Experiments to Study the GaseousDischarge and Filling of Vessels

J. CRAIG DUTTON AND ROBERT E. COVERDILLDepartment of Mechanical and Industrial Engineering, University of Illinois at Urbana-Champaign,Urbana, IL 61801, USA

Two experiments are described that have been developed to demonstrate the fundamentals ofunsteady, compressible flow. The experiments involve the discharge of gas from a pressurized vesseland the filling of an initially evacuated vessel. The hardware, software, and procedures for theexperiments are summarized. In addition, theoretical solutions for the entire vessel filling anddischarge process (choked and unchoked operation) are developed using both adiabatic andisothermal models of the processes. Example measurements from the discharge and fillingexperiments are presented and compared to the adiabatic and isothermal theories. The data arefound to agree well with the theoretical predictions and follow the expected trends with respect tothe rapidity of the processes.

AUTHOR QUESTIONNAIRE

1. The paper describes new training concepts inmechanical and aerospace engineering instru-mentation.

2. The paper is useful in thermodynamics, fluidmechanics, or gas dynamics courses.

3. Level of students to be involved in the use ofthe equipment: junior or senior undergraduatestudents.

4. This paper highlights the development of ana-lytical solutions, hardware, and data acquisi-tion software to demonstrate the principles ofunsteady, compressible flow.

5. The material presented can be incorporated inengineering teaching as a laboratory experienceor classroom demonstration to be used in con-junction with thermodynamics, fluid mechanics,or gas dynamics lecture courses or a thermalscience laboratory course.

6. The laboratory manuals cited as Refs. 1 and 5 inthe paper provide additional support material;these manuals can be made available uponrequest.

7. The experiments have been used in the currentformat for the last five years. Student feedbackon the experiments has been very positive.

8. These experiments can also be formulated asopen-ended experimental design experiences.The analytical solutions are also useful in anumber of practical engineering applications.

INTRODUCTION

EXPERIMENTS have been developed for theinvestigation of the discharge of compressed gasfrom a pressure vessel and the filling (charging) ofan initially evacuated vessel. In each case theprocess occurs through a converging or conver-ging-diverging nozzle. These experiments areused in a required senior-level course, `ThermalScience Laboratory', in the mechanical engineer-ing curriculum at the University of Illinois atUrbana-Champaign. This course is taken aftercompletion of the introductory thermodynamics,fluid mechanics, and heat transfer lecture coursesand demonstrates, in a laboratory environment,the theories and concepts developed in the class-room. In other curricular arrangements, theexperiments described here may also be usedeffectively in conjunction with an undergraduatefluid mechanics or thermodynamics course or witha first course in gas dynamics.

One of the objectives of these laboratoryexercises is to perform unsteady, compressibleflow experiments, thereby providing a complementto the more usual steady, incompressible flowproblems that an undergraduate student investi-gates. In this context the experiments provide theopportunity to reinforce several compressibleflow concepts, particularly the phenomenon ofchoking and differences in operation between con-verging and converging-diverging nozzles. In addi-tion, the use of a digital data acquisition systembased on a personal computer using graphicalobject-oriented programming software, pressuretransducers, and thermocouples simplifies thecollection of data, provides rapid graphical repre-sentation of the data on the computer monitor,and demonstrates the power and utility of ordinary* Accepted 20 May 1996.

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Int. J. Engng Ed. Vol. 13, No. 2, p. 123±134, 1997 0949-149X/91 $3.00+0.00Printed in Great Britain. # 1997 TEMPUS Publications.

desktop computers in a laboratory environment.The experiments are also relatively inexpensive tofabricate, and yield excellent, repeatable data thatagree well with the theories developed for thevessel filling and discharge processes.

In addition to the usefulness of these experi-ments to engineering educators, the theoreticalsolutions that have been developed have foundapplication in a variety of practical, industrialsituations ranging from analysis of accident sce-narios to prediction of the filling time of air bagsand aircraft evacuation slides. We are unaware ofany previous presentation of unified solutions forthe entire vessel discharging or charging processes(i.e., both choked and unchoked operation). Suchsolutions, incorporating both adiabatic and iso-thermal models for the processes, are describedbriefly in the next section.

THEORETICAL DEVELOPMENT

Discharge analysisThe objectives of the analysis are to predict the

pressure, temperature, and density of the gas inthe tank and the mass flow rate out of the tank asfunctions of time during the discharge process.To accomplish these objectives the control volumeshown in Fig. 1(a), which lies just inside thevessel walls, is used. In addition, the followingassumptions are made:

1. Properties of the gas in the tank are spatiallyuniform at any instant of time (i.e., quasi-steadyor uniform state assumption);

2. Average velocity of the gas in the tank is zero;3. Opening modeled as an ideal converging or

converging-diverging nozzle with isentropicflow to the nozzle throat;

4. One-dimensional flow and properties in thenozzle;

5. Neglect gravitational potential energy;6. No shear or shaft work for the control volume;7. Gas is thermally and calorically perfect;8. Thermodynamic process is either adiabatic or

isothermal.

The adiabatic assumption would be expected tobe a good model for very rapid discharge processesin which case there would be little time for sig-nificant heat transfer between the tank walls andthe gas. On the other hand, the isothermal assump-tion is expected to be appropriate for slow vesseldischarge processes whereby there is sufficient timefor heat transfer to maintain the temperature ofthe gas in the vessel constant.

Applying the integral continuity and energyequations to the control volume for the adiabaticcase, the thermodynamic properties of the gas inthe vessel can be shown to obey isentropic rela-tions. In addition, for a large enough initial tankpressure Pi, compared to the back pressure PB, thenozzle will be choked during the initial portion ofthe discharge process. By starting with the integral

continuity equation, substituting Fliegner's for-mula for the choked mass flow rate, and integrat-ing the resulting ordinary differential equation,the solutions for the adiabatic and isothermalpressure/time histories in dimensionless form canbe found as [1±3]:

Choked adiabatic solution:

P� � 1� ÿ 1

2

� � � 1

2

� �ÿ� �1�2� ÿ1�

t�

24 35ÿ2 � ÿ1�

�1�

Choked isothermal solution:

P� � exp ÿ � 1

2

� �ÿ� �1�2� ÿ1�

t�

24 35 �2�

In the discharge analysis the gas thermodynamicproperties are nondimensionalized with respect totheir initial values so that P� � P=Pi in the expres-sions above. In addition, the dimensionless time isdefined as t� � t=tchar where the characteristictime is given by tchar � V=At ai. The symbols V ,

Fig. 1. Control volumes used for the vessel discharge and fillinganalyses: (a) vessel discharge, (b) vessel charge.

J. C. Dutton and R. E. Coverdill124

At, and ai denote the vessel volume, nozzle throatarea, and speed of sound of the gas initially in thetank, respectively. In this dimensionless P�ÿt�form, the pressure/time history of the gas in thevessel for both models is therefore dependent onlyon the single parameter , the gas specific heatratio, as long as the nozzle is choked.

As the tank pressure falls toward the backpressure, the nozzle will eventually unchoke. Thetheoretical results can be extended through theunchoked regime by writing a mass flow expres-sion at the nozzle exit plane, imposing theboundary condition that the nozzle exit staticpressure must equal the ambient pressure, sub-stituting this result into the integral continuityequation, and integrating the resulting ordinarydifferential equation using the unchoking pointvalues �P�unch; t

�unch� as the initial condition [1]. To

our knowledge closed form solutions can only beobtained for t� as an explicit function of P�, ratherthan vice versa, and only for cases in which the gasspecific heat ratio is the ratio of integers, such as � 7=5 or 5/3. A change of variables suggested byOwczarek [4] has been used in the unchoked analy-sis. The results for the adiabatic and isothermalmodel for � 7=5 are as follows:

Unchoked adiabatic solution:

t� � t�unch �2

ÿ 1

� �1=2At

Ae�P�B �

ÿ� ÿ1�2

��

x3

4� 5

8x

� ��x2 � 1�1=2

� 38

ln �x� �x2 � 1�1=2��xunch

x

�3�

Unchoked isothermal solution:

t� � t�unch �2 2

ÿ 1

� �1=2At

Ae

� �x5unch ÿ x5�

5� 2�x3

unch ÿ x3�3

� �xunch ÿ x�� �

�4�where

x � P�

P�B

� �� ÿ1�= ÿ1

" #1=2

�5�

The unchoked solutions are seen to depend ontwo additional parameters as compared to thechoked solutions: the nozzle throat-to-exit arearatio At=Ae and the dimensionless back pressureP�B � PB=Pi. Also, note that these solutions can beapplied to the situation in which the entire vesseldischarge is unchoked. In that case, equations(3)±(5) are used with P�unch replaced by unity andt�unch replaced by zero.

Charge analysisThe objectives, control volume, Fig. 1(b),

assumptions, and solution methods for the vessel

filling analysis are similar to those for the dis-charge analysis described above. For the adiabaticmodel, however, the relations among the thermo-dynamic properties are no longer isentropic. Thisresult is consistent with the fact that the kineticenergy of the gas entering the tank must bedissipated if the average velocity in the tank iszero. In the tank charging analysis, the thermo-dynamic properties of the gas in the tank (whoseinitial values are Pi, �i, and Ti) are normalized withrespect to the constant source values Ps, �s, and Ts,where atmosphere is used as the source and thetank is initially evacuated in the experimentsdescribed below. Thus, in the following expres-sions, the dimensionless pressure is defined asP� � P=Ps, and the dimensionless time is givenby t� � t=tchar � V=At as and as is the speed ofsound in the source gas. The adiabatic and iso-thermal solutions for choked flow, which willoccur if the initial tank pressure is low enoughcompared to the source pressure, are [2, 5]:

Choked adiabatic solution:

P� � P�i � � 1

2

� �ÿ� �1�2� ÿ1�

t� �6�

Choked isothermal solution:

P� � P�i � T �i � 1

2

� �ÿ� �1�2� ÿ1�

t� �7�

The adiabatic choked P�ÿt� solution is seen todepend on the gas specific heat ratio and theinitial pressure ratio P�i � Pi=Ps. The isothermalsolution for choked flow depends on these twoparameters plus the initial temperature ratioT �i � Ti=Ts. For both choked solutions the pres-sure increase with time is linear, but the rate ofpressure increase for the isothermal case is smallerby the factor =T �i .

As the pressure in the vessel approaches thesource pressure, the nozzle will unchoke and theexpressions above can no longer be used. Adoptinga procedure similar to that described previouslyfor the unchoked discharge analysis, but nowsetting the nozzle exit static pressure equal to thetank pressure for the unchoked case, yields thefollowing results for unchoked vessel filling [5]:

Unchoked adiabatic solution:

P� ��

1ÿ��1ÿ �P�unch�� ÿ1�= �1=2

ÿ ÿ 1

2

� �1=2Ae

At�t� ÿ t�unch�

�2� =� ÿ1��8�

Unchoked isothermal solution:

P� ��

1ÿ��1ÿ �P�unch�� ÿ1�= �1=2

ÿ ÿ 1

2 2

� �1=2

T �iAe

At�t� ÿ t�unch�

�2� =� ÿ1�

�9�

The Gaseous Discharge and Filling of Vessels 125

Note that the two unchoked solutions are identi-cal except that the last term of the isothermalmodel is smaller than that for the adiabaticmodel by the factor =T �i , which is similar to theresults for choked flow. The nozzle exit-to-throatarea ratio is also introduced as an additionalparameter in both unchoked solutions as com-pared to the choked flow results. It should benoted that if these solutions are continuedbeyond the time at which P� � 1, the mass flowwill become negative (i.e., out of the tank) and thepressure will decrease again, which is obviouslyphysically unrealistic. Thus, the solutions shouldbe terminated at P� � 1. As was the case for thedischarge analysis, the solutions given above canbe used for the situation in which the entire vesselfilling process is unchoked. In that case, theequations for the unchoked regime are used withP�unch replaced by P�i and t�unch replaced by zero.

In addition to the pressure/time history solutionspresented above for the discharge and fillingprocesses, similar time history expressions for thedimensionless density, temperature, and mass flowrate can also be developed from the thermo-dynamic relations that apply for the adiabaticand isothermal models. Further details about thetheoretical analyses may be found in the labora-tory manuals that have been developed for these

experiments [1, 5]; these manuals are availablefrom the authors upon request.

EXPERIMENTAL EQUIPMENT ANDMETHODS

ApparatusA schematic diagram of the apparatus for the

discharge experiment is shown in Fig. 2. Twoseparate vessels are available; the smaller onehas a volume of 4920 cm3 while the larger tankhas a volume of 29 100 cm3. The vessels haveseveral fittings, one each at the top and bottomand several on the sides. The lower and sideports are used, respectively, to mount a type Tthermocouple, a pressure transducer (Sensotec0±1.4 MPa(abs) strain gauge-type), a connectionfor pressurizing the tank, and a pressure reliefvalve. The upper port is the location at which anozzle, either converging or converging-diverging,is mounted, and through which the gas dischargeoccurs. As shown in Table 1, six nozzles areavailable, ranging from 1.63 to 6.36 mm in throatdiameter. A small flange fastened with socket headscrews holds the nozzle securely to its seat while anO-ring is used to seal the nozzle against the seat. Aflat-faced plug with an O-ring that is attached to a

Fig. 2. Schematic diagram of the vessel discharge experimental apparatus.

J. C. Dutton and R. E. Coverdill126

fast-acting toggle clamp seals tightly against theouter face of the nozzle when it is placed in theclosed position.

A standard bottle of compressed air equippedwith a regulator is used to pressurize the test vessel.A second regulator on a calibration stand is usedto adjust the initial pressure in the vessel. A flexiblehose with a quick-disconnect type of fitting couplesthe calibration stand to the vessel. A three-wayvalve on the test vessel stand (not shown) is used toallow air to flow into the vessel during charging,and also to isolate the vessel from the calibrationstand when charging is complete. The third posi-tion of the valve can be used to vent the gas in thevessel to atmosphere. The pressure in the vessel isdisplayed on a Bourdon tube gauge on the calibra-tion stand and is monitored during vessel charginguntil the pressure has reached the desired initialvalue, typically around 1 MPa. Since the pressuredata are nondimensionalized with respect to thisinitial value, the actual starting pressure used isunimportant, as long as it is sufficiently high thatthe nozzle will be choked initially (the usual caseof interest). As stated above, a thermocouple issituated in each of the vessels to monitor thetemperature of the air. However, the thermo-couples have neither been sized nor located tofollow the transient behavior of the dischargeprocess; the thermocouple data are used primarilyto determine the initial gas temperature. Once thevessel is pressurized, the temperature of the air inthe tank is allowed to return to the ambient valuebefore discharging it through the nozzle. Dischargeof the vessel occurs when the fast-acting toggleclamp is actuated, removing the sealing plug fromthe face of the nozzle.

InstrumentationA computerized data acquisition system that

allows for rapid collection of pressure, temperature,and time data has been developed for this experi-ment. The system consists of an Apple Macintoshcomputer with 8 MB of RAM, an Apple colormonitor, a data acquisition card (ours is a multi-purpose card purchased from National Instru-ments, model NB-MIO-16H), and LabVIEW 2software, also from National Instruments. Thesignals that are input to the A/D card are thevoltage outputs from the pressure transducer and

the thermocouple that are located in the vessel.Since the time for complete discharge can last froma few seconds to several minutes depending onthe vessel/nozzle combination being tested, thesampling interval of the LabVIEW applicationmust be user selectable. This requires that thecharacteristic time tchar of the event be calculated,based on the tank and nozzle being investigated, tohave a reasonably sized data set when completed(typically 50 data points are adequate). Since theA/D card is capable of greater than a 40 kHzsampling rate, this is an important step in theprocess. The sampling interval is entered in soft-ware from the `front panel' of the `virtual instru-ment' that is written in LabVIEW. A reproductionof the front panel for the discharge experiment isshown in Fig. 3. Displays of the pressure trans-ducer output voltage and air temperature areincluded on the panel. In addition, the user maystart, stop, or toggle between any of the threemodes used to calibrate the transducer, monitortank charging, or record data during the discharge.

After the process has ended, the data acquisi-tion program is terminated and the raw voltagedata from the pressure transducer are plottedversus time on the monitor by the LabVIEWprogram to verify that the event occurred properly(Fig. 3). The data are then saved to a spreadsheetfile. Final data reduction is accomplished in astraightforward manner using the spreadsheet.

The apparatus and instrumentation for thevessel filling experiment are essentially identicalto that described above for the discharge experi-ment. The only differences are that the com-pressed air bottle and calibration stand arereplaced by a two-stage vacuum pump and aBourdon type absolute pressure gauge to monitorthe tank pressure, and 0±140 kPa(abs) Sensotecstrain gauge pressure transducers are used insteadof 0±1.4 MPa(abs) transducers. In addition, thenozzles are installed with their rounded entrancesection facing outward (rather than into the tank asfor the discharge experiment).

EXAMPLE RESULTS AND DISCUSSION

Example measurements and comparisons totheory will now be presented for both the vessel

Table 1. Nozzle dimensions and characteristic times

Dimensions tchar for V � 4920 cm3 tchar for V � 29 100 cm3

Nozzle No. Description (mm) (sec)* (sec)*

QN1.1 Converging Dt � 1:63 6.85 40.5QN1.2 Converging Dt � 3:19 1.79 10.6QN1.3 Converging Dt � 4:79 0.79 4.69QN1.4 Converging Dt � 6:36 0.45 2.66QN2.1 Converging- Dt � 3:18 1.80 10.6

Diverging De � 4:11QN2.2 Converging- Dt � 4:78 0.80 4.71

Diverging De � 6:17

* Assumes Ti � Ts � 295 K and that the gas is air.

The Gaseous Discharge and Filling of Vessels 127

discharge and filling experiments. In all casesexperimental uncertainties are specified in thefigure captions. These values have been determinedusing the uncertainty propagation procedureoutlined by Coleman and Steele [6], together withthe definitions of the plotted dimensionless vari-ables: P� � P=Pref and t� � �tAt aref�=V . As dis-cussed earlier, the reference conditions for thedischarge experiment are the initial values of thegas in the tank, while for the charge problem theyare the constant values of the source gas. Esti-mates of the bias and precision limits to 95%confidence have been made for each of the

component quantities in the definitions of thedimensionless quantities that are plotted.

Example vessel discharge results are shown inFig. 4 where both the experimental data and theadiabatic and isothermal theories have beenplotted. Figure 4(a) corresponds to the mostrapid discharge possible with our hardware: thenozzle with the largest throat diameter mounted onthe smaller tank (see Table 1 for nozzle dimensionsand characteristic times). This discharge occurs ina little over 2 s (approximately five characteristictimes), and the data are seen to agree well with theadiabatic theoretical results for the entire duration

Fig. 3. Reproduction of the LabVIEW front panel for the discharge experiment.

J. C. Dutton and R. E. Coverdill128

of the process. At the other extreme is the smallestthroat diameter nozzle used in conjunction withthe large tank, Fig. 4(b). In this case the processrequires about 200 s. During the initial stages ofthe discharge, the data follow the adiabatic theoryquite closely, as there is little time elapsed and onlya small temperature difference between the gas andvessel walls, so that significant heat transfer doesnot occur. However, as the discharge proceeds,

heat transfer does occur, the gas tends to remainat constant temperature, and the P�ÿt� resultsmore closely follow the isothermal theory. Thethermocouple measurements, which are admittedlyqualitative for the reasons discussed above, agreewith this reasoning.

Figure 5 presents composite results for twoseries of experiments that can be performed withthis hardware. In Fig. 5(a) the initial tank pressure,

Fig. 4. Example single experiment data for the discharge experiment: (a) nozzle QN1.4Ðsmall tank, (b) nozzle QN1.1Ðlarge tank;uncertainty in P� � �0:0075 and in t� � �0:15 to 95% confidence.

The Gaseous Discharge and Filling of Vessels 129

and therefore P�B � PB=Pi, are held approximatelyconstant and several vessel/nozzle combinationsare examined. Although the characteristic timesfor the extreme cases differ by nearly two orders ofmagnitude (Table 1), when plotted in this dimen-sionless format, the data for all cases collapse to afairly narrow band about the adiabatic and iso-thermal theoretical predictions. This result is peda-gogically useful in reinforcing dimensional analysisconcepts. However, the trends described above,that the faster discharges agree more closely with

the adiabatic theory while the slower ones agreebetter with the isothermal theory, are also discern-ible in Fig. 5(a). Figure 5(b) shows the results of aseries of experiments in which the initial pressure,and therefore P�B , are varied for the same vessel/nozzle combination. These experiments demon-strate that a single curve describes the dimension-less pressure/time history for choked flow, but thatthe unchoking point and the asymptotic value ofP� at long times depend on P�B . Since thedischarges plotted in Fig. 5(b) are all relatively

Fig. 5. Example composite data for the discharge experiment: (a) variable nozzle-tank combinations and constant P�B , (b) variable P�Band constant nozzle-tank combination; uncertainties same as in Fig. 4.

J. C. Dutton and R. E. Coverdill130

fast ones, taking on the order of 10 s or less, onlythe adiabatic theory has been plotted to avoidclutter. The agreement between the data and thetheoretical predictions is excellent.

Results from typical vessel filling experimentsare shown in Fig. 6. As was done for the dischargeresults, Fig. 6(a) presents data and predictions forthe fastest charging experiment (approximatelyone second), while Fig. 6(b) does so for the slowestone (about 100 s). Clearly, the agreement between

the data in Fig. 6(b) for the slow chargingprocess agree very closely with the isothermaltheory. While the data in Fig. 6(a) for the fastfilling process are shifted somewhat toward theprediction of the adiabatic model, they still liecloser to the isothermal prediction. This resultcan be explained by the observation that forvessel filling enhanced forced convective heattransfer occurs, compared to vessel discharge,due to jet impingement phenomena on the walls

Fig. 6. Example single experiment data for the filling experiment: (a) nozzle QN1.4Ðsmall tank, (b) nozzle QN1.1Ðlarge tank;uncertainty in P� � �0:015 and in t� � �0:08 to 95% confidence.

The Gaseous Discharge and Filling of Vessels 131

of the tank. In addition, the heat capacity of thetank walls is estimated to be more than an order ofmagnitude greater than that of the gas. Thus, evenfor rapid filling, substantial heat transfer betweenthe gas and the vessel walls occurs and the gastemperature remains approximately constant. Thishypothesis is again qualitatively confirmed by thethermocouple measurements.

Composite results for two series of experimentsin which the vessel/nozzle geometry and initial

pressure ratio P�i � Pi=Ps were varied are shownin Figs 7(a) and 7(b), respectively. In Fig. 7(a)the data for four vessel/nozzle combinations at anapproximately constant value of P�i are seen tocollapse near the isothermal theory, although theexpected trends with experiment characteristictime can be discerned. Figure 7(b) presents resultsin which P�i was varied for a given vessel andnozzle, including the upper two curves for whichthe entire filling process was unchoked. For this

Fig. 7. Example composite data for the filling experiment: (a) variable nozzle/tank combinations and constant P�i , (b) variable P�i andconstant nozzle/tank combination; uncertainties same as in Fig. 6.

J. C. Dutton and R. E. Coverdill132

vessel and nozzle, the experiments require afilling time of about 15 s or less. In all cases theisothermal theory, which is clearly the superiorone for the cases investigated here, is in closeagreement with the data.

All of the experimental results presented herehave been for cases in which converging nozzleswere used. This is because these nozzles providethe extremes in the experimental characteristictimes with the current equipment (Table 1). How-ever, use of both the converging and converging-diverging nozzles illustrates the differences inchoking characteristics of these two designs, inparticular that the converging-diverging nozzlesremain choked over a larger range of pressureratios than do the converging nozzles.

SUMMARY AND CONCLUSIONS

Experiments to study the discharge of com-pressed gas from a pressure vessel and filling ofan initially evacuated tank are described. Theoreti-cal solutions for the two processes, incorporatingboth adiabatic and isothermal models, are alsopresented and compared to example measurementsfrom the experiments. In each case, the agreementbetween the experimental data and theoreticalpredictions is found to be quite good.

In addition to demonstrating the accuracy of theone-dimensional theories developed here, theseexperiments can be used in open-ended experi-mental design situations. One possibility wouldbe to introduce the students to the theoreticalsolutions and the available equipment and thenask them to design experiments that determine therange of parameters over which each model, adia-batic or isothermal, is the more accurate. Anotherpossibility would be to pose an industrial applica-tion, such as a vessel discharge or filling accidentscenario, for which the parameters (such as vessel

size, opening area, initial pressure, or initial tem-perature) are far outside those that can be achievedin the laboratory. The students can then be askedto design experiments that answer questions con-cerning the time for vessel discharge or filling,the pressure, temperature, and mass flow timehistories, etc. for the posed scenario. To answerthese questions, the students obviously must iden-tify the pertinent dimensionless variables, either bynon-dimensionalizing the governing equations orby using the Buckingham Pi procedure, beforeproceeding with the experiments. Other open-ended experimental design experiences are alsopossible.

These experiments have been used in their cur-rent format for the last several years in a requiredsenior-level thermal science laboratory course atthe University of Illinois at Urbana-Champaign.In general, student feedback on the experimentsis very positive. The experiments require sub-stantial hands-on interaction, they make noise,and the students are particularly interested in theuse of the digital data acquisition system andobject-oriented LabVIEW programming languagefor acquiring the measurements. In addition, thedata reduction is straightforward and is easilyaccomplished on a spreadsheet. Although safetyis obviously a concern for the discharge experi-ment, because of the use of compressed gas, thefilling experiment is extremely safe since onlysubatmospheric pressures occur. In summary, itis our experience that these experiments areexcellent vehicles for demonstrating the funda-mentals of unsteady, compressible flow. In addi-tion, the analytical solutions that have beendeveloped for the charging and dischargingprocesses are useful in a number of practicalapplications.

AcknowledgmentsÐWe would like to acknowledge ChristopherP. LaMothe for his help in developing the LabVIEW virtualinstrument and in obtaining the example experimental results.

REFERENCES

1. J. C. Dutton and R. E. Coverdill, Sudden discharge of a pressure vessel, Laboratory Manual forME 250: Thermal Science Laboratory, Department of Mechanical and Industrial Engineering,University of Illinois at Urbana-Champaign (1994).

2. A. L. Addy and B. J. Walker, Rapid discharging of a vessel through a nozzle or an orifice, ASMEPaper 72-FE-40 (1972).

3. M. A. Saad, Compressible Fluid Flow, 2nd Ed., Prentice-Hall, Englewood Cliffs, New Jersey (1993)pp. 103±109.

4. J. A. Owczarek, Fundamentals of Gas Dynamics, International Textbook Co., Scranton,Pennsylvania (1964) pp. 254±256.

5. J. C. Dutton and R. E. Coverdill, Rapid filling of an evacuated vessel, Laboratory Manual forME 250: Thermal Science Laboratory, Department of Mechanical and Industrial Engineering,University of Illinois at Urbana-Champaign (1993).

6. H. W. Coleman and W. G. Steele, Jr., Experimentation and Uncertainty Analysis for Engineers,Wiley, New York (1989).

J. Craig Dutton is the W. Grafton and Lillian B. Wilkins Professor of MechanicalEngineering at the University of Illinois at Urbana-Champaign. He received his B.S.from the University of Washington, his M.S. from Oregon State University, and his Ph.D.from the University of Illinois, all in Mechanical Engineering. His research activities consistof experimental studies of compressible fluid flows. He teaches undergraduate courses in

The Gaseous Discharge and Filling of Vessels 133

fluid mechanics and gas dynamics and graduate courses in gas dynamics. In addition, hehas helped to develop the senior-level thermal science laboratory course. Two of theexperiments from this course are the subject of the current paper.

Robert E. Coverdill is a Senior Research Engineer and Adjunct Lecturer in the Departmentof Mechanical and Industrial Engineering at the University of Illinois at Urbana-Champaign. He received a B.S. and M.S. in Mechanical Engineering from the Universityof Illinois. His research activity consists of engineering support for a wide range of projectsin the department. He helped develop, and now teaches, the senior-level thermal sciencelaboratory course. With several faculty members he has prepared many laboratoryexperiments and manuals in both thermal science and materials behavior for use withundergraduate courses.

J. C. Dutton and R. E. Coverdill134