Investigation of High-Speed Flow Control from CD Nozzle Using Design of Experiments and CFD Methods


In high-speed fluid dynamics, the control of base pressure finds many engineering applications such as automobile industry and defense applications. Several studies have been reported on passive control using devices like cavities, ribs, aerospikes, etc. in the last three decades. Therefore, the present research focuses on active control uses the microjets in the form of an orifice of a 1 mm diameter to inject the air in the base flows and located at base area of 90° intervals as a control mechanism. Since the air is drawn from the main settling chamber, the NPR will be the same as the respective NPRs used for tests. Experiments were conducted in the presence and absence of the microjets for area ratio 3.24 and L/D ratios from 10 to 1 at Mach numbers 1.87, 2.2, and 2.58. The parameters were optimized using the design of experiments (DOE) approach. Three parameters have been selected for the flow and the DOE. An L9 orthogonal array, multiple linear regression, and confirmation tests were performed to analyze the experimental results. The developed models are statistically suitable and accomplished in producing reasonable predictions for both cases. Besides, a computational fluid dynamics method has been utilized and validated by the experimental results. The k–Ɛ turbulent model is used to analyze the simulation results. According to the present results, it is evident that for a given parameter, an L/D ratio is the most significant impacting to a maximum increment or decrement of a base pressure.

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P b :

Base pressure

P w :

Wall pressure

P a :

Atmospheric pressure


Mach number

ρ :


k :

Turbulent kinetic energy

μ :

Dynamic viscosity




Backward-facing steps


Computational fluid dynamics




Degree of freedom


Design of experiments


Finite volume method

L/D :

Length-to-diameter ratio


Mesh independence study


Nozzle pressure ratio


Partial differential equation


Pressure regulating valve


Reynolds average Navier–Stokes


  1. 1.

    Vikramaditya, N.S.; Viji, M.; Verma, S.B.; Ali, N.; Thakur, D.N.: Base Pressure Fluctuations on typical missile configuration in the presence of base cavity. J. Spacecr. Rockets. 55(2), 335–345 (2017)

    Article  Google Scholar 

  2. 2.

    Viswanath, P.R.: passive devices for axisymmetric base drag reduction at transonic speeds. J. Aircr. 25(3), 258–262 (1988)

    Article  Google Scholar 

  3. 3.

    Viswanath, P.R.: Flow management techniques for base and afterbody drag reduction. Prog. Aerosp. Sci. 32(95), 3–8 (1996)

    Google Scholar 

  4. 4.

    Singh, N.K.; Rathakrishnan, Ε.: Sonic jet control with tabs. Int. J. Turbo Jet Engines. 19, 107–118 (2002)

    Article  Google Scholar 

  5. 5.

    Vijayaraja, K.; Senthilkumar, C.; Elangovan, S.; Rathakrishnan, E.: Base pressure control with annular ribs. Int. J. Turbo Jet Engines. 31(2), 111–118 (2014)

    Article  Google Scholar 

  6. 6.

    Khurana, S.; Suzuki, K.; Rathakrishnan, E.: Flow field around a blunt-nosed body with spike. Int. J. Turbo Jet Engines. 29, 217–221 (2012)

    Article  Google Scholar 

  7. 7.

    Khurana, S.; Suzuki, K.: Towards heat transfer control by aerospikes for lifting- body configuration in hypersonic flow. In: 44th AIAA Thermophysics Conference, p. 2898 (2013)

  8. 8.

    Khurana, S.; Suzuki, K.: Assessment of aerodynamic effectiveness for aerospike application on hypothesized lifting-body in hypersonic flow. In: Fluid Dynamics and Co-located Conferences, pp. 24–27 (2013)

  9. 9.

    Sinclair, J.; Cui, X.: A theoretical approximation of the shock standoff distance for supersonic flows around a circular cylinder. Phys. Fluids 29, 026102 (2017)

    Article  Google Scholar 

  10. 10.

    Khan, S.A.; Asadullah, M.; Sadhiq, J.: Passive control of base drag employing dimple in subsonic suddenly expanded flow. Int. J. Mech. Mechatron. Eng. 18(July), 3 (2018)

    Google Scholar 

  11. 11.

    Khan, S.A.; Asadullah, M.: Passive control of base drag in compressible subsonic flow using multiple cavity. Int. J. Mech. Prod. Eng. Res. Dev. 8(4), 39–44 (2018)

    Google Scholar 

  12. 12.

    Asadullah, M.; Khan, S. A.: A comparison of the effect of single and multiple cavities on base flows. In: 2018 IEEE 5th International Conference on Engineering Technologies and Applied Sciences (ICETAS), pp. 1–6, (2019)

  13. 13.

    Khan, S.A.; Asadullah, M.: Grooved cavity as a passive controller behind backward facing step. J. Adv. Res. Fluid Mech. Therm. Sci. 53(2), 185–193 (2019)

    Google Scholar 

  14. 14.

    Khan, S.A.; Asadullah, M.; Fharukh, A.G.M.; Jalaluddeen, A.; Baig, M.A.: Flow control with aerospike behind bluff body. Int. J. Mech. Prod. Eng. Res. Dev. 8(3), 1001–1008 (2018)

    Google Scholar 

  15. 15.

    Asadullah, M.; Khan, S. A.; Asrar, W.; Sulaeman, E.: Passive control of base pressure with the static cylinder at supersonic flow. In: International Conference on Aerospace and Mechanical Engineering, pp. 1–9 (2018)

  16. 16.

    Asadullah, M.; Khan, S. A.; Asrar, W.; Sulaeman, E.: Active control of base pressure with counter-clockwise rotating cylinder at Mach 2. In: 2017 4th IEEE International Conference on Engineering Technologies and Applied Sciences (ICETAS), pp. 1–6, (2017)

  17. 17.

    Khan, S.A.; Rathakrishnan, E.: Active control of suddenly expanded flows from underexpanded nozzles. Int. J. Turbo Jet Engines. 21, 233–254 (2004)

    Google Scholar 

  18. 18.

    Khan, S.A.; Rathakrishnan, E.: Active control of suddenly expanded flows from underexpanded nozzles-part II. Int. J. Turbo Jet Engines. 22, 163–183 (2005)

    Article  Google Scholar 

  19. 19.

    Fharukh, A.G.M.; Ullah, M.A.; Khan, S.A.: Experimental study of suddenly expanded flow from correctly expanded nozzles. ARPN J. Eng. Appl. Sci. 11(16), 10041–10047 (2016)

    Google Scholar 

  20. 20.

    Quadros, J. D.; Khan, S. A.; Antony, A. J.: Investigation of effect of process parameters on suddenly expanded flows through an axi-symmetric nozzle for different mach numbers using design of experiments. In: IOP Conf. Series: Materials Science and Engineering. 1–8 (2017).

  21. 21.

    Quadros, J.D.; Khan, S.A.; Antony, A.J.: Study of effect of flow parameters on base pressure in a suddenly expanded duct at supersonic mach number regimes using CFD and design of experiments. J. Appl. Fluid Mech. 11(2), 483–496 (2018)

    Article  Google Scholar 

  22. 22.

    Khan, S.A.; Aabid, A.; Saleel, C.A.: Influence of micro jets on the flow development in the enlarged duct at supersonic mach number. Int. J. Mech. Mechatron Eng. 19(01), 70–82 (2019)

    Google Scholar 

  23. 23.

    Ahmed, F.; Khan, S.A.: Investigation of the efficacy of low length-to-diameter ratio and nozzle pressure ratio on base pressure in an abruptly expanded flow. MATEC Web Conf. 01004, 1–6 (2018)

    Google Scholar 

  24. 24.

    Kostic, O.; Stefanovic, Z.; Kostic, I.: CFD modeling of supersonic airflow generated by 2D nozzle with and without an obstacle at the exit section. FME Trans. 43(2), 107–113 (2015)

    Article  Google Scholar 

  25. 25.

    Khan, S.A.; Mohiuddin, M.; Saleel, C.A.; Fharukh, G.M.: Investigation of the effects of nozzle exit mach number and nozzle pressure ratio on axisymmetric flow through suddenly expanded nozzles. Int. J. Eng. Adv. Technol. 8(3), 570–578 (2019)

    Google Scholar 

  26. 26.

    Fharukh, A.G.M.; Alrobaian, A.A.; Aabid, A.; Khan, S.A.: Numerical analysis of convergent-divergent nozzle using finite element method. Int. J. Mech. Prod. Eng. Dev. 8(6), 373–382 (2018)

    Google Scholar 

  27. 27.

    Pathan, K.A.; Dabeer, P.S.; Khan, S.A.: An investigation to control base pressure in suddenly expanded flows. Int. Rev. Aerosp. Eng. 11(4), 162–169 (2018)

    Google Scholar 

  28. 28.

    Aabid, A.; Afifi, A.; Ali, F.A.G.M.; Nishat, A.M.; Khan, S.A.: CFD analysis of splitter plate on bluff body. CFD Lett. 11, 25–38 (2019)

    Google Scholar 

  29. 29.

    Afifi, A.; Aabid, A.; Khan, S. A.: Simulation of splitter plate on bluff body using finite volume method. Materials Today: Proceedings, 12 (2020)

  30. 30.

    Sajali, M.F.M.; Aabid, A.; Khan, S.A.; Mehaboobali, F.A.G.; Sulaeman, E.: Numerical investigation of the flow field of a non-circular cylinder. CFD Lett. 11(5), 37–49 (2019)

    Google Scholar 

  31. 31.

    Sajali, M.F.M.; Ashfaq, S.; Aabid, A.; Khan, S.A.: Simulation of effect of various distances between front and rear body on drag of a non-circular cylinder. J. Adv. Res. Fluid Mech. Therm. Sci. 62(1), 53–65 (2019)

    Google Scholar 

  32. 32.

    Khan, S.A.; Rathakrishnan, E.: Control of suddenly expanded flows with micro-jets. Int J Turbo Jet Engines 20, 63–82 (2003)

    Article  Google Scholar 

  33. 33.

    Fischer, R.A.: Statistical Methods for Research Workers, 5th edn. Oliver and Boyd, London (1934)

    Google Scholar 

  34. 34.

    Fischer, R.A.: Statistical Methods for Research Workers. Oliver and Boyd ed., London (1925)

    Google Scholar 

  35. 35.

    Montgomery, D.C.: Design and Analysis of Experiments, 8th edn. Hoboken, New York (2013)

    Google Scholar 

  36. 36.

    Zhang, H.; Craft, T.; Iacovides, H.: The formulation of the RANS equations for hypersonic turbulent flows. In: Proceedings of the World Congress on Mechanical, Chemical, and Material Engineering, pp. 1–9, (2019)

  37. 37.

    Scharnowski, S.; Kähler, C.J.: Investigation of a transonic separating/reattaching shear layer by means of PIV. Theor Appl Mech Lett. 5(1), 30–34 (2015)

    Article  Google Scholar 

  38. 38.

    Launder, B.E.; Sharma, B.I.: Application of the energy-dissipation model of turbulence to the calculation of flow near a spinning disc. Lett Heat Mass Transf. 1, 11–30 (1974)

    Article  Google Scholar 

  39. 39.

    ANSYS Inc: ANSYS FLUENT 18.0: Theory Guidance. Canonsburg PA, (2017)

  40. 40.

    Khan, S.A.; Aabid, A.: CFD analysis of CD nozzle and effect of nozzle pressure ratio on pressure and velocity for suddenly expanded flows. Int. J. Mech. Prod. Eng. Res. Dev. 8(June), 1147–1158 (2018)

    Google Scholar 

  41. 41.

    Sutherland, W.: LII. The viscosity of gases and molecular force. Dublin Philos. Mag. J. Sci. 36(223), 507–531 (1893)

    Article  Google Scholar 

  42. 42.

    Barth, T. J.; Jespersen, D. C.: The design and application of upwind schemes on unstructured meshes. In: 27th Aerospace Sciences Meeting, pp. 1–13, (1989)

  43. 43.

    Rehman, S.; Khan, S.A.: Control of base pressure with micro-jets: part I. Aircr Eng Aerosp. Technol. 80(2), 158–164 (2008)

    Article  Google Scholar 

  44. 44.

    Rathakrishnan, E.; Sreekanth, A. K.: Flow in pipes with sudden enlargement. In: Proceedings of the 14th International Symposium on Space Technology and Science, pp. 491–496, (1984)

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The authors wish to acknowledge and thank to Indian Institute of Technology, Kanpur, India, for allowing us to use their research facility of high-speed aerodynamics laboratory.

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Correspondence to Abdul Aabid.

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Aabid, A., Khan, S.A. Investigation of High-Speed Flow Control from CD Nozzle Using Design of Experiments and CFD Methods. Arab J Sci Eng 46, 2201–2230 (2021).

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  • Base pressure
  • Supersonic flow
  • CFD
  • Mach number
  • Microjet control
  • DOE