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Propulsion and aerodynamic performance evaluation of jet-wing distributed propulsion
Aerospace Science and Technology 14 (2010) 1–10
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Propulsion and aerodynamic performance evaluation of jet-wing distributed propulsion Joseph A. Schetz a,1 , Serhat Hosder b,∗,2 , Vance Dippold III a,3 , Jessica Walker a,4 a b
Virginia Polytechnic Institute and State University, Blacksburg, VA 24061, United States 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 2006 Accepted 17 June 2009 Available online 17 September 2009 Keywords: Jet-wing Propulsion Distributed propulsion Computational fluid dynamics Aerodynamics
Distributed propulsion is the idea of redistributing the thrust across the drag producing elements of a vehicle. Our configuration has a modest number of engines with part of the exhaust flow vented from thick trailing edges of the wings to cancel the local profile drag and the rest of the exhaust flow providing thrust to cancel the induced drag and drag of the fuselage and tails. CFD studies were performed on two-dimensional wing sections in transonic, viscous flow to (1) investigate the effect of jet-wing on propulsion efficiency and the flow field (2) determine design changes for achieving efficient distributed propulsion, and (3) investigate the effect of jet-flaps with small jet deflection angles on aerodynamic parameters. The jet-wing distributed propulsion can give propulsive efficiencies on the order of turbofan engine aircraft and if the trailing edge of a conventional Outboard airfoil is expanded, efficiency can be increased by 7.5%. An increase in propulsion efficiency was achieved without expanding the trailing edge for a thicker Inboard airfoil. The results of the Outboard airfoil jet-flap cases support the idea of using deflected 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 Cayley arrangement where the thrust is concentrated just behind each engine. This results in a non-uniform wake behind the vehicle, where the wakes behind the wings, tails, and fuselage have a momentum deficit that is balanced by momentum excess behind the engines. This leads to a loss in theoretical propulsion efficiency. Distributed propulsion would have the thrust distributed across all or most of the drag producing elements of the vehicle with one major aim of producing a more uniform wake and thus higher propulsion efficiency that would lead to lower fuel consumption with an attendant reduction in emissions. Another aim would be to minimize control surfaces by vectoring the thrust, which could reduce aircraft weight, noise and complexity. Further, a reduction in engine
*
Corresponding author. Address for correspondence: Missouri University of Science and Technology, Mechanical and Aerospace Engineering Department, 290B Toomey 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 doi:10.1016/j.ast.2009.06.010
© 2009 Elsevier Masson
SAS. All rights reserved.
Fig. 1. Kuchemann’s jet-wing aircraft concept [1].
noise might be anticipated as a result of the change in exhaust nozzle size and shape. With these important potential advantages, the concept of distributed propulsion has received considerable recent attention. The basic concept, however, is not new. Kuchemann [1,15] suggested the idea for jet aircraft in the 1940’s, and his suggested arrangement is shown in Fig. 1. This arrangement incorporates the propulsion system into the aircraft by burying the engines in the wing and blowing the engine exhaust out of the trailing edge. Kuchemann [15] proposes that the jet-wing arrangement may be more efficient than a conventional engine arrangement, in which the engine nacelles are located some distance away from the wing and body. See Ref. [14] for more on that topic. Kuchemann never performed any detailed studies with the jetwing [1]. However, a number of analytical, numerical, experimental, and flight test studies have been performed on jet-flaps [5,7,
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Nomenclature TE b c CD C D Net CJ CL C L Net Cp D D Net hjet L Net ˙ m M∞ M jet
Trailing edge Wing span Chord length Drag coefficient Net drag coefficient, includes jet thrust Jet thrust coefficient Lift coefficient Net lift coefficient, includes jet thrust Pressure coefficient Drag Net drag, includes jet thrust Jet height Net lift, includes jet thrust Mass flow rate of the jet Free-stream Mach number Jet Mach number
Fig. 2. Present jet-wing distributed propulsion concept.
10,12,16,19,21], which are similar to jet-wings. In contrast to jetwings, which have small jet deflection angles and are associated with cruise situations, jet-flaps typically have large jet deflection angles and are found in high-lift applications. In 1972, Boeing and NASA conducted a flight test with a modified de Havilland C-8A Buffalo military turboprop transport research aircraft to investigate the STOL characteristics of an augmented jet-flap configuration [16]. In the same decade, a Navy Grumman A-6A Intruder was modified to become the A-6A/CCW flight circulation control wings (CCW) test demonstrator with trailing edge blowing [5]. Yoshihara and Zonars [21] considered jet-flaps in viscous, transonic flow. However, they applied this concept to only high-lift configurations and no cruise configurations were presented. We have adopted the distributed propulsion configuration shown in Fig. 2 for our study. The arrangement has a modest number of engines with part of the exhaust flow vented from thick trailing edges of the wings to cancel the local profile drag and the rest of the exhaust flow providing thrust to cancel the induced drag and drag of the fuselage and tails. In this paper, we mainly focus on the propulsion efficiency evaluation of a jet-wing section away from the engine (Fig. 2b), which includes the trailing edge exhaust of a jet that is taken from cold (by-pass) air of a turbofan engine shown in Fig. 2a. Our configuration does not have the engines embedded in the wing as originally suggested by Kuchemann or arranged in a shallow planar duct as has been suggested in some schematics recently. We feel that those schemes
p∞ p jet p TE Re Rec
Free-stream pressure Jet pressure Pressure at trailing edge Reynolds number Reynolds number based on chord t Thickness ratio c Thrustjet Jet thrust T∞ Free-stream temperature U ∞ , Uinf Free-stream velocity magnitude U jet Jet velocity magnitude α Airfoil angle of attack ηP Froude propulsion efficiency ρ∞ Free-stream density ρjet Jet flow density τ Jet deflection angle
will have poor engine performance especially for turbofans. In Ref. [14], it was shown that the theoretical gains in propulsion efficiency are substantial. Multidisciplinary design and optimization (MDO) studies presented in Ref. [13] indicate that real improvements in transport aircraft design are possible. But, as always, achieving these potential improvements rests on the details of the implementation. One such important detail is the aerodynamics of the flow near the thick trailing edges of the wings. Can one efficiently exhaust sufficient air out of the trailing edge of the usual airfoils used for wings? If not, how is the aerodynamic performance of the wing affected if a thicker trailing edge must be employed? Further, how well can one “fill in the wake” behind the wing to thereby attain the desired gains in propulsion efficiency? An initial study of some of these questions was presented in Ref. [3]. This paper will include some of the important results obtained from that study and provide further results by considering a wider range of parameters and conditions such as the Reynolds number and the airfoil geometry. Also, new results for deflected exhaust jets (jetflaps with small jet deflection angles) as a possible replacement for conventional control surfaces will be presented. The goals of this study are: (1) to ascertain the effect of jet-wing distributed propulsion on propulsion efficiency, (2) to observe how jet-wing distributed propulsion affect the flow-field, (3) to determine design changes that might be implemented for achieving efficient distributed propulsion, and (4) to investigate the effect of the jetflaps with small deflection angles on aerodynamic parameters. To achieve these goals, we use computational fluid dynamics (CFD) as the analysis tool in our studies. 2. Improvement of the propulsion efficiency by distributed propulsion The propulsion efficiency is improved by distributed propulsion, since a jet exiting out the trailing edge of the wing ‘fills in’ the wake directly behind the wing. Propulsion efficiency loss is a consequence of any net kinetic energy left in the wake (characterized by non-uniformities in the velocity profile) compared to that of a uniform velocity profile. Naval architects implement this concept on ships and submarines by installing a propeller directly behind a streamlined body. This tends to maximize the propulsion efficiency of the ship-propeller system, even though the wake is typically not perfectly filled in (see Ref. [17]). The concept of “filling in the wake” superficially resembles to the wake ingestion studied by Smith [18], which aims to improve the propulsion efficiency by
J.A. Schetz et al. / Aerospace Science and Technology 14 (2010) 1–10
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Fig. 5. Outboard 1 × TE airfoil geometry.
Fig. 3. The velocity profile of a perfect distributed propulsion body/engine system [14].
Fig. 6. Inboard airfoil geometry.
Fig. 4. The velocity profile of a realistic distributed propulsion body/engine system [14].
taking part or all of the propulsive fluid from the wake of the craft being propelled. However, in our distributed propulsion model we do not have wake ingestion in the sense of Smith [18], since in a jet-wing none of the wake fluid passes through the propulsor. In our jet-wing configuration, we try to improve the propulsion efficiency by filling in the wake of the wing sections with the jet exhausted from the trailing edge. The Froude Propulsion Efficiency, η P , is defined as the ratio of useful power out of the propulsor to the rate of kinetic energy added to the flow by the propulsor. For a jet engine isolated from an aircraft wing, the familiar result is:
ηP =
2 U jet U∞
+1
(1)
For a typical high-bypass-ratio turbofan at Mach 0.85, the Froude Propulsion Efficiency is about 80% [9]. Consider the distributed propulsion system shown in Fig. 3, in which the jet and the wake of 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 to that of a uniform velocity profile is zero, and the propulsion efficiency is η P = 100%. However, the jet does not fully ‘fill in’ the wake in practice, but rather creates smaller non-uniformities in the velocity profile, as illustrated in Fig. 4. The resulting velocity profile contains a smaller net kinetic energy than that of the case where the body and engine are independent. Ko, Schetz, and Mason [14] present an analysis of the propulsion efficiency of a distributed propulsion system of this type. The efficiency of a distributed propulsion system will be bounded by the efficiency of the body/engine configuration (nominally 80%) and the perfect distributed propulsion configuration of 100%. Note, however, that the effect of the jet on the overall pressure distribution of the body was not included. 3. Airfoils used in computational studies For our studies, we have selected two representative spanwise stations on a typical transport aircraft wing. The first airfoil, referred to as the “Outboard” airfoil, is a representative of the wing sections found on the outboard portion of a transport wing. The Outboard airfoil has a thickness ratio of t /c = 11%, a 2-D design lift
coefficient of C L = 0.69 at a 2-D Mach number of 0.72, and a chord length of c = 6.77 m. The Outboard airfoil was developed by modifying a SC(2)-0410 supercritical airfoil [8] by adding small cubic bumps along the upper surface and stretching the lower surface. The modifications were performed in order to reduce the shock strength and to reduce the aft loading. Complete details of the development process can be found in Ref. [2]. The Outboard airfoil model has a trailing edge thickness of 0.49% of the chord and is pictured in Fig. 5. A second airfoil was developed to be representative of the thicker Inboard wing sections on a transport aircraft wing. This “Inboard” airfoil has a thickness ratio of 16%, a 2-D design lift coefficient of C L = 0.62 at a 2-D Mach number of 0.67, and a chord length 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 CFD calculations using Simple Sweep Theory described in Ref. [2]. The Inboard airfoil has a trailing edge thickness of 0.66% of the chord and is shown in Fig. 6. One more airfoil development technique was performed in this research, namely expanding the trailing edge of the airfoil. One of the goals of the jet-wing distributed propulsion concept study is to increase the propulsion efficiency of the aircraft. As will be discussed later, the propulsion efficiency of the baseline Outboard airfoil with the jet-wing applied was slightly lower than the 80% that is typical of turbofans [9]. Therefore, an attempt was made at decreasing the jet exit speed by increasing the height of the airfoil trailing edge. The trailing edge of the Outboard airfoil was expanded by truncating the airfoil at the location of desired trailing edge height and then linearly stretching the airfoil to the correct chord length. The trailing edge expansion of the Outboard airfoil increased the trailing edge height from 0.49% to 0.98% of the chord. The Outboard airfoil with the original trailing edge thickness is now referred to as the “Outboard 1 × TE” airfoil, and the Outboard airfoil 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 performed using the Reynolds-averaged, three-dimensional, finitevolume, Navier–Stokes code GASP [6]. The three representative airfoils were modeled using conventional two-zone C-grids. The details of the Outboard airfoil grids are described in Ref. [2] and the details of the Inboard airfoil grid are given in Ref. [20]. Each CFD case was run at three grid levels: coarse, medium, and fine. Medium and coarse grid levels were obtained from the fine grid by reducing the number of grid points by a factor of two at each direction. The fine grid around Outboard 1 × TE airfoil (Fig. 7) had 493 × 65 grid points in the airfoil zone including the airfoil sur-
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Fig. 7. Two-zone C-grid around Outboard 1 × TE airfoil. Table 1 Free-stream properties used in the computations.
Free-stream Mach, M ∞ Free-stream temp., T ∞ Free-stream density, ρ∞ Angle of attack, α Reynolds number, Rec
Outboard 1 × TE airfoil
Outboard 1 × TE airfoil
Outboard 2 × TE airfoil
Inboard airfoil
0.72 218.93 K 0.3807 kg/m3 2.66◦ 5.67 × 106 (low Rec )
0.72 218.93 K 0.3807 kg/m3 2.66◦ 38.40 × 106 (design Rec )
0.72 218.93 K 0.3807 kg/m3 3.00◦ 38.40 × 106 (design Rec )
0.67 218.93 K 0.3807 kg/m3 0.521◦ 62.96 × 106 (design Rec )
face and the wake region and 85 × 41 grid points in the trailing edge region. At each grid level, except the coarsest one, the initial solution estimates were obtained by interpolating the primitive variable values of the previous grid solution to the new cell locations. This technique, known as grid sequencing, was used to reduce the number of iterations required to converge to a steady state solution at finer mesh levels. All the results presented in this manuscript were obtained with the finest mesh level. With the results of the medium and fine grid levels, the discretization errors at the fine grid level were estimated for the output quantities of interest using Richardson’s extrapolation method. For the cases presented in this manuscript the estimated discretization errors were less than 1.0% for the lift coefficient and less than 8% for the drag coefficient. In the CFD simulations, inviscid fluxes were calculated with 3rd order upwind biased Roe’s flux difference splitting scheme. The physical model included all the viscous terms (thinlayer and cross-derivative terms) and used Menter’s Shear Stress Transport turbulence model with compressibility corrections. The free-stream flow properties used in the CFD simulations for each of the three airfoils models are given in Table 1. Note that the design Reynolds number (based on the chord length and the flow conditions specified in Table 1) is Rec = 38.40 × 106 for the Outboard airfoil and Rec = 62.96 × 106 for the Inboard airfoil. These Reynolds numbers are typical values for conventional transport aircraft at cruise conditions. Runs with the design Reynolds numbers included 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 simulations were performed at a lower Reynolds number (Rec = 5.67 × 106 ) with the Outboard 1 × TE airfoil. These runs used the same freestream values, but had a scaled airfoil chord length of 1 m. Low Reynolds number runs included a no-jet case, a jet-wing case, and three jet-flap cases with different jet deflection angles (see Table 2). In the computations, airfoil chords are aligned with the x-axis of an x– y Cartesian coordinate system which defines the coordinates of the airfoil and the grid points in the physical domain. The free-stream flow, having a velocity magnitude of U ∞ , is specified in GASP with an angle of attack α . The lift and drag forces are aligned with a coordinate system rotated an angle α from the x– y coordinate system. The jet deflection angle (τ ) is defined as the
Table 2 Jet flow properties of airfoil models obtained at design and low Reynolds numbers. Outboard 1 × TE airfoil Reynolds number, Rec Jet Mach number, M ∞ Jet angle, τ (degrees)
Outboard Inboard 2 × TE airfoil airfoil
5.67 × 106 1.22 0.0
38.40 × 106 38.40 × 106
1.22 1.28
−2.66 5.0
1.34 1.199 10.0
0.0
62.96 × 106
1.021
1.059
0.0
3.0
angle between the jet direction and the airfoil chordline, and measured positive in the clockwise direction. The jet flow properties were determined using the results of the no-jet airfoil cases obtained with GASP. To simplify the modeling, it was assumed that the jet would use exhaust from the engine fan and that it would be at the same temperature as the free-stream. Furthermore, the pressure of the jet flow was set equal to the average of pressures on the upper and lower surfaces of the airfoil at the trailing edge. The jet flow Mach number M jet was determined from the thrust of the jet. Since the jet-wing is locally self-propelled, the jet thrust component 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
2 · ρ∞ · U ∞ ·c
(2)
Here we consider a unit wing span (b = 1 m). The jet thrust was found from the thrust equation
Thrustjet = ρjet · U jet · hjet · (U jet − U ∞ ) + ( p jet − p ∞ ) · hjet
(3)
Using Eq. (3) in Eq. (2), we obtained 2 C D · ( 12 · ρ∞ · U ∞ · c)
Cos(α + τ )
= ρjet · U jet · hjet · (U jet − U ∞ ) + ( p jet − p ∞ ) · hjet
(4)
Eq. (4) was solved for the jet exit velocity, U jet , and thus M jet . The jet flow properties for the airfoil cases presented in this paper are
J.A. Schetz et al. / Aerospace Science and Technology 14 (2010) 1–10
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Table 3 Jet-wing results obtained at design Reynolds numbers. Airfoil
Outboard 1 × TE, no-jet
Outboard 1 × TE, jet-wing
Outboard 2 × TE, no-jet
Outboard 2 × TE, jet-wing
Inboard no-jet
Inboard, jet-wing
Angle-of-attack, α Jet Mach number, M jet Propulsion efficiency, η P Jet coefficient, C J Net lift coefficient, C L Net Net drag coefficient, C D Net
2.66◦ 0.0 N/A 0.0 0.6276 0.0124
2.75◦ 1.199 75.1% 0.0115 0.6230 0.0002
3.00◦ 0.0 N/A 0.0 0.6303 0.0136
3.13◦ 1.021 82.8% 0.0122 0.6389 −0.0001
0.521◦ 0.0 N/A 0.0 0.5824 0.0118
0.521◦ 1.059 81.0% 0.0089 0.4684 0.0008
listed in Table 2. The net force coefficients on the airfoil, including the effects of the jet thrust, were calculated using the formulas
C L Net = C D Net =
L Net 1 2
2 ·c · ρ∞ · U ∞
D Net 1 2
2 ·c · ρ∞ · U ∞
(5)
The jet thrust coefficient, C J , is defined as:
CJ =
˙ · U jet m 1 2
2 ·c · ρ∞ · U ∞
(6)
˙ is the mass flow rate of the jet. In our calculations to apHere m proximate the drag of a jet-wing section, we start with the drag of the no-jet case and use this value as an initial guess to obtain the required jet velocity. Then the results of the CFD simulations are used for the jet-wing case to calculate the net drag value, which should be ideally equal to zero or to a very small value for the wing section to be self-propelled. Depending on the value of the net drag, more iterations are performed if needed. We have seen that, in most cases, the estimate of the drag from the no-jet case was a good first approximation for the calculation the net drag of the jet-wing case. When no jet is present at the trailing edge, a no-slip boundary condition is applied to the trailing edge, just like the rest of the airfoil. However, when a jet is exhausted from the trailing edge, the primitive variables at the trailing edge (density, velocity components in x and y directions, and the static pressure) were kept fixed with the jet flow parameters. This boundary condition is appropriate for a supersonic jet flow ( M jet > 1) and have worked well for all the models, even when M jet was very close to 1. For the inflow and outflow boundaries, a Riemann subsonic, inflow/outflow boundary condition was used. 5. Design Reynolds number results 5.1. Outboard 1 × TE airfoil The CFD analysis with GASP gave a lift coefficient value of C L = 0.628 and a drag coefficient of C D = 0.0124 for the Outboard 1 × TE no-jet airfoil (see Table 3). This lift coefficient was 9% less than the design value of C L = 0.69. This difference originated due to the fact that the angle of attack (which was used in GASP simulations) for the design lift coefficient was obtained using MSES [4], an Euler + Boundary Layer Code to reduce the computational expense of the determination of the design angle of attack, which is an iterative procedure. From the results of the Outboard 1 × TE no-jet airfoil case (C D and p TE in particular), the jet conditions were calculated so as to produce a self-propelled jet-wing. The required jet flow Mach number was calculated as M jet = 1.199. Using Eq. (1), the propulsion efficiency of the Outboard 1 × TE jet-wing airfoil was obtained as η P = 75.1%. The resulting force coefficients for the no-jet and jet-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 C L Net = 0.63 at the design Reynolds number.
the pressure distributions are shown in Fig. 8. It should be noted that it was necessary to increase the angle of attack by a small amount in order to compare the no-jet and jet-wing airfoils at the same net lift coefficient. The pressure distributions for the no-jet and jet-wing case at the same lift coefficient are nearly identical, including the shock region. Fig. 9 shows the velocity profile located 1.0% downstream of the trailing edge of the airfoil. This figure helps to explain why the propulsion efficiency is low (η P = 75.1%) compared to a typical high-bypass-ratio turbofan enh
gine aircraft (η P typical = 80%). The jet is rather thin ( cjet = 0.49%) and does not exhibit good performance of ‘filling in’ the wake behind the airfoil. Also, note that the jet velocity is much greater than the free-stream velocity. The streamlines at the trailing edge of the Outboard 1 × TE no-jet airfoil can be seen in Fig. 10. A complex 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 in the same figure. The jet-wing fills in the flow on the trailing edge base and eliminates the vortex seen in the no-jet case. This example exhibits one of those rare cases when adding something to a flow problem actually simplifies the flow-field. 5.2. Outboard 2 × TE airfoil The Outboard 2 × TE airfoil was studied to determine how the expanded trailing edge affects the propulsion efficiency. As tabulated in Table 3, the drag of the Outboard 2 × TE no-jet airfoil is 9.7% higher than that of the Outboard 1 × TE no-jet airfoil. Although the net lift coefficients vary by only a small amount, the pressure distribution of the Outboard 2 × TE airfoil, plotted in Fig. 11, differs significantly from that of the Outboard 1 × TE airfoil especially in the shock region and on the lower surface close to the trailing edge. The shock is shifted approximately 4% aft of the 1 × TE airfoil shock location. The flow-field near the trailing edge of 2 × TE airfoil is pictured in Fig. 10. Compared to the flow-field of the Outboard 1 × TE no-jet airfoil, a larger vortex structure can be seen on the base of the Outboard 2 × TE airfoil.
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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
x c
= 1.01 at the design Rec .
Fig. 10. Streamlines and Mach number contours at the trailing edge of Outboard airfoils at design Reynolds number.
efficiency of the Outboard 2 × TE jet-wing airfoil was calculated using Eq. (1) and found to be η P = 82.8%. The pressure distribution is pictured in Fig. 12. As before, the jet-wing has a minimal effect on the pressure distribution. The velocity profiles in Fig. 9 show why the propulsion efficiency has been increased. The Outboard 2 × TE jet-wing has a lower jet speed than that of the Outboard 1 × TE jet-wing and provides a better ‘fill in’ of the wake behind the airfoil. The complex structure on the base of the Outboard 2 × TE no-jet airfoil is eliminated by the jet, as shown in Fig. 10. For this 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 increases substantially (nearly 10%). This could be a problem for an engineout situation. Therefore, expanding the trailing edge height is not a trivial modification and should be done in a multi-objective fashion by considering the other performance parameters. Fig. 11. Outboard 1 × TE and Outboard 2 × TE no-jet airfoil pressure distributions for C L Net = 0.63 at the design Reynolds number.
The results of the Outboard 2 × TE no-jet case were used to calculate the required jet flow to produce a self-propelled vehicle. The required jet flow Mach number was M jet = 1.021. The propulsion
5.3. Inboard airfoil The main objective of the Inboard airfoil study was to investigate the jet-wing distributed propulsion flow field around a thicker airfoil (t /c = 16%). Outboard airfoil studies showed that it was possible to increase the propulsion efficiency by enlarging the trail-
J.A. Schetz et al. / Aerospace Science and Technology 14 (2010) 1–10
Fig. 12. Outboard 2 × TE no-jet and jet-wing airfoil pressure distributions for C L Net = 0.63 at the design Reynolds number.
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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 Inboard airfoil used in this study has a thickness of 0.66% of the chord. Since the trailing edge of this airfoil has sufficient thickness, it was not necessary to double the trailing edge in order to increase the propulsion efficiency. With no jet, the drag coefficient for the Inboard airfoil was obtained as C D = 0.018. Using this value and the static pressure at the trailing edge, the jet Mach number was found to be M jet = 1.059, which was the required value for the airfoil to be self-propelled. The propulsion efficiency for the Inboard jetwing airfoil was calculated as η P = 81.0%. Fig. 13 shows the downstream velocity profile for the jet and no-jet cases. It can be seen that by adding the jet, the wake is partially filled in, which explains the increase in the propulsion efficiency. The velocity profiles for the two cases differ slightly outside the wake and the jet regions due to the difference in circulation, which originates from the difference in the lift coefficient values between two cases (see Table 3). As also observed in the Outboard no-jet airfoil cases, a vortex stands on the base of the Inboard airfoil when there is no jet (Fig. 14). With the injection of the jet from the trailing edge, this vortex is eliminated and the streamlines on the upper and the lower surface of the airfoil are pulled towards the trailing edge region to smoothly blend with the jet. Since the increase in propulsion efficiency was achieved without expanding the trailing edge, no drag penalty is expected for the Inboard airfoil in case of an engine-out situation. Because of this reason, this Inboard airfoil and the other similar transonic wing sections can be thought of as good candidates for the jet-wing application.
6. Low Reynolds number results The low Reynolds number results obtained with the Outboard 1 × TE airfoil show the effectiveness of the distributed propulsion jet-wing configuration when applied to smaller vehicles, such as UAVs. In addition to the baseline jet-wing configuration, in which the jet deflection angle is τ = 0.0◦ , jet-flaps were also studied, with the jet deflection angles of τ = −2.66◦ , τ = 5.0◦ , and τ = 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 nojet Outboard 1 × TE airfoil was obtained as C D = 0.0128. Using this value and the trailing edge pressure, the jet flow Mach number and the jet flow density were calculated (M jet = 1.22 and ρjet = 0.4038 kg/m3 ) for the jet-wing calculations to obtain a selfpropelled airfoil. The propulsion efficiency was found to be η P = 74.3%, which is slightly lower than that of the design Reynolds number case, η P = 75.1%. The force coefficients of the Outboard 1 × TE jet-wing airfoil at the lower Reynolds number are presented in Table 4. The lift coefficient of the jet-wing airfoil was within 0.7% of that of the no-jet airfoil, so increasing the angle of attack was not necessary. Fig. 15 compares the downstream velocity profiles of the design Reynolds number and the low Reynolds number jet-wing cases. The two jet velocity profiles are comparable. Overall, the results indicate that there is no significant difference between the propulsion efficiency, drag, and the lift coefficients of the design and the low Reynolds number cases.
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Table 4 Jet-wing results obtained with Outboard 1 × TE airfoil at low Reynolds number.
Angle-of-attack, α Jet Mach number, M jet Propulsion efficiency, η P Jet coefficient, C J Net lift coefficient, C L Net Net drag coefficient, C D Net
Outboard 1 × TE, no-jet
Outboard 1 × TE, jet-wing
2.66◦ 0.000 N/A 0.0000 0.6106 0.0128
2.66◦ 1.220 74.3% 0.122 0.6067 0.0001
Fig. 16. Trends in lift, drag, pitching moment with jet deflection angle at constant angle of attack and low Reynolds number. Note that the drag coefficient C D presented in this figure does not include the jet thrust.
Fig. 15. Velocity profiles downstream (x/c = 1.01) of Outboard jet-wing airfoil at design and low Reynolds numbers. Table 5 Outboard 1 × TE jet-wing and jet-flap airfoil results for Rec = 5.67 × 106 .
Angle-of-attack, α Jet angle, τ Jet Mach number, M jet Propulsion efficiency, η P Jet coefficient, C J Net lift coefficient, C L Net Net drag coefficient, C D Net Net pitch. mom. coeff., C mNet
Jet-wing
Jet-flap 1
Jet-flap 2
Jet-flap 3
2.66◦ 0.0◦ 1.220 74.3% 0.122 0.6067 0.0001 0.0341
2.66◦ −2.66◦ 1.220 74.3% 0.121 0.5642 0.0001 0.0268
2.66◦ 5.0◦ 1.280 72.1% 0.142 0.7003 −0.0009 0.0505
2.66◦ 10.0◦ 1.340 70.0% 0.160 0.7996 −0.0005 0.0702
Fig. 17. Comparison of pressure distributions for Outboard 1 × TE jet-wing/-flap airfoil at constant angle of attack and low Reynolds number.
6.2. Outboard 1 × TE airfoil jet-flap studies at low Reynolds number In addition to the usual jet-wing studies, several jet-flap cases were run at the lower Reynolds number to see how the jet influences vehicle performance when deflected to different angles. Attinello [1] and Yoshihara and Zonars [21] both studied high deflection angle (e.g. τ = 80◦ ) jet-flaps applied to high-lift situations. The jet-flap cases examined in this study used small jet deflection angles (τ = −2.66◦ , τ = 5.0◦ , and τ = 10.0◦ ) applied to the Outboard 1 × TE airfoil at cruise conditions and an angle of attack of α = 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 deflecting the jet and producing a self-propelled jet-flap airfoil was not straightforward and required several iterations. In fact, more iterations were required as the jet deflection angle was increased. For this reason, the additional complexity of maintaining a constant lift was not considered. The performance results of the jet-flap cases are shown in Table 5 for the three jet deflection angles. Note that the jet deflection angle of τ = −2.66◦ aligns the jet with the freestream flow. In Table 5 and Fig. 16, it is observed that even as the jet deflection τ is increased away a small amount, the net lift increases significantly (by up to 31% for τ = 10◦ ). As indicated in Fig. 16, the pitching moment also increases as the jet deflection angle increases, by 100% for a jet deflection angle of τ = 10◦ . However, the increased lift and pitching moment performance do come
Fig. 18. Comparison of pressure distributions near the trailing edge of the Outboard 1 × 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 jet produces some interesting effects on the flow around the airfoil. The pressure distributions for the jet-wing and jet-flap airfoils are compared in Fig. 17. Compared to the baseline jet-wing (τ = 0◦ ), deflecting the jet-flap downward moves the shock aft, while deflecting the jet-flap upward moves the shock forward. This helps explain the changes in lift produced by the jet-flap, as seen in Table 5. Furthermore, the jet-flap alters the pressure at the trailing edge, as shown in Fig. 18. Although the airfoils and even the jet-wings presented in this study typically experience equal pressures 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
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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, the pressure of the lower surface is actually less than the pressure on the upper surface at the trailing edge. Meanwhile, for positive jet deflection angles, the pressure distribution at the trailing edge spreads out. This phenomenon was also observed by Yoshihara and Zonars [21]. Fig. 19 shows the flow field near the trailing edge of the 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 moment of a jet-wing vehicle. These results support the idea of using deflected exhaust jets from trailing edges as a possible replacement for conventional control surfaces. Recall however, there is also 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-dimensional wing sections in transonic, viscous flow to analyze the jet-wing distributed propulsion flow fields at a range of flow conditions with different airfoil geometries. The goals of these numerical studies were: (1) to ascertain the effect of jet-wing distributed propulsion on propulsion efficiency, (2) to observe how jet-wing distributed propulsion affect the flow-field, (3) to determine design changes that might be implemented for achieving efficient distributed propulsion, and (4) to investigate the effect of the jetflaps with small jet deflection angles on aerodynamic parameters. Numerical studies were performed using two supercritical airfoils corresponding to the Inboard and Outboard wing sections of a conventional transport wing. In addition to the Outboard airfoil with the original trailing edge thickness (Outboard 1 × TE airfoil) of 0.49% of the chord, a modified version of Outboard airfoil with double trailing edge thickness (Outboard 2 × TE) was also used in the numerical studies. The design Reynolds number (based on the chord length) was Rec = 38.40 × 106 for the Outboard airfoil and Rec = 62.96 × 106 for the Inboard airfoil. Runs with the design Reynolds numbers included 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 simulations were performed at a lower Reynolds
number (Rec = 5.67 × 106 ) with the Outboard 1 × TE airfoil. Low Reynolds number runs included a no-jet case, a jet-wing case (a jet deflection angle of τ = 0◦ ), and three jet-flap cases with different jet deflection angles (τ = −2.66◦ , τ = 5.0◦ , and τ = 10.0◦ ). At the design Reynolds number, when the jet-wing was applied to the Outboard 1 × TE airfoil, the resulting propulsion efficiency was found to be η P = 75%. This performance was due to the insufficient jet height and relatively large velocity of the jet, which failed to “fill in” the wake efficiently. For the airfoil with the double trailing edge thickness, propulsion efficiency increased by 7.5%, however, the drag on the airfoil for the no-jet case also increased substantially (nearly 10%). This could be a problem for an engine-out situation. Therefore, expanding the trailing edge height is not a trivial modification and should be done in a multi-objective fashion by considering the other performance parameters. The propulsion efficiency for the Inboard jet-wing airfoil was calculated as η P = 81.0%. Since the increase in propulsion efficiency was achieved without expanding the trailing edge, no drag penalty is expected for the Inboard airfoil in case of an engine-out situation. Because of this reason, this Inboard airfoil and the other similar transonic wing sections can be thought as good candidates for the jet-wing application. The low Reynolds number jet-wing results indicate that there is no significant difference between the propulsion efficiency, drag, and the lift coefficients obtained at the design and the low Reynolds number cases. 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 moment of a jet-wing vehicle. These results support the idea of using deflected exhaust jets from trailing edges as possible replacement for conventional control surfaces. However, there is also a drag penalty associated with positive jet deflection angles. This is the same situation as for real flap deflections. Acknowledgement This work was supported by the NASA Langley Research Center under Grant NAG-1-02024.
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References [1] J.S. Attinello, The jet wing, in: IAS 25th Annual Meeting, IAS Preprint No. 703, January 28–31, 1957. [2] V.F. Dippold, Numerical assessment of the performance of jet-wing distributed propulsion on blended-wing-body aircraft, Master’s thesis, Virginia Polytechnic Institute and State University, 2003. Available at http://etd.vt.edu, September 2004. [3] V. Dippold, S. Hosder, J.A. Schetz, Analysis of distributed propulsion by engine exhaust from thick trailing edges, AIAA 2004-1205, January 2004. [4] M. Drela, MSES multi-element airfoil design/analysis software – Summary, Massachusetts Institute of Technology, MA, http://raphael.mit.edu/drela/ msessum.ps, May 1994. [5] R.J. Englar, R.A. Hemmerly, W.H. Moore, V. Seredinsky, W. Valckenaere, J.A. Jackson, Design of the circulation control wing STOL demonstrator aircraft, in: Aircraft Systems and Technology Meeting, AIAA-1979-1842, New York, NY, August 20–22, 1979. [6] GASP Version 4.1.1 Reference Guide, Aerosoft, Inc., Blacksburg, VA, 2003. [7] H. Hagendorn, P. Ruden, Wind tunnel investigation of a wing with junkers slotted flap and the effect of blowing through the trailing edge of the main surface over the flap, Report by Institut für Aeromechanik and Flugtechnik der Technischen Hochschule, Hannover LGL Bericht A64, 1938. Available as R.A.E. Translation No. 422, December 1953. [8] C.D. Harris, NASA supercritical airfoils: A matrix of family related airfoils, NASA TP 2969, March 1990. [9] P. Hill, C. Peterson, Mechanics and Thermodynamics of Propulsion, 2nd ed., Addison–Wesley, New York, 1992. [10] D.C. Ives, R.E. Melnik, Numerical calculation of the compressible flow over an airfoil with a jet flap, in: 7th AIAA Fluid and Plasma Dynamics Conference, AIAA-74-542, Palo Alto, CA, June 17–19, 1974.
[11] Peter F. Jacobs, B. Blair Gloss, Longitudinal aerodynamic characteristics of a subsonic energy-efficient transport configuration in the national transonic facility, NASA TP-2922, August 1989. [12] R.D. Kimberlin, Performance flight test evaluation of the Ball-Bartoe JW-1 JetWing STOL research aircraft, in: Flight Testing in the Eighties: 11th Annual Symposium Proceedings of the Society of Flight Test Engineers, August 27–29, 1980. [13] Y. Ko, L. Leifsson, J. Schetz, W. Mason, B. Grossman, MDO of a blended-wingbody transport aircraft with distributed propulsion, AIAA 2003-6732, September 2003. [14] A. Ko, J.A. Schetz, W.H. Mason, Assessment of the potential advantages of distributed-propulsion for aircraft, in: XVIth International Symposium on Air Breathing Engines (ISABE), Cleveland, OH, Paper 2003-1094, August 31– September 5, 2003. [15] D. Kuchemann, The Aerodynamic Design of Aircraft, Pergamon Press, New York, 1978, p. 229. [16] H.C. Quigley, R.C. Innis, S. Grossmith, A flight investigation of the STOL characteristics of an augmented jet flap STOL research aircraft, NASA TM X-62334, May 1974. [17] Herbert Lee Seward (Ed.), Marine Engineering, vol. 1, Society of Naval Architects and Marine Engineers, 1942, pp. 10–11. [18] L.H. Smith, Wake ingestion propulsion benefit, Journal of Propulsion and Power 9 (1) (1993) 74–82. [19] D.A. Spence, The lift coefficient of a thin, jet-flapped wing, Proceedings of the Royal Society of London, Series A, Mathematical and Physical Sciences 238 (112) (December 1956) 46–68. [20] J.N. Walker, Numerical studies of jet-wing distributed propulsion and a simplified trailing edge noise metric method, Master’s thesis, Virginia Polytechnic Institute and State University, August 2004. [21] H. Yoshihara, D. Zonars, The transonic jet flap: A review of recent results, in: National Aerospace and Manufacturing Meeting, ASE-751089, November 1975.
Contents lists available at ScienceDirect
Aerospace Science and Technology www.elsevier.com/locate/aescte
Propulsion and aerodynamic performance evaluation of jet-wing distributed propulsion Joseph A. Schetz a,1 , Serhat Hosder b,∗,2 , Vance Dippold III a,3 , Jessica Walker a,4 a b
Virginia Polytechnic Institute and State University, Blacksburg, VA 24061, United States 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 2006 Accepted 17 June 2009 Available online 17 September 2009 Keywords: Jet-wing Propulsion Distributed propulsion Computational fluid dynamics Aerodynamics
Distributed propulsion is the idea of redistributing the thrust across the drag producing elements of a vehicle. Our configuration has a modest number of engines with part of the exhaust flow vented from thick trailing edges of the wings to cancel the local profile drag and the rest of the exhaust flow providing thrust to cancel the induced drag and drag of the fuselage and tails. CFD studies were performed on two-dimensional wing sections in transonic, viscous flow to (1) investigate the effect of jet-wing on propulsion efficiency and the flow field (2) determine design changes for achieving efficient distributed propulsion, and (3) investigate the effect of jet-flaps with small jet deflection angles on aerodynamic parameters. The jet-wing distributed propulsion can give propulsive efficiencies on the order of turbofan engine aircraft and if the trailing edge of a conventional Outboard airfoil is expanded, efficiency can be increased by 7.5%. An increase in propulsion efficiency was achieved without expanding the trailing edge for a thicker Inboard airfoil. The results of the Outboard airfoil jet-flap cases support the idea of using deflected 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 Cayley arrangement where the thrust is concentrated just behind each engine. This results in a non-uniform wake behind the vehicle, where the wakes behind the wings, tails, and fuselage have a momentum deficit that is balanced by momentum excess behind the engines. This leads to a loss in theoretical propulsion efficiency. Distributed propulsion would have the thrust distributed across all or most of the drag producing elements of the vehicle with one major aim of producing a more uniform wake and thus higher propulsion efficiency that would lead to lower fuel consumption with an attendant reduction in emissions. Another aim would be to minimize control surfaces by vectoring the thrust, which could reduce aircraft weight, noise and complexity. Further, a reduction in engine
*
Corresponding author. Address for correspondence: Missouri University of Science and Technology, Mechanical and Aerospace Engineering Department, 290B Toomey 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 doi:10.1016/j.ast.2009.06.010
© 2009 Elsevier Masson
SAS. All rights reserved.
Fig. 1. Kuchemann’s jet-wing aircraft concept [1].
noise might be anticipated as a result of the change in exhaust nozzle size and shape. With these important potential advantages, the concept of distributed propulsion has received considerable recent attention. The basic concept, however, is not new. Kuchemann [1,15] suggested the idea for jet aircraft in the 1940’s, and his suggested arrangement is shown in Fig. 1. This arrangement incorporates the propulsion system into the aircraft by burying the engines in the wing and blowing the engine exhaust out of the trailing edge. Kuchemann [15] proposes that the jet-wing arrangement may be more efficient than a conventional engine arrangement, in which the engine nacelles are located some distance away from the wing and body. See Ref. [14] for more on that topic. Kuchemann never performed any detailed studies with the jetwing [1]. However, a number of analytical, numerical, experimental, and flight test studies have been performed on jet-flaps [5,7,
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Nomenclature TE b c CD C D Net CJ CL C L Net Cp D D Net hjet L Net ˙ m M∞ M jet
Trailing edge Wing span Chord length Drag coefficient Net drag coefficient, includes jet thrust Jet thrust coefficient Lift coefficient Net lift coefficient, includes jet thrust Pressure coefficient Drag Net drag, includes jet thrust Jet height Net lift, includes jet thrust Mass flow rate of the jet Free-stream Mach number Jet Mach number
Fig. 2. Present jet-wing distributed propulsion concept.
10,12,16,19,21], which are similar to jet-wings. In contrast to jetwings, which have small jet deflection angles and are associated with cruise situations, jet-flaps typically have large jet deflection angles and are found in high-lift applications. In 1972, Boeing and NASA conducted a flight test with a modified de Havilland C-8A Buffalo military turboprop transport research aircraft to investigate the STOL characteristics of an augmented jet-flap configuration [16]. In the same decade, a Navy Grumman A-6A Intruder was modified to become the A-6A/CCW flight circulation control wings (CCW) test demonstrator with trailing edge blowing [5]. Yoshihara and Zonars [21] considered jet-flaps in viscous, transonic flow. However, they applied this concept to only high-lift configurations and no cruise configurations were presented. We have adopted the distributed propulsion configuration shown in Fig. 2 for our study. The arrangement has a modest number of engines with part of the exhaust flow vented from thick trailing edges of the wings to cancel the local profile drag and the rest of the exhaust flow providing thrust to cancel the induced drag and drag of the fuselage and tails. In this paper, we mainly focus on the propulsion efficiency evaluation of a jet-wing section away from the engine (Fig. 2b), which includes the trailing edge exhaust of a jet that is taken from cold (by-pass) air of a turbofan engine shown in Fig. 2a. Our configuration does not have the engines embedded in the wing as originally suggested by Kuchemann or arranged in a shallow planar duct as has been suggested in some schematics recently. We feel that those schemes
p∞ p jet p TE Re Rec
Free-stream pressure Jet pressure Pressure at trailing edge Reynolds number Reynolds number based on chord t Thickness ratio c Thrustjet Jet thrust T∞ Free-stream temperature U ∞ , Uinf Free-stream velocity magnitude U jet Jet velocity magnitude α Airfoil angle of attack ηP Froude propulsion efficiency ρ∞ Free-stream density ρjet Jet flow density τ Jet deflection angle
will have poor engine performance especially for turbofans. In Ref. [14], it was shown that the theoretical gains in propulsion efficiency are substantial. Multidisciplinary design and optimization (MDO) studies presented in Ref. [13] indicate that real improvements in transport aircraft design are possible. But, as always, achieving these potential improvements rests on the details of the implementation. One such important detail is the aerodynamics of the flow near the thick trailing edges of the wings. Can one efficiently exhaust sufficient air out of the trailing edge of the usual airfoils used for wings? If not, how is the aerodynamic performance of the wing affected if a thicker trailing edge must be employed? Further, how well can one “fill in the wake” behind the wing to thereby attain the desired gains in propulsion efficiency? An initial study of some of these questions was presented in Ref. [3]. This paper will include some of the important results obtained from that study and provide further results by considering a wider range of parameters and conditions such as the Reynolds number and the airfoil geometry. Also, new results for deflected exhaust jets (jetflaps with small jet deflection angles) as a possible replacement for conventional control surfaces will be presented. The goals of this study are: (1) to ascertain the effect of jet-wing distributed propulsion on propulsion efficiency, (2) to observe how jet-wing distributed propulsion affect the flow-field, (3) to determine design changes that might be implemented for achieving efficient distributed propulsion, and (4) to investigate the effect of the jetflaps with small deflection angles on aerodynamic parameters. To achieve these goals, we use computational fluid dynamics (CFD) as the analysis tool in our studies. 2. Improvement of the propulsion efficiency by distributed propulsion The propulsion efficiency is improved by distributed propulsion, since a jet exiting out the trailing edge of the wing ‘fills in’ the wake directly behind the wing. Propulsion efficiency loss is a consequence of any net kinetic energy left in the wake (characterized by non-uniformities in the velocity profile) compared to that of a uniform velocity profile. Naval architects implement this concept on ships and submarines by installing a propeller directly behind a streamlined body. This tends to maximize the propulsion efficiency of the ship-propeller system, even though the wake is typically not perfectly filled in (see Ref. [17]). The concept of “filling in the wake” superficially resembles to the wake ingestion studied by Smith [18], which aims to improve the propulsion efficiency by
J.A. Schetz et al. / Aerospace Science and Technology 14 (2010) 1–10
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Fig. 5. Outboard 1 × TE airfoil geometry.
Fig. 3. The velocity profile of a perfect distributed propulsion body/engine system [14].
Fig. 6. Inboard airfoil geometry.
Fig. 4. The velocity profile of a realistic distributed propulsion body/engine system [14].
taking part or all of the propulsive fluid from the wake of the craft being propelled. However, in our distributed propulsion model we do not have wake ingestion in the sense of Smith [18], since in a jet-wing none of the wake fluid passes through the propulsor. In our jet-wing configuration, we try to improve the propulsion efficiency by filling in the wake of the wing sections with the jet exhausted from the trailing edge. The Froude Propulsion Efficiency, η P , is defined as the ratio of useful power out of the propulsor to the rate of kinetic energy added to the flow by the propulsor. For a jet engine isolated from an aircraft wing, the familiar result is:
ηP =
2 U jet U∞
+1
(1)
For a typical high-bypass-ratio turbofan at Mach 0.85, the Froude Propulsion Efficiency is about 80% [9]. Consider the distributed propulsion system shown in Fig. 3, in which the jet and the wake of 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 to that of a uniform velocity profile is zero, and the propulsion efficiency is η P = 100%. However, the jet does not fully ‘fill in’ the wake in practice, but rather creates smaller non-uniformities in the velocity profile, as illustrated in Fig. 4. The resulting velocity profile contains a smaller net kinetic energy than that of the case where the body and engine are independent. Ko, Schetz, and Mason [14] present an analysis of the propulsion efficiency of a distributed propulsion system of this type. The efficiency of a distributed propulsion system will be bounded by the efficiency of the body/engine configuration (nominally 80%) and the perfect distributed propulsion configuration of 100%. Note, however, that the effect of the jet on the overall pressure distribution of the body was not included. 3. Airfoils used in computational studies For our studies, we have selected two representative spanwise stations on a typical transport aircraft wing. The first airfoil, referred to as the “Outboard” airfoil, is a representative of the wing sections found on the outboard portion of a transport wing. The Outboard airfoil has a thickness ratio of t /c = 11%, a 2-D design lift
coefficient of C L = 0.69 at a 2-D Mach number of 0.72, and a chord length of c = 6.77 m. The Outboard airfoil was developed by modifying a SC(2)-0410 supercritical airfoil [8] by adding small cubic bumps along the upper surface and stretching the lower surface. The modifications were performed in order to reduce the shock strength and to reduce the aft loading. Complete details of the development process can be found in Ref. [2]. The Outboard airfoil model has a trailing edge thickness of 0.49% of the chord and is pictured in Fig. 5. A second airfoil was developed to be representative of the thicker Inboard wing sections on a transport aircraft wing. This “Inboard” airfoil has a thickness ratio of 16%, a 2-D design lift coefficient of C L = 0.62 at a 2-D Mach number of 0.67, and a chord length 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 CFD calculations using Simple Sweep Theory described in Ref. [2]. The Inboard airfoil has a trailing edge thickness of 0.66% of the chord and is shown in Fig. 6. One more airfoil development technique was performed in this research, namely expanding the trailing edge of the airfoil. One of the goals of the jet-wing distributed propulsion concept study is to increase the propulsion efficiency of the aircraft. As will be discussed later, the propulsion efficiency of the baseline Outboard airfoil with the jet-wing applied was slightly lower than the 80% that is typical of turbofans [9]. Therefore, an attempt was made at decreasing the jet exit speed by increasing the height of the airfoil trailing edge. The trailing edge of the Outboard airfoil was expanded by truncating the airfoil at the location of desired trailing edge height and then linearly stretching the airfoil to the correct chord length. The trailing edge expansion of the Outboard airfoil increased the trailing edge height from 0.49% to 0.98% of the chord. The Outboard airfoil with the original trailing edge thickness is now referred to as the “Outboard 1 × TE” airfoil, and the Outboard airfoil 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 performed using the Reynolds-averaged, three-dimensional, finitevolume, Navier–Stokes code GASP [6]. The three representative airfoils were modeled using conventional two-zone C-grids. The details of the Outboard airfoil grids are described in Ref. [2] and the details of the Inboard airfoil grid are given in Ref. [20]. Each CFD case was run at three grid levels: coarse, medium, and fine. Medium and coarse grid levels were obtained from the fine grid by reducing the number of grid points by a factor of two at each direction. The fine grid around Outboard 1 × TE airfoil (Fig. 7) had 493 × 65 grid points in the airfoil zone including the airfoil sur-
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Fig. 7. Two-zone C-grid around Outboard 1 × TE airfoil. Table 1 Free-stream properties used in the computations.
Free-stream Mach, M ∞ Free-stream temp., T ∞ Free-stream density, ρ∞ Angle of attack, α Reynolds number, Rec
Outboard 1 × TE airfoil
Outboard 1 × TE airfoil
Outboard 2 × TE airfoil
Inboard airfoil
0.72 218.93 K 0.3807 kg/m3 2.66◦ 5.67 × 106 (low Rec )
0.72 218.93 K 0.3807 kg/m3 2.66◦ 38.40 × 106 (design Rec )
0.72 218.93 K 0.3807 kg/m3 3.00◦ 38.40 × 106 (design Rec )
0.67 218.93 K 0.3807 kg/m3 0.521◦ 62.96 × 106 (design Rec )
face and the wake region and 85 × 41 grid points in the trailing edge region. At each grid level, except the coarsest one, the initial solution estimates were obtained by interpolating the primitive variable values of the previous grid solution to the new cell locations. This technique, known as grid sequencing, was used to reduce the number of iterations required to converge to a steady state solution at finer mesh levels. All the results presented in this manuscript were obtained with the finest mesh level. With the results of the medium and fine grid levels, the discretization errors at the fine grid level were estimated for the output quantities of interest using Richardson’s extrapolation method. For the cases presented in this manuscript the estimated discretization errors were less than 1.0% for the lift coefficient and less than 8% for the drag coefficient. In the CFD simulations, inviscid fluxes were calculated with 3rd order upwind biased Roe’s flux difference splitting scheme. The physical model included all the viscous terms (thinlayer and cross-derivative terms) and used Menter’s Shear Stress Transport turbulence model with compressibility corrections. The free-stream flow properties used in the CFD simulations for each of the three airfoils models are given in Table 1. Note that the design Reynolds number (based on the chord length and the flow conditions specified in Table 1) is Rec = 38.40 × 106 for the Outboard airfoil and Rec = 62.96 × 106 for the Inboard airfoil. These Reynolds numbers are typical values for conventional transport aircraft at cruise conditions. Runs with the design Reynolds numbers included 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 simulations were performed at a lower Reynolds number (Rec = 5.67 × 106 ) with the Outboard 1 × TE airfoil. These runs used the same freestream values, but had a scaled airfoil chord length of 1 m. Low Reynolds number runs included a no-jet case, a jet-wing case, and three jet-flap cases with different jet deflection angles (see Table 2). In the computations, airfoil chords are aligned with the x-axis of an x– y Cartesian coordinate system which defines the coordinates of the airfoil and the grid points in the physical domain. The free-stream flow, having a velocity magnitude of U ∞ , is specified in GASP with an angle of attack α . The lift and drag forces are aligned with a coordinate system rotated an angle α from the x– y coordinate system. The jet deflection angle (τ ) is defined as the
Table 2 Jet flow properties of airfoil models obtained at design and low Reynolds numbers. Outboard 1 × TE airfoil Reynolds number, Rec Jet Mach number, M ∞ Jet angle, τ (degrees)
Outboard Inboard 2 × TE airfoil airfoil
5.67 × 106 1.22 0.0
38.40 × 106 38.40 × 106
1.22 1.28
−2.66 5.0
1.34 1.199 10.0
0.0
62.96 × 106
1.021
1.059
0.0
3.0
angle between the jet direction and the airfoil chordline, and measured positive in the clockwise direction. The jet flow properties were determined using the results of the no-jet airfoil cases obtained with GASP. To simplify the modeling, it was assumed that the jet would use exhaust from the engine fan and that it would be at the same temperature as the free-stream. Furthermore, the pressure of the jet flow was set equal to the average of pressures on the upper and lower surfaces of the airfoil at the trailing edge. The jet flow Mach number M jet was determined from the thrust of the jet. Since the jet-wing is locally self-propelled, the jet thrust component 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
2 · ρ∞ · U ∞ ·c
(2)
Here we consider a unit wing span (b = 1 m). The jet thrust was found from the thrust equation
Thrustjet = ρjet · U jet · hjet · (U jet − U ∞ ) + ( p jet − p ∞ ) · hjet
(3)
Using Eq. (3) in Eq. (2), we obtained 2 C D · ( 12 · ρ∞ · U ∞ · c)
Cos(α + τ )
= ρjet · U jet · hjet · (U jet − U ∞ ) + ( p jet − p ∞ ) · hjet
(4)
Eq. (4) was solved for the jet exit velocity, U jet , and thus M jet . The jet flow properties for the airfoil cases presented in this paper are
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Table 3 Jet-wing results obtained at design Reynolds numbers. Airfoil
Outboard 1 × TE, no-jet
Outboard 1 × TE, jet-wing
Outboard 2 × TE, no-jet
Outboard 2 × TE, jet-wing
Inboard no-jet
Inboard, jet-wing
Angle-of-attack, α Jet Mach number, M jet Propulsion efficiency, η P Jet coefficient, C J Net lift coefficient, C L Net Net drag coefficient, C D Net
2.66◦ 0.0 N/A 0.0 0.6276 0.0124
2.75◦ 1.199 75.1% 0.0115 0.6230 0.0002
3.00◦ 0.0 N/A 0.0 0.6303 0.0136
3.13◦ 1.021 82.8% 0.0122 0.6389 −0.0001
0.521◦ 0.0 N/A 0.0 0.5824 0.0118
0.521◦ 1.059 81.0% 0.0089 0.4684 0.0008
listed in Table 2. The net force coefficients on the airfoil, including the effects of the jet thrust, were calculated using the formulas
C L Net = C D Net =
L Net 1 2
2 ·c · ρ∞ · U ∞
D Net 1 2
2 ·c · ρ∞ · U ∞
(5)
The jet thrust coefficient, C J , is defined as:
CJ =
˙ · U jet m 1 2
2 ·c · ρ∞ · U ∞
(6)
˙ is the mass flow rate of the jet. In our calculations to apHere m proximate the drag of a jet-wing section, we start with the drag of the no-jet case and use this value as an initial guess to obtain the required jet velocity. Then the results of the CFD simulations are used for the jet-wing case to calculate the net drag value, which should be ideally equal to zero or to a very small value for the wing section to be self-propelled. Depending on the value of the net drag, more iterations are performed if needed. We have seen that, in most cases, the estimate of the drag from the no-jet case was a good first approximation for the calculation the net drag of the jet-wing case. When no jet is present at the trailing edge, a no-slip boundary condition is applied to the trailing edge, just like the rest of the airfoil. However, when a jet is exhausted from the trailing edge, the primitive variables at the trailing edge (density, velocity components in x and y directions, and the static pressure) were kept fixed with the jet flow parameters. This boundary condition is appropriate for a supersonic jet flow ( M jet > 1) and have worked well for all the models, even when M jet was very close to 1. For the inflow and outflow boundaries, a Riemann subsonic, inflow/outflow boundary condition was used. 5. Design Reynolds number results 5.1. Outboard 1 × TE airfoil The CFD analysis with GASP gave a lift coefficient value of C L = 0.628 and a drag coefficient of C D = 0.0124 for the Outboard 1 × TE no-jet airfoil (see Table 3). This lift coefficient was 9% less than the design value of C L = 0.69. This difference originated due to the fact that the angle of attack (which was used in GASP simulations) for the design lift coefficient was obtained using MSES [4], an Euler + Boundary Layer Code to reduce the computational expense of the determination of the design angle of attack, which is an iterative procedure. From the results of the Outboard 1 × TE no-jet airfoil case (C D and p TE in particular), the jet conditions were calculated so as to produce a self-propelled jet-wing. The required jet flow Mach number was calculated as M jet = 1.199. Using Eq. (1), the propulsion efficiency of the Outboard 1 × TE jet-wing airfoil was obtained as η P = 75.1%. The resulting force coefficients for the no-jet and jet-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 C L Net = 0.63 at the design Reynolds number.
the pressure distributions are shown in Fig. 8. It should be noted that it was necessary to increase the angle of attack by a small amount in order to compare the no-jet and jet-wing airfoils at the same net lift coefficient. The pressure distributions for the no-jet and jet-wing case at the same lift coefficient are nearly identical, including the shock region. Fig. 9 shows the velocity profile located 1.0% downstream of the trailing edge of the airfoil. This figure helps to explain why the propulsion efficiency is low (η P = 75.1%) compared to a typical high-bypass-ratio turbofan enh
gine aircraft (η P typical = 80%). The jet is rather thin ( cjet = 0.49%) and does not exhibit good performance of ‘filling in’ the wake behind the airfoil. Also, note that the jet velocity is much greater than the free-stream velocity. The streamlines at the trailing edge of the Outboard 1 × TE no-jet airfoil can be seen in Fig. 10. A complex 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 in the same figure. The jet-wing fills in the flow on the trailing edge base and eliminates the vortex seen in the no-jet case. This example exhibits one of those rare cases when adding something to a flow problem actually simplifies the flow-field. 5.2. Outboard 2 × TE airfoil The Outboard 2 × TE airfoil was studied to determine how the expanded trailing edge affects the propulsion efficiency. As tabulated in Table 3, the drag of the Outboard 2 × TE no-jet airfoil is 9.7% higher than that of the Outboard 1 × TE no-jet airfoil. Although the net lift coefficients vary by only a small amount, the pressure distribution of the Outboard 2 × TE airfoil, plotted in Fig. 11, differs significantly from that of the Outboard 1 × TE airfoil especially in the shock region and on the lower surface close to the trailing edge. The shock is shifted approximately 4% aft of the 1 × TE airfoil shock location. The flow-field near the trailing edge of 2 × TE airfoil is pictured in Fig. 10. Compared to the flow-field of the Outboard 1 × TE no-jet airfoil, a larger vortex structure can be seen on the base of the Outboard 2 × TE airfoil.
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Fig. 9. Velocity profiles downstream of Outboard no-jet and jet-wing airfoils at
x c
= 1.01 at the design Rec .
Fig. 10. Streamlines and Mach number contours at the trailing edge of Outboard airfoils at design Reynolds number.
efficiency of the Outboard 2 × TE jet-wing airfoil was calculated using Eq. (1) and found to be η P = 82.8%. The pressure distribution is pictured in Fig. 12. As before, the jet-wing has a minimal effect on the pressure distribution. The velocity profiles in Fig. 9 show why the propulsion efficiency has been increased. The Outboard 2 × TE jet-wing has a lower jet speed than that of the Outboard 1 × TE jet-wing and provides a better ‘fill in’ of the wake behind the airfoil. The complex structure on the base of the Outboard 2 × TE no-jet airfoil is eliminated by the jet, as shown in Fig. 10. For this 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 increases substantially (nearly 10%). This could be a problem for an engineout situation. Therefore, expanding the trailing edge height is not a trivial modification and should be done in a multi-objective fashion by considering the other performance parameters. Fig. 11. Outboard 1 × TE and Outboard 2 × TE no-jet airfoil pressure distributions for C L Net = 0.63 at the design Reynolds number.
The results of the Outboard 2 × TE no-jet case were used to calculate the required jet flow to produce a self-propelled vehicle. The required jet flow Mach number was M jet = 1.021. The propulsion
5.3. Inboard airfoil The main objective of the Inboard airfoil study was to investigate the jet-wing distributed propulsion flow field around a thicker airfoil (t /c = 16%). Outboard airfoil studies showed that it was possible to increase the propulsion efficiency by enlarging the trail-
J.A. Schetz et al. / Aerospace Science and Technology 14 (2010) 1–10
Fig. 12. Outboard 2 × TE no-jet and jet-wing airfoil pressure distributions for C L Net = 0.63 at the design Reynolds number.
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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 Inboard airfoil used in this study has a thickness of 0.66% of the chord. Since the trailing edge of this airfoil has sufficient thickness, it was not necessary to double the trailing edge in order to increase the propulsion efficiency. With no jet, the drag coefficient for the Inboard airfoil was obtained as C D = 0.018. Using this value and the static pressure at the trailing edge, the jet Mach number was found to be M jet = 1.059, which was the required value for the airfoil to be self-propelled. The propulsion efficiency for the Inboard jetwing airfoil was calculated as η P = 81.0%. Fig. 13 shows the downstream velocity profile for the jet and no-jet cases. It can be seen that by adding the jet, the wake is partially filled in, which explains the increase in the propulsion efficiency. The velocity profiles for the two cases differ slightly outside the wake and the jet regions due to the difference in circulation, which originates from the difference in the lift coefficient values between two cases (see Table 3). As also observed in the Outboard no-jet airfoil cases, a vortex stands on the base of the Inboard airfoil when there is no jet (Fig. 14). With the injection of the jet from the trailing edge, this vortex is eliminated and the streamlines on the upper and the lower surface of the airfoil are pulled towards the trailing edge region to smoothly blend with the jet. Since the increase in propulsion efficiency was achieved without expanding the trailing edge, no drag penalty is expected for the Inboard airfoil in case of an engine-out situation. Because of this reason, this Inboard airfoil and the other similar transonic wing sections can be thought of as good candidates for the jet-wing application.
6. Low Reynolds number results The low Reynolds number results obtained with the Outboard 1 × TE airfoil show the effectiveness of the distributed propulsion jet-wing configuration when applied to smaller vehicles, such as UAVs. In addition to the baseline jet-wing configuration, in which the jet deflection angle is τ = 0.0◦ , jet-flaps were also studied, with the jet deflection angles of τ = −2.66◦ , τ = 5.0◦ , and τ = 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 nojet Outboard 1 × TE airfoil was obtained as C D = 0.0128. Using this value and the trailing edge pressure, the jet flow Mach number and the jet flow density were calculated (M jet = 1.22 and ρjet = 0.4038 kg/m3 ) for the jet-wing calculations to obtain a selfpropelled airfoil. The propulsion efficiency was found to be η P = 74.3%, which is slightly lower than that of the design Reynolds number case, η P = 75.1%. The force coefficients of the Outboard 1 × TE jet-wing airfoil at the lower Reynolds number are presented in Table 4. The lift coefficient of the jet-wing airfoil was within 0.7% of that of the no-jet airfoil, so increasing the angle of attack was not necessary. Fig. 15 compares the downstream velocity profiles of the design Reynolds number and the low Reynolds number jet-wing cases. The two jet velocity profiles are comparable. Overall, the results indicate that there is no significant difference between the propulsion efficiency, drag, and the lift coefficients of the design and the low Reynolds number cases.
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Table 4 Jet-wing results obtained with Outboard 1 × TE airfoil at low Reynolds number.
Angle-of-attack, α Jet Mach number, M jet Propulsion efficiency, η P Jet coefficient, C J Net lift coefficient, C L Net Net drag coefficient, C D Net
Outboard 1 × TE, no-jet
Outboard 1 × TE, jet-wing
2.66◦ 0.000 N/A 0.0000 0.6106 0.0128
2.66◦ 1.220 74.3% 0.122 0.6067 0.0001
Fig. 16. Trends in lift, drag, pitching moment with jet deflection angle at constant angle of attack and low Reynolds number. Note that the drag coefficient C D presented in this figure does not include the jet thrust.
Fig. 15. Velocity profiles downstream (x/c = 1.01) of Outboard jet-wing airfoil at design and low Reynolds numbers. Table 5 Outboard 1 × TE jet-wing and jet-flap airfoil results for Rec = 5.67 × 106 .
Angle-of-attack, α Jet angle, τ Jet Mach number, M jet Propulsion efficiency, η P Jet coefficient, C J Net lift coefficient, C L Net Net drag coefficient, C D Net Net pitch. mom. coeff., C mNet
Jet-wing
Jet-flap 1
Jet-flap 2
Jet-flap 3
2.66◦ 0.0◦ 1.220 74.3% 0.122 0.6067 0.0001 0.0341
2.66◦ −2.66◦ 1.220 74.3% 0.121 0.5642 0.0001 0.0268
2.66◦ 5.0◦ 1.280 72.1% 0.142 0.7003 −0.0009 0.0505
2.66◦ 10.0◦ 1.340 70.0% 0.160 0.7996 −0.0005 0.0702
Fig. 17. Comparison of pressure distributions for Outboard 1 × TE jet-wing/-flap airfoil at constant angle of attack and low Reynolds number.
6.2. Outboard 1 × TE airfoil jet-flap studies at low Reynolds number In addition to the usual jet-wing studies, several jet-flap cases were run at the lower Reynolds number to see how the jet influences vehicle performance when deflected to different angles. Attinello [1] and Yoshihara and Zonars [21] both studied high deflection angle (e.g. τ = 80◦ ) jet-flaps applied to high-lift situations. The jet-flap cases examined in this study used small jet deflection angles (τ = −2.66◦ , τ = 5.0◦ , and τ = 10.0◦ ) applied to the Outboard 1 × TE airfoil at cruise conditions and an angle of attack of α = 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 deflecting the jet and producing a self-propelled jet-flap airfoil was not straightforward and required several iterations. In fact, more iterations were required as the jet deflection angle was increased. For this reason, the additional complexity of maintaining a constant lift was not considered. The performance results of the jet-flap cases are shown in Table 5 for the three jet deflection angles. Note that the jet deflection angle of τ = −2.66◦ aligns the jet with the freestream flow. In Table 5 and Fig. 16, it is observed that even as the jet deflection τ is increased away a small amount, the net lift increases significantly (by up to 31% for τ = 10◦ ). As indicated in Fig. 16, the pitching moment also increases as the jet deflection angle increases, by 100% for a jet deflection angle of τ = 10◦ . However, the increased lift and pitching moment performance do come
Fig. 18. Comparison of pressure distributions near the trailing edge of the Outboard 1 × 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 jet produces some interesting effects on the flow around the airfoil. The pressure distributions for the jet-wing and jet-flap airfoils are compared in Fig. 17. Compared to the baseline jet-wing (τ = 0◦ ), deflecting the jet-flap downward moves the shock aft, while deflecting the jet-flap upward moves the shock forward. This helps explain the changes in lift produced by the jet-flap, as seen in Table 5. Furthermore, the jet-flap alters the pressure at the trailing edge, as shown in Fig. 18. Although the airfoils and even the jet-wings presented in this study typically experience equal pressures 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
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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, the pressure of the lower surface is actually less than the pressure on the upper surface at the trailing edge. Meanwhile, for positive jet deflection angles, the pressure distribution at the trailing edge spreads out. This phenomenon was also observed by Yoshihara and Zonars [21]. Fig. 19 shows the flow field near the trailing edge of the 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 moment of a jet-wing vehicle. These results support the idea of using deflected exhaust jets from trailing edges as a possible replacement for conventional control surfaces. Recall however, there is also 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-dimensional wing sections in transonic, viscous flow to analyze the jet-wing distributed propulsion flow fields at a range of flow conditions with different airfoil geometries. The goals of these numerical studies were: (1) to ascertain the effect of jet-wing distributed propulsion on propulsion efficiency, (2) to observe how jet-wing distributed propulsion affect the flow-field, (3) to determine design changes that might be implemented for achieving efficient distributed propulsion, and (4) to investigate the effect of the jetflaps with small jet deflection angles on aerodynamic parameters. Numerical studies were performed using two supercritical airfoils corresponding to the Inboard and Outboard wing sections of a conventional transport wing. In addition to the Outboard airfoil with the original trailing edge thickness (Outboard 1 × TE airfoil) of 0.49% of the chord, a modified version of Outboard airfoil with double trailing edge thickness (Outboard 2 × TE) was also used in the numerical studies. The design Reynolds number (based on the chord length) was Rec = 38.40 × 106 for the Outboard airfoil and Rec = 62.96 × 106 for the Inboard airfoil. Runs with the design Reynolds numbers included 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 simulations were performed at a lower Reynolds
number (Rec = 5.67 × 106 ) with the Outboard 1 × TE airfoil. Low Reynolds number runs included a no-jet case, a jet-wing case (a jet deflection angle of τ = 0◦ ), and three jet-flap cases with different jet deflection angles (τ = −2.66◦ , τ = 5.0◦ , and τ = 10.0◦ ). At the design Reynolds number, when the jet-wing was applied to the Outboard 1 × TE airfoil, the resulting propulsion efficiency was found to be η P = 75%. This performance was due to the insufficient jet height and relatively large velocity of the jet, which failed to “fill in” the wake efficiently. For the airfoil with the double trailing edge thickness, propulsion efficiency increased by 7.5%, however, the drag on the airfoil for the no-jet case also increased substantially (nearly 10%). This could be a problem for an engine-out situation. Therefore, expanding the trailing edge height is not a trivial modification and should be done in a multi-objective fashion by considering the other performance parameters. The propulsion efficiency for the Inboard jet-wing airfoil was calculated as η P = 81.0%. Since the increase in propulsion efficiency was achieved without expanding the trailing edge, no drag penalty is expected for the Inboard airfoil in case of an engine-out situation. Because of this reason, this Inboard airfoil and the other similar transonic wing sections can be thought as good candidates for the jet-wing application. The low Reynolds number jet-wing results indicate that there is no significant difference between the propulsion efficiency, drag, and the lift coefficients obtained at the design and the low Reynolds number cases. 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 moment of a jet-wing vehicle. These results support the idea of using deflected exhaust jets from trailing edges as possible replacement for conventional control surfaces. However, there is also a drag penalty associated with positive jet deflection angles. This is the same situation as for real flap deflections. Acknowledgement This work was supported by the NASA Langley Research Center under Grant NAG-1-02024.
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