Gregory P. Herrick

Glenn Research Center, Cleveland, Ohio

Assessing Fan Flutter Stability in Presence of

Inlet Distortion Using One-Way and Two-Way

Coupled Methods

NASA/TM—2014-218447

December 2014

AIAA–2014–3733
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Gregory P. Herrick

Glenn Research Center, Cleveland, Ohio

Assessing Fan Flutter Stability in Presence of

Inlet Distortion Using One-Way and Two-Way

Coupled Methods

NASA/TM—2014-218447

December 2014

National Aeronautics and

Space Administration

Glenn Research Center

Cleveland, Ohio 44135

Prepared for the

50th Joint Propulsion Conference

cosponsored by AIAA, ASME, SAE, and ASEE

Cleveland, Ohio, July 28–30, 2014

AIAA–2014–3733
Available from

NASA STI Information Desk

Mail Stop 148

NASA Langley Research Center

Hampton, VA 23681-2199

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Available electronically at http://www.sti.nasa.gov

Level of Review: This material has been technically reviewed by technical management. 
Abstract

Concerns regarding noise, propulsive efficiency, and fuel burn are inspiring aircraft

designs wherein the propulsive turbomachines are partially (or fully) embedded

within the airframe; such designs present serious concerns with regard to aerodynamic and aeromechanic performance of the compression system in response to

inlet distortion. Previously, a preliminary design of a forward-swept high-speed fan

exhibited flutter concerns in clean-inlet flows, and the present author then studied

this fan further in the presence of off-design distorted in-flows. Continuing this research, a three-dimensional, unsteady, Navier-Stokes computational fluid dynamics

code is again applied to analyze and corroborate fan performance with clean inlet

flow and now with a simplified, sinusoidal distortion of total pressure at the aerodynamic interface plane. This code, already validated in its application to assess

aerodynamic damping of vibrating blades at various flow conditions using a one-way

coupled energy-exchange approach, is modified to include a two-way coupled timemarching aeroelastic simulation capability. The two coupling methods are compared

in their evaluation of flutter stability in the presence of distorted in-flows.

1 Introduction

Since the advent of turbojet propulsion, “clean” intake flow for the fan (or propulsor) of the gas turbine engine has been the desired, elusive, goal of airframe, inlet,

and propulsion system designers alike in the quest for optimal performance of the

propulsion system. As we look to the future, design goals now focus on reduced

emissions, reduced fuel consumption, better propulsive efficiency (of the entire aircraft system), and reduced ambient noise. Among the prominent design concepts

under development for application to future aircraft is the “Blended Wing Body”

(alternatively known as “hybrid wing/body”). Most of these prospective designs

feature propulsion systems wherein the propulsive fan, whether coupled directly to

a Brayton cycle turbine engine or part of a turbo-electric distributed propulsion

system, is partially or fully embedded within the body.

Boundary layer ingestion (BLI) propulsion has the potential for significant reduction in aircraft fuel burn [1]; previous system studies [2–6] have shown that 5-10%

reduction in fuel burn is possible. Recent work [7] has confirmed this potential benefit through a system study focused on the propulsion system and its integration

into the BWB aircraft. The system study indicated that low-loss inlets and highAssessing Fan Flutter Stability in Presence of Inlet Distortion Using 

One-Way and Two-Way Coupled Methods 

Gregory P. Herrick 

National Aeronautics and Space Administration 

Glenn Research Center 

Cleveland, Ohio 44135 

NASA/TM—2014-218447 1
performance, distortion-tolerant turbomachinery are key technologies required to

achieve a 3-5% BLI fuel burn benefit for future aircraft relative to a baseline highperformance, pylon-mounted, propulsion system. A robust aeromechanical design

with respect to dynamic stresses and flutter stability in the presence of distortion is

critical to the successful implementation and application of BLI propulsion systems.

In previous work from Herrick [8], a parallel computational fluid dynamics (CFD)

code was modified and customized to begin studying the issues relevant to aeromechanical response of turbomachinery to distorted inlet flows. In that effort, the

aeroelastic analysis employed in the CFD code was “one-way” coupled: The blades’

motion was prescribed and enforced, perturbing the flow field, while the resultant

changes in blade surface pressures were not fed back to alter the blades’ motions. In

this effort, a “two-way” coupled method of aeroelastic analysis is implemented into

the code and applied in the analysis of the fan subject to distorted inlet flows: The

motion of the blades perturbs the flow field, and the flow field’s unsteady pressures

in turn influence the motion of the blades. Many two-way coupled methods for turbomachinery aeroelasticity have been presented in the literature [9–11]; Br ́eard [12]

et al. applied their integrated model to the study of forced response due to inlet

distortion.

2 Background

The CFD code modified and applied in this study is TURBO, a physics-based simulation tool for multistage turbomachinery. The solver computes the fluid conservation laws without ad hoc modeling of any flow phenomena other than models

required for turbulence. This code solves the unsteady Reynolds-averaged NavierStokes equations and a decoupled k-turbulence model developed by Zhu and

Shih [13]. The code is implemented in a portable, scalable form for distributedmemory parallel computers using MPI message passing. The parallel implementation employs domain decomposition and supports general multi-block grids with

arbitrary grid-block connectivity. The solution algorithm is a Newton iterative

implicit time-accurate scheme with characteristics-based finite-volume spatial discretization. The Newton subiterations are solved using a concurrent block-Jacobi

symmetric Gauss-Seidel (BJ-SGS) relaxation scheme. Because all of the fundamental fluid mechanics are computed, the code is capable of capturing the nonlinear

characteristics of the flow fields of interest. With the actual modeling of grid movement of blade rows in relative motion, this code is capable of computing the unsteady

interactions between blade rows. Details of the flow solver are given by Chen and

Whitfield [14]. The approach to parallelization for large-scale, complex problems

is discussed by Chen and Briley [15]. TURBO has been previously modified for

application to study flutter and forced vibration [16–18]. TURBO has been further

validated in several previous research efforts regarding aeromechanics [19–26].

The fan of interest is comprised of twenty-two blades. The fan was designed

for purposes of noise reduction in a typical podded-engine mounting. Physically,

the average radial tip gap as gridded for this study is about 0.28% of blade radial

span. The fan was never intended to be part of an embedded propulsion system with

distorted inlet flow. Previous aeromechanics analyses [25] of this fan exhibited good

corroboration between computational and experimental performance in clean-inlet

NASA/TM—2014-218447 2
flow conditions.

In his initial study of this fan’s aeroelastic behavior in distorted inlet flows, Herrick [8] modified the code’s total-condition preserved inlet boundary condition to

allow for circumferential nonuniformity at the inlet plane. Application of a throttle

exit boundary condition, allowing the exit flow to attain equilibrium without artificial constraint, showed that inlet distortions do not fully attenuate upon passage

through a single rotor. In the previous work, examination of aeroelastic behavior –

using a prescribed motion, one-way coupled approach – in clean inlet conditions generally yielded clear, consistent solutions. The distorted inlet aeroelastic simulations

(using the same one-way coupled approach, but with an inlet total pressure distribution approximating that of Inlet A [27]) yielded dramatic variation in aerodynamic

damping computations about the annulus, with some annular sectors exhibiting

great aeroelastic stability and other annular sectors indicating significant aeroelastic instability. These intriguing observations prompt further investigation into the

methods used to assess aeroelastic behavior in a distorted flow environment.

This study shall further investigate several issues relevant to the computational

assessment of flutter stability for turbomachinery rotors in distorted flow fields:

“one-way coupled” versus “two-way coupled” motion of the blades in the unsteady

flow field, post-processing/interpretation of computed output (modal force, modal

displacement), and initial conditions. The fan is gridded with a single H-block

topology for the fan passage, with 214 grid points streamwise, 76 grid points radially, and 58 grid points pitchwise; the blade itself has 81 grid points streamwise and 70 points in the spanwise direction. No tip grid is present: Instead, a

lossless multi-point constraint is applied between the suction and pressure sides in

the region between the blade’s radial extent and the casing. Computationally, the

fan is preceded by inlet duct of length-ratio 1.387 with respect to blade-tip axial chord and followed by exit duct of length-ratio 2.365 with respect to blade-tip

axial chord. Again, the total-condition preserved boundary condition, capable of

enforcing circumferentially-varying flow conditions, is applied at the inlet/AIP. The

throttle boundary condition is again applied at the exit plane.

To facilitate the goals of this research effort, some fundamental assumptions

and simplifications are applied in the study regarding operating speed, inlet distortion pattern, blade mode shape, and blade natural frequency. The fan is operated

at 10800 rpm, a part-speed condition. From this part-speed condition the fan’s

aeroelastic behavior is assessed near op-line and near stall. The mode shape and

frequency of interest are artificial; its frequency is dictated to be 220 Hz such that

a blade completes one oscillation cycle in the course of traversing precisely 18 blade

pitches at 10800 rpm. The CFD mesh of the blade, with deflected geometry, is

shown in Fig. 1. The artificial mode shape and frequency, in concert with the partspeed run condition, are chosen with intent to encounter stable and unstable flutter

conditions.

The total pressure distortion at the inlet plane is a simple, single-frequency,

once-per-revoluton spatial distribution. The simulations are performed rotor-alone,

and only one mode is studied, thus the only fundamental frequencies at play are

the blades’ vibrational frequency and the rotor’s rotational frequency. The singlefrequency, once-per-revolution spatial distortion of total pressure is created by applying a 4% (mean-to-peak) sinusoidal variation upon the (circumferentially-constant,

radially-varying) clean flow total pressure profile in a single wave about the inNASA/TM—2014-218447 3
let annulus. No circumferential nonuniformity is applied to total temperature or

flow angles. Simulations reveal that the sinusoidal distortion yields a 0.12% higher

(energy-averaged) integrated total pressure at the inlet plane than the clean, axisymmetric pressure distribution. The fan characteristic at part-speed is shown in

Fig. 2. The total pressure distributions for clean and distorted in-flow are shown

in Fig. 3. CFD simulations are executed with 15 time steps per blade pitch; for

clean inlet simulations, 6 Newton subiterations are applied at each time step, while

9 Newton subiterations per time step are used for the sinusoidally-distorted inlet

runs.

Figure 1: Mesh and deflected shape

applied to blade in this research.

31 32 33 34 35

Corrected Mass Flow [kg/s]

1.25

1.3

1.35

Total Pressure Ratio [Pte/Pti]

Clean

Distorted

Figure 2: Speedlines: Clean and distorted

inlets, part-speed.

(a) Clean Inlet (b) Sinusoidal Inlet Distortion

Figure 3: Inlet total pressure distributions for the clean and distorted inlets of this

study. Common colorbar, red is high. Azimuthal orientation: 0◦ at 12 o’clock,

increasing clockwise. Fan rotates counterclockwise.

NASA/TM—2014-218447 4
3 One-way Coupled Method for Aeroelastic Analysis

3.1 Description and Implementation

Flutter stability of the fan is first evaluated using the TURBO aeroelastic analysis

code’s one-way coupled method. The energy method [28], or work-per-cycle approach, is used to calculate aerodynamic damping (and hence flutter stability) as

described in Ref. 26; Vasanthakumar [29] used a similar approach in flutter analysis

of a transonic fan. For a clean inflow prescribed at the inlet boundary, the flow

field through the blade row is first calculated with no prescribed blade oscillation.

Starting with this converged steady flow field, blade vibrations are prescribed in

a selected mode, frequency (f), and nodal diameter pattern (ND) or inter-blade

phase angle (σ). Note that the number of different possible nodal diameter patterns

is equal to the number of blades on the rotor of interest. After the transients in the

flow field decay and a periodic flow field is obtained, the work done on the vibrating

blade is calculated as follows:

W = −



surface

p dA ·

∂X

∂t dt (1)

where p is the aerodynamic pressure, A is the blade surface area vector, X is the

displacement vector on the blade surface, and t denotes time. The aerodynamic

damping ratio (ζ) can be approximately related to the work-per-cycle (W) and the

average kinetic energy (KE) of the blade over one cycle of vibration through the

following expression:

ζ ≈ −

W

8KE

(2)

The schematic for this method is shown in Fig. 4. If aerodynamic damping is

negative (i.e., aerodynamic work is positive), flutter may occur. Note that structural

damping (material and mechanical) has not been considered.

Generate new mesh

in accordance

with blade position

Calculate unsteady

flow field on

new mesh

Calculate new

aerodynamic

work acting

on blade

Calculate new

blade position

and velocity

from prescribed

harmonic motion

Figure 4: One-way coupling time marching scheme.

NASA/TM—2014-218447 5
3.2 Application to Distorted In-Flows

In previous research, Herrick [8] and Bakhle [26] et al. have utilized the one-way

coupled method to assess stability of fans in the presence of distorted in-flows. In

each of these endeavors, the temporally- and spatially-averaged damping of all blades

– a single value attributed to an idealized “average” blade – was used to gauge the

flutter stability of the entire rotor in the presence of the circumferentially-varying

flow field.

In the presence of a clean-inlet flow field, this single-value average represents

very well the consistent response of each and every blade as the blade traverses the

flow field. In Fig. 5(a) the convergence time history of the aerodynamic work on

all blades is plotted along with the single-value average; in Fig. 5(b), the annulus

is “unrolled”, and the aerodynamic work distribution for each of the twenty-two

blades is plotted versus each blade’s respective annular position at the end of each

oscillation cycle. In both plots of Fig. 5, the eleven-nodal diameter condition

demonstrates the common occurrence whereby the blade may oscillate through a

few cycles prior to reaching a converged state. As to be expected for a flow condition

with axisymmetric conditions at the inlet plane, Fig. 5(b) shows great consistency

about the annulus in a clean flow field. Analyzing blade-to-blade aerodynamic work

data in the “unrolled” presentation of Fig. 5(b) proves to be particularly useful

when studying a flow condition with inlet distortion.

1234 5

Oscillation Cycle Count

-2e-05

-1.5e-05

-1e-05

-5e-06

0

5e-06

Normalized Aerodynamic Work [-]

0 ND, Blades 1-22

11 ND, Blades 1-22

0 ND, Average Blade

11 ND, Average Blade

(a) Convergence of aerodynamic work for all

blades versus oscillation cycle count.

0 90 180 270 360

Azimuthal Position of Root LE at end of oscillation cycle [deg]

-2e-05

-1.5e-05

-1e-05

-5e-06

0

5e-06

Normalized Aerodynamic Work [-]

0 ND, Cycle 1

0 ND, Cycles 2-5

11 ND, Cycle 1

11 ND, Cycles 2-5

(b) Convergence of aerodynamic work for all

blades versus azimuthal position.

Figure 5: Time-convergence of aerodynamic work at part-speed, near op-line, clean

inlet condition.

In the presence of circumferentially-varying distorted in-flow, the aerodynamic

work done on/by the blade – and hence its damping – varies considerably as the

blade traverses the flow field, see Fig. 6. Note that the ordinates are of identical

scale among all plots in Figures 5 and 6, providing perspective on the constancy of

the aerodynamic work about the annulus for the clean inlet condition and the variation of the aerodynamic work about the annulus for the sinusoidally-distorted inlet

condition. Observe further the close similarity between the converged “average”

blade’s aerodynamic work for both the clean inlet and the sinusoidally-distorted inlet. Recall that the the total pressure distribution of the distorted inlet applied here

was specified to be a sinusoidal variation (of magnitude 4%) about the clean inlet’s

NASA/TM—2014-218447 6
radially-varying profile of total pressure. Close examination of the “average” blade’s

aerodynamic work quantities reveals the sinusoidally-distorted inlet condition to be

marginally/negligibly less stable – but still stable – than the clean inlet condition

near op-line.

In instances of inlet distortion wherein the aerodynamic work computations of

the one-way coupling method vary from cycle to cycle and from blade to blade about

the annulus – and all quantities indicate stability – it is conservative and reasonable

to declare the system to be stable; in Fig. 6, the eleven-nodal pattern is clearly

stable, and in the work of Bakhle [26] et al. the system was clearly stable under

these auspices. However, observe in Fig. 6(b) that a sector spanning approximately

150◦ of the 360◦ annulus exhibits unstable (positive) aerodynamic work for the

zero-nodal diameter pattern. While the “average” blade indicates stability for zero

nodal diameters, one cannot conservatively assert that the system is stable with the

one-way coupling method consistently indicating instability over a defined sector of

the annulus. Similar behavior, not shown here, is observed for for one-, two-, and

three-nodal diameter forward traveling waves with inlet distortion near op-line.

Complemenary one-way coupling aeroelastic analyses are performed for the nearstall condition. Again, the “average” blade aerodynamic work computations (and

hence aerodynamic dampings) are very similar between clean inlet and sinusoidallydistorted inlet conditions, with the sinusoidally-distorted inlet conditions usually

yielding marginally/negligibly less stable dampings than the clean inlet for the partspeed, near-stall condition. For both the clean inlet and sinusodially- distorted inlet,

the near-stall “average” blade dampings are less stable than the op-line “average

blade” dampings. Notably, the 1 ND FTW (one nodal diameter forward traveing

wave) pattern for the part-speed, near-stall condition yields small negative values of

damping (i.e., flutter-unstable) for the “average” blade, whereby the sinsusoidallydistorted inlet is marginally/negligibly more unstable. As shown in Figure 7, for

both clean inlet and distorted inlet for both one- and two-nodal diameter forward

traveling waves, all blades alternate between stable (negative) aerodynamic work

and unstable (positive) aerodynamic work as they circumnavigate the annulus. Each

black line in Fig. 7(a) represents each individual blade as it traverses the annulus of

the clean-inlet flow, while each red line plots the path of individual blades rotating

through the distorted-inlet flow, for the one-nodal diameter forward traveling wave.

Figure 7(b) shows similar behavior for the two-nodal diameter forward traveling

wave.

Nodal diameter sweeps of “average” blade damping from zero-nodal diameter to

three-nodal diameter forward-traveling wave for the part-speed condition – for both

near-stall and near op-line, and for both clean inlet and distorted inlet – are plotted

in Fig. 8. The eleven-nodal diameter pattern is strongly stable in all studies here;

these data points are omitted from Fig. 8 for clarity of the data of nodal diameters

zero through three.

4 Two-way Coupled Method for Aeroelastic Analysis

4.1 Description and Implementation

The two-way coupled method is implemented via a modal superposition framework

similar to Gnesin and Rz ̧adkowski [10], Carstens [9] et al., and Br ́eard [12] et al. In

NASA/TM—2014-218447 7
1234 5

Oscillation Cycle Count

-2e-05

-1.5e-05

-1e-05

-5e-06

0

5e-06

Normalized Aerodynamic Work [-]

0 ND, Blades 1-22

11 ND, Blades 1-22

0 ND, Average Blade

11 ND, Average Blade

(a) Convergence of aerodynamic work for all

blades versus oscillation cycle count.

0 90 180 270 360

Azimuthal Position of Root LE at end of oscillation cycle [deg]

-2e-05

-1.5e-05

-1e-05

-5e-06

0

5e-06

Normalized Aerodynamic Work [-]

0 ND, Cycle 1

0 ND, Cycles 2-5

11 ND, Cycle 1

11 ND, Cycles 2-5

(b) Convergence of aerodynamic work for all

blades versus azimuthal position.

Figure 6: Time-convergence of aerodynamic work at part-speed, near op-line, sinusoidal distortion inlet condition.

0 90 180 270 360

Azimuthal Position of Root LE at end of oscillation cycle [deg]

-6e-06

-4e-06

-2e-06

0

2e-06

4e-06

6e-06

Normalized Aerodynamic Work [-]

(a) 1 ND FTW

0 90 180 270 360

Azimuthal Position of Root LE at end of oscillation cycle [deg]

-6e-06

-4e-06

-2e-06

0

2e-06

4e-06

6e-06

Normalized Aerodynamic Work [-]

(b) 2 ND FTW

Figure 7: Aerodynamic work of all blades versus azimuthal position: Near stall,

both clean (black) and distorted (red) inlets.

0123

Nodal Diameter

-5

0

5

10

15

Aerodynamic Damping [%]

Near-Stall Clean

Near-Stall, Distorted

Op-line, Clean

Op-Line, Distorted

Figure 8: Aerodynamic damping versus nodal diameter using average-blade aerodynamic work from one-way coupled method.

NASA/TM—2014-218447 8
the two-way coupled method, the blade motion and the aerodynamic force acting

on the blade each respond to, and act on, one another in sequential fashion in

accordance with the equation of motion. Mode shapes are unit-mass normalized and

hence modal stiffnesses equate to the squares of the respective frequencies. Modal

forces are computed by taking the inner product of the blade surface pressure forces

with the blade mode shape.

From the original equation of motion,

[M]{X ̈} + [C]{X ̇ } + [K]{X} = {F}−{fs} (3)

Pre-multiply by the mode shape [Φ]T , establish the generalized displacement coordinate η, and normalize to unit modal mass:

[Φ]T [M][Φ] = 1 (4)

{X} = [Φ]{η} (5)

Applying the conservative simplification of neglecting material and structural damping (i.e., assuming C = 0). yields independent second order ordinary differential

equations for each mode i:

η ̈i + ω2

i ηi = [Φi]

T {Fi − fs,i} (6)

Equation 6 represents the equation of motion for the blade in terms of its generalized

displacement coordinate, η. This equation is time-integrated using a Newmark-β

method [30]. This equation applies the modal forces, F, acting on the blades from

the existing flow field (with the blades in their existing orientations) to compute the

resulting deflections of the blades; these deflections are then applied to the blades

to update the grid, and the aerodynamics and modal forces are recomputed and

updated; this sequence is shown in Fig. 9.

For each computation and utilization of modal force in Eq. 6, a datum static

modal force fs – representing the equilibrium loading on the undeformed hot blades

– must be debited such that the blade vibrates about a mean equilibrium position

corresponding to the undeformed hot blade. While for axisymmetric clean inlet flow

Generate new mesh

in accordance

with blade position

Calculate unsteady

flow field on

new mesh

Calculate new

aerodynamic

forces acting

on blade

Calculate new

blade position

and velocity

from aeroelastic

equation of motion

Figure 9: Two-way coupling time marching scheme.

NASA/TM—2014-218447 9
the pressure forces acting on the blades are nominally constant as the blade circumnavigates the annulus, these pressure forces acting on the blade can vary significantly

about the annulus in the presence of distorted in-flows, hence the computation and

utilization of the static modal force demand careful consideration. This variation

in unsteady pressures about the annulus is plotted in Fig. 10. Observe the considerable variation in blade loading – nearly 25% (mean-to-peak) near op-line – as

the blade traverses the annulus in the distorted flow (with an inlet total pressure

variation of 4% mean-to-peak). As expected, the blade is more highly loaded near

stall than near op-line. While the mean modal force for the distorted flow near

op-line is almost equivalent to the nearly-constant modal force for the clean flow

at the near op-line condition, there is greater difference between the mean modal

force of distorted flow and the nearly-constant modal force of clean flow at the near

stall condition. Also, while the variation in modal force within distorted flow near

op-line is nearly sinusoidal, the variation in modal force within distorted flow near

stall is more disorderly.

In the present implementation into TURBO, the two-way coupled method allows

(or requires) user-specification of modal mass, stiffness or frequency of the mode(s),

mechanical damping, initial blade displacements and velocities (or prescription of

an initial nodal diameter pattern [or interblade phase angle] with displacement amplitude), and β and γ parameters for the Newmark-β time integration. The user

must also specify parameters of the “static modal force” for the simulation: retrieving modal force data on rigid blades over a period of one step, one blade pitch, or

one revolution; and then sampling that static modal force data as discrete values,

blade pitch averages, or full revolution averages. The fluid-structure coupling stencil

applied in this study may be classified as conventional serial staggered; improved

serial staggered [31] and predictor-corrector stencils are in validation and shall be

applied in future work.

4.2 Validation

While this two-way coupled method for aeroelastic analysis has been developed and

implemented to facilitate greater insight into aeroelastic behavior of turbomachinery rotors in the presence of highly unsteady flows, it is instructive to first verify

the performance of the algorithm in simpler, more fundamental aeroelastic environments. Given that the one-way coupled analysis procedure deflects the blades in a

prescribed sinusoidal motion (irrespective of the aerodynamic modal forces acting on

the blades), the two-way coupled analysis procedure should produce identical results

when the computed modal forces are set to zero in the solution of Eq. 6. Figure 11

shows the requisite replication of the prescribed motion displacement at the blade

tip, suction side, midchord (part-speed, clean inlet, near-stall shown) when using the

two-way coupled motion procedure with modal forces neglected; this corroboration

verfies that the Newmark-β procedure adequately resolves the displacement-time

evolution of the undamped elastic blade in a clean flow, near-stall environment.

Further validation of the method is evident from examination of its performance

with its typical modal force coupling enforced. Figure 12 shows the blade’s decreasing magnitude of oscillation in the 0 ND pattern near op-line in clean flow. The

prescribed motion analysis conveys dampings of 1.64% for zero-nodal diameters (see

Fig. 8), while logarithmic-decrement analysis of the tightly-coupled method’s blade

NASA/TM—2014-218447 10
0 90 180 270 360

Azimuthal Position of Root LE [deg]

0.002

0.0025

0.003

0.0035

0.004

Normalized Modal Force [-]

Near Op-Line, Clean, Discrete

Near Stall, Clean, Discrete

Near Op-Line, Distorted, Discrete

Near Stall, Distorted, Discrete

Near Op-Line, Distorted, Mean

Near Stall, Distorted, Mean

Figure 10: Static modal force: Modal

force on rigid blades, due to unsteady

pressure loading of clean and distorted

flows. One blade shown.

0 200 400 600 800

Time Step

-0.525

-0.524

-0.523

-0.522

-0.521

-0.52

-0.519

-0.518

Normalized Axial Position of Tip Midchord [-]

One-way coupling

Two-way Coupling, Zero Modal Force

Figure 11: Blade axial motion (suction side tip, midchord) using both oneway prescribed motion procedure and

two-way coupled motion procedure with

modal forces zeroed.

motion time histories yields dampings between 1.60% to 1.80%. The positive aerodynamic damping conservatively indicates flutter stability.

0 0.01 0.02 0.03 0.04

Time [s]

-0.0004

-0.0002

0

0.0002

0.0004

Normalized Generalized Displacement [-]

Figure 12: Two-way coupled simulation with decreasing magnitudes of blade oscillation for all blades, indicative of positive aerodynamic damping. Near op-line,

clean-inlet flow, 0 ND initial condition. Static modal force: full revolution, sampled

discretely.

4.3 Application to Near-stall and Distorted Flows

As discussed previously, the one-way coupling method clearly (and conservatively)

shows flutter stability for this fan at part-speed, near op-line, clean inlet conditions.

The flutter-stability question is less clear near stall for both clean and distorted

inlet conditions, and there is evidence of periodic instability near op-line with distorted inlet conditions. The two-way coupled method shall be applied in further

investigation of these fan operating conditions. For each of the following studies,

the inlet conditions, exit conditions, fan speed, CFD time step, blade frequency, and

blade mode shape are specified identically as for the one-way coupling runs. For

NASA/TM—2014-218447 11
highest fidelity – and with greatest computational expense – the static modal force

application in these studies consists of compiling data from one revolution of fan

operation with rigid blades, and then sampling this data discretely, matching the

annular position of the deflecting blade (the current run) with the annular position

of the static modal force database (a previous run with rigid blades but otherwise

identical conditions).

4.3.1 Near op-line, sinusoidal inlet distortion

For a near op-line condition with a distorted inlet, the zero-nodal diameter pattern

exhibits stability by inspection of the “average” blade, but unrolling the annulus

reveals that a significant portion of the annulus lends itself to positive (unstable)

aerodynamic work computations; see Fig. 6(b). The one-, two-, and three-nodal

diameter forward traveling wave patterns (not shown) have similar character in their

flutter assessment via the one-way coupling method. Applying the two-way coupled

analysis to the zero-nodal diameter pattern near op-line, it is readily evident that

the blade is stable under these distorted inlet conditions; see Fig. 13. Comparison

of Figures 12 and 13 shows little difference in damping for the zero-nodal diameter

pattern, near op-line, between clean and distorted flows; these are nearly-identically

stable conditions.

4.3.2 Near stall, clean and distorted inlets

Near stall, uncertainties regarding flutter stability arise in both clean and distorted

flows with the one-way coupled method, due to the changes in sign of the aerodynamic work from blade to blade and from cycle to cycle; see Fig. 7(a). The one-way

coupled method’s “average” blade indicates negative aerodynamic damping (flutter

instability) of -0.068% and -0.070% for clean and distorted flows, respectively, near

stall (see Fig. 8). In Figures 14(a) and (b), displacements of all blades are plotted

for both clean and distorted inlets for 1 ND FTW near stall. Figure 14(a) shows

blade-to-blade inconsistency about the rotor with a small global trend of increasing

blade displacements. Figure 14(b) shows great blade-to-blade inconsistency about

the rotor and a greater global trend in the growth of blade displacements, indicating

flutter instability.

The two-nodal diameter forward traveling wave pattern is assessed to be minimally stable near stall in both clean (+0.49% damping) and distorted (+0.09%

damping) flows from the “average” blade computations using the one-way coupled

method (see Fig. 8). Like the one-nodal diameter forward traveling wave, this twonodal diameter pattern shows sign-changes about the annulus in its one-way coupled

aerodynamic work computations; see Fig. 7(b). Figures 15(a) and (b) plot the displacements of all blades in both clean and distorted flows near stall upon application

of the two-way coupled method. Like the 1 ND FTW case in clean flow, Fig. 15(a)

shows blade-to- blade nonuniformity of displacements in clean flow; however, for the

two-nodal diameter forward traveling wave pattern in clean flow, sporadic increases

seem to damp again, as would be expected for the flutter-stable system predicted

by the “average” blade using the one-way coupled method. For the 2 ND FTW in

distorted flow, Fig. 15(b), the blades again exhibit nonuniformity of displacement

about the annulus, but now the displacements seem to grow. While the one-way

NASA/TM—2014-218447 12
coupled method’s “average” blade showed minimal stability in clean and distorted

flows for 2 ND FTW near stall, the two-way coupled method shows stability near

stall in clean flow but instability near stall in distorted flow.

0 0.01 0.02 0.03 0.04

Time [s]

-0.0006

-0.0004

-0.0002

0

0.0002

0.0004

0.0006

Normalized Generalized Displacement [-]

Figure 13: Decreasing magnitudes of oscillation of all blades, indicating flutter stability. Near op-line, distorted inlet, 0 ND initial condition. Static modal force: full

revolution sampled discretely.

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1

Time [s]

-0.0008

-0.0006

-0.0004

-0.0002

0

0.0002

0.0004

0.0006

0.0008

Normalized Generalized Displacement [-]

(a) Near stall, clean inlet, 1 ND FTW, all

blades.

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07

Time [s]

-0.0008

-0.0006

-0.0004

-0.0002

0

0.0002

0.0004

0.0006

0.0008

Normalized Generalized Displacement [-]

(b) Near stall, distorted inlet, 1 ND FTW,

all blades

Figure 14: Comparing blade displacements at near-stall, 1 ND FTW, for both clean

and distorted inlets. Static modal force: full revolution sampled discretely.

5 Conclusions and Future Work

An initial comparison between one-way and two-way coupled flutter analysis methods implemented in TURBO has been performed. An existing fan, for which

TURBO’s one-way coupled flutter analysis method has been experimentally corroborated, was used as the computational test article. The fan’s structural dynamics

characterstics (mode shape and natural frequency) were altered, and the fan was

run at part-speed conditions with intention of simulating stable and unstable flutter

environments. The fan was provided with both axisymmetric inlet total pressure

as well as a sinusoidal variation of total pressure about the annulus, such that the

NASA/TM—2014-218447 13
0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09

Time [s]

-0.0008

-0.0006

-0.0004

-0.0002

0

0.0002

0.0004

0.0006

0.0008

Normalized Generalized Displacement [-]

(a) Near stall, clean inlet, 2 ND FTW, all

blades.

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07

Time [s]

-0.0008

-0.0006

-0.0004

-0.0002

0

0.0002

0.0004

0.0006

0.0008

Normalized Generalized Displacement [-]

(b) Near stall, distorted inlet, 2 ND FTW,

all blades

Figure 15: Comparing blade displacements at near-stall, 2 ND FTW, for both clean

and distorted inlets. Static modal force: full revolution sampled discretely.

integrated, mean flow parameters for the distorted flow were equivalent to the clean

flow, and thus the circumferential uniformity (or nonuniformity) of the inlet flow

would be the only difference between the two flow conditions.

As had been demonstrated previously, TURBO’s one-way coupling method provided consistent work-per-cycle computations for all blades across the annulus in

clean flow, while distorted flow caused great variation in aerodynamic work computations from blade to blade and from cycle to cycle. The “average” blade can

be conservatively applied to assess flutter stability in clean flow, provided that all

blades’ aerodynamic work computations indicate stability. Multiple cases were observed wherein the “average” blade was stable, but the full annulus of blades would

oscillate between stability and instability from blade to blade and from cycle to cycle

in an orderly repeating sequence.

The two-way coupling method corroborated the one-way coupling method in

assessing flutter stability in clean flow near op-line. The two-way coupling method

was then used to investigate the flutter stability of clean flow near stall as well as

distorted flow at both near op-line and near stall conditions. In most cases, the twoway coupling corroborated the adequacy of the one-way coupling method’s “average”

blade assessment of flutter stability. In general, the distorted flow was slightly less

stable (or slightly more unstable) than its clean flow counterpart. However, for 1

ND FTW and 2 ND FTW at near stall conditions, the “average” blade’s (one-way

coupling) aerodynamic work oscillated between small values positive and negative in

clean flow and among large values positive and negative in distorted flow. The twoway coupled method showed blade-to-blade variation at these conditions, but 1 ND

FTW seemed to be minorly unstable in clean flow and more unstable in distorted

flow. Most notably, the two-way coupled analysis of 2 ND FTW showed to be stable

in clean flow but unstable in distorted flow.

While instabilities seem to have been demonstrated, their magnitude was quite

small, and these must be investigated further. Refined gridding, refined timestepping, and longer simulation times would be conducive to more in-depth study

of the fluid mechanics’ role in these potential instabilities. The time-step for these

NASA/TM—2014-218447 14
simulations, though constant between one-way and two-way coupling simulations,

was rather coarse. Different fluid-structure coupling stencils exist which could prove

critical when operating so closely to neutral stability. All two-way coupled flutter simulations discussed herein used a full revolution of “static modal force” data

and sampled it discretely because it was thought to offer the highest fidelity (at

the highest computational cost) of the fluid-structure interaction; the “static modal

force” data is generated by running a rigid-blade simulation with identical parameters to the subsequent elastic-blade simulation of primary interest. NASA’s work

in researching developing BLI propulsion systems continues, and in time there will

be experimental aeromechanics data of BLI devices to complement and validate

computational method development.

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