Analytical Method for Prediction of Suction Performance of

Analytical Method for Prediction of Suction Performance of Ejector-Jet*

Kouichiro TANI,1) Susumu HASEGAWA,1) Shuichi UEDA,1) Takeshi KANDA,1) and Harunori NAGATA2)

1)Space Transportation Mission Directorate, Japan Aerospace Exploration Agency, Miyagi 981–1525, Japan2)Department of Mechanical and Intelligent System Engineering, Hokkaido University, Hokkaido 060–0808, Japan

To reduce the cost of space transportation, air-breathing engines are considered to be candidates for propulsion. How-ever, to cover a wide range of flight speeds, the propulsion system has to operate in various modes to be efficient underincoming atmospheric-air conditions. The Japan Aerospace Exploration Agency is proposing a rocket-based combinedcycle engine for operation under various condition, an ejector-jet mode being adopted for the low-speed regime. The suc-tion performance ejector-jets has long been studied experimentally and numerically at JAXA, and little success has beenachieved in explaining the deterioration of suction performance with high-temperature gas or light gas such as helium. Inthe present study, based on former models, a simple one-dimensional model was introduced incorporating the mixingeffects of the primary flow (rocket flow) and secondary flow (induced air flow). The results were compared using severalexperimental and numerical data to check the plausibility of the model. It was found that if greater mixing occurs, suctionperformance is degraded, explaining the actual phenomena of the experiments.

Key Words: Air-breathing Engine, Combined Cycle, Ejector-jet

Nomenclature

A: areaCp: specific heat at constant pressureE: energy

Gr: incompressible growth rate of mixing layerGf: compressible growth rate of mixing layerH: heightK: momentumM: Mach numberP: total pressureR: gas constantT: total temperatureW: width_m: mass flowp: static pressurer: velocity ratios: density ratiot: static temperatureu: velocityw: molecular weight

� ¼ T1w2

T2w1

!12

¢: mixing parameter£: specific heat ratio®: suction rateµ: density

Subscripts1: primary flow (rocket flow)2: secondary flow (induced air flow)

b: rearward facing basec: choke condition or convectivei: initial condition (entrance condition)m: mixing layert: terminal conditionx: intermediate condition

1. Introduction

To reduce the cost of space transportation, engine effi-ciency is an important aspect. However, conventional rocketengines have come close to optimal performance, and thenext step in the evolution of space propulsion has to incorpo-rate a fundamentally more efficient cycle to enhance the ef-fective specific impulse (eIsp). The combined cycle engine,which is a hybrid rocket-jet engine, has been proposed forthis purpose and extensively studied. At the JAXA KakudaSpace Propulsion Center, rocket-base combined cycle en-gines (RBCC) have been studied since the turn of the cen-tury.1) Since all space transporters have to accelerate fromzero to orbital speed, the engine has to operate in a widerange of flight speeds. The rocket can inherently achieve thisrequirement but with limited eIsp. On the other hand, air-breathing engines can produce thrust with a much highereIsp, but their range of speed in which high performancecan be achieved is rather limited, depending on the operationcycle. JAXA’s RBCC uses both a rocket and several types ofair-breathing cycles to maintain higher performance through-out the entire ascent flight (Fig. 1). In the supersonic or hy-personic region, the RBCC operates a ram/scramjet combus-tion cycle, while in the subsonic or transonic region, whereram pressure is not sufficient, it uses a rocket as the mainthrust generator. To enhance the specific impulse even insuch a low-speed region, the air induced into the RBCC flowduct by the rocket exhaust is used as an oxidizer for extra

© 2015 The Japan Society for Aeronautical and Space Sciences+Received 29 August 2014; final revision received 16 January 2015;accepted for publication 9 February 2015.

Trans. Japan Soc. Aero. Space Sci.Vol. 58, No. 4, pp. 228–236, 2015

228

fuel. The operation cycle is designated as the “ejector-jet”mode. Ram and scramjet engines had been studied at Kakudafor several years2,3) prior to the RBCC research. However,the ejector-jet had not been well explored at Kakuda.

To study the ejector-jet and ejector effect, several tests us-ing small-scale models with room temperature gas as rocketexhaust have been carried out.4,5) Also large-scale enginetests with hydrogen/oxygen rockets have been conducted.6)

The results showed that the choked air flow (secondary flow)can be established with nitrogen gas at room temperature. Onthe other hand, with the very same geometrical configuration,the choked condition is hard to establish when using lightermolecular weight gas (light gas), such as helium or high-tem-perature gas. Since the amount of the intake-air is directly re-lated to the performance of the ejector-jet, it is imperative tostudy the reason for the degradation of suction performancein order to design an RBCC engine with high performance.In 2009, to study the suction performance under low subson-ic conditions, experiments with a hybrid sounding rocket,CAMUI,7) were carried out8) in cooperation with HokkaidoUniversity and the Hokkaido Aerospace Science and Tech-nology Incubation Center. A cylindrical duct was attachedaround the nozzle section of the CAMUI to form an ejectorduct. Comparing the small-scale tests with nitrogen gas, nodegradation of suction performance was observed in the CA-MUI experiments. The results further confused the under-standing of the ejector mechanism.

Along with the experiments, several models of ejectorflow field have been examined. Aoki et al.9) proposed a sim-ple momentum transfer model based on the Fabri model.10,11)

However, that method does not explain the difference of suc-tion performance caused by the difference in the nature of theprimary gas. The present study aims to enhance this methodby considering the effect of mixing rocket gas (primary flow)and air flow (secondary gas). In short, Aoki’s method as-sumes the pressure of the choked secondary flow at the ter-minal point where the momentum exchange of two flowsis completed. The present method assumes higher pressuredue to the mixing of two flows at the terminal point. Analysiswith the present method was carried out to compare the ex-perimental results and to see if mixing is the reason for thedegradation of suction performance.

2. Analytical Model

Aoki et al.9) proposed a momentum transfer model whichconsiders the exchange of momentum between the primaryand secondary flow at the contact surface. It is assumed that,through the contact surface, the momentum which equals theproduct of the pressure and contact area is exchanged, where-as no other properties (mass flow or energy) remain constantfor each flow. At the end of the interaction, the pressure oftwo flows matches, and the secondary flow reaches itschoked condition (i.e., sonic condition). The suction per-formance (initial condition of the secondary flow) is itera-tively determined, so that pressure matching and choked con-dition are simultaneously achieved. The model is applicableif the secondary flow is in the subsonic condition, and so istrue for the present model described below.

In the present study, it is assumed that primary and sec-ondary flows form a mixing layer. At some distance fromthe initial contact point, primary, secondary and tertiary(mixed) flows complete an exchange of mass, momentumand energy, and reach a uniform pressure condition. To cal-culate the flow properties, momentum exchange and masstransfer to the mixing layer should be simultaneously consid-ered, but this would require an intricate calculation process.

To avoid complexity, in the present method, two processes(momentum transfer and mixing) are separately modeled andare assumed to occur in two steps. In the first step, only mo-mentum transfer is considered. In the second step, startingfrom the momentum-transferred conditions, the mixing proc-ess of two flows is considered. The present procedure is out-lined in Figs. 2 and 3.

The primary aim of the present analysis was to study thedegradation of suction performance due to the pressure risecaused by mixing. Neither physical mechanism of mixingnor the mixing rate were sufficiently modeled in this proce-dure. Instead, a single mixing parameter was introduced,and the relation between the parameter and the suction per-formance was calculated in the analysis. Here, the mixing pa-rameter ¢ is defined as the ratio of half of the mixing layerthickness (Hm) to the smaller duct height (H1 or H2) of theprimary or secondary flow.

� ¼ Hm

MINðH1; H2Þ; ð1Þ

where MINð Þ is a function that gives the smaller numberfrom arguments. At the beginning of the procedure, the in-coming secondary flow condition (i.e., the Mach number,M2i) is assumed. The momentum exchange is then evaluatedto obtain the intermediate state of the two flows. UnlikeAoki’s method, the secondary flow does not necessarilyreach the choked condition and only pressure matching ofthe two flows is imposed. After the momentum exchange,the mixing process is calculated from the intermediate state.In this process, an arbitrary Hm(¢) is given and the threelayers of flow field are equalized in pressure at the terminalpoint. If a match is established, it is considered that the as-sumed incoming secondary flow condition is the solution

Fig. 1. Operation modes of the RBCC engine.

Trans. Japan Soc. Aero. Space Sci., Vol. 58, No. 4, 2015

229©2015 JSASS

for the given ¢. If the mixing procedure does not yield anequalized pressure state, the secondary flow condition is iter-atively changed, and the solution is sought.

For the detailed mathematical procedure of each model,the unknowns and equations are summarized in the follow-ing subsections. In general, mass, momentum and energyof the flow ( _m; K and E, respectively) are evaluated by thefollowing equations in the subsections.

_m ¼ �uA ð2Þ

K ¼ pAþ _mu ð3Þ

E ¼ _m Cp � t þ u2

2

!; ð4Þ

where Cp is specific heat at constant pressure.

2.1. Momentum transfer processAssuming that the initial condition of the secondary flow

is known, five parameters for each primary and secondaryflow (�; p; t; u and A) at the intermediate condition areobtained in the process. Each flow satisfies the mass,momentum and energy conservation from the initial stateto the intermediate state. Additionally, the ideal gas law,p ¼ �Rt, is adopted (four equations for each flow). Formomentum conservation, it is assumed that the pressureforce on the contact surface transfers momentum from oneflow to the other;

A1iðp1i þ �1iu21iÞ � pc�A ¼ A1xðp1x þ �1xu

21xÞ; ð5Þ

where subscripts 1 and 2 denote the primary and secondaryflow, respectively. Also note that the subscript i indicatesan initial (incoming) condition, and x indicates an intermedi-ate state. pc is the pressure along the boundary of the twolayers and �A is the variance of area between A1i and A1x.In this process, it is assumed that a flow with higher pressureexpands to the lower pressure stream. Thus, if p1i > p2i, pri-mary flow expands, and pc�A is positive. If otherwise, sec-ondary flow expands and pc�A becomes negative. In all,eight equations for 10 parameters are given. However, sincethe pressure matches at the intermediate state and overall areaat the intermediate state is also known, two more relationscan be incorporated. Thus, all quantities can be obtained.2.2. Mixing process

The mixing model assumes that the mixing layer developswith the same heightHm into both the primary and secondaryflows. The mass of the primary flow and that of the sec-ondary flow that go into the mixing layer, _m1m and _m2m, areobtained from the initial state of the flow (i.e., �1iu1iHmW

and �2iu2iHmW where W is the width of flow field), whichis constant for both primary and secondary flow passagefor the sake of simplicity. The mass conservation of the mix-ing layer is written as follows:

_m1 þ _m2 ¼ _mm

¼ �mumAm

ð6Þ

Here, subscript m denotes the mixing layer condition. As forthe properties in the mixing layer, the unknown parametersare five; namely, �m; pm; tm; um and Am. The flows out ofthe mixing layer (i.e., primary and secondary flows that areleft unmixed) are assumed to change isentropically. Thesetwo flows satisfy mass conservation and ideal gas law (twoequations for each flow).

�1iu1iA1 � _m1m ¼ �1tu1tA1t ð7Þp1t ¼ �1tR1t1t; ð8Þ

where subscript t denotes the terminal condition. If flow isassumed to be in an isentropic condition, static pressureand temperature can be written in isentropic relations (twoequations):

p1t ¼ p1x

�2þ ð�1 � 1ÞM2

1x

2þ ð�1 � 1ÞM21t

� �1�1�1

ð9Þ

Start

Hm given

Assume M2i

End

P1x=P2x?

Assume ΔA

No

Yes

Calculate momentum transferred model

Calculate mixing model

P1t=P2t = Pm?No

Yes

Fig. 3. Analytical procedure.

ΔA

inp1x

p2x

out

pm

= Hm/min(H1,H2)=p ΔA

Momentum transfer model Mixing model

Momentumtransferred

Mixingparamter

p

p

Secondary flow (air)

Primary flow (rocket)

p1t

p2t

c

c

cHm

Hm

= β

m1m

m2m

H1

H2

Intermediate

p2xp1x = p2t

p1t

= pm=

Fig. 2. Analysis model.


230©2015 JSASS

t1t ¼ t1x

�2þ ð�1 � 1ÞM2

1x

2þ ð�1 � 1ÞM21t

�ð10Þ

By adding the Mach number relation, M ¼ u= �Rt� �1=2,

five equations can be obtained for the flow out of the mixinglayer, which has six unknowns (�t; pt; tt; ut; At and Mt). Fur-thermore, the sum of momentum and energy of primary, sec-ondary and tertiary flows are conserved (two equations):

K1i þK2i ¼ K1t þKm þK2t ð11ÞE1i þ E2i ¼ E1t þ Em þ E2t ð12Þ

For the flow inside the mixing layer, the ideal gas relationis imposed. Thus, 14 equations for 17 unknowns are ob-tained. However, since the pressure matches at the terminalpoint, two pressure values can be neglected and unknownsare reduced to 15.

pm ¼ p1t ¼ p2t ð13ÞIn this analysis, for the sake of simplicity, the entire flow

area is constant from initial to terminal points, giving a 15thequation:

ðH1 þH2ÞW ¼ A1i þ A2i ¼ A1t þ Am þ A2t ð14ÞThus, there are 15 equations for 15 unknowns. If the inter-

mediate state is given, terminal values can be solved.

3. Experiments and CFD Analysis

Figure 4 shows a typical diagram of the measurement sys-tem. Wall pressures were measured by various pressuretransducers (300 kPa, 700 kPa FS) which were electricallyscanned. The signal was then A/D converted and stored ina computer. The total pressure of the primary gas was ob-tained with a sensor of 5MPa FS, separately from measure-ment of the wall pressures. To synchronize the time of thetwo systems, the starting signal was recorded in both systemsand matching of the time lines was manually established bysignal pattern comparison. The suction performance was es-timated based on the wall pressure at the throat of the modelassuming the isentropic process in the inlet section. Prior tothe experiments, the measurement system was calibrated,and its end-to-end uncertainty was confirmed to be less than0.5% of full scale.

To investigate the growth of a mixing layer, a gas sam-pling was conducted. The gas was sampled at several loca-tions downstream of the nozzle exit, with nitrogen as the pri-mary flow. A gas chromatograph, with an accuracy of 0.2 vol%, was utilized for analyzing the flow composition. The mix-ing layer thickness was evaluated based on the distribution ofthe nitrogen. The uncertainty of the location of sampling was� 0.5 mm for each probe.

Computational fluid dynamics (CFD) analysis of the ejec-tor jet was also carried out to validate the present method.The Reynolds averaged Navier-Stokes equation was solvedon a structured grid. The in-house code is based on the con-trol volume method, with the Spalart-Allmaras turbulencemodel.12) The computational domain was 2-dimensionaland had a simple rectangular shape like the one shown inFig. 2. The length of the ejector duct was 19 times the ductheight of the flow passage (H1 þH2 in Fig. 2), four timesthat upstream and 15 times that downstream from the pointwhere the mixing initiated. The total amount of nodes insidethe duct was about 57,000.

4. Results

In some experiments, the suction performance varied bychanging the chemical or thermal condition of the primaryflow. In general, the higher the temperature of the primarygas, or the lighter the molecular weight of the species for pri-mary flow, the more the suction performance was degraded.This phenomenon cannot be explained solely by the momen-tum transfer model. In this section, the present analysismethod is applied to actual experimental conditions and itis confirmed whether degradation can be explained by con-sidering mixing.

Hereafter, suction rate, ®, is defined by the ratio of themass flow:

� ¼ _m

_mc

; ð15Þ

where _m is the mass flow of the secondary flow, and _mc isalso the mass of secondary flow under choked condition atthe entrance (i.e M2i ¼ 1). By definition, ® varies from 0to 1.4.1. Effect of mixing

Before applying actual experimental conditions, thepresent procedure was applied to a virtual simple geometryejector jet model in order to check the general tendency ofthe mixing effect.

The duct had a constant rectangular section, and the ratioof the primary and secondary flows was set to 2 to 1. TheMach number of the primary flow was 3.0 and the propertyof pure nitrogen gas was assumed. The total pressure of theprimary flow was 2.0MPa. As for the secondary flow, the to-tal pressure and temperature were 101.3 kPa and 300K (at-mospheric condition), respectively. Figure 5 shows the effectof the temperature of the primary flow on suction perfor-mance. The vertical axis denotes the mixing parameter, ¢.As the temperature increased, the suction performance of

PC

Manualstartingsignal

Amp A/DScanner

Computer

N2

Bottle

Electricvalve

sensors

A/D data logger

Rocketblock

Amp

(He)(Ar)

300 kPa

5 MPasensor

Gas sampler

M

Pitot tube

Wall pressure

Amp

sensors700 kPa

Fig. 4. Measurement diagram.


231©2015 JSASS

the flow was drastically reduced. At 1,000K or less, the dropin suction performance was virtually non-existent. The bro-ken line shows the results of the CFD. The CFD also showedno loss in suction performance at temperatures less than1,000K, whereas at 2,000 or 3,000K, deterioration in per-formance occurred. By comparing the CFD and the presentanalysis, ¢ of 20 to 45% gives a match.

The effect of molecular weight was also surveyed with thepresent procedure using the same geometry. The total tem-perature and pressure were 2,000K and 1.2MPa, respec-tively. The Mach number was 3.0. Atmospheric conditionswere assumed for the secondary flow. As can be seen inFig. 6, the suction performance decreased with the increaseof ¢. The defect was greater with the gas of lighter molecularweight. Helium showed significant sensitivities to ¢, but ni-trogen and argon did not show such different tendencies,though argon is much heavier than nitrogen. The additionalcomparison with total temperature at 300K showed that ni-trogen and argon do not have any sensitivities to ¢, while he-lium showed the a deterioration of performance with higher¢. The higher sensitivity of helium will be reexamined in sec-tion 4.3.

By these evaluations, it was concluded that suction per-formance is affected by the difference in natures of the twoflows. When the natures of the two flows widely differ, thesuction performance becomes quite sensitive to ¢, resultingin large degradation of performance with a small amountof mixing.4.2. The comparison with experiments of scale models

The present procedure was also examined by comparisonwith the experimental results. In all of the experiments withsmall engine models conducted at JAXA, nitrogen gas atroom temperature was used for the primary flow. Also,helium was used to check the effect of gas species.

Figure 7 shows a simple schematic of the models tested. Arocket nozzle is located at the mid-point of the model. Theprimary flow is accelerated through the conical nozzle. Inthe actual configuration, however, there was a rearward face(base area) around the nozzle exit, which the present modelcannot explicitly incorporate. In reality, Ad, the downstreamduct area, should be

Ad ¼ A1 þ A2 þ Ab; ð16Þwhere Ab is the base area, and A1 and A2 are the upstreamprimary and secondary flow areas, respectively. In thepresent analysis, the base area was neglected and the geom-etry was modified as follows:

Ad ¼ A1 þ A2 ð17ÞFrom the results of the previous section, mixing is the key

phenomena that affects suction performance. The base area(i.e., both its size and shape) contributes to form a secondaryflow that alters the mixing process. A larger base area delaysthe formation of the mixing layer (small ¢) and a complexbase geometry enhances mixing (large ¢). In the present anal-ysis, the value of ¢ is the effect produced by the base area.

Figure 8 shows the model geometry and suction perfor-mance using a light gas for the rocket. The total pressureof the primary gas was 1.6MPa and the Mach number atthe exit of the conical nozzle was estimated to be 2.3 fromthe area ratio. Broken lines denote the experimental data.In the experiments, the secondary flow achieved a chokedcondition using nitrogen gas as the primary flow. However,a 5% loss in suction performance was observed with heliumas the primary flow. If 15% of ¢ is assumed, the present pro-cedure can reproduce the loss.

At JAXA, a 3-m-long rocket-based combined cycle engine(RBCC, designated as E36)) has been tested in the ramjet en-gine test facility (RJTF). A configuration of the model is pro-vided in Fig. 9.

0.0 0.2 0.4 0.6 0.8 1.00.80

0.85

0.90

0.95

1.00

β

μ2,000 K (0.981)

3,000 K(0.905)

CFD

1,200 K1,500 K2,000 K2,500 K3,000 K

Fig. 5. Effect of temperature of primary flow.

0.0 0.2 0.4 0.6 0.8 1.00.5

0.6

0.7

0.8

0.9

1.0

β

μ

He

H2O

N2

Ar

Fig. 6. Effect of molecular weight of primary flow.

A d

A

AA 2

1

b

Induced flow

Rocket

Inlet Isolator Combustor

Fig. 7. Simple schematic of models.


232©2015 JSASS

The model consists of a double-staged ramp inlet, an iso-lator that enfolds the rockets and an expanding combustor. Ithas several ram fuel injection holes in the combustor section,as well as a pair of rockets with a gas (oxygen and hydrogen)propellant. By changing the rockets and ram fuel injectionmethod, the model can be operated in the ejector-jet, ram

and scramjet modes. As for the ejector-jet mode, the chamberpressure of the rocket was 3MPa. To compare the results, aone-fifth-scale model with nitrogen gas rocket flow was alsotested under static condition at sea level.13) The scale modeleasily achieved choked condition with nitrogen gas injectedat 2 or 3MPa. However, E3 could not achieve the chokedcondition at the same pressure level. With the present proce-dure, there was relatively little degradation on suction per-formance with nitrogen gas, whereas the loss of suctionwas obtained with a hydrogen and oxygen mixture, as is in-dicated in Fig. 9. It should be noted that the physical quanti-ties of the combustion gas were estimated by chemical equi-librium with applications (CEA).14) The experimentalsuction performance is indicated by broken lines in the figurefor 2 and 3MPa cases. The loss in suction performance co-incides with the condition in which 20% of ¢ is assumed.

To check the suction performance with low-speed incom-ing flow, an ejector-jet experiment was conducted with amodified CAMUI sounding rocket in 2009.8) CAMUI9) is ahybrid propellant rocket using polyethylene as a fuel andliquid oxygen as an oxidizer. In that experiment, a shroudduct was mounted around the rocket nozzle, thus formingan ejector flow passage (see Fig. 10). In this case, the shapeof the ejector jet was cylindrical. Since the present analysisassumes one-dimensional preservation of the total amountof mass, momentum and energy, inherently, the shape ofthe flow geometry should not affect the results of the analy-sis. For pre-checking the actual flight test, a 1/3-scale modelwas prepared and tested in a low subsonic wind tunnel.Again, the rocket gas was simulated using nitrogen gas. Ad-ditionally, a ground test having an actual rocket motor with ashrouded duct was carried out. For comparison with these

19022 8

Nozzle angle 20Throat φ2Exit φ3

20 7

N2

N2

(Ar,He)

(Ar, He)10

Hth = 9,8,7

10 Hth

Dimensions in mm

0.0 0.1 0.2 0.3 0.4 0.50.85

0.90

0.95

1.00

β

μ

0.78 MPa (0.942)

0.87 MPa (0.965)

Experiments

He 0.78 MPaHe 0.87 MPa

Fig. 8. Comparison to small-scale model with He injection.

11401390

2700

5.4 14150

100

3000

200

20

0

180

280

220

80A

A

Throat φ26Exit φ70

110

Section A-A

105Dimensions in mm

0.0 0.2 0.4 0.60.6

0.7

0.8

0.9

1.0

β

μ 1.96 MPa (0.785)

2.93 MPa (0.723)

Experiments

H2O 2.93 MPa

H2O 1.96 MPa

Fig. 9. Comparison to E3 models.

0φ9

0

φ102

φ17

φ38

φ76

φ69

φ102

φ90

φ 114

71 160

190

279

641

CAMUI nozzle

Ejector duct

Dimensions in mm

0.0 0.2 0.4 0.60.6

0.7

0.8

0.9

1.0

βμ

2.0 MPa2.5 MPa

Fig. 10. Comparison to CAMUI models.


233©2015 JSASS

tests, physical quantities of gas were estimated by CEA. Un-like the E3 cases, the difference of rocket gas had no effect onsuction performance. Even a hot gas produced maximumsuction (i.e., choked flow in the CAMUI configuration).On the other hand, the present procedure resulted in a lossof suction as ¢ becomes greater with hot gas. This result sug-gests that mixing in the actual model was poor.4.3. Effects of total temperature and molecular weight

on the mixing processAs was observed in the previous sections, the differences

in nature of the primary and secondary gases affected suctionperformance. In this section, two properties of the gas, totaltemperature and molecular weight, were investigated analyti-cally for their effect on mixing parameter, ¢, and the pressurerise due to mixing.

As for ¢, it was simply assumed that ¢ is related to themixing layer growth rate because a larger growth rate resultsin larger ¢. The growth rate,Gf, is evaluated as follows15,16):

Gf ¼ GrfðMc1Þ; ð18Þwhere Gr is an incompressible growth rate of the mixinglayer described as:

Gr ¼2Hm

x

¼ 0:17ð1� rÞ 1þ s

12

� �1þ rs

12

ð19Þ

r denotes the ratio of flow velocity (u2=u1) and s is theratio of density (�2=�1). Hm is half of the mixing layer thick-ness, as was defined in the former section.

fðMc1Þ is the function of a convective Mach number,Mc1,to adjust the compressible effect on Gr.

fðMc1Þ ¼ 0:2þ 0:8e�3M2c1 ; ð20Þ

where Mc1 is defined as follows:

Mc1 ¼u1 � uc

a1ð21Þ

uc ¼u1 þ s

12u2

1þ s12

ð22Þ

Since the pressure of two flows is assumed to be identical,s can be describes as the product of the molecular weight ra-tio and the total temperature ratio.

s ¼ �2

�1

¼ w2

w1

t1

t2

¼ w2

w1

T1

T2

2þ ð�2 � 1ÞM22

2þ ð�1 � 1ÞM21

ð23Þ

By introducing ¡, which is defined as:

� ¼ T1w2

T2w1

!12

; ð24Þ

Eqs. (19) and (20) can be described as follows:

Gr ¼ 0:17

1� M2

M1

�2t2w1

�1t1w2

!12

8<:

9=; 1þ w2t1

w1t2

!12

8<:

9=;

1þ w2t1

w1t2

!12M2

M1

�2t2w1

�1t1w2

!12

¼ 0:17

1þ �� 1

��

�2M22

�1M21

!12

� �2M22

�1M21

!12

1þ �2M22

�1M21

!

ð25Þ

Mc1 ¼ M1

w2t1

w1t2

!12

1þ w2t1

w1t2

!12

1� M2

M1

�2t2w1

�1t1w2

!12

8<:

9=;

¼ M1

�

1þ �� 1

�

�2M22

�1M21

!12

8<:

9=;;

ð26Þ

where ¤ denotes:

� ¼�2þ ð�2 � 1ÞM2

2

2þ ð�1 � 1ÞM21

�12

ð27Þ

As can be seen, both Gr and Mc1 (and thus fðMc1Þ) arefunctions of ¡. From the definition, when the total tempera-ture of the primary gas becomes greater, or the molecularweight of the primary gas becomes lighter, ¡ becomesgreater and the effect results in greater Gf as is depicted inFig. 11. With the fixed secondary flow condition (atmo-spheric air at M2 ¼ 0:5, T2 ¼ 300K and w2 ¼ 28:8) andthe fixed total pressure of the primary flow (P1 ¼ 2MPa),three cases were evaluated and the results are shown in thisfigure. The solid line with circle symbols shows the case withnitrogen as the primary gas, varying its total temperature.The other two lines correspond to the cases where the totaltemperature of the primary gas was fixed to be 300 K, vary-ing the molecular weight with a different specific heat ratio.For clarity, additional axes show the equivalent total temper-ature or the molecular weight of the primary gas. In any case,the minimum Gf appeared around � ¼ 1 and Gf becamegreater roughly proportional to ¡. Thus, it is expected qual-itatively that ¢ becomes larger as the value of ¡ increases.It should be noted that the local maximum was observed at� ¼ 0:6, but that ¡ corresponds to an unpractical condition(primary gas of extremely low temperature or heavy molecu-lar weight) for an ejector-jet application.

As for the pressure rise due to mixing, one-dimensionalanalysis for two flows forming a mixed flow was carriedout. Here, for the sake of simplicity, it is assumed two flowshave the same sectional area, A, and the mixed flow has anarea twice the size, 2A. The conservation equations and idealgas relation were assumed for the mixing process, and thesupersonic solution for the mixing flow was evaluated.

_m1 þ _m2 ¼ _m ¼ �mum2A ð28Þ


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K1 þK2 ¼ K ¼ pm2Aþ _mum ð29Þ

E1 þ E2 ¼ E ¼ _m Cpmtm þ u2m2

!ð30Þ

pm ¼ �mRmtm ð31Þ

The properties of the mixed flow, Rm and Cpm, were ob-tained as a mole weighted average of the two flows. To fur-ther simplify the relation, the following relation is alsoadopted from Mayer’s relation:

Rm

Cpm¼ �m � 1

�mð32Þ

As a result, pm can be described as follows:

pm ¼K�

�K2�2

m � 2 _mEð�2m � 1Þ

�12

2Að�m þ 1Þ ð33Þ

The sum of the momentum and the product of mass andenergy of two flows are described as follows:

K ¼ K1 þK2

¼ pAþ �1u21Aþ pAþ �2u

22A

¼ pA 2þ �1M21 þ �2M

22

� � ð34Þ

_mE ¼ _m1 þ _m2Þð _m1Cp1T1 þ _m2Cp2T2� �

¼ _m21Cp1T1 þ _m2

2Cp2T2 þ _m1 _m2 Cp1T1 þ Cp2T2� � ð35Þ

By substituting these values in Eq. (32), the normalizedpressure, pm=p, is derived as follows:

2 �m þ 1� �pm

p¼ 2þ �1M

21 þ �2M

22

� �

�*�2m 2þ �1M

21 þ �2M

22

� �2�2 �2m � 1

� �� 21M

21

�1 � 1

1þ �1 � 1

2M2

1

þ �2

2M22

�2 � 1

1þ �2 � 1

2M2

2

þM1M2

��1�2

1þ �1 � 1

2M2

1

1þ �2 � 1

2M2

2

�12

�1

�1 � 1�þ �2

�2 � 1

1

�

�+12

ð36Þ

Here again, the parameter ¡ is incorporated to see its effecton the pressure rise. If further simplification is adopted by as-suming the identical specific heat ratio of two flows, the pres-sure rise is degenerated to the function of �þ 1=�, whichgives minimum value at � ¼ 1. In Fig. 12, the pressure risewas evaluated with the same three conditions as those inFig. 11. The results indicate that the pressure rise due to mix-ing takes the minimum value at � ¼ 1; namely, identicalT=w of two flows. In other words, if the total temperatureand/or molecular weight of two flows differ, then an increasein pressure is expected.

From these two analyses, in a qualitative way, it was foundthat larger ratios of total temperature and molecular weightcause a wider mixing layer and higher pressure, and thus, de-grades suction performance, as found in Figs. 5 and 6.

It should also be noted that the molecular weight of the pri-mary gas non-linearly affects the rise in pressure, as can beseen in Fig. 12. Gases of heavier molecular weight than air(like argon) produce a limited change of pressure, whilelighter gases like helium show a significant pressure rise.As was mentioned in section 4.2, only the helium showedlarge degradation in suction performance, with the very same

¢. This phenomena can be explained as resulting from alarger rise in pressure.4.4. Mixing layer observation in CAMUI geometry

To check the actual formation of a mixing layer, an experi-ment was conducted using the scale model of CAMUI de-scribed in section 4.2. The gas sampling was carried out atthe end of the constant area section, downstream of the noz-zle exit with a distance of roughly seven times the size of theheight of the secondary flow passage.

Pure nitrogen was used for the primary gas and its totalpressure was 2.0MPa, which is high enough to establishthe choked condition of the secondary flow. It should alsobe noted that the theoretical pressure at the exit of the nozzleroughly coincided with the pressure of the choked secondaryflow. Figure 13 shows the distribution of nitrogen along theradial direction. Pure nitrogen was observed in the regionexactly downstream of the nozzle exit. The dissipation ofnitrogen gas was rather restricted, roughly comparable withthe error of the probe location. From the distribution ofnitrogen, the mixing layer thickness was estimated to beroughly 1mm, which can be translated into 0.13 of ¢. FromFig. 10, ® can be as high as 0.9, which corresponds to the

0 1 2 3 40.04

0.06

0.08

0.10

α

Gf

T1300 1200 2100 3000

w190 30 12 4

N2, T1 = 300 - 3,300 K

γ1 = 1.4, w1 = 2 - 100

γ1 = 1.67, w1 = 2 - 100

Fig. 11. Effect of ¡ on the mixing layer growth rate.


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good suction performance observed in the experiments.

5. Conclusion

To explore the reason for the degradation of suction per-formance in an ejector-jet, a mixing model was incorporatedin the momentum transfer model. This model resulted in aloss of suction, thus indicating that mixing of the primaryand secondary flows could affect suction performance. Thefollowing results were obtained by the present analysis.

1. As the temperature of the primary flow becomeshigher, loss of suction performance becomes greater. Thisis also true with light molecular gases. The present analysisshowed that, as the difference in the physical nature of twoflows becomes greater, the loss of suction performance iskeenly affected by the quantity of the mixing flow.

2. In the case of the CAMUI experiment, it was suggestedthat mixing the two flows was minimal since the analysisshowed that a loss in performance would occur when mixingthe two flows.

3. Analytical investigations showed that the ratios of thetotal temperature and molecular weight of two flows arethe major parameter for determining the mixing layer thick-ness and pressure rise. The degradation of suction perfor-mance is also affected by this parameter.

4. Analytical investigation also indicated that the molecu-lar weight non-linearly affects pressure rise due to mixing.The result explains the extreme degradation of suction per-formance when helium is used for the primary flow.

5. Nitrogen distribution at the exit of the CAMUI modelshowed limited growth of the mixing layer. Good suctionperformance was achieved due to poor mixing, as predictedby the present method.

References

1) Kanda, T., Tomioka, S., Ueda, S., Tani, K., and Wakamatsu, Y.: De-sign of Sub-scale Rocket-Ramjet Combined Cycle Engine Model, IACPaper IAC-05-C4.5.03, 2005.

2) Tomioka, S., Ueda, S., Tani, K., and Kanda, T.: Scramjet Engine Testsat Ramjet Engine Test Facility in JAXA-KSPC, AIAA Paper 2007-1040, 2007.

3) Itoh, K.: Aerothermodynamic and Scramjet Tests in High EnthalpyShock Tunnel, AIAA Paper 2007-1041, 2007.

4) Tani, K., Kanda, T., and Tokudome, S.: Aerodynamic Characteristicsof the Combined Cycle Engine in an Ejector Jet Mode, AIAA Paper2005-1210, 2005.

5) Tani, K., Kanda, T., and Tokudome, S.: Aerodynamic Characteristicsof the Modified Combined Cycle Engine in an Ejector Jet Mode, AIAAPaper 2006-224, 2006.

6) Tomioka, S., Takegoshi, M., Kudo, K., Kato, K., Hasegawa, S., andKobayashi, K.: Performance of a Rocket-Ramjet Combined-CycleEngine Model in Ejector Mode Operation, AIAA Paper 2008-2618,15th AIAA International Space Planes and Hypersonic Systems andTechnologies Conference, Dayton, OH, 2008.

7) Nagata, H., Ito, M., Maeda, T., Watanabe, M., Uematsu, T., Totani, T.,and Kudo, I.: Development of CAMUI Hybrid Rocket to Create a Mar-ket for Small Rocket Experiments, IAC-05-C4.P.21, 56th InternationalAstronautical Congress of IAF/IAA/IISL, Fukuoka, Japan, 2005.

8) Ueda, S., Hiraiwa, T., Takegoshi, M., Tani, K., and Kanda, T.:Subsonic Flight Experiments of Ejector-Rocket using Hybird-RocketCAMUI, AIAA Paper 2009-7298, 16th AIAA/DLR/DGLR Interna-tional Space Planes and Hypersonic and Technologies Conference,Bremen, Germany, 2009.

9) Aoki, S., Lee, J., Masuya, G., Kanda, T., and Kudo, K.: AerodynamicExperiment on an Ejector-Jet, J. Propul. Power, 21, 3 (2005),pp. 496–503.

10) Fabri, J. and Siestrunck, R.: Supersonic Air Ejectors, Adv. Appl. Mech.,5 (1958), pp. 1–34.

11) Fabri, J. and Paulon, J., Theory and Experiments on Supersonic Air toAir Ejectors, NACA TM 1410, 1958.

12) Spalart, P. R. and Allmaras, S. R.: A One-Equation Turbulence Modelfor Aerodynamic Flows, AIAA Paper 92-0439, 30th Aerospace Sci-ences Meeting & Exhibits, Reno, NV, 1992.

13) Tani, K., Kouchi, T., Kato, K., Sakuranaka, N., and Watanabe, S.:Aerodynamic Experiments of Small Scale Combined Cycle Enginein Various Mach Numbers, ISTS 2008-a-41, 26th International Sym-posium on Space Technology and Science, Hamamatsu, Japan, 2008.

14) Gordon, S. and McBride, B. J.: Computer Program for Calculation ofComplex Chemical Equilibrium Compositions and Applications, I.Analysis, NASA RP-1311, 1994.

15) Papamoschuou, D. and Roshuko, A.: The Compressible TurbulentShear Layer: An Experimental Study, J. Fluid Mech., 197 (1988),pp. 453–477.

16) Dimotakis, P.: Turbulent Free Shear Layer Mixing and Combustion,Proc. of the 9th International Symposium on Air Breathing Engines,AIAA, Washington, DC, 1989, pp. 58–79.

I.-S. JeungAssociate Editor

080 90 100

-5

5

10

15

20

Dis

tanc

e fr

om a

xis

(mm

)

N2

Air

Measurementposition

N2 mole fraction (%)

Nozzle

Ejector duct

Fig. 13. Primary gas distribution in the CAMUI configuration.

0 2 4 6 80.4

0.6

0.8

1.0

1.2

α

p m/p

T1300 1200 2100 3000

w190 30 12 4

N2, T1 = 300 - 3,300 K

γ1 = 1.4, w1 = 2 - 100

γ1 = 1.67, w1 = 2 - 100

Fig. 12. Effect of ¡ on the pressure rise due to the mixing.


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