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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


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


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.


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


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


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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