tema 6 - hp axial flow turbine

8/10/2019 Tema 6 - HP Axial Flow Turbine

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VKI Lecture Series 2006 Mark D Taylor2006

HP Axial Flow TurbineAerodynamic Design

Dr Mark Taylor Senior Project Engineer

Advanced Propulsion System DesignRolls-Royce Aerospace,

Derby, U.K.

email: [email protected]


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Preliminary Annulus Design

Velocity Triangle, Basic Rules, Efficiency Charts One-Dimensional Mean Line Methods

Preliminary Annulus/Vortex Design

Two-Dimensional Throughflow & Correlations2D Aerofoil Design

Design of a Passage Prescribed Velocity Distribution - Inverse Design

3D Aerofoil Design

Aerofoil Stacking Contoured Endwalls

Lecture Overview


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Performance Data

New TurbineDesign Concept

Parallel Activityfor Each Blade Row

2D & 3D Flow Features,Blade Row Interactions,Temperature Traverse,Forced Response, etc.

Detailed ExperimentalUnderstanding

& CFD Validation

Turbine Design Concepts,Velocity Triangles,

Performance Correlation's,Previous Experience, etc.,

2D Axi-SymmetricThroughflow

Model of Whole Turbine

Turbine Rig/Engine Test

Detailed Design ofBlade Row No1

Detailed Design ofBlade Row No2

Detailed Design ofBlade Row n

2D/3D CFD Design Codes

Advanced Projects WholeEngine Design Studies

Black Box Components

1 2

3

4

5

IntroductionHow Do We Undertake an Aerodynamic Design?


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Improved Mechanical and Manufacturing Technologies, Disk technology limits blade speed U B mean ! exit Mach number and blade turning Blade and disc stress limits annulus area (AN 2) ! axial Mach number Casting technology (yield) limits trailing edge size Tip clearance control (shroudless rotor) efficiency improvements available from increasedUB mean , i.e., reduced number of blades, etc., offset by tip leakage increase

Seal leakage proportionally greater ! mechanical features do not scale Casting technology limits cooling hole size and internal feed geometry ! reduced cooling

effectiveness/efficiency

Improved Aerodynamic Component Efficiencies ( " row) Secondary flows - reverse rotation, contoured endwalls Improved cooling design Reduced leakage flows Improved trailing edge designs and thinner trailing edges

IntroductionFactors Influencing Turbine Efficiency

Turbine Efficiency Improvements Resulting From


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At the beginning of the design process the aerothermal designer is faced with his firstchallenge, how do you optimise a turbine(s) when you apparently do not have enough detailedinformation to make quantitative decisions.

This is where the skill and knowledge of the designer are most needed, as an incorrectdecisions made at this stage of the design could have major consequence later in the designprocess. A basic rule is that;

80% of the final product is decided in the first 20% of the design time

There are two main ways to proceed with a preliminary design;

Begin from an existing design (engine throughflow model),

Start from scratch using velocity triangles (basic relationships and 1-D mean line methods),Swindell (Smith) charts, simple correlations, experience, etc.,

Preliminary - Annulus DesignDesign Options


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The first approach tends to be used when the new design is similar to that ofan existing design, and is therefore usually based on information/data, which

has a relatively high degree of certainty. Hence, the designer is able tooptimise the new design relatively quickly and is able to provide quantitative

assessments of efficiency, weight and cost early in the design process.


The second approach tends to be used when the design is significantly differentthat it would take considerable resource and time to explore the new design spaceusing the relatively complex throughflow model. In addition, as this design will be atthe boundaries or outside current design experience, it will probably not be possible

early in the design phase to obtain the necessary detailed information to set up athroughflow model. Many of the design decision made will have to be taken based

on limited information and will require engineering judgement and gut feel.


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Starting with the simple velocity triangles approach (and working through to 2-Dthroughflow) let us explore what information each step in the preliminary design process

requires, along with the level of confidence you have in your design at that stage, andhow you can make simple checks to substantiate your efficiency claims.



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Rotor ExitVane Exit (Rotor Inlet)

VABS

VREL VABS

VREL

Blade Speed U

VAxial

Delta V W

Turbine Velocity Triangle

Preliminary - Annulus DesignVelocity Triangles, Basic Rules and Efficiency Charts

Velocity Triangles


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Specific Work

Stage Loading

Flow Coefficient (Flow Function)

Stage Reaction

Non-Dimensional MechanicalSpeed & Non-Dimensional Blade

Speed

where, Cp specific heat at constant pressure Jkg -1K-1 , P o total pressure kPa, T o total temperature K, t static temperature K,N rotational speed rpm, U blade velocity ms -1, H specific enthalpy Jkg -1K-1 , Va axial velocity ms -1 , m mass flow rate kgs -1.

Inlet Capacity


Turbine Design Parameters


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Compressor WorkmC p# To

Turbine InletTemperature T o

Compressor

Shaft Speed N

Turbine

Fixed Specific Work,

Inlet Capacity &

Non-DimensionalMechanical Speed


Cycle Requirements


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As the work done by the turbine equals the energy extracted from the fluid, combining theabove equations and simplifying;

From the above equation it is clear that stage loading is the width of the velocity triangles tothe length of the base. Note: For fixed flow coefficient (Va/U), high stage loading leads tohigh turning in both the vane and the blade.

Dividing the above equation by U 2 and multiplying through by, , gives;


Work Equation


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Hence, the stage loading is equal to the specific work divided by the square of turbine non-dimensional blade speed.


Work Equation

Dividing the above equation by U 2 and multiplying through by, , gives;


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As the Advanced Projects Department (preliminary cycle design) will not have set the meandiameter, the mean blade speed U is still free to be adjusted by the turbine designer.


Stage Loading

The stage loading of the turbine can now be set with an appropriate mean diameter.

Typical stage loading are;

Mean Radius R


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Note: As stage loading is proportional to the width of the triangles to the length of the base,, therefore;

High stage loading leads to higher turning and an increase in Mach number, however there ismore work per stage (at fixed non-dimensional blade speed), which can lead to fewer stages.

Low stage loading leads to lower turning and a decrease in Mach number, however you maynot be getting the best out of the turbine (at fixed non-dimensional blade speed).

High Stage Loading ! High angles & increased Mn

Low stage loading ! Lower angles & decrease in Mn


Stage Loading

HP Turbine 1.5 to 2.0 @ CpdT/T stage $ 0.05IP Turbine 1.5 to 2.0 @ CpdT/T stage $ 0.05LP Turbine 2.0 to 3.0 @ CpdT/T stage $ 0.02


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As 2-D loss is approximately proportional to the square of Mach number, from the velocitytriangles you might expect that minimum loss will occur when the triangles are symmetrical(assuming vane " row = rotor " row).

This is the condition of 50% reaction, i.e., the same expansion over the vane as the rotor. Asreaction is the amount of expansion over the rotor, low reaction (< 50%) leads to increasedexpansion over the nozzle and reduced expansion over the rotor and visa-versa.

U

U U

Low Reaction High Reaction

V ABS

VREL

VREL

V ABS

V ABS

VREL

VREL

V ABS


Reaction


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For a conventional HP turbine it is common practice to use 45% reaction as this leads toreduced relative total temperature (and pressure) in the rotor ( , V abs reduces morethan V rel), reduced inlet angles to the following nozzle (less turning) and reduced bearing loads.This is a compromise and will not necessary lead to the best design.

Flow Coefficient , is the height of the velocity triangles to the length of the base.

Once this parameter is selected the velocity triangles are effectively locked up. As the mean

diameter is fixed, changing V A adjusts the height of the annulus, and hence the hub and casediameters (hub/tip ratio).

Fixed Mean Radius& Blade SpeedU

U


Reaction and Flow Coefficient


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Increased flow coefficient , leads to increased Mach numbers, reduced exit angles andturning in both the vane and rotor, and a smaller annulus height. This will result in increasedaerofoil chord and/or numbers off (increased trailing edge loss) to achieve the required work(sail area) and potentially increased cost.

In addition the aspect ratio of the aerofoils will be reduced, resulting in increased secondaryloss. However, the turbine is smaller and lighter and the blade stress will be reduced (i.e., AN 2

will reduce). As the hub diameter will increase, there is the potential for more leakage loss due to theincreased area of the seals. At the casing the overall result depends on two opposing effects,as the area of the seals is reduced there is the potential for reduced leakage, however,assuming the tip gap is fixed, the tip gap to height ratio of the rotor will increase, providing thepotential for increased tip leakage flow per unit area.

Due to the size and weight constraints of military aircraft, and the fact that efficiency (thrust/weight is the main design target) and cost are not as high priority, many military turbine are highVa/U designs.


High Flow Coefficient (Va/U)


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Reduced flow coefficient , leads to reduced Mach Numbers, increased exit angles andturning in both the vane and rotor, and a larger annulus height. This will result in reducedaerofoil chord and/or numbers off (reduced trailing edge loss) to achieve the required work (sail area) and reduced cost.

In addition the aspect ratio of the aerofoils will be increased, resulting in reduced secondaryloss. However, the turbine is larger and heavier and the blade stress will be increased (i.e., AN 2

will increase).

As the hub diameter will reduce, there is the potential for reduced leakage loss due to thereduced area of the seals. At the casing the overall result depends on two opposing effects, asthe area of the seals is increased there is the potential for increased leakage, however,assuming the tip gap is fixed, the tip gap to height ratio of the rotor will reduced, providing thepotential for reduced tip leakage flow per unit area.


Low Flow Coefficient (Va/U)


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Due to the civil aircraft markets desire to minimise the aircraft's fuel consumption and maximiserevenues, a civil engine design is primary driven on the requirement to minimise the specificfuel consumption (SFC), i.e., maximise the efficiency. However, although a low Va/U designcan result in reduced cost, the corresponding increase in weight and size has to be balanced inorder to achieve the optimum design for a particular airframe and mission requirement.

Typical values for flow coefficients are;


Low Flow Coefficient (Va/U)

HP turbine 0.4 - 0.6IP turbine 0.4 - 0.6


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Given a few simple mechanical constraints, i.e., stress limits (AN 2) and a maximum meanblade speed U, a range of possible turbine designs can be generated using the previouslyoutlined design rules. However, unless the designer can relate how the choice of theseparameter effect turbine efficiency, it will be impossible to optimise the design.

There are two simple approaches to solving this problem,

(i) Choose design parameters close to a turbine which you already have a goodunderstanding of its measured efficiency, and then apply engineering judgement and/orefficiency charts, correlations, etc., to correct this efficiency for any differences betweenthe two designs,

(ii) Utilise one of the many efficiency against stage loading ( # H/U2), flow coefficient (Va/U),turning, etc., charts, which have been generated using measured data from a wide rangeof different turbine designs.


Simple Turbine Optimisation


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Although a design based on the second option should capture more design experience,efficiency charts should be used with caution.

Firstly, turbine efficiency is not simply a function of two variable, i.e., in the case of Swindell(and Smith) chart, stage loading ( # H/U2) and flow coefficient (Va/U), it is dependant on manyfactors (as will be discussed later) and therefore such charts can be extremely misleading.

Secondly, as these charts usually contain a range of different design styles (and measurement

techniques) the peak efficiency ridge could be a different shape and/or in a different locationdepending on the individual design of turbine.

And thirdly, they are usually derived from rig data and should not therefore be used to quotevalues of in-engine efficiency.

In my opinion efficiency charts are only a guide, or a visual aid to show that your design is notout with acceptable boundaries. Modifying a design to sit on the top of the efficiency ridge linemaybe unnecessary, as the error in the chart may be significantly bigger than the improvementyou believe you are making.




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Although a designer relies on the turbineefficiency correlations to undertake the finaloptimisation of a particular preliminaryturbine design, it is common practice to plotthe final design on a Swindell (Smith) chart.

The Swindell chart, plots contours ofefficiency against turbine loading and flowcoefficient. The efficiency contours wereevaluated from many rig tests and show thatthere is a ridge along which turbines have amaximum efficiency.

Although, the chart is a useful guide to aim aparticular design, it is only as good as thedata it was generated from (circa 1960-70).Current rig results show that its shape andefficiency ridge do not match current designstyles (third axis - specific work).

Stage EfficiencyContours

High Efficiency


Efficiency Charts Swindell (Smith)


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Whether you have used either of these options, it is good engineering practise to compare youdesign to other turbines, and see if you efficiency estimate passes the eyeball test, i.e.,

Cp # To/To

# H/U2

Va/U

Mn Vane

Mn Rotor

Efficiency %



Existing Design 1

200

1.70

0.85

0.90

0.88

87.0

Existing Design 2

210

1.80

0.60

0.87

0.85

88.2

New Turbine Design

210

1.80

0.66

0.88

0.87

87.8


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The next level of preliminary design is based on the application of one-dimensional mean linemethods. These methods use simple bulk values of pressure, temperature, Mach numbers, etc.,to represent the flow within a turbine and are usually linked to some form of simple efficiencycorrelation.

Using a combination of one-dimensional mean line methods, simple assumptions and the stageefficiency equation, important understanding can be gained into how the turbine designparameters (Cp # To/To, U/T o0.5 , Va/U, etc.,) influence both the design and the overall efficiency of a turbine.

Consider the following Equations;

where, at exit of blade row - T oex total temperature, t ex static temperature, t ex isentropic statictemperature, Mn ex Mach Number, P oIN Inlet total pressure, # P o Total pressure change over blade row.

Preliminary - Annulus DesignOne-Dimensional Mean Line Methods

Row Efficiency and Pressure Loss Coefficient


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2


Row Efficiency and Pressure Loss


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Stage Efficiency Against Specific Work Series of HP Turbine Designs - Fixed Row Efficiencies U/T 0.5 = 10.8, Va/U = 0.49, % = 0.45, mT o 0.5 /P o = 1.34, N/T 0.5 = 300

82.00

83.00

84.00

85.00

86.00

87.00

88.00

0 50 100 150 200 250 300 350 400 Specific Work J/kgK

S t a g e

E f f i c i e n c y

%


Stage Efficiency vs Specific Work


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Stage Efficiency vs Specific Work

Pressure Loss = f (Mexit

2)

Mnexit = 0.95 @ 250J/kgK


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Stage Efficiency vs Specific Work Effect of Row Efficiency

No Change in Efficiency PeakRow Efficiency Little Effect on Mn exit

Stage EfficiencySensitive to Row

Efficiency


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(ii) As a consequence of these reduced Mach numbers (resulting from increased U), itis possible to operate a turbine at higher values of specific work whilst achievingcomparable values of stage efficiency, i.e., the probability of designing anefficient high work turbine is significantly improved if the design incorporates ahigh values of U/T o0.5 .

Overall these results show that turbine non-dimensional speed U/T 0.5 has a significant effect

on the Mach numbers within a turbine and hence the stage efficiency.


Stage Efficiency vs Specific Work Effect of U/T 0.5


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Stage Efficiency vs Specific Work Effect of U/T 0.5


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Stage Efficiency vs Specific Work Effect of Va/U

Increased Va/U Moves PeakEfficiency to Higher CpdT/T

Stage Efficiency Is ReducedDue to Increased Axial and

Hence Increased Exit Mn

Overall these results show that Flow Coefficient has a strong effect on turbine stage efficiency.


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Although changes in stage reaction will change the balance of the exit Mach numbers in aturbine stage, this does not usually have a significant effect on stage efficiency.

The exception to this rule occurs when one of the blade row efficiencies is considerabledifferent to the other, and/or a low or high reaction design is required. For example if the rowefficiency of a nozzle was 95% and the rotor was 84%, and the exit Mach numbers of bothblade rows were the same (50% reaction), it is apparent from the row efficiency equation that

this would lead to a higher pressure loss in the rotor than in the vane. By reducing the reaction(increased vane exit Mach number, reduced rotor exit Mach number) a more optimum valuecould be found where the overall pressure loss (vane + rotor) would be at a minimum. As therow efficiencies of vanes are usually higher than rotors, it is common practice to use reaction inthe range 40 to 50%.

When dealing with designs which require extremely low (< 0.3) or high (> 0.7) reactions, carefulconsideration must be made to ensure that the blade row with the high exit Mach number is the

one with the highest row efficiency and visa-versa, or the design may not deliver an acceptablelevel of stage efficiency.


Stage Efficiency vs Specific Work Effect of Stage Reaction


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Utilising a 1-D mean line design program and the assumption of fixed row efficiencies, it hasbeen possible to demonstrate how each of the principle design parameters influence the Machnumbers within a turbine and subsequently the stage efficiency.

From these results it is possible to develop powerful preliminary design rules, for example,

If you are designing a turbine and you discover that the exit Mach > 1.2 ( loss & M2), and yourmean blade speed U and inlet temperature are fixed (U/T o0.5 fixed), you are unlikely to achieve

acceptable Mach numbers on both blade rows (and efficiency) unless you significantly reduceyour specific work (Cp # To/To) and/or flow coefficient (Va/U). As the latter will lead to anincreased in the annulus area, high angles, possible increased weight and mechanical stress(AN2), it is unlikely that this option will offer much scope for change. Hence, you will havechange the engine cycle to reduce the specific work over the turbine, or split the required workover two stages.

Simple design rule;

Blade row exit Mach numbers are primarily a function of Cp To /To , U/To 0.5 , Va/U and


Summary

Alters Locationof Peak Efficiency

Equal Influence Weaker Mn Influence,Strong Effect on Angles

Adjusts the BalanceBetween Vane and

Rotor Exit Mns


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$ 100 Degreesof Turning

$ 40 DegreesInlet Angle


Efficiency Chart Understanding - Fixed Row Efficiencies

Chart Dominated by Work andMach Number Relationship

Peak Efficiency at dH/U 2 = 1and minimum Va/U


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Utilising the equation for entropy production rate in a two dimensional boundary layer(assuming turbulent from LE), along with a square box lift distribution (Loss Mechanisms InTurbomachines Denton 1993),

Profile Loss = f (inlet & exit velocities, inlet & exit angles, loss factor C d )


Efficiency Chart Understanding


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Fixed Row Efficiency Row Efficiency = f(profile loss)

Inclusion of profile loss correlationleads to efficiency ridge

Profile loss = f(inlet & exit velocities,inlet & exit angles, and C d)


Efficiency Chart Understanding - Row Efficiencies = f(profile loss)

Profile loss correlation leads

to reduction in efficiencyat low Va/U, high dH/U 2

- high Mn and turning


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If we now invoke a simple secondary loss model utilising representative HP turbine values oflift coefficient and aspect ratio, i.e.,

Secondary Loss = f (C L, aspect ratio, turning, velocity ratio)




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Fixed Row Efficiency Row Efficiency = f(Secondary Loss)

Secondary loss = f(C L, aspect ratio, turning, velocity ratio)


Efficiency Chart Understanding - Row Efficiencies = f(secondary loss)

Analysis shows for HP style turbine turning is the dominantfactor, i.e., +110 degrees.

Secondary loss correlation leads

to reduction in efficiencyat low Va/U, high dH/U 2,

resulting from increased turning HP style turbine $ +110 degrees


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If we now invoke a simple trailing edge loss model utilising representative HP turbine values oftrailing edge thickness to throat blockage ratio, and exit Mach numbers, i.e.,

Trailing Edge Loss = f (C base , te/throat blockage, exit Mach number)




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Fixed Row Efficiency Row Efficiency = f(Trailing Edge Loss)

Trailing edge loss = f(C base , te/throat blockage, exit Mach N o)


Efficiency Chart Understanding - Row Efficiencies = f(trailing edge loss)

Trailing edge loss correlation leadsto reduction in efficiency at low Va/U, high dH/

U2, resulting from increasedte/throat blockage (at fixed te size)

Reduction in efficiency over the righthand side of chart is the direct result of

the increased exit Mach number


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Fixed Row Efficiency Row Efficiency = f(profile, secondary & trailing edge)


Efficiency Chart UnderstandingRow Efficiencies = f(profile, secondary & trailing edge loss)

Ridge line corresponds to $ 100 degrees of rotorturning and $ 40 degrees of rotor inlet angle


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Specific Work = 100 J/kgK Specific Work = 280 J/kgK


Efficiency Chart Understanding Effect of Specific Work

Change in specific work result in both anefficiency level and ridge location change


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A number of conclusions and design rules can be drawn from this study;

The underlying shape of the standard turbine efficiency chart appears to be primarilydominated by the work and Mach number relationship (fixed row efficiencies),

The top left hand side of the chart is influenced by secondary loss through high aerofoilturning,

The top left hand side of the chart is influenced by profile loss through increased Machnumbers and turning. The effect of trailing edge loss is to further reduce the efficiency in the top left hand side ofthe chart through an increase in the trailing edge to throat blockage ratio, and to reduce theefficiency over the entire right hand side of the chart due to the increased aerofoil exit machnumbers.

It is possible using the simple design rules, i.e., rotor turning < 100 degrees, rotor inlet angle< 40 degrees to place a turbine close to the predicted/measured efficiency ridge,


Efficiency Chart Understanding Conclusions


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Turbine efficiency charts are effectively multi-dimensional, i.e., they are also a function ofspecific work (and other parameters), and should therefore only be used to optimises a designwhen the quality and standard of data used to generate them is known.

Consider the following example.


Efficiency Chart Understanding Conclusions


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Cycle Constraints

Inlet Total Temperature 1800 K U/T 0.5 = 10.6Inlet Total Pressure 45 Bar DH/U2 = 1.78Inlet Mass Flow Rate 140 kg/s mT 0.5 /P = 1.32Specific Work (CpDT/T) 200 J/kgKHP Shaft Speed 12000 rpm

HP Turbine Constraints

MechanicalMaximum Mean Blade Speed 450 m/s

AN 2 Limit (inch 2*rpm2) 2.5E10 Aerodynamic

Maximum Rotor Turning 120 degreesRotor Inlet 50 degreesRoot Velocity Ratio > 1.2

Exit Mn Vane & Rotor < 0.95Reaction 0.45Nozzle " row (Exit Mn = 0.9) 0.93Rotor " row (Exit Mn = 0.9) 0.88

Preliminary - Annulus DesignOne-Dimensional Mean Line Methods Worked Example

Design Constraints


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VKI Lecture Series 2006 Mark D Taylor2006Figure 21a


(7) Rotor Turning > 120 degrees

(6) Exit Angle > 75 degrees

(8) Inlet Angle > 50 degrees

(5) AN 2 > 2.5E10

(1) Input Performance Data and Mechanical Constraints

(2) Set Inlet Velocity& Mn From Combustor

(3) No Axial Expansion in Vane or Rotor

(4) Radius Set to Achieve 450m/s Mean Blade Speed


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VKI Lecture Series 2006 Mark D Taylor2006Figure 21b


(1) Adjusting Axial Velocity Ratios, i.e., Annulus Area

(2) Satisfy AN 2 < 2.5E10

(5) Rotor Root Velocity Ratio > 1.2

(6) Reasonable Annulus Hade Across HP Rotor

$ 15 degrees Hub & Case(3) Inlet Angle < 50 degrees

(4) Exit Angles < 75 degrees

(7) Efficiency Reduced Due to AN 2 and Rotor Turning Constraint


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VKI Lecture Series 2006 Mark D Taylor2006Figure 21c



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Up until this point in the design we have utilised the basic relationships and simple models toundertake the first stage in the preliminary design. This process mainly relied on theunderstanding and previous experience that the turbine designer has of what is possibleaerodynamically, and how these aerodynamic requirements relate to the mechanical, stress,cooling and weight requirements of the turbine and whole engine.

Before finalising these decisions the designer must develop a more complex model of theturbine. Within Rolls-Royce turbines this is done by developing a 2-D axi-symmetricthroughflow model, which represent the desired flow conditions throughout the turbines.Utilising this model along with the Rolls-Royce turbine performance correlation's, the designer

is able to optimise the requirements of the aerodynamic design, against those of themechanical, stress and cooling designers.

This is a key stage in the design process, as decisions

taken now will fix the main architecture of the turbine(s).

Preliminary Annulus/Vortex DesignTwo-Dimensional Throughflow Methods

Introduction


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In order to develop this model the designer must decide on what aerodynamic conditions hewants to achieve in each of the blade rows. It is at this point that he must decide if thereare new detailed aerodynamic concepts which he wants to utilise. For example,

(1) A rig test has shown that a particular exit angle profile (resulting from a new aerofoilshape) improves the efficiency.

(2) 3-D CFD has predicted that a particular distance between two adjacent aerofoils maybebeneficial to reduce blade row interaction (forced response and reduced unsteady loss),etc.

HP TurbineIP Turbine

LP Turbine

Typical Throughflow Annulus Diagram


Utilisation of New Concepts


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3D Aerofoil Design

Straight Stacked Aerofoil3D Aerofoil


Utilisation of New ConceptsExit Angle Profile Leading to Improved Efficiency


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3D Blading Design - Unsteady CFD - Unsteady Interaction Loss

Steady 3D CFD Prediction of AxialVelocity at Exit from Turbine Rotor

Flow Field Looks Good !


Utilisation of New Concepts Increased Axial Spacing Leading to Reduced Unsteady Interaction


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Steady 3D CFD Prediction of Total

Pressure at Exit from Turbine NGVFlow Field Looks Good !




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Unsteady 3D CFD Prediction of Axial

Velocity at Exit from an Turbine Rotor,Time-Averaged in Absolute Frame

Strong Rotor Root Unsteady InteractionDesign Rule Increase Axial Gap and/or

Reduce Aerofoil Lift




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The designer can then combine these new ideas along with previously measured (orpredicted) data on angle profile deviations, efficiency profiles, coolant and tip leakage flows,etc, to develop the target gaspath throughflow model.

In addition, turbine efficiency correlations allow an initial number of aerofoils to selected,however, this usually is not the final numbers as mechanical, cooling and cost have a stronginfluence on aerofoil numbers.

By developing this model the designer can verify (in a 2-D representation) if the requireddesign concept, i.e., turbine type, specific work, stage loading, numbers off, etc, are feasible,and if not what parameters must be change to achieve (utilising efficiency correlations andother evidence to numerate) the required overall aerodynamic specification.

This model represents the target gaspath flowfield against which each of the individual bladerows are to be designed (to match), and allows the detailed aerodynamics of each blade rowto be designed independently and in parallel.


Target Gaspath Model


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Once each blade row has been designed (2-D and 3-D CFD), the results are fed back into thetarget gaspath throughflow model (angle deviations, loss profiles, etc.). A new target gaspaththroughflow model is generated and the process is repeated until an acceptable aerodynamicdesign of the whole turbine is achieved.


Target Gaspath Model


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Turbine efficiency correlations are a mixture of physical models, measured exchange ratesand correlations. They are developed over many years and are usually based on an extensiveexperimental database (low and high speed turbine rig tests). They provide a pre-profileestimation of the stage efficiency of a particular turbine design, and are used extensively in theaerodynamic efficiency bid process (2-D throughflow ! flow conditions ! correlation - rowefficiencies ! stage efficiency). Typical factors considered are;

Secondary Loss - Lift coefficient , aspect ratio ,aerofoil turning, velocity ratio, etc.

Trailing Edge Loss - Exit Mach number, trailing edge thickness, boundary layerthickness, etc.

Profile Loss - Lift distribution, lift coefficient, blade area, etc.

Over Tip Leakage Loss - Shrouded/shroudless, height of tip gap, tip liftcoefficient, etc.


Efficiency Correlations


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Aft-Loaded

M a c

h N u m

b e r

Axial Chord

Forward-Loaded

Shroudless Shrouded




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Disk Windage Loss Turbine disc diameter and speed, etc.

Wetted Area Loss - Hub and casing endwall Mach Numbers, endwall areas, etc.

Cooling Exchange Rates - Experimental measured exchange rates for a seriesof different cooling flows which, reflect the change inturbine efficiency as a percentage of coolant flow. Asthese exchange rates are very dependant on thelocation at which the flow enters the annulus greatcare must be taken when applying them in a designand bid process (typical range 0.1% to 1% change inefficiency for 1% change in coolant flow).

Leakage Exchange Rates - As above - platform, blade root seals, over tipleakage, etc.

Pumping Losses - The energy required to pump the coolant and leakageflows from a source to the point where it enters theannulus.


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S t a g e

E f f i c i e n c y

Exit Mach Number = f (Cp # T/T, U/T o0.5, Va/U, %)

2nd IterationImprove Efficiency by

Increasing Number of Aerofoils

1

Improved AR- Reduction in

Secondary Loss

Increased TrailingEdge Loss 1a

1bReduced Va/U

- Reduced Mn &Trailing Edge Loss

Increased Turning- Increased Secondary

& Profile Los

2

2a

Annulus Design Changes- Work/Mn Relationship

Detailed Blading Changes- Row Efficiency Changes


Summary


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The primary function of 2-D blading is to satisfy the flow condition calculated from thethroughflow model, i.e., inlet and exit flow angles and Mach numbers. As an estimation of theloss within the blade row will have been input to the throughflow model, it is important that thisloss is also taken into account when designing the 2-D aerofoil sections. It is usual to specifythe loss as a function up to and downstream of the aerodynamic throat, in order that theaerofoil is designed with the correct inlet flow capacity (mT o0.5 /P o) and exit angle.

Consider the following;

If we use the continuity equation on a control surface which stretches from a plane infinitelyfar ahead of an aerofoil cascade to a plane infinitely far behind the aerofoil cascade(homogeneous entry and exit flow), the exit flow angle can be calculated from the other flowparameters.

With the assumption that the flow between inlet and exit exchanges no energy with the aerofoil,the fluid behaves like an idea gas, and that density and temperature ratios are a function ofMach number, the above equation can be written in the following form;

2D Blading DesignIntroduction

Control Volume Analysis


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' inlet

M inlet

' exit

Mexit




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Utilising the above equation the variation of exit angle can be calculated for a range of loss

levels and over a range of exit Mach numbers, for fixed inlet conditions, i.e., Minlet = 0.15, ' inlet =0o.

Exit Angle Against Exit Mach Number Effect of Blade Row Loss

Fixed Inlet Conditions Mn = 0.1, Angle = 0 o

68 69 70 71 72 73 74 75 76 77 78

0.4 0.5 0.6 0.7 0.8 0.9 1 Exit Mach Number

E x i

t A n g

l e D e g r e e s

No Loss 1% Loss 5% Loss 10% Loss




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Blade row exit angle is sensitive to variations in the blade row loss, i.e., a 1 degree change inexit angle for a 6% change in loss. As errors in exit angle will result in the blade row delivering

the wrong value of exit swirl velocity and hence stage work, it is important that the 2-D bladingdesign is undertaken with a representative level of overall loss.

The distribution of loss through the blade row will influence both the profile shape and thethroat width and hence blade row inlet capacity (size of turbine, non-dimensional mass flowrate).

As approximately 30% of a blade row loss occurs upstream of the throat plane, the aboveerror in overall loss (and exit angle) would represent around a 2% change in the blade row inletcapacity. As this level of errors could lead to a significant re-matching of the engine, it isessential that a representative pre-throat loss be applied when undertaking 2-D profile design.

Although not directly related to the above discussion, the results presented, highlight why themeasurement of efficiency should be bias towards total pressure measurements and shouldonly rely on angle distributions, and not the absolute values of angle, i.e., typical probe absoluteaccuracy 1 degree.




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The design of a turbine aerofoil differs from that of an external aerofoil (wing), inthat you are designing a flow passage rather than an isolated aerofoil.

Hence in the design of turbine blades both the curvature of the aerofoil (andendwalls) and the aerodynamic blockage have a significant effect on the

design, the former being the dominant effect on external (wing) aerofoil design.

2D Blading DesignDesign of a Passage

A valuable insight into the design of turbine aerofoils can be gained if we startingwith a constant area passage (impulse turbine - low reaction design) and

develop it into a convergent passage reaction design.


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AX

Vabs

Vrel Vabs

Vrel

# Vw

' 1 ' 2

V A

Reduced turning leads to a thinner aerofoil

Limits diameter of service pipes

Reduced cross-sectional area for structural support

Difficult cooling geometry's


Impulse Blading Effect of Aerofoil Turning

U


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Large suction and pressure surface diffusionsPossibility of separated flows

Mn

Cax

Inlet Exit

Large suction and pressure surface diffusions

Flow separation(s) leading to increased loss, enhancedheat transfer at re-attachment points

Diffusion on suction surface limits amount of availablelift, i.e., low lift coefficient leads to high number ofaerofoils and/or blade chord

Consider: Inlet and exit relative Mn = 0.6, max diffusionlevel = 35%, therefore peak Mn $ 0.8

# p/D = (p end of diffusion - p start of diffusion )/(P o- p) start of diffusion


Impulse Blading Limitations

l d


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As the change in whirl velocity ( # VW) and hence turbine power (mU # VW) is limited by the constraint that no

expansion can take place over the rotor (Mn relative inlet = Mn relative exit) the specific power (per kg massflow) available from an impulse turbine will always be lower then an equivalent reaction design with equalrelative exit Mach numbers on both the vane and rotor.

In addition, the requirement to do all of the expansion over the nozzle leads to high inlet angle to the rotor,which tends to increase the levels of pressure surface diffusion previously highlighted.

These limitations along with the difficulties previously outlined (separations, low lift coefficient, etc) meanthat most modern aero gas turbine designs are based on reaction styles of turbine blading.

Vabs

Vrel

U

Vabs

Vrel

# Vw

' 1 ' 2

V A

Inlet Exit Increased# Vw


Impulse Blading Limitations

2D Bl di D i


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However, as # Vw has been reduced by thereduction in inlet angle, the exit angle must

be increased to restore the work

Vabs

Vrel

U

Vabs

Vrel

# Vw

' 1 ' 2

V A

Ax

Ax

' 1 ' 2


Reaction Blading Reduced Inlet Angle

At constant axial velocity (and hence axial area),it is clear from the diagram that there is a

corresponding flow area increase (reduced inletMn) as the inlet angle is reduced

This leads to a fatter front portion of the aerofoil(increased wedge angle)

2D Bl di D i


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Ax

Vabs

Vrel

U

Vabs

Vrel

# Vw

' 1 ' 2

V A Ax


Reaction Blading Increased Exit Angle

2D Bl di D i


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Fatter front portion of aerofoil leads to increased convexcurvature and blockage on front half of the suction surface

and hence a more rapid rise in the suction surface Mach number

Mn

Cax

Inlet Mn

Reduced

Exit MnIncreased

Fatter front portion reduces concave curvature on pressuresurface which leads to reduced pressure surface diffusion


Reaction Blading

2D Bl di D i


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Mn

Cax

Inlet MnReduced

Exit MnIncreased

Aerofoil remains forward loaded as the location of peaksuction (peak suction surface Mach number) has not altered

Suction surface diffusion can be significantly reduced by aftloading the aerofoil, i.e., moving the location of peak suction

rearwards (reducing stagger angle)

Formation of a convergent passage and increasedtrailing edge wedge angle leads to increasedacceleration on rear part of pressure surface


Reaction Blading Aft loading

2D Bl di g D ig


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Suction surface curvature modified to move peaksuction rearwards, i.e., Mach number distribution

change due to both curvature and blockage

Aerofoil has clearly defined geometric throat at orclose to peak suctionMn

Cax

Inlet MnReduced

Exit MnIncreased

Aerofoil X-sectional area reduction maybe undesirable,hence pressure surface concave curvature can be reducedto restore X-sectional area and eliminate pressure surface

diffusion (blockage and curvature changes on pressuresurface have weaker effect as Mach numbers are lower)


Reaction Blading Aft loading

2D Bl di g D ig


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Positive IncidenceSuction Surface Diffusion

Negative IncidencePressure Surface Diffusion

Mach Number

Cax

Inlet Mn

Exit Mn

Small wedge angle at leading edge of aerofoil gives littleincidence tolerance, i.e., suction and pressure surface spikes

and diffusions

As aerofoil will be subjected to incidence variation fromupstream blade row (potential interaction, wakes, secondary

flows, etc), careful design of the leading edge must beundertaken to minimise the loss associated with these forms of unsteady interaction loss


Reaction Blading Incidence

2D Blading Design


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d) /dsGradient

s

)

s

d2) /ds 2Curvature

s

)

s

Positive IncidenceSuction Surface Diffusion

Negative IncidencePressure Surface Diffusion

Mach Number

Cax

Inlet Mn

Exit Mn


Reaction Blading Small Wedge Angle

2D Blading Design


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s

)

s

s

)

s

Suction and Pressure SurfaceDiffusions Reduced at Positive and

Negative Incidence

Mach Number

Cax

Inlet Mn

Exit Mn

Blockage Leads to Increased Suctionand Pressure Surface Mach Numbers

Increased leading edge wedge angle leads to

increased blockage and reduced curvature.

Resulting in increased lift and improved incidence tolerance.


Reaction Blading Large Wedge Angle

d) /dsGradient

d2) /ds 2Curvature

2D Blading Design


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Mach Number

Axial Chord Cax

Inlet Mn

Exit Mn

Smooth velocity distributions - steady accelerating flow

No predicted flow separations

Minimised loss Maximise lift

Margin for skew Contracting passages

Minimised straight line diffusion No separation

Back surface diffusion < 35%

Minimise peak Mn < 1.2

Subsonic if possible Peak opposite throat

Off-loaded nose Design for incidence 10 0

Minimised suction and pressure surfacediffusion at incidence, including skew margin.

Subsonic exitMach number.


Reaction Blading Design Objectives

2D Blading Design


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Although as the previous slides have show, a good understanding can be gained into how thegeometric shape of a passage (curvature and blockage) influence an aerofoil Mach numberdistribution, it is more convenient to design an aerofoil to meet a desired lift distribution.

This is usually undertaken using an inverse design technique known as Prescribed VelocityDistribution (PVD), i.e., a desired velocity distribution is chose and the resulting geometry tomeet this requirement is automatically generated.

Although this is a more convenient method by which to design a row of aerofoil, the designermust still understand the simple rules developed earlier, if he is to design an aerofoil which alsomeet the many mechanical and cooling requirements.

For example, the wedge angle at the leading edge of a HP turbine is significantly greater than isrequired aerodynamically. The thickness requirement is predominantly there in order that thereis enough physical space to accommodate the complex cooling arrangement within the leadingedge.


Prescribed Velocity Distribution - Inverse Design

2D Blading Design


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Improved BacksurfaceDistribution

Improved PressureSurface Acceleration

Figure highlights the type of modifications to the velocity distributions, which can be easily

undertaken using a prescribed velocity distribution method.



2D Blading Design


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Based on the rules presented previously (and particular lift style) 2-D aerofoil profiles are

designed at a number of spanwise locations. A typical final summary of the 2-D aerofoilparameters is given below.



2D Blading Design


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Large Leading Edge Circle Size Stagnation Point Control and TBC

TE Definition

Increase PS & SSMach Numbers


HP Vane and Rotor 2-D Design

Full Lift Distribution Aerofoil NumbersChosen For Cost and Forced Response

Large Trailing Edge Wedge AngleLeads to Reduced Pressure Surface Lift

Lift Coefficient Limited by Peak Mn

Large Leading Edge Wedge Angle toSatisfy Cooling Geometry Requirements

3D Blading Design


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Currently 3-D CFD cannot be used directly to predict the aerodynamic performance of aturbine, i.e., loss predictions are unreliable (unsteady stage calculations are within 1 to 2%

of experimental measurements).

Hence, the fundamental design of turbines is based on performance correlations producedfrom extensive rig/engine testing.

3-D CFD is used to undertake the detailed aerodynamic design of each blade row, usingboundary condition data defined from a target gaspath throughflow (axi-symmetric) modelof the whole turbine (losses, deviations, etc, from empirical/experimental data).

The objective of a 3-D aerofoil design being to match the predicted exit conditions to thosein the target gaspath throughflow model.

The designer uses flow parameters which he/she knows the 3-D CFD code can accuratelypredict (static pressure, angle deviations, SKEH, etc.), along with design concepts (styles)which experimental studies have shown produce high aerodynamic efficiencies, i.e., bladelean, exit flow angle variation, etc.

3-D CFD is used in conjunction with experimental data to understand particular flowfeatures identified by rig testing.


3D Blading Design


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Turbine Blade 3D Flow Phenomena


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3D Blading Design


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LeadingEdge

TrailingEdge

No Axial Lean(View from side of engine)

Single Axial Leanor visa-versa

Compound Axial Leanor visa-versa

LeadingEdge

TrailingEdge

LeadingEdge

TrailingEdge

% Height

Exit Angle

Linear Variationin Exit Angle (Vortex) % Height

Metal Exit Angle

Parabolic or Brand XExit Angle (Vortex)

3D Blading Design Aerofoil Stacking and Vortex

3D Blading Design


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Each of these stacking concepts have different effects on the flow field, for example consider

the effect of compound lean (convex pressure surface, concave suction surface).

Increased Static Pressure

Mass flow

EndwallMach

Number

Chord Air Exit Angle (At TE)

% Height

WithoutWith

Increased staticpressure in the endwall

regions

Mass flow within passagemoves from

endwalls to mid-height

Less turning at endwalls(reduced lift)

More turning mid-height(increase lift)

Loss & V3endwalls Endwall loss reduced

Overall Loss ?


Compound Lean

3D Blading Design


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Both of the exit angle (vortex) concepts have different effect on the flow field, for exampleconsider the effect of Brand X (reduced exit angles at endwalls, increased exit angles at mid-height).

Reduce angles at endwallsIncrease angle at mid-height

Exit mass flow moves frommid-height to the endwall

regions

More turning at endwalls(increased lift)

Reduced turning mid-height(reduced lift)

Air Exit Angle

EndwallMach

Number

Chord

% Height

WithoutWith

More uniform distributionof massflow into

following blade rowImproved stage efficiency

% Height

Metal Exit Angle

Reduced Exit Angles

IncreasedExit Angle


Brand X

3D Blading Design


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It is worth noting that there are several different schools of thought on how, or even if, these

3D flow concepts actually work. As it is difficult, if not impossible, to prove mathematically thatthey do, the majority of evidence is based on experimental rig testing.

A quick glance at published research will show that a number of these concepts appear to alsowork when applied in exact opposite ways, i.e., some researches say that compound leandefined as convex pressure surface, concave suction surface improves stage efficiency, othershave found the exact opposite. Although impossible to prove, it is generally believed theseapparent contradiction result from the differences in the initially design to which the concept isapplied, and the level to which a particular concept can effect the overall value of loss within aturbine stage.

For example, if an initial design contained a strong Brand X (open endwall, closed mid-height)distribution, and a designer applied a compound lean which encourages mass flow rate to theendwalls within the vane, i.e., the opposite of that presented here, this should lead to anincrease in the vane endwall loss (loss & V3), and a slight improvement in the mass distributionentering the following rotor. However, if the designer applied compound lean which encouragedmass flow rate away from the endwalls, to the same strongly Brand X design, the effect wouldbe a reduction in vane endwall loss, and a slight deterioration in the mass distribution enteringthe following rotor.


Discussion

3D Blading Design


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Clearly both these design have the potential to improved the stage efficiency, whether they door not, depends on the initial level of Brand X and the strength and resulting effect that thecompound lean has on the overall loss within the turbine stage and not just the vane loss.

g g Aerofoil Stacking and Vortex

Discussion

3D Blading Design


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Target Exit Angle

g g Aerofoil Stacking and VortexVane 3-D Stack and Vortex

3-D Predicted Distribution

3D Blading Design


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As the requirement to reduce cost tends to lead to a reduction in aerofoil numbers, an importantconstraint on HP turbine design is forced response. In the preliminary design stage this ismainly undertaken using simple models such as the Campbell diagram.

The objective of the diagram being to show graphically where a particular mechanical modes(resonant frequency) will cross a particular engine order (EO) excitation frequency (frequency =number of nozzles * shaft rps what a single blade experiences).


Forced Response

3D Blading Design


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Engine Speed100% NHIdle

Frequency Hz

30 EO

25 EO

35 EO

1 st Flap

1st Torsion

Mode resonant frequencies function (No blades,shape of blades, blade/disc assembly, etc.)

Number of Nozzles


Forced Response Campbell Diagram

3D Blading Design


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Engine Speed100% NHIdle

Turbine InletTotal Pressure

Flight Condition

Take-OffCruise


Forced Response Turbine Inlet Pressure

3D Blading Design


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Combining the information contained in the figures, the designer can quickly make anassessment on whether a design is practical or not, for example;

In order to reduce cost the project team would like to change the number of HP nozzles from 35to either 30 or 25. As this could have a significant effect on the forced response of the HPturbine, it is essential that an early assessment be made.

Previous experience has shown that the blade numbers chosen, blade design, disk assembly,

etc., will result in two main modes of vibration, i.e., 1st

torsion and 1st

flap.

Lowering the number of HP nozzles from 35 + 30,

Increased engine speed at which the resonance crossing points occur. Increased inlet pressure ! greater aerodynamic forcing, i.e, aerodynamic forcing directlyrelated to absolute pressure level

Larger signature per aerofoil ! greater aerodynamic forcing

1 st torsion mode resonance at 100% NH


Forced Response

3D Blading Design


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Lowering the number of nozzles from 35 + 25,

Increased engine speed at which the resonance crossing points occur Further increase in the aerodynamic forcing increased inlet pressure & aerofoil signature 1 st torsion resonance has moved outside running range However, possible problems now with 1 st flap mode

Although the above assessment does not allow the actual mechanical displacements andstresses to be calculated, it does clearly identify the potential resonance points, and based on asimple scaling of the inlet pressure and number off relationships, can provide a preliminaryassessment of the change in aerodynamic forcing (based on previous data).

Aerofoil Stacking and VortexForced Response

3D Blading Design


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Mid-height nozzle section Mid-height lift plot

Conventional Low Number Off$ 50% Conventional

Low Number Off$ 50% Conventional

Conventional

Aerofoil Stacking and VortexForced Response Lift Styles

3D Blading Design


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In addition to 2-D lift style, other techniques can be used to minimise forced response, i.e.,aerofoil stack and endwall contouring. Figure shows a low number off HP nozzle guide vanedesign where the aerofoil stack and endwalls have been optimised to reduce the unsteadyaerodynamic forcing onto the HP rotor.

Irrespective of whether you utilise one or all of the above techniques to minimise the unsteadyinteraction between two blade rows, the designer must have a reliable method to predict theresulting unsteady pressure field.

Experience has shown that although 3-D unsteady CFD codes do not accurately predictaerodynamic loss ( 2%), they do allow a good assessment of the unsteady aerodynamicforcing to be made. Comparison with measured unsteady static pressure data has shown thatamplitude can be predicted to a high level of accuracy, however errors in the relative phaseacross the aerofoil tends to reduce the overall accuracy of the prediction.

Aerofoil Stacking and VortexForced Response

3D Blading Design


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3D Stack and Profiled Endwall

Aerofoil Stacking and VortexForced Response Stack and Profiled Endwalls

tema 6 - hp axial flow turbine

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