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 As an object moves through a gas, the gas molecules near the object are disturbed and move around the object. Aerodynamic forces are generated between the gas and the object and the magnitude of these forces depend on many factors associated with the object and the gas. The speed of the object relative to the gas introduces many significant effects. We characterize the speed of the object by a non-dimensional number called the Mach number; the Mach number is the ratio of the speed of the object to the speed of sound in the gas. The speed of "sound" is actually the speed of transmission for small, isentropic disturbances in the gas. As shown on the figure, the physical state of the gas depends on the Mach number of the object. In our discussions, we will use the Mach number of the object and the Mach number of the flow interchangeably. If we travel with the object as it moves through the air, the air moves past the object at the speed of the object. So, the Mach number of the object and the Mach number of the flow are the same number. For a moving flow of gas, there are several different values of the temperature of the gas. The static temperature is the temperature of the gas if it had no ordered motion and was not flowing. From kinetic theory, static temperature is related to the average kinetic energy of the random motion of the molecules of the gas. The value of the static temperature of air depends on the altitude. For a moving flow, there is a dynamic temperature associated with the kinetic energy of ordered motion of the flow in the same way that the static temperature is related to the kinetic energy of the random motion of the molecules. The total temperature is the sum of the static temperature and the dynamic temperature. and the value of total temperature depends on the Mach number of the flow. If the moving flow is isentropically brought to a halt on the body, we measure a stagnation temperature. The stagnation temperature is important because it is the temperature that occurs at a stagnation point on the object. Because the total temperature does not change through a shock wave, the stagnation temperature and and the total temperature have the same value at a stagnation point. The red line on the figure shows the general trend of the stagnation temperature of air as a function of the Mach number. A more detailed relation for Mach numbers from zero to eight is shown on a separate page. In the process of slowing the flow, the gas is heated due to the kinetic energy of flow. The amount of the heating depends on the specific heat capacity of the gas. If the specific heat capacity is a constant value, the gas is said to be calorically perfect and if the specific heat capacity changes, the gas is said to be calorically imperfect. At subsonic and low supersonic Mach numbers, air is calorically perfect. But under low hypersonic conditions, air is calorically imperfect. Derived flow variables, like the speed of sound and the isentropic flow relations are slightly different for a calorically imperfect gas than the conditions predicted for a calorically perfect gas as described below. On this page, we have indicated some important real gas effects that occur as the Mach number of the flow increases. Air is a mixture of gases with the major components being diatomic nitrogen and diatomic oxygen. For very low Mach numbers, the density of the air is a constant. But as the Mach number increases into the supersonic regime, some of the energy associated with the motion of the object compresses the gas and changes the density from its static value. Compressibility effects, such as shock waves, are present in supersonic airflows. As the Mach number increases into the low hypersonic regime, some of the energy of the flow excites the vibrational modes of the diatomic molecules. The molecules vibrate as illustrated in this computer model: This page shows an interactive Java applet which demonstrates the vibrational mode of a diatomic molecule. Click on the slider bar, hold the mouse button down and drag to the right to increase the temperature. Both the nitrogen and the oxygen experience vibrational excitation. There are mathematical models determined from statistical mechanics and the kinetic theory of gases that account for this effect on isentropic flows, oblique, and normal shocks. In all of these cases, the excitation of the vibrational modes cause the specific heat capacity to become a function of temperature and no longer a single constant value. The value of the total temperature of the flow is less for a calorically imperfect gas than for a perfect gas since some of the kinetic energy of the flow is converted to vibrational energy. As the Mach and temperature are further increased, some of the energy of the flow goes into breaking the molecular bonds holding the diatomic nitrogen and oxygen. We then have a mixture of dissociated atomic nitrogen and oxygen which is both calorically imperfect and thermally imperfect. A gas that follows the ideal equation of state is said to be thermally perfect and a gas that does not follow the ideal equation of state is thermally imperfect. With even more speed and temperature, some of the electrons surrounding the nitrogen and oxygen atoms are stripped free to produce a mixture of ionized nitrogen, oxygen, and free electrons. The resulting plasma can conduct an electric current and is influenced by electro-magnetic forces. Activities: Guided Tours Navigation .. Beginner's Guide Home Page

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