Rotating Stall Control in a High-Speed Stage with Inlet Distortion, Part II Circumferential Distortion

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1 THE AMERICAN SOCIETY OF MECHANICAL ENGINEERS 345 E. 47th St., New York, N.Y S The Society shll not be responsible for sttements or opinions dvnced in ppers or discussion t meetings of the Society or of its Divisions or Sections, or printed in its publictions. Discussion is printed only it the pper is published in n ASME Journl. Authoriztion to photocopy for internl or personl use is grnted to librries nd other users registered with the Copyright Clernce Center (CCC) provided $3/rticle or $4/pge is pid to CCC, 222 Rosewood Dr., Dnvers, MA Requests for specil permission or bulk reproduction should be ddressed to the ASME Technicl Publishing Deprtment. Copyright 1998 by ASME All Rights Reserved Printed in U.S.A. Rotting Stll Control in High-Speed Stge with Inlet Distortion, Prt II Circumferentil Distortion Z. S. Spkovszky C. M. vn Schlkwyk Gs Turbine Lbortory Scientific Systems Co., Inc. Deprtment of Aeronutics nd Astronutics Woburn, MA 181 Msschusetts Institute of Technology Cmbridge, MA 2139 H. J. Weigl, J. D. Pduno K. L. Suder, M. M. Bright Gs Turbine Lbortory NASA Lewis Reserch Center Deprtment of Aeronutics nd Astronutics Clevelnd, OH Msschusetts Institute of Technology Cmbridge, MA 2139 Abstrct This pper presents the first ttempt to stbilize rotting stll in single-stge trnsonic xil flow compressor with inlet distortion using ctive feedbck control. The experiments were conducted t the NASA Lewis Reserch Center on single-stge trnsonic core compressor inlet stge. An rry of 12 jet injectors locted upstrem of the compressor ws used for forced response testing nd feedbck stbiliztion. Results for circumferentil totl pressure distortion of bout one dynmic hed nd 12 extent (DC(6)=.61) re reported in this pper. Prt I (Spkovszky et l. (1998)) reports results for rdil distortion. Control lws were designed using empiricl trnsfer function estimtes determined from forced response results. Distortion introduces coupling between the hrmonics of circumferentil pressure perturbtions, requiring multivrible identifiction nd control design techniques. The compressor response displyed strong first sptil hrmonic, dominted by the well known incompressible Moore- Greitzer mode. Stedy xisymmetric injection of 4% of the compressor mss flow resulted in 6.2% reduction of stlling mss flow. Constnt gin feedbck, using unstedy symmetric injection, yielded further rnge extension of 9%. A more sophisticted robust H controller llowed reduction in stlling mss flow of 1.2% reltive to stedy injection, yielding totl reduction in stlling mss flow of 16.4%. 1. Introduction For better understnding of the coupled compressor dynmics short overview of undistorted flow compressor modeling is given. The clssic Moore-Greitzer formultion (Moore nd Greitzer (1986)) considers n incompressible two-dimensionl flow field with n xisymmetric, sptilly uniform (undistorted) inlet flow, nd linerized pproch for the perturbtions. The rotting stll dynmics for the nth mode re described by \ +t I - = ^ jna b, (1) ( '9'P ts where Tts is the totl-to-sttic pressure rise coefficient of the entire compressor nd nd Jo re the compressor fce flow coefficient nd its perturbtion respectively. The inerti prmeters re the fluidic inerti in the rotors A, in the rotors plus sttors p, nd in the inlet nd exit ducts where cr/f,^ =cx/f cos. + 2 COS 2 (2) rotors sttors ' Presented t the Interntionl Gs Turbine & Aeroengine Congress & Exhibition Stockholm, Sweden June 2-June 5,1998 This pper hs been ccepted for publiction in the Trnsctions of the ASME Discussion of it will be ccepted t ASME Hedqurters until September 3,1998 Downloded From: on 1/3/218 Terms of Use:

2 c, f, nd l; re the xil chord, men rdius, nd stgger ngle respectively. Solving Eqution (1) with yields &(9,t) = (3) n=-oo 8(9,t) = ne(,. nwn)tene, n=-oo where 9 nd t re the ngle round the nnulus nd the time respectively. The growth rte vn nd rottion rte wn re given by (4) The other gols of this pper re identifiction nd stbiliztion of the compression system with inlet distortion. Our frmework will be, s in Prt I (Spkovszky et l. (1998)), multi-vrible input-output chrcteriztion where mesurements nd ctution re expressed s complex sptil Fourier coefficients (Pduno et l. (1993)). This frmework is consistent with the stbility nlysis of Hynes nd Greitzer (1987), except their nlysis ws homogeneous insted of forced, nd nonliner stedy-stte condition ws found numericlly (ours is chieved experimentlly). The frequency domin input-output mp, or trnsfer function mtrix, for the first three hrmonics is written: q1ts yo(s) Goo(s) Goi(s) G2(s) 1 -(S) ^n =wn = (5) 1(s) = G`1 (s) G'i^ (s) G12 (s) u^ (s), (6) ( ^n^ + ^/ \ In + ^/ [ 2(S ] ) G2(s) G21(s) G22 (S) v2(s) This solution describes sptil wves of sinusoidl shpe (hrmonics) tht trvel round the nnulus t rottion rte wn, nd grow or decy in time with growth rte v n. Compressor stbility is determined by the growth rte of these modes. In this model, the xil velocity perturbtions S&(9) re xilly uniform throughout the compressor. Furthermore, the flow field for the nth mode consists only of the nth sptil hrmonic. Tht is, the hrmonics re ll decoupled (independent of one nother). In the presence of circumferentilly nonuniform inlet flow the pressure rise,ts, nd therefore the slope, is no longer constnt but strong function of. This nonliner coupling between the stedy inlet flow field nd the compressor mp strongly influences the linerized behvior of the flow field perturbtions. The mode shpes re no longer purely sinusoidl but hve contributions of other hrmonics. In other words, distortion introduces coupling between the hrmonics. Hynes nd Greitzer (1987) hve extended the Moore-Greitzer model to describe incompressible dynmics with inlet distortion. The ccurcy of this model hs been verified experimentlly by Vn Schlkwyk et l. (1997) on low-speed three-stge compressor. If n nlysis ccounting for compressibility is done, coustic modes with xil structure re introduced. In this cse, ech compression system mode hs both circumferentil nd xil structure. Modeling of this kind ws conducted by Bonnure (1991), Hendricks et l. (1993), nd Feulner et l. (1994). To dte, no control-theoretic compressible model exists which ccounts for inlet distortion. Thus it is one of the gols of this pper to investigte the effects of inlet distortion on high-speed compressor pre-stll behvior. or, in compct form, y(s) = G(s)ii(s), (7) where the output vector y is vector contining the system's primry outputs: the complex sptil Fourier coefficients (SFCs) of the pressure perturbtions (nlogous to Eqution (3)). The input vector ii contins the corresponding SFCs of the injection profile, which is the system input. Coupling between hrmonics due to circumferentil distortion is indicted by nonzero off-digonl elements of G(s) (G22 (s), for ll i 54 j). The strength of this coupling cn be determined by the mgnitudes of the off-digonl trnsfer functions. The consequence of this coupling is tht the individul trnsfer functions of G cnnot be treted independently; thus controller design becomes multi-input-multioutput (MIMO) problem. This increses the complexity of the controller nd complictes system identifiction. After describing the stedy-stte conditions, we will use these concepts to interpret the identifiction nd control results. 2. Experimentl Setup The experiments described in this pper were ll conducted t the NASA Lewis Reserch Center in the singlestge xil compressor test fcility. A detiled description of the NASA Stge 35 test compressor nd the ctution nd instrumenttion is given in Prt I (Spkovszky et l. (1998)), s well s other documents, Reid nd Moore (1978), Berndt et l. (1995), Weigl et l. (1997), nd will not be repeted here. For our purposes it suffices to sy tht set of twelve evenly spced injectors, blowing high pressure ir in the tip region of the rotor, provide the ctution, nd set of 8 Downloded From: on 1/3/218 Terms of Use:

3 sttic pressure trnsducers locted immeditely upstrem of the rotor provide sensing. Both the ctution nd sensing signls re decomposed into sptil Fourier coefficients, nd treted s such in the reminder of the pper. 3. Circumferentil Inlet Distortion An erly effort using stedy blowing nd bleeding devices to determine if tip boundry lyer control ws n effective mens of incresing the unstlled weight flow rnge of trnsonic single-stge compressor with nd without inlet flow distortion ws conducted by Koch (197). The experiments reveled tht the blowing device ws more effective thn the bleed device nd tht the unstlled rnge could be improved. Circumferentil inlet irflow distortion tht is cused by phenomen such s flow seprtion or nonxisymmetric intke duct geometry hs been studied by instlling circumferentil distortion screen: fine mesh ws mounted in the inlet duct, locted pproximtely 2.2 men rdii upstrem of the rotor (s in Prt I). The screen cn be indexed through 35 round the nnulus to llow more detiled mpping of stedy stte compressor performnce. The extent of the screen ws 12 nd covered the full blde spn. 3.1 Stedy Stte Experiments Circumferentil totl nd sttic pressure nd totl temperture profiles were mesured with probes positioned between the distortion screen nd the rotor. In ddition, four circumferentilly distributed wll sttic pressure tps t the hub nd csing, nd totl pressure nd totl temperture rke provided dt on the flow field downstrem of the compressor. The stedy pressure nd temperture probes were geometriclly fixed nd the screen ws rotted in five degree increments to obtin the profiles. Figure 1 shows the totl nd sttic pressure profiles t the inlet, pproximtely 1.1 men rdii upstrem of the rotor inlet, nd the sttic pressure profile t the compressor exit. The men exit sttic pressure hs been subtrcted from ll these curves to show the reltive offset of the pressure profiles. The distortion screen blocked the flow between 12 nd 24 circumferentilly; these ngles re mrked with the dotted verticl lines in the figure. The totl pressure drop generted by the distortion screen ws bout one dynmic hed, tht is Apt 2y1. (8) The distortion mgnitude cn lso be described by prmeter commonly used in engine intke erodynmics clled.5 ept Ps.5 Spoiled Sector D.2s -.3 D inlet Pt inlet Ps Circumferentil Angle, Figure 1: Totl nd sttic pressure t the compressor inlet nd sttic pressure t the compressor exit for 1 dynmic hed distortion t moor? = 16.5 kg/s without blowing. U) C) CO CO Cl) c v m 't3 fyd C mm Ui.55.5 CO.45 N C).4 Z Y.35 o U ^ >.3 > `o ' Spoiled Sector Circumferentil Angle, Figure 2: Mesured velocity profile for 1 dynmic hed distortion t rh o.,. = 16.5 kg/s without blowing. the DC(6) descriptor (Willims (1991)). The DC(6) descriptor is defined by Pt 136 i A Iw rst 6. DC(6) (9) pv2 In the idel cse where the sttic pressure is uniform, DC(6)=1 corresponds to zero-velocity flow within the 6 sector, giving very poor inlet erodynmics. The distortion screen designed for Stge 35 with 1 dynmic hed distortion mgnitude corresponds to DC(6)=.61, representing poor inlet conditions, s shown in the velocity profile in Figure 2. Downloded From: on 1/3/218 Terms of Use:

4 The inlet sttic pressure shown in Figure 1 is pproximtely uniform round the nnulus, while the exit sttic pressure is circumferentilly nonuniform with n incresed pressure rise in the rnge 12 < 9 <_ 24. This contrdicts the bsic Hynes-Greitzer theory (Hynes nd Greitzer (1987)) which ssumes tht the flow ngle from the sttor vnes is uniform nd tht the downstrem duct hs constnt re. In two-dimensionl (incompressible) flow field these ssumptions imply uniform exit sttic pressure nd nonuniform inlet sttic pressure. This discrepncy between the theory nd mesurements cn be explined by considering the compressor plus downstrem diffuser, nd using prllel compressor type rgument s follows (see Longley nd Greitzer (1992)): In the spoiled sector the diffuser is operting with low inlet totl pressure nd thus low velocity, producing lower pressure rise thn the diffuser in the unspoiled sector. Since the sttic pressure t the diffuser exit must be uniform, the sttic pressure t the compressor exit must be higher in the spoiled sector thn in the unspoiled sector. ^ 1 D 3 N ^ 1 Ce U) c H o, e. no distortion ^b circ. distortion (no blowing) circ. distortion (5% blowing).8 ' Corrected Mss Flow [kg/s] Figure 3: Speed lines for undistorted inlet (solid), circumferentil distortion no blowing (dsh), nd with 5% stedy blowing (dsh-dot). Speed lines were mesured for undistorted inlet flow s well s with circumferentil inlet distortion. The effect of stedy blowing (stedy vlve opening of 5%, injected corrected mss flow of.65 kg/sec) on the pressure rtio ws then mesured. The speed lines re constructed s described in Prt I: totl corrected mss flow is the sum of n upstrem orifice mss flow nd the injected mss flow, the upstrem totl pressure is the mss verge of totl pressure probes between the distortion screen nd the ctutors, nd the Qb downstrem pressure is from mss verged hub nd csing sttic pressure mesurements. In Figure 3 we see tht the circumferentil distortion resulted in pek pressure rtio drop. However, with stedy blowing the pek pressure rtio cn be recovered nd even considerble rnge extension of 6.2% in stlling mss flow cn be obtined. Although the pressure rtio of the compressor is recovered by blowing, there is no chnge in the inlet distortion, becuse the distortion screen is upstrem of the compressor, nd there is considerble non-uniformity in the compressor fce flow field, s evidenced by the system identifiction results in the next section. 4. Open Loop Compressor Dynmics Hving chrcterized the stedy-stte behvior, we turn to the dynmic behvior ner stll. Using sinusoidl frequency sweeps on ech sptil hrmonic, we quntify the dominnt eigenmodes of the system, their circumferentil structure, nd the degree of coupling between hrmonics tht exists in the input-output dynmics. The ltter is importnt for control lw design; it is lso of interest to determine the degree of coupling between hrmonics in compressible pre-stll modes. Using stndrd frequency sweep methods (see Ljung (1987)), we mesured the trnsfer function mtrix (Eqution (6)). The of digonl elements, G2j (jw) for i # j, were found to hve mgnitudes of bout.1 to 1. times the digonl elements, indicting strong coupling between some hrmonics. A subset of the trnsfer functions is shown in Figure 4. The mgnitudes of the off-digonl trnsfer functions G1(jw) nd G1(jw) re of the sme order s the digonl trnsfer functions Goo(jw) nd G11(jw). To find the eigenvlues, nd for control lw design, stte-spce models were identified bsed on the mesured trnsfer functions using n MIT-developed method clled FORSE (Jcques (1994)). The trnsfer functions of the identified stte spce model re plotted s dshed lines in Figure 4. The peks in the trnsfer functions indicte tht there re severl lightly dmped modes in the pressure perturbtions. Due to compressibility, severl modes with similr circumferentil structure cn exist, ech hving different xil structure. Therefore we denote the modes by [n, m], where n is inferred from the circumferentil hrmonic tht is lrgest in the mode, nd m indictes the postulted xil mode number (higher vlues of m indicte higher frequency, usully ssocited with more xil mode structure, s in coustics) 1. 'The mode nmes used here re primrily for conveying the physicl effects involved, nd do not effect controller design t ll; controllers 4 Downloded From: on 1/3/218 Terms of Use:

5 ) Goo(jw) Trnsfer Function -1 (, ) [,1] [,2] M i m -1 c C c) G1 Uo) Trnsfer Function [1,-3] [1,] c\ fl to 2 r c^4 m CO o_ N b) G1 (jco) Trnsfer Function - 1 [,21. m -^, ^ [1.1] flh ^; Al C : 2 (ci m d) G11(jw) Trnsfer Function (1,-4] [1,1] [12] [1. 3] I1: 1 ] [1 2] Frequency Normlized by Rotor Frequency Frequency Normlized by Rotor Frequency Figure 4: MIMO trnsfer functions Goo(jw), Goi(jw), Gio(jw), nd G11(jw), with circumferentil inlet distortion t tn orr 16. kg/s nd 85% corrected design speed. = mesured, - - = identified model. Mode number ssignment requires creful dt reduction nd nlysis. First, to visulize the sptil structure of the modes, we reconstruct the mode shpes using the eigenstructure of the identified stte-spce model (Spkovszky (1998)). Figure 5 shows some of the reconstructed mode shpes, including the hrmonic content in ech. For these experiments the distortion screen rnged from 18 to 3 - this is mrked with x's in Figure 5. Next, we ssign the number n bsed on the hrmonic which contributes most to the mode shpe. The first two modes in Figure 5 hve strong th hrmonics, indicting tht overll compression system re bsed only upon the input-output model prmeters (such s duct lengths nd plenum size) will hve strong influence on their stbility. The second two modes hve strong 1st hrmonics, nd we will see tht stbiliztion of these modes cn be chieved by controlling the first hrmonic of the flow perturbtions. Finlly, the "coustic" mode number m is ssigned by looking t vrious fctors. Higher frequencies re considered to be more cousticlly coupled, nd re given lrger vlues of m. We note tht the mode shpes, nd therefore the hrmonic contents of ech mode, is function of time. Figure 5 thus portrys the modes t severl specific instnts in time. Eigenvlues obtined without distortion Weigl et l. (1997) (lso see Weigl 5 Downloded From: on 1/3/218 Terms of Use:

6 (1997)) re compred to those found here, to judge how distortion hs ltered their frequency, stbility, nd hrmonic content; this lso helps to ssign the mode numbers. In ddition, low speed modeling (Vn Schlkwyk (1996)) is employed to help ssocite mode numbers with the peks when strong coupling is present. The results re summrized in Figure 6, which shows the identified poles nd ssigned mode numbers. Mode Shpe Mode # Hrmonic Contribution [,].5 fl i `o [,1] [1,].5 _niilri [1,1] Circumferentil Angle Hrmonic Figure 5: Left: mode shpes for the four primry modes of the identified dynmics, plotted in severl positions s the eigenmode trvels round the nnulus. Right: mplitude of the hrmonic contribution to ech mode, indicting which hrmonic domintes nd the degree of coupling between hrmonics. Verticl scles re rbitrry, since only the mode shpe is shown. Severl sttements cn be mde bsed on Figure 5. First, note tht mode [1,] hs minimum t pproximtely 25, which is bout in the middle of the distorted region. This behvior is predicted by the low-speed model nd hs been observed in low-speed compressor by Vn Schlkwyk et l. (1997). Furthermore, the Fourier decompositions of the mode shpes, shown in the right hnd grphs of Figure 5, indicte tht severl hrmonics re present in ech mode; this is lso predicted by incompressible theory. The compressible modes [,1] nd [1,1], on the other hnd, represent n effect which hs not yet been modeled: it ppers tht these higher frequency, compressible dynmics re lso coupled, to n extent very similr to the incompressible dynmics, by inlet distortion. Finlly, we note tht the richness of the dynmics displyed in Figure 4 nd Figure 5 mkes the control problem more complex, but this complexity is mitigted by the fct tht some of the high frequency is C o Growth Rte, Figure 6: Identified poles of the multi-vrible trnsfer function system t 7n CO,.r = 16. kg/s. modes re reltively well dmped, nd do not tend to go unstble s mss flow is reduced. To study the reltive stbility nd sensitivity to mss flow of the vrious compressor modes, we conducted system identifiction t vrious mss flows. By compring ll of the trnsfer functions t ll the tested mss flows, it ws found tht the [1,] mode is primrily responsible for system stbility. To summrize our conclusion, Figure 7 shows the mgnitude nd phse of G 11 mesured t four different mss flows. The [1, ] mode is prticulrly visible in this trnsfer function. Only the positive frequency (forwrd trveling wve) portion of the trnsfer functions re shown. As the mss flow is decresed, the mgnitude of the pek t.4w,. increses, indicting lightly dmped mode. At the lowest mss flow tested this mode is ctully unstble. This cn be determined by looking t the corresponding phse plot: for rh =14. kg/s (solid line), the phse increses in the rnge.3 < w,. <.6, indicting tht the pole ssocited with this mode is unstble. For m =15. kg/s (dsh-dot) nd 14.7 kg/s (dsh) the respective phses decrese in the sme frequency rnge, indicting tht t these mss flows the mode is stble. Note tht for rh =16. kg/s (dotted) the phse lso increses in this frequency rnge. However, t this high mss flow the mode is stble. The increse in the phse is result of zero t.35w, which is clerly visible s deep vlley in the mgnitude of the trnsfer function. Note tht the compressible modes in Figure 7 (lbeled [1, 1] nd [1, 2]) do not chnge significntly with mss Downloded From: on 1/3/218 Terms of Use:

7 1-1 C -2 v (D -2 (CS [1.1] [1,21 C Q) (C U ) U) ), Frequency, Normlized by Rotor Frequency Figure 7: Mesured Gil(jw) t 16. kg/s (dotted), 15. kg/s (dsh-dot), 14.7 kg/s (dsh) nd 14. kg/s (solid) totl corrected mss flow. flow. These eigenmodes cuse peks in the trnsfer function which chnge only slightly s the mss flow is decresed, indicting tht their degree of stbility is not gretly ffected by the decrese in mss flow. Similr conclusions were drwn bout other pre-stll modes by looking t the relevnt trnsfer functions nd studying eigenvlue migrtion with mss flow. Throttle rmps into stll reveled tht indeed the [1, ] mode resontes strongly s the stll point is pproched. This mode cn be relted to the incompressible Moore- Greitzer mode, nd hs lso been observed with rdil distortion in Prt I (Spkovszky et l. (1998)). The spectrogrm of the first hrmonic of the pressure perturbtions during stll event is plotted in Figure 8. We note tht, even right up to stll, there is reltively little ctivity t 1w, nd 1.6w,. This indictes the [1,1] nd [1,2] compressible modes re well dmped nd tht it is the [1,] mode tht loses stbility. In summry, in the presence of circumferentil distortion, the stbility of the compression system is determined by the [1,] mode. This behvior is nlogous to tht observed in low-speed compressors. The dditionl compressible modes were lso observed with rdil distortion by Spkovszky et l. (1998). Unlike rdil distortion, there is strong coupling between the hrmonics, tht is, ech mode contins severl hrmonics. This coupling is considered during design nd testing of controllers to stbilize the compression system, discussed in the next section. --"ter Imormlized by Rotor Fre quency 2 T^ Figure 8: Spectrogrm of the 1st hrmonic perturbtions during n open loop stll rmp. 5. Active Control Results In this section we discuss ctive control of rotting stll in high-speed single-stge compression system with circumferentil distortion. Two different controllers were tested: constnt gin controller, nd dynmic, model bsed controller. The two controllers re discussed in the following sections. 5.1 Constnt Gin Control Constnt gin control hs been used successfully by severl reserchers to stbilize rotting stll in low-speed compressors. Pduno et l. (1993) developed the experimentl design procedure on single-stge compressor, nd Hynes et l. (1994) pplied it to three-stge compressor. The sme pproch ws used by Vn Schlkwyk et l. (1997) to stbilize three-stge compressor with circumferentil distortion of the inlet totl pressure. However, Weigl et l. (1997) showed tht constnt gin controllers re not effective in high-speed compressors with uniform inlet flow. A similr result ws obtined in Prt I (Spkovszky et l. (1998)) with rdil distortion. However, s we will see momentrily, constnt gin control ws very effective on this mchine in the presence of circumferentil distortion. The ide behind constnt gin control is s follows. The circumferentil pressure perturbtion bp(9) is mesured nd decomposed in Fourier series nlogous to Eqution (3). The nth hrmonic is then sptilly rotted by n experimentlly optimized ngle (3n, multiplied by constnt gin k to form the nth hrmonic of the control signl. For ex- 7 Downloded From: on 1/3/218 Terms of Use:

8 mple, for sensed first hrmonic perturbtion y l = bpl the constnt gin control lw is ul = _k 1e yq^6p 1 (1) where ul is the corresponding first hrmonic SFC of the injection wve. Finlly, the individul ctutor commnds re reconstructed bsed on the Fourier coefficients. A first hrmonic constnt gin control lw ws found to be effective t stbilizing the circumferentil distortion cse investigted here. When the gin nd phse were set to k1 = 1 nd,(31 = is respectively, the stlling mss flow ws reduced by 6.8% reltive to stedy blowing. The totlto-sttic speed lines re plotted in Figure 9 for undistorted inlet flow (solid), circumferentil distortion without blowing (dsh), nd with 5% stedy blowing (dsh-dot). The stll >, Cl) C, Cs U D iy -^ ^y worrrtlized by 2 "cove y Rotor Frequency ' 1( ^J^y co x x + o,. Q ro^q Figure 1: Spectrogrm of the first hrmonic pressure perturbtions with first hrmonic constnt gin control U Cs 51 O ro o.9.8 o open loop tests + 1st hrm. constnt gin ^b * oth,lst nd 2nd hrm. constnt gin b x 1st hrm, robust control ^?p Corrected Totl Mss Flow [kg/s) C Cs U ) CD d Figure 9: Speed lines for undistorted inlet flow (solid), circumferentil distortion without blowing (dsh), nd with 5% stedy blowing (dsh-dot). Stll points with control re: 1st hrmonic constnt gin control (+), th-1st-2nd hrmonic constnt gin control (*), nd 1st hrmonic H control (x). point with the first hrmonic constnt gin control lw is mrked with + in this figure. Spectrogrms of the first nd second hrmonics of the pressure perturbtions, immeditely prior to the control-on stll point, re shown in Figures 1 nd 11 respectively. The [1, ] mode ppers to be reltively well dmped during the first 1 revolutions in Figure 1, while the [1, 1] mode nd the [2, ] mode (Figure 11) re resonting strongly during the entire pre-stll period. Other evidence indictes tht the [2, ] mode goes unstble first, nd in fct dding '7..c JU ormlized by Rotor Frequency,^ije' Figure 11: Spectrogrm of the second hrmonic pressure perturbtions with first hrmonic constnt gin control. second hrmonic constnt gin feedbck with k2 = 1 nd,32 = it dmped out the second hrmonic mode nd chieved further rnge extension of 2.2% in stlling mss flow reltive to the first hrmonic constnt gin control cse. The mesured mss flow nd pressure rtio is mrked with * in Figure 9. A zeroth hrmonic feedbck, with gin k o = 1, is lso in opertion during this run. These results clerly show tht constnt gin control is effective in the presence of circumferentil distortion. Since compressible, distorted flow, control theoretic model I 8 Downloded From: on 1/3/218 Terms of Use:

9 does not exist, it is difficult to explin these phenomen. The system identifiction experiments indicte tht single mode with dominnt first hrmonic nd incompressible fetures determines the stbility, suggesting the pplicbility of constnt gin control strtegy. This ws lso qulittively nd quntittively verified using incompressible modeling methods (Vn Schlkwyk (1996)). However, the mesurements in Figure 4 show tht there re compressible modes tht hve significnt mgnitudes in the coupled (off-digonl) trnsfer functions (e.g. the [1, 1] mode hs the sme mgnitude in G11 (j) s in Glo(jw)). Such coupling is typiclly detrimentl to ny control lw which does not explicitly tke it into ccount. Even without this coupling, the [1, 1] mode in this compressor hs invribly been destbilized by constnt gin control without circumferentil distortion (Weigl et l. (1997), Spkovszky et l. (1998)). Apprently the effect of distortion in this mchine is such tht the constnt gin control lw, tuned for mode [1, ] stbiliztion, does not destbilize the other lightly dmped modes. It is not cler whether this fortuitous effect will exist in other compressors with inlet distortion. 5.2 Robust He Control In this section the performnce improvement obtined using robust H control is investigted. As in Prt I (Spkovszky et l. (1998)), the lck of theoreticl model requires the use of n identified model for the design of these model-bsed dynmic control lws. This is prticulrly difficult when circumferentil distortion is present, becuse the compressor becomes MIMO dynmic system in which one common set of eigenmodes describes the coupled compressor dynmics; in other words, one cnnot tret one hrmonic t time. This complictes system identifiction nd significntly increses the order of the controller. Becuse of this dded complexity, initil tests of MIMO H. controller did not show n improvement in stlling mss flow over constnt gin control (Spkovszky (1998)). Although further itertion nd improvement of the MIMO controller design should be possible, time did not permit this pproch to be pursued. Therefore n lterntive method, described below, ws investigted. The dominnce of the first hrmonic in the [1,] mode nd the presence of resonnce in the [1,1] mode in Figure 1 suggests tht robust controller which ignores coupling, nd is designed for the first hrmonic only, might yield improvement in performnce. Fortuntely, such controller lredy existed t the time of these tests, becuse the frequencies ssocited with the [1,] mode for both circumferentil nd rdil distortion re pproximtely the sme (.4wr). In fct, the eigenvlue loction of the unstble [1,] mode used for design of the rdil distortion controller ws lmost identicl to the identified eigenvlue loction for this mode with distortion. Figure 12 shows the identified eigenvlues with circumferentil distortion, together with circles indicting the rnge of eigenvlues which the first hrmonic H., rdil distortion controller from Prt I (Spkovszky et l. (1998)) ws designed to stbilize. The 3 > io c 6 _ e: 1.5 c^ ' 1 O ++ [1,1] ).5 (l,o]t t,o] ) Growth Rte, Figure 12: Identified coupled unstble dynmics t ynco,r = 14. kg/s nd perturbtion circles of H control lw designed for rdil distortion. [1,] mode perturbtion circle includes the unstble pole ssocited with circumferentil distortion, indicting tht the controller should be ble to stbilize this mode. Although the [1, 1] mode with circumferentil distortion is more lightly dmped thn in the design model, the frequency is ccurtely cptured by the design model. This proves to be sufficient for success of the controller, indicting tht this pole remins stble for the mss flows of interest. Bsed on these rguments the controller originlly designed for rdil distortion ws tested experimentlly nd showed lrge rnge extension. The stlling mss flow ws reduced by 1.2% reltive to stedy blowing, resulting in totl reduction in stlling mss flow of 16.4%. This is indicted in Figure 9. Of ll the methods tested, this first hrmonic robust control lw chieved the lrgest reduction in stlling mss flow, which is comprble to the reduction in stlling mss flow with rdil inlet distortion shown in Prt I (Spkovszky et l. (1998)). TT Downloded From: on 1/3/218 Terms of Use:

10 6. Concluding Remrks nd Summry This pper presents the first experimentl investigtion of coupled compressible stll dynmics nd it is the first time tht trnsonic compressor with circumferentil inlet distortion ws ctively stbilized. The distortion mgnitude ws bout one dynmic hed, corresponding to DC(6)=.61. Forced response experiments reveled strong coupling between the hrmonics of the pressure perturbtions. Anlysis showed tht single mode of the compression system determines its stbility this behvior is similr to tht of low-speed compressors. Constnt gin control chieved lrge rnge extension. The dominnce of n incompressible mode, together with fortuitous coupling between the hrmonics, ppers to chnge the stll dynmics in such wy tht (unlike the undistorted flow cse) constnt gin feedbck does not destbilize lightly dmped compressible modes. Thus, lthough the detils of the mesured dynmics re strongly ffected by compressibility, the control strtegy pplied here ws the sme s tht used in low-speed compressors. The mximum reduction in stlling mss flow with zeroth, first nd second hrmonic constnt gin controllers ws 9.% reltive to stedy blowing, giving totl reduction in stlling mss flow of 15.2%. In generl, MIMO control lw is indicted when coupled multi-vrible dynmics re present. In this experiment, however, the dominnce of the first hrmonic in the destbilizing mode suggested tht SISO H controller for the first hrmonic might work well. This in fct proved to be the cse: controller originlly designed for rdil distortion chieved totl reduction in stlling mss flow of 16.4%, thus demonstrting robustness with respect to chnge in inlet flow from rdil to circumferentil distortion. Time did not permit compring this performnce to MIMO controller. These results, together with the results of Prt I (Spkovszky et l. (1998)), show tht ctive control of rotting stll in high-speed compressor results in significnt increse in the stble operting rnge of compressor operting in the presence of inlet distortion. These results re very promising for future work nd pplictions. Much work remins to be done, however. In prticulr, the dependence of the dynmics on nonliner coupling between the compressor nd (typiclly unknown) inlet distortion dd degree of uncertinty which is ddressed in our pproch only to the extent tht our control lw is robust to modeling errors. More explicitly designing for, nd subsequently testing ginst, unknown distortion scenrios re needed. It is lso necessry to investigte nd better understnd the interply between distortion nd lightly dmped compressible dynmics. This interply ws beneficil in these experiments, but my not lwys be so. Finlly, one would like to use s few ctutors nd s little mss flow s possible to chieve results like those presented here, nd do so in multistge high-speed environment. 7. Acknowledgments This project ws conducted under collbortion between the NASA Lewis Reserch Center, Scientific Systems Co., Inc., nd MIT. The uthors would like to thnk T. Strzisr nd J. Chi for their very useful input, s well s D. Willims, R. Brokopp, nd B. Piendl for their help during compressor testing. Specil thnks lso to M. Crroll nd D. Prk for prepring this mnuscript. This work ws conducted under NASA funding NAG nd NAS References Berndt R., Weigl H., Pduno J., nd Epstein A., "Experimentl Techniques for Actution, Sensing, nd Mesurement of Rotting Stll Dynmics in High Speed Engines." In J.D. Pduno (editor), Sensing, Actution, nd Control in Aeropropulsion, vol SPIE. Bonnure L., Modelling High Speed Multistge Compressor Stbility. Mster's thesis, Deprtment of Aeronutics nd Astronutics, MIT. Feulner M., Hendricks G., nd Pduno J., "Modeling for Control of Rotting Stll in High Speed Multi-Stge Axil Compressors." In ASME Gs Turbine nd Aeroengine Congress nd Exposition, The Hgue, The Netherlnds, Pper 94-GT-292. Hynes J., Hendricks G., nd Epstein A., "Active Stbiliztion of Rotting Stll in Three-Stge Axil Compressor." ASME J. of Turbomchinry, vol. 116 pp Hendricks G., Bonnure L., Longley J., Greitzer E., nd Epstein A., "Anlysis of Rotting Stll Onset in High Speed Axil Flow Compressors." In AIAA/SAE/ASME/ASEE 29th Joint Propulsion Conference, Pper AIAA Hynes T. nd Greitzer E., "A method for ssessing Effects of Circumferentil Flow Distortion on Compressor Stbility." ASME J. of Turbomchinry, vol. 19 pp Jcques R., On-line System Identifiction nd Control Design for Flexible Structures. Ph.D. thesis, Deprtment of Aeronutics nd Astronutics, MIT. 1 Downloded From: on 1/3/218 Terms of Use:

11 Koch C.C., 197. "Experimentl Evlution of Outer Cse Blowing or Bleeding of Single-Stge Axil Flow Compressor." Tech. Rep. CR-54592, NASA. Ljung L., System Identifiction: Theory for the User. Prentice-Hll, Inc. Longley J. nd Greitzer E., "Inlet Distortion Effects in Aircrft Propulsion System Integrtion." Stedy nd Trnsient Performnce Prediction of Gs Turbine Engines, AGARD-LS-183 pp Weigl H.J., Active Stbiliztion of Rotting Stll nd Surge in Trnsonic Single Stge Axil Compressor. Ph.D. thesis, Deprtment of Aeronutics nd Astronutics, MIT. Willims D., "Engine Comptibility." Tech. rep., Rolls-Royce PLC. Moore F. nd Greitzer E., "A Theory of Post-Stll Trnsients in Axil Compressors: Prt I Development of the Equtions." ASME J. of Engineering for Gs Turbines nd Power, vol. 18 pp Pduno J., Epstein A., Vlvni L., Longley J., Greitzer E., nd Guenette G., "Active Control of Rotting Stll in Low-Speed Axil Compressors." ASME J. of Turbomchinry, vol. 115 pp Reid L. nd Moore D., "Performnce of Single-Stge Axil-Flow Trnsonic Compressor With Rotor nd Sttor Aspect Rtios of 1.19 nd 1.26, Respectively, nd With Design Pressure Rtio 1.82." Tech. Rep. TP-1338, NASA. Spkovszky Z., "Active Control of Rotting Stll in NASA Compressor Stge 35 with Inlet Distortion." Mster's thesis in preprtion, Deprtment of Aeronutics nd Astronutics, MIT. Spkovszky Z., Weigl H., Pduno J., Vn Schlkwyk C., Suder K., nd Bright M., "Rotting Stll Control in High-Speed Stge with Inlet Distortion, Prt I Rdil Distortion." In ASME Gs Turbine nd Aeroengine Congress nd Exposition, Stockholm, Sweden. Vn Schlkwyk C., Active Control of Rotting Stll with Inlet Distortion. Ph.D. thesis, Deprtment of Aeronutics nd Astronutics, MIT. Also vilble s Gs Turbine Lb Report #222. Vn Schlkwyk C., Pduno J., Greitzer E., nd Epstein A., "Active Stbiliztion of Axil Compressors with Circumferentil Inlet Distortion." In ASME Gs Turbine nd Aeroengine Congress nd Exposition, Orlndo, FL, Pper 97-GT-279. Weigl H., Pduno J., Frechette L., Epstein A., nd Greitzer E., "Active Stbiliztion of Rotting Stll nd Surge in Trnsonic Single Stge Axil Compressor." In ASME Gs Turbine nd Aeroengine Congress nd Exposition, Orlndo, FL, Pper 97-GT Downloded From: on 1/3/218 Terms of Use: