Aircraft Propulsion I - Lecture1

Aircraft Propulsion I IntroductionNGUYEN ANH THI, PhDDepartment of Aeronautical EngineeringUniversity of Technology HCMC National University

@ 2008 Nguyen Anh Thi, Ph.D.

Contents /1Introduction to Aerospace Propulsion SystemsPropeller engineEngines: internal combustion engine, turbine engine (turbo-propeller engine, eg. ATR72 PW..)Propeller Assignment: Propeller designTurbomachineryCompressor: axial compressor, centrifugal compressorTurbine: axial turbine


ReferencesE.L. Houghton and P.W. Carpenter, Aerodynamics for Engineering Students, 5th Eds., BH Editor (2003) --- > [Chapter 9]

J. Roskam et al. Airplane Aerodynamics and Performance, DARCorporation Editor (2003) --- > [Chapter 6] & [Chapter 7]


Propeller /1Propeller:Froude momentum theoryBlade element theoryComputational Fluid Dynamics (Solution of 3D Navier-Stokes equations)FLUENT software : Navier-Stokes solverGRIDGEN software : mesh generation


Propeller engine


Propeller /2


Propeller /3Pressure distribution downstream of propeller


Introduction to Propulsion systems In the frame of this lecture, We will consider only thermal engine.

Which propulsion system will be adopted depends on the vehicle performances required, i.e. flight altitude and velocity!

We will briefly discuss all the engine concepts figured out on the left figure.


Introduction to Propulsion systems


Propeller design variables / 1For any given aircraft, the propeller is selected (designed) to satisfy 5 following performance conditions:Take-off performanceClimb performance Cruise performance Maximum speed capabilityFAR 36 noise requirement


Propeller design variables / 2When selecting or designing a propeller, one must specify following fundamental variables:Propeller diameter,Activity factor, and number of blades,Blade airfoil section and design lift coefficient Other propeller selection (or design) consideration are:

WeightComplexity Blade stress & vibrationCost (variable pitch mechanism?)


Propeller design variables/ diameter /1 The propeller diameter should be as large as possible for high propulsive efficiency,The upper bound of propeller diameter is determined by ground clearance, noise, compressibility, and blade stress levelsNoise, compressibility and blade stress levels are all related to the tip speed (tip Mach number) of propeller. For low noise, a helical tip Mach number limit could be 0.72 (~800 ft/sec at sea level).


Propeller design variables/ diameter /2 Neglecting the propeller induced velocity, one has:

Here, is the rotational speed in rad/s. In terms of tip Mach number, this becomes:

At pre-determined tip Mach number, forward speed and rotational speed, the propeller diameter is frozen by:


Activity factor (AF) and number of blades (B) / 1The activity factor and the number of blades are closely related to the amount of power absorded by a propeller.

The activity factor and number of blades are not independent. Typical activity factors vary between 70 and 200!Plot the propeller efficiency versus the activity factor (70:200)?


Activity factor (AF) and number of blades (B) / 2

Airplane or propeller designNumber of blades, BBlade activity factor, AFIntegragted design lift coefficient, CLintCessna 310290RAF-6Hamilton standard 6903A with WAC R-3350 compound engine31030.50 (NACA-26 series)Hamilton standard 6921A with WAC R-3350 compound engine31320.586 (NACA-26 series)Hamilton standard 4D15A3 with WAC R-3350 compound engine32000.427Cessna 40431070.55Cessna 337 (font pro)21120.51


Activity factor (AF) and number of blades (B) / 2Data obtained from Roskam J. L. (1997)

Airplane or propeller designNumber of blades, BBlade activity factor, AFIntegragted design lift coefficient, CLintCessna 337 (rear prop)21050.57Cessna 108K21000.50Cessna S172E 21040.53Cessna 150M2770.60


Introduction to Propulsion systems


Introduction to Propulsion systemsA turbo/ ram jet engine


Axial turbomachinery


Aircraft Propulsion I Turbomachinery


Axial turbomachinery

CMF56-3 Turbofan, lower half side viewRolls-Royce RB211 Turbofan mounted on a Boeing 747


Axial turbomachineryThe design of axial turbo-machine invokes different contradictory objectives: Power (maxi. via a turbine)

Thrust (mini. via a compressor) Performances (specific fuel consumption)Minimum volumeMinimum frontal surface (reduction of external drag)

high mass flow rate/ surface unity high axial velocity high rotational speed- Compressibility problem- Problem of resistance mechanics


Axial turbomachineryThe design of axial turbo-machine invokes different contradictory objectives (cont.): Minimum volume (cont.)Minimum length (reduction of weight and friction drag)

reduce the number of stages obtain high compression ratio/ stage with high efficiency face to stall problem and shock-induced separation Reliability and manufacturing commodityVibration and fatigueMaintenance commodityLow cost


Principal characteristics of turbomachines flow /1 Let consider, in permanent regime (mass flow and pressure ratios are independent with time), the flow at the entry of a cascade of blades is:Highly three-dimensionalNon-uniformTurbulent (viscous effects)Unsteady

existence of pressure, energy, and velocity VARIATIONS in all spatial directionsRadial direction due to:Radial distribution of upstream cascadeReduction of flow channel to compensate density variationBoundary layers on the hub, casing and bladesFlow related to the gap between blades tip and the casing.


Principal charactics of turbomachines flow /2 In azimuthal direction:Radial distributions # along azimuthal positions linked to pressure # between lower and upper surfaces of blades. Wakes of upstream blades

Unsteady nature induced by the defilement of blades of upstream cascades.

Viscous effects that becomes predominant in the stages with very low span (dominance of boundary layers developed on the casing and the hub in the last stages of compressor)


Objective hierarchy /1Classification of objectives is required to define appropriate design point that depends on aircrafts missions.

Civil aircarftsMilitary aircrafts1Performances1Manoevrability2Mass2Mass3Cost3Cost4Maintenance commodity4Maintenance commodity55Performances


Objective hierarchy /2Flight times in different phases of a short range civil aircraft

Flight phaseRange: 650 kmRange: 1000 kmTaxi6%6%Take-off7%7%Climbing48%32%Cruising30%42%Descent5%8%Approach4%5%100%100%


Manoevrability and flexibility of operating The manoevrability and flexibility of operating are defined by following factors:

Large operating domain with high efficiency

The capacity to adopt certain distortion level at the entry

Acceleration time


Fundamental equations / 1

Cylindrical coordinatesRotational speed around z-axisPosition vectorAbsolute velocityEntrainment velocityEntrainment accelerationRelative velocityCoriolis acceleration


Crocco equation/ relative velocity / 1Linear momentum equation/ relative velocity

Here, is the viscous forces per unity of mass:

with the strain tensor, is the unique tensor and is the total stress tensor


Crocco equation/ relative velocity / 2

Taking into account the fact that the rotational vector , the momentum equation can be rewritten as:

From the thermodynamic relation , one can deduce

Taking into account the fact that , one obtain finally the generalized Crocco equation:


Crocco equation/ relative velocity / 3

The term is called rothalpy (rotational stagnation enthalpy) and the Crocco equation can be finally rewritten as follows:

(1)


Kinetic energy balance

The equation representing the specific kinetic energy balance can be obtained by multiplying equation (1) with

One obtain finally

(1)


Consequences / 1For steady, adiabatic, non-viscous and reversible flow, one has:

and

The equation (2) then reduces to:

The rothalpy does conserve along a stream-tube of relative flow.


Consequences / 2The total enthalpy in the absolute frame

The rothalpy can be rewritten:

With the projection of absolute velocity on the direction of the entrainment velocity. If the inlet condition so that:

i.e. the flow is iso-nergtique in the Galelian frame and homentropique, the solution depends on upstream conditions. and


Consequences / 3If the flow upstream is purely axial (Vu = 0 ), the rothalpy is thus constant in total part of the flow upstream. The rothalpy does conserve along a streamline of the rotational frame, and we have .The momentum equation (1) reduces to:

If the upstream flow is not axial (e.g. the rotor is placed downstream of a range of guide valves that produce a tangential component Vu )

(3)(4)


Consequences / 4For the static guide valves, one has . One can obtain the momentum equation by replacing by and by . For a steady, non-viscous flow, the momentum equation or the Crocco equation reduces to:

If flow is adiabatic, total enthalpy conserves along streamlines. If the flow is adiabatic and reversible, entropy conserves along the streamlines too. If total enthalpy and entropy are constant in total part of flow field, the Crocco equation reduces to:


Circulation and Kelvin theoremLet consider an adiabatic, non-viscous, reversible flow (without shock): entropy conserves along streamlines. If the upstream conditions are such that the entropy are constant throughout the flow field, i.e. the flow is barotrope . The gradient term of the pressure can be written as:

In the absolute reference, one defines:

with


Circulation and Kelvin theorem / 2We can deduce:

The momentum equation can be rewritten as follows:

By applying the rotational operator to this equation, one has:


Circulation and Kelvin theorem / 3One finally deduces:

This constitutes the Kelvin theorem.

(5)


Circulation and Kelvin theorem / 4If we are now in the relative (rotational) frame and consider the evolution of circulation along a closed line that is in motion in relative flow. We define:

This equation can be rewritten as follows:


Circulation and Kelvin theorem / 5In the relative frame, the momentum equation can be written as follows:

By applying the rotational operator to this equation, one has:

The circulation of relative velocity in the rotational frame changes due to the Coriolis acceleration.

(6)


The S1/S2 decomposition / 1In 1952, WU introduced a simplified decomposition of tri-dimensional flow in turbo-machines. This approach consists in approximating unsteady tri-dimensional flow by a combination of two steady bi-dimensional flows on two surface families. The stream tubes that are typically formed by the streamlines crossing an arc like . Generally, this surface is not revolutionary and could round off due to the presence of corner vortices (e.g. the vortices generated by the flow in the gap between the carter and blades). One important simplification is that the surface is a revolution one: one can for example produce the revolution surface by rotating a streamline, i.e. around the rotational axis. If we suppose that is cylindrical, one can develop this surface and directly apply the results of bi-dimensional range of fixed blades. Investigating the flow on surfaces is commonly qualified as blade-to-blade problem.


The S1/S2 decomposition / 2(Cont.)The second family of surface is constituted by the streamlines formed by the streamlines passing by the same radial distance at the inlet. This surface is in general twisted and does not coincide with the surfaces of blades after a rotation that transforms into . A common simplification consists in consider only a mean surface we have azimuthal step and suppose that the flow is axi-symmetrical (this is justified as the number of blades tends to infinity): It is then enough to consider the meridian flow in the meridian plan defined by the radial distance and the rotation axis of machine. In this type of approximation, we commonly suppose that the flow is adiabatic and non-viscous (Euler equation) and the viscous effects (losses due to the boundary layers on blades, flow in the gap between fixed and rotational parts,) are indirectly taken into account.


The S1/S2 decomposition / 3


The S1/S2 decomposition / 4


Flow in a range of fixed bladesLet us consider a steady, isonergtique and homentropique, the Crocco equation reduces to:

Let expand this equation in a curvilinear orthogonal coordinates

built on the revolution surface . The unity vectors are in the direction azimuthal, tangent to in the meridian plane and normal to . The components of velocity in this coordinates are in the azimuthal direction, along and along the normal . This curvilinear coordinate system is characterized by the transversal curvature radius and longitudinal curvature


Flow in a range of fixed blades /1The rotational of velocity can be explicitly written as follows:

If we suppose that the surface coincides with the stream tubes surface, then the expression of is widely simplified:


Flow in a range of fixed blades /2If we suppose that the surface coincides with the stream tubes surface, then the expression of is widely simplified:


Flow in a range of fixed blades /3One obtains finally the vector product :


Flow in a range of fixed blades /4The Crocco equation leads to:

The irrotational condition leads to:


Flow in a range of rotational blades /1According to equation (3), for an isonergtique, homentropique and purely axial flow, one has:

In addition, by taking into account The expression of can be obtain as previously. If the surface

coincides with a stream tube, then :


Flow in a range of rotational blades /3One can finally obtain the explicit expression of :


Flow in a range of rotational blades /2The components of vector can be obtained knowing that

with :

One can finally obtain the explicit expression of :


Flow in a range of rotational blades /4One can prove the correctness of two equations:

The continuity equation can be written as follows:

(7)(8)


Flow in a range of rotational blades /5One has with designates the height of stream

sheet ( being independent of due to the axi-symmetric hypothesis)

Note that the mass flow rates are in the direction and

in the azimuthal direction, perpendicular to the plane of figure. One can then introduce a stream function defined by:

Introducing these expressions into equation (7), one obtains the partial differential equation of that depends on that must be determined by taking into account (8) representing compability condition in the radial direction.


Simplified radial equilibrium /1Hypotheses:perfect gasInviscid, adiabaticsteady, axisymmetric , negligible radial component In the absolute frame , the velocity components are . The momentum equation projected on the radial direction is:

This does reduce to:


Simplified radial equilibrium /2Suppose that we know the radial pressure total and the temperature total . The momentum equation can be rewritten as follows:

From the definition of total temperature , one can draw:

One defines a total Mach number

(9)


Simplified radial equilibrium /3One has:

One deduces finally:

By defining , the momentum equation reduces to:


Simplified radial equilibrium /4Let denote:

Then,

The momentum equation can be finally rewritten as follows:


Simplified radial equilibrium /5One can show that the integration of momentum equation leads to:

The integration constant is iteratively determined by the condition of mass flow rate conservation between minimum radius (moyeu) and maximum radius (carter):


Simplified radial equilibrium /6With more severe hypotheses, one can find the explicit expression of the axial velocity:AxisymmetricNegligible radial component,Negligible radial gradients of enthalpy and entropy, The radial component of Crocco equation in absolute frame results in:

The solution of this equation is:


Simplified radial equilibrium /6Different simple solutions can be found according to the adopted distribution of : Irrotational flow

The axial and rotational components vanishes:

constant in radial distance


Simplified radial equilibrium /7Different simple solutions can be found according to the adopted distribution of : Solid rotational flow

This flow type is characterized by: One then has:

Then:

One finally obtains the distribution of axial velocity


Simplified radial equilibrium /8Different simple solutions can be found according to the adopted distribution of : Constant angle of attack

This flow type is characterized by: The momentum equation can be then written as follows:


Simplified radial equilibrium /9Different simple solutions can be found according to the adopted distribution of : Constant angle of attack

One finally obtains the solution:


Blade cascade / 1Definitions:Profile defined by a mean line giving camber line that is covered by a sheet of material giving the definition of profile thickness. Chord having length and connecting the trailing edge and leading edge of profile.Stagger angle is the angle formed by airfoil chord and the direction normal to cascade front plan (One sometimes uses the angle between airfoil chord and cascade front). Space-chord ratio Relative aspect ratio with being the dimension of blade in the radial direction. One denotes the and the angles defined by the mean line at the entrance and the exit, respectively (with respect to the plan normal to the cascade front, i.e. axis of machine). One sometimes refers to the camber line angle . If the camber line is a arc of circle, one has:


Blade cascade / force balance / 1The flow enters the cascade with absolute velocity at mean pressure and leaves the cascade with absolute velocity at mean pressure . Let and the components of aerodynamic forces acting by fluid on a period of cascade.


Blade cascade / force balance / 2The momentum balance results in:

If we suppose that the flow is incompressible, the mass conservation condition results in:

By denoting

(10)(11)


Load coefficient of blade / 1If we suppose that flow is incompressible, one has:

By introducing the mean velocity , one deduces:

The module of total force is then:


Load coefficient of blade / 2If we normalize the total force by (i.e. we are now in the situation that the blade is, at its exit, subjected to a total pressure

on the lower surface and a static pressure ), one define the ZWEIFFEL coefficient:

The common values of are:

That permits, in the preliminary design phase to select the space-chord ratio


Lift and drag / 1The effort on a period of cascade can be decomposed into lift force

normal to the mean flow direction defined by and drag parallel to this direction. Here, the angle of attack of the mean flow is defined as follows:


Lift and drag / 1One can express as function of :

The lift and drag coefficients are defined as follows:

(12)(13)


Losses / 1Due to the viscosity, the fluid (as it passes through the cascade) is subjected to different sources of losses that are characterized by a drop of total pressure . If one supposes the flow is incompressible:

Car , one has:


Losses / 2By using (10) and (11), one obtains:

One can define the loss coefficient as follows:

OR

(14)


Losses / 3Let introduce a pressure coefficient and a tangential force coefficient as follows:

One can rewrite equation (14):

(15)


Lift-to-drag ratio / 1 Equation (13) results in:

By taking into account (14), one has:

One can then express the drag coefficient as function of loss coef.


Lift-to-drag ratio / 2 By doing the same, one can deduce from equation (14):

Introducing this equation into (12), one obtains:

One can then deduce the expression of lift coefficient:


Lift-to-drag ratio / 3 One deduce finally the expression of lift coefficient:

In practice, and is rarely higher than , the term

is then negligible. On obtains finally:

Discussions?


Efficiency / 1 The efficiency of a diffusser is defined as follows:

One has:


Efficiency / 2One then obtains:

One has:

One note that if


Efficiency / 2If one supposes that is independent of and is large enough:

If


Axial turbines / 1STATORROTOR123Chiu dng cc gc !


Axial turbines / 2 losses in stator


Axial turbines /3 losses in rotorhS23


Axial turbines /4 losses in turbinehS123


Axial turbines /5 losses in turbineFriction losses on turbine bladesLoss due to finite thickness at the blades trailing edgeLoss due to shock wavesLoss due to the cooling of blades, casing and rotor disks Loss due to the gap between blade tip and casing


Axial turbines /5 losses in turbineFriction losses on turbine blades


Axial turbines /5 losses in turbineLoss due to shock waves

2D turbine cascade


Axial turbines /5 losses in turbineIf one supposes that the isobars are parallel (this assumption is fine for one stage):

Isentropic efficiency:


Axial turbines /6 losses in turbineEULER theorem:

with


Axial turbines /7 losses in turbine5 design variables:

Optimize ?

directly affect the isentropic efficiency, the turbine:One fixes One fixes and changes


Axial turbines /8 losses in turbineRemark:for An error of 0.2 degree results in a reduction of 1% of throat section


Axial turbines /8 Degree of reactionDefinition

Enthalpy reduction in the isentropic transformation from Enthalpy reduction in the isentropic transformation from


Axial turbines /8 Typical HP turbine at stator exit : ~ 75o 78oMach number at stator exit : ~ 1.05Absolute Mach number at rotor exit: ~ 0.45Relative Mach number at rotor exit : ~1.0Mean degree of reaction : ~ 0.4


Axial turbines /8 Typical multistage LPT

CFM56-type 100kN Engine at the lowest rotational speed (this corresponds to tip Mach number of the Fan ~1.4)

Rule for determining the number of stages:

Stage #12340.280.300.330.353.12.72.51.3


Axial compressors /1ROTORSTATOR


Axial compressors /2Input dataCompression ratioMass flowTotal pressure and temperature a entryChoicesShape of flow channel through stagesNumber of stages and distribution of charge/ stagesDegree of reaction (repartition between rotor and stator)Radial variation of velocity triangles anglesNumber of blades and their span


Axial compressors /3Following is a typical velocity triangles of axial compressor with constant axial velocity


Axial compressors /4From velocity triangle at the entry of rotor, one can deduce:


Axial compressors /4According to Euler theorem, one has:


Axial compressors /5From velocity triangle at the exit of rotor, one can deduce:


Axial compressors /6From the velocity triangles, one can also deduce:


Axial compressors /7Work coefficient / stage

Flow coefficient

Degree of reaction


Axial compressors /8From velocity triangles, one can deduce:

One notes that velocity triangles (i.e. element of rotor geometry) are completely defined based on three parameters .


Axial compressors /9


Axial compressors /10


Axial compressors /11For the case of a constant circulation (ir-rotational) OR free vortex flow, from the simplified radial equilibrium theory, one draws:

The work per unity of mass received by fluid is independent of radial position:

Inconvenience: W is highest at the tip of blades = risk to surpass the critical Mach number of blades profile (on the first stage, since the static temperature at the downstream stages increases = the sound speed increases = Mach number reduces)


Axial compressors /11How to overcome this inconvenience?Reduce Wmax by reducing the load factor (i.e. the circulation)Use appropriate profiles (think bi-circular airfoils)Reduce (but 1- is a decreasing function of radial distance r == this solution is infeasible)

Abandon free vortex flow, i.e. and adopt rotational compressor concept.


Origin of losses in axial compressor/1Simplified radial equilibrium approach (that results in radial evolution of absolute angles and relative angles ) depends on losses through compressor: Loss due to friction on profilesLoss due to shock wavesLoss due to secondary flows Boundary layers at hub and casingGap between blades tip and casing After-body loss associated with blunt trailing edges of profiles


Loss due to friction /1Associated with boundary layersCharacterized by diffusion factorExist correlations between loss due to friction and diffusion factor, for example:

How to evaluate diffusion factor


Loss due to friction /2The maximum velocity over profile can be expressed as follows:

with due to the circulation around profile due to obstruction of profileThe circulation is determined by

By neglecting the last term and with


Loss due to compressibility /1If upstream flow is subsonic

Exist a critical Mach number Choking (flow rate is limited)Increase of losses (due to shock waves)Loss due to shock waves in inviscid flowsLoss due to shock waves in viscous flows (boundary layer/ shock wave interaction)If upstream flow is supersonic

One can not specify at the same time upstream Mach number and incidence (unique incidence notion)


Choking of flow through cascade /1

The mass flow rate is defined as follows:


Choking of flow through cascade /2One can finally deduces:

The critical throat is:In practice, the actual throat > 4-5% higher that critical throat. This margin is required to compensate the boundary layer, the fluctuations of incidence, machining error (stagger angle error), .

Max. for


Compressor with super. upstream flow Unique incidence notion /1

ABAAThe supersonic flow in region is completely defined by the upstream Mach number M1 and the geometry of the part AB of profile.


Compressor with super. upstream flow Unique incidence notion /2The conservation of mass results in:

This can be rewritten as follows:

This is a function of and for a predefined geometry of AB of profileOne cannot impose at the same time upstream Mach number and incidence


Losses due to secondary flows / 1Boundary layers on the internal and external walls between the channel formed by two consecutive blades.Phenomena associated with the gap between rotors blade tips and casing (= leakage + boundary layer perturbations) Recirculation due to complex gaps at the tips of stators


Isentropic efficiency /of rotor/ 1The loss coefficient is defined as follows:

If one supposes that the flow is incompressible:


Isentropic efficiency /of rotor/ 2Since , one has::

and,


Isentropic efficiency /of rotor/ 3One then deduces:

Finally, one has:


Isentropic efficiency /of stator/ 1The loss coefficient is defined as follows:

If one supposes that the flow is incompressible:


Isentropic efficiency /of stator/ 2Since , one has::

Since


Isentropic efficiency /of stator/ 3One finally deduces:

The increase of pressure through a stage of compressor is the sum of ones through rotor and stator:


Isentropic efficiency /1Isentropic efficiency is defined as follows:

where (since by hypothesis ) According to second principle of thermodynamics, one has:


Isentropic efficiency /2Let introduce the flow coefficient into the formula of pressure increases through rotor and stator:


Isentropic efficiency /3


Optimization of isentropic efficiency as function of degree of reactionLet freeze:The work coefficientThe flow coefficient

and try to find the optimum isentropic efficiency as function of . 1/ One has: then, from 2/ One can the diffusion factor D as function of and .3/ One can finally deduce loss coefficients of rotor and stator


Off-design operating / 1Hypotheses: Compressor is defined by a set of predefined parameters (On-design conditions)

What will happen if we keep constant while flow coefficient

is changing!

defined by defined by


Off-design operating / 21/ When


Off-design operating / 32/ One has

3/ One has

4/ One has WhenWhenWhen


Off-design operating / 4One has

In conclusion:

WhenIf the flow coefficient


Off-design operating / 5The working (load) coefficient but the incident angles to rotor (|1| ) and stator (1 ) and deceleration over profiles becomes too severe.

risk to fall into unstable regimes (surge, rotating separation) Problem:is too high/separation on rotorRemedity:Increase Variable Stator Vanes

Bleed Vanes


Variable stator vanes


Bleed vanes


Axial compressors perfomance map

Surge lineN1N2N3N4Corrected mass flow rate [kg/s]Pressure ratioworking line


Different unstable regimes / 1Rotating separation

Rotation direction1234Separation propagation directionMECHANISM separation on upperside of blade #1

choking of flow between blade #1 and blade #2

deviation of the incoming flow of blade #2

Increase of incidence angle at blade #2

Speration on upperside of blade #2

Etc.


Different unstable regimes / 2Rotating separation .

Surge

Flutter (Aeroelasticity)

The rotating separation induces a spatial fluctuation of mass flow rate (a fraction of rotor is separated) but the total mass flow rate remains unchanged (stabilized regime). Strong fluctuation of total mass flow rate and pressure ratio due to separation on blades and casing. Coupling between fluid/ and structure.


Surge criteria / 1

Surge lineN1N2N3N4Corrected mass flow rate [kg/s]Pressure ratioWorking lineTransient working lineFull throttleSurge margin defines acceptable acceleration time of engine! Surge margin


Surge criteria / 2Surge in compressor influenced by different factors:Internal factorsDiffusion factor,

To avoid separation on the casing, the following condition must be fulfilled:

The incidence to rotor becomes too high at low regime need to help variable stator valves.


Surge criteria / 3Surge in compressor influenced by different factors:External factors

Surge may be provoked by heterogeneity produced by:Side wind, and Excessive climbing gradient


Some typical values... / 1Conditions for velocity triangleIncoming Mach number on mini. radius (minimizing secondary losses)

Flow decelerationOn the blades, diffusion factorFor boundary layer on the casing Flow deviation (secondary phenomenon)For subsonic flow:For supersonic flow: just some degrees.

or


Some typical values... / 2Axial velocity at entry of compressor

For one-dimensional flow, one has:

In practice, ifandthrough first stage of a multi-stage compressor or fanthrough first stage of a multi-stage compressor or fanat entry of HP compressor (reduction of effective cross area due to presence of boundary layer+ wake of BP blades )


Some typical values... / 3Variation of axial velocity Mach number at entry of combustor ~ 0.25 to 0.3

EntryEntryExitAxial Mach numberIt needs to be optimized to limit the diffusion in rotor.


Some typical values... / 4Rotational regime and pressure ratio

It has been shown in the beginning of this chapter that the velocity triangle is full defined by a set of , and

It clears that, for a pre-defined , the pressure ratio is defined by


Aircraft Propulsion I - Lecture1

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