Wave tank/basin CFD simulations

Canad

National Research Conseil national Council Canada de recherches Canada Institute for Institut de

Marine Dynamics dynamique marine

SYMPOSIUM ON

SELECTED TOPICS OF

MARINE HYDRODYNAMICS

St. John's, Newfoundland

August 7, 1991

WAVE TANK/BASIN CFD SIMULATIONS

M.J. Hinchey

Ocean

Engineering

Research Centre

National Researcs, Council

I'U Cthada

InStitute fOr Mame Dynamics

Conseil national dé recherches Canada Institut de dnarnique manne

SYMPOSJiJM ON

SELECTED

_{TOPICS OF}

MARINE

_{llYDRODyNA?JCS}

St. John's, Newfôundjand

August 7, 1991

A3SAC

Computational Fluid Dynamics (CPD) is a very active research area. Most wave tank/basin CFD simulations are based _{ot a potential} f low formulation. This paper _{describes CPD} 3imulations based on a Návjer-Stokes _(NS) förmujatjon. _{It describes a 2D finita} lifference NS code bown _{as SOLA-voy that} ias been used for vaya tank simulations and recent 3D NS code known as FLOW-3D that ould be used fOr wave basin _simulations. 30th codes were developed by Hirt and his

:oileagues at the Los Alas

_Scientific

Caboratorjes. Neither code is _{set up for} luid

interaction

_{with bodies ündergoing} trbitrary motions. So, they _{cannot handle} ¿ave interactions with floating bodies. The 'apar describes so _{coda modifications that} ìight allow such _{interactions.}

dvantages/Disadvg

of the codes elative to Panel Iethod codes are briefly eviewed.

BACKGROUND

rost wave tank/basin sjmulatjons are based rn a boundary integral

formulation and a 'anel Method djscretizatjon. _{The starting}

oint for this is _{Laplace's equation for}

)otential water flow. This _{is basically a} ;tatement of _{corervatjon of mass for} .nviscid incomprethle _{water undergoing an} .rrotatjonal motion. This paper describes a_injt difference _{dtscretjzatjon of the} rimitjve variable form of the Wavier-stokes

NS)

equations that coùld also be uséd for

ank/basjn

sirnulatj.

_{In terms of the}

rimitjve _variables,

_conservation

of omentum considerations _give:

p _{( au/at + u 8u/x}

+ y auiay + w au/az ) - - ap/ax _{+ 1 a/ax (u au/ax)}

+

_{/y (}

_òu/8y)

_{+ a/az}

au/az)]

WAVE TANK/BASIN CFD SIMULATIONS

N.J. Hinchey

Ocean Engineering Research Centre Memorial University of Newfouzdland

32

p _{( av/at + u av/ex + V}

av/ay

4

w av/az ) - ap/ay + _{a/er öv/8x)}

+ _{a/a7 ( av/ay) + a/az}

( av/az)]

av/at + av/ex + _{8w/ay + w av/a}

z )

- ap/as - pg + ( a/ax

(14 au/ax) + _{a/ai (p av/ay) +}

a/az (u av/ez)]

where u,v,v are velocity

_components

_{in the} x,y,z directions, _{p is prèssure,}

p is the

density of Vater and _{p is its effective} Viscosity. Similarly, _{to conserve}

mass, the velocities and _{Pressure must Satisfy:}

ap/at + a,'a _{+ av/ay + aw,'az}

) - o

where a is the _{speed of Sound in}

water. Although Vater is

basically incompressible

for mass _{conservation,}

the Ns/cpo codes

(l2J take it to _{be compressible..}

A spécial function known _{as the volume of fluid}

(VOF)

function P _{is used to locate}

the water surface. Vithin the _{water, the VOP function} is unity : _outside

the water it is

zero.

Material volume _{considerations give,}

for it the governing _equation:

a,at +

aP/ex + y aP/ay _{+ w eF/as - O}

Codes based on these

equations would have to use an extremely fine _{mesh to accurately} model

_turbulent

_flows

such as _those generat _{by waves breaking on a beach. This} is because the scales of turbulence _{are very} small. Turbulence is

characterized by small lumps of fluid known as eddies moving

arouzd in a rand _{fashion. Like the}

molecules in a gas, eddies cause a diffusion of

_moment.

They make the fluid _{appear more viscous.}

Now, _{gineers are usually not interested in} the tails of the eddy metioñ. Instead, they steed models which account for the

difts..v character of turbulence. Such

modes can be obtained from the momentum

equa.n.s

by a complex time _averaging

pro. One popular two equation model

obtA±d in this way is known as the

_k-e

aode. :3], wher.

k is

th. local intensity of

tur..nca and e

is its dissipation _rate. FLCW-1 [2] uses this model _{: SOL-VOp (1]} does t. Its governing equations _are:

èk,?t + u 8k/ax + V _{8k/ay + w 8k/8z}

-T- Td

+ (8/8x (p/ak 8k/8x) + 8,'8y (u/a 8k/8y) + a/az (js/c 8k/8z)]/p

8e19t + u

8e/8x

_{+ V}

_8c/8y

_{+ V}

_8c/8z

D -

Dd + (8/8x (p/a1 8c/8x) + 8/8v (p/a1 8e/8y) + a/az _{(p/a1 8e/òz)]/p}

where

T, = G p / p

T C1 e / k

e

whee ak(l.0), a,(l.3), _{Cb(l.0), C1(l.44),}

C2(l.92) and C1(O.9) _{are universal constants} based _{on data}

from geometrically simple experients, p1 is the laminar Viscosity of water, p _{is its apparent Viscosity due to} eddy _{'otion and G is a}

production function

(3]. _{The k-c equations}

account for the

convection, _{diffugjon, production}

and

dissjtjo

of _{turbulence. Th time} averaç _process

introduces source-like ter _{into the momentum equations. Special}

wall fctjos

_{are often used to simplify}

consjãeratjon of the _{sharp normal gradients} in ve..ocitje3 _{and turbulence}

near walls. Ever $lflce their

introduction back in the early seventies,

turbulence models, such as

the

k-ode1, hava been and still are quite one.rsja1, mainly because _{the so-called}

univeaj

_{Constants seem to be}

geometry

1epen.

ach coverning

equation can be put into the

form:

- B

[1,,2J, _{each is integrated}

numerically

tcrs a time step

to get new A from old A:

A(t + ¿t) _{A(t) + Lt B(t)}

where _{th. various derivatives}

_{in B are}

discretized using finite difference approximations. _{The discretizatjon gives} algebraic equations for the _{scalars p,P,k} and e at points where _{grid lines cr.s and} equations for Velocity components at staggered positions between the grid points. Central differences _{are used to disetize}

the viscous terms. To

ensure nrica1

stability, a combination of central ¡ upvind differences is used for the _corrvectïve terms. Collocation or lumping is u.sed for each of the T and D terms. The details of the discretjzatjon can be found. in [1,2]. To march the uniciowne forward in time, _the momentum equations are used to update the velocities, the continuity equation is used to update pressure and the turi.lence equations are used to update the local intensity and dissipation rate of turbulence.

2. WAVE TANI SDWLATIONS

The SOL&-Vop code has been. used _{for 2D vave} simulations (4]. In (5], we used it to study the wave attenuation characteristj _{of a} number of breakwaters. In (6;7], we used it to study the waves generated by a hovercraft undergoing a pure sinusoidal heave motion overwater. Recall that hovercraft are

amphibious

yehicles which float on

_{a shion}

of pressurized air contained by a flexible

structure known as a skirt. Lift _{air is}

typically supplied by one or more fans or blowers, and it leaks _{away to atmoephere} through a gap beneath the skirt. _{For the} breakwater study, waves were generated by imposing a periodic flap-like _horizontal velocity profile at the left hand e of a tank. For the hovercraft _{study, they 'vere} generated by imposing a periodic _pressure over a section of the water surface at the left and: _{this vas taken to be uniform} beneath the craft and undergo a linear fall-off to atmospheric pressure at the edge of the cushion. Group speed _{concepts vere used} to stop each simulation before the profiles of interest could get _{contaminated by beach} or end wall reflection.

Fig 1 shows a typical wave profile from the breakwater study. The breakwater was nonporous and was generated by blocking out specific cells _{in, the finite difference} mesh. Note the superposition of incident and reflected waves just upstream of the breakwater. This was used to determina the reflection coefficient of the _breakwater. Comparison with its transmission

coefficient showed that there was coña_{iderable energy.} dissipation. Runs for this case typically

took several hours of

_{VAX CPU time}

:

however, runs for a porous geometry often took. days, _{especially when to}

ccuracy an automatic tine step reduction ras employed by the code. For the breakWater tudy, the water was typically dlscretjzed .'y 25 horizontal grid lines and 200 vertical rid lines.

'ig 2 shows a typical result fr the overcraft study. For this, the hydrostatic rough normally found beneath a craft vas ot allowed to form. The figure gives the ave profiles generated near a craft by a ure heave motion with frequency i cps: IN e fers to a component in phase with pressure hile OUT refers to a component 90° out of hase. The left half of each profile orresponds to the region directly beneath he craft while the right half corresponds o the region just outside. One vili note hat the. waves beneath the craft are asicaily standing waves vtiile outside they re propagating waves. As can be seen, the refiles beneath compare favorably with orresponding potential flow profiles enerated by Lamb (8] and shown in Fig 3. he duration of each simulation in real time as typically 10 seconds and the profiles iven are for the last second or cycle of his. By this time, start-up transients _were significant. For each simulation, the ater was _{discretized typically by 20} orizonta]. grid, lines and 250 vertical grid

ines : about 20 of the vertical lines _were

riside the cuShion. This _{was considered to} e adequate for the wavelengths generated.

ic grid vas uniform throughout except for e far right end where it vas allowed to pand horizontally so that reflected waves rom a vertical wall there did not have _a hance to form. For the profiles, _the drop-tf in pressure at the édge of the cushion curred across the 4 vertical _{lines just}

utside the edge. _{Similar profiles were} tained with a nonzero hydrostatic trough.

have also used the. simulation to study e heave stability of hovercraft hovering

d-erwatar, _{where the waves}

generated by aave motion modulate the cushion volume and e flow of air beneath _{the skirt (6,7]. We}

3und that Water _{compliance can improve} ability at high _{Cushion pressures but} tuse many stability _{transitions at low}

essures. For this work, _{the hydrostatic} rough beneath the craft vas not allowed to ,ra because with it motions _{were erratic.}

Fig i Wave Interaction with Nonporous Breakwater : SOLA-VO? Simulation.

34

In reality, this trough nay degrade stability at high cushion pressures. Some of the stability trends at low cushiön pressureswere recently confirmed iñ _{a wave} tank setup at ¿(UN (7].

WAVE BASIN SIMULATIONS

The FLOW-3D code could be _{used for wave}

basin simulations. Procedures _{used in} SOLA-VOY to generate and dissipate waves should also work in FLOW-3D. Unfortunately, we have not been able to check this _{because the} FLOW-3D code costs approximately $50, 000 US (SOlA-Voy $800 US)! It should be _possible with the code to study the diffraction of wave fields by complex 3D shapes. _According to (9], several research _{institutes in the.} UK are working on this.

BODY MOTIONS TE TO WAVES

Neither NS/CPD code can handle bodies undergoing arbitrary motions in waves. However, they can handle special _{cases such} as constant speed body motions. For example, ve used SOLA-Vop to study the _{impact of} submersible capsules onto the ocean surface following free fall from the deck of an oil rig. Hirt and his colleagues have used FLOW-3D in a similar way (10]. _{A typical result} from their work is shown in Fig 4. They are nov attempting to extend the _{code to the.} arbitrary motion case (il] _{: unfortunately,} success to date with this has

_been

_very modest. _{It might be possible to}

setup a pressure iteration over _{a section of the} water surface that _{over a time step would} move the water the way a moving body would. This is something that Hirt and his colleagues have not tried.

DISCUSSION

Probably the major advantage of the NS/CFD codes relative to Panel Method codes is they can handle nonlinear phenomenon _{such as}

breaking waves and turbulence. Their major disadvantage is they presently cannot handle arbitrary body notions such _{as those of} floating bodies in waves. _Another disadvantage is in 3D they discretjze the

OUT

M**.

W%WW

*

w

w w

Fig 2 Water Waves near Hovercraft undergoing Pure Heave Motion : SOLA-VO? Siu.1ation.

DISTANCE OUT FROM CRAÉT CENTfl ()

space occupied by a fluid while the Panel

'(ethods discretize s or all of the 3urface surrounding the space : thus Panel '(ethod codes are potentially caputationally nora efficient. Also, Panel Method codes

pproxizate colex shapes

better than IS/CPD codes, which generally employ ectangular grids. Curvilinear coordinates r finite element geometry mappings could ?robably b.

Used to ctaract this. Por

3ome geometries, r VAX SOL-VOP impact & reakwater computations were

quite cu

intensive.

So, a ercomputer woúld

robably be needed for 3D computations.

.nothar problem with NS/CYD codes is iomething called false diffusion : because

the upwind difference treatment of the ;onvective terms in the transport equations,

.ha Vater appears more viscous than _it

eally is : so, XS/C?D acouracy can be low.

;kew upwind difference schemes can :ounteract this somewhat : however, these

re not used by the NS/D codes.

COWLEbGEMENT

his work was funded by NSERC through perating Grant A4955(Hinchey).

ZPER.ENcEs

Nichols, B.D., Hirt, C.W. and Hotchkiss,

.5. (1980): SOLA-VO? : .A Solution

lgoritbm for Transient Fluid Plow with

ultip1e Free Boundaries", Los Alamos ;cientjfjc Laboratories, Los Alamos, New (exico, USA.

Hirt, C.W. (1991):

"FLOW3D User

anual", Plow Science Incorporated, Los lamos, New Mexico, USA.

Launder, B.E. and Spa.lding, D.B. (1972): Lectures in Mathematical Models of .'urbulence", Acadeiic Press.

Su, T. (1984): 'Wave Breaking on Sloping eaches', Fourth International Conference on .pplied Numerical Modelling, Taiwan, ROC.

Yetman, R. and Rinchey, fl.J. (1990): Wave Attenuation by the Deltaport Floating rea)cwater", CS _{Mechanical Engineering} orum 1990, Toronto.

Hinchey, *.J. (1989): _"Numejca1 imulatjon of Overvater Heave Motion Of 2D overcraft", CACTS 89, Transport Canada, TDC .eport TP 8979.

Hinchey, X.?. and Sullivan, P.A. (1991): Experiments on _{Hovercraft Overwater} tability", _{POAC 91, st.}

John's, ewfoundland, Canada.

36

Lamb, H. (1904): "On Deep Water Waves", Proceedings of the London Mathematical Society, Series 2, Volume 2.

Eatock-Taylor, R. (1991) : Oxford University, UK, Private Communication.

Hirt, C.W. (1990): "Water Entry of High Speed _{Projectiles", Flow Science} Incorporated, New Mexico, (ISA, FSI-90-TN23.

li. Sicilian, 3. (1990): "A FAVOR Based Moving Obstacle Treatment for _{FLOW-3D", Flow} Science Incorporated, New Mexico, USA, PSI-90-00-TN24.