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Chapter 10 Drying of Solids

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IntroductionIntroduction

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Introduction1.Methods for removing liquid from solid materials1.Methods for removing liquid from solid materials

(1)Mechanically: By presses or centrifuges(1)Mechanically: By presses or centrifuges ,, etc. etc.

(2)By physical-chemical process: Only small (2)By physical-chemical process: Only small amounts of liquid removed. amounts of liquid removed.

(3)Thermally: Liquid is heated and vaporized, and (3)Thermally: Liquid is heated and vaporized, and then removed---Drying. then removed---Drying. ••It is generally cheaper to remove liquid It is generally cheaper to remove liquid mechanically than thermally, and thus it is mechanically than thermally, and thus it is advisable to reduce the liquid content as much as advisable to reduce the liquid content as much as practicable before feeding the material to a practicable before feeding the material to a heated dryer.heated dryer.

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Introduction2.Purposes and applications of drying2.Purposes and applications of drying

••Purposes: Drying makes materials more Purposes: Drying makes materials more convenient in packaging, transporting, convenient in packaging, transporting, preserving, fabricating, and applying; preserving, fabricating, and applying; and improves quality of products. and improves quality of products. ••Applications: ….Applications: ….

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Introduction

3.Classification of drying processes 3.Classification of drying processes (1)Atmospheric and vacuum drying processes. (1)Atmospheric and vacuum drying processes. Question: why no drying process with pressure greatQuestion: why no drying process with pressure great

er than 1 atm?er than 1 atm? (2)continuous and batchwise drying processes. (2)continuous and batchwise drying processes. (3)According to the heat transfer manners: (3)According to the heat transfer manners: 1)Indirect dryers/dryers in which heat is trans1)Indirect dryers/dryers in which heat is trans

ferred to the solid from an external mediumferred to the solid from an external medium(condensing steam, etc)(condensing steam, etc)

2)Convective/direct dryers/Dryers in which th2)Convective/direct dryers/Dryers in which the solid is directly exposed to a hot gase solid is directly exposed to a hot gas

6

Introduction

3)Drying by radiant energy3)Drying by radiant energy4)Drying by dielectric/microwave energy4)Drying by dielectric/microwave energy5)Freeze-drying5)Freeze-drying6)Combining drying6)Combining drying••Most common used: Convective/direct dryersMost common used: Convective/direct dryers••Common used drying medium: air; Common used drying medium: air; ••Common liquid existing in solids: Water.Common liquid existing in solids: Water.

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4.Drying conditions for convective dryers

0)(

:

ppforceDriving

ppNecessary

w

w

：

••Question: Is the drying process Question: Is the drying process a combination of heat transfer a combination of heat transfer and mass transfer?Why? What and mass transfer?Why? What is the effect of drying medium?is the effect of drying medium?

••Heat transfer is the means, Heat transfer is the means, and mass transfer is the end.and mass transfer is the end.

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Schematic diagram of convective drying processSchematic diagram of convective drying process

• 4.Drying conditions for convective dryers4.Drying conditions for convective dryers

Schematic diagram of convective drying processSchematic diagram of convective drying process

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• 5.Problems discussed in this chapter(1)Properties of Moist air; (1)Properties of Moist air;

(2)Material balances——Air flow rate; (2)Material balances——Air flow rate;

(3)Heat balances——Flow rate of heating steam, (3)Heat balances——Flow rate of heating steam, heat transfer area of heater; heat transfer area of heater;

(4)Calculation of drying rates and drying time; (4)Calculation of drying rates and drying time;

(5)Equilibrium relationship; (5)Equilibrium relationship;

(6)Selection of drying equipment; (6)Selection of drying equipment;

(7)Operation and enhancement of drying (7)Operation and enhancement of drying equipment.equipment.

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(1)Properties of Moist air; (1)Properties of Moist air;

(2)Phase equilibria of drying process;(2)Phase equilibria of drying process;

(3)Drying curve and drying rate curve under (3)Drying curve and drying rate curve under constant drying conditions; constant drying conditions;

(4) Material and heat balances, calculation of d(4) Material and heat balances, calculation of drying rates and drying time; rying rates and drying time;

(5)Principles and structures of typical drying e(5)Principles and structures of typical drying equipmentquipment..

Principal subject matter of this chapter

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•1 Properties of Moist Air and Humidity-enthalpy Chart （ H-I ） or temperature-humidity(t-H) chart[Reading Materials:596-608]

••Moist air=Dry air+water vaporMoist air=Dry air+water vapor

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(1)Moist air can be considered as ideal gas, I.e., m(1)Moist air can be considered as ideal gas, I.e., mixtures of gas and vapor follow the ideal gas laixtures of gas and vapor follow the ideal gas laws. ws.

(2)The usual basis for engineering calculations: (2)The usual basis for engineering calculations: (a)A unit mass of vapor-free air/dry air[(a)A unit mass of vapor-free air/dry air[ 计算基准计算基准

：单位质量的绝干空气：单位质量的绝干空气 ], ], where where vaporvapor means the gaseous form of the comp means the gaseous form of the comp

onent that is also present as liquid and onent that is also present as liquid and gasgas is th is the component present only in gaseous form;e component present only in gaseous form;

(b)A unit mass of bone-dry material[(b)A unit mass of bone-dry material[ 单位质量的单位质量的绝干物料绝干物料 .].]

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g

v

gg

vv

n

n

nM

nM

airmoistofmassairdry

airmoistofmassvaporwaterH

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1. Moist air properties1. Moist air properties (1. a).Humidity H [(1. a).Humidity H [kgkg water vapor/ water vapor/kgkg dry air] dry air]

)25(622.0

pP

pH

pP

p

p

p

n

n

g

v

g

v

p=pp=pvv—partial pressure of water vapor in moist air, N/m—partial pressure of water vapor in moist air, N/m22; p; pgg—partial p—partial p

ressure of dry air in moist air; P—total pressure of moist air, N/mressure of dry air in moist air; P—total pressure of moist air, N/m22..

H=fH=f （（ PP ，， pp ））

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•Difficult points:

1) Understanding 1) Understanding adiabatic saturation adiabatic saturation temperaturetemperature tastas and and wet-bulb tempewet-bulb temperaturerature tw tw; ;

2)Heat balances of non-ideal drying p2)Heat balances of non-ideal drying process. rocess.

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Where p=ps=f(t), ps=vapor pressure of water, Where p=ps=f(t), ps=vapor pressure of water, Hs=f(P, t) Hs=f(P, t)

(1(1. . b).Saturation humidity Hs: [kg water vapor/kg b).Saturation humidity Hs: [kg water vapor/kg dry air] or[ kgdry air] or[ kg 水气水气 /kg/kg 干空气干空气 ], when ], when p=pp=pss

),()(

)35(622.0

tPfHtfp

pP

pH

ss

s

ss

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•(2)Specific volume of moist air :Specific volume of dry airSpecific volume of dry air::

（（ 5-65-6 ））

••Specific volume of water vapor:Specific volume of water vapor:

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•(3) Relative humidity

pp and and ppss are under the same temperature. are under the same temperature.

Saturated air is air in which Saturated air is air in which =100%. air capacity of ab=100%. air capacity of absorbing water vaporsorbing water vapor

When p=0,When p=0,=0=0 ，湿空气不含水，为绝干空气。，湿空气不含水，为绝干空气。When When p= pp= pss,,=100%,=100%, 空气中水气已饱和，无干燥能力空气中水气已饱和，无干燥能力。。

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(5)Total enthalpy of moist air(5)Total enthalpy of moist air ： ： I I 焓 焓 [kJ/kg dry air] [kJ/kg dry air] 。。

)75(88.101.1

)]/([88.1

)]/([01.1

aHC

CvaporwaterkgkJC

CairdrykgkJC

HCCC

H

v

g

vgH

(4)Humid Heat C(4)Humid Heat CHH ： ： [KJ/[KJ/ （（ kg dry air·kg dry air·

℃℃）） ]]

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Assignment: Problem5-1Assignment: Problem5-1

•Attention: Enthalpy is a relative value. •Datum temperature: 0 . At 0 , enthalpy of dry ℃ ℃air or liquid water is zero.

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•Problem5-1. The total pressure of moist air at 600C and 40% relative humidity is 50kPa. Calculate, (1)Partial pressure of water vapor in the moist air; (2)Humidity; (3)Density of the moist air.

./493.0)3(

;/118.0)2(

;97.7)1(

:

1

3 airmoistmkg

airdrykgvaporwaterkgH

kPap

Key

v

H

H

HH

Hint:Hint:

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• Example5-1. The humidity of moist air at 1 atm and 20 is ℃0.014673kg/kg dry air, and ps(at 20 )℃is 2.3346kPa. Calculate: (1) Relative humidity of the moist air; (2)Humid specific volume; (3)Humid heat;(4)Total enthalpy. If the moist air is heated to the temperature of 50 , calculate the above items respectively. ℃

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. (6)Dry-bulb temperature t and wet-bulb temperature tw

tt Under steadUnder steady- state, ty- state, tww<<

t. Whyt. Why ？？Make-up water

tw

u>5m/s (Turbulent flow)

teTemperatur

HHumidity

Const

Air

Dry-bulb Dry-bulb temperature t: the temperature t: the actual gas actual gas temperature.temperature.

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•The liquid temperature when steady state is reached is the wet bulb temperature.

Meanings of the symbols refer to p.247-248Meanings of the symbols refer to p.247-248

••If air is not saturated, If air is not saturated, some liquid some liquid evaporates, cooling the evaporates, cooling the remaining liquid until remaining liquid until the rate of heat the rate of heat transfer to the liquid transfer to the liquid just balances the heat just balances the heat needed for needed for evaporation.evaporation.

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When steady state is reached, When steady state is reached,

Combining above equations gives,Combining above equations gives,

Mass transfer coefficient based on Mass transfer coefficient based on

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Implications of Implications of Eq.(5-12):Eq.(5-12):

HH

nnH

nn

wtwwtws

w

Ck

uku

tfrtfH

Htft

09.1

Re,Re

)(),(

),()1

,

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When measuring tw:When measuring tw: In order to ensure In order to ensure /k/kHH=Const=Const ，， air flow must bair flow must b

e kept in turbulent state. Experiments prove the kept in turbulent state. Experiments prove that when u>5m/s, the radiant and conduction effat when u>5m/s, the radiant and conduction effects can be omitted. ects can be omitted.

3)When 3)When <1 , t<1 , tww<t; When <t; When =1, t=1, tww=t.=t.Measurement of tMeasurement of tas as of air (tof air (tww))

2)Measurement of humidity H:

),(),,( ww ttfHHtft

A very common method of measuring H is to determine simultaA very common method of measuring H is to determine simultaneously the tneously the tw w and t.and t.