American Institute of Aeronautics and Astronautics1

Examination of Fabri-Choking in a SimulatedAir Augmented Rocket

D. R. Gist1 T. J. Foster2 and D. J. DeTurris3

California Polytechnic State University, San Luis Obispo, CA, 93407

ABSTRACT

A simulated Air Augmented Rocket (AAR), operating as a mixer-ejector, was tested in a cold-flow, planar 2D configuration. The simulated primary rocket ejector was supplied by nitrogen at a maximum chamber stagnation pressure of 1690 psi, and maximum flow rate of 2.8 lbm/s. Secondary air was entrained directly from ambient, providing primary to secondary Total Pressure Ratios as high as 115. The primary ejector nozzle exit area was 0.75 in2, with an expansion ratio of 10, generating an exit Mach number of 3.92. An examination of the mixing duct flow field was conducted using pressure and temperature instrumentation, as well as direct flow visualization. The 2D mixer-ejector was observed to exhibit Fabri-choking at Total Pressure Ratios above 80. An analytic approximation based on 1D isentropic flow was generated to model theFabri-choke and saturated supersonic modes. The model included an empirical correction to reflect the 2D nature of the shock structure in the primary plume. The test results were in agreement with the corrected equations for Fabri-choking to within 12% experimental uncertainty. Experimental evidence showed that the transition from Fabri-choke to saturated mode occurs near the optimally expanded Pressure Ratio, as predicted by the model. The highest secondary entrainment (0.32 lbm/s) was obtained in the saturated supersonic mode. Flow visualization verified the cyclic 2D shock/expansion structure of the primary plume and the location of the Fabri-choke point. The visualization also supported measurement evidence of secondary flow unchoke, which resulted in flow field asymmetry.

NomenclatureA Area (ft2, in2)a Speed of Sound (ft/s)d Hydraulic Equivalent Diameter (ft)FR Force Ratio -Isp Specific Impulse (s)K Discharge Coefficient -Kexpand Plume Expansion Correction Factor -M Mach Number -N Number of Data Points in a Set -w Mass Flow Rate (lbm/s)P Pressure (lbf/in

2), (psia or psig)PRtotal Total Pressure Ratio = P0p/P0s -R Universal Gas Constant (lbf-ft/lbm°R)Re Reynolds NumberT Temperature (°F, °R)t Time (s)tb Primary Nozzle Base Thickness (in)V Velocity (ft/s)x Longitudinal Position From Mixing Plane (in)xi Measured Data Point -x Mean Value -Y Compressibility Coefficient -

1 Graduate Student, Aerospace Engineering Department, San Luis Obispo, AIAA Student Member2 Graduate Student, Aerospace Engineering Department, San Luis Obispo, AIAA Student Member3 Associate Professor, Aerospace Engineering Department, San Luis Obispo, AIAA Senior Member

43rd AIAA/ASME/SAE/ASEE Joint Propulsion Conference & Exhibit 8 - 11 July 2007, Cincinnati, OH

AIAA 2007-5392

Copyright © 2007 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.

American Institute of Aeronautics and Astronautics2

Γ Specific Heat Ratio group -

Φ Entrainment Ratio = PS ww -

γ Ratio of Specific Heats -ε Nozzle Expansion Ratio = Aexit/A

* -µ Dynamic Viscosity (slug/ft-s)ρ Density (slug/ft3)σ 1st Standard Deviation -

Subscripts0 Longitudinal Station (upstream source), Stagnation Conditions1 Longitudinal Station (mixing plane)2 Longitudinal Station (location of Fabri-choke)3 Longitudinal Station (mixing duct exit)i Ideal Conditionsp Primary Streams Secondary Stream

I. Introduction

An air-augmented rocket (AAR) is essentially a rocket firing within a duct, where secondary air from the atmosphere is entrained into the rocket exit plume. The goal of this research was to develop a relatively simple and inexpensive test environment for simulated 2D planar AAR testing, and to generate 1st order analytic correlations to better understand the experimental results. A cold-flow survey of an AAR operating as a mixer-ejector was performed with primary Mach numbers and primary to secondary Pressure Ratios beyond those previously tested. Also evaluated were the conditions required to establish Fabri-choke mode in a 2D configuration.

The main application for the AAR is in hypersonic airbreathing propulsion, and specifically in “combined cycle” propulsion systems, which incorporate multiple operational modes.1 In the context of hypersonic air-breathing vehicles, most combined cycle designs have included a ramjet/scramjet combined with either a rocket or a gas turbine (jet engine). The goal of recent hypersonic research projects like DARPA’s Force Application and Launch from Continental U.S. (FALCON) has been to develop a vehicle capable of operating in a variety of flight regimes from either a conventional takeoff (Mach 0) or an air launch (Mach 0.7) up through the hypersonic regime. In order to transition through these diverse conditions, an efficient propulsion system must be capable of operation through several distinct modes. One solution is a rocket based combined cycle (RBCC) system, which includes the air-augmented rocket, ejector-ramjet, pure ramjet, scramjet, and exo-atmospheric rocket.

The geometry and performance characteristics of the AAR are analogous to the better-known “mixer-ejector” or “induction pump.”2 In such devices, the slower moving secondary air is entrained into the mixing duct by the faster moving, lower pressure primary stream. The two streams experience some level of mixing, wherein the secondary flow is energized by the primary. The combined flow can then be ejected to create thrust. A typical mixer-ejector arrangement is shown in Figure 1. Note that the exit flow is not necessarily uniform or fully mixed.

Primary Flow (Rocket)

Secondary Flow (Air)

Secondary Flow (Air)

Mixing Duct

Primary Plume Boundary

Figure 1: Typical 2D Mixer Ejector Configuration

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The entrained secondary air provides thrust augmentation and a source of additional oxidizer which can be burned with fuel rich rocket exhaust. While air augmentation can provide significantly increased performance, aerodynamic blockage of the secondary by the primary rocket plume can cause substantial performance loss. During the initial phase of flight in the AAR mode, maximum thrust is desired to accelerate the vehicle into the more efficient ramjet mode. This scenario implies a high throttle setting, which means high chamber pressures and a large primary plume. Under some circumstances the secondary air flow is aerodynamically choked between the large primary plume and the mixing duct wall. This phenomenon, known as Fabri-choking, limits the amount of entrained secondary air and reduces the benefits of secondary entrainment. At the extreme case, the secondary flow can be severely blocked and even re-circulate back upstream; causing possible damage to the engine.

For these reasons it is imperative that a reliable prediction of the plume interaction is correlated to relevant experimental data. While a large body of analysis and experimental data exists for mixer-ejectors with subsonic and low supersonic primary ejectors,3,4,5,6,7, similar research into high Mach number systems is more limited. The primary to secondary Pressure Ratios that have been well characterized are also limited to lower values. Even more scarce is scalable research into flows where the primary and secondary gases have different composition and compressibility, or significantly different total temperatures. These types of flows must be better understood in order to implement rocket combustion gases as the primary ejector fluid for RBCC. Additionally, the overwhelming majority of experiments have utilized axis-symmetric configurations. Theoretical analysis has suggested that axis-symmetric configurations are more efficient than planar 2D arrangements8,9, but recent vehicle level trade studies have called for modular propulsion systems that can be easily produced and tailored for specific missions.10 The packing efficiency of 2D planar configurations is much better than axis-symmetric, thus the 2D configuration warrants renewed consideration. Accurate experiments investigating this plume interaction can quickly become prohibitively complex and expensive, one of the primary reasons for the lack of available research.

II. Analysis

A. Mixer-Ejector Theory

From an analytic point of view, there are two unique forms of the AAR or mixer-ejector. The “ejector” analysis is used when the secondary entrainment is unknown and must be calculated. This is the classical problem of an induction pump which motivates and entrains fluid from a supply reservoir. In the ejector analysis the secondary flow rate is calculated in order to satisfy the governing equations of an inviscid control volume. The “mixer” analysis is used when the secondary flow is forced into the mixing duct at a known rate. The simulated AAR used in this research will operate as an “ejector”, though reference to general “mixer-ejector” modeling will be used. Within the “ejector” configuration there exists three distinct modes depending on the conditions at the mixing duct inlet and exit.11,12,13

First, if the secondary flow and downstream pressures are high enough, (or conversely the primary pressure is low enough) the primary nozzle will be over-expanded and oblique shock waves will form. The shocks will eventually terminate in a normal shock and the two streams will become subsonic and fully mixed. The entrainment is thus dictated by the ambient pressure at the mixing duct exit plane. Mixing of the two streams takes place downstream of the normal shock, but the normal shock and full mixing usually occur only in mixing ducts of sufficient length and back pressure.

Secondly, if the mixer is too short or insufficient mixing is caused by some other mechanism often two separate streams will persist through the length of the mixing duct. This mode, often called the “mixed” mode, consists of a supersonic primary stream and subsonic secondary stream with a pronounced slip line in between.

Finally, for sufficiently low back pressure and low secondary pressure (or conversely very high primary pressure) the primary nozzle will be highly under-expanded. The primary flow will expand from the nozzle lip through a Prandtl-Meyer expansion. In this mode it is possible for the initially subsonic secondary stream to be aerodynamically contracted by the primary plume. This reduced flow area will cause the secondary to expand

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(accelerate) to a sonic throat and then become supersonic. This aerodynamic choking effect, seen in Figure 2, is known as “Fabri” choking after the French scientist who first published the concept.3 The two streams are then mixed in a combined supersonic flow. This is also known as the “supersonic” condition. In this mode the secondary entrainment is independent of downstream conditions and is instead only a function of primary to secondary Pressure Ratio, mixer-ejector geometry, and the fact that the flow has indeed choked.

Figure 2: Fabri Choke Ejector Operation Mode

B. Fabri-Choke Analysis and Empirical Plume CorrectionThe primary plume size, the secondary choking area, and the entrained mass flow rate for the Fabri Choke mode will be predicted using a quasi-1D control volume model which is based on the isentropic 1D assumption but with an empirical correction to reflect some of the higher order effects. The model originated with suggestions by engineers from Pratt & Whitney Rocketdyne and Aerojet (Personal Conversations, July to September, 2006).

The governing equations of motion for the expansion and compression waves which form in the primary plume reveal that waves reflect as like entities from a solid boundary or symmetry line, but are reflected as opposite waves from a pressure-matched free boundary (that is, a compression wave is reflected as an expansion wave).14 Applying this knowledge to the case of an under-expanded primary nozzle flow that expands to a known pressure-matched boundary yields a picture similar to the 2D depiction in Figure 3.

Expansion Fans

Compression Fan

Normal ShockFree Jet

Boundary

Oblique Shocks

Nozzle

Figure 3: Expansion and Recompression of Supersonic Primary Plume15

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A Prandtl-Meyer expansion fan emanates from the lip of the under-expanded nozzle, and is reflected as a like expansion fan by the symmetry line. When this reflected fan encounters the free boundary of the plume it is reflected as a family of compression waves that begin to coalesce. Both a strong normal shock and a reflected compression wave are formed by the coalesced waves. The compression wave is reflected again from the free boundary as a new expansion fan, and the process continues. The entropy change and total pressure loss across each compression wave is the dominant inviscid plume decay mechanism. This process, along with viscous dampening, eventually brings the plume flow to equilibrium with the surrounding gas. The results of these reflections are the cyclic exhaust plume structures, often called “barrel shocks” or “shock diamonds”.

Note that the first expansion and reflection cycle creates the largest cross-sectional plume area and a highly 2D flow region. The result is a pressure matched free-jet boundary with a significantly lower core plume pressure. The average plume pressure in the transverse plane (the approximate 1D pressure) is significantly lower than the boundary pressure. As compared to an ideal 1D analysis, the actual 2D plume, shown in Figure 4; is larger in area for a given boundary pressure.

Aideal Aactual 2D

PsPs

P = PsP < Ps

Aideal Aactual 2D

PsPs

P = PsP < Ps

IdealIsentropic

Actual

Figure 4: Ideal Isentropic versus Actual 2D Plume Area

To generate an empirical correction factor for the actual plume area, the basic mixer ejector parameters and geometry must first be defined. The geometry is planar 2D, with flow properties assumed constant in the z-direction as shown in Figure 5. Subscripts 0,1,2,3 are used to designate the upstream stagnation conditions, primary nozzle exit plane (beginning of mixer), minimum secondary flow area (Fabri choke point), and mixing duct exit plane, respectively. The subscripts p and s denote primary and secondary streams when they are distinct. A superscript * will be used to denote choked conditions at the primary nozzle throat and secondary aerodynamic throat.

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11 22 3300

Ms < 1

Mp > 1Primary Flow

Secondary Flow

Mixing Duct Wall

Aerodynamic Throat

Plume Boundary

Primary Nozzle

XY

Figure 5: Fabri Choked Mixer-Ejector Analysis Model

The mixing analysis begins with the primary and secondary streams fully defined at station 1 (the mixing plane), though information from the upstream station 0 is required to fully characterize each flow. The primary stream is defined by solving the 1D isentropic equations using the primary chamber conditions and the fixed primary nozzlegeometry. The primary mass flow rate, exit Mach number at station 1, and static pressure at station 1 can all be obtained from the chamber conditions (pressure and temperature) and nozzle geometry. The secondary stream is defined by the ambient air inlet conditions and the Fabri choke assumption.

The primary mass flow rate is determined by knowing the flow area at the nozzle throat. Then an iterative solver is used to determine the supersonic Mach number that satisfies Equation 1 for the known exit area ratio. With the exit Mach number and stagnation conditions known, the exit flow properties at station 1 can be obtained.

( ) 11

212

1

2

*

1

2

11

1

21−+

−++

=

γγγ

γ ppp

p MMA

A(1)

To characterize the secondary flow entering the mixing duct requires the assumption that the flow is choked downstream, and that the choking area can be determined. If the secondary is assumed to choke, then the static pressure at which it becomes sonic can be determined using ambient air pressure as the secondary stagnationpressure (P0s). Knowing the static pressure at which the secondary will choke, we can then assume a pressure matched boundary between the plume and secondary air, such that P2p = P2s and perform an isentropic expansion of the primary plume from the exit pressure to this external pressure. This expansion is calculated by solving for Mach number using the newly determined P2p. With the primary Mach number at station 2 known the primary flow area can be determined as shown in Equation 2.

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( )

1

21

1

2

1

2

0

12

11

2

0

*2

−

−

+

=−

−+

−

γ

γ

γγ

γγ

γγ

p

p

p

p

pp

P

P

P

P

AAi

(2)

Recall, however, that the natural expansion and recompression process will generate a plume area that is larger than the ideal 1D plume area predicted by Equation 2. At this point we introduce a correction factor to account for this larger plume. For now the correction will be treated as a parameter, which will later be compared with experimental results to create an empirical correction factor. Let Kexpand be this parameter. Based on an equation generated by engineers at Pratt & Whitney Rocketdyne we can write the corrected actual plume area as Equation 3.16

( ) bppandpp tAAKAAiactual

212exp12 −−+= (3)

A1p is the primary nozzle exit area, and A2pi is the ideal primary plume area at station 2 as predicted by Equation 2. This equation corrects the expanded portion of the plume from the exit area of the primary nozzle to the new cross-sectional area based on boundary pressure matching. In his original analysis, Fabri subtracted the base thickness of the primary nozzle lip (tb) from the available secondary flow area. The same concept is applied again here, but with more consequence, due to the large base area of the experimental nozzle. Essentially the base thickness term is an attempt to model the thickness of the wake shed at the nozzle base, without specifically modeling the mixing characteristics of the turbulent wake area.

Again, Kexpand is a parameter at this point and can be arbitrarily assigned. An array of Kexpand values will be analyzed and compared to experimental results to determine which value, if any, is appropriate as an empirical correction. Setting the Kexpand parameter will now allow for a determination of the secondary choke area. Subtracting the total duct area by the corrected plume area gives the cross sectional area of the choked secondary flow. This area is assumed to be evenly distributed to each side of the plume (symmetric).

Using the known stagnation conditions and the secondary throat area, the flow at the Fabri-choke point can be fully characterized. Using again isentropic equations, the secondary static temperature (T2s) and density (ρ2s) can be obtained. This temperature determines the local speed of sound and the continuity equation used to obtain the mass flow rate of the secondary stream.

The most common performance parameter used for mixer-ejector analyses is the Bypass Ratio or Entrainment Ratio (Φ), defined as the ratio of secondary to primary mass flow rate. The Entrainment Ratio is a measure of how well the primary mass flow is being used to entrain secondary flow. The Entrainment Ratio is a function of many case-specific variables, but it is convenient to simply plot the Entrainment Ratio versus the Total Pressure Ratio. The Total Pressure Ratio is the ratio of stagnation pressure in the primary to that of the secondary.

Using the correction factor Kexpand as a parameter we can generate several Entrainment Ratio versus Pressure Ratio curves to compare with the experimental results. These plots are often called performance curves, as the Entrainment Ratio provides a basic measure of mixer-ejector performance.4 Within the Fabri-choke regime, higher Pressure Ratios will produce a larger plume and thus a smaller aerodynamic throat for the secondary flow. If the secondary stagnation pressure is held constant (such is the case when the secondary inlets are exposed to ambient) the secondary mass flow rate, and thus the Entrainment Ratio, will decrease with increasing Total Pressure Ratio. Figure 6 shows the ideal isentropic Fabri-choke performance curve (Kexpand = 1.0) curve, as well as modified curves for higher values of Kexpand.

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En

trai

nm

ent R

atio

(Φ)

Kexpand = 1.0Kexpand = 1.5Kexpand = 2.0Saturated Case

OP

TIM

AL

EX

PA

NS

ION

Fabri Mode

Figure 6: Theoretical Fabri-Choke Performance Curves

Note that the effect of Kexpand is to decrease the amount of secondary entrainment at high Total Pressure Ratios. Varying values of Kexpand also changes the rate of Entrainment Ratio decrease, seen as a change in slope.

A special case of the Fabri-choke condition can occur when the physical secondary flow passage is of minimum area at the entrance to the mixing duct. At a moderate Total Pressure Ratio it is possible for the secondary stream to choke at this point (station 1) rather than downstream in the duct (station 2). This is known as the “saturated supersonic” mode, because all of the flow entering the mixing duct is now supersonic.11 Under the assumption of ideal isentropic conditions, this case corresponds to an optimally expanded primary nozzle and M1s = 1. In optimally expanded operation the primary exit pressure is matched with the secondary static pressure, and parallel streams exhaust into the mixing duct. The point of intersection of all the curves in Figure 6 is exactly this case. In real flows the saturated mode may persist on either side of the saturated “point”, creating a saturated “region.” The saturated mode has been shown to be the most efficient mode of operation for the mixer-ejector, corresponding to the highest secondary mass flow rate.5

In order to obtain a prediction of the performance curves in the saturated mode the secondary Mach number is assumed to be unity at the mixing plane (Station 1). Applying the choked assumption to the continuity equation for both the primary and secondary streams, and noting that the ratio of specific heats for nitrogen and air are approximately equal; yields Equation 4.

pp

ss

PA

PA

0*

01=Φ (4)

A performance curve can thus be added to account for the possibility of saturated supersonic operation as seen in Figure 6.

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III. Experimental Apparatus

The baseline design parameters were chosen to approximate a single 2D thruster from one of the proposed ISTAR RBCC engines. Early concepts were validated through several analytic and numeric investigations.17,18 The most restrictive requirement in the design process was to maintain the integrity of the hardware during later hot-fire experiments.

The apparatus used for these experiments can best be broken up into three basic elements. The first element is the primary thruster assembly, the second element is the Flow Control System (FCS), and the third element is the Data Acquisition System (DAS).

The primary thruster assembly consists of copper and stainless steel components to endure high heat loads, with aluminum incorporated in lower temperature areas. The size and shape of the assembly was dictated by the available gas supply and the baseline analyses conducted during previous design studies.17,18,19 The mixing duct sidewalls diverge at a 3° angle, to encourage a favorable supersonic pressure gradient. The design CAD model of the thruster assembly is shown in Figure 7.

Manifold (Steel/Aluminum)

Bottom Surface (Copper)

Sidewalls (x2)

(Aluminum)

Upper Surface (Glass)

Thrust Chamber (Copper)

Mixing Duct

Figure 7: 3D Model Depiction of Thruster Assembly Materials

Figure 7 calls out the materials used to fabricate the thruster assembly. A plate of high temperature tempered glass was used as the mixing duct upper surface to allow for direct flow visualization. Copper was used for the primary thrust chamber and mixing duct bottom surface to alleviate the high thermal loads during hot-fire testing. Stainless steel and aluminum were incorporated where the thermal loads are lower.

The Flow Control System (FCS) consists of the high pressure gas supply tanks; stainless steel feed lines, and actuated control valves. The control valves were remotely operated using a pneumatically powered and electronically commanded control system. Eight nitrogen supply tanks, each at 2600 psi, were used to simulate the primary rocket flow.

The Data Acquisition System (DAS) consists of all the hardware and software required to measure, record, and manage the experimental data. Signals from pressure transducers and thermocouples, as well as the power supplyvoltage, were routed to a National Instruments (NI) SCXI-1102 32-channel thermocouple amplifier for signal conditioning. The output signal from the terminal block was sent to a laptop computer via PCMCIA DAQ card-6036E. Labview® software was programmed to read the data channels from the amplifier as input, and display real-time pressures, temperatures, and instrument locations. Labview® recorded the data channels at 1000 Hz.

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Over 25 channels of data were required to properly monitor and document the tests. For pressure measurements,Omega PX302 milivolt type pressure transducers were used. For temperature measurements, omega Type K shielded thermocouples were used. The locations of all the instrumentation points as well as several significant dimensions of the thruster assembly are shown in Figure 8. In addition to the test data described above, a digital video camera was used to document the visible character of the plume.

11 2200

Mixing Duct Wall

Primary Nozzle

1 2 3 4 5 6 7 0inches

Static Pressure PortPitot Probe

Thermocouple

Figure 8: Instrument Locations in Thruster Assembly

IV. Formal Fabri-Choke Testing

After the experimental apparatus was demonstrated, and all the system issues had been resolved dutesting, the formal Fabri-choke testing was initiated. Tests were conducted at the AerospaDepartment’s Propulsion System Test Facility. A total of four formal test runs were completed. Teperformed with 6 high pressure Nitrogen cylinders that provided a maximum Total Pressure Ratioand IV were performed using 8 Nitrogen cylinders, providing a maximum Total Pressure Ratio owere performed for each configuration to ensure repeatability and to rearrange instrumentation.

A number of experimental parameters that were not directly measured were instead calculated fromquantities. The velocity of the flow in the secondary duct was calculated from the recorded pitotusing the Bernoulli equation for incompressible flow. Since the secondary flow likely experiencesabove 0.3, the Bernoulli equation is utilized beyond its incompressible limit, with the knowledgdensity can be determined from direct measurement of the local pressure and temperature, and thecalorically perfect gas.

The mass flow rate through the secondary ducts is obtained from continuity applied in the constanduct. The primary mass flow rate was calculated by two methods. The isentropic choked flow equawell as the corrected Bernoulli equation for flow through a Venturi nozzle, shown below as Equation

Man

ifo

ld

3.164

1.00

0.625

0.25

33

All dimensions in inches

ring preliminary ce Engineering sts I and II were of 95. Tests III f 115. Two tests

other measured -static pressures Mach numbers

e that the actual assumption of a

t area secondary tion was used as 5.

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( )*0

* 2 pppp PPYKAw −= ρ (5)

The * symbol indicates conditions at the primary nozzle throat. The factor Y is an empirical correction for compressibility, and K is a correction for the discharge efficiency of the nozzle. Both values are obtained from charted empirical values.20 The compressibility coefficient is dependent on the pressure drop (P0p – P*p), and the discharge coefficient is dependent on the local Reynolds Number.

The values obtained from Equation 5 agree well with the isentropic choked flow values obtained from continuity. Equation 5 results were used to calculate experimental mixer-ejector performance, using the definition of Entrainment Ratio.

An error source and propagation analysis showed that an experimental uncertainty of 12% would be sufficient to reflect the expected error in mass flow rates and Entrainment Ratio. Errors in other important resultant quantities were very small (< 2%). All pressure measurements presented are precise to less than 0.1% and accurate to less than 1% after mitigation of systematic error.

V. Experimental Results

Of the four tests performed, the higher Total Pressure Ratios achieved in Test III and IV were used to investigate performance in the Fabri choke mode, and behavior of the entrained secondary flow. Tests I and II concentrated on primary plume diagnostics and fundamental flow field structure. Data from Tests III and IV will be correlated to the theoretical models. Pressure data from the mixing duct surfaces, taken from Tests I and II, will be examined and compared with video documentation.

Planar 2-D mixer-ejector geometry was implemented in this research. Care was taken to maintain symmetry during fabrication of the apparatus hardware. Unfortunately, during preliminary testing it became clear that the right and left secondary flows were not precisely symmetric. At the start of the test run the secondary mass flow rates are very similar and both increase in a similar fashion. At a Pressure Ratio of approximately 94 (t = 7.5sec), the mass flow rates diverge asymmetrically. The left side mass flow continues to increase, but the right side begins to decrease.Figure 9 shows that the Mach numbers are initially subsonic and increasing. At about 7.5 seconds, the right side Mach number declines, while the left side increases towards sonic.

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0.80

0.90

1.00

1.10

1.20

-2 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30

Time (sec)

Mac

h N

um

ber

M1s_LeftM1s_RightPR_total/100

Figure 9: Test III Secondary Duct Mach Numbers

The most likely explanation is that both right and left secondary flows are initially aerodynamically choked downstream in the mixing duct; this is the result of Fabri-choking. As the primary plume compresses with reduced Pressure Ratio, the left duct Mach number increases to accommodate the growing aerodynamic throat of the secondary flow. The right secondary duct flow, however, behaves as if it has unchoked and no longer achieves a sonic throat. Initially, while the Pressure Ratio is high, the right and left secondary flows both experience a favorable pressure gradient moving downstream towards the sonic throat. At a critical point, however, the right side flow abruptly transitions and is no longer choked downstream by the primary plume.

Previous research has found that the re-circulation zone emanating from the nozzle base is more predominant as the secondary flow rate increases.21 The implication to the current research is that the shed wake from the nozzle base may have become dominant in the right secondary flow and caused enough viscous disruption to unchoke the right side flow. It has been observed that the left side secondary remains choked much further into the experiment, as predicted using the inviscid theoretical model.

A. Experimental Mixer-Ejector Performance

In evaluating the experimental mixer-ejector performance, it is important to note that the independent axis plots Total Pressure Ratio from low to high, but during each actual run the Pressure Ratio decreases from an initially high value. A reasonably high degree of repeatability among the formal tests existed, with a maximum 14% relative error between Entrainment Ratios from tests III and IV (just outside the experimental uncertainty).

Figure 10 shows the experimental performance curves from Test III. The marked data points are only a subset of the recorded test data. The number of plotted points was chosen to give a clear representative trend of the recorded values. Also shown in Figure 10 are the analytic curves for the saturated supersonic and Fabri-choke modes, with several values of the correction, Kexpand. The theoretical curves provide a physical basis for interpreting the experimental results.

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Figure 10: Test III Experimental and Theoretical Performance Curves

The left side data agrees well with the saturated prediction in the range near the optimally expanded Pressure Ratio. As the saturated model predicts, the Entrainment Ratio near the optimally expanded Pressure Ratio is dependent only on the physical geometry of the mixer. At a point beyond the optimally expanded Pressure Ratio, the experimental results begin to diverge from the saturated prediction. This indicates operation in the Fabri-choke mode, where the secondary entrainment is now limited by the expanded primary plume. At the highest Total Pressure Ratios both right and left secondary flows appear to be Fabri-choked. Here, while the flow field is symmetric, the Fabri model prediction is valid. As observed before, the two mass flow rates diverge abruptly at a Pressure Ratio near 95. The significantly lower performance curve of the right side highlights the inefficiency of the unchoked secondary flow. Less mass flow is convected through the subsonic secondary, even though the flow passage has widened.

The agreement of the Test III results and the theoretical model shown in Figure 10, however, suggests that a value of Kexpand near 1.5 provides a close prediction of the Fabri-choked performance. The results from Test IV also fall nearest to the Kexpand = 1.5 line.

As the data in Figure 10 shows, the left secondary experimental performance curves agree very well with the saturated supersonic prediction near the optimal expansion ratio. By examination of additional parameters we can attain a better understanding of the different mixer-ejector modes exhibited during the experiments, as wells as the transitions between them. Examining again the left secondary Mach number plot in Figure 11 shows that the secondary flow in the fixed duct section is initially subsonic at high Total Pressure Ratios. The dotted lines denote the region where the secondary Mach number is nearly constant and equal to one.

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Ind

uct

ion

Rat

io (Φ) Kexpand = 1.0

Kexpand = 1.5Kexpand = 2.0

Saturated Case

Test III LeftTest III Right

Fabri ModeO

PTIM

AL

EX

PAN

SIO

N

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Time (sec)

Mac

h N

um

ber

M1s_LeftPR_total/100

Figure 11: Test III Secondary Duct Mach Numbers (extended)

Recall that the Mach numbers plotted above are calculated in the fixed area secondary duct (station 0). The smaller the aerodynamic throat caused by Fabri-choking, the lower the Mach number in the fixed duct area must be to satisfy continuity. As the Pressure Ratio is reduced the aerodynamic throat grows closer to the fixed duct area. Thus, the Mach number increases towards unity. At a Pressure Ratio near the optimally expanded value (72), the secondary flow enters the saturated regime, and the secondary duct becomes the choke point.

The Mach number in the duct is observed to remain relatively constant from the optimally expanded pressure ratio of 72 to about 55 (t = 17 to 31sec). Physically, after the flow had transitioned out of the Fabri-choke regime the only way it can remain sonic is if the choke point exists in the fixed area duct (the physical location of minimum area).

As Figure 11 suggests, the saturated mode can only persist for so long and eventually, as the primary flow rate decreases, the entrainment will not be great enough to support sonic flow. At this point the experimental performance curves show a reduction in efficiency. Figure 12 shows the left side performance curves for Test III, extended into the lower Pressure Ratios. The dotted lines denote the same region highlighted in Figure 11.

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0.060.080.100.120.140.160.180.200.220.240.260.280.300.320.340.360.380.40

20 30 40 50 60 70 80 90 100 110 120

Total Pressure Ratio

En

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ent

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Saturated CaseTest III Left

Figure 12: Test III Extended Performance Curves

Figure 12, shows that the best agreement with the saturated prediction occurs while the secondary flow enters the mixing duct at a Mach number close to unity. Recall the mass flow rate also shows maximum secondary entrainment occurring in this range. This agreement shows that Fabri-choke mode has been demonstrated in the planar 2D configuration. The entrainment efficiency in this regime has been shown to fall off as the primary plume size increases, as predicted. For the left side secondary, it has also been shown that the saturated supersonic regime provides the highest entrainment. Unfortunately, these conclusions come with a caveat. The trends could not be duplicated in the right side flow, because of an asymmetry mechanism that is not yet well understood.

B. Plume Flow Field Diagnostics

The pressure ports located along the centerline of the lower mixing duct surface allowed for direct measurement of the internal plume flow field. Using these pressures and the wall surface pressures mentioned previously, together with the video documentation, a complete picture of the primary plume structure was formulated. Centerline pressure profiles and still shots from the video documentation show the mixing duct flow field and shock structure is consistent with the structure described in the analysis section.

A typical centerline pressure profile, taken from Test II, is shown in Figure 13. The figure shows the propagation of pressure phenomenon through the duration of the test run. Each line corresponds to a pressure tap, the location of which is measured from the mixing plane (station 1).

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0.0

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Centerline 1.5 in.Centerline 2.5 in.Centerline 3.5 in.Centerline 4.5 in.Centerline 6.5 in.

Figure 13: Test II Centerline Surface Pressures

The most striking features of Figure 13 are the steady occurrence of pressure spikes which appear to oscillate through time. The oscillations are damped towards the end of the run. Each large spike corresponds to a strong shock wave passing over a particular pressure tap. By noting the location of each tap, one can visualize a single wave beginning downstream, and propagating upstream through time.

The video documentation provides visualization of this shock structure. What is captured by the video is the condensation which occurs due to decreasing pressure and temperature as the gas expands. Figure 14 shows a still shot from the raw video and an enhanced image with wave lines superimposed. The image was recorded from Test II at (t = 65sec). Expansion waves are shown in yellow and compression waves in orange. These wave lines are purely qualitative and represent the author’s best judgment. The exact locations and number of wave lines cannot be determined from this imagery.

The cyclic shock structure suggested in Figure 13 is supported by the video frame in Figure 14. As the primary stagnation pressure falls towards the end of the test runs, the wavelength of the wave cycles shrinks and the number of cycles within the mixing duct increases.

Referenced From Station 1

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Figure 14: Video Frame and Superimposed Shock Structure from Test II at t = 65 sec

As a final confirmation of the shock structure, consider the core plume pressure compared to the boundary pressure. The secondary flow can be considered to behave similar to 1D and inviscid flow such that the pressure measured along the mixing duct wall is essentially equal to the plume boundary pressure. By examining the centerline surface pressures (internal plume) and the mixer wall surface pressures (plume boundary), one can verify the basic concept used to make the plume size correction in the theoretical model. Specifically, the pressure on the plume boundary is higher than in the plume core when the plume is at its maximum size. Figure 15 shows the time history of the wall pressures at 3 in. as well as the centerline pressures at 2.5 in. and 3.5 in. This region was chosen because it captures the plane of first maximum expansion near the beginning of the test. The maximum expansion passes over the 3 in. wall ports at approximately 5 seconds.

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0.0

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Centerline 2.5 in.Centerline 3.5 in.Left Wall 3 in.Right Wall 3 in.

Figure 15: Internal and External Plume Pressure Comparison

The important thing to note about Figure 15 is that the external pressures at 3.0 in. are significantly higher than either of the internal pressures at 2.5 and 3.5 inches during the beginning of the test (no transducer was available at 3.0 in.). The internal pressure does not overtake the external pressure until the first re-compression wave front passes over the 3.5 in. centerline pressure port, which occurs near 10 seconds. The pressure rise corresponds with the strong oblique shock movement shown in Figure 13. This result is consistent with the expected wave reflection and propagation structure. The pressure evidence supports the existence of a 2D plume which is over-expanded at its core, and larger than the 1D isentropic equations would predict. This larger plume restricts the secondary flow in the Fabri-choke mode.

VI. Conclusion

A survey was conducted of a cold-flow simulated AAR operating as a mixer-ejector. A first order inviscid model was created to predict the mixer-ejector performance in both the Fabri-choke and saturated supersonic modes. Empirical corrections to the isentropic Fabri-choke model were compared with experimental results.

It was found that the 2D planar mixer ejector configuration operating at high Total Pressure Ratio and high primary Mach number exhibits a Fabri-choke mode similar to axis-symmetric mixer-ejectors previously investigated. At high Total Pressure Ratios the primary plume expands further and limits the secondary entrainment more than the isentropic equations predict. An empirical correction, which is non-isentropic yet still inviscid, was used to model the larger plume and better predict the performance curve in the Fabri-choke regime. The current research suggests a value of 1.5 for the correction factor Kexpand. The saturated supersonic condition can be used to estimate mixer-ejector performance for supersonic primary flows near the optimally expanded pressure ratio. The saturated mode is the most efficient mode of operation, producing the highest secondary mass flow entrainment.

The 2D planar mixer-ejector was susceptible to flow asymmetry and it was seen that the two secondary flows werecapable of operating in different modes (subsonic, mixed, saturated, Fabri-choke) simultaneously. Video documentation of the visible plume showed cases of asymmetry. In addition, the condensation in the mixing duct captured on the video provides a qualitative observation of the plume shock structure. The video visualization,

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paired with the mixing duct pressures, shows a cyclic shock structure that moves through the duct and reduces in wavelength as the primary supply pressure is reduced.

References

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14. Zucrow, M.J. & Hoffman, J.D., Gas Dynamics, Wiley Publishing, New York, 1976

15. Aerospaceweb, Shock Diamonds and Mach Discs. Website: http://www.aerospaceweb.org/ , 2006

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18. Hafeman, D. “Fabri-Choking Analysis of an Ejector” Senior Project, Cal Poly Aerospace Engineering Dept., San Luis Obispo, CA., 2003

19. Foster, T. “Air Augmented Rocket Plume Modeling”, Design Project in support of Masters Thesis, Cal Poly Aerospace Engineering Dept., San Luis Obispo, CA., 2004

20. DeTurris, D. & Tso, J. Experimental Aerothermodynamics, Lab Manual for Aero 304 course, January 2006

21. Gujarathi, A., Li, D., Anderson, W., & Sankaran, V. “CFD Modeling of a Ducted Rocket Combined with a Fuel-Rich Primary Thruster”, 42nd Joint Propulsion Conference. AIAA 4577, July 2006