What are shock waves?

Shock waves are common in continuum mechanics, and their dominance is attributable to the fact that they are stronger (or even less) compressible. Substantial perturbations propagated as sudden dynamic changes of a compressible medium supersonically. Shock waves are all around us in our daily lives. Lightning, earthquakes, volcanic eruptions, and meteorite impact all produce them in nature. Even the earth, which is protected by its magnetic field, generates a shock wave as in solar wind that travels around 20 Earth radiuses. These shock waves might be either constant, linked to the body, or unsteady, i.e., moving around with time. All of the shocks mentioned above can be damaging, so precautions must be taken to reduce their impact.

Shock wave transmission in channels situations

Shock wave transmission in arbitrary geometry channels is important in various engineering fields, including mines in which dangerous shocks induced through exploding coal dust perpetuate along mine shafts affecting irreparable damage, and also long pipelines transporting natural gas, for instance, can cause unintentional explosions. This is also found inside the exhaust pipes for multi-cylindrical reciprocating engines, including the channels leading to underground bunkers designed to protect personnel and equipment against shock or explosion waves. This wave must diminish before reaching the safety space, thus ducts leading to subterranean shelters must be constructed specially to ensure this. Several governments have invested much in the construction of secure subterranean bunkers.

The interaction of shock/blast waves with buildings above ground level is a separate issue. In most cases, the important needs are to reduce the propagating shock's strength and the rapid pressure-time rise over the shock front to reduce the shock's damaging effects. Rough duct walls or, better still, internal baffles that create energy and momentum dissipation from the flow are excellent ways to accomplish this aim. Other options include adding branches and deflections to the duct system or increasing the cross-section of the duct by inserting expansion chambers.

Nevertheless, in other applications, including such compacted operations, namely the production of diamonds using graphite, or even in the wider field of shock wave focused, raising the strength of a propagated shock wave is desired. Working with extremely powerful shock waves was also supposed to be a way to start nuclear fusion. The contraction of the channel is an excellent way for producing a large shock amplification in this case.

Types of shock waves

Shock waves could be of three types: normal, oblique, and bow.

Normal Shocks

A shock wave is described as a discontinuity in elementary fluid mechanics using ideal gases, where entropy grows across a virtually minuscule span.  Since no working fluid is continuous, a controlling volume is built around the blast wave, with control surfaces that seem to be parallel to a blast wave. This shock is entirely contained between both the two surfaces since they are split with such a tiny space. At these control surfaces, mass flow, momentum, and energy are consistent; within the ignition, detonations may be regarded as heat introduction via a blast wave. The system is considered to be adiabatic (no heat leaves or enters the system), and that no work is being performed. These considerations lead to the Rankine–Hugoniot conditions.

In a system, the downstream properties are becoming subsonic, where fluid's upstream and downstream flow properties are considered isentropic, taking into consideration the given assumptions. The stagnation enthalpy remains constant in both locations because the total quantity of energy in the system is constant. Though entropy is growing, this must be explained by a decrease in the downstream fluid's stagnation pressure.

Oblique shocks

This shock is characterized as a sonic boom that detracts at such an arbitrary angle from a stream-wise direction while examining shocks in a fluid flow that seem to be related to the body. Components vector assessment of a flow is required for such shocks, which permits the stream to be regarded as a normal shock in such an orthogonal direction towards the oblique shocks.

Bow shocks

A nonlinear phenomenon happens whenever an oblique shock originates during an angle which thus prevents this from resting upon that surface, causing the shock wave to create a continuous pattern around the subject referred to as bow shocks. Within those cases, the 1D flow model is inaccurate, and further research is needed to predict the pressure force applied upon that surface.

Supersonic flows

The shock pulse abrupt change throughout medium properties can be thought of as a phase converting the pressure-time curve of such a moving supersonic object shows how well the shock pulse transformation is comparable to a dynamic phase transformation.

Whenever a disturbance travels faster than that of the information in the fluid medium, that fluid cannot reply in time even before disruption arrives. These fluid properties (e.g. density, temperature, and Mach number) vary rapidly in a shock wave.

Shock waves differ from ordinary sound waves in that they are marked by a rapid change in gas characteristics. Shock waves in the air generate a loud "snap" (or crack) sound. When a shock wave warms the air and loses energy over extended distances, it degrades into a normal sound wave, converting from a nonlinear to a linear wave. The sound wave is distinguished by the distinctive "thud" (or thump) of a sonic boom, which is generally produced by supersonic aircraft.

When a pressure front advances at supersonic speeds and presses on the surrounding air, shock waves system.  Sound waves moving against the river come to a point where they would no longer go upstream, causing pressure to build up in the region, leading to a high shock wave.

The powerful sound that happens once the shock wave travels on the bottom is understood as a shock wave (or sonic boom). The shock wave's angle is also determined as

$sin\theta \approx \frac{vt}{\left(v_{s}t\right)}=\frac{1}{M}$

whereas,

$$\begin{gathered} v=speed of sound; \\ {v}_s=velocity of a source; \\ \theta =shock wave angle; \\ t=time \end{gathered}$$

Shock wave compression causes a loss of total pressure, creating it a less economical suggests that of pressing gases for a few applications, like during a scramjet's intake. The action of shock compression on the flow is primarily responsible for the emergence of pressure drag on supersonic aircraft.

Mach number  is that the source speed divided by the sound speed written as

$M=\frac{v_s}{v}$

whereas

$$\begin{gathered} sourcespeed=v_s \\ soundspeed=v \\ M =mach number, \end{gathered}$$ 

Typically, this shock wave analysis is completed by utilizing the propagation of a moving source along with the stationary observer, which is Doppler effect, which imply that the determined observed frequency for the source which is moving approaches a stationary observer as

$$\begin{gathered} f_o=f_s\frac{v}{v-v_s} \\ whereas \\ {f}_o=observed frequency \\ {f}_s=source frequency \\ v=speed of the sound \\ {V}_s=source velocity \end{gathered}$$

Shock wave compression causes a loss of total pressure, creating it a less economical suggests that of pressing gases for a few applications, like during a scramjet's intake. The development of pressure w.r.t. drag forces on supersonic aircraft is largely due to the impact of shock compress upon that flow.

The amplitude of a strong shock wave, due to an explosion, decreases to the inverse square of the distance. It becomes so weak that it obeys the laws of acoustic waves.

Usage of shock waves

• Shock waves are mostly useful in recompression shock applications such as transonic wings, turbines, and pipe flow.
• It is useful in supersonic propulsion such as ramjet, scramjet, unstart, and inflow control applications such as needle valve, choked venturi.
• Shock waves can compress a gas. For example,Isentropic compressions, such as Prandtl–Meyer compressions, offer another option. 
• Shocks area unit created unnaturally during a form of ways that, as well as nuclear or chemical explosions, the shock wave of supersonic aircraft and any supersonic flying projectile, a bullet pushing the air during a rifle barrel, bow waves around an associate obstacle during a supersonic wind tunnel, or shock waves around a re-entry vehicle.
• NASA's Armstrong Flight Research Center captures images of shockwaves created by supersonic aircraft by Background Oriented Schlieren using Celestial Objects (BOSCO) technology. These images will help to develop a supersonic aircraft. Instead of a disruptive sonic boom, a soft "thump" will be produced by such aircraft. The aircraft with X-1 series were launched by NASA.
• It is used in Lithotripsy a procedure to break up stones in the kidney and parts of the ureter

Context and Application

This topic is useful for the students who are undertaking the following courses:

• Bachelors in Technology (Civil engineering, Mechanical engineering, chemical engineering)
• Masters in Technology (Civil engineering, Mechanical engineering, chemical engineering)
• Doctor of Philosophy in Physics
• Bachelors in Science in Physics
• Masters in Science in Physics

Practice Problem

Q. 1 What type of shock waves can be treated as perpendicular to the flow direction of the shock medium?

a) Normal shocks

b) Oblique shocks

c) Both

d) None of these

Ans. Option (a)

Explanation: Normal shock waves can be treated as perpendicular to the flow direction of the shock medium.

Q. 2 What type of shock waves flow direction of the shock medium?

a) Normal shocks

b) Oblique shocks

c) Both

d) None of these

Ans. Option (b).

Explanation: Oblique shocks waves can be treated as the flow direction of the shock medium.

Q. 3 What is the Mach number?

$a. v-v_s$

$b. \frac{v_s}{v_{}}$

$c.\frac{v}{v_s}$

d. none

Ans. Option (b)

Explanation: The Mach number is the ratio of the source speed to the sound speed.

Q. 4. What is the shock wave's angle is equal to?

$a. M+1$

$b. M-1$

$c. M$

$d. \frac{1}{M}$

Ans. Option (d)

Explanation: The shock wave's angle is equal to the inverse of the Mach number or inverse of the source speed by the sound speed.

Q. 5. What is the Doppler effect relationship?

a. $f_0=f_s\frac{v}{v-v_s}$

b. $f_s=f_0\frac{v}{v-v_s}$

c. $f_0=f_s\frac{v}{v+v_s}$

d. None of these

Ans. Option (a)

Explanation: Doppler effect is the ratio of observed frequency for the source which is moving approaches a stationary observer or $f_0=f_s\frac{v}{v-v_s}$.