# Effect of dependent variables to the performance of water injection vacuum drying system.

IntroductionVacuum drying is one method to increase the drying efficiency. Yang and Atallah (1985) concluded that vacuum will lower the boiling point of water and the absence of oxygen during the dehydration process is a prefer method for drying food sensitive to both heat and oxidation. The dried product so obtained show better retention of the nutrition (or medical) quality. Montgomery, et al. (1998) suggested that lowering the drying temperatures offer lesser waste heat for drying process.

This method does not popular due to higher both in term of the first installation and extra operating cost. Sapakie and Renshaw (1984) compared that the vacuum dryer system may cause approximately five folds of installation cost and two folds of operation cost when compared to the conventional forced air-drying system. However, the vacuum method is restricted for some certain kind of high quality drying products. One factor affecting to the decision to use is the equipment for inducing vacuum. Ranken and Kill (1995) recommended that proper value should not lower than 20 kPa, of which a water ejector is suitably be used. With merit of simplicity and reliability of operation, virtually no mechanical moving parts involved and using fluid media (water) for inducing vacuum, therefore it may be considered as an added-in system to the existing industrial plants with plenty of water circulation.

The objective of this study was to investigate the effect of some variables to vacuum drying water ejection type.

Theoretical Consideration

In order to induce vacuum in the control volume of a vessel, let consider Figure 1 the relation of diminishing pressure with respect to time and relationships of drying were derived (Holkeboer, 1993). When the gas supply from pressure [P.sub.2] through a conductance [F.sub.2], the left side (Figure 1a) shows a steady-state gas load limits the system to ultimate pressure (atmospheric). While the right-side (Figure 1a) shows the effect of trapped volume [V.sub.2], on the system pressure [P.sub.1].

[FIGURE 1 OMITTED]

Express a relationship as, P = [P.sub.0][e.sup.(-St/V)] - [Q.sub.L] / S (1)

Consider into 2 distinctive phenomena that,

The 1st portion, is not considering the effect of air quantity flow into the control chamber ([Q.sub.L]) (as [Q.sub.L] very small compared to the quantity being pulled out of the chamber), therefore equation (1) will be

P = [P.sub.0] [e.sup.(-St/V)] (2)

The 2nd successive portion, after a certain period of operation that the air being pulled out is very small compared to [Q.sub.L]

Hence P = [Q.sub.L]/S (3)

The gas flow through a vacuum component may be considered analogous to the current flow through an electrical circuit element. The conductance [F.sub.2] is defined as

[F.sub.2] = [Q.sub.L]/[P.sub.1]-[P.sub.2] (4)

Equations (1) to (4) are used for describing the evaporation loss in vacuum drying system.

[FIGURE 2 OMITTED]

Thermal dehydration as shown in Figure 2 explains that the heat for drying, at first transfers from the outer body of the product, causes evaporation of water (by latent heat of evaporation). The vapor transfuses to the air film adjacent to the surface then being carried away by the moving hot air. If the situation is sustained, therefore the surface vapor pressure of the product is lower than the vapor pressure inside. The moisture migration is going on due to the vapor pressure difference, until the product reaches its equilibrium moisture content where the inside moisture is equal to the moisture of the hot air surrounded (Langsartthong, 2002).

The total pressure of moist air (P) is the sum of partial pressures of the dry air ([P.sub.a]) and vapor pressure of water in the air ([P.sub.v])

i.e., P = [P.sub.a] + [P.sub.v] (5)

Where, [P.sub.a][V.sub.a] = ([m.sub.a]/[M.sub.a])R[T.sub.abs] (6)

[P.sub.v][V.sub.v] = ([m.sub.v]/[M.sub.v])R[T.sub.abs] (7)

The saturated vapor pressure ([P.sub.vs]) with respect to temperature were described as following relationships (Soponronnarit, 1997)

ln([P.sub.vs]) = 24.2779 - 6238.64/[T.sub.abs] - 0.344438ln([T.sub.abs]);233,16 [less than or equal to] [T.sub.abs](K) [less than or equal to] 273.16 (8)

And

ln([P.sub.vs]) = - 6238.64/[T.sub.abs] + 89.63121 + 0.023998970([T.sub.abs]) 1.2810336 x [10.sup.8]([T.sup.3.sub.abs]) + 2.0998405 x [10.sup.-11] ([T.sup.4.sub.abs]) - 12.150799ln([T.sub.abs]); 273.16[less than or equal to][T.sub.abs](K)[less than or equal to]3993.16 (9)

The relative humidity (%RH) can be expressed, at any particular temperature as

%RH = [P.sub.v]/[P.sub.vs] x 100 (10)

[FIGURE 3 OMITTED]

At the constant drying rate, Soponronnarit (1997) suggested for the material on drying tray has heat transmission by convection at the upper free surface, while at the bottom tray heat conduction combine with radiation is existed. This case appears to suit well with the water pan experiment. Refer to Figure 3, it can be written for the relationship of moisture loss in the water pan per unit area as,

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (11)

And [[??].sub.w]/[A.sub.cv] = [h'.sub.D] [[rho].sub.a] ([W.sub.vs][W.sub.[infinity]) (12)

Latent heat of vaporization is equal to the heat supply to the product, therefore the equilibrium of heat is concluded as

[[??].sub.w] = [h'.sub.D] [[rho].sub.a] A([W.sub.Wb]-[W.sub.[infinity]]) (13)

And [[??].sub.w] = h'A([T.sub.[infinity]]-[T.sub.Wb])/[h.sub.fg] (14)

For air-water system h'/[h'.sub.D] = [[rho].sub.a][C.sub.a] (15)

Knowing that [W.sub.wb] = [[M.sub.w]/[M.sub.a]] x [[P.sub.v,wb]/[P.sub.a]] (16)

And [W.sub.wb] = [[M.sub.w]/[M.sub.a]] x [[P.sub.v,[infinity]]/[P.sub.a]] (17)

Therefore, heat require for drying is

q = [[??].sub.w][h.sub.fg] = [[h'.sub.D]A[M.sub.W]([P.sub.v,wb][P.sub.v,[inifinity]])/[RT.sub.abs]] x [h.sub.fg] (18)

Experimental Method

A sketch of experiment apparatus is show in Figure 4

[FIGURE 4 OMITTED]

The system simulates some variables effecting at the steady state (or constantrate drying rate) of water in a tray dryer chamber (exclude time to created vacuum pressure), i.e. vacuum, temperature, water pressure and make-up air quantity on the moisture removal in a drying chamber was studied.

Four temperatures at 40, 50, 60 and 70[degrees]C and four vacuum pressures at 17, 44, 70 and 97 kPa, were used respectively. Two alternative methods indirectly controlled vacuum pressure for this experiment was used; either by controlling water pressure inlet ejector at 373 kPa, or controlling the make-up air quantity to vacuum chamber.

Experimental Results

Water Ejector Performance

Figure 5 show performances of the water ejector used in vacuum drying system, in term of Jet Pump Efficiency, Pressure Ratio (P/R), Suction Pressure with respect to the Air/Water Volumetric Flow Ratio. Result so obtained by setting the feeding water pressure at 373 kPa at the flow rate of 1.51 [m.sup.3]/hr.

[FIGURE 5 OMITTED]

Vacuum Chamber Characteristic

Further experiment shown with Figure 6 (with tabulated data) the controlled vacuum pressure inside vacuum chamber, by combining effect of the water pressure supplied to ejector and the air quantity fed into the chamber.

[FIGURE 6 OMITTED]

Figure 6 revealed that in side the vacuum chamber, the average air velocity is a dependence proportion to the vacuum pressure. Nevertheless, the water pressure supplied to the ejector has less effect to the change of the air velocity.

Evaporating Experimental Results

The experimental results of MER and SMER with a water pan in vacuum drying chamber are shown in Figure 7 to Figure 11, at various predetermined conditions.

[FIGURE 7 OMITTED]

[FIGURE 8 OMITTED]

[FIGURE 9 OMITTED]

[FIGURE 10 OMITTED]

[FIGURE 11 OMITTED]

Conclusion

At any particular temperature of drying, the average values of MER and SMER are concluded as follows,

(1) In the case of vacuum pressure is controlled by water pressure shown by Figure 7 (when compared to the base reference at 17 kPa),

At 44 kPa, MER and SMER are lower than at 17 kPa about 10 and 2%, respectively.

At 70 kPa, MER and SMER are lower than at 17 kPa about 3 and 3%, respectively.

(2) In the case of vacuum pressure is controlled by make-up air quantity shown by Figure 8 (when compared to the base reference at 44 kPa),

At 70 kPa, MER and SMER are higher than at 44 kPa about 9 and 9%, respectively.

At 97 kPa, MER and SMER are higher than at 44 kPa about 20 and 21%, respectively.

Consider for the effect of make-up air to the performance of drying. By direct comparison base on a same vacuum pressure that was indirectly controlled by the water pressure supplied to the ejector (Figures 9 and 10). Following conclusion can be made for any particular temperature of drying, for the average values of MER and SMER,

(1) At vacuum of 44 kPa (Figure 9), the average MER and SMER at no make-up air condition are lower than that with make-up air about 18 and 27% respectively.

(2) At vacuum of 70 kPa (Figure 10), the average MER and SMER at no make-up air condition are lower than that with make-up air about 30 and 37% respectively.

Effect of air temperatures on the performance for drying system (base on experiments result at 40[degrees]C), can be observed in Figure 11. Of which reveals that considering at any particular combinations of [P.sub.v] and [P.sub.w], the MER at 50, 60 and 70[degrees]C are higher than at 40[degrees]C by average about 50, 120 and 200 % respectively. Whereas the SMER at 50, 60 and 70[degrees]C are also higher than at 40[degrees]C by average about 50, 100 and 150 %, respectively.

Refer to equations (8) to (10), are obvious that the saturated vapor pressure ([P.sub.vs]) and the relative humidity (RH) each is sole dependent upon the air temperature. If the air temperature increases then the RH diminishes but the [P.sub.vs] increases, causes the increasing of moisture absorption capacity of the air inside vacuum chamber.

The MER and SMER obtained from this vacuum drying experiment of the water tray offer comparative performances for further study of the possibility of optimizing use of vacuum drying in existing industries.

It can be concluded that, the most factor affecting (in terms of MER and SMER) to the vacuum drying system using water ejector is the air temperature in the chamber, second by the quantity of make-up air and the third least effect is air velocity.

Nomenclature A = Area of exchanging heat ([m.sup.2]) [A.sub.cd] = Area of conductivity ([m.sup.2]) [A.sub.cv] = Evaporation surface area (only free surface of water on water pan) ([m.sup.2]) [A.sub.r] = Area of radiation ([m.sup.2]) g = Gravitational acceleration (m/[sec.sup.2]) h = Enthalpy of dry air (kJ/kg) [h.sub.fg] = Enthalpy of evaporation at the pressure in vacuum chamber (kJ/kg) h' = Convection heat transfer coefficient (W/[m.sup.2]) [h'.sub.D] = Mass transfer coefficient (W/m2) [h.sub.r] = Radiation heat transfer coefficient (W/[m.sup.2]) [k.sub.p] = Thermal conductivity (W/m[degrees]C) L = Length (m) l = Thickness (m) M = Molecular weight MER = Moisture extraction rate ([kg.sub.water]/hr) [M.sub.wf] = Final moisture content (wet basis) [M.sub.wi] = Initial moisture content (wet basis) m = Mass flow rate (kg/sec) [[??].sub.W] = Water removal rate (kg/hr) P = Pressure (kPa) [P.sub.v,wb] = Saturated vapor pressure (kPa) [P.sub.v,[infinity]] = Vapor pressure (kPa) Q = Volumetric flow rate ([m.sup.3]/sec) Re = Reynolds number S = Pumping speed (liter/sec) SMER = Specific moisture extraction rate ([kg.sub.water]/kW-h) T = Temperature ([degrees]C) t = time (sec) V = Velocity (m/sec) [W.sub.d] = Dry material (kg) [W.sub.f] = Final weight product (kg) [W.sub.i] = Initial weight product (kg) [W.sub.vs] = Saturated moisture ratio to dry air at temperature of [T.sub.vs] ([kg.sub.water]/ [kg.sub.dry air]) [W.sub.w] = Wet material (kg) [W.sub.wb] = Saturated moisture ratio at wet bulb temperature ([kg.sub.water]/[kg.sub.dry air]) [W.sub.wf] = Water removed (kg) [W.sub.[infinity]] = Moisture ratio ([kg.sub.water]/[kg.sub.dry air]) [[empty set].sub.0] = Volumetric flow ratio (air/water) [[eta].sub.jp] = Water jet pump efficiency [rho] = Density (kg/[m.sup.2]) [mu] = Liquid viscosity (N-sec/[m.sup.2]) Subscript Description a air abs Absolute atm Atmosphere cd Material of tray eq Equation exp Experiment g Gas partial pressure ke Kinetic energy m Mass, or mixing loss p Product r Radiation t Tray tb Outside surface of tray tt Inside surface of tray v vapor vs saturated vapor wb wet basis w Water vs Saturated vapor at product surface [infinity] Air

Acknowledgement

The authors are grateful to the research-supporting fund, Faculty of Engineering, Chiang Mai University for providing of financial support for this work.

Reference

[1] Boonsit P. (2002). Design and Performance Evaluation of a Water Ejection Type Vacuum Drying System, Thesis of Master Engineering, Chiang Mai University, Thailand

[2] Cunningham, R.G. (1974). Gas Compression with the Liquid Jet Pump", Journal of Fluids Engineering, 203-215.

[3] Cunningham, R.G. and Doping, R.J. (1974). "Jet Breakup and Mixing Throat Lengths for the Liquid Jet Gas Pump", Transactions of the ASME: 216-226.

[4] Holkeboer D.H., Jones D.W., Pagano F. and Santeler D.J. (1993). "Vacuum Technology and Space Simulation", American Vacuum Society Classics. AERO VAC CORP.: New York.

[5] Kogphimai D. (1999). A Design of Vacuum Cooling System Using Steam Jet Ejector., Thesis of Master Engineering, Chiang Mai University, Thailand.

[6] Langsartthong. (2002). Food Processing Technology. King Mongkut's Institute of Technology North Bangkok. (In Thai)

[7] Montgomery, S.W., Goldschmidt, V.W. and Franchek, M.A. (1998). "Vacuum Assisted Drying of Hydrophilic Plates: Static Drying Experiments". Journal of Heat Mass Transfer, Vol.415: 735-744

[8] Mujumdar, A.S. (1987). Handbook of Industrial Drying. McGill University: Montreal.

[9] Power R.B. (1993). Steam Jet Ejectors for the Process Industries, McGrawHill: London.

[10] Soponronnarit, S. (1997). Drying Grains and Some Food. Bangkok, King Mongkut's Institute of Technology Thonburi. (In Thai)

[11] Ranken, M.D., and Kill, R.C. (1995). Food Industries Manual 23rd Edition, New York : Chapman & Hall: 471-473.

[12] Sapakie, S.F and Renshaw, T.A. (1984). "Economics of Drying and Concentration of Food". Engineering and Food Volume 2 Process. New York: Elsevier Applied Science.

[13] Yang, C.S.T. and Atallah, W.A.A., (1985). "Effect of Four Drying Method on the Quality of Intermediate Lowbush Blueberries". Journal of Food Science, Vol 50: 1233-1237

(1) Sumpun Chaitep, (2) Payungsak Boonsit and (3) Pipatpong Watanawanyoo

(1,2) Department of Mechanical Engineering, Faculty of Engineering, Chiang Mai University, Chiang Mai, Thailand, 50200

(1) E-mail: svmpvn@hotmail.com

(3) College of Engineering, Rangsit University, Patumthani, Thailand, 12000 E-mail : tum1879@hotmail.com

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Author: | Chaitep, Sumpun; Boonsit, Payungsak; Watanawanyoo, Pipatpong |
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Publication: | International Journal of Applied Engineering Research |

Article Type: | Report |

Geographic Code: | 1USA |

Date: | Oct 1, 2009 |

Words: | 2569 |

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