windloads on offshore structures
TRANSCRIPT
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Wind oads on Offshore Structures
van Walree Maritime Research Institute Netherlands MARIN),
P.O. Box 28, 6700 Wageni,ngen, he Netherlands
Willemsen National
Aerospace Laboratories NLR,
P.O. Box 153, 8300
D
Emmeloord, The Netherlands
SUMMARY
A new computational model for determining the wind loads on off-
shore structures is described. This model aims to bridge the gap
between calculation procedures provided by the classification
societies and wind tunnel testing. The new model is based on the
so-called building block approach, whereby the structure is thought
to be composed of standard components with known force characteris-
tics. Special attention is given to the modelling of the wind flow
field, component interaction and lift forces on elevated and in-
clined main decks. Three comparisons between experimental and cal-
culated results are given for typical offshore structures. These
comparisons show that the results obtained by using the new compu-
tational model are much closer to the experimental values than
those obtained from the classification society rules.
1. INTRODUCTION
Wind forces contribute significantly to the total environmental
loads on offshore structures. Drag forces are of importance for
moori.ng, dynamic positioning and manoeuvring of floating struc-
tures. Stability of floating and fixed structures may be affected
by overturning moments due to drag and lift forces. Knowledge of
these loads is therefore indispensable for the design and operation
of such structures.
From the point of view of the wind flow field and wind induced
pressures, offshore platforms and vessels are rather complex. Semi-
submersible drilling rigs, jack-ups with huge cantilever legs,
floating production and storage units and crane vessels, to mention
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only a few, display a large variety of columns, work decks, super-
structures, derricks, heli decks etcetera.
-
Commonly followed routes to obtain the wind force data for such
complicated shapes are:
-
simple calculation methods as provided by classification
societies
see ABS [ l]
and DnV [ 21
)
- wind tunnel tests.
The first method is easily applicable and requires little time but
the accuracy is limited, primarily because lift effects on decks
and interaction effects between adjacent members are neglected.
Wind tunnel tests, when performed correctly, provide realistic re-
sults but are rather time-consuming and expensive. For further in-
sight into these matters reference is made to Boonstra and Leynse
[3]
and Macha and Reid
[ ] -
l
In order to bridge the gap between the methods outlined above, in
1987 a joint industry development study was carried out. This study
aimed at the development of an advanced computational model for de-
termining wind forces on arbitrary offshore structures. The project
was carried out by M RIN in close cooperation with NLR as part of
the Netherlands Marine Technological Research MaTS) program. The
project was sponsored and supervised by the following companies:
De Hoop ~obith);
GUSTO Engineering;
Maritime Project Engineering;
Rijkswaterstaat;
Shell Internationale Petroleum Maatschappij;
Verolme Trust;
WijsmulLer Engineering.
In
an early stage of the study, detailed requirements as to the
computational mode1 were derived. ~pplications of the mode1 as
foreseen, required the validity of the method for arbitrary off-
shore structures. Wind loads in
6
degrees of freedom for arbitrary
orientations wind directions) and heel angles up to
20 degrees had
to be calculated. Furthermore the accuracy of the model had to be
improved significantly when compared with existing calculation pro-
cedures.
Since the resulting computer program had to be used in various
design and engineering studies at small offshore engineering of-
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fices, the program had to run on mini- and personal computers with
a reasonable performance.
Based on these requirements a new computational model has been de-
veloped, whereby the physical model was derived from classical
aerodynamics and empirical formulations. Data bases with additional
information completed the computational model.
0
The computational model developed in this study has been imple-
mented in a Fortran
77
computer program by MARIN
Extensive wind tunnel experiments have been carried out in the low
speed wind tunnel 3.0 2.25 m) of NLR The experimental program
was carried out, to provide data for derivation of empirical formu-
lations, to complete relevant data bases and in order to verify the
overall model..
2.
COMPUTATIONAL
CONCEPT
The various project demands set the trend of alternative approaches
to the computational model. Possible approaches are:
theoretical methods;
correction methods;
fully empirical methods:
building block methods as applied by ABS and DnV).
Theoretical methods for flows around complex bluff bodies like off-
shore structures are not available, although programs for single
bluff bodies have appeared recently, see Van Oortmerssen et al.
[5]
These programs can only run on large and very fast mainframe
units. As such, application of these methods is out of the ques-
tion.
The correction method is based on wind tunnel test data of struc-
tures similar to the proposed design. By adding and subtracting
certain parts of the construction, and at the same time correcting
the wind load, one can obtain the wind loads on the structure. This
method is based on the availability of suitable test data which may
form a problem especially for new designs. Furthermore, interaction
effects will not be proper1,y accounted for.
Empirical, formulations also need a set of wind tunnel data for each
type of offshore structure. The more data available the higher the
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accuracy of empirical relations. Again, a good prediction for an
unusual or new type of construction is not possible. Also, a com-
parison based on wind loads of a series of prototypes with the same
main dimensions but with for example alternative deck lay outs,
will in general not be possible.
The building block method does not rely on data of similar designs;
it can be applied to any structure provided the characteristics of
its components are known. The accuracy of this method however, is
strongly related to a proper inclusion of several physical flow
phenomena.
Considering these methods, it was thought that the building block
method would be the most promising one. Its flexibility and
physical correctness play an important role. The following items
form the fundamentals of the physical model:
force characteristics of the standard components;
wind velocity field;
determination of component interaction;
forces on inclined structures.
These topics will be discussed in detail in the next section.
3 PHYSICAL MODEL
3.1 Standard Components
The basis of the calculation method is formed by a set of three-
dimensional geometrical components with known force characteris-
tics. These characteristics are reflected by three force coeffi-
cients for the drag, side and lift force) and the centre of effort
of each force component. The characteristics of the components are
mainly obtained from published results of model experiments. By
means of the following five types of standard components, an ade-
quate description of offshore structures can be given:
circular cyli.nders
rectangular prisms;
flat plates;
lattice structures;
ship hulls.
The description of the force characteristics of circular cylinders
includes effects due to the Reynolds number flow separation), sur-
face roughness, flow turbulence, cylinder inclination, aspect ratio
and taper. Fig. 1 shows the drag coefficient for two-dimensional
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(infinite aspect ratio) circular cylinders. The horizontal axis
represents the effective Reynolds number which is corrected for
flow turbulence and surface roughness.
R
= eynolds nunber
E O
= relative surface roughness
Fig. 1. Drag Coeffici.ents for Circular Cylinders
Drag, side and lift force coefficients for rectangular prisms were
derived as a function of the prisms relative dimensions and
inclination angle. The side force may be comparable in magnitude
with the drag force and may therefore add substantially to the
total overturning moment on offshore structures. Surface mounted
prisms may experience an appreciable lift force due to the acceler-
ated flow and accompanying reduced pressure over the top face. As
the boundary layer separation points are fixed at the sharp cor-
ners, no significant Reynolds number effects occur. Also, since the
forces are predominantly determined by pressure forces and not by
skin friction, the surface roughness of the prism s sides is irrel-
evant.
For flat plates normal to the flow, only a drag force arises. At
incidence, a lift and a side force are introduced which are depen-
dent on the incidence angle and the aspect ratio, see Fig. 2. The
tangential force is negligible and Reynolds number effects for full
scale conditi.ons may be neglected. The centre of effort positi.on of
the force component is also dependent on incidence and aspect ra-
tio. The lifting characteristics of flat plates may be of partic-
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ular interest for the prediction of the forces due to helicopter
decks subjected to a platform induced upflow.
A
DYIDX
DY
PL TE
WIDTH
For the prediction
of forces on lattice
structures, a bulk
method is used where
the forces are ob-
tained from empiri-
cal data relating
the force coeffi-
1 6
cient for a single
0 25
framework to it
2 00 overall shape and
solidity ratio. An
allowance is pro-
vided for the effect
111
1 2 3: 4 b
o
70 8 P d*J.i of shielding for
downstream frames.
Fig. 2. Normal Force Coefficients for
Flat Plates
The data base provides force coefficients for a wide variety of
Lattice structures. Three basic arrangements of chord members are
considered: a triangular, a square and a rectangular arrangement.
The bracing configuration is arbitrary since the solidity ratio of
the configuration is the main variable. The structural. members may
either be of the angular flat faced) or the circular type.
Wind load coefficients for ship hulls were again derived from wind-
tunnel tests. The contribution of the several superstructure compo-
nents was subtracted from the total measured wind loads. In this
way, the corrected force coefficients may be used for ships with an
arbitrary superstructure configuration.
3.2 Wind Velocity Field and Component Interaction
For the transfer of a force coefficient for a specific component to
an actual force, knowledge is required of the component area and
mean dynamic pressure. The first follows from the model descrip-
tion; the latter is determined from the mean value over the wind
area A of the component. An component-bounded effective wind speed
ve
is defined:
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V = v2 y,z) dydz 1
For the undisturbed atmospheric boundary layer the wind velocity
increase with height is commonly expressed in t.he power-law repre-
sentation:
where V, denotes the reference wind speed at the reference height
zr.
The exponent value p will range between 0.10 and 0.15 for most
practical purposes.
Local windspeeds may deviate from the power-law profile due to
various effects like the occurrence of separated flow regions, t.he
circulation around a lift generating main deck and the presence of
other deck components. The combined effect of these disturbances
will lead to a highly complex velocity field. For the flow along an
elevated main deck the following equations were derived from Hess
C6
where t is the body thickness and
X
and z are the local coordi-
nates, see Fig. 3
These formulations, basically valid for the potential flow around
flat nosed bodies, agree for the flow outside the separation zone,
along the main deck centre line. Experimental data were used for
corrections of the velocity components V, and V, accounting for
flow separation and three-dimensional effects near the deck
edges). Fig.
3
shows the computed streamlines for two main deck
types.
To account for the reduced velocities in an elements wake, the
following description was taken from Schlichting
[ 7 ] :
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where b is the wake
width, CD is the upstream
component drag coeffi-
cient, dw is the upstream
component width and X and
y denote a local coordi-
nate system, see Figure
4 The exponents pl and
p2 have a value dependent
on the aspect ratio of
the upstream member.
The equations 4)and 5)
may only be used for not
too short distances be-
_U_J
tween the two bodies. For
short distances the wake
of the upstream body is
Fig. 3. Flow Fields along Elevated too much affected by the
Main Decks presence of the
down-
stream one. In that case
data obtained from literature and from special wind tunnel experi-
ments were used. These data also account for effects due to the
bodies aspect ratio, flow enhancement and multiple interaction.
3.3 Forces on Inclined Structures
For the discussion of the various principles, column-supported
structures will be taken as starting point. Surface vessels then
form a group with the limiting condition of a zero airgap. The
basic ideas are drawn from classical aerodynamic theories on lif-
ting bodies, like the wing theory. The features for a specific
platform are a rather linear lift curve with a positive lift in
level condition, a lift induced drag increase at inclined condi-
tions and a lift increase due to the proximity of the sea surface.
As pointed out by various investigators the lift may be rather high
and important because of its contribution to the overturning moment
[8 9]
The present work demonstrates an increased importance of the lift
because of its contribution to the drag. Physically, the lift gene-
rating entity of a platform is the main deck. To compare t.he test
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results of various platforms as available in open literature and at
NLR, the presented drag and lift coefficients were re-cal.culated
with appropriate reference values for area and dynamic pressure.
The applied reference values were the main deck area and the mean
dynamic pressure over the height range of the main deck boundaries.
2
In general the test results showed rather linear CL(a) and C (C )
D
L
relations for inclination angles up to, say 15 degrees.
V Y)
Fig.
4
Velocity Reduction due to Shielding
The lift curves also showed a posi.tive lift at a = 0 degrees (level
condition), indicating that a platform is subjected to an upflow
angle aO, caused by the presence of platform columns and sea boun-
dary. Therefore, an effective pitch angle aeff is defined:
a
eff
= a + a
0
where a is the main deck pitch angle with respect to the wind axes
system.
The relation between CL and
or ff
is calculated from literature,
accounting for the thickness ratio t/c and aspect ratio = b2/~)
of the main deck thickness, excluding the contribution of large
protruding elements.
The definitions of b and c, i.e. platform main deck dimensions in
the wind axes system, imply that for a non-circular main deck and
t/c vary with the wind direction
8
For t/c
< 0.05
the lift curve is assumed to be linear, with a lift
curve slope C calculated by applying the Jones edge-velocity
La
correction to Anderson s formula on basic and additional lift dis-
tribution [l01
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For larger values of t/c this thickness parameter will affect the
lift curve slope in a non-linear way, i.e. also dependent on the
value of aeff. Experimental data [l11 were used to modify the above
relation accordingly.
The upflow angle a is estimated from the calculated drag distribu-
tion along the platform and the airgap geometry by means of an
empirical relation.
For a wide variety of platforms the typical value of
a was 5 to 10
degrees.
Wind tunnel experiments showed that with decreasing airgap between
main deck and simulated sea surface the lift is increasing, without
significantly affecting the drag. This indicates that the main deck
is subjected to a
ground induced upflow angle and that the dynam-
ic pressure remains unaffected. Ground effects on a lifting wing,
which are represented by a bound vortex along the span and trailing
vortices from the tips, result in a dynamic pressure increase from
the plane-imaged bound vortex and in an induced upflow angle from
the plane-imaged trailing vortices. Apparently, for a platform only
the imaged trailing vortices play significant role. To correct
for this phenomenon the following correction formula, valid for a
wing with eliiptic Lift distribution along the span [12], is ap-
plied:
2zeff) 0.768
with ex p (- 2. 4 8( ~
where zeff is the height halfway the wing trailing edge and the
wing aerodynamic centre. Similarly, w define:
It will be clear that. this procedure may be considerably improved
when more is known about the actually non-elliptic lift distribu-
tion and corresponding vortex system of main decks at various
thickness ratios, particularly for the relatively thick main decks
(t/c greater than approximately
0.35).
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W ith t h e a bove d e s c r i b e d p r oc e du r e t h e l i f t c ur ve of a s p e c i f i c
p l a t f o r m
i s
c a l c u l a t e d , w he reb y a l s o d r a g a t . a e f f = 0 i s d e t e r -
mined.
The e a r l i e r m en tio ne d v a l i d i t y o f
0.1
-
2
l i n e a r C C c ur ve s p o i n t s t o
D L
k=
- t / c a / 2
CL
t h e c l a s s i c a l i nd uc ed d r a g con-
c e p t
1 2
CD
. L
1
F r o m c l a s s i ca l a e r o d y n am i cs it
i s
known t h a t t h e p a r am e t e r k
i s
de-
p en de nt on t h e a s p e c t r a t i o
A
For an e l l i p t i c d i s t r i b u t i o n
a l o n g t h e s pa n k i s e qu al t o
n .
H oe rner [ l 31 r e p o r t s f o r l i f t i n g
s u r f a c e s w i t h sm a ll a s p e c t r a t i o s
a v a l u e o f k e qu al t o
n / 2 .
The
wind t un n e l t e s t r e s u l t s , d i s -
c u ss e d e a r l i e r , showed t h a t
k
s h o u l d b e c o r r ec t ed f o r t.h e m ain
d eck t h i ck n es s . T h e f o l l o w i n g
c o r r e c t i o n was a p p l i e d :
t . /c 0 .75 : k
=
l - t / c ) r / 2
F i g . 5 . I nd uced D rag C o e f f i c i e n t s t / c 0 .7 5: k
=
0 .393 12 )
F i g .
5
shows t h e t e s t r e s u l t s f o r a r e c t a n g u l a r m ain de ck
R M D )
wi th d imens ions b
=
500 mm, c
=
750
mm
a t = 0 d eg r ee s ) an d
t
=
300 mm The induced d rag concep t and th e mod i f ied k -va lue ag ree
w e l l w i th t h e t e s t r e s u l t s f o r t h e two t e s t e d w ind d i r e c t i o n s and
v a r i e d a i r g a p v a l u e s . The v a l i d i t y of k
=
0.393 a t t / c
>
0.75 could
n o t be v e r i f i e d , a s no s u f f i c i e n t d a t a a r e a v a i l a b l e f o r t h o se r e -
l a t i v e l y t h i c k t y p e s o f p la tf o rm .
F o r t h e ca l c u l a t i o n o f t h e o v e r t u r n i n g moment, n o t o n l y t h e d rag
a r e a s o f t h e v a r i o u s p l a t f o r m c om pon ents and t h e main de ck l i f t
m ust b e c a l c u l a t e d , b u t a l s o t h e v a ri o u s c e n t r e s of e f f o r t .
The w or ki ng l i n e o f t h e d r ag on a s p e c i f i c p l a t f o r m com ponent
i s
d e t e rm i n ed by t h e h e i g h t o f t h e mean d ynamic p r e s s u r e o v e r t h a t
component. The l i f t i nduced d rag
i s
added t o th e main deck d ra g .
The w orkin g l i n e of t h e l i f t i s c a l c u l a t e d from t h e w e l l- d e s cr i be d
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flat plate data [14], with a correction for the main deck thickness
as deduced from wind tunnel tests:
where X /c denotes the centre of effort of a flat plate.
c
Analysis of the tests showed that for a platform with a smooth main
deck an aerodynamic torque is present. This torque decreases with
increasing ratio of deck thickness and streamwise platform length,
with increasing airgap between main deck and sea surface and with
increasing deck arrangement. The origin of this torque is believed
to be due to the formation of a separation bubble at the main deck
leading edge. Enlargement of this bubble up to even bursting re-
sults in a decreasing torque, increasing lift and a forward shift
of the lift working line. This process il.lustrates the importance
of a properly modelled platform in wind tunnel testing.
4.
CORRELATION OF WINDOS WITH EXPERIMENTAL RESULTS
4.1 Introduction
A computer program (WINDOS) has been developed based on the phy-
sical model discussed. For the correlation between calculated and
experimental results, three comparisons will be given here which
are thought to be representative for typical WINDOS applications.
The comparisons concern:
a semi-submersible consisting of a rectangular main deck, four
circular columns and a helicopter deck located at the main deck s
leading edge. The experimental data are obtained from the NLR
wind tunnel tests;
a so called semi-spar platform, consisting of a circular main
deck and circular columns. The experimental data are obtained
from Willemsen et al.
[ 91
a jack-up platform consisting of a triangular main deck, three
square legs and several superstructure components. The experi-
mental data are obtained from Norton [l5
In the several comparative figures, the calculated results by using
the ABS or DnV method are given too. These methods do not account
for lift effects.
4.2 Semi-submersible with Helicopter Deck
Fig.
6
shows the results for this structure in terms of a drag co-
efficient CD, a lift coefficient L and an overturning moment CO
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aOnV a 0
efficient
CM
Four wind headings
WT a 0
WT.
a
10
8 ) and two platform inclination
WINDOS
a
0 angles a) are given. The corre-
WINDOS; a 1 0
lation between WINDOS and the
HEL IDECK
3
60 90
wind tunnel data is both qualita-
tively and quantitatively good
for the lift and drag coeffi-
cients. The overturning moment
coefficient is somewhat underpre-
dicted a
0
degrees) or over-
predicted a 10 degrees,
0
and
30
degrees) by WINDOS, al-
though the trends with the incli-
nat.ion and wind angle are well
predicted. The gap effect on the
overturning moment needs probably
t.o be extended in the physical
model of WINDOS.
The greater overturning moment
for the inclined platform at a
Fig. 6. Semi-submersib4e with Helideck
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zero degree wind angle is caused by the lift forces on the main-
and helicopter decks. Apart from the flow inclination due to the
structure s pitch angle, the main deck induced velocity field acts
as an inclined flow (see Fig. 3) to this helicopter deck. This
deck, modelled as a flat plate in WINDOS, experiences then a sig-
nificant lift force, which adds to the overturning moment by the
long lever arm.The DnV prediction for the drag at even keel is too
conservative. This overprediction is less pronounced for the
overturning moment.
4.3
Semi-spar Platform
Fig. 7
shows the re-
Wind
sults for this case.
-D
WIN OS
WT o
nV o
~
WIN OS
WT
nV
A
The correlation between
WINDOS and the experi-
ments for the drag and
overturning moment co-
efficients is good.
This indicates a proper
modelling of interac-
tion effects between
circular cylinders in
WINDOS. The resemblance
for the lift coeffi-
cients is not satisfac-
tory. This is due to
the circular shaped
main deck which is not
Fig.
7.
Semi-Spar Platform modelled in WINDOS.
The DnV results for this structure are reasonably good, compared
with the previous case. WINDOS results are more close to the expe-
rimental values than the DnV results due to a better treatment of
Reynolds number and interaction effects on the circular cylinders.
i
4.4
Jack-up Platform
The drag and overturning moment coefficients are shown in Fig.
8.
Lift coefficients are not shown as the experimental arrangement is
judged to be inadequate for a good prediction of the lift forces.
f
The comparison between the WINDOS and experimental results is again
f
reasonably good. The ABS predictions are too conservative, espe- i
cially for the drag coefficients.
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5 CONCLUDING
REMARKS
Fig.
8.
Jack-up Platform
The new developed method
for the computation of
wind loads on offshore
structures is based on
physical principles expe-
rimental data and computer
capabilities.
The main physical princi-
ples used are based on
classical aerodynamic the-
ories on lifting bodies.
An extensive wind tunnel
test program validated the
basic principles enabled
the derivation of empiri-
cal formulations and pro-
vided new data sets.
The final computer program
WINDOS has been verified
with results of several
wind tunnel tests.
A
sig-
ni i.cant improvement of
the correlation was found
when compared with the re-
sults from classification
society rules.
NOMENCLATURE
main deck area; component wind area
b cross main deck dimension; wake width
C
longitudinal main deck dimension
dw component width
CD
drag coefficient
lift coef ici.ent
lift curve slope
CM
overturning moment coefficient
9
mean airgap between main deck and sea surface
k variable in the induced drag relation
P exponent
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main deck thickness
velocity
effective velocity
reference velocity
coordinate system
distance from main deck leading edge to the lift
working line
roughness height
reference height
wind axis pitch angle of main deck
platform induced upflow angle
effective platform inclination angle
wind heading
aspect ratio; b 2 / ~
variable in ground effect formula
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Mobile Offshore Units, 1985.
[2] Det n o r s w ~ u l e sor Classification of Mobile Off-
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[ 31 BOONSTRA, H. and LEYNSE, C., Windtunnel Tests on a Model of
a Semi.submersible Platform and Comparison of the Results with
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MACHA, J.M. and REID, D.F., Semisubmersible Wi.nd Loads and
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OORTMERSSEN, G. VAN, VEGT, J.J.W. VAN DER and WALREE, F. VAN,
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H.,
Boundary Layer Theory, MC Graw-Hill, 7th
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TORENBEEK, E., Synthesis of Subsonic Airplane Design, Delft
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HOERNER,
.F.
and BORST, H.V., Fluid-Dynamic Lift, published
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