The Minimization of Wave Drag on Struts, Using Mathieu Functions

Abstract A new effect related to the evaluation of momentum deposition in conventional parameterizations of orographic gravity wave drag (GWD) is considered. The effect takes the form of an adjustment to the basic-state wind about which steady-state wave solutions are constructed. The adjustment is conservative and follows from wave–mean flow theory associated with wave transience at the leading edge of the wave train, which sets up the steady solution assumed in such parameterizations. This has been referred to as “self-acceleration” and it is shown to induce a systematic lowering of the elevation of momentum deposition, which depends quadratically on the amplitude of the wave. An expression for the leading-order impact of self-acceleration is derived in terms of a reduction of the critical inverse Froude number Fc, which determines the onset of wave breaking for upwardly propagating waves in orographic GWD schemes. In such schemes Fc is a central tuning parameter and typical values are generally smaller than anticipated from conventional wave theory. Here it is suggested that self-acceleration may provide some of the explanation for why such small values of Fc are required. The impact of Fc on present-day climate is illustrated by simulations of the Canadian Middle Atmosphere Model.

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Transient Pressure-Driven Electroosmotic Flow through Elliptic Cross-Sectional Microchannels with Various Eccentricities

Computation ◽

10.3390/computation9030027 ◽

2021 ◽

Vol 9 (3) ◽

pp. 27

Author(s):

Nattakarn Numpanviwat ◽

Pearanat Chuchard

Keyword(s):

Laplace Transform ◽

Electroosmotic Flow ◽

Stokes Equations ◽

Navier Stokes ◽

Mathieu Functions ◽

Navier Stokes Equations ◽

Flow Rates ◽

Elliptic Cross ◽

Flow Through ◽

Relative Errors

The semi-analytical solution for transient electroosmotic flow through elliptic cylindrical microchannels is derived from the Navier-Stokes equations using the Laplace transform. The electroosmotic force expressed by the linearized Poisson-Boltzmann equation is considered the external force in the Navier-Stokes equations. The velocity field solution is obtained in the form of the Mathieu and modified Mathieu functions and it is capable of describing the flow behavior in the system when the boundary condition is either constant or varied. The fluid velocity is calculated numerically using the inverse Laplace transform in order to describe the transient behavior. Moreover, the flow rates and the relative errors on the flow rates are presented to investigate the effect of eccentricity of the elliptic cross-section. The investigation shows that, when the area of the channel cross-sections is fixed, the relative errors are less than 1% if the eccentricity is not greater than 0.5. As a result, an elliptic channel with the eccentricity not greater than 0.5 can be assumed to be circular when the solution is written in the form of trigonometric functions in order to avoid the difficulty in computing the Mathieu and modified Mathieu functions.

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A numerical study on the single pulsed energy addition based unsteady wave drag reduction at varied hypersonic flow regimes

Proceedings of the Institution of Mechanical Engineers Part G Journal of Aerospace Engineering ◽

10.1177/0954410020973134 ◽

2020 ◽

pp. 095441002097313

Author(s):

Dathi SNV Rajasekhar Rao ◽

Bibin John

Keyword(s):

Steady State ◽

Mach Number ◽

Drag Reduction ◽

Shock Layer ◽

Blunt Body ◽

Wave Drag ◽

Flow Features ◽

Energy Pulse ◽

Energy Addition ◽

Wave Drag Reduction

In this study, unsteady wave drag reduction in hypersonic flowfield using pulsed energy addition is numerically investigated. A single energy pulse is considered to analyze the time-averaged drag reduction/pulse. The blast wave creation, translation and its interaction with shock layer are studied. As the wave drag depends only on the inviscid aspects of the flowfield, Euler part of a well-established compressible flow Navier-Stokes solver USHAS (Unstructured Solver for Hypersonic Aerothermodynamics) is employed for the present study. To explore the feasibility of pulsed energy addition in reducing the wave drag at different flight conditions, flight Mach numbers of 5.75, 6.9 and 8.0 are chosen for the study. An [Formula: see text] apex angle blunt cone model is considered to be placed in such hypersonic streams, and steady-state drag and unsteady drag reductions are computed. The simulation results indicate that drag of the blunt-body can be reduced below the steady-state drag for a significant period of energy bubble-shock layer interaction, and the corresponding propulsive energy savings can be up to 9%. For energy pulse of magnitude 100mJ deposited to a spherical region of 2 mm radius, located 50 mm upstream of the blunt-body offered a maximum percentage of wave drag reduction in the case of Mach 8.0 flowfield. Two different flow features are found to be responsible for the drag reduction, one is the low-density core of the blast wave and the second one is the baroclinic vortex created due to the plasma energy bubble-shock layer interaction. For the same freestream stagnation conditions, these two flow features are noted to be very predominant in the case of high Mach number flow in comparison to Mach 5.75 and 6.9 cases. However, the ratio of energy saved to the energy consumed is noted as a maximum for the lower Mach number case.

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Thermal and structural response of aerospike mounted on blunt-nose body

Proceedings of the Institution of Mechanical Engineers Part G Journal of Aerospace Engineering ◽

10.1177/0954410020976488 ◽

2020 ◽

pp. 095441002097648

Author(s):

Zhang ZhunHyok ◽

Won CholJin ◽

Ri CholUk ◽

Kim CholJin ◽

Kim RyongSop

Keyword(s):

Aerodynamic Force ◽

Coupling Effect ◽

Angle Of Attack ◽

Structural Response ◽

Response Characteristic ◽

Wave Drag ◽

Hypersonic Vehicle ◽

Loosely Coupled ◽

Calculation Results ◽

Blunt Nose

The inclusion of aerospike on blunt nose body of hypersonic vehicle has been considered to be the simplest and most efficient technique for a concurrent reduction of both aeroheating and wave drag due to hypersonic speed. However, the thermal and mechanical behavior of aerospike structure under the coupling effect of aerodynamic force and aeroheating remains unclear. In this study, the thermal and structural response of aerospike mounted on the blunt nose body of hypersonic vehicle was numerically simulated by applying 3 D fluid-thermal-structural coupling method based on loosely-coupled strategy. In the simulation, the angle-of-attack and the spike’s length and diameter are differently set as α = 0°–10°, L/D = 1–2 and d/D = 0.05–0.15, respectively. Through the parametric study, the following results were obtained. Firstly, the increase of vehicle’s angle-of-attack and spike’s length unfavorably affect the thermal and structural response of aerospike. Secondly, the increase of spike’s diameter can improve its structural response characteristic. Finally, the aerospike with the angle-of-attack of 0° and the length and diameter of L/D = 1 and d/D = 0.15, respectively, is preferred in consideration of the effect of flight angle-of-attack and spike’s geometrical structure on the thermal and structural response of spike and the drag reduction of vehicle. The numerical calculation results provide a technical support for the safe design of aerospike.

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