Scramjet Isolators. Subscript c core flow t total w wall

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1 Professor Mihael K. Smart Chair of Hypersoni Propulsion Centre for Hypersonis The University of Queensland Brisbane 7 AUSTRALIA m.smart@uq.edu.au ABSTRACT Sramjet operation in the lower hypersoni regime between Mah and 8 is haraterized by what is alled dual-mode ombustion. In this situation disturbanes generated by heat-release in the ombustor an propagate upstream of fuel injetion to affet the operation of the inlet. The method use to alleviate this problem is installation of a short dut between the inlet and the ombustor known as an isolator. This artile desribes the flow phenomenon that exits in the isolator in these situations and presents some of the urrent methodologies and analysis tehniques for sramjet isolator design. NOMENCLATURE A area (m ) p C f D f st F h pr H t M P Q R Re s T speifi heat (J/kgK) skin frition oeffiient hydrauli diameter (m) stoihiometri ratio stream thrust (N) heat of ombustion (J/kg of fuel) total enthalpy (K basis) (J/kg) Mah number pressure (Pa) heat loss to the struture (J/kg) gas onstant (J/kgK) Reynolds number shok train length (m) temperature (K) V veloity (m/s) x axial distane (m) φ equivalene ratio ϑ onstant in mixing urve γ ratio of speifi heats θ boundary layer momentum thikness (m) η ombustion effiieny ρ density (kg/m ) τ shear stress (Pa) Subsript ore flow t total w wall. INTRODUCTION Sramjet operation in the lower hypersoni regime between Mah and 8 is haraterized by what is alled dual-mode ombustion. Figure shows a shemati of a sramjet powered vehile operating in this way. In this instane, flow is ompressed by shok waves in the forebody and inlet, and is supplied to the RTO-EN-AVT-8 -

2 Report Doumentation Page Form Approved OMB No Publi reporting burden for the olletion of information is estimated to average hour per response, inluding the time for reviewing instrutions, searhing existing data soures, gathering and maintaining the data needed, and ompleting and reviewing the olletion of information. Send omments regarding this burden estimate or any other aspet of this olletion of information, inluding suggestions for reduing this burden, to Washington Headquarters Servies, Diretorate for Information Operations and Reports, Jefferson Davis Highway, Suite, Arlington VA -. Respondents should be aware that notwithstanding any other provision of law, no person shall be subjet to a penalty for failing to omply with a olletion of information if it does not display a urrently valid OMB ontrol number.. REPORT DATE SEP. TITLE AND SUBTITLE Sramjet Isolators. REPORT TYPE N/A. DATES COVERED - a. CONTRACT NUMBER b. GRANT NUMBER. PROGRAM ELEMENT NUMBER 6. AUTHOR(S) d. PROJECT NUMBER e. TASK NUMBER f. WORK UNIT NUMBER 7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES) Centre for Hypersonis The University of Queensland Brisbane 7 AUSTRALIA 8. PERFORMING ORGANIZATION REPORT NUMBER 9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES). SPONSOR/MONITOR S ACRONYM(S). DISTRIBUTION/AVAILABILITY STATEMENT Approved for publi release, distribution unlimited. SPONSOR/MONITOR S REPORT NUMBER(S). SUPPLEMENTARY NOTES See also ADA66. High Speed Propulsion: Engine Design - Integration and Thermal Management (Propulsion a vitesse elevee : Coneption du moteur - integration et gestion thermique). ABSTRACT Sramjet operation in the lower hypersoni regime between Mah and 8 is haraterized by what is alled dual-mode ombustion. In this situation disturbanes generated by heat-release in the ombustor an propagate upstream of fuel injetion to affet the operation of the inlet. The method use to alleviate this problem is installation of a short dut between the inlet and the ombustor known as an isolator. This artile desribes the flow phenomenon that exits in the isolator in these situations and presents some of the urrent methodologies and analysis tehniques for sramjet isolator design.. SUBJECT TERMS 6. SECURITY CLASSIFICATION OF: 7. LIMITATION OF ABSTRACT SAR a. REPORT unlassified b. ABSTRACT unlassified. THIS PAGE unlassified 8. NUMBER OF PAGES 9a. NAME OF RESPONSIBLE PERSON Standard Form 98 (Rev. 8-98) Presribed by ANSI Std Z9-8

3 ombustor at supersoni onditions. Combustion of fuel with the inoming air generates a large loal pressure rise and separation of the boundary layer on the surfaes of the ombustor dut. This separation, whih an feed upstream of the point of fuel injetion, ats to further ompress the ore flow by generating a series of shok waves known as a shok-train. A short length of dut, alled the isolator, is usually added to the sramjet flowpath upstream of the ombustor to ontain this phenomenon and stop it from disrupting the operation of the inlet. In some engines, the ombination of diffusion in the isolator and heat release in the ombustor deelerates the ore flow to subsoni onditions. In this instane the ore flow must then re-aelerate through Mah in what is known as a thermal throat. Figure : Shemati of a sramjet operating in dual-mode (NASA). Dual-mode ombustion an produe large pressure levels in the ombustor and nozzle, generating high levels of thrust. This flow is affeted by many parameters, inluding the state of the boundary layer in the isolator, the flow Mah number exiting the inlet, the area distribution of the ombustor, and the position and number of fuel injetion stations. As the separated regions on the surfaes of the isolator and ombustor are seen by the ore flow as blokage, sramjet engines operating in dual-mode an be thought of involving fluid-dynami variable geometry. At speeds above Mah 8, the inreased kineti energy of the airflow through the engine means that the ombustion generated pressure rise is not strong enough to ause boundary layer separation. Flow remains attahed and supersoni throughout in the instane, and the engine operates as a pure sramjet. The artile will first desribe the flow struture that ours in the isolator of a dual-mode sramjet. Next, a diffuser model appliable to the analysis of dual-mode sramjet ombustion will be presented. Some results of the analysis will then be ompared to experiments.. FLOW STRUCTURE IN A SCRAMJET ISOLATOR The struture of the supersoni flow in onfined duts under the influene of a strong adverse pressure gradient is of interest in the design of sramjet isolators. As shown in the shemati of Fig., the pressure gradient is imposed on the inoming supersoni flow in the form of shok waves. If there were no boundary layer, a normal would form in a plane. However, the presene of an inoming boundary layer produes a series of normal or oblique shoks that an spread the pressure rise over a length of many dut diameters. This phenomenon, known as a pseudo shok or shok-train is haraterized by a region of separated flow next to the wall, together with a supersoni ore that experienes a pressure gradient due to - RTO-EN-AVT-8

4 the area restrition of the separation, forming a series of rossing oblique shoks in the ore flow. A mixing region also grows between the ore and separated flows, balaning the pressure rise in the ore against the shear stress on the boundary of the separation. Finally, the flow reattahes at some point and mixes out to onditions that math the imposed bak-pressure. Being able to predit the length sale of this flow struture is the key omponent of isolator design for dual-mode sramjets. Figure : Shemati of flow struture in an isolator. Important work on this phenomenon was performed by MLafferty in the 9 s and by Waltrup and Billig in the early 97 s. In this researh it was observed that for a given imposed pressure rise (ΔP/P), the length over whih the shok train spread varied with D / θ / and inversely with (M )(Re θ ) /, where D is the dut diameter, M is the Mah number of the inflow, θ is the momentum thikness of the boundary layer and Re θ is the Reynolds number based on momentum thikness. Based on experiments in round duts with inoming Mah numbers between. and.7, Waltup and Billig found that thiker boundary layers lead to longer shok trains,and developed the following empirial orrelation for s, the distane over whih the shok struture (or pressure rise) is spread: / sm ( )(Re θ ) P P = Δ + 7 Δ / / D θ P P () Figure below, taken from Ref., shows the form of the simple quadrati orrelation in ΔP/P in omparison to the data used to develop the orrelation. RTO-EN-AVT-8 -

5 Figure : Correlation of experimental shok train data. It has been postulated by many authors that the pressure gradient experiene by the ore flow in the dut must be equal to the pressure gradient that an be supported by shear in the separated region. Based on a large amount of experimental data at different Mah numbers, Reynolds numbers and in different dut geometries, Ortwerth determined that the rate of pressure rise (diffusion) in a dut is diretly proportional to the dynami pressure of the inoming flow and the skin frition oeffiient at the initial point of separation in the dut, and inversely proportional to the dut hydrauli diameter. From this he developed a diffuser model for separated flow in duts whih an be expressed as: dp 89 ρv C f ( ) () dx D H where D H is the hydrauli diameter of the dut, C f is the frition oeffiient at the initial separation point. In essene, this relationship supplies the ability to determine a length sale over whih pressure rise must be spread in a dut. It will be used in the next setion of this paper as the extra equation needed to perform quasi-one-dimensional alulations of flow properties in separated duts.. DIFFUSER MODEL FOR SCRAMJET ISOLATOR FLOW ANALYSIS Analysis of the ombustion proess in a sramjet usually involves quasi-one-dimensional yle analysis methods. While the real ombusting flow in a sramjet is far from uniform at any ross-setion throughout the engine, when used properly, these tehniques provide an effiient means of modeling isolator and ombustor region of a sramjet. While some methods simply jump from the start to the end of the ombusting zone, the method presented in this artile enables predition of the pressure distribution in the entire region of the engine affeted by ombustion, therefore enabling omparison with experimental pressure measurements. These methods follow diretly from the lassial quasi-one-dimensional gasdynamis presented by Shapiro 6, with the addition of Ortwerth s diffuser model to lose the equation set. A differential element of the separated flow in a dut is shown in Fig.. Here the area of the ore flow passing through the dut (A ), is equal to the geometri area of the dut (A) if flow is attahed, but is less - RTO-EN-AVT-8

6 than A for separated flow. Fuel and air are burning in this element, and a frition fore dfr = τ w A w is applied by the walls, together with a heat loss in the amount dq. For simpliity of analysis, the flow is assumed to be that of a alorially perfet gas with onstant ratio of speifi heats, γ, gas onstant R, and speifi heat at onstant pressure, p. Combustion heat release is modeled through the use of a heat of ombustion, h pr, and the hange in total enthalpy of the flow as it traverses the element is: dh = h f dφ dq () t pr st where f st is the stoihiometri fration of fuel to air, and dφ is the equivalene ratio of fuel that ombusts in length dx. The orresponding hange in the total temperature of the flow is therefore dt t = dh t / p. The wall shear stress is related to a skin frition oeffiient through τ w = C f ρv /, and A w = Adx/D, where D is the hydrauli diameter of the dut. dq p+dp m& P T ρ V M A A dfr A + da A + da T+dT ρ+dρ m& V+dV M+dM dx Figure : Differential element of separated flow. The differential onservation equations of mass, momentum and energy for the element, are given by: dρ dv da ρ + V + A = () dp γm Cdx f γm A dv + + = () p D A V dt γ dv γ dtt + M = M + T V T t (6) Note that these equations all apply to the ore flow area, but frition and heat loss are based on the geometri area. Together with the equation of state for the gas and the definition of Mah number (in differential form): dp dρ dt = (7) p ρ T RTO-EN-AVT-8 -

7 dm dv dt + = (8) M V T we have five equations to relate the eight variables. Following Shapiro 6, area hange (da/a) and total temperature hange (dt t /T t ) are treated as independent variables. If the flow is attahed, this loses the equation set and all -D axial property distributions in the dut an be alulated as desribed by the influene oeffiients of Shapiro. For separated flows, however, an extra equation is needed for the extra variable, A. This is supplied by Ortwerth s diffuser relation (eqn ). After a signifiant amount of algebrai manipulation of equations,-7, the following differential relation for Mah number is obtained: dx C dm ( ) / f γ dp p dtt M D = M γ M A A Tt A A (9) This related the hange in Mah number to the amount of diffusion (dp/p), the amount of heat release (dt t /T t ), and the axial distribution of C f. This must be integrated in onjuntion with the following relation for A /A: { ( )} dp ( ) d( A / A) M γ A / A γ M γ dt A A M A A p A A D T + dx t = C + f + + M / γ / / t () To determine the axial distributions of Mah number and A /A in duts with speified area A(x) and prior knowledge of the heat release distribution, T t (x) and C f, these equations an be integrated with a standard ODE solver for multiple equations. This methodology will now be applied to a sramjet vehile flying at Mah 7 and a dynami pressure of kpa. In keeping with the notation of Heiser and Pratt 7, station is in the freestream flow ahead of the vehile, and a streamtube with area A is aptured and proessed by the engine. Station is downstream of the vehile forebody shok and represents the properties of the flow that enters the inlet. Station is at the inlet throat, whih is usually the minimum area of the flowpath, and the length between stations and is referred to as the isolator. Station represents the start of the ombustor, and fuel and air is mixed and burned by the end of the ombustor at station. The nozzle inludes an internal expansion up to station 9, and an external expansion to station at the end of the vehile. Assuming a fairly typial forebody/inlet ompression, the properties at the inlet throat (station ) will be assumed to be M =.6, p = kpa, T = 6 K, H t =. MJ/kg. The axial distribution of properties in a round isolator/ombustor dut with an initial diameter of.6m and a divergene with area ratio of will be alulated for different fuelling levels. The start of the isolator is assumed to be at x =. m, and hydrogen fuel (h pr = M/kg) is injeted at x =. m (the start of the ombustor). The amount of fuel that is allowed to reat with the air at a partiular station is ditated by a mixing effiieny urve, η (Χ), that takes the form: η η ϑχ + ( ϑ ) Χ =, tot () where η,tot is the ombustion effiieny at the end of the ombustor, Χ = (x-x)/(x-x) and ϑ is an empirial onstant of order to whih depends on the rate of mixing 7. For the urrent study η,tot was - 6 RTO-EN-AVT-8

8 set to.8 at all times and a value of ϑ =. was used. These values orrespond to robust ombustion in the engine. Making use of eqn., the heat release urve is therefore: ( φη ) T = T + h f dq () t t pr st / p Skin frition was alulated assuming a onstant skin frition oeffiient of C f =. and heat loss to the struture (dq) was alulated using Reynolds analogy and an assumed wall temperature of T w = 6 K. Given the limitation of onstant γ, R and p in the analysis, eqns. 9 and are integrated in setions along the dut. In the isolator setion upstream of fuel injetion, values of γ =.7, R = 87 J/kg/K and p = 6 J/kg/K were used. In the ombustor, average values of γ =., R = 97 J/kg/K and p = J/kg/K were used, so as to model the properties of the real fuel/air/ombustion produts mixture whih vary along the length of the ombustor. Figure shows alulated -D flow properties in the dut for fuelling at an equivalene ratio of φ =.. In the isolator setion of the dut the Mah number redues and the pressure and temperature inrease due to the ation of frition on the dut surfaes. At the start of the ombustor, flow properties are realulated to be onsistent with the values of γ and R used in the ombustor integration, while onserving fluxes of mass, momentum and total enthalpy aross the boundary between the isolator and ombustor. Fuel is also added, and ombustion along the dut leads to a drop in the Mah number, an inrease in the temperature, and the pressure varies smoothly in response to the ompeting effets of ombustion and area inrease. The peak pressure and temperature in the dut are P/P =.9 and T/T =.6, and the minimum Mah number is M =.8. The analysis results in an estimate of the one-dimensional supersoni properties of the flow as it exits the ombustor at x =. m. M =.6, p =kpa, T = 6 K, H t =.9 MJ/kg, φ =. A/A M p/p T/T. A/A, A /A... M, p/p,t/t Isolator Combustor x(m) Figure : Fuelling at φ =.; attahed flow through the isolator/ombustor dut. As the fuelling level is inreased, the pressure rise in the dut an reah the point where flow separation an our. In the urrent analysis the well known separation riterion of Korkegi 8 are used to determine if this ours. When this does happen, an iterative tehnique is required to determine the axial position of separation, after whih the ore flow area is less than the geometri area until re-attahment ours. It has RTO-EN-AVT-8-7

9 been found that in all instanes there is a unique position for the separation point that allows the flow to re-attah smoothly in the divergent setion. Furthermore, if the ore flow redues to subsoni onditions in the separated region, the flow re-attahes subsonially and then re-aelerates through a thermal throat at an axial position that an be alulated a priori, as outlined in Shapiro 6. Figure 6 shows the alulated properties for a fuelling level of φ =.7. Here the pressure rise is high enough to separate the flow, and the analysis has been iterated to determine a separation point at x =.8 m. The ore flow begins diffusing at this point at a rate ditated by eqn., reahing a minimum area of A /A =.8. Combustion of fuel ats to push the flow towards re-attahment, whih ours at x =. m (downstream of fuel injetion) with M =.7. After re-attahment the Mah number ontinues to drop to a minimum of M =.87, and the pressure ontinues to rise to a maximum of P/P =., after whih the flow aelerates under the ation of the inreasing area to leave the ombustor supersonially. M =.6, p =kpa, T =6K,H t =.9 MJ/kg, φ =.7 A/A, A /A A/A A /A M p/p T/T Separation.... M, p/p,t/t Re-attahment Isolator Combustor x(m) Figure 6: Fuelling at φ =.7; separated flow with a supersoni re-attahment. Figure 7 shows the alulated properties for a fuelling level of φ =.8. One again the pressure rise is high enough to separate the boundary layer, but in this instane the inreased ombustion has pushed the separation well upstream of fuel injetion to x =.99 m. Furthermore, the Mah number of the ore flow has dropped below Mah to form what is known as a thermal throat. After separation the ore flow redues in area to a minimum of A /A =.8 at the start of the ombustor. The ombustion then ats to push the ore flow to re-attahment, and the Mah number drops through M = with re-attahment at x =.8 with M =.96. The pressure also peaks at the point of re-attahment at P/P =.. The flow then re-aelerates through a thermal throat at x =.9 m and leaves the ombustor supersonially. There is an important disussion in Shapiro 6 on the nature of a thermal throat and the manner in whih attahed flow an pass through the soni point. - 8 RTO-EN-AVT-8

10 M =.6, p =kpa, T =6K,H t =.9 MJ/kg, φ =.8 A/A A /A M p/p T/T.. A/A, A /A Separation Re-attahment.. M, p/p,t/t Thermal Throat Isolator Combustor x(m) Figure 7: Fuelling at φ =.8; separated flow with a thermally throated. A omparison of Figs., 6 and 7 shows the upstream progress of the ombustion influene with inreasing heat release. For φ =.8, the separation is approximately half way along the isolator, and a designer would have to deide if extension of the isolator is justified to allow for inreased ombustion. While it is reognized that this analysis involves the signifiant assumption of a perfet gas, it does however ontain all the physial attributes that are exhibited by real flows. Similar analyses of ombustion flows using finite volume tehniques and equilibrium hemistry are presented by Auslender & Smart 9.. CONCLUDING REMARKS The key feature of isolator design is the hoie of the length required to isolate the inlet from influenes propagating upstream from the ombustor. Determination of this length requires modeling of separated, diffusing flows in internal duts. The diffuser model of Ortwerth has been implemented here as part of a quasi-one-dimensional yle ode for the alulation of these flows. Given the distribution of heat release in the ombustor and the isolator/ombustor geometry, this ode predits the length of the upstream influene and hene the required isolator length.. REFERENCES Matsuo, K., Miyazato, Y. and Kim, H., 999, Shok train and pseudo-shok phenomena in internal gas flows, Progress in Aerospae Sienes,, p-. MLafferty, G.H., Theoretial pressure reovery through a normal shok in a dut with initial boundary layer, Journal of the Aeronautial Sienes, Vol., No., 9, p69. Waltrup, P.J. and Billig, F.S., Struture of shok waves in ylindrial duts, AIAA journal, Vol., No., 97, pp -8. Ortwerth, P.J.,, Sramjet Vehile Integration, Sramjet Propulsion, Progress in Astronautis and Aeronautis, AIAA Washington DC, Chapter 7. RTO-EN-AVT-8-9

11 Pandolfini, P.P., 986, Instrutions for using ramjet performane analysis (RJPA) IBM-PC Version., JHU-APL NASP-86-. Shapiro, A.H., 9, The dynamis and thermodynamis of ompressible fluid flow, John Wiley & Sons, New York. Heiser, W.H. and Pratt, D.T., 99, Hypersoni Airbreathing Propulsion, AIAA Eduation Series. Korkegi, R.H., 97, Comparison of shok indued two- and three-dimensional inipient turbulent separation, AIAA Journal (), p-. Auslender, A.H., and Smart, M.K.,, Comparison of Ramjet Isolator Performane with Emphasis on Non-Constant Area Proesses, Joint Army-Navy-NASA-Air Fore (JANNAF) Meeting, Monterey, California. - RTO-EN-AVT-8