1. 1 Shock-induced boundary layer separation in Round C-D nozzles Khairul Zaman Inlets and Nozzles Branch, NASA GRC Cleveland, OH 44135 Co-investigators: Timothy Bencic, Amy Fagan and Michelle Clem Optics and Photonic Branch Supported by Commercial Supersonic Technology and Transformative Tools and Technologies Projects SWBLI Workshop, Dayton, OH April 14-15, 2015 NASA Glenn Research Center SWBLI Wkshp, Dayton, April 14-15, 2015 Zaman/GRC

2. 2 Background: Shock-induced BL separation occurs in Convergent-divergent (C- D) nozzles when run in overexpanded condition. Such condition occurs, e.g., during certain flight regimes and also with rocket nozzles during start-up. These flows are noisy and may involve detrimental unsteady loads. As a first step in any analysis one requires the knowledge of mean shock location within the divergent section for a given nozzle pressure ratio (NPR). NASA Glenn Research Center SWBLI Wkshp, Dayton, April 14-15, 2015 Zaman/GRC

3. 3 Background: Shock location within C-D nozzles have been studied in many previous investigations Stodola experiment (1903) Anderson Data with rocket nozzles Morrisette & Goldberg 1978 However, systematic database especially for lower design Mach number nozzles, typical of aircraft application, is lacking. NASA Glenn Research Center SWBLI Wkshp, Dayton, April 14-15, 2015 Zaman/GRC

4. 4 Objective: Conduct experiment with a set of C-D nozzles to study steady-state shock-location as a function of ‘jet Mach number’ M j (or NPR) Analyze results vis-à-vis an available correlation and 1D theory Experimental method: Pressure sensitive paint static pressure taps and shadowgraph Note: M j is ‘Mach number’ had the jet expanded fully for a given NPR. NASA Glenn Research Center SWBLI Wkshp, Dayton, April 14-15, 2015 Zaman/GRC AIAA Paper 2011-1031 Zaman/Bencic/Clem/Fagan With new data manuscript submitted for Journal publication

5. 5 NASA Glenn Research Center Experimental Facility Open jet rig M D =1.8 Noz SWBLI Wkshp, Dayton, April 14-15, 2015 Zaman/GRC

6. 6 NASA Glenn Research Center Facility: Nozzle characteristics NozzleDesign Mach No., M D Throat diameter D t Div. section length M14 1.4 1.89521.832 M16 1.6 1.79002.382 M18 1.8 1.67022.630 M18L 1.81.67023.351 M22 2.2 1.41483.351 M28 2.8 1.07304.002 For these nozzles: exit diameter = 2”, Length = 7.5” CAD image of M22 SWBLI Wkshp, Dayton, April 14-15, 2015 Zaman/GRC

7. 7 NASA Glenn Research Center Facility Additional nozzles Large M21Lg D E =3.5, D t =2.567 Total length = 15 Div sec length, L=4.2 M D =2.1 Small M18Sm Geometrically Similar to M18 D E =1.485 M D =1.8 SWBLI Wkshp, Dayton, April 14-15, 2015 Zaman/GRC M j [=] 0.4 – 1.7; Re D [=] 0.35x10 6 – 0.58x10 7 covered in experiment

8. 8 NASA Glenn Research Center Sample raw PSP data M18 Nozzle SWBLI Wkshp, Dayton, April 14-15, 2015 Zaman/GRC

9. 9 NASA Glenn Research Center Comparison of PSP data with static pressure tap data M18L Pressure tap data PSP data SWBLI Wkshp, Dayton, April 14-15, 2015 Zaman/GRC

10. 10 NASA Glenn Research Center Profiles of wall pressure from PSP data M18 and M18L At separation, p w /p a  0.5 noted before Papamoschou & Johnson 2010 SWBLI Wkshp, Dayton, April 14-15, 2015 Zaman/GRC

11. 11 NASA Glenn Research Center Morrisette & Goldberg NASA TP 1978 Reshotko & Tucker NACA TN 1955 Shock location vs. M j M18L SWBLI Wkshp, Dayton, April 14-15, 2015 Zaman/GRC Design N. Shock @exit Throat choked 1-D theory

12. 12 NASA Glenn Research Center MGRT correlation (Morrisette & Goldberg 1978 ) Per Reshotko & Tucker (1955) (Eq. 3) assuming H 1 =1.286 and H 2 =2.2, M 2 /M 1 =0.762 is obtained. With M 2 = 0.762M 1 find p 2 /p 1 (oblique shock Eqns. 128 and 132, Ames Table). For a given x-location of the shock, find nozzle diameter at that x. Calculate Mach number assuming fully expanded flow up to this point. This is M 1 (upstream of oblique shock). From M 1, find corresponding wall pressure p 1 /p 0. Assuming p 2 = p a, p 0 /p a is found which yields M j. SWBLI Wkshp, Dayton, April 14-15, 2015 Zaman/GRC

13. 13 NASA Glenn Research Center Shock location vs. M j M14 and M16 SWBLI Wkshp, Dayton, April 14-15, 2015 Zaman/GRC

14. 14 NASA Glenn Research Center Shock location vs. M j M18 and M18L SWBLI Wkshp, Dayton, April 14-15, 2015 Zaman/GRC

15. 15 NASA Glenn Research Center Shock location vs. M j M22 and M28 SWBLI Wkshp, Dayton, April 14-15, 2015 Zaman/GRC

16. 16 NASA Glenn Research Center Shock location vs. M j For the six 2” nozzles SWBLI Wkshp, Dayton, April 14-15, 2015 Zaman/GRC

17. 17 NASA Glenn Research Center Shock location vs. M j For the six 2” nozzles SWBLI Wkshp, Dayton, April 14-15, 2015 Zaman/GRC y=(tanh  (x-0.65))*0.5+0.5, x=M j /M D, y=(x-x*)/L  =5 for M j /M D 0.65

18. 18 NASA Glenn Research Center Shock location vs. M j For the large and small nozzles SWBLI Wkshp, Dayton, April 14-15, 2015 Zaman/GRC

19. 19 NASA Glenn Research Center Acceleration parameter K for different nozzles Thus, BL before separation must be turbulent for M21Lg case For other nozzles cannot be sure but also likely to be turbulent SWBLI Wkshp, Dayton, April 14-15, 2015 Zaman/GRC r /D E Narasimha & Sreenivasan 1979

20. 20 Conclusions: Shock-induced boundary layer separation location documented for C-D nozzles of M D in the range 1.4-2.8. PSP technique satisfactorily provided relative trends of wall pressure. Data compared with a correlation from rocket nozzle literature; it agreed better for nozzles of higher M D but deviated at low M D. All data correlated simply with the ratio of ‘jet Mach number’ to design Mach number (M j /M D ). A correlation equation is provided. The correlation is found to be valid over a wide range of Re (0.35x10 6 – 0.58x10 7 ). An analysis indicates that the state of the boundary layer prior to separation is likely to be turbulent for all cases studied. NASA Glenn Research Center SWBLI Wkshp, Dayton, April 14-15, 2015 Zaman/GRC

21. 21 NASA Glenn Research Center Profiles of wall pressure from PSP data M14 and M16 SWBLI Wkshp, Dayton, April 14-15, 2015 Zaman/GRC Backup 1

22. 22 NASA Glenn Research Center Profiles of wall pressure from PSP data M22 and M28 SWBLI Wkshp, Dayton, April 14-15, 2015 Zaman/GRC Backup 2

23. 23 NASA Glenn Research Center Minimum pressure at static pressure taps M18L AIAA Paper 2011-1031 Zaman/Bencic/Clem/Fagan Backup 3