Note: Descriptions are shown in the official language in which they were submitted.
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PCT/DE97/00049 GR96P3052P
Description
Once-through steam generator and method for designing a
once-through steam generator
The invention relates to a once-through steam
generator with a combustion chamber surrounded by a
containment wall composed of tubes connected to one
another in a gastight manner, a flow medium being
capable of flowing from the bottom upward through the
vertically extending tubes which have a surface
structure on their inside. It relates, further, to a
method for designing a once-through steam generator of
this type.
A steam generator of this type is known from
the paper "Verdampferkonzepte f~r Benson-Dampferzeuger"
["Evaporator concepts for Benson steam generators"] by
J. Franke, W. Kohler and E. Wittchow, published in VGB
Kraftwerkstechnik 73 (1993), No. 4, pages 352 to 360.
In a once-through steam generator of this type, in
contrast to a natural circulation or forced circulation
steam generator with only partial evaporation of the
water/steam mixture, the heating of evaporator tubes
forming the combustion chamber leads to the complete
2S evaporation of the flow medium in the evaporator tubes
- in a single pass. Whereas, in the natural circulation
steam generator, the evaporator tubes are basically
arranged vertically, the evaporator tubes of the once-
through steam generator may be arranged both vertically
a!nd spirally, hence at an inclination.
once-through steam generator, the combustion chamber
~alls of which are composed of vertically arranged
evaporator tubes, can be produced more cost-effectively
than a once-through steam generator having spiral
tubing. Furthermore, once-through steam generators with
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vertical tubing have lower water-side/steam-side
pressure losses than those with evaporator tubes which
are inclined or are arranged so as to ascend spirally.
Furthermore, in contrast to a natural circulation steam
generator, a once-through steam generator is not
subject to any pressure limitation, so that fresh steam
pressures well above the critical pressure of water
(PCrit= 221 bar), where there is only a slight density
difference .......
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_
between the liquid-like and steam-like
~edium. High fresh-steam pressures are necessary in
order to achieve high thermal efficiencies and
consequently low C0z emissions.
A particular problem, in this case, is to
design the combustion-chamber or containing wall of the
once-through steam generator with regard to the tube-
wall or material temperatures which occur there. In the
subcritical pressure range up to about 200 bar, the
temperature of the combustion-chamber wall is
determined essentially by the value of the water
saturation temperature, when wetting of the heating
surface in the evaporation zone can be ensured. This is
achieved, for example, by the use of internally ribbed
tubes. Tubes of this type and their use in steam
generators are known, for example, from European Patent
~pplication 0,503,116. These so-called ribbed tubes,
that is to say tubes with a ribbed inner surface, have
particularly good heat transmission from the inner wall
to the flow medium.
In the pressure range of about 200 to 221 bar,
the heat transmission from the tube inner wall to the
flow medium decreases sharply, so that the flow
velocity - the mass flow density usually being used as
a measure of this - has to be increased
correspondingly, in order to ensure that the tubes are
cooled sufficiently. Consequently, in the evaporator
tubes of once-through steam generators operated at
pressures of approximately 200 bar and above, the mass
flow density and therefore the pressure loss due to
friction must be selected higher than in once-through
;team generators which are operated at pressures of
below 200 bar. Particularly in the case of small tube
inside diameters, the higher pressure loss due to
friction cancels out the advan~ageous property of
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vertical tubing but, when there is multiple heating of
individual tubes, their throughput also rises. However,
since high steam pressures of more than 200 bar are
required in order to achieve high thermal ef~iciencies
and therefore low CO2 emissions, it is necessary, in
this pressure range too, to ensure good heat
transmission. Consequently, once-through steam
generators with a combustion-chamber wall having
vertical tubing are conventionally operated with
relatively high mass flow densities in the tubes, so as
to ensure, in the unfavourable pressure range of about
200 to 221 bar, that there is always suf~iciently high
heat transmission from the tube wall to the flow
medium, that is to say to the water/steam mixture. In
this context, the publication "Thermal Engineering"
I.E. Semenovker, Vol. 41, No. 8, 1994, pages 655 to
661, speci~ies a mass flow density at 100~ load o~
about 2000 kg/m2s consistently both for gas~fired and
for coal-fired steam generators.
The object on which the invention is based is
to specify, for tubes with a containing wall of a once-
through steam generator, a design criterion which is
suitable in terms of a particularly favourable mass
flow density in the tubes.
This object is achieved, according to the
invention, in that the steam generator is designed in
such a way that the mass flow density m in the tubes
of the containing walls at that load at which critical
pressure Pcrit prevails in the tubes conforms to the
relation:
m= qi (kg/m2s),
c ( TmaX ~ Tcrit--~Tw )
in which
qi (kW/M2) is the heat flow density on the inside of the
tube,
Tm~x (~C) is the maximum permissible material
temperature of the tube,
<~
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l'Cri~ (~C) is the temperature of the flow medium at
critical pressure Pcrit~
~ Tw (K) is the temperature difference between the outer
wall and inner wall of the tube, and
C > 7.3 10-3 kWs/kgK is a constant.
The invention proceeds from the consideration
that, in the flow-related design of the internally
ribbed tubes, two basically contradictory conditions
have to be satisfied with regard to the mass flow
density. On the one hand, the mean mass flow density in
the tubes must be selected as low as possible. This is
to ensure that a higher mass flow flows through
individual tubes, to which more heat is supplied than
to other tubes on account of unavoidable heating
differences, than through tubes which have average
heating. This natural-circulation characteristic known
~rom the drum-type boiler leads, at the outlet of the
evaporator heating surface, to an equalization of the
steam temperature and consequently of the tube-wall
temperatures.
On the other hand, the mass flow density in the
tubes must be selected high enough that reliable
cooling of the tube wall is ensured and permissible
material temperatures are not exceeded. High local
overheating of the tube material and the consequential
damage (tube cracks) are thereby avoided. Essential
influencing variables for the material temperature are,
in addition to the temperature of the flow medium, the
external heating of the tube wall and the heat
t:ransmission ~rom the inner tube wall to the flow
medium (fluid). There is therefore a connection between
the internal heat transmission, which is influenced by
the mass flow density, and the external heating of the
tube wall.
The invention, then, proceeds from the finding
l_hat the connection between the internal minimum heat
transmission coefficient ami~ an~ the mass flow density
~ can be described in permissibly simplified form by
l_he relation:
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~~min = C ~m (1)
in which
~Xmin (kW/m2K) iS the heat transmission coefficient,
m (kg/m2s) is the mass flow density in the ribbed
tubes, and
C is a constant with the mean value of
C = 7.3 ~ 10-3 kWs/kgK for commercially available tubes.
Depending on the structure of the inner surface of the
tubes, this constant C can also be selected in the
10 :range between 7.3 ~ 10-3 kWs/kgK and 12 ~ 10-3 kWs/kgK.
The said relation gives an optimum mass flow
density in the tubes which both results in a favourable
throughflow characteristic (natural-circulation
characteristic) and also ensures reliable cooling of
the tube wall and conse~uently adherence to the
permissible material temperatures.
A fundamental consideration in deriving the
said relation for the mass flow density in the tubes is
that, in the case of predetermined external heating of
the tube wall - the so-called heat flow density (kW/M2),
that is to say the heating per unit area, being used
hereafter for this - the material temperature of the
tube wall is only slightly, but definitely, below the
~ermissible value. In this case, it is necessary to
bear in mind the physical phenomenon that the heat
transmission from the inner tube wall to the flow
medium is most unfavourable in the critical pressure
range of about 200 to 221 bar.
Comprehensive tests show that the highest
material stress is obtained when a relatively low mass
flow density is combined with the highest occurring
heat flow density in the evaporation zone at about 200
to 221 bar. This is the case, for example, in that
region of the combustion chamber in which the burners
are arranged. If evaporation is subse~uently terminated
and steam superheating commences, the material stress
on the tubes of a combustion-chamber wall decreases
again. The reason for this is that, in a conventional
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burner arrangement and a conventional combustion cycle,
the heat flow density also decreases.
It wa~ found, furthermore, that, in other
pressure ranges too, no heat transmission problems
arise if, when ribbed tubes are used, sufficient
cooling of the tube wall is ensured in the said
pressure range of 200 to 221 bar. Thus, at low
pressures, that is to say of below approximately
200 bar, the internal ribbing of the tubes causes
critical boiling to commence only at the end of the
evaporation zone, that is to say in a region having a
reduced heat ~low density. Critical boiling no longer
occurs in the supercritical pressure range. Heat
transmission, then, is so intensive that sufficient
cooling of the tube wall is ensured.
To determine the optimum mass flow density m
in the tubes of the tube wall, the said optimum mass
flow density ensuring an advantageous throughflow
characteristic on the one hand and reliable cooling of
the tube wall on the other hand, the following
procedure can be adopted:
Step 1:
Determination of the heat flow density q~ on the
tube outside, based on the thermal calculation of that
load at which a pressure of 210 bar prevails in the
tubes of the tube wall. This heat flow density
determined in this way must be increased by a factor of
between 1.1 and 1.5, in order to allow for local
irregularities in heat transmission.
Step 2:
Calculation of the maximum permissible material
temperature TmaX at the tube apex on the heated side of
the tube wall. If it is assumed that the containing or
combustion-chamber wall has a mean temperature which
corresponds to the mean value of Tm~X and TCrit, the
maximum thermal stress is calculated as:
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T -T
. ~m~= m~2 ~t ~-E~N/n~n2), ~(2)
with
~max maximum thermal stress (N/mm2)
Tmax maximum material temperature (~C)
Tcrit temperature of the fluid at the critical
point (~C)
~ coefficient of thermal expansion (1/K)
E modulus of elasticity (N/mm2)
Since the stresses which are crucial here are
thermal stresses, these can be guarded against as
secondary stresses according to the ASME Code with
triple the value of the permissible stresses ~per~ This
results in the temperature TmaX as
~-E
The permissible stress can be taken from the
particulars supplied by the tube manufacturers.
Step 3:
Conversion of the predetermined heat flow
density q~ (related to the outside of the tube wall) to
a heat flow density qi which is related to the inner
wall of the tubes:
qi = d ~qa (kWlm ) (4)
The determination of the heat redistribution
factor K is based on temperature field calculations and
can be arrived at with sufficient accuracy as follows:
K = A (d~2 q~) + B (5)
with A = 0.45 and B = 0.625 for (d~2 ~ ~) < 0.5 kW
and A = 0.25 and B = 0.725 ~or (d~2 ~ q~) ~ 0.5 and
< 1.1 kW
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and A - 0 and B - l for (d.2 ~ q~) > l.l kW, with
da = tube outside diameter (m)
di = tube inside diameter (m)
~ = heat flow density on the outside (kW/m2)
qi = heat flow density on the inside (kW/m2)
Step 4:
Determination of the temperature difference
~ Tw between the tube outer wall and the tube inner
wall. The temperature difference ~ Tw is determined by
means of the heat conduction equation:
~Tw=( 2 ) qn2~ 1n n (K) (6)
with ~ = thermal conductivity of the tube material
(kW/mK).
Step 5:
Determination of the necessary mass flow
density m according to the relation:
C(Tm~--T --~T ~ (kg/m2s) (7~
An exemplary embodiment of the invention is
explained in more detail by means of a drawing. In
this:
Figure l shows a simplified representation of a once-
through steam generator with vertically
arranged evaporator tubes,
Figure 2 shows an individual evaporator tube in cross-
section,
Figure 3 shows, in a graphical representation, curves
E, F, G and H for the mass flow density in
the case of different geometries of an
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evaporator tube consisting of the material 13
CrMo 44, and
Figure 4 sho~s, in a graphical representation, the
dependence of the maximum permissible
material temperature of 13 CrMo 44 on the
permissible stress (N/mm2).
Parts corresponding to one another are provided
with the same reference symbols in all the figures.
Figure 1 shows diagrammatically a once-through
steam generator 2 of rectangular cross-section, a
vertical gas flue of which is formed from a containing
wall 4 which merges at the lower end into a funnel-
shaped bottom 6. The bottom 6 comprises a discharge
orifice 8, not shown in any more detail, for ash.
A number of burners 10, only one of which can
be seen, for a fossil fuel are mounted, in the lower
region A of the gas flue, in the containing wall or
combustion chamber 4 formed from vertically arranged
evaporator tubes 12. In this region A, the vertically
arranged evaporator tubes 12 are welded to one another
via tube fins or tube webs 14 to form gas-tight
combustion-chamber or containing walls. The evaporator
tubes 12, through which the flow passes from the bottom
upwards when the once-through steam generator 2 is in
operation, form an evaporator heating surface 16 in
this region A.
When the once-through steam generator 2 is in
operation, a flame body 17 occurring during the
combustion of a fossil fuel is located in the
combustion chamber 4, so that this region A of the
once-through steam generator 2 is distinguished by a
very high heat flow density. The flame body 17 has a
temperature profile which, starting from about the
middle of the combustion chamber 4, decreases both
upwards and downwards in the vertical direction and in
the horizontal direction towards the sides, that is to
say towards the corners of the combustion chamber 4.
Located above the lower region A of the gas flue is a
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second flame-distant region B, above which a third
upper region C of the gas flue is provided. Convection
heating surfaces 18, 20 and 22 are arranged in the
regions B and C o~ the gas flue. Located above the
region C of the gas flue is a flue-gas outlet duct 24,
via which the flue gas RG generated as a result of the
combustion of the fossil ~uel leaves the vertical gas
flue.
Figure 2 shows an evaporator tube 12 which is
provided with ribs 26 on the inside and which, while
the once-through steam generator 2 is in operation, is
exposed on the outside, within the co'mbustion chamber
4, to heating at the heat flow density qa and through
which the flow medium S flows internally. At the
critical point, that is to say at the critical pressure
]?crit Of 221 bar, the temperature of the flow medium or
Eluid in the tube 12 is designated by TCrit. The maximum
permissible material temperature TmaX at the tube apex
~8 on the heated side of the tube wall is used for
calculating the maximum thermal stress ~x. The inside
diameter and outside diameter of the evaporator tube 12
are designated by di and d~ respectively. In the case of
internally ribbed tubes, it is necessary to use the
equivalent inside diameter which allows for the
influence of the rib heights and rib valleys. The tube-
wall thickness is designated by dr~
Figure 3 shows, in a system of coordinates,
four curves E, F, G and H for different outside
diameters da (mm) and tube-wall thicknesses dr (mm). For
this purpose, the heat flow density ~ (kW/m2) on the
tube outside is plotted on the abscissa and the
preferred or optimum mass flow density m (kg/m2s) is
plotted on the ordinate. The curve E shows the trend
for a tube outside diameter da of 30 mm in the case of a
tube-wall thickness dr of 7 mm. The curve F represents
the trend for a tube outside diameter d~ of 40 mm in the
case of a tube-wall thickness dr ~f 7 mm The curve G
shows the trend of the mass flow density ~ in
dependence on the heat flow density ~ for a tube 12
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having an outside diameter dA of 30 mm and a tube-wall
thickness dr of 6 mm. The curve H shows the trend o~ a
tube 12 with an outside diameter d~ of 40 mm in the case
of a tube-wall thickness dr o~ 6 mm. The mass flow
densities m are calculated for heat flow densities qa
of 250, 300, 350 and 400 kW/m2 at the critical pressure
Pcrit Of the flow medium S for the tube material 13 CrMo
44 .
An example of the determination of the optimum
mass flow density m is shown below. In this case, the
following conditions are presupposed:
q~ = 250 kW/m2; heat ~Clow densïty on the tube
outside at a pressure of 210 bar,
1.4 as raising factor for allowing for local
irregularities in the heat transmission to the tubes
12,
d~ = 40 mm tube outside diameter, dr = 7 mm
tube-wall thickness, and tube material: 13 CrMo 44.
It follows from da and dr that: di = 26 mm tube
inside diameter.
1st Step: Calculatinq the heat flow density
The heat flow density based on thermal
calculation is multiplied by the raising factor. This
results in:
qa = 350 kW/m2
2nd Step: Determininq the maximum permissible material
temperature
According to equation (3), this temperature is
calculated at TCrit = 374~C (temperature of the fluid at
critical pressure Pcrie)~ with ~ = 16.3 ~ 10-6 (1/K)
~coefficient of thermal expansion of 13 CrMo 44), E =
~78 ~ 103 (N/mm2) (modulus of elasticity of 13 CrMo 44)
and ~per = 68.5 (N/mm2) (permissible stress of 13 CrMo 44
at the maximum permissible material temperature) as:
TmaX = 515~C.
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This determination of TmAX, to be carried out
iteratively, shows the dependence of the permissible
stress ~per on the material temperature. Figure 4
represents graphically this dependence between the
permissible stress ~per on the maximum material
temperature TmaX for the material 13 CrMo 44.
3~d Step: Heat flow density on the tube inside
By means of the equations (4) and (5), there
follows for A = 0.25 and B = 0.725 for the heat flow
density qi on the inside of the tubes 12:
qi = 466 kW/m2.
4th Step: Determininq the temPerature dlfference T~,
between the tube outer wall and tube inner
wall
According to equation (6), with the thermal
conductivity of 13 CrMo 44 of ~ = 38.5 - 10-3 kW/m K:
~ Tw = 73 K.
5th Ste~: Determininq the necessary mass flow density
According to equation (7), with C = 7.3 10-3
kWs/kgK:
m = 939 kg/m2s.
The optimum mass flow density m can thus be
determined by means of the available values for the
heat flow density qa on the tube outside and the maximum
permissible material temperature T~x. This value is
represented by broken lines in Figure 3 for the
specified conditions. It can be seen that, for the
assumed heat flow density qa of the tube outside of
350 kW/m2, optimum mass flow densities m of between 740
and 1060 kg/m2s are obtained in the case of tubes 12
having outside diameters da of between 30 and 40 mm and
wall thicknesses dr of between 6 and 7 mm.
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For the flow-related design of the tubes 12 of
the tube wall or containing wall 4, the mass flow
density m th~s determined can still be converted to
the conditions prevailing under 100~ load. For this
purpose, the operating pressure at the inlet of the
tubes 12 is calculated at 100~. The abovementioned mass
flow densities m are subsequently converted in
proportion to the operating pressure under 100~ load.
If, for example, the operating pressure under 100~ load
is p~ = 270 bar, the mass flow density m increases from
740 to 951 kg/mZ or from 1060 to 1363 kg/m2s.
It may be expedient to allow for uncertainties
in the determination of the heat flow density ~ by
raising the mass flow density m from +15~ to +20~ in
relation to the calculated value.
-
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List of reference symbols
m mass.flow density
~ thermal stress
A, B region
~a outside diameter
dr tube-wall thickness
E,F,G,H curve
Pcr~t pressure
~ heat flow density
qi heat flow density
RG flue gas
S flow medium
TmaX maximum permissible material temperature
2 once-through steam generator
4 containing wall
6 bottom
8 discharge orifice
burner
12 evaporator tube
14 tube web
16 evaporator heating surface
17 flame body
18,20,22 convection heating surface
24 flue-gas outlet duct
26 ribs
28 tube apex
