Steady Flow Unsteady Flow

Unsteady Flow in Axial Turbines: A Shift of Paradigm

Martin Rose

Institut für Luftfahrtantriebe (ILA) Universität Stuttgart September 2013

Steady Flow

Shift Paradigm

Unsteady Flow e.g. Turbomachinery

Streamlines

Particle Paths

Po and To , Toω conserved: if inviscid & adiabatic

Po and To , Toω not conserved

p t  0

Work = 0

Energy Flows Along Streamlines

Wall heat transfer and friction diffuse across the flow. Reynolds limited

Non-uniform in space

Dho 1 p  Dt  t

HPT -ΔTo/To > 20% 350K in 25mm

Energy convects with particles & propagates in any direction: static pressure waves Diffusion Reynolds limited Friction and heat transfer across whole flow

Non-uniform in space & time, walls move Sensitive to reduced frequency.

1 p Is the Turbine Work (Dean 1959)  t So

D 1    1 Dp DK Dho De  p    Dt Dt Dt  Dt Dt

D 1   p       p    2  u v  w  Dt   t x y z 

Stagnation enthalpy is internal energy plus pressure work plus kinetic energy p ho  e 



K

Expanding the pdv term:D 1    p  u v w   p      Dt   x y z 

Using continuity:

Two other forms of the inviscid adiabatic energy equation:De p  u v w        Dt   x y z 

DK 1  p p p     u  v  w  Dt   x y z 

Dho p  u v w  p  u v w             Dt   x y z    x y z  

1  p p p p  1  p p p    u  v  w    u  v  w    t x y z    x y z 

The change in internal energy is perfectly balanced by pdv

Dho 1 p  Dt  t

The change in the kinetic energy perfectly balances all the convective terms of vdp. BUT not the temporal.

If there is a Propagating Pressure Wave

p is finite t U can be any speed from near zero to supersonic

U p x

p

δp

Wave at time = t

If the wave is steady in its frame of reference p p   x x

x  Ut p p   U t x

p 0 t p 0 t

Wave at time = t + δt

x If the wave is weak and not tied to the motion of a body then it is a sound wave and propagation is at a the speed of sound in stagnant flow. Very small changes of enthalpy. But in turbomachinery waves are very strong, discontinuous and often tied to and propagate with the blades at their speed U. Large changes of enthalpy result.

The conventional way of looking at a turbine rotor blade: Steady Flow thinking has enabled very successfull Turbomachinery design. Many loss sources have been understood, quantified and controlled.

Fθ N/m

U m/s

But where is the work? Work done on aerofoil per second per m span

Profile

= Fθ U But where is the necessary flow unsteadiness ?

p t

Misenrel Lift

….its in the other frame of reference. Cx

The Pressure Wave

p p  U t r

Responsible for Time Averaged Work In an Axial Flow Turbine

U

p r

Xm rθ m

Time averaged URANS static pressure mid-height axial turbine rotor

But what if the flow is unsteady in the relative frame? Absolute Frame:

Dho 1 p    Dt  t  abs

Relative Frame:

DI 1 p    Dt  t  rel

I = Rothalpy

In both frames of reference there are unsteady pressure waves due to wake and potential interaction with adjascent rows.

1   p t abs is the turbine work. In the relative frame the integral of 1   p t rel is zero. In the absolute frame the integral of

p  p  p    U t  abs t  rel r

or

DUV p  p      t  abs t  rel Dt

If steady flow in rotor: Euler work Wx  UV

The difference between the two temporal derivatives is controlled by circumferential momentum

In an HP turbine p t abs ≈ 115,000 Atm/sec; p t rel ≈ 10,000 Atm/sec

Is

1 p pdv or vdp ?  t

Tds  dh  vdp Tds  de  pdv

Pressure-work term: cell boundaries: breaks up: two terms when differentiated. Orthogonal. Tds equations:

 pdv controls internal energy: divergence of the fluid (density change).  vdp controls enthalpy: due to convection of fluid

Question: Where is the work?  pdv: volume change times pressure force is a work term.  vdp: work due to convection into cell i.e. velocity provides displacement. Why is there no velocity term in vdp? Because the work is specific i.e. per unit mass.

Force

A

 PA

Distance moved  ut

Work Mass

 PAut

 Aut

Work/Mass 

p



u So

1 p is a pressure-work term of type vdp and is due to the convection of the fluid.  t

Status of Turbomachinery Research Experimental Data Time resolved measurements:  Velocity e.g. hot wires and LDA (1950‘s to date)  Surface; thin film guages, Kulites (30 years)  Unsteady probes pressures and temperatures (20 years) Computational Capability  Industry steady CFD dominated < 1990‘s.  Now design steady CFD, but analysis URANS.  LES and DNS research activities. Recognisable flow structures are reported Thought Processes Areas of existing unsteady thought & research:  Wake blade interaction  Unsteady transition LP Turbines at low Re  Unsteady secondary flow behaviour  +…. BUT The thermodynamics of a distorted flow dominated by unsteady work are not addressed. We already have the tools to build this understanding.

Experimental Evidence NGV Exit: FRAP Total Pressure (non-dim)

FRAP& FENT ETHZ

Mid-height space-time diagram Diagonal lines rotor passing Vertically arranged blobs NGV wake

NGV Exit FRAP data Unsteady Work in the Relative Frame: time averaged in absolute frame

DI 1 p    Dt  t  rel

Location of casing loss core

FRAP total pressure for reference

 p        Po1     t      rel  abs

Location of hub loss core

Location of NGV Wake

The dark regions have rates of change of rothalpy of about 17x106 j/s and the white regions have about -22x106 j/s this is +1000 and -1350 times the absolute kinetic energy per second: time of flight is approx 0.24 ms. So we have approx. +20% and -30% KE in gap

Experimental Evidence Rotor Exit: FRAP Relative Total Pressure (non-dim)

FRAP relative total pressure in the absolute frame

Space-time diagram at rotor exit midheight. RMS of the absolute total pressure. Rotor wake turbulence on diagonal lines. Signature of NGV wake at TR8 dotted ellipse encloses the NGV wake fluid.

Experimental Thermodynamics of wake fluid particle Particle efficiencies Freestream: Rotor Wake: NGV Wake:

97,4% 92,3% 114.1%



Thermodynamic Understanding Ambiguity:Entropy change:loss or heat transfer?

 To 2    1  To1   1     Po 2       1  P     o1    

Efficiencies greater than 100% indicate that heat loss must have occured………

ho  Wx  Q  0

Q  Tds

Enthalpy change: work or heat transfer? Conclusion Wake work is less than 21kJ/Kg Freestream work is less than 27kJ/Kg

Probable implications  Differential work coefficient µ = 0.7  Difference in work as fraction of average work 24%  Wake work is less than freestream work.  Wake looses heat at more than 12% of specific work

Unsteady Work

p   t  rel

Max 5.0 x 107 Pa/s: red Min -4.0 x 107 Pa/s: blue

Turbine rotor 2D URANS

Further evidence: URANS particle paths Animation of Particle Paths Colours: entropy. Trajectory: wake • Negative incidence • Migration to suction side. Entropy falls along particle paths!

Important note: these are not streamlines

Particles Start: points fixed relative frame Integration: t = 34 µs 14 steps per cycle.

Particle path thermodynamic data from URANS Fluid particles as they pass through a turbine rotor.

HEAT

TRANSFER

Dotted lines are high entropy (NGV wake fluid), full lines are freestream.

Where entropy falls we have cooling due to heat transfer The wake work is lower than the free-stream

WORK

Red and Blue are particles introduced at two different instants in time

MIXING

Intra-Fluid Heat Transfer A Strong Mechanism even in cold flow rigs NGV wakes loose heat to the freestream in the rotor. Wake entropy falls significantly. Estimates of wake heat loss per unit mass:



Experimental ETHZ Lisa 12% of specific work



URANS ETHZ Lisa 24% of specific work



URANS LP turbine ILA 40% of specific work (Lower Reynolds)

Questions: how reliable is CFD to predict intra-fluid heat transfer using turbulence modelling with Bousinesq assumption and taking a fixed turbulent Prandtl number? What are the loss consequences of the heat transfer? Mechanical Work Potential Miller (2013) has shown that heat transfer from a region of low static pressure to a region of higher static pressure, the potential of the flow to do work increases. The negative jet deposits the wake segment on the suction side and it looses heat to the free stream (more on the pressure side). This is probably a loss reduction effect: needs research!

p  p  U p     t  abs t  rel r 

NGV Exit Absolute Unsteady Work time averaged in the relative frame

   p     Po1    t      abs  rel

Time Averaging in The Relative Frame

p   Verified 5 orders of    0 magnitude down t  rel  rel



p   U p       t  abs  rel r   rel

Blade Speed U = 103 m/s

NGV Exit circumferential static pressure gradient time averaged in relative frame

  p   P  o1   r    rel

Differential Work Idea (Rose 2000) Free-stream loading UVf

Across a rotor NGV Wake Work



Wake loading UVw

Freestream Work

Steady velocity triangles show wake work low.

h U2



UVw UVf

Velocity Triangles Differential Work Coefficient 

1.4 1.8-2 1.6-1.8

If the wake work is low the wake is partially rectified and mixing losses downstream will reduce

1.2

1.4-1.6 1

1.2-1.4 1-1.2

0.8

0.8-1 0.6-0.8

0.6

0.4-0.6 0.2-0.4 0.6

0.7

0.8

0.9

1

1.1

1.2

1.3

Total Pressure Ratio; Wake to Free-Stream

0.4 1.4

Total Temperature Ratio : Wake to Free-Stream

1.6

Disagreement in the Literature

Axial Velocity

Turbine wake work: higher or lower than free-stream? Wake work high; Smith(1966), Praisner(2006), Hodson etal(2009)

Particle path data from unsteady 2D CFD Wake is shown Dotted

Current work shows the reverse, the wake work is low: 1. Velocity triangles 2. URANS particle tracking 3. Experiment FRAP

But why was Smith wrong? Smith assumed that the wake has a lower axial velocity. But it does not in the passage: There are two reasons for this; Negative Jet and Unsteady Work (Hodson). The migration towards the suction side drops the static pressure &Unsteady work boosts the total pressure. Dynamic head climbs!

„Negative Jet“

Smith and Greitzer have accepted Rose 2009 paper. Now in final process of publication in J.Turbomach.

One-Dimensional Analytic Incompressible Model (J.Turbomach. in review)     

Throat th

Inlet i

Exit e

Approach from Greitzer etal. Linearised 1D Momentum Equation Specified total pressure fluctuation inlet Specified static pressure fluctuation at exit Specified turbine passage with throat

Turbine Passage

 p′ti

ui pti pte   t  

A

p′e

ε i 2π

0

μ

e

ωt

2π

th

Ai

Ae

inlet

throat

0

xth

Ath

φ 0 exit x

L

ωt

1200

Total Pressure Perturbations on three particle paths

c) 1000

Total Pressure Perturbation p't Pa

800 600 400 200

Results of Analytical Modelling

0 -200

0

0,005

0,01

0,015

0,02

0,025

0,03

0,035

0,04

-400

p t

-600 zero p't start high p't start low p't start

-800 -1000

d)

-1200 xm

5,0E+07 4,0E+07

    

38,3

x mm

0,0 0,000216

0,000180

0,000198

0,000144

9,6 0,000162

0,000108

0,000072

0,000126

t sec.

19,1 0,000090

0,000036

0,000054

0,000000

28,7 0,000018

3,0E+07 Work transfer mechanism captured 2,0E+07 Up to 67% attenuation of wave form Unsteady 1,0E+07 Work 0,0E+00 Reduced frequency important Pa/s -1,0E+07 -2,0E+07 Phase of exit static pressure important (19%) -3,0E+07 -4,0E+07 Static pressure fluctuation experimentally -5,0E+07 confirmed  Trajectory of pressure wave poorly predicted  Happens equally in stators and rotors

Space-time diagram

Turbine Optimised for Unsteady Flow: Initial Approach Three Zones To Exploit Unsteady Work (1) Upstream (Medium Strength)

(2) Wake/Suction side Interaction (Low Strength) p   t  rel

p     t  rel  abs

(3) Passage Pulsation (High Strength)

(1)

Important parameters in each zone (1) Leading Edge Lift, Size of Axial Gap, Flow Angles, Blade Pitch, Leading Edge Circle Diameter, von Karman Vortices in Wakes & phase difference between wake and potential interaction.

(2)

(3)

(2) Blade lift distribution (thickness, curvature) Wake momentum and incidence, Boundary layer thickness and state (intermitency) and Mach number (3) Reduced Frequency of Wake passing, Downstream potential field (strength and phase), Flow Coefficient and passage shape (inlet to throat area ratio).

U

Conclusions It is time to shift the paradigm of how turbine flow fields are understood.  Turbine flow is fundamentally & massively unsteady.  Energy can move in any direction in the form of waves.  Wave energy transfer is the dominant flow mechanism.  There are substantially unknown loss consequences.  Very large levels of heat transfer intra-fluid exist.  Particle entropy both increases and decreases.  Reduced frequency and clocking both strongly influence the flow. To fully optimise the design of turbines the thermodynamic behaviour of this unsteady, work dominated, non-adiabatic flow must be understood and exploited.

THINK STEADY

Back Up Foils

Unsteady work and rotors Dho 1 p    Dt  t  abs

 Absolute frame: temporal derivative: static pressure indicates stagnation enthalpy (ho) change.

DI 1 p    Dt  t  rel

 Relative frame: temporal derivative: static pressure indicates rothalpy (I) change.

DUV 1 p  1 p       t  abs  t  rel Dt

or

p  p  U p     t  abs t  rel r 

Relationship: two unsteady work terms. Difference: blade speed times rate of change of circumferential momentum. If rotor flow: steady : Euler work equation. ho  UV

Turbine Wake Mixing Losses As wakes mix out viscous stresses cause dissipation and the entropy rises. Heat is also transferred both increasing and redistributing entropy. The turbine efficiency will fall.

Wake at inlet

MASS: MOMENTUM: ENERGY

Control Volume

 s

Uniform flow exit

We can estimate the wake mixing losses using simple control volume calculations

The simple differential work model using velocity triangles and steady flow suggests large reductions of mixing loss (50 to 80 %). Turbine efficiencies have already benefited from this effect, to some extent.

Summary of Unsteady Work Unsteady Work Rectifies Wakes in Vanes and Blades & Reduces Mixing Loss We have some understanding of the phenomena;      

Velocity triangles: Differential work Experimental FRAP & FENT probes URANS CFD Lagrangian output processing Intra-fluid heat transfer is part of it Experimental measured pulsation in vane passage with kulites & URANS Analytic model 1D incompressible o Reduced frequency matters o Phase of downstream static pulsation matters



Potentially quite large (circa 0.4 to 0.8 %).

But we do not know how sensitive unsteady work is to design parameters. We also don‘t know what additional losses we may cause in trying to reduce the wake mixing loss or what blade forcing and noise may result.

Strategy  Current knowledge will not support improved efficiency design with confidence.  Continue experimental and computational studies. But:

 Now the strong approach is „Design for Research“.  URANS works: Design sensitivity study in 2D.  Turbine operating point & reaction might need to be reconsidered  Sensitivities used to evolve new research design (IPR).  Confirm design sensitivities experimentally (IPR!). o

Low speed rotating rig or bar-passing cascade

o

Efficiency measurement has high uncertainties: so-

o

Diagnostic measurements high spatial and temporal resolution

 Design study to include full 3D effects of ideas: mitigation with endwall contouring  Design of high speed rig  High speed rig test.

Design the Turbine Optimised for Unsteady Flow

DESIGN SYSTEM

Theory

Main loop

Wake Work, Heat transfer & Entropy Rise Lagrangian Thermodynamics URANS

Unsteady Mixing Sum Time Average Performance Assessment

List of Rose Literature on Unsteady Work 1.

Rose, M.G., Harvey, N.W. “ Turbomachinery Wakes: Differential Work and Mixing Losses” 99-GT-249 and Trans ASME Journal of Turbomachinery Jan 2000 Vol. 122 pp 68–77

2.

Mokulys, Thomas, Congiu, Francesco, Rose, Martin G., Abhari, Reza S. “UNSTEADY NUMERICAL INVESTIGATION ON DIFFERENT AXIAL TURBINE AIRFOILS WITH INTERACTION OF WAKES WITH EDDY SHEDDING” Accepted for the I.Mech.E Journal of Power and Energy 2009.

3.

Rose Martin G; Schuepbach Peter; Mansour Michel „The Thermodynamics of Wake Blade interaction in axial flow turbines combined experimental and computational study“ Accepted for publication in ASME J.Turbomach 2012

4.

Rose Martin G; Jenny Philipp; Abhari Reza; Gier Jochen “Experimentally Observed Unsteady Work at inlet to and Exit from an axial flow turbine rotor” TE GT2012 69207 accepted for Journal of Turbomachinery.

5.

Rose, Martin G. “Unsteady Flow in Axial Turbines” Habilitation Thesis October 2010 Institüt für Luftfahrtantriebe Universität Stuttgart. ISBN 978-3-86624-531-0

6.

Marx Martin; Lipfert Martin; Rose Martin; Staudacher Stephan; Gündogdu Yavuz; Engel Karl; “LP TURBINE: UNSTEADY WORK PROCESSES AT LOW REYNOLDS CONDITIONS” GT2013 94234 Under review for Turbo-Expo 2013.

7.

Rose, Martin; Marx, Martin: “Unsteady Work Transfer Within a Turbine Blade Row Passage” under review for Journal of Turbomachinery

Universität Stuttgart

Institut Für Luftfahrtantriebe

GT2012-69207

Experimentally Observed Unsteady Work at Inlet to and Exit from an Axial Flow Turbine Rotor Martin G. Rose, ILA, Uni-Stuttgart:

Germany

FRAP

Philipp Jenny, Reza S. Abhari,

Jochen Gier

LEC-ETHZ

MTU Aero Engines

Zürich, Switzerland

München, Germany

p t Funding: German Government LUFO IV & MTU

Introduction to Unsteady Work The energy equation; adiabatic & inviscid

Dho 1 p  Dt  t

 Dean (1959): Turbomachinery must be unsteady to isentropically extract work.  Smith (1966): Work done by the NGV wakes is different from the work done by the free-stream.  Hodson & Dawes (1998): Cascade-wake interaction: stagnation enthalpy of the fluid on the suction side is ellevated by unsteady work.

 Rose & Harvey (2000): „Differential Work“ turbine wake work is low & this reduces mixing loss.  Thorpe etal. (2005): Unsteady work causes high gas temperature on the casing with over-tip leakage in shroudless turbines.

 Rose etal. (2009): NGV wakes are hot inside turbine rotors, they loose heat by intra-fluid heat transfer and their entropy falls.

Unsteady Work In the Absolute Frame

p   t  rel

ho 1 p    t  t  abs The substantial derivative of stagnation enthalpy is determined by the rate of change of static pressure at a fixed point in space

Unsteady Work in the Relative Frame

DI 1 p    Dt  t  rel Where I is rothalpy, the equivalent of stagnation enthalpy in a rotor: dp/dt)rel is evaluated at a fixed point in the rotor, moving with it. Predicted unsteady work in the relative frame: contours around a rotating turbine blade

What is the Relationship Between Unsteady Work in The Two frames of Reference? The difference between the two unsteady work terms is determined by the substantial derivative of the Euler work group UVθ. Thus is dependent on the absolute circumferential momentum times the blade speed.

DUV 1 p  1 p       t  abs  t  rel Dt

The two temporal gradients of static pressure can be related by the following identity to the instantaneous circumferential static pressure gradient times the blade speed.

p  p  U p     t  abs t  rel r 

(A)

So high levels of work are associated with strong circumferential pressure garadients (of opposite sign: high blade lift force) and the modulus of the absolute temporal gradient of static pressure will be greater than the relative. The remainder of this presentation attempts to visualise and verify these expressions.

FRAP Normalised Total Pressure NGV Exit: time averaged Wake Po

Loss Cores

Po1

Normalised: Divided by NGV inlet total pressure

Wake Effects NGV exit FRAP Normalised Static Pressure time averaged absolute frame

p Po1

Vortex Core

p

NGV exit 4 Hole pneumatic probe Normalised Static Pressure

Po1

Vortex Core Wake Effects

NGV Exit FRAP data normalised static pressure time averaged in the relative frame

Low: Suction side shoulder

High: Rotor Stagnation Region

p Po1

Three Rotors LISA Turbine: 2 NGV for 3 Rotors

Rotor Exit Unsteady Work in the Absolute Frame: Time Averaged in the Relative Frame

ho 1 p    t  t  abs

Location of rotor casing loss core

FRAP relative total pressure for reference

   p    P  o1    t      abs  rel

Approximate location of rotor wake

Location of rotor hub loss core

CFD comparison: no von Karman vortices in NGV wake, pressure field of passage vortices not resolved

FRAP

URANS: 18.5 Mnodes, Y+ ≈ 1.5, 80 steps per cycle

CFD: CFX

p

p     t  rel  abs Relative unsteady work not resolved in wakes and loss cores Maybe: vortices cause unsteady work

Conclusions  Unsteady work: different, absolute and relative frames of reference.  Difference between temporal derivatives: Euler work UVθ & θ momentum.  FRAP: unsteady work field influenced by NGV wake and rotor wake.  Identity verifies experimental data: time averaged unsteady work & circumferential pressure gradients  URANS calc. No von-Karman vortices, NGV wake: different time averaged static pressure field & unsteady work distribution NGV wake.  Speculation: von Karman vortices may play an important role in determining the enthalpy exchange that is unsteady work.

Blade Interaction Inside a turbine the wakes and pressure field of one row interact with the next  Wake interaction  Potential Interaction

 Wake bowing  Negative jet  Wake mixing

 Boundary layer interaction URANS 2D Oneand-a-half Stages T. Mokulys Stage3D ETH Zürich

Dean (1959): Energy Equation

Dho 1 p  Dt  t Hodson & Dawes (1989)  Linear cascade with bar passing  Expectation of high loss on suction side due to „negative jet“  But low loss found on the suction side of passage  Unsteady work responsible

p t

„Unsteady Work“

In inviscid and adiabatic flow the stagnation enthalpy of a fluid particle can only change if the static pressure changes at a fixed point in space