multi-fidelity simulation for a transonic compressor with...

Multi-fidelity simulation for a transonic compressorwith inflow distortionsJiahuan Cui1*, Yunfei Ma1, Bryn Ubald1, Paul Tucker1

SYM

POSI

A

ON ROTATING MACHIN

ERY

ISROMAC 2017

InternationalSymposium on

Transport Phenomenaand

Dynamics of RotatingMachinery

Maui, Hawaii

December 16-21, 2017

Abstracte low and high delity methods are used to study a transonic fan case. is transonic fan casefeatures a distortion generator upstream of the rotor. e low delity methods (immersed boundarymethod and immersed boundary method with smeared geometry) show promising results againsthi- simulation (unsteady RANS) and experiments.

e ow in the tip region, especially the interaction between the distorted inow and tipleakage ow, are investigated in detail. It is found that the tip leakage ow is the dominant owstructure near the casing. It is strong enough to sustain even at the exit of the stator. Apart fromanalysing the tip leakage ow structures, the stalling mechanism is also explored. As mass owdecreases, more rotor blades are contaminated by the distorted ow. A rotating cell starts to developshortly aer all the rotor blade passages are contaminated. e rotating cell is found to be swept incircumferential direction at the 65% speed of the rotor.KeywordsUnsteady ow — Stall mechanism — Inlet distortion

1Department of Engineering, University of Cambridge, Cambridge, United Kingdom

INTRODUCTIONFlow distortions in a modern aero engine system are oen in-duced due to the integration of dierent components. Inowdistortions can reduce the performance and the stall marginof a compression system [1]. Nacelle stall and boundarylayer ingestion are two common scenarios where inowdistortions are interacting with compressors/fan. In thesetwo scenarios, inlet distortion mainly aects the tip regionof the compressors/fan.

Flow in the tip region of the rotor is highly complexand unsteady [2, 3]. Due to the clearance between the ro-tating blade tip and the stationary casing, several vorticesare formed. As demonstrated by You and Moin [4] andalso illustrated in gure 1, tip vortex system consist of 1)tip-leakage vortex, 2) induced vortex, and 3) tip-separationvortex. e tip-leakage vortex is the dominant one.

For a transonic fan/compressor, the tip leakage vortexis strongly aected by the shock. e shock intersects thetrajectory of the tip leakage vortex. As the ow coecientis reduced, the tip leakage vortex strengthens and movesupstream [5]. When the tip leakage vortex cannot overcomethe adverse pressure gradient, the breakdown of the tipleakage occurs. As a result, the blockage in the tip regionincreases, which further reduces the velocity. As less massow travels through the region near the casing, the bladeloading decreases. If the mass ow decreases further, the tipleakage vortex starts to travel tangentially towards the adja-cent blade leading edge[6]. is is also termed leading edgetip clearance ow spillage. At this condition, the rotating

Figure 1. Sketch of the tip vortex system.

stall can occur.e stalling process becomes more complicated in the

presence of a distorted inow. Such highly turbulent and com-plex ow is very challenging to be predicted accurately, evenfor the state of the art of computational uid dynamics[7]. Inthe current study, a transonic fan (the Darmstadt case) willbe used to investigate the interaction between the inow dis-tortion and the downstream rotating blades. e Darmstadtcase is featured by a distortion generator (DG) located twoaxial chord upstream of the compressor. e DG is aachedto the case and it is designed to generate a large separationto represent a stalled engine nacelle [8]. e current paperwill investigate the general ow features in the tip region

Multi-fidelity simulation for a transonic compressor with inflow distortions — 2/7

Figure 2. Computational domain.

aected by the inlet distortion. A range of dierent levels ofdelity modelling strategies will be used to study dierentaspects of the ow. In addition, the stalling mechanism underthe inuence of inlet distortion will be explored.

1. CASE SETUPe Darmstadt transonic compressor case is used in thecurrent study. e case itself has been studied by manyother researchers [8, 9, 10]. It consists of 16 rotor bladesand 29 stator blades. e spool speed is 20,000 rpm. isgives a total pressure ratio around 1.5 at the design condition.To investigate the inlet distortion on the performance andstability margin of the downstream compressor, a distortiongenerator is aached to the casingwith a distance of two axialchord length upstream of the rotor leading edge. e heightof the distortion generator is designed to be 10 % of rotorspan. Such a distorted inow is large enough to inuencethe rotor tip region.

e computational domain used in the current study isshown in gure 2. Depending on the delity level of thesimulation, the blades and distortion generator are modelledby dierent methods.

High delity simulation. A range of unsteady RANSsimulations are carried out to study the detailed ow featuresat dierent total pressure ratio along the performance line,including the stall point. Figure 3 shows the surface mesh ofthe blades and the distortion generator. In total, around 65million cells are used to resolve the whole domain, with 23million cells for the rotor blades and 34 million for the stator.On average, there are around 1.3 million cells for each bladepassage.

Low delity simulation. At the design stage, the abilityto account for the eects of the fan on the ow upstreamis extremely benecial, especially for a short-intake designat the high angle of aack. e low delity method can

Figure 3. Mesh for unsteady RANS calculations.

accurately capture the potential led that created by thefan with a cost only a fraction of the hi- simulations. ecurrent study performed several low delity simulations withthe distortion generator resolved by the immersed boundarymethod (IBM) and the blades by immersed boundary methodwith smeared geometry (IBMSG). Details of these methodsare giving in the Numerical Methods section.

2. NUMERICAL METHODSe numerical solver used by the current study is a Rolls-Royce in-house CFD (Computational Fluid Dynamics) code– HYDRA [11]. HYDRA is a second order nite volumeRANS (Reynolds Average Naiver-Stoke) solver. e solverhas been used to aack a range of changeling problems inaero engines [12, 13, 14]. Here, the IBMSG and IBM aredeveloped within the HYDRA framework. A brief summaryof these two methods are given below in this section.

2.1 IBMIBM is used to avoid meshing the complicated DG geometryin the low delity simulation. In the currently study, thefeedback force method [15] is used to calculate the forceterms:

f = αˆ t

0(v − u)dt + β(v − u) (1)

where, v is the intended velocity on the boundary (zero inthe current study) and u is the actual local velocity on theboundary. e force term is added to the NS equations so thatthe actual local velocity is driven to the intended boundaryvelocity as the solution is converging. e constants, α andβ, can aect the convergence speed.

2.2 IBMSGe immersed boundary method with smeared geometry isused to develop a low-order compressor/fan model. is low-order model is useful in cases where calculations for fullyresolved blades are extremely expensive. For example, at the


12 13 14 15 16 171

1.2

1.4

1.6

PE

NS

mass ow (kg/s)

pressure

ratio

(π)

Exp.low delityhigh delity

Figure 4. Characteristic line for Darmstadt case at 100 %speed; line – experiments, dots: low delity simulation (IBMfor DG and IBMSG for blades), squares: high delitysimulations (URANS)

design stage of an engine nacelle, sometimes the eects ofthe compressor/fan on the ow over the nacelle can not be ig-nored. Under this circumstance, a low-order compressor/fanmodel is highly valuable. Equation 2 is the basic NS equationwith some extra terms for IBMSG.

∂

∂t

ˆΩ

λqdΩ+˛A

λFdS =ˆΩ

λ f ndΩ+ˆΩ

λ f pdΩ+ˆΩ

BdΩ

(2)

where q are the primitive variables. F are the sum of inviscidand viscous terms. f n are the force terms normal to the bladecamber line. f p are the force terms parallel to the bladecamber line. λ is the blockage factor. B are the extra termsdue to blockage. e detailed description and calculation forthe each term can be found in [16].

3. RESULTS AND DISCUSSIONS3.1 Validation.To obtain the characteristic line from numerical simulations,the pressure at the outlet was increased step by step, from thepeak eciency (PE) condition to the near stall (NS) condition.Figure 4 shows the characteristic line at the 100% speed forexperiments (solid line), low delity simulations (dots), andhigh delity simulations (squares). In general, both low andhigh delity simulations agree with the experimental results.Although the choking mass ow and the pressure ratio atnear stall condition are slightly (1-2%) dierent betweenthe numerical results and the experiments, these dierencesare marginal and do not compromise the conclusion of thecurrent study.

Figure 5 shows the total pressure ratio in circumferentialdirection at three measurement stations (S1−S3). ese threestations are illustrated in gure 2. e eects of the distortiongenerator can be seen between 225 − 325, where the total

0 50 100 150 200 250 300 3500.90.95

11.051.1

(a)rotate

Circumferential angle ()

π

Exp. URANS IBMSG

0 50 100 150 200 250 300 3500.90.95

11.051.1

(b)


π

0 50 100 150 200 250 300 3500.90.95

11.051.1

(c)

Circumferential angle ()π

Figure 5. Total pressure ratio (π) in circumferentialdirection at (a) S1, (b) S2 and (c) S3.

0 50 100 150 200 250 300 3501.21.41.6

near hub


π

Exp. URANS IBMSG

0 50 100 150 200 250 300 3501.21.41.6

mid span


π

0 50 100 150 200 250 300 3501.21.41.6

near case


π

Figure 6. Total pressure ratio in circumferentialdirection at S3 for three spanwise locations.


Figure 7. Q-criterion isosurface contoured by absolute Mach number. To have a clear view of the ow structure within theblade passage, the annular cascade is transformed to a linear one as illustrated in the embedded frame.

pressure ratio is lower. e distortion generator creates alarge separation, which dissipates energy and results a lowertotal pressure region downstream.

is lower pressure region is convected downstream. Atthe both rotor and stator exits (gure 5(b, c)), the lowerpressure region is still visible. e distorted region is alsoextended in circumferential direction at the downstream. Asthe blade travels from right to le in the gure, at the exitside of the distorted region (the le side of the lower pressureregion), the total pressure is increased slightly. is is dueto the rotor incidence variation. More details are given insection 3.2.

In gure 6, the total pressure ratio is ploed at threedierent span locations: near hub, mid span and near case.e eects of the inow distortion extends to the whole spanat the exit of the stator. Both the URANS and IBMSG capturesthe distorted region, though the averaged total pressure inthe IBMSG calculation is higher at the mid span and lowernear the case.

3.2 General flow features.In this and the following sections, results from URANS willbe studied in more detail. Figure 7 shows the Q-criterioncoloured by Mach number in the region between 85% - 100%span. To increase the visibility into the blade passage, only15% of span is shown. Also, the annular cascade is trans-formed to a linear one. e y coordinate in gure 7 is thecircumferential distance and the z coordinate is the radius.To calculate the circumferential distance, a xed radius at

92.5 % of span is used rather than the local one. is is tomake sure that the blades at the lower and upper bound ofthe y coordinate are not leaned.

Flow within the separated region immediately downstreamof the DG.e distortion generator creates a large separationupstream of the rotor. e separated ow constantly shedsvortices. is results in a highly unsteady region downstreamof the DG. In this region, the velocity is lower than in theundistorted region. As a result, the rotor blades experience avariation of the incidence in the circumferential direction.

Since the static pressure in the distorted region is lower,the vortices formed at the circumferential end of the DGconverge towards the centre (see gure 7). As a result, thecircumferential velocity increases at the entry side of thedistorted region and decreases at the exit side. Hence, theincidence is higher at the exit and lower at the entry side.is is the reason why the total pressure is higher at the exitin gure 5(b,c). Similar results can be found in section 3.1.

Flow structures within the rotor blade passage. Upstreamof the rotor, the leading edge shocks create vortices on thecasing. ese vortices are relatively small compared to thetip leakage vortex. Similar to the ndings in the literature, allthe three main vortices – induced vortex, tip-leakage vortexand tip-separation vortex are captured in the simulation.However, in the distorted region, the tip leakage vortexbreaks down immediately aer the shock. Aer the rotorexits the distorted region, the ow recovers to the normalstate. Around three/four blade passages are signicantly af-fected by the distortion generator. However, as the mass ow


(a)

(b)

(c)

(d)

Figure 8. Flow at 95% span at PE point; (a) Mach number,(b) total pressure, (c) entropy, and (d) entropy generationrate.

(a)

(b)

Figure 9. Flow at 95% span at NS point; (a) entropy, and (b)local entropy generation rate.

decreases, it takes longer for the distorted ow to convectout of the rotor passage. More blade passages are expectedto be aected.

Flow structures within the stator blade passage. e owstructure in the stator blade passage is relatively cleaner. etip leakage vortex generated in the rotor convects down-stream to the stator passage. ey are not entirely dissipatedeven at the stator exit. In the blade passages that are aectedby the distortion, the secondary ow becomes stronger. Notip leakage vortices can been observed in those blade pas-sages, as the tip vortices have already been broken down inthe rotor.

3.3 Flowat peak eiciency andnear stall points.Aer understanding the general ow features in the bladepassage, the dierence between the ow at the peak eciencypoint and the near the stall point will be examined. Only theregion near the casing is studied here.

Figures 8 and 9 show the ow at 95% of span for the peakeciency point and near stall point, respectively. All thequantities are based in the absolute frame. As mentioned be-fore, for both operating points, the distorted ow convergestowards the middle. is leads to an increase of incidence atthe exit side and an decrease at the entry side of the distortedregion. As a result, higher entropy is observed at the exit sidein the rotor blade passages (gure 8(c)). At the peak eciencypoint, most entropy is generated in the separated regiondownstream of the distortion generator. Around four rotorblade passages are contaminated, where entropy generationrate is higher. Consequently, around ve stator passages arecontaminated. Other loss sources, such as shocks, wakesand secondary ows, can also identied in the gure 8(d).


Figure 10. Stalling process: radial velocity signals at the 95% of span upstream of the rotor tip.

Among them, wakes are the second dominant source of theentropy generation. Interestingly, the interaction of the rotorwakes and the stator suction surface is also a large source ofentropy generation.

At the near stall point, only entropy and entropy gen-eration rate are shown. Note that to highlight the entropygeneration within the blade passages, the colouring levelsare dierent from that in gure 8. At the near stall condition,the axial ow velocity is lower. e convection time for thedistorted ow to travel through the rotor is longer. Hence,more rotor blade passages (around 9) are contaminated bythe distorted ow. Other entropy generation sources alsoincrease due to a higher pressure gradient in the rotor andstator. At this condition, all the boundary layers on thesuction surface of the stator are separated, except for thethree passages at the entry side of the distortion. is is,again, due to the lower incidence and lower pressure rise atthe entry side. e separated boundary layer is also a largesource of entropy generation at near stall condition.

3.4 Stalling process.As mass ow decreases further, more blade passages will becontaminated. Eventually, the compressor would be fullystalled. Figure 10 shows the radial velocity signals at 95%of the span upstream of the rotor. At t0, the mass ow rateis around 13.8 kg/s. At this mass ow rate, rotor passagebetween −1 radian to 3 radian are contaminated, where theradial velocity is oscillating more than that at −3 radian to−1 radian. As the mass ow decreases, the contaminatedregion extends wider in the circumferential direction. At t1,the mass ow rate drops to around 13.5. Almost all the rotorblade passages are contaminated. Shortly aer all the bladepassages are contaminated, a rotating cell starts to develop att2. It rotates along the circumferential direction at the 65% ofthe rotor rotating speed. As the rotating cell starts to develop,the mass ow rate drops faster.

4. CONCLUSIONSe current paper demonstrated the applications of low andhigh delity simulations for a transonic fan. e low delitymethods (IBM and IBMSG) showed promising results againsthi- simulation (URANS) and experiments. ese low order

methods are useful in designing a coupled system wheremesh resolved blades are computationally expensive.

For hi- simulations, the detailed ow features near thecasing were analysed. It was found that the tip leakageow was stable and strong enough to sustain even at thestator exit. Apart from the analysis of ow structures, thestalling mechanism was also investigated. When mass owwas decreased, more rotor blades are contaminated by theincoming distorted ow. As mass ow reduced to the nearstall condition, separation can be observed over most of thestator blade suction surface. A rotating cell started to developshortly aer all the rotor blade passages were contaminated.e rotating cell was swept around at the 65% speed of therotor.

ACKNOWLEDGMENTSe authors would like to acknowledge the insightful dis-cussion and input from Dr. Rob Watson, Dr. James Page, Dr.Yangwei Liu and Mr. Callum Mantell.

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