A heat pipe construction to seperate the freezing and heat absorption compartments in a domestic ice cream maker

Design:

A HEAT PIPE CONSTRUCTION

to separate the freezing and heat absorption compartments in a domestic

ICE CREAM MAKER

'.

,/ /

G

.

Kant

L.F. Kramer

Department of Chemical Engineering, University of Technology Delft

A heat pipe construction

to separate the freezing

and heat absorption compartments in a domestic

ICE CREAM MAKER

G. Kant and L.F. Kramer

Department of Chemical Engineering

University of Technology Delft

Final Report, December 1992

25 isobutane pressure (bars) 20 1.5 1.0 :5 o RR -20 o 20 40 sa 100 110

19-2 Refrigeration Technology Subscripts

A absorber

c condenser ; condensing C Carnot

e etTective: external heat-transfer area el electrical

g geometrie H generator

HP high-pressure; high-stage

indicated; internal heat-transfer area; intercooler I intermediate

lP intermediate-pressure LP low-pressure; low-stage p pump

r rich

R reflux condenser; refrigerant ideal (theoretical)

v volumetrie w wall; weak

o evaporalOr: evaporating

1. Refrigeration [1]-[3], [28], [32], [34] The technology of generating and using

sub-ambient temperatures is divided into three fields: refrigeration, low-temperature technology, and

cryogenics. The boundaries between these fields are not clear cut. Refrigeration is generally un-derstood to mean from ambient temperature down to the standard boiling point of ethylene (ca. 170 K); low-temperature technology is from 170 K down to the melting point of nitrogen (63 K); and cryogenics is below 120 K, as

sug-gested by the Ausschuss für Tieftemperatur-Ter-minologie (Committee for Low-Temperature Terminology). This article deals with refrigera-tion; cryogenics is the subject of a separate

arti-cle (-+ 20. Cryogenic Technology).

The purpose of refrigeration technology is to

cool materials to subambient temperatures or

hold them at such temperatures. The substance to be refrigerated is cooled by a working fluid, which moves in a closed cycle. Most of the

cycli-cal processes employed for refrigeration are

re-versals of processes used in heat engines. In cold-gas processes, the working fluid is

al-ways in the gaseous state; in cold-vapor

process-es, the working fluid changes state from liquid to gas and back to liquid. Cold-gas processes are

energetically less favorable than cold-vapor pro- F

cesses at all temperatures of interest for

refriger-ation, i.e .. down to ca. -100

o

e.

In practice, cold-gas machines are important at lower tem-peratures, and these systems are therefore dis-cussed under -+ 20. Cryogenic Technology.

Cold-"apor systems use the latent heat of evaporation of a liquefied working fluid in a c10sed cyc1e to genera te

Vol. B 3

cold. The fluid (refrigerant) moves continuously through the cycle. The evaporating refrigerant remains at either constant pressure or constant temperature as heat is ab-sorbed from the medium beingcooled; it is then condensed at a higher pressure. The condensing pressure is dictated by the conditions of heat rejection to the surroundings and by the vapor pressure of the refrigerant. To keep the refriger-ant circulating between the two pressures, energy must be supplied to the system in the form of mechanical work or heat.

Cold-vapor machines include the following types:

1) compressor refrigerating systems, 2) absorption refrigerating systems, and 3) steam-jet refrigerating systems.

Mechanicalor electrical energy must be used to drive compressor refrigerating machines; ab-sorption and steam-jet refrigerating systems are powered by thermal energy.

1.1. Compressor Refrigerating Systems

[2], [3], [14], [17], [19], [20], [28], [35]-[43]

The most frequently used class of cold-vapor refrigeration machines is the compressor type. Figure 1 is a schema tic diagram of a single-stage refrigeration system.

A refrigerant enters the suction of a compressor (a) at a low pressure Po, it is compressed to a higher pressure Po' and is then condensed in acondenser (b) by rejection of heat to the surroundings. The liquefied refrigerant is ex-panded to pressure Po in an expansion valve (c). The amount of refrigerant vapor (flash gas) produced depends on operating conditions; this part ofthe refrigerant cannot be used to generate cold. As it absorbs heat, the liquid refrigerant evaporates in the evaporator (d); it then returns to the suction of the compressor.

The thermal balance of the process is then

Qo + P = Qc

where Qo is the rate of cold production (refriger-ating effect) in the evaporator, Pis the

compres-} - - - - , 3

) - - > - - - - ' 4

Figure I. Single-stage compressor refrigerating systcm a) Compressor; b) Condenser; c) Expansion valve: d) Evaporator; el Compressor drive motor

Vol. B 3 'nuously through emains at either re as heat is ab-is then condensed ure is dictated by oundings and by

keep the

refriger-, energy must be Ichanieal work or , the following rns, hs, and ~ must be used machines; ab-~g systems are Ig Systems [35]-[43] lof cold-vapor ~pressor type. r a single-stage :ompressor (al at gher pressure PC' ) by rejection of refrigerant is ex-I valve (c). The roduced depends efrigerant cannot heat, the liquid I); it then returns ~cess is then ttion (refriger-, the compres-ating systcm pansion valve; Vol. B 3

sor drive power, and Qc is the rate of energy rejection in the condenser. _{Wh en referred to the}

mass flow rate, this relation is

qo + w = qc

wh ere IV is the specific work of compression. For

energetic assessment of compressor refrigerating systems, the coefficient of performance (e) is gen-erally used; _{this is the ratio of refrigerating effect}

<20 to the electricalor mechanica I power supplied

P:

<20 qo

e=- =

-P IV

The coefficient of performance can be deter

-mined both for the real refrigeration process and for a suitable ideal (theoretical) reference pro-cess. _{The ratio of the coefficients of performance}

of these processes is ca lied the efficiency factor (r?) :

For the fundamental ideal reference process in refrigeration, _{the Carnot process running}

be-tween the absolute condensing temperature Tc and the absolute evaporating temperature T_o,

the coefficient of performance is

T_o

f._c =

---Tc - T_o

The smaller the temperature difference (Tc -T_o),

the higher is the coefficient of performance.

The ideal process for a compressor refrigerat-ing s_{ystem is described by the temperature-}

en-tropy (T -s) diagram (Fig. 2), which shows the specitic refrigerating effect qo and the specific compressor work IV as separate areas_{. A log} pres-'ure vs. enthalpy diagram (p-h or Mollier dia-~!ram. _{Fig. 3) is more useful because (1) both} '_{pecific quantities are defined as enthalpy}

differ-cnces. (2) the process runs between two fixed press_{ures. and (3) expansion is a}

constant-cnthalpy process. The quantities. now referred to

I _{kg of circulating refrigerant, can be plotted as}

kngths. _{The specific compression work (w), the} '_{pccific refrigerating effect (qo)' and the specific} I_{hcrmal power (qc) are defined as follows:} " = h2 - h,

'I" = h, - h4 'I. = h2 - hJ

\_{\here the numerical subscripts refer to the points} ,hown in Figure 3.

Refrigeration Technology _19-3

Specific entropy, 5 _ Figure 2. Diagram of the single-stage process in a com-pres_{sor refrigerating system (temperature vs. specific}

en-tropy)

1-2 = [sentropie compression; 2-3 = Cooting and

con-densing at constant pressure; 3-4 = Expansion

(isen-thalpie); 4-1 = Evaporation at constant pressure; 1-2

-3-4-1 = Specific work of compression; 1-4-5-6-1

= Specific refrigerating effect

'" o

Specific enthalpy, h _

Figure 3. _{Diagram of the single-stage compressor}

refriger-ating process (log pressure vs. specific enthalpy) 1-:2 = [sentropie compression; 2 -3 = Cooling and

con-densing at constant pressure; 3 -4 = Expansion (isen

-thalpic); 4-1 = Evaporation at constant pressure

Performance Figures. The ma ss flow rate of refrigerant for a given refrigerating effect 00 is

The specific refrigerating effect per unit specific volume qov is given by

ht - h4 qov =

..

19-4 Refrigeration Technology

where VI is the specific volume of refrigerant va-por at the suction. The volume flow rate at the suction of the compressor is thus

~

=

00

=

~

VI = m_R VI

qov hl - h4

The coefficient of performance el ofthe ideal pro-cess is

The power consumption of the ideal process for a given refrigerating effect can be determined: p. = 00 = 00 h2 - h,

el hl - h4

The necessary rate of heat rejection needed in the condenser for the ideal process is

In practice, compression is not an isentropic pro

-cess, but a polytropic one in which the entropy increases. This nonideal behavior is described by the indicated efficiency I'/i of the compressor used. The indicated power consumption Pi for a refrigerating effect 00 is th us

When frictionallosses in the compressor are tak-en into account, the effective power consump-tion p. is

Subcooling. The liquefied refrigerant can be subcooled by heat exchange with the cold vapor from the evaporator. A system with a heat ex-changer provided for this purpose is depicted in Figure 4.

Subcooling the refrigerant results in a gain in specific refrigerating effect. The increase for some halocarbon refrigerants is greater than the increase in specific compressor work because compression is started in the superheating re-gion instead of at saturation. The process is de-scribed by the p-h diagram in Figure 5. This heat-exchange step can also be used to prevent liquid droplets from being entrained from the

Vol. B 3

3' r - - - . y " .rl---~ 3

e d

Figure 4. Single-stage compressor refrigerating system with internal heat exchange

a) Compressor; b) Condenser; c) Evaporator; d) Expan-sion valve; e) Heat exchanger; f) Compressor drive motor

t

Ol o

Specific enthalpy, h _

Figure 5. Diagram of the compressor refrigerating process with internal heat exchange (log pressure vs. specific en-thalpy)

hl' - hl = h3 - h"~

evaporator into the compressor. Valve dam-age in reciprocating compressors can thus be

avoided.

Compound Compression. In positive-dis-placement compressors, the volumetrie and the indicated efficiencies of the compressor fall ofT sharply at higher compression ratios. In addi-tion, compression temperatures may reach

exces-Vol. B 3

'rigerating system

orator; d)

Expan-ressor drive motor

'igerating proccss

'e vs. specific

en-Valve dam-can thus be

positive-dis-letric and the 'essor fall 01T jos. In addi-y reach exces-Vol. B 3 4,---, 3~---_, 2,---~ 7 ) - - - ' 8 d 6 l--iXJ-'S f 1 b

Figure 6. Two-stage _{compound compressor refrigerating} process with two-stage expansion

al High-stage compressor_{; b) Condenser; c)} Intermediate-pressure vessel; d) Evaporator: _{e) Low-stage compressor;}

f) Expansion valve; g) Compressor _{drive motor}

si\'e values _{if the ratio is high. This happens} at

evaporating _{temperatures between ca. - 20}

and

- 45 cC, _{depending on the condensing}

tempera-ture, the refrigerant_{, and the compressor design} . In order to avoid these problems, compound

(two-stage _{and multistage) compression systems}

Q.. ",I O l

-

i

I

I Specific enthalpy, _{h _}

Figure 7. Diagram of compressor _{refrigerating process} wilh two-stage compression _{and two-stage expansion}

(log rressure vs. specific enthalpy)

Refrigeration Technology _19-5 are used. The optimum intermediate pressure for two-stage compression is

Two-Slage Expansion. _{The refrigerating}

ef-fect declines as the compression ratio increases, because of the high vapor content in single-stage expansion. Performance can be greatly improved by expansion in two stages. Figure 6 shows a process with stage compression and two-stage expansion; this arrangement is common in larger refrigerating _{systems th at use ammonia as} the refrigerant. Figure 7 is the corresponding

p-h diagram for this process.

The low-stage compressor _{(Fig. 6,e) takes vapor from} the evaporator (d) _{and compresses it to the intermediate}

pressure. This vapor goes to the intermediate-pressure _tank (c), _{where it is cooled to saturation}

by refrigerant that has been expanded to the intermediate pressure. All the vapor

passes to the suction _{of the high-stage compressor (a),}

where it is compressed and _{then condensed in the}

con-denser (b). An expansion valve (f,) _{allows the condensate}

to ex pand to the _{pressure prevailing in the intermedia}

te-pressure tank; further expansion to the evaporating

pres-sure _{takes place in a second expansion valve}

(f2). The vapor

produced by heat exchange in the intermediate-pressure tank, along with the vapor from expansion_{, results in the} mass flow rate of refrigerant being greater in the

high-pres-sure part of _{the system than in the low-pressure part.}

a

h

e

Figure 8. Two-stage compound compressor refrigerating

system _{with two evaporators at different temperatures and} with interstage _{cooling by cooling water}

and refrigerant

a) _{High-stage compressor; b) Condenser; c)}

Intermediate-pressure vessel; d) High-stage evaporator; e) Low-stage evaporator; f) Low-stage compressor_{; g) Interstage cooler;} h) Expansion valves: i) Compressor drive motor

..

19-6 Refrigeration Technology

4r---~

a b

d

Figure 9. Two-stage compound compressor refrigerating system with vapor cooling by intermediate injection and single-stage expansion

a) High-stage compressor; b) Condenser; c) Evaporator; d) Low-stage compressor; e) Expansion valves; f) Compres-sor drive motor

"" o

Jr---t---;;J:) 4

Specific enthalpy. h _

Figure 10. Diagram of the process iIlustrated in Figure 9 (log pressure vs. specific enthalpy.

Two-Stage Compression with Tiro Evapora-tors. If additional refrigeration is necessary at the temperature corresponding to the interrnediate pressure, another evaporator can be placed in parallel with the intermediate-pressure tank. Figure 8 shows such a system with one evapora-tor for low pressure (e) and one for interrnediate pressure (d). The additional cooling ofthe vapor compressed by the low-stage compressor reduces energy consumption. The power balance for this two-stage process is as follows:

{,?C = QOLP + QOIP + PLP + PHP + Q;

where Qc is the rate of heat rejection in the

con-Vol. B 3 den ser, QOLP is the refrigerating effect in the

evaporator at Po, QOIP is the refrigerating effect in

the evaporator at PI' PLP is the drive power of the

low-stage compressor, PHP is the drive power of

the high-stage compressor, and Q; is the rate of heat rejection in the intercooler.

The refrigerant mass flow rates, the suction volume flow rates, and the effective power con-sumptions for the compressors can be deter-mined from information provided on the single-stage process.

Two-Stage Compression with Single-Stage Expansion. On grounds of design simplicity, two-stage expansion is often not used in small sys-tems with two-stage compression. This process is depicted in Figures 9 (schema tic diagram) and t 0

(p-h diagram). In the low-pressure stage, the va por is compressed from pressure Po to the intermediate pressure PI' The vapor is then cooled by refrigerant from the condenser, which is injected through an expansion valve.

When halocarbon refrigerants are employed, the system shown in Figures 1 t (schematic) and

12 (p-h diagram) is often used. Beforeexpansion at low pressure, the refrigerant is subcooled

al-4r---, a b ~----_15 6 e 2 e d 8

Figure 11. Two-stage compound compressor refrigerating system with single-stage expansion and refrigerant sub-cooling

a) High-stage compressor; b) Condenser; c) Evaporator: d) Low-stage compressor; e) Expansion valves; f) Subcool-er; g) Compressor drive motor

Vol. 83

hg _{effect in the}

I_{gerating effect in}

Bve power of the

e _{drive power of}

I

Qi is the rate of

ates, the suction :tive power con-o can be deter-~d on the single-~h Single-Stage simplicity , two-ed in small sys-l. _{This process is} diagram) and 10

.sure stage, the

Isure Po to the vapor is then mdenser, which , valve. are employed, Ischematic) and ~fore expansion s subcooled al-b 5 e sor refrigerating refrigerant sub-c) Evaporator: Ives; f) SubcoO\' Vol. 83 ~~---_+---~4

t

C>---f<:f--;:I:) ₂ Specific enthalpy, _{h _}

Figure 12. Diagram _{of the process illustrated}

in Figure 11

(log pressure vs. specific enthalpy)

most to the saturation _temperature

correspond-ing to the intermediate pressure. Subcoolcorrespond-ing is accomplished by part of the refrigerant flow evaporating _{at the intermediate pressure}

. Ener -getically, the process is almost equivalent to

two-stage expansion; it offers some advantages with regard to control of _{the refrigerant mass flow}

ra te in the low-pressure section.

Cascade Compressor Refrigerating Systems. At evaporating temperatures between -_-110 70 and

°_{C, the large difference between the} evapo-rating and compressing pressures has unfavor-able effects. _{Depending on the refrigerant, the} pressure on the condenser side may be

excessive-ly _{high or may exceed the critical pressure}

. On the low-pressure side, the pressure can be so low that entry of air into the system becomes a

dan-ger. The use of a _{given refrigerant may by ruled}

High-temper ature loop

d

c Fi~ure 13. Cascade compressor refrigerating system

"I Compressor; _{b) Cascade}

cooler: c) Evaporator: d) Ex

-ransion valves; e) Condenser: f) _{Compressor drive motor}

Refrigeration Technology _19-7 out by its freezing point and by the high specific volume ofthe suction vapor at low temperatures. The process is, therefore, divided into two sepa-rate loops and a suitable refrigerant is chosen in each loop for the pressures occurring there. Fig-ure 13 shows _{a simple cascade system with two}

loops.

The refrigerant in the low-temperature cir-cuit is condensed by evaporating high-tempera-ture circuit refrigerant in the cascade cooler; i.e., the refrigerating effect of the high-temperature circuit is used to remove heat of condensation from the low-temperature circuit. In this way, only the evaporator with the lowest evaporating temperature generates the useful refrigerating ef-fect. _{Depending on the compression ratios in the} circuits ofthe cascade system, the refrigerant can be compressed in several stages.

1.1.1. Refrigerants for Compressor Refrigerating Systems [4], [14], [22], [28], [44]-[47]

The working fluids moving in a closed cycle in compressor refrigerating systems must satisfy many requirements_{. These requirements are} pri-marily concerned with thermodynamic proper

-ties, heat-transfer characteristics, chemical and physiological hehavior, and usability with vari-ous compressor designs.

A _{refrigerant must have good chemical}

sta-bility under working conditions and in the pres-ence of construction materials and lubricants. lts pressure must not be too high, but it should not he lower than atmospheric pressure at standard temperature and, _{if possible, in the evaporator.} Other characteristics of a good refrigerant are low compression ratio (the ratio ofthe condenser pressure Pc to the evaporator pressure Po,

corre-sponding _{to the condensing temperature}

te and the evaporating temperature _{to)' high specific} enthalpy of evaporation, and smal! isentropic exponent (see Table t). _{Furthermore, the}

volu-metrie refrigerating effect (the refrigerating effect per unit refrigerant volume flow rate at the

suction) is a _{crucial factor; it depends on both}

the specific volume of the vapor and the specific enthalpy of evaporation_.

The two main types of refrigerants are am-monia and chlorofluoro derivatives of methane and ethane (halocarbon refrigerants). Pure hy-drocarbons are also _{used in petrochemical}

plants.

I

I.

_j! ,

Vol. B 3 ~r plate

evapora-lfilled vessel. The erves mainly as a

rroduction, espe-nd for cold rises, porator coils is

looling capacity.

round increasing te produced with

p meet peak

day-}ting systems can

~ted load can be be lowered.

:ieces (diameter ca. Iduced in tube iee

:hine. In avertical lorates in the shell-YS _through distribu-Some of the water re a float controller he amount frozen.

the water flow and ienser to start the m the tubes is bro-md through a chute ) an iee hopper or :e maker operating re ca. - 12 0C) and specific cold

lakes is made con-takes plaee on the . Water is sprayed from arevolving the outside by

re-;e is removed by a : cylinder is cooled 19 refrigerant and iees are stationary.

:quipment are

be-m long and weigh a large number of tank. Because the rosive, the iee eells ,tainless steel. An Jbe evaporator in d then circulated

:ure of ca. - 7 °C, block or 19 h for are hoisted out of n water to release )Iaeed by tipping. yalled iee eells are The refrigerant is ing is accelerated inside the iee eell. :1, the jacket and denser side of the , process are the , of the iee eells.

lOt pressure. Thc

11 costs are then

Vol. B 3

lower. Refrigerating systems for this process are single-stage _{ammonia machines with reciprocating compressors.}

Dry /ce. The method most commonly employed for producing dry ice (solid carbon dioxide) consists of

ex-panding pressurized liquid carbon dioxide to ambient

pres-sure; _{the temperature falls below the triple point and}

snow-like carbon dioxide is obtained (-+ _{Carbon Dioxide, A5,} pp. t 77 -t 78). _{Roughly a third of the liquid is transfonned}

to the solid state; the remaining gas is recycled. The carbon dioxide "snow" is molded into 12 -lOO-kg blocks in hy-draulic presses.

Dry ice sublimes at -78.9°C and has a heat of

subli-mation of 573 kj/_{kg. [t is used chiefly in the transport of} deep-frozen products and, to a minor extent, in laboratory chilling apparatus.

2.7. Use of Cold in Construction _{[13], [21],}

[31], [159)-[162)

The heat of setting in concrete gravity dams ranges from 250 to 500 kj/kg, depending on the aggregate used and the cement: sand ratio. This heat must be removed, especially in thick dams,

so _{th at it does not buildup and cause cracking. In}

Pos/cooling, _{chilled water is pumped through}

pipes inside the structure; compact water-chill-ing plants are used for this purpose. About 75000 kj of cold is required per cubic meter of concrete. In preeaaIing, excessive temperatures are prevented either by cooling the aggregate and water before mixing or by adding finely divided (Oaked or tube-frozen) ice during mixing. Aggre-gate cooling is usually performed with chilled water, _{but other methods employing air chilled}

to - 20

c

e

_{also offer some operational} advan-tages.

When tunneling or similar construction work requires shaft sinking in water-bearing ground,

the ground around the planned excavation is sta-bilized by freezing. Double-walled pipes are driv-en into the soi!. A secondary refrigerant (usually brine) at - 20 to -40

o

e

flows down the inner pipe and returns through the outer space. The time required for freezing with these parallel pipes depends on the type and size ofthe excava-tion. the spacing of the pipes, and the tempera-ture of the secondary refrigerant; months are of-ten necessary. Transportable brine-cooling units with reciprocating or screw compressors, using ammonia as primary refrigerant, are employed.

2.8. Air Refrigeration in Mining [13],

[163]-[165]

The temperature and humidity in mines often become so high th at ordinary ventilation with

Refrigeration Technology _19-35

outside air is inadequate. Refrigeration equip-ment can be set up below ground in the shaft, or central cooling plants can be erected at the sur-face to produce cold water, which is then led to air coolers near the working face.

Refrigerating systems for underground in-stallation are compact, transportabie, explosion-proof units that cool air to ca. 18 -20

o

e

and dehumidify it. The air is introduced into the ven-tilation tubing ca. 50-100 m before the road ending. The plants usually have watercooled condensers and employ R 22 or R 12 as refriger-ant. Such machines can be driven by a com-pressed-air motor instead of an electric motor. 2.9. Artificially Cooled Skating Rinks

[13], [21], [31], [166]

An artificially cooled skating rink consists of tubes embedded in a concrete slab that rests on a frost-proof base. The pipes are parallel, spaced some di stance apart, and ca. 25 - 30 mm bel ow the surface. A secondary refrigerant (usually brine), evaporating ammonia, or R 22 is pumped through the pipes. The surface temperature of the ice over the entire rink surface must stay within narrow Iimits; stringent requirements thus apply to both the supply of secondary or primary refrigerant and the control system .

3. Heat Pumps [167)-[172)

Heat pumps operate on the refrigeration principles described in Sections 1.1 and 1.2. The process is shifted toward higher temperatures, and the temperature ofthe rejected heat allows a medium to be heated for a given application.

The economic significance of the heat pump lies in the saving of primary energy in thermo-technical processes. The useful energy consists partly of primary energy and partly of energy

from the surroundings or another heat source.

In a heat pump driven by an electric motor, the heat rejected in the condenser is used for heating. _{The process is assessed from the energy}

stand point in terms of the coefficient of perfor-mance e, _{which is the ratio of thermal power to}

19-36 Refrigeration Technology

It is determined essentially by the temperatures in the heat-source loop and the useful-heat loop. An electrically driven heat pump is evaluated economically over a given span of time in terms of the average coefficient of performance [3, which is the ratio of the heat generated to the electrical work consumed during this period:

In many applications, the compressor is driv-en by an internal-combustion (gas or diesel) en-gine. Heat from the engine coolant and from the engine exhaust is used in addition to that pro-duced in the condenser.

The heating medium absorbs heat in the con-den ser, and is then delivered by a pump to the motor coolant heat exchanger and, subsequent-ly, to the exhaust heat exchanger. In th is way, useful heat is obtained at higher temperatures than in heat pumps with electrical drive.

With regard to primary energy utilization, this heat-pump system is very economical as a heating method because a substantial part of the primary energy applied is available for heating purposes, and heat from the surroundings or some other heat source is also used.

Heat pumps driven with primary energy (in-cluding absorption heat pumps) are character-ized by the performance ratio (. This quantity is the ratio of thermal power to power supplied by the fuel:

(=

~

PF

The average performance ratio y is, accordingly, defined as

y

=~

WF

where Q is the useful heat generated in the inter-val under consideration and WF is the fuel energy

consumed in the same interval.

The components used in heat-pump systems are largely the same as those in compression and absorption refrigerating systems. In heat pumps with intemal-combustion drives, the engines and their control and monitoring equipment are sup-plemented by heat exchangers for recovering heat from the coolant and exhaust. Most such exchangers are of the shell-and-tube type.

With R 114, the therm al stability of the halo-carbon refrigerant limits the temperature of the

Vol. B 3

useful heat to between 100 and 130°C. In gener-al, however, these temperatures are between 50 and 80°C when R 12 is used as refrigerant.

The most important application of heat pumps in industry is the generation of process heat, especially for drying, in the food industry, and for process technology. Heat generation with heat pumps is especially economical when the coupled production of cold and heat is possi-bie, as in galvanizing, plastics fabrication, or food technology.

4. References General References

[1) R. Plank, (ed.): Handbuch der Kältetechnik, vol. I,

1954 Entwicklung, wirtschaftliche Bedeutung,

Werk-stoffe, Springer Verlag, Berlin.

[2] Thermodynamische Gundiagen, vol. 2, 1953 in [1].

[3] Verfahren der Kälteerzeugung und Grundlagen der Wärmeübertragung, vol. 3, 1959 in [I].

[4] Die Kältemillel, vol. 4, 1956 in [I].

[5] Kältemaschinen, Kaltgasmaschinen,

Kaltdampfma-schinen, vol. 5, 1966 in [1].

[6] Auromatik, Zubehör, lnbetriebnahme,

Geräuschbe-kämpfung, Wärmepumpen, vol. 6a, 1969 in [1].

[7] Wärmeaustauscher, vol. 6b, 1988 in [I].

[8] Sorptionskältemaschinen, vol. 7, 1959 in [1].

[9] Erzeugung sehr tiefer Temperaturen, Gasverjlüssigung und Zerlegung von Gasgemischen, vol. 8,1957 in [I).

[10] Biochemische Grundlagen, Lebensmittelfrischhaltung,

vol. 9, 1952 in [1].

[11] Die Anwendung der Kälte in der Lebensmittelindu-strie, vol. 10, 1960 in [I].

[12] Der gekühlte Raum, der Transport gekühlter Lebens-mirtel und die Eiserzeugung, vol. 11, 1962 in [I].

[13] Die Anwendung der Kälte in der Verfahrens- und

K/i-matechnik, Biologie und Medizin.

Sicherheitsvor-schriften. vol. 12. 1967 in [I].

[14] Kältemaschinenregeln, 7th ed., C. F. Müller, Karls-ruhe 1981.

[15] W. Pohlmann, W. Maake, H. J. Eckert: Taschenbuch

for Kältetechniker. 17th ed., C. F. Müller, Karlsruhe 1988.

[16] M. Bäckström, E. Emblik: Kä/tetechnik. 3rd ed .• G. Braun. Karlsruhe 1965.

[17] H. L. v. Cube (ed.): Lehrbuch der Kä/tetechnik.

vol. I, Physik, Chemie, Kä/teerzeugung, Montage.

C. F. Müller, Karlsruhe 1975.

[18] Regelung, Elektrotechnik, Kälteschutz,

Kälteanwen-dung, Lebensmitteltechnik, Scha//schutz, Neue

Ein-heiten, vol. 2 in [17].

[19] H. lungnickel, R. Agsten, W. E. Kraus: Grrmd/agen der Kä/tetechnik, 2nd ed .• Technik. Berlin 1985. [20] International lnstitute of Refrigeration: Sa ving of

Energy in Refrigeration. Paris 1980.

[21] E. Emblik: Kä/teamvendung, G. Braun, Karlsruhe 1971.

[22] H. G. Hirschberg: Kältemittel, C. F. Müller. Karts-ruhe 1966.

[23] M. Mörsel: Taschenbuch Kältean/agen, 3rd ed .. VEB Technik. 1970.

a..

HeC(.,f

P\'p~

«;lAce.pe

~ ~0\.k.~1 I·C

!'-

C

r-~ct.1N\

f,r-

J,ok,~

l..{..se.

G.

l(a..",,~ L.t. Kr-(;(..\1,.1er

NCtK<

Cl

(pro

c

e.s

s

J

~low

c

UG<..~ra."",

(~eWl.p.) PY~.ss.) ~",cl

t

)VWJ a.

",-cl

~

c.I u.ot,

·

V<. ~

.Áold-\Á.?~

b.

'D<-5c-t'ip}-,'Ok

o{ Vlttod-e)

ó1

lrte.cJ.-p'Pe..

(Ce.

u((;o,\...,

~C(,ker

CVl-tre,,-+-

d~s(tip~'-o~ Lru~e.s l::t

,J3)

c..oVCYS:

bc.,jli~J ~ew..p, p"Y~5~u.r(.

h~CLf

It-a.Lt)fer

t"tl,d,öW:>

(UVGl.PI

/ALO'"')

(A..~cl ~ec.J ~JIA.X

Jw)va.p

e. «j u..a.Á-t' 0 \A.

01-

.l

~

c.t-

~ e

\,tv

h

Cl\- i

s

VlA ,. S. ':. Î k~ ~

t

~ ~

cl

~

s

ct ,.

r

U

0 IA

(CU,)

I-0

l.q;t

11 ~ cc. (,,0 'W-p

/.d

~

MOd.J)!

heGt.+

bdC(...lhce

s

tor jee) c..O<:>lIh~ hox w~-rl ~t!H-, ~ l"~(.(ie-l. 5,!Ûe-1A...

v(.(...puu..r)11-1L.L1c.I

~1I.A.iL·br-;Vl'--

"'"

vo..puv..r-/.1'·OjtA..I'rJ...

sy~re""".

-

spec'1ic.o...holA

0

the. de!)1'1"'"

pct\'"CA-IA.A.«et.s

~ H'\~,--ocLJ..

---~---r

~

Cl,vC..e. '""- <lL-

~

,

v..

ct

e cc.,"\A.

c.,~

c.J)

~"

e

0-{

(.l.ûL

cr

€. ve.v-c\.o."-,,

r;

~r

-kc:.J.

U ICj ~ ( '> v\ e

1

h.

€. r'

cl

~ i\ e \

b

C"-eX. r . , .( L{J

..

(S

i

12

~cv-I

b

es:. cc. "

k,

J.

b (. ""

lA.-H e. ~

D

i u.~ r CL \.AA. • ~

b

J

.

.u.-I.A/) /'I h 0 ~ + t. u"'-

cJ

t - h.-~?

\Jol/.e.cl\~L~,'cL

"Ik.

\/--ocL .-\ ..

\jt?lrvc.\r.~'-"-J

/

vev'(\-\~~

L~'J

~

bep~

La-v .

~(.)rpe.t~

.

v

'-.1

~ .e..-~k

hl

d. ;

L

l,\-e '"

t'

''g

e

UO

r-

d..sJ(

~

ep

Cv)

? e.

c

t-e

~

:

.. _ ~ l

vJd

U,:<"v.-,

pl-e

x

i ~

t

t

_ \N\(e\" Ocr

>f'rC\Ak..èLjJvk(J

'Y-t><"-

1

ic.lhr,

'

eh.

\l\A-QCLI' LCVV')v(. \N..t'i'

prcckd.

cl c;-Q

cl...

C(~

0

~

c\.k.

~

cL

v-e

IJ ':> (

(.(...~

..

~l.Ve.Yp

"T

ti--o

k-e

LA v-.. l ~ ( ~ .,Q, ' - •

ra...

b)-.

, . I

i.

I

C

' I

J

do cr

G

.

"

e.cJ

e v 0

cl

< C l cl

v-~'

cl

o-<.J

~

c~o.. cU:'

fl

:.

<) Gt.; \

I

C.l

~

rL-\.t-vklA. /)

\-clrft~r- JA.~

'-

vv(..v) w-,O 'f&(

~lt

Q I Û "" L 0 "'-\J e ~ 0 ~ <:.:fIA

cl

ê.Y ,,,A ... H!. ~

P ;

c~ ~ ~ ~ e cytw"V\.

/

-______ J

1 '

,,

?\"e.f~tr~c1.. C<..deU~,

"

olA.~:

., J.

P \"

Cl cLucJ

.a1A.J.

p

roe e 5:> /;> J=> e ei

f ,-

c CC.k} " t.v..:>

( P

GL~ e.. -i ~ \.A) ~ e IA. ie-€.

'1

u..cU." ~ '( r ~« cA 'j )

• ~ u..cJ

d,

Y

(

~ vu:uJ-d-('

, , .l .

M-t.

~

vJ -

J.,

jlA. i

cl

co

J

C(..

v~

~ Wt-o""-~ f're~~lI\Ar

b-ioVt,

w.r.~. CLolJ"~'-YI·/-.y

01

tt'~I~ht..-""tO

r

\)

0" }- ( e. )( I

b

~

I

C.

l<.'

i ( e

c{'

ct. r -e C0") ,

" 3.

H

~CU-

P

~

P

~

:

COlA c e...

p \:;

I.A

cJ.

ol

y CL w

i

h..cJ

lA; "

t

k

~

i l i",

J

c..u...

cl

c. 0

\'-'.,c

,

L

·

t

I'Cl

~

.. S """ l !. 5. ," v-.~

*"

D i C(..~ r CL

""'-~

P ,T

~

M

Q.~

S. )

e

\A

er

1

'I

.f

10

W

~

,)

h.

0

l

cl.

v...p

S .

" ,

~

r

y-0 C €

~

:>

C-

~

vvJ.

c,( .. ,t-,; 0 IA.../): e j

~

e.-t-J.

ï

a.L

e <j lA..

wh'

0 \.V.) cU' e. """-i :.

~

\ "';)

_ hed

bcJcu..t'L /(

e

"

., t. 0 0 1 i

"'Cf

e

I

-e '-J2 .../ -t /1 I , V C"-

r

IJ I.Á Y' t ' , t ' ,

A

i'1lA"c,[

I ,

VjL

c.. c::? u..

cl

I'

t-

i <:) vv)

P,T

ClM.oI

j

",J

ct

he.

o~

rB,

N~ ~

~ 1

Contents

l. Introduction 1

2. Heat and heat fluxes; the present ice cream maker 2

3. Possible solutions 5

3.1 Metal to metal contact 6

3.2 Metal to liquid contact 9

3.3 Heat Pipe contact between bowl and cooling disk 11

4. Design

4.1 Choice of method

18

4.2 The ice-cream maker 18

4.3 Safety 21

4.4 Economics 22

5

.

Conclusion 23

1. Introdllction

Icecream has been a delicacy for a long time. Now that al most every household has a refrigerator it has become easy to preserve this frozen dessert for a long time. But this has also opened the possibility to make fresh icecream at home. This gives the cook the freedom to decide what kind of recipe he is going to use. And often the fresh icecream is tastier and better textured than the deep frozen commercial product af ter storage.

Several small household apparatus have been developed for the preparation of icecream at home. Often these consist of a bowl and a stirring mechanism, in combination with a separate cooling disk in direct contact with the icecream. Inside the cooling disk is an eutectic, from which the latent heat of melting serves to generate the cooling power for freezing the icecream. The cooling disk is kept frozen in a freezer and is put into the machine when it is going to be used.

The cooling disk is a cheap and rather easy to handle source for cold in making icecream at home. lts use will be a starting point in our design of a new type of icecreammaker, in which two of the drawbacks of this device are eliminated. One disadvantage of the cooling disk is that its cooling power drops during the process of icemaking. The second is, that it is not easy to clean after it has been in direct contact with the icecream during the preparation, because it is not enough heat resistant to be cleaned in a dishwasher. The first requirement for a successful domestic icecream maker is that the product must be as good or even better as commercially available icecream. The product has to be smooth and creamy, it must have a good flavour and a stable texture. This is not only an aspect of the cooling ra te in the machine, but has also to do with the mixture of ingredie-nts. In Appendix I we have given a detailed summary of the effects of the different

ingre-dients and processing conditions on the quality of icecreams. It would be a commercial

advantage if the design of the cooling process allows controlled variation of cooling rates and of the final temperature of the product.

Another very important aspect of making icecream at home is the time it takes to produce

a satisfactory amount of icecream. This preparation time depends on the total heat resistance between the melting eutectic and the freezing mass of icecream, on the temperature difference between these, and on the area through which the heatflux can be transferred. It is an inherent property of the cooling disk that its heat resistance increases as the eutectic melts. The cooling power drops off towards the end of the processing, when the temperature difference between the eutectic melt and the icecream becomes smal!. We have aimed at a design for a domestic icecream maker in which the heat flow between the icecream and the cooling disk is not mediated by direct conductive contact, but can be adapted to process conditions and optimized by variation of the available surface for heat transfer to the cooling disk.

Summarizing, the conditions tor our design study were:

1.

Using the existing cooling disk with eutectic.

2. Separating the cooling disk from the icecream mixture; for hygienic reasons direct

contact is undesirable.

3. The machine must be able to produce 600 grams of icecream in 15 minutes.

2. Heat and heat f1uxesi tlle present iee eream maker

In order to make ice cream, the ice cream mixture, which in general consists of the fo11o-wing substances, has to be frozen:

component mass fraction Cp (kJ/kg*K) water 0.65 4.2 sugar 0.20 1.3 fats 0.10 1.7 proteins 0.05 1.4 TOTAL 1.00 3.2

table I. Composition of an ice cream mixture

Such a mixture does not have one particlllar freezing point, but starts freezing at about -2°C. Actually, only the water in the mixture freezes: the sugar is dissolved in the water; the fats and the proteins are already in their solid state. As the temperature of the mixture decreases more water freezes and the heat capacity of the mixture changes, as shown in the next tabie.

temperature water Cp temperature water frozen frozen (OC) _(%) (kJ/kg*K) (0C)

_(%)

-2.0 0 3.22 -5.6 52 -3.0 21 2.94 -6.1 56 -3.9 33 2.77 -6.7 59 -4.4 41 2.66 -7.0 61 -5.0 47 2.58 -7.8 64

tab1e 2. Approximate percentage of water frozen in the ice cream mixture and the heat capacity of the mixture at various temperatures. (taken from lit. 4)

2 Cp (kJ/kg*K) 2.51 2.46 2.41 2.39 2.35

The desired ice cream temperature is -7°C. To reach this temperature, heat must be

withdrawn for cooling and for freezing. The total amount of heat (Q) that has to be

withdrawn can be calculated using the expression below.

Q = mass '"

J

Cp '" dT + mass'" warerfractioll '" waterfrozelI '" tJi/usi""

with mass = massoficecreammixture(kg),

C = healcapacityoflhemixlure(~) •

p ~",K

~H.... = enthalpyoffusiollofwater = 336 kJ.

,_."" kg

With an initial temperature of 20°C, the following values can thus be calculated:

ice cream heat from heat from tota! heat eutectic mass

mass cooling freezing

Q

needed

(kg) (kJ) (kJ) (kJ) (kg)

0.6 51 80 131 0.52

1.0 85 133 218 0.86

l.2 102 160 262 1.03

Table 3. Calculated heat for different ice cream masses.

(1)

The needed eutectic mass is calculated on the basis of a heat of fusion of 280 kJ/kg and a 10% excess cooling capacity. To meet the demand of making 0.6 kg ice cream in 15

minutes, 131 kJ heat must be withdrawn from the mixture in th at time, so a mean heat

flux of 145 W must be sustained. This heat flux has to be in agreement with Fourier's law: cp

=

U", A'" flT '" with cp '"

=

hearflux (W), U = IOwlheattramfercoefficient (~). tw*K A = areaofheattratlsfer (m2 ), flT = temperaruregradiellt (K)

In the existing ice cream machines, a maximum heat flux is created by:

(2)

1. A maximum total heat transfer coefficient, obtained by the direct contact between

cooling disk and ice cream mixture.

2. A maximum area of heat transfer, because the entire bottom of the bowl is used as

cooling surface.

-I

I

I I

eutecticum

Irrelt layer

aluminum

lee cream

I

I

I

_Tjre

I

I(

I

l

-TSJt

V

I . / ....

r--

..

I

T

dmelt{t)

dAl

t

.

I

~ I

h=~

U-~Lh-i

,

I

d

I

The tota! heat transfer coefficient is composed of three thermal heat resistances (see also fig. i):

1. The melt layer in the cooling disk. Ouring the cooling process the eutectic in the cooling disk melts. Ouring the freezing process the thickness of the melt layer increases up to about 3 mmo The heat conductivity of this melt is very small, so the resistance increases during the freezing process. By means of a large area the resistance can be limited.

*A = 0.53 '" 0.12 = 21 KW

3

*

10-J

(3)

2. The aluminum layer between ice cream mixture and cooling medium. This resistance is very small, because aluminium is a good heat conductor.

ÀAI

*

A =

~_23_5-:--;-

'" 0.0225 = 2115 W

dAl 2.5

*

10-J K

(4)

3. The transfer resistance from ice cream mixture to the aluminium wall. This resistance is a function of the stirring velocity and of the ice cream temperature. The heat transfer coefficient is in the order of 600 to 1000 W/(m2K).

k ... A "'" 800 ... 0.0225 = 18 W

K (5)

Results of experiments (by Philips Drachten) in which the heat transfer coefficient is measured as a function of the temperature at a constant stirring velocity , have been used. [app.2]

The resistance of the aluminium wall is very small compared to the other two resistances, so it can be neglected. As the freezing progresses, the resistance in the melt layer becomes of the same order of magnitude as the resistance of the heat transfer from the ice cream mixture to the aluminium wal!. So then these two resistances limit the heat flux. With an improved heat distribution inside the cooling disk, the heat transfer inside the ice cream mixture would become the sole heat tlux limiting factor.

3. Possible solutions

or

the heat transfer p,"oblem.

Using the present cooling disk, but disconnecting its direct contact with the freezing mass of icecream while retaining the necessary cooling power requires the interposition of a heat conductor of low resistivity between the disk and the bowl. One could think of some possible intermedia:

1. metal-to-metal contact.

2. metal in contact with a t10wing cooling liquid.

3. metal in contact with evaporating and condensing liquid.

Some other solutions for the heat conducting bridge between disk and bowl, like soft heat conducting rubber layers between the disk and the bottom of the icecream bowl were already examined by Philps Drachten, but could not satisfy the condition of not adding a considerable heat resistance. Therefore these wiU not be further discussed here.

In the following paragraphs we will analyse the three possibilities named above, calculate their effect on the heat conduction between the eutectic and the icecream, and draw conclusions about their respective advantages and disadvantages.

3.1 Metal-to-metal contact

The heat flux between any two media is a function of the total heat transfer coefficient, the contact area and the temperature gradient (Fourier's law).

<1>",

=

U

*

A

*

6.T (6)

When two hard metal plates are placed on top of each other there win not be contact between the plates in more than three points, because no plate wiU be perfectly flat. AIso, the plates will not have a·completely smooth surface. As a consequence there is only a small area of real contact between the plates. The overall shape deviation could be reduced by expensive manufacturing or by insertion of a soft elastic metal foil. An average surface roughness is not avoidabie. As an example of such a solution, which aims at increasing the number of contact points, let us examine a "bubbled" soft capper foil between two aluminum layers.

dc..== 1 mrn dAl == 2.5 mm

fig.2. Bubbled copper foil hdwt:t:n aluminium layèrs.

tig.3. Examplè of surface roughness.

The heat flux from one metal layer to another takes place by three mechanisms:

1. SSC Solid Spot Conductance, therm al heat conductance through the solid contact points.

2. GFC Gap Fluid Conductance, thermal heat conductance through the intermedium fluid or gas where the surfaces do not touch.

3. RGC Radiative Gap Conductance across the gap, (which is only effective at high T)

In the article of Jeevanashara [app.3;liL13] measurements are made of the thermal heat transfer between two flat metal plates under light pressure. It is found that at the temperatures of interest the resistance of the air between the two surfaces is toa high to have a positive contribution on the heat tlux; This means that in our case the GFC and RGC are zero. The entire heat tlux is due to contact conductance by SSC.

The total heat conduction through the three metal layers can be calculated in the following way:

u = ( " rh i cklle.\·s -I = ( 2 * 0.0025 0.001 -I = 42058 ~

L.... À 235 + 400 ) m" >I< K (7)

Because of the design-condition not to add a large extra heat resistance, the heat resis-tance through the three metal layers must be small compared to the heat resisresis-tance from the bowl wall into the icecream and the heat resistance from the aluminium wall into the cooling disk.

( 42058 >I< COfl(aCULrea

r

l (8)

From this the real contact area should be at least about 45 cm2 _{(a 5 % larger total heat}

resistance). The total disk surface area is 225 cm2• We estimate that 25 % of this surface

at most is 'on top of the bubbles', sa now we can calclilate how mllch real contact must be made there. 45 cm" = ~ * 25 % * 225 CII/' Aa so A = 80 % Ao (9)

A methad to calculate the lllInIlTIUm pressure for obtaining 80% rea! metal-to-metal contact is found in the baak "Contact Mechanics" by K.L. Johnson [liL 12]. It is a genera! methad to calculate the real area of contact between two flats with a certain surface roughness. The surface is asslimed to be a two dimensional wavy flat with amplitude, a and wavelenght, lambda.

area CJfCOllfllC( =f(.J:...-)

wwL area iJ •

(10) p"

with E· = mean elasticity of the two materials

Because the elasticty of cap per is mllch higher than the elasticity of alliminum we can take Ecopper as value for E".

It is aften assumed [liL 16] that the wavelength and the amplitude are of the same order of

magnitude. This is, of course, a very rough criterium. The shape, frequency and degree of surface rollghness depends on the manufacturing methad for the surface.

p. = 2*7r*E· = 7.359*1011 _Pa

E* = Ecoppcr = 17 millions of psi

= 1.1713*1011 _Pa

~ =

80 % and figure 13.4, (app.3,p.403) gives

p

=

0.65 .

~ p

From this we can calculate the local pressure needed to press the surfaces together. This

calculation is based on two tlat plates, but on microscopic scale, the bubbles can be

regarded as flat so this wi11 not callse a large error.

"ft

= 4.8 * 10" Pa

Conclusion

The necessary pressure of abollt 4.7

*

10ó

atm. is ridiculously high, and we can conclude that direct metal-to-metal contact can not be an option in the design of a new ice cream maker.

Even if our assumptions and estimations are In error by a factor 105, the necessary

pressure will be impossibly high.

That metal-to-metal contact is effective at higher temperatures is caused by the radiative heat transfer between the surfaces across small but resistive air gaps.

3.2 MetaHo-liguid contact

The second idea is cooling with a liquid that flows through the jacket of the ice bowl and

is cooled by contact with the cooling disk. The use of a cooling liquid would leave the

possibility to increase the area of heat transfer in the cooling disk as weU as in the jacket of the ice cream bowl. Reglllation would be possible by changing the flow velocity of the liquid.

A weil known cooling medium

(antifreeze mixture) is water with

40

volume% glycerol. This mixture

stays liquid up to about -25°C

[app.9;lit.9]. The thermal conduc-tivity and other properties of this mixture are: <À>

=

0.391 Wlm.K <p> = 1.065.103 _kglm3 <1/> = 10 ",Pa (-IOQC) T/.C Pr = 77.3 = _ I' À <C> _p

=

3022.4 Jlkg.K

fig. 3. Sketch of an ice cream maker with metal to liquid

contact.

The extra heat resistance in this construction is the resistance of transfer to, through and

from the cooling liquid. This resistance is built up in series by the resistance from the

wall into the liquid, the heat carrying capacity of the flowing liquid and the resistance from the liquid into the wall of the bowl. Conduction through the liquid is negligible,

compared with the transport by flow, and this again ean be made so large that the extra

resistance is determined by heat transfer between the eold and warm metal walls and the flowing liquid. This kind of heat transfer depends on the flow rate of the liquid along the walls.

For a laminar liquid flow through a pipe, with a flow velocity of 1 cmfs there are

empirical expressions for the heat transfer eoefficient like: 'Jo.. 0.391

1I = _ _ = _ _ _ _ _ _ ~ = 1.21

*

10-7

p

*

C _I' 1.065

*

3022.4

*

10J

L = length of the tube over which the heat transfer takes plaee

D = diameter of the tube

9

Choose L "'" 1 mand D = 5 mm, then Gz = 0.484. When Gz

>

0.1 then Nu

=

<

Nu

>

=

3.66.

k = 1.431 W

m*K

(12)

Similar as in the previous paragraph with metal-to-metal contact, the added resistance may not 10wer the total heat transfer by more than 5 %.

À ( 1.431

*

area

r

l _~ 5 %

* (

--=:..

*

A

r

l + (k

*

A. ti d mell ,,.,,11 let (13)

Calculation gives that the necessary area of heat transfer should be at least 125 m2

•

Conclusion

The area of heat transfer should be at least 125 m2•

This is and absurdly high area, considering the fact that the tube has a length of about 1 meter.

Therefore, the idea of metal-to-liquid contact is not a possible solution. The area needed to compensate the low heat transfer of such a liquid is too large.

eooling disk

';' -" _.".

iee erean

bCJvll :

tedicum

~ltla)e'

alurrinum

c

Ic.ecream

evaporation area

aluminum

stirrer

3.3 Heat Pipe Contact between Bowl and Cooling Disk

For boiling, a liquid absorbs the heat of evaporation, and when the vapour condenses the same amount of heat is released again. Like in a destillation column the vapour flow in a heat pipe transports the latent heat of evaporation from the hot (boiling) to the cool (condensation) parts. This is the principle for heat transfer from the icecream bowl to the cooling disk by heat pipe contact.

The icecream mixture can be cooled and frozen by withdrawing heat through the

evaporation of a liquid which is boiling at the desired minimum temperature of -7°C The

vapour flows into the cooling disk where the heat from the icecream mixture is transfe-rred to the eutectic by condensation of the vapour on the metal wall. The flow of gas from hot to cold connects the cooling disk and the icecream bowl. To separate these, the cold and the hot parts of the heat pipe must be disconnected.

A heat pipe is a self stabilizing system. Wh en more heat is extracted at the boiling end than is delivered at the cool surface the vapour pressure would rise. But this increases the boiling temperature and the rate of condensation, so that all the extra heat is rapidly absorbed and the pressure remains normal.

In appendix [4] several possible constructions for an icecream maker are sketched, in which the cooling disk is the cold spot of a heat pipe and the icecream mixture the heat source. The simplest designs put the cooling disk on top of the bowl. The evaporated gas will rise to the cooling disk, whereas the condensed liquid flows back due to gravity

forces. In figure 4 a schematic overview of the construction is given.

One big advantage of using a heat pipe to deliver the heat to the cooling disk is to improve the disks performance. lts shape is no longer dependent on the shape of the bowl, but it can be designed for optimum heat exchange with the gaseous heat carrier. In

this way it becomes possible to reduce the layer thickness of the molten eutectic, which

becomes the limiting factor for cooling power during the process.

Also, by variing the heat exchange area, for condensation or for evaporation, it becomes

possible to externally regulate the heat flux. By increasing the condensation area the

cooling will become faster, decreasing the area slows down the freezing process. With this type of con trol the icecream maker would have "program" settings for different types of icecream (see appendix 1).

To describe and investigate the dynamic behaviour of an icecream maker with a heat pipe

we have made a computer simulation model, written in TurboPascal [appendix 5].

For the quantitative calculations we have introduced a heat transfer medium in the heat pipe with the physical properties of isobutane. This medium has to evaporate at the wall of the bowl, and it must be condensed into a liquid inside or on the cooling disk. So, the

boiling point of the medium must lie between -12°C and -7°C.

The atmospheric boiling point of isobutane is -ll.7°C. Other liquids or mixtures of liquids could be used, but their boiling point must be in the mentioned range, because for price and safety reasons it is preferabie to operate the disconnectable heatpipe at at-mospheric pressure.

Teut

~(----eute::ticum

fflbow

p)

isobutane

fig:S Schematic Overview Heatftow

T

icecream

L--~~X

fig:6Temperature Profile Evaporation Side

,

_I

(

Icecream

In the simulation of the funetioning of the heat-pipe the following expressions have been used.

The tota! heatt1ux is dependent on the temperature dit'ferenee between the eutecticum and the iee eream mixture.

(14)

The heat is transferred by means of eondensation and evaporation of the isobutane. These

are eoupled by the boiling temperature, Tboi1 and pressure, p of the isobutane. (see fig.5)

The iee eream temperature is ealculated from the evaporation heatflux with the following formula.

r

<I> * d(time)

..." _M. = C _" ( T . - T ) +ji·acrio/l. * jiYlcrio/l * 6.H

1(t'.IJt't:1II ,,'<, /rc,:.t'1I ~ •• jJt" 1· Ict with: Cp C1H. fraetion froZt:1l Tjee.begin ~VDP (time=O)

=

heat eapaeity iee eream [J/kg/K]

=

f(fraetionrrozeJ

= heat of melting [J/kg]

= fraetion frozen water in iee eream mixture = f(Tjee)

= beginning temperature iee eream = 293 K

= beginning heat flux = 0

The evaporation heattlux is given in the following formula. <I> _vap = U _'\lap

*

A _mp

*

(T - T _{wt' h,,"} .)

with: Av.p = area of evaporation = eonst.

U_{v• P}

=

total heat transfer eoeftïeient

=

[(Tboi1)

T_boil= f(p)

(15)

(16)

In fig.6 the temperature protïle over the evaporation area is given. Uvap is calculated by

summation of partial heat transfer coeffieients.

U

=<_l_+_l_r

'

..." h ia h is • ., . . . "

(17) with hice

=

heat-trllllsfen:oëjf. jiwt/ iee -miXIUre Iv waLL

and hisobtuaw

=

heat-rral/.lfercvëfj: from wall ro i~ivbuta"e

The heat transfer coeffieient of the aluminum is negleeted (see chapter 2). The heat transfer coefficient from iee mixture to wall is a funetion of the temperature difference and the stirrer speed. The value of this eoeffieient is obtained from experimental data given by Philips (app.2).

In the wall of the ice cream maker, liquid isobutane is boiling. Dependent on the temperature difference between the heated surface and the saturated liquid, different regimes of boiling are possible and give a different heat transfer coefficient. In our case we have a transition regime and the transfer coefficient can be calculated by superposition of two effects. The resulting heat transfer coefficient from wall to boiling isobutane is than calculated with the following relationships [lit.6, 10, 11]:

=

h _Ir" C'CltU'f'C'I;utJ

~*e* *{3*c

with h .

=

0.548

*

(PI f g P)O.2S t:.r:.."!S

'fr ... morr *L

*

"'P

IJ. k

and h.--boiUnl

_~

__

~

* ,

kJ"

*

~

*

~r..."

t:.H;np

*

0.0153

C/

*

",4.1

J

~

The relation between T_boii and p is given by the boiling curve (liL17;app.6). 882.80

log(pressure) = 6.74808 -

---=-=

ll>>i/i/l~ +240

which relates pressure in mm Hg to temperature in

oe.

This formula can be rewritten to:

T

=

-882.80 + 33.15

boiUnl log(pressure * 760) - 6.74808

which relates the boiling temperature in degrees Kelvin to the pressure in bars.

(18)

(19)

(20)

The evaporated isobutane is condensed on the cold surface at the cooling disk. The condensation heat t1ux is also a function of TbOil and is ca1culated by:

(21)

with: U con

=

total heat transfer coefficien t

=

f(T boi.)

Aeon

=

area of condensation

=

con st.

T_boil = f(p) (formula)

Teut

=

eutecticum temperature

=

const.

The total heat transfer coeftïcient is again ca1culated by summation of the partial heat transfer coefficient, and the heat transfer coefficient through the aluminium wall is again neglected.

_ . _

-T

~X

eutedicum

I

melt

I

layer

1lJ:7

~mperature

Profile Condensation Side

. - - - - TOOil

isobutane

l