# Envelopes of the Efficiency of Power Augmentation for a Scheme with a Reentrant Jet

Suggestions to utilize blowing under the main lifting wing of the wing-inground-effect vehicle for improved performance date back to early projects by Warner; see Belavin [1]. The technical development and implementation of the concept for large takeoff weight ground-effect vehicles is due to the effort of Russian engineers R. Bartini and R. Alexeyev. It is known that power augmentation by turbulent jets from upstream engines, directed under the wing, can be used either as a temporary, transitional mode of motion at takeoff and landing or permanently for cruise.

The efficiency of power augmentation (PAR) is determined by two main factors. The first of these factors is the magnitude of the required thrust of PAR engines for a given weight of the vehicle (the inverse quantity equal to the ratio of the lift Ry to the required thrust T can be characterized as the efficiency of power augmentation, later on designated as If par = Ry/T). The second factor is the thrust recovery, representing the excess thrust which can be used for forward motion. Gallington et al. [153, 154, 156] proposed a rather convenient form of diagrams which were called PAR envelopes. The vertical axis of these envelopes represents the PAR efficiency ATpar multiplied by a characteristic relative ground clearance h. Such scaling of the vertical axis of the PAR envelope implies that the order of the lift coefficient is Cy = 0(1) and that of the drag coefficient Cx = 0(h) (or the coefficient of required thrust) assumed and realized within a one-dimensional model of the flow. Hence, the efficiency factor if par should be of the order of 0(1/h) and ifpar. h = 0(1). A simple explanation of the correctness of such a scaling consists of the fact that in strongly deccelerated flow under the wing with a deflected flap, the pressure is close to the dynamic head. In this situation, the lift is directly proportional to the chord length, whereas the drag coefficient should be of the order of the ground clearance. The horizontal axis of the PAR efficiency envelopes represents the thrust recovery fraction, that is, the ratio of excess of thrust over the drag T — Rx to the thrust Тг = (T — Rx)/T = 1 — Rx/T. Having used some of the PAR energy to generate lift, it is important to have a certain reserve of thrust for further acceleration to cruise speed. Using the scheme of PAR flow with a reentrant jet, Gallington and Chaplin [154] analyzed the if par/і — Tr diagram for the simple case of a flat plate with a deflected flap and zero incidence, assuming that there is no leakage from the channel flow region. In the analysis, they employed two parameters, the width of the incoming jet in front of the wing and the width of the jet escaping the channel under the wing 5f, both parameters expressed as fraction of the characteristic ground clearance h (i. e., Sf). As a result, on the diagram were plotted two families of curves, corresponding to the constant magnitudes of each of these parameters when varying another one, namely, a (£j = const., = var.) and (Sf = const., = var.). On the PAR diagram presented by Gallington et al., the domain of points with coordinates if par — Tr is bounded below by a straight line, corresponding to 5f = 0 (zero gap under the flap). The upper boundary of this domain is obtained by using the momentum equation to a surface, including flow cross sections on the incoming jet, outcoming jet and the reentrant jet. This implies a realization of the momentum equation which corresponds to a minimal possible (within the PAR flow model with a reentrant jet) width of the incoming jet <Sj = <5jmin achieved for a jet orientation angle /3j = 7Г. Evidently, the latter case corresponds to maximum of PAR efficiency (ifpar h)max. Practical tasks that can be set forth to extend the approach of Gallington et al. are as follows:

• Using PAR efficiency envelopes based on a scheme of a reentrant jet and applying a mathematical model of the aerodynamics of the wing with small endplate tip clearance in a strong ground effect, analyze the influence of different factors (such as the angle of pitch, the curvature of the wing’s lower surface, the aspect ratio, gaps under the endplates, waves on the underlying surface, etc.) upon the efficiency of power augmentation;

• Consider approaches of modelling the PAR flow scheme with a realization of the Coanda effect with subsequent determination of power-augmentation efficiency;

• Analyze the reserves of enhancing PAR efficiency through an appropriate choice of the geometry and the kinematic parameters of the lifting surface and use of devices, such as rigid and jet flaps, forward flaps, etc., to control the efficiency of power-augmented regimes (e. g., by providing shock-free entry and fuller realization of the suction force);

• Develop a scheme of using PAR efficiency diagrams based on a potential theory for prediction and maximization of the efficiency of blowing the exhaust from the upstream PAR engines. Therewith, account should be taken of the most significant factors, such as momentum losses due to impact of the jet upon the ground, the mixing of turbulent jets, the entrainment of the surrounding air by the turbulent jet ejected by the engine on its way to the leading edge of the wing, the coalescence of a system of initially circular jets into an almost two-dimensional jet, and the space orientation and reciprocal position of engines in the PAR power system in the lateral, horizontal, and vertical directions, as well as their locations with respect to the wing.

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