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Fluid Mechanics
Published in P.K. Jayasree, K Balan, V Rani, Practical Civil Engineering, 2021
P.K. Jayasree, K Balan, V Rani
Compressible flow (gas dynamics) is the branch of fluid mechanics that deals with flows having significant changes in fluid density. Gases, mostly, display such behavior. To distinguish between compressible and incompressible flow, the Mach number (the ratio of the speed of the flow to the speed of sound) must be greater than about 0.3 (since the density change is greater than 5% in that case) before significant compressibility occurs. The study of compressible flow is relevant to high-speed aircraft, jet engines, rocket motors, hyperloops, high-speed entry into a planetary atmosphere, gas pipelines, commercial applications such as abrasive blasting, and many other fields.
Compressible Flow
Published in William S. Janna, Introduction to Fluid Mechanics, Sixth Edition, 2020
From the preceding discussion, it is apparent that two different flow regimes exist in compressible flow: subsonic and supersonic. The criterion used to distinguish between the two is the Mach number, defined as the ratio of flow velocity to the sonic velocity in the medium: M=Va
Force-System Resultants and Equilibrium
Published in Richard C. Dorf, The Engineering Handbook, 2018
Compressible flow is defined as variable density flow; this is in contrast to incompressible flow, where the density is assumed to be constant throughout. The variation in density is mainly caused by variations in pressure and temperature. We sometimes call the study of such fluids in motion gas dynamics. Fluid compressibility is a very important consideration in modern engineering applications. Knowledge of compressible fluid flow theory is required in the design and operation of many devices commonly encountered in engineering practice. A few important examples are the external flow over modern highspeed aircrafts; internal flows through rocket, gas turbine, and reciprocating engines; flow through natural gas transmission pipelines; and flow in high-speed wind tunnels.
Size effect on compressible flow and heat transfer in microtube with rarefaction and viscous dissipation
Published in Numerical Heat Transfer, Part A: Applications, 2019
Figure 4 shows axial distributions of the pressure, streamwise velocity, density, and temperature for decreasing tube diameter. For a constant Reynolds number, if the tube diameter decreases, the velocity magnitude should be increased and the frictional force becomes large because of the presence of high velocity gradients. In this case, a large pressure difference is necessary to overcome the increased friction. This feature can be explained as follows for P/Pin at the centerline in Figure 4a. In small microtubes, increased pressure drops are observed in the flow direction. Figure 4b depicts streamwise velocities at the centerline. The velocity ratio u/Uin develops to about two for large microtubes with D-values of 10 and 5 μm, but it increases nonlinearly for smaller microtubes with D-values of 2 and 1 μm. Thus, flows in small-diameter microtubes are very different from those in large-diameter microtubes. Therefore, for small microtubes, the streamwise acceleration of compressible flow can be considered as one of the factors representing the size effect. The centerline densities observed for a decreasing tube diameter are plotted in Figure 4c, and Figure 4d shows the cross-sectional mean temperature in the streamwise direction. The meaningful reduction of density is higher for smaller diameters. Unlike incompressible flow, the density of compressible flow is very sensitive to pressure and temperature. According to the ideal gas law, the density is directly proportional to the pressure and inversely proportional to the temperature. At the exit x* = 0.4, we have ρ/ρin = 0.45 and Tm/Tin = 0.93. Thus, as the diameter decreases, the density reduction resulting from the increased pressure drop is more dominant than that associated with temperature changes. This result explains the velocity increase in the axial direction. Since the mass flow rate () is constant, naturally, the velocity increases with a decrease in the density in the axial direction. In Figure 4d, the theoretical temperature obtained from the energy conservation for incompressible flow is represented by the black line (obtained from the expression where and denote the surface area and perimeter of the microtube, respectively) for distinguishing the size effect. For a tube diameter of 10 μm, it agrees well with the theoretical temperature. However, as the diameter decreases, the temperature rise decreases. For the smallest diameter (1 μm), the outlet temperature is less than the inlet temperature, although heat transfer is from the wall to the fluid. This implies that the heat energy from the wall is used for changing the fluid state, which is not expected in incompressible flows.