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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.
In fluid dynamics, an isentropic flow is a fluid flow that is both adiabatic and reversible. That is, no heat is added to the flow, and no energy transformations occur due to friction or dissipative effects. For an isentropic flow of a perfect gas, several relations can be derived to define the pressure, density and temperature along a streamline.
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 The isentropic relations are no longer valid and the flow is governed by the oblique or normal shock relations.
See relations between specific heats for the derivation of the thermodynamic relations between the heat capacities. The above definition is the approach used to develop rigorous expressions from equations of state (such as Peng–Robinson ), which match experimental values so closely that there is little need to develop a database of ratios or ...
Three assumptions will be made: the flow from behind the normal shock in the inlet is isentropic, or p t4 = p t2, the flow at the throat (point 4) is sonic such that M 4 = 1, and the pressures between the various point are related through normal shock relations, resulting in the following relation between inlet and throat pressures, [1]
Clausius–Clapeyron relation; Departure functions; Duhem–Margules equation; Ehrenfest equations; Gibbs–Helmholtz equation; Phase rule; Kopp's law; Noro–Frenkel law of corresponding states; Onsager reciprocal relations; Stefan number; Thermodynamics; Timeline of thermodynamics; Triple product rule; Exact differential
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 isentropic flow, so the conditions at point 1 move down vertically to point 3.
The above equation can be manipulated to solve for M as a function of H. However, due to the form of the T/T* equation, a complicated multi-root relation is formed for M = M(T/T*). Instead, M can be chosen as an independent variable where ΔS and H can be matched up in a chart as shown in Figure 1.