E�ect of Fan on Inlet distortion: A Mixed fidelityApproachYunfei Ma1*, Jiahuan Cui1, Nagabhushana Rao Vadlamani1, Paul Tucker1

SYM

POSI

A

ON ROTATING MACHIN

ERY

ISROMAC 2017

InternationalSymposium on

Transport Phenomenaand

Dynamics of RotatingMachinery

Maui, Hawaii

December 16-21, 2017

AbstractInlet distortion is typically encountered during the o�-design conditions on civil aircra�s and inS-ducts in military aircra�s. It is known to severely deteriorate the performance of a gas-turbineengine. As the intakes get shorter, there is an increased interaction between the inlet distortionand the downstream fan. Previous studies in the literature use low-�delity methods (RANS orURANS) to address this unsteady interaction, due the substantial computational cost associatedwith the high �delity methods like LES/DNS. On the other hand, it is well known that the loworder methods like RANS have limitations to accurately represent the distorted �ows. In thispaper, we propose a mixed-�delity approach and employ it to study the intake-fan interaction at ana�ordable computational cost. �e results demonstrate that there are two ways through which thefan a�ects the separated �ow. Firstly, the suction e�ect of the fan alleviates the undesired distortionby ‘directly’ changing the streamline curvature, intensifying the turbulence transport and closingthe recirculation bubble much earlier. Secondly, the enhanced turbulence in the vicinity of thefan feeds back into the initial growth of the shear layer by means of the recirculating �ow. �is‘indirect’ feedback is found to increase the turbulence production during the initial stages of theshear layer. Both the direct and indirect e�ects of the fan signi�cantly suppress the inlet distortion.Keywordsinlet distortion, fan e�ects, mixed �delity1Department of Engineering, University of Cambridge, Cambridge, United Kingdom*Corresponding author: ym324@cam.ac.uk

INTRODUCTIONFlow distortion is typically encountered on the engine in-takes and in the duct �ows under the o�-design conditions.�e �ow over an intake lip separates speci�cally during thetake-o� at high angles of incidence and under severe cross-winds during taxing or landing of an aircra�. �e distorted�ow at the inlet convects downstream and deteriorates theperformance of the fan. In some extreme cases, it can evenlead to the catastrophic events like stall and surge. Interest-ingly, as the inlets become shorter, the proximity of the fan tothe source of the distortion is shown to a�ect the distortionrecovery ([1]). In order to numerically investigate this inter-action, it is crucial to accurately resolve the following �owregimes: (a) the separated �ow domain and (b) the in�uenceof a fan.

Most of the research in the literature addressed the fan-distortion study using low �delity methods such as URANSand RANS [2, 3, 4]. It is well known that the predictive capa-bility of these low �delity approaches are satisfactory at thedesign point. However, they still su�er from severe limita-tions under o�-design conditions, involving �ow separation,distortion and unsteadiness [5, 6, 7]. In particular, whenpredicting �ows with large-scale, low-frequency turbulence,the results may vary signi�cantly among the di�erent RANSmodels [5]. For these �ows, eddy resolving simulations suchas DNS/LES and hybrid LES/RANS are demonstrated to yieldmuch more promising results [7, 8, 9].

On the other hand, the fan in�uence can be representedeither by resolving all fan blades or with a body force. While

the former approach is computationally expensive [10], theBody Force Method (BFM) is much more economical[11] andpractically feasible. BFM can be further classi�ed into thesmeared and standard methods, based on the extent to whichthe geometry has been modelled.

�e Immersed Boundary Method with Smeared Geome-try (IBMSG) is typically used to model the force �eld gener-ated by a set of rotating blades. �is approach assumes anin�nite number of blades in the circumferential direction;which avoids the computational overhead of capturing thedetailed blade geometry and/or incorporating moving bound-aries to represent the fan. In this approach, an inviscid (orwall-normal) force and a viscous (or parallel) force due tothe rotating blades are added to the circumferentially aver-aged Navier-Stokes equations. �e inviscid component ofthe force, formulated by Marble [12], ensures that the �owfollows the blade metal angle. �e viscous component, intro-duced by Xu [13], accounts for the losses encountered overthe blades using a force-velocity relation. Xu [13] has suc-cessfully employed this approach to investigate the distortiontransfer in a high pressure turbine.

On the other hand, the standard Immersed BoundaryMethod (IBM) is generally used to resolve the features of areal geometry. Peskin [14] proposed IBM based on Eulerianand Lagrangian variables, linked by the interaction equationsinvolving smooth appximation of the Dirac-delta function.�is approach has been successfully applied by Fadlun [15]to study the �ow past a backward facing step and by Defoe[16], who modelled a rotor blade and predicted the noise

E�ect of Fan on Inlet distortion: A Mixed fidelity Approach — 2/7

propagation under the in�uence of an inlet �ow distortion.In this paper, a mixed-�delity approach is applied to ac-

curately investigate the in�uence of the fan on the inlet dis-tortion at an a�ordable computational expense. �e standardIBM proposed by Peskin [14] is used to model the distor-tion generator upstream of the fan. �e unsteady separatedregime downstream of the distortion generator is capturedusing a high-�delity eddy resolving approach. Further down-stream, IBMSG is used to model the force �eld due to a ro-tating fan. Subsequently, the recovery of distortion in thepresence of a fan is examined using both the mean and tur-bulent characteristics.

1. NUMERICAL FRAMEWORKFigure 1 illustrates the computational domain and the bound-ary conditions considered in the current study. �is simpli-�ed setup is motivated by the experimental studies on theDarmstadt Rotor [17, 18, 19, 20, 21], albeit under di�erentoperating conditions. In these studies, the distortion gener-ators were designed to reproduce the �ow conditions in areal engine within the laboratory. Measurements by Lieser[17] and Bi�er [20] show that the compressor performanceis largely sensitive to the distortions encountered at the tip.Hence, a periodic distortion generator is placed upstreamof the tip of the fan in order to reproduce the distortion en-countered over the intake lip at high angles of a�ack. �etest case employs the original duct and the rotating fan fromthe Bi�er’s test rig [20, 21], with the periodic beam installedupstream of the fan. It features a 30 deg sector duct with adistortion generator (‘beam’) of height ‘H’ and length ‘1.5H’placed at an axial distance of ‘12.5H’ from the inlet. �efan is positioned at a streamwise distance of 5.25H from thebeam. All the spatial quantities mentioned in the followingsections are normalised by the beam height H. �e velocityis normalised by the velocity, u∞, measured at the maximumheight of the beam (Fig.1), which corresponds to the outeredge velocity of a separated shear layer.

�e primary objective of the current study is to capturethe distortion generated on the lower wall. Hence, an invscidboundary condition is imposed on the upper wall, which en-sures that the pressure distribution due to the spinner is wellrepresented at a reduced computational cost. InternationalStandard Metric Conditions (P0=101325Pa and T0=288.15K)are applied at the in�ow and the mass�ow rate is �xed at10.6kg/s. �is mass�ow rate corresponds to the peak e�-ciency point at 65% rotational speed (1361.31rad/s). A radialequilibrium boundary condition is imposed at the out�ow.Periodicity is imposed in the circumferential direction. �eextent of the sector (30◦ corresponds to 5H) is su�cientenough to ensure that the structres are decorrelated in thecircumferential direction. In a mixed �delity framework, thebeam is represented using the conventional IBM [14]. �eseparated �ow downstream of the beam is captured using theeddy resolving approach, while the force �eld of a rotatingfan is replicated using IBMSG [22]). �is approach avoids theneed to capture detailed blade geometry or incorporate mov-

ing boundaries. Instead, it represents the force �eld generatedby the rotating fan blades and captures the suction e�ect ofthe fan, thereby substantially reducing computational cost.

2. METHOD�e present simulations are carried out using a Rolls-Royce’sin-house CFD code, HYDRA [23, 24]. Both IBM and IBMSGare implemented into the numerical framework and are thor-oughly validated [1]. For the IBM part, the distortion genera-tor is modelled using feedback forcing, proposed by Goldsteinet al. [25]. It has the following expression,

f (x, t) = α∫ t

0∆udt + β∆u,

∆u = u(x0, t) − u0(x0, t)(1)

where the subscript 0 represents the solid boundary. �e co-e�cients α and β are negative constants because essentiallythey function as a proportional-integral (PI) feedback con-troller evaluated by the velocity di�erence. Eventually, thecontroller enforces u = u0 on the immersed boundary. Fromthe viewpoint of control theory, the value of the force is inde-pendent of the two coe�cients α and β, under the conditionthat the computation is convergent. To ensure the conver-gence, the two coe�cients should be carefully selected. Infact, they are associated with two important parameters: the

frequency12π

√|α | and the damping factor −

β

2√|α |

. Hence,

α must be large enough to keep the force frequency12π

√|α |

much larger than any other frequencies in the �ow [15]. �ismeans that the feedback force should change rapidly and �tthe �ow to the desired direction within a unsteady period.Also, to ensure the numerical stability, the time step shouldalso meet the requirement

∆t <−β −

√β2 − 2αkα

, (2)

where the order of k is 1.�e fan modelled with IBMSG can be regarded as a set

of an in�nite number of in�nitesimally thin blades. �eforces are circumferential averaged into every cell in theblade region and turn the �ow to the local desired direction.Cao et al. [22] introduced this method when studying intakeseparation and �nd this model is capable to capture the key�ow features. Hence, we use this normal force model

fn = −ul · n

∆t− RHS · n, (3)

where n is the normal vector of blade surface, and RHS isthe right hand side of Navier-Stokes equation. �e parallelforce from Watson et al. [26] is also used, which is

fp = −K(r)ρu2rel,K(r) = 4k1s2 + k1, (4)

where s is the fraction of span and the coe�cient k1 need tobe calibrated by the existing performance data.�e blockage

E�ect of Fan on Inlet distortion: A Mixed fidelity Approach — 3/7

Figure 1. Experiment se�ings

e�ect is also modelled as [22],

λ = 1 −12(t1 + t2)

S(r) cos β, (5)

where t1 and t2 are the blade thickness for the pressure partand suction part, and S(r) is the surface pitch, as is shown inFigure 2.

Figure 2. Sketch of blade blockage

3. RESULTS3.1 Instantaneous flow fieldFigure 3 shows the contours of the stagnation pressure of theinstantaneous �ow. It demonstrates both the distortion gen-erated in the lee of the beam and an increase in the stagnationpressure due the presence of the fan.

�e iso-surfaces of Q (Q=40) in di�erent views are il-lustrated in Figure 4 and 5, contoured with the local axialvelocity (vx = −150 ∼ 200). �e axial location of the fan isalso shown by means of a sketch. Coherent two-dimensionaldetached shear layer forms at the edge of the beam whichrapidly destabilized downstream. A decrease in the recir-culation region is clearly evident in the presence of the fan.�alitatively, an increase in the length scales of the turbulentstructures due to fan is notable from the top-le� sub�gure inFig. 5.

3.2 Time averaged flow fieldA�er �ushing out the initial transience, statistics are collectedfor around 94H/U∞. �e maximal deviation of 〈u′u′〉 ex-tracted from two di�erent times (with the interval of 50H/U∞)is only 5%, indicating the convergence is acceptable. Figure6 compares the mean velocity pro�les at di�erent stream-wise locations on a carpet plot. A line joining the locus ofin�ectional points of the velocity pro�les is also overlaid. �erecirculation region can be also seen in Figure 7. As notedfrom the instantaneous �ow, the extent of the recirculationzone is signi�cantly reduced due to the fan. �e �ow reat-taches at an axial location which is more than a beam heightupstream of the fan leading edge.

Figure 8a shows the contours of the time-averaged tur-bulent kinetic energy. �e TKE in the shear layer and inthe rea�aching regime has increased by around 40-70% inthe axial direction in the presence of fan. �is is partiallycaused by a higher production in the shear layer (Fig. 8b) andpartially by a stronger convection in the middle-rear part ofthe recirculation region (Fig. 8c).

3.3 MechanismTo further investigate how fan interacts the separation bubblethrough turbulence, this section delves into the mechanismby which the fan has reduced the recirculation region. In theprevious section, Figure 8b and 8c demonstrates a substantialincrease in both the production and convection. However,the location of such increase varies, and consequently maypresent di�erent traits. To examine this in more details, theindividual contributions from the dominant terms (in order):〈u′u′〉 ∂U/∂x, 〈v′v′〉 ∂V/∂y and 〈u′v′〉 ∂U/∂y to the TKEproduction are analysed.

�e results demonstrate that there are two distinct waysthrough which the fan e�ects the separated �ow: shear �owdominant (Zone 1) and strain rate dominant (Zone 2), shownin Figures 9a and 9b. In Zone 2, the primary e�ect of thefan is observable between x = 2H − 4H where the recir-culation region decreases due to the change of the stream-line curvature. Both 〈u′u′〉 and 〈v′v′〉 increase signi�cantlywithin this region by around 40% and 75% respectively. �eincrease in 〈v′v′〉 is much more pronounced than 〈u′u′〉, in-

E�ect of Fan on Inlet distortion: A Mixed fidelity Approach — 4/7

Figure 3. Total pressure distribution

Figure 4. Instantaneous �ow for the cases without/with fan

Figure 5. Lateral view of instantaneous �ow for the caseswithout/with fan

Figure 6. Velocity pro�le

E�ect of Fan on Inlet distortion: A Mixed fidelity Approach — 5/7

Figure 7. Recirculation region

dicating a stronger turbulent transport in the wall-normaldirection. �is is similar to that observed in the context ofcorner separation [27] separating at the leading edge of theblade. Consistent with the observations of Bradshaw [28],we consider this increase in Reynolds stresses to be a ‘directe�ect’ which is a�ributed to the additional strain rate causedby the curvature change.

In zone 1, Figures 9a and 9b also demonstrate an increasein both the streamwise and wall normal �uctuations withinthe shear layer at the edge of the beam between x = 0 − 2H.Clearly, the spreading rate of the shear layer is much morepredominant in the presence of the fan. �is is a�ributed tothe ‘indirect e�ect’ of the fan, where the enhanced turbulencegenerated in the vicinity of the fan feeds back into the originof the shear layer by means of the recirculating �ow. �is isalso evident from the Figures 8a and 8c where an increasein the TKE and TKE convection is observable within therecicurlating region. Consequently, this ‘indirect’ feedback isfound to further intensify the turbulence production withinthe shear layer (Figure 8b) increasing the Reynolds stresses(〈u′u′〉, 〈v′v′〉).

As expected, 〈u′v′〉 ∂U/∂y is found to be the major con-tributor to the total production of TKE in Zone 1 within aspreading shear layer. Figure 10 compares the velocity gra-dients ∂U/∂y to the contours of the Reynolds stress 〈u′v′〉(Fig.9c) without/with fan. It is evident that the contributionto the TKE production is primarily a�ected by an increase inthe Reynolds stress 〈u′v′〉. On the other hand, the change inthe velocity gradients is marginal.

�e increased TKE in Zone 1 is subsequently convecteddownstream into the Zone 2 through the mainstream �owand resulting in the cyclic feedback between both the zones.Hence, although the �ow in the Zone 1 is not a�ected directlyby the fan, it is still a key source of turbulence due to thefeedback from the reverse �ow. It supplements the turbu-lence generated in the vicinity of the fan in the Zone 2 andalso contributes to the earlier rea�achment of the separationbubble.

(a) Contours of TKE

(b) Contours of TKE Production

(c) Contours of TKE convection

Figure 8. Turbulent Kinetic Energy Statistics

E�ect of Fan on Inlet distortion: A Mixed fidelity Approach — 6/7

(a) Reynolds stress 〈u′u′〉

(b) Reynolds stress 〈v′v′〉

(c) Reynolds stress 〈u′v′〉

Figure 9. Main Reynolds stresses

Figure 10. Velocity gradient ∂U/∂y

4. CONCLUSIONIn this paper, we propose a mixed-�delity approach and em-ploy it to study the intake-fan interaction at an a�ordablecomputational cost. �e results demonstrate that there aretwo ways through which the fan e�ects the separated �ow:Firstly, the suction e�ect of the fan (e�ective upto almost halfthe chord length upstream of the fan) alleviates the undesireddistortion by ‘directly’ changing the streamline curvature,intensifying the strain rate and turbulence transport therebyclosing the recirculation bubble much earlier. Secondly, theenhanced turbulence in the vicinity of the fan feeds back intothe initial growth of the shear layer by means of the recircu-lating �ow. �is ‘indirect’ feedback is found to increase theturbulence production and spreading rate of the shear layer.Both these direct and indirect e�ects of the fan signi�cantlysuppress the inlet distortion.

From an engineering perspective, the current study showsthat the loading of the fan blade can be conveninently alteredto maximise the stagnation pressure recovery by suppressingthe distortion. A tip loaded fan can increase the streamlinecurvature driving early rea�achment of the �ow. Furtherstudies will be carried out to address these aspects and ex-plore the possibility of some potential �ow control methodsto alleviate the inlet distortion.

ACKNOWLEDGMENTS�e authors gratefully acknowledge the UK Turbulence Con-sortium grant (EPSRC grant EP/L000261/1), the �nancial sup-port from the Chinese Scholarship Council, and the technicalsupport from Rolls-Royce.

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