Post on 04-Apr-2018
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Vacuum Drying of foods Methods of water removal
to obtain final products of thehigh quality
byreducing air pressure which results in drying at a
lower temperature than is
required at full pressure.
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States of Water
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Industry has grouped pressures
below atmospheric level into
Rough vacuum
is used in about 90% of the chemical,petrochemical, and other processingindustries.
vacuum distillation,
filtration,
crystallization,
reaction,
drying, others.
Medium vacuum
molten metals degassing, moleculesdistillation, freeze drying, and others.High and ultra-high vacuum thin films, research, and space
simulation.(Power,2005)
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Heat Transfer Mechanismsat Low Pressure
fsh TThq
xTkqC
1/1/121
44
21
ss
C
TTq
Convection
Conduction
Radiation
total pressure decreases, heat transfer coefficient (h) decreases
h : negligible, under high vacuum,.
k :lowest value at high vacuum
total pressure decreases, thermal conductivity (k) decreases
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Heat Transfer Mechanismsat Low Pressure
Heat transfer ispoorly transferredunder vacuum.
Heat is generallytransferred to the
product byconduction andsometimes byradiation.
Convection is raresince very few fluid
molecules areavailable undervacuum.
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Ejectors : Vacuum Pump
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Problem of Vacuum Drying Main problem of drying processes under vacuum .
The high operating and maintenance costs
The long drying times under continuous vacuumincrease theirenergy consumption enormously and
make the process considerably more expensive as
compared to drying at atmospheric pressure.
(Ratti, 2008)
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Advantages of EjectorsMechanical Vacuum Pump Ejector
energyconsumption very high lowmaintenance-cost very high Low(No moving part,
Easy to operate)heat convection exhaust air affects its
surrounding of theproduction machines
no heat convection
Space-requirement much more space LessEasy to Install
oil-requirement oil-lubricated, oil separator oil-freeefficency expensive energy high efficency
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Complete system of an ejector
5
6
1
4
2
3
1 Compressed fluid
2 Nozzle3 Suction pipe4 Vacuum connection5 Inlet filter6 Exhaust fluid
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Diffuser and Nozzle (Subsonic Flow)A diffuser
converts high speed, low pressure flowto low speed, high pressure flow
A nozzleconverts high pressure, low speed flow
to low pressure, high speed flow
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Total energy of High-speed flow
Common Assumptions No work or heat transfer
Neglect changes in pe
Energy Balance: Crossing out terms assumed 0
2 2
C CIN OUTIN OUT
h h2
h ke h kg 2g
e
v v
INq
0
INw
0
h ke pe 0
IN
OUTq0
OUTw0
h ke pe 0OUT
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Basic design of an ejector
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Mathematical model The main steps used to establish mathematical
modelsA. assumption proposalB. deriving the governing equations
C. providing auxiliary relation to close the governingequations
D. adopting proper mathematic approach to solve themodel
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A: Assumption proposal1. The inner wall of the ejector is adiabatic.2. The flow inside the ejector is steady and isentropic.3. The primary fluid and secondary fluid are supplied to
the ejector at zero velocity.4. The velocity at the ejectoroutlet is neglected.5. The two fluids begin to mix with a uniform pressure
at the mixing section.
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B: Governing equations
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C: Auxiliary relation1. Boundary conditions:
pressures at inlet and exit of the ejector.
the mass flow rates or the velocities of the primary andsecondary fluids
2. Initial conditions: expansion ratio entrainment ratio
cross section area of the constant-area throat tube Auxiliary relations:
Definition of Mach number
Definition of sonic velocity
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C: Auxiliary relation (Cont.)
3. Auxiliary relations: Based on isentropic assumption, the following gas
dynamic equations are frequently used in thethermodynamic models:
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C: Auxiliary relation (Cont.)
3. Auxiliary relations: (Cont.)
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D: Mathematical Model
Thermodynamicmodel
Single-phase flow
model
Constant-pressure
mixing model
Keenan and Neumann (1942)
Munday and Bagster (1977)
Eames et al.(1995)
Constant-area
mixing model
Keenan and Neumann (1942)
Grazzini and Mariani (1998)
Yapici and Ersoy (2005)
Two-phaseflow model
Sherif et al. (2000)Beithou and Aybar (2000)
Empirical/semi-empirical
model
Huang et al. (1999)Cizungu et al. (2005)Balamurugan et al. (2007)Dessouky et al. (2002)
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Thermodynamic model the model based on thermodynamic analysis is the simplest
solve the equations in one dimension
the isentropic relations and some gas dynamic equations are used to assist in the description of the relationship between
the temperature pressure enthalpy Mach number velocity
Single-phase flow assume that the inlet fluid is superheated and no phase change occurring in the ejector.
Two-phase flow ejector works as a pump
using high pressure liquid to entrain gas
or higher pressure vapor to entrain liquid
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Thermodynamic modelTwo-phase flow model
Beithou and Aybar (2000) employed a one-dimensional control volume method to develop a local
mathematical model
performance prediction of the steam-driven jet pump.
applied the conservation of mass and momentum equation as well as theentropy equation As the fluid is uncompressible,
the Bernoulli equation can be used to calculate the entrained water velocity at thenozzle.
at the mixing section, the steady-state energy equation was used to calculate thevelocity of the mixture with the assumption of
adiabatic mixing process no potential energy change.
Take the head loss into account, the Bernoulli equation was used in thediffuser to find out the pressure and velocity profiles along it.
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Thermodynamic modelTwo-phase flow model
section By usingBernoulli equation between the water tank and the exit of thewater nozzleContinuity equation
WaternozzleMixing
Diffuser
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Effect of design and operatingparameter on suction pressure
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Relationship betweenair (primary) mass flow rate and pressure drop
(Balamurugan et al. 2006)
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Relationship between
water temperature and lowest suction pressure
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Variation of the air entrainment rate
with the pressure difference
between the air entry and the throat exit:
(Kandakureet al. 2005)
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Schematic geometry of an ejector
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Effect of projection ration (LTN/DT) on the rate of entrainment
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Effect of area ratio ((DS2-DN
2)/DN2) on the rate of
entrainment for different values of projection ratios
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Effect of angle on converging section ()on rate of entrainment
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Conclusion Effect of design and operating parameter on suction pressure
Parameter Value of parameter Suction pressureLTN/DT
((DS2-DN
2)/DN2)
mT
Optimal valueOptimal valueOptimal value
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ConclusionSteam ejector Water ejector
Mostly use forVacuum ejector
Expensive Cheap
Design : GEOMETRY