Russian Federation
Vortex devices are effective apparatuses for intensifying heat and mass transfer and separation processes in chemical engineering, energy, and other industrial sectors. One of the key challenges in their design is the accurate assessment of pressure drop, which determines energy consumption. Multi-stage systems present particular complexity, where a swirling flow exiting a lower stage enters the subsequent one. The aim of this work is to develop an analytical method for calculating the pressure drop based on the theory of a centrifugal nozzle, applied to two sequentially arranged vortex elements accounting for pre-swirled flow. The method is founded on a computational scheme dividing the flow into four characteristic sections. The positions of the flow discontinuity surfaces were determined based on the maximum flow rate criterion. A calculated dependence for the pressure drop coefficient of a system of two identical vortex elements was obtained, establishing a relationship with the dimensionless swirl conservation coefficient Φ2. It is shown that the system's pressure drop varies from the sum of the pressure drops of individual elements at Φ2 = 0 to the pressure drop of a single element at Φ2= 1. Analysis of the dependence revealed that preserving 50% of the flow swirl at the inlet to the second stage reduces the overall system pressure drop by 20-40% compared to the mode of complete vortex decay. Comparison with independent experimental data confirmed the adequacy of the proposed method. Managing the degree of swirl conservation between stages is an effective way to reduce hydraulic losses. The developed methodology is intended for engineering calculations and optimization of multi-stage vortex apparatus designs with sequentially arranged identical stages.
PRESSURE DROP, CENTRIFUGAL NOZZLE, SWIRLING FLOW, ENERGY EFFICIENCY
1. S. Pandey, M. Wasilewski, A. Mukhopadhyay, O. Prakash, A. Ahmad, L.S. Brar, Applied Sciences, 14, 5, Article 2034 (2024). DOI:https://doi.org/10.3390/app14052034.
2. A. Kourou, S. Chen, Y. Ouyang, Current Opinion in Chemical Engineering, 46, Article 101056 (2024). DOI:https://doi.org/10.1016/j.coche.2024.101056.
3. G. Chen, G. Jiang, L. Tang, N. Li, International Communications in Heat and Mass Transfer, 158, Article 107907 (2024). DOI:https://doi.org/10.1016/j.icheatmasstransfer.2024.107907
4. O.S. Dmitrieva, V.V. Kharkov, A.N. Nikolaev, Theoretical Foundations of Chemical Engineering, 58, 1755-1759 (2024). DOI:https://doi.org/10.1134/S0040579525601165.
5. T.C. Hsiao, D.R. Chen, L. Li, P. Greenberg, K.W. Street, Aerosol Science and Technology, 44(4), 253-261 (2010). DOI:https://doi.org/10.1080/02786820903575394.
6. V.V. Kharkov, K.Z. Lavrova, A.N. Nikolaev, Herald of Technological University, 28, 8, 106-109 (2025). DOI:https://doi.org/10.55421/3034-4689_2025_28_8_106.
7. K. Bakhronov, A. Akhmatov, J. Dadakhon, Chemistry and Chemical Engineering, 4, Article 8 (2021). DOI:https://doi.org/10.51348/RGIR9524.
8. V.G. Ryabykh, V.Ya. Kozhukhar, L.V. Ivanchenko, V.L. Savich, Proceedings of Odessa Polytechnic University, 1(43), 242-248 (2014).
9. A.N. Musinsky, V.G. Ostrovsky, S.N. Peshcherenko, Territoriya Neftegaz, 9, 38-49 (2019).
10. R.R. Usmanova, G.E. Zaikov, Encyclopedia of Chemical Engineer, 5, 29-35 (2014).
11. V.E. Zinurov, V.V. Kharkov, I.N. Madyshev, Mining Informational and Analytical Bulletin, 10-1, 173-181 (2022). DOI:https://doi.org/10.25018/0236_1493_2022_101_0_173.
12. A.L. Tukmakov, V.V. Kharkov, A.A. Akhunov, Journal of Engineering Physics and Thermophysics, 95, 4, 902-908 (2022). DOI:https://doi.org/10.1007/s10891-022-02549-0.
13. A.N. Nikolaev, O.V. Kozulina, A.A. Ovchinnikov, R.R. Fatychov, Herald of Kazan Technological University, 11, 82-89 (2010).
14. E.S. Vyazovkin, Abstract of PhD Thesis, Kazan Chemical Technological Institute, Kazan, 1972. 24 p.
15. A.S. Karpenkov, N.A. Nikolaev, A.M. Nikolaev, Proceedings of KKhTI, 1, 48-52 (1970).
16. A.N. Nikolaev, Diss. Sci. (Eng.) Dissertation, KSTU, Kazan, 1999. 287 p
