Transonic Wave Drag Research Articles

Estimation of Transport-Category Jet Airplane Maximum Range and Airspeed in the Presence of Transonic Wave Drag

One of the most difficult steps in estimating the cruise performance characteristics of high-subsonic transport-category turbofan-powered airplanes is the estimation of the transonic wave drag. Modern jet airplanes cruise most efficiently in the vicinity of the drag-divergence or drag-rise Mach numbers. In the initial design phase and later when the preliminary wind-tunnel and/or CFD computations and drag polars are known with increased accuracy, a method of estimating cruise performance is needed. In this study, a new semi-empirical transonic wave drag model using modified Lock’s equation was developed. For maximum range cruise estimations, an optimization criterion based on maximizing specific air range was used. The resulting nonlinear equations are of 12th- and 13th-order. Numerical Newton–Raphson nonlinear solvers were used to find real positive roots of such polynomials. The NR method was first tested for accuracy and convergence using known analytical solutions. A methodology for an initial guess was developed starting with the maximum-range cruise Mach without the wave-drag included. This guess resulted in fast quadratic convergence in all computations. Other novel features of this article include a new semi-empirical fuel-flow law, which was also extensively tested. Additionally, a semi-empirical turbofan thrust model usable for a wide range of bypass ratios and the entire flight envelope was developed. Such physics-based semi-empirical model can be used for a wide range of turbofans. The algorithm can be utilized to identify most beneficial input parameter values and combinations for the cruise flight phase. The model represents a powerful tool to estimate important cruise performance airspeeds located in the transonic regime. An intended application is in the conceptual development stages for early design optimizations of future airplanes. It is possible with additional effort to extend existing model capabilities to deal with supersonic transports optimal cruise parameters.

Multidisciplinary optimization of an NLF forward swept wing in combination with aeroelastic tailoring using CFRP

This article introduces a process chain for commercial aircraft wing multidisciplinary optimization (MDO) based on high fidelity simulation methods. The architecture of this process chain enables two of the most promising future technologies in commercial aircraft design in the context of MDO. These technologies are natural laminar flow (NLF) and aeroelastic tailoring using carbon fiber reinforced plastics (CFRP). With this new approach the application of MDO to a NLF forward swept composite wing will be possible. The main feature of the process chain is the hierarchical decomposition of the optimization problem into two levels. On the highest level the wing planform including twist and airfoil thickness distributions as well as the orthotropy direction of the composite structure will be optimized. The lower optimization level includes the wing box sizing for essential load cases considering the static aeroelastic deformations. Additionally, the airfoil shape adaptation based on sectional pressure distribution optimization and inverse design follows for the design point. Thereby, the objective function of the sectional pressure distribution optimization is the minimization of drag to find the best trade-off between profile drag considering NLF and transonic wave drag. First optimization results of the multidisciplinary process chain are presented for a forward swept wing aircraft configuration. At this stage, airfoil shape optimization has not been included yet. Instead, natural laminar flow is considered by prescribing laminar-turbulent transition locations.

Estimation of Performance Airspeeds for High-Bypass Turbofans Equipped Transport-Category Airplanes

Conventional Mach-independent subsonic drag polar does not replicate the real airplane drag characteristics exactly and especially not in the drag-divergence region due to shock-induced transonic wave drag. High-bypass turbofan thrust is a complicated function of many parameters that eludes accurate predictions for the entire operating envelope and must be experimentally verified. Fuel laws are also complicated functions of many parameters which make optimization and economic analysis difficult and uncertain in the conceptual design phase. Nevertheless, mathematical models and predictions have its important place in aircraft development, design, and optimization. In this work, airspeed-dependent turbofan thrust and the new fuel-law model were used in combination with an airplane polynomial drag model to estimate important performance speeds. Except for the airframe-only dependent control airspeeds, all performance speeds are airframepowerplant dependent. In all analytical considerations one ends up with polynomials of the 4 order that have no closed-form solutions. A real positive-root seeking numerical procedure based on the family of Newton-Raphson methods was used to extract performance airspeeds for variable in-flight weights and altitudes in the ISA troposphere. Extensive testing of the accuracy and convergence of the Newton-Raphson nonlinear equation solvers was conducted before performance speed calculations. A fictitious long-range wide-body transport-category airplane was modeled in combination with a pair of high-bypass and ultra-high bypass ratio flat-rated turbofans. Procedure employed here can be easily extended to cases when fitted, measured drag and thrust data is given in arbitrary polynomial forms. Sensitivity analysis is performed on minimum-drag airspeed and maximum aerodynamic efficiency. Transonic wave drag considerations are introduced.

Making Air Travelling More Economical, An Innovative Drag Reduction Approach For A Supercritical Wing Section Using Shock Control Bumps

AbstractAir travelling is the second largest travelling medium used by people. In future it is expected to be the first choice for the travellers. As increase in the price of oil cost of air travelling is getting higher. Engineers are forced to find the cheaper means of travelling by innovating new techniques. This paper presents the new idea to reduce air travelling cost by reducing drag, which is major driving factor of high fuel consumption. Two-dimensional and three-dimensional shock control contour bumps have been designed and analysed for a supercritical wing section with the aim of transonic wave drag reduction. A supercritical airfoil (NACA SC (02)-0714) has been selected for this study considering the fact that most modern jet transport aircraft that operate in the transonic flow regime (cruise at transonic speeds) employ supercritical airfoil sections. It is to be noted that a decrease in the transonic wave drag without loss in lift would result in an increased lift to drag ratio, which being a key range parameter could potentially increase both the range and endurance of the aircraft. The major geometric bump parameters such as length, height, crest and span have been altered for both the two-dimensional and three-dimensional bumps in order to obtain the optimum location and shape of the bump. Once an optimum standalone three-dimensional bump has been acquired an array of bumps has been manually placed spanwise of an unswept supercritical wing and analysed under fully turbulent flow conditions. Different configurations have been tested with varying three-dimensional bump spacing in order to determine the contribution of bump spacing on overall performance. The results show a 14 percent drag reduction and a consequent 16 percent lift to drag ratio rise at the design Mach number for the optimum arrangement of bumps along the wing span. This innovative technique proves to be a bridge between economical problems and engineering solutions and a milestone for aviation engineering.

Conceptual Design Studies of a Strut-Braced Wing Transonic Transport

Recent transonic airliner designs have generally converged upon a common cantilever low-wing configuration. It is unlikely that further large strides in performance are possible without a significant departure from the present design paradigm. One such alternative configuration is the strut-braced wing (SBW), which uses a strut for wing-bending load alleviation, allowing increased aspect ratio and reduced wing thickness to increase the lift to drag ratio. The thinner wing has less transonic wave drag, permitting the wing to unsweep for increased areas of natural laminar flow and further structural weight savings. High aerodynamic efficiency translates into smaller, quieter, less expensive engines and less pollution. A multidisciplinary design optimization (MDO) approach is essential to realize the full potential of this synergistic configuration caused by the strong interdependence of structures, aerodynamics, and propulsion. NASA defined a need for a 325-passenger transport capable of flying 7500 n miles at Mach 0.85 for a 2010 service entry date

Accurate transonic wave drag prediction using simple physical models

A new method is presented to compute the transonic wave drag of airfoils. Coupled with an inverse boundary-layer procedure, the calculated results have an accuracy comparable to experiments. The method is robust and easy to handle without the necessity of tuning; hence, it is an excellent engineering tool for supercritical airfoil design. The inviscid flowfield is assumed to be governed by the full potential equation except at the shock. The solution is obtained by a finite-difference method. At shock points, a shock operator is introduced; it satisfies the kinematic Prandtl relation for normal and oblique shocks, which is the consistent condition for the velocity potential. For each streamline behind the shock, an entropy correction is calculated by the Rankine-Hugoniot equations. The wave drag is given by integrating the entropy rise along the shock. The computational mesh, formed by incompressibl e stream and potential lines, allows easy coupling of the boundary-layer solution at the airfoil and wake. The H-type singularity at the incompressible stagnation point is handled by a finite-volume procedure. For better physical pressure and drag solutions, the condition of the normal shock has to be altered due to the boundary layer. Therefore, an analytic model of the inviscid interference region was developed and the essential features are embedded in the numerical procedure.

Transonic wave drag estimation and optimization using the nonlinear area rule

Nonlinear area ruling procedures based on the transonic slender body and lift-dominated theories are described as a means of providing low-cost wave drag estimates and optima for basepoint definition. The computational implementation is capable of accurately predicting drag rise of realistic configurations and shows applicability to moderate supersonic Mach numbers. An analogy between the zero-lift and liftdominated case establishes a basis for sizeable wave drag due to lift reduction through planform and sectional shaping. Results illustrating the potential benefits are shown for a fighter configuration in which a small movement of the maximum thickness location of the equivalent body of revolution with the volume fixed gives a fourfold reduction in zero-lift wave drag. This benefit can be translated into similar reductions in transonic wave drag due to lift.

On the wave drag integral for slender bodies

A method reported by Eminton (1963) is currently widely used in an evaluation of the transonic wave drag integral derived from linear theory. A description of an alternative approach utilizing Filon's quadrature rule is presented, taking into consideration the wave drag integral for a sufficiently slender body at zero incidence. Numerical results obtained in an application of the new approach are compared with data computed with the Eminton method and with a collocation method.

Numerical evaluation of the transonic wave drag integral

AbstractThis article describes‐a new method, suitable for use on a digital computer, for evaluating the singular double integral of Hayes which determines the transonic wave drag of a slender body. Comparison with known exact results and with an earlier computer program described by Eminton shows the present method to be accurate as well as economic in computer time.

Limitations of the Sonic Area Rule

SummaryRecent free flight tests have provided information on the applicability of the sonic area rule to non-lifting configurations. An analysis of results for the sonic wave drag of swept-back, tapered wings has suggested that the sonic area rule is applicable to thin wing and slender body combinations provided that the product of the wing span/length ratio and the cube root of the thickness /chord ratio is less than unity. The wing span/length ratio was found to be a much more useful slenderness parameter than the aspect ratio.When the wing has a round-nosed section, theoretical considerations predict the existence of a so-called leading edge drag force varying with Mach number. One would expect such a wing to have the same sonic drag-rise as the equivalent body with an identical cross-sectional area distribution. Some test results do not confirm this drag-rise equivalence. It appears that the transonic drag-rise of the leading edge force is much greater than that predicted by theory.Tests on one basic wing-body combination, with different body cross-sectional shapes of the same area, suggest that the cross-sectional shape, of a smooth slender body, has no influence on the transonic wave drag of a configuration.