First Stage of the Centrifugal Compressor Design with Tandem Rotor Blades

1
First Stage of the Centrifugal Compressor Design
with Tandem Rotor Blades

• Daniel Hanus, Tomá Censký
• CZECH TECHNICAL UNIVERSITY
• IN PRAGUE
• Jaromír Neveceral,
• Vojtech Horký
• WALTER ENGINES a.s

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Contents

• Introduction
• Thermodynamics of the Centrifugal Compressor
  Stage
• One Dimensional Design of the Centrifugal
  Compressor Stage
• Indirect Design Method of the Mean Streamline
  Geometry
• Primary LPC Design Parameters
• Impeller Primary Design
• Tandem Blade Design Philosophy
• Tandem Blade Design Procedure
• CFD Calculation of Compressor Characteristics
• First Results and Discussion
• Conclusions and Future Work

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Introduction

• Centrifugal compressors are widely used in
  turbine engines of smaller power outputs
• Advantages
• Higher pressure ratio attainable in one stage
• Higher efficiency at low flow rates
• Higher mechanical resistance
• New project of the two stage single shaft
  centrifugal compressor design at the Walter
  Engines a. s.
• Collaboration with the Department of Automotive
  and Aerospace Engineering of the CTU in Prague

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Thermodynamics of the Centrifugal Compressor
Stage
Centrifugal compressor flow path-station numbering
Isentropic efficiency
One-dimensional flow path thermodynamic state
curve in the temperature-entropy diagram
Total pressure ratio
5
One Dimensional Design of the Centrifugal
Compressor Stage

• Intention - to define basic thermodynamic,
  kinematical, and geometric parameters of the
  compressor flow path and to select preferably
  optimal geometry of the stage even in the very
  beginning of the design
• Input data file needed
• 1) Given basic desired performance parameters of
  the compressor stage
• 2) Data obtained by optimizing procedures
• 3) Data based on the experience gained from
  experimental research
• Design procedure consists of the three main parts
  
• Impeller inducer
• Exducer
• Diffuser.

Results from the 1 D design then form basic input
data file for the following part of the method -
design of the impeller blade geometry and
diffuser geometry.
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Impeller Inducer Design
Impeller inducer significantly influences
impeller operation and thus operation of the
whole compressor stage.This influence is the most
important in case of transonic inlet flow
pattern. Particular attention should be paid to
the inducer within all stages of the design.
Optimization of the inlet area of the inducer
for given air mass flow with regard to Mach
Numbers at the leading edge of the blade is
necessary. Optimization represents here a
selection of such an inlet velocity distribution
to which corresponds to minimum Mach number of
the relative air velocity at the inducer tip.
Relative velocity Mach number at the inducer at
the tip and mean radius as a function of axial
flow velocity for given rotational speed, and
mass rate.
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Impeller Exducer Design
Design philosophy Determine the outlet diameter
D2 and the width N2 of the impeller for given
specified parameters like a mass flow rate G and
rotational speed nK to obtain desired pressure
ratio ? of the compressor stage for the condition
of maximum attainable compressor efficiency ?.
Computational procedure is based on these
specified parameters and gives first
approximation of thermodynamic, kinematical and
geometric parameters at the outlet for estimated
circumferential velocity u2 , and selected blade
geometric angle ?2g at the outlet. Required
design pressure ratio is then attained through
optimisation of the circumferential velocity
given by the requirement to attain optimum
specific speed within limitations given by
specifications. Calculation Procedure Impeller
outlet diameter D2 is determined at first.
Performance coefficient or slip factor ? is
determined from semi-empiric formula. The exducer
height N2 calculation takes in account the effect
of the boundary layer (?2) and blades thickness.
Density of the fluid is determined through an
iteration procedure. Meridional component of the
absolute velocity is selected circumferential
component of the absolute velocity is hereafter
calculated as well as the absolute velocity at
the impeller outlet. Thermodynamic static and
total states of the air at the impeller outlet
are calculated using Eulers equation and
velocity triangle at the impeller tip radius.
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Diffuser Design
Design philosophy Diffuser is considered as an
integral part comprising vaneless diffuser, vaned
diffuser and outlet section. Diffuser losses are
estimated by means of selected polytropic
coefficient. Annulus axial diffuser outlet with
diameters D4k and D5o is considered.
Calculation Procedure Static temperature at
the diffuser system outlet can be determined from
selected or prescribed absolute velocity c5
. Static pressure p5s, density ?5s, and annulus
area A5 at the diffuser outlet are calculated
from continuity equation. Outer diameter of the
compressor outlet is expressed as D5k D2 E.
Constant E is selected in compliance with
compressor installation requirements. Assuming
adiabatic flow at the diffuser the outlet total
temperature is
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Indirect Design Method of the Mean Streamline
Geometry
Design philosophy The spatial shape of the
inter-blades working channel of the impeller as
well as the flow passage through the diffuser
parts is represented by the spatial flow tube
defined by the spatial course of its main
streamline and the course of the cross section
area. The indirect design method of the channel
is based on the calculation of the geometry of
the stream tube for given inlet and outlet
geometric and flow conditions and chosen
fundamental general flow properties that are
essential for the quality of the flow within the
flow channel, its stability and energy losses.
Design procedure comprise the calculation of
the shape of the impeller blades and the shape of
diffuser flow path.
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Design of the Impeller Blades Geometry 1/2
Design philosophy
The design method is based on the solution of the
equation of motion for steady flow of the
inviscid compressible fluid. Its general vector
formularization is
In streamwise coordinate l, normal hub to shroud
coordinate n and bi-normal coordinate b this
equation of motion can be expressed in analytic
terms

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Design of the Impeller Blades Geometry 2/2
Design philosophy
Solution is based 1. On the assumption that
pressure gradient ?p in the normal direction to
mean streamline equals zero
By considering this assumption and by
substituting cu and cm from the velocity triangle
to the component motion equation (in the
direction n)

This equation defines by given cu and cm the
curvature radius (Rm) of the meridional
projection of the mean streamline in each point
of the mean streamline at the radius R .
2. On the assumption that optimum course of the
relative velocity w along the streamline is
defined
3. On the assumption that optimum course of the
angle ß is defined
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Design of the Diffuser Flow Path
Design philosophy
Solution is based on the boundary conditions
resulting from 1 D compressor stage design. Flow
pattern at the impeller outlet and in the
vaneless space is assumed to be close to free
vortex flow. An abrupt change in flow pattern
occurs upstream of the diffuser throat
practically one-dimensional flow forms at the
throat in the direction of the downstream vane
passage axis. Throat area decisively determines
compressor stage mass flow rate and thus matching
of the impeller and diffuser operation. The flow
pattern in the throat is close to one-dimensional
flow i.e. flow field without pressure gradient
from wall to wall. Downstream of the throat
there is a diverging diffuser duct. Diffuser duct
is usually divided into two basic parts with
lengths lI and lII. Angles of the equivalent
conical diffusers are selected with regard to
course of the pressure gradient along flow path
and its influence on growing boundary layers. On
the basis of the experimental experience angle
ranges are selected as follows ?Iequiv4 to 6?
and ?IIequiv9 to 11?. From diffuser loss point
of view it is advantageous when the greatest
deceleration downstream of the throat occurs in
the straight diffuser duct and flow is bent at
speed as low as possible.

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Primary LPC Design Parameters

• Pressure Ratio 4.475
• Efficiency 0.824
• Mass Flow 4.301 kg .s-1
• RPM 37 600
• Temperature Rise 186.2 K
• Preswirl 0
• Inlet Tip Mach Number 1.26
• Outlet absolute velocity
• Mach Number 0.9574
• Circumferential Velocity 526.1 m.s-1
• Outlet Vane Angle 45 deg
• Impeller Outlet Diameter 267.2 mm
• Inducer Hub Diameter 65.0 mm
• Inducer Shroud Diameter 183.8 mm
• Main Blades 14
• Splitter Blades 14
• Specific Speed 127.9

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Impeller Primary Design
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Tandem Blade Design Philosophy 1/2
The rise of the enthalpy of the compressed air in
the compressor and its efficiency are given by
the total increase of the circumferential
momentum of the flow in the impeller and by the
efficiency of the transformation of the kinetic
energy into pressure energy in the working
channels of the compressor stage. In this
transformation the crucial role play the
stability and uniformity of the flow field in the
working channel. In classical design of the
compressor impeller a relatively long working
channel and acting blade to blade pressure
gradient are reasons of important non uniformity
of the velocity distribution at the outlet of the
impeller which is known as a Jet and Wake flow
pattern. The idea of the tandem blade design is
motivated by the need to improve the aerodynamic
characteristics of the impeller. Division of
the impeller blade into two parts and
re-dislocation of the blade load offers an
advantage to shorten the length of the boundary
layers on both parts of the blade and enables to
improve the distribution of the outlet velocity
profile.
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Tandem Blade Design Philosophy 2/2
The tandem blade is composed by the axial part,
that is designed to provide at the design point
maximum rise of the enthalpy at high efficiency,
limited by the stable fluid flow around the
blade. The second radial part of the blade has to
be positioned with regard to the axial blade so
that the wake after axial blade does not affect
the flow at the incidence part of the second
blade. The incidence geometry of the second blade
is designed at the design point of
characteristics for zero incidence angle and its
geometry is further modified to get smooth
transition to the primary designed blade geometry
at the outlet part. Two parts of the blade then
form tandem cascades placed close one by one and
positioned circumferentially in a way so that the
wakes flowing out from the first cascade enter
approximately to the middle of inter-blade
channels of the following cascade.
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Tandem Blade Design Procedure
Axial cascade

• Meridional shape of the axial blade ( hub and
  shroud) is the same as the primary designed
  impeller blade
• Number of axial blades is 14
• The axial blade leading edge is identical to the
  primary designed impeller main blade
• The axial blade trailing edge axial coordinates
  are the same as the axial coordinates of the
  splitter blades of the primary designed impeller.
  
• The incidence axial blade angles are identical to
  the incidence primary designed impeller main
  blade
• The axial blade airfoil is designed in a form of
  bi-circular sector
• The first approximation of the camber of the
  airfoil ( ?2 - ?1) is defined by using empirical
  Howell formulas where S/C is a cascade density,
  a2 is an outlet velocity angle, e is a curvature
  of the flow in the cascade, ? is a deviation
  angle of the outlet flow, P/C is a maximum
  non-dimensional camber position that is in the
  case of circular arc airfoil 0.5.

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Tandem Blade Design Procedure
Radial cascade

• Meridional shape of the radial blade ( hub and
  shroud) is the same as the primary designed
  impeller blade
• Number of radial blades is 28
• The radial blade leading edge axial coordinates
  are the same as the axial coordinates of the
  splitter blades of the primary designed impeller.
  
• The radial blade trailing edge has the same form
  as the blades of the primary designed impeller
• The incidence radial blade angles are given by
  the condition of zero incidence angle of the
  inlet flow. The flow direction is given by the
  calculated angles a2
• The outlet part of the radial blade is of
  identical form as the outlet part of the primary
  designed impeller blade
• Radial cascade is turned with respect to the
  axial cascade so that the trailing edges of the
  axial blades are in the middle of the blade
  spacing of the radial cascade

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Tandem Blade Design Procedure
Axial and Radial Cascade
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CFD Calculation of Compressor Characteristics
solver Fluent 6.2.16 quadrilateral and hybrid
grid, 365000 cells in computational segment
impeller plus diffuser
coupled explicit solver, steady flow, 1eq
Spalart-Allmaras turbulence model,ideal gas, 1st
order discretization scheme, mixing
plane Solution takes approx. 15000 iterations on
SGI Altix computer(24 Itanium2 processors), the
speed with eight parallel processes of Fluent-
1000 iterations per hour
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First Results and Discussion
Reduced Mass Flow
Calculated compressor stage pressure ratio
performance characteristic tandem blade versus
primary blade
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First Results and Discussion
Reduced Mass Flow
Calculated compressor stage total temperature
increase performance characteristic tandem blade
versus primary blade
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First Results and Discussion
Reduced Mass Flow
Calculated compressor stage isentropic efficiency
performance characteristic tandem blade versus
primary blade
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First Results and Discussion
Static pressure distribution at design point
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First Results and Discussion
The axial velocity field at cylindrical surface
in the computational segment at design point
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First Results and Discussion
Detail of the axial velocity field at cylindrical
surface in the computational segment at design
point
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First Results and Discussion
Outlet velocity distribution in the radial plane
in the computational segment at design point
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First Results and Discussion
Absolute velocity distribution in the radial
plane in the outlet part of the impeller and
inlet part of the diffuser in the computational
segment at design point
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First Results and Discussion
Absolute velocity Mach Number distribution in the
radial plane in the outlet part of the impeller
and inlet part of the diffuser in the
computational segment at design point
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First Results and Discussion
Relative velocity Mach Number distribution in the
radial plane in the outlet part of the impeller
and inlet part of the diffuser in the
computational segment at design point
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First Results and Discussion
Relative velocity Mach Number distribution in the
cylindrical surface at the inlet part of the
impeller in the computational segment at design
point
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First Results and Discussion
Detail of the relative velocity Mach Number
distribution in the cylindrical surface at the
inlet part of the impeller in the computational
segment at design point
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Conclusions and Future Work

• First stage of the advanced centrifugal
  compressor was designed and manufactured using in
  house special indirect design method
• Tandem blade impeller as an alternative to
  primary impeller of the centrifugal compressor
  stage was designed in the same construction space
• The performance characteristics of both
  compressor stages were calculated using the
  Fluent solver
• First results arising from the CFD show that
  primary designed stage meets very satisfactory
  design parameters at design rotational speed
• First results arising from the CFD validates the
  original premise of the design philosophy that
  the tandem blade impeller design can improve the
  compressor stage performance characteristics,
  namely the efficiency and extent of the stable
  segment of the performance characteristics.
• The primary stage has been manufactured and is
  currently prepared for testing on special
  experimental stand with turboprop engine
• The alternative tandem blade impeller design will
  be optimized using CAD and CFD and then
  manufactured and physically tested on the same
  experimental test cell as an alternative design
  of the primary compressor

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Thank you for your kind attention