2010

Aerospace Science and Technology 14 (2010) 1–10

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Aerospace Science and Technology

www.elsevier.com/locate/aescte

Propulsion and aerodynamic performance evaluation of jet-wing distributedpropulsion

Joseph A. Schetz a,1, Serhat Hosder b,∗,2, Vance Dippold III a,3, Jessica Walker a,4

a Virginia Polytechnic Institute and State University, Blacksburg, VA 24061, United Statesb Missouri University of Science and Technology, Rolla, MO 65409, United States

a r t i c l e i n f o a b s t r a c t

Article history:Received 10 December 2006Accepted 17 June 2009Available online 17 September 2009

Keywords:Jet-wingPropulsionDistributed propulsionComputational fluid dynamicsAerodynamics

Distributed propulsion is the idea of redistributing the thrust across the drag producing elements of avehicle. Our configuration has a modest number of engines with part of the exhaust flow vented fromthick trailing edges of the wings to cancel the local profile drag and the rest of the exhaust flow providingthrust to cancel the induced drag and drag of the fuselage and tails. CFD studies were performed ontwo-dimensional wing sections in transonic, viscous flow to (1) investigate the effect of jet-wing onpropulsion efficiency and the flow field (2) determine design changes for achieving efficient distributedpropulsion, and (3) investigate the effect of jet-flaps with small jet deflection angles on aerodynamicparameters. The jet-wing distributed propulsion can give propulsive efficiencies on the order of turbofanengine aircraft and if the trailing edge of a conventional Outboard airfoil is expanded, efficiency can beincreased by 7.5%. An increase in propulsion efficiency was achieved without expanding the trailing edgefor a thicker Inboard airfoil. The results of the Outboard airfoil jet-flap cases support the idea of usingdeflected exhaust jets from trailing edges as control surfaces.

© 2009 Elsevier Masson SAS. All rights reserved.

1. Introduction

Modern transport aircraft use two or four engines in a Cayleyarrangement where the thrust is concentrated just behind each en-gine. This results in a non-uniform wake behind the vehicle, wherethe wakes behind the wings, tails, and fuselage have a momentumdeficit that is balanced by momentum excess behind the engines.This leads to a loss in theoretical propulsion efficiency. Distributedpropulsion would have the thrust distributed across all or most ofthe drag producing elements of the vehicle with one major aimof producing a more uniform wake and thus higher propulsionefficiency that would lead to lower fuel consumption with an at-tendant reduction in emissions. Another aim would be to minimizecontrol surfaces by vectoring the thrust, which could reduce air-craft weight, noise and complexity. Further, a reduction in engine

* Corresponding author. Address for correspondence: Missouri University of Sci-ence and Technology, Mechanical and Aerospace Engineering Department, 290BToomey Hall, Rolla, MO 65409, United States.

E-mail address: [email protected] (S. Hosder).1 Fred D. Durham Chair, Aerospace and Ocean Engineering Department.2 Assistant Professor, Mechanical and Aerospace Engineering Department.3 Graduate Student, Aerospace and Ocean Engineering Department. Currently at

NASA Glenn Research Center, Cleveland, Ohio.4 Graduate Student, Aerospace and Ocean Engineering Department. Currently at

Centra Technology, Inc., Arlington, Virginia.

1270-9638/$ – see front matter © 2009 Elsevier Masson SAS. All rights reserved.doi:10.1016/j.ast.2009.06.010

Fig. 1. Kuchemann’s jet-wing aircraft concept [1].

noise might be anticipated as a result of the change in exhaustnozzle size and shape.

With these important potential advantages, the concept of dis-tributed propulsion has received considerable recent attention. Thebasic concept, however, is not new. Kuchemann [1,15] suggestedthe idea for jet aircraft in the 1940’s, and his suggested arrange-ment is shown in Fig. 1. This arrangement incorporates the propul-sion system into the aircraft by burying the engines in the wingand blowing the engine exhaust out of the trailing edge. Kuche-mann [15] proposes that the jet-wing arrangement may be moreefficient than a conventional engine arrangement, in which the en-gine nacelles are located some distance away from the wing andbody. See Ref. [14] for more on that topic.

Kuchemann never performed any detailed studies with the jet-wing [1]. However, a number of analytical, numerical, experimen-tal, and flight test studies have been performed on jet-flaps [5,7,

2 J.A. Schetz et al. / Aerospace Science and Technology 14 (2010) 1–10

Nomenclature

TE Trailing edgeb Wing spanc Chord lengthC D Drag coefficientC DNet Net drag coefficient, includes jet thrustC J Jet thrust coefficientCL Lift coefficientCLNet Net lift coefficient, includes jet thrustC p Pressure coefficientD DragDNet Net drag, includes jet thrusthjet Jet heightLNet Net lift, includes jet thrustm Mass flow rate of the jetM∞ Free-stream Mach numberMjet Jet Mach number

p∞ Free-stream pressurepjet Jet pressurepTE Pressure at trailing edgeRe Reynolds numberRec Reynolds number based on chordtc Thickness ratioThrustjet Jet thrustT∞ Free-stream temperatureU∞ , Uinf Free-stream velocity magnitudeUjet Jet velocity magnitudeα Airfoil angle of attackηP Froude propulsion efficiencyρ∞ Free-stream densityρjet Jet flow densityτ Jet deflection angle

Fig. 2. Present jet-wing distributed propulsion concept.

10,12,16,19,21], which are similar to jet-wings. In contrast to jet-wings, which have small jet deflection angles and are associatedwith cruise situations, jet-flaps typically have large jet deflectionangles and are found in high-lift applications. In 1972, Boeing andNASA conducted a flight test with a modified de Havilland C-8ABuffalo military turboprop transport research aircraft to investi-gate the STOL characteristics of an augmented jet-flap configura-tion [16]. In the same decade, a Navy Grumman A-6A Intruder wasmodified to become the A-6A/CCW flight circulation control wings(CCW) test demonstrator with trailing edge blowing [5]. Yoshi-hara and Zonars [21] considered jet-flaps in viscous, transonic flow.However, they applied this concept to only high-lift configurationsand no cruise configurations were presented.

We have adopted the distributed propulsion configurationshown in Fig. 2 for our study. The arrangement has a modestnumber of engines with part of the exhaust flow vented fromthick trailing edges of the wings to cancel the local profile dragand the rest of the exhaust flow providing thrust to cancel the in-duced drag and drag of the fuselage and tails. In this paper, wemainly focus on the propulsion efficiency evaluation of a jet-wingsection away from the engine (Fig. 2b), which includes the trail-ing edge exhaust of a jet that is taken from cold (by-pass) air ofa turbofan engine shown in Fig. 2a. Our configuration does nothave the engines embedded in the wing as originally suggested byKuchemann or arranged in a shallow planar duct as has been sug-gested in some schematics recently. We feel that those schemes

will have poor engine performance especially for turbofans. InRef. [14], it was shown that the theoretical gains in propulsion ef-ficiency are substantial. Multidisciplinary design and optimization(MDO) studies presented in Ref. [13] indicate that real improve-ments in transport aircraft design are possible. But, as always,achieving these potential improvements rests on the details of theimplementation.

One such important detail is the aerodynamics of the flow nearthe thick trailing edges of the wings. Can one efficiently exhaustsufficient air out of the trailing edge of the usual airfoils used forwings? If not, how is the aerodynamic performance of the wingaffected if a thicker trailing edge must be employed? Further, howwell can one “fill in the wake” behind the wing to thereby at-tain the desired gains in propulsion efficiency? An initial study ofsome of these questions was presented in Ref. [3]. This paper willinclude some of the important results obtained from that studyand provide further results by considering a wider range of pa-rameters and conditions such as the Reynolds number and theairfoil geometry. Also, new results for deflected exhaust jets (jet-flaps with small jet deflection angles) as a possible replacementfor conventional control surfaces will be presented. The goals ofthis study are: (1) to ascertain the effect of jet-wing distributedpropulsion on propulsion efficiency, (2) to observe how jet-wingdistributed propulsion affect the flow-field, (3) to determine de-sign changes that might be implemented for achieving efficientdistributed propulsion, and (4) to investigate the effect of the jet-flaps with small deflection angles on aerodynamic parameters. Toachieve these goals, we use computational fluid dynamics (CFD) asthe analysis tool in our studies.

2. Improvement of the propulsion efficiency by distributedpropulsion

The propulsion efficiency is improved by distributed propulsion,since a jet exiting out the trailing edge of the wing ‘fills in’ thewake directly behind the wing. Propulsion efficiency loss is a con-sequence of any net kinetic energy left in the wake (characterizedby non-uniformities in the velocity profile) compared to that of auniform velocity profile. Naval architects implement this concepton ships and submarines by installing a propeller directly behind astreamlined body. This tends to maximize the propulsion efficiencyof the ship-propeller system, even though the wake is typicallynot perfectly filled in (see Ref. [17]). The concept of “filling inthe wake” superficially resembles to the wake ingestion studiedby Smith [18], which aims to improve the propulsion efficiency by

J.A. Schetz et al. / Aerospace Science and Technology 14 (2010) 1–10 3

Fig. 3. The velocity profile of a perfect distributed propulsion body/engine sys-tem [14].

Fig. 4. The velocity profile of a realistic distributed propulsion body/engine sys-tem [14].

taking part or all of the propulsive fluid from the wake of the craftbeing propelled. However, in our distributed propulsion model wedo not have wake ingestion in the sense of Smith [18], since in ajet-wing none of the wake fluid passes through the propulsor. Inour jet-wing configuration, we try to improve the propulsion ef-ficiency by filling in the wake of the wing sections with the jetexhausted from the trailing edge.

The Froude Propulsion Efficiency, ηP , is defined as the ratio ofuseful power out of the propulsor to the rate of kinetic energyadded to the flow by the propulsor. For a jet engine isolated froman aircraft wing, the familiar result is:

ηP = 2UjetU∞ + 1

(1)

For a typical high-bypass-ratio turbofan at Mach 0.85, the FroudePropulsion Efficiency is about 80% [9]. Consider the distributedpropulsion system shown in Fig. 3, in which the jet and the wakeof the body are combined. In the ideal system, the jet perfectly‘fills in’ the wake, creating a uniform velocity profile. In this case,the kinetic energy added to the flow by the jet compared tothat of a uniform velocity profile is zero, and the propulsion ef-ficiency is ηP = 100%. However, the jet does not fully ‘fill in’ thewake in practice, but rather creates smaller non-uniformities inthe velocity profile, as illustrated in Fig. 4. The resulting veloc-ity profile contains a smaller net kinetic energy than that of thecase where the body and engine are independent. Ko, Schetz, andMason [14] present an analysis of the propulsion efficiency of adistributed propulsion system of this type. The efficiency of a dis-tributed propulsion system will be bounded by the efficiency ofthe body/engine configuration (nominally 80%) and the perfect dis-tributed propulsion configuration of 100%. Note, however, that theeffect of the jet on the overall pressure distribution of the bodywas not included.

3. Airfoils used in computational studies

For our studies, we have selected two representative spanwisestations on a typical transport aircraft wing. The first airfoil, re-ferred to as the “Outboard” airfoil, is a representative of the wingsections found on the outboard portion of a transport wing. TheOutboard airfoil has a thickness ratio of t/c = 11%, a 2-D design lift

Fig. 5. Outboard 1 × TE airfoil geometry.

Fig. 6. Inboard airfoil geometry.

coefficient of CL = 0.69 at a 2-D Mach number of 0.72, and a chordlength of c = 6.77 m. The Outboard airfoil was developed by mod-ifying a SC(2)-0410 supercritical airfoil [8] by adding small cubicbumps along the upper surface and stretching the lower surface.The modifications were performed in order to reduce the shockstrength and to reduce the aft loading. Complete details of the de-velopment process can be found in Ref. [2]. The Outboard airfoilmodel has a trailing edge thickness of 0.49% of the chord and ispictured in Fig. 5.

A second airfoil was developed to be representative of thethicker Inboard wing sections on a transport aircraft wing. This“Inboard” airfoil has a thickness ratio of 16%, a 2-D design lift co-efficient of CL = 0.62 at a 2-D Mach number of 0.67, and a chordlength of 11.93 m. The Inboard airfoil was taken from the EET wing(Ref. [11]) at a spanwise station of 0.23 and modified for 2-D CFDcalculations using Simple Sweep Theory described in Ref. [2]. TheInboard airfoil has a trailing edge thickness of 0.66% of the chordand is shown in Fig. 6.

One more airfoil development technique was performed in thisresearch, namely expanding the trailing edge of the airfoil. Oneof the goals of the jet-wing distributed propulsion concept studyis to increase the propulsion efficiency of the aircraft. As will bediscussed later, the propulsion efficiency of the baseline Outboardairfoil with the jet-wing applied was slightly lower than the 80%that is typical of turbofans [9]. Therefore, an attempt was made atdecreasing the jet exit speed by increasing the height of the airfoiltrailing edge. The trailing edge of the Outboard airfoil was ex-panded by truncating the airfoil at the location of desired trailingedge height and then linearly stretching the airfoil to the correctchord length. The trailing edge expansion of the Outboard airfoilincreased the trailing edge height from 0.49% to 0.98% of the chord.The Outboard airfoil with the original trailing edge thickness isnow referred to as the “Outboard 1 × TE” airfoil, and the Outboardairfoil with the double thickness trailing edge is referred to as the“Outboard 2 × TE” airfoil.

4. Computational model

The computational analyses of the jet-wing models were per-formed using the Reynolds-averaged, three-dimensional, finite-volume, Navier–Stokes code GASP [6]. The three representativeairfoils were modeled using conventional two-zone C-grids. Thedetails of the Outboard airfoil grids are described in Ref. [2] andthe details of the Inboard airfoil grid are given in Ref. [20]. EachCFD case was run at three grid levels: coarse, medium, and fine.Medium and coarse grid levels were obtained from the fine gridby reducing the number of grid points by a factor of two at eachdirection. The fine grid around Outboard 1 × TE airfoil (Fig. 7) had493 × 65 grid points in the airfoil zone including the airfoil sur-

4 J.A. Schetz et al. / Aerospace Science and Technology 14 (2010) 1–10

Fig. 7. Two-zone C-grid around Outboard 1 × TE airfoil.

Table 1Free-stream properties used in the computations.

Outboard1 × TE airfoil

Outboard1 × TE airfoil

Outboard2 × TE airfoil

Inboardairfoil

Free-stream Mach, M∞ 0.72 0.72 0.72 0.67Free-stream temp., T∞ 218.93 K 218.93 K 218.93 K 218.93 KFree-stream density, ρ∞ 0.3807 kg/m3 0.3807 kg/m3 0.3807 kg/m3 0.3807 kg/m3

Angle of attack, α 2.66◦ 2.66◦ 3.00◦ 0.521◦Reynolds number, Rec 5.67 × 106

(low Rec)38.40 × 106

(design Rec )38.40 × 106

(design Rec)62.96 × 106

(design Rec )

face and the wake region and 85 × 41 grid points in the trailingedge region. At each grid level, except the coarsest one, the ini-tial solution estimates were obtained by interpolating the primitivevariable values of the previous grid solution to the new cell lo-cations. This technique, known as grid sequencing, was used toreduce the number of iterations required to converge to a steadystate solution at finer mesh levels. All the results presented in thismanuscript were obtained with the finest mesh level. With theresults of the medium and fine grid levels, the discretization er-rors at the fine grid level were estimated for the output quantitiesof interest using Richardson’s extrapolation method. For the casespresented in this manuscript the estimated discretization errorswere less than 1.0% for the lift coefficient and less than 8% for thedrag coefficient. In the CFD simulations, inviscid fluxes were calcu-lated with 3rd order upwind biased Roe’s flux difference splittingscheme. The physical model included all the viscous terms (thin-layer and cross-derivative terms) and used Menter’s Shear StressTransport turbulence model with compressibility corrections.

The free-stream flow properties used in the CFD simulations foreach of the three airfoils models are given in Table 1. Note that thedesign Reynolds number (based on the chord length and the flowconditions specified in Table 1) is Rec = 38.40 × 106 for the Out-board airfoil and Rec = 62.96 × 106 for the Inboard airfoil. TheseReynolds numbers are typical values for conventional transport air-craft at cruise conditions. Runs with the design Reynolds numbersincluded a no-jet and a jet-wing case for each of the three airfoils.In addition to the runs with the design Rec , some CFD simulationswere performed at a lower Reynolds number (Rec = 5.67 × 106)

with the Outboard 1 × TE airfoil. These runs used the same free-stream values, but had a scaled airfoil chord length of 1 m. LowReynolds number runs included a no-jet case, a jet-wing case, andthree jet-flap cases with different jet deflection angles (see Ta-ble 2).

In the computations, airfoil chords are aligned with the x-axisof an x–y Cartesian coordinate system which defines the coordi-nates of the airfoil and the grid points in the physical domain. Thefree-stream flow, having a velocity magnitude of U∞ , is specifiedin GASP with an angle of attack α. The lift and drag forces arealigned with a coordinate system rotated an angle α from the x–ycoordinate system. The jet deflection angle (τ ) is defined as the

Table 2Jet flow properties of airfoil models obtained at design and low Reynolds numbers.

Outboard 1 × TE airfoil Outboard2 × TE airfoil

Inboardairfoil

Reynoldsnumber, Rec

5.67 × 106 38.40 × 106 38.40 × 106 62.96 × 106

Jet Machnumber, M∞

1.22 1.22 1.28 1.34 1.199 1.021 1.059

Jet angle, τ(degrees)

0.0 −2.66 5.0 10.0 0.0 0.0 3.0

angle between the jet direction and the airfoil chordline, and mea-sured positive in the clockwise direction. The jet flow propertieswere determined using the results of the no-jet airfoil cases ob-tained with GASP. To simplify the modeling, it was assumed thatthe jet would use exhaust from the engine fan and that it wouldbe at the same temperature as the free-stream. Furthermore, thepressure of the jet flow was set equal to the average of pressureson the upper and lower surfaces of the airfoil at the trailing edge.The jet flow Mach number Mjet was determined from the thrustof the jet. Since the jet-wing is locally self-propelled, the jet thrustcomponent in the free-stream direction is equal to the local drag(D) of the wing section:

Thrustjet · Cos(α + τ ) = D

Thrustjet · Cos(α + τ ) = C D ·(

1

2· ρ∞ · U 2∞ · c

)(2)

Here we consider a unit wing span (b = 1 m). The jet thrust wasfound from the thrust equation

Thrustjet = ρjet · Ujet · hjet · (Ujet − U∞) + (pjet − p∞) · hjet (3)

Using Eq. (3) in Eq. (2), we obtained

C D · ( 12 · ρ∞ · U 2∞ · c)

Cos(α + τ )= ρjet · Ujet · hjet · (Ujet − U∞)

+ (pjet − p∞) · hjet (4)

Eq. (4) was solved for the jet exit velocity, Ujet , and thus Mjet . Thejet flow properties for the airfoil cases presented in this paper are

J.A. Schetz et al. / Aerospace Science and Technology 14 (2010) 1–10 5

Table 3Jet-wing results obtained at design Reynolds numbers.

Airfoil Outboard1 × TE, no-jet

Outboard1 × TE, jet-wing

Outboard2 × TE, no-jet

Outboard2 × TE, jet-wing

Inboardno-jet

Inboard,jet-wing

Angle-of-attack, α 2.66◦ 2.75◦ 3.00◦ 3.13◦ 0.521◦ 0.521◦Jet Mach number, Mjet 0.0 1.199 0.0 1.021 0.0 1.059Propulsion efficiency, ηP N/A 75.1% N/A 82.8% N/A 81.0%Jet coefficient, C J 0.0 0.0115 0.0 0.0122 0.0 0.0089Net lift coefficient, CLNet 0.6276 0.6230 0.6303 0.6389 0.5824 0.4684Net drag coefficient, C DNet 0.0124 0.0002 0.0136 −0.0001 0.0118 0.0008

listed in Table 2. The net force coefficients on the airfoil, includingthe effects of the jet thrust, were calculated using the formulas

CLNet = LNet12 · ρ∞ · U 2∞ · c

C DNet = DNet12 · ρ∞ · U 2∞ · c

(5)

The jet thrust coefficient, C J , is defined as:

C J = m · Ujet12 · ρ∞ · U 2∞ · c

(6)

Here m is the mass flow rate of the jet. In our calculations to ap-proximate the drag of a jet-wing section, we start with the drag ofthe no-jet case and use this value as an initial guess to obtain therequired jet velocity. Then the results of the CFD simulations areused for the jet-wing case to calculate the net drag value, whichshould be ideally equal to zero or to a very small value for thewing section to be self-propelled. Depending on the value of thenet drag, more iterations are performed if needed. We have seenthat, in most cases, the estimate of the drag from the no-jet casewas a good first approximation for the calculation the net drag ofthe jet-wing case.

When no jet is present at the trailing edge, a no-slip boundarycondition is applied to the trailing edge, just like the rest of theairfoil. However, when a jet is exhausted from the trailing edge,the primitive variables at the trailing edge (density, velocity com-ponents in x and y directions, and the static pressure) were keptfixed with the jet flow parameters. This boundary condition is ap-propriate for a supersonic jet flow (Mjet > 1) and have worked wellfor all the models, even when Mjet was very close to 1. For the in-flow and outflow boundaries, a Riemann subsonic, inflow/outflowboundary condition was used.

5. Design Reynolds number results

5.1. Outboard 1 × TE airfoil

The CFD analysis with GASP gave a lift coefficient value ofCL = 0.628 and a drag coefficient of C D = 0.0124 for the Outboard1 × TE no-jet airfoil (see Table 3). This lift coefficient was 9% lessthan the design value of CL = 0.69. This difference originated dueto the fact that the angle of attack (which was used in GASP simu-lations) for the design lift coefficient was obtained using MSES [4],an Euler + Boundary Layer Code to reduce the computational ex-pense of the determination of the design angle of attack, which isan iterative procedure.

From the results of the Outboard 1 × TE no-jet airfoil case (C D

and pTE in particular), the jet conditions were calculated so asto produce a self-propelled jet-wing. The required jet flow Machnumber was calculated as Mjet = 1.199. Using Eq. (1), the propul-sion efficiency of the Outboard 1×TE jet-wing airfoil was obtainedas ηP = 75.1%. The resulting force coefficients for the no-jet andjet-wing Outboard 1 × TE airfoil cases are listed in Table 3 and

Fig. 8. Outboard 1 × TE no-jet and jet-wing airfoil pressure distributions for CLNet =0.63 at the design Reynolds number.

the pressure distributions are shown in Fig. 8. It should be notedthat it was necessary to increase the angle of attack by a smallamount in order to compare the no-jet and jet-wing airfoils atthe same net lift coefficient. The pressure distributions for theno-jet and jet-wing case at the same lift coefficient are nearlyidentical, including the shock region. Fig. 9 shows the velocity pro-file located 1.0% downstream of the trailing edge of the airfoil.This figure helps to explain why the propulsion efficiency is low(ηP = 75.1%) compared to a typical high-bypass-ratio turbofan en-

gine aircraft (ηPtypical = 80%). The jet is rather thin (hjet

c = 0.49%)and does not exhibit good performance of ‘filling in’ the wake be-hind the airfoil. Also, note that the jet velocity is much greaterthan the free-stream velocity. The streamlines at the trailing edgeof the Outboard 1 × TE no-jet airfoil can be seen in Fig. 10. A com-plex vortex forms on the trailing edge base when no jet is present.The flow-field of the Outboard 1 × TE jet-wing airfoil is pictured inthe same figure. The jet-wing fills in the flow on the trailing edgebase and eliminates the vortex seen in the no-jet case. This exam-ple exhibits one of those rare cases when adding something to aflow problem actually simplifies the flow-field.

5.2. Outboard 2 × TE airfoil

The Outboard 2 × TE airfoil was studied to determine how theexpanded trailing edge affects the propulsion efficiency. As tabu-lated in Table 3, the drag of the Outboard 2 × TE no-jet airfoil is9.7% higher than that of the Outboard 1 × TE no-jet airfoil. Al-though the net lift coefficients vary by only a small amount, thepressure distribution of the Outboard 2 × TE airfoil, plotted inFig. 11, differs significantly from that of the Outboard 1 × TE airfoilespecially in the shock region and on the lower surface close tothe trailing edge. The shock is shifted approximately 4% aft of the1 × TE airfoil shock location. The flow-field near the trailing edgeof 2 × TE airfoil is pictured in Fig. 10. Compared to the flow-fieldof the Outboard 1 × TE no-jet airfoil, a larger vortex structure canbe seen on the base of the Outboard 2 × TE airfoil.

6 J.A. Schetz et al. / Aerospace Science and Technology 14 (2010) 1–10

Fig. 9. Velocity profiles downstream of Outboard no-jet and jet-wing airfoils at xc = 1.01 at the design Rec .

Fig. 10. Streamlines and Mach number contours at the trailing edge of Outboard airfoils at design Reynolds number.

Fig. 11. Outboard 1 × TE and Outboard 2 × TE no-jet airfoil pressure distributionsfor CLNet = 0.63 at the design Reynolds number.

The results of the Outboard 2×TE no-jet case were used to cal-culate the required jet flow to produce a self-propelled vehicle. Therequired jet flow Mach number was Mjet = 1.021. The propulsion

efficiency of the Outboard 2×TE jet-wing airfoil was calculated us-ing Eq. (1) and found to be ηP = 82.8%. The pressure distribution ispictured in Fig. 12. As before, the jet-wing has a minimal effect onthe pressure distribution. The velocity profiles in Fig. 9 show whythe propulsion efficiency has been increased. The Outboard 2 × TEjet-wing has a lower jet speed than that of the Outboard 1 × TEjet-wing and provides a better ‘fill in’ of the wake behind the air-foil. The complex structure on the base of the Outboard 2 × TEno-jet airfoil is eliminated by the jet, as shown in Fig. 10. Forthis airfoil of moderate thickness, when the trailing edge thickness(and jet height) is doubled, propulsion efficiency increases by 7.5%.However, the drag on the airfoil for the no-jet case also increasessubstantially (nearly 10%). This could be a problem for an engine-out situation. Therefore, expanding the trailing edge height is not atrivial modification and should be done in a multi-objective fash-ion by considering the other performance parameters.

5.3. Inboard airfoil

The main objective of the Inboard airfoil study was to investi-gate the jet-wing distributed propulsion flow field around a thickerairfoil (t/c = 16%). Outboard airfoil studies showed that it waspossible to increase the propulsion efficiency by enlarging the trail-

J.A. Schetz et al. / Aerospace Science and Technology 14 (2010) 1–10 7

Fig. 12. Outboard 2×TE no-jet and jet-wing airfoil pressure distributions for CLNet =0.63 at the design Reynolds number.

Fig. 13. Velocity profiles downstream of Inboard no-jet and jet-wing airfoil at x/c =1.01 at the n Reynolds number.

Fig. 14. Streamlines and Mach number contours at trailing edge of Inboard airfoil at design Reynolds number.

ing edge, but this was achieved with a drag penalty. The Inboardairfoil used in this study has a thickness of 0.66% of the chord.Since the trailing edge of this airfoil has sufficient thickness, it wasnot necessary to double the trailing edge in order to increase thepropulsion efficiency.

With no jet, the drag coefficient for the Inboard airfoil wasobtained as C D = 0.018. Using this value and the static pres-sure at the trailing edge, the jet Mach number was found tobe Mjet = 1.059, which was the required value for the airfoil tobe self-propelled. The propulsion efficiency for the Inboard jet-wing airfoil was calculated as ηP = 81.0%. Fig. 13 shows thedownstream velocity profile for the jet and no-jet cases. It canbe seen that by adding the jet, the wake is partially filled in,which explains the increase in the propulsion efficiency. The ve-locity profiles for the two cases differ slightly outside the wakeand the jet regions due to the difference in circulation, whichoriginates from the difference in the lift coefficient values be-tween two cases (see Table 3). As also observed in the Out-board no-jet airfoil cases, a vortex stands on the base of the In-board airfoil when there is no jet (Fig. 14). With the injection ofthe jet from the trailing edge, this vortex is eliminated and thestreamlines on the upper and the lower surface of the airfoil arepulled towards the trailing edge region to smoothly blend with thejet.

Since the increase in propulsion efficiency was achieved with-out expanding the trailing edge, no drag penalty is expected forthe Inboard airfoil in case of an engine-out situation.

Because of this reason, this Inboard airfoil and the other similartransonic wing sections can be thought of as good candidates forthe jet-wing application.

6. Low Reynolds number results

The low Reynolds number results obtained with the Outboard1 × TE airfoil show the effectiveness of the distributed propul-sion jet-wing configuration when applied to smaller vehicles, suchas UAVs. In addition to the baseline jet-wing configuration, inwhich the jet deflection angle is τ = 0.0◦ , jet-flaps were also stud-ied, with the jet deflection angles of τ = −2.66◦ , τ = 5.0◦ , andτ = 10.0◦ .

6.1. Outboard 1 × TE jet-wing airfoil results at low Reynolds number

At the low Reynolds number, the drag coefficient of the no-jet Outboard 1 × TE airfoil was obtained as C D = 0.0128. Usingthis value and the trailing edge pressure, the jet flow Mach num-ber and the jet flow density were calculated (Mjet = 1.22 andρjet = 0.4038 kg/m3) for the jet-wing calculations to obtain a self-propelled airfoil. The propulsion efficiency was found to be ηP =74.3%, which is slightly lower than that of the design Reynoldsnumber case, ηP = 75.1%. The force coefficients of the Outboard1×TE jet-wing airfoil at the lower Reynolds number are presentedin Table 4. The lift coefficient of the jet-wing airfoil was within0.7% of that of the no-jet airfoil, so increasing the angle of attackwas not necessary. Fig. 15 compares the downstream velocity pro-files of the design Reynolds number and the low Reynolds numberjet-wing cases. The two jet velocity profiles are comparable. Over-all, the results indicate that there is no significant difference be-tween the propulsion efficiency, drag, and the lift coefficients ofthe design and the low Reynolds number cases.

8 J.A. Schetz et al. / Aerospace Science and Technology 14 (2010) 1–10

Table 4Jet-wing results obtained with Outboard 1 × TE airfoil at low Reynolds number.

Outboard 1 × TE,no-jet

Outboard 1 × TE,jet-wing

Angle-of-attack, α 2.66◦ 2.66◦Jet Mach number, Mjet 0.000 1.220Propulsion efficiency, ηP N/A 74.3%Jet coefficient, C J 0.0000 0.122Net lift coefficient, CLNet 0.6106 0.6067Net drag coefficient, C DNet 0.0128 0.0001

Fig. 15. Velocity profiles downstream (x/c = 1.01) of Outboard jet-wing airfoil atdesign and low Reynolds numbers.

Table 5Outboard 1 × TE jet-wing and jet-flap airfoil results for Rec = 5.67 × 106.

Jet-wing Jet-flap 1 Jet-flap 2 Jet-flap 3

Angle-of-attack, α 2.66◦ 2.66◦ 2.66◦ 2.66◦Jet angle, τ 0.0◦ −2.66◦ 5.0◦ 10.0◦Jet Mach number, Mjet 1.220 1.220 1.280 1.340Propulsion efficiency, ηP 74.3% 74.3% 72.1% 70.0%Jet coefficient, C J 0.122 0.121 0.142 0.160Net lift coefficient, CLNet 0.6067 0.5642 0.7003 0.7996Net drag coefficient, C DNet 0.0001 0.0001 −0.0009 −0.0005Net pitch. mom. coeff., CmNet 0.0341 0.0268 0.0505 0.0702

6.2. Outboard 1 × TE airfoil jet-flap studies at low Reynolds number

In addition to the usual jet-wing studies, several jet-flap caseswere run at the lower Reynolds number to see how the jet in-fluences vehicle performance when deflected to different angles.Attinello [1] and Yoshihara and Zonars [21] both studied high de-flection angle (e.g. τ = 80◦) jet-flaps applied to high-lift situations.The jet-flap cases examined in this study used small jet deflectionangles (τ = −2.66◦ , τ = 5.0◦ , and τ = 10.0◦) applied to the Out-board 1 × TE airfoil at cruise conditions and an angle of attack ofα = 2.66◦ . Because the vehicle was modeled to be self-propelled,the jet coefficient was moderate and on the order of C j = 0.14.

When running these cases, it must be mentioned that deflect-ing the jet and producing a self-propelled jet-flap airfoil was notstraightforward and required several iterations. In fact, more itera-tions were required as the jet deflection angle was increased. Forthis reason, the additional complexity of maintaining a constant liftwas not considered. The performance results of the jet-flap casesare shown in Table 5 for the three jet deflection angles. Note thatthe jet deflection angle of τ = −2.66◦ aligns the jet with the free-stream flow. In Table 5 and Fig. 16, it is observed that even as thejet deflection τ is increased away a small amount, the net lift in-creases significantly (by up to 31% for τ = 10◦). As indicated inFig. 16, the pitching moment also increases as the jet deflectionangle increases, by 100% for a jet deflection angle of τ = 10◦ . How-ever, the increased lift and pitching moment performance do come

Fig. 16. Trends in lift, drag, pitching moment with jet deflection angle at constantangle of attack and low Reynolds number. Note that the drag coefficient C D pre-sented in this figure does not include the jet thrust.

Fig. 17. Comparison of pressure distributions for Outboard 1 × TE jet-wing/-flap air-foil at constant angle of attack and low Reynolds number.

Fig. 18. Comparison of pressure distributions near the trailing edge of the Outboard1 × TE jet-wing/-flap airfoils at low Reynolds number.

at a cost of increased drag and decreased propulsion efficiency.The drag increases by 19% for the τ = 10◦ case. The deflected jetproduces some interesting effects on the flow around the airfoil.The pressure distributions for the jet-wing and jet-flap airfoils arecompared in Fig. 17. Compared to the baseline jet-wing (τ = 0◦),deflecting the jet-flap downward moves the shock aft, while de-flecting the jet-flap upward moves the shock forward. This helpsexplain the changes in lift produced by the jet-flap, as seen inTable 5. Furthermore, the jet-flap alters the pressure at the trail-ing edge, as shown in Fig. 18. Although the airfoils and even thejet-wings presented in this study typically experience equal pres-sures on both the upper and lower surfaces at the trailing edge;when the jet is deflected, the upper and lower surface pressures

J.A. Schetz et al. / Aerospace Science and Technology 14 (2010) 1–10 9

Fig. 19. Streamlines and Mach number contours at trailing edge of Outboard 1 × TE jet-wing/-flap airfoils at low Reynolds number.

at the trailing edge diverge. For negative jet deflection angles, thepressure of the lower surface is actually less than the pressureon the upper surface at the trailing edge. Meanwhile, for positivejet deflection angles, the pressure distribution at the trailing edgespreads out. This phenomenon was also observed by Yoshihara andZonars [21]. Fig. 19 shows the flow field near the trailing edge ofthe jet-wing and jet-flap airfoils at the low Reynolds number.

The jet-flap studies show that at a constant angle of attack,a jet deflected even with a small angle can significantly increase(or decrease, if jet deflection is negative) the lift and pitching mo-ment of a jet-wing vehicle. These results support the idea of usingdeflected exhaust jets from trailing edges as a possible replace-ment for conventional control surfaces. Recall however, there isalso a drag penalty associated with positive jet deflection angles.To remain self-propelled, the jet flow velocity must be increased,thereby decreasing the propulsion efficiency.

7. Conclusions

Parametric CFD studies were performed on two-dimensionalwing sections in transonic, viscous flow to analyze the jet-wingdistributed propulsion flow fields at a range of flow conditionswith different airfoil geometries. The goals of these numericalstudies were: (1) to ascertain the effect of jet-wing distributedpropulsion on propulsion efficiency, (2) to observe how jet-wingdistributed propulsion affect the flow-field, (3) to determine de-sign changes that might be implemented for achieving efficientdistributed propulsion, and (4) to investigate the effect of the jet-flaps with small jet deflection angles on aerodynamic parameters.

Numerical studies were performed using two supercritical air-foils corresponding to the Inboard and Outboard wing sections ofa conventional transport wing. In addition to the Outboard airfoilwith the original trailing edge thickness (Outboard 1 × TE airfoil)of 0.49% of the chord, a modified version of Outboard airfoil withdouble trailing edge thickness (Outboard 2 × TE) was also usedin the numerical studies. The design Reynolds number (based onthe chord length) was Rec = 38.40 × 106 for the Outboard airfoiland Rec = 62.96 × 106 for the Inboard airfoil. Runs with the de-sign Reynolds numbers included a no-jet and a jet-wing case foreach of the three-airfoils. In addition to the runs with the designRec , some CFD simulations were performed at a lower Reynolds

number (Rec = 5.67 × 106) with the Outboard 1 × TE airfoil. LowReynolds number runs included a no-jet case, a jet-wing case (a jetdeflection angle of τ = 0◦), and three jet-flap cases with differentjet deflection angles (τ = −2.66◦ , τ = 5.0◦ , and τ = 10.0◦).

At the design Reynolds number, when the jet-wing was ap-plied to the Outboard 1 × TE airfoil, the resulting propulsion ef-ficiency was found to be ηP = 75%. This performance was dueto the insufficient jet height and relatively large velocity of thejet, which failed to “fill in” the wake efficiently. For the airfoilwith the double trailing edge thickness, propulsion efficiency in-creased by 7.5%, however, the drag on the airfoil for the no-jet casealso increased substantially (nearly 10%). This could be a prob-lem for an engine-out situation. Therefore, expanding the trailingedge height is not a trivial modification and should be done in amulti-objective fashion by considering the other performance pa-rameters. The propulsion efficiency for the Inboard jet-wing airfoilwas calculated as ηP = 81.0%. Since the increase in propulsion ef-ficiency was achieved without expanding the trailing edge, no dragpenalty is expected for the Inboard airfoil in case of an engine-outsituation. Because of this reason, this Inboard airfoil and the othersimilar transonic wing sections can be thought as good candidatesfor the jet-wing application.

The low Reynolds number jet-wing results indicate that thereis no significant difference between the propulsion efficiency,drag, and the lift coefficients obtained at the design and the lowReynolds number cases.

The jet-flap studies show that at a constant angle of attack, ajet deflected even with a small angle can significantly increase (ordecrease, if jet deflection is negative) the lift and pitching momentof a jet-wing vehicle. These results support the idea of using de-flected exhaust jets from trailing edges as possible replacement forconventional control surfaces. However, there is also a drag penaltyassociated with positive jet deflection angles. This is the same sit-uation as for real flap deflections.

Acknowledgement

This work was supported by the NASA Langley Research Centerunder Grant NAG-1-02024.

10 J.A. Schetz et al. / Aerospace Science and Technology 14 (2010) 1–10

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