Compressible Waves

What Are Waves in Gas Dynamics?

?Gas flow over a body (or body motion in the gas) creates disturbances which propagate through the fluid domain and interact with other parts of the body.

?These disturbances are called waves , and their motion is referred to as wave motion

? Wave motion has a profound effect on the dynamics of gas flow, and it affects forces and thermal loads on the body.

?Wave motion in compressible flows is a complex phenomenon and its basic physics must be understood and correctly described by predictive methods when analyzing gas flows.

? In this course we will apply one dimensional governing equations of gas dynamics to analyze wave motion in gas flows.

? In this introductory lesson we will describe different types of compressible waves, but without going into details about their physics, which we will expand on in following lessons.

Shock Waves due to Supersonic Motion

?A shock wave is a fluid flow disturbance propagating through the gas faster than the local speed of sound.

?As the object moves through the fluid at a supersonic speed, waves generated by its motion cannot propagate upstream. Instead, they coalesce a short distance in front of the object, forming a very thin wave front called a shock wave (or simply shock).

?The lag of the wave fronts behind the object restricts them to a cone shaped region. Wave fronts at the edge of this cone form a shock wave, which is effectively the downstream part of the upstream shock.

Characteristics of Shock Waves

?Shock waves are very thin. Measurements indicate a typical thickness of a shock wave is on the order of magnitude of the mean free molecule path. Thus, in the continuum description of gas dynamics, they are treated as discontinuities.

? Shock waves are characterized by an abrupt change in flow properties across the shock:

‐An increase in static properties (pressure, temperature, density)

‐A decrease in Mach number and total pressure

‐An increase in entropy Contour

Shock Waves due to a Sudden Release of Energy

?Another mechanism of generating a shock wave is a sudden release of energy. This energy is dissipated into ambient through an expanding

shock, followed by a subsonic flow.

? An obvious example of this type of shock is a blast wave created by an explosion.

Expansion Waves

?Expansion waves (also called expansion fans ) are another type of wave in supersonicflows. They develop when the flow area suddenly expands, e. g., when the flow turns a convex corner.

?The expansion fan is a mechanism for supersonic flow to expand without “violating” laws of thermodynamics.

Normal Shocks

?A normal shock wave is a shock with the wave front normal to the freestream flow.

?Normal shocks occur, for example, in supersonic internal and jet flows.

Mach Number Contours: Shock vs. Design

?For both the cases

‐The air accelerates through the converging section of the nozzle and reaches the sonic speed (M = 1) at the nozzle throat.

‐Downstream of the throat, the flow continues accelerating to become mildly supersonic

Supersonic Flow Over Wedges and Cones

A detached shock wave is created upstream of the blunt cone.

Because of its curved shape, this shock is typically known as the bow shock.

?Flow is brought to rest at the stagnation point on the cone nose. The flow is subsonic in the stagnation region.

?Because of viscous effects, the velocity at the wall is 0 and there is a thin layer near the walls, called subsonic layer , where the fluid velocity is subsonic. Beyond it, the boundary layer becomes supersonic.

? This bow shock can be interpreted as a combination of normal and oblique shocks.

‐Normal shock at point 1: Flow decelerates from supersonic to subsonic.

‐Strong oblique shock at point 2: Flow behind the shock continues to be subsonic.

‐Weak oblique shock at point 3: Flow behind the shock is supersonic.

Expansion Wave

Supersonic Flow over a Diamond Shaped Airfoil

Reflections of 2 D Supersonic Waves

?The static pressure contours show clearly how the shock reflects off the duct walls.

?We can also identify where the expansion fan forms. Looking at the areas of smooth variations of pressure contours color, we can get an idea on how it reflects and widens along the duct.

?This alternating pattern of shock and expansion reflections continue throughout the duct.

The shocks are easy to visualize. However, due to their interactions with the expansion waves the flow turns and the shocks get curved, as highlighted by the black straight line below.

?We can also observe that the shock interacts with the boundary layer.

?At the shock nears the wall, it impinges on the boundary layer and forced it to separate.

?This fascinating phenomenon of the physical shock induced boundary layer separation would be overlooked if we used the inviscid assumption.

?The pathlines show how the flow suddenly changes direction past the shock and its reflections, while it smoothly turns as it crosses the expansion fan and its reflections.

? Interestingly, the fluid experiences a smoother change of direction where the expansion fan and the shock waves interact.

?The reflections in the duct cause the fluid to have an undulatory motion.