Nonlinear effects in the interaction of periodic pulsed energy supply and shock-wave structure during transonic streamlining of wing profiles

2009

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The possibility of controlling the aerodynamic characteristics of airfoils with the help of one-sided pulsed-periodic energy supply is studied. The change in the flow structure near the airfoil and its aerodynamic characteristics are determined as functions of the magnitude of energy supply and of the energy-supply location by means of the numerical solution of two-dimensional unsteady equations of gas dynamics. It is demonstrated that external energy supply can substantially improve the aerodynamic characteristics of airfoils with a high lift-to-drag ratio. The moment characteristics of the airfoil are found.Introduction. The effect of energy supply on the aerodynamic characteristics of a symmetric airfoil in a flow with a free-stream Mach number M ∞ = 0.85 was studied in [1][2][3][4]. At the same Mach number M ∞ , the influence of energy supply on the aerodynamic characteristics of an airfoil was considered in [5]. The effect of energy supply in the case of transonic flows around asymmetric airfoils with a substantially higher lift-to-drag ratio typical for lower Mach numbers, however, was not give proper attention. The aerodynamic characteristics of bodies in transonic flow are known to change substantially. Yuriev (see, e.g., [6]) demonstrated an ambiguous behavior of the drag of the NACA-0012 airfoil with energy supply, depending on the free-stream Mach number varying in the range M ∞ = 0.8-0.9: it can either increase or decrease. In contrast to [1-6], Starodubtsev [7] performed a pioneering study with numerical simulations of a transonic flow around an airfoil with local volume heat supply on the basis of Reynolds-averaged Navier-Stokes equations. Various aspects of the influence of energy supply on the flow around an airfoil were considered, and an upstream shift of the closing shock wave was found, which confirmed the previously established (see, e.g., [1]) character of flow reconstruction. It should be noted that the chosen location, compact shape, and power of the energy source did not improve the lift-to-drag ratio K of the airfoil. The influence of heat transfer between the flow and the surface was considered in the examined range of the free-stream Mach numbers, in addition to the effect of volume energy supply (see, e.g., [8,9]).In the present paper, we study the effect of energy supply on the flow around an optimal airfoil (with respect to its lift-to-drag ratio for the Mach number M ∞ = 0.75 in a certain class of configurations). As the Mach number M ∞ is smaller and the shape is more optimal, the lift-to-drag ratio of this airfoil is substantially higher than that in the cases considered in [1][2][3][4][5][6][7]. Therefore, it seems of interest to study the effect of energy supply as a method of controlling the aerodynamic characteristics of the airfoil.Formulation of the Problem. As a mathematical model for the description of a plane unsteady flow of an inviscid heat-non-conducting gas with a constant ratio of specific heats γ, we use the Euler equations in a conservative form ∂U ∂t + ∂F ∂x + ∂G...

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confidence: 98%

“…The effect of energy supply on the aerodynamic characteristics of a symmetric airfoil in a flow with a free-stream Mach number M ∞ = 0.85 was studied in [1][2][3][4]. At the same Mach number M ∞ , the influence of energy supply on the aerodynamic characteristics of an airfoil was considered in [5].…”

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confidence: 99%

Aerodynamic characteristics of airfoils with energy supply

2009

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“…2) than it is possible with symmetric energy supply [1][2][3]. The pressure behaves nonmonotonically near the energy-supply zone: the pressure is increased ahead of the zone and lower in the zone because of gas spreading.…”

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confidence: 99%

Effect of asymmetric pulsed periodic energy supply on aerodynamic characteristics of airfoils

2007

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The possibility of controlling the aerodynamic characteristics of airfoils in transonic flight regimes by means of local pulsed periodic energy supply is considered. The numerical solution of two-dimensional unsteady equations of gas dynamics allowed determining the changes in the flow structure near a symmetric airfoil and its aerodynamic characteristics depending on the magnitude of energy in the case of its asymmetric (with respect to the airfoil ) supply. The results obtained are compared with the calculated data for the flow around the airfoil at different angles of attack without energy supply. With the use of energy supply, a prescribed lift force can be obtained with a substantially lower wave drag of the airfoil, as compared with the flow around the airfoil at an angle of attack.Introduction. The study of transonic flow around airfoils with pulsed periodic energy supply [1-4] provided the first results on nonlinear effects arising if the energy is supplied in thin zones located along the airfoil. The energy-supply regime proposed in [1-4] made it possible to reduce the wave drag of the airfoil by more than a factor of 2. Such a significant change in the flow structure with moderate consumption of energy was previously observed for supersonic flows only.The energy can be supplied along the airfoil contour, for instance, with the use of a sliding pulsed arc discharge. The corresponding experiments with Mach numbers 1.7 < M < 3.4 were performed in [5]. The experiments described in [6] involved a glow discharge on the wing of an aerodynamic model in a subsonic flow (with a flow velocity of 150 m/sec). In [7], similar experiments were performed at M = 4. Based on a plasma sheet in a transonic flow with a shock wave, a near-surface distributed energy-supply zone was obtained in [8].In the present work, the calculations were performed for asymmetric energy supply, which allowed us to obtain the lift force and pitching moment. This paper continues the investigations of the shock-wave structure of the transonic flow around a symmetric airfoil [1-4, 9, 10]. Asymmetric energy supply in a supersonic flow was considered, for instance, in [11][12][13][14].Formulation of the Problem. A system of two-dimensional unsteady equations of gas dynamics (Euler equations) in conservative form for an ideal gas with a constant ratio of specific heats γ is used as a mathematical model of the flow. A total variation diminishing (TVD) scheme is used in the intervals between instances of energy supply to solve this system numerically. Integration in time is performed by the Runge-Kutta method. The 352 × 320 computational grid in the physical domain is geometrically adapted to the airfoil contour and is refined in the vicinity of the latter. In the model considered, pulsed supply of energy is performed instantaneously, and the gas density and velocity remain unchanged thereby. The energy density of the gas e in energy-supply zones increases by Δe = ΔE/ΔS (ΔE is the total energy supplied in one zone per unit length in the direction per...

“…In the experiments performed in [9, 10], a plasma sheet was used to obtain a near-surface zone of energy supply in a transonic flow with a shock wave. The plasma sheet parameters (layer thickness and amount of the supplied energy) agree with the corresponding parameters of the energy-supply zone in [1,2].…”

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confidence: 75%

“…2) than in the case of symmetric energy supply [1,2]. This fact is responsible for the weak dependence of the lift and wave drag coefficients on the energysupply zone location along the airfoil.…”

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confidence: 78%

Effect of one-sided unsteady energy supply on aerodynamic characteristics of airfoils in a transonic flow

2008

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The possibility of controlling the aerodynamic characteristics of airfoils in transonic flight regimes by means of one-sided pulsed-periodic energy supply is studied. Based on the numerical solution of two-dimensional unsteady gas-dynamic equations, the change in the flow structure in the vicinity of a symmetric airfoil at different angles of attack and the aerodynamic characteristics of the airfoil as functions of the amount of energy supplied asymmetrically (with respect to the airfoil ) are determined. The results obtained are compared with the data calculated for the flow past the airfoil at different angles of attack without energy supply. It is found that a given lift force can be obtained with the use of energy supply at a much better lift-to-drag ratio of the airfoil, as compared to the case of the flow past the airfoil at an angle of attack. The moment characteristics of the airfoil are found.Introduction. In contrast to papers [1-3] dealing with a transonic flow past symmetric airfoils at a zero angle of attack with pulsed-periodic symmetric energy supply, we consider one-sided energy supply, which allows us to obtain the governing forces and moments necessary for controlling the flight of various vehicles. Based on the numerical solution of two-dimensional unsteady gas-dynamic equations, the change in the flow structure in the vicinity of a symmetric airfoil is studied, and the wave drag is obtained as a function of the amount of energy supplied on the lower part of the airfoil in a transonic flow at different angles of attack. The results obtained are compared with the calculations for such an airfoil at different angles of attack without energy supply. It is found that a given lift force can be obtained with the use of energy supply at a much better lift-to-drag ratio of the airfoil, as compared to the case of the flow past the airfoil at an angle of attack. Some results of such a study (for a flow past an airfoil at a zero angle of attack) were published [4,5].The study of a transonic flow past airfoils with pulsed-periodic energy supply [1, 2] revealed some new nonlinear effects observed if energy supply is performed in narrow regions aligned along the airfoil. The regime of energy supply proposed in [1, 2] allowed the wave drag of the airfoil to be more than halved. The energy can be supplied along the airfoil, for instance, by using a sliding pulsed arc discharge. Such a discharge was initiated in a supersonic flow (at Mach numbers 1.7 < M < 3.4) in [6]. The experiments performed in [7] involved a glow discharge on an aerodynamic model wing in a subsonic flow (with a flow velocity of 150 m/sec). Skvortsov et al. [8] performed similar experiments at M = 4. In the experiments performed in [9, 10], a plasma sheet was used to obtain a near-surface zone of energy supply in a transonic flow with a shock wave. The plasma sheet parameters (layer thickness and amount of the supplied energy) agree with the corresponding parameters of the energy-supply zone in [1,2].