bianchinicosimo_phdthesis

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Universita degli Studi di Firenze

Facolta di Ingegneria

Dottorato in

Ingegneria Energetica e Tecnologie Industriali Innovative

Assessment of boundary

conditions for heat transfer and

aeroacoustic analysis

Relatori:

Prof. Bruno Facchini

Prof. Gavin Tabor

Candidato:

Cosimo Bianchini

Anno Accademico 2011



1

Context and aims

With the recently introduced regulations on pollutant emissions for aero-engines, major manufacturers had to move towards the lean premixed com-bustion technology. This introduces a significant reduction of air availablefor cooling purposes which designers needs to face seeking for more and moreefficient (and coolant saving) combustor cooling devices.

Furthermore the stability of the flame is deeply decreased and strongpressure fluctuations are generated within the combustor by an inhomoge-neous heat release. The beneficial role of the perforated plates employed incooling systems in the damping of such acoustic fluctuations can be takeninto account to avoid use of heavy and large additional acoustic dampers.

Accurate and reliable numerical simulations of the heat transfer and theacoustic properties of the cooling systems are therefore fundamental to assistthe design of such components. In order to overcome the known limitations of standard eddy-viscosity RANS models, more complex turbulence treatmentssuch as Large Eddy Simulation or anisotropic RANS models were consideredtogether with the possibility to account for heat conduction in the solidby means of conjugate heat transfer computations. The success of thesemore advanced computational techniques strongly relies on the provisionof adequate boundary conditions. An assessment of “optimal” boundaryconditions is hence proposed to evaluate possible enhancements of the fidelity

of such predictions.

Main achievements

A 3-dimensional numerical study of the heat transfer and acoustics of differ-ent combustor cooling devices, including impingement and effusion systems,was performed with the open-source CFD code OpenFOAM R.

In order to align the OpenFOAMRcode to the most advanced researchcodes for this kind of applications, three different boundary conditions wereimplemented in such a computational environment. The first one is an im-

plicitly coupled non conformal interface to solve for conjugate heat transfer,the second is an auto-recycling turbulent inlet generator with feedback tomaintain prescribed mean flow field while the third one is a non and par-tially reflecting boundary conditions with the possibility to include acous-tic forcing known as the Navier-Stokes Characteristic Boundary Conditions(NSCBC). The capabilities of those boundary conditions to improve the ac-curacy of predictions with respect to standard procedures were tested underconditions relevant for combustor cooling system design.

A conjugate heat transfer analysis of a multiperforated plate with highly



2

inclined conventional and shaped holes for effusion cooling was performed

computing overall effectiveness for both a cold and a hot condition. Ananisotropic correction to the two-layer eddy viscosity Low Reynolds turbu-lence model to augment lateral diffusion was tested showing a lower level of effectiveness.

0 1 2 3 4 5 6 7 8 9 1 0

0 . 5 0

0 . 5 5

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1 . 0 0

E X P - B R 3 . 2

A T L - B R 3 . 6

T L - B R 3 . 7

o

v

e

r

a

X / S

(a) Circular holes

0 1 2 3 4 5 6 7 8 9 1 0

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E X P - B R 3 . 2

A T L - B R 3 . 3

T L - B R 3 . 3

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v

e

r

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X / S

(b) Shaped holes

Figure 1: Spanwise averaged overall effectiveness.

Key factors for correctly predicting the overall effectiveness were foundto be a proper modelling of the heat sink effect and the correct set up of the

metal sheet conditions at the fluid inlet and outlet, as shown in figure 1 wherethe strong overestimation for the hot condition of the conventional geometryis related to the higher criticality of the above mentioned conditions.

An axisymmetric impingement jet with heat transfer was simulated ex-ploiting wall resolved LES turbulence treatment to test the potentiality of auto-recycling turbulent inlet for heat transfer analysis.

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e

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y / D

M a p p e d

M a p p e d F l u c t u a t i o n

E X P

(a) Mean radial velocity

0 . 0 0 . 1 0 . 2 0 . 3 0 . 4

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(

U

' r

U

' r

)

/

U

2 b

M a p p e d

E X P

y / D

(b) Effective radial fluctuation

Figure 2: Flow field in the wall jet zone - r/D=2.



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The auto mapped technique proved its capability in the generation of tur-

bulent inflow conditions while the mapped fluctuations too strongly inhibitsthe onset of turbulent fluctuations in the feeding pipe resulting in an almostlaminar profile with too high potential core inertia. This is highly affectingthe wall jet development as reported in figure 2.

Concerning heat transfer, even though the secondary peak in Nusseltnumber (around r/D = 2) was not reproduced, the primary peak in thestagnation region and the asymptotic behavior are quite well captured, seefigure 3.

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2 0

4 0

6 0

8 0

1 0 0

1 2 0

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1 6 0

1 8 0

2 0 0

2 2 0

M a p p e d

M a p p e d f l u c t u a t i o n s

E X P

N

u

r / D

Figure 3: Nusselt number radial distribution.

Finally, the acoustic behavior of multiperforated plates with bias flowwas studied to evaluate the performance of acoustically excited NSCBC inmodelling the effects of a speaker. Large Eddy Simulation was exploited toresolve the unsteady structures developing in the free and acoustically excited jet configuration. Results obtained for the absorption coefficient were com-pared with available experiments and other computational tools as reportedin figure 4.

1 0 0 2 0 0 3 0 0 4 0 0 5 0 0 6 0 0

0 . 0

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E x p e r i m e n t a l

L E S

H o w e

M o d i f i e d H o w e

f r e q u e n c y ( H z )

A

Figure 4: Absorption coefficient - Bellucci test case



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A Proper Orthogonal Decomposition was applied to the unsteady flow

field permitting a spectral analysis of the most energetic acoustic modesshowing a substantial decoupling between the fluid-dynamic characteristicStrohual numbers and the frequencies characterizing the flame instability.

Conclusions and perspectives for future works

The implemented conditions showed results aligned with the “state of theart” for these kind of computations. The open-source code OpenFOAMR

chosen as the framework where develop and implement the proposed algo-rithms, was found to be as effective as the most advanced research codes for

the computation of the heat transfer and aeroacoustics of the gas turbinecombustor cooling systems and proved to be accurate and fast enough forthe purpose of this work.

In particular the implicit conjugate boundary condition for non confor-mal interfaces permitted to improve convergence rate, especially in case of steady-state calculations, with respect to explicit iterative coupling and torationalize the mesh generation process compared to only conformal inter-faces. The turbulent inflow generator with purely auto-recycling technique,well performed in terms of being able of developing turbulent fluctuations.Anyhow the attempt to force a given mean profile to speed up convergencetowards statistically averaged state failed in generating adequate fluctuationslevel. The NSCBC result to be effective for both free and acoustically ex-cited boundaries. Even with multi-tonal signal superposed, they showed tomaintain the desired non reflecting behavior.

Further work on the proposed boundary conditions should be directedtowards the enhancement of the parallel efficiency of the conjugate interfaceand the NSCBC as well as the proposal of techniques to shorten the transientdevelopment of the flow when subject to mapped inflow conditions. Moreoverthe NSCBC for solid wall should be implemented to make the pressure wavereflection more physical considering both adiabatic and given temperaturewall thermal conditions.

bianchinicosimo_phdthesis

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