Numerical Simulation of Gas Turbine Swirl-Stabilized Injector Dynamics

Transcription

1 Numercal Smulaton of Gas Turbne Swrl-Stablzed Inector Dynamcs Shanwu Wang, Shh-Yang Hseh, Vgor Yang The Pennsylvana State Unversty Unversty Park, P 1680, US I bstract comprehensve numercal analyss has been conducted to nvestgate the vortcal flow dynamcs and acoustc response of a gas-turbne swrlstablzed nector. The theoretcal formulaton s based on the complete conservaton equatons of mass, momentum, and energy n three dmensons. Turbulence closure s acheved by means of the large-eddy-smulaton (LES technque. The compressble verson of the Smagornsky eddyvscosty model s employed to descrbe the subgrdscale turbulent motons and ther effect on large-scale structures. The governng equatons and the assocated boundary condtons are solved by a fntevolume, dam-bashforth predctor-corrector scheme along wth the mplementaton of the message passng nterface (MPI parallel computng archtecture. Detaled flow structures are studed for two dfferent swrl numbers. Results show that the nternal flowfeld n the nector s ntrnscally unsteady and subect to shear and centrfugal nstabltes. The unsteady flow evoluton and vortex breakdown are clearly vsualzed and can be explaned on theoretcal bases. The unsteadness may be related to perodc vortex sheddng, vortex breakdown and breakup, mode competton, and other phenomena that are senstve to the swrl number. Introducton The unsteady flow dynamc nteracton wth chemcal reactons n combuston chamber has hndered the development of gas turbne engnes for years. The resultant flow oscllatons may reach certan level to nterfere wth proper engne operaton and eventually may sgnfcantly shorten the engne lfetme. lthough t s well known that combuston nstablty s a consequence of the transent response of flame dynamcs to local flow oscllatons n a confned volume, the trggerng mechansm that leads to the onset of combuston nstablty s stll unclear. Therefore, t s essental to specfcally dentfy the most mportant physcal processes for drvng nstabltes n order to establsh a knowledge-based desgn methodology for successful development of gas turbne combuston systems. Swrl-stablzed nectors have been commonly used n modern gas turbne engnes as an ad to stablze the hgh ntensty combuston process and to promote effcent clean combuston. One of the most mportant flow characterstcs produced by swrlstablzed nectors s the central torodal recrculaton zone (CTRZ [1], whch serves as a flame stablzaton mechansm. The flows n ths regon are generally assocated wth hgh shear rates and turbulent ntensty resultng from vortex breakdown so that large-scale unsteady flow motons occur. The flow oscllatons may couple resonantly wth fundamental acoustc modes n the combustor, causng combuston nstabltes. Snce the flow felds generated by swrl-stablzed nectors play an mportant role n defnng the stochometry and flud dynamcs of the prmary combuston zone, t s thus necessary to nvestgate the flow response and acoustc couplng n the nectors for dagnosng the cause of the nstablty. The purpose of ths work s to conduct a comprehensve numercal nvestgaton nto the detaled flow structures and the effects of the swrl number on the stablty of a swrl-stablzed nector. Ph.D. Student, Department of Mechancal Engneerng. Research ssocate, Department of Mechancal Engneerng. Professor, Department of Mechancal Engneerng. 1

2 Theoretcal and Numercal Framework Governng equatons The basc concept of LES s that the large-scale turbulent structure s drectly computed and small dsspatve structure s modeled. Mathematcally, the LES methodology begns wth flterng of small-scale effects from large-scale motons n the full conservaton equatons. fltered (or resolved varable, denoted by an overbar, s defned as φ ( x = φ(x G(x, x d x (1 Ω where Ω s the entre doman and G s the flter functon, whch determnes the sze and structure of the small scales. To account for varable densty effects, the flterng operaton gven by Eq. (1 s augmented wth Favre decompostons of the form φ = φ φ, φ = ρφ / ρ ( fter applyng the flterng operaton to the nstantaneous governng equatons, one obtans the fltered equatons of moton to be solved n largeeddy smulatons. The Favre-fltered conservaton equatons of mass, momentum, and energy can be expressed n the followng conservatve forms: ρ ρ u t = 0 ρ u ( ρu u pδ = t ρe t t where [( ρe t p u ] = l ( u τ q u l u τ = µ δ µ ( 3 = λ( T / ( τ τ H u e = e 1/ u u, e = h p / ρ q t (3 (4 (5 In the above equatons, ρ, u, p, T, e t, h, µ, and λ represent the densty, velocty components, pressure, temperature, specfc total energy, specfc enthalpy, vscosty, and thermal conductvty, respectvely, and τ represents the vscous stress tensor. The unclosed subgrd-scale terms n Eqs. (3-(5 are the subgrd stresses and subgrd energy fluxes. S τ Subgrd-scale model u = u, H Turbulence closure of the fltered governng equatons can be acheved wth the mplementaton of an approprate subgrd-scale model. The Favreaveraged generalzaton of the Smagornsky model proposed by Erlebacher et al.[] s employed n the present study. The subgrd stress terms and respectve counterparts n the energy equaton are modeled usng the Smagornsky eddy-vscosty model for compressble flows coupled wth a gradent transport model to smulate energy transport. The subgrd stress τ s modeled as follows: δ τ τ kk = CR ρ S ( S Sll (6 3 3 τ = C ρ S S (7 kk where I δ 1 1/ S = ( SS Here, the dmensonless quanttes C R and C I represent the compressble Smagornsky constants, wth beng the flter wdth. The subgrd energy flux term H H s modeled as C R h u = ρ S u (8 Pr t where the constant Pr t represents the turbulent Prandtl number. The constants C R = 0.01 and C I = are adopted n the current work. The value of 0.5 s employed for Pr t. Numercal method The theoretcal formulaton outlned above s solved numercally by means of a densty-based, fnte-volume methodology. The spatal dscretzaton employs fourth-order and second-order, centraldfferencng schemes for convectve terms and vscous terms, respectvely, n generalzed

3 coordnates. Temporal dscretzaton s obtaned usng a second-order, four-stage Runge-Kutta ntegraton method. Further effcency s obtaned by mplementng an MPI (Message Passng Interface parallel computng archtecture wth a mult-block doman composton technque. Results and Dsscuson The physcal model ncludes the nternal flowfeld n a swrl-stablzed nector. The external regon downstream of the nector s also consdered to provde a complete descrpton of the flow development. The nector [3] conssts of a mxng duct and a fuel nozzle located coaxally upstream of the mxng duct, as shown n Fg. 1. The mxng duct ncludes a center cylndrcal duct, two annular ducts, and three passages correspondng to the three ducts, respectvely. Those passages are spaced radally outward from each other. Three sets of ar swrlers, denoted as S 1, S, and S 3, respectvely, are located upstream of the ar-passages, and the frst and second swrlers are counter-rotatng relatve to the x-axs. The mxng duct measures a length of 8 mm, and the frst duct outlet has a dameter of 3 mm. The computatonal doman s carefully chosen such that the outer boundares n the x and r drectons are suffcently far enough from the nector ext to mnmze the propagaton of boundary-nduced dsturbances nto the computatonal doman. The entre grd system has 1.9 mllon ponts, of whch 0.9 mllon ponts are located wthn the nector. total number of 54 computatonal blocks are used. The baselne flow condton n the current study ncludes an ambent pressure of 1 atm, an nlet temperature of 93 K, and an nlet mass flow rate of kg/s. The correspondng Reynolds number based on the dameter and average velocty at the nector outlet s Calculatons are conducted for two dfferent sets of swrl vane angles. The low swrl-number case has swrl vane angles of S 1 = 30, S = -45, and S 3 = 50, and the hgh swrl-number case has S 1 = 50, S = -60, and S 3 = 70. Fgures 3 and 4 show the snapshots of the vortcty magntude contours on the x-y and y-z planes for the low and hgh swrl-number cases, respectvely. The flow patterns exhbt two common features as follows. The frst s the vortex breakdown due to the radal-entry swrlng flows. CTRZ s found downstream of the center body due to ths vortex breakdown. Because of the strong shear layer between the nlet passage and CTRZ, a strong vortcty layer s produced, whch subsequently rolls, tlts, stretches, and breaks up nto small vortcty bulbs. These vortcty bulbs are then convected downstream and nteract wth the surroundng flow structures. The evoluton of these vortex structures may serve as a source of low-frequency flow oscllatons. Fgure 5 presents the power spectral densty (PSD of pressure oscllatons at the nector ext for both cases, showng a rather broadband behavor. From the experments conducted by Cohen and Hbshman [4], t was found that a swrl-stablzed nector closely smlar to those examned n ths study would cause preferental amplfcaton and nstablty couplng of pressure fluctuatons n the range of Hz. Ths fndng, however, was not observed heren probably because no external forcng was mposed at the nlet n the present calculatons as opposed to the experments. Nonetheless, the flowfelds tend to exhbt low-frequency oscllatons when the swrl number ncreases, as shown n Fg. 5 for the hgh swrl number case. Further study of the dynamcal behavor of the nector and ts response to externally mposed acoustc forcng s currently underway. The second phenomenon s the hgh-frequency vortex sheddng from the tp of the gude vane between the frst and second passages, arsng from the Kelvn-Helmholtz nstablty. Because of the opposton of the swrler vane angles, two hghly swrled counter-rotatng flows wth dfferent veloctes, onng at the rm tp, produce a strong shear layer that promotes mxng process. The flow at the rm tp act as a vortex source,.e., vortces are generated and shed downstream sequentally wth alternatng drecton, smlar to those produced at the tralng edge of an arfol at a hgh angle of attack. The ensung nfluence on the fuel/ar mxng may be sgnfcant because the strong vortcal flow wll nteract wth the thn fuel flm on the surface of the gude vane between the second and thrd passages. Fgures 3 and 4 also present the modecompetton between two maor dynamcal phenomena vortex breakup n the CTRZ and vortex sheddng near the gude vane. For low swrl-number flows, the two phenomena coexst well and the vortex sheddng phenomenon s more organzed, and several well-defned harmoncs n the pressure-frequency spectrum are observed n Fg. 5 When the swrl strength ncreases, the nteractons between the shed vortces and CTRZ flow become stronger, and the mode-competton appears. For hgh swrl flows, the CTRZ sze and strength ncrease, and the vortex streets orgnatng from the tps of the gude vanes are suppressed and become dsordered n the downstream. In addton, the low-frequency content of the pressure spectrum ncreases sgnfcantly. The vortcty felds on the y-z plane n Fgs. 3 and 4 show the asymmetrcal flow oscllatons n the azmuthal 3

4 drecton, further revealng the complcated flow structures. Fgure 6 shows the contours of mean axal velocty supermposed on the streamlne patterns on the x-y plane. CTRZ, where the mean axal velocty s negatve near the center lne, s clearly observed n both cases. The sze and the onset locaton of the CTRZ, however, are qute dfferent. In swrlng flows, an adverse pressure gradent n the axal locaton s requred to balance the centrfugal force. When the swrl strength s large enough, the low-pressure core near the x-axs may nduce vortex breakdown and result n a CTRZ. In the hgh swrlnumber case, because the azmuthal velocty s hgher than that n the low swrl-number case, a larger lowpressure regon s requred to balance the centrfugal force. Ths explans that the sze of the CTRZ n the hgh swrl-number case s much larger than that wth the small swrl number. It s also observed n Fg. 6 that the hghest axal velocty for the low swrlnumber case occurs near the center body of the fuel nozzle, whle n the same regon the axal velocty s negatve for the hgh swrl-number case. The contours of the mean turbulent knetc energy for both cases are presented n Fg. 7. Two hgh turbulent-knetc-energy (tke regons are observed n regons downstream of the center body and the frst gude vane, where the vortex breakdown and vortex sheddng occur. The strong vortcal motons promote locally the mxng between the fuel and ar. The two hgh tke regons almost merge together at the ext of the nector for the hgh swrl-number case, but there stll exsts a gap for the low swrl-number case. of a swrl-stablzed nector. The formulaton treats the unsteady, three-dmensonal conservaton equatons, wth turbulence closure acheved usng the large eddy smulaton technque. Results show that the swrl-stablzed nector consdered n the present study s effectve n mxng the fuel and ar. Varous unsteady flow characterstcs, such as vortex sheddng and vortex breakdown as well as ther nteractons, are nvestgated n depth for cases wth dfferent swrl numbers. cknowledgements Ths work was sponsored by the NS Glenn Research Center under Grant NG The support and encouragement of Kevn Bresacher s greatly apprecated. References 1. Gupta,.K., Llley, D.G., and Syred, N., "Swrlng flows", bacus Press, Erlebacher, G., Hussan, M. Y., Spezale, C. G., and Zang, T.., Toward the Large Eddy Smulaton of Compressble Turbulent Flows, Journal of Flud Mechancs, Vol. 38, 199, pp Graves, C.B., Outer Share Layer Swrl Mxer for combustor, Unted State Patent , Feb Cohen, J., and Hbshman, J.R., n Expermental Study of Combustor r Swrler coustc and Flud Dynamc Senstvtes, presented at PERC 9th Symposum on Propulson, Cleveland, OH, October 1-, 1997 Conclusons comprehensve numercal analyss has been conducted to nvestgate the vortcal flow dynamcs 4

5 r S S3 Swrler Fuel Nozzle 16 mm S1 S S3 S1 r Fg. 1 Schematc dagram of swrl-stablzed nector Ω: 1/s Fg. Grd system t = 1.01 ms t = 1.04 ms t = 1.10 ms Fg. 3 Snapshots of vortcty contours on x-y and y-z planes, low swrl number 5

6 Ω: 1/s t = ms t = ms t = ms Fg. 4 Snapshots of vortcty contours on x-y and y-z planes, hgh swrl number Probe: p3:04 ( x = 0.03 m, y = 0.015m 1.8 Probe: p3:04 ( x = 0.03m, y = 0.015m PSD PSD a frequency, Hz b frequency, Hz Fg. 5 Power spectral densty: a low swrl number and b hgh swrl number 6

7 a u x : m/s b u x : m/s Fg. 6 Contours of mean axal velocty and streamlne pattern: a low swrl number and b hgh swrl number a tke: m /s tke: m /s b 0 Fg. 7 Contours of turbulence knetc energy: a low swrl number and b hgh swrl number