VERTIMAR-2005 Numerical Simulation of the Thermal and Fluid- dynamic behaviour of fuel-oil in sunk...

VERTIMAR-2005

Numerical Simulation of the Thermal and Fluid-dynamic behaviour of fuel-oil in sunk ships

C.D.Pérez-Segarra, R.Consul, R.Capdevila, A.Oliva, J.Castro, E.Mas de les Valls

Heat and Mass Transfer Technological Center (CTTC) Technical University of Catalonia

www.cttc.upc.edu

Edifici TR4, ETSEITC/ Colom, 1108222 Terrassa (Barcelona)Tel. 93 739 81 92 Fax 93 739 81 [email protected] http://www.cttc.upc.edu

http://www.cttc.upc.edu/





Vertimar, Vigo, July 13th-16th, 2005Vertimar, Vigo, July 13th-16th, 2005

Presentation:Presentation:

1. Project objectives and scope of this presentation

2. Preliminar numerical results for a case defined by the CIEMAT

3. Improvements in the computational code developed

a. Unstructured grids

b. Subdomain methods

c. Turbulence modelling: RANS models

d. Turbulence modelling: DNS and LES models

e. Verification of the calculations

4. Conclusions

1. Project objectives and scope of this presentation

11. Project objectives and scope of this presentation. Project objectives and scope of this presentation

Basic objective:Basic objective: Development of a code for the numerical simulation of the

thermal and fluid-dynamic behaviour of the fuel-oil contained in sunk ships

(VEM2003-20046).

Two steps: 1. Development of a computational code; 2. Application of the

code to two characteristics problems.

• Mathematical formulation and discretization procedures of the heat transfer and fluid dynamic phenomena involved

• Efficient numerical resolution. Verification of the codes (MSM).

• Software development and parallelization of the Navier-Stokes equations.

• Validation process: experimental studies, DNS solutions,...

1. Development of a computational code1. Development of a computational code

11. Project objectives and scope of this presentation. Project objectives and scope of this presentation

2. 2. Application of the codeApplication of the code

• Characterization of different cooling conditions in terms of ship sizes, boundary conditions, fuel-oil and sea-water thermophysical properties, ...). First approximations: no leakages.

• Characterization of the fuel-oil leakages through holes. First approximations: isothermal conditions.

L

L

2. Preliminar numerical study of a benchmark case

2. Preliminar n2. Preliminar numerical study of a benchmark caseumerical study of a benchmark case

Modelling of the fuel-oil cooling inside the Prestige tanker.

y

x

19 m

g

7.6 m9.6 m

• Case defined by the CIEMAT.

• 2D approach with specular symmetry on the right

boundary. Left, top and bottom boundaries with

vanishing velocities and constant temperature

(2.6 ºC). Initial temperature 50 ºC.

• Thermophysical properties: =1012 kg/m3;

cp=1700 J/kg K; =0.13 W/m K; =7.40·10-4 K-1.

0

200

400

600

800

1000

1200

1400

1600

0 3,125 5,25 10,25 15,25 20,125 50

temperature (C)

visc

osi

ty (

kg/m

s)


Numerical method

• Finite volume techniques with semi-implicit differentiation in

space and fully implicit in time, using Cartesian staggered grid.

• Pressure-based method (SIMPLEC). PLDS and CDS for

convective and diffusive terms respectively.

• Mesh: (N1 + N2) x M. Mesh concentration near the walls.

Constant t.

• Simulations carried out with an AMD K7 CPU at 1100 Hz.


Preliminar results

• High computational cost:

• Remedies: subdomain (or multiblock) techniques (as a parallelization strategy); variable t; semi-explicit methods; more efficient solvers; dynamic grids (variable grid concentration); ...

• Heat transfer and temperature evolution (ref 2):


Preliminar results (ref 2)

• The phenomenology at the first 20 days is mainly convective but,

once the fluid is cold enough to became very viscous, the velocity

decreases and the phenomenology is diffusive predominant.

• The inner tank is almost one degree hotter than the outer (5th day).


Preliminar results (ref 2)

• 1st day: relatively high velocities at the outer tank, specially at the left boundary due to natural convection. The inferior part of the system is the cooler one, with much more vortex (initial Rayleigh = 3.72·1013). Mean temperature around 39 ºC.

• 5th day: still movement into the tank, but considerably lower. Quite uniform temperature, around 30 ºC.

• From the 20th day velocities are almost null and temperature decrease has the form of an inverse exponential.

Code Development:

3a. Unstructured Grids

3a. Code development: unstructured meshes3a. Code development: unstructured meshes

Computational fluid dynamics and heat transfer (CFD&HT)

• Finite-volume techniques

• Analysis and development of different numerical schemes for the resolution of the convection-diffusion transport equations (Numerical Heat Transfer, two papers in press).

• Pressure-based methods for the pressure-velocity coupling.

• Algebraic multigrid solver for the resolution of the algebraic system of equations.


Smith-Hutton problem. Comparison of different schemes for the convective terms

Pe=103, D2, I2a Pe=, D2, I2a

Pe=, D1b, I2a Pe=, D2, I2a

Algebraic Correction Multigrid (ACM) for linear equation sys. A=b


• Smoothers: iterative (GS, MSIP,...) o direct solvers (used in the levels of the coarsest meshes)

• Correction equations are obtained forcing to zero the residuum of each block.

• Neighbours nodes are grouped according to criteria of more interaction (weight of the discretization coefficients).

Code Development:

3b. Subdomain Methods

3b. Subdomain methods3b. Subdomain methods

General comments

• The whole domain is split into a number of non-

overlapping subdomains.

• Useful strategy for complex systems and/or multi-

mathematical formulations according to the different

regions to be studied.

• Useful paralelization strategy

• Critical aspect: transfer of information between

subdomains (conservative vs. non-conservative

methods). Different strategies have been tested

depending on the transitory formulation (fully implicit

vs. explicit methods)

PCs running Linux: Beowulf cluster Joan Francesc Fernàndez (JFF)

Two clusters: i) 48 processors AMD k7, 900 MHz, switch 100 Mbits/s + 40 processors AMD K7 XP2600+ (1938 MHz), switch 100 Mbits/s; ii) 24 processors

Intel P4, 2800 MHz, switch 1 Gbit/s



Example of a complex geometry and boundary conditions

Code Development:

3c. Turbulence Modelling (RANS models)

Mathematical formulation (RANS models). Incompressible flows or gases at low Mach numbers.

3c. Code development: turbulence modelling (RANS models)3c. Code development: turbulence modelling (RANS models)

0vDt

D1

gTTvvpDt

vDo

TvqDt

TDcp

Linear eddy-viscosity models for the turbulent shear stresses and heat transfer:

k3

22vv t TT

cTv

T

t

p

t

Non-linear eddy-viscosity and explicit algebraic models for the turbulent shear stresses:

klklij2

2t

7klklij2

2t

6

ijnlmnlmmjlmilmjlmil2

2t

5

kllikjljki2

2t

4ijklkljkikt

3

kijkkjikt

2ijklklkjikt

1ijtijji

kc

kc

3

2kc

kc

3

1kc

kc

3

1kc2k

3

2vv

**

*

**

***

where, 2xvxv2xvxv ijjiijijjiij /// ;///


Two additional transport equations for some turbulent quantities (e.g. k-)

kk

k

t GPkDt

Dk

k

fCGfCPfCkDt

Dkk

t2

213311

2kfCt

donde, gTvGvvvP kk

;:


Fully developed turbulent flow in a channel (mean velocity, turbulent kinetic energy, and normal Reynolds stresses in y-z direction , ReDh=43460)


DNS results by R.Moser, J.Kim, M.N.Mansour, Direct numerical simulation of turbulent channel flow up to Re=990, Physics of Fluids, 11:943-945, 1999.

Turbulent impinging

plane jet


Experimental data by A.R.P.Van Heiningen, Heat transfer under impinging slot jet, PhD thesis, McGill University, Montreal, Canada, 1982.

Turbulent natural convection in a differentially heated cavity (A=5, Ra=5.1010, Pr=0.71)


Top: low-Reynolds number k- model by Wilcox (1993)

Right: modified k- model by Peng-Davidson-Holmberg (1999)

Experimental data by R.Cheesewright et al. (1996).

Code Development:

3d. Turbulence Modelling (DNS and LES models)

Governing equations (mass, momentum and energy):

TTvt

T

gTp1

vvvt

v

0v

2

2

Transport equation of the kinetic energy:

where,

vgTvpvvvvet

e Tc

c

PrPr

vvv T :

3d. Code development: turbulence modelling (DNS & LES models)3d. Code development: turbulence modelling (DNS & LES models)

Numerical method

•Explicit Adams-Bashforth methods with high-order spatial schemes

(second and fourth order).

•Spectro-consistent (or symmetry-preserving) discretizations (momentum

and kinetic energy should be exactly satisfied in each CV).

•Pressure-based method: a Poisson equation must be solved. For

incompressible flows this equation is strongly coupled in all the domain.

•Parallelization strategy when Beowulf clusters are used: Direct Schur

Decomposition and Direct Schur-Fourier Decomposition algorithms.

Poisson equation is solved with just one message. Speed-ups greater than

24 have been obtained with conventional 100 Mbits network and 36

processors.


Turbulent natural convection in a differentially heated tall cavity (Ra=6.4.108, Pr=0.71, A=4)

Horizontal section (z=3.75): mean T (top) and mean v (bottom). Two grids: B and A.

Temporal discretization:

Spatial discretization:•C: 16x37x76

•B: 32x76x154

•A: 64x154x310

•106 time-steps

Turbulent heat flux. Two grids: B and A..


Basic aspects of LESBasic aspects of LES


Filtered process (volume average)

0gTp1

vvvt

v 0v 2

;

vvvvgTp1

vvvt

v 0v 2

;

• Most closure models reinforced dissipation (they act to compensate the

convective term in the smallest scales).

• We have followed a different approach (Leroy and NS- models) acting on

the convective term itself. The modified term transfers energy up to a certain

point (no in the smallest scales) in such a way that some properties are

verified (Prof. Verstappen et al., University of Groningen): i) symmetry-

preserving discretization (conservation of kinetic energy); ii) enstrophy

conservation in 2D; iii) helicity conservation in 3D and no viscous dissip.

Closure problem: how to express the commutator in terms of fileterd velocity

New LES vs. DNS. Velocity profile v at z=2.0. Ra=10New LES vs. DNS. Velocity profile v at z=2.0. Ra=101010..


New LES (8x17x40=5440 nodes) vs. DNS (64x138x324=2.9.106 nodes!!)

New LES vs. DNS. Velocity profile w at z=2.0. Ra=10New LES vs. DNS. Velocity profile w at z=2.0. Ra=101010. .



New LES vs. DNS. Temperature profile at z=2.0. Ra=10New LES vs. DNS. Temperature profile at z=2.0. Ra=101010..



4. Conclusions

4. Conclusions4. Conclusions

• A detailed code for the thermal and fluid dynamic behaviour of fuel-oil in

sunk ships is being developed.

• Preliminar results of a benchmark case of the cooling process in the sunk

tanker Prestige have been presented. More effort is needed to obtain grid

independent solutions.

• Different computational topics have been addressed: i) unstructured

meshes to deal with complex geometries; ii) subdomain methods to deal

with complex systems and to allow easy paralelization; iii) turbulence

modelling: RANS vs. DNS vs. LES.

• A new LES method has been tested: a promising alternative to RANS

models!

Code Development:

3e. Verification of the calculations

3e. Code development: verification of the calculations3e. Code development: verification of the calculations

Based on the generalised Richardson extrapolation for mesh refinement and on the Grid Convergence Index (GCI)

Applications to transient problems have seldom been reported

Extension to transient solutions of the method developed at CTTC (Cadafalch et al.,J. Fluids Eng.,124,11-21,2002)

Numerical error given by two different sources: the mesh (h,t) and the numerical scheme (p)

3 solutions obtained by means of mesh refinement on three grids

3 equation system

Estimation of the local value of p, and the GCI

A global observed value of p contained within the expected limits of the theoretical p, shows asymptotically convergence of the numerical solution.

The GCI becomes then a reliable estimator of the absolute discretization error

3e. Code development: verification of the calculations3e. Code development: verification of the calculations

According to the discretization the governing equations, theoretical value of p is bounded by values 1.0 to 3.0

ht-refinement studies showed values of p between 1.5 and 1.0

Maximum values of p in the instants of maximum piston velocity

Maximum values of GCI at the TDP and the BDP

VERTIMAR-2005 Numerical Simulation of the Thermal and Fluid- dynamic behaviour of fuel-oil in sunk...

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