entropynoiseingasturbines - keele university...24of60 generaon"of"entropy"waves"...

Entropy noise in gas turbines -‐ background and challenges

Dr Aimee S. Morgans KTH Workshop in aeroacous=cs in confined flows

of low mach number May 23rd 2014

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What is entropy noise? •  Entropy noise is one (of two) components of combus=on noise •  Unsteady combus=on always generates:

•  Acous=c waves -‐ these propagate within the combustor.

acoustic

waves

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What is entropy noise? •  Entropy noise is one (of two) components of combus=on noise •  Unsteady combus=on always generates:

•  Acous=c waves -‐ these propagate within the combustor.

•  Entropy waves (hot/cold spots) -‐ these are “swept” downstream, advec=ng with the flow. In a non-‐accelera=ng flow they are “silent”.

entropy waves

acoustic

waves

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What is entropy noise? •  Q: If entropy waves are silent, what is “entropy noise”?

•  A: When the flow is accelerated, acous=c, entropy and vor=city waves all become coupled. Thus by accelera=ng entropy waves, new acous=c waves are generated.

noise

Q’ mean flow

source of directcombustion

noise

source of entropy

Regions of fluid with different densi=es undergo different volume contrac=ons

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Entropy noise in gas turbines

•  Q: Are entropy waves accelerated in real combus=on systems?

•  A: Yes! In a gas turbine, as the flow undergoes rapid accelera=on through the combustor exit and first turbine stage. This means that the entropy waves generate acous=c waves, called “entropy noise”, or “indirect combus=on noise”.

Stator exit shock waves from Mee et al. (1992)

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Acousticwaves

Entropywaves

Turbine

blades

Directcombustion

noise

noiseEntropy

release rate Unsteady heat

from flame

unsteady flame

direct noiseturbine blades

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Acousticwaves

Entropywaves

Turbine

blades

Directcombustion

noise

noiseEntropy


from flame

entropy waves


unsteady flame

(hot spots)

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Acousticwaves

Entropywaves

Turbine

blades

Directcombustion

noise

noiseEntropy


from flame

(indirect noise)


unsteady flame

entropy noise

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•  Simplified movie of nozzle response to impulse in unsteady heat release rate.

•  Note the different =me scales for returning to the flame of the “direct” and “indirect” noise.

Combustor flows are low Mach number (M < 0.2) to keep the flame adached. Thus the acous=c waves travel at M≈1, entropy waves travel at flow Mach number M << 1.

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Why is entropy noise important? •  Aeroengine exhaust noise •  Combus=on instability

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Why is entropy noise important? •  Future aero-‐engine noise reduc=ons, as predicted by Snecma.

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Why is entropy noise important? •  Aeroengine exhaust noise •  Combus5on instability

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Entropy noise research Five “stages” of combus=on noise relevant to research: 1.  Genera5on of entropy waves by flame 2.  Advec=on of entropy waves within combustor 3.  Genera=on of acous=c waves as entropy waves accelerated 4.  Passage of acous=c waves through turbine (including subsequent accelera=on of entropy wave) 5.  Effect of reflected component of entropy noise on combus=on instability

1

direct

noiseentropy

noise

combustorturbine stages

flameacoustic

waves

entropywaves

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Entropy noise research Five “stages” of combus=on noise relevant to research: 1.  Genera=on of entropy waves by flame 2.  Advec5on of entropy waves within combustor 3.  Genera=on of acous=c waves as entropy waves accelerated 4.  Passage of acous=c waves through turbine (including subsequent accelera=on of entropy wave) 5.  Effect of reflected component of entropy noise on combus=on instability

2

direct

noiseentropy

noise


flameacoustic

waves

entropywaves

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Entropy noise research Five “stages” of combus=on noise relevant to research: 1.  Genera=on of entropy waves by flame 2.  Advec=on of entropy waves within combustor 3.  Genera5on of acous5c waves as entropy waves accelerated 4.  Passage of acous=c waves through turbine (including subsequent accelera=on of entropy wave) 5.  Effect of reflected component of entropy noise on combus=on instability

3

direct

noiseentropy

noise


flameacoustic

waves

entropywaves

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Entropy noise research Five “stages” of combus=on noise relevant to research: 1.  Genera=on of entropy waves by flame 2.  Advec=on of entropy waves within combustor 3.  Genera=on of acous=c waves as entropy waves accelerated 4.  Passage of acous5c waves through turbine (including subsequent accelera5on of entropy wave) 5.  Effect of reflected component of entropy noise on combus=on instability

4

direct

noiseentropy

noise


flameacoustic

waves

entropywaves

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Entropy noise research Five “stages” of combus=on noise relevant to research: 1.  Genera=on of entropy waves by flame 2.  Advec=on of entropy waves within combustor 3.  Genera=on of acous=c waves as entropy waves accelerated 4.  Passage of acous=c waves through turbine (including subsequent accelera=on of entropy wave) 5.  Effect of reflected component of entropy noise on combus5on instability

5

direct

noiseentropy

noise


flameacoustic

waves

entropywaves

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Entropy noise: history

•  Ini=al research ac=vity in 1970’s e.g. Strahle (1972), Hassan (1974), Chiu & Summerfield (1974), Marble & Candel (1977), Cumpsty & Marble (1977)

•  Research resurgence over last 6 years or so.

Lean premixed low NOX combustors have increased combus=on noise and propensity to combus=on instability.

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Genera=on of entropy waves

1

direct

noiseentropy

noise


flameacoustic

waves

entropywaves

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Genera=on of entropy waves

Let’s remind ourselves of what entropy “is”. It’s defined through the standard thermodynamic rela=on

from which it follows that We are only interested in entropy fluctua=ons: seong and linearising gives that:

which is equivalent to

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Genera=on of entropy waves Consider the standard flow equa=ons of mo=on in a compressible fluid: Mass Momentum Energy Assume inviscid flow, ideal gas, cp and cv constant, and zero mean vor=city. Linearise about steady, uniform mean flow, so that etc.

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Genera=on of entropy waves This linearisa=on of the Euler equa=ons gives 3 equa=ons in pressure, entropy and vor=city. See Dowling and Stow (2003) for more detailed deriva=on

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Genera=on of entropy waves This linearisa=on of the Euler equa=ons gives 3 equa=ons in pressure, entropy and vor=city.

Note 1: In the presence of unsteady heat release q’, the pressure and entropy equa=ons are coupled. The vor=city equa=on is not coupled to the other two.

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Note 2: If q’=0, we recover the “convected wave equa=on” for pressure, and find that entropy fluctua=ons simply advect with the mean flow. All 3 equa=ons are decoupled, meaning acous=c, entropy and vor=city waves are all independent (Chu & Kovasznay 1958)

L (speed c-‐u ) R (speed c+u )

s’ (speed u) ξ ’ (speed u)

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Note 3: If = 0, we recover which is consistent with the “direct” combus=on noise work from the 1970’s (Strahle (1972), Hassan (1974), Chui & Summerfield (1974)). Good overview in “Modern Methods in Analy=cal Acous=cs” book.

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Genera=on of entropy waves This linearisa=on of the Euler equa=ons gives 3 equa=ons in pressure, entropy and vor=city. So unsteady heat release rate, q’, acts as a “source” of both acous=c waves and entropy waves. Once away from the heat release zone, the acous=c waves propagate at speed rela=ve to the flow, while the entropy waves advect at speed

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Genera=on of entropy waves A final note on what an entropy fluctua=on “is”: Away from the heat release, we know (i) that

or equivalently

and (ii) that entropy and pressure fluctua=ons are uncoupled (independent).

Note: this has led to the concept of “excess density”

e.g.Lighthill (52), Morfey (73)

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Genera=on of entropy waves A final note on what an entropy fluctua=on “is”: Away from the heat release, we know (i) that

or equivalently

and (ii) that entropy and pressure fluctua=ons are uncoupled (independent). For an entropy wave in isola=on (no acous=c waves)

In prac=ce, even in the presence of acous=c waves, the acous=c component of temperature and density fluctua=ons is small.

Thus an entropy fluctua=on (wave) is comprised of the (non-‐acous=c component of) the temperature or density fluctua=on.

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Advec=on of entropy waves

2

direct

noiseentropy

noise


flameacoustic

waves

entropywaves

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In prac=ce, the mean flow responsible for entropy wave advec=on is not uniform (Sadelmayer 2004)! Even in a simple geometry like a channel, it varies due to boundary layers.

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In prac=ce, the mean flow responsible for entropy wave advec=on is not uniform (Sadelmayer 2004)! Even in a simple geometry like a channel, it varies due to boundary layers.

? How does this affect the entropy wave strength at the combustor exit (i.e. at accelera=on)?

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The equa=on (retaining non-‐linear and viscous terms) governing entropy wave transporta=on is:

Morgans, Goh & Dahan (2013) considered entropy wave advec=on in direct numerical simula=ons (DNS) of a simple turbulent channel flow.

Define: Dissipa=on: Ds’/Dt = -‐X2 Shear dispersion: reduc=on in wave strength due spa=al varia=ons in velocity field causing smearing

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The entropy wave “impulse response” between flame and channel exit was considered for the area-‐averaged wave strength.

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•  “Smearing” and shortening of wave strength seen •  Entropy wave suffered negligible dissipa=on. •  It suffered shear dispersion due to the mean velocity profile •  Turbulent flow fluctua=ons had lidle effect.

0 1 2 3 4 5 60

0.2

0.4

0.6

0.8

1

x/h

Rel

ativ

e m

agni

tude

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•  “Smearing” and shortening of wave strength seen •  Entropy wave suffered negligible dissipa=on. •  It suffered shear dispersion due to the mean velocity profile •  Turbulent flow fluctua=ons had lidle effect.

0 1 2 3 4 5 60

0.2

0.4

0.6

0.8

1

x/h

Rel

ativ

e m

agni

tude

A Gaussian transfer func=on model was shown to give good fit.

Shear dispersion for flow condi=ons of typical combustor much less than previously thought

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Entropy wave accelera=on

3

direct

noiseentropy

noise


flameacoustic

waves

entropywaves

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•  The Marble & Candel (1977) paper considered what happens to entropy waves when they are accelerated through subsonic and supersonic nozzles

•  Explains direct and indirect noise mechanisms

S

acoustic waveentropy wave

M <11P

P+

P

2M >1P

S

!+1

1 !2

2

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•  Consider a choked nozzle with 1-‐D flow •  Assume acous=cally compact nozzle (very low frequency approxima=on) •  Nozzle then acts as discon=nuity, and linearised Euler equa=ons are quasi-‐

steady giving 3 jump condi=ons across nozzle:

mass flow rate stagna=on temperature entropy Jump condi=ons wriden in terms of acous=c & entropy wave strengths

S


M <11P

P+

P

2M >1P

S

!+1

1 !2

2

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•  Combining these 3 jump condi=ons gives rise to

•  This equa=on acts as a boundary condi=on on both upstream and downstream flow-‐field, rather than matching condi=on across nozzle.

•  Allows reflec=on and transmission coefficients to be found for incident acous=c or entropy wave.

S


M <11P

P+

P

2M >1P

S

!+1

1 !2

2

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S


M <11P

P+

P

2M >1P

S

!+1

1 !2

2

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•  Recent work has focussed on extending concepts to •  higher frequencies for general geometries (Stow et al. 2002, Goh & Morgans

2011) •  Any frequency for specific nozzle geometries (Moase et al. 2007, Giauque et al.

2012)

•  Paper last year (Duran & Moreau 2013) extends to any frequency and any

geometry!

S


M <11P

P+

P

2M >1P

S

!+1

1 !2

2

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Duran & Moreau (2013) start with same quasi 1-‐D linearised Euler equa=ons as Marble & Candel (1977)

Aver a convenient change of variable and considering harmonic varia=ons, these can be recast as

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Entropy wave accelera=on This is solved using a Magnus expansion (Magnus 1954)

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Entropy wave accelera=on Comparing Duran & Moreau’s Magnus expansion method with experiments

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Entropy noise passage through turbine

4

direct

noiseentropy

noise


flameacoustic

waves

entropywaves

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Entropy noise passage through turbine •  Each blade row modelled as discon=nuity -‐ compact assump=on

(Cumpsty & Marble 1977) •  Jump condi=ons applied across this e.g for stator row

•  Similar for rotor row but rota=ng frame used (e.g. rothalpy instead of

enthalpy)

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Entropy noise passage through turbine Interac=ons of successive blade rows then follows from straighworward matrix mul=plica=on (Cumpsty & Marble 1977) Simple wave propaga=on between rows Cumpsty & Marble (1977) compare mesaured & predicted rear arc acous=c power for 3 real gas turbines Good match at low jet veloci=es (when jet noise low)

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Entropy noise passage through turbine

•  Recent results from CERFACS (Toulouse) for 1 stator row followed by 1 rotor row

Reflected wave Transmided wave

___ analy=cal . , + numerical, simple entropy dispersion model (Leyko 2010)

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Effect of entropy noise on combus=on instability

5

direct

noiseentropy

noise


flameacoustic

waves

entropywaves

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Effect of entropy noise on combustor stability

Consider simple model combustor with entropy waves present downstream of flame (Goh & Morgans 2013). Choked upstream and downstream. Assume plane acous=c waves, compact flame.

etc in region 1.

Similar in region 2, except density fluctua=on has entropic component:

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(Linearised) conserva=on of mass, momentum, energy applied across flame. Flame model required for closure

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Simple =me delay spread model for entropy wave dispersion

Area = 1 Area = k (<1)

flame outlet

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Find the combustor modes (frequency and growth rate) by numerically finding poles of relevant transfer func=on

Poles in white

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Entropy noise can (Goh & Morgans 2013): •  Destabilise otherwise stable modes •  Stabilise otherwise unstable modes •  Cause mode switching •  Cause an acous=c-‐entropic instability in which heat release rate amplitudes

stay small

Mode destabilisa=on as entropy waves increasingly accounted for (k increasing from 0 to 1)

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Entropy noise can (Goh & Morgans 2013): •  Destabilise otherwise stable modes •  Stabilise otherwise unstable modes •  Cause mode switching •  Cause an acous=c-‐entropic instability in which heat release rate amplitudes stay

small

Mode switching as entropy wave dispersion varies (k=1)

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Final note: entropy noise experiments

•  Experiments on entropy noise complicated by difficul=es in measuring entropy waves – measuring temperature fluctua=ons at high speed a challenge!

Entropy wave generator DLR Berlin (Bake et. al 2009)

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Conclusions

•  Entropy noise important for aero-‐engine noise and combus=on instability

•  Generated by accelera=on of “hot-‐spots” / “cold-‐spots” resul=ng from unsteady heat release

•  Entropy wave (i) genera=on, (ii) advec=on, (iii) accelera=on, (iv) passage through turbine and (v) effect on combus=on instability all ac=ve research areas!

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Thank you!

entropynoiseingasturbines - keele university...24of60 generaon"of"entropy"waves"...

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