numerical models for sailing yachts: from hull dynamics to ... · pdf filedipartimento di...
TRANSCRIPT
Numerical models for sailing yachts:from hull dynamics to wind/sails FSI
Nicola Parolini, Matteo Lombardi
Dipartimento di MatematicaPolitecnico di Milano
HPC enabling of OpenFOAM for CFD applications
CINECA, Casalecchio di Reno - November 27, 2012
Sport Hydrodynamics: our contribution
America’s Cup Sailing Yachts
Appendage shape optimization
Free-surface hydrodynamics
Sink and trim boat dynamics
(with A. Quarteroni, D. Detomi, S. Piazza, M. Lombardi)
Olympic Rowing Boats
Boat/oar/rower system dynamics
Free-surface hydrodynamics
6-DOF dynamics and control
(with L. Formaggia, E. Miglio, A. Mola, M. Pischiutta)
Swimsuits
Drag reduction
Performance assessment
(with A. Veneziani, E. Foa, F. Biondi)
Collaboration with the Alinghi Design Team
31st America’s Cup
Auckland (NZ), February 2003
Defender: Team New Zealand (NZ)
Challenger: Alinghi (SUI)
Collaboration with the Alinghi Design Team
31st America’s Cup
Auckland (NZ), February 2003
Defender: Team New Zealand (NZ)
Challenger: Alinghi (SUI)
Collaboration with the Alinghi Design Team
31st America’s Cup
Auckland (NZ), February 2003
Defender: Team New Zealand (NZ)
Challenger: Alinghi (SUI)
32nd America’s Cup
Valencia (E), July 2007
Defender: Alinghi (SUI)
Challenger: Team New Zealand (TNZ)
Collaboration with the Alinghi Design Team
31st America’s Cup
Auckland (NZ), February 2003
Defender: Team New Zealand (NZ)
Challenger: Alinghi (SUI)
32nd America’s Cup
Valencia (E), July 2007
Defender: Alinghi (SUI)
Challenger: Team New Zealand (TNZ)
Collaboration with the Alinghi Design Team
31st America’s Cup
Auckland (NZ), February 2003
Defender: Team New Zealand (NZ)
Challenger: Alinghi (SUI)
32nd America’s Cup
Valencia (E), July 2007
Defender: Alinghi (SUI)
Challenger: Team New Zealand (TNZ)
33rd America’s Cup
Valencia (E), February 2010
Defender: Alinghi (SUI)
Challenger: BMW Oracle Racing (USA)
Collaboration with the Alinghi Design Team
31st America’s Cup
Auckland (NZ), February 2003
Defender: Team New Zealand (NZ)
Challenger: Alinghi (SUI)
32nd America’s Cup
Valencia (E), July 2007
Defender: Alinghi (SUI)
Challenger: Team New Zealand (TNZ)
33rd America’s Cup
Valencia (E), February 2010
Defender: Alinghi (SUI)
Challenger: BMW Oracle Racing (USA)
Role of CFD in IACC yacht design
Role of CFD in IACC yacht design
Towing TankWave drag on the
hull
Role of CFD in IACC yacht design
Towing TankWave drag on the
hull
Wind TunnelGlobal forces on sails and
appendages
Role of CFD in IACC yacht design
Towing TankWave drag on the
hull
Wind TunnelGlobal forces on sails and
appendages
Potential FlowInviscid forces on
sails and appendages
Role of CFD in IACC yacht design
Towing TankWave drag on the
hull
Wind TunnelGlobal forces on sails and
appendages
RANS-based CFDViscous and pressureforces on sails and
appendages
Potential FlowInviscid forces on
sails and appendages
Role of CFD in IACC yacht design
Towing TankWave drag on the
hull
Wind TunnelGlobal forces on sails and
appendages
RANS-based CFDViscous and pressureforces on sails and
appendages
Potential FlowInviscid forces on
sails and appendages
For any given design configuration:Experimental tests and CFD simulations on a limited set of boat speed andattitude configurations F (Vi ,Aj );
Data regression on the range of parameters F (V ,A),(Vmin < V < Vmax,Amin < A < Amax);
Compute performance VEq,AEq with a Velocity Prediction Program (VPP).
Role of CFD in IACC yacht design
Towing TankWave drag on the
hull
Wind TunnelGlobal forces on sails and
appendagesVPP
RANS-based CFDViscous and pressureforces on sails and
appendages
Potential FlowInviscid forces on
sails and appendages
For any given design configuration:Experimental tests and CFD simulations on a limited set of boat speed andattitude configurations F (Vi ,Aj );
Data regression on the range of parameters F (V ,A),(Vmin < V < Vmax,Amin < A < Amax);
Compute performance VEq,AEq with a Velocity Prediction Program (VPP).
Velocity Prediction Programs (VPP)
Velocity Prediction Programs (VPP)
Velocity Prediction Programs (VPP)
Velocity Prediction Programs (VPP)
EquilibriumFor a given configuration, the VPP computes boat speed V and attitude A associated tothe force equilibrium state:
M ax = Ta(V ,A)− Dh(V ,A)
M ay = Sa(V ,A)− Sh(V ,A)
I ΩH = MH(V ,A)−MR(V ,A)
Velocity Prediction Programs (VPP)
EquilibriumFor a given configuration, the VPP computes boat speed V and attitude A associated tothe force equilibrium state:
M ax = Ta(V ,A)− Dh(V ,A)
M ay = Sa(V ,A)− Sh(V ,A)
I ΩH = MH(V ,A)−MR(V ,A)
−→
Ta = Dh
Sa = Sh
MH = MR
Velocity Prediction Programs (VPP)
EquilibriumFor a given configuration, the VPP computes boat speed V and attitude A associated tothe force equilibrium state:
M ax = Ta(V ,A)− Dh(V ,A)
M ay = Sa(V ,A)− Sh(V ,A)
I ΩH = MH(V ,A)−MR(V ,A)
−→
Ta = Dh
Sa = Sh
MH = MR
−→ VEq,AEq
Performance evaluation for yacht design
Objective: prediction of aero/hydrodynamic forces
Performance evaluation for yacht design
Objective: prediction of aero/hydrodynamic forces
Wave resistance and boat dynamicsevaluation
Performance evaluation for yacht design
Objective: prediction of aero/hydrodynamic forces
Wave resistance and boat dynamicsevaluation
Laminar-to-turbulent transition regimes onappendages
Performance evaluation for yacht design
Objective: prediction of aero/hydrodynamic forces
Wave resistance and boat dynamicsevaluation
Laminar-to-turbulent transition regimes onappendages
Optimal flying shape of sails
Performance evaluation for yacht design
Objective: prediction of aero/hydrodynamic forces
Wave resistance and boat dynamicsevaluation
Laminar-to-turbulent transition regimes onappendages
Optimal flying shape of sails
Modeling approach:
Multiphase Reynolds-Averaged Navier-StokesEquations
SST k − ω turbulence model
Volume-of-Fluid method for interfacecapturing
Dynamical system for 6DOF boat motion
Fluid-structure interaction for sails
WIND/SAILS FSI
FREE-SURFACE HYDRODYNAMICS
APPENDAGE OPTIMIZATION
WIND/SAILS FSI
Wind/Sails Fluid-Structure interaction
Determination of the flying sail shape is crucial for per-formance evaluation
In Upwind sailing flow is mainly attached
Potential flow model can be adopted
FSI coupling between a sail structural model andpanel method
In Downwind sailing flow is stronglyseparated
Flow around gennaker/spinnaker needsviscous RANS solutions
Development of a RANS based FSIalgorithm required
Wind/Sails FSI: coupling algorithm
FSI problem as a fixed-point:
Fluid(Struct(p)) = pFluid : fluid operator
Struct : structural operator
Given a pressure field pk , the fixed point iteration reads:
(Gk+1,Uk+1) = Struct(pk )
pk+1 = Fluid(Gk+1,Uk+1)
pk+1 = (1− θk )pk + θk pk+1
Steady algorithm
Interest only on converged steadysolution
Sail velocity (Uk+1) set to zero inflow solver
Less FSI iterations required
Steady solution may not be physical
Unsteady algorithm
Interest on transient solution
Unsteady flow solver required
Moving wall BC (Uk+1) in flowsolver
More FSI iterations required
Commercial software integration: the Virtual Wind Tunnel
Simulation of downwind sails: steady algorithm
Analysis of different sail shapesand trimmings
Changing sail trimming, the flowfield can dramatically change
Optimal trimming identification
0
2000
4000
6000
8000
10000
12000
14000
-2 -1.5 -1 -0.5 0 0.5 1
Fx [N
]
Genn Sheet Trimming [m]
MainGennakerTotal Force
Gennaker Sheet Trimming GS=-1 m
Simulation of downwind sails: steady algorithm
Analysis of different sail shapesand trimmings
Changing sail trimming, the flowfield can dramatically change
Optimal trimming identification
0
2000
4000
6000
8000
10000
12000
14000
-2 -1.5 -1 -0.5 0 0.5 1
Fx [N
]
Genn Sheet Trimming [m]
MainGennakerTotal Force
Gennaker Sheet Trimming GS=0.5 m
Wind/Sails FSI: open-source development
Fluid finite-volume model (OpenFOAM)
RANS equations with k − ω turbulence model
SIMPLE/PISO schemes for steady/transient solutions
Shell finite element model
SEDIS solverdeveloped at DIS, Politecnico diMilano (Prof. U. Perego)
MITC4 shell elements (Locking-free)
linear isotropic material
no need for wrinkle model
explicit in time
Fortran with OpenMP
h
Wind/Sails FSI: shell structure solver
Sail wrinkling detected loading the structure with a constant pressure field
Test case proposed in Fluid-structure interactions of anisotropic thin composite
materials for application to sail aerodynamics of a yacht in waves, Trimarchi, D.,Turnock, S.R., Chapelle, D. and Taunton, D. (2009).
Wind/Sails FSI: modelling
Wind/Sails FSI: modelling
A COUPLED PROBLEM !
Wind/Sails FSI: possible coupling strategies
MONOLITHIC APPROACH
Wind/Sails FSI: possible coupling strategies
MONOLITHIC APPROACH
Better stability properties
Wind/Sails FSI: possible coupling strategies
MONOLITHIC APPROACH
Better stability properties
Full matrix (fluid+structure)
Wind/Sails FSI: possible coupling strategies
MONOLITHIC APPROACH
Better stability properties
Full matrix (fluid+structure)
Large memory requirements
Wind/Sails FSI: possible coupling strategies
MONOLITHIC APPROACH
Better stability properties
Full matrix (fluid+structure)
Large memory requirements
PARTITIONED APPROACH
Wind/Sails FSI: possible coupling strategies
MONOLITHIC APPROACH
Better stability properties
Full matrix (fluid+structure)
Large memory requirements
PARTITIONED APPROACH
Modular approach
Wind/Sails FSI: possible coupling strategies
MONOLITHIC APPROACH
Better stability properties
Full matrix (fluid+structure)
Large memory requirements
PARTITIONED APPROACH
Modular approach
Reuse of existing software
Wind/Sails FSI: possible coupling strategies
MONOLITHIC APPROACH
Better stability properties
Full matrix (fluid+structure)
Large memory requirements
PARTITIONED APPROACH
Modular approach
Reuse of existing software
Weakly Coupled
Efficient (1 flow and 1structure solution per timestep)
Can be unstable
Wind/Sails FSI: possible coupling strategies
MONOLITHIC APPROACH
Better stability properties
Full matrix (fluid+structure)
Large memory requirements
PARTITIONED APPROACH
Modular approach
Reuse of existing software
Weakly Coupled
Efficient (1 flow and 1structure solution per timestep)
Can be unstable
Strongly Coupled
Subiterations andrelaxation
Better stability
Wind/Sails FSI: strongly coupled segregated scheme
Structural problem:
Mesh motion problem:
Flow problem:
Wind/Sails FSI: strongly coupled segregated scheme
Wind/Sails FSI: strongly coupled segregated scheme
Convergence test
Wind/Sails FSI: strongly coupled segregated scheme
Convergence test Number of FSI iterations
material properties
deformation magnitude
relaxation scheme
Wind/Sails FSI: implementation
Shell structural solver
• Explicit scheme =⇒ Many sub-time steps required to coverone fluid step
Wind/Sails FSI: implementation
Shell structural solver
• Explicit scheme =⇒ Many sub-time steps required to coverone fluid step
• Fortran code =⇒ OF is master, Fortran routine calledinside OF with fortran/c++ wrappers
Wind/Sails FSI: implementation
Shell structural solver
• Explicit scheme =⇒ Many sub-time steps required to coverone fluid step
• Fortran code =⇒ OF is master, Fortran routine calledinside OF with fortran/c++ wrappers
• OpenMP =⇒ OF Master node calls structural solverwhile other CPUs are idle
Wind/Sails FSI: implementation
Shell structural solver
• Explicit scheme =⇒ Many sub-time steps required to coverone fluid step
• Fortran code =⇒ OF is master, Fortran routine calledinside OF with fortran/c++ wrappers
• OpenMP =⇒ OF Master node calls structural solverwhile other CPUs are idle
⇓Whit more than one sail, structuralsolvers can be run in parallel
Wind/Sails FSI: implementation
Non-conforming mesh (FV/FEM)
different grids
different collocations of DOF
interface interpolation (RBF)
Wind/Sails FSI: implementation
Non-conforming mesh (FV/FEM)
different grids
different collocations of DOF
interface interpolation (RBF)
Mesh motion
moving 3D fluid grid (ALE)
large displacement
different possible approaches:
LaplacianRadial basis function (RBF)Inverse distance weighting (IDW)
RBF: an overview
Global map from a set of control points Cj :
f (x) =
NC∑
j=1
γjφ(|x− xCj|) + q(x),
φ(·): radial basis (based on Euclidean distance)q: additional polynomial term
Imposing
exact mapping of control points f (xCj) = fCj
exact mapping of rigid body motions[BCC PC
PTC 0
] [γ
β
]
=
[fC0
]
RBF: interpolation
General RBF interpolation formula:
fI = [BIC PI ]︸ ︷︷ ︸
RIC
[γ
β
]
= [BIC PI ]
[BCC PC
PTC 0
]−1
︸ ︷︷ ︸
R−1CC
[fC0
]
= HIC fC
Interpolation of displacement from structure (DS) to fluid (DF )
DF = [BFS PF ]︸ ︷︷ ︸
RFS
[γ
β
]
= [BFS PF ]
[BSS PS
PTS 0
]−1
︸ ︷︷ ︸
R−1SS
[DS
0
]
= HFSDS
Control points: structural nodesInterpolation points: fluid nodes
FSI: energy conservation
Exact energy transfer at the interface requires
WS(d) =
∫
Γ
(σSdS) · d =
∫
Γ
(σFdF ) · d = WF (d), ∀ d,
Numerically, the following stress transfer is obtained
ΣS = M−1S H
TFSMFΣF ,
For a finite-element structural solver, we need:
∫
S
(σ · n)ψj =
∫
S
∑
i
(σ · n)iψiψj =⇒ MSΣS = HTFSMFΣF ,
RBF implementation improvements
Optimized libraries for LU factorization
Method OpenFOAM Boost ATLAS
NC = 1925 34.54 19.20 3.08NC = 2850 73.72 60.11 9.29
RBF implementation improvements
Optimized libraries for LU factorization
Method OpenFOAM Boost ATLAS
NC = 1925 34.54 19.20 3.08NC = 2850 73.72 60.11 9.29
... and matrix-vector multiplications (with ATLAS)
# proc. 2 4 8 16
Time (s.) 0.44 0.24 0.13 0.07
Each partition moves its own points and evaluates the local stress contribution:
MSΣS = HTFSMFΣF =
Np∑
k
HTFkS
MFkΣFk
Mesh motion: Laplacian
Mesh motion based on the solution ofa Laplace problem
∇ · (γM∇d) = 0, in Ω,
d = d, on ∂ΩM ,
d = 0, on ∂ΩF ,
γM : variable artificial diffusion coefficient
inversely proportional to cell element size
inversely proportional to distance from moving patches
Mesh motion: RBF
Same RBF map defined for the interface interpolation
more interpolation points (all the 3d mesh points)
very large linear system to solve
to reduce the computational cost
some sampling of the control points (e.g. only one every N points)smooth cut-off function
Mesh motion: IDW
Inverse Distance Weighting (IDW) for multivariate interpolation.
Interpolation map: d(x) =∑NC
i=1|x−xi |
−pdi∑NCi=1
|x−xi |−p
, p = 2, 3, 4 usually
no linear system to solve
large matrix: # surface mesh points × # volume mesh points
local smooth cut-off functions to reduce computational cost
FSI: mesh motion
Laplacian: unsuccessful
RBF: too expensive
IDW: used in most simulations
FSI: benchmark test case
assessment of FSI algorithmsnot easy
comparison with availablebenchmark test cases
grid and time-step convergence
Wind/sail FSI: one sail setup
5.48%
&%U%Boat%
155°%
Wind/sail FSI: one sail simulations
Intial transient due to non-equilibriuminitial configuration
Flow pushing on the edges of the sailbefore starting to stabilize
Wind/sail FSI: one-sail simulations - steady vs transient
Different possible approaches:1 Fully Transient
transient flow solution (PISO scheme)transient structure solutionmany FSI iterations for convergence (50-60)
2 Pseudo Transient
transient FSI solutionbut zero-velocity imposed on the sailfaster convergence (6-8 FSI iterations)smoother flow evolution
3 Steady
alternate steady flow solution (SIMPLE) and steady structuresolutiondisplacement from steady structural solver may be largedisplacement distributed over N sub-stepsmuch faster convergence, meaningful for steady physical solution
Wind/sail FSI: one-sail simulations - steady
Pseudo-Transient vs. Steadymean forces and sail flying shapes veryclose
steady converges to a non oscillatingsolution
Wind/sail FSI: one-sail simulations - transient
Lower gennaker corner attachedto a sheeting rope (i.e. free tomove on a spherical path if undertension)
Pressure waves propagates fromthe corners (fixed and attachedto the sheet)
Wind/sail FSI: one-sail simulations - transient
Wind/sail FSI: two-sail simulations - steady
Different trimming of the gennaker (5m, 6m, 7m, 8m)
Wind/sail FSI: two-sail simulations - steady vs transient
Steady FSI (8 m) Transient FSI (8 m)
Wind/sail FSI: two-sail simulations - transient
1 initial large motion of sheet-attached vertex
2 when sail seems to collapse inward, the sheet gets under tension and sailrecovers
3 sail finally collapses inward due to the too open trimming
Wind/sail FSI: real-life instability
Wind/sail FSI: computational cost
Typical case size:
Fluid: 1.8M elements on 32 cores with MPI
Structure: 1800 nodes on 8 cores with OpenMP
Wind/sail FSI: computational cost
Typical case size:
Fluid: 1.8M elements on 32 cores with MPI
Structure: 1800 nodes on 8 cores with OpenMP
One FSI iteration timing:
Fluid solver =⇒ 8 s (44%)
Mesh motion =⇒ 3 s (17%)
Structural solver =⇒ 5 s (27%)
Other =⇒ 2 s (12%)
Wind/sail FSI: computational cost
Typical case size:
Fluid: 1.8M elements on 32 cores with MPI
Structure: 1800 nodes on 8 cores with OpenMP
One FSI iteration timing:
Fluid solver =⇒ 8 s (44%)
Mesh motion =⇒ 3 s (17%)
Structural solver =⇒ 5 s (27%)
Other =⇒ 2 s (12%)
Fluid/FSI cost comparison:
NS transient solver: 8 s per time step
FSI solver: 18 s × 30=540 s per time step (×70 !)
Wind/sail FSI: computational cost
Typical case size:
Fluid: 1.8M elements on 32 cores with MPI
Structure: 1800 nodes on 8 cores with OpenMP
One FSI iteration timing:
Fluid solver =⇒ 8 s (44%)
Mesh motion =⇒ 3 s (17%)
Structural solver =⇒ 5 s (27%)
Other =⇒ 2 s (12%)
Fluid/FSI cost comparison:
NS transient solver: 8 s per time step
FSI solver: 18 s × 30=540 s per time step (×70 !)
GPU acceleration:
GPU implementation of mesh motion
Hybrid GPU/CPU implementation of structural solver
(Andrea Bartezzaghi’s Master thesis)
FREE-SURFACE HYDRODYNAMICS
Flow equations
Flow equations
Navier–Stokes equations
ρi∂tui + ρi (ui ·∇)ui −∇ · Ti (ui , pi ) = ρig, in Ωi
∇ · ui = 0,
with Ti (ui , pi ) = (µi + µt i )(∇ui +∇uiT )− pi I.
O2
O1
Gt
Flow equations
Navier–Stokes equations
ρi∂tui + ρi (ui ·∇)ui −∇ · Ti (ui , pi ) = ρig, in Ωi
∇ · ui = 0,
with Ti (ui , pi ) = (µi + µt i )(∇ui +∇uiT )− pi I.
O2
O1
Gt
Interface conditions
u1 = u2, on Γ,
T1 · n = T2 · n+ κσn on Γ.
Flow equations
Navier–Stokes equations
ρi∂tui + ρi (ui ·∇)ui −∇ · Ti (ui , pi ) = ρig, in Ωi
∇ · ui = 0,
with Ti (ui , pi ) = (µi + µt i )(∇ui +∇uiT )− pi I.
O2
O1
Gt
Interface conditions
u1 = u2, on Γ,
T1 · n = T2 · n+ κσn on Γ.
One-fluid formulation
∂tρ+ u · ∇ρ = 0,
ρ∂tu+ ρ(u ·∇)u−∇ · T(u, p) = ρg + fΓ, in Ω
∇ · u = 0,
with T(u, p) = (µ+ µt)(∇u+∇uT )− pI.
Flow equations
Navier–Stokes equations
ρi∂tui + ρi (ui ·∇)ui −∇ · Ti (ui , pi ) = ρig, in Ωi
∇ · ui = 0,
with Ti (ui , pi ) = (µi + µt i )(∇ui +∇uiT )− pi I.
O2
O1
Gt
Interface conditions
u1 = u2, on Γ,
T1 · n = T2 · n+ κσn on Γ.
One-fluid formulation
∂tρ+ u · ∇ρ = 0,
ρ∂tu+ ρ(u ·∇)u−∇ · T(u, p) = ρg + fΓ, in Ω
∇ · u = 0,
with T(u, p) = (µ+ µt)(∇u+∇uT )− pI.
ρ = ρ(x)
µ = µ(x)
Flow equations
Navier–Stokes equations
ρi∂tui + ρi (ui ·∇)ui −∇ · Ti (ui , pi ) = ρig, in Ωi
∇ · ui = 0,
with Ti (ui , pi ) = (µi + µt i )(∇ui +∇uiT )− pi I.
O2
O1
Gt
Interface conditions
u1 = u2, on Γ,
T1 · n = T2 · n+ κσn on Γ.
One-fluid formulation
∂tρ+ u · ∇ρ = 0,
ρ∂tu+ ρ(u ·∇)u−∇ · T(u, p) = ρg + fΓ, in Ω
∇ · u = 0,
with T(u, p) = (µ+ µt)(∇u+∇uT )− pI.
ρ = ρ(x)
µ = µ(x)
fΓ = κσδΓn
Flow equations
Navier–Stokes equations
ρi∂tui + ρi (ui ·∇)ui −∇ · Ti (ui , pi ) = ρig, in Ωi
∇ · ui = 0,
with Ti (ui , pi ) = (µi + µt i )(∇ui +∇uiT )− pi I.
O2
O1
Gt
Interface conditions
u1 = u2, on Γ,
T1 · n = T2 · n+ κσn on Γ.
One-fluid formulation
∂tρ+ u · ∇ρ = 0,
ρ∂tu+ ρ(u ·∇)u−∇ · T(u, p) = ρg + fΓ, in Ω
∇ · u = 0,
with T(u, p) = (µ+ µt)(∇u+∇uT )− pI.
ρ = ρ(x)
µ = µ(x)
fΓ = κσδΓn
Initial and boundaryconditions for u and ρ
Boat dynamics
Boat reference (Gc ; x, y, z) Global reference (O; X , Y , Z)
Rotation matrix
R =
cos θ cosψ sinφ sin θ cosψ − cosφ sinψ cosφ sin θ cosψ + sinφ sinψcos θ cosψ sinφ sin θ sinψ + cosφ cosψ cosφ sin θ sinψ − sinφ cosψ− sin θ sinφ cos θ cosφ cos θ
Boat tensor of inertia
IG =
Ixx Ixy IxzIyx Iyy IyzIzx Izy Izz
referred to the body-fixed reference system
Boat dynamics
Linear and angular momentum in the inertial reference system:
mXG = F
RIGR−1
ω + ω ×RIGR−1
ω = MG
Time integration on the system of first order ODE
mYG = F,
XG = YG ,
Adam-Bashforth scheme for the velocity
Yn+1 = Yn +∆t
2m(3Fn − Fn−1),
Crank-Nicolson scheme for the position of the center of mass
Xn+1 = Xn +∆t
2(Yn+1 + Yn).
Dynamical system coupled with the flow solver on a moving domain (in ALEframework).
Dynamics in wavy sea
Wave boundary condition at inlet
Seakeeping analysis in wavy seacan be performed
Dynamic response of the boat fordifferent wave lenghts andamplitudes
Maximum sink vs wave frequency
Free-surface simulation for AC32 and AC33
AC32
Free-surface simulation for AC32 and AC33
AC32
AC33
Free-surface simulation for AC32 and AC33
AC32
AC33
Free-surface solver in OpenFOAM
interFoam class solver
Validation on benchmark cases
Coupling with dynamic module
Implementation of external wavemodel
-0.015
-0.01
-0.005
0
0.005
0.01
0.015
0 0.2 0.4 0.6 0.8 1
Wave e
levation [m
]
X [m]
CoarseMedium
FineExp.
5
6
7
8
9
10
11
12
0 5 10 15 20 25 30D
rag
[N
]Time [s]
Wavy seaFlat sea
-15
-10
-5
0
5
10
15
0 5 10 15 20 25 30
Pitch
ing
Mo
me
nt
[Nm
]
Time [s]
Wavy seaFlat sea
VOF model in interFoam
VOF uses a scalar indicator function to represent the phase of the fluid in each cell
α = α(x, t)
µ(x, t) = µwα+ µa(1− α)
ρ(x, t) = ρwα+ ρa(1− α)
density and viscosity (and, therefore α) are material properties of the fluids:
Dα
Dt= 0 →
∂α
∂t+ u · ∇α = 0 →
∂α
∂t+∇ · (uα) = 0
to keep the interface sharp, consider a modified governing equation
∂α
∂t+∇ · (uα) +∇ · (wα(1− α)) = 0
with w an artificial velocity field oriented normal to and towards the interface.
the relative magnitude of the artificial velocity can be changed (parameter cAlpha)
the α equation is solved using MULES (Multidimensional Universal Limiter withExplicit Solution) method
VOF model in interFoam
Ansys CFX (homogeneous) interFoam
CFX/OpenFOAM for AC33
Experimental vs. numerical drag prediction at different boat speeds
Automated Mesh Generation: snappyHexMesh
blockMesh+ STL geometry
Automated Mesh Generation: snappyHexMesh
blockMesh+ STL geometry
castellatedMesh
Automated Mesh Generation: snappyHexMesh
blockMesh+ STL geometry
castellatedMesh
snap
Automated Mesh Generation: snappyHexMesh
blockMesh+ STL geometry
castellatedMesh
snap
snapEdge (in SHM since v2.0)
Automated Mesh Generation: snappyHexMesh
blockMesh+ STL geometry
castellatedMesh
snap
snapEdge (in SHM since v2.0)
refineMesh
Automated Mesh Generation: snappyHexMesh
blockMesh+ STL geometry
castellatedMesh
snap
snapEdge (in SHM since v2.0)
refineMesh
addLayers
snappyHexMesh: a more complex example
ad-hoc setup of snappyHexMesh
uniform refinement level over surfaces for layers
avoid non-conforming refinement in free-surface region
smooth refinement layer transition
snappyHexMesh: a more complex example
ad-hoc setup of snappyHexMesh
uniform refinement level over surfaces for layers
avoid non-conforming refinement in free-surface region
smooth refinement layer transition
snappyHexMesh: a more complex example
ad-hoc setup of snappyHexMesh
uniform refinement level over surfaces for layers
avoid non-conforming refinement in free-surface region
smooth refinement layer transition
snappyHexMesh: a more complex example
ad-hoc setup of snappyHexMesh
uniform refinement level over surfaces for layers
avoid non-conforming refinement in free-surface region
smooth refinement layer transition
snappyHexMesh: a more complex example
ad-hoc setup of snappyHexMesh
uniform refinement level over surfaces for layers
avoid non-conforming refinement in free-surface region
smooth refinement layer transition
APPENDAGE OPTIMIZATION
Results on appendage design
Simulation campaign on all theappendage components at differentsailing regimes
Parametric studies on different designchoices
Investigation on radical new shapes
Results on appendage design
Simulation campaign on all theappendage components at differentsailing regimes
Parametric studies on different designchoices
Investigation on radical new shapes
Turbulent and transition models requireshighly refined block structured grids(Y+ ≈ 1)
Postprocessing for detection of local flowfeatures (separation and vortices)
Shape optimization: possible strategies
Continuous adjoint approach in OpenFOAM
Drag Minimization
J = −
∫ΓBody
(2νσ(u)n − pn) · ufdγ
Gbody
O
Gin Gout
Continuous adjoint approach in OpenFOAM
Steady Navier-Stokes equations
(u · ∇)u − ∇ · (νσ(u)) + ∇p = 0 in Ω
∇ · u = 0 in Ω
u = uf on ΓIn
u = 0 on ΓBody
−2νσ(u)n + pn = 0 on ΓOut
Drag Minimization
J = −
∫ΓBody
(2νσ(u)n − pn) · ufdγ
Gbody
O
Gin Gout
Continuous adjoint approach in OpenFOAM
Steady Navier-Stokes equations
(u · ∇)u − ∇ · (νσ(u)) + ∇p = 0 in Ω
∇ · u = 0 in Ω
u = uf on ΓIn
u = 0 on ΓBody
−2νσ(u)n + pn = 0 on ΓOut
Adjoint problem
(∇Tv)u − (u · ∇)v − ∇ · (2νσ(v)) + ∇q = 0 in Ω
∇ · v = 0 in Ω
v = −uf on ΓBody
v = 0 on ∂Ω \ ΓBody
Drag Minimization
J = −
∫ΓBody
(2νσ(u)n − pn) · ufdγ
Gbody
O
Gin Gout
Continuous adjoint approach in OpenFOAM
Steady Navier-Stokes equations
(u · ∇)u − ∇ · (νσ(u)) + ∇p = 0 in Ω
∇ · u = 0 in Ω
u = uf on ΓIn
u = 0 on ΓBody
−2νσ(u)n + pn = 0 on ΓOut
Adjoint problem
(∇Tv)u − (u · ∇)v − ∇ · (2νσ(v)) + ∇q = 0 in Ω
∇ · v = 0 in Ω
v = −uf on ΓBody
v = 0 on ∂Ω \ ΓBody
Shape gradient
∇J = −(2νσ(u) : σ(v))n
Drag Minimization
J = −
∫ΓBody
(2νσ(u)n − pn) · ufdγ
Gbody
O
Gin Gout
Continuous adjoint approach in OpenFOAM
Steady Navier-Stokes equations
(u · ∇)u − ∇ · (νσ(u)) + ∇p = 0 in Ω
∇ · u = 0 in Ω
u = uf on ΓIn
u = 0 on ΓBody
−2νσ(u)n + pn = 0 on ΓOut
Adjoint problem
(∇Tv)u − (u · ∇)v − ∇ · (2νσ(v)) + ∇q = 0 in Ω
∇ · v = 0 in Ω
v = −uf on ΓBody
v = 0 on ∂Ω \ ΓBody
Shape gradient
∇J = −(2νσ(u) : σ(v))n
Drag Minimization
J = −
∫ΓBody
(2νσ(u)n − pn) · ufdγ
Gbody
O
Gin Gout
Volume constraint
augmented Lagrangianmethod
a-posteriori correction
Shape parametrization: FFD method
Sensitivity field V:
move the mesh points according to V
project V on a shape parametrization
Shape parametrization: FFD method
Sensitivity field V:
move the mesh points according to V
project V on a shape parametrization
Free-Form Deformation
Th
psi invpsi
P Pt
T
Omega Omegat
D
Shape parametrization: FFD method
Sensitivity field V:
move the mesh points according to V
project V on a shape parametrization
Free-Form Deformation
Map Ψ : (x1, x2) −→ (s, t) such that Ψ(D) = (0, 1)2, with Ω ⊂ D
Th
psi invpsi
P Pt
T
Omega Omegat
D
Shape parametrization: FFD method
Sensitivity field V:
move the mesh points according to V
project V on a shape parametrization
Free-Form Deformation
Map Ψ : (x1, x2) −→ (s, t) such that Ψ(D) = (0, 1)2, with Ω ⊂ D
Control points: Pol,m(µl,m) = Pl,m + µl,m
Th
psi invpsi
P Pt
T
Omega Omegat
D
Shape parametrization: FFD method
Sensitivity field V:
move the mesh points according to V
project V on a shape parametrization
Free-Form Deformation
Map Ψ : (x1, x2) −→ (s, t) such that Ψ(D) = (0, 1)2, with Ω ⊂ D
Control points: Pol,m(µl,m) = Pl,m + µl,m
FFD map: T (x;µ) = Ψ−1(
∑Ll=0
∑Mm=0 b
L,Ml,m
(Ψ(x))Pol,m(µl,m)
)
Th
psi invpsi
P Pt
T
Omega Omegat
D
Shape parametrization: FFD method
Sensitivity field V:
move the mesh points according to V
project V on a shape parametrization
Free-Form Deformation
Map Ψ : (x1, x2) −→ (s, t) such that Ψ(D) = (0, 1)2, with Ω ⊂ D
Control points: Pol,m(µl,m) = Pl,m + µl,m
FFD map: T (x;µ) = Ψ−1(
∑Ll=0
∑Mm=0 b
L,Ml,m
(Ψ(x))Pol,m(µl,m)
)
Deformed domain: Ωo(µ) = T (Ω;µ), with T = T |Ω
Th
psi invpsi
P Pt
T
Omega Omegat
D
Shape optimization: 2D test case
Drag minimization of an airfoil
Initial shape NACA0030
Re=1000
0.17
0.18
0.19
0.2
0.21
0.22
0.23
0.24
0.25
0 10 20 30 40 50
Cd
Iteration
Drag coefficient
Velocity Velocity Adjoint Velocity
Initial geometry Final shape Final Shape
Shape optimization: 3D test case
only very preliminary results obtained
difficult extension to turbulent flows
Dakota/OpenFOAM integration
Dakota library (developed at Sandia Labs)
open-source multiobjctive optimization softwaredifferent optimization algorithms (gradient-based and not)tools for sensitivity analysis and robust design
Integration with external software (e.g. OpenFOAM) based on scripts
Simple example: bulb shape optimization
bulb drag minimization
fixed righting moment constraint
3 global design parameters controlling:
section aspect ratiomean camber linesection CG position
D
W
H
ReferenceconfigurationP1 = P2 = P3 = 0
Simple example: bulb shape optimization
bulb drag minimization
fixed righting moment constraint
3 global design parameters controlling:
section aspect ratiomean camber linesection CG position
D
W
H
Aspect RatioP1 = P1,min = −0.3
Simple example: bulb shape optimization
bulb drag minimization
fixed righting moment constraint
3 global design parameters controlling:
section aspect ratiomean camber linesection CG position
D
W
H
Aspect RatioP1 = P1,max = 0.3
Simple example: bulb shape optimization
bulb drag minimization
fixed righting moment constraint
3 global design parameters controlling:
section aspect ratiomean camber linesection CG position
D
W
H
Mean CamberP2 = P2,min = −0.4
Simple example: bulb shape optimization
bulb drag minimization
fixed righting moment constraint
3 global design parameters controlling:
section aspect ratiomean camber linesection CG position
D
W
H
Mean CamberP2 = P2,max = 0.4
Simple example: bulb shape optimization
bulb drag minimization
fixed righting moment constraint
3 global design parameters controlling:
section aspect ratiomean camber linesection CG position
D
W
H
Section CGP3 = P3,min = −0.4
Simple example: bulb shape optimization
bulb drag minimization
fixed righting moment constraint
3 global design parameters controlling:
section aspect ratiomean camber linesection CG position
D
W
H
Section CGP3 = P3,max = −0.4
Simple example: bulb shape optimization
bulb drag minimization
fixed righting moment constraint
3 global design parameters controlling:
section aspect ratiomean camber linesection CG position
D
W
H
Optimalconfigurationfor draft D=4 m
Simple example: bulb shape optimization
bulb drag minimization
fixed righting moment constraint
3 global design parameters controlling:
section aspect ratiomean camber linesection CG position
D
W
H
Optimalconfigurationfor draft D=2 m
Simple example: bulb shape optimization
bulb drag minimization
fixed righting moment constraint
3 global design parameters controlling:
section aspect ratiomean camber linesection CG position
D
W
H
Optimalconfigurationfor draft D=2 m
(Vittorio Bissaro’s Master thesis)
FREE-SURFACE HYDRODYNAMICS
APPENDAGE OPTIMIZATION
WIND/SAILS FSI
Integration of numerical tools for sailing yacht simulation
Full boat simulations
Integrate different models:
free-surface flow solver
rigid boat motion
wind/sail fluid-structure interaction
longitudinal motion (surge) treated withnon-inertial reference system
Different possible approaches:
one single domain
decoupling hydro and aero domains withsuitable domain interface conditions
Full boat simulations
Integrate different models:
free-surface flow solver
rigid boat motion
wind/sail fluid-structure interaction
longitudinal motion (surge) treated withnon-inertial reference system
Different possible approaches:
one single domain
decoupling hydro and aero domains withsuitable domain interface conditions
Full boat simulations
Integrate different models:
free-surface flow solver
rigid boat motion
wind/sail fluid-structure interaction
longitudinal motion (surge) treated withnon-inertial reference system
Different possible approaches:
one single domain
decoupling hydro and aero domains withsuitable domain interface conditions
Full boat simulations
Integrate different models:
free-surface flow solver
rigid boat motion
wind/sail fluid-structure interaction
longitudinal motion (surge) treated withnon-inertial reference system
Different possible approaches:
one single domain
decoupling hydro and aero domains withsuitable domain interface conditions
(Wibke Wriggers’s Master thesis)
Full boat simulation
Conclusions and perspectives
CFD in yacht design
Increased importance in design process
Acquired confidence from designer and sailors (thanks to proved accuracy)
New boat class (multi-hull) demanding new models (planing, cavitation, ...)
Conclusions and perspectives
CFD in yacht design
Increased importance in design process
Acquired confidence from designer and sailors (thanks to proved accuracy)
New boat class (multi-hull) demanding new models (planing, cavitation, ...)
Development directions
Model integration
sail aerodynamicsfree-surface solver on appended hullFSI for sails and hull
CFD based VPP
Shape optimization and optimal control
References
N. P. and A. Quarteroni, Mathematical Models and Numerical Simulations for the America’s Cup. Comp.
Meth. Appl. Mech. Eng., 194, 1001–1026 (2005).
N. P. and A. Quarteroni. Modelling and numerical simulation for yacht design. In Proceedings of the 26th
Symposium on Naval Hydrodynamics Strategic Analysis, Inc., Arlington, VA, USA, 2007.
L. Formaggia, E. Miglio, A. Mola, and N. P. Fluid-structure interaction problems in free surface flows:application to boat dynamics. Int. J. Num. Meth. Fluids 56(8) 965–978 (2008)
D. Detomi, N. P. and A. Quarteroni, Mathematics in the Wind, in Monografias de La Real Academia de
Ciencias de Zaragoza 31, 35–56 (2009).
D. Detomi, N. P. and A. Quarteroni, Numerical Models and Simulations in Sailing Yacht Design. inComputational Fluid Dynamics for Sport Simulation, Lecture Notes in Computational Science andEngineering, 1–31, Springer, 2009.
M. Lombardi, N. P., A. Quarteroni and G. Rozza, Numerical simulation of sailing boats: dynamics, FSI, andshape optimization, in Variational Analysis and Aerospace Engineering: Mathematical Challenges forAerospace Design, G. Buttazzo and A. Frediani Eds., Optimization and its Applications series, Vol. 66,Springer, in press, 2012.
M. Lombardi, M. Cremonesi, A. Giampieri, N. P. and A. Quarteroni, A strongly coupled fluid-structureinteraction model for sail simulations, to appear in Proceedings of the 4th High Performance Yacht Design
Conference, Auckland, 2012.
M. Lombardi, N. P., A. Quarteroni, Radial basis functions for inter-grid interpolation and mesh motion in FSIproblems, MOX Report 40/2012.
thanks for your attention
thanks for your attention
This work has been partially supported by Regione Lombardia and CILEA througha LISA Initiative grant 2010/2012.
This work is not approved or endorsed by ESI Group, the producer of theOpenFOAM R© software and owner of the OpenFOAM R© trade mark.