A STUDY ON THE PHYSICS OF SUPERSONIC MIXING FIELD WITH INJECTION AT DIFFERENT ANGLES

Transcription

1 Proceedngs of the Internatonal Conference on Mechancal Engneerng 23 (ICME23) December 23 Dhaka Bangladesh ICME3-FL-18 A STUDY ON THE PHYSICS OF SUPERSONIC MIXING FIELD WITH INJECTION AT DIFFERENT ANGLES Mohammad Al and Shakl Ahmed Department of Mechancal Engneerng Bangladesh Unversty of Engneerng and Technology Dhaka 1 Bangladesh. ABSTRACT A numercal study on mxng feld of hydrogen and ar has been performed by solvng two-dmensonal full Naver-Stokes equatons. An explct Harten-Yee Non-MUSCL Modfed-flux-type TVD scheme has been used to solve the system of equatons and a zero-equaton algebrac turbulence model to calculate the eddy vscosty coeffcent. The man obectve of ths study s to study the physcs of the flow feld and fnd out the means of ncreasng the mxng effcency of a supersonc combustor. The flow feld has been studed by varyng the hydrogen necton angle made wth the drecton of ar stream. The results show that n upstream of nector the boundary layer s thckened by the backward-facng step and the necton on thck boundary layer enhances mxng. The necton system changes the angles and postons of dfferent shocks n the flow feld. Incorporatng the varous effects necton wth moderate angle shows hgher penetraton and mxng of hydrogen wth ar and ts large upstream recrculaton regon has a good flame holdng capablty. Keywords: TVD scheme Backward-facng step Bow shock Reattachment shock Flame holdng. 1. INTRODUCTION The fuel necton scheme n hypersonc vehcles ncorporatng Scramet (Supersonc Combuston Ramet) engnes requres specal attenton for effcent mxng and stable combuston. Though a consderable number of researches has been carred out on mxng and combuston of fuel wth oxdzer n Scramet program stll t faces many unresolved problems. The man problems that arse n ths regard concern mxng of reactants gnton flame holdng and completon of combuston. In fact n supersonc combuston hgh penetraton and mxng of nectant wth man stream s dffcult due to ther short resdence tme n combustor as descrbed by Brown et al. [1] and Papamoschou et al. [2]. These nvestgatons showed that good mxng and hgh penetraton of nectant s dffcult for the flow of hgh Mach number. Therefore t s necessary to nvestgate the physcal mechansms that affect the mxng and combuston n Scramet engne. Several nvestgatons have been performed to analyze the mxng feld and ncrease the mxng effcency. In these nvestgatons the authors showed a number of parameters that can affect on penetraton and mxng. In an experment Rogers [3] showed the effect of the rato between et dynamc pressure and freestream dynamc pressure on the penetraton and mxng of a sonc hydrogen et nected normal to a Mach 4 arstream. In smlar flow arrangements Kraemer et al. [4] found that the relatve change n et momentum (product of gap wdth et statc pressure and nectants specfc heat rato) was drectly proportonal to the relatve sze between the flowfeld dsturbance and the upstream separaton dstance. The downstream nectant penetraton heght s drectly proportonal to the upstream separaton dstance and thus the downstream mxng s dependent on the relatve change n et momentum. Smlar conclusons were also drawn by Holdeman et al. [5] and Thayer III et al. [6]. Thayer III et al. [6] also found that the nectant concentraton of the separated regon was hgh at all condtons nvestgated. Hester et al. [7] conducted a calculaton on the penetraton and bow shock shape of a non-reactng lqud et nected transversely nto a supersonc cross flow and obtaned a correlaton between mass loss boundary layer thckness recrculaton and related parameters. Al et al. [8] studed the mxng mechansms and nvestgated mxng and combuston characterstcs for several flow confguratons. On the analyss of mxng the author observed that the backward-facng step n fnte flow confguraton plays an mportant role to enhance mxng and penetraton n both upstream and downstream of nector. Investgaton proved that wthout dffuson nectant can spread n the flow feld due to speces contnuty equatons but does not mx wth man stream. In another study Al et al. [9] searched the enhancement of mxng by varyng the nlet wdth of ar stream and 1 ICME23

2 found that the flow nlet confguraton of a supersonc combustor can play an mportant role on mxng. In present nvestgaton we numercally smulate two-dmensonal mxng flow felds for dfferent nectng angles and study the flow feld characterstcs to search better mxng and good flame holdng capablty n supersonc combustor. The geometrc confguraton of the calculaton doman and the nlet condtons of man and nectng flows are shown n Fg.1. The left boundary conssts of a backward-facng step of heght 5 mm whch was found most effcent n mxng by Al et al. [8]. The nector poston from left boundary backward-facng step heght and the nlet wdth of ar stream are kept constant. For ths study the nectng angle θ s vared from 3 ~ 15 wth 3 nterval n ant-clockwse drecton and defned as Case and 5 sequentally. The nector poston s fxed at 3 mm from left boundary. The nlet condtons of ar are used as Wedner et al. [1] except the Mach number. We choose the Mach number 5. for the man flow as the test program has been conducted over the flght Mach number range from 3. to 7. as descrbed by Rausch et al. [11]. The nlet wdths of ar and sde et are used as Al et al. [9]. Throughout the study the grd system conssts of 194 nodes n horzontal drecton and 121 n transverse drecton. 2. MATHEMATICAL MODELING The unsteady two-dmensonal full Naver-Stokes and speces contnuty equatons have been solved to analyse the mxng flow feld of hydrogen and ar. Body forces are neglected. These equatons can be expressed by U F G Fv Gv + + = + t where U = [ρρuρveρy] T F = [ρuρu 2 +pρuv(e+p)uρyu] T G = [ρvρuvρv 2 +p(e+p)vρyv] T Fv = [σxτxyσxu + τyxv + qx m x] T and Gv = [τyxσyτxyu + σyv + qy m y] T. σ x σy τ xy q x The followng terms are expressed as = λ = λ + + = τ yx = μ + 2μ T ns = κ + ρ D = 1 + 2μ + H Y x q y mx = T ns Y = κ + ρ D H. = 1 y ρd Y my = ρd Y λ = 2 μ. 3 The values of C p and H are consdered as functons of temperature and determned from the polynomal curve fttng developed by Moss [12]. The detals of transport propertes and other dfferent parameters are shown n Al et al. [8]. Temperature s calculated by Newton-Raphson method from energy equaton. The flud dynamcs s solved usng an explct Harten-Yee Non-MUSCL Modfed-flux-type TVD scheme proposed by Yee [13~14]. The backward-facng step makes the flowfeld turbulent at the present Mach number. Partcularly the recrculatons n both upstream and downstream of nector shocks and expanson of both man stream and sde et leads us to use a turbulence model. Therefore to calculate eddy vscosty we selected the zero-equaton turbulence model proposed by Baldwn and Lomax [15]. The model s modfed so that t can avod the necessty for fndng the edge of the boundary layer. Ths has been very helpful because at the necton port and adacent regon t s dffcult to defne boundary layer thckness. Accordng to the model the eddy vscosty µ t s defned as μ t = ( μ t ) ( ) μ t nner outer y y crossover y > y crossover where y s the normal dstance from the wall and y crossover s the smallest value of y at whch the value of vscosty n the outer regon becomes less than or equal to the value of vscosty n the nner regon. The values of the turbulent thermal conductvty of the mxture κ t and turbulent dffuson coeffcent of -th speces D t are obtaned from eddy vscosty coeffcent µ t by assumng a constant turbulent Prandtl and Lews number equal to.91 and 1. respectvely. They can be expressed as μ t Cp ρ D t Cp =.91 and = 1. k t k t The fnal values of µ κ and D m used n the governng equatons are μ = μ l + μ t κ = κ l + κ t D m = D ml + D t where µ l κ l and D ml are the vscosty coeffcent thermal conductvty and dffuson coeffcent for lamnar flow respectvely. More detals about the turbulence model and ts dfferent parameters can be found n Al et al. [8]. 2 ICME23

3 3. RESULTS AND DISCUSSION 3.1 The physcs of flud dynamcs Fgures 2 shows the velocty vector n both upstream and downstream of nector. A par of recrculaton forms at the upstream of the nector; one of whch s large and the other s small n sze. In case 1 the recrculatons are weak whch can be understood by the vector length n recrculaton regon. The ncrease of necton angle makes the recrculatons stronger whch can be found n cases 2 and 3. For further ncrease of nectng angle. e. n cases 4 and 5 they are not sgnfcant. The large prmary clockwse recrculaton s caused by the backward facng step and the secondary small counter-clockwse recrculaton close to nector s caused by the prmary recrculaton and the sucton of necton. The prmary recrculaton ncreases the boundary layer thckness and the necton nto a thck boundary layer causes greater penetraton resultng n hgher mxng. Due to nteracton between man flow and sde et the velocty of man flow decreases and the ar enters the upstream recrculaton. On the other hand by dffuson and convecton due to necton the nected hydrogen enters the recrculaton and mxes well wth ar. So upstream recrculatons play a vtal role on mxng and consequently cases 3 and 4 show better mxng. In downstream there s no strong recrculaton n any case. Case 3 shows a very small recrculaton ust downstream of the nector caused by the sucton of the necton and bendng of the sde et. Ths recrculaton and convecton due to necton cause better mxng n case Characterstcs of the flow feld The characterstcs of the flow feld are shown n Fgs. 3 4 and 5. Fgure 3 shows the pressure dstrbuton along the axs at 8 mm from left wall. In general pressure n downstream near bottom wall s hghest for all cases. Along vertcal drecton the pressure decreases up to the doman heght of 2. cm. Above that heght the pressure remans constant n cases 3~5 whereas n cases 1 and 2 the pressure decreases near the upper boundary of the doman. Another observaton s that wth the ncrease of necton angle pressure decreases n downstream except at the upper part. Ths s caused by the weaker reattachment shock n downstream when necton angle s ncreased. Due to strong suppresson of sde et n cases 1 and 2 caused by the hgh momentum of man flow the reattachment shock becomes stronger resultng n hgher pressure n downstream. As dffuson of hydrogen s nversely proportonal to the pressure therefore lower value of pressure ndcates hgher dffuson at downstream whch results n greater mxng rate for the cases of hgher necton angle. Other characterstc phenomena such as seperaton shock bow shock Mach dsk reattachment shock can be seen n fgures 4 and 5. Fgure 4 shows the pressure contours by whch the pressure dstrbuton and dfferent shocks can be understood. Flow seperaton s ntated by the backward facng step at left boundary. The man flow s deflected upward by the exsstance of wall at the upper part of the left boundary and the momentum of nectng flow along upward drecton. The deflecton angle frst ncreases wth the ncrease of necton angle and then decreases for further ncrease of necton angle. Therefore the deflecton angle of man flow s maxmum for case 3 (θ=9 o ) caused by the nteracton of man flow wth the hghest momentum of nectng flow. It can be ponted out that the momentum of the nectng flow along the upward drecton s maxmum when the necton angle s 9. e. case 3. The under expanded sde et rapdly expands and forms a Mach dsk and a bow shock due to the nteracton wth man flow. The sze of the Mach dsk ncreases wth the ncrease of necton angle frst and then decreases for hgher necton angle as shown n Fg. 5. Ths ncrease of Mach dsk n sze s caused by hgher expanson of sde et. We can see that case 2 has the hghest expanson of sde et n downstream resultng n largest Mach dsk among the cases consdered. For the necton angle θ=9 o the slope of the bow shock s steeper ndcatng hgh teracton between the man flow and sde et. Strong nteracton causes hgh penetraton and more unform mxng of hydrogen n downstream. The maxmum pressure and temperature n the flow feld have been found mmedately behnd the ntersecton of separaton shock and bow shock. The maxmum temperature (n case 3 t s about 243 K) occurs mmedately behnd the ntersecton of separaton shock and bow shock. In the downstream regon the reattachemnt shock s more vsble n the pressure contour of Fg. 4. The reattachemnt shock starts almost at the same poston of the bottom wall for all cases. The pressure s hgher n the upstream recrculaton regon whle t s much lower mmedately behnd the nector caused by the sucton of necton. 3.3 Penetraton and mxng of hydrogen Fgures 6 shows the penetraton and mass concentraton of hydrogen n the flow feld. In ths paper the term penetraton s referred to the edge of mxng regon n the vertcal drecton where the mole fracton of hydrogen s 5%. It can be ponted out that the penetraton and mxng of hydrogen n a numercal smulaton can occur by means of () turbulence and convecton due to recrculaton and () molecular dffuson. The backward facng step assocated wth upstream recrculaton brngs the nected hydrogen up to the left boundary n all cases. The hydrogen penetaton heght at dfferent downstream locatons can be compared from Fgs. 6 (a~e). For example at 1 cm from left boundary the penetraton heght s up to 2 cm n case 1 whereas t s 2.5 cm for case 2 and above 3 cm for cases 3 and 4. The penetraton heght of the hydrogen s hgher n cases 3 and 4 (above 3 cm) ndcatng more unform dstrbuton of hydrogen and consequently hgher mxng. In Fgs. 6 (a~e) ϕ ndcates the contour level of hydrogen mole fracton. The value of the mnmum contour level s.5 and that of the maxmum contour level s 1.. The ncrement of adacent hgher contour level s.5. For all cases (case 1~5) the mole fracton contours of hydrogen are concentrated n a narrow regon on the top of the nector as shown n Fgs. 6 (a~e) whch mght become a hgh heat release zone n the reactng flowfeld. The flame holdng requres longer resdence tme of flame n the 3 ICME23

4 burnng range and ths resdence tme strongly depends on the geometrc expason of the recrculaton zone [16]. Also the equvalence rato of fuel and oxdzer n mxture s an mportant factor for burnng because among the mxtures the stochometrc mxture strength s good for combuston. Therefore longer recrculaton zone contanng stochometrc mxture strength results n a longer resdence tme and leads to a more stable flame. Accordngly cases 3 and 4 have good flame holdng capablty because they can produce larger and elongated upstream recrculaton where most of the regon contans good proporton of hydrogen and oxygen. Agan n cases havng θ = 3 o and 15 o upstream regon contans lower mass cencentraton of hydrogen whch s not good for flame holdng. In downstream hydrogen dstrbuton s seemed to be better n cases 3 and 4 as mentond earler because of hgher expanson of sde et. 4. CONCLUSION In present paper the characterstcs of the mxng feld has been analyzed and dscussed wth numercal smulaton of two-dmensonal full Naver-Stokes equatons. Takng the drecton of ar stream as reference the necton angle was vared from 3 ~ 15 wth 3 nterval ant-clockwse. It was found that wth the ncrease of necton angle from 3 ~ 9 mxng ncreased and further ncrement of necton angle decreased the mxng effcency. Two competng phenomena were observed: ) n upstream of nector mxn was domnated by convecton due to recrculaton and ) n downstream mxng was domnated by mass concentraton of hydrogen. Small necton angle caused hgher expanson of sde et resultng n hgher Mach dsk. The ncrease of necton angle decreased the down stream pressure near the sde wall and ncreased the dffuson of hydrogen. Incorporatng all the effects the confguraton of moderate necton angle had the hgher mxng effcency and ts upstream recrculaton regon wth good proporton of hydrogen and oxygen mght act as a good flame holder n Scramet combustor. For the necton angle θ=9 o the slope of the bow shock s steeper ndcatng hgh nteracton between the man flow and sde et. Strong nteracton causes hgh penetraton and more unform mxng of hydrogen n downstream. The maxmum pressure and temperature n the flow feld was found mmedately behnd the ntersecton of separaton shock and bow shock where chemcal reacton mght start n reactng flow feld. 6. REFERENCES 1. Brown G. L. and Roshko A On Densty Effects and Large Structure n Turbulent Mxng Layer. J. Flud Mechancs vol. 64 no Papamoschou D. and Roshko A Observaton of Supersonc Free Shear Layers. AIAA Paper Rogers R. C A Study of the Mxng of Hydrogen Inected Normal to a Supersonc Arstream. NASA TN D Kraemer G. O. and Twar S. N Interacton of Two-Dmensonal Transverse Jet wth a Supersonc Manstream. NASA CR Holdeman J. D. and Walker R. E Mxng of a Row of Jets wth a Confned Crossflow. AIAA Journal vol. 5 no Thayer III W. J. and Corlett R. C Gas Dynamc and Transport Phenomena n the Two-Dmensonal Jet Interacton Flowfeld. AIAA Journal vol Hester S. D. Nguyen T. T. and Karagozan A. R Modelng of Lqud Jets Inected Transversely nto a Supersonc Crossflow. AIAA Journal vol. 27 no Al M. Fuwara T. and Leblanc J. E. 2. Influence of Man Flow Confguraton on Mxng and Flameholdng n Transverse Inecton nto Supersonc Arstream. Int. Journal Engneerng Scence Al M. and Islam A.K.M.S Effect of Manflow Inlet Wdth on Penetraton and Mxng of Hydrogen n Scramet Combustor. Proceedngs of the Eghth Asan Congress of Flud Mechancs pp December 6-1 Shenzhen Chna. 1. Wedner E.H. and Drummond J.P A Parametrc Study of Staged Fuel Inector Confguratons for Scramet Applcatons. AIAA Paper RauschV.L. McClnton C.R. and Hcks J.W Scramet Breath New Lfe nto Hypersoncs Aerospace Amerca July Moss J. N Reactng Vscous-Shock-Layer Solutons wth Multcomponent Dffuson and Mass Inecton. NASA TR Yee H.C A Class of Hgh-Resoluton Explct and Implct Shock Capturng Methods. NASA TM Yee H. C Upwnd and Symmetrc Shock-Capturng Schemes. NASA TM December. 15. Baldwn B.S. and Lomax H Thn Layer Approxmaton and Algebrac Model for Separated Turbulent Flows. AIAA Paper Tabeamaat S. JU. Y. and Noka T Numercal Smulaton of Secondary Combuston of Hydrogen Inected from Preburner nto Supersonc Arflow. AIAA Journal vol.35 no.9 September. Fg.1 Schematc of physcal model. Case 1: θ = 3 Case 2: θ = 6 Case 3: θ = 9 Case 4: θ = 12 Case 5: θ = 15 4 ICME23

5 Dstance from bottom wall (m) Pressure (N/m 2 ) Fg.3 Pressure dstrbuton at 8. cm from left wall Dstance from bottom wall (m) Dstance from left wall (m) Fg.2 Velocty vector near nector; Case 1 Case 2 Case 3 Case 4 Case5. Dstance frombottomwall (m) Dstance from left wall (m) Fg.4 Pressure (N/m 2 ) contour ϕ (2*1 4 2*1 6 2*1 4 ) ϕ s contour level; Case 1 Case 2 Case 3 Case 4 Case 5. 5 ICME23

6 Dstance from bottom wall (m) Dstance from left wall (m) Dstance from bottom wall (m) Dstance from left wall (m) Fg.5 Temperature (K) contour ϕ ( ) ϕ s contour level; Case-1 Case 2 Case 3 Case 4 Case 5. Fg.6 Mole fracton contour of Hydrogen ϕ(.5 1.); ϕ s contour level Case1 Case2 Case3 Case4 Case5 6 ICME23