BianchiniCosimo PhD dissertation 13 April 2011

University of FlorenceDepartment of Energy Engineering

Assessment of boundary conditions for heat transfer and

aeroacoustic analysis

Cosimo BianchiniHTC group

Energy Engineering Department

Via di S.Marta 3, 50139 Firenze

[email protected]


Cosimo Bianchini – PhD thesis dissertation – 13/04/2011

DNS – near wall LES – far field LES – Advanced RANS – RANS

Effusion cooling – Effusion acoustic – Impingement jet

Outline• Introduction

• Generic grid interface for conjugate heat transfer analysis

• Overall effectiveness of effusion cooling plates

• Auto-recycling turbulent inlet condition

• Heat transfer of axisymmetric impingement jet

• Navier-Stokes Characteristic Boundary Conditions

• Acoustic response of perforated plates

• Conclusions

2/17





Motivation

3/17

Dome cooling

Impingement arrays

Liner cooling

Effusion systems

• Stricter requirements for aero-engine pollutant emission

• Lean Partially Premixed technology

• Reduced amount of air for cooling purposes

• Decreased stability of flames working close to the lean limit

• Perforated plates may absorb acoustic fluctuations

• Present-day aero-engines combustion chambers cooling is obtained by:

• Effusion for the liner

• Impingement in the dome

• Exploit cooling system as passive dampers

• Dual thermal acoustic optimization





Motivation

4/17

• Numerical predictions to reliably help designers needs to

• overcome known failures of standard CFD analysis

• at a computationally affordable level

• Implement methods for

• Conjugate Heat Transfer analysis

• Large Eddy Simulation

• In the context of open-source CFD

• OpenFOAM®

• Increased complexity require adequate boundary treatment

• Energy balance on the interface needs to be respected

• Grid scale turbulence needs to be specified

DNS

Wall resolved

LES

Far field

LES

Advanced

RANS

RANS





Objectives

5/17

• The aim of the thesis is to • implement, validate and assess boundary conditions for the study of heat transfer

and aero-acoustic phenomena connected with combustor cooling

• Technological problems faced• Estimate combined effect of film protection and heat sink in effusion cooling devices

• Evaluate the cooling capabilities of impingement jets

• Assess the potential of perforated liners as acoustic dampers for the stabilization of lean flames

• Computational aspects• Conjugate interface boundary condition to couple fluid and solid domain

• Generation of turbulent fluctuations for inflow boundary

• Non-reflecting inflow and outflow boundaries with acoustic forcing





Conjugate interface• Energy equation solved in terms of temperature (static or total)

• Fluid: convective-diffusive equation • Solid: Fourier equation

• Coupled boundary guarantees• Continuity of temperature• Continuity of heat flux: temperature gradient

• Different mesh requirements for fluid and solid side• No boundary layer in solid domain• Strictly apply only to Low-Reynolds computations• Non conformal interface treatment

6/17

same matrix for solid and fluid domain

fwsw TT ,,

fwf

sws n

Tk

n

Tk

,,





Effusion cooling conjugate analysis

7/17

• Conventional (circular hole) and shaped (circular imprint) holes

• Same porosity, same slanted angle:17°

• High temperature rig (Poiters): heat shield, 17-12 rows

• 3.5 millions cells hybrid mesh for 8 rows

• Steady-state RANS analysis: Two-Layer (TL) and anisotropic Two-Layer (ATL) turbulence models

ConventionalShaped





Turbulent inlet

8/17

• Perfect turbulent inlet should:• “look” like turbulence• allow easy specification of turbulent

integral properties• easily adjust to new inlet conditions• be computationally cheap

• Internal mapping• identify an internal portion of

the domain to apply recycling methods

• Feedback• scaling the mapped field to

satisfy specified integral values• Mapped fluctuation

• same procedure applied to fluctuations

• superposed on desired base profiles





Axisymmetric Impingement Jet

9/17

• Ercoftac database: Re= 23000, H/D=2

• Detailed experimental data

• hexahedral mesh, 84 blocks, 5.2 millions cells

• Incompressible Large Eddy Simulation

• Additional equation for temperature

• One equation sgs model: transport equation for turbulent kinetic energy

• Convective condition on outlet and top boundaries

• Fully developed inlet condition

• Mapped and Mapped fluctuation (from pipe simulation)

0

n

UC

t

U

MappedMapped fluctuation






10/17

• Mean velocity

• Impinging zone

• Wall jet zone

R/D = 0 R/D = 0.5

R/D = 1 R/D = 2 R/D = 3






11/17

• Effective fluctuations

• Radial fluctuations

• Axial fluctuations

''rrUU

R/D = 0.5 R/D = 1 R/D = 2 R/D = 3

''zzUU

R/D = 3R/D = 2.5R/D = 1R/D = 0.5






12/17

• Constant and uniform heat flux: mean Nusselt number

• Controversy on stagnation point dip and secondary peak

• Secondary peak due to periodical impingement of broken ring vortex

• Too low axial fluctuations might have lowered Nu for r/D > 1.5





Non reflecting boundaries

13/17

• Navier Stokes Characteristic Boundary Conditions (NSCBC)

• Characteristic wave analysis on the boundary

• NSE are rewritten on the boundary in terms of wave amplitude variations

• Entering waves: imposed by means of Linear Relaxation Method

• Outgoing waves: extrapolation from internal solution

• NSE are integrated on the boundary

• Introduction of transverse and diffusive terms

• The reflectivity of the boundary is driven by

• Acoustic forcing is introduced with variable target value

c,,,n

p,n

ufL

)( TL

L

)cos( tAT





Acoustic response of perforated plates Bellucci test

14/17

• Periodic circular hole at 90 deg with bias flow

• Pulsed pressure outflow and fully reflecting inlet with NSCBC

• Wall Adaptive Local Eddy (WALE) viscosity model

• Estimate reflection coefficient of perforated plate with bias flow

• Multimicrophone (4 stations) post processing technique

• Reconstruction of progressive and regressive wave

R





Acoustic response of perforated plates Bellucci test

15/17





Acoustic response of perforated plates KIAI test

16/17

• Same set up more realistic geometry and flow conditions

• Multifrequency excitation

• Effect of stagger studied with different cyclic boundary arrangement at 1000 Hz

i

iiT tAp )cos(

in line staggered rhomboidal staggered rectangular





Conclusions

17/17

• Three boundary conditions were implemented in an open-source CFD code

• A conjugate interface with implicit non-conformal coupling

• An internal mapping turbulent inlet generator

• Non and partially reflecting inflow and outflow conditions

• Accuracy of prediction was tested under conditions relevant for combustor liners cooling system design

• An effusion cooling plate at engine like condition

• An axisymmetric impingement jet with heat transfer

• The acoustic response of perforated liners with bias flow

• The implemented conditions showed results aligned with “state of the art” computations

• Further work should be addressed towards:

• Improving efficiency, robustness and stability

• Development of homogeneous model for thermal and acoustic behavior of perforated plates





Publications• Bianchini, Da Soghe, Facchini, Innocenti, Micio, Bozzi, Traverso, “Development of numerical tools for stator-rotor

cavities calculation in heavy-duty gas turbines", 2008, ASME PAPER GT2008-51266, Asme Turbo Expo, Berlin

• Bianchini, Facchini, Mangani, “Conjugate heat transfer analysis of an internally cooled turbine blades with an object oriented cfd code", 2009, European Turbomachinery Congress, Graz

• Andreini, Bianchini, Ceccherini, Facchini, Mangani, Cinque, Colantuoni, “Investigation of circular and shaped effusion cooling arrays for combustor liner application – Part II: Numerical analysis", 2009, ASME PAPER GT2009-60038, Asme Turbo Expo, Orlando

• Boust, Lalizel, Bianchini, Facchini, Cinque, Colantuoni, “Dual investigations on the improvement of effusion cooling by shaped holes", 2009, 7th World Conference on Experimental Heat transfer Fluid mechanics Thermodynamics, Krakow

• Bianchini, Simonetti, Zecchi, “Numerical and experimental investigation of turning flow effects on innovative pin fin arrangements for trailing edge cooling configurations”, 2010, ASME PAPER GT2010-23536, Asme Turbo Expo, Glasgow to appear on Journal of Turbomachinery

• Bianchini, Mangani, Maritano, “Heat transfer performance of fan-shaped film cooling holes. Part II – Numerical analysis”, 2010, ASME PAPER GT2010-22809, Asme Turbo Expo, Glasgow

• Bianchini, Bonanni, Carcasci, Facchini, Tarchi, “Experimental survey on heat transfer in an internal channel of a trailing edge cooling system”, 2010, 65° ATI conference

• Bianchini, Andreini, Facchini, “Numerical analysis of the heat transfer in a trailing edge cooling duct in stationary and rotating conditions”, 2011,9th European Turbomachinery Congress, Istanbul

• Andreini, Bianchini, Armellini, Casarsa, “Flow field analysis of a trailing edge internal cooling channel”, 2011, ASME PAPER GT2011-45724, Asme Turbo Expo, Vancouver, Accepted for publication

• Simonetti, Andreini, Bianchini, “Assessment of numerical tools for the evaluation of the acoustic impedance of multi-perforated plates”, 2011, ASME PAPER GT2011- 46303, Asme Turbo Expo, Vancouver, Accepted for publication


Assessment of boundary conditions for heat transfer and

aeroacoustic analysis

Cosimo BianchiniHTC group

Energy Engineering Department

Via di S.Marta 3, 50139 Firenze

[email protected]





• Multiple implicit coupling - ghost cell mechanism

• Contribution of ghost cell calculated via cell-to-cell addressing and weighting factors αi

• Weighting factors based on face overlapping areas

• Algorithm for overlapping area based on surface integral of the product of the winding number of the two polygons

• Applies to every non self-intersecting polygon, positively oriented: all types of meshes can be used (tetra,hexa,poly,etc..)

,1f p p p i n ii

w w

,i o i fpA A

,n i n iC C

Domain 1

Domain 2 p

n1 n2

Non conformal interface

Generic grid interface

20/20





KIAI test – Flow field analysis

21/20

• Instantaneous axial velocity show typical turbulent behaviour

• Modal analysis performed with Proper Orthogonal Decomposition technique

• Equivalent but symmetric modes at 3 and 5

• Mode 2: vortex rings aligned with hole axis

• Mode 4: vortex rings misaligned with hole axis

POD pressure modes

BianchiniCosimo PhD dissertation 13 April 2011

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