cfd analysis of a captive bullet forced into calm water

CFD Analysis of a Captive Bullet Forced into Calm Water

Rene Bettencourt [email protected]

Instituto Superior Tecnico, Universidade de Lisboa, Portugal

November 2018

Abstract

Loads of a generic free-fall lifeboat, forced into calm water are analysed with different simulationparameters. This captive motion case is studied using the CFD code ReFRESCO [1], which solvesthe RANS equations supplemented by a volume-of-fluid (VoF) model. The influence of numericalparameters is first analysed with laminar solutions. It was found that for a ∆t = 10−4, residualsmust not exceed L2 < 5 × 10−4 and that grid refinements around the tip should expand gradually.Then a two-equation turbulence model was added, to compare laminar and turbulent solutions ofcaptive motions with higher angles of attack and experimental data. It was identified that maximumloads for turbulent solutions, stayed within a 6% deviation of laminar cases for small angles of attack.Furthermore, it was observed that greater angles of attack can contribute to viscous forces becomingof the same order as pressure forces for a short period during the initial dive part.Keywords: Free-fall Lifeboat, Water Impact, Turbulence, Computational Fluid Dynamics, Volume ofFluid

AcknowledgementsThe author would like to thank WavEC -OffshoreRenewables for providing the computational meansfor this work, and MARIN for kindly providing theexperimental data.

1. IntroductionOn July 21st 2005 the Statoil1 owned Veslefrikk Boffshore platform conducted its final test on theirnewly mounted free falling lifeboats, with disastrousconsequences. The lifeboat suffered serious damage,with its superstructure caved in and showing signsof cracks, the bow and stern hatch also deflected,which led to some water folding the vessel. As HansSkeide, the chief safety delegate at the time on theVeslefrikk B platform, put it: ”If there had beenpeople on board when the lifeboat hit the sea, manyof them could have been killed.”. This test hadbeen the last step before the new emergency systemwould become operational. Instead it was the firststep towards an industry-wide pursuit in achievinga new safety standard.

In 2010 this culminated in two norms: the lessstricter ”LSA Code”(updated version [2]) and themore restrictive ”DNV-OS-E406”(new [3]). TheDNV-OS-E406 regulation is as of 2015 applicable

1Statoil is the state-owned Norwegian petroleum com-pany. The company merged in 2007 with Norsk Hydro toform StatoilHydro and is in the process of changing its nameto Equinor as part of its strategy to diversify its presence toa broader energy sector.

to lifeboats on the NCS, including conventionallifeboats.

At present the DNV norm (2016 edition [3]) al-lows for CFD (Computational Fluid Dynamics) toaid in the design process of free-fall lifeboats. Unlikethe structural analysis, which has an appendix ded-icated to providing recommendations for FEM cal-culations, CFD recommendations seem more vagueand do not present concrete guidelines on the nu-merical aspects of simulations.

1.1. ObjectivesThis work goes one step further from results pre-sented by Maximiano in [4] towards systematic in-crease in complexity. The focus of this work will beanalysing the effect of turbulence modelling and nu-merical parameters for different captive trajectories.This work is a summary of the findings presentedin [5].

1.2. Literature ReviewApplying CFD to the lifeboat case, raises tradi-tional CFD questions, and more problem specificissues on how to model the real-life case.

One of the first modelling questions related tothis problem is how to accurately predict the freesurface dynamic. In the majority of cases thisis done via the ”Volume-of-Fluid”(VoF) approach[6, 7, 8], in which both air and water are modelledas a single fluid with physical properties varying lin-early between the two fluids. When using the VoF

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model, attention must be paid to ensure a sharptransition from air to water. In the few works whichshowed the VoF field, most had a transition area oftwo or three cells. However, only [9] presented theVoF field along the lifeboat’s surface, where the FSwas more smeared. Such smearing could lead todifficulties in predicting the lifeboat’s trajectory.

The DNV norm requires some consideration re-garding turbulence modelling. It suggests usingtwo equation models for free-fall lifeboats design.In most literature articles this advice is ignored ordeemed negligible. In [10], [11], [12] and [13] atwo equation model with wall functions was emp-ployed using the STAR CCM+ code and in [14]a minimum-dissipation turbulence LES model wasused in the ComFLOW code. In [10], for a 2D and3D wedge drop case, the influence of adding a tur-bulence model was investigated. It had an impactof less then 3% in the computational results.

Lifeboats will likely be used under extremeweather conditions. Hence, another level of com-plexity must be added to the CFD model, condi-tions such as waves, currents or wind. In [6], [7],[12] and [8] waves were taken into account by mod-elling them as 5th order Stokes waves. In [7] and [8]wind was also contemplated. Berchiche et al. [6] in-vestigated computationally and experimentally, theimpact of a model lifeboat into waves with differ-ent headings. For waves propagating perpendicularto the model, it was reported that the most criticalloading condition occurred for heading angles of 60◦

and 120◦. Mørch et al. studied the influence of par-ticular wave hit-points for waves propagating alongthe lifeboat’s longitudinal axis. In [8] the wind(head wind) was directly considered in the CFDcalculations. This approach predicted a change inimpact pitch angle of 8◦. Note that both cases con-sidered constant wind speeds of 40− 50m/s, whichcorresponds to wind gusts of a category 3 cyclonestorm.

Regarding verification and validation, Maximi-ano et al.[4] used the procedure proposed in [15]to do a formal verification and validation exercise.This work allowed to quantify the numerical un-certainty, which resulted in recommendations re-garding domain size, FS discretization scheme, CFLrange, grid influence and residuals convergence amore reliable foundation. In particular, the at-tention paid to iterative errors should be empha-sized, for in most works this is usually discarded oronly briefly mentioned but not formally analysed.Other works have also compared computational re-sults with experimental ones. In [7],[16],[17],[9],[6]computational results showed reasonable agreementwith scale model experiments, with exception of[17], which presented just qualitative matching toexperiments. In [12, 6, 18] CFD results also demon-

strated reasonable agreement with full-scale test re-sults. It should be noted that only Berchiche etal.[6] had experimental data of model drops intowaves. The remaining experiments were drops intocalm water.

In order for the computational mesh to moveand thus model the lifeboat’s trajectory, four meth-ods stand out: moving grid, overset grids, adap-tive grids and embedded grids. The moving gridmethod involves applying the rigid body motion tothe whole grid. This was done in [4, 9] and willalso be used in calculations presented here. Thebenefits are to only mesh the domain once, withouthaving to re-mesh at each time step. This contrastswith the adaptive grid method in which for eachtime step the grid is locally refined and/or coars-ened. A novel adaptive grid method was devel-oped by Plas et al. [18] for the comFLOW solver,which demonstrated promising results in the free-fall lifeboat case. CFD results showed good agree-ment with experimental results even for grids withjust 90K cells. Another way to improve the mov-ing grid shortcomings relies in using the oversetgrid method. In this method smaller moving gridsof sub domains move freely through a backgroundgrid. Authors who used STAR CCM+ used this ap-proach [6, 7, 8]. In this code, a three cell interfacebetween background and sub domain grid is usedto match both grids. STAR CCM+ also offers thepossibility to use embedded grids, which involves asliding internal interface between a sphere, wherethe lifeboat resides, and the rest of the mesh. Itwas used in [12, 6, 7]

This review shows that great efforts have beenmade in applying CFD to the free-fall lifeboat dropcase. Nonetheless, besides Maximiano [4] no recom-mendation of numerical parameters has been madeso far for the free-fall lifeboat case.

2. Theoretical Background2.0.1 Governing Equations

The fluids motion will be modelled using theRANS2 equations, assuming incompressible fluidflow. Closure of the equations will be achieved bysupplementing a two equation turbulence model,which rely on the Boussinesq hypothesis. To modelthe Free Surface (FS), water and air will be treatedas two immiscible incompressible phases of a sin-gle fluid of density and dynamic viscosity given by(1). The air-volume fraction α is the ratio of airvolume occupied to the total control volume (2).Because the two phases are assumed immiscible theair-volume fraction of each material particle shouldremain constant and convected by a simple convec-tion equation (3). For incompressible fluids thisequation could be recasted in conservative form, but

2Reynolds averaged Navier-Stokes

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due to stability reasons [19] it is used in the presentnon-conservative form.

ρ = αρair+(1−α)ρwater µ = αµair+(1−α)µwater

(1)

α = Vair/VCV (2)

∂α

∂t+ α

∂ui∂xi

= 0 (3)

This modelling approach is known as the Volume-of-Fluid (VoF) method. An important aspect ofusing this method is guaranteeing a sharp transi-tion between phases with little ”smear”. Moreover,at no-slip walls with densely packed viscous-layergrids, the (relative) velocity goes to zero near thewall. In consequence, α is not properly convectedin these regions and can lead to air being ”dragged”into the water during impact. This issue is knownas the contact line problem.

2.1. Problem DefinitionAn axisymmetric bullet is considered as a genericgeometry of a free-fall lifeboat. This generic shapewas chosen to make a more general analysis, ratherthen a specific life-boat design study. The bullet is“forced” into calm water with a constant velocity of3m/s. It’s longitudinal axis (dashed-line) is alignedwith the velocity vector, i.e. with angle of attackγ = 0 (see fig 1). The bullet trajectory has a pitch-ing angle of 55◦, θ = 55◦ (nose-down positive). Theplane of symmetry is the X-Z plane. The bullet ischaracterized by the length between it’s perpendic-ulars, Lpp, and it’s breadth B (see figure 1). Thedomain is a cylinder of height 5 × B and diameter10× Lpp.

The boundary conditions are schematically de-picted in figure 2. Symmetry condition on parallelfaces, no-slip on the bullet’s surface and prescribedpressure on the lateral face, equal to the hydrostaticpressure inside the water and zero outside. At sim-ulation start the velocity field is at rest and thepressure field is set to hydrostatic pressure in waterand zero in air. For the air-volume fraction, a planeperpendicular to the gravity force vector is definedby a given distance from the origin (the origin isin the bullet’s COG). Above the plane α = 1 andbelow α = 0, at the cells containing the interface, αis obtained by the cell’s volume fraction above theplane.

2.2. Numerical ConsiderationsAll CFD analysis done in this thesis will be done us-ing MARIN’s3 code, ReFRESCO [1]. It is a RANSbased CFD code for maritime applications. It solves

3Maritime Research Institute Netherlands

Figure 1: Test Case Schematic Sign Conventions

Figure 2: Boundary Conditions

multiphase (unsteady) incompressible viscous flows.The coupled non-linear equations are solved usingthe SIMPLE algorithm in segregated fashion.

Regarding numerical schemes; time integrationis done implicitly with first order accuracy, con-vective fluxes from momentum equations are dis-cretized with a TVD variant of the QUICK schemeand the convective fluxes of turbulence equationsapply first order upwind for stability reasons. Forthe air-volume convective flux, the ReFRICS [19]compressive scheme was chosen as the best candi-date from a comparison done in [5].

The air-volume equation has specific ”under-relaxation” methods, which keep 0 ≤ α ≤ 1. Thishas the downside of slowing the convergence, whichcan lead to α residuals stagnating.

3. Sensitivity Studies

It is helpful as reference to divide the motion intothree segments, which can be visualized in figure 3and are defined as follows:

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www.refresco.org

Adef= t(ms) ∈ [0; 80] B

def= t(ms) ∈ [80; 270]

Cdef= t(ms) ∈ [270; 600]

During interval A the bullet is entering the wa-ter and the FS has to first accommodate the bullet.Interval B is representative of the time through-out which the bullet simply continues the ”dive”without affecting much the shape of the air-waterinterface. Finally, interval C is the wake collapseinterval.

Figure 3: Iso-surface for the air-volume-fraction, α =0.5

It is generally accepted that besides coding er-rors, there can be errors in the solution due to dis-cretization errors, iterative errors or modelling er-rors. With this in mind, the following laminar re-sults will assess the influence of the discretizationand iterative error only in intervals A and B, whilezone C and turbulence modelling will be addressedlater.

3.1. Iterative Error Influence

The linearized RANS equations are solved itera-tively according to Eq.(4)(the superscript indicatesiteration and should not be confused with expo-nent).

φk+1 = [C]φk (4)

If converged to a certain convergence criteria,these solutions will all fulfil their linearised equa-tions i.e. the right-hand side,of the equations, willbe ”equal” to left-hand side. ”Equal” because ifone were to subtract the right-hand side by theleft-hand side the result would deviate from zero.This deviation is closely related to the concept ofresidual (see Eq.(6)), and is a measure of how farthe solution is, from the exact numerical solution ofEq. (5).

Given a linear system of equations: [A]φ = b (5)

The residual is: Res = [A]φ− b (6)

The difference between the last iteration, of theconvergence process, and the exact numerical solu-tion of Eq. (5), is the iterative error. Even if the it-erative solution process were to be carried out indef-initely, there would still be an error towards the ex-act numerical solution due to finite precision, as theround-off error. Nonetheless, if one had the exactnumerical solution, the computed solution wouldhave an error towards the analytical valued. Thiserror is termed discretization error and is presentbecause the computed solution is obtained from adiscretized form of the original equations. In real-ity, without infinitely precise grids, finite computerprecision and numbered iterative solver iterations,the error between the true analytical solution, φ∗,and the computed solution is due all error types (Eq.(7)).

φ∗ − φcomputed = εiter + εdiscr + εround−off (7)

The convergence criteria naturally affects the it-erative error in a very direct way. The solution willhave less iterative error for stricter the convergencecriteria.

The iterative error can also be influenced by thetime-step magnitude. With decreasing time-stepmagnitude, the changes in all fields , will be smaller.As the field changes become smaller, the iterativeerror becomes relatively more relevant, and it canbecome important enough to pollute the solution.

3.1.1 Time-Step ∆t

For this analysis the original ∆t = 1 × 10−4 wasdoubled four times. The most striking effect of suchincrease in ∆t is that it has a filtering effect (see fig-ure 4). The small noise in B disappeared and thewake collapse interval C, has a different behaviouralso with less high amplitude noise. For the re-sults in figure 4, the percentage of time-steps whichreached the maximum outerloop limit is presentedin table 1. At this point, there are two hypothe-sis with similar outcomes: 1) A smaller ∆t impartsmore resolution, thus possibly contributing to thenoise. 2) A small ∆t increases the relative impor-tance of the iterative error, as explained before, alsopossibly contributing to noise. Therefore, intervalA, was simulated under more rigorous convergencecriteria of the smallest ∆t = 1× 10−4, to see if it’snoise would change, validating the 2nd hypothesis,or not, validating the 1st. The convergence criteriawas set to Linf < 1E−5 and Linf < 1E−6 and sig-nificant reduction in noise was not found (see figure5).

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Figure 4: Influence of using different ∆t values

Table 1: Percentage of time-steps reaching the max.number of outerloops

∆tPercentage of time-steps whichreached max. outerloop number

∆t = 1E − 4 none∆t = 2E − 4 1%∆t = 4E − 4 4.1%∆t = 8E − 4 4.3%∆t = 16E − 4 13%

3.1.2 Convergence Criteria

Four L2 criteria were compared: L2 < 5E − 4;L2 < 1E − 4; L2 < 1E − 5 and L2 < 1E − 7.Figure 6 shows that L2 < 5E − 4 is the limit abovewhich the solution behaviour completely changes,for this reason the influence of the iterative errorcannot be overlooked! In contrast, Figure 7 showsthat L2 < 1E − 5 is the limit below which a morerestrictive convergence factor doesn’t change the so-lution much. From L2 < 1E−4 to L2 < 1E−5 onlythe smaller oscillations in interval B (see figure 7)improved.

Regarding convergence, for the L2 < 1E − 5 case40% of all time-steps exceeded the maximum out-erloop number. Out of those 40% time-steps, 75%where exclusively due to the α-equation. For theL2 < 1E − 7 case, 99% of all time-steps exceededthe limit and from those 99%, 80% where due tothe α equation exclusively. As the outerloop limitwas reached mostly only due to the α equation, itis safe to make conclusions about the pitching mo-ment solution, which are influenced by the resultsfrom the momentum and pressure equation.

Figure 5: Zone A with stricter convergence factors

In conclusion, the iterative error was at most,only responsible for the smallest oscillations in theoriginal solution. It should however, not be under-estimated for there exists a limit above which it hasa greater impact (see figure 6).

Figure 6: Comparison of solutions obtained with L2 <5E−4; L2 < 1E−5 and L2 < 1E−7 for ∆t = 4×10−4

Figure 7: Comparison of solutions obtained with L2 <1E − 4; L2 < 1E − 5 and L2 < 1E − 7

3.2. Grid Topology InfluenceA new grid was created with ”smoother” refinementregions, namely ”Grid3.1”, see figure 8. Figure 9depicts the results obtained with this new grid andin fact the new grid resolved almost all of the highamplitude noise. The new grid solution convergedto L2 < 1E − 5 all time-steps, excluding the air-volume-fraction residuals which exceeded the max-imum number of outerloops 8% of all time-steps.

In post-processing, it was discovered that when-ever the refinement regions of Grid3 traversed theFS, there would be a peak in forces and moment.Grid3 has ”tighter” refinement zones which expandmore rapidly than Grid3.1. Hence, a possible ex-planation would be that making cells, close to thetip, expand too quickly makes the bullet dive intothe water in a less ”continuous”, more discrete way.Thus, from one time-step to another there is a pres-sure force spike. As was noted in section 3.1.1, thismust also be related to the time-step.

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Figure 8: Grid3.1

Figure 9: Comparison between solutions using Grid3and Grid3.1

4. Laminar Vs. Turbulent Flow andExperimental Data

In order to approximate the real free-moving case,three different trajectories will be presented. Theobjective is to evaluate the impact of a turbulencemodel in such flows and compare with experimentaldata. The turbulence model used was the k − ωSST model [20]. In order to minimize the contactline problem, viscous cell layers were set to have ay+1 ∼ 300 in water. This choice is explained in [5].

While the first trajectory did not have angle ofattack, the second and third trajectories have 10◦

and 35◦. The pitch angle for the first, second andthird trajectory are 55◦, 45◦ and 55◦ respectively.Accordingly, the third trajectory represents a verti-cal ”drop” with 55◦ pitch, and should demonstratea more vigorous water impact. Schematics for thethree cases are presented below in figures 10, 11 and12 notice the velocity vectors.

The experimental data was kindly provided byMARIN, and represents the same results previouslyused in [4]. As discussed in [4], the experimentaldata consistently presents an oscillatory behaviourthroughout all three cases, even before water im-pact. For this reason, these oscillations are regardedas vibrations of the experimental set-up. In an ef-fort to minimize the influence of such vibrations onexperimental data, a low-filtered version is also pre-sented.

Figure 10: Case1.

Figure 11: Case2.

Figure 12: Case3.

4.1. Case 1, θ = 55◦ & γ = 0◦

For this particular bullet motion, the turbulencemodel has close to no effect, apart from some non-physical oscillations during the wake collapse. Inrelative terms, Fx shows the greatest difference fromapplying the turbulence model, at t = 70ms (seefigure 14). Nonetheless, aside from that instance,the influence of the turbulence model stays within6% for all quantities.

Regarding experimental results, an excellentagreement with experimental data for Fx (figure 13)and a qualitative good agreement for Fz (figure 15)and Myy (figure 17) is observed. The last two quan-tities, Fz and Myy, were the ones most affected bythe oscillations, which was expected for the type ofvibrations associated with the skid mount set-up.One can conclude the turbulence model had someinfluence concerning Fx, and it should be notedthat this influence improves even more the agree-ment with experimental data. This suggests thatthe model enhances the accuracy Fx, which is likelydue to increased wall shear-stress.

Figure 13: Fx(t) obtained with and without the SSTturbulence model Vs. experimental data for case 1.

Figure 14: Relative difference between laminar and tur-bulent solutions for Fx(%) of case1.

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Figure 15: Fz(t) obtained with and without the SSTturbulence model Vs. experimental data for case 1.

Figure 16: Relative difference between laminar and tur-bulent solutions for Fz(%) of case1.

Figure 17: Myy(t) obtained with and without the SSTturbulence model Vs. experimental data for case 1.

Figure 18: Relative difference between laminar and tur-bulent solutions for Myy(%) of case1.

4.2. Case 2, θ = 45◦ & γ = 10◦

Case two follows a similar trend, of the turbulencemodel having little impact in relative terms, apartfrom a peak during the initial water impact at t =70ms for Fx (figure 20).

Nevertheless, in absolute terms, Fx seems to feelthe collapse of the the FS more abruptly with the

turbulence model. During this 10ms interval, thepressure in the aft part of the bullet, increases by afactor of 3. Such phenomena is associated with anup-tick in Fx at around t = 360ms and has beenconsistently observed, experimentally and numer-ically, by other authors (see section 1.2). There-fore, this behaviour could be indicative of the tur-bulence model rendering a more physically realisticbehaviour.

In terms of experimental results; Fx calculationswith the turbulence model still present a better cor-respondence to experimental results, but at the endresults with experimental data tend to better agreewith the laminar simulations. In opposition, Fz andMyy seem to better agree with experimental resultsin relative terms, which translates into Fz predict-ing experimental maximum loads with superior ac-curacy. However, differences towards experimentalloads are still far greater then what the turbulencemodel can account for.

Figure 19: Fx(t) obtained with and without the SSTturbulence model for case 2.


Figure 21: Fz(t) obtained with and without the SSTturbulence model for case 2.

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Figure 23: Myy(t) obtained with and without the SSTturbulence model for case 2.


4.3. Case 3, θ = 55◦ & γ = 35◦

Case 3 has the greatest angle of attack. Conse-quently, the FS behaviour features two collapses,one on the top part of the bullet (140ms < t <175ms) and another at the aft part of the bullet(t ∼ 340ms). For a visual reference see figure 32.The first collapse leads to Fz (figure 27) deviating10% from the laminar case, while the second onecorrelates with the greater magnitude felt by thelongitudinal force Fx. During the first collapse, inparticular Fz and Myy respond more abruptly, un-derscoring the trend of a more sudden collapse withturbulence. Nonetheless, compared to the laminarcase, deviations remain mostly under 6%.

However, Fx features once more a relative-difference spike during the initial water impact, ex-ceeding 30%. Note that this difference increase isnot related to any FS collapse. Thus, another pat-tern comes into light: as the angle of attack in-creases, during the initial period when the bullet

first touches the water, the relative importance ofhaving a turbulence model also increases. This islikely due to water being initially pushed along hebullet’s walls, causing shear stress. This is similarto the water flow for the free-fall wedge case. Quan-titatively, it translates into viscous forces reachingthe same order of magnitude as pressure forces inxx direction, at least momentarily (see figure 31).

Case three represented a more vigorous impactwith greater angle of attack. Consequently, thewake should have a greater impact in the flow. Ina way, this trajectory case can be seen as havingthe most bluff-body-like wake of all. Thus, from afundamental point of view, applying wall functionsbecomes even more questionable. Moreover, a bluff-body wake can be greatly influenced by the bound-ary layer separation point and flow regime (laminarvs. turbulent), for which wall-function boundaryconditions are also too simplistic.

For all these reasons, it should not come as asurprise that experimental results present a pooreragreement with numerical ones. It is particularlystriking that Fx, which used to display good agree-ment with experimental data, now demonstrate sig-nificant discrepancies. Fz and Myy also demon-strate worse matching to experimental results, withFz reaching a deviation of 38%. Nonetheless, inqualitative terms, the overall behaviour can still bepredicted.

Figure 25: Fx(t) obtained with and without the SSTturbulence model for case 3.


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Figure 27: Fz(t) obtained with and without the SSTturbulence model for case 3.


Figure 29: Myy(t) obtained with and without the SSTturbulence model for case 3.


Figure 31: Ratio of pressure force to viscous force in xxdirection, during the initial period of case 3.

Figure 32: Air-volume fraction field of case 3. Noteboth FS collapses, one on the top and the other at thebullet’s aft part.

5. ConclusionsRegarding the influence of iterative errors, it wasfound that the convergence criteria had a significantimpact. Residuals should not exceed L2 < 5×10−4.Above this limit, the solution would feel significantchanges. It is important to emphasize this find-ing as iterative errors and convergence criteria wererarely discussed in the reviewed literature. In par-ticular the convergence criterion sometimes recom-mended of lowering residuals two orders of magni-tude, proved to be not only time-step dependentbut also less restrictive. According to the find-ings of this work, a more reliable recommendationwould be to identify the upper absolute convergencelimit, above which the solution changes and im-pose a convergence criterion 1.5 orders of magni-tude lower. Furthermore, the numerical parameterswhich seemed to most influence the solution wherethe time-step value and grid topology, which shoulddisplay smoother grid refinements around the tip.

From the two extra captive trajectories with suc-

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cessively greater angles of attack, it was recognizedthat at its core, the turbulence model might onlyhave a significant impact on loads for brief and spe-cific instances like FS collapse or the initial interval.Substituting the model for an uncertainty of ±10%can be considered for a quick conservative estimate(for γ < 10◦). This can be a simple solution forinitial design phases and proved to be especiallyreliable for estimating maximum loads. However,differences during the initial dive period increasedwith angle of attack. This indicated that for greaterangles of attack (γ ≥ 35◦), viscous forces could,momentarily, become of the same order as pres-sure forces. Nonetheless, these findings should beconsidered with caution, because on one hand theywere obtained using wall functions, which tend tooverestimate wall shear stresses, on the other hand,a full-scale free-fall lifeboat should have a Reynoldsnumber 100 times greater, which would make theuse of wall functions more appropriate.

Experimental results displayed qualitatively goodagreement with numerical data. For small angles,Fx also demonstrated exceptional agreement withexperimental results in quantitative terms. Thisquantity was the only one for which a turbulencemodel had an appreciable impact and of the sameorder as deviations between laminar and experimen-tal loads. In general, Fx predictions with turbulencemodel had better correspondence towards experi-ments. However, as the difference between laminarand turbulent results proved to be small in the firstplace, adding a turbulence model might be unnec-essary in terms of accuracy. For greater angles ofattack, all three quantities displayed greater devi-ations from experimental results. A possible ex-planation, would lay on the inadequate use of wallfunctions in zones of massive separations, as is thecase for the wake of case three.

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cfd analysis of a captive bullet forced into calm water

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