Calculation of ship dynamics in ship fixed coordinate system. Fluid dynamics equations in ship fixed reference system

Lecture 11:

Calculation of ship dynamics in ship fixed coordinate system Fluid dynamics equations in

ship fixed reference system

N. Kornev,

Lehrstuhl für Modellierung und Simulation Fakultät für Maschinenbau und Schiffstechnik

Universität Rostock

Motion equations in ship fixed reference system

Navier Stokes equation in ship fixed reference system

General relations

NS equation in ship fixed reference system

General relations

NS equation in ship fixed reference system

URANS equation in ship fixed reference system

Turbulent models in ship fixed reference system

NS equation

URANS equation

Tensor (vector) form Operator form

k j ijk i

i

u p C u

A ^{( , )}   ²  

k j ijk i

i

u p C u

A ^{( , )}   ²  

Intertial ship fixed

m j kjm k

k

u p C u

A ^{( , )}   ²  

m j kjm i k

i k

i

A u p u C u u

u ^{( , )}   ²  

m j ijm k i

k i

k

A u p u C u u

u ^{( , )}   ²  

inertial

Ship fixed inertial

Ship fixed

m j kjm i k

i m j ijm k i

k i

k k

i

A u p u A u p u C u u u C u u

u ^{( , )}  ^{( , )}   ²     ²  

/ /

/

/

2

2 2

2 )

, ( )

,

(

k

i

A u p u A u p u C u C u u u u u u u u

u               

Ship fixed

Ship fixed inertial

m j kjm k

k

u p C u

A ^{( , )}   ²  

m j ijm k i

k i

k

A u p u C u u

u ^{( , )}   ²  

m j kjm i k

i k

i

A u p u C u u

u ^{( , )}   ²  

m j ijm k m

j kjm i i

k k i i

k k

i

A u p u A u p u C u C u u u u

u ^{( , )}  ^{( , )}    ²    ²  

inertial Ship fixed

/ /

/

/

2

2

)) , ( )

, ( (

) , ( )

, (

m j kjm i m

j ijm k

i k k

i

i k k

i

u u

u u

p u A u p

u A u

p u A u p

u A u







 











Contribution from moving coordinates

Ship fixed

K- equation is the same in intertial and ship fixed reference systems !!

Addtional term inertial

0 )

( 2

2

/ /

/ /











u u

u u _{k kjm j m}

 

 





Ship fixed inertial

- equation is the same in intertial and ship fixed reference systems !!

k i m j ijm i

i

k

x

u u C

p u

x A 

 

 

 ( ( , ) 2   )

0 )

( 2

) 2

(

/ /

/

 

 





 







k k

k i m j ijm k

x u u x

x u u

x

 

 







Calculation of rotating propeller

N. Abbas, N.Kornev et al. (2015) Ocean Engineering, Vol. 104, 659–672.

Samples

Computational grid of KVLCC2, (7 million cells).

Computational grids.

Blocks of the boundary layer and the propeller disc.

KVLCC2 with propeller (VP1356),

(27 million cells). KVLCC2 with propeller (MOERI) and rudder, (30 million cells).

Samples

Hydrodynamic force and moment coefficients versus drift angle

N. Abbas, N.Kornev (2015) Ship Technology Research



Longitudinal distribution of lateral forces

Pressure distrubution

N. Abbas, N.Kornev (2015) Ship Technology Research

Experiment k-w SST

IDDES LeMoS

Pressure distribution

   12

Calculation of wake at straight course

N. Abbas, N.Kornev (2015) Ship Technology Research

N. Abbas, N.Kornev (2015) Ship Technology Research

Calculation of wake at 6 ⁰ drift angle

N. Abbas, N.Kornev (2015) Ship Technology Research

Calculation of wake at 12 ⁰ drift angle

Calculation of wake at different drift angle

Thank you very much for your attention!

Literature:

1. Kornev, N. & Cherunova I. (2014). Lectures on computational fluid

dynamics and heat Transfer with applications to human thermodynamics.

Bookboon Publisher.

2. Kornev, N. (2013). Lectures on Ship manoeuvrability. Bookboon

Publisher.