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Numerical investigation of roughness effect on wet steam ejector performance in the refrigeration cycle

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Abstract

Machining operation and presence of water droplets cause increase the surface roughness of wet steam ejector walls and change its performance in the refrigeration cycle. The purpose of this work is to investigate the influences of the primary nozzle surface roughness on wet steam ejectors in the refrigeration cycle with steam water as a working flow. The Eulerian-Eulerian model is validated by a comparison of numerical results with experimental data. Moreover, different surface roughness has been successfully applied to the primary nozzle, and its effect on the entire flow is shown. Six properties of wet steam are selected, including pressure, temperature, Mach number, average droplet radius, droplet growth rate, and liquid mass fraction. The result shows increasing roughness resulted in a shift of the shock chain to the primary nozzle, damping shock strength, and rising temperature in the diffuser. In addition, increment of the primary nozzle surface roughness decreases ER and COP of the refrigeration cycle by 3.67% and 3.8%, respectively. The designers and operators should be considered the roughness effects in the design and operation of wet steam ejectors due to the vital impact of the roughness on the liquid mass fraction, average droplet radius, droplet growth rate, ER, and COP.

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Abbreviations

\({D}_{\omega }\) :

Cross-diffusion term (kgm−1 s−3)

E:

Total energy (J)

ER:

Entrainment ratio (-)

\({f}_{r}\) :

Roughness function (-)

G:

Gibbs free energy (J kg−1)

\({\tilde{G }}_{k}\) :

Turbulence kinetic energy generation (kgm−1 s−3)

\({G}_{\omega }\) :

Generation of ω(kgm−1 s−3)

h:

Enthalpy (J kg−1)

J:

Nucleation rate (m−3 s−1)

k:

Turbulent dissipation rate (m2 s−3)

\({K}_{s}^{+}\) :

Non-dimensional roughness height

\({k}_{s}\) :

Physical roughness height (m)

\({K}_{B}\) :

Boltzmann’s constant

L:

Nozzle length(m)

m:

Mass of one molecule (mg)

\(\dot{m}\) :

Mass flow rate (kg s−1)

Ma:

Mach number

P:

Pressure (Pa)

\(\dot{Q}\) :

Rate of heat exchange (W m−2 s−1)

\({q}_{c}\) :

Condensation coefficient (-)

r∗ :

Critical radius of droplets (μm)

r:

Droplet radius (μm)

\(\dot{r}\) :

Droplet growth rate (μm s−1)

R:

Gas constant (JK−1 mol−1)

S:

Saturation ratio (-)

\({S}_{k}\) :

Source terms of ω (kgm−1 s−3)

\({S}_{\omega }\) :

Source terms of ω (kgm−1 s−3)

T:

Temperature (K)

u:

Velocity (m s − 1)

\({V}_{d}\) :

Mean volume of the droplets (m3)

x:

Spatial component (m)

Yk :

Dissipation of k (kgm−1 s−3)

Yω:

Dissipation of ω (kgm−1 s−3

α:

Thermal conductivity (W m−1 K−1)

β:

Liquid mass fraction (-)

Γ:

Mass generation rate (kg m−3 s−1)

δij:

Rate of mixing layer growth (-)

η:

Number of droplets (m−3)

μ:

Dynamic viscosity (Pa s)

ρ:

Density (kg m−3)

σ:

Liquid surface tension (N m−1)

σk :

Indicate turbulent Prandtl numbers for k

σω :

Turbulent Prandtl numbers for ω

τ:

Stress tensor (Pa)

ω:

Specific turbulence dissipation (s−1)

s:

Secondary

p:

Primary

e:

Exit

g:

Gas (vapor)

eff:

Effective

l:

Liquid

v:

Vapor

CAE:

Constant Area Exit

MCE:

Mixing Chamber Exit

PNE:

Primary Nozzle Exit

-:

Average

References

  1. Edathol J, Brezgin D, Aronson K, Kim HD (2020) Prediction of non-equilibrium homogeneous condensation in supersonic nozzle flows using Eulerian-Eulerian models. Int J Heat Mass Transf 1(152):119451. https://doi.org/10.1016/j.ijheatmasstransfer.2020.119451

    Article  Google Scholar 

  2. Yazdani S, Lakzian E (2020) Numerical simulation and passive control of condensing flow through turbine blade by NVD Method Using Eulerian-Lagrangian Model. Comput Math Appl 80(1):140–160. https://doi.org/10.1016/j.camwa.2020.03.007

    Article  MathSciNet  MATH  Google Scholar 

  3. Ding H, Tian Y, Wen C, Wang C, Sun C (2021) Polydispersed droplet spectrum and exergy analysis in wet steam flows using method of moments. Appl Therm Eng 182:116148. https://doi.org/10.1016/j.applthermaleng.2020.116148

    Article  Google Scholar 

  4. Dykas S, Wróblewski W (2011) Single-and two-fluid models for steam condensing flow modeling. Int J Multiph Flow 37(9):1245–1253. https://doi.org/10.1016/j.ijmultiphaseflow.2011.05.008

    Article  Google Scholar 

  5. Alekseev RA, Gribin VG, Tishchenko AA, Gavrilov IY, Tishchenko VA, Popov VV (2018) Application of PTV method for investigation of polydisperse wet steam flow. In J Phys: Confer Series 1128(1):012093. IOP Publishing. https://doi.org/10.1088/1742-6596/1128/1/012093

  6. Kafaei A, Salmani F, Lakzian E, Wróblewski W, Vlaskin MS, Deng Q (2022) The best angle of hot steam injection holes in the 3D steam turbine blade cascade. Int J Therm Sci 1(173):107387. https://doi.org/10.1016/j.ijthermalsci.2021.107387

    Article  Google Scholar 

  7. Milazzo A, Rocchetti A (2015) Modelling of ejector chillers with steam and other working fluids. Int J Refrig 1(57):277–287. https://doi.org/10.1016/j.ijrefrig.2015.05.015

    Article  Google Scholar 

  8. Besagni G, Cristiani N, Croci L, Guédon GR, Inzoli F (2021) Multi-scale evaluation of ejector performances: The influence of refrigerants and ejector design. Appl Therm Eng 5(186):116502. https://doi.org/10.1016/j.applthermaleng.2020.116502

    Article  Google Scholar 

  9. Pérez BP, Carrillo JA, de La Flor FJ, Lissén JM, Navarro AM (2021) Thermoeconomic analysis of CO2 Ejector-Expansion Refrigeration Cycle (EERC) for low-temperature refrigeration in warm climates. Appl Therm Eng 1(188):116613. https://doi.org/10.1016/j.applthermaleng.2021.116613

    Article  Google Scholar 

  10. Sharifi N, Boroomand M, Sharifi M (2013) Numerical assessment of steam nucleation on thermodynamic performance of steam ejectors. Appl Therm Eng 52(2):449–59. https://doi.org/10.1016/j.applthermaleng.2012.12.003

  11. Aliabadi MA, Bahiraei M (2021) Effect of water nano-droplet injection on steam ejector performance based on non-equilibrium spontaneous condensation: A droplet number study. Appl Therm Eng 5(184):116236. https://doi.org/10.1016/j.applthermaleng.2020.116236

    Article  Google Scholar 

  12. Li A, Yuen AC, Chen TB, Wang C, Liu H, Cao R, Yang W, Yeoh GH, Timchenko V (2019) Computational study of wet steam flow to optimize steam ejector efficiency for potential fire suppression application. Appl Sci 9(7):1486. https://doi.org/10.3390/app9071486

    Article  Google Scholar 

  13. Zhang G, Dykas S, Li P, Li H, Wang J (2020) Accurate condensing steam flow modeling in the ejector of the solar-driven refrigeration system. Energy 1(212):118690. https://doi.org/10.1016/j.energy.2020.118690

    Article  Google Scholar 

  14. Wang C, Wang L, Zhao H, Du Z, Ding Z (2016) Effects of superheated steam on non-equilibrium condensation in ejector primary nozzle. Int J Refrig 1(67):214–226. https://doi.org/10.1016/j.ijrefrig.2016.02.022

    Article  Google Scholar 

  15. Wang X, Dong J, Li A, Lei H, Tu J (2014) Numerical study of primary steam superheating effects on steam ejector flow and its pumping performance. Energy 15(78):205–211. https://doi.org/10.1016/j.energy.2014.10.004

    Article  Google Scholar 

  16. Yang Y, Karvounis N, Walther JH, Ding H, Wen C (2021) Effect of area ratio of the primary nozzle on steam ejector performance considering nonequilibrium condensations. Energy 15(237):121483. https://doi.org/10.1016/j.energy.2021.121483

    Article  Google Scholar 

  17. Ariafar K, Buttsworth D, Al-Doori G, Sharifi N (2016) Mixing layer effects on the entrainment ratio in steam ejectors through ideal gas computational simulations. Energy. 95:380–92. https://doi.org/10.1016/j.energy.2015.12.027

  18. Tang Y, Liu Z, Li Y, Wu H, Zhang X, Yang N (2019) Visualization experimental study of the condensing flow regime in the transonic mixing process of desalination-oriented steam ejector. Energy Convers Manage 1(197):111849. https://doi.org/10.1016/j.enconman.2019.111849

    Article  Google Scholar 

  19. Zou JJ, Zhou J, Lu HQ, Hu Y (2012) Experimental investigation on starting process of supersonic single-stage air ejector. J Therm Sci 21(4):348–353. https://doi.org/10.1007/s11630-012-0554-1

    Article  Google Scholar 

  20. Foroozesh F, Khoshnevis AB, Lakzian E (2020) Improvement of the wet steam ejector performance in a refrigeration cycle via changing the ejector geometry by a novel EEC (Entropy generation, Entrainment ratio, and Coefficient of performance) method. Int J Refrig 1(110):248–261. https://doi.org/10.1016/j.ijrefrig.2019.11.006

    Article  Google Scholar 

  21. Foroozesh F, Khoshnevis AB, Lakzian E (2020) Investigation on the effects of water steam ejector geometry in the refrigeration systems using entropy generation assessment. J Therm Anal Calorim 141(4):1399–1411. https://doi.org/10.1007/s10973-019-09128-1

    Article  Google Scholar 

  22. Lakzian E, Hajian M, Farahmand A (2018) The entropy generation rate minimization for a proposed air ejector for the carpet industry. Meccanica 53(1):145–159. https://doi.org/10.1007/s11012-017-0706-1https://doi.org/10.1007/s11012-017-0706-1

  23. Dong J, Hu Q, Yu M, Han Z, Cui W, Liang D, Ma H, Pan X (2020) Numerical investigation on the influence of mixing chamber length on steam ejector performance. Appl Therm Eng 25(174):115204. https://doi.org/10.1016/j.applthermaleng.2020.115204

    Article  Google Scholar 

  24. Zhang G, Dykas S, Yang S, Zhang X, Li H, Wang J (2020) Optimization of the primary nozzle based on a modified condensation model in a steam ejector. Appl Therm Eng 5(171):115090. https://doi.org/10.1016/j.applthermaleng.2020.115090

    Article  Google Scholar 

  25. Zhang G, Wang X, Pourranjbar D, Dykas S, Li H, Chen J (2022) The comprehensive analysis of the relationship between the latent heat, entrainment ratio, and ejector performance under different superheating degree conditions considering the non-equilibrium condensation. Appl Therm Eng 5(200):117701. https://doi.org/10.1016/j.applthermaleng.2021.117701

    Article  Google Scholar 

  26. Wang C, Wang L, Zou T, Zhang H (2017) Influences of area ratio and surface roughness on homogeneous condensation in ejector primary nozzle. Energy Convers Manag 149:168–74. https://doi.org/10.1016/j.enconman.2017.07.025

  27. Mahmoudian J, Mazzelli F, Milazzo A, Rocchetti A (2020) Experimental and numerical activity on a prototype ejector chiller. In J Phys: Confer Series 1599(1):012056. IOP Publishing. https://doi.org/10.1088/1742-6596/1599/1/012056

  28. Zhang H, Wang L, Jia L, Wang X (2018) Assessment and prediction of component efficiencies in supersonic ejector with friction losses. Appl Therm Eng 25(129):618–627. https://doi.org/10.1016/j.applthermaleng.2017.10.054

    Article  Google Scholar 

  29. Zhang H, Wang L, Jia L, Zhao H, Wang C (2018) Influence investigation of friction on supersonic ejector performance. Int J Refrig 1(85):229–239. https://doi.org/10.1016/j.ijrefrig.2017.09.028

    Article  Google Scholar 

  30. Wang L, Yan J, Wang C, Li X (2017) Numerical study on optimization of ejector primary nozzle geometries. Internatl J Refrige 76:219–29. https://doi.org/10.1016/j.ijrefrig.2017.02.010

  31. Brezgin DV, Aronson KE, Mazzelli F, Milazzo A (2017) The surface roughness effect on the performance of supersonic ejectors. Thermophys Aeromech 24(4):553–61. https://doi.org/10.1134/S0869864317040060

  32. Pillai A, Prasad BV (2018) Effect of wall surface roughness on condensation shock. Int J Therm Sci 1(132):435–445. https://doi.org/10.1016/j.ijthermalsci.-2018.06.028

    Article  Google Scholar 

  33. Han X, Liu X, Yuan Y, Han Z (2019) Effect of blade surface roughness on condensation process in a stator cascade. Int J Numer Meth Heat Fluid Flow. https://doi.org/10.1108/HFF-10-2019-0736

    Article  Google Scholar 

  34. Ding H, Li Y, Lakzian E, Wen C, Wang C (2019) Entropy generation and exergy destruction in condensing steam flow through turbine blade with surface roughness. Energy Convers Manage 15(196):1089–1104. https://doi.org/10.1016/j.enconman.2019.06.066

    Article  Google Scholar 

  35. Esfe HB, Kermani MJ, Avval MS (2015) Effects of surface roughness on deviation angle and performance losses in wet steam turbines. Appl Therm Eng 5(90):158–173. https://doi.org/10.1016/j.applthermaleng.2015.07.007

    Article  Google Scholar 

  36. Ruangtrakoon N, Aphornratana S, Sriveerakul T (2011) Experimental studies of a steam jet refrigeration cycle: effect of the primary nozzle geometries to system performance. Exp Thermal Fluid Sci 35(4):676–683. https://doi.org/10.1016/j.expthermflusci.-2011.01.001

    Article  Google Scholar 

  37. Ebrahimi-Fizik A, Lakzian E, Hashemian A (2020) Numerical investigation of wet inflow in steam turbine cascades using NURBS-based mesh generation method. Int Commun Heat Mass Transfer 1(118):104812. https://doi.org/10.1016/j.icheatmasstransfer.-2020.104812

    Article  MATH  Google Scholar 

  38. Mazzelli F, Little AB, Garimella S, Bartosiewicz Y (2015) Computational and experimental analysis of supersonic air ejector: Turbulence modeling and assessment of 3D effects. Int J Heat Fluid Flow 1(56):305–316. https://doi.org/10.1016/j.ijheatfluidflow.-2015.08.003

    Article  Google Scholar 

  39. Cebeci T, Chang KC (1978) Calculation of incompressible rough-wall boundary-layer flows. AIAA J 16(7):730–735. https://doi.org/10.2514/3.7571

    Article  Google Scholar 

  40. Bolduc CP, Van Dam N (2021) Development of a four-fluid model for condensing steam flows. Ann Nucl Energy 1(151):107893. https://doi.org/10.1016/j.anucene.2020.-107893

    Article  Google Scholar 

  41. Federico M, Francesco G, Adriano M (2017) CFD modelling of the condensation inside a Supersonic Nozzle: implementing customized wet-steam model in commercial codes. Energy Procedia 1(126):34–41. https://doi.org/10.1016/j.egypro.2017.08.053

    Article  Google Scholar 

  42. Senguttuvan S, Lee JC (2019) Numerical study of wet-steam flow in Moore nozzles. J Mech Sci Technol 33(10):4823–4830. https://doi.org/10.1007/s12206-019-0923-8

    Article  Google Scholar 

  43. Kermani MJ, Gerber AG (2003) A general formula for the evaluation of thermodynamic and aerodynamic losses in nucleating steam flow. Int J Heat Mass Transf 46(17):3265–3278. https://doi.org/10.1016/S0017-9310(03)00096-6

    Article  MATH  Google Scholar 

  44. White FM (2016) Fluid Mechanics 8th Edition, McGraw-Hill Education

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Authors and Affiliations

  1. Center of Computational Energy, Department of Mechanical Engineering, Hakim Sabzevari University, Sabzevar, Iran

    Mehdi Pouyan Rad & Esmail Lakzian

  2. Рeoples’ Friendship University of Russia (RUDN University), 6 Miklukho-Maklaya Street, 117198, Moscow, Russian Federation, Russia

    Esmail Lakzian

  3. School of Energy Systems, LUT University, Yliopistonkatu 34, P.O. Box 20, 53851, Lappeenranta, Finland

    Aki Grönman

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  1. Mehdi Pouyan Rad
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Correspondence to Esmail Lakzian.

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Rad, M.P., Lakzian, E. & Grönman, A. Numerical investigation of roughness effect on wet steam ejector performance in the refrigeration cycle. Heat Mass Transfer 58, 1545–1560 (2022). https://doi.org/10.1007/s00231-022-03197-z

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