CFD MODELLING BY DHI

Statement of Qualifications

CFD Modelling by DHI/hkh/hec-ybr/pot/ShortDescriptions – 08/10

CFD MODELLING BY DHI

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CFD Modelling by DHI

The capability of understanding and investigating

the motions of liquids and gasses in detail is of great

importance in a wide range of engineering disci-

plines and applications. Within recent years, the use

of Computational Fluid Dynamics (CFD) methods

has expanded and today it is a widely used tool in

the engineering design and the analysis of fluid

dynamics.

DHI provides state-of-the-art CFD services within

this field. We have developed our own CFD code,

NS3, and apply this code together with the open

source system, OpenFOAM, in services to our

clients.

Clients are offered fully dynamic as well as steady

state CFD analyses of hydrodynamic performance of

internal and external flow problems. A focal point in

the development of our in-house code, NS3, has

been the development of an accurate description of

the free surface, which is encountered in many of

our projects.

Examples of validation of NS3 are provided in

Mayer et al. (1998), Nielsen & Mayer (2001),

Christensen (2006) and Bredmose et al. (2006),

Nielsen et al. (2008), and Christensen et al. (2009).

The theoretical basis of all CFD modelling is the

Navier-Stokes equations, which are applied to

describe single phase as well as multiphase flow

conditions. On top of the hydrodynamics foundation

we have developed advanced facilities, which

interact with the basic flow description. These

advanced facilities cover for example sediment

transport including a morphological model and

models for transport of conservative constituents.

DHI mainly applies CFD systems, where we have

full access to the source code, as this means that we

are able to adapt and extend the code on an “as

needs” basis project to project.

Characteristic of many of our CFD based services is

that we are applying a phased approach where the

CFD model is used in combination with other DHI

software products. Typically, our leading MIKE by

DHI modelling technology is applied in large-scale

models and the results of such coarse grid model are

used as boundary conditions for the refined CFD

analyses.

All CFD codes applied by DHI are able to run on

high performance computers in 64 bit Windows or

Linux environments.

DHI is extensively using advanced CFD modelling in R&D as well as a direct design tool for our clients in a wide range of engineering disciplines covering internal flow and free surface flow challenges - often in combination or as a supplement to physical model testing. The illustration shows the wave overtopping on a sea dike for an obliquely incident irregular wave train during a possible future climate scenario.

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DHI provides state-of-the art CFD modelling. Example of flow around a velocity cap, cooling water intake.

Features of a CFD Model CFD modelling is today considered the most exact

numerical modelling toll for the analysis of flow

problems. It is recognized that the role of numerical

simulations in the engineering design process is

constantly expanding since the „virtual test‟ is

conducted under controlled environmental

conditions and the amount of information available

is orders of magnitude higher than any complex

physical model test. With the increasing

computational power, CFD modelling is often

considered as an alternative to physical laboratory

tests.

CFD results provide a detailed picture of the hydro-dynamics. Example of pressure distribution on the wind turbine foundation due to a breaking wave

A key feature of CFD modelling is that it provides a

complete insight into the physics of the investigated

problem. Results of the model are not limited to few

measuring points but present a complete picture of

the hydrodynamic performance. The complete

picture of the physics is highly valuable and can be

used to optimise designs, whether for example for

the design wind turbine foundations exposed to

extreme wave loads, flow-induced vibrations of a

riser or operational performance of an industrial

process installation.

However, there is still a large number of engineering

design processes where physical modelling is the

only reliable and accurate optimisation tool, eg for

design of rubble mound breakwaters or structures

using concrete armour layers.

For design and optimisation of rubble mound breakwaters physical model testing is the only reliable and accurate tool.

Application Areas DHI has developed and applied advanced CFD

simulation tools for more than two decades. Our

comprehensive record of experience covers areas

such as:

wave and current-induced design loads on

various type of structures

wave run-up and green water effects

wave overtopping

sedimentation in waves and currents

wave breaking and associated sediment transport

in the surf zone

self-induced vibrations of free spanning

pipelines in currents and wave-induced flow

free-surface waves around piers

flow over spillways

CSO structures

multi-phase flow problems

dam-breaks and other transient problems

moving bodies in flow fields

assessment of structural flow resistance

A number of selected projects where we applied

CFD are illustrated and discussed in the following.

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Wave Run-up on a Wind Turbine Foundation

During recent years, numerous offshore wind farms

have been constructed. One of these is located at

Horns Rev, a reef in the Danish sector of the North

Sea. Observations and measurements from the wind

farm have clearly shown that the wave run-up on the

turbine tower shaft can be quite significant, and the

objective of the project was to evaluate the impact of

wave run-up under extreme wave conditions.

Especially the state of breaking may have a large

influence on the run-up.

The in-house CFD software, NS3, was applied to

study the run-up on the structure for a number of

layouts.

CFD simulation of wave run-up on offshore wind turbine. The scour protection enhances the wave run-up.

The CFD simulations revealed enhanced run-up,

especially for short waves. The run-up was found to

be much larger than found from conventional

potential diffraction theories.

Labyrinth Weir

One of the main objectives of this study was to

investigate the performance of a proposed labyrinth

weir connected to a spillway on a planned dam in

Ecuador. The space available for a weir at the site

was limited, and in order to increase the flow

capacity a labyrinth weir was applied. The purpose

of the model was to verify whether the theoretical

expression developed by Tullis is applicable for the

weir. The formula developed by Tullis is a semi-

empirical model developed on the basis of a large

series of model tests.

CFD simulation of a large labyrinth weir

The labyrinth weir was modelled in DHI‟s three-

dimensional CFD model, NS3. Two sections of the

weir were included in the set-up. The approach flow

upstream of the dam/weir was modelled by the

MIKE 21 HD model and the results of the MIKE 21

model were applied as boundary conditions for the

CFD model.

Free surface flow over one tooth of the labyrinth weir

CFD simulation results are very close to the Tullis

expression and demonstrated that this formula is

valid and applicable for the actual weir.

Comparison of the CFD simulated flow over one tooth of the labyrinth weir with theoretical formula developed by Tullis.

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CFD Modelling of Artificial Surfing Reefs

During the last decade there has been a growing

interest in multipurpose reefs as a solution to provide

coastal protection while also creating favourable

surfing conditions at the same time. Assessing the

surfing quality of a submerged reef requires highly

detailed information on the wave breaking

characteristics such as the shape of the overturning

wave and the propagation velocity of the moving

breakpoint. In addition the powerful and highly non-

uniform wave breaking conditions across the reef

induce strong return currents and areas of high local

velocities, both of which strongly affect the wave

breaking characteristics and represents crucial reef

design parameters, when assessing structural

stability, induced erosion issues and adjacent beach

safety.

NS3 can be coupled with DHI‟s MIKE 21 BW wave

model to provide the 3D offshore boundary

conditions hence effectively decreasing the

necessary NS3 model domain size and allowing the

representation of regional effects such as non-

uniform refraction around adjacent headlands and

offshore focusing generated by offshore

bathymetrical features.

Visual comparison between model results and camcorder recordings of the wave breaking characteristics at three different locations along the reef

The NS3 model was used to reproduce the wave

transformation processes captured in a large-scale

physical model of an artificial surfing reef presented

in Henriquez (2004). Calculations of the wave

breaking height and wave pealing velocity along the

reef were in excellent agreement with physical

model measurements. A visual comparison between

the numerical model predictions and physical model

video records of the surfing wave shape and

breaking characteristics also demonstrated excellent

agreement.

Coupling of MIKE 21 BW and NS3

Boussinesq wave models have been increasingly

popular for coastal engineering applications during

the last decade, with considerable improvement of

linear and non-linear accuracy. Overturning waves,

splash zone dynamics and extreme run-up on

structures, however, are beyond the capabilities of

this model class. A reliable description of such

phenomena requires a more flexible treatment of the

free surface such as a fully non-linear Navier-Stokes

solver with VOF (Volume of Fluid).

DHI’s MIKE 21 BW is used for calculation of the far-field waves for offshore wind farms and other offshore renewable systems

In Christensen et al (2009), the Boussinesq model is

used for the far-field waves, while the inner region

surrounding the structure is modelled by the Navier-

Stokes solver. The inner solution handles wave

breaking as well as the loads on the structure. The

combined model is applied to wave loads on

offshore wind turbine foundations.

Wave pressure and flow field around a gravity based foundation of an offshore wind turbine.

The transfer of waves from the Boussinesq model to

the Navier-Stokes solver requires specification of the

free surface elevation and the velocity field over the

entire coupling boundary.

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Sequence of horizontal force and overturning moment from the irregular waves: - - Wheeler stretching + Morison equation, ----- BW+ Morison, ____CFD

Comparison of maximum overturning moments found from zero-crossing analyses.

Model Equations The basic equations of all CFD models are the three-

dimensional Navier-Stokes equations.

The Navier-Stokes equations for a one phase

incompressible flow are given by:

i

j

j

i

i

i

i

j

jii

i

i

x

u

x

u

x

x

pg

x

uu

t

u

x

u

0

Where ui are the three velocity components, g the

gravitational acceleration, p the pressure, the fluid

density, and the dynamical viscosity. The first of

two equations is the continuity equation, while the

second equation is the momentum equation.

Most flows encountered in engineering practice are

turbulent. In principle the Navier-Stokes equation

can be applied directly on a turbulent flow (Direct

Numerical Simulation), but such an approach would

require a very detailed computational mesh and very

fine temporal discretisation. From a practical point,

this is only possible for low Reynolds numbers.

In many applications, the main interest is to gain

information about the average performance of the

turbulent flow. This is accomplished by averaging

the basic equations to filter out the many scales of

the turbulent flow and selecting a turbulent closure

model that models the effect of turbulence on the

mean flow.

A common averaging method is the ensemble

averaging leading to the Reynolds Average Navier-

Stokes equations (RANS):

i

j

j

it

i

i

i

j

jii

i

i

x

u

x

u

x

x

pg

x

uu

t

u

x

u

)(

0

where iu are the three average velocity components,

g the gravitational acceleration, p the average

pressure, and t the dynamical eddy viscosity.

The result of this approach is that in the momentum

equation averaged scales appear as the Reynolds

stress tensor. The eddy viscosity hypothesis relates

the turbulent stresses to the velocity gradients of the

mean flow. The modelling is then reduced to the

specification of the eddy or turbulent viscosity

(exchange coefficient for momentum) in terms of the

local turbulence in the flow. Several different

models of the turbulent viscosity have been

developed.

RANS model of the turbulent energy in an injector pump

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The most common models relate the eddy viscosity

to two scalars which are representative of the

turbulence in the flow. These scalars are normally

the turbulent kinetic energy and its dissipation or

specific dissipation. For each of the additional two

scalars, an additional transport equation is solved in

which further modelling assumptions are

incorporated.

The k-ε model is an example of a two-equation

model. This model has been applied with success in

many different simulations, but it has some

disadvantages. The most serious one is perhaps the

lack of sensitivity to adverse pressure gradients.

Another two-equation model is the k- model. This

model performs better than the k-ε model under

adverse pressure gradient conditions, but the model

depends on the free stream values that are specified

for the specific turbulent dissipation rate, .

Another method is the Shear Stress Transport (SST)

k- model, which is a conglomeration of the k-ε and

k- model. In this model, the k- model is applied

in the near wall region, while the k-ε model is

applied in the far-field.

Turbulent flows contain typically a wide range of

time and length scales. The turbulent large-scale

motions contain generally much more energy than

the small scales, which are utilised in the so-called

Large Eddy Simulation method (LES). In the LES

method, the small-scale turbulence is filtered out of

the Navier-Stokes equation, and a set of equations

which is very similar to the Reynolds Average

Navier-Stokes equations is obtained. Closure of the

LES model requires a model of the sub-grid scale

Reynolds Stress. Details of the LES model are for

example given in Christensen (2006).

At the boundaries, appropriate conditions for the

flow field as well as the variables of the turbulence

model must be specified. Simulation of the boundary

layer requires a very fine mesh resolution and this

together with the fact that many turbulence models

are not able to predict flow in the boundary layer

correctly causes that a wall function is often applied

in this zone. With the wall function approach, flow

and turbulence in the boundary layer are predicted

on the basis of assumptions, for example a

logarithmic velocity profile, and the Navier-Stokes

equation together with the turbulence model are

matched to the wall function a certain distance above

the fixed boundary.

Flow with a free surface is a class of flows with

moving boundaries. The position of the boundary is

only known initially, and the solution must track the

position of the free surface. In NS3, tracking of the

surface is based on the VOF method. The position of

the free surface is calculated by solving a transport

equation of the void fraction, f:

𝜕𝑓

𝜕𝑡+

𝜕(𝑢𝑖𝑓)

𝜕𝑥𝑖= 0

F=0.5 track the free surface in a CFD model of super-critical flow in a river

where f=1 in the fluid and f=0 in the air. The

position of the free surface is defined by f=0.5. The

kinematic and dynamic boundary conditions are

imposed along the free surface. The kinematic

condition constraints fluid particles at the free

surface to follow the local fluid velocity, and the

dynamic boundary condition expresses the

equilibrium of stresses across the free surface.

In general, DNS and LES require a fine resolution

and the CPU-time for such calculations is rather

excessive. This in combination with the fact that

information about average performance of the

turbulent flow is often adequate, causes that the

RANS approach is applied in most applications.

Numerical Methods The numerical schemes of the CFD solvers are based

on the finite volume approach. NS3 requires

discretisation of domain in a structured multi-block

mesh, while OpenFOAM supports unstructured as

well as structured mesh.

Space Integration

The spatial domain is discretised by subdivision of

the continuum into non-overlapping cells. Each cell

is bounded by a set of flat faces, and each face is

shared with only one neighbouring cell. Flow

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variables, ui and p, are cell-centred. The Finite

Volume method is based on the Navier-Stokes

equations in an integral form, where the integration

is carried over each cell volume:

dtdvx

u

x

u

xdtdv

x

p

dtdvgdtdvx

uudv

t

u

dtdvx

u

tt

t i

j

j

i

i

tt

t i

tt

t

i

tt

t j

jii

tt

t i

i

0

Using the Gauss theorem on these equations results

in relation between the cell and face-centred values

of ui and p. Finally, applying differencing schemes

to express the face-centred values as a function of

the variables in the neighbouring cells results in a

large set of equations, which express the relation

between p and ui throughout the domain.

Computational mesh of an ejector pump

Time Integration

The time integration is based on a fractional step

approach. Firstly, a propagation step is performed

calculating an approximation solution to the velocity

field, ui, by solving the momentum equation.

Secondly, applying the continuity equation on the

approximated velocity field results in an equation

which is used to predict the pressure field‟s new time

step and the new pressure field is applied to correct

the velocity field.

The propagation in time can be carried out by

different schemes such as an implicit Euler scheme,

explicit Euler scheme, etc.

Model Input The necessary input data to run a CFD model can be

derived into the following groups:

Domain and time parameters

- Computational grid

- Simulation length and time steps

Equations, discretisation and solutions technique

- Turbulence model

- Numerical scheme

- Wall function

- Transport models (sediment)

- Solution techniques

Initial conditions

- Cold start (initial values of flow variables)

- Hot start

Parameters

- Models parameters (for example turbulence

model parameters)

- Body forces

Boundary conditions

- External domain boundary conditions

(inflow, outflow, symmetry, periodic)

- Fixed wall boundary conditions

Providing a CFD model with a suitable grid is

essential for obtaining reliable results from the

model. Setting up the mesh includes appropriate

selection of the flow domain, adequate model

resolution and specification of boundary conditions.

It is often possible to take advantage of symmetrical

conditions and hereby reduce the computational

domain.

Selection of appropriate numerical schemes is an

important part of the model set-up. Selection of these

schemes is often a trade off between stability

considerations versus accuracy. For example an

upwind scheme is typically more stable than a

central difference scheme but, on the other hand,

anupwind scheme tends to introduce numerical

diffusion in the solution.

Selection of an appropriate turbulence model is also

important. The selected model must be able to catch

important features of the flow.

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Model Output At each mesh point and for each time step, the

following type of input is saved in an NS3

simulation:

Velocities

Pressure

Turbulence model variables

Effective viscosity

F (void fraction)

Results of a CFD simulation can be presented in

different ways such as:

Contour plots

Vector plots

Tracer plots

Animations

Output from CFD simulations is often post-

processed using different tools. The post-processing

includes several various analysis tools such as

integration of pressure fields over surfaces in order

to calculate forces and momentum, creations of time

series plots of a flow variable at a single point,

integration of fluxes over surfaces in times, etc.

Validation The NS3 model has successfully been applied to a

number of basic test cases where the results can be

compared with analytical solutions, experimental

tests or information from literature. These tests cover

basic hydraulic aspects such as:

Standing waves

Travelling waves

Shoaling

Wave-current interactions

Simulation of boundary layer flow

Details of the above can be obtained from the

references listed in the section “Reference on Basic

Tests”.

Use of Purpose-built Software Tools based on the Open-source Library, OpenFOAM The OpenFOAM system has been validated in

numerous PhD theses and papers for a range of

physical models and cases. This includes anything

from fluid flow, free surface, multi-phase,

DNS/LES, turbulence modelling to stress analysis,

and solid-fluid interaction. An example of the use at

DHI is given below. It shows the generation of an

internal wave in a fluid with varying salinity. The

analysis is a part of hydrographic services for

Femern Bælt A/S in the environmental investigation

of the impact of a fixed link between Denmark and

Germany.

Internal wave between layers with different salinity generated by the presence of a future bridge pier.

References Bredmose, H, Skourup, J, Hansen, EA, Christensen,

ED, Pedersen, LM, and Mitzlaft, A (2006):

”Numerical reproduction of extreme wave loads on a

gravity wind turbine foundation”. Proc. of OMAE

25th Int. Conf. on Offshore Mechanics and Arctic

Eng., 4-9 June 2006, Hamburg, Germany.

Buxbom, IP, Fredsøe, J, Sumer, BM, Conley, DC,

and Christensen, ED (2003): “Large eddy simulation

of turbulent wave boundary layer subject to constant

ventilation”. In Coastal Sediments 03, 18-23 May

2003. Sheraton Sand Key Resort, Clearwater Beach,

Florida, USA.

Christensen, ED, Bredmose, H, and Hansen, EA

(2009): “Transfer of Boussinesq waves to a Navier-

Stokes solver. Application to wave loads on an

offshore wind turbine foundation”. In Proceedings of

the ASME 28th International Conference on Offshore

Mechanics and Arctic Engineering (10 pages).

Honolulu, Hawaii: ASME.

Christensen, ED (2006): “Large eddy simulation of

spilling and plunging breakers”, Coastal

Engineering, Volume 53, Issues 5-6, April 2006,

Pages 463-485.

Christensen, ED, Bredmose, H, and Hansen, EA

(2005a): “Extreme wave forces and wave run-up on

offshore wind-turbine foundations”, In Proc. of

Copenhagen Offshore Wind Conference, 10 pages.

CFD MODELLING BY DHI

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Christensen, ED, and Hansen, EA (2005b):

”Extreme wave run-up on offshore wind-turbine

foundations”, In Proc. of Int. Conf. on

Computational Methods in Marine Engineering

(MARINE 2005), Oslo, Norway, 27-29 June 2005,

pp 293-302.

Christensen, ED, Zanuttigh, B and Zyserman, J

(2003): “Validation of numerical models against

laboratory measurements of waves and currents

around low-crested structures”. In Coastal Structures

03, 26-29 August 2003, Portland, Oregon, USA.

Christensen, ED, D-J Waltra and N Emerat (2002):

”Vertical variation of the flow across the surf zone”,

Coastal Engineering, Vol 45, No 3-4, pp 169-198.

Christensen, ED, Jensen, JH, and Mayer, S (2000):

“Sediment transport under breaking waves”. Proc.

27th, ICCE00, Sydney, Australia.

Emarat, N, Christensen, ED, Forehand, DIM and

Mayer, S (2000): "A study of plunging breaker

mechanics by PIV measurements and a Navier-

Stokes solver", In Proc. of the 27th Int. Conf. Coastal

Eng., ASCE, Vol 1, pp 891-901, Sydney, Australia.

Hansen, EA and Meyer, S (2001): “A numerical

model for current-induced vibrations of multiple

risers”. In Proc. of the 20th Conference on Offshore

Mechanics and Artic Engineering, OMAE‟01, Rio

de Janeiro, Brazil.

Hansen, EA, Bryndum, M, Mørk, K, Verley, R,

Sortland, L, and Nes, H: “Vibrations of a free

spanning pipeline located in the vicinity of a trench”.

In Proc. of the 20th Conference on Offshore

Mechanics and Artic Engineering, OMAE‟01, Rio

de Janeiro, Brazil.

Jensen, JH and Fredsøe, J (2001): “Sediment

transport and Backfilling of Trenches in oscillatory

Flow”. Journal of Waterway, Port, Coastal and

Ocean Engineering, ASCE, Sep-Oct 2001, pp 272-

281.

Jensen, JH, Madsen, EØ, and Fredsøe, J (1999):

“Oblique flow over dredged channels. II: Sediment

Transport and Morphology”. J. Hyd. Engrg, ASCE,

125(11), pp 1190-1198.

Jensen, JH, Madsen, EØ, and Fredsøe, J (1999a):

“Oblique flow over dredged channels. Part I: Flow

Description”. Journal of Hydraulic Engineering,

ASCE, 125(11), pp 1181-1189.

Kawamura T, Mayer, S, Garapon, A, Sørensen, LS

(2001): “Large Eddy Simulation of the Flow past a

free-surface piercing circular Cylinder”. In:

Transactions of the ASME. Journal of Fluids

Engineering, Vol 124, Issue 1, pp 91-101.

Mayer, S, Nielsen, KB, and Hansen, EA (2005):

“Numerical prediction of wave impact loads on

multiple rectangular beams”, Coastal Engineering

Journal, Vol 45, No 1, pp 41-65.

Mayer, S, Garapon, A and Sørensen, LS (1998):

“A fractional step method for unsteady free-surface

flow with application to non-linear wave dynamics”.

Intl. Journal for Numerical Methods in Fluids,

Vol 28, No 2, pp 293-315.

Nielsen, KB, and Mayer, S (2004): “Numerical

prediction of green water incidents”, Ocean

Engineering, Vol 31, pp 363-399.

Nielsen KB and Mayer, S (2001a): “VOF

simulations of green water load problems”. 4th

Numerical Towing Tank Symposium, September

2001, Hamburg, Germany.

Nielsen, KB, Mayer, S (2001b): “Numerical

simulation of tank sloshing”, SRI-TUHH mini-

Workshop on Numerical Simulation of Two-Phase

Flows, Tokyo, Japan.

Tullis, JP, Amanian, N, and Waldron, D (1995):

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Hydraulic Engineering, Vol 121, No 3, pp 247-255.

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Agern Allé 5 Tel: +45 4516 9200

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E-mail: dhi@dhigroup.com

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