1 / 76

Method of Characteristics, Minimum Length Nozzle, and Aerospike Nozzle Contour Design

Method of Characteristics, Minimum Length Nozzle, and Aerospike Nozzle Contour Design. Stephen A. Whitmore Mechanical and Aerospace Engineering Department (Not in Sutton and Biblarz). The NASA Need? (1). NASA RFI Solicitation Number NNC09Z005: MARS ASCENT VEHICLE TECHNOLOGIES FOR

jamesz
Download Presentation

Method of Characteristics, Minimum Length Nozzle, and Aerospike Nozzle Contour Design

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Method of Characteristics, Minimum Length Nozzle, and Aerospike Nozzle Contour Design Stephen A. Whitmore Mechanical and Aerospace Engineering Department (Not in Sutton and Biblarz)

  2. The NASA Need? (1) NASA RFI Solicitation Number NNC09Z005: MARS ASCENT VEHICLE TECHNOLOGIES FOR DEVELOPMENT, DUE JAN 30, 2009. • NASA’s In-Space Propulsion Technology (ISPT) project has been assigned the responsibility of developing propulsion technologies needed to enable future sample return missions. • In recognition of the high interest of the science community in the return of samples from Mars the ISPT project, working in conjunction with the Mars Technology Program (MTP), will be starting an effort to develop long lead and critical technologies necessary for a Mars Ascent Vehicle (MAV). http://prod.nais.nasa.gov/cgi-bin/eps/synopsis.cgi?acqid=133093

  3. The NASA Need? (2) • Areas of interest include: Component technologies offering improvements in specific impulse or offer significant reduction in mass for operations including propulsive maneuvers, … thrust vector control (TVC), guidance and communication, …integrated TVC, valves, actuators, flex seals, composite motor case, lightweight avionics, etc. • Concepts must be above TRL 2 with rapid demonstration to TRL 4 expected and development to TRL 6 practical within a 4-6 year horizon. • Submissions are intended to aid in future NRA (NASA Research Announcement) preparation. NRA figures of merits would emphasize reductions in mass and risk.

  4. Proposed Technology Thrust (1) • Aerospike Nozzle as Technology for Low-mass, high-performance Space Thrusters

  5. Proposed Technology Thrust (2) • High Expansion ratio for smaller mass/volume • Enhanced Thrust and Specific Impulse • Simple, More reliable operation

  6. Why Aerospike for in-Space Thrusters? • Truncated aerospike nozzles can be as short as 25% the length of a conventional bell nozzle. • Provide savings in packing volume and weight for space vehicles. • Aerospike nozzles allow higher expansion ratio than conventional nozzle for a given space vehicle base area. • Increase vacuum thrust and specific impulse. • For missions to the Moon and Mars, advanced nozzles can increase the thrust and specific impulse by 5-6%, resulting in a 8-9% decrease in propellant mass. • Lower total vehicle mass and provide extra margin for the mass inclusion of other critical vehicle systems. • New nozzle technology also applicable to RCS, space tugs, etc…

  7. Spike Nozzle … Other advantages (cont’d) • Higher expansion ratio for smaller size II Credit: Aerospace web

  8. Spike Nozzle … Other advantages (cont’d) “Passive” 2-D Thrust Vectoring Using thruster chamber pressure 2-D aerospike Circumferential Nozzle Blowing Results in Significant Flow Deflection … Potential for semi-passive Thrust Vectoring

  9. Spike Nozzle … Disadvantages) • • Only 1 …….. • Low TRL Level: No aerospike engine has ever flown on an • Operational rocket application. • As a result, little flight design experience has been gained. • High Fidelity, comprehensive ground test data also limited. • Almost no correlation of experimental and analytical results • Fidelity and controllability data is non existent • Current TRL Level 2-3 tops!

  10. ALTAIR Configuration (Firestar Engineering Concept) Firestar Engineering Proprietary

  11. So Let’s Design One! Credit: Aerospace web

  12. An Introduction to theTwo-Dimensional Method of Characteristics • Anderson, Chapter 11 pp. 377-403 12

  13. Isentropic Nozzle Flow? • What Conditions are Required for Isentropic Supersonic Nozzle Flow? • We are going to have to review method of characteristics to get there 13

  14. Expansion Waves • “Pin point” disturbance in supersonic flow • Mach Angle m = 1/sin(M) 14

  15. Expansion Waves (concluded) • Then it follows that for an “expansion corner” q<0 .. We get an expansion wave (Prandtl-Meyer) • Flow accelerates around corner • Continuous flow region … sometimes called “expansion fan” • Each mach wave is infinitesimally weak isentropic flow region • Flow stream lines are curved and smooth through fan 15

  16. Prandtl-Meyer Expansion Fan: MathematicalAnalysis Revisited • Consider flow expansion around an infinitesimal corner • From Law of Sines

  17. Prandtl-Meyer Expansion Fan: MathematicalAnalysis (cont’d) • Expanding sin(p+m), sin(p-m-dq), and collecting terms • Letting dq is considered be infinitesimal

  18. Prandtl-Meyer Expansion Fan: MathematicalAnalysis (cont’d) • Exploiting the form of the power series (expanded about dV/V=0) • … truncate after first order term

  19. Prandtl-Meyer Expansion Fan: MathematicalAnalysis (cont’d) • Solve for dq in terms of dV/V • Since disturbance is infinitesimal (mach wave)

  20. Prandtl-Meyer Expansion Fan: MathematicalAnalysis (cont’d) • “ Differential form” of Prandtl-Meyer wave • For an infinitesimal disturbance (mach wave)

  21. Prandtl-Meyer Expansion Fan: MathematicalAnalysis (cont’d) • and …. This time we keep + sign

  22. Prandtl-Meyer Expansion Fan: MathematicalAnalysis (cont’d) • As demonstrated in section 6.2 in MAE 5420 • Extension of Prandtl Meyer expansion theory

  23. Method of Characteristics Revisited • Left and Right running characteristic lines Slope: q  m • C- “right running” characteristic Line is a Generalization For infinitesimal expansion corner flow 23

  24. Method of Characteristics Revisited(cont’d) • Left and Right running characteristic lines Slope: q + m • C+ “left running” characteristic Line is a Generalization infinitesimal compression corner flow 24

  25. Method of Characteristics Revisited • Supersonic “compatibility” equations • Apply along “characteristic lines” in flow field, and insure isentropic flow … 25

  26. “Method of Characteristics” • Basic principle of Methods of Characteristics -- If supersonic flow properties are known at two points in a flow field, -- There is one and only one set of properties compatible* with these at a third point, -- Determined by the intersection of characteristics, or machwaves, from the two original points. *Root of term “compatibility equations”

  27. “Method of Characteristics” (cont’d) • Compatibility Equations relate the velocity magnitude and direction along the characteristic line. • In 2-D and quasi 1-D flow, compatibility equations are Independent of spatial position, in 3-D methods, space Becomes a player and complexity goes up considerably • Computational Machinery for applying the method of Characteristics are the so-called “unit processes” • By repeated application of unit processes, flow field Can be solved in entirety

  28. Supersonic Nozzle Design • Strategic contouring will “absorb” mach waves to give isentropic flow in divergent section 28

  29. Supersonic Nozzle Design (cont’d) • Rocket Nozzle (Minimum Length) • Wind tunnel diffuser (gradual expansion) • Find minimum length nozzle with shock-free flow 29

  30. Method of Characteristics • Supersonic “compatibility” equations • Apply along “characteristic lines” in flow field, and insure isentropic flow … 30

  31. Minimum Length Nozzle Design (cont’d) • Along C+ characteristic {d,c, exit} • Find minimum length nozzle with shock-free flow • Along C- characteristic {a,c, exit} C+ • Add C-

  32. Minimum Length Nozzle Design (cont’d) • Find minimum length nozzle with shock-free flow • Along C- characteristic {a,c} at point a • But from Prandtl-Meyer expansion at point a C+ 0 C- 32

  33. Minimum Length Nozzle Design (cont’d) But as already shown C+ C-

  34. Minimum Length Nozzle Design (concluded) • Criterion for Minimum Length Nozzle 34

  35. Typical Conical Nozzle Contour e --> expansion ratio (Aexit/A*) Dt = Throat diameter R1 = Radius of curvature of nozzle contraction N = Transition point from circular contraction to conical nozzle LN = Nozzle Length De = Exit diameter • R1 ~ 0.75Dt is typical 35 Credit: Georgia Tech

  36. Typical Conical Nozzle Contour(Cont’d) • Solve for Nozzle length in terms of other parameters 36

  37. Typical Conical Nozzle Contour(Cont’d) • Using trig identities • R1 ~ 0.75Dt is typical 37

  38. Minimum Length Conical Nozzle • Example… given Dthroat = 1 cm Ae/A* = 8  = 1.2 = 8.0 = Mexit = 3.122 38

  39. Minimum Length Conical Nozzle(cont’d) Mexit = 3.122 = = 33.53 = 67.06 39

  40. Minimum Length Conical Nozzle(cont’d) • R1 ~ 0.75Dt is typical …. R1=0.75 cm • Any shorter and you have “problems” = 33.53 = = 1.606 cm 40

  41. What happens when a nozzle expandstoo quickly? • i.e. …. A mess … for a given Operating condition there is only so fast we can expand a Conventional Nozzle • Is there an alternative to the minimum length nozzle? 41

  42. Apply Method of Characteristics to Aerospike Nozzle 42

  43. Apply Method of Characteristics to Aerospike Nozzle (1) 43

  44. Apply Method of Characteristics to Aerospike Nozzle (2) Throat Throat Exit Angle Fixed by Spike Design expansion ratio 44

  45. Apply Method of Characteristics to Aerospike Nozzle (3) Along spike surface 45

  46. Plug Geometry At position X 46

  47. Apply Continuity equation 47

  48. Apply Method of Characteristics to Aerospike Nozzle (5) • Solving for Ax • Divide by throat area 48

  49. Apply Method of Characteristics to Aerospike Nozzle (6) • Simplifying 49

  50. Apply Method of Characteristics to Aerospike Nozzle (7) • Simplifying again 50

More Related