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Consider elements of the subject of high-speed aerodynamics, from subsonic to supersonic.

does a change in angle of attack affect the critical mach number? can you explain the underlying physics as well as how the prandtl-glauert rule may be used to confirm the result?

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User Grucha
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Answer:

Step-by-step explanation:

Yes, a change in angle of attack does affect the critical Mach number of an airfoil or aircraft. The critical Mach number is the airspeed at which the local airflow over a point on the airfoil reaches the speed of sound, resulting in a shock wave and loss of lift. At lower airspeeds, the airflow is subsonic, while at higher airspeeds, the airflow becomes supersonic.

When the angle of attack of an airfoil is increased, the airflow over the upper surface of the airfoil is accelerated, which can lead to an earlier onset of supersonic flow and shock wave formation. As a result, the critical Mach number is reduced for a given airfoil or aircraft configuration at higher angles of attack.

The Prandtl-Glauert rule is a mathematical relationship that describes the effect of compressibility on the lift and drag characteristics of an airfoil or aircraft as it approaches the speed of sound. The rule is based on the assumption that the flow can be treated as incompressible by applying a compressibility correction factor to the lift and drag coefficients.

The Prandtl-Glauert rule predicts that as the speed of an airfoil or aircraft approaches the speed of sound, the lift coefficient initially increases with increasing Mach number, reaches a maximum value at the critical Mach number, and then decreases rapidly due to the formation of shock waves. The rule also predicts that the drag coefficient initially decreases with increasing Mach number, reaches a minimum value at the critical Mach number, and then increases due to the formation of shock waves.

Thus, the Prandtl-Glauert rule can be used to confirm the effect of angle of attack on the critical Mach number. If the angle of attack is increased, the onset of supersonic flow and shock wave formation occurs at a lower Mach number, which results in a reduction of the maximum lift coefficient and an increase in drag. This can be seen in the compressibility correction factor used in the Prandtl-Glauert rule, which is proportional to the square root of 1 - M², where M is the Mach number. Therefore, a reduction in the critical Mach number due to an increase in angle of attack leads to a decrease in the compressibility correction factor, which in turn affects the lift and drag coefficients predicted by the Prandtl-Glauert rule.

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User Art Shendrik
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