EXPERIMENTAL DETERMINATION OF UNSTEADY LIFT[41]

Many methods have been used in measuring the unsteady aerodynamic forces (lift, moment, or pressure distribution) acting on an airfoil which is moving or is situated in a nonuniform flow. One may speak of “direct” and “indirect” measurements. If the forces are measured directly by dynamometers, manometers or strain gages, the measurement is said to be direct. If they are determined from their effect on the motion of the airfoil, air density, or other quantities, it is said to be indirect.

The requirements imposed on direct-measuring instruments are not easy to meet. The influence of the measuring instruments on the phenomena under examination must be kept as small as possible. The installation must not affect the flow to any appreciable degree. The variation of forces with time must be recorded with sufficient accuracy. In particular,

the time lag in the recording instrument due to the mass inertia of the sensing elements must be kept small.

In some of the indirect methods of measurement, the mass-inertia time-lag problem is completely eliminated. These methods are listed as follows:

1. Indirect Methods, (a) Determination of circulation from photo­graphs of the flow. In Walker15-119 and Farren’s experiments,15-112 a wing model is drawn through a glass vessel filled with water. The flow is made visible by small drops of olive oil and ethylene dibromide, and can be photographed. The velocity of the fluid particles can be deter­mined from the time of exposure and from the streak lines of the oil drops. The circulation about the wing is then obtained from the velocity field by a numerical integration.

(b) Determination of pressure from the variation of air density. Since the index of refraction of light varies with the density of a fluid, which in turn is related to the pressure field, the pressure can be determined optically. The variable index of refraction is measured by light inter­ference. Zender-Mach interferometer can be used for this purpose. This method is effective for high-speed flow, in the transonic and super­sonic ranges.

(c) Determination of unsteady forces from the motion influenced by these forces. The lift acting on an airfoil in entering a gust can be calcu­lated from the motion of the airfoil. The gust response may be verified by measuring the trajectory of an airfoil in passing through a jet stream (e. g., by dropping an airfoil through the test section of an open-jet wind tunnel). This method has been applied with certain degree of success by Kiissner.15110

A more commonly used method is based on forced oscillations. The wing model is excited by harmonic external forces, and the aerodynamic forces are determined from the kinematic quantities involved. Generally, the aerodynamic forces are not large compared to the inertia and elastic forces. Hence, the model must be built as light as possible (yet sufficiently rigid to prevent appreciable distortions) or a water tunnel must be used. See the works of Cicala,15-125 Dresher,15128 Greidanus,15,128 etc.

Flutter experiments may be considered as another approach. But, owing to the large number of parameters involved, it is unsuitable for an exact determination of the aerodynamic forces.

2. Direct Methods, (a) Spring balances. The transient force to be measured is opposed by a spring whose deflection is converted, for instance, into a rotation of a mirror, which is recorded by a pencil of reflected light. Various versions of spring balances are used by Farren,15111 Silverstein,15131 Scheubel,15117 Reid and Vincenti,15130 etc.

(b) Electric measuring elements. Forces can be measured by a number of electromagnetic devices, such as: (i) Piezoelectric gages (Kramer15115), (ii) Wire-resistance strain gages, (iii) Inductance transducers (Wiesels – berger15,120).

A piezoelectric gage measures the electric charges (or their voltages) produced on the end surfaces of certain crystal (e. g., quartz) when it is subject to pressure. It has been used for stationary models in a flow whose direction is changed at constant velocity.

A wire-resistance strain gage measures the change of resistance of a fine wire (e. g., tungsten) due to elastic strain. It can be used to measure the elastic deflections of springs. If the wire is attached to a thin metal membrane which deflects under pressure, it can be used as a pressure gage. Wire-resistance gages are used extensively both in wind-tunnel and in flight testing.

There are many types of inductance transducers. Either the air gap or the position of an iron core may be varied, and the corresponding change in inductance is measured. The displacement of the air gap or the iron core can be made proportional to the deflection of a spring, thus measuring a force. Very high accuracy can be achieved in certain designs.

Use of electrical means for measuring forces often involves a compli­cated electronic system. To improve the accuracy and ease the analysis, various ingenious schemes have been invented. As an example, one may name the “wattmeter” harmonic analyzer of Bratt, Wight, and Tilly,15,121 in measuring the aerodynamic damping for pitching oscillations. The modulated output from the stress indicator is first rectified and then analyzed electrically by means of an electronic wattmeter; the damping coefficient is obtained directly from meter readings.

The electrical measurements have the important advantage of min­imizing the mass-inertia effect of the sensing elements. With proper electronic equipment and circuits, it is probably the most convenient, accurate, and versatile of all methods.

(c) Manometers. Pressure distribution over the model surface can be measured by manometers. Drescher15,110 describes a successful multiple manometer used in measuring unsteady pressure distribution over an airfoil in a water tunnel.

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