Relativity Research of Total Pressure and Regulating Valve in Continuous Wind Tunnel and Its Application

As the main adjusting means of the total pressure for the continuous transonic wind tunnel, the characteristics of regulating valve directly affect the flow field performance of the wind tunnel, therefore, it is important to analyze and establish the correlation between the regulating valve and the total pressure, and it is necessary to select the appropriate regulating valve and its combination accordingly. Firstly, in terms of the pressure regulation principle of the wind tunnel pressure regulating system, combining with the flow characteristics of the regulating valve, the correlation between the position control of the regulating valve and the total pressure control of the wind tunnel is established, then the static test is conducted to verify the relationship. In order to shorten the flow field stability time under the negative pressure of 0.6m continuous transonic wind tunnel, based on the established theory, the valve system is optimized and reformed, and the blowing test is carried out. The results show that the time of optimized Mach number polar curve decreases by 40%~50%, which greatly improves the test efficiency, which further proves that the present analysis is correct and effective, and can provide reference for the design of pressure regulating system in continuous transonic wind tunnel.

Plane branches with Newton non-degenerate polars

To an equisingularity class of complex plane branches, described by its multiplicity [Formula: see text] and characteristic exponents [Formula: see text], [Formula: see text], there is a naturally associated family [Formula: see text] of equations containing a complete set of analytic representatives for all branches of the class. We show in this paper that the general polar curve of any member of [Formula: see text] is Newton degenerate, except when [Formula: see text], in which case the general member of [Formula: see text] corresponds to a curve which has a Newton non-degenerate general polar curve with a fixed Newton polygon, or when [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], with [Formula: see text] and [Formula: see text] is odd, in which case [Formula: see text] has a subset containing a complete set of analytic representatives for all branches of the class whose general member has also a Newton non-degenerate general polar curve with a fixed Newton polygon. In both cases, we give explicit Zariski open sets the points of which represent branches with Newton non-degenerate polars and describe the topology of their general polars.

A Degree Formula for Secant Varieties of Curves

Using the Stückrad–Vogel self-intersection cycle of an irreducible and reduced curve in pro-jective space, we obtain a formula that relates the degree of the secant variety, the degree and the genus of the curve and the self-intersection numbers, the multiplicities and the number of branches of the curve at its singular points. From this formula we deduce an expression for the difference between the genera of the curve. This result shows that the self-intersection multiplicity of a curve in projectiveN-space at a singular point is a natural generalization of the intersection multiplicity of a plane curve with its generic polar curve. In this approach, the degree of the secant variety (up to a factor 2), the self-intersection numbers and the multiplicities of the singular points are leading coefficients of a bivariate Hilbert polynomial, which can be computed by computer algebra systems.

AERODYNAMICS OF GLIDING FLIGHT IN A HARRIS' HAWK, PARABUTEO UNICINCTUS

1. A Harris' hawk with a mass of 0.702 kg and a maximum wing span of 1.02 m glided freely in a wind tunnel at air speeds between 6.1 and 16.2ms−1. The glide angle varied from 8.5% at the slowest speed to a minimum of 5% at speeds between 8.0 and 14.7 ms−1. The maximum ratio of lift to drag was 10.9 and the minimum sinking speed was 0.81ms−1 2. Wing span decreased when either air speed or glide angle increased. Wing area was a parabolic function of wing span 3. Lift and profile drag coefficients of the wings fell in a polar area similar to that for a laggar falcon (Falco jugger) and a black vulture (Coragyps atratus). A single polar curve relating lift coefficients to minimum profile drag coefficients can predict the maximum gliding performance of all three birds when used with a mathematical model for gliding flight 4. The parasite drag values that have been used with the model are probably too high. Thus, the profile drag coefficients determined from the polar curve mentioned above are too low, and the predicted wing spans for gliding at maximum performance are too large. The predicted curve for maximum gliding performance is relatively unaffected 5. The maximum lift coefficient for the Harris' hawk in the wind tunnel was 1.6. This value is probably less than the maximum attainable, since the hawk's wings never appeared to stall. The best estimate of the minimum profile drag coefficient is 0.026 at a lift coefficient of 0.60.

Gliding Birds: The Effect of Variable Wing Span

The equilibrium gliding performance of a bird is described by the relationship between sinking speed (V8) and air speed (V). When V9 is plotted against V, the points fall in a ‘performance area’ because the wing span is changed during gliding. The lowest V3 for each V in the performance area defines a ‘maximum performance curve’. This curve can be predicted by a mathematical model that changes the wing span, area and profile drag coefficient (CD, pr) of a hypothetical bird to minimize drag. The model can be evaluated for a particular species given (a) a linear function relating wing area to wing span, and (b) a ‘polar curve’ that relates CDpr and the lift coefficient (CL) of the wings. For rigid wings, a single polar curve relates CDpr to CL values at a given Reynolds number. The position and shape of the polar curve depend on the aerofoil section of the wing and the Reynolds number. In contrast, the adjustable wings of a laggar falcon (Falco jugger) and a black vulture (Coragyps atratus) gliding in a wind tunnel have CL, and CD,pr values that fall in a ‘polar area’ rather than on a curve. The minimum values of CD,pr at each CL bound the polar area and define a polar curve that is suitable for evaluating the model. Although the falcon and the vulture have wings that are markedly different in appearance, the data for either bird are enclosed by the same polar area, and fitted by the same polar curve for minimum CD,pr at each CL value. This curve is a composite of the polar curves for rigid wings with aerofoils similar to those found in avian wings. These observations suggest that the polar curves of other gliding birds may be similar to that of the falcon and the vulture. Other polar curves are defined by CL and CD,pr values for the falcon and the vulture gliding at a constant speed but at different glide angles. Each speed has a different polar curve; but for a given speed, the same polar curve fits the data foreither bird. The falcon and the vulture gliding in the wind tunnel at a given speed were found to increase their drag by decreasing their wing span. This change increases induced drag and probably increases CD,pr for the inner parts of the wing because of an unusual property of bird-like aerofoil sections: wings with such sections have minimum values of CDpr at CL values near 1, while conventional wings have minimum values of CD,Pr at CL values near 0.