CFD Simulations of Unsteady LHA Ship Airwake in OpenFOAM

KTH ROYAL INSTITUTE OF TECHNOLOGY SCHOOL OF ENGINEERING SCIENCES

CFD Simulations of Unsteady

LHA Ship Airwake in OpenFOAM ^®

MATÚŠ CVENGROŠ

CFD Simulations of Unsteady LHA Ship Airwake in

OpenFOAM ^®

MATÚŠ CVENGROŠ

KTH Royal Institute of Technology

BEN THORNBER

Associate Professor at School of Aerospace, Mechanical and Mechatronic Engineering

The University of Sydney

AUTHOR

SUPERVISOR

PHILIPP SCHLATTER

Associate Professor at KTH Mechanics KTH Royal Institute of Technology

EXAMINER

Master Thesis

KTH Royal Institute of Technology School of Engineering Sciences KTH Mechanics

Stockholm, Sweden

Abstract

Extensive research in the past two decades has shown that ow around the sharp edges of blu bodies, such as the superstructure of a ship, can cause large scale shear-layer sepa- rations with increased turbulence, generating a highly unsteady ow in the airwake region.

Such separations aect the control margins and handling loading of a rotorcraft, mainly if operating from the vicinity of a ight deck, and therefore negatively in uence the rotorcraft operating limits, which is one of the main reasons for the study of ship airwakes. Current work focuses on CFD analysis of the US Landing Helicopter Assault (LHA) ship airwake, both through Reynolds-Averaged Navier Stokes (RANS) simulations and Improved Delayed Detached-Eddy Simulations (IDDES), particularly focusing on IDDES. Simulations involved an increasing number of grid resolutions (with a total of 7) for thorough convergence and grid independence study of the inherently turbulent ow, with the highest resolution being the largest computation to date of the LHA ship airwake. Computations were undertaken using the open-source unstructured grid Navier-Stokes CFD software OpenFOAM. The work thoroughly discusses the results for 7 independent wind-over-deck (WOD) angles and wind velocities of 30 knots, and shows quantitative data and analysis of numerous ow quantities.

Abstrakt

Omfattande forskning under de senaste tva decennierna har visat att öde runt skarvkrop-

pens skarpa kanter, som ett skepps överbyggnad, kan orsaka storskaliga skjuvskiktsskillnader

med ökad turbulens och generera ett mycket ostabilt öde i luftvagsomradet. Sadana sep-

arationer paverkar kontrollmarginalerna och hanteringen av en rotorkraft, huvudsakligen

om de körs fran närheten av ett ygdäck och därmed negativt paverkar driftsgränserna

för rotorcraften, vilket är en av huvudorsakerna till studien av ygvagor. Nuvarande ar-

bete är fokuserat pa CFD-analys av US Airways Landing Helicopter Assault (LHA), bade

genom Reynolds-Averaged Navier Stokes (RANS) -simuleringar och Improved Delayed De-

tached Eddy Simulations (IDDES), med inriktning pa IDDES. Simuleringar involverade ett

ökande antal nätresolutioner (totalt 7) för grundlig konvergens och gridoberoende studie av

det inneboende turbulenta ödet, där beräkningen med högst upplösning är den största som

gjorts pa LHA-fartygets luftvag. Beräkningar gjordes med hjälp av open-source ostruktur-

erat nät Navier-Stokes CFD-program OpenFOAM. Arbetet diskuterar grundligt resultaten

för 7 oberoende vind-över-däck (WOD) vinklar och vindhastigheter pa 30 knop, och visar

kvantitativ data och analys av manga ödesmängder.

Acknowledgements

First and foremost, I would like to give thanks to my supervisor Ben Thornber, who has been leading me throughout this project. When I rst came to Australia as an exchange stu- dent, I had no idea what to do, and I remember the day when I simply strolled into your oce with a question if I can do some research. After a brief moment of bewilderment and following discussion, you have accepted me as one of your research students, and thus unknowingly set in motion a wave of life-changing moments and opportunities that span far beyond the scope of this project. For all of that, I will be forever thankful.

Second, I would like to give thanks to Daniel Linton, who has trained me in the ways of OpenFOAM, and withstood the innite barrage of questions I always had. Without your help, I would not know nearly as much as I do now.

I would also like to thank my examiner Philipp Schlatter, who has been my guide overseas while I stayed in Australia, and who was always willing to help me when I needed it, either in person or e-mail.

Special thanks go to my friends that I made along this journey, both in Sweden and Aus- tralia. To the special few such as Chris and Pete that made my Australian stay so much more warmer in an already warm summer, and especially to the Bad Boys in Sweden { Matias, Toni, Juanjo, Federico and most importantly, Adrian. I will never forget the days when we stayed inside of Shire during the cold Swedish winters, and all the crazy fun that followed. I will especially remember the gathering on Friday morning of June 9, 2017, and the amazing memory of what happened has to be repeated. I would also like to thank Shegufta, Irina and particularly Cristina. I have got to know you while we were trying to solve the problems of the World, and although we were unsuccessful in the end, you have stayed my friends forever since. There are many more I would like to name, however these pages are not long enough and I hope you will forgive me. It has been a very colorful ride, and would not be the same without you. Thank you, for being there.

Special thanks goes to my brother Robert, which prepared an awesome cover page graph- ics of my super-pretty ship.

Finally, I would like to thank my brothers Dodo and Robert, my Father, and especially

my Mom, to whom I would like to dedicate this thesis to. Without your support, I would not

be who I am today.

Contents

Abstract iii

Acknowledgements v

List of Figures ix

List of Tables xix

Nomenclature xxiv

I Theoretical Introduction 1

1 Introduction 3

1.1 Literature Review . . . . 4

1.2 Thesis Outline . . . 17

2 Theory 19 2.1 General Equations for Incompressible Flow . . . 19

2.1.1 Conservation of Mass . . . 19

2.1.2 Conservation of Momentum . . . 21

2.1.3 The Role of Incompressibility . . . 22

2.2 Turbulence and Turbulence Modeling . . . 23

2.2.1 Direct Numerical Simulation . . . 24

2.2.2 Reynold-Averaged Navier-Stokes Simulation . . . 25

2.2.3 Large Eddy Simulation . . . 30

2.2.4 Detached Eddy Simulation . . . 33

2.3 Introduction to Boundary Layer Theory . . . 34

2.3.1 Momentum Thickness, Wall Shear . . . 34

2.3.2 Laminar and Turbulent Layer Thickness . . . 36

2.3.3 Friction Velocity, Dimensionless Velocity and Dimensionless Wall Dis- tance . . . 36

2.3.4 Law of the Wall . . . 36

II Simulation Setup, Mesh & Results 39 3 Mesh Generation 41 3.1 Introduction to Mesh Generation . . . 41

3.1.1 Mesh Quality . . . 41

3.1.2 Structured & Unstructured Meshes . . . 43

3.2 Structured Meshing Approach for LHA . . . 44

3.2.1 Boundary Surfaces . . . 45

3.2.2 Meshing Strategy . . . 46

3.2.3 Final Mesh Topology . . . 49

3.3 Conclusion . . . 53

4 Grid Convergence 55 4.1 Steady-State Analysis . . . 55

4.1.1 Boundary Conditions . . . 56

4.1.2 Solution Strategy . . . 56

4.1.3 Convergence Results . . . 57

4.2 Unsteady Analysis . . . 60

4.2.1 Courant-Friedrichs-Lewy Independence . . . 60

4.2.2 Boundary Conditions . . . 64

4.2.3 Solution Strategy . . . 64

4.2.4 Convergence Results . . . 65

4.3 Conclusion . . . 70

5 Validation 73 5.1 Conclusion . . . 77

6 Results 79 6.1 Headwind . . . 81

6.1.1 Temporal Spectral Analysis . . . 104

6.1.2 Spatial Spectral Analysis . . . 109

6.1.3 Further Comparison of Turbulence Solved on a Coarser Grid . . . 111

6.1.4 Discussion . . . 115

6.2 Green 30 ^◦ . . . 116

6.3 Green 60 ^◦ . . . 125

6.4 Green 90 ^◦ . . . 133

6.5 Red 30 ^◦ . . . 140

6.6 Red 60 ^◦ . . . 147

6.7 Red 90 ^◦ . . . 155

6.8 Conclusion . . . 162

6.8.1 Further Discussion and Improvements . . . 164

References 167 A OpenFOAM Dictionary Files 171 A.1 Steady-State Analysis (RANS) . . . 171

A.1.1 Initial and Boundary Conditions . . . 171

A.1.2 System Dictionaries . . . 176

A.1.3 Constant Dictionaries . . . 179

A.2 Unsteady Analysis (IDDES) . . . 181

A.2.1 Initial and Boundary Conditions . . . 181

A.2.2 System Dictionaries . . . 185

A.2.3 Constant Dictionaries . . . 189

A.3 Post-Processing . . . 191

A.3.1 Field Operations . . . 191

A.3.2 Sampling . . . 195

List of Figures

1.1 USS Saipan (LHA-2) Amphibious Assault Ship (a) and DI (b) in Pacic Ocean (Nov. 10, 2006) - Pilots hover in an SH-60B Seahawk assigned to the

"Wolfpack" of Helicopter Anti-Submarine Squadron Light Four Five (HSL- 45) while waiting for the perfect time to land aboard the Arleigh Burke-class guided missile destroyer USS Preble (DDG 88) during rough seas. . . . 3 1.2 Dierent ship types that were subject to airwake studies over the years. . . . 5 1.3 Simple Frigate Shape (SFS). . . . 5 1.4 Dramatic change of the airwake caused by the superstructure of the LHA ship

due to various WOD angles. Source: Polsky et al. [29]. . . . 6 1.5 The geometry of CPF and MCPF together with the measured volumes. Source:

Syms [46]. . . . 7 1.6 Unstructured mesh of the domain and a visualization of the DI volume.

Source: Lee et al. [17]. . . . 8 1.7 Dynamic F/A-18 C/D CFD calculation. Plane colored by velocity magnitude.

Source: Polsky et al. [26]. . . . 9 1.8 Streaklines for headwind direction of wind for SFS 1. Source: Syms [45]. . . . 10 1.9 Surface mesh of the SFS 2 geometry. Source: Forrest et al [8]. . . 10 1.10 Experimental model of 1:100 scale mounted in NRC 2 m × 3 m low-speed

wind tunnel. Source: Forrest et al [8]. . . 11 1.11 Contours of mean (top) and instantaneous (bottom) velocity magnitude for a

headwind, plotted on a plane at z/h = 1.15 above the deck. Source: Forrest et al. [8]. . . 12 1.12 Contours of mean (top) and instantaneous (bottom) velocity magnitude for

a headwind WOD condition of ow eld around T23. Plotted on a plane y/b = 0 . Source: Forrest et al. [8]. . . 13 1.13 Structured grids of the Type 23 Frigate and Wave Class Auxiliary Oiler.

Source: Thornber et al. [52]. . . 14 2.1 Fixed control volume. Source: Anderson [3, p. 45]. . . 19 2.2 Reynolds Averaging, producing mean and uctuating components. Source:

Moukalled et al. [24, p. 695]. . . 25 2.3 The famous Kolmogorov ve-thirds law, showing a range of wavenumbers

(spatial frequencies) with a constant slope of energy decrease. Longer wave lengths (left of k 1 ) are in the energy containing range, interval between k 1

and k 2 is the inertial subrange and smaller wave lengths (right of k 2 ) are in the dissipation range. Source: Lewandowski et al. [19]. . . 30 2.4 Homogeneous decaying turbulence. Domain scale L ³ . Source: Wikipedia. . . 31 2.5 Attenuation factors ˆ G(κ) ² : box lter, dashed line; Gaussian lter, solid line;

sharp spectral lter; dot-dashed line. Source: Pope [31, p. 569]. . . 31

2.6 Boundary layer growth. Figure shows freestream velocity U and development of the velocity prole u(x, y) close to the wall. Pressure p equals to the atmospheric pressure p a in the outside region of the boundary layer growth.

Figure shows wall shear τ w and boundary layer thickness δ. Source: White [22]. 34

2.7 Universal distribution of u ⁺ (y ⁺ ) near a smooth wall. Source: White [37]. . . 36

3.1 Non-orthogonality measured as an angle between the cell centroids and shared face normal vector of two adjacent cells. . . 41

3.2 Changing aspect ratio of cells. . . 42

3.3 Dierent volume ratios of neighbouring cells. . . 42

3.4 Dierent types of unstructured meshes. . . 43

3.5 Structured mesh consisting of hexahedral faces. . . 44

3.6 Side view of the 3D model used for LHA mesh generation. . . 44

3.7 Domain (to scale) used in CFD simulations. . . 45

3.8 Coordinate system used for all CFD simulations. . . 45

3.9 Domain and LHA model (actual size) used in CFD simulations. Individual colors represent the surfaces. Inlet represented by the cylindrical surface in the background. Sky symmetric (same geometry as sea; not visible in the picture). . . 46

3.10 Multi-block division of the computational domain. . . 46

3.11 Detail of the multi-block topology for the close proximity of the LHA ship and ship surfaces. Picture was generated as a post-script le, with certain export issues, which can be seen near the deck region right behind the ship bow. . . 47

3.12 Dierent mesh topology at the bow islands. . . 47

3.13 Strong pressure gradient at the ship bow, potentially causing grid convergence issues. Colored by pressure coecient C p . . . 48

3.14 Dierent grid resolution for the ship bow. . . 48

3.15 Computational domain for a grid resolution corresponding to 1.5 m edge length at the entirety of the ship deck, creating 2.3 million cells total. . . 50

3.16 Top view of the LHA close-up and computational domain expansion. Mesh with 2.3 million cells selected for visualisation purposes. Blue grid represents the SEA surface, whereas black grid represents the LHA and DECK surfaces. 50 3.17 Expansion of the boundary layer throughout the computational domain. . . . 51

3.18 Comparison of mesh resolution of the deck and superstructure for 17.4 million and 92.8 million cells. . . 51

3.19 Comparison of mesh resolution of the deck and superstructure horns for 17.4 million and 92.8 million cells. . . 52

3.20 Comparison of the non-orthogonal grid regions at ship bow. . . 52

3.21 Non-orthogonality of the ship bow. Decrease of non-orthogonality in prob- lematic regions means increase of non-orthogonality in a dierent region. . . . 53

4.1 Dierence between the boundary layer expansion for the same mesh topolo- gies, where max (L cell = 3 m) at the deck. . . 58

4.2 Dierence between the cases of non-consistent and consistent boundary layers. 58 4.3 Convergence of velocity eld for various mesh densities at the ship centerline. 59 4.4 Location of the landing spots along the ship deck. . . 59

4.5 Convergence of velocity eld for various mesh densities above the locations

of landing spots. . . 61

4.6 Comparison between the mean velocity magnitudes for dierent CFL numbers through ship centerline at z = 3 m. First: t = 5 ms. Second: t = 2.5 s. Third:

t = 5 s . Fourth: t = 10 s. Error bars were omitted for plot clarity, however quantitative analysis showed all lines within uncertainty bounds of others. . . 62 4.7 Comparison between the mean velocity magnitudes for dierent CFL numbers

through ship centerline at z = 6 m. First: t = 5 ms. Second: t = 2.5 s. Third:

t = 5 s . Fourth: t = 10 s. Error bars were omitted for plot clarity, however quantitative analysis showed all lines within uncertainty bounds of others. . . 63 4.8 Convergence of velocity eld magnitudes for various mesh densities at the

ship centerline. . . 66 4.9 Convergence of velocity eld magnitudes for various mesh densities at the

longitudinal position of landing spots. . . 67 4.10 Top view of the LHA and the ship deck, showing dierent grid resolutions.

The white line at the center represents centerline with diameter of 1 m. . . 68 5.1 Comparison of time-averaged velocity magnitudes at the ship centerline for

z = 3 m . . . 73 5.2 Comparison of time-averaged velocity magnitudes at the ship centerline for

z = 6 m . . . 74 5.3 Comparison of time-accurate velocity magnitudes at the ship centerline for

z = 3 m at t = 4 s. . . 75 5.4 Comparison of mean velocity magnitudes normal to the ship surface at the

spot 8 location. Experimental results scaled from 40 knots to 30 knots. . . 75 5.5 Convergence of velocity eld magnitudes for various mesh densities at the

ship centerline. . . 76 5.6 Convergence of velocity eld magnitudes for various mesh densities at the

ship centerline. . . 76 5.7 Comparison of surface pressure coecient at 50 s. . . 77 6.1 Comparison of vorticity magnitude for all presented WOD cases with fre-

quency of 2 Hz and 17.4 million cells. The ow represents, from left to right:

Red 90 ^◦ , Red 60 ^◦ , Red 30 ^◦ , Headwind, Green 30 ^◦ , Green 60 ^◦ , Green 90 ^◦ . . . . 79 6.2 Location of cutting planes for data gathering and visualisation. Red lines

represent cutting planes with 4 ms write time. Blue lines represent write time of 1 s. . . 80 6.3 Comparison of mean velocity magnitude for 17.4 million and 92.8 million

simulation case at the ship centerline and throughout the landing spots. Both lines taken at the height of 3 m and 6 m. . . 81 6.4 Comparison of time-accurate velocity magnitude for 17.4 million and 92.8

million simulation case at the ship centerline and throughout the landing spots, both at the height of 3 m and 6 m. Snapshot at time of 60 s. . . 82 6.5 Comparison of mean velocity magnitude across the ship beam. . . 83 6.6 Turbulence intensity through beam width for the location of landing spots. . 84 6.7 Time-averaged contours of pressure coecient ¯ C _p , normalized with velocity

of 30 knots (≈ 15.43 m/s). . . 84 6.8 Time-accurate contours of pressure coecient C p at t = 60 s, normalized with

velocity of 30 knots (≈ 15.43 m/s). . . 84 6.9 Time-accurate contours of wall shear stress τ w at t = 60 s with units in N/m ² . 85 6.10 Time-accurate contours of wall shear stress τ w in the superstructure region.

Time at 60 s with units in N/m ² . . . 85

6.11 Time-averaged contours of wall shear stress τ w at the ship deck. Units in N/m ² . 85 6.12 Time-averaged contours of wall shear stress τ w

at the ship deck. Units in

N/m ² . . . 86 6.13 Time-accurate contours of pressure coecient above the ship deck. Time

equal to 60 s in both cases. Contours purposefully left without discretisation to highlight small uctuations. . . 87 6.14 Time-accurate contours of velocity magnitude above the ship deck. Time

equal to 60 s in both cases. . . 88 6.15 Time-averaged contours of pressure coecient above the ship deck. Contours

discretized to 32 values in order to provide more clarity and contrast. . . 89 6.16 Time-averaged contours of velocity magnitude above the ship deck. Contours

discretized to 32 values in order to provide more clarity and contrast. . . 90 6.17 The U RMS velocity (also a standard deviation for the given case), created from

30 time-averaged samples with 1 s of temporal resolution. Planes parallel to the ship deck at dierent heights. Units in m/s. . . 91 6.18 Turbulence intensity at planes parallel to the ship deck. Logarithmic scale. . . 92 6.19 Time-accurate contours of wall shear stress at the port side of the LHA ship.

Units in N/m ² . . . 92 6.20 Time-accurate contours of pressure coecient and velocity magnitude through

the ship centerline. Snapshot at 60 s. . . 93 6.21 Time-averaged contours of pressure coecient, velocity magnitude and root-

mean-square velocity through the ship centerline. . . 93 6.22 Time-accurate results of C p and U contours for plane parallel to ship super-

structure. . . 94 6.23 Time-averaged results of ¯ C _p , ¯ U and U RMS contours for plane parallel to ship

superstructure. . . 94 6.24 Time-accurate results of C p and U contours for plane parallel to location

of ship landing spots. Contours purposefully left without discretisation to highlight small uctuations. . . 95 6.25 Time-averaged results of ¯ C _p , ¯ U and U RMS contours for planes parallel to

location of ship landing spots. Dataset of 30 samples. . . 95 6.26 Time-accurate turbulence uctuations. Snapshot at 60 s. . . 96 6.27 Turbulence intensity (in percentage) of dierent locations on the ship. . . 96 6.28 Vorticity magnitude of ow eld in dierent locations on the ship. Snapshot

at 60 s. . . 97 6.29 Time-accurate pressure coecient at LHA surface and velocity magnitude

through landing spots at time t = 60 s. . . 98 6.30 Time-averaged pressure coecient at LHA surface and mean velocity magni-

tude through landing spots. . . 99 6.31 Dierent structures of burbles for vorticity magnitude of 1 Hz based on mesh

density. Time-accurate snapshot at 60 s. . . 99 6.32 Frontal LHA ship view with volumetric surfaces of vorticity magnitude. Time-

accurate snapshot at 60 s. . . 100 6.33 Frontal view of LHA with volumetric surfaces of vorticity magnitude. Time-

accurate snapshot at 60 s. . . 101 6.34 View of the LHA ship from the port side, with volumetric surfaces of vorticity

magnitude. Time-accurate snapshot at 60 s. . . 102 6.35 Time-averaged vorticity magnitude above the ship deck in 3 m height, clearly

showing the dierent frequency regions. . . 102

6.36 Time-accurate pressure coecient at LHA surface and vorticity magnitude through landing spots at time t = 60 s. . . 103 6.37 Time-averaged pressure coecient at LHA surface and mean vorticity mag-

nitude through landing spots. . . 103 6.38 Temporal evolution of velocity magnitude for all landing spots throughout

the 60 s of simulation time. . . 104 6.39 Histogram showing the distribution of sampling frequencies, with mean value

at approximately 196.99 Hz and median at 184.08 Hz. Values were rounded to 197 Hz and 184 Hz, respectively. . . 105 6.40 Spectrum of velocity magnitude U at all landing spots with FFT. . . 106 6.41 Spectrum of turbulence uctuations at all landing spots with FFT. . . 106 6.42 Power spectral density of the whole range of frequencies of the velocity mag-

nitude. Created with periodogram and with applied hanning window with length of the whole signal (no averaging neither overlapping). . . 107 6.43 Power spectral density of the landing spots based on the Welch's method.

Hanning window with 1/4th of NFFT signal length used (averaging and 50

% signal overlapping). . . 108 6.44 Spectrograms of PSD of turbulence uctuations U ⁰ of all landing spots for

the height of 3 m. . . 109 6.45 PSD of velocity magnitude over line at centerline and through the location of

landing spots. Averaged with hanning window with length of 1/2 of the zero- padded signal length and 50% overlap. Time-accurate frequency spectrum for one snapshot at 60 s shown in the left column. . . 110 6.46 Spectrograms of PSD of velocity magnitude U of all centerline and spotsline

timesteps at the height of 3 m. FFT of each timestep averaged over hanning window with the length of half of zero-padded signal length and with 50%

overlap. . . 110 6.47 PSD of time-averaged velocity magnitude in landing spots with data gathered

through lateral beam wide lines. Welch's method with hanning window and 50% overlap. . . 111 6.48 PSD of time-averaged velocity magnitude in landing spots with data gathered

over lines normal to the ship deck. Welch's method with hanning window and 50% overlap. . . 112 6.49 Comparison of turbulence intensity for the two dierent resolution cases.

Plane follows ship centerline. Legend shows percentage on logarithmic scale. . 113 6.50 U RMS magnitude throughout the ship centerline and location of landing spots.

Full line represents the height of 3 m, while dashed line the height of 6 m. . . 113 6.51 Comparison between the 17.4 million cells and 92.8 million cells in the plane

3 m above the ship deck and parallel to it. Legend shows percentage of tur- bulence intensity on a logarithmic scale. . . 114 6.52 Turbulence intensity throughout the landing spots and ship centerline. Full

line represents the height of 3 m, while dashed line the height of 6 m. . . 114 6.53 Time-averaged velocity magnitude normal to the ship deck. . . 115 6.54 Comparison of time-accurate and time-averaged velocity magnitude, root-

mean-square velocity and turbulence intensity longitudinally throughout the ship centerline and along the location of landing spots. Time-accurate snap- shot at the upper left corner at 60 s. . . 116 6.55 Time-averaged contours of pressure coecient ¯ C p . Normalized with velocity

of 30 knots. . . 117

6.56 Time-averaged contours of wall shear stress ¯τ w at the ship deck. Normalized with velocity of 30 knots. . . 117 6.57 Time-averaged contours of velocity magnitude in planes above the ship deck

(upper row), together with the corresponding turbulence intensity in the same locations (lower row). . . 118 6.58 Time-averaged contours of velocity magnitude (left column) and turbulence

intensity (right column) at dierent planes perpendicular to the ship deck. . . 118 6.59 Velocity magnitude and turbulence intensity gathered laterally over line, beam

wide at all 4 longitudinal locations of landing spots. From left column to right:

spot 2, 4, 7 and 8. Third row represents velocity magnitude prole in direc- tion normal to the ship deck. Data gathered at 3 m and 6 m height for the lateral samples. . . 119 6.60 Visualisation of time-averaged velocity magnitude contours going through

planes parallel to ship deck at dierent locations of landing spots. . . 120 6.61 Visualisation of contours of turbulence intensity going through planes parallel

to ship deck at dierent locations of landing spots. . . 121 6.62 Isosurface contours of vorticity magnitude for value of 2 Hz at snapshot of

60 Hz. . . 121 6.63 Isosurfaces of vorticity showing the \tiny burbles" with magnitude of 2 Hz.

Snapshot at 60 s. . . 122 6.64 Isosurface contours of vorticity magnitude for value of 2 Hz at snapshot of

60 Hz. . . 122 6.65 Evolution of probes at the landing spots locations for height of 3 m and 6 m. . 123 6.66 Spectrum of the U ⁰ probe signal for all landing spots. Second row shows the

PSD through Welch's method of velocity magnitude. . . 123 6.67 Spectrogram of velocity magnitude of the probe signal for all landing spots

at the height of 3 m. . . 124 6.68 Isosurfaces of vorticity magnitude at 60 s for surface value of 2 Hz. . . 124 6.69 Isosurfaces of vorticity magnitude of 2 Hz and isolated view of the superstruc-

ture. Snapshot at 60 s. . . 125 6.70 Time-averaged contours of pressure coecient ¯ C _p . Normalized with velocity

of 30 knots. Sampled over 750 samples. . . 125 6.71 Time-averaged contours of wall shear stress ¯τ w at the ship deck. Normalized

with velocity of 30 knots and sampled over dataset of 750 samples. . . 125 6.72 Time-averaged contours of velocity magnitude in planes above the ship deck,

together with the corresponding turbulence intensity in the same locations. . 126 6.73 Time-averaged contours of velocity magnitude (left column) and turbulence

intensity (right column) at dierent planes perpendicular to the ship deck. . . 127 6.74 Comparison of time-accurate and time-averaged velocity magnitude, root-

mean-square velocity and turbulence intensity longitudinally throughout the ship centerline and along the location of landing spots. Time-accurate snap- shot at 60 s. . . 127 6.75 Visualisation of vorticity magnitude. Snapshot at 60 s. . . 128 6.76 Visualisation of vorticity magnitude. Snapshot at 60 s. . . 128 6.77 Visualisation of time-averaged velocity magnitude contours going through

planes parallel to ship deck at dierent locations of landing spots. . . 129 6.78 Gradient of time-averaged velocity magnitude for cutting plane through land-

ing spot 4. Logarithmic scale showing frequency in Hz. . . 129

6.79 Visualisation of contours of turbulence intensity going through planes parallel to ship deck at dierent locations of landing spots. . . 130 6.80 Time-averaged velocity magnitude and turbulence intensity beam wide over

line. From left column to right: spot 2, 4, 7 and 8. Last row represents the velocity prole in direction normal to the ship deck. . . 130 6.81 Spectrum of turbulence uctuations and PSD of time-accurate velocity mag-

nitude at probe locations. From left column to right: spot 2, 4, 7 and 8. . . . 131 6.82 Spectrogram showing time-frequency space and its evolution. . . 131 6.83 Vorticity magnitude isosurface with treshold value of 2 Hz. Snapshot at 60 s. . 132 6.84 Vorticity magnitude isosurface with treshold value of 2 Hz with focus on the

ship superstructure. Snapshot at 60 s. . . 132 6.85 Time-averaged contours of pressure coecient ¯ C _p . Normalized with velocity

of 30 knots. . . 133 6.86 Time-averaged contours of wall shear stress ¯τ w at the ship deck. Normalized

with velocity of 30 knots. . . 133 6.87 Time-averaged contours of velocity magnitude in planes above the ship deck,

together with the corresponding turbulence intensity in the same locations. . 134 6.88 Gradient of velocity magnitude at cutting plane parallel to the ship deck in

6 m height. . . 134 6.89 Time-averaged contours of velocity magnitude (left column) and turbulence

intensity (right column) at dierent planes perpendicular to the ship deck. . . 135 6.90 Comparison of time-accurate and time-averaged velocity magnitude, root-

mean-square velocity and turbulence intensity longitudinally throughout the ship centerline and along the location of landing spots. Time-accurate snap- shot at 60 s. . . 135 6.91 Visualisation of vorticity magnitude with isosurface treshold value of 2 Hz.

Snapshot at 60 s. . . 136 6.92 Vorticity magnitude isosurface with value of 2 Hz. View at the starboard side

of the superstructure. . . 136 6.93 Visualisation of time-averaged velocity magnitude contours going through

planes parallel to the ship deck at dierent locations of landing spots. . . 137 6.94 Time-averaged velocity magnitude and turbulence intensity beam wide over

line. From left column to right: spot 2, 4, 7 and 8. Last row represents the velocity prole in direction normal to the ship deck. . . 137 6.95 Visualisation of contours of turbulence intensity going through planes parallel

to ship deck at dierent locations of landing spots. . . 138 6.96 Spectrum of turbulence uctuations and PSD of time-accurate velocity mag-

nitude at probe locations. From left column to right: spot 2, 4, 7 and 8. . . . 139 6.97 Spectrogram showing time-frequency space and its evolution. . . 139 6.98 Time-averaged contours of pressure coecient ¯ C p . Normalized with velocity

of 30 knots. . . 140 6.99 Time-averaged contours of wall shear stress ¯τ w at the ship deck. Normalized

with velocity of 30 knots. . . 140 6.100 Comparison of time-accurate and time-averaged velocity magnitude, root-

mean-square velocity and turbulence intensity longitudinally throughout the ship centerline and along the location of landing spots. Time-accurate snap- shot at the upper left corner at 60 s. . . 141 6.101 Magnitude vorticity with surface contours equal to a value of 2 Hz. Snapshot

at 60 s. . . 141

6.102 Isosurface contours of vorticity magnitude for value of 2 Hz at snapshot of 60 Hz. Top view. . . 142 6.103 Time-averaged contours of velocity magnitude in planes above the ship deck,

together with the corresponding turbulence intensity in the same locations. . 142 6.104 Time-accurate turbulence uctuations at the plane parallel to ship deck at

3 m height. . . 143 6.105 Time-averaged contours of velocity magnitude (left column) and turbulence

intensity (right column) at dierent planes perpendicular to the ship deck. . . 143 6.106 Time-averaged velocity magnitude and turbulence intensity beam wide over

line. From left column to right: spot 2, 4, 7 and 8. Last row represents the velocity prole in direction normal to the ship deck. . . 144 6.107 Visualisation of time-averaged velocity magnitude contours. . . 145 6.108 Isosurfaces of vorticity magnitude of 2 Hz and isolated view of the port island

past the superstructure. Snapshot at 60 s. . . 145 6.109 Visualisation of contours of turbulence intensity. . . 146 6.110 Spectrum of turbulence uctuations and PSD of the velocity magnitude. . . . 146 6.111 Spectrogram of trubulence uctuations for probes at the locations of landing

spots. . . 147 6.112 Time-averaged contours of pressure coecient ¯ C p . Normalized with velocity

of 30 knots. . . 147 6.113 Time-averaged contours of wall shear stress ¯τ w at the ship deck. Normalized

with velocity of 30 knots. . . 148 6.114 Isosurfaces of vorticity magnitude of 2 Hz and isolated view of the port island

past the superstructure. Snapshot at 60 s. . . 148 6.115 Time-averaged contours of velocity magnitude in planes above the ship deck,

together with the corresponding turbulence intensity in the same locations. . 149 6.116 Isosurface contours of vorticity magnitude for value of 2 Hz at snapshot of

60 Hz. . . 149 6.117 Comparison of time-accurate and time-averaged velocity magnitude, root-

mean-square velocity and turbulence intensity longitudinally throughout the ship centerline and along the location of landing spots. Time-accurate snap- shot at the upper left corner at 60 s. . . 150 6.118 Isosurfaces of vorticity magnitude of 2 Hz and the view of the whole ship from

the port side. Snapshot at 60 s. . . 150 6.119 Time-averaged contours of velocity magnitude (left column) and turbulence

intensity (right column) at dierent planes perpendicular to the ship deck. . . 151 6.120 Comparison of the apparent height of the enveloping ow. Snapshot at 60 s. . 151 6.121 Visualisation of time-averaged velocity magnitude at the landing spots. . . 152 6.122 Visualisation of turbulence intensity contours at the landing spots. . . 153 6.123 Time-averaged velocity magnitude and turbulence intensity beam wide over

line. From left column to right: spot 2, 4, 7 and 8. Last row represents the velocity prole in direction normal to the ship deck. . . 153 6.124 Spectrum of turbulence uctuations and PSD of the velocity magnitude. . . . 154 6.125 Spectrogram of trubulence uctuations for probes at the locations of landing

spots. . . 154 6.126 Time-averaged contours of pressure coecient ¯ C _p . Normalized with velocity

of 30 knots. . . 155 6.127 Time-averaged contours of wall shear stress ¯τ w at the ship deck. Normalized

with velocity of 30 knots. . . 155

6.128 Time-averaged contours of velocity magnitude in planes above the ship deck, together with the corresponding turbulence intensity in the same locations. . 156 6.129 Contours of vorticity magnitude with surface value of 2 Hz, showing the at-

tached vortex and ow emanating from the port side island. . . 156 6.130 Comparison of time-accurate and time-averaged velocity magnitude, root-

mean-square velocity and turbulence intensity longitudinally throughout the ship centerline and along the location of landing spots. Time-accurate snap- shot at the upper left corner at 60 s. . . 157 6.131 Time-averaged contours of velocity magnitude (left column) and turbulence

intensity (right column) at dierent planes perpendicular to the ship deck. . . 157 6.132 Contours of vorticity magnitude with surface value of 2 Hz. . . 158 6.133 Visualisation of time-averaged velocity at the locations of landing spots. . . . 158 6.134 Contours of vorticity magnitude with surface value of 2 Hz. Red line repre-

sents the transition border. . . 159 6.135 Visualisation of turbulence intensity at the locations of landing spots. . . 159 6.136 Time-averaged velocity magnitude and turbulence intensity beam wide over

line. From left column to right: spot 2, 4, 7 and 8. Last row represents the velocity prole in direction normal to the ship deck. . . 160 6.137 Spectrum of turbulence uctuations and PSD of the velocity magnitude.

From left to right: spot 2, 4, 7 and 8. . . 160 6.138 Spectrogram of turbulence uctuations for probes at the locations of landing

spots. . . 161

List of Tables

1 Dierent mesh densities used for grid independence study. . . 49

1 Boundary conditions for RANS simulations. . . 56

2 Summary for computational statistics for RANS grid convergence cases. . . 57

3 Coordinates of the landing spots. . . 60

4 Summary for computational statistics for varying CFL numbers for the coarsest case of 1 million cells. Maximum simulation time for all cases t = 10 s. Some of the statistics were not retrieved, however the relation stays mostly linear. . . 64

5 Boundary conditions for IDDES simulations. . . 64

6 Summary for computational statistics for IDDES grid convergence cases. Max-

imum simulation time for all cases t = 60 s. . . 65

Nomenclature

ACRONYMS

CFD Computational Fluid Dynamics CFL Courant-Friedrichs-Lewy CPU Central Processor Unit DES Detached Eddy Simulation DDES Detached Eddy Simulation DFT Discrete Fourier Transform FFT Fast Fourier Transform

IDDES Improved Delayed Detached Eddy Simulation ILES Implicit Large Eddy Simulation

LES Large Eddy Simulation LHA Landing Helicopter Assault LHS Left-hand-side

RHS Right-hand-side SA Spalart-Allmaras SFS Simple Frigate Shape SGS Subgrid-scale

SHOL Ship-Helicopter Operating Limits

WOD Wind-Over-Deck

OPERATORS AND FRAME DECORATIONS

Symbol Denition

.. Double dot product

∆ Increment or dierence in the quantity div Divergence operator

h·i Average of a quantity or ltering operation max(·) Maximum value of a quantity

∇· Divergence operator

tr(·) Trace of tensor

LATIN LETTERS

Symbol Denition Unit

A Fluid property {

C _p Pressure coecient {

C CFL Courant-Friedrichs-Lewy number {

C ^k Class of functions smooth up to k-th derivative {

D Drag N

dS Surface element m ²

dS Normal surface element m ²

dV Volume element m ³

∂V Boundary of control volume V m ²

f Sum of all force densities N × m ⁻³

f s Sampling frequency Hz

f _viscous Sum of all viscous force densities N × m ⁻³

F Sum of all forces N

F viscous Sum of all viscous forces N

G Convolution kernel {

I Unity matrix {

k Turbulence kinetic energy m ² × s ⁻²

L box Length scale of the domain m

L _cell Maximum cell edge length m

L _int Integral length scale m

L s Ship length m

m Fluid mass kg

N Natural numbers {

n Normal vector m

N _samples Number of FFT samples {

N t Number of time iterations {

N _x Number of spatial iterations {

N _zp Number of zero-padded FFT samples {

p Pressure Pa

p _T Turbulent pressure Pa

R Real numbers {

Re Reynolds number {

S Surface m ²

T ij Viscous stress tensor Pa

T _sim Simulation time s

t Time s

y _wall First-cell height to surface m

x Coordinate along the x axis m

y Coordinate along the y axis m

z Coordinate along the z axis m

V Velocity vector m × s ⁻¹

V Control volume m ³

u Boundary layer velocity prole m × s ⁻¹

U Freestream velocity m × s ⁻¹

u ⁺ Dimensionless velocity {

y ⁺ Dimensionless wall distance {

u _τ Friction velocity m × s ⁻¹

GREEK LETTERS

Symbol Denition Unit

δ _ij Kronecker delta {

δ Boundary layer displacement thickness m

 Rate of dissipation of turbulence energy m ² × s ⁻³

η K Kolmogorov scale m

λ Bulk viscosity Pa × s

µ Molecular (dynamic) viscosity Pa × s

ν Kinematic viscosity m ² × s ⁻¹

ν _T Turbulent eddy viscosity m ² × s ⁻¹

˜

ν Turbulent eddy viscosity used for Spalart-Allmaras model m ² × s ⁻¹ ω Turbulence energy specic dissipation rate to thermal energy Hz

φ Variable of interest representing uid property {

ρ Density kg × m ⁻³

Σ Total stress tensor Pa × m ⁻¹

Σ _ij Total stress tensor component Pa × m ⁻¹

τ Viscouss stress tensor Pa

τ _ij ^s Wall shear stress Pa

τ w Wall shear stress Pa

θ Boundary layer momentum thickness m

SUBSCRIPTS AND SUPERSCRIPTS

Symbol Denition

∂ _(·) Partial derivation with respect to a coordinate (·) ⁰ Fluctuations or residuals

() i Variable and its i-th coordinate

(·) _n Normal projection

Part I

Theoretical Introduction

Chapter 1

Introduction

The beginning of Landing Helicopter Assault (LHA) ship airwake studies dates to January 1999, in which the V-22 aircraft experienced an uncommanded roll while on the deck of the LHA during compatibility trials, with its rotors turning. Thus began the investigation of rotorcraft/ship interaction, and in the past 18 years, substantial time and eort was dedicated to modeling and analysis of unsteady ship airwakes and their in uence on helicopter shipboard operations.

The ship airwake is an unsteady, vortical, three-dimensional and highly separated ow created by the superstructure and deck of a ship. The importance of the airwake is closely tied with helicopters present in the near region of the ship, as it has tremendous in uence on a dynamic interface (DI) { a coupled relationship between the ship and a rotary aircraft during sea-based launch and recovery operations. The LHA ship and SH-60B Seahawk in DI can be seen in Figure 1.1. The most challenging scenarios are engagement and disengagement of

(a) (b) Source: Polsky et al. [30]

Figure 1.1: USS Saipan (LHA-2) Amphibious Assault Ship (a) and DI (b) in Pacic Ocean (Nov. 10, 2006) - Pilots hover in an SH-60B Seahawk assigned to the "Wolfpack" of Helicopter Anti-Submarine Squadron Light Four Five (HSL-45) while waiting for the perfect time to land aboard the Arleigh Burke-class guided missile destroyer USS Preble (DDG 88) during rough seas.

the rotor system (blade-sailing), takeo, landing and station-keeping (hoovering over a ight

deck). Two primary factors impact the aircraft in DI { the wind-over-deck (WOD) condition

(wind speed and angle) and the ship motion. Additional problems involve coupling of the ship

and rotorcraft wake, changing the fuselage loading, handling loading, aircraft performance and

consequently a pilot workload. It is because of these problems that led to development of safe

helicopter operating limits (SHOL), which are usually dened in terms of WOD envelopes.

Obtaining the WOD envelope is essentially possible with in-situ full-scale measurements, wind tunnel scaled model measurements and computational uid dynamics (CFD) simula- tions. Full-scale experiments can produce highly valuable data, however due to atmospheric conditions, availability of ship personnel, the need of dedicated equipment including specic helicopter type, a pilot trained for DI operations and the need to repeat tests in small numer- ous increments of wind speed and azimuth, these experiments can prove to be costly, limited and arguably unsafe, while still being bounded to a specic helicopter type. Wind tunnel ex- periments can provide good quality data and control over the WOD conditions, however they cannot reproduce the intricate coupling eects between the wake of a ship and rotorcraft, with subsequent performance changes. Due to large ship dimensions, the scaled model required to perform these tests are in the range of 1/100th. Furthermore, since the dimensions change so much, so do some elements of scaled frequencies of the unsteady ow phenomena. The ow separation and vortex structures are also shown to be of larger sizes, and although it has been argued and to some extent shown that Reynolds number independence applies, one should still be careful when interpreting results obtained through such measurements. CFD has proven to be a reliable candidate in the past two decades of ship airwake studies and has the ability to compute both scaled and full-scale solutions, resolve higher unsteady ow frequencies and provide data also for o-body analysis.

However, CFD simulations come with drawbacks of their own, such as mesh generation and turbulence modeling. Complex ship geometries are in many cases the driving factor for their simplication, in order to obtain a satisfactory mesh quality. The mesh resolution is of importance for adequately resolving the smaller vortex structures which are a driving factor for larger eddies, together with the temporal resolution to resolve ow unsteadiness and shedding frequencies. In order to properly resolve higher velocity gradients near walls, an in ation boundary layer has to be dened, which considerably increases the mesh resolution and bounds the upper value of discrete time in order to maintain the Courant-Friedrichs-Lewy (CFL) condition, increasing the computational time considerably. These are the main reasons why CFD simulations of ship airwake are still of concern even today and a very interesting domain of research.

1.1 LITERATURE REVIEW

The very rst common eorts for shipboard launch and recovery simulations were per- formed by Joint Helicopter Integration Process (JSHIP) (Polsky et al. [30]), in the year 2000, as a Joint Test and Evaluation program (JT&E) (Advani et al. [2]), sponsored by the Oce of the Secretary of Defense Deputy Director, Developmental Test and Evaluation. Its spe- cic purpose was to increase the interoperability of joint shipboard operations for helicopter units that are not specically designed to go aboard NAVY ships (e. g. Army and Air Force helicopters). The program consisted of man-in-the-loop ight simulations at NASA Ames Vertical Motion Simulator (VMS), simulating the DI of LHA ship and UH-60 Blackhawk.

At that time, just the stochastic turbulence models were available to represent the ship airwake. Recognizing the importance of ship aerodynamics on pilot workload, the development of temporally and spatially correlated airwake models representative of LHA ship class were undertaken by NAVAIR (Polsky et al. [29]). A database was created that consisted of 15 ^◦ increments in azimuth and integrated into the VMS simulation.

LHA was not the only ship to be studied with regards to airwakes. The Simple Frigate

Shape (SFS) was a collaborative venture set up under the auspices of The Technical Co-

operation Programme (TTCP), in order to develop ship airwake validation database and to

facilitate the dissemination of best-practices amongst the DI simulation community [8, 56].

(a) Type 23 Frigate. (b) Wave Class Auxiliary Oiler.

(c) Canadian Patrol Frigate. (d) Arleigh Burke-class Destroyer.

Figure 1.2: Dierent ship types that were subject to airwake studies over the years.

An updated version, SFS2, incorporated a pointed bow, with National Research Council of Canada performing a series of wind tunnel tests on both geometries [8]. Thornber et al. [52]

examined the Type 23 Frigate and Wave Class Auxiliary Oiler, Lee at al. [18] and Syms [46] studied the Canadian Patrol Frigate (CPF) and Polsky also studied the US Navy DDG Arleigh Burke-class Flight II-A destroyer [27].

SFS and SFS2 in particular were extensively studied by numerous authors in the past, due to the fact that both geometries had an extended validation database with geometries being similar to ships such as LHA. The dierence in both geometries is shown in Figure 1.3.

Liu et al. [21] focused on SFS, and used as one of the rst papers, used some new techniques in order to simulate the airwake unsteadiness, such as the usage of Nonlinear Disturbance Equations (NLDE). These equations were developed from perturbation theory and would be essentially equal to Reynolds Averaged Navier-Stokes if time-averaged. The approach was to

(a) Version 1. (b) Version 2.

Figure 1.3: Simple Frigate Shape (SFS).

Figure 1.4: Dramatic change of the airwake caused by the superstructure of the LHA ship due to various WOD angles. Source:

Polsky et al. [29].

solve for a steady-state solution and use the data for NLDE unsteady simulations. Therefore, two solvers were used; one being the CFL3D developed by NASA Langley and Ames research centers and the other the NLDE. These calculations were conducted at 41 knot wind speed with zero yaw angle and hard wall boundary. Massive recirculation and separation regions with severe reversed ow were observed behind the vertical wall separating the hangar, and even these early studies have shown the highly-unsteady nature of the wake. Fourth-order numerical method was used for both time and space, with Runge-Kutta being the former.

Finite Dierence Method (FDM) was used for discretization of the Navier-Stokes equations spatially for the NLDE solver, whereas Finite Volume Method (FVM) was used for CFL3D.

The grid was structured with roughly two million cells. Simulations for this paper were run in parallel with Message Passing Interface (MPI) and Liu et al. [21] also tested the performance of code on various systems. One of the authors of this paper (Long) also spent three days aboard of USS Saipan (LHA-class ship) and conducted measurements that told of highly unsteady ow over the ship deck, where in some places in the range of 12 feet, velocity ranged from zero up to 40 knots. The results from this paper were later used in [33]. It is important to mention that all the results made in that time for the published paper were for inviscid ows.

One of the rst papers for LHA-class was published in the year 2000 by Polsky et al.

[29], in an attempt to perform time-accurate CFD simulations to characterize the unsteady nature of the airwake created by the superstructure of LHA. After examining a series of WOD conditions, Polsky et al. [29] concluded that the general character of the airwake changes dramatically if the conditions change, as shown in Figure 1.4. The airwake was found to be highly unsteady, with some strongly periodic features present. These simulations were performed at full-scale conditions with second-order time accuracy and the COBALT CFD code on an unstructured grid. The rst wind-tunnel measurements of the LHA ship were also described by Polsky et al. [29], performed on a 1/120 ^th test article. Polsky performed both wind tunnel scale and full-scale CFD simulations, with full-scale WOD conditions of 15 knots and 30 knots and various WOD angles. One of the major contributions by Polsky was a demonstration of Reynolds number independence from 15 knots to 30 knots, however only for starboard 330 ^◦ WOD angles, not including the headwind condition out of concern that reattachment might prove the independence to not be true. This was later disproved in additional paper by Polsky et al. [25] and Reynolds number independence for WOD of 0 ^◦ was proven to hold, however Polsky mentioned that although ow eld remained similar, the velocity traces began to diverge and that vortex shedding frequency is probably dependent to Reynolds scaling to some extent. The only in-situ measurement to date performed was also described in paper by Polsky et al. [25].

Reddy et al. [33] presented results of SFS for steady ow conditions with k −  turbulence

model, where k is the kinetic energy of turbulent uctuations and  is the dissipation per unit mass. The turbulence model was based on Renormalization Group (RNG) method. Reddy used the FLUENT Version 4.3 ¹ solver, which at the time supported only the structured grids, and so was the grid choice for the paper. However, Reddy conducted the CFD analysis of 6 dierent grid resolutions, where he concluded that qualitatively, the ow features of coarser grids were similar to those of more ner grids, however quantitative variations were dierent. In this paper, Reddy also showed dierent steady-state ow features of the SFS ship airwake for dierent WOD conditions. In the conclusion, Reddy compared the results to other simulation [21] and experimental results.

In a paper by Lee et al. [18], a dierent approach is discussed { an experimental wind- tunnel testing of the Sea King helicopter, measuring the unsteady aerodynamic fuselage loads, where the fuselage was immersed both in the downwash of a spinning motor and airwake of Canadian Patrol Frigate (CPF) ship. In these results, it was shown that variation of unsteady loading changed with speed and interaction of the airwake with the rotor downwash. This experiment also showed an interesting fact that the unsteady loading in low hover was on par with the high hover in the case where rotor downwash was incorporated, compared to the rotorless case.

Another study of CPF was conducted by Syms [46]. Syms discussed that larger lengths of turbulence are those that aect the loading and performance of a rotorcraft in maritime operations with capability to change the SHOLs, while the smaller turbulent lengths are viewed only as vibrations. The study compared the experimental data from Zan et al [59] to the computational analysis presented in the paper, for which a Modied CPF (MCPF) model was created in order to better accommodate for the multi-block structured grid generated and for the complexity in the grid structure. The comparison between the CPF and MCPF alongside the measurement volumes is in the Figure 1.5, in order to illustrate what types of simplications take place in practice. The solver used was CFD-ACE { a Finite Volume

(a) CPF. (b) MCPF.

Figure 1.5: The geometry of CPF and MCPF together with the measured volumes. Source: Syms [46].

Method cell-centered solver, using SIMPLEC pressure correction algorithm and second-order upwind scheme to resolve the convective terms in Navier-Stokes equations. The turbulence model applied WAS the k −  model as in [33], however this time with wall-functions and y ⁺ in the range between 10 to 50. The grid was consisting of a little less than million points.

Very good set of validation data including the look at DI of UH-60A Black Hawk helicopter and LHA ship airwake was done by Lee et al. [17]. The airwake calculated with the use of PUMA2 solver was for full 3D both steady and unsteady simulations of ow elds for the LHA geometry to predict the unsteady vortical ow. It is important to say that the simulations assumed inviscid conditions. The grid and DI is visualized in Figure 1.6. Results

1

Current version of the FLUENT software at the time when this document is being written is 18.2.

(a) Plane cuts of the domain showing the unstructured

mesh used for inviscid calculations. (b) Volumetric domain of CFD data for the case of DI simulations.

Figure 1.6: Unstructured mesh of the domain and a visualization of the DI volume. Source: Lee et al. [17].

were integrated into the mathematical model based on GENHEL model, describing the ight dynamics of Black Hawk helicopter. Results had shown that time-varying airwake has visible impact on the aircraft response and pilot control activity, with the dierences most notable if helicopter is operating in or near hover state above the deck of the vessel. Lee also successfully implemented a control model of the human pilot in order to solve the inverse simulation problem. Lee described some practical issues when integrating simulations results to dynamic model, as the model requires a history of every velocity component for every grid point. This can become an issue when talking about the memory storage. Also, for real-time simulations, pilot may want to choose a dierent landing spot on the deck; in that case, Lee argues that the use of stochastic airwake model might be an attractive alternative.

Sezer-Uzol et al. [38] published the results of work that featured an LHA-class and LPD-17 ship airwake simulation and analysis. Unstructured grid on full-scale model was used in order to conduct the CFD calculations. Document covers wide range of topics including the previous work conducted by other researchers. Sezer-Uzol used relative wind speed of 15.43 m/s (30 knots) and several WOD angles. Numerical scheme used for time integration was fourth-order explicit Runge-Kutta with Roe's ux-dierence scheme with CFL numbers of 2.5 and 0.8 for steady and unsteady computations, respectively. This implies that the discretization scheme used was Finite Dierences, with CFL condition needed in order to satisfy the convergence criteria needed by explicit methods. The work focuses on capturing the massively separated ow from sharp edges of blunt bodies while ignoring the viscous eects, therefore presenting only inviscid results both for steady and time-accurate solutions, such as the case of Lee et al. [17]. Solver PUMA2 was written in C++ and the LHA model Sezer-Uzol used was 250 m long and approximately 36 m wide, with the ight deck height of approximately 20 m.

Computational domain is also well described, extending up to 2.4 times in front and aft of the ship length. In total, 6 WOD angles were analyzed.

An extensive study of steady-state simulations had been carried out by Roper et al. [34]

on the SFS and modied SFS (SFS2) geometry and partially validated against wind tunnel

data produced by the National Research Council of Canada (NRC) and according to Roper,

showed a good agreement. The resulting airwake data were interpolated onto suitable grids

and attached to the FLIGHTLAB ight-simulation environment as look-up tables; the Liver-

pool ight full-motion simulator was then used in order to conduct a simulation exercise with

a human pilot to develop the SHOL for a Lynx-like helicopter and the SFS2. A steady-state

SHOL were developed for SFS2/generic helicopter combination, however the lack of unsteadi- ness in the airwake data, together with the simplied ship geometry that was stationary on the sea resulted in lower workloads then normally experienced, however the nature of the airwake and trends of wind strength and direction were, according to Roper, correctly pre- dicted. Roper assumed Reynolds number independence because of the large ship size. The solver used was Fluent with SIMPLEC algorithm for pressure-velocity coupling and the higher order QUICK scheme for momentum and turbulence. The ow was modeled as viscous with the k − ω and k −  model, later compared. The grid was unstructured.

Polsky [26] examined the initial steps taken through the High Performance Computing Modernization Program (HPCMP) Grand Challenge to model the coupled ship and aircraft interface. In the coupled interface problem, the aircraft is no longer simply submerged into unsteady ship airwake, but directly in uences the airwake though motor loading, or dynamic movement, such as approach and landing. This in particular increases the complexity of simulations. Where the former analysis focused on modeling the incompressible unsteady phenomena, such as in [29], this works models coupled interaction in a quasi-steady sense in which the vehicle is moved in incremental steps along an approach path with time-averaged results to produce the aircraft performance data. Work discusses the methodology used, such as the use of commercially available Cobalt and CRUNCH CFD solvers with unstructured grids, where Cobalt is Euler/Navier-Stokes solver optimized to run in parallel environment.

Both codes were running in a laminar mode with no turbulence models applied. However, grid-scale turbulent eddies were modeled using MILES approach. Time steps were chosen based on the physics of the oweld and varied from 0.01 seconds for ship-alone to 0.0009259 seconds for cases modeling blade rotation. Two test cases were selected in order to study the characteristics of unsteady ow over ship acting on the body of the aircraft; the cases being V-22 and F/A-18/CV xed wings, with V-22 having rotorcraft capabilities. For V- 22, examination of a decent from static hover using quasi-steady techniques was conducted.

This included a series of hover heights and WOD of 22 kts, 355 ^◦ using Cobalt. The F/A-18 C/D simulation included a dynamic approach of the aircraft towards to LHA ship. First, the modeling complexity was eased by using quasi-steady aircraft motion and culminating into fully unsteady aircraft motion. In this case, dynamic mesh motion techniques were employed, that included a combination of mesh motion and mesh adaptation techniques.

The visualization of the approaching aircraft is in Figure 1.7 and the work demonstrated the feasibility of coupled ship-aircraft calculations.

(a) Approach at time 0.2 s. (b) Approach at time 0.8 s.

Figure 1.7: Dynamic F/A-18 C/D CFD calculation. Plane colored by velocity magnitude. Source: Polsky et al. [26].

Expanded work on previous SFS calculations was made by Syms [45], in which Syms

examined the aspects of steady and unsteady o-body ow elds of SFS2. The novelty of

this publication is that it features gridless lattice-Boltzmann (LB) method, a completely

dierent approach that does not rely on discretization of the Navier-Stokes equations, but

(a) CFD. (b) Experiment.

Figure 1.8: Streaklines for headwind direction of wind for SFS 1. Source: Syms [45].

uses discrete particles and particle interactions instead. LB is a form of kinetic gas theory operating on microscopic and mesoscopic scales, where paricles are positioned at discrete locations with discrete velocities at discrete intervals. These particles move through the lattice (a so-called advection phase) and then undergo a collision process, which drives the ow towards equilibrium. LB method is therefore a sequence of particle advections and collisions. The solver used to apply the method was PowerFLOW, where it was not feasible to simulate all scales. Therefore, PowerFLOW used VLES approach to turbulence, which simulates resolvable scales and models the unresolved. Syms created the simulations of both SFS 1 and SFS 2 o-body ows, for both 0 ^◦ and 45 ^◦ Yaw angle (headwind and Green 45 { wind from bow-starboard side). In these simulations, he showed the separation of ow from the hangar, reattachment and the creation of horseshoe vertices formed by the shear layer.

These simulations can be seen in Figure 1.8. Syms argues comparison of the CFD results to experimental data shows that lattice-Boltzmann method is a viable candidate to simulate the unsteady ow of an airwake. Syms (same as Polsky et al. [29]) also argued that steady-state solvers are perhaps inappropriate [46] as they do not represent the time-averaged phenomena of the unsteady ow.

Forrest et al. [8] created an important and well-written paper in 2010 that started with introduction to previous studies on the subject. Forrest mentioned that many articles con- tained inadequate validation, where either just qualitative comparison is made [23], turbulent characteristics are neglected [13], or analysis is limited to a single WOD [4, 47]. Publication presented by Forrest focused on DI simulations used Detached-Eddy Simulation (DES) tur- bulence modeling and made a signicant step forward in the application. Forrest claimed that DES simulations are a relatively new approach that is feasible for airwake simulations due to the ability to resolve turbulent structures for massively separated high Reynolds number ows around blu bodies, citing previous publications; comparable to LES, but computationally cheaper and closer to URANS in CPU time. Forrest generated airwake data for University

Figure 1.9: Surface mesh of the SFS 2

geometry. Source: Forrest et al [8].

of Liverpool HELIFLIGHT simulation environment. Simulations presented in the paper were created using nite-volume method within commercial software FLUENT, employing DES with Menter's [32] k − ω Shear Stress Transport (SST) turbulence model for closure. Solver used was pressure-based Navier-Stokes, with second-order interpolation scheme. Convective terms were discretized using third-order Monotone Upstream-centered Schemes for Conserva- tion Laws (MUSCL) scheme [54], which consisted of blended central dierencing/second-order upwind formulation. Time integration was implicit and of second-order with dual time step- ping. Forrest used steady-state solution before the unsteady solver was activated, with a baseline ∆t = 1.88 × 10 ⁻² he had chosen based of [41] and through comparison with non- dimensionalized time-steps used in other DES studies such as [14, 9]. Using mean ow statis- tics, comparison to experimental data showed that changing the time-step had little eect on the solution. However, spectral analysis of velocity uctuations over the ight deck showed that smaller time-steps resolved progressively more energies at frequencies above 10 Hz, with majority of the turbulent energy at full-scale in the range from 0.1 Hz to 1 Hz. However, Forrest mentioned that above 2 Hz, the turbulent uctuations had little eect on the pilot workload [58]. Forrest had chosen 10 iterations per time-step with a motivation that more iteration per time-step did not increase convergence much, however did increase computation time considerably. In order to remove transients before the unsteady simulation was run, 23 time units were computed. The ow statistics were then averaged over next 90 time units.

Complete run took 6000 time-steps, of which 4800 were used for sampling. The domain used for simulations was cylindrical, with radius equal to 4.5 multiples of the length of the ship and depth of 0.75 ship length multiples. Ship surface was modeled with no-slip boundary condition. The grid itself was a hybrid of structured and unstructured approach in order to serve as a validation exercise for DES to be applied to ship airwakes based on mesh for ships with more intricate and complex geometries. The detail of this hybrid grid approach is in Figure 1.9. The unstructured part of the grid was modeled with triangular elements with 15 layers for the viscous boundary layer. Values of y ⁺ were of O(10) normal to the wall with ex- pansion ratio of 1.3. Grid independence was tested in accordance to [41] with a scaling factor of √

2 from baseline spacing ∆ 0 . The test computations were performed for a headwind 40 knots and for dierent spacings, where Forrest found little dierence between the three sizes of grid spacings he used. The medium grid density was selected. Data presented were rstly normalized with respect to the free-stream magnitude and positions were normalized with regards to particular ship dimensions. Experimental data were chosen from the experiments of Aerodynamics Laboratory (AL) of the National Research Council (NRC), Canada, in the 2 m × 3 m wind tunnel, conducted by Cheney et al [5] and Zan [57]. Hot-lm anemometry was used to obtain the u − v and u − w data, which consisted of mean velocities and turbulence intensities along a series of experimental maps over the SFS2. The model of SFS2 was in the scale of 1:100 and how such a model looked like is shown in Figure 1.10.

Figure 1.10: Experimental model of 1:100

scale mounted in NRC 2 m × 3 m low-speed

wind tunnel. Source: Forrest et al [8].