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The initial conditions exist at point 1. Point 2 exists at the nozzle throat, where M = 1. Point 3 labels the transition from isentropic to Fanno flow. Points 4 and 5 give the pre- and post-shock wave conditions, and point E is the exit from the duct. Figure 4 The H-S diagram is depicted for the conditions of Figure 3. Entropy is constant for ...
The intersection points occur at the given initial Mach number and its post-normal shock value. For Figure 3, these values are M = 3.0 and 0.4752, which can be found the normal shock tables listed in most compressible flow textbooks. A given flow with a constant duct area can switch between the Rayleigh and Fanno models at these points.
In aerodynamics, the normal shock tables are a series of tabulated data listing the various properties before and after the occurrence of a normal shock wave. [1] With a given upstream Mach number, the post-shock Mach number can be calculated along with the pressure, density, temperature, and stagnation pressure ratios.
By definition, at Mach 1, the local flow velocity u is equal to the speed of sound. At Mach 0.65, u is 65% of the speed of sound (subsonic), and, at Mach 1.35, u is 35% faster than the speed of sound (supersonic). An F/A-18 Hornet creating a vapor cone at transonic speed just before reaching the speed of sound.
For homogeneous fluids, the physical point at which the choking occurs for adiabatic conditions is when the exit plane velocity is at sonic conditions; i.e., at a Mach number of 1. [1] [2] [3] At choked flow, the mass flow rate can be increased only by increasing the upstream density of the substance.
Dimensionless numbers (or characteristic numbers) have an important role in analyzing the behavior of fluids and their flow as well as in other transport phenomena. [1] They include the Reynolds and the Mach numbers, which describe as ratios the relative magnitude of fluid and physical system characteristics, such as density, viscosity, speed of sound, and flow speed.
A different area rule, known as the supersonic area rule, developed by NACA aerodynamicist Robert Jones in "Theory of wing-body drag at supersonic speeds", [2] is applicable at speeds beyond transonic, and in this case, the cross-sectional area requirement is established with relation to the angle of the Mach cone for the design speed.
Since there is an increase in area, therefore we call this an isentropic expansion. If a supersonic flow is turned abruptly and the flow area decreases, the flow is irreversible due to the generation of shock waves. The isentropic relations are no longer valid and the flow is governed by the oblique or normal shock relations.