found to be very encouraging. The specific impulse was cal-culated to be 298 s, assuming chemical equilibrium in thenozzle, an expansion ratio of 80, and a combustion chamberpressure of about 100 atm. Although finite rate chemical re-actions in the nozzle may reduce the specific impulse by sev-eral percent, the resulting performance will still be compa-rable to the best solid rocket propellants and only about 10%lower than for kerosene and LOX, for example. In view ofthe potential savings of energy, the production of cryogenicCO and LOX from the Martian atmosphere merits consid-eration for missions with long stay times on the planet's sur-face. For example, a 100-m2 solar array provides enough powerto produce sufficient propellant during 1 Earth year to launchthe crew and 1000 kg of samples into Martian orbit.
References'Tauber, M. E., Bowles, J., and Yang, L., "The Use of Atmos-
pheric Braking During Mars Missions," Journal of Spacecraft andRockets, Vol. 27, No. 5, 1990, pp. 514-521.2Clark, B., "Manned Mars Missions for the Year 2000," AIAAPaper 89-0512, Jan. 1989.3Owen, T., Biemann, K., Rushneck, D. R.; Biller, J. E., Howarth,D. W., and LaFleur, A. L., "The Composition of the Atmosphereat the Surface of Mars," Journal of Geophysical Research, Vol. 82,No. 8, 1977, pp. 4633-4639.
4Ash, R. L., Dowler, W. L., and Varsi, G., "Feasibility of RocketPropellant Production on Mars," Acta Astronautica, Vol. 5, 1978,pp. 705-724.
5Ash, R. L., Huang, J. K., and Johnson, P. B., "Elements ofOxygen Production Using Martian Atmosphere," AIAA Paper 86-1586, June 1986.6Ramohalli, K., Lawton, E., and Sash, R., "Recent Concepts inMissions to Mars: Extraterrestrial Processes," Journal of Propulsionand Power, Vol. 5, March-April 1989, pp. 181-187.
7Barron, R., Cryogenic Systems, McGraw-Hill, New York, 1966.8Gordon, S., and McBride, B. J., "Computer Program for Cal-
culation of Complex Chemical Equilibrium Compositions, RocketPerformance, Incident and Reflected Shocks, and Chapman-JouguetDetonations," NASA SP-273, Interim Revision, March 1976.
9Taylor, J. W. R. (ed.), Jane's All the Worlds Aircraft, Jane'sPublishing Co., London, England, 1989.
10Gubanov, B., "Energiya Looks to Mars and Beyond," AerospaceAmerica, July 1990, pp. 66-73.
Indicial Method Calculating DynamicStall on a Vertical Axis Wind Turbine
Stephane R. Major* and Ion ParaschivoiutEcole Polytechnique de Montreal,
Montreal, Quebec, Canada
Introduction
T HE critical need for new sources of energy is a vitalproblem, now that worldwide petroleum reserves are
slowly drying out and respect for the environment is a majorconcern. The use of wind energy is a very practical solutionto this problem. Wind turbines are classified in two families,horizontal and vertical axis, and use either lift or drag forcesto generate power. The Darrieus rotor is a high-speed vertical
*Graduate Student, Department of Mechanical Engineering.Member AIAA.
tJ.-A. Bombardier Aeronautical Chair Professor. Member AIAA.
axis wind turbine rotating by the means of the lift generatedon its blades.
The performance and the design of wind turbines are in-fluenced by natural factors such as the average speed of thewind and its possible change in direction, the gusts, and soforth. Unsteady aerodynamic phenomena, including dynamicstall, must also be taken into account during performanceevaluation.
Dynamic stall of oscillating airfoils is characterized by theshedding and passage over the upper surface of the airfoil ofa vortex-like disturbance and has been extensively studied.1Dynamic stall affects the aerodynamic characteristics of theairfoil, and must be accounted for during the performanceprediction of a vertical axis wind turbine. The evaluation ofthese performances is done using the double-multiple stream-tube model which was developed by Paraschivoiu et al.2~4
The purpose of this work is to introduce a new subroutinefor the prediction of dynamic stall using the indicial method.This method is based on the model developed by Beddoesand Leishman5"8 in the early 1980s, and is a new alternativeto the Gormont9 and MIT10 models already implemented inthe performance program. Typical cases are computed andthe results are compared with the other models ami withexperimental data obtained on a SANDIA 17-m wind turbine.
Double-Multiple Streamtube ModelAn aerodynamic model for a vertical axis wind turbine must
be able to calculate the performances of the turbine, and mustprovide a good prediction of the aerodynamic blade loads.Some models may predict quite accurately the mean loads,but not local aerodynamic loads. An example is the modeldeveloped by Templin,11 where the rotor is considered as anactuator disk enclosed in a single streamtube. This modelassumes a constant induced velocity through the swept volumeof the turbine, and all the calculations are based on airfoildata for a single Reynolds number. The model gives accept-able results for lightly loaded blades where the induced ve-locity is relatively uniform.
Templin's model has been improved by Strickland12 whosupposed the swept volume of the turbine to be a series ofadjacent aerodynamically independent streamtubes. This ap-proach is known as the Multiple Streamtube Model. Betterresults for a wider range of cases were obtained, but localblade loads are still not predicted properly.
The Double-Multiple Streamtube Model, used in this work,allows the prediction of good global and local results. Thismodel was developed by Paraschivoiu,2-4 and it assumes thata Darrieus rotor may be represented by a pair of actuatordisks in tandem according to Lapin's concept.13 This modelworks as a multiple streamtube model dividing the rotor cycleinto an upstream and a downstream half-cycle. Basically theblade element and momentum theories are employed for eachstreamtube. The normal and tangential force coefficients arecalculated using the indicial method for each streamtube.
Indicial MethodThe main feature of dynamic stall, when compared with
static stall, is the shedding of a vortex in the leading-edgeregion of the airfoil. After its formation the vortex startsmoving aft on the upper surface and induces a strong unsteadypressure and a significant increase of lift well in excess of thestatic values. When the vortex passes the trailing edge, theairfoil stalls and the lift may drop well below static valuesuntil reattachment of the flow. It is also noticeable that dy-namic stall leads to the creation of a large nose-down pitchingmoment.
Recent experimental and numerical research has been per-formed to quantify the problems related to dynamic stall andother unsteady airfoil behavior. For practical reasons, a num-ber of fairly sophisticated semiempirical models have beenalso developed. Most models were created for helicopter rotor
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analysis. In the dynamic stall regime, Gormont and MIT modelsusually depend on the reduction and resynthesis of aerody-namic test data from unsteady airfoil tests. The indicial methodis different; indicial functions are used to replace the completephenomenon by a summation of distinct effects. An indicialfunction is the response of a system to a disturbance which isapplied at an initial time and held constant thereafter. Ingeneral, an indicial function may take any mathematical form;for the development of the present model an exponentialfunctional form is assumed.
The model performs its calculations in three steps. First,the unsteady aerodynamic model must be able to representcorrectly the attached flow behavior. This is done by a po-tential flow computation which is the sum of a circulatorycomponent related to the change in the angle of attack andan impulsive component being the result of an induced ve-locity, perpendicular to the airfoil surface and generated bythe airfoil movement. Once the potential solution is known,some empirical correlations are inserted into the model tointroduce unsteady nonlinear viscous effects. In this secondstep, leading-edge and trailing-edge separation as well as tem-poral effects must be accounted for. The third step is to takeinto account the effect of the dynamic stall vortex. Forcesgenerated by the vortex allow the lift to keep on increasinglinearly with the angle of attack until the vortex leaves theairfoil. The vortex is also an obstacle on the surface of theairfoil, increasing the total drag. This third step also appliesflow reattachment conditions.
The original model presented by Beddoes and Leishmanuses a step function to represent the variation of the angle ofattack with time. Our subroutine uses an original ramp func-tion which starts from an at time step n and varies linearly toreach the value an + l at the time step n + 1 and finally staysconstant afterward. This ramp function gives good resultsbecause it yields a smoother fitting of the variation of a withtime than a regular step function for the same time step.
Results and DiscussionThe results presented were obtained using the CARDAAV
program3 implemented with the indicial method for wind speedsvarying from 4.0-20.0 m/s. Typical results were computedfor angular velocities of 38.7 and 50.6 rotations per minute.Comparisons are performed with experimental values andwithin available models. The SANDIA 17-m turbine, on whichresults were obtained, has two blades of section NACA 0015,the radius at equator is 8.368 m, and the swept area is 187.1m2.
Predicted and experimental values of the local normal forcecoefficients on a blade element rotating at equator level vslocal angle of attack are compared in Fig. 1. The indicial
Omega = 50.6 RPM,Xeq = 2.87
Omega = 38.7 RPM, Xeq = 2.6
2.5
1.0
-0.5
-2.0
Indicial modelMIT modelGormont modelExperiment
-30 -15 0Angle of attack (deg)
1 5 30
34 r
25
-2
Indicial modelGormont modelExperiment
-90 -45 0 45Azimuth (deg)
90
Fig. 2 Aerodynamic torque vs azimuthal angle at low tip speed ratio.
Omega = 50.6 RPM
100 r
75
I 50
25
>o°oo
• Indicial modela Gormont modelA MIT modelo Experiment
Fig. 1 Normal force coefficient vs angle of attack.
5 10 15 20 25Freestream velocity (m/s)
Fig. 3 Power output vs wind velocity.
method brings improvement in the representation of deep stall(a > 15 deg); it is especially noticeable around the maximumangle of attack. All models predict a maximum CN higherthan the experimental value, but the indicial method offersan improved prediction compared with the other two models.The best evaluation of the local angles of attack is given bythe indicial method. In the downstream region (a; < 0 deg),the MIT model offers the best representation, correspondingclosely to experiment; the indicial method and the Gormontmodel generate a small zone of dynamic stall which does notexist in reality. It seems that the indicial method offers a globalimprovement in the prediction of this coefficient.
Results of the torque were not available for the MIT model;the comparison is then reduced to the two remaining modelsand the experiment (see Fig. 2). At low tip speed ratio, whendynamic stall is present on a large scale, the indicial methodclearly gives better results than the Gormont model, but thereis a peak around 15 deg that does not correspond to reality.As the tip speed ratio grows (decreasing wind speed), theadvantage of the indicial method over the Gormont model isless evident.
It is observed in Fig. 3 that progression of power output islinear for low wind speeds and reaches an almost constantvalue at high wind speeds when there is dynamic stall occur-rence. The power output is the most important informationresulting from the performance program; accuracy is then vitalfor the validation of a new dynamic stall model. For low windvelocities (Vx < 8 m/s) all models give a quite good approx-imation, close to experimental values. For stronger winds (8m/s < VM < 12 m/s), the best results come from the indicialmethod; the MIT model has an overestimation problem atthese speeds. For high wind velocities (Vx > 12 m/s) theGormont model does not predict a constant power value,
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instead it keeps on increasing almost linearly. The two othermodels give good results. Finally it should be noted that MITand the indicial method calculate a transition between linearand constant values that is not as smooth as the real transition.
Comparison of 15-kWe Water-CooledArcjet Test Results at Two Different
Facilities
ConclusionsThe objective behind this work has been to improve the
global performance and local blade loads prediction. It hasbeen reached by implementing a new semiempirical model,the indicia! method, in the CARD A AV performance evalu-ation program. The results presented lead to the followingconclusions:
Improvements1) The indicial method offers a better representation of
dynamic stall, therefore the local blade loads prediction ismore accurate.
2) The indicial method gives the best overall power outputprediction and is at least as good as the other models for agiven wind velocity.
3) The improvements obtained with the indicial method donot imply longer computation time (total time for a windvelocity computation is less than 10 s CPU on IBM main-frame).
Limitations1) The indicial method calculates a small dynamic stall hys-
teresis loop in the downwind in contrast to the experimentalmeasurements. Only the MIT model represents this phenom-enon properly.
2) The maximum torque is overestimated at all tip speedratios (also true for the Gormont model).
References'Can, L. W., "Progress in Analysis and Prediction of Dynamic
Stall," Journal of Aircraft, Vol. 25, No. 1, 1988, pp. 6-17.2Paraschivoiu, I., "Aerodynamic Loads and Performance of the
Darrieus Rotor," Journal of Energy, Vol. 6, No. 6, 1982, pp. 406-412.
3Paraschivoiu, I., and Delclaux, F., -'Double Multiple StreamtubeModel with Recent Improvement," Journal of Energy, Vol. 7, No.3, 1983, pp. 250-255.
4Paraschivoiu, L, Delclaux, F., Fraunie, P., and Beguier, C,"Aerodynamic Analysis of the Darrieus Rotor Including SecondaryEffects," Journal of Energy, Vol. 7, No. 5, 1983, pp. 416-422.
5Beddoes, T. S., "Representation of Airfoil Behaviour," Vertica,Vol. 7, No. 2, 1983, pp. 183-197.
6Beddoes, T. S., "Practical Computation of Unsteady Lift," Ver-tica, Vol. 8, No. 1, 1984, pp. 55-71.
7Leishman, J. G., and Beddoes, T. S., "A Generalized Model forAirfoil Unsteady Aerodynamic Behaviour and Dynamic Stall Usingthe Indicial Method," Westland Helicopters, AHS 42nd Annual Forum,Washington, DC, June 2-4, 1986.
8Beddoes, T. S., and Leishman, J. G., "A Semi-Empirical Modelfor Dynamic Stall," Journal of American Helicopter Society, Vol. 34,No. 3, 1989.
9Gormont, R.-E., "A Mathematical Model of Unsteady Aerody-namics and Radial Flow for Application to Helicopter Rotors," U.S.Army Air Mobility Research & Development Lab., Vertol Division,Rept. DAAJO2-71-C-0045, May 1973.
10Noll, R. B., and Ham, N. D., "Dynamic Stall of Small WindSystems," Aerospace Systems Inc., Rockwell International Corp.Subcontract PF02535F, Feb. 1983.
nTempliri, R. J., "Aerodynamic Performance Theory for the NRCVertical Axis Wind Turbine," National Research Council of CanadaTR, LTR-LA-160, 1974.
12Strickland, J. H., "The Darrieus Turbine: A Performance Pre-diction Model Using Multiple Streamtubes," Sandia Labs., Rept.SAND 75-041, 1975.
13Lapin, E. E., "Theoretical Performance of Vertical Axis WindTurbines," ASME paper 75-WA/ENER-l, Houston, TX, 1975.
E. Tosti*BPD Difesa e Spazio, Colleferro, Italy
H. O. SchradetInstitut fur Raumfahrtsysteme,Universitat Stuttgart, Germany
andC. Petagnaij:
ESAIESTEC, Noordwijk, The Netherlands
Introduction
I N late 1986 the European Space Agency (ESA) started aprogram aimed at developing laboratory model, moderate-
power arc jet thrusters. The main objective of the programwas to obtain design guidelines for the development of flightmodel, 1-N-class arcjet thrusters. These engines are beingdeveloped as a possible advanced technology upgrade for theColumbus Man-Tended Free-Flyer Platform propulsion sys-tem.
A water-cooled, 1-N-class, laboratory model arcjet thrusterwas designed on the basis of test results obtained at otherlaboratories1-5 and featured a coaxial, segmented, water-cooledelectrode system. This feature enabled the evaluation of thethermal load distribution along the nozzle and variation ofthe anode configuration by means of proper selection of theelectrically connected segments. Moreover, the thruster wasdesigned to enable geometrical modification of the thrusterconfiguration by simple replacement of parts.
After parametric testing with different thruster geometries,the most promising thruster configuration, (based on per-formance) was duplicated and tested at a separate laboratory,in order to compare results from testing at two different fa-cilities. This technical note summarizes the results of thatcomparison.
Water-Cooled Arcjet DesignThe basic water-cooled arcjet design used in these tests is
shown in Fig. 1. The two engines, designated MOD-1 andMOD-1', respectively, are briefly described below. They weremade up of a stack of water-cooled coaxial, copper segments,which were insulated from each other, so that each could beused independently or in combination as the anode. The seg-ments of the stack were internally contoured to form theplenum chamber, constrictor, and nozzle. The stack designprovided flexibility for variations in the axial termination pointof the arc, geometry of the injectors, and geometry of thethroat and nozzle. Segment 5 contained the constrictor. Theengine configuration used for the tests was selected from thosestudied during a parametric performance investigation withdifferent thruster geometries arid is described below. In par-ticular, this parametric study showed that the segments mustbe connected properly to obtain a current-voltage character-
