2. Prediction of Minimum Drag
2.3 Analytic estimations / Numerical simulations
PART A Analytic Estimation
One of the oldest, however still useful for preliminary estimation, method was provided by Hoerner [1]; his semi-empirical form of equations covers various form of already-exist designs as shown in Fig. 2.51. Marino [4] evaluated various drag reduction technique for subsonic transport aircraft which is very sensitive to skin-friction drag. Indeed, most of the technique focused on delay of transition using wall-jet or other momentum addition techniques.
Fig. 2.51. Drag estimation of various form of tails, strut, pylon, and cooler inlets [1]
Fig. 2.52. Drag estimation of viscous drag reduction techniques for subsonic transport [4]
Fig. 2.53. Drag estimation of viscous drag reduction techniques for subsonic transport. CONTINUED [4]
Other than semi-empirical ones, Page [28] uses transonic small-disturbance equations to evaluate the wave drag. While the conventional linear theory underestimates the drag, modified one shows better result. However, both methods still have discrepancy for the experiment result as shown in Fig. 2.54. Fig. 2.55 presents another analytic estimation result for the drag related to the nose shape [29]. In order to evaluate drag efficiently, harmonic transform had conducted [30]. Lomax [31] proposed linearized theory which represent drag in terms of areas and oblique planes while similarity laws, specially used for hypersonic condition, were proposed by Miele [32]. Adams [33] determines drag of boattail bodies for minimum wave drag based on these theories.
Fig. 2.54. Drag estimation of various wing-body combination for experiment, linear, modified theory [28]
Fig. 2.55. Drag estimation of nose shape change [29]
Fig. 2.56. Drag estimation theory in terms of harmonic analysis [30]
Fig. 2.57. Drag estimation theory in terms of linearized flow [31]
Fig. 2.58. Determination of boattail drag for minimum wave drag [33]
PART B Numerical Simulation (CFD)
Recently, usage of CFD for the drag estimation is in rapid growth [34] as shown in Fig. 2.59. Kulfan’s [35] hybrid approach using both CFD(panel) and far-field method is used to optimize the drag of the supersonic transport aircraft as shown in Fig. 2.60. More specifically, sting correction of wind-tunnel experiment [36] had been conducted which is importantly considered in the previous part.
In jet fighter’s case, sting should be installed at the nozzle part, then it makes hard that engineer measures precise drag evaluation of thrust-drag book-keeping. Willhite et al. [37] used CFD for the correction of the sting; they evaluated pressure distortion of sting and nozzle propulsion. Wing-tip mounted sting was used to simulate the mass flow of nozzle as shown in Fig. 2.62-63. With proper correction, difference among the method is about few counts (~0.0001) which is reasonable range of drag prediction.
Slator [38] proposed general design and analysis tool for external compression supersonic inlets in given shapes as shown in Fig. 2.64. He organized inlet as types, mass-flow, and other few parameters to analyze it, and CFD method is well used to design it. Now, even the effect of aero-elastic for the minimum drag prediction is introduced [39] as shown in Fig. 2.65; FSI (fluid-structure-interaction) method is now available as computational power is significantly increased. Gregg [40] summarized these recent efforts of CFD for aerodynamic design.
From now on, I will talk about ramjet/scramjet or hypersonic topic as next one. In that topic, method or approach is basically same as high AoA or CDmin prediction. Indeed, I will not repeat the review of the method as shown in these Chap. 1 and 2. With the connection of Missile-SIM, I practically design some missiles with ramjet/scramjet while I naturally introduce the background of the ramjet/scramjet or hypersonic issues.
Fig. 2.59. CFD analysis for supersonic jet [34]
Fig. 2.60. Hybrid approach using far-field and CFD method for drag optimization of supersonic transport [34]
Fig. 2.61. Wind-tunnel experiment sting correction via CFD [36]
Fig. 2.62. Wind-tunnel experiment sting correction via CFD [37]
Fig. 2.63. Wind-tunnel experiment sting correction via CFD. CONTINUED [37]
Fig. 2.64. Inlet design framework [38]
Fig. 2.65. Aero-elastic effect considered CFD for transport aircraft [39]
Fig. 2.66. Summary of CFD usage on airliner design [40]
Fig. 2.67. Summary of CFD usage on airliner design. CONTINUED [40]
* Reference
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[2] Mason, W. H., 2006, ConfigAeroDrag
[3] Jobe, C. E., 1984, Prediction of Aerodynamic Drag, AFWAL-TM-84-203
[4] Marino, A ., et al., 1975, Evaluation of Viscous Drag Reduction Schemes for Subsonic Transport, NASA CR-132718
[5] Sawyer, R. H., and Trant, Jr. J. P., 1950, Effect of Various Modifications on Drag and Longitudinal Stability and Control Characteristics at Tansonic Speeds of a Model of the XF7U-1 Tailess Airplanes, NACA RM SL50D18
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[7] Katz, E., 1949, Flight Investigation from high subsonic to supersonic speeds to determine the zero-lift drag of a transonic research vehicle having wings of 45 deg sweepback, aspect ratio 4, taper ratio 0.6, and NACA65A006 airfoil sections, NACA RM L9H30
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[9] Hoffman, S., and Chaubin, L. T., 1961, Aerodynamic Heat Transfer and Zero-Lift Drag of a Flat Windshield Canopy on the NACA RM-10 Research Vehicle at High Reynolds Numbers for a Flight Mach Number Range from 1.5 to 3.0, NACA RM L56G05
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[29] Fuller, F. B., and Briggs, B. R., 1951, Minimum Wave Drag of Bodies of Revolution with a Cylindrical Section, NACA TN 2325
[30] Holdaway, G. H., and Mersman, W. A., 1956, Application of Tchebichef Form of Harmonic Analysis to the Calculation of Zero-Lift Wave Drag, NACA RM A55J28
[31] Lomax, H., 1955, The Wave Drag of Arbitrary Configurations in Linearized Flow as Determined By Areas and Forces in Oblique Planes, NACA RM A55A18
[32] Miele, A., 1966, Similarity Laws for Lifting Wings of Minimum Drag at Hypersonic Speed, NASA CR70729
[33] Adams, M. C., 1951, Determination of Shapes of Boattail Bodies of Revolution for Minimum Wave Drag
[34] Llorca, I. B., 2015, CFD Analysis and Assessment of the Stability and Control of a Supersonic Business Jet, KTH
[35] Kulfan, B., 2009, New Supersonic Wing Far-Field Compsite Element Wave-Drag Optimization Method, J. Aircraft
[36] Cartieri, A., and Boyet, M. G., 2010, Study of Support Interference Effects at S1MA Wind Tunnel within the “SAO” Project, ICAS 2010
[37] Willhite, P., et al., 1995, A Critical Evaluation of CFD Predictions of Full Aircraft Drag Increments, 26th AIAA Fluid Dynamics Conference, AIAA 95-2289
[38] Slater, J. W., 2012, Design and Analysis Tool for External-Compression Supersonic Inlets, NASA/TM-2012-217660
[39] Keye, S., and Gammon, M. R., 2017, Development of Deformed Computer-Aided Design Geometries for the Sixth Drag Prediction Workshop, J. Aircraft
[40] Gregg, R., 2014, CFD and Aircraft Design, Boeing
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