design and validation of a hilsch-ranque vortex tube

DESIGN AND VALIDATION OF A HILSCH-RANQUE VORTEX TUBE THROUGH EXPERIMENTATION AND COMPUTER SIMULATION

ANDRES H. BILBAO

Advisor

OSCAR F. DELGADO MSc Mechanical Engineer

UNIVERSIDAD DE LOS ANDES MECHANICAL ENGINEERING DEPARTMENT

BOGOTA

2007

Contents Table

Contents Table .................................................................................................................. 2 Figures............................................................................................................................ 3 Tables ............................................................................................................................. 3 Photographs................................................................................................................... 3

1. Introduction................................................................................................................... 4 2. Objectives....................................................................................................................... 6 3. Designing Uniandes Vortex Tube ................................................................................ 7

3.1 Various Designs ....................................................................................................... 7 3.2 Flow dividing, adiabatic vortex tube theory......................................................... 9 3.3 Flow dividing vortex tube’s rough dimensions .................................................. 11 3.4 Uniandes Vortex tube ........................................................................................... 12 3.5 Simulation .............................................................................................................. 15

4. Experimental Setup .................................................................................................... 19 4.1 Preliminary Considerations ................................................................................. 19 4.2 Setup I .................................................................................................................... 22 4.3 Setup II................................................................................................................... 22 4.4 Setup III ................................................................................................................. 23

5. Results .......................................................................................................................... 24 5.1 Preliminary UVT results ...................................................................................... 24 5.2 Generator A results............................................................................................... 25 5.3 Generator B results............................................................................................... 30

6 Future Works ............................................................................................................... 35 7 Conclusions ................................................................................................................... 37 8 Nomenclature ............................................................................................................... 38 9 Bibliography ................................................................................................................. 39 10 Annexes ....................................................................................................................... 40

Thermodynamic Equations and Conversion Equations ......................................... 40 Error Sources .............................................................................................................. 41 Raw Data...................................................................................................................... 49

Generator A .............................................................................................................. 49 Generator B .............................................................................................................. 55

Figures Figure 1. Ranque’s vortex tube patent. ............................................................................... 7 Figure 2. Compact air separation system............................................................................ 7 Figure 3. Ranque’s axial entry vortex tube......................................................................... 8 Figure 4. Shematic diagrams of vortex tubes. Taken from Khodorkov [4]........................ 8 Figure 5. Schematic cut view of a vortex tube. Inspired by Ahlborn and Gordon’s schematics [5] ................................................................................................................... 10 Figure 6. Uniandes Vortex Tube (UVT)........................................................................... 12 Figure 7. UVT section view.............................................................................................. 12 Figure 8. Photographs and three-dimensional model of the central tube ......................... 13 Figure 9. Uniandes Needle Valve (UNV)......................................................................... 15 Figure 10. UNV section view ........................................................................................... 15 Figure 11. UVT mesh ....................................................................................................... 16 Figure 12. UVT simulation streamlines............................................................................ 17 Figure 13. UVT simulation of a single particle. ............................................................... 18 Figure 16. Preliminary results, inlet pressure effect on temperature drop........................ 24 Figure 17. Generator A, cold mass fraction Vs (Tline – Tcold). ...................................... 25 Figure 18. Generator A, cold mass fraction Vs hot temp raise......................................... 26 Figure 19. Generator A, cold mass fraction Vs outlet temperatura difference ................. 27 Figure 20. Cold mass fraction Vs cooling capacity .......................................................... 28 Figure 21. Generator A, cold mass fraction Vs delta entropy .......................................... 30 Figure 22. Generator B, Temperatura drop Vs cold mass fraction................................... 31 Figure 23. Generator B, mass fraction Vs cooling capacity. ............................................ 32 Figure 24. Generator A and B, cold temperature drop Vs cold mass fraction.................. 33 Figure 25. Generator A and B, cooling capacity Vs cold mass fraction........................... 33 Figure 26. Gen A and B, cold temp Vs cold mass fraction. ............................................. 34

Tables Table 1. UVT parts ........................................................................................................... 14 Table 2. Simulation conditions. ........................................................................................ 17 Table 3. Instruments used in the experimental setups. ..................................................... 19 Table 4. Volumetric and mass flow estimates for generator A........................................ 21 Table 5. Volumetric and mass flor estimates for generator B. ......................................... 21 Table 6. Various thermodinamic variables for generator A. ........................................... 29

Photographs Photograph 1. Manufactured UVT ................................................................................... 13 Photograph 2. Two flowmeter xperimental setup............................................................ 20 Photograph 3. Experimental setup I.................................................................................. 22 Photographs 4,5. Cold outlet thermocouple..................................................................... 23

1. Introduction

First patented in 1934 by J.G Ranque, the vortex tube proved to be a truly surprising

invention, capable of obtaining two separate streams of hot and cold air out of a single

line of compressed gas. A particular arrangement for this device, the counter flow vortex

tube, can roughly be described as a T-shaped pipe with a small inlet through which

pressurized gas is injected and two outlets where a hot stream and a cold stream are

ejected (See Figure 1). Gas enters tangentially into a spiral shaped chamber creating a

complex vortex that separates into two streams. The hotter outer stream naturally tends to

heat the colder inner swirl, but this energy transfer rate is far smaller than the rate at

which kinetic energy is transferred from the cold inner particles to the hotter outer

particles. The net result is a group of hotter molecules exiting the tube through a needle

valve, and a group of colder molecules exiting in the other direction. The unexpected

temperature separation makes understandable why the vortex tube was advertised, shortly

after it was invented, as a device that defied thermodynamics’ fundamental laws. It is

obvious that there would no longer be such things as thermodynamic laws, or that they at

least would have been changed, if this apparatus had in fact broken them. This does not

mean that this invention is not still worthy of study, optimization, manufacturing and

commercializing. Proof of this is its increasing commercial divulgation for spot cooling

applications where refrigeration of small components or specific areas is required.

In 1943, Rudolf Hilsch published a systematic study of similar vortex tubes. His work is

very important, not only because it caught the scientific community’s attention, but

because it set a starting point from which a tube with verifiable performance could be

manufactured. He also produced several graphics relating inlet diameters, tube length,

and distance between the inlet ad the spiral’s axis among other geometric variables, with

the difference in outlet temperatures and the tube’s efficiency. The present document uses

this and other researcher’s publications as a base from which to create a vortex tube for

the university.

This project’s main objective is to design, manufacture and validate a vortex tube. Such

task must not be approached lightly due to strong geometric restrictions that should be

followed if a vortex tube with a marked temperature separation effect is to be produced.

The work of Hilsch [1] and Cockerill [2] are clearly very important to the project as the

said geometric restrictions can be implied from their publications, insuring the tube to be

designed will show the expected flow and temperature separation. Following the design

and manufacture of the apparatus, quantitative estimation of its performance and

validation of the confined vortex effect through experimentation will be done. Finally one

of the geometric variables decisive to the tube’s performance will be altered and studied.

Air will be the working fluid injected in the apparatus for all experiments present in this

document.

2. Objectives

Primary

* To design and manufacture a vortex tube that can be validated through experimentation

and computer simulations.

* To obtain performance characteristics for the designed apparatus.

Secondary

* To verify the apparatus follows the first and second law of thermodynamics.

* To set a base simulation, from which different variables relevant to the performance of

vortex tubes can be studied and possible optimizations to this device may be achieved.

* To study through experimentation the effect of altering one of the key variables

relevant to the tube’s performance.

3. Designing Uniandes Vortex Tube

3.1 Various Designs

Since it was first invented so many variations to the original vortex tube were developed,

that a classification for these alternatives became necessary. An acceptable categorization

can be based mainly on the device’s geometry, but should also include streams directions,

number of inlets, and whether the apparatus works under adiabatic or nonadiabatic

conditions. Figure 1 presents the original schematic drawing Ranque patented in 1934

which considering the parameters just stated would be classified as a cylindrical, flow

dividing, single inlet adiabatic configuration. The ‘cylindrical’ adjective was added after

the appearance of various patents that relied on conic geometries for both cold and hot

exits. Some deviations from the initial design were conceived to suit the particular

applications they intend perform. Such is the case of the compact air separation system

[3] (figure 2), where a larger taper angle facilitates de recollection of purer oxygen in the

outer regions at the tube’s hot end.

Figure 1. Ranque’s vortex tube patent.

Figure 2. Compact air separation system

Ranque himself considered variations to his counter flow design. Some included multiple

inlets, cold and hot streams that flowed in the same direction (opposite rotation

nevertheless), and a particular unidirectional arrangement that lacked the usual tangential

inlet (figure 3).

Figure 3. Ranque’s axial entry vortex tube

There are five types of vortex tubes widely studied and commercialized for various

industrial applications. Schematic diagrams for these are presented in figure 4, and

descriptions addressing each variation’s main characteristics were published by

Khodorkov [4].

Figure 4. Shematic diagrams of vortex tubes. Taken from Khodorkov [4]

μ is defined as the cold mass flow fraction. Relation of mass flow that exits the vortex tube at a colder temperature to the total mass flow that enters it. 0<μ< implies cold mass flow regulation by a sort of valve, for μ=1 all mass flow entering exits through one exit, μ>1 additional cold stream enters. a) Dividing vortex tube. b) Cooled vortex tube. c) Self-evacuating vortex tube. d) Dividing vortex tube with additional stream. e) Triple stream vortex tube.

Controversy surrounds the vortex tube. There is no consensus on the effect of conic

geometries on its efficiency or temperature separation phenomenon in the global sense.

Publications dedicated to the study of the effect of taper angles on the hot exit tube have

stated conflicting results [2]. This work will not bring more controversy to the matter

because it is not its intention to tackle the purely theoretical aspects of the forced vortex

phenomena. Efforts will focus on designing a simpler, more conventional flow dividing

vortex tube with geometric dimensions supported on previous work and observation of

currently commercialized tubes.

3.2 Flow dividing, adiabatic vortex tube theory

Despite the fact that no pure theoretical investigation will be addressed by this

investigation, having a certain level of understanding of the complex phenomena

generated inside a flow dividing vortex tube is necessary. It can prove very useful in

getting a feel for the geometric limits intrinsic to this apparatus.

It is not yet fully understood how the vortex tube works. The complex heat and mass

transfer phenomena that gaseous fluids experiment while forced through it have not been

modeled to an extent where consensus has been achieved. Ahlborn and Gordon [5]

proposed an interesting theory to help explain the paths followed by different gas

particles within the tube and also the temperature separation effect.

Figures 5 and 6 present illustrations inspired on those produced by this researchers to

help visualize their theory. As they explained, a number of gas molecules maintain a

circularly motion near the wall after entering the tube. Because flow inside the tube and

therefore near the wall is somewhat turbulent, some molecules are pushed inwards into a

sort of toroid shaped secondary circulation. While remaining within this secondary flow,

molecules help transfer energy in the form of heat from the inner colder backflow to the

outer primary circulatory flow. Some small gas volumes become part of the secondary

circulation momentarily, later return to the primary circulation and exit through the cold

or hot end of the tube. Others remain close enough to the wall as to exit the tube through

the hot end without ever having formed a part of the secondary circulation. Finally some

molecules go straight from the peripheral flow into the backflow due to turbulence

present in the tube.

Energy separation takes place as follows. Air enters tangentially into the spiral shaped

chamber creating a complex vortex that separates into two streams. The hotter outer

stream naturally tends to heat the colder inner swirl, but this energy transfer rate is far

smaller than the rate at which kinetic energy is transferred from the cold inner particles to

the hotter outer particles. In-between these two regions the secondary azimuthal

circulation receives considerable amounts of energy provided by momentum exchange

with the inner backflow and continuously convects to the peripheral circulation. The net

result is a group of hotter molecules exiting the tube through a needle valve, and a group

of colder molecules exiting in the other direction. There is a pressure gradient that

increases from the center of the tube in a radial direction. That is to say that pressure is

higher near the walls. This can help explain why backflow molecules which exit close to

the center of the tube do so at larger speeds than those that exit at the hot end according

to various publications.

Figure 5. Schematic cut view of a vortex tube. Inspired by Ahlborn and Gordon’s schematics [5]

Ahlborn and Gordon’s explanation for the energy separation phenomena that occurs

within a vortex tube, however ingenious as it may be, is but merely one of many which

scientists have conceived to decipher such intriguing condition. Cockerill [2] summarized

a vast amount of research sometimes even contradictory that relied on viscous dissipation

effects, momentum transfer and even complex acoustics to explain the effect. A

Mathematical model for the temperature separation produced by this devise has not yet

been developed to a point of consensus either. It is therefore clear that experimental data

is the main source of information from which theories meant to explain the vortex tube

phenomena are derived.

3.3 Flow dividing vortex tube’s rough dimensions

Having decided to design a flow dividing vortex tube, it is good that researchers seem to

agree a little more in regards to the dimensions that assure a perceivable temperature

separation for this configuration. Total length L, inner radius R and cold outlet radius r,

are the main critical variables to be defined when attempting to create a vortex tube from

scratch. Alekseev and Martynovskii [6] talk of a 40 to 50 L/(2R) relation for optimum

performance. Hilsch [1] suggests a value around 50 for this same quotient, and Cockerill

[2] summarized these along with other findings from different scientists regarding vortex

tube’s dimensions. He also highlighted that most authors use a cold outlet radius to tube

radius ratio (r/R) ranging from 0.3 to 0.6. Most common commercial tubes found on the

web have an inner radius close to 1 cm and have a total length anywhere from 60 mm to

300 mm. Many tubes with applications in spot cooling have a total length close to a 120

mm, size which will approximate the tube to be developed in this work. We will call this

device UVT, short for Uniandes Vortex Tube.

Certainly there are many more variables aside from L, R, and r that define a vortex tube.

The entry nozzle, hot exit valve and circular chamber must all play their part. Because of

patent restrictions, no attempt was made to reproduce an already existing apparatus, and

the design for these last mentioned items was left to be the product of thought and

imagination. Naturally the needle valve and circular chamber designed serve the same

purposes Hilsch first patented, and therefore resemblance is undeniable. Nevertheless no

commercial vortex tube was manipulated or its dimensions reproduced when designing

the UVT.

3.4 Uniandes Vortex tube

Figure 6. Uniandes Vortex Tube (UVT)

Figure 6 shows an exploded view of the main parts that constitute the UVT. Short tube,

vortex generator, central tube and long tube where the names assigned to the pieces there

present, and they will continue being used throughout the rest of this document. No

custom needle valve was initially planned since the use of a regular commercial valve

was being considered.

Figure 7. UVT section view

The UVT was designed as an assembly of parts that can be easily manipulated.

Manufacturing the apparatus would have extremely difficult otherwise. The assembly

also facilitates future study of the effect of altering geometric variables such as cold

outlet diameter, long tube length or inlet diameter among others by simply changing the

generator, long tube, or central tube for one designed with the desired modification.

Assembly between parts is achieved by NPT threads.

Photograph 1. Manufactured UVT

The UVT was predominantly manufactured in stainless steel expecting many months of

future use. It is key to this design to minimize possible leaks and therefore maintain

acceptable efficiency for the device. The generator acts as a seal that allows air exiting at

the cold end of the tube, to do so only through its orifice. It is pushed against the central

tube’s conic interior by the short tube. NPT regular threads had to be modified reach to

full contact between these surfaces. Regular NPT threads are designed to produce a seal

between the third and fifth turn. This seal is caused by a small deformation of the thread

produced after the said number of turns. Figure 7 shows the short tube completely

penetrates the central tube and pushes the generator against it, which could not be

possible if the NPT thread in the short tube had not been deepened.

Figure 8. Photographs and three-dimensional model of the central tube

Other components necessary for the operation of the UVT are two pneumatic connectors,

a female ¼-NPT to male M5 thread connector and a hose. They are required to connect

the tube to the university’s pressurized air line. The experimental setup also involves a

short tube with a ¼-NPT male thread to connect to the flowmeters used. Table 1

illustrates a summary of all UVT parts including those used for the experimental setup

and drafts annexed contain detailed drafts for every non commercial part used in the

experiment.

# Name Threads Material 1 Short Tube 3/8-NPT male, hexagon, 1/4-NPT male Bronze 1 Short Tube 3/8-NPT hexagon Stainless Steel 2 Connectors 1/4-NPT male, hexagon, 1/4-NPT male Bronze 1 Connector M5 female, 1/4-NPT male Stainless Steel 2 Pneumatic connectors 1/4 OD, M5 male ----------------------- 1 Generator A D 4mm Empack 1 Generators B D 3mm Empack 1 Valve A Shruemann 5M4N50 ----------------------- 1 Uniandes Needel Valve

(UNV) 1/4-NPT male, 16MX0,8 1020 Steel

Table 1. UVT parts

The central tube design is decisive to the temperature separation expected from the UVT.

It has a tangential inlet with a 2mm diameter. No particular nozzle was designed for this

entry, so air expands adiabatically as it flows from a small orifice into the comparatively

large opening in the central tube.

Initially the tube was tested with a commercial flow regulating valve; a Shruemann

5M4N50 model which will be referred to as valve A. Some preliminary results were

obtained to corroborate the energy separation effect. This valve did not allow a proper

study of the influence of the ratio at which cold air exits the tube at the cold end to that at

which air enters (cold mass fraction), on outlet temperatures. For this reason no more

measurements were taken with using this model.

A new needle valve more consistent with Hilcsh’s initial design was developed (figure 9).

It consists of two pieces; a hollow cylinder with a ¼-NPT female thread at one end,

where the long tube fits, and a 16MX0.8 female thread at the other end where the second

part (conic portion) is screwed in and out to allow less or more hot flow to exit. The

second part has a conic geometry at the end that seals the long tube.

Figure 9. Uniandes Needle Valve (UNV)

If it were assembled, the long tube would connect with the UNV at the ¼-NPT threaded

opening (see Figure 10). The cylindrical part of the UNV and the long tube would remain

fixed and the conic part of the valve would be unscrewed (moved to the right as placed in

figure 10), to allow more air to exit, or screwed to a point where no flow would get

through. Air would enter the valve through the ring shaped section formed between the

long tube and conic part and would continue to flow through any of the four orifices in it

and finally exit through the larger orifice at its end.

Figure 10. UNV section view

3.5 Simulation

The possibility of having an accurate simulation where various alterations to the initial

geometry could be made and its consequences on the device’s performance approximated

is very appealing. This task is very difficult due to a number of complications. The fact

that there are two outlets and a single inlet in the vortex tube makes it feasible to obtain

highly unlikely results. This could be avoided if approximated variables measured from

the working apparatus were set as input to the new simulation. This implies that

experimental data would always be necessary in order to calibrate the initial simulation

and obtain trustworthy results. Every simulation requires a mesh formed bye a large

amount of nodes and elements (figure 11). A small opening of the needle valve

constitutes a very different geometry at the tube’s hot outlet and therefore a different

mesh. In order to maintain accuracy, a single mesh would have to be simulated and

calibrated for every needle valve position. This means that to approximate via CFD

simulations the effect on a vortex tube of a given alteration to its geometry, and relate it

to the cold mass fraction, at least dozens of meshes and simulations would be required.

Despite mentioned complications a mesh that approximated the hollow volume within the

UVT was created in the CFD simulating package CFX (figure 11). That is the space

enclosed bye the tube through which air would flow. The mesh was composed of roughly

26.000 nodes.

Figure 11. UVT mesh

A simulation of the UVT working at 50 Psig and 40% cold mass fraction with a 4mm

cold outlet diameter (generator A) was carried out. The objective was to visualize flow

streamlines, and evaluate the possibility of continuing efforts looking to reach a

successful CFD model that could prove useful to future optimization of the UVT. Initial

conditions for this simulation are stated in table 2. Simulation Boundary Conditions

Simulation type General Inlet 18.8ºC, 50 Psig Working fluid Air at 0.745 atm, 18.8 ºC Hot outlet 7.4 SCFM, 0 Psig

Pressure referente 0.745 atm Cold outlet 6.9 SCFM, 0 Psig Turbulence model low scale walls Adiabatic, No slip

Energy model k-epsilon Advection écheme High resolution

Table 2. Simulation conditions.

The results for this simulation are presented in figures 12 and 13. They were satisfactory

in the sense that streamlines were clearly visualized. A streamline is the path a

differential element of air would travel according to the simulation results. Figure 13

shows streamlines generated from 50 points at the tube’s inlet. As expected circular

motion is exhibited, and midway through the tube some streamlines turn around forming

backflow which circulates in opposite sense to the initial circulation. Air seems to enter

the tube at about 2.4E4 meters per second which seems reasonable. Exit speed at the hot

end also appears reasonable. This is not the case for the cold end. 8 E4 meters per second

is too large a velocity to consider it plausible.

Figure 12. UVT simulation streamlines.

In figure 13 a streamline was formed starting from single point about an inch from the

inlet in the hot end direction. All the spiraling observed was generated by that sole

streamline. It is very interesting how initially the point moves towards the cold end of the

tube, then gains some speed as it rotates in the opposite sense as it heads for the hot end

of the tube. Again it turns around and travels once more towards the cold end also

switching its sense of rotation.

Figure 13. UVT simulation of a single particle.

No evidence was found in this simulation that could prove an azimuthal secondary

circulation resembling Ahlborn and Gordon theory. This simulation did not produce

realistic results for either outlet temperature. 18.8ºC was the temperature observed

throughout all the tube including its exits. This outcome is then very different from the

expected 4ºC and 40ºC from the cold and hot outlets respectively. In conclusion, the

turbulence and energy models used for this simulation were not a good approximation of

the real operating situation. Because the results obtained were not very off no real

conclusions regarding the UVT performance can be drawn from them. After considering

the volume of work necessary to achieve an acceptable simulation and little available

time the decision was made not continue with the attempt to simulate the UVT, but to

concentrate efforts on the experimental verification of the devise and its performance

analysis.

4. Experimental Setup 4.1 Preliminary Considerations

The basic purpose of the following experimental setups was to observe the influence of

pressure on outlet temperatures, and to relate these variables to cold mass fraction and

therefore obtaining a complete characterization for the device’s performance. A list the

instruments used is presented in table 3.

Instruments Model Range Presicion Accuracy Omega flowmeter FLA2918A 0-5 SCFM 0.25 2%FS Omega flowmeter FL2904A 2-20 SCFM 0.25 2%FS Omega digital thermometer TH15B4 within experriment's limits 0.05 1%FS Zamnac Pressure regulator 2900MN4 0-140 Psig 2.5 2% Omega Channel selector CH23N6 %%% 6 Channels %%%% instrument's instrument's

Table 3. Instruments used in the experimental setups.

Because flowmeters only measure volumetric flow, mass flow had to be estimated so that

cold mass fraction could be related to other variables. This estimation used the ideal gas

law to approximate air’s density at the measured point, and regular unit conversion to

obtain a result in kg/min units. Since volumetric flow is strongly influenced by pressure,

and temperature, it was expected that flowmeter readings at the cold outlet, having colder

temperature and lower pressure conditions, were much higher.

One of the complications that arose as an experimental setup was being planned was the

fact that when both flowmeters were being used (photograph 2), and UNV was

manipulated, inlet volume flow was affected. When the valve was completely shut, less

air entered the tube than when it was slightly or fully opened. The reason for is the

flowmeter operation principle. Since it is based on a spring that is contracted, a strong

resistance diminishes flow’s momentum as air passes through the instrument. When the

valve was fully closed and the second flowmeter was placed at the cold outlet, resistance

was exerted by the two instruments and the tube’s short passages restrictions. As the

valve opened and not as much pressure was placed on the second flowmeter, the overall

resistance reduced and more air could enter the tube. When only one flowmeter was used,

inlet flow remained unaffected by needle valve manipulation. The short range

instrument’s readings (flowmeter 1) were used to estimate inlet mass flow for pressures

10-60 Psig and generators A and B. These estimates were compared to those obtained by

using the flowmeter with a larger range (flowmeter 2) on the cold outlet and having the

needle valve completely closed. Because only one flowmeter was being used at a time

which could be approximated as an equal spring resistance for both cases, and because

the UNV was fully closed, mass flow at the inlet should be very close to mass flow at the

cold outlet. Table 4 and Table 5 show the obtained estimations for generator A and

generator B respectively.

Photograph 2. Two flowmeter xperimental setup.

To better estimate inlet mass flows, high resolution pictures of the operating flowmeter

were taken (figure 14) and inserted in a CAD package where they were measured,

therefore obtaining readings with better precision than that offered by the device’s

original scale.

Inlet Cold Exit

Pressure Flowmeter Temperature Mass Flow Flowmeter Temperature Mass Flow Relación

Flujo (Psig) Reading (SCLM) (ºC) (kg/min) Reading (SCLM) (ºC) (kg/min) Error %

10 2.0 18.7 0.0221 2.6 17.5 0.021 5.8 20 3.1 19.0 0.0416 5.0 17.2 0.040 3.7 30 3.6 18.6 0.0557 7.2 16.2 0.058 4.0 40 4.1 18.8 0.0707 9.3 15.9 0.075 5.9 50 4.8 19.0 0.0905 11.5 15.4 0.093 2.5 60 5.0 19.2 0.1016 13.0 15.6 0.105 3.1

Table 4. Volumetric and mass flow estimates for generator A.

Inlet Cold Exit Pressure Flowmeter Temperature Mass Flow Flowmeter Temperature Mass Flor Relación Flujo

(Psig) Reading (SCLM) (ºC) (kg/min) Reading (SCLM) (ºC) (kg/min) Error %

10 1.9 18.7 0.0210 2.5 17.5 0.0200 4.6

20 2.8 18.8 0.0376 4.8 17.2 0.038 2.3

30 3.4 18.7 0.0526 6.7 16.2 0.054 2.5

40 3.9 18.9 0.0672 8 15.9 0.064 4.2

50 4.4 18.7 0.0830 10.9 15.4 0.088 5.9

60 4.8 18.4 0.0978 12.8 15.6 0.103 5.4

Table 5. Volumetric and mass flor estimates for generator B.

Flowmeters used in these experiments use a conversion chart which helps quickly

translate an initial reading to the ‘real’ value for different pressure conditions. This chart

and Omega’s suggested pressure conversion equations were estimated for sea level

conditions (figures 14). Because these experiments were conducted in Bogotá, where

ambient pressure is about 74% of that at sea level, a different conversion had to be used

(Annex, Equations). Temperature conversion remained the same.

Figure 14. High resolution photo and original Omega conversion factors

4.2 Setup I

For this experiment, only temperature readings for the tube’s outlets were taken. These

were registered at pressures ranging from 10-80 Psig (Photograph 3). Valve A was used

and it remained fully opened during the completion of the experiment. This valve has a

very small inlet and outlet, therefore stating that that it was fully open does not imply that

no flow was exiting the tube through the cold outlet. A thermocouple was placed 2 mm

away from valve A’s outlet and another 7mm away from the tube’s cold outlet. The

objective of this experiment was the corroboration of temperature separation produced by

the UVT, and to observe how it was affected altering only inlet pressure.

Photograph 3. Experimental setup I.

4.3 Setup II

For the second setup, temperature readings were taken at the cold and hot outlets and at

the pressurized air line just after exiting the regulator. Generator A was inserted in the

tube. The instrument configuration for this setup is very similar to that presented in

Figure 15. Omega flowmeter conversion chart and section cut.

photograph 3 with the exception that the flowmeter connected to the pressurized air line

was not used since inlet mass flows had already been approximated.

The Uniandes Needle Valve was fully closed at the beginning of the experiment.

Temperatures and volume flow at the cold exit were registered. This last reading was that

which approximated to mass flow at the exit, and compared to mass flow at the inlet in

table XXX. The valve was then gradually opened and temperature and mass volume

readings taken up to the point of complete overture. The channel selector was used to

facilitate the registering of the three temperatures. The thermocouple placed in the cold

end outlet was located approximately 5mm from the generator’s exit and the one

positioned at the hot exit was just outside the valve.

Photographs 4,5. Cold outlet thermocouple

4.4 Setup III

This configuration is an exact reproduction of setup II with the difference that generator

B was used instead of generator A.

5. Results 5.1 Preliminary UVT results

The following inlet mass flows were estimated under setup II.

Generator A, Valve A fully open, Temperature as a funtion of inlet pressure

-10

0

10

20

30

40

50

10 20 30 40 50 60 70 80

Pressure (Psig)

Tem

pera

tura

(ºC

)

TcoldThotTin

Figure 16. Preliminary results, inlet pressure effect on temperature drop.

Results presented in figure 16 correspond to experimental setup I.

Despite the impossibility of using valve A for a good range of cold mass fraction, it was

practical for observing the influence of inlet pressure on outlet temperatures for a fixed

valve position. As it can be observed, inlet pressure is decisive for both temperature rise

at the hot outlet and temperature drop at the cold outlet. The data shows that for a fixed

cold mass fraction at a higher inlet pressure a larger temperature and temperature rise are

produced. This first observation verifies that temperature separation is proportional to

inlet pressure for the UVT. No airflow measurements were directly taken in this setup but

using the cold temperature registered at a given pressure, say 60 Psig, it can be inferred

that cold mass fraction was around 0.5.

5.2 Generator A results

The following results correspond to experimental setup II.

Generator A, Cold Mass Fraction Vs (Tline-Tcold)

-3

2

7

12

17

22

27

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Cold Mass Fraction

Col

d Te

mp.

Dro

p [C

]

60 Psig50 Psig40 Psig30 Psig2010

Figure 17. Generator A, cold mass fraction Vs (Tline – Tcold).

Figure 17 represents the cold temperature drop as a function of cold mass fraction at

various inlet pressures. It is clear that an altering cold mass fraction reflects strongly on

the temperature exhibited in the cold outlet. It is also clear that higher pressures produce

larger temperature drops as it was confirmed earlier. All the trend lines obtained from this

data coincide in that they have a large interval where temperature drop varies almost

linearly with cold mass fraction. When all the air that enters the tube exits through the

cold outlet, temperature drop is very poor. As fewer air exists at the cold end for a set

pressure (cold mass fraction reduces), temperature drop increases linearly up to a point

where it reaches its maximum value and then decreases describing a sort of parabola.

Generatos A, Cold Mass Fraction Vs Hot Temp Raise

-1

4

9

14

19

24

29

0 0.2 0.4 0.6 0.8 1Cold Mass Fraction

Hot

Tem

p. R

aise

(ºC

)

60 Psig50 Psig40 Psig30 Psig20 Psig10 Psig

Figure 18. Generator A, cold mass fraction Vs hot temp raise

Figure 18 shows the hot temperature drop raise as a function of cold mass fraction at

various inlet pressures. Temperature rise trend lines were arbitrarily defined as linear.

Some data obtain was considerably far from the tendency as is the case of some points

midway through the 60 Psig pressure line. Temperature difference in both hot and cold

end was consistently larger at higher inlet pressures, suggesting that a lower inlet pressure

produces not only lower temperature differences, but also a smaller overall temperature

difference.

Generator A, Cold Mass Fraction Vs Outlet Temperature Difference

5

10

15

20

25

30

35

40

0 0.2 0.4 0.6 0.8 1

Cold Mass Fractions

Thot

- Tc

old


Figure 19. Generator A, cold mass fraction Vs outlet temperatura difference

Overall temperature difference is presented in figure 19. This data is not very consistent

in the sense that trend lines for various inlet pressure differ considerably from each other

showing no consistent pattern. It cannot be concluded that a larger overall temperature

difference is obtained close to a certain value of cold mass fraction. It is clear however

that every curve has a minimum value close to zero cold mass fraction, a maximum

somewhere in the middle and another low point towards the end. As expected, once more

higher inlet pressures account for larger overall temperature differences.

Generator A, Cold Mass Fraction Vs Cooling Capacity

-1.3

-1.1

-0.9

-0.7

-0.5

-0.3

-0.1

0.1

0.3

0 0.2 0.4 0.6 0.8 1

Cold Mass Fraction

Coo

ling

Cap

acity

(kJ/

min

)


Figure 20. Cold mass fraction Vs cooling capacity

Figure 20 shows estimated cooling capacity data approximated from registered

temperatures and cold outlet mass flows. Cooling capacity is defined as the rate at which

heat is withdrawn from a body or space. As expected, the tube worked as a more

powerful chiller as it received a stronger input in the form of higher inlet pressure and

therefore bigger mass flow. Cooling capacity reacts very differently to temperature drop

in the sense that it grows as cold mass fraction grows and not the opposite. This

demonstrates that when it comes to its application as a chiller what is truly relevant to the

vortex tube’s performance is the temperature drop reached at larger cold mass fraction

values. Despite however low a temperature is produced in the cold outlet at very low cold

mass fraction values, it is above 0.5 where the tube does its best work. Clearly the

volume of mass flow has a larger effect than temperature on the tube’s capacity to extract

heat. This leads to believe that efforts on improving the UVT should be directed towards

lower temperatures at 50% or larger volume flow split, and not on achieving minimum

overall temperatures. The best cooling capacity obtained from the UVT was close to 1.0

kJ/min at 60 Psig, meaning that this is the largest rate at which the device can cool air. If

compared with commercial vortex tubes of similar dimensions, the UVT performs around

at 25 % of their capabilities for the same inlet pressure. This considered a satisfactory

performance for an initial design of the apparatus. Compared to commercial chillers

based of different technologies such as air conditioners, the UVT and even commercial

vortex tubes for that matter have very poor capabilities. A regular refrigeration unit

produces anywhere from 100 to 500 kJ/min depending on the model and space to be

cooled [9]. This characteristic helps explain why vortex tubes have such specific

applications and are not an advisable technology in most cases.

Table 5 presents summary of the thermodynamic properties results obtained for UVT using

generator A and an inlet pressure of 20 Psig. The total change in enthalpy for all values in the

table regardless of flow rate is always negative. This data indicates that no matter what cold

mass fraction is applied, there will always be a loss of heat energy in the system. Similar data

can be obtained for operation at different pressures which indicates that total enthalpy

reduction occurs regardless of inlet pressure also. This loss of energy is part of the price that

is paid to produce the hot and cold streams. The values for ∆H were obtained using

experimental data and a balance from the first law of thermodynamics, proving that the

apparatus does follow this law.

Inlet Flow Tcold Thot ∆Hcold ∆Hhot ∆Htot m^3/min ºC ºC kJ/min kJ/min kJ/min 0.04434 17.2 30.3 -0.113 0.044 -0.069 0.04212 16.2 29.9 -0.146 0.039 -0.107 0.03990 15 30.1 -0.182 0.036 -0.146 0.03769 14.1 30.3 -0.204 0.034 -0.170 0.03547 13.9 29.7 -0.199 0.030 -0.169 0.03325 13.6 29.6 -0.196 0.027 -0.168 0.03104 13.2 29.2 -0.194 0.024 -0.170 0.02882 12.6 28.9 -0.197 0.021 -0.176 0.02660 11.9 28 -0.199 0.017 -0.182 0.02439 11.1 27.7 -0.201 0.014 -0.187 0.02217 10.8 27.2 -0.189 0.012 -0.177 0.01995 10 26.6 -0.186 0.010 -0.176 0.01773 9.4 26.1 -0.175 0.008 -0.168 0.01552 9 25.7 -0.159 0.006 -0.153 0.01330 8.8 25 -0.139 0.005 -0.135 0.01108 8.5 24.2 -0.119 0.003 -0.116 0.00887 8.3 23.1 -0.097 0.002 -0.095 0.00665 8.2 22.6 -0.074 0.001 -0.072 0.00443 8.4 22 -0.048 0.001 -0.048 0.00222 8.9 21.4 -0.023 0.000 -0.023

Table 6. Various thermodinamic variables for generator A.

Generator A, Cold Mass Fraction Vs Delta Entropy

4

6

8

10

12

14

16

0 0.2 0.4 0.6 0.8 1

Cold Mass Fractio

Del

ta E

ntro

py (J

/min

*K)


Figure 21. Generator A, cold mass fraction Vs delta entropy

Having verified that the UVT does abide to the first law of thermodynamics,

corroboration for the second law follows. Figure 21 confirms that for all inlet pressures

and cold mass fractions, total entropy change for the UVT is always positive. This piece

of information in accordance with previous observations verifies that for the UVT as

pressure increases so does the cold temperature drop, the hot temperature rise, the cooling

capacity and the system’s entropy as well.

5.3 Generator B results

Looking to analyze the effect of altering a geometric variable on the UVT performance,

generator B added to the device. This second generator’s orifice is 3mm in and identical

to generator A in every other dimension. The following results correspond to

experimental setup III.

Generator B, Cold Mass Fraction Vs (Tline - Tcold)

0.0

5.0

10.0

15.0

20.0

25.0

30.0

35.0

0.0 0.2 0.4 0.6 0.8 1.0

Cold Mass Fraction

Tem

pera

ture

Dro

p (C

)


Figure 22. Generator B, Temperatura drop Vs cold mass fraction

Figure 4 presents the temperature drop as a function of the cold mass fraction for

generator B. As expected was verified for generator A. temperature drop increases as

inlet pressure increases and cold mass fraction reduces. These curves once more describe

an approximate linear behavior for the best part and a concave parabolic rise and descent

at lower cold mass fraction values. This data is consistent with that obtained using

generator A at the same conditions.

Generator B, Cold Mass Fraction Vs Cooling Capacity

-1.40

-1.20

-1.00

-0.80

-0.60

-0.40

-0.20

-0.0 0.2 0.4 0.6 0.8 1.0

Mass Fraction

Coo

ling

Cap

acity

(kJ/

min

)


Figure 23. Generator B, mass fraction Vs cooling capacity.

As expected from the cooling capacity estimated from experimental data and presented in

figure 23, it increases hand in hand with inlet pressure and cold mass fraction. Vortex

tube manufactures state that their devices work best for mass fractions between 0.6 and

0.8. This is corroborated in the UVT by results obtained for 60 , 50, 20 and 10 Psig inlet

pressure in generator B, all inlet pressures except 50 Psig in generator A, but not for the

rest. This leads to believe that a good deal of error intrinsic both the experiment and

assumptions made to calculate cooling capacity does not make a possible irrefutable

conclusion, but still the UVT would probably work best at a cold mass fraction close to 0.7.

Figure 24 presents the temperature drop as a function of cold mass fraction for generators

A and B at different pressures. Generator A is represented in the graph by a circle, and

generator B by a star. The intention of this populated graph is to make visible the fact that

there are no definitive differences between the data obtained from either generator. It is

apparent that at some pressures generator A achieved a larger temperature drop while at

others generator B did. The same situation occurs for higher cold mass fractions where

the tube is expected to have a better performance. Figure 25 contributes to the confusion

as it evidences that no generator consistently surpassed the other in cooling capacity. As a

consequence the data does not provide clear enough information that would allow a

certain generator over the other.

Figure 24. Generator A and B, cold temperature drop Vs cold mass fraction

Figure 25. Generator A and B, cooling capacity Vs cold mass fraction

Cold Mass Flow Vs Cold Temp, 60Psig

-10.0

-5.0

0.0

5.0

10.0

15.0

20.0

0.000 0.020 0.040 0.060 0.080 0.100

Cold Mass Flow (kg/min)

Col

d Te

mp

(C)

Gen BGen A

Figure 26. Gen A and B, cold temp Vs cold mass fraction.

Figure 26 has the intention to present actual temperatures obtained from the cold outlet

for generations A and B. The pressurized air line’s temperature surrounded the 18.7 ºC.

6 Future Works

A great deal of future work can use the UVT as its foundation. It is important however

that better instruments are used so that small variations in outcomes can be effectively

perceived and conclusions may be drawn from them. Instruments that accurately measure

mass flow would be very useful. A data acquisition card hopefully compatible with mass

flow measuring device and also a number of thermocouples would allow precise readings

required to estimate the system’s response to variations in inlet pressure or ambient

temperature.

This experiment assumed flowmeters were subjected to ambient pressure. It would be

best if the setup included pressure readings at the outlets, which could then also be related

to temperature, cooling capacity and flow. A more accurate and stable pressure regulator

could avoid loosing hours of work due to unexpected pressure drops in the air line.

Inserting some probes at different lengths in the long section of the tube could be

considered, though performance would probably suffer due to flow disruption. The

influence of humidity on the devise could also be verified.

In regards to actual variations to the tube, the possibility of analyzing different

geometries for the vortex generator would be very interesting. Some commercial vortex

tubes include a sort of helix through which air flows as it enters the tube, therefore

generating a more aggressive vortex. To study the effect of a taper angle on the long

section of the tube is also advisable. The central tube could be altered in many ways to

study the effect of inlet nozzles, inner radius, length and taper angle among other

geometries on the tube’s performance. A completely different geometry could be

conceived considering that the conic interior for the actual central piece was thought as to

work as an effective seal which was easy to manufacture, but the influence of such a

geometry on the vortex achieved was not given much thought. Care must be taken when

altering the design due to specific length and diameter restrictions. The reason for this is

that too short a tube would not give the stream enough surface or time to friction and heat

up. A tube with exceeding length would cause the vortex to collapse, as would a large

inside diameter also.

Evidently many more aspects of the tube can be studied and even an application for it in

the university laboratory could be given some thought. It is only the authors wish that his

creation and this document may be of assistance to anyone who continues to study the

apparatus or use it in any way.

7 Conclusions Design and Manufacturing

- The device manufactured exhibited satisfactory performance and clearly distinguishable

temperature separation.

- No definitive differences could be obtained from altering the cold outlet diameter by the

use of a second generator. This inconvenience is caused by the large errors with which

the experiment was inevitably carried out.

Validation

- It was experimentally verified that the Uniandes Vortex Tube follow the first law of

thermodynamics, for it always produces a negative enthalpy change, as can be verified

from table 6.

- Inlet pressures and cold mass fraction have effects on the temperature difference

between the hot and cold outlet streams. Increasing the inlet pressures produce larger

temperature differences.

Performance

- The cooling capacity of the device is inefficient compared to commercial refrigeration

units. The maximum cooling capacity obtained from the UVT in this investigation was

1.03 kJ/min while normal refrigeration units produce anywhere from 100-500 kJ/min

depending on the model and space to be cooled [9].

Simulations

- A satisfactory mesh which can be used for future investigation was attained.

- The initial objective set to characterize the UVT steady state working conditions

through CFD simulation was not achieved. Time availability was the main cause for this

underachievement.

8 Nomenclature The following variables defined were used throughout this document:

Cp specific heat capacity at constant pressure (psig) D tube diameter (in) H the standard thermodynamic variable representing enthalpy (J / kg) ∆H state variable representing changes in enthalpy (J / kg) K kinetic energy (J) min mass flow rate of the inlet stream (g/min) mh mass flow rate of the hot outlet stream (g/min) mc mass flow rate of the cold outlet stream (g/min) P pressure of the compressed air in the pressure regulator (psig) Pa atmospheric pressure (mmHg) Pc cold outlet stream pressure (mmHg) Ph hot outlet stream pressure (psig) Pin inlet stream pressure (psig) Q the standard thermodynamic variable representing heat added / removed (J) Qc volumetric flow rate of the compressed air at the cold outlet (SCFM) R the ideal gas law constant (L atm / mol K) Rmax radius of the tube from the tube axis to the tube wall (in) S the standard thermodynamic variable representing entropy (J / kg *K) Sgen entropy generated by the system (J / kg *K) ∆Stot total change in entropy for a system (J / kg *K) ∆Sh entropy change in the hot stream (J / kg *K) ∆Sc entropy change in the cold stream (J / kg *K) Tref reference temperature used to calculate ∆H; in this case Tref = T1 (oC) Tin temperature of the compressed air just before entering the tube (oC) Thot temperature of the hot outlet stream (oC) Tcold temperature of the cold outlet stream (oC) T4 temperature of the air prior to entering the pressure regulator (oC) T5 an unused temperature meter variable (oC)

9 Bibliography 1. R Hilsch. “The use of expansion gases in a centrifugal field as a cooling process.”

The review of scientific instruments, February 1947.

2. Cockerill T. “Thermodynamics and fluid mechanics of a Ranque-Hilsch”.

Universidad de Cambridge. 1998.

3. Crocker A., White S., Bremen F., Space A. Jr., “Experimental Results of a Vortex

Tube Air Separador for Advanced Space Transportation”. 39th Joint Propulsion

Conference & Exhibit, July 2003.

4. K hodorkov L., Poshernev N. V., Zhidkov M. A. “The Vortex Tube – A Universal

Device for Heating, Cooling, Cleaning, and Drying Gases And Separating Gas

Mixtures”. Chemical and Petroleum Engineering, Vol. 39, No. 7–8, 2003.

5. Ahlborn K. Boye, Gordon M. Jeffrey. “The Vortex Tube as a Classic

Thermodynamic Refrigeration Cycle”. Journal of Applied Physics. Vol. 88, No. 6.

Septiembre de 2000.

6. Martynovskii V., Alekseev V., “Investigation of the vortex termal separation effect

for gases and vapors.” Soviet Physics: Technical Physics, 1957.

7. Kulkarni R. Manohar, Sardesai R. Chetan. “Enrichment of Methane

Concentration via Separation of Gases using Vortex Tubes”. Journal of Energy

Engineering. Abril 2002.

8. Trofimov, V.M. “Physical Effect in Ranque Vortex Tubes”. Institute of Theoretical

and Applied Mechanics, Siberian Division, Russian Academy of Sciences,

Institutskaya ul. 4/1, Novosibirsk, 630090 Russia. Agosto 2003.

9. Incopera, P. Frank. “Fundamentals of Heat Transfer”. Cuarta Edicion. Prince Hall.

1999

10. Streeter L. Victor, Wylie Benjamin E. “Fluid Mechanics” Octava Edicion. 1998.

11. Bechwith G. Thomas, Marangony D. Roy. “Mechanical Measurements”. Quinta

Edicion. Addison-Wesley. 1993.

12. American Society of Mechanical Engineers, Thermo King Model C Transport

Refrigeration Unit, October 1996.

13. CFX Analysis Package Manual.

10 Annexes Thermodynamic Equations and Conversion Equations

87.11087.101

+=

Pf

( ) ( )( )

( )incPc

refin

refinPin

refcPcrefhPh

TTCmCC

TTTTCm

TTCmTTCmHHQ

−=

=

−−

−+−=ΔΔ=

&

&

&&

CAPACITYCOOLING

lettingby simplify can

refref

inincchhoverall

gensys

outoutinin

PPnR

TTn

SmSmSmS

STQmSmS

dtdS

ll

&&&

&&

&&

−=Δ

Δ−Δ+Δ=Δ

++−= ∑ ∑

PCS

gas idealan For

Error Sources

Two experiments were performed for every group of data present in every pressure curve.

The error bars observed on all graphs are 12% of the data taken, which was the average

error estimated. For a single data on the curve to be obtained from a cold fraction value

and temperature drop registered, two points were taken. The difference between these

two points was calculated and averaged with all the differences computed from every two

points taken for a single cold mass fraction at every inlet pressure. The overall average

was 12%.

There were different sources of errors for this experiment. Inlet pressure strongly affects

the experiment, and the device used as a pressure regulator was not precise enough as to

assure reproducible conditions for every second experiment. Clearly ideal gas, as the

model from which cold mass fraction was estimated was another big source of error.

Flowmeter readings were not too precise and a bias error due to the experimenter’s

interpretation of such reading was always included.

Drafts

Raw Data

Generator A

Gen A, 60 Psig, First Experiment

Gen A, 60 Psig, Second Experiment

Flow Reading Real Flow Real Flor Tcold Thot Tline Tc-Tl Th-Tl Th-Tc Cold Mass Cold Mass Cooling ∆Entropy SCFM SCFM m^3/min ºC ºC ºC ºC ºC ºC Flow (kg/min) Flow (%) Cap (kJ/min) (J/min*K) 12.5 3.91 0.111 10.0 42.6 19.0 9.0 23.6 32.6 0.103 97.9 -0.93 14.36 11.8 3.68 0.104 8.5 35.8 19.1 10.6 16.7 27.3 0.097 92.5 -1.03 14.37 11.2 3.51 0.099 7.8 35.2 19.1 11.3 16.1 27.4 0.093 88.4 -1.05 14.35 10.8 3.38 0.096 7.0 33.6 19.1 12.1 14.5 26.6 0.090 85.5 -1.09 14.36 10.3 3.23 0.091 7.2 33.9 19.0 11.8 14.9 26.7 0.086 81.4 -1.01 14.30 10.0 3.13 0.089 6.5 33.6 19.0 12.5 14.6 27.1 0.083 79.3 -1.04 14.31 9.5 2.97 0.084 6.1 33.1 19.0 12.9 14.1 27.0 0.079 75.4 -1.03 14.28 9.0 2.82 0.080 5.9 32.7 19.0 13.1 13.7 26.8 0.075 71.5 -0.99 14.24 8.8 2.74 0.078 5.9 32.2 18.9 13.0 13.3 26.3 0.073 69.5 -0.95 14.23 7.5 2.35 0.067 4.8 31.5 18.9 14.1 12.6 26.7 0.063 59.8 -0.89 14.16

Flow Reading Real Flow Real Flow Tcold Thot Tline Tc-Tl Th-Tl Th-Tc Cold Mass Cold Mass Cooling ∆Entropy SCFM SCFM m^3/min ºC ºC ºC ºC ºC ºC Flow (kg/min) Flow (%) Cap (kJ/min) (J/min*K) 13.0 4.07 0.115 15.6 42.0 18.7 3.1 23.3 26.4 0.105 99.8 -0.33 14.13 12.5 3.91 0.111 10.8 35.9 18.7 7.9 17.2 25.1 0.102 97.6 -0.81 14.32 11.8 3.68 0.104 7.7 35.3 18.8 11.1 16.5 27.6 0.097 92.7 -1.09 14.41 10.0 3.13 0.089 6.1 33.7 18.7 12.6 15.0 27.6 0.083 79.4 -1.05 14.32 8.8 2.74 0.078 5.4 34.0 18.8 13.4 15.2 28.6 0.073 69.6 -0.98 14.22 7.5 2.35 0.067 4.7 33.7 18.8 14.1 14.9 29.0 0.063 59.8 -0.89 14.12 6.3 1.96 0.055 0.1 33.2 18.7 18.6 14.5 33.1 0.053 50.7 -0.99 14.13 5.3 1.64 0.047 -0.5 32.7 18.7 19.2 14.0 33.2 0.045 42.7 -0.86 14.04 5.0 1.57 0.044 -1.1 32.2 18.7 19.8 13.5 33.3 0.043 40.7 -0.85 14.03 4.8 1.49 0.042 -2.0 31.5 18.7 20.7 12.8 33.5 0.041 38.8 -0.85 14.04 4.5 1.41 0.040 -2.6 30.2 18.7 21.3 11.5 32.8 0.039 36.9 -0.83 14.05 4.3 1.33 0.038 -3.1 26.4 18.7 21.8 7.7 29.5 0.037 34.9 -0.80 14.14 4.0 1.25 0.035 -4.3 26.2 18.7 23.0 7.5 30.5 0.035 33.0 -0.80 14.14 3.8 1.17 0.033 -5.2 25.8 18.7 23.9 7.1 31.0 0.033 31.0 -0.78 14.13 3.5 1.10 0.031 -5.4 26.0 18.8 24.2 7.2 31.4 0.030 29.0 -0.74 14.10 3.3 1.02 0.029 -5.6 25.0 18.8 24.4 6.2 30.6 0.028 26.9 -0.69 14.10 3.0 0.94 0.027 -5.7 24.5 18.7 24.4 5.8 30.2 0.026 24.9 -0.64 14.09 2.8 0.86 0.024 -5.2 24.0 18.7 23.9 5.3 29.2 0.024 22.7 -0.57 14.07 2.5 0.78 0.022 -4.7 23.3 18.7 23.4 4.6 28.0 0.022 20.6 -0.51 14.06 2.3 0.70 0.020 -5.2 22.9 18.7 23.9 4.2 28.1 0.020 18.6 -0.47 14.05 2.0 0.63 0.018 -5.4 22.3 18.6 24.0 3.7 27.7 0.017 16.6 -0.42 14.05 1.8 0.55 0.016 -5.9 21.8 18.6 24.5 3.2 27.7 0.015 14.5 -0.37 14.04 1.5 0.47 0.013 -6.0 21.2 18.6 24.6 2.6 27.2 0.013 12.4 -0.32 14.04 1.3 0.39 0.011 -5.4 20.9 18.6 24.0 2.3 26.3 0.011 10.3 -0.26 14.02 1.0 0.31 0.009 -4.5 20.6 18.6 23.1 2.0 25.1 0.009 8.3 -0.20 14.00 0.8 0.23 0.007 -3.2 20.0 18.7 21.9 1.3 23.2 0.006 6.2 -0.14 14.00 0.5 0.16 0.004 -1.3 19.8 18.7 20.0 1.1 21.1 0.004 4.1 -0.09 13.98 0.3 0.08 0.002 1.8 19.8 18.7 16.9 1.1 18.0 0.002 2.0 -0.04 13.95

6.4 2.00 0.057 3.2 30.2 18.9 15.7 11.3 27.0 0.054 51.3 -0.85 14.12 5.3 1.66 0.047 1.2 29.4 18.9 17.7 10.5 28.2 0.045 42.8 -0.80 14.08 5.0 1.57 0.044 -1.5 28.8 18.9 20.4 9.9 30.3 0.043 40.8 -0.88 14.12 4.8 1.49 0.042 -2.6 28.2 19.0 21.6 9.2 30.8 0.041 38.9 -0.89 14.13 4.5 1.41 0.040 -2.4 27.3 19.0 21.4 8.3 29.7 0.039 36.8 -0.83 14.12 4.3 1.33 0.038 -2.8 26.2 19.0 21.8 7.2 29.0 0.037 34.8 -0.80 14.13 4.0 1.25 0.035 -4.1 25.1 19.1 23.2 6.0 29.2 0.035 33.0 -0.81 14.16 3.8 1.17 0.033 -4.5 24.6 19.1 23.6 5.5 29.1 0.032 30.9 -0.77 14.16 3.5 1.10 0.031 -5.0 24.1 19.1 24.1 5.0 29.1 0.030 28.9 -0.73 14.15 3.3 1.02 0.029 -5.1 23.5 19.2 24.3 4.3 28.6 0.028 26.9 -0.69 14.14 3.0 0.94 0.027 -5.4 23.0 19.2 24.6 3.8 28.4 0.026 24.8 -0.64 14.13 2.8 0.86 0.024 -5.5 22.6 19.2 24.7 3.4 28.1 0.024 22.8 -0.59 14.12 2.5 0.78 0.022 -5.0 22.5 19.2 24.2 3.3 27.5 0.022 20.7 -0.53 14.09 2.3 0.70 0.020 -5.1 22.1 19.2 24.3 2.9 27.2 0.020 18.6 -0.48 14.08 2.0 0.63 0.018 -5.6 22.0 19.3 24.9 2.7 27.6 0.017 16.6 -0.43 14.06 1.8 0.55 0.016 -6.4 21.5 19.3 25.7 2.2 27.9 0.015 14.5 -0.39 14.06 1.5 0.47 0.013 -6.1 21.1 19.3 25.4 1.8 27.2 0.013 12.5 -0.33 14.04 1.3 0.39 0.011 -5.4 20.6 19.3 24.7 1.3 26.0 0.011 10.3 -0.27 14.03 1.0 0.31 0.009 -5.0 20.8 19.2 24.2 1.6 25.8 0.009 8.3 -0.21 14.00 0.8 0.23 0.007 -3.9 20.5 19.2 23.1 1.3 24.4 0.006 6.2 -0.15 13.98 0.5 0.16 0.004 -0.8 19.8 19.2 20.0 0.6 20.6 0.004 4.1 -0.09 13.98 0.3 0.08 0.002 1.3 19.8 19.2 17.9 0.6 18.5 0.002 2.0 -0.04 13.95


Flow Reading Real Flow Real Flor Tcold Thot Tline Tc-Tl Th-Tl Th-Tc Cold Mass Cold Mass Cooling ∆Entropy SCFM SCFM m^3/min ºC ºC ºC ºC ºC ºC Flow (kg/min) Flow (%) Cap (kJ/min) (J/min*K) 11.5 3.60 0.102 15.1 39.4 19.5 4.4 19.9 24.3 0.093 102.6 -0.41 13.02 10.0 3.13 0.089 14.8 36.6 19.5 4.7 17.1 21.8 0.081 89.3 -0.38 12.92 8.8 2.74 0.078 12.3 35.2 19.6 7.3 15.6 22.9 0.071 78.8 -0.52 12.92 7.5 2.35 0.067 10.9 33.8 19.6 8.7 14.2 22.9 0.061 67.9 -0.54 12.88 6.1 1.91 0.054 7.4 32.7 19.6 12.2 13.1 25.3 0.051 55.9 -0.62 12.88 5.7 1.78 0.051 4.1 31.0 19.5 15.4 11.5 26.9 0.048 52.9 -0.74 12.95 5.3 1.66 0.047 3.4 30.0 19.5 16.1 10.5 26.6 0.045 49.3 -0.72 12.95 5.0 1.57 0.044 1.8 29.4 19.5 17.7 9.9 27.6 0.042 46.8 -0.75 12.97 4.8 1.49 0.042 1.1 28.5 19.5 18.4 9.0 27.4 0.040 44.5 -0.74 12.97 4.5 1.41 0.040 0.5 27.8 19.4 18.9 8.4 27.3 0.038 42.3 -0.73 12.97 4.3 1.33 0.038 0.0 27.2 19.4 19.4 7.8 27.2 0.036 40.0 -0.71 12.97 4.0 1.25 0.035 -2.3 26.8 19.4 21.7 7.4 29.1 0.034 38.0 -0.75 13.00 3.8 1.17 0.033 -3.0 26.7 19.5 22.5 7.2 29.7 0.032 35.7 -0.73 12.99 3.5 1.10 0.031 -3.6 26.4 19.5 23.1 6.9 30.0 0.030 33.4 -0.70 12.97 3.3 1.02 0.029 -3.6 25.8 19.5 23.1 6.3 29.4 0.028 31.0 -0.65 12.96 3.0 0.94 0.027 -3.9 25.1 19.4 23.3 5.7 29.0 0.026 28.7 -0.61 12.95 2.8 0.86 0.024 -3.8 24.4 19.4 23.2 5.0 28.2 0.024 26.3 -0.55 12.94 2.5 0.78 0.022 -3.5 23.5 19.3 22.8 4.2 27.0 0.022 23.8 -0.49 12.94 2.3 0.70 0.020 -3.3 22.6 19.3 22.6 3.3 25.9 0.019 21.4 -0.44 12.93 2.0 0.63 0.018 -3.8 21.9 19.4 23.2 2.5 25.7 0.017 19.1 -0.40 12.93 1.8 0.55 0.016 -3.6 21.7 19.4 23.0 2.3 25.3 0.015 16.7 -0.35 12.91 1.5 0.47 0.013 -3.5 21.2 19.4 22.9 1.8 24.7 0.013 14.3 -0.30 12.90 1.3 0.39 0.011 -3.6 21.0 19.4 23.0 1.6 24.6 0.011 11.9 -0.25 12.88 1.0 0.31 0.009 -2.9 20.6 19.5 22.4 1.1 23.5 0.009 9.5 -0.19 12.87

0.8 0.23 0.007 -2.2 20.0 19.6 21.8 0.4 22.2 0.006 7.1 -0.14 12.86 0.5 0.16 0.004 -1.1 19.8 19.5 20.6 0.3 20.9 0.004 4.7 -0.09 12.85 0.5 0.16 0.004 -0.1 19.3 19.5 19.6 -0.2 19.4 0.004 4.7 -0.08 12.86 0.3 0.08 0.002 1.2 19.2 19.5 18.3 -0.3 18.0 0.002 2.3 -0.04 12.85


Flow Reading Real Flow Real Flor Tcold Thot Tline Tc-Tl Th-Tl Th-Tc Cold Mass Cold Mass Cooling ∆Entropy SCFM SCFM m^3/min ºC ºC ºC ºC ºC ºC Flow (kg/min) Flow (%) Cap (kJ/min) (J/min*K) 11.5 3.60 0.102 14.3 38.9 18.8 4.5 20.1 24.6 0.093 102.9 -0.42 0.02 10.8 3.38 0.096 14.1 32.3 18.7 4.6 13.6 18.2 0.088 96.7 -0.40 0.02 10.0 3.13 0.089 14.8 32.2 18.7 3.9 13.5 17.4 0.081 89.3 -0.32 0.01 9.4 2.94 0.083 13.5 32.4 18.7 5.2 13.7 18.9 0.076 84.3 -0.40 0.02 8.8 2.74 0.078 12.3 32.4 18.8 6.5 13.6 20.1 0.071 78.8 -0.47 0.02 7.5 2.35 0.067 10.9 31.1 18.8 7.9 12.3 20.2 0.061 67.9 -0.49 0.02 6.3 1.96 0.055 6.5 30.6 18.8 12.3 11.8 24.1 0.052 57.5 -0.64 0.03 5.8 1.82 0.051 4.1 29.1 18.7 14.6 10.4 25.0 0.049 53.8 -0.71 0.03 5.0 1.57 0.044 1.5 28.3 18.7 17.2 9.6 26.8 0.042 46.8 -0.73 0.03 4.8 1.49 0.042 1.3 27.3 18.7 17.4 8.6 26.0 0.040 44.5 -0.70 0.03 4.5 1.41 0.040 0.8 26.5 18.6 17.8 7.9 25.7 0.038 42.2 -0.68 0.03 4.3 1.33 0.038 0.3 26.1 18.6 18.3 7.5 25.8 0.036 40.0 -0.66 0.03 4.0 1.25 0.035 -2.7 26.4 18.6 21.3 7.8 29.1 0.034 38.0 -0.74 0.03 3.8 1.17 0.033 -3.5 26.0 18.6 22.1 7.4 29.5 0.032 35.8 -0.72 0.03 3.5 1.10 0.031 -4.0 25.5 18.6 22.6 6.9 29.5 0.030 33.4 -0.69 0.03 3.3 1.02 0.029 -3.7 24.0 18.7 22.4 5.3 27.7 0.028 31.0 -0.63 0.03 3.0 0.94 0.027 -3.7 24.1 18.7 22.4 5.4 27.8 0.026 28.6 -0.58 0.03 2.8 0.86 0.024 -3.9 23.6 18.9 22.8 4.7 27.5 0.024 26.3 -0.54 0.02 2.5 0.78 0.022 -3.4 23.1 18.9 22.3 4.2 26.5 0.022 23.8 -0.48 0.02 2.3 0.70 0.020 -3.3 22.2 18.9 22.2 3.3 25.5 0.019 21.4 -0.43 0.02 2.0 0.63 0.018 -4.2 21.5 18.9 23.1 2.6 25.7 0.017 19.1 -0.40 0.02 1.8 0.55 0.016 -4.6 21.0 18.9 23.5 2.1 25.6 0.015 16.8 -0.36 0.02 1.5 0.47 0.013 -4.8 20.6 18.8 23.6 1.8 25.4 0.013 14.4 -0.31 0.01 1.3 0.39 0.011 -4.5 20.2 18.8 23.3 1.4 24.7 0.011 12.0 -0.25 0.01 1.0 0.31 0.009 -4.0 20.1 18.8 22.8 1.3 24.1 0.009 9.6 -0.20 0.01 0.8 0.23 0.007 -3.6 19.6 18.7 22.3 0.9 23.2 0.006 7.2 -0.15 0.01 0.5 0.16 0.004 -1.6 19.7 18.7 20.3 1.0 21.3 0.004 4.7 -0.09 0.00 0.5 0.16 0.004 -0.7 19.2 18.7 19.4 0.5 19.9 0.004 4.7 -0.08 0.00 -1.1 -0.34 -0.010 -9.0 17.2 18.8 27.7 -1.6 26.1 -0.010 -10.5 -0.29 0.01


Flow Reading Real Flow Real Flor Tcold Thot Tline Tc-Tl Th-Tl Th-Tc Cold Mass Cold Mass Cooling ∆Entropy SCFM SCFM m^3/min ºC ºC ºC ºC ºC ºC Flow (kg/min) Flow (%) Cap (kJ/min) (J/min*K)

9.3 2.91 0.082 15.8 37.3 18.3 2.5 19.0 21.5 0.075 106.0 -0.19 11.66 7.5 2.35 0.067 9.8 33.9 18.3 8.5 15.6 24.1 0.062 87.3 -0.53 11.73 6.3 1.96 0.055 8.7 35.0 18.3 9.6 16.7 26.3 0.052 73.0 -0.50 11.63 5.4 1.69 0.048 7.4 34.1 18.4 11.0 15.7 26.7 0.045 63.4 -0.49 11.59 5.0 1.57 0.044 6.1 33.4 18.3 12.2 15.1 27.3 0.042 58.9 -0.51 11.58 4.8 1.49 0.042 5.1 31.7 18.3 13.2 13.4 26.6 0.040 56.2 -0.53 11.60 4.5 1.41 0.040 4.6 30.8 18.3 13.7 12.5 26.2 0.038 53.3 -0.52 11.60 4.3 1.33 0.038 4.1 29.8 18.3 14.2 11.5 25.7 0.036 50.5 -0.51 11.60

4.0 1.25 0.035 3.7 28.5 18.2 14.5 10.3 24.8 0.034 47.6 -0.49 11.60 3.8 1.17 0.033 1.6 27.8 18.2 16.6 9.6 26.2 0.032 44.9 -0.53 11.63 3.5 1.10 0.031 1.7 26.9 18.2 16.5 8.7 25.2 0.030 41.9 -0.49 11.62 3.3 1.02 0.029 -0.1 26.4 18.2 18.3 8.2 26.5 0.028 39.2 -0.51 11.63 3.0 0.94 0.027 -0.6 26.1 18.1 18.7 8.0 26.7 0.026 36.2 -0.48 11.62 2.8 0.86 0.024 -1.3 25.4 18.1 19.4 7.3 26.7 0.024 33.3 -0.46 11.61 2.5 0.78 0.022 -1.5 25.2 18.1 19.6 7.1 26.7 0.021 30.3 -0.42 11.59 2.3 0.70 0.020 -1.6 24.4 18.1 19.7 6.3 26.0 0.019 27.3 -0.38 11.58 2.0 0.63 0.018 -1.8 23.2 18.1 19.9 5.1 25.0 0.017 24.3 -0.34 11.58 1.8 0.55 0.016 -1.8 22.2 18.2 20.0 4.0 24.0 0.015 21.2 -0.30 11.58 1.5 0.47 0.013 -1.8 21.8 18.2 20.0 3.6 23.6 0.013 18.2 -0.26 11.57 1.3 0.39 0.011 -2.0 21.3 18.2 20.2 3.1 23.3 0.011 15.2 -0.22 11.55 1.0 0.31 0.009 1.9 20.9 18.2 16.3 2.7 19.0 0.008 12.0 -0.14 11.52 0.8 0.23 0.007 -1.5 20.2 18.2 19.7 2.0 21.7 0.006 9.1 -0.13 11.53 0.5 0.16 0.004 -1.0 19.8 18.2 19.2 1.6 20.8 0.004 6.0 -0.08 11.52 0.3 0.08 0.002 1.3 18.8 18.2 16.9 0.6 17.5 0.002 3.0 -0.04 11.53



9.3 2.91 0.082 15.5 37.0 19.1 3.6 17.9 21.5 0.075 106.1 -0.27 11.67 8.8 2.74 0.078 12.4 34.8 19.1 6.7 15.7 22.4 0.071 100.9 -0.48 11.75 7.5 2.35 0.067 9.1 34.3 19.1 10.0 15.2 25.2 0.062 87.5 -0.62 11.76 6.3 1.96 0.055 8.3 34.4 19.1 10.8 15.3 26.1 0.052 73.1 -0.56 11.65 5.7 1.78 0.051 7.8 34.0 19.1 11.3 14.9 26.2 0.047 66.8 -0.54 11.61 5.4 1.69 0.048 7.5 33.7 19.0 11.5 14.7 26.2 0.045 63.3 -0.52 11.59 5.0 1.57 0.044 6.0 33.3 19.0 13.0 14.3 27.3 0.042 59.0 -0.54 11.58 4.8 1.49 0.042 4.6 31.1 19.1 14.5 12.0 26.5 0.040 56.3 -0.58 11.62 4.5 1.41 0.040 4.8 30.2 19.1 14.3 11.1 25.4 0.038 53.3 -0.54 11.60 4.3 1.33 0.038 3.6 29.2 19.1 15.5 10.1 25.6 0.036 50.6 -0.56 11.62 4.0 1.25 0.035 3.5 27.7 19.2 15.7 8.5 24.2 0.034 47.6 -0.53 11.62 3.8 1.17 0.033 1.3 27.7 19.2 17.9 8.5 26.4 0.032 45.0 -0.57 11.64 3.5 1.10 0.031 1.1 27.9 19.2 18.1 8.7 26.8 0.030 42.0 -0.54 11.60 3.3 1.02 0.029 0.3 27.7 19.2 18.9 8.5 27.4 0.028 39.1 -0.52 11.59 3.0 0.94 0.027 -0.6 27.3 19.1 19.7 8.2 27.9 0.026 36.2 -0.51 11.59 2.8 0.86 0.024 -1.8 26.7 19.2 21.0 7.5 28.5 0.024 33.4 -0.50 11.59 2.5 0.78 0.022 -1.9 26.5 19.2 21.1 7.3 28.4 0.021 30.3 -0.46 11.56 2.3 0.70 0.020 -2.0 25.4 19.2 21.2 6.2 27.4 0.019 27.3 -0.41 11.56 2.0 0.63 0.018 -2.0 24.0 19.2 21.2 4.8 26.0 0.017 24.3 -0.36 11.56 1.8 0.55 0.016 -1.9 22.9 19.3 21.2 3.6 24.8 0.015 21.2 -0.32 11.56 1.5 0.47 0.013 -2.1 22.3 19.3 21.4 3.0 24.4 0.013 18.2 -0.28 11.55 1.3 0.39 0.011 -2.0 21.6 19.2 21.2 2.4 23.6 0.011 15.2 -0.23 11.54 1.0 0.31 0.009 -1.6 21.4 19.2 20.8 2.2 23.0 0.009 12.1 -0.18 11.52 0.8 0.23 0.007 -1.5 20.8 19.2 20.7 1.6 22.3 0.006 9.1 -0.13 11.51 0.5 0.16 0.004 -0.8 20.5 19.3 20.1 1.2 21.3 0.004 6.0 -0.09 11.49 0.3 0.08 0.002 1.0 19.5 19.3 18.3 0.2 18.5 0.002 3.0 -0.04 11.50


Flow Reading Real Flow Real Flor Tcold Thot Tline Tc-Tl Th-Tl Th-Tc Cold Mass Cold Mass Cooling ∆Entropy

SCFM SCFM m^3/min ºC ºC ºC ºC ºC ºC Flow (kg/min) Flow (%) Cap (kJ/min) (J/min*K) 7.2 2.25 0.064 16.4 36.1 19.3 2.9 16.8 19.7 0.058 103.9 -0.17 9.95 6.3 1.96 0.055 14.8 34.3 19.3 4.5 15.0 19.5 0.051 90.7 -0.23 9.92 5.6 1.75 0.050 13.7 33.1 19.3 5.6 13.8 19.4 0.045 81.6 -0.26 9.91 5.3 1.64 0.047 13.1 327.0 19.4 6.3 307.6 313.9 0.043 76.6 -0.27 9.90 4.8 1.49 0.042 12.3 32.3 19.5 7.2 12.8 20.0 0.039 69.5 -0.28 9.88 4.5 1.41 0.040 11.8 31.6 19.5 7.7 12.1 19.8 0.037 66.0 -0.28 9.87 4.3 1.33 0.038 10.9 31.7 19.5 8.6 12.2 20.8 0.035 62.5 -0.30 9.87 4.0 1.25 0.035 9.1 31.0 19.5 10.4 11.5 21.9 0.033 59.2 -0.34 9.89 3.8 1.17 0.033 7.9 29.6 19.6 11.7 10.0 21.7 0.031 55.8 -0.37 9.91 3.5 1.10 0.031 7.8 29.0 19.6 11.8 9.4 21.2 0.029 52.1 -0.34 9.89 3.3 1.02 0.029 6.9 28.7 19.6 12.7 9.1 21.8 0.027 48.5 -0.34 9.89 3.0 0.94 0.027 6.0 28.4 19.7 13.7 8.7 22.4 0.025 44.9 -0.34 9.89 2.8 0.86 0.024 5.0 27.3 19.7 14.7 7.6 22.3 0.023 41.3 -0.34 9.89 2.5 0.78 0.022 4.3 26.2 19.7 15.4 6.5 21.9 0.021 37.7 -0.32 9.90 2.3 0.70 0.020 3.8 25.5 19.6 15.8 5.9 21.7 0.019 33.9 -0.30 9.89 2.0 0.63 0.018 3.0 24.9 19.6 16.6 5.3 21.9 0.017 30.3 -0.28 9.89 1.8 0.55 0.016 2.8 24.4 19.7 16.9 4.7 21.6 0.015 26.5 -0.25 9.88 1.5 0.47 0.013 2.8 23.8 19.7 16.9 4.1 21.0 0.013 22.7 -0.21 9.86 1.3 0.39 0.011 2.5 22.9 19.7 17.2 3.2 20.4 0.011 18.9 -0.18 9.86 1.0 0.31 0.009 2.6 22.2 19.7 17.1 2.5 19.6 0.008 15.2 -0.15 9.86 0.8 0.23 0.007 2.6 21.5 19.8 17.2 1.7 18.9 0.006 11.4 -0.11 9.85 0.5 0.16 0.004 3.5 20.3 19.7 16.2 0.6 16.8 0.004 7.6 -0.07 9.86 0.3 0.08 0.002 4.9 20.1 19.7 14.8 0.4 15.2 0.002 3.8 -0.03 9.85



7.2 2.25 0.064 16.2 35.9 19.4 3.2 16.5 19.7 0.058 104.0 -0.19 9.95 4.9 1.53 0.043 12.6 33.4 19.4 6.8 14.0 20.8 0.040 71.7 -0.27 9.87 4.8 1.49 0.042 11.6 32.7 19.4 7.8 13.3 21.1 0.039 69.7 -0.30 9.89 4.5 1.41 0.040 10.2 32.0 19.4 9.2 12.6 21.8 0.037 66.4 -0.34 9.90 4.3 1.33 0.038 9.3 31.8 19.3 10.0 12.5 22.5 0.035 62.9 -0.35 9.90 4.0 1.25 0.035 8.6 31.2 19.3 10.7 11.9 22.6 0.033 59.3 -0.36 9.90 3.8 1.17 0.033 7.9 29.8 19.4 11.5 10.4 21.9 0.031 55.8 -0.36 9.91 3.5 1.10 0.031 7.3 29.3 19.4 12.1 9.9 22.0 0.029 52.1 -0.35 9.90 3.3 1.02 0.029 6.3 29.0 19.4 13.1 9.6 22.7 0.027 48.6 -0.36 9.90 3.0 0.94 0.027 5.6 29.0 19.4 13.8 9.6 23.4 0.025 45.0 -0.35 9.88 2.8 0.86 0.024 4.6 28.5 19.5 14.9 9.0 23.9 0.023 41.4 -0.34 9.88 2.5 0.78 0.022 4.0 28 19.5 15.5 8.5 24.0 0.021 37.7 -0.33 9.87 2.3 0.70 0.020 3.5 26.9 19.6 16.1 7.3 23.4 0.019 34.0 -0.31 9.87 2.0 0.63 0.018 2.9 25.6 19.6 16.7 6.0 22.7 0.017 30.3 -0.28 9.87 1.8 0.55 0.016 2.6 24.9 19.6 17.0 5.3 22.3 0.015 26.5 -0.25 9.87 1.5 0.47 0.013 2.6 24.1 19.5 16.9 4.6 21.5 0.013 22.7 -0.21 9.86 1.3 0.39 0.011 2.4 23.6 19.5 17.1 4.1 21.2 0.011 19.0 -0.18 9.85 1.0 0.31 0.009 2.5 23.0 19.5 17.0 3.5 20.5 0.008 15.2 -0.14 9.84 0.8 0.23 0.007 2.7 22.5 19.4 16.7 3.1 19.8 0.006 11.4 -0.11 9.83 0.5 0.16 0.004 3.2 21.8 19.4 16.2 2.4 18.6 0.004 7.6 -0.07 9.82 0.3 0.08 0.002 5.2 21.1 19.4 14.2 1.7 15.9 0.002 3.8 -0.03 9.82



5.0 1.57 0.044 17.2 30.3 19.0 1.8 11.3 13.1 0.040 96.3 -0.07 7.80 4.8 1.49 0.042 16.2 29.9 19.0 2.8 10.9 13.7 0.038 91.8 -0.11 7.81 4.5 1.41 0.040 15.0 30.1 19.0 4.0 11.1 15.1 0.036 87.4 -0.15 7.82 4.3 1.33 0.038 14.1 30.3 19.1 5.0 11.2 16.2 0.034 82.8 -0.17 7.82 4.0 1.25 0.035 13.9 29.7 19.1 5.2 10.6 15.8 0.032 78.0 -0.17 7.81 3.8 1.17 0.033 13.6 29.6 19.1 5.5 10.5 16.0 0.030 73.2 -0.17 7.80 3.5 1.10 0.031 13.2 29.2 19.1 5.9 10.1 16.0 0.028 68.4 -0.17 7.79 3.3 1.02 0.029 12.6 28.9 19.0 6.4 9.9 16.3 0.026 63.6 -0.17 7.79 3.0 0.94 0.027 11.9 28.0 19.0 7.1 9.0 16.1 0.024 58.9 -0.17 7.79 2.8 0.86 0.024 11.1 27.7 19.0 7.9 8.7 16.6 0.023 54.1 -0.18 7.78 2.5 0.78 0.022 10.8 27.2 18.9 8.1 8.3 16.4 0.020 49.3 -0.17 7.78 2.3 0.70 0.020 10.0 26.6 18.9 8.9 7.7 16.6 0.018 44.5 -0.17 7.77 2.0 0.63 0.018 9.4 26.1 19.0 9.6 7.1 16.7 0.016 39.6 -0.16 7.77 1.8 0.55 0.016 9.0 25.7 19.0 10.0 6.7 16.7 0.014 34.7 -0.14 7.76 1.5 0.47 0.013 8.8 25.0 18.9 10.1 6.1 16.2 0.012 29.8 -0.13 7.75 1.3 0.39 0.011 8.5 24.2 18.9 10.4 5.3 15.7 0.010 24.8 -0.11 7.75 1.0 0.31 0.009 8.3 23.1 18.9 10.6 4.2 14.8 0.008 19.9 -0.09 7.75 0.8 0.23 0.007 8.2 22.6 18.8 10.6 3.8 14.4 0.006 14.9 -0.07 7.74 0.5 0.16 0.004 8.4 22.0 18.8 10.4 3.2 13.6 0.004 9.9 -0.04 7.74 0.3 0.08 0.002 8.9 21.4 18.8 9.9 2.6 12.5 0.002 5.0 -0.02 7.73



5.0 1.57 0.044 17.4 28.0 19.4 2.0 8.6 10.6 0.040 96.3 -0.08 7.80 4.8 1.49 0.042 16.4 28.3 19.4 3.0 8.9 11.9 0.038 91.8 -0.11 7.81 4.5 1.41 0.040 15.3 28.6 19.4 4.1 9.2 13.3 0.036 87.3 -0.15 7.82 4.3 1.33 0.038 14.4 28.1 19.4 5.0 8.7 13.7 0.034 82.7 -0.17 7.83 4.0 1.25 0.035 14.0 27.8 19.3 5.3 8.5 13.8 0.032 77.9 -0.17 7.82 3.8 1.17 0.033 13.8 27.5 19.3 5.5 8.2 13.7 0.030 73.1 -0.17 7.81 3.5 1.10 0.031 13.6 27.3 19.3 5.7 8.0 13.7 0.028 68.3 -0.16 7.80 3.3 1.02 0.029 12.8 26.8 19.3 6.5 7.5 14.0 0.026 63.6 -0.17 7.80 3.0 0.94 0.027 12.7 25.7 19.4 6.7 6.3 13.0 0.024 58.7 -0.16 7.80 2.8 0.86 0.024 11.6 25.0 19.4 7.8 5.6 13.4 0.022 54.0 -0.18 7.80 2.5 0.78 0.022 11.2 24.7 19.5 8.3 5.2 13.5 0.020 49.2 -0.17 7.80 2.3 0.70 0.020 10.2 24.5 19.5 9.3 5.0 14.3 0.018 44.4 -0.17 7.80 2.0 0.63 0.018 9.8 23.6 19.4 9.6 4.2 13.8 0.016 39.5 -0.16 7.79 1.8 0.55 0.016 9.2 23.6 19.4 10.2 4.2 14.4 0.014 34.7 -0.15 7.78 1.5 0.47 0.013 9.1 22.7 19.3 10.2 3.4 13.6 0.012 29.7 -0.13 7.78 1.3 0.39 0.011 8.6 22.3 19.5 10.9 2.8 13.7 0.010 24.8 -0.11 7.78 1.0 0.31 0.009 8.4 20.6 19.5 11.1 1.1 12.2 0.008 19.9 -0.09 7.79 0.8 0.23 0.007 8.7 19.9 19.5 10.8 0.4 11.2 0.006 14.9 -0.07 7.79 0.5 0.16 0.004 8.8 19.5 19.5 10.7 0.0 10.7 0.004 9.9 -0.04 7.78 0.3 0.08 0.002 9.6 19.5 19.5 9.9 0.0 9.9 0.002 4.9 -0.02 7.77

Gen A, 10 Psig, First Experiment Flow Reading Real Flow Real Flor Tcold Thot Tline Tc-Tl Th-Tl Th-Tc Cold Mass Cold Mass Cooling ∆Entropy

SCFM SCFM m^3/min ºC ºC ºC ºC ºC ºC Flow (kg/min) Flow (%) Cap (kJ/min) (J/min*K) 2.6 0.81 0.023 16.2 27.0 18.7 2.5 8.3 10.8 0.021 94.6 -0.05 4.89 2.5 0.78 0.022 15.4 25.1 18.7 3.3 6.4 9.7 0.020 91.2 -0.07 4.89 2.3 0.70 0.020 14.5 24.0 18.8 4.3 5.2 9.5 0.018 82.4 -0.08 4.89 2.0 0.63 0.018 14.0 24.0 18.8 4.8 5.2 10.0 0.016 73.4 -0.08 4.89 1.8 0.55 0.016 13.4 23.6 18.7 5.3 4.9 10.2 0.014 64.3 -0.08 4.88 1.5 0.47 0.013 13.1 23.2 18.7 5.6 4.5 10.1 0.012 55.2 -0.07 4.88 1.3 0.39 0.011 13.1 22.2 18.7 5.6 3.5 9.1 0.010 46.0 -0.06 4.87 1.0 0.31 0.009 12.8 21.8 18.7 5.9 3.1 9.0 0.008 36.8 -0.05 4.86 0.8 0.23 0.007 12.8 21.5 18.7 5.9 2.8 8.7 0.006 27.6 -0.04 4.86 0.5 0.16 0.004 13.0 21.0 18.7 5.7 2.3 8.0 0.004 18.4 -0.02 4.85 0.3 0.08 0.002 13.0 20.6 18.8 5.8 1.8 7.6 0.002 9.2 -0.01 4.84



2.6 0.81 0.023 17.1 27.5 18.9 1.8 8.6 10.4 0.021 94.3 -0.04 4.89 2.5 0.78 0.022 15.6 26.1 18.9 3.3 7.2 10.5 0.020 91.2 -0.07 4.89 2.3 0.70 0.020 14.8 25.2 18.8 4.0 6.4 10.4 0.018 82.3 -0.07 4.89 2.0 0.63 0.018 14.4 24.6 18.8 4.4 5.8 10.2 0.016 73.2 -0.07 4.89 1.8 0.55 0.016 13.9 24.0 18.7 4.8 5.3 10.1 0.014 64.2 -0.07 4.88 1.5 0.47 0.013 13.8 24.0 18.7 4.9 5.3 10.2 0.012 55.1 -0.06 4.88 1.3 0.39 0.011 13.8 23.4 18.6 4.8 4.8 9.6 0.010 45.9 -0.05 4.87 1.0 0.31 0.009 13.5 23.6 18.6 5.1 5.0 10.1 0.008 36.7 -0.04 4.86 0.8 0.23 0.007 13.3 23.3 18.6 5.3 4.7 10.0 0.006 27.6 -0.03 4.86 0.5 0.16 0.004 13.5 21.4 18.6 5.1 2.8 7.9 0.004 18.4 -0.02 4.85 0.3 0.08 0.002 13.2 21.4 18.7 5.5 2.7 8.2 0.002 9.2 -0.01 4.84

Generator B

Gen B, 60 Psig, First Experiment Flow Reading Real Flow Real Flow Tcold Tline Tc-Tl Cold Mass Cold Mass Cooling

SCFM SCFM m^3/min ºC ºC ºC Flow (kg/min) Flow (%) Cap (kJ/min) 12.8 4.01 0.114 17.5 18.5 1.0 0.102 1.0 -0.16 12.5 3.91 0.111 9.8 18.5 8.7 0.103 1.1 -0.79 11.8 3.68 0.104 8.0 18.5 10.5 0.097 1.0 -1.02 10.0 3.13 0.089 5.1 18.5 13.4 0.084 0.9 -1.06 8.8 2.74 0.078 2.0 18.4 16.4 0.074 0.8 -1.14 7.5 2.35 0.067 1.3 18.4 17.1 0.064 0.7 -1.02 6.3 1.96 0.055 0.0 18.4 18.4 0.053 0.5 -0.90 5.0 1.57 0.044 -0.1 18.4 18.5 0.043 0.4 -0.87 4.8 1.49 0.042 -0.5 18.4 18.9 0.041 0.4 -0.81 4.5 1.41 0.040 -1.3 18.4 19.7 0.039 0.4 -0.82 4.3 1.33 0.038 -1.8 18.4 20.2 0.036 0.4 -0.83 4.0 1.25 0.035 -2.4 18.5 20.9 0.034 0.4 -0.79 3.8 1.17 0.033 -3.4 18.5 21.9 0.032 0.3 -0.75 3.5 1.10 0.031 -4.0 18.5 22.5 0.030 0.3 -0.72

3.3 1.02 0.029 -4.7 18.6 23.3 0.028 0.3 -0.71 3.0 0.94 0.027 -5.6 18.6 24.2 0.026 0.3 -0.68 2.8 0.86 0.024 -7.8 18.6 26.4 0.024 0.2 -0.67 2.5 0.78 0.022 -8.2 18.6 26.8 0.022 0.2 -0.62 2.3 0.70 0.020 -8.6 18.6 27.2 0.020 0.2 -0.56 2.0 0.63 0.018 -8.7 18.6 27.3 0.018 0.2 -0.49 1.8 0.55 0.016 -8.6 18.7 27.3 0.015 0.2 -0.43 1.5 0.47 0.013 -8.4 18.7 27.1 0.013 0.1 -0.36 1.3 0.39 0.011 -7.7 18.7 26.4 0.011 0.1 -0.29 1.0 0.31 0.009 -5.5 18.7 24.2 0.009 0.1 -0.23 0.8 0.23 0.007 -3.0 18.7 21.7 0.006 0.1 -0.17 0.5 0.16 0.004 -0.4 18.7 19.1 0.004 0.0 -0.09 0.3 0.08 0.002 1.0 18.8 17.8 0.002 0.0 -0.05

Gen B, 60 Psig, Second Experiment

Flor Reading Real Flow Real Flow Tcold Tline Tc-Tl Cold Mass Cold Mass Cooling SCFM SCFM m^3/min ºC ºC ºC Flow (kg/min) Flow (%) Cap (kJ/min) 12.7 3.98 0.113 17.2 18.8 1.6 0.102 1.0 -0.10 12.5 3.91 0.111 11.1 18.8 7.7 0.102 1.0 -0.90 11.8 3.68 0.104 8.3 18.8 10.5 0.097 1.0 -1.03 10.0 3.13 0.089 6.1 18.8 12.7 0.083 0.9 -1.13 8.8 2.74 0.078 3.4 18.8 15.4 0.074 0.8 -1.22 7.5 2.35 0.067 2.8 18.8 16.0 0.063 0.6 -1.09 6.3 1.96 0.055 1.7 18.7 17.0 0.053 0.5 -0.98 5.0 1.57 0.044 -1.6 18.7 20.3 0.043 0.4 -0.79 4.8 1.49 0.042 -1.2 18.7 19.9 0.041 0.4 -0.77 4.5 1.41 0.040 -2.4 18.6 21.0 0.039 0.4 -0.76 4.3 1.33 0.038 -4.0 18.6 22.6 0.037 0.4 -0.74 4.0 1.25 0.035 -3.9 18.7 22.6 0.035 0.4 -0.72 3.8 1.17 0.033 -4.4 18.7 23.1 0.032 0.3 -0.71 3.5 1.10 0.031 -4.9 18.7 23.6 0.030 0.3 -0.68 3.3 1.02 0.029 -6.3 18.7 25.0 0.028 0.3 -0.66 3.0 0.94 0.027 -7.0 18.8 25.8 0.026 0.3 -0.63 2.8 0.86 0.024 -8.9 18.8 27.7 0.024 0.2 -0.64 2.5 0.78 0.022 -9.2 18.8 28.0 0.022 0.2 -0.59 2.3 0.70 0.020 -9.4 18.8 28.2 0.020 0.2 -0.54 2.0 0.63 0.018 -9.0 18.8 27.8 0.018 0.2 -0.48 1.8 0.55 0.016 -8.9 18.8 27.7 0.015 0.2 -0.42 1.5 0.47 0.013 -8.4 18.9 27.3 0.013 0.1 -0.36 1.3 0.39 0.011 -7.7 18.8 26.5 0.011 0.1 -0.29 1.0 0.31 0.009 -7.0 18.8 25.8 0.009 0.1 -0.21 0.8 0.23 0.007 -6.3 18.8 25.1 0.007 0.1 -0.14 0.5 0.16 0.004 -2.3 18.8 21.1 0.004 0.0 -0.08 0.3 0.08 0.002 -3.0 18.8 21.8 0.002 0.0 -0.04

Gen B, 50 Psig, First Experiment

Flor Reading Real Flow Real Flow Tcold Tline Tc-Tl Cold Mass Cold Mass Cooling SCFM SCFM m^3/min ºC ºC ºC Flow (kg/min) Flow (%) Cap (kJ/min)

11.2 3.51 0.099 15.4 18.9 3.5 0.090 0.9 -0.32

10.0 3.13 0.089 11.8 19.0 7.2 0.082 0.8 -0.59 8.8 2.74 0.078 10.1 19.0 8.9 0.072 0.7 -0.64 7.5 2.35 0.067 9.8 19.0 9.2 0.062 0.6 -0.57 6.3 1.96 0.055 6.4 19.0 12.6 0.052 0.5 -0.66 5.2 1.63 0.046 6.2 19.0 12.8 0.043 0.4 -0.56 5.0 1.57 0.044 4.6 18.9 14.3 0.042 0.4 -0.60 4.8 1.49 0.042 4.4 18.8 14.4 0.040 0.4 -0.58 4.5 1.41 0.040 3.8 18.8 15.0 0.038 0.4 -0.57 4.3 1.33 0.038 4.1 18.8 14.7 0.036 0.4 -0.53 4.0 1.25 0.035 2.9 19.0 16.1 0.034 0.3 -0.55 3.8 1.17 0.033 2.1 19.0 16.9 0.032 0.3 -0.54 3.5 1.10 0.031 1.2 19.0 17.8 0.030 0.3 -0.53 3.3 1.02 0.029 -0.4 19.0 19.4 0.028 0.3 -0.54 3.0 0.94 0.027 -2.1 19.0 21.1 0.026 0.3 -0.55 2.8 0.86 0.024 -2.6 19.0 21.6 0.024 0.2 -0.51 2.5 0.78 0.022 -3.6 19.0 22.6 0.022 0.2 -0.49 2.3 0.70 0.020 -4.4 19.0 23.4 0.019 0.2 -0.46 2.0 0.63 0.018 -4.2 19.0 23.2 0.017 0.2 -0.40 1.8 0.55 0.016 -3.9 19.0 22.9 0.015 0.2 -0.35 1.5 0.47 0.013 -3.9 19.1 23.0 0.013 0.1 -0.30 1.3 0.39 0.011 -3.5 19.1 22.6 0.011 0.1 -0.25 1.0 0.31 0.009 -3.1 19.1 22.2 0.009 0.1 -0.19 0.8 0.23 0.007 -2.4 19.1 21.5 0.006 0.1 -0.14 0.5 0.16 0.004 -1.3 19.1 20.4 0.004 0.0 -0.09 0.3 0.08 0.002 1.4 19.1 17.7 0.002 0.0 -0.04


Flor Reading Real Flow Real Flow Tcold Tline Tc-Tl Cold Mass Cold Mass Cooling SCFM SCFM m^3/min ºC ºC ºC Flow (kg/min) Flow (%) Cap (kJ/min)

11.2 3.51 0.099 15.0 18.8 3.8 0.090 0.9 -0.35 10.0 3.13 0.089 10.5 18.9 8.4 0.082 0.8 -0.69 8.8 2.74 0.078 8.4 18.9 10.5 0.072 0.7 -0.76 7.5 2.35 0.067 7.8 18.8 11.0 0.062 0.6 -0.69 6.3 1.96 0.055 6.4 18.9 12.5 0.052 0.5 -0.65 5.2 1.63 0.046 5.1 18.8 13.7 0.043 0.4 -0.60 5.0 1.57 0.044 4.9 18.8 13.9 0.042 0.4 -0.58 4.8 1.49 0.042 3.7 18.7 15.0 0.040 0.4 -0.60 4.5 1.41 0.040 3.2 18.7 15.5 0.038 0.4 -0.59 4.3 1.33 0.038 1.6 18.8 17.2 0.036 0.4 -0.62 4.0 1.25 0.035 0.8 18.8 18.0 0.034 0.3 -0.61 3.8 1.17 0.033 -0.1 18.9 19.0 0.032 0.3 -0.61 3.5 1.10 0.031 -0.6 18.9 19.5 0.030 0.3 -0.58 3.3 1.02 0.029 -1.0 19.0 20.0 0.028 0.3 -0.56 3.0 0.94 0.027 -1.2 19.0 20.2 0.026 0.3 -0.52 2.8 0.86 0.024 -1.8 19.0 20.8 0.024 0.2 -0.49 2.5 0.78 0.022 -2.1 18.9 21.0 0.021 0.2 -0.45 2.3 0.70 0.020 -2.4 18.9 21.3 0.019 0.2 -0.41 2.0 0.63 0.018 -4.3 18.9 23.2 0.017 0.2 -0.40

1.8 0.55 0.016 -5.3 18.9 24.2 0.015 0.2 -0.37 1.5 0.47 0.013 -5.3 18.8 24.1 0.013 0.1 -0.32 1.3 0.39 0.011 -5.4 18.8 24.2 0.011 0.1 -0.26 1.0 0.31 0.009 -5.2 18.8 24.0 0.009 0.1 -0.21 0.8 0.23 0.007 -4.3 18.8 23.1 0.006 0.1 -0.15 0.5 0.16 0.004 -4.0 18.8 22.8 0.004 0.0 -0.10 0.3 0.08 0.002 -1.2 18.8 20.0 0.002 0.0 -0.04


Flow Reading Real Flow Real Flow Tcold Tline Tc-Tl Cold Mass Cold Mass Cooling SCFM SCFM m^3/min ºC ºC ºC Flow (kg/min) Flow (%) Cap (kJ/min)

9.2 2.88 0.082 17.1 18.4 1.3 0.074 1.1 -0.10 8.8 2.74 0.078 15.1 18.4 3.3 0.071 1.0 -0.23 7.5 2.35 0.067 12.1 18.4 6.3 0.061 0.9 -0.39 6.8 2.13 0.060 12.3 18.4 6.1 0.055 0.8 -0.34 6.5 2.04 0.058 11.5 18.4 6.9 0.053 0.8 -0.37 5.4 1.69 0.048 11.4 18.4 7.0 0.044 0.6 -0.31 5.0 1.57 0.044 10.6 18.5 7.9 0.041 0.6 -0.33 4.8 1.49 0.042 10.4 18.5 8.1 0.039 0.6 -0.32 4.5 1.41 0.040 9.8 18.5 8.7 0.037 0.5 -0.32 4.3 1.33 0.038 8.8 18.6 9.8 0.035 0.5 -0.35 4.0 1.25 0.035 6.7 18.6 11.9 0.033 0.5 -0.40 3.8 1.17 0.033 5.4 18.6 13.2 0.031 0.5 -0.42 3.5 1.10 0.031 5.3 18.6 13.3 0.029 0.4 -0.39 3.3 1.02 0.029 4.1 18.6 14.5 0.027 0.4 -0.40 3.0 0.94 0.027 2.6 18.6 16.0 0.025 0.4 -0.41 2.8 0.86 0.024 2.1 18.6 16.5 0.023 0.3 -0.39 2.5 0.78 0.022 1.4 18.6 17.2 0.021 0.3 -0.37 2.3 0.70 0.020 0.4 18.6 18.2 0.019 0.3 -0.35 2.0 0.63 0.018 0.5 18.5 18.0 0.017 0.2 -0.31 1.8 0.55 0.016 -0.6 18.5 19.1 0.015 0.2 -0.29 1.5 0.47 0.013 -0.7 18.5 19.2 0.013 0.2 -0.25 1.3 0.39 0.011 -0.5 18.4 18.9 0.011 0.2 -0.20 1.0 0.31 0.009 0.4 18.5 18.1 0.009 0.1 -0.16 0.8 0.23 0.007 1.0 18.4 17.4 0.006 0.1 -0.11 0.5 0.16 0.004 2.3 18.5 16.2 0.004 0.1 -0.07 0.3 0.08 0.002 3.3 18.5 15.2 0.002 0.0 -0.03



9.2 2.88 0.082 17.1 18.6 1.5 0.074 1.1 -0.11 8.8 2.74 0.078 16.6 18.6 2.0 0.070 1.0 -0.14 7.5 2.35 0.067 14.6 18.6 4.0 0.061 0.9 -0.24 6.8 2.13 0.060 13.8 18.7 4.9 0.055 0.8 -0.27 6.5 2.04 0.058 14.0 18.7 4.7 0.053 0.8 -0.25 5.4 1.69 0.048 12.4 18.7 6.3 0.044 0.6 -0.28

mailto:4@40

mailto:4@40

5.0 1.57 0.044 12.1 18.7 6.6 0.041 0.6 -0.27 4.8 1.49 0.042 11.9 18.7 6.8 0.039 0.6 -0.26 4.5 1.41 0.040 10.0 18.6 8.6 0.037 0.5 -0.32 4.3 1.33 0.038 10.1 18.6 8.5 0.035 0.5 -0.30 4.0 1.25 0.035 9.2 18.6 9.4 0.033 0.5 -0.31 3.8 1.17 0.033 7.1 18.6 11.5 0.031 0.5 -0.36 3.5 1.10 0.031 6.8 18.7 11.9 0.029 0.4 -0.35 3.3 1.02 0.029 5.6 18.7 13.1 0.027 0.4 -0.36 3.0 0.94 0.027 4.1 18.8 14.7 0.025 0.4 -0.37 2.8 0.86 0.024 3.8 18.8 15.0 0.023 0.3 -0.35 2.5 0.78 0.022 3.4 18.8 15.4 0.021 0.3 -0.33 2.3 0.70 0.020 1.8 18.8 17.0 0.019 0.3 -0.33 2.0 0.63 0.018 1.4 18.8 17.4 0.017 0.2 -0.30 1.8 0.55 0.016 0.2 18.8 18.6 0.015 0.2 -0.28 1.5 0.47 0.013 -1.2 18.8 20.0 0.013 0.2 -0.26 1.3 0.39 0.011 -1.6 18.8 20.4 0.011 0.2 -0.22 1.0 0.31 0.009 -1.8 18.7 20.5 0.009 0.1 -0.18 0.8 0.23 0.007 -1.0 18.7 19.7 0.006 0.1 -0.13 0.5 0.16 0.004 0.5 18.7 18.2 0.004 0.1 -0.08 0.3 0.08 0.002 4.8 18.7 13.9 0.002 0.0 -0.03



7.1 2.22 0.063 15.9 18.2 2.3 0.057 1.1 -0.13 6.3 1.96 0.055 15.1 18.2 3.1 0.050 1.0 -0.16 5.8 1.80 0.051 14.8 18.2 3.4 0.046 0.9 -0.16 5.3 1.64 0.047 14.4 18.4 4.0 0.042 0.8 -0.17 5.0 1.57 0.044 14.0 18.2 4.2 0.041 0.8 -0.17 4.5 1.41 0.040 13.5 18.3 4.8 0.037 0.7 -0.18 4.3 1.33 0.038 13.0 18.3 5.3 0.035 0.7 -0.18 4.0 1.25 0.035 12.2 18.3 6.1 0.033 0.6 -0.20 3.8 1.17 0.033 11.4 18.4 7.0 0.031 0.6 -0.22 3.5 1.10 0.031 11.2 18.4 7.2 0.029 0.5 -0.21 3.3 1.02 0.029 10.7 18.4 7.7 0.027 0.5 -0.21 3.0 0.94 0.027 10.1 18.4 8.3 0.025 0.5 -0.21 2.8 0.86 0.024 9.6 18.4 8.8 0.023 0.4 -0.20 2.5 0.78 0.022 8.6 18.4 9.8 0.021 0.4 -0.20 2.3 0.70 0.020 7.5 18.4 10.9 0.019 0.4 -0.20 2.0 0.63 0.018 5.0 18.4 13.4 0.017 0.3 -0.22 1.8 0.55 0.016 2.0 18.3 16.3 0.015 0.3 -0.24 1.5 0.47 0.013 2.3 18.3 16.0 0.013 0.2 -0.20 1.3 0.39 0.011 1.8 18.3 16.5 0.011 0.2 -0.18 1.0 0.31 0.009 1.7 18.3 16.6 0.008 0.2 -0.14 0.8 0.23 0.007 3.0 18.3 15.3 0.006 0.1 -0.10 0.5 0.16 0.004 4.0 18.3 14.3 0.004 0.1 -0.06 0.3 0.08 0.002 4.1 18.3 14.2 0.002 0.0 -0.03



7.1 2.22 0.063 16.0 18.3 2.3 0.057 1.1 -0.13 6.3 1.96 0.055 15.1 18.3 3.2 0.050 1.0 -0.16 5.8 1.80 0.051 14.0 18.3 4.3 0.047 0.9 -0.20 5.3 1.64 0.047 13.6 18.4 4.8 0.043 0.8 -0.21 5.0 1.57 0.044 13.4 18.4 5.0 0.041 0.8 -0.20 4.5 1.41 0.040 12.1 18.5 6.4 0.037 0.7 -0.24 4.3 1.33 0.038 11.6 18.3 6.7 0.035 0.7 -0.23 4.0 1.25 0.035 11.1 18.3 7.2 0.033 0.6 -0.24 3.8 1.17 0.033 10.4 18.3 7.9 0.031 0.6 -0.24 3.5 1.10 0.031 10.3 18.3 8.0 0.029 0.5 -0.23 3.3 1.02 0.029 9.1 18.3 9.2 0.027 0.5 -0.25 3.0 0.94 0.027 8.6 18.3 9.7 0.025 0.5 -0.24 2.8 0.86 0.024 7.2 18.3 11.1 0.023 0.4 -0.25 2.5 0.78 0.022 5.3 18.3 13.0 0.021 0.4 -0.27 2.3 0.70 0.020 3.9 18.4 14.5 0.019 0.4 -0.28 2.0 0.63 0.018 3.1 18.4 15.3 0.017 0.3 -0.26 1.8 0.55 0.016 1.9 18.4 16.5 0.015 0.3 -0.25 1.5 0.47 0.013 1.5 18.4 16.9 0.013 0.2 -0.22 1.3 0.39 0.011 1.6 18.4 16.8 0.011 0.2 -0.18 1.0 0.31 0.009 1.5 18.4 16.9 0.008 0.2 -0.14 0.8 0.23 0.007 1.8 18.4 16.6 0.006 0.1 -0.11 0.5 0.16 0.004 3.8 18.4 14.6 0.004 0.1 -0.06 0.3 0.08 0.002 4.6 18.4 13.8 0.002 0.0 -0.03



4.8 1.50 0.043 16.4 18.7 2.3 0.039 1.0 -0.09 4.8 1.49 0.042 15.7 18.7 3.0 0.038 1.0 -0.12 4.5 1.41 0.040 14.9 18.7 3.8 0.036 1.0 -0.14 4.3 1.33 0.038 13.9 18.7 4.8 0.034 0.9 -0.17 4.0 1.25 0.035 13.6 18.7 5.1 0.032 0.9 -0.17 3.8 1.17 0.033 13.1 18.7 5.6 0.030 0.8 -0.17 3.5 1.10 0.031 12.6 18.7 6.1 0.029 0.8 -0.17 3.3 1.02 0.029 12.3 18.7 6.4 0.026 0.7 -0.17 3.0 0.94 0.027 11.9 18.7 6.8 0.024 0.7 -0.17 2.8 0.86 0.024 11.4 18.7 7.3 0.022 0.6 -0.17 2.5 0.78 0.022 11.1 18.6 7.5 0.020 0.5 -0.15 2.3 0.70 0.020 10.8 18.6 7.8 0.018 0.5 -0.14 2.0 0.63 0.018 9.4 18.6 9.2 0.016 0.4 -0.15 1.8 0.55 0.016 8.8 18.6 9.8 0.014 0.4 -0.14 1.5 0.47 0.013 7.6 18.7 11.1 0.012 0.3 -0.14 1.3 0.39 0.011 7.2 18.7 11.5 0.010 0.3 -0.12

1.0 0.31 0.009 6.9 18.6 11.7 0.008 0.2 -0.10 0.8 0.23 0.007 7.1 18.6 11.5 0.006 0.2 -0.07 0.5 0.16 0.004 7.0 18.7 11.7 0.004 0.1 -0.05 0.3 0.08 0.002 7.6 18.7 11.1 0.002 0.1 -0.02

Gen B, 20, Second Experiment


5.0 1.57 0.044 16.1 18.7 2.6 0.040 1.1 -0.10 4.8 1.49 0.042 15.3 18.7 3.4 0.038 1.0 -0.13 4.5 1.41 0.040 14.6 18.7 4.1 0.036 1.0 -0.15 4.3 1.33 0.038 13.7 18.7 5.0 0.034 0.9 -0.17 4.0 1.25 0.035 13.5 18.7 5.2 0.032 0.9 -0.17 3.8 1.17 0.033 12.9 18.7 5.8 0.031 0.8 -0.18 3.5 1.10 0.031 12.3 18.7 6.4 0.029 0.8 -0.18 3.3 1.02 0.029 12.0 18.7 6.7 0.027 0.7 -0.18 3.0 0.94 0.027 11.4 18.7 7.3 0.025 0.7 -0.18 2.8 0.86 0.024 11.2 18.7 7.5 0.023 0.6 -0.17 2.5 0.78 0.022 10.7 18.6 7.9 0.020 0.5 -0.16 2.3 0.70 0.020 9.8 18.6 8.8 0.019 0.5 -0.16 2.0 0.63 0.018 9.4 18.6 9.2 0.016 0.4 -0.15 1.8 0.55 0.016 8.7 18.6 9.9 0.014 0.4 -0.14 1.5 0.47 0.013 8.0 18.7 10.7 0.012 0.3 -0.13 1.3 0.39 0.011 8.2 18.7 10.5 0.010 0.3 -0.11 1.0 0.31 0.009 7.5 18.6 11.1 0.008 0.2 -0.09 0.8 0.23 0.007 7.1 18.6 11.5 0.006 0.2 -0.07 0.5 0.16 0.004 7.6 18.7 11.1 0.004 0.1 -0.05 0.3 0.08 0.002 8.2 18.7 10.5 0.002 0.1 -0.02



2.5 0.78 0.022 17.2 18.7 1.5 0.020 1.0 -0.03 2.3 0.70 0.020 15.2 18.6 3.4 0.018 0.9 -0.06 2.0 0.63 0.018 14.7 18.6 3.9 0.016 0.8 -0.06 1.8 0.55 0.016 14.2 18.6 4.4 0.014 0.7 -0.06 1.5 0.47 0.013 13.9 18.7 4.8 0.012 0.6 -0.06 1.3 0.39 0.011 13.5 18.7 5.2 0.010 0.5 -0.05 1.0 0.31 0.009 13.4 18.7 5.3 0.008 0.4 -0.04 0.8 0.23 0.007 13.2 18.7 5.5 0.006 0.3 -0.03 0.5 0.16 0.004 13.2 18.7 5.5 0.004 0.2 -0.02 0.3 0.08 0.002 13.4 18.7 5.3 0.002 0.1 -0.01



2.5 0.78 0.022 17.0 18.7 1.7 0.020 1.0 -0.03

2.3 0.70 0.020 15.2 18.6 3.4 0.018 0.9 -0.06 2.0 0.63 0.018 14.4 18.6 4.2 0.016 0.8 -0.07 1.8 0.55 0.016 13.8 18.6 4.8 0.014 0.7 -0.07 1.5 0.47 0.013 13.2 18.7 5.5 0.012 0.6 -0.07 1.3 0.39 0.011 12.8 18.7 5.9 0.010 0.5 -0.06 1.0 0.31 0.009 12.7 18.7 6.0 0.008 0.4 -0.05 0.8 0.23 0.007 12.8 18.7 5.9 0.006 0.3 -0.04 0.5 0.16 0.004 13.1 18.7 5.6 0.004 0.2 -0.02 0.3 0.08 0.002 13.8 18.7 4.9 0.002 0.1 -0.01

design and validation of a hilsch-ranque vortex tube

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