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A numerical investigation of simulating moisture in motive steam in a thermal-vapor compressor with DPM method

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Abstract

One of the prevalent phenomena that significantly affects thermal-vapor compressors is the moisture in the motive steam. It has a dominant effect on the thermodynamic and design parameters of a thermal-vapor compressor (TVC), such as entrainment ratio, compression ratio, and flow density. This study investigates a numerical simulation of a thermal-vapor compressor operated with a two-phase flow motive steam that is composed of saturated water vapor and dispersed water droplets. The droplets injected into the computational domain are represented as the second phase and are simulated by the discrete phase model. In this method, transport equations are solved for the continuous phase, whereas droplets regarded in the Lagrangian frame are involved through interaction in source terms. Three critical factors for understanding the effect of moisture on TVC are studied: the mass flow rate, the diameter, and the number of droplets. It will be shown that the presence of moisture in motive steam, which is inevitable to be ignored in the desalination industry and vapor lines, has a negative impact on the efficiency of the thermal-vapor compressors. Eventually, the numerical results are compared with the experimental data, which are accepted with less than 5% error from the actual TVC.

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Abbreviations

\(a_{1}\), \(a_{2}\), \(a_{3}\) :

Constant experimental parameters

B.C.:

Boundary condition

C D :

Drag coefficient

C m :

Momentum exchange coefficient

c p :

Specific heat capacity (J/kg. K)

CFD:

Computational fluid dynamics

CR:

Compression ratio

C s :

Thermal slip coefficient

C t :

Temperature jump coefficient

DPM:

Discrete phase model

DNS:

Direct numerical simulation

D T,P :

Thermophoretic coefficient

d P :

Particle diameter (m)

ER:

Entrainment ratio

F:

Momentum source term (kg/m2s2)

F Saff :

Saffman's lift force (N/kg)

F T :

Thermophoretic force (N/kg)

F v :

Virtual mass force (N/kg)

F x :

Additional acceleration force (N/kg)

g :

Gravitational acceleration (m/s2)

G k :

Generation of turbulence kinetic energy (kg/ms3)

h :

Convective heat transfer coefficient (W/m2K)

h fg :

Latent heat of vaporization (J/kg)

HMI:

Human–machine interface

kn:

Knudsen number

Kr:

The ratio of thermal conductivity

M:

Mass source term (kg/m3s)

m p :

Particle mass (kg)

ṁ :

Mass flow rate (kg/s)

MED:

Multi-effect desalination

MDP:

Maximum discharge pressure (KPa)

P :

Pressure (Pa)

P CO :

Cut-off pressure (KPa)

Q :

Energy source term (J/m3s)

Red :

Relative Reynolds number

S ε :

Source terms for dissipation rate (kg/ms3)

S k :

Source terms for turbulent kinetic energy (kg/ms3)

t :

Time (s)

T :

Temperature (K)

T p :

Particle temperature (K)

TVC:

Thermal-vapor compressor

u :

Fluid velocity (m/s)

u p :

Particle velocity (m/s)

\(\varepsilon\) :

Turbulent kinetic energy dissipation rate (m2/s3)

k :

Turbulence kinetic energy (m2/s2)

ρ :

Density (Kg/m3)

ρ p :

Particle density (Kg/m3)

μ :

Dynamic viscosity (Kg/m.s)

τ :

Stress tensor (Pa)

ν :

Kinematic viscosity (m2/s)

dis:

Discharge

mot:

Motive

p :

Particle (water droplet)

Saff:

Saffman's lift force

suc:

Suction

T:

Thermophoretic

References

  1. Noori Rahim Abadi MA, Kouhikamali R, Atashkari K (2015) Two-fluid model for simulation of the supersonic flow of wet steam within high-pressure nozzles. Int J Therm Sci 96:173–182

    Article  Google Scholar 

  2. Sharifi N, Boroomand M, Kouhikamali R (2012) Wet steam flow energy analysis within thermo-compressors. Energy 47:609–619

    Article  Google Scholar 

  3. Morsi SA, Alexander AJ (1972) An investigation of particle trajectories in two-phase flow systems. J Fluid Mech 55(2):193–208

    Article  MATH  Google Scholar 

  4. Bhabhe AS (2012) Experimental study of condensation and freezing in a supersonic nozzle. The Ohio State University, USA

    Google Scholar 

  5. Bakhtar F (1991) A study of nucleating flow of steam in a cascade of supersonic blading by the time-marching method. Int J Heat Fluid Flow 12:54–62

    Article  Google Scholar 

  6. Gerber AG (2002) Two-phase Eulerian/Lagrangian model for nucleating steam flow. J Fluids Eng 124:465–475

    Article  Google Scholar 

  7. Wojtan L, Ursenbacher T, Thome JR (2005) Investigation of flow boiling in horizontal tubes: part II-development of a new heat transfer model for stratified wavy, dry-out and mist flow regimes. Int J Heat Mass Transf 48:2970–2985

    Article  Google Scholar 

  8. O’Rourke PJ, Amsden A (2000) A spray/wall interaction sub-model for the KIVA-3 wall film model. SAE Paper 109:281–298

    Google Scholar 

  9. Dhanasekaran TS, Wang T (2012) Numerical model validation and prediction of mist/ steam cooling in a 180-degree bend tube, International Journal of. Heat Mass Transf 55:3818–3828

    Article  Google Scholar 

  10. Huang LX, Kumar K, Mujumdar AS (2006) A comparative study of a spray dryer with rotary disc atomizer and pressure nozzle using computational fluid dynamic simulations. Chem Eng Process 56:461–470

    Article  Google Scholar 

  11. Zahari NM, Zawawi MH, Sidek LM, Daud M, Zarina I, Ramli MZ, Agusril S, Rashid M (2018) Introduction of discrete phase model (DPM) in fluid flow: a review. Am Inst Phys 2030:20–34

    Google Scholar 

  12. Li X, Gaddis JL, Wang T (2001) Mist/steam heat transfer in confined slot jet im**ement. Trans, ASME 123:1086–1092

    Article  Google Scholar 

  13. Chrigui M, Sadiki A, Ahmadi G (2004) Study of interaction in spray between evaporating droplets and turbulence using second-order turbulence RANS modeling and a Lagrangian approach. Prog Comput Fluid Dyn 4:162–174

    Article  Google Scholar 

  14. Ebrahimian V, Gorji M (2008) Two-dimensional modeling of water spray cooling in superheated steam. Int J Therm Sci 12:79–88

    Article  Google Scholar 

  15. Kouhikamali R, Hesami H, Ghavamian A (2012) Convective heat transfer in a mixture of cooling water and superheated steam. Int J Therm Sci 60:205–211

    Article  Google Scholar 

  16. Torfeh S, Kouhikamali R (2015) Numerical investigation of mist flow regime in a vertical tube. Int J Therm Sci 95:1–8

    Article  Google Scholar 

  17. Lee JW, Jung KJ, Sherman M, Kim HS, Kim YJ (2020) Experimental and numerical analysis on the performance of spiral two-fluid atomizer using DPM method. In: ASME 2020 fluids engineering division summer meeting collocated with the ASME 2020 heat transfer summer conference and the ASME 2020 18th International Conference on Nanochannels, Microchannels, and Minichannels, vol 3. 219–226

  18. Zhang Y, Chang Q, Ge W (2021) Coupling DPM with DNS for dynamic interphase force evaluation. Chem Eng Sci 231:1051–1062

    Article  Google Scholar 

  19. Shafaee M, Tavakol M, Riazi R, Sharifi N (2015) An investigation on the supersonic ejectors working with a mixture of air and steam. Mech Sci Technol 11:4691–4700

    Article  Google Scholar 

  20. Chandra V, Ahmed MR (2014) Experimental and computational studies on a steam jet refrigeration system with constant and variable area ejectors. Energy Convers Manag 79:377–386

    Article  Google Scholar 

  21. Dutton JC, Carroll BF (1986) Optimal supersonic ejector designs. Fluids Eng 108:414–420

    Article  Google Scholar 

  22. ANSYS FLUENT v 20 R1 theory Guide. ANSYS Inc., 2020.

  23. Venkatesan G, Kulasekharan N, Iniyan S (2014) Numerical analysis of curved vane demisters in estimating water droplet separation efficiency. Desalination 339:40–53

    Article  Google Scholar 

  24. Givler RC (1987) An interpretation of solid-phase pressure in slow, fluid-particle flows. Int J Multiph Flows 13(5):717–722

    Article  Google Scholar 

  25. Toumi I, Kumbaro A (2006) An approximate linearized Riemann solver for a two-fluid model. J Comput Phys 124:286–300

    Article  MathSciNet  MATH  Google Scholar 

  26. Stewart HB, Wendroff B (1984) Two-phase flow models and methods. J Comput Phys 56:363–409

    Article  MathSciNet  MATH  Google Scholar 

  27. Niu Y (2001) Numerical approximations of a compressible two-fluid model by the advection upwind splitting method. Int J Numer Methods Fluids 36:351–371

    Article  Google Scholar 

  28. Stuhmiller J (1997) The influence of interfacial pressure forces on the character of two-phase flow model equations. Int J Multiph Flow 3:551–560

    Article  MATH  Google Scholar 

  29. Drew D, Cheng L, Lahey T (1979) The analysis of virtual mass effects in two-phase flow. Int J Multiph Flow 5:233–242

    Article  MATH  Google Scholar 

  30. Saurel R, Abgrall R (1999) A multi-phase method for compressible multi-fluid and multi-phase flows. J Comput Phys 150:425–467

    Article  MathSciNet  MATH  Google Scholar 

  31. Sussman M, Smereka P, Osher S (1994) A level set approach for computing solutions of incompressible two-phase flows. J Comput Phys 114:146–159

    Article  MATH  Google Scholar 

  32. Niu Y (2000) Simple conservative flux splitting for multi-component flow calculations. Numer Heat Transf Part B 38:203–222

    Article  Google Scholar 

  33. Chang C, Sushchikh S, Nguyen L, Liou M, Theofanous T (2007) Hyperbolicity, discontinuities, numerics of two-fluid model, Fifth Joint ASME/JSME fluids engineering summer conference, San Diego, U.S.A., 30 July–2 August 2007.

  34. Yan J, Cai W, Li Y (2012) Geometry parameters effect for air-cooled ejector cooling systems with R134a refrigerant. Renew Energy 46:155–163

    Article  Google Scholar 

  35. Min D, Lee H, Kim H, Kim C, Accurate and efficient prediction on suction performance of thermal vapor compressor using multi-phase flow computations. In: Proceedings of 23rd AIAA computational fluid dynamics conference, 5–9 June 2017, Denver, Colorado.

  36. Kim H, Computational methods for homogeneous multi-phase real fluid flows at all speed (Ph.D. thesis), Seoul National University, 2017

  37. Gerber AG (2002) Two-phase Eulerian/Lagrangian model for nucleating steam flow. J Fluids Eng 124(2):465–475

    Article  Google Scholar 

  38. Huang BJ, Jiang CB, Hu FL (1985) Ejector performance characteristics and design analysis of jet refrigeration system. J Eng Gas Turbine Power 107(3):792–802

    Article  Google Scholar 

  39. Dong J, Hu Q, Yu M, Han Z, Cui W, Liang D, Pan X (2020) Numerical investigation on the influence of mixing chamber length on steam ejector performance. Appl Therm Eng 14:115–204

    Google Scholar 

  40. Xue H, Wang L, Jia L, **e C, Lv Q (2020) Design and investigation of a two-stage vacuum ejector for MED-TVC system. Appl Therm Eng 167:114–713

    Article  Google Scholar 

  41. Park IS (2009) Robust numerical analysis-based design of the thermal vapor compressor shape parameters for multi-effect desalination plants. Desalination 242:245–255

    Article  Google Scholar 

  42. Talbot L, Cheng RK, Schefer RW, Willis DR (1980) Thermophoresis of particles in a heated boundary layer. J Fluid Mech 101:737–758

    Article  Google Scholar 

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Author information

Authors and Affiliations

  1. Faculty of Mechanical Engineering, University of Guilan, Rasht, Iran

    M. Hakimi

  2. Department of Mechanical Engineering, Isfahan University of Technology, Isfahan, Iran

    R. Kouhikamali

  3. Isfahan Science and Technology Town, Isfahan, Iran

    M. Hassani

  4. Faculty of Technology and Engineering, East of Guilan, University of Guilan, Rudsar, Iran

    N. Sharifi

Authors
  1. M. Hakimi
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  4. N. Sharifi
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Correspondence to R. Kouhikamali.

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Hakimi, M., Kouhikamali, R., Hassani, M. et al. A numerical investigation of simulating moisture in motive steam in a thermal-vapor compressor with DPM method. J Braz. Soc. Mech. Sci. Eng. 45, 89 (2023). https://doi.org/10.1007/s40430-023-04018-y

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  • DOI: https://doi.org/10.1007/s40430-023-04018-y

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