Aerodynamic noise in aero-engine LP turbines - Application of CFD techniques

Introduction 
In the following, an introduction to the research performed 
in this thesis is provided. The motivation of the growing 
interest on aircraft and aero-engine noise is given, as 
well as a general overview of the techniques applied, in an 
industrial perspective, for turbomachinery acoustic design. 
I. Background and motivation 
Aircraft noise is a growing problem for communities near 
airports. Air traffic is constantly increasing and is 
expected to increase even faster over the next years. This 
implies the number of airports and the extension of airport 
areas will increase, as well as the number of flights from 
each airport. This means that the concern about airport 
noise will involve more people, and the demand for quieter 
aircrafts will keep increasing.  
Noise pollution associated with take-off and approach may 
cause physical or psychological harm and studies have 
associated excessive noise with sleep deprivation, high 
blood pressure, and poor learning habits of children. In 
some cases, airports are paying millions of dollars to 
soundproof school classrooms to avoid being sued. 
Residential real estate and other properties surrounding 
airports are seeing declines in value as a result of 
aircraft noise. 
To assist with the problems, airports are cooperating to 
change flight procedures for 
take-off and landing. For example, pilots can only use 
certain amounts of thrust at take off and they must be at 
certain altitudes to make certain manoeuvres.  
Nevertheless noise reduction targets cannot be reached by 
improving aircraft traffic management alone. Noise 
reduction at source has to be considered, and here aircraft 
and engine manufacturers will still play a fundamental 
role. This is still more evident, as one thinks that 
aircraft noise regulations are becoming even more stricter.
Introduction 
 
 
 
 
 
 
 
XIII 
In modern turbofans, fan and jet noise are being 
substantially lowered due to the lower rotational speed and 
jet velocity, respectively. Hence, it is expected that to 
further reduce the engine noise other noise sources, like 
turbine and compressor, will have to be addressed. In 
particular, due to the increasing power of the fan 
resulting from an increased by-pass-ratio, the contribution 
of the low-pressure turbine to the overall engine noise 
will increase.  
Nowadays the main contribution of the turbine to the engine 
noise spectrum is related to the unsteady aerodynamic 
interaction between adjacent rows, that generates the so-
called tone noise.  
The objective of this thesis, carried out with the support 
of Avio, is to gain a deeper insight into the physics of 
noise generation in the turbine, in particular focusing on 
unsteady aerodynamic interaction between adjacent rows. 
Both wake-interaction and potential-interaction mechanisms 
will be addressed, that are the tone noise sources in the 
turbine. Moreover, a comparison among the acoustic 
behaviour of different turbines, corresponding to different 
aerodynamic design solutions, will be provided. 
II. Why Aeroacoustics analysis is 
needed 
Important goals in the aero-engine design are nowadays 
weight and cost reduction.  
The motivation is twofold. On one side, the reduction of 
the life cycle cost. On the other side, the reduction of 
the emissions, becoming more and more important due to the 
exponential growth of air transport and growing attention 
to environmental problems such as global warming. 
Another key issue related to the reduction of air transport 
environmental impact is the reduction of both aircraft and 
engine noise.  
Weight and cost reduction is achieved by reducing the 
number of mechanical parts and by adopting thin and highly 
loaded blades. 
These trends increase the relevance of rows aerodynamic 
interactions, including vibration problems, but also noise 
by rows interaction. 
Blade row design always starts from its hot geometry 
definition: “hot” means in design temperature and rotating 
velocity conditions. Once the initial aerodynamic geometry 
definition is completed, the mechanical and thermal
Introduction 
 
 
 
 
 
 
 
XIV 
analyses are put into action. First aeroacoustic analysis 
is also performed. The final hot geometry definition is 
obtained through an iterative redesign process that 
involves aerodynamic, thermal, acoustic, mechanical and 
aeroelastic phases. 
In this context, it is easier to understand the reason why 
in the last years Aeroacoustics and the development of 
aeroacoustc design tools have become an important research 
field, aiming, on one hand, to understand noise generation 
and transmission mechanisms, and  identify innovative 
technologies to reduce noise. On the other hand, to develop 
design tools that allow a multidisciplinary optimization 
process, fundamental to identify the best compromise 
between often competing design requirements, as well as to 
identify a “safe” design, able to address the 
interdependencies between aerodynamics and aeroelastic / 
noise phenomena in the design phase and avoid unexpected 
problems during test and certification.  
III. Analysis process 
The aeroacustic behavior of three different low-pressure 
turbines was investigated in detail by means of CFD 
aeroacoustic analyses. Each one of the analyzed turbine was 
representative of a kind of aerodynamic design concept (HL, 
UHL).  
Acoustic analyses were performed at the same operating 
points tested in aero-engine noise certification, referred 
as Approach, Cutback and Sideline, and representing the 
typical operating range during the aircraft taking off and 
approaching procedures.  
The first step of the analysis process was an aerodynamic 
CFD steady computation of the whole turbine. Then, a 
preliminary aeroacoustic-analysis was performed, aimed to 
point out potentially generated acoustic waves, 
distinguishing the cut-on ones, which can propagate along 
the duct and finally radiate into the far field, by the 
cut-off ones. This analysis was carried out, according to 
the Hanson and Tyler-Sofrin theories [25, 27]. Attention 
was focused on two adjacent rows whose interaction produces 
cut-on modes for the three turbines over the whole 
investigated operating range. 
To analyze the behaviour of these interactions, the outlet 
disturbance was circumferentially decomposed splitting the 
non-uniform steady flow field upstream and downstream to
Introduction 
 
 
 
 
 
 
 
XV 
the blade row into vorticity and pressure waves by means of 
a Fourier analysis.  
The objective of wave splitting analysis was twofold: 
gaining a deeper insight into the spatial and frequency 
content of the circumferential non-uniformities (velocity, 
pressure) produced by the interaction between two adjacent 
rows and providing the inlet boundary conditions needed by 
the aeroacoustic computation tools. 
Finally, a Q3D aeroacoustic computation was performed and 
results were exploited in details in the following 
sections. The previous analyses allowed evaluating noise 
generation sources and, successively, sound propagation 
features from source to turbine outlet. It is clear that 
these tools are becoming even more relevant for LPT design 
due to the fact that noise reduction represent an important 
target for aircrafts of the next generation. 
  
 
Figure I.1 - Unsteady real pressure in a blade row 
 
In Figure I.1, an example of a typical noise analysis 
output is shown: a contour line distribution for the real 
part of the unsteady pressure phasor field of a LP turbine 
bladerow. The acoustic wave fronts impinging the blade and 
transmitted downstream are clearly visible. The acoustic 
energy of these waves, expressed in terms of SPL, and their 
propagating behavior (cut-on, cut-off), will be the main 
object of study in the present thesis. 
Once reached turbine exit, acoustic waves spread in the far 
field each one with their frequency and directivity path.
Introduction 
 
 
 
 
 
 
 
XVI 
To evaluate a perceived noise level it must be taken into 
account of all the different acoustic waves. The sum of all 
disturbances merges into the EPNL index following the 
international FAR rules, and this represents an important 
parameter for engine noise certification. From this point 
of view, the next step will consist in evaluating this 
parameter, directly starting from CAA analyses. 
Consequently, these analyses are suitable not only in a LPT 
design context, but are relevant for the engine 
certification, too. 
IV. Structure of this thesis 
Chapter 1 gives a general and theoretical review of the 
subject this thesis refers to, that is Aeroacoustics. 
Chapter 2 is dedicated to investigate the generating 
mechanism in turbomachinery noise, giving some information 
regarding noise reduction techniques. Moreover, in this 
chapter the Tyler-Sofrin formulation about rotor-stator 
interaction is provided, introducing acoustic mode concept. 
The latter is resumed in chapter 3, where acoustic duct 
theory is explained, and the preliminary aeroacoustic 
analysis tool is presented. 
Chapter 4 provides some information on Computational 
Aeroacoustics (CAA), focusing on wave splitting methods and 
the aeroacoustic simulation tool exploited in the present 
work. 
Chapter 5 points out the relevance of noise measurement 
techniques, exploited in the context of engine 
certification. The way EPNL is evaluated is then described 
in more details. 
Finally, results gained by the several calculations are 
reported in the final chapter, arranged as described in 
section III.
1 
 
 
Chapter 1 
Aeroacoustics and Fluid-
dynamics 
1.1 Acoustics and Aeroacoustics 
Aeroacoustic phenomena consist in fluctuations in the field 
of pressure, which propagate with a particular frequency in 
an elastic medium, typically air. 
When the human ear perceives these perturbations, the head 
interprets those ones like a sound: however, it is 
necessary that frequency and intensity are appropriate 
(this aspect will be clarified later). The pressure 
fluctuations are accompanied by other ones of velocity and, 
(nearly undetectable) of density. 
Therefore, even if air is at rest, Aeroacoustics is closely 
related to Fluid Dynamics, and the acoustic field will be 
directed by the same general gas-dynamics equations 
governing the aerodynamic field. 
In theory, one could investigate acoustic field by means of 
the exact solutions of the compressible fluid-dynamic one. 
However, this is possible only if the air is at rest, 
otherwise the solution would contain both great effects 
(macroscopic airflow) and the smallest ones (acoustics 
flow), and the last ones would be hidden by the first due 
to the accuracy of the calculations. 
This is the reason why direct solution of fluid-dynamic 
equations has been so far a not practicable way in 
Aeroacoustics, that is in that field where noise is made by 
the fluid-dynamics motions and one cannot investigate the 
first (i.e. noise) without the latter. 
In order to avoid this problem, it is possible to look at 
analogical theories, which separate a source region (of 
sound), where the macroscopic flow is confined, from the 
acoustics field, where propagation medium at rest. 
In these analogical theories, the source’s action on fluid 
at rest is often represented by temporal variations of mass 
and energy, or by the application of a variable force.
2 
Therefore, it is opportune to come back to classical 
acoustics about a medium at rest and deduce in this context 
the sound field’s equations starting from the fluid- 
dynamics ones (equations of Navier-Stokes), with the non 
frequent hypothesis of energy and mass injections. Apart 
from the mathematical aspects, which will be treated in 
this chapter, now one can comprehend the reason why 
computational tools exploited in this work are the same 
ones of aerodynamic design, like CFD codes.  
 
However, Computational Aeroacoustics (CAA) presents some 
requirements that have led to developments of specific 
techniques with respect to Computational Fluid Dynamics 
methods. 
These requirements are connected to the nature of 
Aeroacoustics, and will be clarified in chapter 4. 
1.2 Navier-Stokes equations in the 
presence of mass and   energy 
injections 
The starting point is the differential form of Reynolds 
Transport Equation, used in formulating the basic laws of 
fluid-dynamics 
 
 



ij
i
j
j
x
f
t 

 


                   
(1.1) 
 
where symbols take the follow meaning: 
 
j
 is the specific value (per volume unit) of the 
physical variable A about which the   equations is 
written. 
 
j
f is the local production of 
j
 per time unit and 
includes the eventual interactions with external 
fields of forces. 
  


ij
is the i
th
 factor of the flow of the j
th
 component 
of A, positive if outgoing of the infinitesimal 
surface enclosing the point about which the (1.1) is 
valid. 
Outgoing flow  


ij
 is the sum of three possible terms: 
1. a macroscopic contribution due to convective 
transport of  the mass 
j
 is related to, this term 
is always given by 
j i
u  (being 
i
u the mass speed);
1. Aeroacoustics and Fluid-dynamics 
 
 
 
 
 
 
2 
2. a microscopic contribution (molecular)  


ij
 due to 
diffusion of A around the point, which doesn’t 
involve mass transport; 
3.   a possible mixed contribution  

ij
c . 
To summarize: 
     
a
ij ij j i ij
c u   
 
   
but this depends on the physical meaning of A. 
 
 
1.2.1 The continuity equation 
In this case A is the mass and    his specific (with the 
previous meaning) value. 
One considers a local mass generation 
m
Q per volume unit, 
it follows that 
m i
Q f  . The only contribute to the flow is 
the macroscopic convective one (since 
i
u is the mass 
speed,
i
u  represents its flow) .Equation (1.1) becomes: 
 
 
i
i
m
u
x
Q
t




 


                                                  
(1.2) 
 
 
which can be also expressed as follows 
 
 
i
i m
x
u Q
Dt
D


 



1
      
(1.3) 
 
1.2.2 The momentum equation 
Momentum per volume unit is a vector entity: 
j j
u    
It can be modified by an external field strength whose 
intensity is
j
H . Therefore, assuming a mass generation (at  
i
u velocity) 
m
Q too, it follows that 
 
j m j i
u Q H f   
1. Aeroacoustics and Fluid-dynamics 
 
 
 
 
 
 
3 
 


ij
 term consists in turn of two terms: the convective 
contribute 
j i j i
u u u    and the microscopic momentum flow from 
the faster layers to the slower ones, due to the viscosity. 
The latter is indicated 
ij
  .Therefore 
 
 
ij j i ij
u u   

  
 
where 
ij
 is the stress tensor . 
To summarize, (1.1) equation becomes now: 
 
   
ij j i
i
j m j j
u u
x
u Q H u
t
    


  


 
which developed 
 
 
i
ij
i
j
i i
i
j j m j j
j
x x
u
u u
x
u u Q H
t
u
t
u








  




 
  

 
 
Underlined terms give no contribute for (1.2), so 
 
i
ij
j
j
x
H
Dt
Du


 


1
             
(1.4) 
1.2.3 Equation of energy 
Now  is a scalar, representing fluid energy per volume 
unit. 
Assuming E the energy per mass unit, equal to the sum of 
the internal one e and the kinetic energy  
2 2
2
i i
u u V
  
it follows that 








  
2
2
V
e E    
j
f consists of three terms: 
w m i i i
Q E Q H u f     
 
where the first one is the power due to the external field 
strength; the second one is connected with local mass 
production (assuming that 
m
Q is generated with the same 
local energy E of the fluid); and the third is a locally 
generated heat power: this last becomes important during
1. Aeroacoustics and Fluid-dynamics 
 
 
 
 
 
 
4 
combustion processes, but will give no contribute at noise 
generation in the case of turbomachinery noise. 
 


ij
 is now a vector: 
 
ij j i i ij
u q E u   

   
The first term is the macroscopic one; the second is the 
molecular one and expresses the heat outgoing flow. The 
last term is the work of 
ij
 stresses. It follows by (1.2): 
 
   
ij j i i
i
w m i i
u q E u
x
Q E Q H u E
t
     


   


 
Developing the previous equation: 
 
   
ij j
i i
i
i
i i
i
w m i i
u
x x
q
x
E
u u
x
E Q E Q H u
t
E
t
E
   













   





 
 
where underlined terms disappear once again for (1.2) 
equation. 
To summarize, the equation of energy becomes 
 
 
ij j
i i
i
w i i
u
x x
q
Q H u
Dt
DE
  





   
 
By subtracting from the previous equation the (1.3) 
multiplied by 
j
u it can be obtained the equation of internal 
energy: 
 
  
i
j
ij
i
i
w
x
u
x
q
Q
Dt
De





        
(1.5) 
1.2.4 Constitutive equations 
Constitutional relations state the link between viscous 
stresses and strain velocity on the one hand, and between 
thermal flows and temperature field on the other one. 
The first is the constitutional equation of Newtonian 
flows: 
 
ij kk v ij ij
S S     






  
3
2
2 
 
where  is the dynamic viscosity,
v
 is called bulk 
viscosity coefficient , important in the case of
1. Aeroacoustics and Fluid-dynamics 
 
 
 
 
 
 
5 
combustion; 
ij
S is the strain velocity tensor (it is here 
remembered that in fluid-dynamics there is not a link 
between stress and strain tensor, like in solid mechanics, 
but between the first and the strain velocity tensor). 
The latter constitutional equation is the classic Fourier’s 
law: 
 
i
i
x
T
k q


  
 
where T is the temperature and k  the conductibility 
coefficient. 
By assuming fluid as ideal gas, it follows that T C e
v
 with 

v
C constant. 
Furthermore in the next equations it will be assumed that 
stress tensor 
ij
 is the sum of a reversible part 
ij
p   ( pbeing the thermodynamic pressure) and a 
irreversible viscous one 
ij
 , also called deviatoric stress 
tensor. 
1.2.5 Navier-Stokes equations 
By putting together equations (1.3),(1.4) and (1.5)  it is 
finally obtained: 
 
 



















 





 


 
i
j
ij
i
i
i
i
w v
j
ij
i
i
i
i
i m
x
u
x
u
p
x
q
Q T C
Dt
D
x x
p
H
Dt
Du
x
u Q
Dt
D
 

 



1
 
1.3 Acoustics field in a medium at rest 
Consider now the case of a small perturbation of a fluid at 
rest. By indicating with subscript 0 quantities (not time-
dependent) of the state at rest (so,   0
0

i
u ), and with an 
apex the concerning perturbations: 
 
 
; ;
; ; ;
0
0 0 0
i i
u u
T T T p p p
    
        
  
  