40th AIAA/ASME/SAE/ASEE Joint Propulsion Conference and Exhibit11 - 14 July 2004, Fort Lauderdale, Florida

AIAA 2004-3547

This material i

Validation of Stream Thrust Probes for Direct-ConnectTurbine Engine Testing*

Robert Hiers† and Heather MacKinnon‡

Aerospace Testing Alliance, Arnold Engineering Development Center, Arnold AFB, Tennessee

A technique for determining the thrust of a turbine engine during static testing is dis-cussed. The technique relies upon inferring the local stream thrust from pitot pressure mea-surements. The local stream thrust can be spatially integrated to determine the total thrust.The influences of probe geometry and size on the thermochemistry of the probe flow field areaddressed. The probe has a unique aerodynamic shape that automatically compensates forflow direction. This paper compares the fundamentals of both the standard scale forcemethod and the “probe-based stream thrust” method of determining gross thrust. This paperalso describes the validation of the probe technique against standard thrust stand data to beacquired during direct-connect static testing in Propulsion Development Test Cell J-1 at theU.S. Air Force Arnold Engineering Development Center (AEDC).

I. Introduction

A simplified turbine engine direct-connect statictest configuration is shown schematically in Fig. 1.

With the control volume indicated, the measuredscale force (Fs) is given by

(1)

By convention1 the gross thrust is defined as theexit plane stream thrust, which is simply the firstterm in Eq. (1), where stream thrust (σ) is definedas (from Ref. 2)

(2)

Equations (1) and (2) provide the basis for the probe-based stream thrust measurement concept. The differencebetween the exit and inlet stream thrusts is the thrust of the system.

The probe-based stream thrust technique involves using gasdynamic probes to measure the pitot pressure distribu-tion at the exit of the propulsion device and gasdynamic theory to relate the pitot pressure to the stream thrust. Probe-based thrust measurement techniques are attractive for several reasons. Whereas turbine engine and rocket enginethrust stands are expensive to maintain and calibrat, probe-based techniques should be less costly. Also, probe-basedtechniques can be used to separate the thrust contributions of various engine components.In a turbine engine test, forexample, the contributions of the augmentor and the nozzle can be determined separately. While the facility thruststand can determine only the net force (also called the scale force—i.e., thrust minus drag) acting on the vehicle, the

* The research reported herein was performed by the Arnold Engineering Development Center (AEDC), Air Force MaterielCommand. Work and analysis for this research were performed by personnel of Aerospace Testing Alliance, the operations,maintenance, information management, and support contractor for AEDC. Further reproduction is authorized to satisfy needs ofthe U. S. Government.† Senior Member, AIAA.‡ Member, AIAA.

Fs p p∞–( ) ρu2+[ ]exitAexit=

p p∞–( ) ρu2+[ ]inletAinlet–

σ p ρu2+=

Aexit (p + ρu2)exitAinlet (p + ρu2)inlet

Fs

(Ainlet − Aexit)p∞

p∞

Bellmouth

Labyrinth Seal

Figure 1. Simplified Schematic of Turbine Engine Static Test

1American Institute of Aeronautics and Astronautics

s declared a work of the U.S. Government and is not subject to copyright protection in the United States.

probe-based technique can determine the thrust alone. The ability to determine the “installed” thrust of this type ofpropulsion device is a unique benefit of the probe-based technique.

In a previous paper,3 a derivation was given to determine the local stream thrust from a measured pitot pressure.Ideal, perfect gas behavior was assumed to illustrate the technique. A subsequent paper4 addressed the influence ofprobe size on the thermochemistry of the probe flow field. The pressure sensed by the probe was shown to be sensi-tive to the size of the probe; larger probes result in higher pitot pressure, and smaller probes produce lower pressuresthat approach the frozen chemistry limit. A computational fluid dynamics (CFD) model that incorporated chemicalkinetics was used to compute the flow field about various-sized probes to determine the size limits for flow condi-tions typical of a storable propellant rocket. The aerodynamic design of stream thrust probes was addressed in Ref. 5.A probe shape that automatically compensates for flow angle was determined.

II. Theoretical Development of Probe-Based Stream Thrust for an Ideal, Perfect Gasand the Effect of Thermochemistry

The theoretical development in Ref. 3 assumed ideal gas behavior (i.e., constant specific heats). In this section, theeffect of variable specific heats is addressed computationally. As stated in Eq. (2), σ = P + ρu2.

Multiplying and dividing Eq. (2) by the pitot pressure (P02) yields

(3)

The term in the brackets is termed the pitot pressure thrust function, f. In Ref. 3 the pitot pressure thrust function isderived for perfect gas flows as a function of Mach number and the ratio of specific heats (γ). The function is given by

(4)

or

(5)

for supersonic or subsonic flows, respectively. (See the appendix for the mathematical details of this derivation.) Thisfunction is shown in Fig. 2 over a range of Mach num-bers and ratios of specific heat.

Note that the function is relatively insensitive toMach number—particularly at higher Mach num-bers—and is also fairly insensitive to the ratio of spe-cific heat. Reference 3 also dealt with the uncertaintyin the pitot pressure thrust function attributable touncertainty in Mach number. Reference 4 addressedthe uncertainty in the pitot pressure thrust functionattributable to thermochemical effects. In other words,even if the freestream Mach number and composition(and thus γ) are known precisely, how the pitot pres-sure thrust function is influenced by the thermochemi-cal processes in the shock and stagnation regionsbehind the shock remains unknown. Since the stream

σ P02=P ρu2

+P02

------------------- P02f=

f γ M 1≥,( ) 2

γ 1+( )M2------------------------

γγ 1–-----------

2γM2 γ 1–( )–γ 1+

------------------------------------

1γ 1–-----------

γM2 1+( )=

f γ M 1<,( ) 1 γ 1–2

-----------M2+

γ–γ 1–-----------

γM2 1+( )=

Figure 2. Pitot Pressure Thrust Function as a Function ofMach Number and Ratio of Specific Heats

1.000

1.025

1.050

1.075

1.100

1.125

1.150

1.175

1.200

1.225

1.250

1.275

Mach Number

Pito

t Pre

ssur

e F

unct

ion,

f

1.15

1.25

1.35

Ratio of Specific Heats

1 2 3 4 50 6 7 8 9 10

2American Institute of Aeronautics and Astronautics

thrust is to be inferred from the pitot pressure, the authors’ fundamental concern is with the influence of thermochem-istry on the measured pitot pressure.

Figure 3 illustrates the shock/stagnation processes that occur infront of the pitot probe. Also indicated on the figure is a typical staticpressure distribution on the stagnation streamline.

The composition is assumed frozen for the shock jump processsince shocks are typically only a few mean free paths thick. If thechemical composition is assumed to be in equilibrium for the stagna-tion process in front of the pitot probe, then the pitot pressure istermed the “equilibrium” pitot pressure. If the composition isassumed frozen behind the shock, the pitot pressure is termed the“frozen” pitot pressure. The equilibrium pitot pressure is typicallysomewhat higher than the frozen pitot pressure. For large probes, theshock stands a large distance away from the probe tip, allowing moretime for reactions to proceed between the shock and theprobe tip. Therefore, the pressure sensed by a sufficientlylarge probe might be expected to approach the equilibriumpitot pressure. As the probe size is decreased, the reactionswill not have time to proceed to equilibrium, and kineticrates become important. As the size is decreased further, afrozen plateau is reached where there is insufficient resi-dence time behind the shock for chemical reactions to takeplace between the shock and the probe.

As the probe size is decreased, low Reynolds numberviscous effects become important.6 If the probe size isdecreased even further, to the point that the probe diame-ter is on the order of the mean free path, rarefaction effectscan become important.7-9 This dependence of pitot pres-sure on probe size is indicated schematically in Fig. 4.

If the intent is to infer the freestream stream thrust(which is, of course, independent of probe size) from thepitot pressure measurement, then the uncertainties attributable to thermochemistry must be accounted for. Ideally, onewould choose a probe size sufficiently large or small to produce the equilibrium or the frozen limit. However, it wasshown in Ref. 4 that, because of irreversibilities generated behind the shock, the equilibrium limit cannot be reached.In addition, a small probe typically is desirable in order to provide high spatial resolution data. Therefore, it isexpected that, generally, an investigator will desire a probe small enough to produce the frozen limit. If it is knownthat the probe size is small enough to produce the frozen limit pitot pressure in a given reacting flow field, then oneuncertainty associated with inferring the stream thrust from the pitot pressure is removed. An optimum probe sizemay be selected by computing the chemically reacting flow field about the probe tip for varying tip sizes. On theother hand, if the frozen and equilibrium pitot pressure limits are essentially indistinguishable, then the pitot pressurewill be insensitive to probe size.

III. Aerodynamic Considerations

Determining the local stream thrust (a vector quantity) from a measured pitot pressure (a scalar quantity) requireseither knowledge of the flow direction or a probe shape that compensates for flow direction. This compensation ide-ally would make the measured pressure directly proportional to the component of momentum along the probe axis. Aderivation of the flow angle sensitivity required to resolve this component of momentum is given in Ref. 5. Thedesired distribution is given by

(6)PαP02-------- 1 γM2cos2α+

1 γM2+

----------------------------------=

Figure 3. Schematic of Probe Shock FlowField

Figure 4. General Dependence of Pitot Pressure onProbe Size

Freestream

Pre

ssur

e

StagnationRegion

Shock

P02

/P02

, equ

il

ViscousandRarefactionEffects

FrozenLimit

KineticEffects

EquilibriumLimit

Probe Diameter

1.0

3American Institute of Aeronautics and Astronautics

where α is the flow angle, Pα is the measured pressure, and P02 is the pitot pressure that would be measured at zeroflow angle. A parabolic nose shape was found to agree with the desired distribution to within 0.5 percent to flowangles up to 15 deg. Probes with this nose shape will be designed and fabricated for testing at Arnold EngineeringDevelopment Center (AEDC).

IV. Facility Gross Thrust Measurement

Referring to Fig. 1, the momentum equation for the indicated control volume yields

(7)

where Fs is the measured scale force. In Eq. (7), one-dimensional flow is assumed, but that is not a general limitation.Gross thrust (FG) is defined as

(8)

and Net thrust (FN) is defined as

(9)

where RAM is the ram drag. Both the scale force and stream thrust procedures first determine the gross thrust andthen adjust the gross thrust by the computed ram drag to determine the net thrust. Since the ram drag will be com-puted in precisely the same manner for both procedures, the fundamental concern is with the gross thrust comparisonof the two methods. For completeness, note that

(10)

where is the inlet mass flow and V0 is the simulated freestream velocity.Rearranging Eq. (7) as

(11)

and comparing with Eq. (8) makes it obvious that the gross thrust is also given by

(12)

Equation (12) is, in fact, the relationship used in the AEDC Turbine Engine Test Analysis Standard (TETAS). TheTETAS procedure does incorporate a boundary-layer correction in the inlet momentum term. However, for thepresent purposes, Eq. (12) is used to represent the “Scale Force Method” fordetermining gross thrust. The scale force is measured using the thrust stand, andthe inlet mass flow, velocity, and pressure/area terms are determined using pres-sure rakes and taps in the inlet bellmouth.

V. High-Temperature Probe Design

The main body of the stream thrust probes is made of 304 stainless steel. How-ever, the tip typically is made of copper or nickel, because of their high conduc-tivity. The tip was machined to match the ideal parabolic shape determined byCFD and theoretical analysis. Figure 5 shows a closeup view of the stream thrustprobes installed in a standard rake.

The probes are internally cooled with high-pressure water. The cooling wateris supplied to a water manifold with lengthwise grooves that carry water to and

Fs pinletAinlet pexitAexit p∞ Ainlet Aexit–( )––+ m· V( )exit m· V( )inlet–=

FG m· V( )exit Aexit pexit p∞–( )+=

FN FG RAM–=

RAM m· inletV0=

m· inlet

m· V( )exit Aexit pexit p∞–( ) FS m· V( )inlet pinlet p∞–( )+ + Ainlet=+

FG FS m· V( )inlet pinlet p∞–( )Ainlet+ +=

Figure 5. Closeup View of StreamThrust Probes

CopperParabolicNose

StreamThrustProbe

4American Institute of Aeronautics and Astronautics

from each probe. The water travels up the probethrough a small line, encircles the probe tip, and isfed back down the opposite side of the probe via awater return line. The cooling scheme allows theprobes to be exposed to very high-temperature envi-ronments. Internal cooling of the probes eliminatesthe need for expensive materials for probe fabrica-tion, thereby greatly reducing the manufacturingcost. The probes have previously been cooled inde-pendently of the rake, but designs are under way tointegrate the cooling scheme. Figure 6 shows a cut-away view of the probe to illustrate the coolingscheme.

VI. Turbine Engine Testing at the Arnold Engineering Development Center

The probe-based thrust measurement system has been validated with a variety of engines, including a scramjetengine, a rocket engine,10 and an afterburning turbine engine.11 The final test planned to demonstrate this methodwill be that of a large-scale turbine engine in Propulsion Development Test Cell J-1 of the Engine Test Facility (ETF)at the AEDC. The test is planned for late summer of this year (2004).

A. J-1 Facility DescriptionTest Cell J-1 is 16 ft in diameter and 65 ft long. This test cell is used primarily for direct-connect performance and

stability testing of large, airbreathing propulsion systems, although free-jet testing can be accommodated. Airflowrates up to 500, 700, and 1,400 lb/sec can be provided through the heated air inlet to the test cell at 120, 85, and 35psia, respectively. This engine inlet air can be conditioned from −65 to 750°F, depending on airflow rate and supplypressure. Using the heated air inlet source, the facility can provide true simulated flight conditions over the entireflight envelope of most turbojet engines, up to Mach 3.2 and 80,000 ft, in either a free-jet or adirect-connect test con-figuration. A schematic of the test facility is shown in Fig. 7.

Through the refrigerated air inlet, airflow rates up to 1300 lb/sec can be provided at plenum pressures up to 13.0psia. High-accuracy measurement systems for multicomponent thrust (axial, vertical, and side forces), pressure, flowrates, temperature, and speeds are available in the J-1 test complex for the accurate determination of engineperformance. The test cell inlet airflow measuring system consists of five fixed and four remotely operated venturis.High-response data acquisition systems are available for the assessment of engine stability in a dynamic inflowenvironment.

Figure 6. Cutaway of Stream Thrust Probe Cooling Scheme

Figure 7. Simple Schematic of J-1 Test Cell

Drawing Not to Scale

Water In

Water Out

Flow MeasurementVenturis (5 Fixed,4 Remote Actuated)

Inlet Air FiltersRemoved (BasketsLeft as Flow Conditioner)

Overhead Thrust Standw/In-Place Calibrator 6-ft-diam

ExhausterDiffuser

8-ft-diam InletPlenum w/50-MeshFOD Screen

AugmentorTV Camera

16 ft diam

40-ft Hatch Opening

83 in.

65 ft

60 in.

FLOW

CL

5American Institute of Aeronautics and Astronautics

TraversingTable

Rake

Probes

B. Test SetupThe military augmented turbofan engine will be tested at various power

settings, including maximum afterburning. Exit plane temperatures at maxi-mum afterburning are expected to be approximately 3800°F. The 15 pitotpressure probes and one Mach flow angularity probe will be mounted insidea water-cooled rake. Figure 8 shows a typical turbine engine setup.

The rake movement will be controlled by a traversing table that isdesigned to move at various speeds and stop in order to obtain sufficientdata. The pressures will be measured via a cooled, soft-mounted pressuremodule installed inside the test cell. Posttest analysis will include calibrationfactor applications and extensive uncertainty and sensitivity analyses. Theseresults will then be incorporated into a final, probe-based stream thrust valueand compared to the axial thrust values measured on the facility’s thruststand.

VII. Summary

Pitot pressure will be measured at the exit plane of an afterburning turbineengine installed in the J-1 test cell. The pressure will be measured via a suiteof water-cooled probes installed in a rake. The stream thrust will then beinferred via an integral equation. Following posttest analysis, the finalprobe-based thrust value will be compared to the facility axial stream thrustmeasurement. The probe-based method has been developed through CFDand theoretical analysis and modeling, studies of aerodynamics and thermochemical effects, and sensitivity analyses.The probe-based thrust measurement method has been validated for a scramjet, a rocket, and a turbine engine. Theprobe-based thrust for each of these tests was within 2 percent of the facility-measured thrust. This comparison errorlimit is expected for this test.

References

1Kimzey, W. F., Wehofer, S., and Covert, E. E., “Gas Turbine Engine Performance Determination,” in Thrust andDrag: Its Prediction and Verification, from the series "Progress in Astronautics and Aeronautics," Vol. 98, E. E.Covert, Editor. American Institute of Aeronautics and Astronautics, New York, 1985.

2Bore, C. L., “Some Contributions to Propulsions Theory – The Stream Force Theorem and Applications toPropulsion,” Aeronautical Journal, April 1993, pp. 138-144.

3Hiers, R. S., and Pruitt, D. W., “Determination of Thrust from Pitot Pressure Measurements,” AIAA 2001-3314,38th AIAA/ASME/SAE/ASEE Joint Propulsion Conference and Exhibit, Salt Lake City, UT, 8-11 July 2001.

4Hiers, R. S. III, and Lankford, D. W., “Design of Stream Thrust Probes in Reacting Flows.” AIAA-2002-3735,38th AIAA/ASME/SAE/ASEE Joint Propulsion Conference and Exhibit, Indianapolis, IN, 7-10 July 2002.

5Hiers, R. S. III, and Sirbaugh, J. R., “The Aerodynamics of Stream Thrust Probes,” AIAA 2003-1092, 41st

Aerospace Sciences Meeting and Exhibit, Reno, NV, 6-9 January 2003.6Chue, S. H., “Pressure Probes for Fluid Measurement,” Progress in Aerospace Sciences, Vol. 16, No. 2 , 1975, pp.

147-223. 7Daum, F. L., Shang, J. S., and Elliott, G. A., “Impact Pressure Behavior in Rarefied Hypersonic Flow,” AIAA

Journal, Vol. 3, No. 8, August, 1965, pp. 1546-1548.8Kannenberg, K. C., and Boyd, I. D., “Monte Carlo Computation of Rarefied Supersonic Flow into a Pitot Probe,”

AIAA Journal, Vol. 34, No. 1, January 1996, pp. 83-88.9Stephenson, W. B., “Use of the Pitot Tube in Very Low Density Flows.” AEDC-TR-81-11, Arnold Air Force

Base, TN, October 1981.10Hiers, R. S., III, and Hiers, R. S. Jr., “Validation of Stream Thrust Probes for Rocket Engine Thrust

Measurement,” AIAA-2003-5183, 39th AIAA/ASME/SAE/ASEE Joint Propulsion Conference and Exhibit,Huntsville, AL, 20-23 July 2003.

11Hiers, R. S., III, MacKinnon, H. M., and Whitney, R., “Validation of Stream Thrust Probes for Turbine EngineThrust Measurement,” AIAA-2004-1297, 42nd AIAA Aerospace Sciences Meeting and Exhibit, Reno, NV, 5-8January 2004.

Figure 8. Test Setup of J85 ProbeStream Thrust Test

6American Institute of Aeronautics and Astronautics

APPENDIX: The Theoretical Development for an Ideal Perfect Gas

The vacuum thrust (Fv) of a jet propulsion device, assuming ideal, one-dimensional flow, can be shown to be

(A-1)

where ue, Pe, and Ae are the exit plane velocity, static pressure, and area, and is the mass flow. Since the mass flowmay be written as

(A-2)

where ρe is the exit plane density, Equation (A-1) becomes

(A-3)

where the term within the parentheses is referred to as the stream thrust. Applying the ideal gas law yields

(A-4)

where R is the specific gas constant and Te is the exit plane static temperature. Multiplying and dividing the first termby the ratio of specific heats (γ) yields

(A-5)

Recognizing that the exit plane speed of sound (ae) is given by

(A-6)

and the exit Mach number (Me) by

(A-7)

Equation (A-5) may be written as

(A-8)

Equation (A-8) could be used to infer thrust from an exit plane static pressure measurement. However, it is obviousthat this relation is sensitive to errors in both γ and Me—both quantities that would have to be approximated either bycalculations or by other measurements—in addition to measurement errors in Pe. The thrust varies essentially linearlywith γ and goes approximately as the square of the Mach number. Therefore, small errors in either γ or Me would con-tribute large errors to the inferred thrust.

However, if one measures pitot pressure (P02) rather than the static pressure, Eq. (A-8) may be written as

(A-9)

Fv m· ue PeAe+=

m·

m· ρeueAe=

Fv ρeu2e Pe+( )Ae=

FvPe

RTe---------u2

e Pe+⎝ ⎠⎛ ⎞Ae=

Fv γu2

e

γRTe------------ 1+

⎝ ⎠⎜ ⎟⎛ ⎞

PeAe=

ae γRTe=

Meueae-----=

Fv γM2e 1+( )PeAe=

Fv γM2e 1+( )

PeP02--------P02Ae=

7American Institute of Aeronautics and Astronautics

where (assuming now a constant γ) the ratio of the static pressure to the pitot pressure is given by

(A-10)

for supersonic (Me ≥ 1) conditions and

(A-11)

for subsonic (Me < 1) flow.Equation (A-9) may now be written as

(A-12)

where

(A-13)

or

(A-14)

for supersonic or subsonic flows, respectively. The function f is termed the pitot pressure thrust function.The thrust measured on a static test stand (F) under nonvacuum conditions would be given by

(A-15)

where P∞ is the ambient atmospheric pressure.The relations above all assume uniform, one-dimensional flow. If instead one assumse axisymmetric (radially

varying) flow, Eq. (A-15) becomes

(A-16)

where Re is the nozzle exit radius.Note that the function f(γ,Me) given by Eqs. (A-13) and (A-14) exhibits an absolute maximum at Me = 1, which is

given by

(A-17)

PeP02-------- 2

γ 1+( )M2e

------------------------

γγ 1–----------- 2γM2

e γ 1–( )–

γ 1+-----------------------------------

1γ 1–-----------

=

PeP02-------- 1 γ 1–

2-----------M2

e+

γ–γ 1–-----------

=

Fv P02Aef γ Me,( )=

f γ Me 1≥,( ) 2γ 1+( )M2

e

------------------------

γγ 1–----------- 2γM2

e γ 1–( )–

γ 1+-----------------------------------

1γ 1–-----------

γM2e

1+( )=

f γ Me 1≥,( ) 1 γ 1–2

-----------M2e

+

γ–γ 1–-----------

γM2e

1+( )=

F P02Aef γ Me,( ) P∞Ae–=

Fv 2π P02f γ Me,( )r rd P∞Ae–

0

Re

∫=

f γ Me, 1=( ) 2γ 1+-----------⎝ ⎠⎛ ⎞

γγ 1–-----------

γ 1+( )=

8American Institute of Aeronautics and Astronautics

The high Mach number asymptote of the function f(γ,Me) is given by

(A-18)

The low Mach number limit is given by

(A-19)

f γ Me ∞→,( ) 2γ 1–-----------⎝ ⎠⎛ ⎞

γ 1+γ 1–-----------

γ

γγ 1–-----------

=

fγ Me 0=( ), 1=

9American Institute of Aeronautics and Astronautics