Tural Tunay 18.04.2001
12 Temmuz 2007
Tural Tunay 18.04.2001
2000674
HMW # -a
PRESSURE AND VELOCITY MEASUREMENTS AT HIGH MACH NUMBERS:
Static-pressure measurements can be made using conventional static-pressure taps on a surface or a probe. If the boundary layer is disturbed by the presence of a shock wave in the vicinity of the pressure tap, the reading may not give the correct static pressure.
stagnation presssure can be measured with a stagnation tube aligned with the local velocity vector. If the flow is supersonic, however, a shock wave will form around the tip of the probe, as shown in fig. 1, and the stagnation pressure measured is that downstream of the shock wave and not of the free stream. The stagnation pressure in the free stream can be calculating using the normal shock relationships provided the free-stream Mach number is known.
A Pitot-static tube can be used to measure Mach numbers in compressible flows. Taking the measured stagnation pressure as the total pressure, the Mach number in subsonic flows can calculated from the total-to-static-pressure ratio according to eq.(1), namely
(1)
If the flow is supersonic, then the indicated stagnation pressure is the pressure behind the shock wave standing off the tip of the tube. By taking this pressure as the total pressure downstream of a normal shock wave and measuring the static pressure upstream of the shock wave, the Mach number of the free stream ( ) can be determined from the static-to-total-pressure ratio ( ) according to the expression,
(2)
which is called the Rayleigh supersonic Pitot formula. One notes, however, that is an implicit function of the pressure ratio and must be determined graphically or by some numerical procedure. Many normal shock tables have tabulated vs. , which enables one to find quite easily by interpolation.
Once the Mach number is determined, more information is needed to evaluate the velocity: namely, the local speed of sound. This can be done by inserting a probe into the flow to measure total temperature and calculating the static temperature using the following equation ,
(3)
The local speed of sound is then determined by
(4)
and the velocity is calculated from
(5)
the hot-wire anemometer can also be used to measure velocity in compressible flows provided it is calibrated to account for Mach-number effects.
Tural Tunay 18.04.2001
2000674
HMW # -b
1)
Figure 1. Schematic representation pf a Pressure-transmitting system
Consider a system shown in figure 1. The fluctuating pressure has a frequency of w an amplitude of Po and impressed on the tube of length L and radius r. The mass of fluid vibrates under the influence of fluid friction in the tube, which tends to dampen the motion.
The Natural Frequency wn is given below;
c: represents the velocity of sound in the fluid
2)
The Phase Angle: when both pressure signals and pressure transmitting system have the same frequency but do not oscillate together, the time difference (lag or lead) between their motions maybe expressed by an angle referred to as the phase angle,
h: represents the damping ratio
3)
The Resonance Frequency: frequency corresponding to maximum effect is known as the resonance frequency and for a transmitting fluid, it is taken as
4) In many cases it is convenient to use a noninertial, or accelerating, coordinate system. An example would be coordinates fixed to a rocket during takeoff. A second example is any flow on the earths surface, which is accelerating relative to fixed star because of the rotation of the earth. Atmospheric and oceanograhips flows experience the so-called Coriolis Acceleration, outlined below. It is typically less than 10-5 g, where g is the acceleration of gravity, but it is accumulated effect over distances of many kilometers can be dominant in geophysical flows. By contrast, the Coriolis Acceleration is negligible in small-scale problems like pipe or airfoil flows.
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