Efficient Multiobjective Optimization of Amphibious Aircraft Fuselage

Efficient Multiobjective Optimization of Amphibious Aircraft Fuselage Steps with Decoupled Hydrodynamic and Aerodynamic Analysis Models Downloaded from ascelibrary.org by Shanghai Jiaotong University on 10/27/15. Copyright ASCE. For personal use only; all rights reserved.

Liangjun Qiu 1 and Wenbin Song 2

Abstract: This paper proposes an efficient framework for multiobjective optimization of the fuselage step on a large amphibious aircraft using a combination of computational aerodynamic and hydrodynamic methods. Both cruise drag and water take-off resistance and distance are calculated to evaluate the effects of the two key parameters, the longitudinal location and the depth of the step. A Reynolds-averaged Navier-Stokes (RANS) model was used for the calculation of cruise drag of the wing body configuration. Water take-off resistance and distance required for the baseline configuration were calculated using a volume of fluid method for hydrodynamic calculation and RANS method for aerodynamic calculation, respectively. A drag breakdown method was adopted to improve the efficiency of the hydraulic calculations. The method can achieve an accuracy of less than 5% difference compared to fully viscous calculations with only half of the computational time. The optimization is achieved using a combination of design of experiment and the response surfaces method. The optimized step configuration achieved an 18% improvement in take-off distance while maintaining similar cruise performance. The proposed method is generic and can be used in the optimizations of other components such as wings and fuselage geometries of amphibious aircraft. DOI: 10.1061/(ASCE)AS.1943-5525.0000557. © 2015 American Society of Civil Engineers. Author keywords: Amphibious aircraft; Lift-to-drag ratio; Take-off performance; Optimization; Computational fluid dynamics (CFD).

Introduction Amphibious aircraft can be operated on both water and land. There has been over 80 years of history in the development and operation of amphibious aircraft. The development of amphibious aircraft expanded rapidly in the period between the First and Second World War. The goal of amphibious operations is to move more effectively from the sea to the land (and, if necessary, back again). Amphibious airplanes were commonly used in tasks such as water rescue, reconnaissance, and antisubmarine warfare missions. The potential military applications of these aircraft were quickly recognized and large numbers were put into service in air-sea rescue and antisubmarine patrol roles during the Second World War (Knott 1979). Interest in amphibious aircraft design has declined since the beginning of the jet aircraft age as more land infrastructures were built. Advanced modifications or new designs on amphibious aircraft have not been seen very often since the 1950s (Syed 2009). However, amphibious aircraft remain attractive in countries with long waterways or with large number of remote islands where tourism or logistic support is a major part of the economy. The number of people traveling as tourists around the world is increasing, often attracted by the natural beauty or historical significance of some remote areas. Therefore, some natural tourism places otherwise 1

Graduate Student, School of Aeronautics and Astronautics, Shanghai Jiao Tong Univ., No. 800 Dong Chuan Rd., Shanghai 200240, China; presently, Engineer, GE, Shanghai, China. 2 Associate Professor, School of Aeronautics and Astronautics, Shanghai Jiao Tong Univ., No. 800 Dong Chuan Rd., Shanghai 200240, China (corresponding author). E-mail: [email protected]; wenbin.song@ outlook.com Note. This manuscript was submitted on May 23, 2014; approved on July 23, 2015; published online on October 21, 2015. Discussion period open until March 21, 2016; separate discussions must be submitted for individual papers. This paper is part of the Journal of Aerospace Engineering, © ASCE, ISSN 0893-1321/04015071(14)/$25.00. © ASCE

inaccessible by cars, buses, trains, and even landplanes can be accessed conveniently by using amphibious aircraft (Canamar and Smrcek 2009). Amphibious aircraft can also be used in firefighting due to its high efficiency in water loading and discharging processes, for example, a Beriev BE-200 can carry up to 12,000 L of fluid to combat forest fires. In addition, according to studies carried out by Cronin Millar Consulting Engineers to Harbour Air Ireland (Millar 2009), amphibious aircraft cause very little environmental impact since the vehicle usually takes off and lands over water, leading to less demand for land infrastructures. For this wide range of potential applications, Europe has initiated the research project Future Seaplane Traffic (FUSETRA 2013), to investigate these various related issues. When it comes to the design of amphibious aircraft, some important issues need to be taken into consideration. A good compromise should be made between water stability, spray, seaworthiness, good aerodynamic and hydrodynamic performance, sufficient buoyancy, and ease of manufacturing and operation (Tomaszewskl 1943). In addition to typical design criteria used on land operated transport aircraft, the design of amphibious aircraft may also need to consider some special requirements. For example, anticorrosion coating must be added to aircraft’s skin to prevent water corrosion, and the engine must be configured higher to avoid water spray. Amphibious commercial aircraft must also meet certification regulations for water operations as well as regulations applied to typical land aircraft. Due to the hydrodynamic design requirements, the typical configurations of amphibious aircraft differ from those of land aircraft. A float or boat hull should be added close to the wing tips to provide sufficient lateral stability on the water since the metacenter is below the center of gravity (CG) for most amphibious aircraft (Cary 2011). The metacenter of the amphibious fuselage is defined by Nelson (1934) as the intersection between a vertical line from the heeled center of buoyancy and a vertical line of the original center of buoyancy. However, floating devices will add extra

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structure weight and aerodynamic parasite drag. A good compromise between aerodynamic drag and hydrodynamic stability might be achieved from the use of retractable floats, which will be retracted into the fuselage during cruise. While a smooth and streamlined fuselage bottom is the design choice on land aircraft to reduce profile drag, one or more steps on the bottom of the fuselage are often a distinct and important shape characteristic. In the design of an amphibious aircraft fuselage hull, at least one step in the bottom is necessary to break the suction of the water and to facilitate the aircraft’s balance during take-off (Husa 2000). Some amphibious aircraft are even designed with double break steps at the fuselage bottom. One of the most notable designs is the PBY Catalina (GmbH 2011), which played an important role for the U.S. Navy during the Second World War. There has been renewed interest in the design of amphibious aircraft in recent years due to its advantages in certain scenarios and the fact that improved modeling and simulation capabilities developed over the last few decades have provided some opportunities to assist in the development. Most of the research work on amphibious aircraft design were conducted during the 1930s to 1950s and largely relied on experimental and empirical methods. With the development of computational fluid dynamics (CFD) methods in the last few decades, the design of modern aircraft has shifted towards increasing use of CFD in aerodynamic analysis and optimization. The CFD method is also increasingly used in the design of ships in recent years. In the current work, the CFD method is adopted in the analysis and optimization of aerodynamic and hydrodynamic characteristics of amphibious aircraft. This study is a continuation from previous work (Qiu and Song 2012) in which the focus was on the development of a drag breakdown approach involving both hydrodynamic and aerodynamic analysis using a hybrid method of empirical approach and computationally expensive numerical models. The focus of the current paper is on the further use of this model to develop an efficient optimization framework.

This paper is organized as follows. The next section discusses related work about amphibious aircraft and design methods. This is followed by an introduction to the computational models used. Descriptions on optimization framework and problem formulations are given afterward along with results and analysis. Conclusions and remarks are presented in the last section.

Related Work Extensive research activities on amphibious aircraft related topics were carried out during the period between the First and Second World War. Most of those studies were carried out using experimental and empirical methods since reliable CFD methods were not available at the time. The most notable experimental studies on amphibious aircraft were conducted by the NACA Langley Memorial Aeronautical Laboratory, and the extensive data set obtained play an important role even today. Parkinson et al. (1943) performed a series of experimental research on the effects of some of the key hull shape parameters including height of bow, height of stern, angle of dead rise at bow and afterbody, depth of step, and angle of afterbody keel on hydrodynamic and aerodynamic performance for the NACA 84 Series Flying-boat. These parameters along with other typical design features for amphibious aircraft are shown in Fig. 1. These results provided valuable data for amphibious aircraft design. Carter (1949) studied the effects of an increase in the length-beam ratio from 6 to 15 on the aerodynamic performance on high length to beam ratio hull. The length of a hull is defined as the distance from the bow to the sternpost and the beam is defined as the widest section of the float. He found out that the aerodynamic drag coefficient can be decreased by 29% without a significant effect on the hydrodynamic performance of the hull through the length-beam ratio variation. However, Shoemaker and Parkinson (1933) pointed out that a shorter beam may lead to excessive water spray and reduce the lateral stability.

Fig. 1. Some characteristic design parameters of a typical flying boat © ASCE

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Bell (1935) studied the influence of depth of step on the hydrodynamic performance of amphibious aircraft hull during water take-off and found that small depth of step give lower resistance at speeds below and at hump speed of the model, while greater depth of step leads to lower resistance at high speeds. In addition to considerations for water take-off, amphibious aircraft designers should also focus more on cruise drag to increase payload and range. For example, Riebe and Naeseth (1948) conducted a wind tunnel test for a hull with step fairing, hull with rounded bottom, and streamlined body, respectively, and results showed that a flying-boat hull of the type tested can be flown to a Mach number of 0.825 without any sharp drag increase resulting from critical shock conditions. In addition, other studies suggested a step fairing for aerodynamic drag consideration (Yates and Riebe 1947; Riebe and Naeseth 1947). At angles of attack for minimum drag, fairing the step for a distance nine times the depth of the step at the keel resulted in about 0.0008 reduction in drag coefficient at around M ¼ 0.4. Rounding the hull bottom completely to the shape gave a 0.0020 minimum drag coefficient reduction at zero angle of attack. However, rounding the step may increase the resistance for a high speed of water take-off period, since more water will be sucked in at the rounding or step fairing and increase the frictional resistance. To compromise cruise and water take-off performance, Benson recommended the use of a retractable planing step to replace the fixed step (Benson and Lina 1943). Shoemaker and Bell (1936) conducted a water tank test of pointed step configuration (NACA Model 22-A and 35) and reported that the pointed-step type of hull with low dead rise is capable of giving somewhat better take-off performance than any hull of conventional type tested until then in the NACA tank. Allison and Ward (1936) also studied the effect of longitudinal steps on water take-off resistance and found that the models with longitudinal steps have smaller resistance at high speed and higher resistance at low speed than the model that had the same afterbody but with a conventional V-section forebody. The models with a single longitudinal step had better performance at hump speed and low high-speed resistance except at low take-off loads (Allison and Ward 1936). In early plans, amphibious aircraft were designed primarily using empirical methods with experimental water tank tests for the hull’s hydrodynamic design and a wind tunnel test for aerodynamic design. Regarding the boat hull and float device deign, hydrodynamic resistance, stability, spray effect, and sufficient buoyancy are typically considered. Many design criteria and equations were introduced by Langley (1935). For instance, it was suggested that the weight of a float device calculation is based on maximum takeoff weight of the aircraft (MTOW) as follows: W f ¼ MTOW × 0.0365 þ 43.5

0.075 ðln × R − 2Þ2

ð3Þ

where αw and αg denote the volume fraction of water and air, respectively. αw þ αg ¼ 1 for the two-phase flow of water and air. The VOF method can be used to obtain a full viscous flow result but is less efficient than the potential flow method. The computational models for both the cruise and take-off calculations are presented next.

Computational Analysis Models Baseline Model A parametric model was first built in computer aided threedimensional interactive application (CATIA) environment based on a nonparametric geometry of a baseline aircraft’s hull shape. The volume of the baseline model is 195.296 m3 and the intersection volume of the parametric model and baseline model is 195.057 m3 . The volume discrepancy between the parametric model and nonparametric baseline model is 0.1223%, which is calculated by αerror ¼

V base − V inter × 100% V base

ð4Þ

where αerror ; V base ; and V inter stand for the parametric modeling volume discrepancy, baseline geometry volume, and intersection volume of parametric geometry and baseline geometry. Two well-documented benchmark cases are used in the validation of the calculation CFD methods. The Wigley model is used to verify the full viscous ship resistance calculation (Kajitani 1983) and F6 is used to validate the aerodynamic calculation. Detailed comparisons between computational results and experimental data are shown in a previous paper by the authors (Qiu and Song 2012).

ð2Þ Aerodynamic Calculation for Cruise

where Cf and R denote for the skin frictional resistance coefficient and Reynolds number, respectively. Viscous pressure resistance © ASCE

∂αw ∂α þ ui w ¼ 0 ∂t ∂xi

ð1Þ

where W f stands for the weight of float device in pounds. For hydrodynamic resistance prediction, the experience obtained from high-speed ship design can be used. Froude proposed that the hydrodynamic resistance of a ship hull can be divided into three parts: frictional resistance (Rf ) caused by fluid viscosity, viscous pressure resistance (Rvp ) caused by flow separation, and wave resistance (Rw ) caused by fluid’s potential energy. For frictional resistance calculation, the ITTC-57 equation proposed by Lu (2007) be used Cf ¼

accounts for about 10% at low speed and 5% at high speed of the total drag. Froude suggested that the viscous pressure resistance coefficient (Cvp ) remains constant for a certain hull shape configuration. In 1898, Michelle proposed an integration equation to calculate the wave resistance. Frictional resistance can be calculated from Eq. (2), however, since the shape function cannot be easily obtained from an irregular hull shape and the longitudinal gradient value does not follow a certain kind of pattern, wave resistance cannot be easily calculated. With the recent development of CFD methods, aircraft designers are able to rely more on modern numerical tools instead of the time-consuming experimental methods. The Reynolds-averaged Navier-Stokes (RANS) method is commonly used now for steady aerodynamic calculations. For ship design, the volume of fluid (VOF) method and potential flow method are widely used. The potential flow method treats wave movement as irrotational movement of ideal flow (Xia 2003). The potential flow method is used for wave resistance calculation and wave contour of air-water interface pattern capture. It can efficiently produce flow field results without accounting for viscous resistance and frictional resistance information. The VOF method is an interface capture method (Park et al. 2009). Interface is determined by the volume fractional function for each phase in each mesh cell. At each iteration, a volume fraction continuity function is calculated in addition to the typical NS equation

A structured mesh is used to evaluate the aerodynamic performance of aircraft cruise configuration, and the thickness of the first layer

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Table 1. Mesh Convergence Study in Aerodynamic Calculation for Wing/ Body (W/B) CL

Cd

Lift-to-drag ratio

0.572237639 0.572338251 0.573595045 0.573990466 0.573565808 0.573469655

0.030787545 0.030273595 0.02964748 0.029248866 0.029124086 0.029087479

18.58666021 18.90552624 19.34717684 19.62436657 19.6938648 19.71534402

Mesh quantity Calculation (million) time (h)


7.68 11.35 14.17 17.23 20.46 23.42

9.5 15.66 19 25 30.25 36.5

Fig. 3. (Color) Comparison of pressure coefficient (Cp) of different mesh sizes

difference except at pressure peak areas on the wing upper surface. This led to the choice of the mesh size with 17.23 million cells for aerodynamic analysis at cruise conditions.

Fig. 2. (Color) Topology of block structured mesh for CFD calculations: (a) general view of mesh; (b) airfoil section

of boundary layer mesh is 1 × 10−5 m with yþ ≈ 1. The Reynolds number based on mean aerodynamic chord (MAC) is about 24 million. Illustrations of block-structure mesh topology and resolution of cruise calculation mesh are shown in Fig. 2. The first is the three-dimensional view of the mesh, and the second is the mesh topology for one airfoil section. Mesh was generated using ANSYS/ ICEM. Six different mesh sizes were used in the mesh convergence study. The RANS solver and SST turbulence model from ANSYS/ CFX were used in the calculation. Free stream velocity is set to 130 m=s with zero incidence angle and the physical time step is 5 × 10−4 s. All the simulations in the paper were carried out on a cluster of eight-core computing nodes configured with a 2GHz CPU and 24G memory. All the mesh convergence results for the cruise condition are shown in Table 1. The chordwise pressure coefficient for three different mesh sizes at span location of 12 m from the symmetric plane is given in Fig. 3. It can be seen from the mesh convergence study that the lift coefficient, drag coefficient, and lift-to-drag ratio converged for a mesh with 20 million mesh cells for the wing body configuration (W/B). Furthermore, for a mesh with 17.23 million grid cells, the discrepancies for lift coefficient, drag coefficient, and lift-to-drag ratio are −0.09%, −0.55%, and 0.46, respectively, while the calculation time is 35% less. Also, it can be seen from Fig. 3 that the pressure coefficient for medium and fine mesh size has very little © ASCE

Water Take-Off Simulation A decoupled method was introduced to simulate the amphibious aircraft’s water take-off process. The method is based on the combination of a volume of fluid (VOF) calculation for the boat shape using FLUENT and a separate RANS calculation using ANSYS/ CFX for the wing body configuration. The two separated calculations are repeated for every physical time step during take-off and steady calculations are assumed for each time step. The calculation using the VOF method is to obtain the waterline and the associated resistance drag, while the other calculation is to obtain the aerodynamic drag. Results from both calculations are combined in each physical time step and the waterline and velocity are updated for each time step using models from flight mechanics based on engine data, hydrodynamic, and aerodynamic results from the previous time step. The VOF method is an explicit method; therefore, the appropriate Courant number needs to be used taking into consideration the minimum mesh size and time step size in the calculation. In order to obtain accurate aerodynamic analysis results, around 10 million mesh cells and a first layer thickness of 1 × 10−5 m should be used. However, those requirements will significantly increase the time for convergence in hydrodynamic calculations since requirements for mesh resolution and first layer thickness of the boundary layer mesh are different for hydrodynamic and aerodynamic calculations. Therefore, a decoupled approach was adopted considering the trade-off between accuracy of the results and computational efficiency. The complete flowchart of the decoupled approach is given in Fig. 4.

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Table 2. Typical Value for ΔTEL

Start

Lift coefficient increments Baseline aircraft configuration

Hydro calculation

Input:(t=ti,Velocityvi, Waterline height Li)

Flap type Plain Single slotted Double slotted and fowler Triple slotted

Aero calculation (+ground effect)

Engine power Fi (t=ti)

Take-off (unstick) ΔTEL

Landing (approach) ΔTEL

0.3 0.5 0.7 0.8

0.6 1.0 1.35 1.55


Solving kinematic equation i=i+1

Update waterline height at t=ti

Update velocity at t=ti

Reach take-off requirment?

No

Yes

End

Fig. 4. Flowchart of water take-off process decoupled calculation method

The calculation process for water take-off is divided into several small time steps. In each time step ti , the hydrodynamic and aerodynamic calculation is repeated. Boat hull shape is extracted for hydrodynamic calculation by the VOF method and a full takeoff configuration is evaluated for aerodynamic calculation. The aerodynamic drag is a very small portion of the total resistance during the water take-off process before rotation. In addition, when the waterline location is approaching the fuselage bottom and the water wetted area becomes very small, aerodynamic drag accounts for a large portion of total resistance. In other words, extra aerodynamic drag from the water wetted hull causes very little difference in the final total resistance data, which is the primary concern for aircraft designers. Meanwhile, the ground effect is also considered. A ground effect study is performed beforehand to evaluate the ground effect on the aerodynamic lift force. Then, a ground effect factor is used to correct the lift force at each time step ti . The kinematic equation is solved based on hydrodynamic resistance, aerodynamic drag, ground effect, and engine thrust to obtain the velocity and waterline height for the next time step tiþ1 . The take-off distance can then be calculated by the integration of velocity and the time curve. Moreover, aircraft rotation is added when the take-off speed reaches rotation speed, which is assumed to be 1.3 times the stall speed for the take-off configuration. The stall speed is calculated using both the empirical method and CFD method. Howe (2000) suggested that for aircraft with large aspect ratios (A ≥ 5), the maximum lift coefficient can be obtained from Eq. (5) (Howe 2000) CLMAX ¼ ð1.5 ∼ 2.0 þ ΔLEL þ ΔTEL Þ cos Λ1=4

ð5Þ

where ΔLEL is the incremental value when leading edge high-lift devices are deployed and ΔTEL is the incremental value when trailing edge high-lift devices are deployed. For aircraft without aleading edge device, ΔLEL ¼ 0. Typical values for ΔTEL are listed © ASCE

Fig. 5. (Color) Maximum CL calculation result by CFD method: (a) CL AOA curve; (b) streamline result

in Table 2 for 3D wings. For the main wing, typical variations for the maximum lift coefficient are between 1.5 and 2.0 depending on the curvature of main wing. Based on Howe’s (2000) method, ΔLEL ¼ 0 (without leading edge high lift device), ΔTEL ¼ 0.5 (single slotted trailing edge high lift device), and cos Λ1=4 ¼ 1 (zero sweep angle). The maximum lift coefficient varies from 2.0 to 2.5. Then, the stall velocity can be derived from 1 W ¼ ρv2S ACLMAX 2

ð6Þ

where W, ρ, vs , and A represent the weight of aircraft, density of air, stall speed, and wing reference area, respectively. The rotation speed calculated based on the empirical method is from 60 to 66.85 m=s. Another method to determine the maximum lift coefficient is the CFD method. The lift coefficient for a different incidence of angle is calculated from the wing-body configuration. The CL-AOA curve and streamline and velocity result at 12 degrees of AOA are shown in Fig. 5. The maximum lift coefficient calculated by the

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Table 3. Mesh Convergence Study of Water Take-Off Aerodynamic Calculation Mesh quantity


7,353,788 10,670,072 13,689,825 15,310,381 18,569,722

Calculation time per step (min=step)

Lift coefficient (CL )

Drag coefficient (Cd )

1.68 2.24 2.75 3.17 3.74

1.492 1.475 1.422 1.419 1.424

0.15034 0.14863 0.14811 0.14769 0.14795

CFD method is 2.0 and the rotation speed is therefore calculated as being 66.85 m=s. An unstructured volume mesh with prism layer mesh is used for the aerodynamic calculation during water take-off (with flap deflected 35°). Five different mesh sizes are used to study the convergence characteristics of the lift and drag forces. The ANSYS/ CFX RANS solver and SST turbulence model are used in the calculation. Free stream velocity is set to 60 m=s with zero incidence of angle and a physical time step of 5 × 10−4 s. The calculation results are shown in Table 3. The surface mesh and prism layer mesh at the nose section is shown in Fig. 6. The drag and lift coefficient converged with 13 million mesh cells and the calculation time are greatly reduced with respect to 18 million mesh cells. Therefore, 13 million mesh cells were used for the aerodynamic calculation in the water take-off process. The boat hull shape of the amphibious aircraft is first extracted to evaluate the hydrodynamic force by the VOF method in FLUENT 6.3. A 3D hexahedral mesh shown in Fig. 7 is generated for the hydrodynamic analysis. To evaluate the effects of different

turbulence models and mesh sizes, calculations were carried out using six turbulence models available in FLUENT and five different mesh sizes. These turbulence models include Spalart-Allmaras (SA), Standard, Renormalized Group (RNG), Realized k − ε, and standard and shear stress transport (SST) k − ω. The URANS solver in FLUENT is used in the calculation and inlet velocity is set to 40 m=s, a median value in the whole take-off process. The interface between air and water is captured using the VOF model, and hydrodynamic drag force is calculated from the resulting flow field. A comparison of results between turbulence and mesh quantity difference can be found in a previous paper by the authors (Qiu and Song 2012). Based on these observations, the SST turbulence model with 1 million mesh quantity is used in the water takeoff hydrodynamic calculation. Following the flowchart shown in Fig. 4, the entire water takeoff process for the baseline step configuration is calculated. Wave patterns at different speeds are given in Fig. 8. With the increase in water cruise speed, wave height at the hull’s fore part increases. In addition, the angle between two front waves becomes sharper with the increase in speed. These are consistent with the hull’s wave generating phenomena reported in the literature (Ni et al. 2010). Fig. 9 shows the aerodynamic drag, wave resistance, viscous resistance, and engine’s thrust against the Froude number during the water take-off process. From the figure, it can be seen that at the beginning of water take-off run, water resistance increases rapidly with the increase in speed, as does the aerodynamic and hydrodynamic lift, but at a slower pace. This process continues until the sum of lift forces overcomes the weight, when the waterline starts to drop and this leads to a drop in hydrodynamic drag. The speed at this point is often referred to as hump speed. After hump speed, the

Fig. 6. (Color) Surface mesh and prism layer at nose section

Fig. 7. Mesh for hydrodynamic calculations © ASCE

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Fig. 9. (Color) Variation of resistance and thrust for water take-off process

(a)

rear bottom surface is free of water suction so that the water resistance is not increased rapidly because of rotation. Viscous resistance accounts for a higher percentage of total drag at low speed. However, with the increase in speed, wave resistance starts to increase faster than viscous resistance. Water resistance starts to drop after hump speed and aerodynamic drag increases linearly before rotation. After rotation, both water resistance and aerodynamic drag jumped because of the increase of the incidence angle. After that, water resistance starts to decrease due the drop of waterline height and aerodynamic drag increase with the speed increase before the aircraft becomes airborne. More details on the time-varying nature of various forces can be found in Qiu and Song (2012). Drag Breakdown for Water Take-Off Hydrodynamic Analysis The idea for the drag breakdown method originally came from Froude’s assumption, in which Froude believed that the ship resistance can be decomposed into three components: resistance due to wave drag, viscous pressure drag, and frictional drag. Viscous drag is caused by fluid’s viscosity, viscous pressure drag is caused by the separation of flow, and wave drag is caused by the wave movement of fluid. The viscous pressure drag coefficient Cvp remains constant for a certain given hull shape at any speed. For low-speed water cruise, frictional resistance accounts for around 60–80% of total water resistance and viscous pressure accounts for around 10%. For high-speed water cruise, wave resistance increases dramatically with the increase of cruise speed. Frictional resistance accounts for 20% or less and viscous pressure resistance accounts for around 5%. Therefore, Froude’s assumption can be expressed by the following equation:

(b)

R ¼ Rw þ ðCvp þ Cf Þ × Swetted (c) Fig. 8. (Color) Wave pattern at different speeds: (a) V ¼ 4 m=s Fn ¼ 0.21; (b) V ¼ 7.66 m=s Fn ¼ 0.4; (c) V ¼ 14.8 m=s Fn ¼ 0.77

displacement hull turns into a planing hull, and hydrodynamic resistance drops much rather faster than the increase of aerodynamic drag. When the amphibious aircraft starts to rotate just after reaching the hump speed, both hydrodynamic resistance and aerodynamic drag increase due to the increase in the angle of incidence of the hull. A fuselage step must be introduced to ensure that the © ASCE

ð7Þ

where Rw is the wave resistance and can be obtained from the inviscid flow field calculation. Cf is the frictional resistance coefficient that can be obtained from the empirical method based on ITTC equation. Swetted is the the wetted area that can be obtained from inviscid flow field calculations. Cvp is the viscous pressure resistance coefficient and can be determined by the following equation: Cvp ¼

R − Rw − Cf Swetted

ð8Þ

Since viscous pressure drag Cvp remains constant for a given hull shape, only one calculation using full viscous flow at each physical time step ti is necessary to obtain the total resistance using

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Eq. (7). For other components of the total resistance and at other time steps, only the inviscid flow field calculation is required to obtain the total resistance. A pressure viscous drag coefficient of 0.00043 for the baseline configuration is used in the study. The complete procedures of the drag breakdown method for the analysis of water take-off process and water resistance component structure based on Froude assumption are given in Fig. 10. Using the drag

breakdown method, Ni and Yu predicted wave drag for Series No. 60 and a KCS hull using the inviscid model and laminar turbulent model in a more efficient manner than using full-scale viscous RANS calculation; the results satisfy the accuracy requirements for engineering design (Ni et al. 2010; Yu and Liao 2009). The drag breakdown method and viscous method were both calculated at the same waterline height and velocity to analyze the accuracy of the drag breakdown method. By using this drag breakdown method, computational efficiency is improved significantly. The calculation time and discrepancy between results from viscous calculation and drag breakdown calculation are given in Table 4. With the increase in mesh resolution, the difference between the drag breakdown method and viscous calculation will drop. At the same time, the calculation time based on the drag breakdown method decreases by about 45%. The savings in computing time using the drag breakdown method is very beneficial, especially for optimization studies in the preliminary design stage.

Efficient Optimization Framework An efficient optimization framework is described in this section. The framework couples the RANS calculation for cruise configuration and an efficient drag evaluation method described in the previous sections. This method provided notable improvements in design efficiency and accuracy compared to the experimental methods. The water take-off resistance, take-off distance, cruise lift, and drag performance are calculated to evaluate the influence of location and size of the fuselage step. In the calculation, a wing body with flap deflection of 35 degrees was used for take-off analysis and cruise configuration was represented by wing body configuration with the flaps retracted. To improve the hydrodynamic calculation efficiency, a hydrodynamic drag breakdown method was used. Finally, 17 sets of different step geometries obtained using the design of experiments (DOE) method were analyzed to obtain the hydrodynamic resistance and water take-off distance. The complete flowchart of this analysis framework is shown in Fig. 11. The optimization objective here is to obtain the best fuselage step geometry shape for both cruise aerodynamic lift and drag characteristics and water take-off distance and resistance characteristic with respect to the parameter range and design constraints. The optimization objective functions used here are as follows:

fobj

Fig. 10. Details about drag breakdown method: (a) drag breakdown method flow chart; (b) component of water resistance © ASCE

8 < minðSdist Þðfor wate rtake-off conditionÞ ¼ : max DL ðfor cruise conditionÞ

ð9Þ

where Sdist is the water take-off distance and L=D is the lift to drag ratio for the cruise configuration. For some parameter combinations, the performance criteria from water take-off distance and cruise performance lead to contradictory requirements on the step dimensions. The two objective functions in f obj may not be simultaneously optimized and some trade-offs are necessary. In addition, the sum of hydrodynamic resistance and aero drag should not exceed the power of the engine during water take-off in order to meet the basic requirements, which is the constraint in the optimization problem. Based on Langley’s (1935) point of view on the choice of amphibious aircraft’s fuselage step parameters, the location of the step is generally placed approximately 1=16 of the length off the hull’s center of buoyancy and the depth of the step is approximately 4–8% of the breadth of the hull (Xia 2003). The range of the

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Table 4. Drag Breakdown Method Result and Calculation Efficiency Mesh quantity

Wave resistance (N)

Total resistance from drag breakdown method

Total resistance from viscous calculation

246,427 297,597 295,192 290,684 285,383

384,723 421,308 426,893 416,255 404,893

432,000 390,939 402,533 399,349 390,940

472,572 738,478 1,006,873 1,334,146 1,756,652

Difference (%)

Time for viscous calculation (min=step)

Time for drag breakdown method (min=step)

0.54 0.84 1.04 1.35 2.02

0.29 0.43 0.62 0.88 1.11

−10.94 7.77 5.80 4.23 3.57


longitudinal location and depth of fuselage step are decided according to such empirical rules, as shown in Table 5.

Results and Discussions Cruise Performance

Fig. 11. Flowchart of the complete optimization framework

Table 5. Parameter Ranges of Fuselage Step Used in Optimization Study Step parameters Longitudinal location

Depth

Minimum value

Maximum value

−1=16 length off center of buoyancy (16,501.1 mm) 4% beam length

þ1=16 length off center of buoyancy (18,778.9 mm) 8% beam length

Baseline configuration value Center of buoyancy (17,640 mm)

6.69% beam length

Nine sets of representative step parameter combinations are selected manually in the design space to study the relationship between fuselage geometry characteristics and aircraft cruise performance. The ANSYS/CFX solver and SST turbulence model are used in the calculation. Free stream velocity is set to 130 m=s with the same zero incidence angle and the physical time step is 5 × 10−4 s. CFD results are given in Table 6. The pressure coefficient of case 1 and case 9, representing cases with the highest and lowest values for lift-to-drag ratios among the nine calculations, are shown in Fig. 12. It can be seen from Fig. 12 that the fuselage step configuration will affect both the flow characteristics behind the step and the pressure distribution at the fuselage bottom surface. However, the side surface of the fuselage is less sensitive to the changes in step sizes. There is almost no difference in the pressure distribution on the lower surface of the wing between the two cases. In other words, the fuselage step geometry parameter change has little effect on flow characteristics of the wing. Fig. 13 shows the single variable sensitivity study of cruise performance and fuselage parameter change. The result was produced using the response surface model built based on the nine CFD results. It can be seen that the drag coefficient will decrease and L/D ratio will increase when the fuselage step moves forward. Better cruise performance will be obtained when the fuselage step moves forward from the location of gravity since the wetted area as well as viscous drag will drop. However, the longitudinal location is also limited by considerations of aircraft stability during cruise. In addition, a deep step will strengthen the flow separation behind the fuselage step so as to increase both the drag and lift coefficient and lead to a lower L/D ratio and worsened cruise performance. The changes in L/D ratio are from 19.29 to 20.06 for the step parameter range under the current given aircraft configuration.

Table 6. Step Size Influence on Cruise Performance Case number 1 2 3 4 5 (base design) 6 7 8 9 © ASCE

Step longitudinal location (mm)

Step depth (percentage of beam length) (%)

Lift coefficient (CL )

Drag coefficient (Cd )

L/D

16,501.1 16,501.1 16,501.1 17,640 17,640 17,640 18,778.9 18,778.9 18,778.9

4 6.69 8 4 6.69 8 4 6.69 8

0.572536968 0.572952242 0.57321346 0.573593484 0.573990466 0.57424913 0.571031906 0.571515843 0.571881277

0.028539615 0.028794277 0.028919774 0.029039343 0.029248866 0.029345941 0.029375774 0.029542784 0.029647242

20.06113158 19.89812891 19.820814 19.75228858 19.62436657 19.5682642 19.438872 19.34536168 19.28952737

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Fig. 12. (Color) Contours of pressure coefficient for cruise condition: (a) bottom view (case 1 and case 9); (b) side view (case 1 and case 9)

Water Take-Off Distance In addition to the cruise performance, attention should also be given to the water take-off performance for amphibious aircraft designers. Short take-off distance and sea bookkeeping ability and low resistance at hump speed and high speed are preferred. As discussed earlier, small step depth leads to lower resistance at speeds below and at hump speed of the model, and greater step depth leads to lower resistance at high speeds. A small depth of step will cause less turbulence at lower and hump speed, which results in lower resistance. However, at high speed, especially after rotation, a deeper step ensures that there is enough space at the fuselage bottom surface after the step to be free from water suction, therefore leading to lower resistance at later stages of the water takeoff process. Water resistance after hump speed for different step depths is © ASCE

given in Fig. 14 (step longitudinal location is 17,640 mm in both cases). Meanwhile, when the longitudinal location of the fuselage step moves backward, the wetted surface area is increased and frictional resistance is increased before rotation. In addition, the angle of fuselage bottom surface before and after step will increase, leading to less water suction after rotation. Seventeen combinations of fuselage step parameters are first generated using the DOE method with manual addition of the base design. Based on the analysis and water process calculation method, water resistance is calculated at the same waterline height obtained by the baseline configuration water take-off calculation result. Water take-off distance is calculated by the time integration of velocity. A response surface model is built using the results. The shortest water take-off distance and corresponding fuselage step parameters were obtained from the response surface model. Then,

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Fig. 13. (Color) Single value analysis of cruise performance and step parameter: (a) CL and CD variation with step location; (b) L=D variation with step location; (c) CL and CD variation with step depth; (d) L=D variation with step depth

Fig. 14. (Color) Resistance after hump speed for two fuselage step depth sizes

a new CFD calculation is conducted with the step parameters achieving the shortest water take-off distance. Two more iterations of hydrodynamic calculations of step configuration are calculated to improve the accuracy of the response surfaces. The results of these additional calculations are given in Table 7 along with those for the base design. The difference between results calculated by the response surface model and CFD method become less than 0.2% at the second iteration and no more iterations were necessary. The optimized response surface result is shown in Fig. 15. The original configuration (17,640 mm for longitudinal location and 6.69% for step depth) water take-off distance is 663.75 m. The water take-off distance is reduced by 120 m after the optimization while similar cruise performance is maintained. © ASCE

Meanwhile, from Fig. 16 the response surface result for the lift-to-drag ratio at cruise condition is produced from the nine aforementioned cruise calculations. The lift-to-drag ratio varies monotonically with changes in the step location and depth. The optimized design and base design produced similar L/D performance. Tradeoff and Optimization Study To provide a better comparison of the effects of step configurations on both the lift-to-drag ratio at cruise and take-off distance, another plot was produced by overlapping the L/D response surface over the drag contour. This overlapped contour is shown in Fig. 17, in

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Table 7. Response Surface Accuracy Improvement Longitudinal location (mm)

Depth of step (percentage of beam length)

CFD calculated take-off distance (m)

Response calculated take-off distance (m)

Discrepancy (%)

Base design 1 2

17,640 17,963.05284 17,943.54309

6.69 4.762396147 5.097157023

663.75 547.6122252 544.2153105

— 524.3702 543.3702

— 4.43 0.15


Iteration number

Fig. 15. (Color) Response surface result of take-off distance and step parameter

Fig. 16. (Color) Response surface result of L=D at cruise condition

which contour lines show the lift-to-drag values and color contours are used to show the take-off distance values. It can be seen from the figure that the take-off distance can be improved without an apparent penalty in cruise performance. In addition to the shortest water take-off distance achieved by the hybrid response surface and efficient drag computation method, the parameter design space can also be refined. Given that the total resistance should not exceed engine’s thrust at any point during the water take-off process from practical engineering perspective, the actual design space for the step parameters is shown in Fig. 18, © ASCE

which is slightly different from that initially given. The bottom-left and top-right corners represent the high-speed and low-speed constraints imposed by excessive engine power, respectively. At low speed during take-off, a backward shift of the fuselage step will lead to more frictional drag and a deeper step will introduce more turbulence, both of which will lead to an increase in the total drag. The total drag is constrained by the thrust available from the engine for a successful takeoff. The top-right corner in Fig. 18 represents the design boundary at low-speed conditions. With the increase in speed during take-off, a smaller step and forward

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Fig. 17. (Color) Overlapped contour plot of L=D and cruise drag

Notation

Fig. 18. (Color) Design boundary for water take-off process

shift of the fuselage step will leave insufficient space to be free of water suction after the rotation point. Therefore, the bottom-left corner in Fig. 18 represents the design boundary at higher speed conditions.

Concluding Remarks In this paper, the effects of the size and location of fuselage step on an amphibious aircraft is analyzed and optimized for both cruise and water take-off performance. For the cruise condition, the variation of step parameter produced a change in L/D ratio from 19.29 to 20.06. A deep step produced more turbulence and therefore led to a worsened cruise performance. In addition, a backward shift of fuselage step location led to an increase in frictional drag. The water take-off process was calculated by a combined hydrodynamic and aerodynamic calculation method. The drag breakdown method was used to improve the calculation efficiency. Based on the hybrid approach, a water take-off distance optimization was determined. The response surface result converged after two more iterations, and take-off distance is reduced by 120 m compared to that of the original configuration. This improvement represents more than 18% change relative to the base design. The proposed methods can be further used in optimization studies involving more geometric parameters and different configurations. © ASCE

The following symbols are used in this paper: A = wing reference area, m2 ; CL = lift coefficient; CLMAX = maximum lift coefficient; Cd = drag coefficient; Cf = frictional resistance coefficient; Cvp = viscous pressure resistance coefficient; Fn = Froude number; f obj = optimization objective function; fx ðx; zÞ = longitudinal gradient of the hull’s shape function; L=D = lift-to-drag ratio; R = total water resistance, N; Rf = frictional resistance, N; Rvp = viscous pressure resistance, N; Rw = wave resistance, N; R = Reynolds number; S = wetted area, m2 ; Sdist = water take-off distance, m; vs = stall speed, m=s; W = weight of aircraft, kg; W f = weight of the float device, pounds; αw = volume fraction of water; αg = volume fraction of air; ΔLEL = incremental value when a leading edge high-lift device is deployed; ΔTEL = incremental value when a trailing edge high-lift device is deployed; Λ1=4 = iweepback angle at 1=4 chord, degrees; and ρ = density of air, kg=m3 .

References Allison, J. M., and Ward, K. E. (1936). “Tank tests of models of flying boat hulls having longitudinal steps.” National Advisory Committee for Aeronautics (NACA) T.N. No. 574, Washington, DC. ANSYS/FLUENT [Computer software]. Academic Research, ANSYS, Canonsburg, PA. ANSYS/ICEM [Computer software]. Academic Research, ANSYS, Canonsburg, PA.

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Bell, J. W. (1935). “The effect of depth of step on the water performance of a flying-boat hull model.” National Advisory Committee for Aeronautics (NACA) Model 11-C T.N. No. 535, Washington, DC. Benson, J. K., and Lina, L. J. (1943). “The use of a retractable planning flap instead of a fixed step on a seaplane.” National Advisory Committee for Aeronautics (NACA) L-257, Washington, DC. Canamar, A. C., and Smrcek, I. L. (2009). Seaplane design and configuration, Dept. of Aerospace Engineering, Univ. of Glasgow, Glasgow, U.K. Carter, A. W. (1949). “Recent N.A.C.A. research on high length-beam ratio hulls.” J. Aeronaut. Sci., 16(3), 167–183. Cary, J. W. (2011). Preliminary design optimization of an amphibian aircraft, Dept. of Aerospace Engineering, Auburn Univ., AL. FUSETRA (Future Seaplane Traffic). (2013). “Seventh framework program.” 〈http://www.fusetra.eu/〉 (Feb. 12, 2013). Howe, D. (2000). Aircraft conceptual design synthesis, Professional Engineering Publishing, Cranfield, U.K. Husa, B. (2000). “Stepped hull development for amphibious aircraft.” Aerosp. Des. Eng., 1–15. Kajitani, H. (1983). The summary of the cooperative experiments on Wigley parabolic model in Japan, Tokyo Univ., Tokyo. Knott, R. C. (1979). The American flying boat: An illustrated history, Naval Press Institute, Annapolis, MD. Langley, M. (1935). Seaplane float and hull design, Sir Isaac Pitman & Sons, London. Lu, X. (2007). Principles of warships, Beijing Industry of National Defense Press, Beijing. Millar, C. (2009). Seaplane environmental impact information report, Mews Cobh Co. Cork, Lakeland, Australia. Nelson, W. (1934). Seaplane design, 1st ed., McGraw-Hill Book Company, New York. Ni, C., Zhu, R., Miao, G., and Fan, S. (2010). “A method for ship resistance prediction based on CFD computation.” J. Hydrodyn., 25(5), 579–586 (in Chinese). Park, I. R., Kim, K. S., and Kim, J. A. (2009). “Volume of fluid method for incompressible free surface flows.” Int. J. Numer. Method Fluids, 61(12), 1331–1362.

© ASCE

Parkinson, B., Elson, R. E., Drallet, E. C., and Luoma, A. A. (1943). “Aerodynamic and hydrodynamic tests of a family of models of flying-boat hulls derived from a streamline body.” NACA Model 84 series, N.A.C.A. Rep. No. 766, Washington, DC. Qiu, L., and Song, W. (2012). “Efficient decoupled hydrodynamic and aerodynamic analysis of amphibian aircraft water take-off process.” J. Aircr., 50(5), 1369–1379. Riebe, J. M., and Naeseth, R. L. (1947). “Effect of aerodynamic refinement on the aerodynamic characteristics of a flying-boat hulls.” N.A.C.A. T.N. No. 1307, N.A.C.A., Washington, DC. Riebe, J. M., and Naeseth, R. L. (1948). “High-speed wind-tunnel investigation of a flying-boat hull with high length-beam ratio.” N.A.C.A R.M. No. L7K28, N.A.C.A., Washington, DC. Shoemaker, J. M., and Bell, J. W. (1936). “Complete tank tests of two flying-boat hulls with pointed steps—N.A.C.A. Models 22-A and 35, N.A.C.A. Model No. 22-A.” T.N. No. 504, N.A.C.A., Washington, DC. Shoemaker, J. M., and Parkinson, J. B. (1933). “A complete tank test of a model of a flying-boat hull-N.A.C.A. Model No. 11.” NACA TN-464, N.A.C.A., Washington, DC. Syed, H. (2009). Amphibian aircraft concept design study, Dept. of Aerospace Engineering, Univ. of Glasgow, Glasgow, U.K. Tomaszewskl, K. M. (1943). “Hydrodynamic design of seaplane floats.” C.P. No. 15 A.R.C Technical Rep., Aeronautical Research Council, London. Wang, S., Wang, C., Chang, X., and Huang, S. (2010). “Ship resistance prediction by CFD methods.” J. Wuhan Univ. Technol., 32(21), 77–80. Xia, G. (2003). Fluid dynamics of ship, Huazhong University of Science and Technology Press, Wuhan, China. Yates, C. C., and Riebe, J. M. (1947). “Effect of length-beam ratio on the aerodynamic characteristics of float hulls.” N.A.C.A. T.N. No. 1305, N.A.C.A., Washington, DC. Yu, J., and Liao, G. (2009). Ship resistance calculation and prediction based on CFD method, Shanghai Jiao Tong Univ., Shanghai, China.

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