Numerical Simulation of Aircraft Ditching of a Generic Transport

Aircraft: Implementation of an Aerodynamic Model

Joel Bruno Gomesjoel.gomes@tecnico.ulisboa.pt

Instituto Superior Tecnico, Lisboa, Portugal

November 2015

Abstract

Aircraft certification requires the analysis of water emergency landing (ditching) with respect topassenger safety. In order to support the design and certification processes, models for numericalsimulation of aircraft ditching are being developed. Following the work developed in the SMAESproject (SMart Aircraft in Emergency Situations, 2011-2014), which consisted in the enhancing ofsimulation capabilities for aircraft ditching analysis, DLR is transferring the acquired knowledge tofull-scale aircraft ditching. Due to the complexity involved in full-scale modeling, a pre-processingtool is currently under development for an automatic model generation of full-scale aircraft ditchingmodels for the explicit solver Virtual Performance Solution (VPS). The overall goal of this work is toimplement and validate an aerodynamic model in the numerical simulation to allow an improvement inthe state of the art of full-scale aircraft ditching. The developed model physically calculates the loadswith proper aerodynamic equations and strongly improves the predictability of loads occurring duringa ditching simulation. For the implementation of the aerodynamic model in the numerical simulation,the creation of a new module in the pre-processing tool is proposed. The aerodynamic calculationof lift, drag and pitch moment, based on the evolution of the angle of attack and flight velocity, isaccomplished with the implementation of an external user subroutine within the numerical simulation.The superiority of the developed aerodynamic model over the state of the art is demonstrated basedon comparison of results of sensitivity and parameter studies.Keywords: Fixed-wing aircraft ditching, numerical simulation, aerodynamic model, external usersubroutine.

1. Introduction

With the number of overwater operations rising andalso as many airports are close to water, the poten-tial for a water emergency landing increases. Al-though impact on water of an aircraft (ditching) isa very rare event, it is an aspect that needs to beaccounted for within aircraft certification. Aircraftmanufacturers must show compliance to the specificairworthiness regulations associated with ditching.These specify that the aircraft must provide struc-tural integrity to protect all occupants, provide ap-propriate means for evacuation (doors and emer-gency exits operative) and float enough time to al-low for evacuation of all passengers and crew.

In order to guarantee conformity with ditch-ing regulations, engineers typically perform experi-mental test campaigns with scaled aircraft models.These test campaigns are naturally very expensiveand time consuming, which led the aircraft industryto search for new ways to certificate planned wa-ter impact. Therefore, the use of simulation toolscapable of predicting the response of aeronautical

components has increased over the years, aimingto support experimental tests for ditching certifi-cation. Moreover, the progress of computation ca-pabilities along with the development of multidisci-plinary tools such as Finite Element Method (FEM)and Smooth Particle Hydrodynamics (SPH) aims togradually replace experimental model test by pow-erful numerical tools.

Several projects aim to improve the state of theart concerning numerical tools for ditching. From2011 to 2014, the project SMAES (SMart Aircraftin Emergency Situations) was held with the over-all objective to develop a set of simulation tools topermit cost effective and entry-into-service of air-craft able to protect its occupants during ditching.In the project, water impact was investigated us-ing the coupled FE-SPH method: FE for the struc-ture and SPH for water domain. The results werevalidated with data originating from guided ditch-ing tests, in which representative plates were ex-perimentally investigated under realistic ditchingconditions and test campaigns with sub-scaled air-

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craft models. Within this project, the hybrid FE-SPH explicit code VPS (formerly known as PAM-CRASH) from ESI-Group was extended by variousfeatures for improvement of water modeling andreproduction of Fluid-Structure Interaction (FSI)phenomena [1].

Following the achievements of the SMAESproject, the DLR Institute of Structures of Design istransferring the acquired knowledge into full-scaleaircraft ditching. Due to the complexity involvedin full-scale modeling, a pre-processing tool is cur-rently under development for an automatic modelgeneration of full-scale aircraft ditching models forVPS. This pre-processing tool (AC-Ditch), devel-oped for preliminary design stage, automaticallygenerates the pre-processing of all the input cardsnecessary to the numerical simulation in VPS, andall what is left to the user is the post-processingof the results. Besides the automatic feature, twoother features of AC-Ditch are important to high-light. First, the parametric feature which allowsthe conduction of parameter variations in the pre-liminary design phase, and second the modular lay-out of the code, which allows new functionalities beadded or modified in the future, without big effort,through inclusion of new modules.

AC-Ditch comprises four main modules: the Air-craft module, which is responsible for the aircraftmodel generation; the Water module responsiblefor the generation of the water pool; the Mastermodule, which includes the global settings of thesimulation and the contact definitions; and finally,the Start module responsible for the start of thesimulation at the end of the pre-processing phase.The Aircraft module is further divided in two mod-ules: Fuselage and Wing/Empennage. In the Fuse-lage module the generation of the FE model forthe fuselage is performed by AC-Crash, an auto-matic design tool developed by the DLR Instituteof Structures and Design, using the aircraft fuselagegeometry contained in a CPACS file. The wing andempennage structures are modeled as representa-tive beam elements in the Wing/Empennage mod-ule, where rigid and flexible options are provided.Also in this module, the aerodynamics are modeledby a simple lift model where at the beginning ofthe simulation the lift force compensates the air-craft weight, and then the lift is reduced linearly tozero by the end of the simulation time (see Figure1).

This simple linear assumption of lift reveals somelimitations and raises a number of unanswered ques-tions. First, this model only considers the aerody-namic lift. Therefore, other aerodynamic loads, asdrag and pitch moment are not considered. The liftforce is approximated to be a linear function; nev-ertheless, no experimental results are available to

substantiate this assumption, which may not cor-respond to the true evolution of this aerodynamicload. Finally, even if the linear prediction is as-sumed correct, it is not possible to predict a suitableslope for the lift function.

Lift L [kN]

L=mg

Time t [s]tend

L=0

Figure 1: Linear lift model implemented within AC-Ditch.

As consequence of the limitations of the currentlift model and knowing that more complete aerody-namic models can be accomplished in a numericalsimulation of aircraft ditching, the present researchaims to implement a more complete aerodynamicmodel within AC-Ditch. The desired aerodynamicmodel should include lift, drag and pitch moment.These loads, contrary to the lift model that is pre-scribed, are physically calculated with proper aero-dynamic equations based on the evolution of veloc-ity and angle of attack of the aircraft model.

For the implementation of the aerodynamicmodel in the numerical simulation the creation ofa new module in AC-Ditch is proposed. The in-clusion of this new module cannot compromise theautomatic and parametric features of the tool. Theaerodynamic calculation of lift, drag and pitch mo-ment, based on the evolution of the angle of attackand flight velocity, is accomplished with the imple-mentation of an external user subroutine within thenumerical simulation.

2. Aerodynamics

During flight an aircraft is subjected to aerody-namic loads in all six degrees of freedom. In thepredictive ditching simulation tool, developed forpreliminary design, only rectilinear flight with zeroroll, sideslip, and yaw angles is considered, allow-ing to greatly simplify the aerodynamic modelingwith a good level of accuracy to only three loads:lift, drag and pitch moment. In Figure 2 the aero-dynamic loads applied on aircraft center of gravityare illustrated.

2

D

L

v

M

Figure 2: Aerodynamic loads acting on aircraft cen-ter of gravity.

The aerodynamic lift, drag and pitch moment aregiven by the following relations:

L =1

2ρV 2SCL(α,Ma,Re) , (1)

D =1

2ρV 2SCD(α,Ma,Re) , (2)

M =1

2ρV 2SCM (α,Ma,Re)l (3)

where ρ is the density of air, V the flight velocityalong the flight path, S the wing area and l the air-craft reference length. CL, CD and CM are, respec-tively, the lift, drag and pitch moment aerodynamiccoefficients, which are dependent on Mach numberMa, Reynolds number Re and angle of attack α.

All the physical complexity of the flow fieldaround the aerodynamic body is implicitly buried inCL, CD and CM . Therefore the appropriate aerody-namic coefficients must be established. One meansfor this purpose is presented in the next subsection.

2.1. Aerodynamic dataThe aerodynamic coefficients are obtained with theLIFTING LINE tool. This physical-based tool usesa multi-lifting-line method, capable of calculatingforce and moment coefficients for almost arbitrarynon-planar configurations of multiple thin wings.The obtained aerodynamic data is organized in an“Aero Performance Map” and it is included in theCPACS file containing all aircraft data. The “AeroPerformance Map” includes the aerodynamic coef-ficients for loads in all the six degrees of freedom,and it is generated for a set of yaw angles, Machand Reynolds numbers.

During ditching, the aircraft will naturally en-counter low flight velocities, in a similar manneras in a typical landing condition, making thereforenecessary the use of high-lift devices. The LIFT-ING LINE tool, only allows the calculation of aero-dynamic coefficients for a clean configuration, whichrestrains their use in a ditching simulation. To cir-cumvent this limitation, a correction of the lift coef-ficient data is made using real flight data of an Air-bus A320-232, which is of similar size as the genericaircraft investigated in this research.

Finally, the influence of the ground on the aero-dynamic loads acting on the aircraft throughout aditching event was considered in the course of thiswork. For this effect, which is not covered by theLIFTING LINE tool, no experimental data or flighttest results are available to quantify its influence onthe aerodynamic loads for the aircraft considered.Hence, a literature review on this topic has beenperformed. The survey, based on experimental testcampaigns and simple mathematical models usingthe Prandtl lifting-line concept, has shown that asconsequence of the high angles of attack and high-lift devices employment, ground effect is assumedto have a minor influence on aerodynamics duringditching. For this reason, ground effect is not con-sidered on the aerodynamic data used on the im-plemented aerodynamic model.

2.2. Aerodynamic module

The focus of this work is to implement an aerody-namic model in the pre-processing tool, AC-Ditch,developed for automated model generation. One ofthe main features of this tool, as described in sec-tion 1, is the modular layout of the code, which al-lows new modules to be implemented. Within thiscontext, a new module was created to account arealistic aerodynamic model. This module, namedAerodynamics is qualified to model aerodynamicsthrough a simple lift model (previously inside theWing/Empennage module) or through a more com-plex and complete aerodynamic model developed aspart of this work. A description in how the Aero-dynamics module generates the aerodynamic modelfor a rigid aircraft is here presented.

During a ditching simulation, the kinematics ofthe aircraft is changing. Consequently, even thoughthe aerodynamic forces are not explicitly dependenton time, they are dependent on angle of attack andflight velocity, which change with time during thesimulation. Therefore, despite simple aerodynamicequations are considered, see equations (1–3), dueto the indirect dependency of aerodynamic loads ontime, the way of modeling aerodynamics in VPS isnot trivial.

The aerodynamic model comprises two majorparts: specific VPS input cards, which allow theaerodynamic modeling in the simulation, and anexternal user subroutine that performs the aerody-namic calculation during the simulation run time.The Aerodynamics module is responsible for gener-ating these two components fully automatic, when-ever the aerodynamic model is requested by theuser.

Concerning the input data, VPS uses input cardswith fixed format. These contain the necessary datafor the model, the simulation setup, as well as thedefinition of the desired outputs of the simulation.

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A special input card is used to treat the dependencyof aerodynamics on time: the user data definition.When the user data card is executed, the simula-tion expects an external user subroutine. The nodalkinematics transmitted by the user data card allowthe subroutine to perform the aerodynamic calcu-lations at each simulation cycle. The aerodynamicloads calculated in the external user subroutine aretransmitted to the user data cards, which store theresults in function cards, by modifying the ordinatesof respective curves. The modified curve ordinatesoverwrite the original values, even for the very firstcycle, allowing the aerodynamic loads to be updatedat each cycle of the solution phase. This processmakes it possible for the aerodynamic loads to becalculated during the simulation run time based onaircraft kinematics, as illustrated in Figure 3. Thereader should note that each user data and func-tion card pair only includes one aerodynamic load,and as Figure 3 portrays, each pair calls the usersubroutine once per simulation cycle.

Udata card

External user subroutine

Solution phase (per simulation cycle)

Function card

Aerodynamic load Aerodynamic load

Nodal kinematics

Udata card

Function card

Aerodynamic load Aerodynamic load

Nodal kinematics

Figure 3: User data card and external user subrou-tine interaction.

Y

Z

X

y z

x

L

DM

Figure 4: Aircraft-fixed, local frame of reference,{xyz}.

The aerodynamic forces are applied on the air-craft center of gravity, making use of concentratednodal loads cards. Each of these cards is depen-dent on a function card, where forces and momentsare defined. Consequently, nodal loads cards invokethe function cards that are responsible for storing

the aerodynamic loads calculated in the externaluser subroutine. The directions of the concentratedloads refer to a aircraft-fixed local frame of refer-ence {xyz}, defined with the local coordinate framecard of VPS. The Figure 4, illustrates the aircraft-fixed local frame of reference {xyz} and the globalframe {XY Z}.

2.3. External user subroutineUntil the current subsection, the external user sub-routine is being treated as a black box whose func-tion is to calculate aerodynamic loads. The subrou-tine is automatically generated by AC-Ditch andinteracts with the simulation in the solution phase.Therefore, the Aerodynamics module writes thesubroutine with all the inputs necessary for theaerodynamic calculation, i.e. aerodynamic coeffi-cients, wing-fuselage relative incidence angle, den-sity of air, wing area and reference length. Besidesthe inputs defined by the Aerodynamics module,the subroutine also receives the nodal kinematicsfrom the simulation. This data comes from the userdata cards and is listed below.

• Center of gravity velocity, v = [vX , vY , vZ ]

• N1 and N2 coordinates

As portrayed in equations (1–3), the aerodynamicloads are dependent on flight velocity and angle ofattack. The velocity is computed as magnitude ofthe center of gravity (COG) velocity vector, V = |v|and the angle of attack must be calculated usingthe nodal kinematics. The angle of attack can bewritten as the difference between the pitch angleθ and flight path angle γ, plus the wing fuselagerelative incidence angle β, leading to

α = θ − γ + β . (4)

The pitch angle θ is defined as the angle betweenthe longitudinal axis of the aircraft, in this case thex -axis, and the horizontal, i.e. the X -axis. Consid-ering this definition and the illustration in Figure5, it is possible to write

θ = arctan

(ZN1 − ZN2

XN1 −XN2

). (5)

The flight path angle γ, is the angle between thehorizontal and the velocity vector, which describeswhether the aircraft is climbing or descending. Con-sequently, one can write

γ = arctan

(vZvX

). (6)

The aerodynamic coefficients are given as a set ofpoints in an array format, where each component ofthe array corresponds to an angle of attack. There-fore, after the angle of attack has been calculated

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using equation 4, the code selects the correspondingcomponents of the aerodynamic arrays. If the exactangle of attack does not exist, the code interpolatesbetween the two nearest points. This guaranteesthat the aerodynamic coefficients used in the cal-culation are given with a good level of precision.When the calculated angle of attack exceeds themaximum allowed value, the code writes a stall alertin the output file and prescribes α = αmax withinthe aerodynamics computation. Hence, this modelapproximates the stall by limiting the lift coefficientto CL,max, which is the CL of α = αmax.

Once the aerodynamic coefficients are selectedbased on the angle of attack, the aerodynamic loadsare finally calculated using equations (1–3), wherethe absolute value of velocity is given by

V =√v2X + v2Y + v2Z . (7)

Lift and drag forces act in direction normal andparallel to the flight path, respectively. However,defining a system of reference that follows the flightpath is hardly possible, since the velocity vector isone of the problem variables. Thus, the aerody-namic loads are projected in the aircraft-fixed localframe of reference {xyz}, see Figure 4. The projec-tion angle is the difference between the pitch andthe flight path angle. The projection yields

Lx = −L sin(θ − γ) , (8)

Lz = L cos(θ − γ) , (9)

Dx = D cos(θ − γ) , (10)

Dz = D sin(θ − γ) , (11)

My = M . (12)

Due to the direction of the x -component of lift inthe local frame of reference, equation 8 has a minussign. As one can see in Figure 5, for a positive angleof attack the Lx component is contrary to the x -axis, whereas the opposite situation is verified for anegative angle.

L +Dx x

L +Dz z

vCoG

θ

γ

α

z

x

z

N1

N2M

Z

X

Figure 5: Aerodynamic loads projected in theaircraft-fixed local frame of reference.

As the reader can verify in Figure 5, in total thereare five loads to be applied to the model. This

means that five sets of user data, function and con-centrated loads cards are necessary in the aerody-namic model. Each user data card invokes the usersubroutine once, which means that five user datacards are executed per simulation cycle. Everytimethe subroutine is called the five loads are calculated,but only the respective one is given to the simula-tion and written in the external file.

3. ValidationIn order to run trustworthy ditching numerical sim-ulations with the implemented aerodynamic model,it is crucial to perform a model validation. There-fore, the numerical results obtained using the imple-mented aerodynamic model in VPS are comparedwith theoretical ones obtained from the solution ofthe equations of motion. For the solution of theseequations a semi-analytical tool was developed dur-ing the course of this research.

An excellent agreement between the theoreticaland numerical results has been obtained for all theflight conditions used in the validation process. Forinstance, in Figure 2 the pitch angle time histo-ries are in excellent agreement for a typical ditchingcondition. Similar results were obtained for all theanalyzed parameters in different flight conditions.

0 1 2 3 4 5Time t [s]

−15

−10

−5

0

5

10

Pitc

hA

ngle

θ[◦

]

Theoretical Numerical

Figure 6: Validation - Pitch angle time histories.

4. Numerical investigationsNumerical investigations are performed in order toassess the influence of the aerodynamic model onthe ditching behaviors of a generic transport air-craft model.

The aircraft model consists of a generic transportaircraft geometry with a capacity to hold approxi-mately 150 passengers. The fuselage of the aircraftis generated by AC-Crash and converted to a rigidbody by AC-Ditch. The fuselage length is approx-imately 36.5m with a maximum height of 4.1m.The aircraft rigid wing and tail are modeled as rep-resentative beam elements with a wingspan around32m, a sweep back angle of 25◦ and a vertical tail

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9.5m high from the lowest fuselage point. No land-ing gear or engines are modeled. The aircraft totalmass is assigned to the aircraft COG, where differ-ent mass load cases are offered by AC-Ditch.

For the water model, the investigations per-formed in [2] were taken as reference. The watermodel is constituted by a hybrid FE-SPH model asportrayed in Figure 7. Classic FE are placed in thearea where less deformation is expected, whereasSPH particles fill the central section of the waterbasin where splash and larger deformations are ex-pected. The total cross-section of the pool is con-stant with H = 5m and W = 10m, and the SPHdomain measures H = 1m and W = 5m (H-height,W-width). The pool length is computed as the sumof the aircraft length and the product of the ini-tial horizontal velocity with the simulated time, i.e.lT = aircraft length +vX ·time. The ratio betweenparticle spacing and individual finite element lengthis 1:2, with 100mm particle spacing and 200mm forthe FE. Finally, according to reference [2], the ac-tive box is the modeling option (offered within AC-Ditch) that showed the lowest computational timeand therefore it is selected for the present investi-gations.

t = 0 ms t = 250 ms

l (t)A

active

inactive

transition

lT

Y

Z

X

l (t)A

FE fluiddomain

SPH fluiddomain

Figure 7: Water model with adaptive active box.

The active box consists of a virtual box whereSPH particles are active. This box moves withthe aircraft and deactivates particles over a certaintransition region where no water impact is happen-ing. This process is illustrated in Figure 7, wherethe dark blue portion corresponds to the active SPHparticles, red the transition region and gray the de-activated particles. The initial length of the activebox is lA(t = 0) = 16m, as only a small part ofthe aircraft structure is in contact with the water.Throughout the simulation the box grows linearly,and in the end of the simulation, when the aircraftfuselage is completely in contact with the water, thelength of the box is lA(t = tfinal) = 40m. Devia-tions from the presented water model are referredin the following sections, when justified.

Interaction between the fluid, constituted by SPHparticles, and the aircraft structure is modeled witha standard penalty contact, see [3].

All the simulations are performed with zero roll,sideslip and yaw angles, accordingly the velocitycomponent in Y -direction (vY ) is set to zero. The

remaining initial conditions, namely pitch angle θ,horizontal and descent velocities vX and vZ are se-lected depending on the case studied. During theapproach phase it is required that the aircraft holdsa trim condition, i.e. L = W . The old lift model,as consequence of its definition imposes a trim con-dition in the beginning of the simulation regardlessof the initial conditions prescribed by the user. Onthe other hand, the aerodynamic model, which isbased on aerodynamic equations (1–3), only holdsthe trim condition in the beginning of the simula-tion, if a suitable set of initial conditions is pre-scribed to allow the fulfillment of L = W .

4.1. Sensitivity analysisThe influence of the aerodynamic model on aircraftkinematics during ditching is investigated througha sensitivity analysis. For this study, the air-craft model presents a Maximum Takeoff Weight(MTOW) of m = 72547 kg and a COG position onthe x-direction of xCOG = 16.5m. The initial con-ditions are set to vX = 70m/s and vZ = −1.5m/sand θ = 8◦, and allow a trim condition in the be-ginning of the simulation when the aerodynamicmodel is used. The lift model assumes a linear evo-lution, where the slope is predefined by the user.For the current investigation the slope was chosenso that lift equals zero in the end of the simulationat t = 1000ms.

Comparison of conventional lift modelagainst aerodynamic model

To investigate the differences between the twomodeling options, a comparison of results is herepresented. The simulations last 1000ms and theaircraft motion comprehends different phases. Firstthe aircraft impacts the water domain and thenbounces off to impact again several meters aheadof the first impact. At the first impact only therear part of the aircraft fuselage contacts the waterparticles, while at the second impact the aircraftbottom contacts the water and the aircraft finallylands.

The lift force evolution with time for the regardedmodels are compared in Figure 8. The lift forcecomputed by the aerodynamic model is illustratedin a black solid line, whereas the red one illustratesthe linear evolution of the lift model where the curveequals zero at the end of the simulation. As can beseen, at the initial time of the simulation, the air-craft is trimmed using both models. The resultsshow that the lift calculated by the aerodynamicmodel is higher than the one prescribed by the liftmodel during all the simulation time. The differ-ence between the curves increases with time and,at the end the simulation, the lift force computedby the aerodynamic model still equals 400 kN , whilethe one computed by the lift model equals zero.

The lift curve obtained by the aerodynamic

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model shows a quasi-linear behavior. As such, alinear curve in solid blue was added to the resultsin order to compare the lift force coming from theaerodynamic model to a prescribed linear lift force.The slope of this blue line was chosen so that liftequals zero at t = 2000ms. Figure 8 demonstrateshow the lift model is subjected to engineering judg-ment, since according to the slope defined by theuser: the lift model will allow a more or less realis-tic aerodynamic modeling.

0 100 200 300 400 500 600 700 800 900 1000Time t [ms]

0

100

200

300

400

500

600

700

800

Lift

L[kN

]

Aerodynamic Model Lift Model, slope 1 Lift Model, slope 2

Figure 8: Comparison of lift force time histories.

The acceleration time histories of the center ofgravity of the aircraft model are portrayed in Fig-ure 9. The acceleration curves are filtered with aCFC60 filter [4]. As result of the trim condition inthe beginning of the simulation, the acceleration inboth models starts in zero. Accordingly, the accel-eration deviation results from the impact on waterand the change provoked by it in the aircraft kine-matics.

The first peak in the acceleration curves is dueto the first impact, between 10ms and 200ms. Forthis impact the models are in good agreement. Af-ter this, when the aircraft bounces, the curves as-sume a linear behavior, where the acceleration re-sulting from the lift model decreases more than theone coming from the aerodynamic model. This isa consequence of the higher lift in the aerodynamicmodel than in the lift model, as shown in Figure 8.At the second impact the acceleration curve com-ing from the lift model increases almost until 3.5 g,considerably more than the almost 2 g coming fromthe aerodynamic model. Moreover, as the simula-tion using the aerodynamic model has more lift theaircraft flies longer and, as consequence, the secondimpact is delayed about 100ms for the aerodynamicmodel. The acceleration histories obtained from thetwo models show a clear difference in the results.

0 100 200 300 400 500 600 700 800 900 1000Time t [ms]

−1.0

−0.5

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

Acc

eler

atio

naZ

[g](

CFC

60)

Aerodynamic Model Lift Model

Figure 9: Comparison of acceleration time histories.

Influence of aerodynamic drag and pitchmoment

In order to investigate the influence of the aero-dynamic drag on the aircraft kinematics two simula-tions are compared: a reference case using the aero-dynamic model, and a simulation using the aerody-namic model with the drag force set to zero, i.e.where only lift and pitch moment are modeled. Asa full agreement was verified for the majority of theparameters investigated, it is possible to affirm thatthe aerodynamic drag has a minor influence on theaircraft behavior during a ditching simulation.

Analogously, the influence of pitch moment isevaluated through a comparison of two simulations:a reference case using the aerodynamic model, anda simulation using the aerodynamic model with thepitch moment set to zero, i.e. where only lift anddrag are modeled. The obtained results have shownclear differences between the two simulations for thepitch angle and acceleration time histories. There-fore, an influence of the pitch moment on the air-craft kinematics during a ditching simulation can beclaimed. This is an important result since it high-lights one of the limitations of the lift model, whichdoes not include pitch moment.

Comparison of lift model against aerody-namic model with presence of suction

Suction effects can play an important role on air-craft kinematics during ditching, see [5]. In fact,due to the high horizontal velocity the pressure dropin the rear part of the lower fuselage originates asuction force that induces a nose up attitude andresults in the attachment of the aircraft to the wa-ter during the ditching event. In the previous in-vestigations, suction effects were not modeled whichresulted in a nose down attitude and a ricochet afterthe first water impact. To model suction effects inthe simulation, the separation stress feature avail-able in VPS is used, see [2].

Since suction effects are not correctly portrayedfor small SPH particle spacing, a few changes were

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performed in the water model. The SPH particlespacing was increased from 100mm to 200mm, inthe water model used in the numerical investiga-tions, when suction effects are modeled. The ratiobetween particle spacing and individual finite el-ement length was kept at 1:2, with 200mm SPHparticle spacing and 400mm for the FE.

The lift force time histories are presented in Fig-ure 10. The results show, in an identical manner asin Figure 8, that the lift force calculated by the aero-dynamic model is higher than the one prescribedby the lift model throughout all the computationaltime. The larger difference is verified in the begin-ning of the simulation due to the larger pitch angle,caused by suction effects in the simulation. The in-crease in the pitch angle led to an increase in the liftforce calculated by the aerodynamic model, whilethe lift model decreases the lift regardless of theevolution of the pitch angle. Contrary to observa-tions in the lift comparison without suction effectsin Figure 8, the quasi-linear behavior is not foundin the results of the aerodynamic model in Figure10. Moreover, it is possible to verify that the solidblue line, representing the linear lift model endingin 2000ms, is now quite far from matching the re-sults of the aerodynamic model. This exposes thestrength of the aerodynamic model, which is ableto physically calculate the lift force for any motionof the model in the simulation, contrarily to the liftmodel that it is not versatile and strongly dependson its setup (engineering judgment).

0 100 200 300 400 500 600 700 800 900 1000Time t [ms]

0

100

200

300

400

500

600

700

800

Lift

L[kN

]

Aerodynamic Model Lift Model, slope 1 Lift Model, slope 2

Figure 10: Comparison of lift force time historieswith suction model.

4.2. Parametric analysis

Due to the parametric and automatic features ofAC-Ditch, it is possible to conduct parameter vari-ations in the preliminary design phase without thegeneration of numerous different, though similar,models. Based on this premise, a parametric studyis performed for different COG positions and im-pact conditions. In all the following simulations

suction effects are considered due to their impor-tant role during ditching. Consequently, the simula-tion model previously presented, together with themodifications introduced on the water model in thesensitivity analysis with suction model, is adopted.The modeling of aerodynamic loads in the simula-tion is performed using the aerodynamic model.

COG positionTo assess the COG influence, two simulations are

compared: a reference case with the same aircraftmass, COG position and initial conditions as in thesensitivity analysis and another simulation with thesame aircraft mass and initial conditions, but dif-ferent COG position. The reference case presents aCOG position of xCOG = 16.5m and is comparedwith a model with xCOG = 17.14m.

The pitch angle time histories are shown in Figure11. The results portray that the aircraft with theforward COG presents a higher decrease of the pitchangle throughout the simulation. The overpressureregion creates forces that cause a nose down pitchmoment at the aircraft COG, while the suctionforces cause a nose up pitch moment. Dependingon the position of the COG, the lever arm of theseforces can be larger or smaller. As can be seen inFigure 12 this lever arm is bigger for the aircraftwith the forward COG. Therefore, the pitch angleevolution of the simulation with COG position at16.5m results in a lower pitch angle. The differencebetween the pitch angle curves increase throughoutthe time, with the biggest difference at the end ofthe simulation.

0 100 200 300 400 500 600 700 800 900 1000Time t [ms]

−2

0

2

4

6

8

10

Pitc

hA

ngle

θ[◦

]

Reference: COG = 16.5 m COG = 17.14 m

Figure 11: COG investigation: comparison of pitchangle time histories.

The differences in the pitch angle evolutiondemonstrated in Figure 11 induce dissimilarities inthe lift force. The aircraft with the forward COGposition has lower lift force due to the lower pitchangle. The differences in the lift forces increasethroughout the simulation, as the difference in thepitch angle curves increases. Finally, the presented

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investigation shows that the COG position has aclear effect on the aircraft kinematics during ditch-ing. As previously discussed, the difference in theresults arise from the different lever arms for suc-tion and overpressure forces related to the COG po-sition.

16.5 m17.14 m

Figure 12: Typical pressure distribution on rearpart of the lower fuselage during impact with twoCOG positions. Overpressure represented in blackand suction in red.

Impact conditionsThe investigation of different impact conditions is

extremely important due to the influence that thesecan have in the ditching event; for instance, it isexpected that water impact with higher velocitiescause larger structural damages.

Therefore, simulations with different initial ve-locities are performed in this investigation to eval-uate the kinematics of the aircraft. The same air-craft model is used for the three compared simu-lations. The impact conditions were investigatedvarying the initial horizontal velocity 5m/s higherand lower than the reference condition of 70m/s.The initial vertical velocity is kept constant at−1.5m/s as suggested by ditching regulations, andthe velocity component in the Y -direction is keptat zero, as only rectilinear flight is considered inthe model. In order to fulfill the trim condition atthe beginning of the simulation, any change in theinitial velocity implies a change in the initial pitchangle or in the weight configuration. As the weightis kept constant for the three cases (m = 72547 kg),higher horizontal velocities imply lower pitch an-gles, and vice versa. Therefore, the impact con-dition 1 presents the lower pitch angle of 5.25◦,whereas the impact condition 2 yields the higherone with 11◦.

The pitch angle time histories are plotted in Fig-ure 13 as the difference between the pitch angle θand its initial value θ0. Since all the three sim-ulations present different initial pitch angles, thisnormalization was necessary to make a proper com-parison of the obtained results. The highest (θ−θ0)difference is obtained for the impact condition 1with the lowest initial pitch angle (5.25◦), whereasthe impact condition 2 with the highest initial pitchangle (11◦) present the lowest change of pitch angle.

0 100 200 300 400 500 600 700 800 900 1000Time t [ms]

−2

0

2

4

6

8

10

12

Pitc

hA

ngle

θ[◦

]

Reference: θ0 = 8◦, vX = 70m/sImpact condition 1: θ0 = 5.25◦, vX = 75m/sImpact condition 2: θ0 = 11◦, vX = 65m/s

Figure 13: Impact conditions investigation: com-parison of pitch angle time histories.

Depending on the pitch angle upon impact, thewetted structure can be larger or smaller. For lowerpitch angles the structure in contact with the wa-ter particles is bigger, which causes more particlesto remain attach to the fuselage structure (suctionmodel, see [5]). As consequence, there is a highernose up pitch moment, leading to a larger changeof the pitch angle. Moreover, the pressure gradi-ent along the wetted fuselage is strongly affectedby the horizontal velocity component of the aircraft.Therefore, suction effect has a greater influence onthe aircraft kinematics for impact conditions withhigher velocities and lower pitch angles as observerin reality (see [6] and [7]).

The presented investigation permits to inferthe influence of different impact conditions duringditching. In particularly, it could be noticed thatsimulations with higher initial velocities are moreaffected by the suction forces in the rear part of thelower fuselage.

5. Conclusions

In the present work an aerodynamic model was de-veloped, which computes aerodynamic forces andmoments acting during ditching as a function offlight velocity and angle of attack during the simula-tion. The developed model allows for an increase ofthe predictability of loads occurring during ditch-ing. The main achievements of this research arehere presented, followed by a summary of the ma-jor findings.

The Aerodynamics module has shown to be ef-fective in generating the specific VPS cards and theexternal user subroutine required for the aerody-namic modeling, without compromising the auto-matic and parametric features of the tool. More-over, the module proved to be well prepared forhandling different aerodynamic data provided in theCPACS data file. This important feature allows acontinuous improvement of the aerodynamic model,

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since more accurate data could be obtained withina multidisciplinary environment and passed to theaerodynamic model using the developed module.

An excellent agreement between the semi-analytical solution of the equations of motion andnumerical results has been demonstrated for allthe flight conditions used in the validation process.Therefore, it is possible to conclude that the aero-dynamic model is correctly implemented and thata correct computation of aerodynamic forces andmoments acting during ditching, based on flight ve-locity and angle of attack, is achieved. Finally, nu-merical investigations were conducted in a set ofsensitivity and parametric studies, from which somemajor findings can be highlighted.

In the sensitivity analysis the conventional liftmodel was compared with the aerodynamic model.Although a quasi-linear behavior was obtained forthe lift curve computed by the aerodynamic model,considerable differences in the magnitude of the liftforce were verified between the lift curves obtainedwith the two models. Moreover, the lift force timehistories have clearly shown how the lift model issubjected to engineering judgment. For the accel-erations it was verified that at the second impact,the acceleration value obtained with the lift model isthe double of the one obtained by the aerodynamicmodel. Moreover, studies concerning the influenceof drag and pitch moment revealed that the formerhas a minor influence on the aircraft behavior dur-ing ditching, whereas for the second an importantinfluence on the aircraft kinematics during a ditch-ing simulation can be claimed. This is an importantresult since it highlights one of the limitations of thelift model. Finally, the sensitivity study with pres-ence of suction effects exposed the strength of theaerodynamic model, which is able to physically cal-culate the aerodynamic loads for whichever motionof the model in the simulation, contrarily to the liftmodel that is not versatile and strongly dependson engineering judgment. Despite no experimen-tal results exist to perform a validation, the resultsobtained with the aerodynamic model showed a sig-nificant improvement in the predictability of loadsduring ditching, since the aerodynamic loads arephysically calculated based on the aircraft kinemat-ics.

The parametric analysis has shown that differ-ent parameters can significantly change the aircraftbehavior during ditching. From the analyzed pa-rameters, the impact conditions are the ones thatclaim the biggest influence on the ditching behav-ior. Nevertheless, the COG position have shown aconsiderable influence on the aircraft kinematics, inparticularly on the pitch angle.

Other important findings relate with the compu-tational time. Studies regarding this topic have

shown that, despite the frequent interaction be-tween the external user subroutine and the solver,the computational cost of the aerodynamic model isinsignificant. Moreover, it was also verified that theaerodynamic model does not increase the executiontime of the model generation tool, i.e. AC-Ditchtakes the same time to generate a model with thelift or the aerodynamic model.

References[1] Martin H. Siemann, Dieter Kohlgruber, Luis

Benıtez Montanes, and Alessandro Iafrati. Nu-merical Simulation and Experimental Valida-tion of Guided Ditching Tests. 11th WorldCongress on Computational Mechanics (WCCMXI), 2012.

[2] Maria Ines Costa Cadilha. Numerical Simula-tion of Aircraft Ditching of a Generic Trans-port Aircraft: Contribution to Accuracy andEfficiency. Master thesis, Instituto SuperiorTecnico, 2014.

[3] Paul H. L. Groenenboom, James Campbell, LuisBenıtez Montanes, and Martin Siemann. Inno-vative SPH Methods for Aircraft Ditching. 11thWorld Congress on Computational Mechanics(WCCM XI), 2014.

[4] ESI-Group. Solver Notes Manual. Virtual Per-formance Solution, 2009.

[5] Luis Benıtez Montanes, Hector Climent Manez,Martin H. Siemann, and Dieter Kohlgruber.Ditching Numerical Simulations: Recent Stepsin Industrial Applications. Aerospace Struc-tural Impact Dynamics International Confer-ence, 2012.

[6] Ellis E. McBride and Lloyd J. Fisher. Experi-mental Investigation of Effect of Rear-FuselageShape on Ditching Behavior. Technical Report2929, National Advisory Committee for Aero-nautics, 1953.

[7] Margaret F Steiner. Accelerations and bottompressures measured on a B-24D airplane in aditching test. Technical report, National Advi-sory Committee for Aeronautics (NACA), 1944.

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