Globalization

Supersonic Jet Engine Design Name: Institution: Supersonic Jet Engine Design Problem Description As a new engineer at a large aerospace company, I have been assigned a position in the engine design division as a result of a renewed interest to design a commercial supersonic aircraft, which will fly from New York to London under three hours by comparing and contrasting two competitive systems for thrust delivery in a preliminary design approach. Preliminary process of the engine design The process of the engine design will commence with specification of the engine. The description requirements presented by the manufacturer meet the market requirements and needs. The primary step in preliminary engine design process will begin with analysis of the thermodynamic cycle. Subsequently, the engine configuration along with cycle parameters and the components of the chosen performance and assessed to have the required description. By setting up the major parameters through thermodynamic analysis, the subsequent design aerodynamic design of the respective turbomachinery and related components. Also, we are going to determine the overall sizes, number of stages, efficiencies, rotational speeds and the rest f the aerodynamic parameters. On completion of the aerodynamic design, then the mechanical design components, where the mechanical features like vibrations and stress will be assessed. Figure 1: Preliminary of the process of the engine design The process will require continuous response between the various disciplines, alterations in one possibly will result to variations in another. The above illustration depicts a schematic diagram illustrating an overall design procedure. Thermodynamic Analysis Design point and the performance computations During the design point initially, the respective performance and thermodynamics of the engine will be assessed at an operating condition that is fixed. In our case, I opt for the MJ and Haran S14 with an operating state of a speed of the supersonic which ranges at M 1.5 at about 50000ft, in which this condition is where the engine is expected to cruise mostly. Ostensibly, a change in the operating condition at the design point phase would lead to a various engine with a complete geometrical difference which should be used as a locus point. The next phase comprises running off the design performance and respective calculations. Considering that the engine geometry is on a fixed position and the engine performance at various conditions evaluated for operations. The off design will be employed to trace the engine performance achieves the entire operation range. In addition, the design point and its performance along with the off-design computations will involve an engaging iterative procedure. Aerodynamic design For this design, everything will commence after definition of the flow properties from the respective analysis of the thermodynamic. This process will entail pressure losses, effectiveness, the dimensions and the rest of the parameters for aerodynamic components which can be resolved and undergo assessment. Software description I will use MATLAB for geometric computing and as a programming language appropriate for applications range. This is because it has a capability to draw data from various external sources, with inbuilt functions, with a cutting-edge plotting functions and its general documentation makes it a prime project option. Design Approach and Principles In the process of designing the jet engine with a complete logic positioning algorithm, feed and control, then is necessary segment it into subsystems. The most suitable task for this system to be executed is to create a simple model and seamless enough to epitomize an ideal system. The design approach will either be prescriptive or descriptive through morphological method or rather a mathematical model for system analysis. As earlier sated, the descriptive process comprises a design task sequence practice and with an open focus on the concepts being analysed and refinement. The engine system design for the aerospace company may develop problems if it lacks an adequate research strategy and implementation procedure. Therefore, the engine has to be fitted with modern sophisticated system of integrated fuel. Correspondingly, the main functional design mode and principles of the modern supersonic engine will include: Engine feed, Fuel pressurization, Fuel jettison, Ground and Air refuelling, Fuel transfer, Vent system, Fuelling and Defueling flow as well as heat sink. Also, a time range is allocated to the corresponding flow process while the entire system of fuel is modelled on MATLAB-Simulink through compilation of the control system pumping status, aircraft fuel tank geometry, input variables, aircraft fuel tank parameters. Combustion chamber Engine Dynamic System of Equations Where: K implies gain. τ1, τ2 represent the engine time constants. τ1 signify the engine coefficients. τ2 signifies the engine valve coefficients Engine Control Concept To avert any issues, the thrust cannot be measured and changes made in an ambient condition or during airplane maneuvers that causes engine distortion through the compressor and fan which need to be put under control. In addition, there will be need to shield the engine against harsh operational environment especially those with high temperatures and huge vibrations of the engine which ideally needs a safe operation to circumvent any instances of stall and a blow out in the combustor. Additional purpose that to deliver long hours of operation of about 20,000 hours with the engine components degrading with the level of usage for a reliable performance during the operational life since Thrust (T) as the, use fuel flow to control shaft speed, or other measured variable that correlates with thrust: T = F (N) …… Limits are executed through limitation of the fuel flow according to the rotor peed. Apparently, the optimal fuel limit shields stall and engine surges, over speed and overheating and excess-pressure and that may cause combustor blowout. Integral Controllers As it suggests, the integral controllers hold the output. It is also known as actuating signal which is directly proportionate to the respective error signal integral, Using the Oswatisch principle (1980), we can analyze and mathematically compute the integral controller. The output for the integral controller has direct proportional feature to the error signal integration, s we get Eliminating the proportionality sign, we have, We then determine the system stability by finding the root locus using the MATLAB interface. The above values provide the varying stability range ( -10, -100) as illustrated below: Figure : Root Locus Formulas Propulsive efficiency Thermal efficiency Core efficiency Transfer efficiency Overall efficiency Specific fuel consumption OPR FPR TIT ?????? = ??04 BPR Thrust coefficient Angularity coefficient Gross thrust Stage loading Corrected mass flow Flow coefficient Degree of reaction De Haller number Diffusion factor Deflection ?? = ??1 − ??2 Combustor loading Residence time Loading Combustor volume will be derived in consideration of the load combustor at a flight number of settings. Essentially, at static sea level, the highest and maximum power for the combustor loading should be less than: . This is a critical point for the combustion burner and its ability to regenerate during wind milling in the case of an engine flameout. For this to be achieved, the designs should ensure that the respective combustor loading during its highest compulsory altitude as well as its lowest Mach number for the flight and relight does not go above board (Oswatitsch, 1980). To lower the burner volume, the loading should not exceed 300 at The available wind-milling conditions. Residence time The residence time will depend on the liner length as well as the Mach number and diffuser, and should typically surpass 3ms. Long residence times nevertheless, can result in increased NOx. Figure 6: Typical burner [22] Pressure loss This may occur in the combustion chamber caused by skin friction causing a temperature rise which is known cold loss which will account for about ninety percent of the overall loss of pressure. This loss occurs due to a temperature rise is known as important loss and of remaining 10 percent. The pressure loss will be projected using the technique reference defined and is reliant on the burner optimum area, the PLF as the well and the inlet ??0 as well as ??0. Essentially, the PLF refers to a presumed value and typically ranges between 20 to 25. Efficiency The burner efficiency will be found from the combustion products chemical analysis. Referring to the fuel to air ratio as well as the constituents incompletely burnt and proportion, it is probable to compute the actual energy proportion released to the theoretic quantity accessible. Internal ducts The ducts will have a cubic splines design to let the smooth platform between the gear mechanisms in an attempt to lower the loss of pressure. Nevertheless, if there will be no loss of pressure computations to be completed, then the losses will have assumptions based on the design strategies. Inlet We will only use the basic 2D or the axisymmetric inlet that uses shocks for the purpose of diffusing the inbound air. The tabularized values of the usual shock feature applied compute the entire loss of pressure as well as Mach numbers for the subsequent shocks. Apparently, the inlet will be designed to generate an inlet solid shock initially, while lowering the Mach number to a lower value, thereafter, the venturi normal shock may decrease the number to less than one. Henceforward, the speed will be diffused in different part applying the continuity equation to a suitable value. Consequently, these calculations will undertake a flow of isentropic. To recompense, the respective absolute loos of pressure will be multiplied by a factor of 0,997 to ensure the subsonic region accounts for the entire pressure losses occurring due to skin friction. Nozzle A designed nozzle will allow the flow expansion to an absolute pressure, where the process of isentropic generates an optimum thrust. Though, owing to the losses the skin friction and the additional length and mass, a nozzle will be the only a feasible choice if the nozzle ratio of the engine pressure exceeds three, a likely case for a supersonic engine linked to pressure ratio (Goldsmith, & Seddon, 1993). Apparently, the loss of thrust allied to angularity flow surges gradually at inordinate angles of exhaust, thus the divergent section angle will be less than thirty degrees.  Discs The first stage of designing the HPC disc will incorporate the considering some stress data. The optimum design will comprise a hyperbolic disc with some Inconel solid. Nevertheless, the disc is a heavy and wide material which meets the target security line owed to rapid rotational velocities, which may cause a geometrical issue on the second stage disc. The problem will be solved by creating an opening between the central engine axis and the internal disc rim known as bore radius. For the HPC disc, we will design with the material Inconel 718 and the hyperbolic disc with a bore radius of about 4 cm as shown below: Figure 31: First stage HPC disc output file from T-AXI DISC Mechanical Design Description of Software The design was executed using the T – AXI DISK Version 2.5 where the entire system can be employed to project a multistage turbines and compressors from a limited parametric for the physical design. Target safety line The respective target safety line refers to a safety margin available until the entire material begins to give out with a default of about 10 percent. Optimization Optimization was performed using the T – AXI DISK which has an in-built function and a parametric disc through optimization of the disc to realize a design which equals the target safety line and the lowermost probable weight. Shafts For the shafts, the mechanical effectiveness of the shafts will be depending on the input parameter for the analysis of thermodynamic cycle and in this work, we assumed a 99.5 percent for the shafts. No additional shaft calculations and assumptions that were made. Baseline Engine The improved performance data for the baseline engine that served as an initial point for optimization cycle. Also, the schematic 2D engine view of the engine is attached below. Figure : Baseline engine key data Figure 9: Section baseline engine view Cycle Optimization A duo-spool axial flow with low turbofan by-pass outline was configured in the Haran S14-MJ. The entire engine design with the flow positions can be understood. Figure 10: Engine layout design with the flow stations Final Design- Comparisons of the engines Optimization for TIT and OPR The optimum OPR for the two engines TIT. The SFN as well as polytropic effectiveness are kept constant. Additional parameters are varied to maintain optimum interconnectedness between the two engine components. The figure illustrates how increasing the TIT and OPR raises the core effectiveness. The entire designs are nevertheless limited by respective temperatures of the blade metal in the turbines. The table shows the cooling flow values to keep the temperature in the respective HPT, together with the inlet uncooled LPT temperature for the respective TIT. Figure 11: Optimum OPR at different TIT: s. Figure : Required HPT cooling flow and the LPT inlet temperature The above table depicts the maximum available TIT in keeping the chosen 1644K as the LPT inlet temperature has an HPT cooling flow that is within the acceptable parameters. From this, the entire TIT was calibrated at 1644K while the OPR at 38. Consequently, these calculations will undertake a flow of isentropic. To recompense, the respective absolute loos of pressure to ensure the subsonic region accounts for the entire pressure losses occurring due to skin friction (Goldsmith, & Seddon, 1993). The figure below illustrates the association between thermal efficiency, core efficiency, overall efficiency besides SFC at the selected TIT. The transfer and propulsive effectiveness are comparatively constant along the range, and are exempted in the respective diagram. Figure : Efficiencies over the OPR With the TIT and the OPR set, the rest of the parameters with interrelationships defined below Figure : Key parametric for the design point cycle A 2D schematic view of the two engines engine is depicted below. The engine inlet is illustrated in the corresponding figure. Figure 13: Overview of MJ – Haran S14 Figure 14: Supersonic section overview of the MJ – Haran S15 inlet Component Design Supersonic Inlet Design An inlet has a 2D view, with the shocks signified in dotted lines as seen below. The total recovery pressure is 0.983 with the total length of 2,088 m. Consequently, the angle ?? of deflection was set to 9.26° to attain absolute pressure recovery combination contains a normal shock at the design point. The equivalent angle β is 55°.. Figure 15: Supersonic inlet along with some flow stations Internal ducts The presumed pressure ratios and the internal ducts lengths is seen below and a schematic interpretation is the corresponding figure. Figure : Internal Duct Data Figure : Ducts Figure 16: Ducts Compressors To employ the HPT, we lowered the inlet temperature to the respective LPT. Subsequently, the tip clearance is set to about 1 percent of the height of the blade. Also, the blade spacing is set at 20 percent of the respective upstream chord on an average stage load as well as low coefficient as shown below. Figure 17: Stage load over flow coefficient for the FAN and HPC Figure : Stage load over the flow coefficient for the HPC and FAN The supersonic jet engine will draw its thrust through a high acceleration of air mass, which passes through the engine. Given that a high “jet” velocity will be essential in obtaining a high thrust, the engine turbine will be designed to draw only sufficient power from the burning gas rivulet to drive the entire compressor and its accessories. Figure : Sections of the Turbo Jet Engine Coolant Injection Supersonic Engine Combustor Coolant injection of the Supersonic jet engine into the combustor has an accomplished injection system set in the burner can’s rear part close to the wall. It ensures a burner’s wall additional cooling by facilitating the vaporized coolant mix into the gases burnt. Correspondingly, if the air compressor air mass flow rate surpasses the combustor’s essential due to the coolant injection, so as to avert compressor flow, in addition to an unbalanced engine operation, where the combustor rate of air flow to by-pass duct and evacuation of the excess air. Figure : Gas-turbine-engine combustor Both the exhaust nozzle and mass flow of the burned gases’ velocity causes an increase in thrust extension at about 25 percent for the coolant flow rate segment of about 5 percent while the exact fuel consumption rises up to 15 percent, which is a tolerable value bearing in mind the thrust upsurge advantage. Before the project ends, much skills will be earned and significant knowledge learnt. The entire overlap occurring between the electronics and programming makes it deserves to spend the time on it to apply and manage the engineering work. Conclusions In this research design, a supersonic jet engine preliminary design for our large aerospace company, the jet is expected to be in operational service soonest. Correspondingly, the engine is expected to offer better performance as compared to the current one opted for aircraft propulsion. Referring to the provided requirements for the engine, the thermodynamic cycle is enhanced with the fundamental sizing as well as performance of the aerodynamic design. The output is a smaller engine of analogous diameter with an enhanced efficiency. Besides, a comparison weighted flow of fuel of the respective two engines at the prime operational points indicates a fuel burn enhancement of about 12 percent for the new developed engine. This improves the commercial features of aeroplane operations while lowering the emission levels to lower the environmental impact. On the converse, it follows that the aircraft motion with the jet engine depends mostly on moments of Inertia and mass of which it significantly varies, in consideration, the mass variation. If there exists a variation, a comparative fuel mixture motion in a connected coordinates aircraft system, then in the aircraft motion has a variability consideration of mass and the extra members and consideration of the restrain impact on aircraft of comparative fuel mixture motion. Essentially, the procedure of designing a jet engine involves a quite complex procedure which touches numerous diverse fields with a no apparent solution as an upgrade of a single parameter frequently carry an expense of a different one. References Goldsmith, E. L., & Seddon, J. (1993). Practical intake aerodynamic design. Amer Inst of Aeronautics &. Oswatitsch, K. (1980). Pressure recovery for missiles with reaction propulsion at high supersonic speeds (the efficiency of shock diffusers). In Contributions to the Development of Gasdynamics (pp. 290-323). Vieweg+ Teubner Verlag. Appendices MATLAB program output files -----------------------------FAN----------------------------- Entry Into Service: As soon as it’s complete Stages: 4 Av. Stage loading 2dH/Umid2: 1.0223 1st stage Flow coefficient Cax/Umid: 0.76598 1st stage Mtip,rel: 1.4837 1st stage Utip,in: 455.1531 1st stage Utip,in,corr: 435.7497 1st stage Umid,in: 289.5909 1st stage Cax,in: 221.8209 1st stage Hade angle: 21 (rhub/rtip)in: 0.2725 (rhub/rtip)out: 0.69474 AR,in 2.4 AR,out 2.3 M,ax,in 0.65 M,ax,in 0.38 Total length [m]: 0.9876 RNI: 0.35315 Mcorr: 238.1475 dETAEIS: 0.016354 dETARe: -0.012639 dETAM: 0 ETA*: 0.89693 ETApol: 0.90065 -----------------------------HPC----------------------------- Stages: 5 1:st stg Flow function HPC: 0.42313 Avg. Stage load HPC: 0.7074 1:st stg(hub/tip)-ratio: 0.70373 last stg(hub/tip)-ratio: 0.94776 1:st stg Mtip,rel no IGV: 1.5247 AR,in 1.6325 AR,out 0.9325 M,ax,in 0.517 M,ax,in 0.329 Total length [m]: 0.37088 RNI: 0.80258 Mcorr: 54.9092 dETAEIS: 0.018391 dETARe: -0.0021124 dETAM: -0.0014644 ETA*: 0.9258 ETApol: 0.94062 -----------------------------Combustor----------------------- At Cruise conditions Pattern Factor: 0.35259 dp: 4.1152 burning time: 0.004021 Vcc [m^3]: 0.058889 Vcc [m^3]: 0.029445 Total length [m]: 0.195 At windmilling conditions Loading: 230.9597 -----------------------------HPT----------------------------- Stages: 1 1:st stg Flow function HPT: 0.41448 Avg. Stage load HPT: 3.1288 AN2: 7247.5 AR,in 1.16 AR,out 1.16 M,ax,in 0.15852 M,ax,in 0.4 Total length [m]: 0.097334 RNI: 1.822 Mcorr: 9.0066 dETAEIS: 0.0084819 dETARe: 0.0056299 dETAM: -0.034234 ETA*: 0.95693 ETApol: 0.9099 -----------------------------LPT----------------------------- Stages: 2 1:st stg Flow function LPT: 0.75935 Avg. Stage load LPT: 2.1106 Last stg AN2: 5114.8347 AR,in 1.835 AR,out 6.7225 M,ax,in 0.35 M,ax,in 0.5 Total length [m]: 0.089104 RNI: 0.64113 Mcorr: 38.6614 dETAEIS: 0.016457 dETARe: -0.0045817 dETAM: -0.0082715 ETA*: 0.93012 ETApol: 0.93372 -----------------------------Engine-------------------------- OPR: 38.0 BPR: 0.39702 FPR: 3.9283 HPC P-ratio: 10.0381 Inlet Diameter [m]: 1.2418 Inlet Area [m]: 1.2112 Engine Length [m]: 4.2305 Core length: FANstart-LPTend [m]: 2.0971 LowSpeedShaft [rps]: 116.6667 HighSpeedShaft [rps]: 225 -----------------------------Ducts--------------------------- ICD length [m]: 0.14886 ITD length [m]: 0.1067 LPT exhaust length [m]: 0.15 BP duct length [m]: 1.1627 Jet pipe length [m]: 0.5 Mixer length [m] 0.2 -----------------------------Nozzle-------------------------- Nozzle length [m] 1.1834 Petal angle [deg]: 35.2059 Divergent angle [deg]: 12.5 Throat Diameter [m]: 0.75978 Exit Diameter [m]: 1.1515 Ain/Athroat: 2.4249 Athroat/Aexit: 0.43538 Athroat: 0.45338 Aexit: 1.0414 Ain: 1.0994 -----------------------------Inlet--------------------------- Total Pressure recovery Inlet: 0.98342 Total length Inlet: 2.0884 Total Engine length with Inlet: 6.3189 Venturi Area [m^2]: 0.99211 Oblique shock angle "beta" [deg]: 55 Deflection angle "theta" [deg]: 9.2563 Mach number after oblique shock: 1.1517 Mach number after normal shock: 0.87387 Mach number inlet FAN: 0.65 ----------------------------Velocity Diagram FAN------------ Mtip,rel: 1.4297 Average Stage Load: 0.81845 Average Flow coefficient: 0.62704 Average Temp rise: 42.2583 Stage Hubradii Midradii Tipradii _____ ________ ________ ________ beta1 1 51.128 52.549 63.069 beta2 1 -10.74 34.427 55.205 alpha1 1 -32.218 0 5.216 alpha2 1 41.505 34.311 34.031 Deflection 1 61.868 18.122 7.864 C-axial in 1 203.19 221.82 220.97 C-axial out 1 254.59 221.82 203.29 Uin m/s 1 124.03 289.59 455.15 Uout m/s 1 176.99 303.42 429.84 V1 m/s 1 323.77 364.78 487.89 V2 m/s 1 259.13 268.92 356.26 C1 m/s 1 240.17 221.82 221.89 C2 m/s 1 339.95 268.55 245.31 Reaction 1 0.60803 0.73863 0.82703 Diffusion 1 0.38456 0.33965 0.2986 de Haller 1 0.63877 0.73721 0.7937 Flow coefficient 1 1.6383 0.76598 0.48549 Stage load 1 5.1384 0.94255 0.38156 Stage Temp-rise K 1 39.258 39.258 39.258 Stage Hubradii Midradii Tipradii _____ ________ ________ ________ beta1 2 44.776 52.446 59.916 beta2 2 2.009 27.241 50 alpha1 2 2.742 11.984 17.446 alpha2 2 43.977 44.945 46.873 Deflection 2 42.767 25.204 9.9159 C-axial in 2 218.11 212.15 203.43 C-axial out 2 248.13 212.15 182.76 Uin m/s 2 226.85 320.97 415.1 Uout m/s 2 248.13 330.52 412.92 V1 m/s 2 307.25 348.07 405.83 V2 m/s 2 248.28 238.62 284.32 C1 m/s 2 218.36 216.88 213.24 C2 m/s 2 344.81 299.74 267.34 Reaction 2 0.44926 0.6 0.68797 Diffusion 2 0.43885 0.45729 0.37939 de Haller 2 0.71031 0.68555 0.77984 Flow coefficient 2 0.96145 0.66097 0.49009 Stage load 2 1.7776 0.88795 0.53092 Stage Temp-rise K 2 45.258 45.258 45.258 Stage Hubradii Midradii Tipradii _____ ________ ________ ________ beta1 3 50.622 56.374 61.686 beta2 3 12.93 34.122 51.766 alpha1 3 6.5513 12.817 17.186 alpha2 3 45.27 46.494 48.377 Deflection 3 37.692 22.252 9.9208 C-axial in 3 202.08 196.95 190.49 C-axial out 3 224.99 196.95 172.61 Uin m/s 3 269.41 340.95 412.49 Uout m/s 3 278.78 346.06 413.33 V1 m/s 3 318.51 355.65 401.62 V2 m/s 3 230.85 237.91 278.91 C1 m/s 3 203.4 201.98 199.39 C2 m/s 3 319.7 286.08 259.86 Reaction 3 0.53541 0.63 0.69312 Diffusion 3 0.49431 0.47296 0.39589 de Haller 3 0.65094 0.66892 0.76638 Flow coefficient 3 0.75006 0.57765 0.4618 Stage load 3 1.268 0.79169 0.54089 Stage Temp-rise K 3 45.258 45.258 45.258 Stage Hubradii Midradii Tipradii _____ ________ ________ ________ beta1 4 51.145 57.728 63.452 beta2 4 17.476 38.639 55.698 alpha1 4 16.638 21.913 26.171 alpha2 4 47.237 49.873 53.432 Deflection 4 33.669 19.088 7.754 C-axial in 4 186.71 176.87 166.42 C-axial out 4 207.95 176.87 147.88 Uin m/s 4 287.56 351.22 414.88 Uout m/s 4 290.32 353.22 416.12 V1 m/s 4 297.62 331.25 372.35 V2 m/s 4 218.01 226.43 262.4 C1 m/s 4 194.87 190.64 185.43 C2 m/s 4 306.27 274.43 248.21 Reaction 4 0.51202 0.6 0.66118 Diffusion 4 0.49207 0.46819 0.39644 de Haller 4 0.65771 0.68358 0.79309 Flow coefficient 4 0.64929 0.50357 0.40113 Stage load 4 0.97205 0.65163 0.46701 Stage Temp-rise K 4 39.258 39.258 39.258 ----------------------------Velocity Diagram Compressor----- IGV angle: 18 First stage Mtip,rel: 1.3421 Average Stage Load: 0.58116 Average Flow coefficient: 0.37835 Average Temp rise: 89.8067 Stage Hubradii Midradii Tipradii _____ ________ ________ ________ beta1 1 59.191 67.066 68.265 beta2 1 46.582 51.759 61.289 alpha1 1 11.848 18 20.69 alpha2 1 47.102 47.582 49.396 Deflection 1 12.609 15.306 6.9764 C-axial in 1 228.95 221.24 212.68 C-axial out 1 238.25 221.24 205.13 Uin m/s 1 431.95 522.88 613.8 Uout m/s 1 508.18 560.99 613.8 V1 m/s 1 447 567.76 574.31 V2 m/s 1 346.63 357.44 427.01 C1 m/s 1 233.93 232.63 227.34 C2 m/s 1 350 327.99 315.19 Reaction 1 0.64761 0.69971 0.73964 Diffusion 1 0.38034 0.47122 0.34827 de Haller 1 0.74519 0.62956 0.77085 Flow coefficient 1 0.53003 0.42313 0.34649 Stage load 1 0.96328 0.65739 0.47705 Stage Temp-rise K 1 86.807 86.807 86.807 Stage Hubradii Midradii Tipradii _____ ________ ________ ________ beta1 2 65.382 66.703 67.942 beta2 2 54.619 57.398 60.589 alpha1 2 13.717 15.017 16.21 alpha2 2 45.398 45.763 46.162 Deflection 2 10.762 9.3045 7.3534 C-axial in 2 226.76 224.67 222.5 C-axial out 2 231.52 224.67 218.02 Uin m/s 2 550.22 582.01 613.8 Uout m/s 2 560.78 587.29 613.8 V1 m/s 2 544.35 568.06 592.48 V2 m/s 2 399.87 416.98 443.97 C1 m/s 2 233.42 232.61 231.72 C2 m/s 2 329.72 322.04 314.78 Reaction 2 0.73637 0.75 0.76235 Diffusion 2 0.37158 0.36042 0.33478 de Haller 2 0.71946 0.73405 0.76474 Flow coefficient 2 0.41213 0.38602 0.3625 Stage load 2 0.63967 0.5717 0.51401 Stage Temp-rise K 2 91.807 91.807 91.807 Stage Hubradii Midradii Tipradii _____ ________ ________ ________ beta1 3 64.154 65.349 66.49 beta2 3 51.159 54.142 57.217 alpha1 3 24.576 25.624 26.638 alpha2 3 51.163 51.895 52.671 Deflection 3 12.995 11.207 9.2734 C-axial in 3 226.09 222.66 219.18 C-axial out 3 231.05 222.66 214.32 Uin m/s 3 570.14 591.97 613.8 Uout m/s 3 573.93 593.87 613.8 V1 m/s 3 518.61 533.83 549.47 V2 m/s 3 368.4 380.1 395.81 C1 m/s 3 248.62 246.94 245.21 C2 m/s 3 368.43 360.8 353.43 Reaction 3 0.65764 0.67 0.68152 Diffusion 3 0.42826 0.41595 0.39781 de Haller 3 0.69513 0.71203 0.73672 Flow coefficient 3 0.39656 0.37613 0.35709 Stage load 3 0.60805 0.56402 0.52461 Stage Temp-rise K 3 91.807 91.807 91.807 Stage Hubradii Midradii Tipradii _____ ________ ________ ________ beta1 4 66.495 67.293 68.063 beta2 4 54.411 56.763 59.071 alpha1 4 19.353 20.196 21.006 alpha2 4 50.423 50.924 51.45 Deflection 4 12.084 10.53 8.9918 C-axial in 4 217.95 216.04 214.1 C-axial out 4 222.22 216.04 209.93 Uin m/s 4 577.69 595.75 613.8 Uout m/s 4 579.35 596.58 613.8 V1 m/s 4 546.48 559.66 573.09 V2 m/s 4 381.84 394.16 408.44 C1 m/s 4 231 230.19 229.34 C2 m/s 4 348.79 342.73 336.86 Reaction 4 0.70106 0.71 0.71843 Diffusion 4 0.4306 0.41636 0.39987 de Haller 4 0.68531 0.70429 0.72686 Flow coefficient 4 0.37728 0.36264 0.34881 Stage load 4 0.60446 0.56837 0.53542 Stage Temp-rise K 4 91.807 91.807 91.807 Stage Hubradii Midradii Tipradii _____ ________ ________ ________ beta1 5 67.134 67.912 68.663 beta2 5 55.841 58.116 60.285 alpha1 5 23.151 23.952 24.731 alpha2 5 51.863 52.449 53.064 Deflection 5 11.293 9.7957 8.378 C-axial in 5 207.58 205.4 203.2 C-axial out 5 211.7 205.4 199.14 Uin m/s 5 580.98 597.39 613.8 Uout m/s 5 581.61 597.71 613.8 V1 m/s 5 534.2 546.24 558.49 V2 m/s 5 377.03 388.87 401.75 C1 m/s 5 225.76 224.76 223.72 C2 m/s 5 342.8 337.02 331.39 Reaction 5 0.69157 0.7 0.70798 Diffusion 5 0.42568 0.4114 0.39632 de Haller 5 0.69205 0.71191 0.73404 Flow coefficient 5 0.35729 0.34383 0.33106 Stage load 5 0.57551 0.54432 0.51561 Stage Temp-rise K 5 86.807 86.807 86.807 -----------------------------Velocity Diagram HPT------------ Avg. Stage load 3.101 Avg. Flow coefficient 0.41135 Stage Hubradii Midradii Tipradii _____ ________ ________ ________ beta2 1 58.989 51.748 42.042 beta3 1 66.991 68.206 70.037 alpha2 1 75.772 74.874 73.983 alpha3 1 4.2634 4 3.6162 Deflection 1 8.0023 16.458 27.995 C-axial in 1 259.33 259.33 259.33 U m/s 1 591.35 630.43 669.52 V2 m/s 1 503.36 418.86 349.2 V3 m/s 1 663.47 698.49 759.58 C2 m/s 1 1055.1 993.8 939.85 C3 m/s 1 260.05 259.96 259.85 Relative Mach # 1 0.42712 0.35277 0.2923 Reaction 1 0.19342 0.25351 0.3572 Flow coefficient 1 0.41135 0.41135 0.41135 Stage load 1 3.101 3.101 3.101 Stage Temp-drop K 1 494.16 494.16 494.16 P2/Pchoke < 1 1 0.85975 0.85975 0.85975 -----------------------------Velocity Diagram LPT------------ Avg. Stage load 2.056 Avg. Flow coefficient 0.80783 Stage Hubradii Midradii Tipradii _____ ________ ________ ________ beta2 1 21.753 4.1707 -12.257 beta3 1 49.486 52.837 56.013 alpha2 1 57.493 54.309 51.36 alpha3 1 0 0 0 Deflection 1 27.732 48.666 68.27 C-axial in 1 253.6 253.6 253.6 U m/s 1 296.77 334.54 372.31 V2 m/s 1 273.04 254.27 259.51 V3 m/s 1 390.37 419.8 453.66 C2 m/s 1 471.9 434.68 406.13 C3 m/s 1 253.6 253.6 253.6 Relative Mach # 1 0.43013 0.3978 0.40403 Reaction 1 0.35946 0.47236 0.59675 Flow coefficient 1 0.75804 0.75804 0.75804 Stage load 1 2.1106 2.1106 2.1106 Stage Temp-drop K 1 99.661 99.661 99.661 P2/Pchoke < 1 1 0.73794 0.73794 0.73794 Stage Hubradii Midradii Tipradii _____ ________ ________ ________ beta2 2 18.955 0.046184 -16.582 beta3 2 45.207 49.383 54.209 alpha2 2 53.485 49.402 45.763 alpha3 2 0 0 0 Deflection 2 26.252 49.337 70.79 C-axial in 2 294.64 294.64 294.64 U m/s 2 296.77 343.55 390.32 V2 m/s 2 311.53 294.64 307.42 V3 m/s 2 418.19 452.59 503.79 C2 m/s 2 495.16 452.77 422.34 C3 m/s 2 294.64 294.64 294.64 Relative Mach # 2 0.47108 0.44216 0.45906 Reaction 2 0.36351 0.49965 0.68916 Flow coefficient 2 0.85763 0.85763 0.85763 Stage load 2 2.0014 2.0014 2.0014 Stage Temp-drop K 2 99.661 99.661 99.661 P2/Pchoke < 1 2 0.73757 0.73757 0.73757 Output files for the T-AXI DISK  &INPUT_OUTPUT TYPE= 2 DRQR= 1.00010000169277191E-002 WWEB= 0.44678959250450134 DRQB= 0.57624977827072144 WBOR= 0.23997600376605988 RBOR= 4.00040000677108765E-002 DSF= 0.16814558207988739 PR1= 0.50000000000000000 PR2= 0.50000000000000000 PT1= 1.00000000000000000 PT2= 0.25000000000000000 PT3= 0.25000000000000000 S12= 0.50000000000000000 C4="*****************DISK_MATERIAL******************" MATNAME="INCONEL718.dmat" C5="**********DEAD_WEIGHT_SPECIFICATION*************" DEAD_WEIGHT_FLAG= 1 M_B= 1.1856651650167098 R_CG_B= 0.35306778472642797 C6="**************ANALYSIS_CONDITIONS***************" RPMO= 13500.000000000000 TADDER= 0.0000000000000000 RIMT= 150.00000000000000 TAXIS= 145.00000000000000 SFACT= 1.1000000000000001 C7="*****************OTHER_VALUES*******************" BNUM= 65.000000000000000 BIRR= 0.30900000000000000 BERR= 0.35899999999999999 WRIM= 7.79999999999999999E-002 BSPN= 0.12500000000000000 BSHR= 2 BRHO= 8000.0000000000000 BTHP= 7.0000000000000000 RTQB= 0.25000000000000000 WBOR_MAX= 0.23997599999999999 RBOR_MIN= 4.00039999999999979E-002 BFILENAME="none" BSCALE= 1.00000000000000000 / 2nd Engine HPC Engine disc DRQR= 1.00010000169277191E-002 WWEB= 0.10898753255605698 DRQB= 1.1600420475006104 WBOR= 5.99999986588954926E-002 RBOR= 9.00089964270591736E-002 DSF= 0.10001000016927719 PR1= 0.50000000000000000 PR2= 0.50000000000000000 PT1= 1.00000000000000000 PT2= 0.25000000000000000 PT3= 0.25000000000000000 S12= 0.50000000000000000 C4="*****************DISK_MATERIAL******************" MATNAME="INCONEL718.dmat" C5="**********DEAD_WEIGHT_SPECIFICATION*************" DEAD_WEIGHT_FLAG= 1 M_B= 0.11507518039625086 R_CG_B= 0.39494879717528664 C6="**************ANALYSIS_CONDITIONS***************" RPMO= 13500.000000000000 TADDER= 0.0000000000000000 RIMT= 150.00000000000000 TAXIS= 145.00000000000000 SFACT= 1.1000000000000001 C7="*****************OTHER_VALUES*******************" BNUM= 60.000000000000000 BIRR= 0.38900000000000001 BERR= 0.39700000000000002 WRIM= 2.99999999999999989E-002 BSPN= 4.49999999999999983E-002 BSHR= 2 BRHO= 8000.0000000000000 BTHP= 7.0000000000000000 RTQB= 0.20000000000000001 WBOR_MAX= 6.99930000000000135E-002 RBOR_MIN= 9.00089999999999918E-002 BFILENAME="none" BSCALE= 1.00000000000000000 / 3rd HPC Engine disc DRQR= 9.99999974737875164E-005 WWEB= 8.00120010972023010E-002 DRQB= 1.2000399827957153 WBOR= 2.49975007027387619E-002 RBOR= 4.00040000677108765E-002 DSF= 0.18009099364280701 PR1= 0.50000000000000000 PR2= 0.50000000000000000 PT1= 1.00000000000000000 PT2= 0.25000000000000000 PT3= 0.25000000000000000 S12= 0.50000000000000000 C4="*****************DISK_MATERIAL******************" MATNAME="INCONEL718.dmat" C5="**********DEAD_WEIGHT_SPECIFICATION*************" DEAD_WEIGHT_FLAG= 1 M_B= 5.81338048435073584E-002 R_CG_B= 0.40494046444841159 C6="**************ANALYSIS_CONDITIONS***************" RPMO= 13500.000000000000 TADDER= 0.0000000000000000 RIMT= 150.00000000000000 TAXIS= 145.00000000000000 SFACT= 1.1000000000000001 C7="*****************OTHER_VALUES*******************" BNUM= 60.000000000000000 BIRR= 0.40300000000000002 BERR= 0.40600000000000003 WRIM= 2.29999999999999996E-002 BSPN= 3.09999999999999998E-002 BSHR= 2 BRHO= 8000.0000000000000 BTHP= 7.0000000000000000 RTQB= 0.20000000000000001 WBOR_MAX= 2.99969999999999994E-002 RBOR_MIN= 4.00039999999999979E-002 BFILENAME="none" BSCALE= 1.00000000000000000 / Fourth HPC Engine Disc  WWEB= 6.81580975651741028E-002 DRQB= 0.86708587408065796 WBOR= 2.46679987758398056E-002 RBOR= 4.00040000677108765E-002 DSF= 0.15354484319686890 PR1= 0.50000000000000000 PR2= 0.50000000000000000 PT1= 1.00000000000000000 PT2= 0.25000000000000000 PT3= 0.25000000000000000 S12= 0.50000000000000000 C4="*****************DISK_MATERIAL******************" MATNAME="INCONEL718.dmat" C5="**********DEAD_WEIGHT_SPECIFICATION*************" DEAD_WEIGHT_FLAG= 1 M_B= 4.14624665236959580E-002 R_CG_B= 0.40971401261695956 C6="**************ANALYSIS_CONDITIONS***************" RPMO= 13500.000000000000 TADDER= 0.0000000000000000 RIMT= 150.00000000000000 TAXIS= 145.00000000000000 SFACT= 1.1000000000000001 C7="*****************OTHER_VALUES*******************" BNUM= 60.000000000000000 BIRR= 0.40899999999999997 BERR= 0.40999999999999998 WRIM= 2.19999999999999987E-002 BSPN= 2.29999999999999996E-002 BSHR= 2 BRHO= 8000.0000000000000 BTHP= 7.0000000000000000 RTQB= 0.20000000000000001 WBOR_MAX= 2.49975000000000024E-002 RBOR_MIN= 4.00039999999999979E-002 BFILENAME="none" BSCALE= 1.00000000000000000 / Fifth HPC disc WWEB= 6.48523047566413879E-002 DRQB= 0.90963256359100342 WBOR= 2.29748580604791641E-002 RBOR= 4.00040000677108765E-002 DSF= 0.16116099059581757 PR1= 0.50000000000000000 PR2= 0.50000000000000000 PT1= 1.00000000000000000 PT2= 0.25000000000000000 PT3= 0.25000000000000000 S12= 0.50000000000000000 C4="*****************DISK_MATERIAL******************" MATNAME="INCONEL718.dmat" C5="**********DEAD_WEIGHT_SPECIFICATION*************" DEAD_WEIGHT_FLAG= 1 M_B= 4.39481341670272668E-002 R_CG_B= 0.41129828749125069 C6="**************ANALYSIS_CONDITIONS***************" RPMO= 13500.000000000000 TADDER= 0.0000000000000000 RIMT= 150.00000000000000 TAXIS= 145.00000000000000 SFACT= 1.1000000000000001 C7="*****************OTHER_VALUES*******************" BNUM= 60.000000000000000 BIRR= 0.41099999999999998 BERR= 0.41099999999999998 WRIM= 2.29999999999999996E-002 BSPN= 2.29999999999999996E-002 BSHR= 2 BRHO= 8000.0000000000000 BTHP= 7.0000000000000000 RTQB= 0.20000000000000001 WBOR_MAX= 2.39976000000000009E-002 RBOR_MIN= 4.00039999999999979E-002 BFILENAME="none" BSCALE= 1.00000000000000000 / HPT Engine disc WWEB= 0.15955232083797455 DRQB= 0.90005499124526978 WBOR= 0.16498349606990814 RBOR= 3.00030000507831573E-002 DSF= 0.14009299874305725 PR1= 0.50000000000000000 PR2= 0.50000000000000000 PT1= 1.00000000000000000 PT2= 0.25000000000000000 PT3= 0.25000000000000000 S12= 0.50000000000000000 C4="*****************DISK_MATERIAL******************" MATNAME="INCONEL718.dmat" C5="**********DEAD_WEIGHT_SPECIFICATION*************" DEAD_WEIGHT_FLAG= 1 M_B= 0.18910831139661863 R_CG_B= 0.42570518476269659 C6="**************ANALYSIS_CONDITIONS***************" RPMO= 13500.000000000000 TADDER= 0.0000000000000000 RIMT= 600.00000000000000 TAXIS= 145.00000000000000 SFACT= 1.1000000000000001 C7="*****************OTHER_VALUES*******************" BNUM= 68.000000000000000 BIRR= 0.41799999999999998 BERR= 0.41799999999999998 WRIM= 4.39999999999999974E-002 BSPN= 5.39999999999999994E-002 BSHR= 2 BRHO= 8000.0000000000000 BTHP= 7.0000000000000000 RTQB= 0.14999999999999999 WBOR_MAX= 0.16498350000000001 RBOR_MIN= 3.00029999999999984E-002 BFILENAME="none" BSCALE= 1.00000000000000000/ 29 PAGE \* MERGEFORMAT 12 PAGE \* MERGEFORMAT 12 &INPUT_OUTPUT C1="*******T-AXI_DISK_INPUT_FILE:_VERSION_2.4*******" C2="*******PARAMATERIZATION_TYPE********************" TYPE= 2 C3="*****************PARAMETERS*********************" PAGE \* MERGEFORMAT 12 PAGE \* MERGEFORMAT 12 C1="*******T-AXI_DISK_INPUT_FILE:_VERSION_2.4*******" C2="*******PARAMATERIZATION_TYPE********************" C3="*****************PARAMETERS*********************" 34 GLOBALIZATION 36