CFD STUDY OF AIR-LAYER DRAG REDUCTION ON A PLATE WITH DIFFERENT KINDS OF CAVITY DESIGN
Xiaosong Zhang Computational Marine Hydrodynamics Lab (CMHL)
School of Naval Architecture, Ocean and Civil Engineering, State Key Laboratory of Ocean Engineering, Shanghai Jiao Tong University,
Shanghai 200240, China CSIC Shanghai Marine Energy Saving
Technology Development Co.,Ltd No.185 Gao Xiong Road, Shanghai, China
Decheng Wan* Computational Marine Hydrodynamics Lab (CMHL),
School of Naval Architecture, Ocean and Civil Engineering, State Key Laboratory of Ocean Engineering, Shanghai Jiao Tong University,
Shanghai 200240, China *Corresponding author
Email: [email protected] URL: https://dcwan.sjtu.edu.cn/
ABSTRACT Air-Layer Drag Reduction (ALDR) technique is one of the
most effective air lubrication techniques, which creates a
complete air layer to separate the hull surface from the water.
Drag reduction effect has been proved to be over 80% for a flat
plate in previous experiments. However, how to form an air-layer
as complete as possible attached to the bottom of the ship has not
yet been completely understood, holding back the practical
application on ships. In this context, CFD method can be useful
to simulate the air layer evolution process and analyze the two-
phase flow field in detail. A few simulations using RANS models
have been presented, but there is no related simulation work
using LES model. Therefore, the primary goal of this work is to
check the effect of an LES model and develop methodology for
effective CFD simulation of air-layer flows. Bottom plate of ship
is simplified to a flat plate in the numerical simulation, and air is
ejected from circular jet holes at the front of the plate. An
important condition for the formation of air-layer is the design of
bottom air cavity. In the present work, the influence of two key
parameters of the cavity is investigated, which are the direction
of injector and the height of front wedge. Through the simulation
of air layer at different wedge height, it was found that the wedge
height has a major effect on the thickness of air layer, which in
turn exerts an obvious influence on the drag reduction effect.
INTRODUCTION With the further implementation of Energy Efficiency
Design Index (EEDI) [1] requirements, energy saving has
become an important factor in modern ship design and
manufacturing. Air lubrication is a very promising technique for
reducing ship drag resistance and saving energy. There have been
many researches on different forms of air lubrication drag
reduction. Bubble Drag Reduction (BDR) is the earliest form of
air lubrication, which takes advantage of microbubbles injected
into the turbulent boundary layer to reduce density of mixed flow
and inhibit turbulent vortex. Many previous experimental [2,3]
and numerical studies [4,5,6] using BDR technique obtained
approximately 20%-30% drag reduction effect on a plate. In the
last decade, Air-Layer Drag Reduction (ALDR) technology was
proposed [7] and considered as a potential alternative to bubble
drag reduction. A complete air layer is created in the ALDR
technique to separate the hull surface from the water. The
theoretical frictional resistance reduction effect of the area
covered by air layer can be up to 100%. Because of its excellent
drag reduction effect and can be effective on various rough
surfaces, the ALDR technique has promising application on large
transport ships.
Elbing et al. [7] was the first to define the air-layer drag
reduction. Their team originally carried out a bubble drag
reduction experiment with Reynolds number as high as 210
million [8]. In their experiments, they found that at low flow
velocity and high air flow rate, the bubbles were confined to a
layer and could reduce drag by more than 90%. This remarkable
drag reduction effect led them to further study the transition
conditions from BDR to ALDR [7]. The shape of air under
different injection flow rate was divided into three regions:
bubble region, transitional region and air layer region. More
recently, Elbing et al. [9] adopted the same experiment facilities
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Proceedings of the ASME 2020 39th International Conference on Ocean, Offshore and Arctic Engineering
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to study the influence of surface roughness and the scaling.
Experiments mentioned above were all conducted in the USA
Navy’s William B. Morgan Large Cavitation Channel. Huang et
al. [10] carried out experimental study of air-layer drag reduction
in a high Relynolds number flat plate turbulent boundary layer.
A clear visualization of the air layer was presented in their paper.
All the experimental studies introduced above presented
abundant physical phenomenon and data. However, detail flow
analysis still requires numerical simulation. Kim and Moin [11]
performed DNS simulation on the air layer drag reduction over
a backward-facing step. The total number of grid points was
about 271 million although the length of computational domain
was only 0.4m. The air layer was simulated perfectly, but the
calculation cost was also very high. More numerical works were
based on RANS model. Wang et al. [12] simulated the air layer
formation in a high Reynolds-number flat plate turbulent
boundary layer. The effect of drag reduction was basically
consistent with the trend of experimental results. Montazeri and
Alishahi [13] combined the linear stability and URANS model
to simulate the air layer flow. Simulation results showed the
effectiveness of the proposed method.
To summarize the above numerical simulation studies, only
DNS method can simulate the air layer very well, and RANS
simulations are all aiming at improving numerical prediction of
the amount of drag reduction. In fact, it is more important for the
analysis to simulate the air layer clearly. In this paper, the authors
use the LES model to simulate the air layer. The influence of
different kinds of cavity design is investigated in detail. Two key
parameters are the direction of injector and the height of front
wedge block.
The present paper is organized as follows. The numerical
approach is presented first with emphasis on the turbulence
modeling and the two-phase simulation method. The geometry
model and computational grids are introduced next. The
investigation of air layer shape and control mechanism are
shown in the numerical simulation section. The effect of air
injection direction and wedge block height are analyzed in detail.
A brief conclusion and future works are given in the end.
NUMERICAL APPROACH In order to better solve the turbulence fluctuation, Large
Eddy Simulation (LES) model is adopted. The governing
equations are incompressible, immiscible, two-phase N-S
equations. The filtered expression is:
0U (1)
( ) ( )rgh ij ij
UUU p gh p k
t
(2)
where the overbar identifies filtered quantities. U is velocity
vector, p is pressure, is fluid density, g is gravity. The last
term is surface tension term, in which is surface tension
coefficient, k is curvature and is phase fraction. ij and ij
represent the viscous stress and sub-grid scale stress tensor,
respectively. The dynamic Smagorinsky model proposed by
Germano et al.[14] is used to model the SGS stress. The classical
Smagorinsky model can be written as:
1( )
3ij kk ij sgs ijS u (3)
where sgs is the sub-grid scale viscosity coefficient, which is
defined as: 2( ) ( )sgs sC S u (4)
where Cs is a constant parameter, is filtered scale. Cs has
different value for different problems. But it is really hard to
determine a constant value for a complex flow. Thus, the
dynamic Smagorinsky model was proposed. Cs in this model is
a value that adjusts with the flow changes, which satisfies:
2 1
2
ij ij
s
mn mn
L MC
M M (5)
( )r r t rt rt
ij i j i jL u u u u (6)
2 2( ) ( ) ( )t rt rt r r r t
ij ij ijM S S S S (7)
where superscript r and t represent grid-filter and test filter
respectively.
There is obvious stratification characteristic for the two
phase flow in air layer drag reduction problem. Therefore, it is
necessary to capture the two-phase interface accurately. The
volume of fluid (VOF) method with artificial compressive term
is applied for locating and tracking the air-water interface[15].
The effect of artificial compressive term is to counteract the
phase interface fuzziness caused by the numerical dissipation to
obtain a sharper interface. The phase fraction transport equation
can be written as:
( ) ( (1 ) ) 0U c Ut
(8)
where c represents compressive factor. There is no compressive
effect when c equals to 0.
The two phase flow solver interFoam in open source
platform OpenFOAM is used to perform the simulations. As for
the numerical schemes, the computational domain is discretized
by unstructured grids with finite volume method for space
discretization. In addition, the pressure-velocity coupling
equations is solved by the PIMPLE algorithm. Second-order
scheme is used for both temporal discretization and spatial
discretization.
GEOMETRY AND GRIDS The flat section of the bottom of ship is simplified to a
rectangular flat plate as modeled in a companion set of
experiments discussed below. The geometry of the plate model
is shown in Figure1. The full length of the plate is Louter=2.275m,
with an oval transition at the head. Width of the plate is B=0.3m.
Under the plate is an air cavity whose length is Linner=2m,
consisting of a wedge block and two side boards. These
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structures are used to help form stable air layer under reasonable
air flow rate. Heights of the side boards are Hs=0.035m.
Similarly, height of the wedge block is Hw=0.035m initially. In
the following investigation, the height of wedge block will be
modified to 0.015 to study its effect. The air flow is injected from
a row of 10 circular holes with a diameter of 0.005m and a
distance of 0.03m from the wedge block.
(a) Overall view
(b) Side view
(c) Upward view
(d) Wedge block and side board
Figure1 Geometry of the plate model with cavity.
(a) Computational domain
(b) Grid distribution
Figure 2 Computational domain and grid distribution.
Computational domain and grid distribution are shown in
Figure 2. Unstructured hexahedral grids generated by pre-
processing software Hexpress are used to discretize the whole
domain. Two region refinements and one surface refinement are
performed around the geometry. The first grid refinement region
surrounds the air cavity in three directions and its height is twice
the wedge height. The second grid refinement region is the same
width as the first, and the height is equal to the wedge height.
Aspect ratio of the grids in the inner refinement region is 4:4:1
(x : y : z). There are 10 layers of boundary layer grids in the near-
wall region of the air cavity. The viscous sub-layer flow is
resolved by using wall-bounded grid layers to ensure that the
body-surface y+ is in the order of 1. Wall function is not
applied in the present simulation.
NUMERICAL CONDTIONS Boundaries of the computational domain are shown in
Figure 3 and the corresponding boundary types are identified in
the figure. Water flow enters from the left boundary of the
computational domain. Air flow is injected from a row of 10
holds on the flat plate surface. Both water and air can outflow
freely from the outlet boundary. At the beginning of the
simulations, U.air is set to be zero and cases are run for a long
time without air injection to reach a stable flow field. Then, the
jet velocity of air at the injection holes increases from 0 to the
target velocity within 0.1s. Conditions of the present simulation
are based on our recently completed experiment tests.
Unfortunately, the results of the experiments have not been
published. Typical pictures will be given in the following
section. The speed of inflow water in the present work is
U=2m/s. Total air flow rate is Q=10L/s, the corresponding air
flow velocity at the injector is 50.93m/s. Detailed boundary
conditions can be seen in Table 1, where alpha is volume
fraction, pd is dynamic pressure.
Table 1 Detailed boundary conditions
Boundary type Key parameters
Water Inlet
alpha.water=1
U=U.water=2m/s
∇pd=0
Air Inlet
Alpha.water=0
U=U.air=50.93m/s
∇pd=0
Outlet
∇U=0
∇alpha=0
pd=0
Wall Surface
U=0
∇alpha=0
∇pd=0
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Figure 3 Boundaries of the computational domain.
In the present simulation, time step is set to be-51.8 10t s .
The Courant number remains stable during the calculation, and
the specific value can be seen in Table 2. There are two key
Courant numbers in the calculation of such a complex two phase
flow. Courant number Co is defined as Co u t x , while
Interface Courant number CoI is defined asI I
Co u t x . Iu
andIx are the velocity and size of air-water interface grids,
respectively. The maximum Co occurs at the Air Inlet boundary
because that the air injection velocity is extremely high. Air flow
velocity decreases rapidly after it is injected into the flow field.
So that Co is below 1 except the air injection boundary.
Table 2 Courant numbers in the calculation.
Mean value Maximum value
Co -31.5 10 3.0
CoI -67.0 10 0.3
The velocity U and pressure p are discretized to form
algebraic equations. Gauss-Seidel and PCG methods are used to
solve U and p equations. The final convergence criterion of p and
U in each time step is the residual less than-81 10 . The
convergence criteria can be achieved by several iterations of p
and U in each time step. After velocity correction, volume
fraction α is solved explicitly. The accuracy of the velocity
solution ensures that alpha can be accurately solved at each time
step. On the other hand, by monitoring solving process, the error
of mass conservation at each time step is on the order of 10-14,
which further confirms the convergence of α equation.
RESULTS AND DISCUSSION In the post-processing of simulation results, isosurface of
α=0.5 is used to represent the air/water interface. Figure 4 shows
three typical air layer shapes in t=0.6s, 1.2s and 1.8s. It should
be noted that t=0 is the time at which the air injection started.
The air-water interface is colored by blue in the figures. Initially,
when the air flow is injected into the water flow field, it will
spread downstream evenly. Then, violent fluctuation appears
when air flow reaches a certain position. It can be seen from
Figure 4 (b), in the position where fluctuation occurs, the air flow
moves downstream from both sides of the cavity and converges
into a thinner layer. In Figure 4 (c), the air flow has pass the
whole plate and most areas of the plate are covered by air layer.
However, the air passes through the side boards and escapes from
the cavity. The loss of air will lead to instability of air flow
behind, holding back the formation of a better air layer. At the
same time, there is a very interesting phenomenon that instead of
failing downstream, the air layer appears to have a distinct blank
region at the center of the plate. The blank region is
approximately triangular in shape, causing the air flow to bypass
it from both sides. We have observed this phenomenon in
experiments several times. Figure 5 shows an example picture
taken from our experiment. The air-water interface looks blue in
the experiment and the surface of the plate is painted yellow.
Triangular blank region can be seen clearly in the figure. At the
same time, the air layer in front is significantly thicker than that
behind the blank region, which is similar to the simulation
results.
(a) t=0.6s
(b) t=1.2s
(c) t=1.8s
Figure 4 Air layer at typical moments.
Figure 5 Triangular blank region phenomenon in experiment.
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The distribution of air layer thickness on the middle
longitudinal section of the cavity is plotted in Figure 6. It can be
seen obviously that there is a large bubble in the front of the air
layer, which is almost twice as thick as the wedge block height.
This large bubble is the main reason causing the escape of air
away from the cavity. And the amount of air reaching the
downstream decreases, resulting in unstable air layer. Figure 7
shows three typical air-water interfaces and the stream line
patterns. When air is injected into the flow field from the jet
holes, the air-water interface is highly unstable. The interface is
broken at the end of air layer due to the flow impact, while water
and air mix with each other. As the air injection continues, the air
layer develops downstream and the interface becomes stable
gradually. However, although the water and air have reached a
basically stable state of separation, the flow state inside and
outside the interface is very different. It can be seen from Figure
7 that the stream line outside the interface is smooth, while the
flow inside the interface is very chaotic. There are a large amount
of vortex structures in the large front bubble, leading to
significant fluctuation of the air flow. This phenomenon may be
resulted from two factors, one is the impact of the air flow, and
the other is the vortex shedding of the front wedge block. In order
to find out the control mechanism of the large front bubble, the
authors firstly study the effect of the injection direction of air
flow.
Figure 6 Air layer thickness on the middle longitudinal section
of the plate.
(a) t=0.6s
(b) t=1.2s
(c) t=1.8s
Figure 7 Air-water interface and stream line.
In order to verify whether the impact of vertical injection of
air flow is the main reason for the formation of the front large
bubble, cases with two kinds of air injection are performed.
Illustration is shown in Figure 8. Type (a) in Figure 8 is named
VI (Vertical injection) and type (b) is named PI (Parallel
injection), respectively.
Figure 8 Two kinds of air injection. (a) Vertical injection. (b)
Parallel injection.
When air flow is just injected into the water flow field,
significant difference can be seen in Figure 9. As expected, air
flow in the case PI develops faster downstream than that in the
case VI. At the same time, air flow in the case PI is smoother in
the downstream direction, which indicates that the air layer in
the cavity can be more homogeneous. However, air flows in both
cases appear a trend to roll over at the end, which is not
conducive to the stability of the air layer.
Figure 9 Air-water interface at t=0.06s. (a) VI. (b) PI.
The development process of air layer in case PI is shown in
Figure 10. In contrast with the results of case VI at the same time
plotted in Figure 4, the formation of air layer is better in general.
The blank region at the center of the plate is disappeared and the
whole plate is coved by air layer at the time t=2.4s. And the
whole air layer seems to be more smooth and stable. However,
at the time t=3s, the air flow passes through the side boards and
escapes from the cavity again, leading to the instability of the
downstream air layer. This phenomenon indicates that the
problem of large front bubble has not been solved by the
adoption of parallel injection. But there are still many differences
for the final shape of air layer between these two cases. The
position where air escaped in the case PI is further back than that
in the case VI, the corresponding amount of escaped air is
smaller, which demonstrate that the type of parallel injection
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does have a certain improvement effect for the formation of air
layer.
(a) t=0.6s
(b) t=1.2s
(c) t=1.8s
(d) t=2.4s
(e) t=3.0s
Figure 10 Development process of air layer in case PI.
Figure 11 the comparison of air layer thickness on the middle
longitudinal section of the plate
Figure 11 presents the comparison of air layer thickness on
the middle longitudinal section of the plate between case VI and
case PI. In general, the adoption of parallel injection will
improve the uniformity of the whole air layer. But this method
has little effect on the problem of the large front bubble. Inspired
by the air flow pattern in Figure 9, the vortices formed by the
water flow pass the wedge block are thought to be another
important reason for the formation of large bubble in the front
and the instability of the flow behind.
The geometry of wedge block is modified. The height of
wedge block is reduced from 35mm to 15mm and other
geometric parameters remain unchanged. The comparison of
original geometry and modified geometry is plotted in Figure 12.
Figure 12 The modified wedge block.
Both VI and PI simulations are carried out using the
modified wedge block. The comparison of air layer with original
wedge block and modified wedge block is shown in Figure 13.
Figure 13 The effect of modified wedge block height on the air
layer shape.
Figure 13 (a) and (b) are taken at t=1.8s, and figure (c) and
(d) are taken at t=3.0s. It can be seen that by using the modified
wedge block, the shape of air layer changes significantly. The
height of the large front bubble is reduced and the uniformity of
air layer has been further improved. The whole plate is covered
by the air layer all the time and there is no air escape at the side
of cavity. This kind of air layer is satisfactory and can reduce the
frictional drag by nearly 100%.
The quantitative analysis of the effect of wedge block height
on the air layer thickness can be seen in Figure 14 and Figure 15.
For the case VI, the large front bubble is still exist, but the height
of the bubble is reduced by 33%. The excess air thickens the air
6 Copyright © 2020 ASME
layer downstream and the blank region in the center of the plate
disappears completely. For the case PI, the large front bubble is
nolonger obvious. The thickness of the whole air layer is almost
uniform, at the same time with some fluctuations. All of the
above results prove that the height of wedge block playes an
important role in the formation of air layer. The wedge block
with 15mm height performs much better than that with 35mm
height. Whether there is a optimal height for various plate length
still needs further investigation.
Figure 14 Comparison of air layer thickness using vertical
injection between original and modified wedge block.
Figure 15 Comparison of air layer thickness using parallel
injection between original and modified wedge block.
CONCLUSIONS
In this paper, CFD simulation is carried out for air layer drag
reduction research on a flat plate. VOF model combined with
artificial compressive method is used to capture the air-water
interface, while LES model is applied to simulate the turbulence.
In the simulation with the initial geometry, the air layer is
found to be incomplete. There is a distinct blank region in the
center of the plate, which also has been seen in experiments.
Also, a large bubble appears in the front part of the cavity,
leading to air escape from both sides. Based on these phenomena,
the effect of air injection direction and the height of wedge block
was investigated. Results show that the parallel injection mode
is better than the vertical injection mode for the formation of air
layer, but the effect is limited. However, the height of wedge
block plays an important role in the formation of air layer. The
stability and uniformity of the gas layer have been improved by
reducing the height of wedge block.
Air layer drag reduction is a complex two phase flow
problem. There is a lack of sufficient verification and validation
for the numerical simulation in this study. Therefore only
qualitative analyses are carried out. Future works will be devoted
to checking numerical algorithm and comparing with
comprehensive experimental results. In addition, “moving
contact line” problem may has important effect on the coverage
of air layer. Future research will be analyzed from this
perspective.
ACKNOWLEDGMENTS
This work is supported by the National Natural Science
Foundation of China (51879159), The National Key Research
and Development Program of China (2019YFB1704200,
2019YFC0312400), Chang Jiang Scholars Program (T2014099),
Shanghai Excellent Academic Leaders Program
(17XD1402300), and Innovative Special Project of Numerical
Tank of Ministry of Industry and Information Technology of
China (2016-23/09), to which the authors are most grateful.
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