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Numerical investigation of a fleet of towed AUVs
Ocean Engineering 80 (2014) 25–35
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Numerical investigation of a fleet of towed AUVs Pareecha Rattanasiri n, Philip A. Wilson, Alexander B. Phillips Fluid Structure Interactions Group, Engineering and the Environment, University of Southampton, Southampton SO17 1BJ, United Kingdom
art ic l e i nf o
a b s t r a c t
Article history: Received 26 April 2013 Accepted 4 February 2014
This paper investigates the influence on the fleet of the drag of multiple towed prolate spheroids to determine the hydrodynamic effect of the viscous interaction between hulls and to study the influence of the configuration's shape of multiple hulls in the vee and echelon formations. A series of CFD RANS-SST simulations has been performed at the Reynolds Number 3.2 106 by a commercial code ANSYS CFX 12.1. Mesh convergence is tested and then validated with experimental and empirical results. The drag of each spheroid is compared against the benchmark drag of a single hull. The results show that the spacing between two hulls determines the individual drag and combined drag. The dominant spacing has been classified into seven zones based on the drag characteristic of twin towed models. Regions are characterised to parallel, echelon, no gain, push, drafting, low interaction, and no interaction. Both the multi-vehicle vee and echelon configurations show limited influence against that of the entire fleet's energy budget. For an individual spheroid where a lower propulsion cost is required, then the use of three/four in vee or echelon formation should be considered. Based on this numerical information, operators can determine the optimal fleet configuration based on energy considerations. & 2014 Elsevier Ltd. All rights reserved.
Keywords: Co-operative AUVs Fleet of AUVs Towed model Vee formation Echelon formation CFD RANS-SST simulation
1. Introduction Autonomous Underwater Vehicles (AUVs) are self-propelled robots which perform missions without requiring external powering or an umbilical control. Current AUVs have the capability to perform missions such as pipeline inspection (Labbe et al., 2004; Weiss et al., 2003), mine-sweeping (Edwards et al., 2004), and oceanographic exploration (Botelho et al., 2005; Martins et al., 2003). Proposed missions for the next generation of AUVs require them to acquire both high quantity and quality temporal and spatial data. This enhanced performance may be achieved by either homogeneous or heterogeneous fleets of vehicles. By carrying different sensors, the surveying performance of multiple small vehicles may have a performance equal to or exceeding that of a single larger vehicle, with improved levels of robustness and redundancy for a specific task. This has led to studies of manoeuvring and path planning of fleets by Aguiar et al. (2011), Bean et al. (2007), Burger et al. (2009), Cui et al. (2009, 2010), Reeder et al. (2004), and Vanni (2007). Since the range of an AUV is dictated by its finite energy source, minimising the energy consumption is required to maximise
n Correspondence to: Fluid Structure Interactions Group (Room 28/1021), Engineering and the Environment, Highfield Campus, University of Southampton, Southampton SO17 1BJ, United Kingdom. Tel.: þ 44 23 8059 5097. E-mail addresses: [email protected] (P. Rattanasiri), [email protected] (P.A. Wilson), [email protected] (A.B. Phillips).
http://dx.doi.org/10.1016/j.oceaneng.2014.02.001 0029-8018 & 2014 Elsevier Ltd. All rights reserved.
endurance. The total power consumed by an AUV can be split into propulsion power and the hotel load required to power nonpropulsion related electronics and sensors (Phillips et al., 2012). This study only considers propulsion power. For an individual AUV the propulsion power may be reduced by obtaining the optimum hydrodynamic design of such as hull, propeller and surface control (Bellingham and Willcox, 1996; Bradley, 1992; Bradley et al., 2001; Dalton and Zedan, 1980; Huggins and Packwood, 1994; Jagadeesh and Murali, 2005, 2006; Jagadeesh et al., 2009; Kinsey, 1998; Parsons, 1972; Parsons et al., 1974; Phillips, 2009; Sarkar et al., 1997a; Stevenson et al., 2007). For a fleet of multiple AUVs, minimising the energy consumption may be targeted for both individuals and the entire fleet. Previous experimental studies of flow past bodies in close proximity such as two circular cylinders, two slender bodies, a car with trailer and cars in convoy demonstrate the effect of relative distance between the bodies on the fleet drag as a whole (Hoerner, 1965; Hucho and Ahmed, 1998). When slipstreaming in cycling, the trailing riders experience a 38% reduction in wind resistance (Kyle, 1979). Drafting in swimming, the relative drag of the second swimmer in line is approximately 56% and 84% lower than the leading swimmer, when the distance between the swimmers is 0.5 m and 6.0 m, respectively (Silva et al., 2008). Observation of animal motion such as fish in schools, dolphins in pods or birds in flocks suggests some energy benefit may be obtained by certain fleet configurations (Alexander, 2004; Andersson and Wallander, 2003; Hanrahan and Juanes, 2001; Partridge et al., 1983; Weihs, 2004).
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Nomenclature 1þ k the form factor of a single spheroid 1þ βk the form factor of twin spheroids Aw wetted surface area (m2) B1 leading spheroid B2, B3, and B4 following spheroid %B1, %B2, %B3, and %B4 individual drag of B1, B2, B3, and B4 referred to a single hull drag %CB combined drag refer to sum of two single hull drags CD total drag coefficient, Total drag/(0.5ρV2Aw) CD(B1) and CD(B2) drag coefficient of B1 and B2 in fleet CD(B3) and CD(B4) drag coefficient of B3 and B4 in fleet CD(s) drag coefficient of a single hull CF skin friction drag coefficient, Skin friction drag/ (0.5ρV2Aw) (CF)1957 ITTC'57 skin friction line CPx pressure drag coefficient, Pressure drag/(0.5ρV2Aw) CSF coefficient of side-force
dm D D/L dh S/L L Re V Ui xi ν ρ μ k ε ϕ Ru
maximum diameter of the body of revolution (m) longitudinal offset (m) non-dimensional longitudinal offset maximum hull diameter (m) transverse separation length of the body from nose to tail (m) length Reynolds number, VL/ν vehicle speed (m/s) Cartesian mean velocity components (Ux, Uy, Uz) represents Cartesian co-ordinates (X, Y, Z) (m) fluid kinematic viscosity, μ/ρ (m2/s) fluid density (kg/m3) fluid dynamic viscosity (kg/m s) fluid turbulent kinetic energy (m2/s2) rate of dissipation of turbulent energy (m2 s 3) the advection scheme the vector from the upwind node to the integration point
For mother and calf dolphins, the calf derives a 60% energy benefit by taking up a hydrodynamically advantageous position in close proximity to its mother (Weihs, 2004). This assumption has agreed with the experimental results of twin prolate spheroids in the wind tunnel (Weihs et al., 2007). Recently, Husaini et al. (2009) numerically illustrated the influence of distance among multiple towed torpedo shape AUVs to their individual drags. These results suggest the energy benefit by using a fleet of AUVs may be obtained at the optimal configuration with the optimal distance and lead to the underlying questions of:
Does a fleet configuration provide energy benefits for just an individual AUV or the whole fleet?
What is the optimal configuration and optimal distances of the fleet? The purpose of this paper is to provide guidance for operators on suitable spacing for multiple vehicles' configurations. Based on this numerical information, operators can determine the potential configuration with the optimal distances based on the energy consideration. To achieve this aim, two main hydrodynamic processes of twin towed hulls: the body-to-body interference (or viscous interaction) and the increase of drag of following hulls due to the wake of a leading hull must be numerically investigated, firstly, the effect of various configurations to the individual drag, the fleet drag and the interference drag of a series of two prolate spheroids. Secondly, the influence of the number of spheroids in the fleet including the shape of the configuration must be numerically investigated.
Fig. 1. Physical flow problem: (a) flow passes a single hull, (b) flow passes twin hulls in parallel configuration, and (c) flow passes twin hulls in drafting configuration.
to the viscous drag (Cv) and can be estimated as 2. Theoretical approach
C D C v ¼ ð1 þ kÞC F ¼ ðTotal dragÞ=ð0:5ρV 2 Aw Þ
2.1. Drag estimation
where ρ is the fluid density, Aw is the wetted surface area and V is the fluid velocity and a form factor (1 þk) was introduced to estimate the ratio of total viscous drag (Cv) to the skin friction drag (CF). CF may be estimated by the ITTC'57 correlation line (ITTC, 1957):
The flow pass a single bare hull, twin hulls in parallel configuration and twin hulls in drafting configuration being considered here are sketched in Fig. 1a, b and c, respectively. To estimate total drag coefficient for fluid flow pass a single hull can be obtained by C D ¼ C wave þ C v
ð1Þ
Assuming the AUV is fully submerged in deep water, there will be no wave resistance (Cwave E0), the total drag is therefore only due
ðC F Þ1957 ¼ 0:075=ðlog 10 ðReÞ 2Þ2
ð2Þ
ð3Þ
For streamlined shapes, Hoerner (1965) suggests an estimated form factor in terms of the body length (L) and the maximum body
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diameter (dm) as 3=2
ð1 þ kÞ ¼ 1 þ 1:5ðdm =LÞ
þ 7ðdm =LÞ
3
ð4Þ
In the case of parallel twin hulls in close proximity, the conventional form factor for a single hull cannot establish an accurate prediction due to the accelerated flow velocity between twin hulls, as shown in Fig. 1b. This is called a viscous interaction effect which results in an increase of the drag of both hulls. In case of drafting twin hulls in close proximity, the pressure distribution around the tail of the leading hull interacts with that around the stagnation point of following hull (as shown in Fig. 1c). The pressure distribution of each hull is then changed which cause the individual drag to increase/decrease. By combining a viscous resistance factor β, the estimation of a more accurate form factor (1 þβk) for twin hulls can be obtained (Molland and Utama, 2002), hence the total drag of twin hulls can be estimated as C D ¼ ð1 þ βkÞC F
ð5Þ
To predict the hydrodynamic forces acting on an AUV's hull, a steady-state Reynolds Averaged Navier Stokes (RANS) simulation has proved to provide reasonably accurate results when compared against the experimental results (Jagadeesh et al., 2009; Karim et al., 2009; Phillips et al., 2008, 2007, 2010b; Sarkar et al., 1997b). However, to obtain a high fidelity result needs an appropriate mesh resolution to capture the effect of the boundary layer, bodyto-body interaction and the wake behind the body. 2.2. Reynolds Averaged Navier Stokes (RANS)
The momentum equation can be written as ! ( !) ∂ui'uj' ∂U i ∂U i U j ∂P ∂ ∂U i ∂U j þ μ þ þf i ρ ¼ þ ρ ∂xi ∂xj ∂xj ∂t ∂xj ∂xj ∂xi
ð6Þ
ð7Þ
where the tensor xi represents Cartesian co-ordinates (X, Y, Z) and Ui are the Cartesian mean velocity components (Ux, Uy, Uz). The Reynolds stress tensor ðρu0i u0j Þ is represented the turbulence closure and f i is the external force. The RANS equations are implemented in the commercial CFD code ANSYS (2010) CFX. The governing equations are discretised using the finite volume method. The high-resolution advection scheme was applied for the results presented which varies between first- and second order accuracy depending on spatial gradient. For a scalar quantity ϕ the advection scheme is written in the form of ϕip ¼ ϕup þ b∇ϕ URu
Fig. 2. Set up of twin prolate spheroids in the 14 m long, 70 50 wind tunnel. source: Figure adapted from Molland and Utama (1997).
where ϕip is the value at the integration point, ϕup the value at the upwind node and Ru the vector from the upwind node to the integration point. The model reverts to first order when b¼0 and is a second-order upwind biased scheme for b¼1. The highresolution scheme calculates b using a similar approach to that of Brath and Jesperson (1989), which aims to maintain b locally to be as close to one as possible without introducing local oscillations. Collocated (nonstaggered) grids are used for all transport equations, and pressure velocity coupling is achieved using an interpolation scheme based on that proposed by Rhie and Chow (1982). Gradients are computed at integration points using trilinear shape functions defined in ANSYS (2010) CFX. The linear set of equations that arise by applying the finite volume method to all elements in the domain are discrete conservation equations. The system of equations is solved using a coupled solver and a multigrid approach. The shear stress transport (SST) turbulence closure model (Menter, 1994) which blends k ε and k ω was selected to close the mathematical model for this study. Previous investigations have shown that it is better able to replicate the flow around the ship and submarine hull form than either k ε or k ω model, notably with a moderate accuracy (Larsson and Baba, 1996; Phillips et al., 2010a).
3. Case study 3.1. Base experiment
By assuming the flow is incompressible, the continuity equation becomes ∂U i ¼0 ∂xi
27
ð8Þ
Molland and Utama (1997) performed a series of experiment on twin prolate spheroids to characterise the side-force and yawing moment interactions. Tests were carried out in the 70 50 (2.20 m 1.57 m) low speed wind tunnel at the University of Southampton. The overall length (L) of each model was 1200 mm with maximum diameter (dh) of 200 mm and a surface area (Aw) of 0.601 m2. The top spheroid was placed at the middle breadth and 1.07 m height from the floor. It was fitted to the overhead wind tunnel dynamometer for measuring the total drag and side-force. The lower spheroid (B2) was placed at the transverse separation (S/L) of 0.27, 0.37 and 0.47 away from the centerline of B1. The noses of both spheroids are aligned with zero longitudinal offset (D/L ¼0) as shown in Fig. 2. 3.2. Present study To verify the numerical strategies and results, Molland and Utahan's (1997) experiment of twin towed bare prolate spheroids with transverse separations, where D/L ¼0 and S/L¼ 0.17, 0.27, 0.37 and 0.47, are selected. Where D is the longitudinal distance between each nose of bodies, S is the transverse distance between
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Fig. 3. Fleets of prolate spheroids with the body length L where S/L is the transverse separation and D/L is the longitudinal offset: (Left) twin hulls configuration, (Middle) vee formation and (Right) echelon formation.
centre lines of each bodies and L is the body length. As shown in Fig. 3, the cases have been extended to study the following:
Firstly, the effect of longitudinal spacing on the drag. The
distances between two hulls are considered at various combinations between 0 oD/L r1.77 and 0.27 oS/Lr0.47. The result is shown in Section 4. Secondly, the effect of the configuration's shape of multiple hulls on the drag. The symmetry configuration and the echelon configuration are considered. The result is shown in Section 5. The case details are as follows: Fleets of three spheroids in vee formation for S/L¼ 0.17, 0.27 and 0.37 and D/L¼ 0.27, 0.57, 0.87 and 1.17. Fleets of the three/four spheroids in echelon for S/L ¼0.17 and D/L ¼0.27 and 0.57.
3.3. Numerical settings To replicate the experiment of Molland and Utama (1997), the dimension of fluid domain is modelled at 1.4L 12L 1.8L. Free slip wall conditions (ANSYS, 2010) are used for the roof, floor and walls. The air inlet velocity (V) is set at 40 m/s related to a length Reynolds number (Re) 3.2 106 (typical AUV operates at Re between 105 and 107) with the zero relative pressure outlet boundary condition. The air density (ρair) and the air kinematic viscosity (υair) at room temperature are 1.185 kg/m3 and 1.545 10 5 m2/s, respectively. Both hulls are modelled by using no slip wall condition (ANSYS, 2010). 3.4. Mesh strategy The sample of meshes cut in the ZX plane and the YZ plane is shown in Fig. 4a and b, respectively. The model domain, boundary condition and mesh strategies used in this simulation are illustrated in Fig. 5. The results of drag components; the total drag coefficient (CD), the pressure drag coefficient (CPx) and the skin friction drag coefficient (CF) and form factor (1 þ k), for each cases are shown in Table 1. A series of eleven meshes ranging from 1.2 to 22.7 million elements were made for an example case, where the 1.2, 8.6 and 22.7 million element is considered as the coarse mesh, the medium mesh and the fine mesh, respectively. With 2.0% difference of total drag between the medium mesh (case f) and the fine mesh (case j), the computational cost of using the medium mesh is approximately 8 h which is 10 times lower than that of fine mesh when using the 64 bit operating computational system, 2.53 GHz, two Core Processors with 12 GB RAM. Thus the mesh parameters of global mesh size and the local refinement case f is selected as appropriate. The computational parameters are provided in Table 2. 3.5. Results and validation The twin towed bare hulls are compared against the experimental results (Molland and Utama, 1997), the numerical results
Fig. 4. Mesh cut around a pair of spheroids for S/L ¼0.27 and D/L ¼0 for medium mesh (case f). (a) ZX plane at the centre line at Y ¼ 0 with the fluid flow from left to right and (b) YZ plane at X ¼ 0.6 m from the noses.
(Molland and Utama, 2002) and empirical results (Hoerner, 1965) are as follow. 3.5.1. Pressure distribution The distribution of the pressure coefficient, CP ¼(P P1)/ (0.5ρU2), is shown in Fig. 6a–c. Where, X/L is a position on the longitudinal axis of the body. A good agreement is observed between the numerical trend lines and the experimental results for the three separated separations. 3.5.2. Side-force coefficient The side-force is defined as an attraction force between the hulls (Fz). The side-force coefficient (CSF) is defined by CSF ¼ Fz/ (0.5ρU2). In Fig. 7, the numerical results of CSF of B1 show excellent agreement with the experimental results and show that previous numerical demonstrations were deficit because of the lack of high
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Fig. 5. (Top) Boundary condition and mesh refinement around a pair of prolate spheroids and (Bottom) eleven mesh strategies.
Table 1 The result of drag components; the total drag coefficient (CD), pressure drag coefficient (CPx), skin friction drag coefficient (CF) and form factor (1 þ k), for each mesh strategies.
Table 2 Computational parameters. Parameters
Setting Unstructured with local refinement around spheroids and in wake regions Average 30 8–15 M with 15–20 prism layers in the boundary layer Shear stress transport 1%
Case
CD 103
CPx 103
CF 103
(1 þ k)
Mesh type
a b c d e f g h i j k
4.325 4.307 4.260 4.231 4.180 4.168 4.154 4.139 4.124 4.086 4.076
0.635 0.625 0.571 0.550 0.493 0.481 0.449 0.388 0.379 0.355 0.344
3.718 3.714 3.717 3.713 3.715 3.711 3.724 3.751 3.745 3.730 3.730
1.163 1.160 1.146 1.140 1.125 1.123 1.115 1.103 1.101 1.095 1.093
yþ No. of elements Turbulence model Inlet turbulent intensity Wall modelling Spatial discretisation Timescale control Convergence criteria Computing Run type Simulation time
performance computers at that time. The rapidly decrease of the side-force ratio with an increase of separation, is due to the lower flow velocity through the construction between the hulls.
3.5.3. Form factor For the length–diameter ratio 6:1 spheroid, estimates of (1 þk) from Eq. (4) gives 1.135. The comparison of form factor between the experimental results and the numerical results based on the ITTC correction line is shown in Fig. 8. The numerically predicted (1 þk) of B1 is within 1.5% error of Hoerner's estimation. The increment of form factor (1 þβk) compared with the single hull illustrates the influence of viscous resistance factor (βk) due to close proximity. The 8% error between the experimental result and Hoerner's estimation and 16% error between the experimental result and numerical result show some interference of the tunnel wall to the single hull and twin hulls experiment, respectively.
Automatic wall function (ANSYS, 2010) High resolution (ANSYS, 2010) Auto timescale (ANSYS, 2010) RMS residualo 10 6 3 Linux cluster Parallel (12 partitions run on 4 dual core nodes, each with 2 GB RAM) 2.0–2.5 Wall clock hours (medium mesh)
3.5.4. Total drag coefficient of towed B1 The drag results are evaluated in terms of the total drag coefficient (CD), the pressure drag coefficient (CPx) and the skin friction drag coefficient (CF). Fig. 9 shows the numerical results of the total drag coefficient (CD) at various transverse separations. The CD of a single hull in the present study is 10% lower compared to the experimental drag (Molland and Utama, 1997). A good agreement of the trend line is observed at S/L r0.37. At S/L Z0.47, Molland and Utama (2002) suggested that some interference from the tunnel wall may occur, and consequently, increase the total drag of B1. This is not observed in either numerical study. The experimental result is 16% higher than the current numerical prediction at S/L¼0.27 and 0.37. This may be partially attributed to interference drag due to the experimental mounting system, which is not recreated in the numerical simulations. With these positive evaluations of the CFD with the experiment results and
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Fig. 7. CSF as proportion of CD at various transverse separation.
Fig. 8. Comparison a form factor between the experimental and numerical prediction of a single hull and twin hulls.
Fig. 6. Pressure drag coefficient of B1. (a) S/L ¼0.27, (b) S/L ¼ 0.37, and (c) S/L ¼0.47.
the mesh validation, this selected numerical method and the mesh strategy has been proved to be effective and sufficient for the further studies.
4. Impact of spacing on drag By varying the spacing of the fleet, the results suggest some energy beneficial configurations exist for both individuals and the whole fleet. However, some configurations lead to a significant
Fig. 9. Comparison of CD of towed bare B1, experimental data made available at the reference (Molland and Utama, 1997).
increase in the drag of individual members of the fleet. These results may be classified into seven regions by the different sign of %B1, %B2 and %CB as shown in Table 3 and are shown in Fig. 10. %B1 and %B2 is defined as the percentage difference of the individual drag of B1 and B2 referenced to a single hull drag, respectively. In this paper, %CB is defined as the combined drag which considered as a percentage difference of the fleet drag referenced to the sum
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of two single hull drags. Where CD(B1) and CD(B2) is the drag coefficient of B1 and B2 in fleet, respectively. CD(s) is the drag coefficient of a single hull. %B1 ¼ fðC DðB1Þ C DðsÞ Þ=C DðsÞ g 100; %B2 ¼ fðC DðB2Þ C DðsÞ Þ=C DðsÞ g 100; %CB ¼ fðC DðB1Þ þ C DðB2Þ 2C DðsÞ Þ=2C DðsÞ g 100
ð9Þ
The individual change in the total drag, the skin friction drag and the pressure drag for twin case compare with a single case are illustrated in Fig. 11a, b and c, respectively.
31
4.2. Echelon region With a transverse separation and a limited longitudinal offset within one body length, the configuration is similar to echelon or part of a vee formation. In Fig. 13a and c, the results suggest the change in total drag is dominated by the pressure drag and the skin friction drag at the close proximity at S/L¼0.17 and D/L¼ 0.27. Fig. 13a shows that while both hulls experience interaction, the follower B2 experiences a drag reduction due to the change in its pressure recovery profile and skin friction profile on the surface of B2 at40.6L, the leader B1 experiences a drag augment due to the change of the pressure profile and skin friction profile. The results show a similar magnitude of B1's total drag augment and B2's total drag reduction (Fig. 10). The bigger the longitudinal offset, the smaller the total drag increase.
4.1. Parallel region 4.3. No gain region The parallel region is where both hulls are parallel to the inflow, noses aligned with zero longitudinal offset (D/L¼ 0), both hulls experience a drag increment. In an infinite domain, both hulls are expected to experience an equal drag increase, however, due to the asymmetric finite numerical fluid domain, the tunnel walls result in slightly differing interference drag on each hull. Fig. 12a–d illustrates the longitudinal pressure and skin friction coefficient along the hull. It can be seen that the drag increase experience is due to an increased skin friction drag rather than a change in pressure drag. The change in skin friction drag is due to an accelerated flow regime between the hulls. As the transverse separation increases up to 0.47L, the accelerated flow reduces towards the free-stream velocity, resulting in less than a 2% drag increase. These results and the previous studies (Hoerner, 1965; Hucho and Ahmed, 1998; Molland and Utama, 2002) suggested that the distance of 0.5L is required as the minimum transverse separation to preclude body-to-body interaction. Table 3 The body-to-body interaction region classified by spacings and drags. The sign þand indicates increasing and decreasing of the drag, respectively. Name
S/L
D/L
%B1
%B2
%CB
Parallel region Echelon region No gain region Push region
0.17–0.47 0.17–0.47 0.37–0.47 0.17 0 0 0.17 0.27 0.37–0.47 0.37–0.47
0 0.27–0.57 0.87 0.87–1.17 o 1.37 4 1.37 Z 1.47 Z 0.87 1.17–1.47 Z 1.77
þ þ þ
þ þ
þ þ þ
þ
E0
E0
E0
Drafting region Low interaction region
No interaction region
The individual drag of B1 and B2 is similar to the echelon region; however, the combined drag in this region shows the minimal benefit of the fleet. 4.4. Push region The push region is where the nose of B2 is positioned close to the trailing edge of B1. The combined drag can be reduced by 1–7%; B1 experiences a moderate reduction in drag due to the presence of B2. There is insignificant change in skin friction (Fig. 14c) and pressure distribution along the main body of both hulls (Fig. 14a), the variation in drag is dominated by the pressure drag at the stagnation points (Rattanasiri et al., 2012). The pressure distribution at the bow stagnation point of B2 reinforces the high pressure at the stern of B1 leading to an increased pressure recovery. The results show the same effects as cars in convoy at D/L ¼1.40L (Hucho and Ahmed, 1998). For example, at D/L E1.17L, the combined drag of twin spheroids is reduced by 7% while for cars in convoy are reduced by 15%. The individual drag of the leader is decreased by 20% and 30% for the spheroid and the car, respectively, whilst the follower is increased by 7% and 20% for the spheroid and the car, respectively. At S/L¼0, the drag of B1 is reduced by 20% whilst drag of B2 is increased by 7%. Since the cars in the study of Hucho and Ahmed (1998) are less streamlines and therefore have a higher form factor (i.e. pressure drag), they experience more significant overall drag changes. 4.5. Drafting region By placing B2 directly behind B1 for D/L41.37, the combined drag can be reduced by 5–6% with individual drag reduction
Fig. 10. The effect of twin hulls' spacing on individual drags and combined drag of B1 and B2 at Re¼ 3.2 106.
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by 7–8% for B2 and 2–4% for B1. Considering Fig. 11a–c, as the longitudinal offset increases, the results suggest a loss of energy benefit. For D/L Z5, the drag reduction for B2 tends towards the free stream drag value as wake recovery occurs (Rattanasiri et al., 2012). This hydrodynamic behaviour is similar to cars in a convoy with a slipstream at S/L 41.5 (Hucho and Ahmed, 1998). This goes some-way to explain the energy benefit of cycling and swimming in the slipstream (Kyle, 1979; Silva et al., 2008). 4.6. Low interaction region Outside the previously proposed regions, the boundary of the low interaction region is constructed, the detail of longitudinal offset and transverse separation configurations are shown in Table 3. The results in Fig. 10 show a minimal change of the combined drag, less than 1% of drag reduction. It also suggests that the larger the spacing between two hulls, results in less force interaction. Individually, B2 gets a small drag increase whilst B1 gains some benefit. However, on average, the individual drag exchange is less than 2%. 4.7. No interaction region The results in Fig. 10 show almost no change of the individual drag values and the combined drag due to both hulls experience the free stream drag value as wake recovery occurs. The dominant studies of spacing between twin hulls shows that the echelon region, the no gain region, the low interaction region and the no interaction region could potentially be used to lower propulsion costs of an individual in the fleet. 5. Impact of configuration's shape on drag Following the two hull study in the previous section, three and four hulls configuration will now be considered. With the available space of the domain, the three hulls in symmetry configuration and the three/four hulls in echelon configuration can be studied to determine the effect of the configuration's shape on drag. As before %B3 and %B4 is defined as the percentage difference of the individual drag of B3 and B4 referenced to a single hull drag, respectively. Where CD(B3) and CD(B4) is the drag coefficient of B3 and B4 in fleet, respectively. The same consideration is applied to the combined drag (%CB) for three and four hulls. %B3 ¼ fðC DðB3Þ C DðsÞ Þ=C DðsÞ g 100 %B4 ¼ fðC DðB4Þ C DðsÞ Þ=C DðsÞ g 100
:
ð10Þ
5.1. Impact of vee formation By placing the two spheroids, B2 and B3, symmetrically along the centre line of the leading B1, the results show that the drag of both following hulls (%B2 and %B3) is approximately the same. Similar to the study of twin hulls, the effect of spacing among three hulls can be classified into the same regions at the same specific spacings. The comparison of the drag of twin hulls and the three hulls in vee formation (Table 4) shows that, with similar results of both B2 in the three arrangements, the drag increase of B1 is twice as much as that of B1 in the twin formation. 5.2. Impact of echelon formation In Table 5, similar results to the twin hulls at S/L¼ 0.27 and D/L¼ 0.27 and 0.57 configuration, show that the combined drag of three and four hulls has no energy benefit for the entire fleet.
Fig. 11. Effect of body-to-body interaction on forces acting on the drafting configuration B1 and B2 at various longitudinal offsets. (a) Total drag coefficient, (b) pressure drag coefficient, and (c) skin friction drag coefficient.
The individual results show the similar number between the leading member's drag reduction and the last member's drag increase. Physically, 100% of individual drag reduction means hull experiences the zero drag. For four hulls with a configuration of S/L ¼0.27 and D/L ¼0.27, the drag reduction of the last B4 is 129.3%, the first 100% of drag reduction means that all of B4's hull resistance is eliminated, the rest of the drag reduction (29.3%) illustrates the additional force from those leading hulls which resulting in pulling B4 forward. For the three and four bodies with the configuration of S/L¼ 0.27 and D/L ¼0.57, both middle hulls (B2) experience an approximately zero drag.
P. Rattanasiri et al. / Ocean Engineering 80 (2014) 25–35
33
Fig. 12. Parallel configuration at D/L ¼ 0: the skin friction drag coefficient (CF) and the pressure coefficient (Cp). Where black line is a result of B1 as a single hull. The red dash and blue dot lines are results of B1 and B2 in twin cases, respectively. (a) Cp at S/L ¼ 0.17, (b) Cp at S/L ¼0.37, (c) CF at S/L ¼ 0.17, and (d) CF at S/L ¼ 0.37. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
Fig. 13. Echelon configuration at S/L ¼0.17 and 0.37 for fixed D/L ¼0.27: the skin friction drag coefficient (CF) and the pressure coefficient (Cp). Where black line is a result of B1 as a single hull. The red dash and blue dot lines are results of B1 and B2 in twin cases, respectively. (a) Cp at S/L ¼ 0.17 and D/L ¼ 0.27, (b) Cp at S/L ¼0.37 and D/L ¼ 0.27, (c) CF at S/L ¼ 0.17 and D/L ¼ 0.27, and (d) CF at S/L ¼ 0.37 and D/L ¼ 0.27. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
6. Conclusion The purpose of this paper was to determine firstly, the hydrodynamic effect of the viscous interaction between two hulls on
drag and secondly, the influence of fleet configuration with multiple hulls in the vee formation and the echelon formation. The dominant results for twin hulls' configurations show that the spacing between hulls determines the drag of the entire fleet.
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Fig. 14. Drafting configuration at S/L ¼ 0: the skin friction drag coefficient (CF) and the pressure coefficient (Cp). Where black line is a result of B1 as a single hull. The red dash and blue dot lines are results of B1 and B2 in twin cases, respectively. (a) Cp at D/L ¼ 1.17, (b) Cp at D/L ¼ 1.77, (c) CF at D/L ¼ 1.17, and (d) CF at D/L ¼1.77. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
Table 4 Comparison of drags for the configuration of twin, three spheroids in vee formation at S/L ¼ 0.17, 0.27 and 0.37 and D/L ¼0.27, 0.57, 0.87 and 1.17. Where %B2 and %B3 are approximately the same. S/L
D/L
0.27 Twin
0.57 Sym three
Twin
0.87 Sym three
Twin
Table 5 Comparison of drags for the configuration of twin, three and four prolate spheroids in echelon at S/L ¼ 0.17 and D/L ¼ 0.27 and 0.57. D/L
1.17 Sym three
15.8 38.9 12.8 19.4 1.5 0.0
Twin
Sym three
11.9 24.2 10.3 14.1 0.8 1.4
0.17 %B1 107.3 217.4 %B2 93.9 92.1 %CB 6.7 11
64.0 126.8 62.4 59.1 0.8 2.8
0.27 %B1 55.6 112.8 %B2 49.7 48.3 %CB 3.0 5.3
38.1 76.6 37.3 35.5 0.4 1.8
2.2 0.7 0.7
5.7 3.1 0.2
6.4 13.0 5.4 7.3 0.5 0.6
0.37 %B1 33 68.7 %B2 28.7 28.2 %CB 2.2 3.9
26.0 54.6 25.1 24.6 0.5 1.6
3.5 4.1 0.3
7.3 3.0 0.4
2.5 1.7 0.4
5.4 3.3 0.4
Increasing the spacing results in lower the interaction. The dominant spacing has been characterised into seven zones based on the drag's characteristic of twin towed models. These are the parallel region, echelon region, no gain region, push region, drafting region, low interaction region and finally the no interaction region. The parallel region results in a drag increase for both hulls with the smaller the spacing, the larger the drag increase caused by viscous interactions. The echelon configuration could potentially be used to lower propulsion costs of an individual in the fleet at the expense of the leading hull. Applications where close proximity is required means that, the low interaction region can be indicated as the minimum spacing for minimum drag increase. In these simulations, the drafting region provides the optimum configuration to minimise the overall fleet drag.
0.27
0.57
Twin
Three
Four
Twin
Three
Four
%B1 %B2 %B3 %B4
107.3 93.9
135.6 12.1 199.6
145.2 43.6 13.9 129.3
64 62.4
63.2 0.6 60.2
63.8 0.4 3.4 61.7
%CB
6.7
9.5
11.4
0.8
1.3
1.4
The multi-vehicle configurations show limited influence over the entire fleet's propulsive energy budget. However, for applications where lower propulsion cost for an individual is required, the three ‘vee’ formation in the low interaction region could be considered. Based on this numerical information, operators can determine the optimal fleet configuration in transverse separation and longitudinal offset based on energy considerations. The propeller's wake region is excluded from this simulation which by re-energising the wake region will impact on the drafting vehicle. This is a topic for further study.
Acknowledgement The authors acknowledge the use of the IRIDIS High Performance Computing Facility and associated support services at the University of Southampton, in the completion of this work. The Ph.D. studentship of P. Rattanasiri was financed by the Royal Thai Government.
P. Rattanasiri et al. / Ocean Engineering 80 (2014) 25–35
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Larsson, L., Baba, E., 1996. Advances in Marine Hydrodynamics, vol. 5. Computational Mechanics Publications, Ohkusu, southampton, pp. 1–75 (Chapter: Ship resistance and flow computations). Martins, A., Almeida, J.M., Silva, E., 2003. Coordinated maneuver for gradient search using multiple AUVs. In: Proceedings of OCEANS, vol. 1, pp. 247–352. Menter, F.R., 1994. Two-equation eddy-viscosity turbulence models for engineering applications. Am. Inst. Aeronaut. Astronaut. J. 32 (8), 1598–1605. Molland, A.F., Utama, I.K.A.P., 1997. Wind Tunnel Investigation of a Pair of Ellipsoids in Close Proximity. Technical Report 98. Ship Science, University of Southampton. Molland, A.F., Utama, I.K.A.P., 2002. Experimental and numerical investigations of a pair of ellipsoids in close proximity. Proc. Inst. Mech. Eng., Part M: J. Eng. Marit. Environ. 216 (2), 107–115. Parsons, J.S., 1972. The Optimum Shaping of Axisymmetric Bodies for Minimum Drag in Incompressible Flow (Ph.D. thesis). School of Mechanical Engineering, Purdue University, Lafayette, IN. Parsons, J.S., Goodson, R.E., Goldschmied, F.R., 1974. Shaping of axisymmetric bodies for minimum drag in incompressible flow. J. Hydronaut. 8, 100–107. Partridge, B.L., Johansson, J., Kalish, J., 1983. The structure of schools of giant bluefin tuna in cape cad bay. Environ. Biol. Fishes 9, 253–262. Phillips, A., Haroutunian, M., Man, S., Murphy, A., Boyd, S., Blake, J., Griffiths, G., 2012. Further Advances in Unmanned Marine Vehicles. In: Roberts, G.N., Sutton, R. (Eds.), The Institution of Engineering and Technology, Stevenage, GB, pp. 373–405 (Chapter: Nature in engineering for monitoring the oceans: comparison of the energetic costs of marine animals and AUVs). Phillips, A., Turnock, S., Furlong, M., 2008. Comparisons of CFD simulations and inservice data for the self propelled performance of an Autonomous Underwater Vehicle. In: Proceedings of the 27th Symposium of Naval Hydrodynamics. Seoul, Korea, 05–10 October 2008. Phillips, A.B., 2009. Cost Effective Hydrodynamic Concept Design of Autonomous Underwater Vehicle (Ph.D. Thesis). School of Engineering Sciences, University of Southampton, uk. Phillips, A.B., Furlong, M., Turnock, S.R., 2007. The use of computational fluid dynamics to assess the hull resistance of concept autonomous underwater vehicles. In: Proceedings of OCEANS 2007 – Europe. Institute of Electrical and Electronics Engineers. Richardson, TX, USA. Phillips, A.B., Turnock, S.R., Furlong, M., 2010a. Influence of turbulence closure models on the vortical flow field around a submarine body undergoing steady drift. J. Mar. Sci. Technol. 15 (3), 201–217. Phillips, A.B., Turnock, S.R., Furlong, M., 2010b. The use of computational fluid dynamics to aid cost-effective hydrodynamic design of autonomous underwater vehicles. Proc. Inst. Mech. Eng., Part M: J. Eng. Marit. Environ. 224, 239–254.. Rattanasiri, P., Wilson, P.A., Phillips, A.B., 2012. Numerical investigation of the drag of twin prolate spheroid hulls in various longitudinal and transverse configurations. In: Proceedings of AUV 2012. Southampton, GB, 24–27 September 2012. Reeder, C.A., Odell, D.L., Okamoto, A., Anderson, M.J., Edwards, D.B., 2004. Two hydrophone heading and range sensor applied to formation-flying for AUVs. In: Proceedings of OCEANS'04. MTTS/IEEE TECHNO-OCEAN '04, pp. 517–523. Rhie, C.M., Chow, W.L., 1982. A Numerical Study of the Turbulent Flow Past an Isolated Airfoil with Trailing Edge Separation. AIAA Paper 82-0998. Sarkar, T., Sayer, P.G., Fraser, S.M., 1997a. Flow simulation past axisymmetric bodies using four different turbulence model. Appl. Math. Model. 21, 783–792. Sarkar, T., Sayer, P.G., Fraser, S.M., 1997b. A study of autonomous underwater vehicle hull forms using computational fluid dynamics. Int. J. Numer. Methods Fluids 25, 1301–1313. Silva, A.J., Rouboa, A., Moreira, A., Reis, V.M., Alves, F., Vilas-Boas, J.P., Marinho, D.A., 2008. Analysis of drafting effects in swimming using computational fluid dynamics. J. Sports Sci. Med. 7, 60–66. Stevenson, P., Furlong, M., Dormer, D., 2007. AUV shapes – combining the practical and hydrodynamic considerations. In: Proceedings of OCEANS 2007 – Europe. Vanni, F.V., 2007. Coordinated Motion Control of Multiple. Autonomous Under Vehicle (Master's thesis). Technical University of Lisbon, Lisbon, Portugal. Weihs, D., 2004. The hydrodynamics of dolphin drafting. J. Biol. 3, 8. Weihs, D., Ringel, M., Victor, M., 2007. Aerodynamic interactions between adjacent slender bodies instrumentation and wind tunnel testing. In: Proceedings of the 22nd International Congress on Instrumentation in Aerospace Simulation Facilities, ICIASF, pp. 1–28. Weiss, P., Mascarelli, J.V.C., Grossnet, D., Brignone, L., Labbe, D.F.L., Wilson, P.A., 2003. Freesub: dynamic stabilization and docking for autonomous underwater vehicles. In: Proceedings of the 13th International Symposium on Unmanned Untethered Submersible Technology. Durham, USA.
Contents lists available at ScienceDirect
Ocean Engineering journal homepage: www.elsevier.com/locate/oceaneng
Numerical investigation of a fleet of towed AUVs Pareecha Rattanasiri n, Philip A. Wilson, Alexander B. Phillips Fluid Structure Interactions Group, Engineering and the Environment, University of Southampton, Southampton SO17 1BJ, United Kingdom
art ic l e i nf o
a b s t r a c t
Article history: Received 26 April 2013 Accepted 4 February 2014
This paper investigates the influence on the fleet of the drag of multiple towed prolate spheroids to determine the hydrodynamic effect of the viscous interaction between hulls and to study the influence of the configuration's shape of multiple hulls in the vee and echelon formations. A series of CFD RANS-SST simulations has been performed at the Reynolds Number 3.2 106 by a commercial code ANSYS CFX 12.1. Mesh convergence is tested and then validated with experimental and empirical results. The drag of each spheroid is compared against the benchmark drag of a single hull. The results show that the spacing between two hulls determines the individual drag and combined drag. The dominant spacing has been classified into seven zones based on the drag characteristic of twin towed models. Regions are characterised to parallel, echelon, no gain, push, drafting, low interaction, and no interaction. Both the multi-vehicle vee and echelon configurations show limited influence against that of the entire fleet's energy budget. For an individual spheroid where a lower propulsion cost is required, then the use of three/four in vee or echelon formation should be considered. Based on this numerical information, operators can determine the optimal fleet configuration based on energy considerations. & 2014 Elsevier Ltd. All rights reserved.
Keywords: Co-operative AUVs Fleet of AUVs Towed model Vee formation Echelon formation CFD RANS-SST simulation
1. Introduction Autonomous Underwater Vehicles (AUVs) are self-propelled robots which perform missions without requiring external powering or an umbilical control. Current AUVs have the capability to perform missions such as pipeline inspection (Labbe et al., 2004; Weiss et al., 2003), mine-sweeping (Edwards et al., 2004), and oceanographic exploration (Botelho et al., 2005; Martins et al., 2003). Proposed missions for the next generation of AUVs require them to acquire both high quantity and quality temporal and spatial data. This enhanced performance may be achieved by either homogeneous or heterogeneous fleets of vehicles. By carrying different sensors, the surveying performance of multiple small vehicles may have a performance equal to or exceeding that of a single larger vehicle, with improved levels of robustness and redundancy for a specific task. This has led to studies of manoeuvring and path planning of fleets by Aguiar et al. (2011), Bean et al. (2007), Burger et al. (2009), Cui et al. (2009, 2010), Reeder et al. (2004), and Vanni (2007). Since the range of an AUV is dictated by its finite energy source, minimising the energy consumption is required to maximise
n Correspondence to: Fluid Structure Interactions Group (Room 28/1021), Engineering and the Environment, Highfield Campus, University of Southampton, Southampton SO17 1BJ, United Kingdom. Tel.: þ 44 23 8059 5097. E-mail addresses: [email protected] (P. Rattanasiri), [email protected] (P.A. Wilson), [email protected] (A.B. Phillips).
http://dx.doi.org/10.1016/j.oceaneng.2014.02.001 0029-8018 & 2014 Elsevier Ltd. All rights reserved.
endurance. The total power consumed by an AUV can be split into propulsion power and the hotel load required to power nonpropulsion related electronics and sensors (Phillips et al., 2012). This study only considers propulsion power. For an individual AUV the propulsion power may be reduced by obtaining the optimum hydrodynamic design of such as hull, propeller and surface control (Bellingham and Willcox, 1996; Bradley, 1992; Bradley et al., 2001; Dalton and Zedan, 1980; Huggins and Packwood, 1994; Jagadeesh and Murali, 2005, 2006; Jagadeesh et al., 2009; Kinsey, 1998; Parsons, 1972; Parsons et al., 1974; Phillips, 2009; Sarkar et al., 1997a; Stevenson et al., 2007). For a fleet of multiple AUVs, minimising the energy consumption may be targeted for both individuals and the entire fleet. Previous experimental studies of flow past bodies in close proximity such as two circular cylinders, two slender bodies, a car with trailer and cars in convoy demonstrate the effect of relative distance between the bodies on the fleet drag as a whole (Hoerner, 1965; Hucho and Ahmed, 1998). When slipstreaming in cycling, the trailing riders experience a 38% reduction in wind resistance (Kyle, 1979). Drafting in swimming, the relative drag of the second swimmer in line is approximately 56% and 84% lower than the leading swimmer, when the distance between the swimmers is 0.5 m and 6.0 m, respectively (Silva et al., 2008). Observation of animal motion such as fish in schools, dolphins in pods or birds in flocks suggests some energy benefit may be obtained by certain fleet configurations (Alexander, 2004; Andersson and Wallander, 2003; Hanrahan and Juanes, 2001; Partridge et al., 1983; Weihs, 2004).
26
P. Rattanasiri et al. / Ocean Engineering 80 (2014) 25–35
Nomenclature 1þ k the form factor of a single spheroid 1þ βk the form factor of twin spheroids Aw wetted surface area (m2) B1 leading spheroid B2, B3, and B4 following spheroid %B1, %B2, %B3, and %B4 individual drag of B1, B2, B3, and B4 referred to a single hull drag %CB combined drag refer to sum of two single hull drags CD total drag coefficient, Total drag/(0.5ρV2Aw) CD(B1) and CD(B2) drag coefficient of B1 and B2 in fleet CD(B3) and CD(B4) drag coefficient of B3 and B4 in fleet CD(s) drag coefficient of a single hull CF skin friction drag coefficient, Skin friction drag/ (0.5ρV2Aw) (CF)1957 ITTC'57 skin friction line CPx pressure drag coefficient, Pressure drag/(0.5ρV2Aw) CSF coefficient of side-force
dm D D/L dh S/L L Re V Ui xi ν ρ μ k ε ϕ Ru
maximum diameter of the body of revolution (m) longitudinal offset (m) non-dimensional longitudinal offset maximum hull diameter (m) transverse separation length of the body from nose to tail (m) length Reynolds number, VL/ν vehicle speed (m/s) Cartesian mean velocity components (Ux, Uy, Uz) represents Cartesian co-ordinates (X, Y, Z) (m) fluid kinematic viscosity, μ/ρ (m2/s) fluid density (kg/m3) fluid dynamic viscosity (kg/m s) fluid turbulent kinetic energy (m2/s2) rate of dissipation of turbulent energy (m2 s 3) the advection scheme the vector from the upwind node to the integration point
For mother and calf dolphins, the calf derives a 60% energy benefit by taking up a hydrodynamically advantageous position in close proximity to its mother (Weihs, 2004). This assumption has agreed with the experimental results of twin prolate spheroids in the wind tunnel (Weihs et al., 2007). Recently, Husaini et al. (2009) numerically illustrated the influence of distance among multiple towed torpedo shape AUVs to their individual drags. These results suggest the energy benefit by using a fleet of AUVs may be obtained at the optimal configuration with the optimal distance and lead to the underlying questions of:
Does a fleet configuration provide energy benefits for just an individual AUV or the whole fleet?
What is the optimal configuration and optimal distances of the fleet? The purpose of this paper is to provide guidance for operators on suitable spacing for multiple vehicles' configurations. Based on this numerical information, operators can determine the potential configuration with the optimal distances based on the energy consideration. To achieve this aim, two main hydrodynamic processes of twin towed hulls: the body-to-body interference (or viscous interaction) and the increase of drag of following hulls due to the wake of a leading hull must be numerically investigated, firstly, the effect of various configurations to the individual drag, the fleet drag and the interference drag of a series of two prolate spheroids. Secondly, the influence of the number of spheroids in the fleet including the shape of the configuration must be numerically investigated.
Fig. 1. Physical flow problem: (a) flow passes a single hull, (b) flow passes twin hulls in parallel configuration, and (c) flow passes twin hulls in drafting configuration.
to the viscous drag (Cv) and can be estimated as 2. Theoretical approach
C D C v ¼ ð1 þ kÞC F ¼ ðTotal dragÞ=ð0:5ρV 2 Aw Þ
2.1. Drag estimation
where ρ is the fluid density, Aw is the wetted surface area and V is the fluid velocity and a form factor (1 þk) was introduced to estimate the ratio of total viscous drag (Cv) to the skin friction drag (CF). CF may be estimated by the ITTC'57 correlation line (ITTC, 1957):
The flow pass a single bare hull, twin hulls in parallel configuration and twin hulls in drafting configuration being considered here are sketched in Fig. 1a, b and c, respectively. To estimate total drag coefficient for fluid flow pass a single hull can be obtained by C D ¼ C wave þ C v
ð1Þ
Assuming the AUV is fully submerged in deep water, there will be no wave resistance (Cwave E0), the total drag is therefore only due
ðC F Þ1957 ¼ 0:075=ðlog 10 ðReÞ 2Þ2
ð2Þ
ð3Þ
For streamlined shapes, Hoerner (1965) suggests an estimated form factor in terms of the body length (L) and the maximum body
P. Rattanasiri et al. / Ocean Engineering 80 (2014) 25–35
diameter (dm) as 3=2
ð1 þ kÞ ¼ 1 þ 1:5ðdm =LÞ
þ 7ðdm =LÞ
3
ð4Þ
In the case of parallel twin hulls in close proximity, the conventional form factor for a single hull cannot establish an accurate prediction due to the accelerated flow velocity between twin hulls, as shown in Fig. 1b. This is called a viscous interaction effect which results in an increase of the drag of both hulls. In case of drafting twin hulls in close proximity, the pressure distribution around the tail of the leading hull interacts with that around the stagnation point of following hull (as shown in Fig. 1c). The pressure distribution of each hull is then changed which cause the individual drag to increase/decrease. By combining a viscous resistance factor β, the estimation of a more accurate form factor (1 þβk) for twin hulls can be obtained (Molland and Utama, 2002), hence the total drag of twin hulls can be estimated as C D ¼ ð1 þ βkÞC F
ð5Þ
To predict the hydrodynamic forces acting on an AUV's hull, a steady-state Reynolds Averaged Navier Stokes (RANS) simulation has proved to provide reasonably accurate results when compared against the experimental results (Jagadeesh et al., 2009; Karim et al., 2009; Phillips et al., 2008, 2007, 2010b; Sarkar et al., 1997b). However, to obtain a high fidelity result needs an appropriate mesh resolution to capture the effect of the boundary layer, bodyto-body interaction and the wake behind the body. 2.2. Reynolds Averaged Navier Stokes (RANS)
The momentum equation can be written as ! ( !) ∂ui'uj' ∂U i ∂U i U j ∂P ∂ ∂U i ∂U j þ μ þ þf i ρ ¼ þ ρ ∂xi ∂xj ∂xj ∂t ∂xj ∂xj ∂xi
ð6Þ
ð7Þ
where the tensor xi represents Cartesian co-ordinates (X, Y, Z) and Ui are the Cartesian mean velocity components (Ux, Uy, Uz). The Reynolds stress tensor ðρu0i u0j Þ is represented the turbulence closure and f i is the external force. The RANS equations are implemented in the commercial CFD code ANSYS (2010) CFX. The governing equations are discretised using the finite volume method. The high-resolution advection scheme was applied for the results presented which varies between first- and second order accuracy depending on spatial gradient. For a scalar quantity ϕ the advection scheme is written in the form of ϕip ¼ ϕup þ b∇ϕ URu
Fig. 2. Set up of twin prolate spheroids in the 14 m long, 70 50 wind tunnel. source: Figure adapted from Molland and Utama (1997).
where ϕip is the value at the integration point, ϕup the value at the upwind node and Ru the vector from the upwind node to the integration point. The model reverts to first order when b¼0 and is a second-order upwind biased scheme for b¼1. The highresolution scheme calculates b using a similar approach to that of Brath and Jesperson (1989), which aims to maintain b locally to be as close to one as possible without introducing local oscillations. Collocated (nonstaggered) grids are used for all transport equations, and pressure velocity coupling is achieved using an interpolation scheme based on that proposed by Rhie and Chow (1982). Gradients are computed at integration points using trilinear shape functions defined in ANSYS (2010) CFX. The linear set of equations that arise by applying the finite volume method to all elements in the domain are discrete conservation equations. The system of equations is solved using a coupled solver and a multigrid approach. The shear stress transport (SST) turbulence closure model (Menter, 1994) which blends k ε and k ω was selected to close the mathematical model for this study. Previous investigations have shown that it is better able to replicate the flow around the ship and submarine hull form than either k ε or k ω model, notably with a moderate accuracy (Larsson and Baba, 1996; Phillips et al., 2010a).
3. Case study 3.1. Base experiment
By assuming the flow is incompressible, the continuity equation becomes ∂U i ¼0 ∂xi
27
ð8Þ
Molland and Utama (1997) performed a series of experiment on twin prolate spheroids to characterise the side-force and yawing moment interactions. Tests were carried out in the 70 50 (2.20 m 1.57 m) low speed wind tunnel at the University of Southampton. The overall length (L) of each model was 1200 mm with maximum diameter (dh) of 200 mm and a surface area (Aw) of 0.601 m2. The top spheroid was placed at the middle breadth and 1.07 m height from the floor. It was fitted to the overhead wind tunnel dynamometer for measuring the total drag and side-force. The lower spheroid (B2) was placed at the transverse separation (S/L) of 0.27, 0.37 and 0.47 away from the centerline of B1. The noses of both spheroids are aligned with zero longitudinal offset (D/L ¼0) as shown in Fig. 2. 3.2. Present study To verify the numerical strategies and results, Molland and Utahan's (1997) experiment of twin towed bare prolate spheroids with transverse separations, where D/L ¼0 and S/L¼ 0.17, 0.27, 0.37 and 0.47, are selected. Where D is the longitudinal distance between each nose of bodies, S is the transverse distance between
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Fig. 3. Fleets of prolate spheroids with the body length L where S/L is the transverse separation and D/L is the longitudinal offset: (Left) twin hulls configuration, (Middle) vee formation and (Right) echelon formation.
centre lines of each bodies and L is the body length. As shown in Fig. 3, the cases have been extended to study the following:
Firstly, the effect of longitudinal spacing on the drag. The
distances between two hulls are considered at various combinations between 0 oD/L r1.77 and 0.27 oS/Lr0.47. The result is shown in Section 4. Secondly, the effect of the configuration's shape of multiple hulls on the drag. The symmetry configuration and the echelon configuration are considered. The result is shown in Section 5. The case details are as follows: Fleets of three spheroids in vee formation for S/L¼ 0.17, 0.27 and 0.37 and D/L¼ 0.27, 0.57, 0.87 and 1.17. Fleets of the three/four spheroids in echelon for S/L ¼0.17 and D/L ¼0.27 and 0.57.
3.3. Numerical settings To replicate the experiment of Molland and Utama (1997), the dimension of fluid domain is modelled at 1.4L 12L 1.8L. Free slip wall conditions (ANSYS, 2010) are used for the roof, floor and walls. The air inlet velocity (V) is set at 40 m/s related to a length Reynolds number (Re) 3.2 106 (typical AUV operates at Re between 105 and 107) with the zero relative pressure outlet boundary condition. The air density (ρair) and the air kinematic viscosity (υair) at room temperature are 1.185 kg/m3 and 1.545 10 5 m2/s, respectively. Both hulls are modelled by using no slip wall condition (ANSYS, 2010). 3.4. Mesh strategy The sample of meshes cut in the ZX plane and the YZ plane is shown in Fig. 4a and b, respectively. The model domain, boundary condition and mesh strategies used in this simulation are illustrated in Fig. 5. The results of drag components; the total drag coefficient (CD), the pressure drag coefficient (CPx) and the skin friction drag coefficient (CF) and form factor (1 þ k), for each cases are shown in Table 1. A series of eleven meshes ranging from 1.2 to 22.7 million elements were made for an example case, where the 1.2, 8.6 and 22.7 million element is considered as the coarse mesh, the medium mesh and the fine mesh, respectively. With 2.0% difference of total drag between the medium mesh (case f) and the fine mesh (case j), the computational cost of using the medium mesh is approximately 8 h which is 10 times lower than that of fine mesh when using the 64 bit operating computational system, 2.53 GHz, two Core Processors with 12 GB RAM. Thus the mesh parameters of global mesh size and the local refinement case f is selected as appropriate. The computational parameters are provided in Table 2. 3.5. Results and validation The twin towed bare hulls are compared against the experimental results (Molland and Utama, 1997), the numerical results
Fig. 4. Mesh cut around a pair of spheroids for S/L ¼0.27 and D/L ¼0 for medium mesh (case f). (a) ZX plane at the centre line at Y ¼ 0 with the fluid flow from left to right and (b) YZ plane at X ¼ 0.6 m from the noses.
(Molland and Utama, 2002) and empirical results (Hoerner, 1965) are as follow. 3.5.1. Pressure distribution The distribution of the pressure coefficient, CP ¼(P P1)/ (0.5ρU2), is shown in Fig. 6a–c. Where, X/L is a position on the longitudinal axis of the body. A good agreement is observed between the numerical trend lines and the experimental results for the three separated separations. 3.5.2. Side-force coefficient The side-force is defined as an attraction force between the hulls (Fz). The side-force coefficient (CSF) is defined by CSF ¼ Fz/ (0.5ρU2). In Fig. 7, the numerical results of CSF of B1 show excellent agreement with the experimental results and show that previous numerical demonstrations were deficit because of the lack of high
P. Rattanasiri et al. / Ocean Engineering 80 (2014) 25–35
29
Fig. 5. (Top) Boundary condition and mesh refinement around a pair of prolate spheroids and (Bottom) eleven mesh strategies.
Table 1 The result of drag components; the total drag coefficient (CD), pressure drag coefficient (CPx), skin friction drag coefficient (CF) and form factor (1 þ k), for each mesh strategies.
Table 2 Computational parameters. Parameters
Setting Unstructured with local refinement around spheroids and in wake regions Average 30 8–15 M with 15–20 prism layers in the boundary layer Shear stress transport 1%
Case
CD 103
CPx 103
CF 103
(1 þ k)
Mesh type
a b c d e f g h i j k
4.325 4.307 4.260 4.231 4.180 4.168 4.154 4.139 4.124 4.086 4.076
0.635 0.625 0.571 0.550 0.493 0.481 0.449 0.388 0.379 0.355 0.344
3.718 3.714 3.717 3.713 3.715 3.711 3.724 3.751 3.745 3.730 3.730
1.163 1.160 1.146 1.140 1.125 1.123 1.115 1.103 1.101 1.095 1.093
yþ No. of elements Turbulence model Inlet turbulent intensity Wall modelling Spatial discretisation Timescale control Convergence criteria Computing Run type Simulation time
performance computers at that time. The rapidly decrease of the side-force ratio with an increase of separation, is due to the lower flow velocity through the construction between the hulls.
3.5.3. Form factor For the length–diameter ratio 6:1 spheroid, estimates of (1 þk) from Eq. (4) gives 1.135. The comparison of form factor between the experimental results and the numerical results based on the ITTC correction line is shown in Fig. 8. The numerically predicted (1 þk) of B1 is within 1.5% error of Hoerner's estimation. The increment of form factor (1 þβk) compared with the single hull illustrates the influence of viscous resistance factor (βk) due to close proximity. The 8% error between the experimental result and Hoerner's estimation and 16% error between the experimental result and numerical result show some interference of the tunnel wall to the single hull and twin hulls experiment, respectively.
Automatic wall function (ANSYS, 2010) High resolution (ANSYS, 2010) Auto timescale (ANSYS, 2010) RMS residualo 10 6 3 Linux cluster Parallel (12 partitions run on 4 dual core nodes, each with 2 GB RAM) 2.0–2.5 Wall clock hours (medium mesh)
3.5.4. Total drag coefficient of towed B1 The drag results are evaluated in terms of the total drag coefficient (CD), the pressure drag coefficient (CPx) and the skin friction drag coefficient (CF). Fig. 9 shows the numerical results of the total drag coefficient (CD) at various transverse separations. The CD of a single hull in the present study is 10% lower compared to the experimental drag (Molland and Utama, 1997). A good agreement of the trend line is observed at S/L r0.37. At S/L Z0.47, Molland and Utama (2002) suggested that some interference from the tunnel wall may occur, and consequently, increase the total drag of B1. This is not observed in either numerical study. The experimental result is 16% higher than the current numerical prediction at S/L¼0.27 and 0.37. This may be partially attributed to interference drag due to the experimental mounting system, which is not recreated in the numerical simulations. With these positive evaluations of the CFD with the experiment results and
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Fig. 7. CSF as proportion of CD at various transverse separation.
Fig. 8. Comparison a form factor between the experimental and numerical prediction of a single hull and twin hulls.
Fig. 6. Pressure drag coefficient of B1. (a) S/L ¼0.27, (b) S/L ¼ 0.37, and (c) S/L ¼0.47.
the mesh validation, this selected numerical method and the mesh strategy has been proved to be effective and sufficient for the further studies.
4. Impact of spacing on drag By varying the spacing of the fleet, the results suggest some energy beneficial configurations exist for both individuals and the whole fleet. However, some configurations lead to a significant
Fig. 9. Comparison of CD of towed bare B1, experimental data made available at the reference (Molland and Utama, 1997).
increase in the drag of individual members of the fleet. These results may be classified into seven regions by the different sign of %B1, %B2 and %CB as shown in Table 3 and are shown in Fig. 10. %B1 and %B2 is defined as the percentage difference of the individual drag of B1 and B2 referenced to a single hull drag, respectively. In this paper, %CB is defined as the combined drag which considered as a percentage difference of the fleet drag referenced to the sum
P. Rattanasiri et al. / Ocean Engineering 80 (2014) 25–35
of two single hull drags. Where CD(B1) and CD(B2) is the drag coefficient of B1 and B2 in fleet, respectively. CD(s) is the drag coefficient of a single hull. %B1 ¼ fðC DðB1Þ C DðsÞ Þ=C DðsÞ g 100; %B2 ¼ fðC DðB2Þ C DðsÞ Þ=C DðsÞ g 100; %CB ¼ fðC DðB1Þ þ C DðB2Þ 2C DðsÞ Þ=2C DðsÞ g 100
ð9Þ
The individual change in the total drag, the skin friction drag and the pressure drag for twin case compare with a single case are illustrated in Fig. 11a, b and c, respectively.
31
4.2. Echelon region With a transverse separation and a limited longitudinal offset within one body length, the configuration is similar to echelon or part of a vee formation. In Fig. 13a and c, the results suggest the change in total drag is dominated by the pressure drag and the skin friction drag at the close proximity at S/L¼0.17 and D/L¼ 0.27. Fig. 13a shows that while both hulls experience interaction, the follower B2 experiences a drag reduction due to the change in its pressure recovery profile and skin friction profile on the surface of B2 at40.6L, the leader B1 experiences a drag augment due to the change of the pressure profile and skin friction profile. The results show a similar magnitude of B1's total drag augment and B2's total drag reduction (Fig. 10). The bigger the longitudinal offset, the smaller the total drag increase.
4.1. Parallel region 4.3. No gain region The parallel region is where both hulls are parallel to the inflow, noses aligned with zero longitudinal offset (D/L¼ 0), both hulls experience a drag increment. In an infinite domain, both hulls are expected to experience an equal drag increase, however, due to the asymmetric finite numerical fluid domain, the tunnel walls result in slightly differing interference drag on each hull. Fig. 12a–d illustrates the longitudinal pressure and skin friction coefficient along the hull. It can be seen that the drag increase experience is due to an increased skin friction drag rather than a change in pressure drag. The change in skin friction drag is due to an accelerated flow regime between the hulls. As the transverse separation increases up to 0.47L, the accelerated flow reduces towards the free-stream velocity, resulting in less than a 2% drag increase. These results and the previous studies (Hoerner, 1965; Hucho and Ahmed, 1998; Molland and Utama, 2002) suggested that the distance of 0.5L is required as the minimum transverse separation to preclude body-to-body interaction. Table 3 The body-to-body interaction region classified by spacings and drags. The sign þand indicates increasing and decreasing of the drag, respectively. Name
S/L
D/L
%B1
%B2
%CB
Parallel region Echelon region No gain region Push region
0.17–0.47 0.17–0.47 0.37–0.47 0.17 0 0 0.17 0.27 0.37–0.47 0.37–0.47
0 0.27–0.57 0.87 0.87–1.17 o 1.37 4 1.37 Z 1.47 Z 0.87 1.17–1.47 Z 1.77
þ þ þ
þ þ
þ þ þ
þ
E0
E0
E0
Drafting region Low interaction region
No interaction region
The individual drag of B1 and B2 is similar to the echelon region; however, the combined drag in this region shows the minimal benefit of the fleet. 4.4. Push region The push region is where the nose of B2 is positioned close to the trailing edge of B1. The combined drag can be reduced by 1–7%; B1 experiences a moderate reduction in drag due to the presence of B2. There is insignificant change in skin friction (Fig. 14c) and pressure distribution along the main body of both hulls (Fig. 14a), the variation in drag is dominated by the pressure drag at the stagnation points (Rattanasiri et al., 2012). The pressure distribution at the bow stagnation point of B2 reinforces the high pressure at the stern of B1 leading to an increased pressure recovery. The results show the same effects as cars in convoy at D/L ¼1.40L (Hucho and Ahmed, 1998). For example, at D/L E1.17L, the combined drag of twin spheroids is reduced by 7% while for cars in convoy are reduced by 15%. The individual drag of the leader is decreased by 20% and 30% for the spheroid and the car, respectively, whilst the follower is increased by 7% and 20% for the spheroid and the car, respectively. At S/L¼0, the drag of B1 is reduced by 20% whilst drag of B2 is increased by 7%. Since the cars in the study of Hucho and Ahmed (1998) are less streamlines and therefore have a higher form factor (i.e. pressure drag), they experience more significant overall drag changes. 4.5. Drafting region By placing B2 directly behind B1 for D/L41.37, the combined drag can be reduced by 5–6% with individual drag reduction
Fig. 10. The effect of twin hulls' spacing on individual drags and combined drag of B1 and B2 at Re¼ 3.2 106.
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by 7–8% for B2 and 2–4% for B1. Considering Fig. 11a–c, as the longitudinal offset increases, the results suggest a loss of energy benefit. For D/L Z5, the drag reduction for B2 tends towards the free stream drag value as wake recovery occurs (Rattanasiri et al., 2012). This hydrodynamic behaviour is similar to cars in a convoy with a slipstream at S/L 41.5 (Hucho and Ahmed, 1998). This goes some-way to explain the energy benefit of cycling and swimming in the slipstream (Kyle, 1979; Silva et al., 2008). 4.6. Low interaction region Outside the previously proposed regions, the boundary of the low interaction region is constructed, the detail of longitudinal offset and transverse separation configurations are shown in Table 3. The results in Fig. 10 show a minimal change of the combined drag, less than 1% of drag reduction. It also suggests that the larger the spacing between two hulls, results in less force interaction. Individually, B2 gets a small drag increase whilst B1 gains some benefit. However, on average, the individual drag exchange is less than 2%. 4.7. No interaction region The results in Fig. 10 show almost no change of the individual drag values and the combined drag due to both hulls experience the free stream drag value as wake recovery occurs. The dominant studies of spacing between twin hulls shows that the echelon region, the no gain region, the low interaction region and the no interaction region could potentially be used to lower propulsion costs of an individual in the fleet. 5. Impact of configuration's shape on drag Following the two hull study in the previous section, three and four hulls configuration will now be considered. With the available space of the domain, the three hulls in symmetry configuration and the three/four hulls in echelon configuration can be studied to determine the effect of the configuration's shape on drag. As before %B3 and %B4 is defined as the percentage difference of the individual drag of B3 and B4 referenced to a single hull drag, respectively. Where CD(B3) and CD(B4) is the drag coefficient of B3 and B4 in fleet, respectively. The same consideration is applied to the combined drag (%CB) for three and four hulls. %B3 ¼ fðC DðB3Þ C DðsÞ Þ=C DðsÞ g 100 %B4 ¼ fðC DðB4Þ C DðsÞ Þ=C DðsÞ g 100
:
ð10Þ
5.1. Impact of vee formation By placing the two spheroids, B2 and B3, symmetrically along the centre line of the leading B1, the results show that the drag of both following hulls (%B2 and %B3) is approximately the same. Similar to the study of twin hulls, the effect of spacing among three hulls can be classified into the same regions at the same specific spacings. The comparison of the drag of twin hulls and the three hulls in vee formation (Table 4) shows that, with similar results of both B2 in the three arrangements, the drag increase of B1 is twice as much as that of B1 in the twin formation. 5.2. Impact of echelon formation In Table 5, similar results to the twin hulls at S/L¼ 0.27 and D/L¼ 0.27 and 0.57 configuration, show that the combined drag of three and four hulls has no energy benefit for the entire fleet.
Fig. 11. Effect of body-to-body interaction on forces acting on the drafting configuration B1 and B2 at various longitudinal offsets. (a) Total drag coefficient, (b) pressure drag coefficient, and (c) skin friction drag coefficient.
The individual results show the similar number between the leading member's drag reduction and the last member's drag increase. Physically, 100% of individual drag reduction means hull experiences the zero drag. For four hulls with a configuration of S/L ¼0.27 and D/L ¼0.27, the drag reduction of the last B4 is 129.3%, the first 100% of drag reduction means that all of B4's hull resistance is eliminated, the rest of the drag reduction (29.3%) illustrates the additional force from those leading hulls which resulting in pulling B4 forward. For the three and four bodies with the configuration of S/L¼ 0.27 and D/L ¼0.57, both middle hulls (B2) experience an approximately zero drag.
P. Rattanasiri et al. / Ocean Engineering 80 (2014) 25–35
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Fig. 12. Parallel configuration at D/L ¼ 0: the skin friction drag coefficient (CF) and the pressure coefficient (Cp). Where black line is a result of B1 as a single hull. The red dash and blue dot lines are results of B1 and B2 in twin cases, respectively. (a) Cp at S/L ¼ 0.17, (b) Cp at S/L ¼0.37, (c) CF at S/L ¼ 0.17, and (d) CF at S/L ¼ 0.37. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
Fig. 13. Echelon configuration at S/L ¼0.17 and 0.37 for fixed D/L ¼0.27: the skin friction drag coefficient (CF) and the pressure coefficient (Cp). Where black line is a result of B1 as a single hull. The red dash and blue dot lines are results of B1 and B2 in twin cases, respectively. (a) Cp at S/L ¼ 0.17 and D/L ¼ 0.27, (b) Cp at S/L ¼0.37 and D/L ¼ 0.27, (c) CF at S/L ¼ 0.17 and D/L ¼ 0.27, and (d) CF at S/L ¼ 0.37 and D/L ¼ 0.27. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
6. Conclusion The purpose of this paper was to determine firstly, the hydrodynamic effect of the viscous interaction between two hulls on
drag and secondly, the influence of fleet configuration with multiple hulls in the vee formation and the echelon formation. The dominant results for twin hulls' configurations show that the spacing between hulls determines the drag of the entire fleet.
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Fig. 14. Drafting configuration at S/L ¼ 0: the skin friction drag coefficient (CF) and the pressure coefficient (Cp). Where black line is a result of B1 as a single hull. The red dash and blue dot lines are results of B1 and B2 in twin cases, respectively. (a) Cp at D/L ¼ 1.17, (b) Cp at D/L ¼ 1.77, (c) CF at D/L ¼ 1.17, and (d) CF at D/L ¼1.77. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
Table 4 Comparison of drags for the configuration of twin, three spheroids in vee formation at S/L ¼ 0.17, 0.27 and 0.37 and D/L ¼0.27, 0.57, 0.87 and 1.17. Where %B2 and %B3 are approximately the same. S/L
D/L
0.27 Twin
0.57 Sym three
Twin
0.87 Sym three
Twin
Table 5 Comparison of drags for the configuration of twin, three and four prolate spheroids in echelon at S/L ¼ 0.17 and D/L ¼ 0.27 and 0.57. D/L
1.17 Sym three
15.8 38.9 12.8 19.4 1.5 0.0
Twin
Sym three
11.9 24.2 10.3 14.1 0.8 1.4
0.17 %B1 107.3 217.4 %B2 93.9 92.1 %CB 6.7 11
64.0 126.8 62.4 59.1 0.8 2.8
0.27 %B1 55.6 112.8 %B2 49.7 48.3 %CB 3.0 5.3
38.1 76.6 37.3 35.5 0.4 1.8
2.2 0.7 0.7
5.7 3.1 0.2
6.4 13.0 5.4 7.3 0.5 0.6
0.37 %B1 33 68.7 %B2 28.7 28.2 %CB 2.2 3.9
26.0 54.6 25.1 24.6 0.5 1.6
3.5 4.1 0.3
7.3 3.0 0.4
2.5 1.7 0.4
5.4 3.3 0.4
Increasing the spacing results in lower the interaction. The dominant spacing has been characterised into seven zones based on the drag's characteristic of twin towed models. These are the parallel region, echelon region, no gain region, push region, drafting region, low interaction region and finally the no interaction region. The parallel region results in a drag increase for both hulls with the smaller the spacing, the larger the drag increase caused by viscous interactions. The echelon configuration could potentially be used to lower propulsion costs of an individual in the fleet at the expense of the leading hull. Applications where close proximity is required means that, the low interaction region can be indicated as the minimum spacing for minimum drag increase. In these simulations, the drafting region provides the optimum configuration to minimise the overall fleet drag.
0.27
0.57
Twin
Three
Four
Twin
Three
Four
%B1 %B2 %B3 %B4
107.3 93.9
135.6 12.1 199.6
145.2 43.6 13.9 129.3
64 62.4
63.2 0.6 60.2
63.8 0.4 3.4 61.7
%CB
6.7
9.5
11.4
0.8
1.3
1.4
The multi-vehicle configurations show limited influence over the entire fleet's propulsive energy budget. However, for applications where lower propulsion cost for an individual is required, the three ‘vee’ formation in the low interaction region could be considered. Based on this numerical information, operators can determine the optimal fleet configuration in transverse separation and longitudinal offset based on energy considerations. The propeller's wake region is excluded from this simulation which by re-energising the wake region will impact on the drafting vehicle. This is a topic for further study.
Acknowledgement The authors acknowledge the use of the IRIDIS High Performance Computing Facility and associated support services at the University of Southampton, in the completion of this work. The Ph.D. studentship of P. Rattanasiri was financed by the Royal Thai Government.
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