25 Figure 29. Mach = 1.71, Reft = 4.31 million/ft with trip dots (red highlight).
Figures 30-33 show transition patterns from flight 456 with the 2-D forward-facing steps. A yellow line showing the transition line for the clean test article from flight 452 at similar Reynolds numbers (figures 22-24) has been added to the figures for comparison. On this flight, the upper step had a height of 0.0135 inches (0.0343 cm) and consisted of three layers of film. The lower step had a height of 0.0045 inches (0.0114 cm) and consisted of a single layer of film. Figure 30 shows the transition pattern at the beginning of the descent at Reft = 2.23 million/ft (7.32 million/m). The leading edges of both steps show up as a dark vertical line just downstream of the leading edge. The trailing edge of the upper step shows up as white vertical line located several inches behind the camera-pod shock. The trailing edge of the bottom step has the same longitudinal location as that of the upper step, but is not visible in the figure. A large turbulent wedge originating from the test article leading edge exists on the upper step. A post-flight inspection of the test article revealed a nick on the leading edge at this location. Runway debris kicked up from the airplane nose gear is thought to have caused the nick. A second turbulent wedge on the upper step is located at approximately 28 percent chord. This wedge is a direct effect of the disturbance caused by the step height. At approximately mid-span, a large turbulent wedge has formed from the bottom right corner of the forward face of the upper step. Even though both steps were tapered toward the trailing edge to account for turbulent wedge formation from the corners of the leading edge of each step, the bottom half of this turbulent wedge has encroached onto the upper portion of the lower step test area. A small section of the flow over the lower step remains laminar past the aft portion of the step and beyond the camera-pod shock. An incipient wedge can be seen approximately midway down the lower step, but the majority of the flow over the lower step is laminar. Two small turbulent wedges are apparent near the test article tip upstream of the step. The source of these wedges is not known at this time.
There are four primary instability mechanisms associated with swept wings: attachment-line, streamwise, crossflow, and centrifugal. Attachment-line contamination can occur on swept wings with large leading edge radii. This form of instability causes transition at the leading edge if the attachment-line Reynolds number exceeds a critical value that is dependent on the initial flow condition (laminar or turbulent) at the wing root junction. The streamwise instability is caused by the linear amplification of disturbances, referred to as Tollmien-Schlichting waves, which propagate in the boundary layer parallel to the wall. Tollmien-Schlichting waves are amplified by an adverse pressure gradient, which is common on conventional high-speed designs. The crossflow instability is an inflectional instability and is the dominant form of instability for wings with moderate to high sweep (sweep angles greater than approximately 25 deg). Swept wings can generate a significant spanwise pressure gradient on the wing. This pressure gradient results in the formation of a velocity component in the boundary layer or crossflow that is perpendicular to the inviscid streamline. The crossflow velocity component must be zero both at the wall and at the edge of the boundary layer, resulting in an inflection point in the boundary layer velocity profile. This inflection point is a source of instability that occurs as a pair of co-rotating vortices whose axes are aligned within a few degrees of the local inviscid streamlines . The centrifugal instability, commonly referred to as Görtler instability, is associated with surface concavity and results in the formation of counter- rotating vortices that are destabilizing to the boundary layer. This mode of instability can be controlled through configuration design. A more thorough description of these four transition mechanisms can be found in , while a detailed review of boundary layer stability theory and transition in general can be found in [4-6].
NASA and Aerion have partnered to study S-NLF since 1999
Series of S-NLF experiments flown on the NASA F-15B research test bed airplane Infrared (IR) thermography used to characterize transition
– Non-intrusive, global, good spatial resolution – Captures significant flow features well
In supersonic applications, CF and TCF disturbances are the most dominant modes in the leading-edge region of wings. Historically, these disturbances are controlled through either limiting the leading-edge sweep to less than 20 degrees or introducing a flow control system. To reach supersonicflight conditions, the leading-edge sweep of a wing is typically much more than 20 degrees, although some aircraft such as the F-104 and Aerion’s proposed supersonic business jet 4 with naturallaminarflow (NLF) have wings with fairly low leading-edge sweep. The application of NLF is limited by a combination of Reynolds number based on streamwise transition location (ReT) and the leading-edge sweep (ΛLE). Presently, one of the highest published combinations of transition Reynolds number and leading-edge sweep in flight was on the F-14 VSTFE flight test 5 . This represents the boundary, shown in Figure 1, between aircraft with NLF and laminarflow control (LFC). An LFC system employs suction at the leading edge through a porous or slotted surface to damp the CF instability. While such systems have proven to successfully delay transition due to CF, the added system complexity and weight have rendered this solution too costly for practical use in many situations. The major benefit of controlling transition due to CF waves with the present method is that it allows the vehicle to obtain the benefits of laminarflow (such as reduced skin friction drag), while permitting high leading-edge sweeps and removing the added cost associated with a complex suction system. The goal of this research is to push the current NLF boundary to higher combinations of transition Reynolds numbers and leading-edge sweep on supersonic commercial transports.
Figure 14 shows the control effect of the DRE2 pattern at a higher Reynolds number flight condition, unit Re = 10.8 million/m. Zones two (h/dDRE»0.10) and four (h/dDRE»0.30) show transition delays similar to unit Re = 8.5 million/m. It is interesting to note the transition delay above zone one. This delay in transition is not due to any DRE control effect. Although some suggest this may result from a temperature effect (i.e., freestream static temperature for the DRE2 configuration is 9 K cooler than the baseline), it is not yet clear what actually causes this uncontrolled transition delay to occur in this area. We believe this level of temperature difference between the baseline and control configurations is not sufficient to cause this transition front difference. The next set of IR images of Fig. 15 support this belief by presenting a comparison with a temperature difference of similar magnitude but with the opposite sign. Figure 15 presents the control effect of the DRE3 pattern on the unpainted wing leading edge at a flight unit Re = 7.4 million/m. The control effect shown for the unpainted wing leading edge configuration has a freestream static temperature difference with the DRE3 configuration 8 K warmer than the baseline. Even with the DRE3 configuration exposed to a warmer freestream condition, a similar DRE control effect appears. This DRE3 pattern consisted of a single zone of DREs that span most of the wing leading edge. Because this pattern is consistent, we expected to see laminarflow regions extended over more of the wing model span. The overlay image shown in Fig. 15 has a consistent band of cyan along the transition front as expected. Note we changed the wing leading-edge part to the unpainted leading-edge configuration with a completely new DRE pattern application and still achieved a transition delay effect comparable to earlier flight configurations. The elements of this new pattern are the shortest used in the flight test, nominally 18 µm tall (h/dDRE»0.07).
This result suggests that SST designers can choose a high swept-back planform or a low swept-back planform for the mission and the flight profile of the designed SST. However, researchers have mainly focused on high swept-back wings such as swept wings, delta wings, and cranked arrow wings, and only a few studies have ex- amined low swept-back wings. In addition, the CFD results also suggest that different optimum airfoils should be used depending on the planform because the trends of aerodynamic performance differ according to the planform. The several researches have been carried out regarding supersonic wing design  . In reference , a naturallaminarflow wing was designed by the inverse design. In reference , the multi-disciplinary de- sign which was considered the interaction between the aerodynamics and the structure by an evolutionary algo- rithm was discussed. These studies could find optimum results for a planform. However, the influence by the difference of the planform was not investigated. Therefore, it is necessary to obtain design knowledge regarding the differences in the aerodynamic performance of high and low swept-back wings for the optimum airfoil for a given planform.
theless, the vast NACA experience in the development of laminar-flow airfoils in the late 1930s and early 1940s, the British flighttests of naturallaminar-flow airfoils on the King Cobra and Hurricane air- planes in the mid-1940s, and the NACA and other previously mentioned tests of laminar-flow control through porous surfaces and slots in the late 1940s convinced the NACA that the inability to manufacture and maintain sufficiently wave-free and smooth surfaces was the principal impediment to the attainment of extensive regions of laminarflow for most airplane missions then conceived. The primary focus of the NACA (at least until its transformation in 1958 into the National Aeronautics and Space Adminis- tration [NASA]) was on the business of advancing the understanding of aeronauti- cal phenomena and not on solving manu- facturing or operational problems, which it considered to be the province of the manufacturer and user. The NACA, therefore, turned its attention away from LFC per se and concentrated its laminar- flow activities on expanding the under- standing of the quantitative effects of surface roughness on transition, with and without suction. Based on these NACA data and pertinent data from numerous other researchers, a correlation was
Fluorescent oil surface flow visualization 32 was also performed on the S414 airfoil model in its baseline configuration at Re = 1.8 × 10 6 , and M = 0.18 at α = 0° and α = 15°. At α = 0°, the flowfield is fairly uniform, indicating the presence of a laminar boundary layer across most of the fore element upper surface. At roughly x/c = 0.75, the change in the oil droplet patterns indicate transition has occurred on the fore element upper surface. The LSB can also be seen quite clearly on the aft element upper surface, in the same location identified at Re = 1.0 × 10 6 , M = 0.10 in Fig. 3.14. At α = 15°, the flowfield has well defined streaking oil droplet structures, indicating turbulent flow across most of the fore-element upper surface. The effects of the large leading edge suction peak from x/c = 0.0 to approximately x/c = 0.20 can also be seen. The LSB can be seen once again on the aft-element upper surface, with turbulent flow present downstream. It should be noted that for both Re = 1.8 × 10 6 , M = 0.18 oil surface flow visualization cases, a portion of contact paper was prone to slight separation off the aft element leading edge. This resulted in the typically laminar boundary layer being immediately tripped to turbulent, which can be seen to disrupt the LSB. Due to the location of the contact paper separation and the geometric constraints of the slot between the fore and aft element, the contact paper could not be reapplied in between tests. Both the oil flow visualization images and the C p distribution at each respective angle of attack can be
For the determination of stability properties of the boundary layer, it is im- portant to base the computations of the boundary-layer profiles on accurate boundary conditions. The most realistic boundary conditions are obtained from the pressure measurements, by using Bernoulli’s equation (2.4) to derive the necessary velocity distribution. As shown in Chapter 2.3.1, for unsteady flows the use of the steady Bernoulli equation introduces systematic errors, which, however, remain small for the investigated reduced frequencies. The limited number of pressure sensors does not allow direct linear interpolations to obtain a reasonably smooth distribution. Thus, a smooth interpolation or an accurate curve fitting procedure is necessary. Further complication is introduced due the abrupt changes of the pressure distribution in the vicinity of the stagnation point as shown in Figure 3.9(a). Data interpo- lation with elaborate local procedures such as Akima (1970) polynomials showed an unsuppressible tendency to overshoot in the region of rapidly changing gradients. Therefore, a procedure was developed, which combines the viscous-inviscid method described in Section 3.2 with the experimental results. To obtain a smooth and accurate solution at the leading edge, an XFOIL computation is employed using the specific flight Reynolds number. A MATLAB interface iterates the XFOIL solutions for various angles of at- tack until the computed distribution matches the experimental mean data of 14 specified pressure gauges in the leading edge region. In this region the boundary-layer is thin and a good coincidence between the panel solution and the measurements is to be expected. The sum of the least squares be- tween the third to the tenth sensor on the lower and the upper side of the wing glove is chosen as an iteration criterion. The angle of attack is varied in increments of 0.01 ◦ . Once convergence is achieved, simple fifth order polyno-
Overall Discussion & Future Work
The initial two dimensional analysis gave insight into how the concept of a supersonic channel airfoil could be applied to a generic cambered airfoil. Initial efforts to improve the airfoil by using rounded leading edges showed some improvement with large channel heights. The rounded leading edges were initially used because of concerns of heat transfer. At hypersonic speeds, the rounding of sharp edges is required to inhibit aerodynamic heating. However, at the low supersonic speeds, the heat transfer benefit of the rounded leading edge is negligible. By switching to a sharp leading edge, two benefits were seen. First, the sharp leading edge gave better shock performance. The sharp leading edge allows weaker oblique shocks to be formed than the detached normal shock formed at the channel entrance for a rounded channel. The second benefit was that more of the chord length was recovered. When the rounded channel airfoils were analyzed, the amount of lift was much lower than that of the baseline airfoil at supersonic speeds. From thin airfoil theory, the amount of lift at Mach numbers greater than one is dependent on the length of the chord of the airfoil. When the sharp airfoil was used, less of the chord was removed and the amount of lift produced increased.
Aircraft design of modern combat fighters had evolved around maneuverability at high angle of attack which extended the flight envelope to the stall and post stall region . This was accomplished through design of slender delta wings that leverage leading edge planform vortices to generate large magnitude of lift at high angle of attack by keeping the vortices to the extent possible attached to the wing surface. However, it was found that the lift and the maximum angle of attack can be further enhanced by incorporating high swept leading edge root extensions. It is worth noting that time scales  associated with vortex wing separation are larger than time scales associated with shear layer instabilities, wake instabilities and vortex breakdown instabilities which are considered unsteady flow phenomena that are responsible for the dynamics of aero-elasticity effects. At the extremes, angle of attack the phenomenon of
The channel geometry was also examined to try and improve the performance by obtaining a propulsive force out of the high pressure air in the channel. Two channels were created that started with an 8% channel at the inlet and the exit as a 16.6% channel. One channel had the
normal two kink configuration at the spar locations and the other had a straight channel edges from the 8% inlet to the 16.6% outlet. The number of kinks in the channel only caused a difference in L/D of 0.2%, which could be attributed to the coarseness of the grid. Overall, the growth of the channel gave the effect of a diverging nozzle because the expansion was much greater than the 0.1° used for a normal channel. However, since the flow exit was much larger than the inlet, the flow did not choke at the end of the channel but at the narrowest point of the channel, the inlet point of the channel as seen in Figure 7. This caused supersonicflow throughout the entire length of the duct. The bow shock structure correlated with a constant channel height of 8%. The viscous drag was similar in magnitude to an 8% channel, but the pressure drag did decrease when compared to an 8% channel. The pressure in the channel of an effect, but at high Mach numbers, the disparity between the baseline airfoil and the rounded channel airfoil lift forces was on the order of a few kilonewtons. An increase in L/D was 5.5 seen for 16.6% channel at Mach 2.0, which is a reasonable
Design of a geometry such that the laminar portion is increased or maximized is commonly denoted NaturalLaminarFlow (NLF) design. In terms of practi- cal implementations, NLF is probably the simplest approach. Once a feasible geometry is found no additional devices such as e. g. suction systems, sensors or actuators need to be mounted. One approach to NLF design is, in a ﬁrst step, to generate a pressure distribution (target) that delays transition, then, in a second step, design a wing that results in a pressure distribution as close as possible to the target. In addition constraints on e. g. lift, pitch, volume, minimum thickness et cetera must be handled. Green & Whitesides (1996) took an iterative approach which uses a target pressure-N-factor relationship to compute the desired pressure distribution, and an inverse method to ﬁnd the geometry which satisﬁes the computed pressure distribution. The N -factor method has also been used in multidisciplinary optimization problems of whole aircraft conﬁgurations where aerodynamics is considered as one discipline. In Lee et al. (1998), it was used to predict the onset of transition in order to deter- mine where to turn on a chosen turbulence model in the Reynolds-Averaged- Navier-Stokes equations, enabling calculation of the friction drag. In Manning & Kroo (1999), a surface panel method was coupled with an approximative boundary layer calculation, and stability analysis. Note however, that none of these investigations explicitly calculates the sensitivity of a quantity obtained from the stability analysis such as the N -factor or disturbance kinetic energy, with respect to variations of the geometry. In paper 5, the sensitivity of the disturbance kinetic energy with respect to the geometry is used for the purpose of optimal NLF design.
The trade results represent a range of test article thrusts from 1000 N to 5000 N, flight path angles from 0.0 degrees to -80.0 degrees, deployment altitude from 40 km to 70 km altitude, and burn times from 15 to 25 seconds. Due to the range of the test article thrust and burn time, the mass of the test article would be expected to vary substantially. To capture this, the mass of the system was estimated through the use of Mass Estimating Relations (MERs) for a Hypergolic rocket engine. The structure mass and communication mass was assumed to be constant across all cases. The engine mass was determined from a curve fit of existing hypergolic engines ranging in thrust from 100 N to 4000 N, which provided the engine mass as a function of the engine thrust. Finally, the fuel tanks were determined from the thrust, specific impulse of the engine, and the burn duration. In taking this approach, the objective was not to predict the precise mass of the test article but, instead, to capture the trends of the system.
operator is normally responsible for handling the necessary contacts with the air safety authorities, but in this case the operator delegated the responsibility to SAAB. In part this was because the aircraft is both owned and maintained by SAAB for operations by SAS.
The manufacturing issues were mainly related to the test specimen on the starboard wing, i.e. the "active" panel. Because of the relatively simple nature of the port panel, it was more or less a matter of simply exchanging the ordinary non de-iced panel with the "passive", multi- sectional panel. In the "active" panel case, however, a complex fluid system had to be built into the aircraft wing and nacelle affecting structure, electrical system, etc. Several disciplines were involved: mechanical systems, structures, electrical/avionics, production, maintenance etc. Structural integrity had to be ensured and since the aircraft has fully electronic flight instruments, stringent electrical interference requirements had to be met. Only flight qualified components were used. In some instances, where the required certification was not available, special qualifying tests had to be performed at considerable cost. Of the man-hours spent at SAAB on this project, 55% were on mechanical design issues, 10% on electrical system, 10% on direct manufacturing and installation and 25% on co-ordination and certification issues.
The objective of inverse airfoil design has traditionally been the determination of the airfoil shape that results in desired aerodynamic characteristics. Under this general classiﬁcation, inverse methods have progressed a great deal over the past few decades. With modern inverse methods, it is possible to prescribe velocity and/or boundary-layer characteristics along with desired geometric constraints in the design of airfoils. In spite of these advances, inverse airfoil design still involves a certain amount of trial and error when a designer attempts to ﬁne tune the drag polar of the airfoil or when attempting to tailor the airfoil for a particular application. The research presented in this thesis makes two speciﬁc advances to the state of the art in inverse design. The ﬁrst part of the research describes the development of an approach by which a desired boundary-layer transition curve can be speciﬁed as an input to inverse design. The second part presents an approach for incorporating aircraft performance considerations in the inverse design process. The two advances can help reduce the design cycle time for airfoil and aircraft design by reducing the amount of trial and error in the design process. The motivation factor for the ﬁrst part of the research (inverse design via speci- ﬁcation of the boundary-layer transition curve) was the strong connection between the transition curve and the airfoil drag polar. In the approach developed, a mul- tidimensional Newton iteration is used to adjust the velocity distribution until the transition lift coeﬃcient at several locations on the airfoil are within a given tolerance of the speciﬁcations. It is shown that the shape of the drag bucket as well as the camber and extents of laminar ﬂow on the airfoil can be controlled through the speciﬁcation of the transition-curve. This method represents an en- hancement over previous inverse airfoil design methods since it allows for a single speciﬁcation that spans multiple operating points.
The studies of free-convective flow along a vertical cylinder are important due to its applications in the field of geothermal power generation, drilling operations, geological formulation. Pop, Ingham and Cheng  investigated the growth of the free convection boundary- layer on an isothermal horizontal circular cylinder embedded in a porous medium. El-Shaarawi and Sarhan  have considered the fully developed free convective flow in the vertical annuli with one boundary isothermal and opposite adiabatic boundary. Bhadram  have considered the combined free and forced convective flow and heat transfer in vertical annulus when a radial magnetic field is applied. Singh and Jha  studied the fully developed natural convective flow in the presence of a radial magnetic field by obtaining a unified solution when the thermal boundary condition at the inner cylinder is of mixed kind while outer one is kept on constant temperature. Kumar and Singh  studied the Effect of induced magnetic field on natural convection in vertical concentric annuli heated/cooled asymmetrically. Timol and Kalthia  is probably first to develop systematic analysis of natural convection flows of all non-Newtonian visco-inelastic fluids characterized by the special functional relationship of stress strain components.
American Institute of Aeronautics and Astronautics 6
The results for the evolution of various modes in a nonlinear computation for Re c = 24 x 10 6 are described first.
To initiate the nonlinear computation, the mode shape is first computed for the target mode of wavelength 8 mm using LPSE. The chordwise velocity component for this mode is assigned an initial amplitude of 10 –4 , i.e., .01% of the free-stream velocity. For stationary crossflow computations, the number of Fourier modes used in the spanwise direction is 40, i.e. -40 < n < 40 in Eq. 2. Figure 7(a) presents the results for the case without control. The primary mode (0, 1) initially follows the linear PSE result until its harmonics grow to significant enough amplitudes for the primary mode to saturate, as indicated by the flattening out of the amplitudes in Fig. 7 (a). It can be seen that the disturbance energy cascades into the harmonics (0, 2), (0, 3), etc. The mean flow distortion (0, 0) mode also gains significance, and it attains amplitude equivalent to the first harmonic (i.e., 0, 2) mode. These results are similar to the nonlinear crossflow disturbance evolution computed in Ref. 11 for a canonical problem and in Ref. 12 for a low speed swept-wing flow. The results for the case with DRE control using a control wavelength of 4 mm ((0, 2) mode) are shown in Fig. 7(b), with an initial amplitude for the control mode of .015 (i.e., 1.5% of the free-stream velocity). In contrast with the results in Fig. 7(a), initial amplitude of (0, 2) mode is much higher than the (0, 1) mode. It can be seen that the control mode initially grows but eventually decays within a short chordwise distance, as expected from the LPSE results. The target mode growth is delayed, as discussed in detail in the following paragraphs. Here, one should note that after a period of decay, the control mode picked up again further downstream as a harmonic of the target mode which, by then, had attained a large amplitude.
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It is observed from the above results that, with increase in injection velocity coefficient, the flow separation is delayed. For a given chord length, the injection velocity coefficient can vary with in a certain range. If the injection velocity coefficient is beyond the range, it de-stabilizes the pressure and velocity distribution around the airfoil. The modification near the suction slot has improved the flow performance at the trailing edge by reducing turbulence. But the modification at the suction slot causes flow separation occurs at low angles of attack due to pressure difference between the upper and lower surface of airfoil.