Computational Study on the Effect of Vane Design in Enhancing the Mixing of Subsonic Jet and Sonic Jet

Document Type : Regular Article

Authors

1 Department of Aerospace Engineering, MIT Campus, Anna University, Chennai 600044, India

2 Department of Aerospace Engineering, IIT Kharagpur 721302, India

3 Department of Aerospace Engineering, IIT Kanpur 208016, India

Abstract

The purpose of this study is to numerically analyze the effect of vortex generators that are shaped like vanes in enhancing the mixing of subsonic and sonic jet and to determine the best design which yields maximum reduction in jet potential core length and minimum thrust loss at the nozzle exit.  Four different nozzle designs namely, models A, B, C and D are designed and compared with a base nozzle which is a plain circular nozzle without any vanes. The simulation is performed in ANSYS Fluent using the S-A turbulence model. The centerline pressure decay and radial pressure decay from models A to D are compared with that of the base nozzle to determine the ability of the vane to enhance the jet mixing characteristics. To evaluate the thrust loss, the total pressure at the exit plane of models A to D is measured and compared with that of the base nozzle. When comparing all the designs, it is observed that Model B produces the highest reduction in potential core length which is 66.4% at Mach no. 1 and Model D produces minimum total pressure loss which is 0.47% at Mach no. 0.4. In contrast to the conventional method, this design introduces a novel approach by placing the vanes parallel to the flow instead of the usual perpendicular arrangement. This unique configuration allows the vanes to redirect the flow rather than hinder it, resulting in a total pressure loss of less than 3%.

Keywords

Main Subjects


Akram, S., & Rathakrishnan, E. (2017). Control of supersonic elliptic jet with ventilated tabs. International Journal of Turbo & Jet-Engines ISSN (Online), 2191–0332, ISSN. Print 0334-0082. https://doi.org/10.1515/tjj-2017-0033
Akram, S., & Rathakrishnan, E. (2019). Corrugated tabs for enhanced mixing of supersonic elliptic jet. Journal of Aerospace Engineering, 32(1), 04018140(1-14). https://doi.org/10.1061/(ASCE)AS.1943-5525.0000970
Aravindh, K. S. M., & Rathakrishnan, E. (2017). Control of elliptic supersonic jet of aspect ratio 3. Journal of Aerospace Engineering. 30(5), 1943-5525.0000762. https://doi.org/10.1061/(ASCE)
Ahmed, R. A., Thanigaiarasu, S., Santhosh, J., Elangovan, S., & Rathakrishnan, E. (2013). Study of slanted perforated jets. International Journal of Turbo & Jet-Engines, 30(4), 347–357. https://doi.org/10.1515/tjj-2013-0015
Berrueta, T., & Rathakrishnan, E. (2017). Control of subsonic and sonic jets with limiting tabs. International Journal of Turbo and Jet-Engines, 34(1), 103–113. https://doi.org/10.1515/tjj-2016-0037
Billant, P., Chomaz, J. M., & Huerre, P. (1998). Experimental study of vortex breakdown in swirling jets. Journal of Fluid Mechanics, 376, 183-219. https://doi.org/10.1017/S0022112098002870
Bradbury, L. J. S., & Khadem, A. H. (1975). The distortion of a jet by tabs. Journal of Fluid Mechanics, 70(4), 801–813. https://doi.org/10.1017/S0022112075002352
Chand, D. S., Thanigaiarasu, S., Elangovan, S., & Rathakrishnan, E. (2011). Perforated arc-tabs for jet control. International Journal of Turbo and Jet Engines, 28(2), 133–138. https://doi.org/10.1515/tjj.2011.012
Chauvet, N., Deck, S., & Jacquin, L. (2007). Numerical study of mixing enhancement in a supersonic round jet. AIAA Journal, 45(7), 1675–1687. https://doi.org/10.2514/1.27497
Dhakshnamoorthy, M., Chand, D. S., Thanigaiarasu, S., & Elangovan, S. (2014, April 19–20). Numerical simulation of subsonic jet control with perforated tabs. International Conference on Recent Advances in Mechanical Engineering, Chennai, India.
Elangovan, S., & Rathakrishnan, E. (2004). Studies on high-speed jets from nozzles with internal grooves. Aeronautical Journal, 108(1079), 43–50. https://doi.org/10.1017/S000192400000498X
Ezhilmaran, G., Khandai, S. C., Sinha, Y. K., & Thanigaiarasu, S. (2019). Numerical simulation of supersonic jet control by tabs with slanted perforation. International Journal of Turbo & Jet-Engines. ISSN (Online), 2191-0332, ISSN. Print 0334-0082 https://doi.org/10.1515/tjj-2019-0015
Gandhinathan, B., & Subramanian, T. (2022). Control of subsonic jets using vanes as vortex generators. International Journal of Turbo and Jet-Engines. https://doi.org/10.1515/tjj-2022-0062
Ishii, T., Oinuma, H., Nagai, K., Tanaka, N., Oba, Y., & Oishi, T. (2011). Experimental study on a notched nozzle for jet noise reduction. Proceedings of the ASME Turbo Expo Vancouver, British Columbia, Canada. https://doi.org/10.1115/GT2011-46244
Jabez Richards, S. B., Thanigaiarasu, S., & Kaushik, M. (2023). Experimental study on the effect of tabs with asymmetric projections on the mixing characteristics of subsonic jets. Journal of Applied Fluid Mechanics, 16(6), 1208–1217. https://doi.org/10.47176/jafm.16.06.1584
Lovaraju, P., & Rathakrishnan, E. (2006). Subsonic and transonic jet control with cross-wire. AIAA Journal, 44(11), 2700–2705. https://doi.org/10.2514/1.17637
Mali, A. K., Jana, T., Kaushik, M., & Mishra, D. P. (2023). Influences of semi-circular, square, and triangular grooves on mixing behavior of an axisymmetric supersonic jet. Physics of Fluids, 35(4). https://doi.org/10.1063/5.0146672
Manigandan, S., Vijayaraja, K., Durga Revanth, G., & Anudeep, A. V. S. C. (2018). Mixing and entrainment characteristics of jet control with crosswire. Advances in Machine Learning and Data Science (pp. 121–128). https://doi.org/10.1007/978-981-10-8569-7_13
Maruthupandiyan, K., & Rathakrishnan, E. (2018). Shifted triangular tabs for supersonic jet control. Journal of Aerospace Engineering, 31(5), 04018067(1-8). https://doi.org/10.1061/(ASCE)AS.1943-5525.0000893
Naren, S. R., Thanigaiarasu, S., & Rathakrishnan, E. (2016). Numerical characterization of lip thickness on subsonic and correctly expanded sonic co-flowing jets. Transactions of the Japan Society for Aeronautical and Space Sciences, 59(3), 134–141. https://doi.org/10.2322/tjsass.59.134
Pannu, S. S., & Johannesen, N. H. (1976). The structure of jets from notched nozzles. Journal of Fluid Mechanics, 74(3), 515–528. https://doi.org/10.1017/S0022112076001924
Patil, R., & Rathakrishnan, E. (2019). Sonic elliptic jet control with corrugated limiting tab. Journal of Aerospace Engineering, 32(2), 04018151(1-18). https://doi.org/10.1061/(ASCE)AS.1943-5525.0000976
Powell, A. (1954). The reduction of choked jet noise. Proceedings of the Physical Society. Section B, 67(4), 313–327. https://doi.org/10.1088/0370-1301/67/4/306
Rathakrishnan, E. (2013). Corrugated tabs for subsonic and sonic jet control. Journal of Aeronautics and Aerospace Engineering, 02(5). https://doi.org/10.4172/2168-9792.1000120
Rathakrishnan, E. (2019). Applied gas dynamics. John Wiley & Sons.
Reddy, D. R., & Zaman, K. B. M. Q. (2006). Computational study of effect of tabs on a jet in a cross flow. Computers and Fluids, 35(7), 712–723. https://doi.org/10.1016/j.compfluid.2006.01.011
Sathish, K. K., & Senthilkumar, C. (2018). Jet flow control using semi-circular corrugated tab. International Journal of Turbo & Jet-Engines https://doi.org/10.1515/tjj-2018-0014
Spalart, P. R., & Allmaras, S. R. (1992). A one-equation turbulence model for aerodynamic flows In 30th aerospace sciences meeting and exhibit (pp. 92–0439). https://doi.org/10.2514/6.1992-439
Suseela Moorthi, A. K., Perumal, A. K., & Rathakrishnan, E. (2023). Jet mixing manipulation with asymmetric orientation of tabs. Proceedings of the Institution of Mechanical Engineers, Part G, 237(7), 1571–1581. https://doi.org/10.1177/09544100221132653
Thangaraj, T., Kaushik, M., Deb, D., Unguresan, M., & Muresan, V. (2022). Survey on vortex shedding tabs as supersonic jet control. Frontiers in Physics, 9, 789742. https://doi.org/10.3389/fphy.2021.789742
Thanigaiarasu, S., Jayaprakash, S., Elangovan, S., & Rathakrishnan, E. (2008). Influence of tab geometry and its orientation on under-expanded sonic jets. Proceedings of the IMech e Part G. Proceedings of the Institution of Mechanical Engineers, Part G, 222(3), 331–339. https://doi.org/10.1243/09544100JAERO299
Vignat, G., Durox, D., & Candel, S. (2022). The suitability of different swirl number definitions for describing swirl flows: Accurate, common and (over-) simplified formulations. Progress in Energy and Combustion Science, 89, 100969.
Vishnu, J., & Rathakrishnan, E. (2003). Jets from grooved nozzles. Proceedings of the 39thAIAA/ASME/SAE/ASEE Joint Propulsion Conference and Exhibit Huntsville, Alabama. AIAA, 4402. https://doi.org/10.2514/6.2003-4402
Wan, C., & Yu, S. C. M. (2013). Numerical investigation of the air tabs technique in jet flow. Journal of Propulsion and Power, 29(1), 42–49. https://doi.org/10.2514/1.B34534
Wilcox, D. C. (1993). Turbulence modeling for CFD. DCW Industries, Inc.
Akram, S., & Rathakrishnan, E. (2017). Control of supersonic elliptic jet with ventilated tabs. International Journal of Turbo & Jet-Engines ISSN (Online), 2191–0332, ISSN. Print 0334-0082. https://doi.org/10.1515/tjj-2017-0033
Akram, S., & Rathakrishnan, E. (2019). Corrugated tabs for enhanced mixing of supersonic elliptic jet. Journal of Aerospace Engineering, 32(1), 04018140(1-14). https://doi.org/10.1061/(ASCE)AS.1943-5525.0000970
Aravindh, K. S. M., & Rathakrishnan, E. (2017). Control of elliptic supersonic jet of aspect ratio 3. Journal of Aerospace Engineering. 30(5), 1943-5525.0000762. https://doi.org/10.1061/(ASCE)
Ahmed, R. A., Thanigaiarasu, S., Santhosh, J., Elangovan, S., & Rathakrishnan, E. (2013). Study of slanted perforated jets. International Journal of Turbo & Jet-Engines, 30(4), 347–357. https://doi.org/10.1515/tjj-2013-0015
Berrueta, T., & Rathakrishnan, E. (2017). Control of subsonic and sonic jets with limiting tabs. International Journal of Turbo and Jet-Engines, 34(1), 103–113. https://doi.org/10.1515/tjj-2016-0037
Billant, P., Chomaz, J. M., & Huerre, P. (1998). Experimental study of vortex breakdown in swirling jets. Journal of Fluid Mechanics, 376, 183-219. https://doi.org/10.1017/S0022112098002870
Bradbury, L. J. S., & Khadem, A. H. (1975). The distortion of a jet by tabs. Journal of Fluid Mechanics, 70(4), 801–813. https://doi.org/10.1017/S0022112075002352
Chand, D. S., Thanigaiarasu, S., Elangovan, S., & Rathakrishnan, E. (2011). Perforated arc-tabs for jet control. International Journal of Turbo and Jet Engines, 28(2), 133–138. https://doi.org/10.1515/tjj.2011.012
Chauvet, N., Deck, S., & Jacquin, L. (2007). Numerical study of mixing enhancement in a supersonic round jet. AIAA Journal, 45(7), 1675–1687. https://doi.org/10.2514/1.27497
Dhakshnamoorthy, M., Chand, D. S., Thanigaiarasu, S., & Elangovan, S. (2014, April 19–20). Numerical simulation of subsonic jet control with perforated tabs. International Conference on Recent Advances in Mechanical Engineering, Chennai, India.
Elangovan, S., & Rathakrishnan, E. (2004). Studies on high-speed jets from nozzles with internal grooves. Aeronautical Journal, 108(1079), 43–50. https://doi.org/10.1017/S000192400000498X
Ezhilmaran, G., Khandai, S. C., Sinha, Y. K., & Thanigaiarasu, S. (2019). Numerical simulation of supersonic jet control by tabs with slanted perforation. International Journal of Turbo & Jet-Engines. ISSN (Online), 2191-0332, ISSN. Print 0334-0082 https://doi.org/10.1515/tjj-2019-0015
Gandhinathan, B., & Subramanian, T. (2022). Control of subsonic jets using vanes as vortex generators. International Journal of Turbo and Jet-Engines. https://doi.org/10.1515/tjj-2022-0062
Ishii, T., Oinuma, H., Nagai, K., Tanaka, N., Oba, Y., & Oishi, T. (2011). Experimental study on a notched nozzle for jet noise reduction. Proceedings of the ASME Turbo Expo Vancouver, British Columbia, Canada. https://doi.org/10.1115/GT2011-46244
Jabez Richards, S. B., Thanigaiarasu, S., & Kaushik, M. (2023). Experimental study on the effect of tabs with asymmetric projections on the mixing characteristics of subsonic jets. Journal of Applied Fluid Mechanics, 16(6), 1208–1217. https://doi.org/10.47176/jafm.16.06.1584
Lovaraju, P., & Rathakrishnan, E. (2006). Subsonic and transonic jet control with cross-wire. AIAA Journal, 44(11), 2700–2705. https://doi.org/10.2514/1.17637
Mali, A. K., Jana, T., Kaushik, M., & Mishra, D. P. (2023). Influences of semi-circular, square, and triangular grooves on mixing behavior of an axisymmetric supersonic jet. Physics of Fluids, 35(4). https://doi.org/10.1063/5.0146672
Manigandan, S., Vijayaraja, K., Durga Revanth, G., & Anudeep, A. V. S. C. (2018). Mixing and entrainment characteristics of jet control with crosswire. Advances in Machine Learning and Data Science (pp. 121–128). https://doi.org/10.1007/978-981-10-8569-7_13
Maruthupandiyan, K., & Rathakrishnan, E. (2018). Shifted triangular tabs for supersonic jet control. Journal of Aerospace Engineering, 31(5), 04018067(1-8). https://doi.org/10.1061/(ASCE)AS.1943-5525.0000893
Naren, S. R., Thanigaiarasu, S., & Rathakrishnan, E. (2016). Numerical characterization of lip thickness on subsonic and correctly expanded sonic co-flowing jets. Transactions of the Japan Society for Aeronautical and Space Sciences, 59(3), 134–141. https://doi.org/10.2322/tjsass.59.134
Pannu, S. S., & Johannesen, N. H. (1976). The structure of jets from notched nozzles. Journal of Fluid Mechanics, 74(3), 515–528. https://doi.org/10.1017/S0022112076001924
Patil, R., & Rathakrishnan, E. (2019). Sonic elliptic jet control with corrugated limiting tab. Journal of Aerospace Engineering, 32(2), 04018151(1-18). https://doi.org/10.1061/(ASCE)AS.1943-5525.0000976
Powell, A. (1954). The reduction of choked jet noise. Proceedings of the Physical Society. Section B, 67(4), 313–327. https://doi.org/10.1088/0370-1301/67/4/306
Rathakrishnan, E. (2013). Corrugated tabs for subsonic and sonic jet control. Journal of Aeronautics and Aerospace Engineering, 02(5). https://doi.org/10.4172/2168-9792.1000120
Rathakrishnan, E. (2019). Applied gas dynamics. John Wiley & Sons.
Reddy, D. R., & Zaman, K. B. M. Q. (2006). Computational study of effect of tabs on a jet in a cross flow. Computers and Fluids, 35(7), 712–723. https://doi.org/10.1016/j.compfluid.2006.01.011
Sathish, K. K., & Senthilkumar, C. (2018). Jet flow control using semi-circular corrugated tab. International Journal of Turbo & Jet-Engines https://doi.org/10.1515/tjj-2018-0014
Spalart, P. R., & Allmaras, S. R. (1992). A one-equation turbulence model for aerodynamic flows In 30th aerospace sciences meeting and exhibit (pp. 92–0439). https://doi.org/10.2514/6.1992-439
Suseela Moorthi, A. K., Perumal, A. K., & Rathakrishnan, E. (2023). Jet mixing manipulation with asymmetric orientation of tabs. Proceedings of the Institution of Mechanical Engineers, Part G, 237(7), 1571–1581. https://doi.org/10.1177/09544100221132653
Thangaraj, T., Kaushik, M., Deb, D., Unguresan, M., & Muresan, V. (2022). Survey on vortex shedding tabs as supersonic jet control. Frontiers in Physics, 9, 789742. https://doi.org/10.3389/fphy.2021.789742
Thanigaiarasu, S., Jayaprakash, S., Elangovan, S., & Rathakrishnan, E. (2008). Influence of tab geometry and its orientation on under-expanded sonic jets. Proceedings of the IMech e Part G. Proceedings of the Institution of Mechanical Engineers, Part G, 222(3), 331–339. https://doi.org/10.1243/09544100JAERO299
Vignat, G., Durox, D., & Candel, S. (2022). The suitability of different swirl number definitions for describing swirl flows: Accurate, common and (over-) simplified formulations. Progress in Energy and Combustion Science, 89, 100969.
Vishnu, J., & Rathakrishnan, E. (2003). Jets from grooved nozzles. Proceedings of the 39thAIAA/ASME/SAE/ASEE Joint Propulsion Conference and Exhibit Huntsville, Alabama. AIAA, 4402. https://doi.org/10.2514/6.2003-4402
Wan, C., & Yu, S. C. M. (2013). Numerical investigation of the air tabs technique in jet flow. Journal of Propulsion and Power, 29(1), 42–49. https://doi.org/10.2514/1.B34534
Wilcox, D. C. (1993). Turbulence modeling for CFD. DCW Industries, Inc.
Akram, S., & Rathakrishnan, E. (2017). Control of supersonic elliptic jet with ventilated tabs. International Journal of Turbo & Jet-Engines ISSN (Online), 2191–0332, ISSN. Print 0334-0082. https://doi.org/10.1515/tjj-2017-0033
Akram, S., & Rathakrishnan, E. (2019). Corrugated tabs for enhanced mixing of supersonic elliptic jet. Journal of Aerospace Engineering, 32(1), 04018140(1-14). https://doi.org/10.1061/(ASCE)AS.1943-5525.0000970
Aravindh, K. S. M., & Rathakrishnan, E. (2017). Control of elliptic supersonic jet of aspect ratio 3. Journal of Aerospace Engineering. 30(5), 1943-5525.0000762. https://doi.org/10.1061/(ASCE)
Ahmed, R. A., Thanigaiarasu, S., Santhosh, J., Elangovan, S., & Rathakrishnan, E. (2013). Study of slanted perforated jets. International Journal of Turbo & Jet-Engines, 30(4), 347–357. https://doi.org/10.1515/tjj-2013-0015
Berrueta, T., & Rathakrishnan, E. (2017). Control of subsonic and sonic jets with limiting tabs. International Journal of Turbo and Jet-Engines, 34(1), 103–113. https://doi.org/10.1515/tjj-2016-0037
Billant, P., Chomaz, J. M., & Huerre, P. (1998). Experimental study of vortex breakdown in swirling jets. Journal of Fluid Mechanics, 376, 183-219. https://doi.org/10.1017/S0022112098002870
Bradbury, L. J. S., & Khadem, A. H. (1975). The distortion of a jet by tabs. Journal of Fluid Mechanics, 70(4), 801–813. https://doi.org/10.1017/S0022112075002352
Chand, D. S., Thanigaiarasu, S., Elangovan, S., & Rathakrishnan, E. (2011). Perforated arc-tabs for jet control. International Journal of Turbo and Jet Engines, 28(2), 133–138. https://doi.org/10.1515/tjj.2011.012
Chauvet, N., Deck, S., & Jacquin, L. (2007). Numerical study of mixing enhancement in a supersonic round jet. AIAA Journal, 45(7), 1675–1687. https://doi.org/10.2514/1.27497
Dhakshnamoorthy, M., Chand, D. S., Thanigaiarasu, S., & Elangovan, S. (2014, April 19–20). Numerical simulation of subsonic jet control with perforated tabs. International Conference on Recent Advances in Mechanical Engineering, Chennai, India.
Elangovan, S., & Rathakrishnan, E. (2004). Studies on high-speed jets from nozzles with internal grooves. Aeronautical Journal, 108(1079), 43–50. https://doi.org/10.1017/S000192400000498X
Ezhilmaran, G., Khandai, S. C., Sinha, Y. K., & Thanigaiarasu, S. (2019). Numerical simulation of supersonic jet control by tabs with slanted perforation. International Journal of Turbo & Jet-Engines. ISSN (Online), 2191-0332, ISSN. Print 0334-0082 https://doi.org/10.1515/tjj-2019-0015
Gandhinathan, B., & Subramanian, T. (2022). Control of subsonic jets using vanes as vortex generators. International Journal of Turbo and Jet-Engines. https://doi.org/10.1515/tjj-2022-0062
Ishii, T., Oinuma, H., Nagai, K., Tanaka, N., Oba, Y., & Oishi, T. (2011). Experimental study on a notched nozzle for jet noise reduction. Proceedings of the ASME Turbo Expo Vancouver, British Columbia, Canada. https://doi.org/10.1115/GT2011-46244
Jabez Richards, S. B., Thanigaiarasu, S., & Kaushik, M. (2023). Experimental study on the effect of tabs with asymmetric projections on the mixing characteristics of subsonic jets. Journal of Applied Fluid Mechanics, 16(6), 1208–1217. https://doi.org/10.47176/jafm.16.06.1584
Lovaraju, P., & Rathakrishnan, E. (2006). Subsonic and transonic jet control with cross-wire. AIAA Journal, 44(11), 2700–2705. https://doi.org/10.2514/1.17637
Mali, A. K., Jana, T., Kaushik, M., & Mishra, D. P. (2023). Influences of semi-circular, square, and triangular grooves on mixing behavior of an axisymmetric supersonic jet. Physics of Fluids, 35(4). https://doi.org/10.1063/5.0146672
Manigandan, S., Vijayaraja, K., Durga Revanth, G., & Anudeep, A. V. S. C. (2018). Mixing and entrainment characteristics of jet control with crosswire. Advances in Machine Learning and Data Science (pp. 121–128). https://doi.org/10.1007/978-981-10-8569-7_13
Maruthupandiyan, K., & Rathakrishnan, E. (2018). Shifted triangular tabs for supersonic jet control. Journal of Aerospace Engineering, 31(5), 04018067(1-8). https://doi.org/10.1061/(ASCE)AS.1943-5525.0000893
Naren, S. R., Thanigaiarasu, S., & Rathakrishnan, E. (2016). Numerical characterization of lip thickness on subsonic and correctly expanded sonic co-flowing jets. Transactions of the Japan Society for Aeronautical and Space Sciences, 59(3), 134–141. https://doi.org/10.2322/tjsass.59.134
Pannu, S. S., & Johannesen, N. H. (1976). The structure of jets from notched nozzles. Journal of Fluid Mechanics, 74(3), 515–528. https://doi.org/10.1017/S0022112076001924
Patil, R., & Rathakrishnan, E. (2019). Sonic elliptic jet control with corrugated limiting tab. Journal of Aerospace Engineering, 32(2), 04018151(1-18). https://doi.org/10.1061/(ASCE)AS.1943-5525.0000976
Powell, A. (1954). The reduction of choked jet noise. Proceedings of the Physical Society. Section B, 67(4), 313–327. https://doi.org/10.1088/0370-1301/67/4/306
Rathakrishnan, E. (2013). Corrugated tabs for subsonic and sonic jet control. Journal of Aeronautics and Aerospace Engineering, 02(5). https://doi.org/10.4172/2168-9792.1000120
Rathakrishnan, E. (2019). Applied gas dynamics. John Wiley & Sons.
Reddy, D. R., & Zaman, K. B. M. Q. (2006). Computational study of effect of tabs on a jet in a cross flow. Computers and Fluids, 35(7), 712–723. https://doi.org/10.1016/j.compfluid.2006.01.011
Sathish, K. K., & Senthilkumar, C. (2018). Jet flow control using semi-circular corrugated tab. International Journal of Turbo & Jet-Engines https://doi.org/10.1515/tjj-2018-0014
Spalart, P. R., & Allmaras, S. R. (1992). A one-equation turbulence model for aerodynamic flows In 30th aerospace sciences meeting and exhibit (pp. 92–0439). https://doi.org/10.2514/6.1992-439
Suseela Moorthi, A. K., Perumal, A. K., & Rathakrishnan, E. (2023). Jet mixing manipulation with asymmetric orientation of tabs. Proceedings of the Institution of Mechanical Engineers, Part G, 237(7), 1571–1581. https://doi.org/10.1177/09544100221132653
Thangaraj, T., Kaushik, M., Deb, D., Unguresan, M., & Muresan, V. (2022). Survey on vortex shedding tabs as supersonic jet control. Frontiers in Physics, 9, 789742. https://doi.org/10.3389/fphy.2021.789742
Thanigaiarasu, S., Jayaprakash, S., Elangovan, S., & Rathakrishnan, E. (2008). Influence of tab geometry and its orientation on under-expanded sonic jets. Proceedings of the IMech e Part G. Proceedings of the Institution of Mechanical Engineers, Part G, 222(3), 331–339. https://doi.org/10.1243/09544100JAERO299
Vignat, G., Durox, D., & Candel, S. (2022). The suitability of different swirl number definitions for describing swirl flows: Accurate, common and (over-) simplified formulations. Progress in Energy and Combustion Science, 89, 100969.
Vishnu, J., & Rathakrishnan, E. (2003). Jets from grooved nozzles. Proceedings of the 39thAIAA/ASME/SAE/ASEE Joint Propulsion Conference and Exhibit Huntsville, Alabama. AIAA, 4402. https://doi.org/10.2514/6.2003-4402
Wan, C., & Yu, S. C. M. (2013). Numerical investigation of the air tabs technique in jet flow. Journal of Propulsion and Power, 29(1), 42–49. https://doi.org/10.2514/1.B34534
Wilcox, D. C. (1993). Turbulence modeling for CFD. DCW Industries, Inc.