperature recorded with IR thermal camera is 2%, Nusselt number and reference temperature is around 12%. 3. Data reduction 3.1. Isothermal air jets The Reynolds number of the jet is given by
Re ¼
rvj d 4rQ_ ¼ pdm m
(1)
where, r is the density of the fluid in kg/m3, vj is the jet velocity in m/s, d is the pipe nozzle diameter in m and m is the dynamic viscosity of the fluid in Pa s. All the fluid properties are evaluated at the jet temperature, Tj. Average of ten thermal images is considered for analysis. For each Re, Z/d and jet temperature, the impingement plate is subjected to five different electrical heat fluxes by varying the power input to the plate. The plate loses heat to the surrounding by natural convection and the radiation depending on its surface temperature. There is only forced convection heat transfer due to the impingement of the jet. Thus, the energy balance across the plate surfaces assuming one dimensional heat conduction would be
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405
Fig. 2. Schematic of experimental setup for premixed flame jet impingement heat transfer studies.
00
00
00
00
00
qelec ¼ qconv þ qncðtÞ þ qradðtÞ þ qradðbÞ 00
(2)
9 VI 00 00 > = ; qconv ¼ h Tref Tw ; qncðtÞ ¼ hnc ðTw T∞ Þ; > A > 00 > 4 4 4 4 ; and qradðbÞ ¼ s3 ðbÞ Tw ¼ s3 ðtÞ Tw T∞ T∞
qelec ¼ 00
qradðtÞ
(3) where, V is the voltage across the target plate, I is the current flow, A is the surface area of the target plate, T∞ is the ambient temperature, 3 (t) ¼ 0.99 and 3 (b) ¼ 0.25 are respectively emissivities of top and bottom surfaces of target plate and hnc is the natural convection heat transfer coefficient equal to 10 W/m2 K. The top and the bottom surface temperature of the plate are taken equal to Tw. For a known electrical power input to the plate with the measured wall temperature, the convection heat flux of the impinging jet is given by
00 00 00 00 00 qconv ¼ h Tref Tw ¼ qelec qncðtÞ þ qradðtÞ þ qradðbÞ |fflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflffl} |fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl} Unknown
(4)
Known
By varying the electrical power input to the plate, the wall temperature of the plate changes. Let the five different convection heat fluxes and the corresponding wall temperatures obtained by 00 00 00 00 00 varying the electrical heat input to the plate be, q1 ; q2 ; q3 ; q4 ; q5 and Tw1, Tw2, Tw3, Tw4, Tw5 respectively. Now by rearranging Eq. (4) a 00 linear fit between qðiÞ and Tw(i) is obtained. 00
TwðiÞ ¼
qðiÞ h
þ Tref
(5)
Thus, for a linear curve fit with the convective heat flux along the abscissa and the wall temperature along the ordinate axes, the slope of the line will be negative of inverse of the heat transfer coefficient and the intercept along the ordinate axis will be the reference temperature. The reference temperature for the room temperature jet is nearly ambient temperature. The heat transfer coefficient and the reference temperature are non-dimensionalised to get Nusselt number and effectiveness.
Nu ¼
h¼
hd k
(6)
Tref T∞ Tj T∞
(7)
where, h is the convective heat transfer coefficient in W/m2 K, d is the nozzle diameter in m, k is the thermal conductivity (W/m K) of the fluid at mean film temperature, Tm ¼ ðTw þ Tref Þ=2. 3.2. Flame jets 3.2.1. Mixture parameters The mixture density, viscosity and the Reynolds number at burner exit are given by Eqs. (8)e(10) respectively.
rmix ¼
X
ri
(8)
pffiffiffiffiffiffi mi Xi Mi ¼ P pffiffiffiffiffiffi Xi Mi
(9)
i
P
mmix
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Re ¼
rmix vmix d mmix
(10)
3.2.2. Steady state technique for the measurement of heat transfer coefficient and reference temperature In this technique, the steady state surface temperature of the plate is measured for two different situations for the same flame jet impingement parameters (Re and Z/d) namely. The bottom side of the plate exposed to the impinging flame jet and the top side exposed to the ambient as shown in Fig. 3. The energy balance for this situation is given by 00
00
00
00
qconvð1Þ ¼ qncðtÞ þ qradðtÞ þ qradðbÞ |fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl} Known
4 4 ¼ hnc Twð1Þ T∞ þ 2s3 Twð1Þ T∞ |fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl} ¼ h Tref Twð1Þ
Known
(11) Fig. 4. Local energy balance for top insulated quartz plate impinged by flame jet.
The bottom surface of the plate is exposed to the flame jet and the top surface is insulated with a thick ceramic blanket as shown in Fig. 4. The energy balance for this situation is given by
00 00 4 4 qconvð2Þ ¼ qradðbÞ ¼ s3 Twð2Þ T∞ ¼ h Tref Twð2Þ |fflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflffl} Known Known
the plate for the two situations. Due to the low emissivity of the premixed flame jet, the radiation from the flame to plate is neglected [39]. The heat transfer coefficient for both the cases is assumed to be same as the radial temperature distribution is observed to be parallel resulting same temperature gradient within the plate.
(12) 00
00
where, ðqconvð1Þ ; Twð1Þ Þ and ðqconvð2Þ ; Twð2Þ Þ are respectively convective flame heat flux and corresponding wall temperature of
Eqs. (11) and (12) have two unknowns h and Tref which can be solved simultaneously to get,
00
00
qconvð1Þ qconvð2Þ h¼ Twð2Þ Twð1Þ
!
00
Tref ¼
qconvð1Þ h
(13)
þ Twð1Þ
!
00
¼
qconvð2Þ h
þ Twð2Þ
(14)
The reference temperature can be non-dimensionalised as effectiveness given by
h¼
Tref T∞ Tf T∞
(15)
For premixed flame, the thermo-physical properties of the combustion products at different temperatures are obtained from CEARUN (Chemical Equilibrium Applications), an online program developed by NASA. The thermo-physical properties of the combustion products are to be taken at the mean film temperature. The flame temperature for the methaneeair premixed (stoichiometric mixture) jet varies from 1800 K to 1950 K [41] for the range flame Reynolds numbers studied in the present work. In the present study, the flame temperature is taken an average of 1875 K all Reynolds numbers. 4. Results and discussions 4.1. Comparison of heat transfer distribution for cold jet and hot jet
Fig. 3. Local energy balance for uncovered quartz plate impinged by flame jet.
The Nusselt number and effectiveness distributions for isothermal air jets are obtained from the analysis of the steady
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state surface temperature by performing the local energy balance. The Reynolds number of the jet is varied from 500 to 1500 in steps of 250 for nozzle tip to the impingement surface distances of 2d, 4d and 6d. The cold jet represents the jet at room temperature. The hot jet has a temperature of 100 C at the exit of the nozzle. Fig. 5(aee) shows the comparison between cold and hot jet Nusselt number distributions for Z/d ¼ 2 for various Reynolds number of the jet flow. The Nusselt number distributions for the hot and cold jets follow a Gaussian profile with a maximum value at the stagnation point. The cold and hot jet Nusselt number distributions match reasonably well for a fixed Reynolds number. This suggests that the heat transfer characteristics of the impinging air jet are independent of the jet temperature provided an appropriate reference temperature is chosen for hot jet. Maximum deviation in Nu of 7% is observed for cold and hot jet for Re ¼ 1500 at the
407
stagnation region. This deviation is within the uncertainty limits. With the increase in the jet Reynolds number, the Nusselt number increases. Fig. 5(f) shows the radial effectiveness distribution for Z ¼ 2d for various jet Reynolds numbers. The effectiveness represents the thermal dilution of the impinging air jet due to the mass entrainment of the surrounding fluid into the main stream. For a fixed nozzle tip to plate distance, it is observed that the effectiveness at the stagnation point is independent of Reynolds number up to an r/d of 4 [23]. For radial distances greater than 4d, the effectiveness is dependent on Reynolds numbers. The effectiveness is lower for higher Reynolds number of 1500. This may be because of the thermal dilution of hot air caused by the entrainment of the ambient air into the hot air. This entrainment increases with the increase in the Reynolds number. Ricou and Spalding's relation [42] between the mass flow rate entrained to
(a) Re = 500
(b) Re = 750
(c) Re = 1000
(d) Re = 1250
(e) Re = 1500
(f) Effectiveness (hot jet)
Fig. 5. Heat transfer characteristics of clod and hot impinging air jets for various Reynolds numbers with Z/d ¼ 2.
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the mass flow rate at the exit of the nozzle suggests this increase in the entrainment.
0:5 r z m_ z ¼ 0:32 1 d r0 m_ 0
(16)
where, m0 is the mass flow rate of the jet fluid at the nozzle exit in kg/s, mz is the mass flow rate of the jet fluid at a distance of z from the nozzle exit due to entrainment in kg/s, r0 is the density of the jet fluid in kg/m3, r1 is the density of the surrounding fluid entraining into the jet in kg/m3 and d is the diameter of the nozzle in m. Fig. 6(aec) gives the comparison of Nusselt number distributions for cold and hot jets for nozzle tip to plate distances of 2d, 4d and 6d for a Reynolds number of 1000. Fig. 6(d) shows the radial distribution of effectiveness for nozzle to plate spacing of 2d, 4d and 6d for a jet Reynolds number of 1000. With the increase in the nozzle tip to impingement plate, the cold or hot jet stagnation point Nusselt number remains almost constant (from Z ¼ 2d to 6d) for Re ¼ 1000. This is due to the fact that the potential core region with in the free jet extends till certain length which depends on the jet Reynolds number [43]. The effectiveness of the jet decreases with the increase in the nozzle to the plate distance. This is because of increased surrounding air entrainment that thermally dilutes the jet as understood from Eq. (16). For a nozzle to plate distance of 2d, the effectiveness at the impingement point is around 0.9 (closer to unity). For smaller jet to plate spacings, the thermal entrainment is less and the effectiveness is closer to unity.
4.2. Comparison of heat transfer distribution of premixed flame jets with heated air jets The hot jet heat transfer characteristics (Nu and effectiveness) are independent of the jet temperature as both the potential core length and the entrainment characteristics are not functions of jet temperature [21]. Thus, for flame jets, the gas temperature is taken equal to temperature of flame along the centreline proximity to the flame tip as reported by Hindasageri et al. [41]. The flame temperature is averaged over the Reynolds number range of the study and a constant flame temperature of 1875 K is assumed for all the Reynolds numbers. Fig. 7(aee) shows the comparison of the premixed flame jet Nusselt number with cold and hot jet for various Reynolds numbers for burner to plate spacing of 6d. The Nusselt number distribution of premixed flame jet matches reasonably well with cold and hot jets. This suggests that the reference temperature (shown in the form of effectiveness) measured is quantified appropriately. The deviation between the Nusselt number for flame jet with that of hot jet is less than 8% for all Reynolds number except lower Reynolds number of 500 (deviation is around 18%). With the increase in the mixture Reynolds number, for a fixed burner to plate distance, the premixed flame cone height increases as shown in Table 1. This increases the Nusselt number as the flame tip approaches the plate. The premixed flame cone height plays an important role in heat transfer characteristics of impinging premixed flame jets similar to the potential core length of isothermal air jets. The premixed flame jet effectiveness is compared with that of hot jet in Fig. 8(aee) for various Reynolds numbers for burner to
(a) Z/d = 2
(b) Z/d = 4
(c) Z/d = 6
(d) Effectiveness (hot jet)
Fig. 6. Heat transfer characteristics of cold and hot impinging air jets for various nozzle to plate spacing at a Reynolds number of 1000.
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(a) Re = 500
(b) Re = 750
(c) Re =1000
(d) Re = 1250
409
(e) Re = 1500 Fig. 7. Comparison of Nusselt number for cold, hot and premixed flame jet for Z/d ¼ 6 at different Reynolds numbers.
Table 1 Premixed flame cone height for various Reynolds numbers. Reynolds number, Re
Premixed flame cone height, Lf in mm
500 750 1000 1250 1500
9.2 13.8 18.6 22.8 28.0
plate spacing of 6d. It is observed that the effectiveness of premixed flame jet is lower in comparison with the hot jet for same Re and Z/ d. In reacting flows, the heat release and velocity field have strong interaction. This interaction substantially affects the combustion process. In flame jets due to instantaneous heat release, the combustion
products undergo a substantial stretching, causing higher entrainment (recirculation bubbles are formed between inflow and the outgoing products of combustion) of the ambient fluid into the flame jet in comparison with non-reacting hot jet [44]. This results in dilution of the combustion products and reduction in the reference temperature. The density of the products of combustion is less than the density of the hot air at the same temperature. Thus, from Eq. (16), it can be observed that the mass entrainment is more for the premixed flame jets resulting in a lower effectiveness. The effect of the burner to plate spacing on the jet Nusselt number and effectiveness for Re ¼ 1500 are shown in Figs. 9(aec) and 10(aec) respectively. For Re ¼ 1500 and Z/d ¼ 2, the premixed flame cone touches the impingement plate resulting in cool central core flame. Thus, the stagnation point of the plate in contact with cold unburnt mixture results a decrease in Nusselt number and effectiveness distribution in the stagnation region. This
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(a) Re = 500
(b) Re = 750
(c) Re =1000
(d) Re = 1250
(e) Re = 1500 Fig. 8. Comparison of effectiveness for hot and premixed flame jet for Z/d ¼ 6 at different Reynolds numbers.
phenomenon is observed for all Reynolds numbers having the flame heights higher than the burner to plate spacing. For Z/d ¼ 4, the premixed flame cone is located very closer to the impingement surface. Due to the reaction taking just on the surface of the plate, the effectiveness is higher than that of the hot jet. For Z/d ¼ 6, the flame tip is located at a farther distance with respect to the plate causing a decrement in the Nusselt number. This may be attributed to the increase in the entrainment causing thermal dilution which is more effective at higher Z/d. 4.3. Generalisation of the heat flux and wall temperature reported in the literature by calculating Nusselt number The radial distributions of steady state convective flame heat flux and wall temperature (measured with micro-heat flux sensor HFM) for premixed methane (CH4)eair flame jets impinging over copper plate are reported by Chander and Ray [30]. Zhao et al. [35]
reported the wall temperature and the steady state convective for heat fluxes (measured with heat flux transducer) for butane (C4H10)eair premixed flame jets impinging over brass and stainless steel plates. It may be observed that the heat flux and the wall temperatures reported by Zhao et al. [35] for stainless steel plate and brass plate are very different. Thus, the data reported in the literature is too specific and applicable to a particular plate material, thickness and the heat transfer condition on the rear side of the plate. The generalisation of the heat flux and the wall temperature data reported in the literature is carried out by using the reference temperatures from the present study and thereby calculating the heat transfer coefficient. The heat transfer coefficient is nondimensionalised in terms of Nusselt number with the properties of combustion products evaluated at mean film temperature. Fig. 11(aed) shows the comparison of the methaneeair flame jet Nusselt number from the present study with the Nusselt number
P. Kuntikana, S.V. Prabhu / International Journal of Thermal Sciences 100 (2016) 401e415
(a) Z/d = 2
(b) Z/d = 4
(c) Z/d = 6 Fig. 9. Comparison of cold, hot and premixed flame jet Nusselt numbers for different burner to plate spacing at a Reynolds number of 1500.
(a) Z/d = 2
(b) Z/d = 4
(c) Z/d = 6 Fig. 10. Comparison of hot air jet and premixed flame jet effectiveness for different burner to plate spacing at a Reynolds number of 1500.
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(a) Re = 500
(b) Re = 1000
(c) Re = 1250
(d) Re = 1500
Fig. 11. Comparison of present study with Chander and Ray [30] e impinging premixed methane (CH4)eair flame jets.
calculated with the heat flux and wall temperatures of Chander and Ray [30] for burner to plate spacing of 4d for various Reynolds numbers (Re ¼ 600, 1000, 1200 and 1600). It may be observed that the Nusselt number distribution obtained from data of Chander and Ray [30] is reasonably matching with the present flame and hot jet results. However, data of Chander and Ray [30] underpredicts the stagnation region Nusselt number and overpredicts Nusselt number in the wall jet region. This may be due to the higher thermal conductivity of the plate material (copper) and higher heat transfer coefficient of water in the rear side resulting in radial diffusion of the heat imparted by the flame to the plate. Hence, the Nusselt number profile is more uniform. The flame temperature for butane (C4H10)eair flame is taken as 2150 K [45] for calculating the reference temperature from the effectiveness distribution (independent of fuel) for premixed methaneeair flame jet. Fig. 12(aee) shows the comparison of the Nusselt number calculated from heat flux and wall temperature data of Zhao et al. [35] for premixed butaneeair flame jets (using the effectiveness data of the current study to calculate the reference temperature) with the hot jet of the present study for various Reynolds numbers for a fixed burner to plate distance of 5d. The Nusselt number and the effectiveness of present study for Z ¼ 4d and 6d are averaged for Z ¼ 5d. In the wall jet region, Nusselt numbers of the flame jet and the hot jet match reasonably well. However, in the stagnation region, Nusselt number for flame jets is lower than that of hot jet. This is similar to that as observed in methaneeair flame jets of present study. It may be emphasized that, in general, the Nusselt number and effectiveness distribution for premixed flame jet is independent of the fuel provided an appropriate flame temperature is taken.
4.4. Practical significance/usefulness of present results Nusselt number and effectiveness distributions of the present study can be utilised for determining the steady state convective heat flux and wall temperatures for impinging cold jets, hot jets and premixed-flame jets. The data is valid for Reynolds number ranging from 500 to 1500 and nozzle or burner to plate distance of 2d to 6d. The strength of this generalisation is that, the present results can be used for any wall material, any surface heat transfer conditions (heat transfer coefficient and emissivity) of the plate on the front and rear surfaces and for any plate thickness, given the proper boundary conditions based on the practical application. This is demonstrated through a case study carried out using CFD package (FLUENT). The gas or flame temperature is appropriately taken and with the radial distribution of the effectiveness, the reference temperature distribution is obtained. Similarly, the heat transfer coefficient distribution is obtained from the Nusselt number distribution with the thermo-physical properties of gas or combustion products evaluated at the reference temperature. A user defined function (UDF) is written for the radial profiles of reference temperature and heat transfer coefficient on the jet impingement side of the plate. Suitable boundary conditions with the material and thermal properties are specified on all the surfaces. With the proper numerical model, the energy equation is solved for steady state by setting proper convergence criterion. When the solution is converged, the wall temperature on the impingement side is taken and the heat transfer coefficient profile in the UDF is modified with the thermo-physical properties of the gas or combustion products evaluated at mean film temperature. Then, the energy equation is solved with the modified UDF to get the wall temperature. The
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(a) Re = 500
(b) Re = 750
(c) Re = 1000
(d) Re = 1250
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(e) Re = 1500 Fig. 12. Comparison of present study with Zhao et al. [35] e impinging premixed butane (C4H10)eair flame jets.
process of modifying the UDF for heat transfer coefficient based on corrected mean film temperature and solving the energy equation is repeated until the wall temperatures of two successive iterations are within 2%. By using the steady state wall temperature, reference temperature and the heat transfer coefficient, the local steady state flame heat flux can be estimated. A quartz plate (1 mm thick, 150 mm 150 mm) is modelled. Tetrahedron body mesh was generated with minimum element size of 0.0002 m. Mixed boundary condition (h and Tref from UDF, 3 ¼ 0.93, T∞ ¼ 300 K) is specified on the impingement surface (IS) of the plate. Side surface is subjected to convection (hnc ¼ 10 W/m2 K, T∞ ¼ 300 K) boundary condition. Rear surface (RS) is subjected to mixed boundary condition (hnc ¼ 10 W/m2 K, T∞ ¼ 300 K and 3 ¼ 0.93). The energy equation is solved with second order upwind scheme. The residual for energy equation is set to 1010. For Chander and Ray's [30] case, the material of the plate is copper with the rear surface boundary condition of constant temperature of
310 K (assuming flowing water maintains constant temperature of the plate). Impingement surface is subjected to mixed boundary condition (hnc ¼ 10 W/m2 K, T∞ ¼ 300 K) and 3 ¼ 0.99 (for black paint coated over the sensor). Side surface is subjected to convection (hnc ¼ 10 W/m2 K, T∞ ¼ 300 K) boundary condition. Fig. 13(a) shows the steady state wall temperature for 10 mm diameter burner with impinging methaneeair premixed flame jet having Re ¼ 1000 and Z/d ¼ 4 impinging over a quartz plate (present study) and copper plate (Chander and Ray [30]). The wall temperatures from the numerical simulation match reasonably well with the experimentally measured wall temperatures. The wall temperatures measured by Chander and Ray [30] is very low compared with the present study due to cooling of the plate. Fig. 13(b) shows the comparison of the steady state convective flame heat flux obtained from the numerically computed steady state wall temperature, heat transfer coefficient and reference temperature with that obtained by the one-dimensional energy
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(a)
(b)
Fig. 13. Comparison of numerically computed steady state wall temperature and convective flame heat flux with the experimentally measured values for methaneeair premixed flame jet (Re ¼ 1000 and Z/d ¼ 4).
balance of the plate with the experimentally obtained wall temperature. Chander and Ray [30] measured the steady state flame heat flux with the heat flux sensor. The numerically predicted flame heat flux matches well with the experimental flame heat flux of the present study. Numerically predicted values for Chander and Ray [30] deviate from the experimental flame heat flux. This is due to the constant temperature boundary condition assumed during the numerical simulation, which may not be actually constant. The wall temperature profile on the top surface measured with thermocouples is not reported by Chander and Ray [30]. Thus, an approximate constant profile is assumed. It may be observed that the flame heat flux mainly depends on the wall temperature which is a function of thermal properties of plate material and thermal conditions. 5. Conclusions The present study compares the heat transfer characteristics of impinging isothermal air jets and premixed flame jets. The heat transfer characteristics of isothermal air jets are investigated with thin foil technique. The jet Reynolds numbers of 500, 750, 1000, 1250 and 1500 with nozzle to plate spacing's of 2d, 4d and 6d are considered for both impinging isothermal air jet and premixed flame jet studies. A steady state method is proposed to determine the heat transfer coefficient and the reference temperature of the impinging premixed flame jet (cone flame). The major findings of the present study are: i. For a fixed Reynolds number of the isothermal air jet, the local Nusselt number and effectiveness (for hot jet) distributions are independent of the difference in the jet and surrounding fluid temperature. ii The Nusselt number distributions for isothermal air jets and premixed flame jets match reasonably well for a fixed jet Reynolds number. Thus, the heat transfer characteristics of impinging premixed flame jet are analogous to that of isothermal air jet. The potential core length of isothermal air jets and the premixed flame cone height of premixed flame jets play a significant role in jet impingement heat transfer.
iii For a fixed jet Reynolds number, as the reacting flame jets entrain much surrounding fluid into them compared with the isothermal air jets, the impinging isothermal air jets have higher effectiveness than impinging premixed flame jets. iv For a fixed nozzle or burner to plate spacing, the effectiveness distributions for various jet Reynolds numbers overlap. As the spacing is increased, the thermal entrainment dilutes the jet temperature and the effectiveness decreases. 6. Contributions of the present work The present work suggests that the premixed flame can be visualized as an isothermal jet. This is because the Nusselt number distribution and the effectiveness of isothermal jet compares reasonably well with the premixed flame jet. The outcome of present study can be utilised for various industrial and domestic heating applications as benchmark data. The steady state wall temperature and the convective heat flux can be predicted numerically for any target surface material of any thickness for a circular isothermal air jet or premixed flame jet (of any fuel) impingement by appropriately taking gas or flame temperature. A steady state technique is proposed for determining the premixed flame jet heat transfer coefficient and reference temperature simultaneously. By using this reference temperature, the flame jet impingement data available in the literature is generalised in terms of Nusselt number. Acknowledgements The authors are thankful to Aeronautical Research and Development Board, India for partial funding of this work. The ARDB project sanction number is DARO/08/1041685/M/I. Authors are grateful to Mr. Rahul Shirsat for his assistance in building the experimental setup. References [1] K. Jambunathan, E. Lai, M.A. Moss, B.L. Button, A review of heat transfer data for single circular jet impingement, Int. J. Heat Fluid Flow 13 (1992) 106e115.
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