Aeroelastic assessment of a highly loaded high pressure compressor exposed to pressure gain combustion disturbances [original]

Aeroelastic assessment of a highly loaded high pressure

compressor exposed to pressure gain combustion

disturbances

Victor Bicalho Civinelli de Almeida

1,*

, Dieter Peitsch

Technical University of Berlin, Marchstr. 12-14, Berlin 10587, BE, Germany

Abstract

A numerical aeroelastic assessment of a highly loaded high pressure com-

pressor exposed to ﬂow disturbances is presented in this paper. The distur-

bances originate from novel, inherently unsteady, pressure gain combustion

processes, such as pulse detonation, shockless explosion, wave rotor or

piston topping composite cycles. All these arrangements promise to reduce

substantially the speciﬁc fuel consumption of present-day aeronautical

engines and stationary gas turbines. However, their unsteady behavior must

be further investigated to ensure the thermodynamic efﬁciency gain is not

hindered by stage performance losses. Furthermore, blade excessive vibra-

tion (leading to high cycle fatigue) must be avoided, especially under the

additional excitations frequencies from waves traveling upstream of the

combustor.

Two main numerical analyses are presented, contrasting undisturbed with

disturbed operation of a typical industrial core compressor. The ﬁrst part of

the paper evaluates performance parameters for a representative blisk stage

with high-accuracy 3D unsteady Reynolds-averaged Navier-Stokes compu-

tations. Isentropic efﬁciency as well as pressure and temperature unsteady

damping are determined for a broad range of disturbances. The nonlinear

harmonic balance method is used to determine the aerodynamic damping.

The second part provides the aeroelastic harmonic forced response of the

rotor blades, with aerodynamic damping and forcing obtained from the

unsteady calculations in the ﬁrst part. The inﬂuence of blade mode shapes,

nodal diameters and forcing frequency matching is also examined.

Introduction

Increase in overall efﬁciency of aeronautical engines and stationary gas

turbines, reducing speciﬁc fuel consumption, is being extensively

researched. Since traditional engine conﬁgurations are reaching saturation

development state, novel technological breakthroughs are sought. Among

these radical changes, the most signiﬁcant tackle either the core/bypass

ﬂows or the combustor losses. To address core ﬂow hurdles, intercool-

ing, Rankine bottoming and recuperation might be viable options.

Reheating is also particularly developed for land-based applications.

Concerning bypass losses, geared turbofan and open rotor concepts are

receiving considerable attention (Grönstedt et al., 2013,2016;Gülen,

2017).

With respect to the combustion losses, several innovative approaches

have been proposed. Most of them aim at improving current constant-

pressure (in fact, pressure-loss) combustion with a pressure-increase

process. This so-called pressure gain combustion (PGC) can be

Original article

Article history:

Accepted: 16 July 2018

Published: 15 October 2018

This paper was originally presented at the

GPPS Montreal 18 Conference, in Montreal,

May 7–9 2018.

*Correspondence:

VB: [email protected]-berlin.de

Peer review:

Single blind

Peitsch This is an open access article

distributed under the Creative Commons

Attribution Non Commercial No Derivatives

License (CC BY-NC-ND 4.0). Unrestricted

use, distribution, and reproduction of the

original work are permitted for

noncommercial purposes only, provided it

is properly cited and its authors credited.

No derivative of this work may be

distributed.

Keywords:

aeroelasticity; forced response; unsteady

performance; axial compressor; high

pressure compressor; pressure gain

combustion

Citation:

Bicalho Civinelli de Almeida V., Peitsch D.

(2018). Aeroelastic assessment of a highly

loaded high pressure compressor exposed

to pressure gain combustion disturbances.

Journal of the Global Power and Propulsion

Society. 2: 477–492.

https://doi.org/10.22261/JGPPS.F72OUU

J. Glob. Power Propuls. Soc. | 2018 | 2: 477–492 | https://doi.org/10.22261/JGPPS.F72OUU 477

JOURNAL OF THE GLOBAL POWER AND PROPULSION SOCIETY

journal.gpps.global/jgpps

accomplished by different means. The leading paths are pulse detonation (Roy et al., 2004;Pandey and

Debnath, 2016), rotating detonation (Zhou et al., 2016;Kailasanath, 2017;Paxson and Naples, 2017), wave

rotors (Akbari and Nalim, 2009;McClearn et al., 2016) and shockless explosion (Bobusch et al., 2014;Reichel

et al., 2016) combustion. Some other concepts are the piston topping (Kaiser et al., 2015) and the nutating disk

(Meitner et al., 2006). All these setups are theoretically supported by substantial thermodynamic gains, described

in detail, e.g., by (Heiser and Pratt, 2002;Gray et al., 2016).

Despite fairly different construction and engine-integration characteristics, all these PGC processes introduce

additional unsteadiness into the adjacent turbomachinery components, namely, the compressor upstream and the

turbine downstream. This unsteadiness is directly linked with the inherently periodic nature of the combustion

mechanisms, and affect the operation of both stationary and rotating parts (traditionally designed by steady state

workﬂows). The integration between combustion units and engine (most likely through plena interfaces) is key

to estimate proper boundary conditions for the neighboring components, such as perturbation signatures, oper-

ation frequencies and amplitudes.

Although fundamental combustion research on pulse detonation had been restricted to low frequency pro-

cesses, massive increase in the number of ignitions per second has been achieved. Kilohertz pulse detonation

frequencies were recently reported by (Taki et al., 2017). As for rotating detonation, it already takes place in the

few kilohertz range (Lu and Braun, 2014;Bluemner et al., 2018). Similar periodicity is reported for the other

PGC devices. This frequency range is also expected to be pushed up, once PGC technology takes off.

With respect to the amplitudes of such disturbances, they are strongly linked to the PGC operation (such as

ﬁlling, ignition and purging phases), but also to the plena interfaces. Limited PGC experimental data with

upstream measurements is available, such as (Roy et al., 2004;Rasheed et al., 2005). Some numerical work used

pressure amplitude values at the combustor interfaces of a few percent up to approximately 40% (Van Zante

et al., 2007;Fernelius, 2017;Liu et al., 2017). This disturbance amplitude range is already signiﬁcant from the

turbomachinery point of view, justifying detailed investigations.

The need for assessing the performance and aeroelasticity effects of these disturbances has been recognized by

the combustion and turbomachinery academic community (Kailasanath, 2003;Roy et al., 2004;Rasheed et al.,

2009;Lu and Braun, 2014;Gülen, 2017). However, quantitative information to evaluate the extent of these

changes is scarce, especially for state-of-the-art industrial machines. Up to the current date, there has been no full

integration between those PGC cores to commercial engines. Therefore, the current exploratory research sheds

some light into the effects of this interfacing (speciﬁcally upstream), by numerical means. Both performance and

aeroelasticity assessments will be presented.

The manuscript is organized as follows. In the case description section, the simulated high pressure compressor

geometry is characterized. Next, the numerical methodologies both for the computational ﬂuid dynamics (CFD)

and computational solid mechanics (CSM) are presented. Subsequently, results are given for a broad range of dis-

turbance amplitudes and frequencies, followed by the main outcomes.

Case description

A modern industrial high pressure compressor, depicted in Figure 1 is here used for the simulations (Klinger et al.,

2008,2011). Practical 3D geometries and operation points have been provided by an industrial partner. It is

important to say that the whole engine has been designed for traditional deﬂagration combustion, without speciﬁc

considerations for PGC and its effects on turbomachinery components. Therefore, the present study analyzes how

this traditional setup would potentially react to unsteady disturbances and depart from the reference design.

The simulated domain is the HPC 6th stage, the last with a bladed disk (blisk) design. Although it is not the

very last stage right before the combustion chamber, it has been chosen considering that blisk manufacturing

becomes increasingly more common in axial compressor design (Peitsch et al., 2005;Honisch et al., 2012;

Mayorca et al., 2012;Zhao et al., 2015). Due to conﬁdentiality constraints, the speedline itself and some abso-

lute design quantities will not be disclosed here, but rather normalized values, enough for full comprehension

and comparative evaluations.

Numerical methodology

For brevity purposes, neither the ﬂuid nor the solid domain state and constitutive equations will be derived here.

Rather, focus will be given to the interface treatment of necessary aeroelastic quantities, such as aerodynamic

work or pressure harmonics. The next sections describe respectively the CFD (steady and unsteady) and CSM

J. Glob. Power Propuls. Soc. | 2018 | 2: 477–492 | https://doi.org/10.22261/JGPPS.F72OUU 478

Bicalho Civinelli de Almeida and Peitsch | Aeroelastic assessment of a HPC exposed to PGC disturb https://journal.gpps.global/a/F72OUU

methodologies used along this work. The space and time independence studies for the grids are likewise

presented.

Computational ﬂuid dynamics

Due to the unsteady behavior associated with the new combustion processes, 3D unsteady viscid ﬂuid dynamics

simulations are employed, both in time and frequency domain. Time-domain calculations are here used to deter-

mine performance parameters, unsteady damping and blade surface pressure harmonics, to be later used in the

structural simulations. Frequency-domain runs determine the aerodynamic damping.

(i) Steady state: the Navier-Stokes equations are boundary-layer resolved with the ﬁnite volumes solver CFX®

(ANSYS Academic Research, Release 18.1), with air (ideal gas) as compressible medium. Fourth-order Rhie

& Chow smoothing is employed (Rhie and Chow, 1983), while Reynolds stresses are computed by the

two-equation Menter’s SST turbulence model (Menter, 1994). Since the simulated stage is located substan-

tially far from the engine inlet, the ﬂow is safely assumed to be fully turbulent, so no transition models were

shown necessary. Double-precision, properly converged steady state solutions (with root-mean-square residuals

lower than 10

−5

, and imbalances lower than 5·10

−6

) are used as initial conditions for the unsteady runs.

The 3D geometries were meshed with AutoGrid5® developed by Numeca (IGG™/AutoGrid5™v11.1). Both

root ﬁllet and tip gap have been modeled. Multi-block structured hexaedra meshes were employed, with direc-

tional boundary-layer reﬁnement on all walls (dimensionless wall distance yþ1), keeping the expansion ratio

below 1.2. The topology for both rotor blades and stator vanes is the O4H. The tip gap was modeled with at

least 30 cells in the radial direction.

Several meshes were generated in order to perform a proper grid independence study, done separately for rotor

and stator. The grids were reﬁned as uniformly as practical, however always keeping the boundary layer on the

walls resolved. Figure 2 displays three chosen meshes for rotor (labeled from coarsest to ﬁnest as R-A, R-B and

R-C) and stator (labeled as S-A, S-B and S-C), with isentropic efﬁciency and mass ﬂow values normalized by the

ﬁnest grid, as a function of cell count. The deviation between the ﬁnest- and coarsest-grid values is less than 1%

for both domains, in the sense that all displayed grids capture the global ﬂow behavior accurately enough. The

Grid Independence Index (Celik, 2008), formally derived based on the Richardson extrapolation (Roache,

1994), has been calculated and showed no oscillatory behavior. For the isentropic efﬁciency, the index between

ﬁnest and medium meshes is GCI

= 0.24%, with apparent order of 1.94. The grids utilized for the current

stage are assembled together and shown in Figure 3. The number of nodes for the stage (if using one passage for

rotor and one for stator) is approximately 1.3 million.

As inlet boundary conditions, total pressure and temperature along with ﬂow direction are implemented,

while on the outlet the static pressure is prescribed. Both on inlet and outlet, radial proﬁles experimentally

validated by the manufacturer are utilized. For the steady runs only, mixing-plane interface, with constant total

pressure (that is, no loss in through the interface), is used to account for the non-unitary pitch ratio.

(ii) Unsteady: two types of time-resolved simulations are performed, with and without the PGC disturbances.

The time discretization scheme utilized is the second order backward Euler, with a bounded high-resolution

Figure 1. The E3E high pressure compressor rotor.

J. Glob. Power Propuls. Soc. | 2018 | 2: 477–492 | https://doi.org/10.22261/JGPPS.F72OUU 479

Bicalho Civinelli de Almeida and Peitsch | Aeroelastic assessment of a HPC exposed to PGC disturb https://journal.gpps.global/a/F72OUU

discretization for advection and viscous terms. The solution is deemed periodically converged when the rela-

tive difference between two consecutive periods for some globally integrated parameter (such as compression

ratio or efﬁciency) or pressure probe falls below 0.05%. The attainment of quasi-convergence depends not

only on the blade passing frequency (BPF), but also on the combustion-originated frequency and intensity,

which in turn determines the required total run time.

The time resolution must be properly chosen to model the necessary phenomena without excessively consum-

ing computational resources. For the present case, the main (a priori known) frequencies to be modeled by the

time march are the rotor BPF and the disturbance frequency. A temporal resolution study was performed to

determine the minimum time discretization required, using the number of time steps per rotor passing period

(TSRPP) as a parameter. Pressure time traces of two points located between rotor and stator (one in each

domain, respectively P1 and P2) are shown in Figure 4 (after periodic convergence is achieved). For both

domains, 50 TSRPP are enough to accurately capture the unsteady behavior. To enhance resolution for the dis-

turbed runs, a slightly higher value of 55 TSRPP has been chosen.

It is important to highlight that, under unsteady disturbances (additional to the rotor-stator frequency), the

required time step could become smaller. To assess whether 55 TSRPP is enough for the outlet disturbance with

the highest frequency here simulated (3.0 times the BPF), an extra run with halved time step (i.e., 110 TSRPP)

was carried out, for an extra full rotor revolution. In comparison with the 55 TSRPP setup, a relative difference

of 0.09% and 0.005% for isentropic efﬁciency and compression ratio, respectively, was found. Unsteady

damping, as well as modal forcing (both deﬁned further), showed similar minimal changes. From that, the

current time resolution was deemed enough within the simulated disturbance range. Higher frequency distur-

bances could possibly require further time step reﬁnement.

Figure 2. Grid independence study for ﬂuid system, normalized by ﬁnest grid values.

Figure 3. Grids R-B and S-B for the simulated stage (rotor on the front and stator on the back), obtained after grid

independence study. Geometry is rescaled.

J. Glob. Power Propuls. Soc. | 2018 | 2: 477–492 | https://doi.org/10.22261/JGPPS.F72OUU 480

Bicalho Civinelli de Almeida and Peitsch | Aeroelastic assessment of a HPC exposed to PGC disturb https://journal.gpps.global/a/F72OUU

For the transient calculations, the number of rotor blades was reduced by one unit, so that 3 rotor passages

and 4 stator passages yield a unitary pitch ratio. This modiﬁcation prevents phase errors which would incur

when using for example the proﬁle-scaling method (Galpin et al., 1995). Time-inclining or -shifted methods,

such as (Giles, 1988)or(Gerolymos et al., 2002), are not physically consistent when disturbance frequencies dif-

ferent from the BPF are present in the system. In summary, the current unsteady simulation setup does not

induce frequency or phase errors due to non-unitary pitch ratio, with sliding meshes accurately modeling the

transient phenomena that takes place between rotor and stator. All unsteady disturbances are modeled by the

time marching scheme without further simpliﬁcations. The total number of nodes for this setup is approximately

4.6 million.

To model the PGC disturbances, time periodic boundary conditions at the stage outlet have been implemen-

ted. To the knowledge of the authors, no effective test rig or prototype coupling industrial axial compressor and

turbine to a pressure gain combustor has been built, in a fully coupled fashion. Ongoing investigations focus on

how to connect these components through adequate plena geometries, to minimize unsteadiness and therefore

prevent extra losses. Accordingly, due to the lack of more precise plenum information, it is assumed that the

unsteadiness reaching the compressor/combustor interface does not vary circumferentially, being here described

by harmonic ﬂuctuations, as in Equation (1).

p(x,t)¼p(x)[1 þAdsin(2πfdt)] (1)

Here, Adand fdstand respectively for amplitude and frequency of the imposed harmonic disturbance on the

static pressure distribution p(x). Indeed, since the pressure is in this work prescribed radially, p(x)¼p(r) for

radius r. This approach assumes that the number of blades and vanes is rather larger than the number of com-

bustion units downstream, so that no disturbance wave interaction among combustor units is modeled.

(iii) Time-spectral: the frequency-domain method employed here is the nonlinear harmonic balance (Hall

et al., 2002) (also known as time spectral method (Gopinath and Jameson, 2005)). The time and

spatial dependent state variables are written as a Fourier series for a predetermined fundamental fre-

quency, whose ﬁrst harmonics are iteratively and simultaneously solved with a pseudo time march.

Along this work, 3 harmonics (producing 7 time levels) have been used, after parametric studies

showed that more harmonics did not change the solution substantially. Additionally, 20 pseudo time

steps per oscillation period were enough to achieve the desired computational accuracy at rapid conver-

gence. The nonlinear harmonic balance is here utilized to determine the aerodynamic work Waero,as

deﬁnedinEquation(2).

Waero ¼ðtþT

tð‘

pv^

nd‘dt (2)

Here, pis the static pressure, vthe wall velocity vector and ^

nthe wall outwards pointing normal versor. The

surface integral takes place along the blade walls ‘. The aerodynamic work is integrated in time tduring one

Figure 4. Pressure probe periodically converged time trace, on rotor (P1) and stator (P2) domains. Several values for

time steps per rotor passing period (TSRPP) are shown.

J. Glob. Power Propuls. Soc. | 2018 | 2: 477–492 | https://doi.org/10.22261/JGPPS.F72OUU 481

Bicalho Civinelli de Almeida and Peitsch | Aeroelastic assessment of a HPC exposed to PGC disturb https://journal.gpps.global/a/F72OUU

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