Glossary

3.4 Normal and oblique shock waves

11 min read•august 20, 2024

Normal and oblique shock waves are critical phenomena in . These abrupt changes in flow properties occur when supersonic flow encounters obstructions or changes direction. Understanding shock waves is essential for analyzing and designing supersonic vehicles and propulsion systems.

Shock waves cause sudden increases in pressure, temperature, and density while decreasing velocity. The describe these changes mathematically. Oblique shocks, inclined to the flow direction, are weaker than normal shocks and allow downstream flow to remain supersonic.

Properties of normal shock waves

  • Normal shock waves are thin regions where flow properties change abruptly
  • Occur when supersonic flow encounters an obstruction or a sharp change in flow direction
  • Characterized by a discontinuous increase in pressure, temperature, and density across the shock

Pressure ratio across shock

Top images from around the web for Pressure ratio across shock

  • Shock Waves – University Physics Volume 1 View original

    Is this image relevant?

  • Chapter 1. Introduction to Aerodynamics – Aerodynamics and Aircraft Performance, 3rd edition View original

    Is this image relevant?

  • Shock Waves – University Physics Volume 1 View original

    Is this image relevant?

1 of 3

Top images from around the web for Pressure ratio across shock

  • Shock Waves – University Physics Volume 1 View original

    Is this image relevant?

  • Chapter 1. Introduction to Aerodynamics – Aerodynamics and Aircraft Performance, 3rd edition View original

    Is this image relevant?

  • Shock Waves – University Physics Volume 1 View original

    Is this image relevant?

1 of 3
  • Pressure increases significantly across a
  • Pressure ratio depends on the upstream
  • Higher upstream Mach numbers result in larger pressure ratios across the shock
  • Pressure ratio can be calculated using the Rankine-Hugoniot relations

Temperature ratio across shock

  • Temperature also increases across a normal shock wave
  • Temperature ratio is a function of the upstream Mach number
  • Higher upstream Mach numbers lead to higher temperature ratios
  • Temperature increase is due to the conversion of kinetic energy into thermal energy

Density ratio across shock

  • Density increases across a normal shock wave
  • Density ratio is related to the pressure and temperature ratios
  • Can be calculated using the equation of state for an ideal gas
  • is necessary to satisfy conservation of mass

Mach number change

  • Flow velocity decreases across a normal shock wave
  • Upstream Mach number is always supersonic (M > 1)
  • Downstream Mach number is always subsonic (M < 1)
  • Mach number decrease is due to the increase in speed of sound across the shock

Entropy increase

  • Entropy increases across a normal shock wave
  • Entropy increase is irreversible and indicates a loss of available energy
  • Amount of entropy increase depends on the strength of the shock (upstream Mach number)
  • Entropy increase is a measure of the irreversibility of the shock process

Rankine-Hugoniot relations

  • Set of equations that describe the relationship between flow properties across a shock wave
  • Derived from the conservation laws of mass, momentum, and energy
  • Used to calculate the downstream flow properties given the upstream conditions and shock strength

Conservation of mass

  • Mass flow rate is conserved across a normal shock wave
  • Product of density and velocity must be equal on both sides of the shock
  • Equation: ρ1u1=ρ2u2\rho_1 u_1 = \rho_2 u_2, where ρ\rho is density and uu is velocity
  • Subscripts 1 and 2 denote upstream and downstream conditions, respectively

Conservation of momentum

  • Momentum is conserved across a normal shock wave
  • Sum of pressure and momentum flux must be equal on both sides of the shock
  • Equation: p1+ρ1u12=p2+ρ2u22p_1 + \rho_1 u_1^2 = p_2 + \rho_2 u_2^2, where pp is pressure
  • Pressure increase across the shock balances the decrease in momentum flux

Conservation of energy

  • Energy is conserved across a normal shock wave
  • Total enthalpy (sum of static enthalpy and kinetic energy) is constant across the shock
  • Equation: h1+12u12=h2+12u22h_1 + \frac{1}{2}u_1^2 = h_2 + \frac{1}{2}u_2^2, where hh is specific enthalpy
  • Kinetic energy is converted into thermal energy (static enthalpy) across the shock

Normal shock in ideal gas

  • Normal shock waves in an ideal gas exhibit specific behavior and properties
  • Ideal gas assumption simplifies the analysis and allows for closed-form solutions

Upstream and downstream states

  • Upstream (pre-shock) state is characterized by high Mach number, low pressure, low temperature, and low density
  • Downstream (post-shock) state has low Mach number, high pressure, high temperature, and high density
  • Ratio of downstream to upstream properties depends on the upstream Mach number
  • Property ratios increase with increasing upstream Mach number

Mach number limits

  • Normal shock waves can only occur in supersonic flow (upstream Mach number > 1)
  • Downstream Mach number is always subsonic (< 1) for a normal shock in an ideal gas
  • Maximum downstream Mach number is limited to 1, which occurs for an infinitely strong shock
  • Minimum upstream Mach number for a normal shock is 1, corresponding to a weak shock

Stagnation pressure ratio

  • Stagnation pressure (total pressure) decreases across a normal shock wave
  • (downstream to upstream) is always less than 1
  • Stagnation pressure ratio decreases with increasing upstream Mach number
  • Stagnation pressure loss is a measure of the irreversibility of the shock process

Maximum entropy increase

  • Entropy increase across a normal shock wave has a maximum value
  • occurs at a specific upstream Mach number (approximately 1.245 for air)
  • Upstream Mach numbers above or below this value result in lower entropy increases
  • Maximum entropy increase is an important consideration in the design of supersonic diffusers

Moving normal shock waves

  • Normal shock waves can be either stationary or moving relative to an observer
  • Moving shocks introduce additional complexity in the analysis of flow properties

Stationary vs moving shocks

  • Stationary shocks are fixed in space and the flow moves through the shock
  • Moving shocks propagate through a stationary or moving fluid
  • Reference frame can be changed to convert a moving shock into a stationary shock and vice versa
  • Flow properties across the shock are the same in both reference frames

Shock velocity relative to flow

  • Velocity of a moving shock wave is superimposed on the flow velocity
  • Upstream and downstream velocities relative to the shock are different
  • Relative velocity upstream of the shock is supersonic, while downstream is subsonic
  • Shock velocity can be determined using the Rankine-Hugoniot relations

Shock propagation in ducts

  • Moving normal shocks can propagate through ducts or channels
  • Shock propagation is influenced by the duct geometry and flow conditions
  • Shock velocity in a duct is affected by the change in cross-sectional area
  • Converging ducts accelerate the shock, while diverging ducts decelerate it

Oblique shock waves

  • Oblique shock waves are inclined at an angle to the flow direction
  • Occur when a supersonic flow encounters a concave corner or a compression ramp

Oblique vs normal shock waves

  • Oblique shocks have a non-zero angle with respect to the flow direction, while normal shocks are perpendicular
  • Flow downstream of an oblique shock remains supersonic, while it becomes subsonic after a normal shock
  • Oblique shocks are weaker than normal shocks for the same upstream Mach number
  • Oblique shocks can be attached to the surface or detached, depending on the flow conditions

Shock wave angle

  • Angle between the and the upstream flow direction
  • Shock wave angle depends on the upstream Mach number and the of the surface
  • Increases with increasing upstream Mach number and deflection angle
  • Can be calculated using the theta-beta-Mach relation

Deflection angle

  • Angle through which the flow is turned by the oblique shock wave
  • Deflection angle is determined by the geometry of the surface (ramp angle or corner angle)
  • Maximum deflection angle exists for a given upstream Mach number, beyond which the shock becomes detached
  • Deflection angle is related to the shock wave angle through the theta-beta-Mach relation

Weak vs strong solutions

  • For a given upstream Mach number and deflection angle, there are two possible shock wave angles
  • has a smaller shock wave angle and a higher downstream Mach number
  • has a larger shock wave angle and a lower downstream Mach number
  • Weak shock solution is usually observed in practice, unless the flow is highly disturbed or the deflection angle is large

Oblique shock relations

  • Flow properties across an oblique shock wave can be calculated using
  • Relations are derived from the Rankine-Hugoniot equations and the geometry of the oblique shock

Pressure ratio across oblique shock

  • Pressure increases across an oblique shock wave
  • Pressure ratio depends on the upstream Mach number and the shock wave angle
  • Pressure ratio increases with increasing Mach number and shock wave angle
  • Can be calculated using the oblique shock pressure ratio equation

Density ratio across oblique shock

  • Density also increases across an oblique shock wave
  • Density ratio is related to the pressure ratio and the upstream Mach number
  • Can be calculated using the oblique shock density ratio equation
  • Density ratio is always greater than 1

Temperature ratio across oblique shock

  • Temperature increases across an oblique shock wave
  • Temperature ratio depends on the upstream Mach number and the shock wave angle
  • Can be calculated using the oblique shock temperature ratio equation
  • Temperature ratio is always greater than 1

Downstream Mach number

  • Mach number downstream of an oblique shock wave is lower than the upstream Mach number
  • Downstream Mach number depends on the upstream Mach number, shock wave angle, and deflection angle
  • Can be calculated using the oblique shock Mach number equation
  • Downstream Mach number is always supersonic for an attached oblique shock

Supersonic flow over wedges

  • Wedges are simple geometries that produce oblique shock waves in supersonic flow
  • Wedge flow is a fundamental problem in compressible aerodynamics

Attached vs detached shocks

  • Oblique shock wave can be attached to the wedge apex or detached from it
  • Attached shock occurs when the deflection angle is less than the maximum deflection angle for the given Mach number
  • Detached shock occurs when the deflection angle exceeds the maximum deflection angle
  • Detached shock is curved and stands off from the wedge apex

Wedge angle for attached shock

  • Wedge angle is the angle between the wedge surface and the freestream direction
  • For an attached shock, the wedge angle is equal to the deflection angle
  • Maximum wedge angle for an attached shock depends on the freestream Mach number
  • Can be calculated using the theta-beta-Mach relation and the maximum deflection angle

Maximum deflection angle

  • Maximum angle through which the flow can be turned by an attached oblique shock
  • Depends on the upstream Mach number and the specific heat ratio of the gas
  • Increases with increasing Mach number
  • Flow cannot be turned by an angle greater than the maximum deflection angle without creating a detached shock

Reflection of oblique shocks

  • Oblique shock waves can reflect from solid surfaces or interact with other shock waves
  • Reflection patterns depend on the incident shock strength and the flow conditions

Regular vs Mach reflection

  • Regular reflection occurs when the incident and reflected shocks meet at the surface
  • Mach reflection occurs when the incident and reflected shocks meet above the surface, forming a Mach stem
  • Transition from regular to Mach reflection depends on the incident and the flow deflection angle
  • Mach reflection is more likely to occur for strong incident shocks and large deflection angles

Shock-shock interaction

  • Oblique shocks can interact with each other, resulting in complex flow patterns
  • Interaction can be between two oblique shocks or between an oblique shock and a normal shock
  • Shock-shock interaction can lead to the formation of a triple point, where three shocks meet
  • Flow properties and shock angles change discontinuously across the triple point

Shock polars

  • Graphical representation of the relationship between the flow deflection angle and the shock wave angle
  • Used to analyze and predict the behavior of oblique shocks and their interactions
  • Different branches of the shock polar correspond to different shock solutions (weak, strong, or detached)
  • Intersection of shock polars determines the flow conditions and shock angles in shock-shock interactions

Shock wave-boundary layer interaction

  • Interaction between shock waves and boundary layers can significantly affect the flow field
  • Shock-boundary layer interaction can lead to , unsteadiness, and increased drag

Shock-induced separation

  • Adverse pressure gradient imposed by a shock wave can cause the boundary layer to separate
  • Separation occurs when the boundary layer cannot overcome the pressure rise across the shock
  • Shock-induced separation can lead to the formation of a recirculation bubble and increased flow unsteadiness
  • Severity of separation depends on the shock strength, boundary layer state, and surface geometry

Lambda shock structure

  • Characteristic shock pattern that forms when a shock wave interacts with a boundary layer
  • Consists of a normal shock near the surface, followed by an oblique shock that merges with the incident shock
  • Lambda shock structure is associated with shock-induced separation and the formation of a recirculation bubble
  • Can occur in supersonic inlets, transonic airfoils, and other flow situations where shocks interact with boundary layers

Shock train in supersonic flow

  • Series of successive shock waves that form in a supersonic flow with a boundary layer
  • Shock train is caused by the interaction between the shocks and the boundary layer
  • Each shock in the train is weaker than the previous one, and the spacing between shocks decreases downstream
  • Shock trains can occur in supersonic diffusers, isolators, and other flow passages with adverse pressure gradients

Applications of shock waves

  • Shock waves have numerous applications in aerospace engineering and other fields
  • Understanding and controlling shock waves is crucial for the design and operation of supersonic vehicles and devices

Supersonic inlets

  • Inlets are used to decelerate and compress the flow before it enters the engine of a supersonic vehicle
  • Shock waves are employed in supersonic inlets to efficiently reduce the Mach number and increase the pressure
  • Inlet design must balance the conflicting requirements of high pressure recovery and low flow distortion
  • Shock wave-boundary layer interaction and shock stability are major challenges in supersonic inlet design

Shock tubes and tunnels

  • Shock tubes and tunnels are experimental facilities used to study shock waves and high-speed flows
  • Shock tube consists of a high-pressure driver section and a low-pressure driven section separated by a diaphragm
  • When the diaphragm is ruptured, a shock wave propagates into the driven section, followed by an expansion wave
  • Shock tunnels use the high-temperature, high-pressure flow behind the reflected shock to simulate hypersonic flight conditions

Shock wave lithotripsy

  • Medical application of shock waves for the non-invasive treatment of kidney stones and other calculi
  • Focused shock waves are generated outside the body and propagate through tissue to the target stone
  • Shock waves induce stress and fracture in the stone, leading to its fragmentation into smaller pieces
  • Fragmented stones can then be easily passed through the urinary tract or dissolved by the body's natural processes

Key Terms to Review (24)

Compressibility effects: Compressibility effects refer to the changes in fluid density that occur when a fluid flows at high velocities, particularly when approaching or exceeding the speed of sound. These effects become crucial in understanding phenomena like shock waves and flow behavior in supersonic and hypersonic regimes, where traditional assumptions of incompressible flow no longer apply.
Deflection Angle: The deflection angle is the angle through which a flow direction is altered as it passes through a shock wave, either normal or oblique. This angle is crucial in understanding the behavior of fluid flow around obstacles and how it changes due to shock waves, impacting pressure, temperature, and density in the fluid. Analyzing the deflection angle helps engineers design more efficient aerodynamic structures and predict flow behavior.
Density Increase: Density increase refers to the rise in mass per unit volume of a fluid, which occurs as it experiences a compression, particularly in the context of shock waves. In compressible fluid dynamics, when a shock wave travels through a medium, it compresses the fluid particles, leading to an increase in density. This phenomenon is crucial when analyzing the behavior of gases in high-speed flows, where changes in density significantly influence flow properties and shock behavior.
Design of supersonic aircraft: The design of supersonic aircraft involves the engineering and aerodynamic considerations necessary to create vehicles capable of flying faster than the speed of sound, typically over Mach 1. This design process must account for unique aerodynamic phenomena, such as shock waves, drag, and stability challenges that arise at these high speeds. Effective designs incorporate advanced materials and technologies to manage thermal loads and structural integrity while ensuring efficient performance and safety.
Expansion fans: Expansion fans are a type of flow phenomenon that occurs when a supersonic flow expands around a corner or a wedge, resulting in a decrease in pressure and an increase in flow area. This process is characterized by a series of weak discontinuities that allow the fluid to adjust its state while maintaining supersonic conditions. Understanding expansion fans is crucial for analyzing how compressible flows behave, especially in relation to shock waves and other flow features.
Flow Separation: Flow separation occurs when the smooth flow of fluid over a surface breaks away from that surface, typically resulting in a wake region behind the object. This phenomenon is crucial as it affects lift, drag, and overall aerodynamic performance of bodies moving through fluids, influencing many aspects of fluid dynamics including stability and control.
Mach number: Mach number is a dimensionless quantity that represents the ratio of the speed of an object to the speed of sound in the surrounding medium. It is a key concept in fluid dynamics, especially when analyzing how objects move through air at different speeds, such as subsonic, transonic, and supersonic conditions.
Maximum Entropy Increase: Maximum entropy increase refers to the principle that in any irreversible process, the total entropy of a closed system will tend to increase until it reaches equilibrium. In the context of normal and oblique shock waves, this principle helps describe the energy dissipation and changes in thermodynamic properties as fluid flows transition from supersonic to subsonic speeds, resulting in a significant increase in entropy across the shock wave.
Normal shock wave: A normal shock wave is a type of shock wave that occurs when supersonic flow encounters a sudden change in pressure or velocity, resulting in a rapid transition to subsonic flow. This phenomenon is crucial in aerodynamics, as it affects the behavior of air around objects moving at high speeds and plays a significant role in the analysis of both normal and oblique shock waves in supersonic flow scenarios.
Oblique Shock Relations: Oblique shock relations describe the behavior of flow characteristics when a supersonic flow encounters a wedge or an angled surface, leading to the formation of an oblique shock wave. This phenomenon allows for a change in flow direction and pressure while maintaining the supersonic nature of the flow. Understanding these relations is crucial for analyzing how different geometries affect the aerodynamic performance of bodies moving at high speeds.
Oblique Shock Wave: An oblique shock wave is a type of shock wave that forms when supersonic flow encounters a surface at an angle, resulting in a change in the flow direction and an increase in pressure, temperature, and density of the fluid. This phenomenon is significant in understanding how air flows around sharp edges or surfaces, particularly in supersonic conditions, where the fluid experiences rapid compressions and expansions that lead to these shock formations.
Pressure Jump: A pressure jump refers to the sudden increase in pressure that occurs across a shock wave, where fluid properties change abruptly. This phenomenon is critical in understanding how shock waves impact airflow, particularly in compressible fluid dynamics, leading to changes in velocity, density, and temperature across the shock front.
Ramjet Operation: Ramjet operation refers to a type of air-breathing jet engine that utilizes the forward motion of the aircraft to compress incoming air for combustion, allowing it to achieve supersonic speeds without moving parts. This design relies heavily on the principles of normal and oblique shock waves to manage airflow, providing efficient thrust as high-speed air enters the engine. Understanding how ramjets harness shock waves is crucial for optimizing their performance at various speeds.
Rankine-Hugoniot Relations: Rankine-Hugoniot relations describe the conservation laws that govern the behavior of fluid flow across a discontinuity, such as a shock wave. These relations link the flow properties on either side of a shock wave, ensuring that mass, momentum, and energy are conserved during the transition from one state to another. They are essential for understanding both normal and oblique shock waves as well as for applying appropriate boundary conditions in fluid dynamics.
Shock angle: The shock angle is the angle formed between the oncoming flow direction and the shock wave itself, which occurs when a supersonic flow encounters a change in conditions, such as a solid surface or a change in area. This angle is crucial in determining the behavior of shock waves, specifically normal and oblique shocks, as it influences the flow properties behind the shock and affects overall aerodynamic performance.
Shock wave boundary layer interaction: Shock wave boundary layer interaction refers to the complex phenomena that occur when a shock wave interacts with the boundary layer of a fluid flow. This interaction can significantly affect the flow characteristics, such as velocity, pressure, and temperature, and can lead to flow separation or changes in the shock structure. Understanding this interaction is critical in aerodynamics, particularly in designing vehicles that travel at supersonic speeds.
Shock-induced flow instability: Shock-induced flow instability refers to the phenomena where the presence of shock waves in a fluid flow can lead to unpredictable and unsteady flow behavior. This instability can occur in various aerodynamic conditions, especially when dealing with normal and oblique shock waves that can create abrupt changes in pressure, temperature, and velocity, resulting in a complex interaction with the surrounding flow field.
Stagnation Pressure Ratio: The stagnation pressure ratio is the ratio of the stagnation pressure to the static pressure in a fluid flow. This ratio is crucial for understanding how energy changes as a flow passes through shock waves, as it helps characterize how shock waves affect the pressure and velocity of the flow, influencing both normal and oblique shocks.
Strong shock solution: A strong shock solution refers to a specific mathematical description of the flow behavior and properties in a strong shock wave, where there is a significant increase in pressure, density, and temperature across the shock front. This type of shock typically occurs in compressible flows where the Mach number exceeds one, resulting in abrupt changes in flow conditions. Understanding strong shock solutions is essential for analyzing the behavior of normal and oblique shock waves in various aerodynamic applications.
Subsonic flow: Subsonic flow refers to fluid motion where the velocity of the fluid is less than the speed of sound in that medium. This type of flow exhibits certain predictable characteristics, including smooth and streamlined behavior, which are important when analyzing various aerodynamic phenomena, such as pressure changes, shock wave interactions, and expansion waves. Understanding subsonic flow is crucial for applications involving aircraft design, nozzle performance, and fluid measurement techniques.
Supersonic Flow: Supersonic flow refers to the condition where the speed of a fluid, typically air, exceeds the speed of sound in that medium. This phenomenon is crucial for understanding various aerodynamic behaviors, including shock waves, pressure changes, and flow characteristics in high-speed flight and propulsion systems.
Temperature Rise: Temperature rise refers to the increase in temperature that occurs across a shock wave as a result of the compressive processes in fluid dynamics. This phenomenon is crucial for understanding how shock waves affect flow properties, including pressure and density, which play significant roles in aerodynamic design and analysis. The rise in temperature can influence the behavior of gases, leading to changes in their thermodynamic properties, and can impact the performance of aircraft and other vehicles traveling at high speeds.
Wave drag: Wave drag is a form of aerodynamic resistance that occurs when an object moves through a fluid at high speeds, particularly as it approaches and exceeds the speed of sound. This phenomenon is closely linked to the creation of shock waves, which are caused by the compression of air in front of the object, resulting in increased drag as the object transitions between subsonic and supersonic speeds.
Weak Shock Solution: A weak shock solution refers to a type of shock wave that occurs in compressible fluid flow when the change in pressure and density across the shock front is relatively small. This solution is characterized by small disturbances and is usually applied in situations where the flow remains subsonic on one side of the shock. Weak shocks are essential in understanding normal and oblique shock waves, as they provide a basis for analyzing the behavior of flows that experience minimal changes in properties.
© 2024 Fiveable Inc. All rights reserved.
AP® and SAT® are trademarks registered by the College Board, which is not affiliated with, and does not endorse this website.
Back
Practice QuizGlossary
Practice QuizGlossary
Next guide