International Journal of Applied Engineering Research ISSN 0973-4562 Volume 11, Number 2 (2016) pp 1273-1281
© Research India Publications. http://www.ripublication.com
A New Method for Prediction of Local Heat Flux on Membrane Waterwall
with Rifled Tubes of Subcritical Boilers
Sankar G
Engineer, Bharat Heavy Electricals Ltd.,
Tiruchirappalli, Tamil Nadu, India.
E-mail: sankarg@bheltry.co.in
Chandrasekhara Rao A
Deputy General Manager, Bharat Heavy Electricals Ltd.,
Tiruchirappalli, Tamil Nadu, India.
E-mail: chandra@bheltry.co.in
Kartikeyan V R
Engineer, Bharat Heavy Electricals Ltd.,
Tiruchirappalli, Tamil Nadu, India.
E-mail: vrkarti@bheltry.co.in
Seshadri P S
Addl. General Manager, Bharat Heavy Electricals Ltd.,
Tiruchirapalli, Tamil Nadu, India.
E-mail: pss@bheltry.co.in
Balasubramanian K R
Assistant Professor, National Institute of Technology,
Tiruchirappalli, Tamil Nadu, India.
E-mail: krbala@nitt.edu
the powerplant. A furnace model capable of predicting heat
flux based on the specified operating parameters will be able to
mitigate this problem. A thoroughly validated model with a set
of experimental results will be an effective tool in the
determination of boiler furnace heat flux for a variety of
operating variables.
A review of heat flux measurement techniques adopted by
various researchers resulted in a conclusion that, the use of
chordal thermocouples for measurement of tube crown
temperature and then arriving at the surface absorbed heat flux
by using heat transfer equations is a more viable solution. In
that direction, an attempt has been made to develop a new
method to calculate the applied local outside heat flux (Q/Ao)
of the membrane waterwall of boiler with rifled tubing. An
inverse heat conduction problem was solved using an iterative
procedure. ‘Predicted’ temperatures required for the inverse
problem were artificially generated by solving a direct heat
conduction problem using ANSYS-FLUENT software. The
calculated Q/Ao is compared with that of the Q/Ao used for
generation of ‘predicted’ temperatures.
Abstract
A simplified procedure for prediction of local heat flux on the
membrane waterwall rifled tubes of a sub-critical boiler is
presented which requires the measurement of metal
temperature at the tube crown using a chordal thermocouple.
An inverse problem of heat conduction was solved using an
iterative procedure to calculate the outside heat absorption rate
from conduction and convection related heat transfer equations.
The temperature distribution over the cross-section of the tube
was found using ANSYS-FLUENT software for different range
of values of outside heat flux, inside heat transfer coefficient
and operating pressures. ‘Predicted’ temperatures obtained
from the solution of direct heat conduction problem has been
used to solve for the outside heat flux.
Keywords: Heat flux measurement, Furnace modelling and
heat flux prediction, Heat flux distribution, Indian-coal fired
boilers, Inverse heat conduction problem
Introduction
A boiler furnace is an enclosure of tubes carrying water/steam.
Tube failures are imminent when there is excessive heating due
to reduction of flow in the furnace wall or due to a sudden
increase in incident heat flux.. Judicious selection of waterwall
tube thickness is required to avoid these failures. Moreover, the
fluid pressure drop in the furnace wall is also affected by the
thickness of the tube. Hence arriving at an optimum thickness
is required to achieve a trade-off between pressure drop and
metal temperatures. This requires a lucid understanding of heat
flux profile in the furnace, especially for boilers firing high ash
Indian coal. Heat flux and temperature are to be measured for a
large permutation of operating variables like furnace size,
operating load, water wall flow, type of coal fired, and ash
deposition for a complete understanding of the absorption
phenomenon. But a large scale experimentation requires
meticulous planning and a sufficiently large number of
measurements which will lead to the temporary shutdown of
Literature review
Previous work done by researchers in the areas of furnace
modeling, heat flux prediction, heat flux measurement
techniques and effect of ash deposit on thermal performance
are discussed in the forthcoming section.
A. Furnace modeling
S. Rajaram and K. U. Abraham [1] described an iterative
procedure for the calculation of furnace heat flux from
measured metal temperatures using finite-difference equations
formulated using the procedure given by Adams and Rogers [2]
and solving the same using relaxation technique to obtain the
relationship between outside heat flux and total temperature
drop. Martins et al. [3, 4] worked on a hemispherical radiation
heat flux meter to measure the difference between
hemispherical radiation heat flux and convective heat flux and
1273
International Journal of Applied Engineering Research ISSN 0973-4562 Volume 11, Number 2 (2016) pp 1273-1281
© Research India Publications. http://www.ripublication.com
experimentally verified the same for measuring totalhemispherical radiation with the range of heat flux 40-150
kW/m2. Yuh-Long Hwang and John R. Howell [5] calibrated a
furnace model based on PCGC-3 code developed by Brigham
Young University using measurements of local gas temperature
distributions, local radiative and total wall heat flux
distributions, and stack NOX. Modeling of the effect of ash
deposition is discussed by many authors [6-15], [25]. The
models included the effects of ash formation, growth rate and
particle sticking on heat transfer. Various other authors [16-24]
have also worked on developing a numerical model for
predicting furnace performance parameters like gas
temperatures and heat flux pattern. A few authors [26-28] have
attempted thermal-hydraulic modelling of boiler wherein the
waterwall of the boiler is treated as a flow network containing
series and parallel loops, pressure grids and connecting tubes
and a mathematical model is developed based on mass,
momentum and energy conservation of the above said
components. Mathematical model for studying performance of
CFB boiler was developed by [29, 30].
But, very few research articles are available on accurate
prediction of heat flux for high ash coal fired boilers especially
in super-critical range. Hence, a research involving prediction
of heat flux for high ash coal fired boilers and validation of the
same will be of high importance in arriving at optimum boiler
design.
transfer and surrounding atmosphere like ash deposition is
satisfied by tubular instruments. The EPRI report [34] throws
light on two of the currently manufactured sensors namely
Applied Synergistics' Heat flux sensor and Chordal
thermocouples. Chordal thermocouples are widely used in heat
flux evaluation by measuring tube wall temperatures where
holes are drilled along the chords of a tube wall and the
thermocouple wire is installed through these holes.
Measurement of heat flux has been widely used in the boiler
industry for monitoring of ash deposition on water wall tubes
and the development of smart soot blowing system as discussed
in [36], [37], [41-44], [55-63]. Optimization of soot-blowing is
the end requirement in many of these researches.
The measurement techniques discussed are also based on
deriving heat flux from basic conduction principle by
measuring temperature at two different points. Various authors
have used different locations for measurement. Since only an
indication of ash fouling is required, none of the above
techniques explained above will result in an accurate
measurement of heat flux. Hence, there is a need to develop a
technique concerning the application of understanding the heat
flux variation in the furnace waterwall. This requires
measurement of heat flux either directly or temperature using
chordal thermocouple placed on the tube crown. However, the
latter area needs to be explored further.
Direct heat conduction problem
B. Heat flux measurement techniques
Different techniques available for measurement of heat flux are
outlined by various researchers [31-34]. The authors explain
regarding heat flux measuring devices using two major
principles viz. radial disk principle and guarded cylinder
technique. Even though the radial disk principle is easy to use,
the method does not always guarantee an accurate
measurement of heat flux since it is mounted on the surface of
the tube. This is because, the measurement depends on the heat
flux on the top and bottom surface of the device. Any change
in the varied operating conditions mainly due to ash deposition
will lead to a considerably erroneous indication of heat flux.
The guarded cylinder technique does not have this limitation,
but it is difficult to implement owing to requirement of high
manufacturing accuracies. According to Taler et al. [35], three
types of heat flux measurement devices can be used broadly in
boiler water-walls: (1) portable heat flux meters inserted in
inspection ports (2) Gardon type heat flux meters welded to the
section of boiler tubes (3) tubular type instruments placed
between two adjacent boiler tubes. A device named fluxprobe
[37] was designed for measuring values of incident radiation
flux primarily in membrane walls with an accuracy of +5%.
Gardon type heat flux meters have been the subject of research
of many researchers [38-45]. These are heat flux measuring
devices welded to the surface of the boiler tube. They
predominantly work on radial disc principle. Since these
devices are mounted to the surface of the waterwall tube, the
effect of non-uniform ash deposition on the measuring device
and the tube leads to inaccuracies in the computed values of
heat flux. Tubular type instruments have been explored by [33],
[35], [46-54]. The requirement that the heat flux instrument
used for measuring absorbed heat flux should represent the
boiler tube as closely as possible in terms of both radiant heat
A linear direct heat conduction problem was formulated and
solved using ANSYS-FLUENT code to obtain the temperature
distribution across the cross section of the boiler tube. The
following assumptions were made in the analysis.
 Heat transfer coefficient on the inner surface of the
boiler tube (h i) does not vary along the circumference of
the tube.
 Rear side of the boiler tube is thermally insulated.
 Thermal conductivity (k) of the tube material is constant
(40. 5 W/mK).
 Heat flux distribution on the outer surface is dependent
on the view factor computed using equations (1) and (2).
 Effect of ash deposition is neglected.
Analysis was performed using ANSYS-FLUENT code for the
following conditions:
 Operating pressure (PDRUM) range: 120 bar to 160 bar
 Outside heat flux (Q/Ao): 220, 000 to 355, 000 W/m2
 Inside heat transfer coefficient (h i): 46, 000 to 55, 000
W/m2K
A. View factor determination
Radiation heat transfer between surfaces depends on the
orientation of those surfaces relative to each other in addition
to their temperatures, emissivity and transmissivity of the
medium in between them. Effect of view factor on radiation
incident on tube outer surface was considered using the
procedure furnished by Ganapathy [67] as depicted in Fig. 1.
The following set of equations have been adopted separately
for view factor (ψ) on fin and tube
View factor on tube outer surface=
1274
(1+ cos ϕ)
2
(1)
International Journal of Applied Engineering Research ISSN 0973-4562 Volume 11, Number 2 (2016) pp 1273-1281
© Research India Publications. http://www.ripublication.com
View factor on fin outer surface=
( cos ϕ1 + cos ϕ2 )
2
(2)
View factor variation on tube & fin outer surface
1.2
For the purpose of computation of view factor at a point on the
tube surface, the angle (φ) between the tangents to the particular
tube of interest and to its adjacent tube to the corresponding
point is found out. Relation between the view factor of the
boiler tube at the particular point of interest and the angle
subtended by the line connecting the point from the center of
the tube with the horizontal was arrived. Similarly for the fin, a
relation between the view factor of the tube-fin at the particular
point of interest and the distance between that point and the
vertical axis of the tube. The above relations were coded into
ANSYS-FLUENT for analysis [68]. The view factor variation
on the outer surface of the tube and fin as a function of curve
length is shown in Fig. 2
View factor
1
0.8
0.6
0.4
0.2
0
0
0.01
0.02
0.03
0.04
0.05
Curve length (m)
Figure 2: View factor variation on tube and fin outer surface
B. Solution procedure
After computing the view factor as mentioned previously, the
direct heat conduction problem was solved using ANSYSFLUENT code. Tube temperature distribution is expressed by
the following heat conduction equation:
k ∇2T = 0
(3)
The boundary condition at the tube outside surface may be
expressed as:
k
∂T
|
∂r (r= ro)
= q̇ m
(4)
The absorbed outside surface heat flux (q̇ m ) as a function of
Q
applied heat flux (A ) and view factor (ψ) is expressed in the
0
form of the following equation:
q̇ m =
Q
A0
ψ
(5)
The boundary condition at the tube inside surface may be
expressed as a convection boundary condition:
A) Estimation of View For Tube
-k
∂T
|
∂r (r= ri )
= hi (Tf – Ti)
(6)
The above direct heat conduction problem was solved using
ANSYS-FLUENT software with the following mesh
configuration: Tetrahedral mesh with 2751077 elements,
524163 nodes
C. Grid independence study
A grid independence study was carried out with the grids as
shown in Fig. 3. The values of temperature at the thermocouple
location points for the three grids are tabulated in Table 1. As
it can be noted, the variation in temperature is very low across
the three types of grids. For generating the temperatures
mentioned in the Table 1, heat flux of 2, 50, 000 W/m2, inside
heat transfer coefficient of 54, 000 W/m2 K and a fluid
temperature of 363 °C was used.
B) Estimation of View Factor for Fin
Figure 1: View factor estimation for membrane wall
tubes [67]
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International Journal of Applied Engineering Research ISSN 0973-4562 Volume 11, Number 2 (2016) pp 1273-1281
© Research India Publications. http://www.ripublication.com
Figure 5: Temperature distribution across the tube
circumference and fin
Inverse heat conduction problem
A. Analytical Procedure for inverse heat conduction problem
The iterative procedure for computation of boiler tube outside
surface heat flux (Q/Ao) is discussed. The tube material, outside
diameter (Do), major inside diameter (Dmajor), minor inside
diameter (Dminor) and the thermocouple installation diameter
(Dc) are the known physical dimensions as shown in Fig. 6.
Figure 3: Division of geometrical model of tube into elements
(a) Hexahedral mesh with 77410 elements, 53100 nodes (b)
Tetrahedral mesh with 334028 elements, 68314 nodes (c)
Tetrahedral mesh with 2751287 elements, 524218 nodes
Table 1: Temperature at measuring points computed for
different meshes in Fig. 3
Sl. No.
1
2
3
Temperature (°C)
400. 98
401. 21
401. 55
Mesh type
3 (a)
3 (b)
3 (c)
D. Results
Total surface heat flux i. e Applied local outside heat flux
(Q/Ao) variation across the tube and fin surface for a sample
case (P=120 bar, Q/Ao = 2, 80, 000 W/m2 and hi = 51, 000 W/m2
K) is shown in Fig. 4. The effect of view factor on the tube and
fin is clearly visible. The temperature distribution in the tube is
shown in Fig. 5.
Figure 6: Schematic representation of the tube and
thermocouple location
In the sub-critical operating range, it is appropriate to take the
saturation temperature as the bulk fluid temperature (T f) and
assume the region of operation in nucleate boiling regime. An
initial assumption for tube inside surface temperature (T i) and
inside heat transfer coefficient (h i) is required for further
computations. Average metal temperature (Tav) is computed
using one-dimensional heat conduction equation as given by
Cengel [64] with the temperature dependence of thermal
conductivity, heat generation and unsteady terms neglected.
1
∂
r ∂r
Figure 4: Heat flux variation across the tube circumference
and fin
(r k
∂T
∂r
) +ġ = ρ Cp
∂T
∂t
(7)
The tube metal thermal conductivity (k) is computed based on
average temperature in case of non-linear heat conduction
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International Journal of Applied Engineering Research ISSN 0973-4562 Volume 11, Number 2 (2016) pp 1273-1281
© Research India Publications. http://www.ripublication.com
problem and is constant in case of linear heat conduction
problem. From the known values of thermal conductivity and
temperature difference between outside and inside metal
temperatures, inside surface heat flux (Q/Ai) is calculated based
on heat conduction equation given below:
∂T
=- k
|
∂r (r= ri )
(8)
Further, the film temperature drop (ΔTsat) is calculated using
Jens-Lottes equation as suggested in [65] using inside surface
heat flux (Q/Ai) and drum pressure (PDRUM).
ΔTsat =
60 (
e
1/4
Q⁄Ai
⁄ 6)
10
PDRUM
⁄
900
Jens-Lottes
(9)
Thom et. al
Computed outside surface heat lux
(W/m2)
Q
Ai
B. Results
Since both the equations, (9) and (10) are used to calculate the
film temperature drop, outside heat flux (Q/Ao), computed
using both the equations are compared in Fig. 8. The data
shown is for the case with a pressure of 120 bar corresponding
to the 'predicted' temperatures obtained from solving the direct
heat conduction problem. It is clear that usage of Jens-Lottes
equation (Eq. 9) leads to a higher value of computed heat flux
for the same 'predicted’ temperature when compared to Thom
et al. equation (Eq. 10).
360000
Alternatively, Thom et al. equation [66] has also been used.
ΔTsat =
72 (
e
1/2
Q⁄Ai
⁄ 6)
10
PDRUM
⁄
1260
320000
(10)
The above calculated value of film temperature drop (ΔT sat) is
used to calculate new values Ti and hi. This iterative procedure
is repeated until specified tolerance limits are achieved. The
outside surface heat flux (Q/Ao) is calculated from inside
surface heat flux (Q/Ai) after correcting suitably for
circumferential heat flow.
The temperature obtained at the thermocouple measuring point
at the tube crown after solving the direct heat conduction
problem is termed as 'predicted' temperature. From the
predicted temperature, the outside heat flux (Q/Ao) is computed
by the procedure described above.
A flow chart depicting the suggested calculation procedure is
shown in Fig. 7.
280000
240000
200000
355
360
365
370
375
380
Predicted themocouple temperature (°C)
385
Figure 8: Heat flux calculation: Comparison between heat
flux calculated Jens-Lottes and Thom equations
Fig. 9 shows the comparison between actual values of outside
heat flux (Q/Ao) used for generating the predicted temperatures
and the computed values of (Q/Ao) arrived by solving the
inverse heat conduction problem using the 'predicted'
temperatures. The values are shown for 120 bar operating
pressure. It can be seen that the calculated heat flux matches
closely with that of the actual heat flux.
Thom et. al
Actual
Computed outside surface heat lux (W/m2)
Jens-Lottes
360000
320000
280000
240000
200000
350
360
370
380
390
Predicted themocouple temperature (°C)
Figure 9: Heat flux calculation: Comparison with actual
values
Figure 7: Flow chart for calculation of heat flux
1277
International Journal of Applied Engineering Research ISSN 0973-4562 Volume 11, Number 2 (2016) pp 1273-1281
© Research India Publications. http://www.ripublication.com
The uncertainties (95% confidence interval) for predicted heat
flux through the iterative procedure is given in the Table 2
below. From the table, it can be inferred that at 120 bar, Jens
Lottes correlation has a lesser uncertainty. At operating
pressures higher than 120 bar Thom’s correlation can be used
for better accuracy.
with rifled tube configuration. It has been found that, outside
heat flux in the membrane waterwall of a boiler can be
computed with reasonable accuracy with the measurement of
only one temperature at the tube crown for lower sub-critical
pressures.
Acknowledgement
Table 2: Uncertainties (95 % confidence interval) for
predicted heat flux
Operating
pressure
(bar)
Uncertainties in
heat flux calculated
using Jens-Lottes
equation (W/m2 )
120
140
160
±9704
±12820
±19364
The authors wish to thank the management of Bharat Heavy
Electricals Limited for having granted permission to publish
this paper.
Uncertainties in
heat flux
calculated using
Thom equation
(W/m2 )
±10679
±6231
±10801
List of symbols and abbreviations
B
Fin width (m)
Cp
Specific heat of tube material (kJ / (kg K))
Dc
Thermocouple installation diameter (m)
Dmajor
Major inside diameter of waterwall tube (m)
Dminor
Minor inside diameter of waterwall tube (m)
Do
Outside diameter of waterwall tube (m)
The calculation procedure was used to compute the outside heat
flux for the parameters specified by Duda and Taler [49] which
are specified below:
 Outside radius: 0. 03 m
 Inside radius: 0. 025 m
 Thermocouple location radius: 0. 029 m
 Thermal conductivity: 40. 5 W/ mK
 Fluid temperature: 318. 2 ˚C
 ‘Measured’ temperature: 349. 17 ˚C
ġ
Rate of heat generation (W/m3)
hi
Inside heat transfer coefficient (W/ (m2 K))
k
Thermal conductivity of the tube material
q̇ m
Absorbed outside surface heat flux (W/ m2)
Table 3 shows the comparison of calculated values of outside
heat flux with that of the values obtained in [49]. The calculated
values are closer to that of values furnished in [49]
Q/Ao
Applied local outside surface heat flux (W/
(W/ (m K))
PDRUM
Eq. (9) and Eq. (10)
m2)
Q/Ai
1
2
Parameter
Outside heat
flux (W/m2)
Inside heat
transfer
coefficient
(W/ m2 K)
Taler
and
Duda
[49]
220135.
3
37105. 5
JensLottes
equation
Thom
equation
221302. 2
219792.
6
37443. 8
38622. 3
Inside surface heat flux (W/ m2) or (Btu / (hr
ft2)) in Eq. (9) and Eq. (10)
Table 3: Comparison of results with Duda and
Taler paper [49]
Sl.
No.
Drum operating pressure (bar) or (psi (a)) in
r
radius of the waterwall tube (m)
ro
Outside radius of waterwall tube (m)
ri
Inside radius of waterwall tube (m)
T
Temperature of waterwall tube (°C)
Tav
Average wall temperature of the tube (°C)
Tc
Temperature
measured
by
chordal
thermocouple (°C)
Tf
Bulk fluid temperature (°C)
Ti
Inside surface temperature of waterwall tube
(°C)
Conclusion
ΔTsat
The sizing of a furnace necessitates an extensive study of heat
flux distribution in the furnace both along the height of the
furnace and laterally (along the width and depth). Measuring
the metal temperature using a chordal thermocouple inserted
into a hole drilled at the crown of the waterwall tube and then
computing the absorbed heat flux is a more viable and simple
method for sub-critical boilers in the operating pressure range
of 120-160 bar. An iterative procedure for calculation of heat
flux from the measured metal temperatures has been proposed
and validated for the membrane waterwall of sub-critical boiler
Film temperature drop (°C) or (°F) Eq. (5)
and Eq. (6), ΔTsat = (Tf – Ti)
Greek Symbols
θ, ϕ, ϕ1 and ϕ2 Angles as shown in Fig. 1
1278
ρ
Density of tube material (kg/m3)
ψ
View factor
International Journal of Applied Engineering Research ISSN 0973-4562 Volume 11, Number 2 (2016) pp 1273-1281
© Research India Publications. http://www.ripublication.com
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