MECH 535-CHAPTER 6-AERODYNAMIC LOSSES MECHANISMS & EFFECTS-SLIDES-13
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MECH 535TURBOMACHINERYCHAPTER 6AERODYNAMIC LOSSES: MECHANISMS AND EFFECTSMECH 535 TURBOMACHINERY & PROPULSION Dr. WG. HabashiChapter 6 – Slide 1
•Some important concepts of viscous and inviscid fluid dynamics•Energy addition in terms of geometry•Energy addition in terms of thermodynamics•T & P changes in a multistage compressor: total temperature riseis additive, total pressure ratiois multiplicative•Degree of reaction is an indication of the split in static pressure rise between stator and rotor, can be anywhere from –ve (a horrible design), to over 100% (another horrible design)•Stage loading: an indication of work done per flow rate•Work done factor: a fudge factor •Shape of blades: twist and stagger•Effect of inlet guide vane (IGV)•Effect of engine flare•The ideal and actual 𝚿𝚿vs 𝚽𝚽stage loading characteristic What did we learn in Chapter 5?MECH 535 TURBOMACHINERY & PROPULSION Dr. WG. HabashiChapter 6 – Slide 2
What is covered in Chapter 6, 16.1 AERODYNAMIC LOSSES: IDENTIFICATIONIdentifying the total pressure loss mechanisms6.2 TOWARD BETTER UNDERSTANDING BOUNDARY LAYERSLaminar, transition, turbulentOver external bodies, in internal flowsOver streamlined, bluff, contaminated bodiesWith and without pressure gradientAttached, separated over clean and contaminated profilesB/L thickness, displacement thickness, momentum thicknessViscous-inviscid interaction methodsDrag: profile/friction, form/parasite, inducedLaminar vs. Turbulent flows: what to chooseMECH 535 TURBOMACHINERY & PROPULSION Dr. WG. HabashiChapter 6 – Slide 3
What is covered in Chapter 6, 26.3 AERODYNAMIC LOSSES: QUANTIFICATIONFlow and blade angles mismatch at L.E. : incidenceBoundary layers: friction, flow separation, T.E. deviationShocksSecondary flows Clearances and gaps6.4 AERODYNAMIC LOSSES: EFFECTS, MEASUREMENTRotor and stage non-isentropy ; loss coefficientsDetermining losses by measuring P, V, T at inlet/exitOverall effect of losses on a characteristic6.5 MOLLIER DIAGRAM FOR AN AXIAL-FLOW COMPRESSORMECH 535 TURBOMACHINERY & PROPULSION Dr. WG. HabashiChapter 6 – Slide 4
What is covered in Chapter 6, 3The chapter is qualitative in nature but will, for those who will absorb its contents, crystallize “concepts” such as boundary layers and shocks covered in Fluids course(s) and now shown how applied in practiceMECH 535 TURBOMACHINERY & PROPULSION Dr. WG. HabashiChapter 6 – Slide 5
A Gentle Reminder•Have you gone through the •Flipped Learning of this Chapter?•If you do it regularly, the course will be “enjoyable”•If not, the course will slowly become more “painful”MECH 535 TURBOMACHINERY & PROPULSION Dr. WG. HabashiChapter 6 – Slide 6
Section 6.1Aerodynamic losses: identificationMECH 535 TURBOMACHINERY & PROPULSION Dr. WG. HabashiChapter 6 – Slide 7
•All fluids are viscous, some more than others•When we mention inviscid, we mean the assumption that the flowcan be treated as inviscid, not the fluid•This, in general applies only at high speeds•Thus, in FD, we make the distinction : hydrodynamics, fluid mechanics, fluid dynamics, aerodynamics and gas dynamics, to distinguish increasing speeds starting from statics•The boundary layer (B/L) is as an important concept to understand how fluids behave near a wall, causing friction and aerodynamic losses•The B/L is the enemy of the aerodynamicist•Up to the late 1990s most computer codes were based on what is known as viscous-inviscid interaction methods or B/L (to become clearer later in this chapter)•Most flows nowadays are solved by the Reynolds-Averaged Navier-Stokes (RANS) equations•Almost no B/L codes are used in today’s practiceSome important fluid dynamics (FD) conceptsMECH 535 TURBOMACHINERY & PROPULSION Dr. WG. HabashiChapter 6 – Slide 8
•Every newclass of engines is designed to meet the requirements of a newclass of aircraft•The engine has to be designed, tested, and certificated by the time the aircraft is ready for its first test flight•In general, the cycle for designing a new aircraft is 3 years and the engine OEM therefore, 3 years ahead of its own final product, has to guarantee a certain performance in order to be commissioned to produce that new engine•The new engine could be a derivative or could also be a brand-new engine or concept (vide the Geared Turbofan as an example)•The engine manufacturer has to commit to a specified performance in terms of thrust, SFC, surge, maintainability, serviceability, etc.•Thrust and SFC are the basic aerodynamic items the designers have to contend with•For 3 years, these aerodynamicists are fighting an invisible enemy:Aerodynamic LossesSome important jet engines performance conceptsMECH 535 TURBOMACHINERY & PROPULSION Dr. WG. HabashiChapter 6 – Slide 9
The aerodynamic loss mechanisms: descriptionMECH 535 TURBOMACHINERY & PROPULSION Dr. WG. HabashiChapter 6 – Slide 10
The major aerodynamic (total pressure) losses in a jet engine are due to:A.Flow and blade mismatch at L.E. due to incidence during acceleration/decelerationB.Boundary layers: causing friction(momentum losses) on all 4 surfaces (2 blade surfaces, hub, shroud), and trailing edge deviationC. Shocks,if the relative Mach number exceeds unityD.Secondary flows due to turning of the flow causing regions with motion not in the direction of the main flowE. Leakagelosses due to flow crossing at tips of rotor blades and stator vanes and through seals of various typesThese are illustrated in the next slideThe aerodynamic loss mechanisms: identificationMECH 535 TURBOMACHINERY & PROPULSION Dr. WG. HabashiChapter 6 – Slide 11
Shock LossesL.E. Incidence SeparationBoundary Layers: frictionTip Clearance FlowsSecondary FlowsT.E. Deviation due to B/LThe aerodynamic loss mechanisms: illustration
Foreign Object Damage (FOD) lossesMECH 535 TURBOMACHINERY & PROPULSION DR. W.G. HABASHIChapter 13.1 – Slide 13
Impact of an ice slab on the Fan Blades – Side ViewThe ice slab (0.5x12x20 inches) impacts the rotating fan blades at 200 m/sThe fan blades slice the ice slab into pieces that disintegrate into dustTotal time ~5 millisecondsMECH 535 TURBOMACHINERY & PROPULSION DR. W.G. HABASHIChapter 13.1 – Slide 14
Deformation of the fan blades by the ice impactThe ice impact causes significant deformation, but the deformation is elastic, and the blades do not sustain permanent damageMECH 535 TURBOMACHINERY & PROPULSION DR. W.G. HABASHIChapter 13.1 – Slide 15
UAVs and air mobility: an accident waiting to happen?MECH 535 TURBOMACHINERY & PROPULSION DR. W.G. HABASHIChapter 13.1 – Slide 16
UAVs and air mobility: an accident waiting to happen?MECH 535 TURBOMACHINERY & PROPULSION DR. W.G. HABASHIChapter 13.1 – Slide 17
January 1997 crash of COMAIR 3272 EMB 120 while attempting to land at DetroitAirspeed 146 kts; AoA 9.2, Flap Angle 0°CFD showing the separation effect of a 3 mm ice ridge near LE, with boots off, boots onFlow separation over ice contaminated profilesMECH 535 TURBOMACHINERY & PROPULSION Dr. WG. HabashiChapter 6 – Slide 18
Ice Ingestion (SAS), Boots (EMB120), SLD (ATR72), Ice Crystals (A330)MECH 535 TURBOMACHINERY & PROPULSION Dr. WG. HabashiChapter 6 – Slide 19
COMAIR 3272, Over Detroit, EMB 120 (landing)MECH 535 TURBOMACHINERY & PROPULSION Dr. WG. HabashiChapter 6 – Slide 20
American Eagle 4184, Over Chicago, ATR72(holding)Appendix O icing conditions (SLD) running back on wing surface MECH 535 TURBOMACHINERY & PROPULSION Dr. WG. HabashiChapter 6 – Slide 21
Air France 447, Over Pacific, Airbus 330(cruising)Dr. Habashi:I went from my happiest moment in life to the deepest darknessafter losing my only daughter and my son-in-law in the AF447 flight hours after their fairy tale marriage, on their way to their Paris honeymoon.Your friend, Dr. R.C.MECH 535 TURBOMACHINERY & PROPULSION Dr. WG. HabashiChapter 6 – Slide 22
Ethiopian-Malaysian-United-Alaskan-Southwest: Boeing + Boeing…Crashes…Doors…Engines…Wheels...Fasteners…Dutch Roll…What next?andWhy?The FAA and OEMs: an ill-defined relationship that includes company-employed DERS. Imagine a sports event where the referee is a player from one of the two teams!MECH 535 TURBOMACHINERY & PROPULSION Dr. WG. HabashiChapter 6 – Slide 23
Section 6.2Toward better understanding boundary layers(a boost to your fluid dynamics knowledge)MECH 535 TURBOMACHINERY & PROPULSION Dr. WG. HabashiChapter 6 – Slide 27
Assumptions under which the boundary layer equations are derived [Ludwig Prandtl, 1875-1953]:in B/L= given by the inviscid solution outside the B/L. Profile Losses or Drag:A boundary layer always grows on a body, even on a flat plate with no curvature or pressure gradient. A profile occurs from the free stream of the flow up to the body where the velocity is reduced to zero. Friction at wall gives shear stresscausing total pressure drop and profile drag.¶p¶y»0¶p¶x=μ¶u¶yThe boundary layer concept and assumptionsMECH 535 TURBOMACHINERY & PROPULSION Dr. WG. HabashiChapter 6 – Slide 28
The boundary layer equations•The B/L assumptions result in a set of governing equations that are much simpler to solve than the Navier-Stokes equations, by rendering the equations system parabolic, thus allowing a marching scheme from left to right, as the boundary layer grows (similar to a heat propagation problem)•https://web.mit.edu/fluids-modules/www/highspeed_flows/ver2/bl_Chap2.pdf•These equations are not part of the course but have been added for graduate students or students who may later on decide to pursue graduate studies”MECH 535 TURBOMACHINERY & PROPULSION Dr. WG. HabashiChapter 6 – Slide 29
B/L: laminar, transition, turbulentMECH 535 TURBOMACHINERY & PROPULSION Dr. WG. HabashiChapter 6 – Slide 30
B/L turbulence leads to more lossesMECH 535 TURBOMACHINERY & PROPULSION Dr. WG. HabashiChapter 6 – Slide 31
B/L over a streamlined body (sb)AttachedSeparatedOn a streamlined body with separation, the B/L assumptions are not valid anymore: must solve the Navier-Stokes equations MECH 535 TURBOMACHINERY & PROPULSION Dr. WG. HabashiChapter 6 – Slide 32
B/L over a bluff body (bb)Always separatedOn a bluff body, separation will occur and the B/L assumptions are not valid anymore: must solve the Navier-Stokes equations MECH 535 TURBOMACHINERY & PROPULSION Dr. WG. HabashiChapter 6 – Slide 33
PlenumB/L development in an internal flowThe flow progresses from an inviscid profile to a fully viscous one (Poiseuille Flow)MECH 535 TURBOMACHINERY & PROPULSION Dr. WG. HabashiChapter 6 – Slide 34
On a body with zero pressure gradient:no change in velocity “profile”.On a body with an adverse pressure gradient, i.e., pressure downstream > pressure upstream (as in a compressor)separation mayoccur, with a region of reverse/recirculating flow. B/L with and without pressure gradientMECH 535 TURBOMACHINERY & PROPULSION Dr. WG. HabashiChapter 6 – Slide 35
Flow separation in external and internal flowsCompressor caseTurbine caseExternal flows: potential separation over a streamlined body and over a bluff bodyInternal flows: potential separation in convergent and divergent nozzlesMECH 535 TURBOMACHINERY & PROPULSION Dr. WG. HabashiChapter 6 – Slide 36
B/L “thickness” concept99% UMECH 535 TURBOMACHINERY & PROPULSION Dr. WG. HabashiChapter 6 – Slide 37That definition used in all textbooks is valid for flow over a flat plate. It is inaccurate if not altogether confusing as it is difficult to define the “edge of a freestream” for a non-uniform flow over an arbitrarily shaped bodyThe B/L “displacement thickness” is more meaningful and quantifiable.
B/L momentum loss concept (quantified in slide 63)MECH 535 TURBOMACHINERY & PROPULSION Dr. WG. HabashiChapter 6 – Slide 38
B/L displacement and momentum thickness conceptsMECH 535 TURBOMACHINERY & PROPULSION Dr. WG. HabashiChapter 6 – Slide 39
Displacement Thicknessis a meaningful parameter : at a point x: is the distance the streamline entering the B/L at that x-position has been displaced outwards in the y-direction creating a totally stagnated region that has the same integrated velocity deficit as the actual B/L. In other words, it is the thickness by which we have to augment the body profile in order to include the viscous flow effects in otherwise inviscid calculations. The new results foron the augmented body can be compared to the previous one and the iteration continued until a certain tolerance is reached between successive thicknesses.udy0¥ò=uedyd*¥òd*=1-uueæèçöø÷dy0¥òB/L displacement thickness calculationδ*δ*δ*to augment body profile and carry on inviscid flow calculationsMECH 535 TURBOMACHINERY & PROPULSION Dr. WG. HabashiChapter 6 – Slide 40
A typical viscous-inviscid interaction method1.The flow is thought of as a purely inviscid flow over a body once augmented by the displacement thickness (B/L solution, much simpler equations than Navier-Stokes)2.Since the displacement thickness depends on the pressure gradient it is not known as priori.3.Inviscid equations solution is needed for flow outside of the B/L to determine the pressure gradientHence the concept of an iterative viscous-inviscid interaction approacha. Solve the inviscid (Euler or Potential) equations on the original body outside the B/L and establish a pressure gradient, dp/dxb. Solve the boundary layer equations with this imposed pressure gradient and determine δ*(s) along the entire airfoil profilec. Augment the body shape all along s by δ*(s)d. Repeat from (a) and stop when change ∆[δ*(s)] is below a selected thresholdDistance “s” is measured along suction and pressure surfaces of the body from the LE stagnation pointMECH 535 TURBOMACHINERY & PROPULSION Dr. WG. HabashiChapter 6 – Slide 41
Momentum Thickness,: Associated with the total momentum deficit in the B/L: (derived in a comprehensive way for cascades in slide 64)Thus, , in accounting for the total momentum in the flow is like assuming a region of that thickness, in which the velocity is zero, and hence there is no difference between static and dynamic pressures in that region.ue2θ*=u ue−u()dy0∞∫θ*=uue1−uue⎛⎝⎜⎞⎠⎟dy0∞∫B/L momentum thickness calculationθ*θ*MECH 535 TURBOMACHINERY & PROPULSION Dr. WG. HabashiChapter 6 – Slide 42
Types of drag: profile drag (skin friction)MECH 535 TURBOMACHINERY & PROPULSION Dr. WG. HabashiChapter 6 – Slide 43
Types of drag: form or parasite dragparasitic drag on an object is proportional to the square of the airspeedMECH 535 TURBOMACHINERY & PROPULSION Dr. WG. HabashiChapter 6 – Slide 44
This is what the local airfoil sees, and not simply the geometric angle of attack.The trailing vortex (really drag/ wasted energy) induces a small downward component of air velocity in the neighborhood of the wing itself. This downward component is called "downwash". In turn, downwash combines with the freestream velocity to produce a local relative wind which is canted downward - differently - ahead of each airfoil section of the wing: the resultant is the "local aerodynamic angle"Types of drag: induced drag as with a finite wingMECH 535 TURBOMACHINERY & PROPULSION Dr. WG. HabashiChapter 6 – Slide 45
Interpretation of the induced drag due to incidenceinduced drag on an airfoil is proportional to the square of the airspeedMECH 535 TURBOMACHINERY & PROPULSION Dr. WG. HabashiChapter 6 – Slide 46
B/L : laminar vs. turbulent characteristics, 1Difference in thickness Difference in profile Difference in shear stress MECH 535 TURBOMACHINERY & PROPULSION Dr. WG. HabashiChapter 6 – Slide 47
LAMINARTURBULENTfor a flat plateFor lower drag, a laminar B/L is preferred to a turbulent B/L.But is a laminar flow always desired?And, is a laminar flow always achievable?δ∝xRexδ∝xRex()1/5Cf∝1RexCf∝1Rex()1/5B/L : laminar vs. turbulent characteristics, 2MECH 535 TURBOMACHINERY & PROPULSION Dr. WG. HabashiChapter 6 – Slide 48
B/L: laminar vs turbulent for a wingThe choice for the airplane designer comes down to how important the parasite drag of the wing is in the overall mission performance of the airplane and whether or not the materials and manufacturing processes used to build the airplane are compatible with maintaining the conditions for laminar flow.https://www.kitplanes.com/laminar-vs-turbulent-flow-airfoils/For airplanes where the maximum speed isn’t a primary consideration or the environment is likely to be dirty, more forgiving turbulent-flow airfoils are preferredTrying for the drag reduction of laminar flow is worthwhile for fast cross-country airplaneslike this Lancair Legacy.MECH 535 TURBOMACHINERY & PROPULSION Dr. WG. HabashiChapter 6 – Slide 49
B/L: laminar vs turbulent for a bb like a golf ballIf the bb is too smooth the air over the bb won't cling to it, producing a large wakeFor a bb with a rougher surface, the air will more readily cling to the surface and produce a narrower wakeOverall effects on golf ball due to travel + spinning: 1.Increased profile drag due to roughness; 2. Decreased form drag due to weaker wake; 3. If the ball is spinning then Magnus effect: lift due to higher speed at top than bottom (Bernoulli).MECH 535 TURBOMACHINERY & PROPULSION Dr. WG. HabashiChapter 6 – Slide 50
B/L: why do gold balls have dimples?https://youtu.be/fcjaxC-e8oYMECH 535 TURBOMACHINERY & PROPULSION Dr. WG. HabashiChapter 6 – Slide 51
B/L: laminar vs turbulent in a turbomachineTransitioning from laminar to turbulent flow is very fast in a turbomachineMaintaining laminar flow is thus a virtual impossibilityMECH 535 TURBOMACHINERY & PROPULSION Dr. WG. HabashiChapter 6 – Slide 52
Flow out of a helicopter tail rotor (the power of CFD)3 mm ice ridge, boots off, boots onMECH 535 TURBOMACHINERY & PROPULSION Dr. WG. HabashiChapter 6 – Slide 53
Flow over a high-lift wing system (the power of CFD)3 mm ice ridge, boots off, boots onMECH 535 TURBOMACHINERY & PROPULSION Dr. WG. HabashiChapter 6 – Slide 54
Section 6.3Aerodynamic losses: quantificationMECH 535 TURBOMACHINERY & PROPULSION Dr. WG. HabashiChapter 6 – Slide 55
The major aerodynamic (total pressure) losses in a jet engine are caused by the following processes:A.Flow separation due to high incidence at leading edgeB.Boundary layer friction (loss of momentum) on all surfaces, and in addition causing a flow deviationat the trailing edgeC. Shocks,if the inlet relative Mach number exceeds unityD.Secondary flows due to turning of the flowE. Leakagelosses due to flow crossing at the tip of rotor blades and stator vanes and through seals of various typesThe aerodynamic loss mechanisms: quantificationMECH 535 TURBOMACHINERY & PROPULSION Dr. WG. HabashiChapter 6 – Slide 56
VUhigher m•lower m•!!Cx (design)Positive incidencedue to lower than design mass flow rateleads to stall or surge: forbidden zone on left of characteristic peak. Positive incidenceincreases amount of diffusion.Negative incidencedue to higher than design mass flow rateleads to choking: vertical line on right of characteristic peak.Negative incidencecan be tolerated because the flow accelerates instead of diffusing up to the throat but the loss eventually rises very rapidly when the minimum area (throat) chokes and a shock is formed behind it.A. Incidence effects : can lead to stall or chokingMECH 535 TURBOMACHINERY & PROPULSION Dr. WG. HabashiChapter 6 – Slide 57VUhigher m•lower m•!!Cx (design)
+ve incidence causing flow stall: CFDhttps://www.ccj-online.com/combined-cycle-journal-number-50/gas-turbine-compressors-understanding-stall-surgeA. Incidence effects : individual blade stall, 1MECH 535 TURBOMACHINERY & PROPULSION Dr. WG. HabashiChapter 6 – Slide 58
A. Incidence effects : rotating stall, 2Once a single blade stalls, stall starts propagating rotationallyhttps://www.ccj-online.com/combined-cycle-journal-number-50/gas-turbine-compressors-understanding-stall-surge/MECH 535 TURBOMACHINERY & PROPULSION Dr. WG. HabashiChapter 6 – Slide 59
A. Incidence effects : -ve incidence can cause choking-ve incidence choking of a cascade: CFDMECH 535 TURBOMACHINERY & PROPULSION Dr. WG. HabashiChapter 6 – Slide 60
A. Designing “with/for” incidence, 1Note that minimum loss is never at zero incidence, as the flow ahead of cascade, same as the flow ahead of a wing, has an induced angle of attackSo, one can possibly design the flow to come at incidence in the freestream such that “by the time the flow reaches the blade” its incidence with the leading edge is zero!MECH 535 TURBOMACHINERY & PROPULSION Dr. WG. HabashiChapter 6 – Slide 61
If α1is fixed, the actual blade angle is given from the desired incidence (see previous slide)A good working rule is to use zero-incidence as this allows the highest critical Mach number. However, the minimum loss as can be seen from the figure is never at zero incidence.The use of positive incidence is safe with high solidity blades and negative incidence with low solidity cascades. An approximate guiding rule is given by:i, incidence_________________________________2+5° to 0°10° to -2.5°0.66 -2.5° to -5°So, incidence considerations help us determine the inlet angle.cs=sA. Designing “with/for” incidence, 2β1MECH 535 TURBOMACHINERY & PROPULSION Dr. WG. HabashiChapter 6 – Slide 62
B. B/L friction (momentum) losses in a cascade, 1MECH 535 TURBOMACHINERY & PROPULSION Dr. WG. HabashiChapter 6 – Slide 63A wake of zero velocity and width θ*represents the momentum loss.Within that wake, the pressure (since V=0) is the static pressureThe geometrical average of the downstream stagnation pressure would then be:inviscid region wakepo2r=po1rscosβ2−θ*()+p2θ*⎡⎣⎤⎦scosβ2Note that this figure taken from a book is slightly incorrect: the region indicated by the double arrow is notbut is The correctis between the middle of hatched areas (green )
ρV122=ρCx122cos2β1B. B/L friction (momentum) losses in a cascade, 2ϖ=cosβ1cosβ2⎛⎝⎜⎞⎠⎟2σcosβ2⎛⎝⎜⎞⎠⎟θ*c⎛⎝⎜⎞⎠⎟ϖcosβ2σ!"#$%&cosβ2cosβ1!"#$%&2=fDi()where σ = c/sis the soliditypo2ri−po2r≈ρV222=ρCx22cos2β2This is a correlation in the form of a diffusion coefficient (see next slide):MECH 535 TURBOMACHINERY & PROPULSION Dr. WG. HabashiChapter 6 – Slide 64Loss=⎡⎣⎢⎤⎦⎥po2ri−po2r()Defining p0loss, geometrically, as in figure:ϖ=θ∗scosβ2⎡⎣⎢⎤⎦⎥po2ri−po2r()ρV12/ 2Defining , a non-dimensional loss coefficient:ϖSubstituting:;Yields:
B. B/L friction (momentum) losses in a cascade, 3MECH 535 TURBOMACHINERY & PROPULSION Dr. WG. HabashiChapter 6 – Slide 65This rises rapidly above Di= 0.6 (drag rise), indicating separationϖcosβ2σ!"#$%&cosβ2cosβ1!"#$%&2=fDi()
B. B/L losses due to T.E. deviation effects, 1 +veMECH 535 TURBOMACHINERY & PROPULSION Dr. WG. HabashiChapter 6 – Slide 66
The differencebetween the fluid and blade inlet angles at cascade inlet is under the arbitrary control of the designer. At cascade outlet however, the difference between the fluid and blade angles, called the deviation, is a function of blade camber, blade shape, space-chord ratio and stagger angle. The deviation is drawn as positive; almost without exception it is in such a direction that the deflection of the fluid, is reduced. The deviation is due to the fact that the suction surface of a blade has a higher adverse pressure gradient than the pressure surface, hence the B/L displacement thickness on top is larger than bottom. The deviation may be of considerable magnitude, and it is important that an accurate estimate is made of it. How? Empirical rules or CFD!B. B/L losses due to T.E. deviation effects, 2 dδ=β2−β2'()β2−β2'MECH 535 TURBOMACHINERY & PROPULSION Dr. WG. HabashiChapter 6 – Slide 67
Here is an empirical rule to relate the nominal deviation to the camber and space-chord ratio,CARTERwhere n =1/2 for compressor cascadesand n=1 for compressorinlet guide vanes. The value of mdepends upon the shape of the camber line and the blade setting. For a compressor cascade (i.e., diffusing flow):where a is the distance of the maximum camber from the leading edge. For inlet guide vanes, which are essentially turbine nozzles (i.e., accelerating flow):m = constant = 0.19d*=mqs c()nm=.23 2a c()2+a2*500B. B/L losses due to T.E. deviation effects, 3δ*MECH 535 TURBOMACHINERY & PROPULSION Dr. WG. HabashiChapter 6 – Slide 68
C. Aerodynamic losses due to shock waves, 1MECH 535 TURBOMACHINERY & PROPULSION Dr. WG. HabashiChapter 6 – Slide 69Compression shocks occur from supersonic to subsonic flows.Expansion shocks from subsonic to supersonic cannot occur, as proven by a decrease in entropy.Across a shock:•T0remains constant•P0decreases (irreversible process: total pressure loss, increased entropy)•P(static pressure increases)•The static pressure rise across the shock may cause rapid growth of the B/L thickness (slowest moving part of fluid) and increase the risk of separation
For a transonic flow (flow subsonic ahead of blade, with a supersonic region on the blade) there must be the development of a supersonic bubble which must terminate in a shock. Across a normal shock with a shock foot M1 :The higher the shock foot M1, the higher the loss in total pressure (lower po2).The entropy generated across a shock is: with T02=T01across a shock.Shock losses are tabulated in gas dynamics/thermodynamics books against M1(next slide) po2po1=γ+1()2M122γM12−γ−1()γ+1⎡⎣⎢⎢⎢⎢⎤⎦⎥⎥⎥⎥γγ−1Δs=cvlnTo2To1⎛⎝⎜⎞⎠⎟−Rlnpo2po1⎛⎝⎜⎞⎠⎟∴po2=po1e−Δs/RC. Aerodynamic losses due to shock waves, 2MECH 535 TURBOMACHINERY & PROPULSION Dr. WG. HabashiChapter 6 – Slide 70
C. Aerodynamic losses due to shock waves, P02/P01 , 3MECH 535 TURBOMACHINERY & PROPULSION Dr. WG. HabashiChapter 6 – Slide 71
D+E Combined losses due to secondary flows MECH 535 TURBOMACHINERY & PROPULSION Dr. WG. HabashiChapter 6 – Slide 72
D: A vivid CFD demonstrationseparated streamlineseparation boundaryshockMECH 535 TURBOMACHINERY & PROPULSION Dr. WG. HabashiChapter 6 – Slide 73
D. Aerodynamic losses due to secondary flows, 1MECH 535 TURBOMACHINERY & PROPULSION Dr. WG. HabashiChapter 6 – Slide 74CentrifugalAxial
1. Secondary flow at shroud because fluid migrates from the high pressure to the low pressure.2. The vorticity created by fluid gradient due to the boundary layer at the inlet of a row is:This creates a vortex pointing atbottom and pointing attop. When a fluid particle possessing rotation is turned (i.e., by a cascade) its axis of rotation is deflected in a manner analogous to the motion of a gyroscope, i.e., in a direction ⊥to the direction of turning [right-hand rule]. The result of turning the rotation (vorticity) is the formation of secondary flows normal to it in a plane.If the deflection of Ω1is ε, the secondary vorticity Ωs(outlet stream direction) isIf C1(z)is known one can calculate ΩsIt is clear the the flow is overturned near hub and shroud and underturned away from the walls. If the height pitch is not very high the two vortices may merge!W1=dC1dzΩs≈ −2εdC1dzD. Aerodynamic losses due to secondary flows, 2→←MECH 535 TURBOMACHINERY & PROPULSION Dr. WG. HabashiChapter 6 – Slide 75
•Fluid will go anywherethere are gaps•Any flow that is not in the direction of the mainstream is dissipating energy idly•Example (other than leaks) is the fluid passing between blade tip and shroud without having any work done on it•The clearance flow, because of rotation, will form vortices exactly like at a wing tip: hence this is another manifestation of secondary flows•This can be reduced, but not totally eliminated, by shrouding the blade•Examples in the next slideE. Aerodynamic losses due to clearances, gapsMECH 535 TURBOMACHINERY & PROPULSION Dr. WG. HabashiChapter 6 – Slide 76
E. Aerodynamic losses due to tip clearance (CFD)MECH 535 TURBOMACHINERY & PROPULSION Dr. WG. HabashiChapter 6 – Slide 77UnshroudedShrouded: 1-seal labyrinth (left) ; 2-seal labyrinth (right)
Section 6.4Aerodynamic losses: effects, measurementMECH 535 TURBOMACHINERY & PROPULSION Dr. WG. HabashiChapter 6 – Slide 78
Because of the small stage temperature rise, the density change is also small and it is reasonable to assume incompressibility for the fluid.This approximation is applied only to the stageand a mean stage density is implied. Not valid across a multistage compressor, i.e., density varies from a stage to next.2 ways of expressing non-isentropic effects:a) Rotor and stage isentropic efficiency ηR=To2i−To1To2−To1;po2po1=1+ηRTo2−To1To1⎡⎣⎢⎢⎤⎦⎥⎥γγ−1ηS=To3i−To1To3−To1;po3po1=1+ηSTo3−To1To1⎡⎣⎢⎢⎤⎦⎥⎥γγ−1Non-isentropy expressed as an efficiencyMECH 535 TURBOMACHINERY & PROPULSION Dr. WG. HabashiChapter 6 – Slide 79
b)Defining non-dimensional loss coefficients for relative total pressureor alternately:note that for an incompressible fluid and for stationary components (stators) relative and absolute quantities are the same.v=po2ri-po2rpo1r-p1Z1=po2ri-po2r1/2rV12;Z2=po2ri-po2r1/2rCx12po1r-p1=1/2rV12and hence v=Z1Non-isentropy expressed as a loss coefficientMECH 535 TURBOMACHINERY & PROPULSION Dr. WG. HabashiChapter 6 – Slide 80
Given experimental measurements of relative temperature To2rand relative pressure Po2rat the exit of a machine (measure T and pand V and then calculate relative quantities) we can determine the actual loss coefficient:To2rTo1r=po2ripo1r⎛⎝⎜⎞⎠⎟γ−1γ∴po2ri=po1rTo2rTo1r⎛⎝⎜⎞⎠⎟γ γ−1Determining losses from experimental measurementsandZ=po1rTo2rT01r⎛⎝⎜⎞⎠⎟γ γ−1−po2r⎡⎣⎢⎢⎤⎦⎥⎥1/ 2ρV12All what one needs to determine losses is to measure at inlet and exit T, p, and the 3 components of VMECH 535 TURBOMACHINERY & PROPULSION Dr. WG. HabashiChapter 6 – Slide 81
Determining losses from experimental measurementsMECH 535 TURBOMACHINERY & PROPULSION Dr. WG. HabashiChapter 6 – Slide 82
Compendium of losses: stall and choking limitsChokedMECH 535 TURBOMACHINERY & PROPULSION Dr. WG. HabashiChapter 6 – Slide 83
Section 6.5Mollier diagram for an axial-flow compressorMECH 535 TURBOMACHINERY & PROPULSION Dr. WG. HabashiChapter 6 – Slide 84
Absolute quantities at 1 (start with rotor): knowing p1, h1get Ho1 , po1Relative quantities at 1:Ho1=h1+C122po1=p1Ho1h1⎛⎝⎜⎞⎠⎟γγ−1;isentropicHo1r=h1+V122po1r=p1ho1rh1⎛⎝⎜⎞⎠⎟γγ−1Mollier diagram for an axial-flow compressor, 1MECH 535 TURBOMACHINERY & PROPULSION Dr. WG. HabashiChapter 6 – Slide 851/2V221/2V12Stator lossRotor loss
Relative quantities at 2:Absolute quantities at 2: po2ri=por1po2r=po2ri−ϖpor1−p1()Ho2r=Ho1rh2=Ho2r−V222Ho2=h2+C222Mollier diagram for an axial-flow compressor, 2MECH 535 TURBOMACHINERY & PROPULSION Dr. WG. HabashiChapter 6 – Slide 86p2=por2ih2/Hor2()γ γ−11/2V221/2V12Stator lossRotor loss
Mollier diagram for an axial-flow compressor, 3MECH 535 TURBOMACHINERY & PROPULSION Dr. WG. HabashiChapter 6 – Slide 87The calculation of all quantities at 3,from those at 2, follow the same logic if the is given.This is a “necessary” exercise for students.P.S.: The lossesare obtained experimentallyor by solving the Navier-Stokes equations (CFD), which would yield V, p, T, 𝜌𝜌at all points.Stator loss1/2V221/2V12Stator lossRotor loss
Mini-quiz: can you answer these questions?•Aerodynamic losses in a multistage turbomachine are said to be “cumulative”: why?•We have characterized the losses in a turbomachine as “actual overall output”/”ideal overall output”. However, could these losses be measured stage-by-stage to identify a culprit stage? Scour the web if this could be done•Do the different non-dimensionalizations of the loss coefficient(s) have an impact on applying them?•Do you expect the losses in the rotor to be higher than the stator, less, or the same? Why?•Would the losses through a centrifugal be higher, lower, or the same as in an axial with the same overall pressure ratio?•How does the aerodynamic loss in a single compressor stage compare to the loss of energy around an airplane wing?•What does “designing with incidence” mean to you? Can you sketch an example?•What is the difference between a stall and a rotating stall? In which category does surge fall?•How would you identify surge if you were a pilot or a passenger on an aircraft?https://youtu.be/QRY42OjaUS0MECH 535 Turbomachinery & Propulsion Dr. W.G. Habashi Chapter 6 – Slide 88
Mini-quiz: can you answer these questions?•What are modern means of measuring T, P, and Vin an engine test cell? •Can any of these means be used between stages? Explain•What fluid dynamics concepts you already knew were “reinforced” in this course?•What fluid dynamics concepts did you learn that were “not covered” in other courses?•A student in a course evaluation opined that he would have preferred for 2D losses to be covered before 3D losses. Do you think this critique is justified? Is it even correct? Why?•In an extremely well-designed turbomachine can losses be eliminated? If yes, which ones?•The change in gaspath area is an obvious cause of 3D flows: give at least another 2 causes.•The hub of the compressor section is curved: why?•How do you define secondary flows in a turbomachine?•Do secondary flows exist only in axial, or only in centrifugal compressors, or both?•Give “3” examples of secondary flows in turbomachines (typical interview question)•For flow in a curved duct, would static pressure be higher on the outer periphery of the duct or the inner one? (typical interview question).MECH 535 Turbomachinery & Propulsion Dr. W.G. Habashi Chapter 6 – Slide 89