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When an object or a disturbance moves so fast that fluid particles cannot move out of the way, the molecular structure of the fluid permits the relative position of the molecules to move closer together or to compress. Thus, as the mean free path of the molecules is shortened, layers of spherical (3-D) disturbances come together to form a shock wave. A pressure build up or pressure pulse is created which grows larger and larger until it becomes a shock wave resulting in a rise in temperature and pressure. In short, as a disturbance approaches the speed of sound, gas molecules pack closer and closer together until a region of compressed fluid results called a shock wave. A shock wave is actually a wave-front of compressed gas molecules with some unique properties. Some engineers and researchers define a shock wave as an infinitely thin discontinuity. Actually, a shock wave is not discontinuous (i.e. a shock wave is NOT infinitely thin) because a shock wave has a finite thickness where fluid properties vary continuously across the region defined by the shock wave. According to this analysis, shock wave thickness tends to become smaller as Mach number is increased. For the example presented below shock wave thickness is approximately 40% smaller at Mach 10 than it is at Mach 1.

SPECIAL NOTE: Contrary to common belief, shock thickness is not unchanging as a function of Mach number. This analysis illustrates that shock thickness decreases significantly as Mach number increases and is not an absolute and unchanging discontinuity.

John Cipolla
Chief Aerodynamicist, AeroRocket

Cone-Cylinder-Flare pressure contours
AeroCFD Pressure Contours, Cone-Cylinder-Flare, M = 2.81, AOA = 0.5 degrees

Upstream of a normal shock wave the flow is supersonic, whereas downstream of a normal shock wave the flow is always subsonic. In addition, upstream and downstream of a shock wave the flow is isentropic but the flow is not isentropic in a region defined by the shock wave. The flow is not isentropic in a shock wave because friction or shear stress cause the flow to be internally irreversible. In a shock wave internal irreversibility (losses) due to friction cause the entropy, ds to be greater than 0.0. Whereas, before and after a shock wave ds = 0.0.

A shock wave has a finite but very small thickness, dX caused by "packing" of the molecules during the compression process as the shock wave moves through a fluid. The density of the fluid in the region of the shock wave tries to distribute itself evenly during the passage of the shock wave into undisturbed fluid. The distribution of density, pressure, etc is governed by fluid viscosity. This analysis assumes that for a control volume of fluid around the shock wave, the shear stress, Pyx within the shock wave is of the same magnitude as the normal stress, DP acting on the shock wave. Please refer to figure 1 below that graphically illustrates the control volume around the shock wave. Finally, figure 2 illustrates the derivation of the equations required to compute shock wave thickness as a function of Mach number plotted in figure 3. Please see the reference, "Fluid Mechanics", page 845, by R.A. Granger.

Figure 1. Control volume around the shock

Figure 2. Equations for determining shock thickness

The viscosity of air at 1 atm and 100 degrees F is n = 1.80 E-4 ft^2/sec. In figure 3 the shock wave thickness is plotted as a function of Mach number. Please see example on page 845 of the book "Fluid Mechanics" by R.A. Granger where the flow velocity is Mach = 2.71 (2000 ft/sec) and the resulting shock wave thickness is 9.0 E-8 ft (2.743E-5mm).

Shock thickness analysis
Figure 3. Complete MathCAD analysis for shock thickness as a function of Mach number in air.

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