清华大学航空学院符松流体力学第九章.ppt

清华大学工程力学系 IX. COMPRESSIBLE FLOW 符 松 清华大学 航天航空学院 COMPRESSIBLE FLOW Compressible flow is the study of fluids flowing at speeds comparable to the local speed of sound. This occurs when fluid speeds are about 30% or more of the local acoustic velocity. Then, the fluid density no longer remains constant throughout the flow field. This typically does not occur with fluids but can easily occur in flowing gases. Two important and distinctive effects that occur in compressible flows are choking where the flow is limited by the sonic condition that occurs when the flow velocity becomes equal to the local acoustic velocity and shock waves that introduce discontinuities in the fluid properties and are highly irreversible. COMPRESSIBLE FLOW Since the density of the fluid is no longer constant in compressible flows, there are now four dependent variables to be determined throughout the flow field. These are pressure, temperature, density, and flow velocity. Two new variables, temperature and density, have been introduced and two additional equations are required for a complete solution. These are the energy equation and the fluid equation of state. These must be solved simultaneously with the continuity and momentum equations to determine all the flow field variables. Equations of State and Ideal Gas Properties Two equations of state are used to analyze compressible flows: the ideal gas equation of state and the isentropic flow equation of state. The first of these describe gases at low pressure (relative to the gas critical pressure) and high temperature (relative to the gas critical temperature). The second applies to ideal gases experiencing isentropic (adiabatic and frictionless) flow. Equations of State and Ideal Gas Properties The ideal gas equation of state is In this equation, R is the gas constant, and P and T are the absolute pressure and absolute temperature respectively. Air is the most commonly incurred compressible flow gas and its gas constant is