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Heat transfer distribution for impinging methane–air premixed flame jets
Accepted Manuscript Heat transfer distribution for impinging methane –air premixed flame jets Vijaykumar Hindasageri, Rajendra P. Vedula, Siddini V. Prabhu PII:
S1359-4311(14)00664-4
DOI:
10.1016/j.applthermaleng.2014.08.002
Reference:
ATE 5856
To appear in:
Applied Thermal Engineering
Received Date: 26 March 2014 Revised Date:
30 July 2014
Accepted Date: 1 August 2014
Please cite this article as: V. Hindasageri, R.P. Vedula, S.V. Prabhu, Heat transfer distribution for impinging methane –air premixed flame jets, Applied Thermal Engineering (2014), doi: 10.1016/ j.applthermaleng.2014.08.002. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
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Heat transfer distribution for impinging methane –air premixed flame jets Vijaykumar Hindasageri2, Rajendra P. Vedula3 and Siddini V. Prabhu1 Department of Mechanical Engineering, Indian Institute of Technology, Bombay, India
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[email protected], [email protected], [email protected]
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ADDRESS FOR CORRESPONDENCE Dr. S.V. PRABHU1, Professor, Department of Mechanical Engineering, Indian Institute of Technology, Bombay Powai, Mumbai – 400 076 INDIA E-mail:[email protected]; Telephone : (+91) 22-25767515 Fax: (+91) 22-2572 6875, 2572 3480
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ABSTRACT Heat transfer by flame jet impingement is extensively used in industrial and domestic heating applications. The present experimental study proposes the application of an inverse heat
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conduction (IHCP) technique to obtain the heat flux distribution for methane-air premixed flame jet impinging on a flat plate. The heat flux distribution is studied for burner tubes of circular shape (d = 10 mm and 8.75 mm), square shape (width = 10 mm and 7.65 mm) and rectangular shape (19 mm × 9mm). Methane-air premixed flame jet of Reynolds number varying from 600 to
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2200 and an equivalence ratio of 1 is considered. The nozzle to burner tip distance is varied from 2 to 6. Axis switching is observed for non-circular shaped burner flame jets. Correlations for local Nusselt number and effectiveness distribution are proposed for circular and square burners
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by direct measurement of the adiabatic wall temperature. The heat transfer coefficients and adiabatic wall temperatures are validated with the experimental heat flux data available in the literature. The non-dimensional flame premixed cone height (ratio of flame premixed cone height to the distance of the burner tip from the impingement wall) alone governs the Nusselt number and effectiveness.
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thermography
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Keywords: flame jet, local heat flux, adiabatic wall temperature, tube burner, infrared
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NOMENCLATURE Meaning
A
Area (m2)
A/F
Air to fuel ratio
Cp
Specific heat (J/kgK)
d
Hydraulic diameter (m)
I
Current (Amps)
k
Thermal conductivity (W/m K)
L
Flame inner cone length (m)
M
Molecular weight
Nu
Nusselt number
Pe
Peclet Number
Pr
Prandtl number
qʺ
Heat flux (W/m2K)
Q
Volumetric heat (W/m3)
r
Arbitrary radius (m)
R
Maximum radius of the burner tube (m)
Re
Reynolds number
Su
Burning velocity (m/s)
t
Time (sec)
T
Temperature (K)
Square burner width (m)
x, y, r, z
Coordinate directions
X
Mole fraction
Y
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Voltage (V)
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w
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Average velocity of fuel-air mixture (m / s)
um V
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Symbol
Mass fraction
z
Burner tip to target plate distance (m)
Z
Quartz plate thickness/depth (m)
Greek symbols
3
α
Thermal diffusivity (m / s2)
β
Radial velocity gradient (1/s)
μ
Absolute viscosity (Pa-s)
ρ
Density (kg / m3)
φ
Equivalence ratio
η
Effectiveness
Subscripts/
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Superscripts
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Adiabatic wall
conv
convection
e
Edge of boundary layer
f
flame
FJ
Flame jet
i ,init
Initial
j
Component of the mixture
m
Mixture
NC
Natural convection
rad
Radiation
0
Stagnation point
w
Wall
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aw
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1. Introduction Heat transfer by flame jet impingement is extensively used in several industrial and domestic
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applications like melting of metal billets in a closed heating furnace, glass processing, domestic gas geysers and others. The phenomenon of flame jet impingement heating is dependent on four different mechanisms of heat transfer- forced convection, radiation, thermochemical heat release (TCHR) and condensation of water vapor in the burnt gas. Amongst the four mechanisms of heat
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transfer, forced convection is the most dominant and accounts for nearly 90% of the heat transferred in flames with air as oxidizer. Reviews by Viskanta [1], Baukal and Gebhart[2-3] and Chander and Ray [4] give substantial information of the flame jet impingement studies. These
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studies are mostly experimental in nature. Recently analytical expressions are reported by Remie et al. [5] for two-dimensional and axisymmetric cases of impinging flame jets. These analytical expressions are based on isothermal plug flow concept for the flame jet valid for a radial distance, r < R and nozzle-tip distance, z < 2R. For two-dimensional case with non-viscous assumption, they have reported a simple expression given by Eq. (1). Remie et al. [5] are further able to arrive at an expression (Eq. 2) for viscous flow case by adjusting the analytical
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expression result with numerical simulation result carried out in a commercial CFD package FLUENT.
k (Tf − Tw )
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q0" =
z
where, Pe =
k (Tf − Tw )
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z
(1)
Pe
v e ρ zCp k
(
Pe ⋅ exp − 0.28 Pr0.4
)
(2)
The fluid properties for Pe are evaluated at an average temperature (maximum temperature within the boundary layer and target plate surface temperature). The fluid velocity (ve) is the velocity at the edge of the boundary layer. In the subsequent work by Remie et al.[6], they matched the results obtained by analytical expression with the numerical solution from FLUENT. They found that the ratio of the two results decay in an exponential fashion for region away from the stagnation region (r > R) and therefore corrected their analytical expression by an 5
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exponential multiplication factor. However, in order to use the Eqs. (1) and (2), the flame temperature needs to be measured near the edge of the boundary layer. The measurement of flame at the edge of the boundary layer is difficult as this requires proper location of
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thermocouple. Furthermore, this intrusion of thermocouple would disturb the boundary layer. Studies on numerical investigation of this problem are reported by Conolly and Davies [7], Som et al.[8], Chander and Ray [9] and Remie et al.[6]. Different burner geometries (single, multiple and annular) are used along with inverse diffusion flame (IDF) burners and swirl induced burners
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[10-18]). Almost all these reported studies are on the estimation of convective heat transfer characteristics while studies on radiation heat transfer characteristics [19-21] and emissions [21-
i)
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24] are limited. Following conclusions can be drawn from the reported literature: The heat transfer distribution is strongly dependent on the nozzle-plate spacing [1-24], burner shape [17], Reynolds number [1-25], equivalence ratio, oxygen enhancement [19], jet incidence angle [26], impingement plate material [27] and inter-jet spacing [14, 16]. ii) The effect of surface characteristics of the impingement plate on the heat transfer characteristic is less significant [21].
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iii) Thermochemical heat release is a dominant mechanism of heat transfer contributing by more than 40% for oxygenated methane flames [25]. This may be neglected for methane-air flames [25].
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The heat flux reported in the literature is measured by a ring calorimeter [2, 3] and heat flux sensors [4, 9, 10-18]. The size of the heat flux sensor is around 4 to 6 mm in diameter. Hence,
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the measured heat flux is averaged over this area. Furthermore, this heat flux sensor is to be traversed to different locations to measure the heat flux at different locations. Hence, the heat flux distribution reported in the literature lacks sufficient resolution, except the approach using inverse heat conduction (IHCP) method of Norteshaur and Millan [28] and Loubat et al. [29]. High spatial resolution enables one to understand important physical phenomenon like the axisswitching (Gutmark et al. [30] and Lou [31]). Use of inverse heat conduction method using liquid crystals are extensively used in the estimation of heat transfer coefficient for impinging air jets (Baughn [32], Talib et al. [33], Sagheby and Kowsary [34]) and film cooling problem (Ai et
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al.[35], Chen et al. [36]). In the present work, an IHCP method using analytical solution for semi-infinite medium is used to get high resolution heat flux using a thermal infrared camera. Nusselt number distribution is of engineering importance for the flame jet impingement heat
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transfer process. Correlations for Nusselt number distributions are reported in the literature based on analytical and semi-analytical studies. A collection of these correlations is available in the review papers of Viskanta [1] and Baukal and Gebhart [2-3]. Van der Meer [37] compared the Nusselt number distribution of isothermal non-reacting jets with that of the flame jets. He
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showed that if the properties of the burnt gases are taken at the temperature corresponding to the average enthalpy in the boundary layer formed on the plate, then the Nusselt number distribution
defined as given in Eqs. (3) and (4).
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of flame jets matches reasonably well with isothermal jets. The heat flux and Nusselt number are
q ′′ = h (Taw − Tw )
Nu =
hd k
(3) (4)
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The evaluation of Nusselt number requires the accurate data of the adiabatic wall temperature (Taw). Hence, most of the heat transfer correlations reported in the literature [2,3] are basically semi-analytical, which are modified form of the Sibulkin’s equation [38] given in Eq. (5). (5)
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q "s = 0.763 ( β s ρ e µ e ) 0.5 Pre−0.6 Cp e ( Te − T w )
Even then, there are difficulties involved in the evaluation of βs and Te since these parameters are
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to be estimated at the edge of the boundary layer. Therefore the utility of these correlations is difficult. Although Nusselt number correlations are reported in some studies in the literature, the adiabatic wall temperature is evaluated in an arbitrary manner. For instance, Van der Meer [37] defines the Nusselt number based on the adiabatic wall temperature evaluated as the temperature of the flame at the axis of the burner. In another study by Chander and Ray [9], the adiabatic wall temperature is evaluated as the adiabatic flame temperature. Therefore, the reported Nusselt number correlations are not the true values. In the present investigation, the adiabatic wall temperature is measured using thermal infrared camera. The objectives of the present work are as follows 7
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i) Application of an inverse heat conduction (IHCP) technique to obtain localized heat flux distribution with high spatial resolution in short time ii) Obtain heat flux distribution for circular (d = 8.7 mm and 10 mm) and non-circular burners (square of sides 7.6 mm and 10 mm and rectangular burner of size: 19 mm × 9 mm)
on experimentally measured adiabatic wall temperature
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2. EXPERIMENTAL DETAILS
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iii) Obtain Nusselt number and effectiveness distribution for circular and square burners based
2.1 Description of experimental setup
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Figure 1 is the schematic of the experimental set-up used in studying the flame jet impingement
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heat transfer.
Fig. 1 Schematic of the experimental setup
Mass Flow controllers (MFC) of accuracy 1.5% of full scale are used to meter the flow of methane gas (99.5% purity) and air from compressed air storage tank. The mass flow controllers used are of Aalborg make, USA. The air mass flow controller is calibrated with DryCal (DCLITE H) calibrator, BIOS International make whose accuracy is 1% of the reading traceable to NIST standards. The methane mass flow controller is calibrated by Soap bubble meter of PCI
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Analytics make, India whose accuracy is 2% of reading traceable to FCRI standards, India. Methane and air are mixed in a mixing tube. The stainless steel balls ensure that the two fluids find enough time for mixing and reduce the flow fluctuations. The accuracy of the flow metering is further validated by the measurement of the burning velocity (Vijaykumar et al. [39]).The
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dimensions of the burners used in the present study are given in Table 1. Table 1 Details of the burner geometry Area (mm2)
Dimension (mm) 8.7
59.45
Circle
10
78.55
Square
7.6 × 7.6
57.76
Square
10 × 10
100
Rectangle
19 × 9
8.7
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Circle
Hydraulic diameter (mm)
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Shape
171
10 7.6 10 12.2
The length to diameter ratio (l/d) of all tube burners are maintained as 50 which is based on the requirement for fully developed flow criterion, l/d > 30. The impingement plate is made of
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quartz whose size is 150 mm × 150 mm. Three plates of different thicknesses namely 1 mm, 3 mm and 5 mm are considered in this study. The emissivity of the quartz plate reported in the literature is 0.93 [40, 41]. The temperature distribution of the quartz plate is measured by the use of thermal infrared camera (Thermoteknix make VisIR® Ti 200). Specifications of this camera
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are given in Table 2.
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Table 2 Specifications of uncooled thermal cameras used in the present study Model Detector Spectral range Pixel Resolution FOV Minimum focus distance Temperature range Accuracy Frames per second
VisIR Ti 200 Microbolometer Uncooled FPA 7.5 – 13 µm 320 × 240 25 × 19 0.3 m -20°C to 1200°C ± 2% of reading 25
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This camera can record 25 thermal images in a second. As infrared camera transforms the incident radiation into temperature readings, few parameters like emissivity of the emitting body, atmospheric temperature between camera and object are to be necessarily introduced during post-processing the thermal images. The spectral range of IR cameras is 7.5 µm to 13 µm.
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Although, the main part of the response lies between 7.5 µm and 13µm, the camera is actually sensitive to radiation in a larger spectrum, namely from 6.5 µm to 17.8µm. This camera is further calibrated with a black body calibrator of TEMPSENS Make, CALsys 1500BB model. The
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accuracy of curve fit expression from calibration is 2% of reading. 2.2 Data reduction 2.2.1 Technique for heat flux measurement
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A typical heat flux distribution, when the premixed cone does not touch the plate, is shown in the Fig. 2. In the present methodology, the impingement plate is modeled as a semi-infinite medium governed by the following equation (Eq. 6) and boundary conditions.
∂ 2T 1 ∂T = ∂z 2 α ∂t
(6)
At t = 0 : Tw1(r, t) = Tw2(r, t) = T∞
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At t = t : Tw2 (r, t) = T∞, At z = 0 q ′′(r ) = q ′FJ′ (r ) The temperature distribution, T (Z, t) with time (t) at a given depth (Z) in a semi-infinite medium for a constant heat flux (qʺ) is given by Eq. (7).
− Z 2 q ′′Z 2q ′′ αt / π Z − exp erfc k k 2 αt 4αt
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T (Z ,t ) − Ti =
(7)
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The temperature distribution on the back side of the quartz plate is recorded using the infrared thermal camera. This recorded temperature T (Z, t) is then matched with that of Eq. (7) at different time intervals, for a short time, by varying the heat flux value (qʺ) such that the square root of the sum of squares, RSS =
∑ (T n
i =1
analytical
2
− Texperimental ) is minimum. Since this is the inverse
way of estimation of heat flux, the sensitivity coefficient (dT(Z, t)/dqʺ) has to be studied (Beck et al. [42]). On differentiating the Eq. (7), the sensitivity coefficient is expressed as Eq. (8).
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Convection loss = 0
Radiation loss = 0
Tw2 (t)
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Z Tw1 (t)
Radiation loss = 0
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z
d
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′ (r ) Heat flux from flame, q′FJ
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r
Fig. 2 Schematic representation of the heat exchange process for the axisymmetric flame jet impinging on a flat plate
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−Z2 dT ( Z ,t ) 2 αt / π = exp dq ′′ k 4αt
Z Z − erfc 2 αt k
(8)
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The sensitivity coefficients for different depths (Z) are same for all the thicknesses at varying time as presented by Beck et al. [42]. The thermal conductivity (k) and thermal diffusivity (α) of the quartz plate is computed at varying temperatures (T (K)) as per Eqs. (9 and 10). k = 0.0015T + 0.8956 (W/m K)
(9)
α = (9 × 10-9 T 2 – 1 × 10-5T + 0.0108) × 10-4 (m2/s)
(10)
Figure 3a shows the temperature distribution of the quartz plate of thickness 3mm impinged by a flame jet at time t = 10 seconds for a burner diameter of 10 mm at z/d = 4 and Re = 1000. The heat flux mapping for z/d = 4, ϕ = 1 and Re = 1000 on the back side of the plate is shown in Fig. 3b. 11
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(a)
(b)
Fig. 3 Circular burner of diameter 10 mm (z/d = 4, Re = 1000 and φ = 1)
a) Temperature (K) distribution on back side of plate at t = 10 s b) Temperature mapping of experimental data measured on back side with that of Eq. (7)
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This mapping is done for short initial time. For the present quartz plates, the matching of experimental and analytical temperatures values is for less than 5 seconds for 1.1 mm thick plate, 15 seconds for 3 mm thick plate and 30 seconds for 5 mm thick plate. The temperature data for the first 1/3rd of total mapping time is considered in the analysis. Temperature mapping over a
temperature measurement with the infrared camera.
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short time period rather than at a single time instant would nullify the uncertainties in
The comparison of heat flux estimated at Re = 1000, z/d = 4 and ϕ = 1 for different plate
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thicknesses is shown in Fig. 4a.
Fig. 4 Comparison of present experimental heat flux for circular burner of diameter 10 mm:
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a) for different plate thicknesses, b) flame side and back side measurements, Z = 3mm There is a good match of heat flux values for the thicknesses considered. However, for Z = 1
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mm, the estimated heat flux is more scattered which could be due to magnification of noise in the experimental data. The 3 mm thick quartz plate is used for the data presented in further sections of this study.
The backside measurement would enable capturing thermal images of the
impingement plate without loss of aspect ratio, which is the case for flame side measurement, due to obstruction of image by the burner tube. The backside temperature measurement does violate the mathematical constraint of Eq.(6)through the requirement of the backside boundary condition (At t = t : Tw2 (r, t)). Two separate measurements are done: i) based on front side temp measurement when Tbackside = T∞ and ii) based on back side temp measurement when Tbackside
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marginally higher than T∞. The quartz plate selected is 3mm thick and the test case is Re = 1400, z/d = 4 and ϕ = 1. The flame side temperature is measured for time less than 2 seconds when the heat has not diffused to backside wall (Tbackside = T∞). The estimated heat fluxes from the flame
2.2.2 Method for measurement of adiabatic wall temperature
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side and the backside measurements are in good agreement as shown in Fig.4b.
The adiabatic wall temperature is defined as the steady state impingement side wall temperature when the other sides are insulated. This is experimentally measured by insulating the top side of
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the impingement plate by using an insulating material (Ceramic blanket) as shown in Fig. 5. Insulation material (Ceramic blanket)
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Insulation box
Thermal camera
Tube burner
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Quartz plate
Fig. 5 Schematic of direct measurement of adiabatic wall temperature using thermal infrared camera
The transmissivity of premixed flames is nearly unity. Hence, the steady state adiabatic wall temperature is measured by a thermal camera from the front side. A total of 10 images is taken at steady state from the thermal camera and then averaged at each pixel in the Thermagram software.
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2.2.3 Nusselt number and effectiveness distribution The heat transfer coefficient is calculated using Eq. (3) with the wall temperature (Tw1) being taken as the average temperature on the impingement side of the plate for the short time (5 seconds). Nusselt number is calculated using Eq. (4) with the thermal conductivity taken at
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adiabatic wall temperatures using CEA software developed by NASA [43]. Effectiveness for the flame impingement process is given by Eq. (11).
Taw − T∞ Tadf − T∞
(11)
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η=
2.2.4 Mixture parameters
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The mixture density is calculated from Eq. (12), the mixture viscosity is calculated from Eq. (13) and the mixture Reynolds number (Re) is calculated from Eq. (14).
ρm = ∑Yjρ j
(12)
∑µ X ∑X
(13)
µm =
j
j
Mj
ρ mum d µm
(14)
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Re =
Mj
j
The uncertainties in the measured parameters are estimated by the method of Moffat [44]. Table 3 gives the uncertainties of various parameters reported in the present study.
1
Parameter
Minimum
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Sl No.
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Table 3 Uncertainties in various parameters reported in the present study
uncertainty (%)
Maximum uncertainty (%)
Equivalence ratio
5
10
Reynolds number
5
10
Temperature from thermal camera
2
2
4
Heat flux
6
12
5
Nusselt number
8
16
6
Effectiveness
4
8
2 3
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2.3 Validation of the present IHCP technique Chander and Ray [17] have reported heat flux measurements using heat flux sensor. The burner diameter for the present study and that reported by Chander and Ray [17] is same. However, the experimental conditions for the present case (transient) and that of Chander and Ray [17] (steady)
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are different.
The reported heat flux data of Chander and Ray [17] is compared by the following two different methods
The estimated heat flux by IHCP method in the present study (green line in Fig. 6)
•
Heat flux is estimated from Eq. (3) using the phenomenon constants – the heat transfer
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•
coefficient (h) and adiabatic wall temperature (Taw) measured from the present study. The
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wall temperatures are taken from reported data of Chander and Ray [17] (red line in Fig. 6)
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Fig. 6 Comparison of recalculated and reported heat flux of Chander and Ray [17] at z/d = 4, ϕ = 1, Re = 600 and1800 There is a reasonably good match of heat flux values from both steady state and transient methods. This is because the wall temperatures of present IHCP study and that of Chander and Ray [17] are comparable (around 100°C) and the wall heat flux solely depends on this parameter as per Eq. (3). The advantages of the present IHCP method of heat flux estimation are – o
It has high spatial resolution (nearly 60,000 data points) unlike the use of a sensor reported in literature. Even with the IHCP method employing numerical method (Loubat et al. [28]), sufficient resolution is not possible due to the requirement of huge memory and
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computational time. To reduce the computational time, the experimental input data points are reduced by techniques like Discrete Cosine transform (DCT). However, this would greatly reduce the resolution of the measured data and would fail to capture the steep gradients in the
rectangular burners which show multiple elliptical hot spots. o
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estimated parameter especially for multiple jet impingement and impingement with
It requires vey less computational time (less than 15 minutes), since simple analytical solution for semi-infinite medium (1-D transient equation) is to be computed. Numerical IHCP techniques are based on assumptions of the initial spatial heat flux boundary condition
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which is again assumed temporally and spatially by methods like the Function specification method. To arrive at the proper heat flux value, one has to do several iterations and this
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consumes time. So, the philosophy of applying DCT now comes into picture that takes values that are average of neighboring data. In the present analytical IHCP technique the heat flux is obtained by directly applying the analytical solution for semi-infinite medium. Hence, no substantial iterations are required. The only iterations for the present analytical IHCP technique is done to get the least square fit for small varying time (5 seconds interval in a step size of 1/5th sec). It is found to take less than 15 minutes of computational time for the contour
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maps shown in the present investigation. The computational platform is a desktop of i5 series Pentium processor of 8 GB RAM and 64 bit Windows 7 Operating system o
Accurate estimation of heat flux is possible. In the case of heat flux sensor, the accuracy is limited due to the size of the sensor. For the IHCP method using numerical method, accurate
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material properties of the impingement plate are to be used. In most instances, the material property of the plate itself needs to be determined, again by IHCP method [42].
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3. Distribution of heat flux, Nusselt number and effectiveness The spatial distribution of heat flux for varying Reynolds number, nozzle-burner tip distance and equivalence ratio is presented for square, circular and rectangular burners. The flame jet for noncircular burners is found to switch their axis and is captured in the contour plots. The radial distribution of Nusselt number (Nu) and effectiveness (η) is presented and correlations for circular and square burners are provided. The adiabatic flame temperature is taken as 2200K and the ambient temperature as 300K.
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3.1 Heat flux distribution 3.1.1 Circular and Square burners The contour plots of heat flux distribution for circular and square burners is shown in Figs. 7 and
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8 at a Reynolds number of 1000, equivalence ratio of 1 at different nozzle plate spacing (2 to 6). Referring to Fig. 7, perfect circular symmetric heat flux distribution pattern is observed for circular flame jet issuing from the burners of diameter 10 mm and 8.7 mm. For the burner of diameter 10 mm at Re = 1000, the heat flux decreases with the increase in z/d from 2 to 4. For
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further increase in z/d from 4 to 6, the change in heat flux is negligible. For the burner of diameter 8.7 mm at z/d = 4, the heat flux increases with the increase in Re from 600 to 1400. However, for square burners, axis switching is observed as shown in Fig. 8 and is believed to be
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reported for the first time for impinging flame jet. This phenomenon is due to vortex formation at the corners of the burner wall tip. The detailed information on the development of these vortices and their structure for square jets is reported by Grinstein et al. [45] and Grinstein and DeVore [46] and Miller et al. [47]. For the square jets, the axis is switched by 45° in the present experimental results (Fig. 8).
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This outcome is in agreement with the observations reported by Grinstein and DeVore [46] and Miller et al. [47]. Furthermore, the axis switching is more predominant in square burner of larger dimension. This is because larger size vortices would be generated in the larger burner and hence more the strength of axis switching. For the smaller burner, the heat flux distribution is rather in
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concentric circles shaped away from stagnation region with short region near stagnation depicting a subdued diamond shaped pattern. The location of inner premixed cone influences the
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heat flux distribution on the target plate. Flame jets with the premixed cone nearer to the target plate produce higher heat flux unless the inner premixed cone does not touch the target plate. The experimentally measured inner premixed cone height for the square and circular burners at different Reynolds number is given in Table 4. The flame cone height can be obtained by a simple expression in terms of the mixture velocity and the burning velocity given by Eq. (15), derived by Kleijn [17]. Lf =
u mix d 2 Su
(15)
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Table 4 Premixed flame cone heights (mm) for different burners square, d = 10mm Eq. measured (15) 15.2 16.9 21.9 22.5 27.4 28.1 32.4 33.8 37 39.4
circle, d = 8.7mm Eq. measured (15) 15.1 14.95 20 19.93 25.5 24.91 30.3 29.9
square, d = 7.6mm Eq. measured (15) 15.2 16.9 21.6 22.5 27.7 28.1 32.7 33.8
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circle, d = 10mm Eq. measured (15) 600 15.3 14.95 800 19.8 19.93 1000 25.4 24.91 1200 30 29.9 1400 35.1 34.9
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Re
Flame cone height (Lf) computed by Eq. (15) is also given in Table 4. For the square burner the
4 umix d For the square and circular π 2 Su .
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diameter, d is calculated based on equivalent area, i.e., L f =
shaped burners of same hydraulic diameter (d = 10 mm), it is observed from Table 4 that the cone heights are equal with a slightly higher value for the square burner. Therefore, the heat flux for a square burner is slightly higher than that of circular burner as shown in Figs. 7-8. Furthermore, the location of the premixed cone tip from the impingement plate for same shape
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(circular or square) is different for different hydraulic diameters. Smaller diameter tubes have their premixed cone located much closer to the target plate for a given Reynolds number and equivalence ratio. Hence, the heat flux distribution for smaller diameter tubes is higher unless the
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premixed cone touches the impingement plate.
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(d)
(e)
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(c)
(f)
Fig. 7 Heat flux (kW/m2) distribution for circular burners; diameter 10 mm at Re = 1000; a) z/d = 2, b) z/d = 4, c) z/d = 6 and diameter 8.7mm at z/d = 4; d) Re = 600, e) Re = 1000, f) Re = 1200 20
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(c)
(f)
Fig. 8 Heat flux (kW/m2) distribution for square burners; Re =1000: a) d = 10 mm; z/d =2, b) d = 10 mm; z/d = 4, c) d = 10 mm; z/d = 6, d) d = 7.6 mm; z/d = 2, e) d = 7.6 mm; z/d = 4, f) d = 7.6 mm; z/d = 6; Burner orientation 21
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3.1.2 Rectangular burner Contour plots of rectangular burner for Reynolds number varying from 800 to 2200 at an equivalence ratio =1 and z/d = 4 is shown in Fig. 9. Axis switching is clearly observed in all the
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cases studied. In Fig. 9, the orientation of the burner is shown in the caption of the figure. Grinstein [48] reported on the vortex ring dynamics for rectangular burners of different aspect ratios. The axis is found to switch by 90° for aspect ratios of 2 and 3. A similar study by Miller et al. [47] also concluded that the axis is found to switch by 90° for rectangular nozzle of aspect
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ratios of 2. In the present experimental study, for a rectangular burner of aspect ratio of 2.1, the axis switched by 90° as shown in Fig. 9. Two circular hot spots are observed along the maximum dimension of the burner as shown in Fig. 9. The region between these hotspots has relatively
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lower heat flux. The distance between these two hot spots increases with the increase in z/d. There is no substantial decrease (from 75% to 77%) in the heat flux gradient between the two hot spots for Re = 800 to 1400. However, there is substantial decrease (from 77% to 30%) of heat flux gradient between the two hot spots from Re = 1400 to 2200.The central elliptical minima could be due to reduction of the flame gas velocity at the center due to the vortex formation that tends to flush out the gases in a radially outward direction. For x/d > 3 and y/d > 2, the multi-
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elliptical pattern vanishes and a single ellipse is observed. For Re = 1000, the maximum heat flux is observed for the lowest z/d. At z/d = 2, the inner premixed cone of the flame is closest to the target plate as compared to higher z/d. For z/d = 4, the heat flux increases with the increase in the
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Reynolds number. The maximum heat flux is observed for Re = 2200. The increase in the heat flux with increase in Re is due to increase in the premixed cone height. With the increase in the
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Re, the premixed cone tip is closer to the impingement plate and therefore the heat flux increases.
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(f)
Fig. 9 Heat flux distribution (kW/m2) for rectangular burner; a) Re =1000; z/d =2, b) Re =1000; z/d = 4, c) Re =1000; z/d = 6, d) Re =800; z/d = 4, e) Re =1400; z/d = 4, f) Re =2200; z/d = 4; Burner orientation -
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3.2 Nusselt number and Effectiveness distribution Nusselt number and effectiveness distribution for circular, square and rectangular burner is presented. The adiabatic flame temperature (Tadf) for methane air flame of equivalence ratio of 1
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is 2200 K. The ambient temperature (T∞) in the present study is taken as 300 K for the calculation of effectiveness. 3.2.1 Circular and square burners
The Nusselt number and effectiveness distributions for circular and square tube burners of
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hydraulic diameter 10 mm, impinging on a quartz plate are shown in Figs. 10 and 11. The equivalence ratio of the fuel-air mixture is 1. The Reynolds number (Re) range covered is 600 to
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1400 while the nozzle-tip to impingement plate distance (z/d) is varied from 2 to 6. The stagnation point Nusselt number and effectiveness is found to increase with the increase in the Reynolds number unless the inner premixed cone height touches the impingement plate. Furthermore, the Nusselt number and effectiveness have peak values at the stagnation point and exhibit radial decay, when the inner premixed cone is not touching the impingement plate. With the increase in the impingement distance (z/d), both Nusselt number and effectiveness decrease
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and the radial distribution pattern tends to flatten.
Three empirical correlations are used to fit the present data for stagnation point Nusselt number for circular and square burners as given in Eqs.(16 - 18).
c
(16)
Lf Nu0 = a Re z
c
(17)
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Lf Nu0 = a Pe z b
b
Lf Nu0 = a z
+ b
(18)
Equation (16) is based on the analytical solution (Eq.5) of Remie et al [5]. Furthermore, it is evident that the inner premixed cone plays an important role and hence the non- dimensional parameter, Lf /z is introduced in Eq. (16). Lf measured by direct photographs is used in the present correlations.
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Fig. 10 Nusselt number and effectiveness distribution for Circular burner of d = 10 mm
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Fig.11 Nusselt number and effectiveness distribution for Square burner of d = 10 mm
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Equation (17) is based on the empirical form assumed by Chander and Ray [9] and Eq. (18) is based on the present hypothesis that the ratio of location of the cone tip from the impingement plate to the distance of the burner tip from the impingement plate is the sole parameter to correlate the Nusselt number and effectiveness. The maximum deviation for all three correlations
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is found to be 15%. Hence, knowing only the flame cone height, it is sufficient enough to predict the Nusselt number. The expression for radial distribution of Nusselt number is given by Eq. (19). Similar expressions for effectiveness are given by Eqs. (20) and (21).
L
(20)
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η 0 = a f + b z
(19)
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Nu r =c +d Nu 0 d
η r = c + d η0 d
(21)
Table 5 gives the curve fit constants for the square and circular burners for r/d < 4. Table 5 Curve fit constants for Eqs. (18-21)
Eq. No.
a
b
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Circular burners c
Square burners d
a
b
c
d
-51
111
----
----
26.7
15.3
-0.099
1.04
-0.106
0.48
----
-----
0.141
0.32
-0.052
1.08
Lf /z > 1.1
-36
20
10
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18, 19
80
20, 21
-0.22
0.151
---
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18
0.69
0.283
---
Lf /z < 1.1
-0.086
0.99 Lf /z > 1.1
---
--Lf /z < 1.1
-0.053
1.03
The Nusselt number and effectiveness increases for increasing Lf / z until it reached a value of 1.1 and thereafter the trend reverses. For Lf / z < 1.1, the maximum deviation in the curvefit correlation for Nusselt number given by Eq. (19) for circular and square burners is 25% and 27
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22%. For the curvefit correlation, for effectiveness given by Eq. (21) for circular and square burners the maximum deviation is 10% and 8%. For Lf /z >1.1, the maximum deviation in the curvefit correlation for Nusselt number given by Eq. (19) for circular and square burners is 25% and 30%. For the curvefit correlation, for effectiveness given by Eq. (21) for circular and square
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burners the maximum deviation is 7% and 8%. For Lf /z >1.1, the radial Nusselt number and effectiveness curvefits have significantly higher deviations and therefore are not presented.
A comparison of Nusselt number and effectiveness is done between circular and square burners
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based on same hydraulic diameter and same equivalent area as shown in Fig. 12.
Fig. 12 Nusselt number and effectiveness distribution for circular and square burners based on same hydraulic diameter and same equivalent area
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There is a good agreement in Nusselt number and effectiveness distribution for the same hydraulic diameter case and significantly large deviation for the same equivalent area. This is due to the influence of the non-dimensional inner premixed cone height (Lf /z). For same hydraulic diameter case, the Lf /z differs only by a small magnitude but for same equivalent area
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Lf /z differs by a large magnitude. However, the small difference in Lf /z leads to significant deviations in Nusselt number and effectiveness for same hydraulic diameter case when the inner premixed cone tip is nearer to the impingement plate, for instance Re =1400, z/d = 4 shown in
deviation in the actual and the curve fit data is 5%.
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4. Conclusions
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Fig. 12. The data presented in Figs. (10-12) is obtained from a polynomial fit of 10th order. The
Heat flux distribution for premixed methane-air flame jet is studied for Reynolds number varying from 600 – 1400 at an equivalence ratio of 1 for nozzle tip-target plate distance varying from 2 to 4. An inverse heat conduction technique is applied with semi-infinite medium assumption for the target plate. The thermal infrared camera enables high resolution temperature measurement of the backside of the impingement plate. The measured initial-short time transient temperature is
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then analyzed to get the heat flux in an inverse way. The condition of minimization of sum of squares for the difference between the measured and predicted temperatures is applied by varying the heat flux. The adiabatic wall temperature has been estimated by direct measurement.
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Following are the outcomes of the present investigation. Heat flux distribution with high spatial resolution, short computational time and good accuracy is obtained
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Axis switching is observed in non-circular burners, for square burner it is more predominant in burner with larger dimension
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Stagnation point and radial Nusselt number distribution correlations are given for
circular and square burners
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The non-dimensional flame cone height, Lf /z is the sole parameter that correlates the Nusselt number and effectiveness distribution
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•
There is a good agreement in Nusselt number and effectiveness distribution for circular and square burners based on same hydraulic diameter and significantly large deviation for same equivalent area.
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Acknowledgements The first author would like to acknowledge the support of MHRD, Govt. of India for sponsoring him to pursue Ph.D at Indian Institute of Technology, Bombay. The authors are also grateful to
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Aeronautical Research and Development Board for funding this work.
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premixed annular flame jet, Applied Thermal Engineering 36 (2012) 386e392. [14] Dong L., Leung C.W., and Cheung C. S., Heat transfer Characteristics of a Pair of
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Management 46 (2005) 941–958. [27] Zhao Z., Wong T.T., Leung C.W., Probert S.D., Wok design: thermal-performance influencing parameters, Applied Energy 83 (2006) 387–400. [28] Nortershauser D., Millan P., “Resolution of a three-dimensional unsteady inverse problem by sequential method using parameter reduction and infrared thermography measurements”, Num. Heat Transfer, Part A, 37 (2000) 587-611.
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[32] Baughn J. W., Liquid crystal methods for studying turbulent heat transfer, Int. J. Heat and
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Fluid Flow 16 (1995) 365-375.
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heat transfer coefficientin jet impingement using transient inverse heat conduction problem, Experimental Heat Transfer 22 (2009) 300–315.
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[36] Chen P, Ding P., Ai D., An improved data reduction method for transient liquid crystal thermography on film cooling measurements, International Journal of Heat and Mass Transfer 44 (2001) 1379 -1387.
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[40] Wentink T., Planet W. G., Infrared Emission Spectra of Quartz, Journal of the optical society of America, 51 (6) (1960) 595-600.
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[42] Beck J. V., Blackwell B., Clair C. R., Inverse heat conduction – Ill-posed Problems, Wiley,
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[44] Moffat R.J., Using Uncertainty Analysis in the Planning of an Experiment, Journal of Fluids Engineering, Transactions of the ASME (1986).
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[45] Grinstein F. F., Gutmark E., and Parr T.,Near field dynamics of subsonic free square jets- A computational andexperimental study, Phys. Fluids 7 (1995)1483. [46] Grinstein F. F. and DeVore C. R., Dynamics of coherent structures and transition to
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turbulence in free square jets, Phys. Fluids 8 (1996) 1237. [47] Miller R. S., Madnia C. K. and Givi P., Numerical Simulation of Non-circular jets,
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Computers & Fluids 24 (1)(1995) l -25. [48] Grinstein F. F., Selfinduced vortex ring dynamics in subsonic rectangular jets, Phys. Fluids 7, (1995) 2519.
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Figure captions Fig. 1 Schematic of the experimental setup
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Fig. 2 Schematic representation of the heat exchange for the axisymmetric jet impinging on a flat plate Fig. 3 Circular burner of diameter 10 mm (z/d = 4, Re = 1000 and φ = 1)
a) Temperature (K) distribution on back side of plate at t = 10 s b) Temperature mapping of experimental data measured on back side with that of Eq. (7)
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Fig. 4 Comparison of present experimental heat flux for different plate thicknesses for circular burner of diameter 10 mm
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Fig. 5 Schematic of direct measurement of adiabatic wall temperature using thermal infrared camera
Fig. 6 Comparison of recalculated and reported heat flux of Chander and Ray [17] at z/d = 4, ϕ = 1, Re = 600 and1800 Fig. 7 Heat flux distribution for circular burners; diameter 10 mm at Re = 1000; a) z/d = 2, b) z/d = 4, c) z/d = 6 and diameter 8.7mm at z/d = 4; d) Re = 600, e) Re = 1000, f) Re = 1200
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Fig. 8 Heat flux distribution for square burners; Re =1000: a) d = 10 mm; z/d =2, b) d = 10 mm; z/d = 4, c) d = 10 mm; z/d = 6, d) d = 7.6 mm; z/d = 2, e) d = 7.6 mm; z/d = 4, f) d = 7.6 mm; z/d = 6; Burner orientation -
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Fig. 9 Heat flux distribution for rectangular burner; a) Re =1000; z/d =2, b) Re =1000; z/d = 4, c) Re =1000; z/d = 6, d) Re =800; z/d = 4, e) Re =1400; z/d = 4, f) Re =2200; z/d = 4; Burner orientation -
Fig. 10 Nusselt number and effectiveness distribution for Circular burner of d = 10 mm Fig.11 Nusselt number and effectiveness distribution for Square burner of d = 10 mm Fig. 12 Nusselt number and effectiveness distribution for circular and square burners based on same hydraulic diameter and same equivalent area
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Highlights IHCP technique to obtain local heat flux distribution using thermal camera
•
Adiabatic wall temperature and heat transfer coefficient are given
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Circular, square and rectangular burners are used
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Axis switching is observed in non-circular burners
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Correlations for local Nusselt number and effectiveness are given
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S1359-4311(14)00664-4
DOI:
10.1016/j.applthermaleng.2014.08.002
Reference:
ATE 5856
To appear in:
Applied Thermal Engineering
Received Date: 26 March 2014 Revised Date:
30 July 2014
Accepted Date: 1 August 2014
Please cite this article as: V. Hindasageri, R.P. Vedula, S.V. Prabhu, Heat transfer distribution for impinging methane –air premixed flame jets, Applied Thermal Engineering (2014), doi: 10.1016/ j.applthermaleng.2014.08.002. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
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Heat transfer distribution for impinging methane –air premixed flame jets Vijaykumar Hindasageri2, Rajendra P. Vedula3 and Siddini V. Prabhu1 Department of Mechanical Engineering, Indian Institute of Technology, Bombay, India
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[email protected], [email protected], [email protected]
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1
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ADDRESS FOR CORRESPONDENCE Dr. S.V. PRABHU1, Professor, Department of Mechanical Engineering, Indian Institute of Technology, Bombay Powai, Mumbai – 400 076 INDIA E-mail:[email protected]; Telephone : (+91) 22-25767515 Fax: (+91) 22-2572 6875, 2572 3480
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ABSTRACT Heat transfer by flame jet impingement is extensively used in industrial and domestic heating applications. The present experimental study proposes the application of an inverse heat
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conduction (IHCP) technique to obtain the heat flux distribution for methane-air premixed flame jet impinging on a flat plate. The heat flux distribution is studied for burner tubes of circular shape (d = 10 mm and 8.75 mm), square shape (width = 10 mm and 7.65 mm) and rectangular shape (19 mm × 9mm). Methane-air premixed flame jet of Reynolds number varying from 600 to
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2200 and an equivalence ratio of 1 is considered. The nozzle to burner tip distance is varied from 2 to 6. Axis switching is observed for non-circular shaped burner flame jets. Correlations for local Nusselt number and effectiveness distribution are proposed for circular and square burners
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by direct measurement of the adiabatic wall temperature. The heat transfer coefficients and adiabatic wall temperatures are validated with the experimental heat flux data available in the literature. The non-dimensional flame premixed cone height (ratio of flame premixed cone height to the distance of the burner tip from the impingement wall) alone governs the Nusselt number and effectiveness.
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thermography
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Keywords: flame jet, local heat flux, adiabatic wall temperature, tube burner, infrared
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NOMENCLATURE Meaning
A
Area (m2)
A/F
Air to fuel ratio
Cp
Specific heat (J/kgK)
d
Hydraulic diameter (m)
I
Current (Amps)
k
Thermal conductivity (W/m K)
L
Flame inner cone length (m)
M
Molecular weight
Nu
Nusselt number
Pe
Peclet Number
Pr
Prandtl number
qʺ
Heat flux (W/m2K)
Q
Volumetric heat (W/m3)
r
Arbitrary radius (m)
R
Maximum radius of the burner tube (m)
Re
Reynolds number
Su
Burning velocity (m/s)
t
Time (sec)
T
Temperature (K)
Square burner width (m)
x, y, r, z
Coordinate directions
X
Mole fraction
Y
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Voltage (V)
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w
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Average velocity of fuel-air mixture (m / s)
um V
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Symbol
Mass fraction
z
Burner tip to target plate distance (m)
Z
Quartz plate thickness/depth (m)
Greek symbols
3
α
Thermal diffusivity (m / s2)
β
Radial velocity gradient (1/s)
μ
Absolute viscosity (Pa-s)
ρ
Density (kg / m3)
φ
Equivalence ratio
η
Effectiveness
Subscripts/
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Superscripts
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Adiabatic wall
conv
convection
e
Edge of boundary layer
f
flame
FJ
Flame jet
i ,init
Initial
j
Component of the mixture
m
Mixture
NC
Natural convection
rad
Radiation
0
Stagnation point
w
Wall
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1. Introduction Heat transfer by flame jet impingement is extensively used in several industrial and domestic
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applications like melting of metal billets in a closed heating furnace, glass processing, domestic gas geysers and others. The phenomenon of flame jet impingement heating is dependent on four different mechanisms of heat transfer- forced convection, radiation, thermochemical heat release (TCHR) and condensation of water vapor in the burnt gas. Amongst the four mechanisms of heat
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transfer, forced convection is the most dominant and accounts for nearly 90% of the heat transferred in flames with air as oxidizer. Reviews by Viskanta [1], Baukal and Gebhart[2-3] and Chander and Ray [4] give substantial information of the flame jet impingement studies. These
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studies are mostly experimental in nature. Recently analytical expressions are reported by Remie et al. [5] for two-dimensional and axisymmetric cases of impinging flame jets. These analytical expressions are based on isothermal plug flow concept for the flame jet valid for a radial distance, r < R and nozzle-tip distance, z < 2R. For two-dimensional case with non-viscous assumption, they have reported a simple expression given by Eq. (1). Remie et al. [5] are further able to arrive at an expression (Eq. 2) for viscous flow case by adjusting the analytical
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expression result with numerical simulation result carried out in a commercial CFD package FLUENT.
k (Tf − Tw )
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q0" =
z
where, Pe =
k (Tf − Tw )
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z
(1)
Pe
v e ρ zCp k
(
Pe ⋅ exp − 0.28 Pr0.4
)
(2)
The fluid properties for Pe are evaluated at an average temperature (maximum temperature within the boundary layer and target plate surface temperature). The fluid velocity (ve) is the velocity at the edge of the boundary layer. In the subsequent work by Remie et al.[6], they matched the results obtained by analytical expression with the numerical solution from FLUENT. They found that the ratio of the two results decay in an exponential fashion for region away from the stagnation region (r > R) and therefore corrected their analytical expression by an 5
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exponential multiplication factor. However, in order to use the Eqs. (1) and (2), the flame temperature needs to be measured near the edge of the boundary layer. The measurement of flame at the edge of the boundary layer is difficult as this requires proper location of
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thermocouple. Furthermore, this intrusion of thermocouple would disturb the boundary layer. Studies on numerical investigation of this problem are reported by Conolly and Davies [7], Som et al.[8], Chander and Ray [9] and Remie et al.[6]. Different burner geometries (single, multiple and annular) are used along with inverse diffusion flame (IDF) burners and swirl induced burners
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[10-18]). Almost all these reported studies are on the estimation of convective heat transfer characteristics while studies on radiation heat transfer characteristics [19-21] and emissions [21-
i)
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24] are limited. Following conclusions can be drawn from the reported literature: The heat transfer distribution is strongly dependent on the nozzle-plate spacing [1-24], burner shape [17], Reynolds number [1-25], equivalence ratio, oxygen enhancement [19], jet incidence angle [26], impingement plate material [27] and inter-jet spacing [14, 16]. ii) The effect of surface characteristics of the impingement plate on the heat transfer characteristic is less significant [21].
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iii) Thermochemical heat release is a dominant mechanism of heat transfer contributing by more than 40% for oxygenated methane flames [25]. This may be neglected for methane-air flames [25].
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The heat flux reported in the literature is measured by a ring calorimeter [2, 3] and heat flux sensors [4, 9, 10-18]. The size of the heat flux sensor is around 4 to 6 mm in diameter. Hence,
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the measured heat flux is averaged over this area. Furthermore, this heat flux sensor is to be traversed to different locations to measure the heat flux at different locations. Hence, the heat flux distribution reported in the literature lacks sufficient resolution, except the approach using inverse heat conduction (IHCP) method of Norteshaur and Millan [28] and Loubat et al. [29]. High spatial resolution enables one to understand important physical phenomenon like the axisswitching (Gutmark et al. [30] and Lou [31]). Use of inverse heat conduction method using liquid crystals are extensively used in the estimation of heat transfer coefficient for impinging air jets (Baughn [32], Talib et al. [33], Sagheby and Kowsary [34]) and film cooling problem (Ai et
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al.[35], Chen et al. [36]). In the present work, an IHCP method using analytical solution for semi-infinite medium is used to get high resolution heat flux using a thermal infrared camera. Nusselt number distribution is of engineering importance for the flame jet impingement heat
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transfer process. Correlations for Nusselt number distributions are reported in the literature based on analytical and semi-analytical studies. A collection of these correlations is available in the review papers of Viskanta [1] and Baukal and Gebhart [2-3]. Van der Meer [37] compared the Nusselt number distribution of isothermal non-reacting jets with that of the flame jets. He
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showed that if the properties of the burnt gases are taken at the temperature corresponding to the average enthalpy in the boundary layer formed on the plate, then the Nusselt number distribution
defined as given in Eqs. (3) and (4).
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of flame jets matches reasonably well with isothermal jets. The heat flux and Nusselt number are
q ′′ = h (Taw − Tw )
Nu =
hd k
(3) (4)
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The evaluation of Nusselt number requires the accurate data of the adiabatic wall temperature (Taw). Hence, most of the heat transfer correlations reported in the literature [2,3] are basically semi-analytical, which are modified form of the Sibulkin’s equation [38] given in Eq. (5). (5)
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q "s = 0.763 ( β s ρ e µ e ) 0.5 Pre−0.6 Cp e ( Te − T w )
Even then, there are difficulties involved in the evaluation of βs and Te since these parameters are
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to be estimated at the edge of the boundary layer. Therefore the utility of these correlations is difficult. Although Nusselt number correlations are reported in some studies in the literature, the adiabatic wall temperature is evaluated in an arbitrary manner. For instance, Van der Meer [37] defines the Nusselt number based on the adiabatic wall temperature evaluated as the temperature of the flame at the axis of the burner. In another study by Chander and Ray [9], the adiabatic wall temperature is evaluated as the adiabatic flame temperature. Therefore, the reported Nusselt number correlations are not the true values. In the present investigation, the adiabatic wall temperature is measured using thermal infrared camera. The objectives of the present work are as follows 7
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i) Application of an inverse heat conduction (IHCP) technique to obtain localized heat flux distribution with high spatial resolution in short time ii) Obtain heat flux distribution for circular (d = 8.7 mm and 10 mm) and non-circular burners (square of sides 7.6 mm and 10 mm and rectangular burner of size: 19 mm × 9 mm)
on experimentally measured adiabatic wall temperature
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2. EXPERIMENTAL DETAILS
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iii) Obtain Nusselt number and effectiveness distribution for circular and square burners based
2.1 Description of experimental setup
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Figure 1 is the schematic of the experimental set-up used in studying the flame jet impingement
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heat transfer.
Fig. 1 Schematic of the experimental setup
Mass Flow controllers (MFC) of accuracy 1.5% of full scale are used to meter the flow of methane gas (99.5% purity) and air from compressed air storage tank. The mass flow controllers used are of Aalborg make, USA. The air mass flow controller is calibrated with DryCal (DCLITE H) calibrator, BIOS International make whose accuracy is 1% of the reading traceable to NIST standards. The methane mass flow controller is calibrated by Soap bubble meter of PCI
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Analytics make, India whose accuracy is 2% of reading traceable to FCRI standards, India. Methane and air are mixed in a mixing tube. The stainless steel balls ensure that the two fluids find enough time for mixing and reduce the flow fluctuations. The accuracy of the flow metering is further validated by the measurement of the burning velocity (Vijaykumar et al. [39]).The
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dimensions of the burners used in the present study are given in Table 1. Table 1 Details of the burner geometry Area (mm2)
Dimension (mm) 8.7
59.45
Circle
10
78.55
Square
7.6 × 7.6
57.76
Square
10 × 10
100
Rectangle
19 × 9
8.7
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Circle
Hydraulic diameter (mm)
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Shape
171
10 7.6 10 12.2
The length to diameter ratio (l/d) of all tube burners are maintained as 50 which is based on the requirement for fully developed flow criterion, l/d > 30. The impingement plate is made of
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quartz whose size is 150 mm × 150 mm. Three plates of different thicknesses namely 1 mm, 3 mm and 5 mm are considered in this study. The emissivity of the quartz plate reported in the literature is 0.93 [40, 41]. The temperature distribution of the quartz plate is measured by the use of thermal infrared camera (Thermoteknix make VisIR® Ti 200). Specifications of this camera
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are given in Table 2.
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Table 2 Specifications of uncooled thermal cameras used in the present study Model Detector Spectral range Pixel Resolution FOV Minimum focus distance Temperature range Accuracy Frames per second
VisIR Ti 200 Microbolometer Uncooled FPA 7.5 – 13 µm 320 × 240 25 × 19 0.3 m -20°C to 1200°C ± 2% of reading 25
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This camera can record 25 thermal images in a second. As infrared camera transforms the incident radiation into temperature readings, few parameters like emissivity of the emitting body, atmospheric temperature between camera and object are to be necessarily introduced during post-processing the thermal images. The spectral range of IR cameras is 7.5 µm to 13 µm.
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Although, the main part of the response lies between 7.5 µm and 13µm, the camera is actually sensitive to radiation in a larger spectrum, namely from 6.5 µm to 17.8µm. This camera is further calibrated with a black body calibrator of TEMPSENS Make, CALsys 1500BB model. The
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accuracy of curve fit expression from calibration is 2% of reading. 2.2 Data reduction 2.2.1 Technique for heat flux measurement
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A typical heat flux distribution, when the premixed cone does not touch the plate, is shown in the Fig. 2. In the present methodology, the impingement plate is modeled as a semi-infinite medium governed by the following equation (Eq. 6) and boundary conditions.
∂ 2T 1 ∂T = ∂z 2 α ∂t
(6)
At t = 0 : Tw1(r, t) = Tw2(r, t) = T∞
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At t = t : Tw2 (r, t) = T∞, At z = 0 q ′′(r ) = q ′FJ′ (r ) The temperature distribution, T (Z, t) with time (t) at a given depth (Z) in a semi-infinite medium for a constant heat flux (qʺ) is given by Eq. (7).
− Z 2 q ′′Z 2q ′′ αt / π Z − exp erfc k k 2 αt 4αt
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T (Z ,t ) − Ti =
(7)
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The temperature distribution on the back side of the quartz plate is recorded using the infrared thermal camera. This recorded temperature T (Z, t) is then matched with that of Eq. (7) at different time intervals, for a short time, by varying the heat flux value (qʺ) such that the square root of the sum of squares, RSS =
∑ (T n
i =1
analytical
2
− Texperimental ) is minimum. Since this is the inverse
way of estimation of heat flux, the sensitivity coefficient (dT(Z, t)/dqʺ) has to be studied (Beck et al. [42]). On differentiating the Eq. (7), the sensitivity coefficient is expressed as Eq. (8).
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Convection loss = 0
Radiation loss = 0
Tw2 (t)
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Z Tw1 (t)
Radiation loss = 0
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z
d
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′ (r ) Heat flux from flame, q′FJ
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r
Fig. 2 Schematic representation of the heat exchange process for the axisymmetric flame jet impinging on a flat plate
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−Z2 dT ( Z ,t ) 2 αt / π = exp dq ′′ k 4αt
Z Z − erfc 2 αt k
(8)
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The sensitivity coefficients for different depths (Z) are same for all the thicknesses at varying time as presented by Beck et al. [42]. The thermal conductivity (k) and thermal diffusivity (α) of the quartz plate is computed at varying temperatures (T (K)) as per Eqs. (9 and 10). k = 0.0015T + 0.8956 (W/m K)
(9)
α = (9 × 10-9 T 2 – 1 × 10-5T + 0.0108) × 10-4 (m2/s)
(10)
Figure 3a shows the temperature distribution of the quartz plate of thickness 3mm impinged by a flame jet at time t = 10 seconds for a burner diameter of 10 mm at z/d = 4 and Re = 1000. The heat flux mapping for z/d = 4, ϕ = 1 and Re = 1000 on the back side of the plate is shown in Fig. 3b. 11
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(a)
(b)
Fig. 3 Circular burner of diameter 10 mm (z/d = 4, Re = 1000 and φ = 1)
a) Temperature (K) distribution on back side of plate at t = 10 s b) Temperature mapping of experimental data measured on back side with that of Eq. (7)
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This mapping is done for short initial time. For the present quartz plates, the matching of experimental and analytical temperatures values is for less than 5 seconds for 1.1 mm thick plate, 15 seconds for 3 mm thick plate and 30 seconds for 5 mm thick plate. The temperature data for the first 1/3rd of total mapping time is considered in the analysis. Temperature mapping over a
temperature measurement with the infrared camera.
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short time period rather than at a single time instant would nullify the uncertainties in
The comparison of heat flux estimated at Re = 1000, z/d = 4 and ϕ = 1 for different plate
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thicknesses is shown in Fig. 4a.
Fig. 4 Comparison of present experimental heat flux for circular burner of diameter 10 mm:
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a) for different plate thicknesses, b) flame side and back side measurements, Z = 3mm There is a good match of heat flux values for the thicknesses considered. However, for Z = 1
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mm, the estimated heat flux is more scattered which could be due to magnification of noise in the experimental data. The 3 mm thick quartz plate is used for the data presented in further sections of this study.
The backside measurement would enable capturing thermal images of the
impingement plate without loss of aspect ratio, which is the case for flame side measurement, due to obstruction of image by the burner tube. The backside temperature measurement does violate the mathematical constraint of Eq.(6)through the requirement of the backside boundary condition (At t = t : Tw2 (r, t)). Two separate measurements are done: i) based on front side temp measurement when Tbackside = T∞ and ii) based on back side temp measurement when Tbackside
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marginally higher than T∞. The quartz plate selected is 3mm thick and the test case is Re = 1400, z/d = 4 and ϕ = 1. The flame side temperature is measured for time less than 2 seconds when the heat has not diffused to backside wall (Tbackside = T∞). The estimated heat fluxes from the flame
2.2.2 Method for measurement of adiabatic wall temperature
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side and the backside measurements are in good agreement as shown in Fig.4b.
The adiabatic wall temperature is defined as the steady state impingement side wall temperature when the other sides are insulated. This is experimentally measured by insulating the top side of
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the impingement plate by using an insulating material (Ceramic blanket) as shown in Fig. 5. Insulation material (Ceramic blanket)
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Insulation box
Thermal camera
Tube burner
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Quartz plate
Fig. 5 Schematic of direct measurement of adiabatic wall temperature using thermal infrared camera
The transmissivity of premixed flames is nearly unity. Hence, the steady state adiabatic wall temperature is measured by a thermal camera from the front side. A total of 10 images is taken at steady state from the thermal camera and then averaged at each pixel in the Thermagram software.
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2.2.3 Nusselt number and effectiveness distribution The heat transfer coefficient is calculated using Eq. (3) with the wall temperature (Tw1) being taken as the average temperature on the impingement side of the plate for the short time (5 seconds). Nusselt number is calculated using Eq. (4) with the thermal conductivity taken at
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adiabatic wall temperatures using CEA software developed by NASA [43]. Effectiveness for the flame impingement process is given by Eq. (11).
Taw − T∞ Tadf − T∞
(11)
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η=
2.2.4 Mixture parameters
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The mixture density is calculated from Eq. (12), the mixture viscosity is calculated from Eq. (13) and the mixture Reynolds number (Re) is calculated from Eq. (14).
ρm = ∑Yjρ j
(12)
∑µ X ∑X
(13)
µm =
j
j
Mj
ρ mum d µm
(14)
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Re =
Mj
j
The uncertainties in the measured parameters are estimated by the method of Moffat [44]. Table 3 gives the uncertainties of various parameters reported in the present study.
1
Parameter
Minimum
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Sl No.
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Table 3 Uncertainties in various parameters reported in the present study
uncertainty (%)
Maximum uncertainty (%)
Equivalence ratio
5
10
Reynolds number
5
10
Temperature from thermal camera
2
2
4
Heat flux
6
12
5
Nusselt number
8
16
6
Effectiveness
4
8
2 3
15
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2.3 Validation of the present IHCP technique Chander and Ray [17] have reported heat flux measurements using heat flux sensor. The burner diameter for the present study and that reported by Chander and Ray [17] is same. However, the experimental conditions for the present case (transient) and that of Chander and Ray [17] (steady)
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are different.
The reported heat flux data of Chander and Ray [17] is compared by the following two different methods
The estimated heat flux by IHCP method in the present study (green line in Fig. 6)
•
Heat flux is estimated from Eq. (3) using the phenomenon constants – the heat transfer
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•
coefficient (h) and adiabatic wall temperature (Taw) measured from the present study. The
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wall temperatures are taken from reported data of Chander and Ray [17] (red line in Fig. 6)
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Fig. 6 Comparison of recalculated and reported heat flux of Chander and Ray [17] at z/d = 4, ϕ = 1, Re = 600 and1800 There is a reasonably good match of heat flux values from both steady state and transient methods. This is because the wall temperatures of present IHCP study and that of Chander and Ray [17] are comparable (around 100°C) and the wall heat flux solely depends on this parameter as per Eq. (3). The advantages of the present IHCP method of heat flux estimation are – o
It has high spatial resolution (nearly 60,000 data points) unlike the use of a sensor reported in literature. Even with the IHCP method employing numerical method (Loubat et al. [28]), sufficient resolution is not possible due to the requirement of huge memory and
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computational time. To reduce the computational time, the experimental input data points are reduced by techniques like Discrete Cosine transform (DCT). However, this would greatly reduce the resolution of the measured data and would fail to capture the steep gradients in the
rectangular burners which show multiple elliptical hot spots. o
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estimated parameter especially for multiple jet impingement and impingement with
It requires vey less computational time (less than 15 minutes), since simple analytical solution for semi-infinite medium (1-D transient equation) is to be computed. Numerical IHCP techniques are based on assumptions of the initial spatial heat flux boundary condition
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which is again assumed temporally and spatially by methods like the Function specification method. To arrive at the proper heat flux value, one has to do several iterations and this
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consumes time. So, the philosophy of applying DCT now comes into picture that takes values that are average of neighboring data. In the present analytical IHCP technique the heat flux is obtained by directly applying the analytical solution for semi-infinite medium. Hence, no substantial iterations are required. The only iterations for the present analytical IHCP technique is done to get the least square fit for small varying time (5 seconds interval in a step size of 1/5th sec). It is found to take less than 15 minutes of computational time for the contour
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maps shown in the present investigation. The computational platform is a desktop of i5 series Pentium processor of 8 GB RAM and 64 bit Windows 7 Operating system o
Accurate estimation of heat flux is possible. In the case of heat flux sensor, the accuracy is limited due to the size of the sensor. For the IHCP method using numerical method, accurate
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material properties of the impingement plate are to be used. In most instances, the material property of the plate itself needs to be determined, again by IHCP method [42].
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3. Distribution of heat flux, Nusselt number and effectiveness The spatial distribution of heat flux for varying Reynolds number, nozzle-burner tip distance and equivalence ratio is presented for square, circular and rectangular burners. The flame jet for noncircular burners is found to switch their axis and is captured in the contour plots. The radial distribution of Nusselt number (Nu) and effectiveness (η) is presented and correlations for circular and square burners are provided. The adiabatic flame temperature is taken as 2200K and the ambient temperature as 300K.
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3.1 Heat flux distribution 3.1.1 Circular and Square burners The contour plots of heat flux distribution for circular and square burners is shown in Figs. 7 and
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8 at a Reynolds number of 1000, equivalence ratio of 1 at different nozzle plate spacing (2 to 6). Referring to Fig. 7, perfect circular symmetric heat flux distribution pattern is observed for circular flame jet issuing from the burners of diameter 10 mm and 8.7 mm. For the burner of diameter 10 mm at Re = 1000, the heat flux decreases with the increase in z/d from 2 to 4. For
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further increase in z/d from 4 to 6, the change in heat flux is negligible. For the burner of diameter 8.7 mm at z/d = 4, the heat flux increases with the increase in Re from 600 to 1400. However, for square burners, axis switching is observed as shown in Fig. 8 and is believed to be
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reported for the first time for impinging flame jet. This phenomenon is due to vortex formation at the corners of the burner wall tip. The detailed information on the development of these vortices and their structure for square jets is reported by Grinstein et al. [45] and Grinstein and DeVore [46] and Miller et al. [47]. For the square jets, the axis is switched by 45° in the present experimental results (Fig. 8).
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This outcome is in agreement with the observations reported by Grinstein and DeVore [46] and Miller et al. [47]. Furthermore, the axis switching is more predominant in square burner of larger dimension. This is because larger size vortices would be generated in the larger burner and hence more the strength of axis switching. For the smaller burner, the heat flux distribution is rather in
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concentric circles shaped away from stagnation region with short region near stagnation depicting a subdued diamond shaped pattern. The location of inner premixed cone influences the
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heat flux distribution on the target plate. Flame jets with the premixed cone nearer to the target plate produce higher heat flux unless the inner premixed cone does not touch the target plate. The experimentally measured inner premixed cone height for the square and circular burners at different Reynolds number is given in Table 4. The flame cone height can be obtained by a simple expression in terms of the mixture velocity and the burning velocity given by Eq. (15), derived by Kleijn [17]. Lf =
u mix d 2 Su
(15)
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Table 4 Premixed flame cone heights (mm) for different burners square, d = 10mm Eq. measured (15) 15.2 16.9 21.9 22.5 27.4 28.1 32.4 33.8 37 39.4
circle, d = 8.7mm Eq. measured (15) 15.1 14.95 20 19.93 25.5 24.91 30.3 29.9
square, d = 7.6mm Eq. measured (15) 15.2 16.9 21.6 22.5 27.7 28.1 32.7 33.8
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circle, d = 10mm Eq. measured (15) 600 15.3 14.95 800 19.8 19.93 1000 25.4 24.91 1200 30 29.9 1400 35.1 34.9
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Re
Flame cone height (Lf) computed by Eq. (15) is also given in Table 4. For the square burner the
4 umix d For the square and circular π 2 Su .
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diameter, d is calculated based on equivalent area, i.e., L f =
shaped burners of same hydraulic diameter (d = 10 mm), it is observed from Table 4 that the cone heights are equal with a slightly higher value for the square burner. Therefore, the heat flux for a square burner is slightly higher than that of circular burner as shown in Figs. 7-8. Furthermore, the location of the premixed cone tip from the impingement plate for same shape
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(circular or square) is different for different hydraulic diameters. Smaller diameter tubes have their premixed cone located much closer to the target plate for a given Reynolds number and equivalence ratio. Hence, the heat flux distribution for smaller diameter tubes is higher unless the
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premixed cone touches the impingement plate.
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(e)
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(c)
(f)
Fig. 7 Heat flux (kW/m2) distribution for circular burners; diameter 10 mm at Re = 1000; a) z/d = 2, b) z/d = 4, c) z/d = 6 and diameter 8.7mm at z/d = 4; d) Re = 600, e) Re = 1000, f) Re = 1200 20
(e)
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(c)
(f)
Fig. 8 Heat flux (kW/m2) distribution for square burners; Re =1000: a) d = 10 mm; z/d =2, b) d = 10 mm; z/d = 4, c) d = 10 mm; z/d = 6, d) d = 7.6 mm; z/d = 2, e) d = 7.6 mm; z/d = 4, f) d = 7.6 mm; z/d = 6; Burner orientation 21
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3.1.2 Rectangular burner Contour plots of rectangular burner for Reynolds number varying from 800 to 2200 at an equivalence ratio =1 and z/d = 4 is shown in Fig. 9. Axis switching is clearly observed in all the
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cases studied. In Fig. 9, the orientation of the burner is shown in the caption of the figure. Grinstein [48] reported on the vortex ring dynamics for rectangular burners of different aspect ratios. The axis is found to switch by 90° for aspect ratios of 2 and 3. A similar study by Miller et al. [47] also concluded that the axis is found to switch by 90° for rectangular nozzle of aspect
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ratios of 2. In the present experimental study, for a rectangular burner of aspect ratio of 2.1, the axis switched by 90° as shown in Fig. 9. Two circular hot spots are observed along the maximum dimension of the burner as shown in Fig. 9. The region between these hotspots has relatively
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lower heat flux. The distance between these two hot spots increases with the increase in z/d. There is no substantial decrease (from 75% to 77%) in the heat flux gradient between the two hot spots for Re = 800 to 1400. However, there is substantial decrease (from 77% to 30%) of heat flux gradient between the two hot spots from Re = 1400 to 2200.The central elliptical minima could be due to reduction of the flame gas velocity at the center due to the vortex formation that tends to flush out the gases in a radially outward direction. For x/d > 3 and y/d > 2, the multi-
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elliptical pattern vanishes and a single ellipse is observed. For Re = 1000, the maximum heat flux is observed for the lowest z/d. At z/d = 2, the inner premixed cone of the flame is closest to the target plate as compared to higher z/d. For z/d = 4, the heat flux increases with the increase in the
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Reynolds number. The maximum heat flux is observed for Re = 2200. The increase in the heat flux with increase in Re is due to increase in the premixed cone height. With the increase in the
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Re, the premixed cone tip is closer to the impingement plate and therefore the heat flux increases.
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(c)
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(f)
Fig. 9 Heat flux distribution (kW/m2) for rectangular burner; a) Re =1000; z/d =2, b) Re =1000; z/d = 4, c) Re =1000; z/d = 6, d) Re =800; z/d = 4, e) Re =1400; z/d = 4, f) Re =2200; z/d = 4; Burner orientation -
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3.2 Nusselt number and Effectiveness distribution Nusselt number and effectiveness distribution for circular, square and rectangular burner is presented. The adiabatic flame temperature (Tadf) for methane air flame of equivalence ratio of 1
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is 2200 K. The ambient temperature (T∞) in the present study is taken as 300 K for the calculation of effectiveness. 3.2.1 Circular and square burners
The Nusselt number and effectiveness distributions for circular and square tube burners of
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hydraulic diameter 10 mm, impinging on a quartz plate are shown in Figs. 10 and 11. The equivalence ratio of the fuel-air mixture is 1. The Reynolds number (Re) range covered is 600 to
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1400 while the nozzle-tip to impingement plate distance (z/d) is varied from 2 to 6. The stagnation point Nusselt number and effectiveness is found to increase with the increase in the Reynolds number unless the inner premixed cone height touches the impingement plate. Furthermore, the Nusselt number and effectiveness have peak values at the stagnation point and exhibit radial decay, when the inner premixed cone is not touching the impingement plate. With the increase in the impingement distance (z/d), both Nusselt number and effectiveness decrease
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and the radial distribution pattern tends to flatten.
Three empirical correlations are used to fit the present data for stagnation point Nusselt number for circular and square burners as given in Eqs.(16 - 18).
c
(16)
Lf Nu0 = a Re z
c
(17)
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Lf Nu0 = a Pe z b
b
Lf Nu0 = a z
+ b
(18)
Equation (16) is based on the analytical solution (Eq.5) of Remie et al [5]. Furthermore, it is evident that the inner premixed cone plays an important role and hence the non- dimensional parameter, Lf /z is introduced in Eq. (16). Lf measured by direct photographs is used in the present correlations.
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Fig. 10 Nusselt number and effectiveness distribution for Circular burner of d = 10 mm
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Fig.11 Nusselt number and effectiveness distribution for Square burner of d = 10 mm
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Equation (17) is based on the empirical form assumed by Chander and Ray [9] and Eq. (18) is based on the present hypothesis that the ratio of location of the cone tip from the impingement plate to the distance of the burner tip from the impingement plate is the sole parameter to correlate the Nusselt number and effectiveness. The maximum deviation for all three correlations
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is found to be 15%. Hence, knowing only the flame cone height, it is sufficient enough to predict the Nusselt number. The expression for radial distribution of Nusselt number is given by Eq. (19). Similar expressions for effectiveness are given by Eqs. (20) and (21).
L
(20)
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η 0 = a f + b z
(19)
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Nu r =c +d Nu 0 d
η r = c + d η0 d
(21)
Table 5 gives the curve fit constants for the square and circular burners for r/d < 4. Table 5 Curve fit constants for Eqs. (18-21)
Eq. No.
a
b
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Circular burners c
Square burners d
a
b
c
d
-51
111
----
----
26.7
15.3
-0.099
1.04
-0.106
0.48
----
-----
0.141
0.32
-0.052
1.08
Lf /z > 1.1
-36
20
10
26
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18, 19
80
20, 21
-0.22
0.151
---
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18
0.69
0.283
---
Lf /z < 1.1
-0.086
0.99 Lf /z > 1.1
---
--Lf /z < 1.1
-0.053
1.03
The Nusselt number and effectiveness increases for increasing Lf / z until it reached a value of 1.1 and thereafter the trend reverses. For Lf / z < 1.1, the maximum deviation in the curvefit correlation for Nusselt number given by Eq. (19) for circular and square burners is 25% and 27
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22%. For the curvefit correlation, for effectiveness given by Eq. (21) for circular and square burners the maximum deviation is 10% and 8%. For Lf /z >1.1, the maximum deviation in the curvefit correlation for Nusselt number given by Eq. (19) for circular and square burners is 25% and 30%. For the curvefit correlation, for effectiveness given by Eq. (21) for circular and square
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burners the maximum deviation is 7% and 8%. For Lf /z >1.1, the radial Nusselt number and effectiveness curvefits have significantly higher deviations and therefore are not presented.
A comparison of Nusselt number and effectiveness is done between circular and square burners
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based on same hydraulic diameter and same equivalent area as shown in Fig. 12.
Fig. 12 Nusselt number and effectiveness distribution for circular and square burners based on same hydraulic diameter and same equivalent area
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There is a good agreement in Nusselt number and effectiveness distribution for the same hydraulic diameter case and significantly large deviation for the same equivalent area. This is due to the influence of the non-dimensional inner premixed cone height (Lf /z). For same hydraulic diameter case, the Lf /z differs only by a small magnitude but for same equivalent area
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Lf /z differs by a large magnitude. However, the small difference in Lf /z leads to significant deviations in Nusselt number and effectiveness for same hydraulic diameter case when the inner premixed cone tip is nearer to the impingement plate, for instance Re =1400, z/d = 4 shown in
deviation in the actual and the curve fit data is 5%.
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4. Conclusions
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Fig. 12. The data presented in Figs. (10-12) is obtained from a polynomial fit of 10th order. The
Heat flux distribution for premixed methane-air flame jet is studied for Reynolds number varying from 600 – 1400 at an equivalence ratio of 1 for nozzle tip-target plate distance varying from 2 to 4. An inverse heat conduction technique is applied with semi-infinite medium assumption for the target plate. The thermal infrared camera enables high resolution temperature measurement of the backside of the impingement plate. The measured initial-short time transient temperature is
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then analyzed to get the heat flux in an inverse way. The condition of minimization of sum of squares for the difference between the measured and predicted temperatures is applied by varying the heat flux. The adiabatic wall temperature has been estimated by direct measurement.
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Following are the outcomes of the present investigation. Heat flux distribution with high spatial resolution, short computational time and good accuracy is obtained
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Axis switching is observed in non-circular burners, for square burner it is more predominant in burner with larger dimension
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Stagnation point and radial Nusselt number distribution correlations are given for
circular and square burners
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The non-dimensional flame cone height, Lf /z is the sole parameter that correlates the Nusselt number and effectiveness distribution
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There is a good agreement in Nusselt number and effectiveness distribution for circular and square burners based on same hydraulic diameter and significantly large deviation for same equivalent area.
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Acknowledgements The first author would like to acknowledge the support of MHRD, Govt. of India for sponsoring him to pursue Ph.D at Indian Institute of Technology, Bombay. The authors are also grateful to
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Aeronautical Research and Development Board for funding this work.
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Figure captions Fig. 1 Schematic of the experimental setup
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Fig. 2 Schematic representation of the heat exchange for the axisymmetric jet impinging on a flat plate Fig. 3 Circular burner of diameter 10 mm (z/d = 4, Re = 1000 and φ = 1)
a) Temperature (K) distribution on back side of plate at t = 10 s b) Temperature mapping of experimental data measured on back side with that of Eq. (7)
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Fig. 4 Comparison of present experimental heat flux for different plate thicknesses for circular burner of diameter 10 mm
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Fig. 5 Schematic of direct measurement of adiabatic wall temperature using thermal infrared camera
Fig. 6 Comparison of recalculated and reported heat flux of Chander and Ray [17] at z/d = 4, ϕ = 1, Re = 600 and1800 Fig. 7 Heat flux distribution for circular burners; diameter 10 mm at Re = 1000; a) z/d = 2, b) z/d = 4, c) z/d = 6 and diameter 8.7mm at z/d = 4; d) Re = 600, e) Re = 1000, f) Re = 1200
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Fig. 8 Heat flux distribution for square burners; Re =1000: a) d = 10 mm; z/d =2, b) d = 10 mm; z/d = 4, c) d = 10 mm; z/d = 6, d) d = 7.6 mm; z/d = 2, e) d = 7.6 mm; z/d = 4, f) d = 7.6 mm; z/d = 6; Burner orientation -
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Fig. 9 Heat flux distribution for rectangular burner; a) Re =1000; z/d =2, b) Re =1000; z/d = 4, c) Re =1000; z/d = 6, d) Re =800; z/d = 4, e) Re =1400; z/d = 4, f) Re =2200; z/d = 4; Burner orientation -
Fig. 10 Nusselt number and effectiveness distribution for Circular burner of d = 10 mm Fig.11 Nusselt number and effectiveness distribution for Square burner of d = 10 mm Fig. 12 Nusselt number and effectiveness distribution for circular and square burners based on same hydraulic diameter and same equivalent area
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Highlights IHCP technique to obtain local heat flux distribution using thermal camera
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Adiabatic wall temperature and heat transfer coefficient are given
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Circular, square and rectangular burners are used
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Axis switching is observed in non-circular burners
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Correlations for local Nusselt number and effectiveness are given
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