Oblique shock waves and expansion waves are crucial phenomena in supersonic flow. These waves occur when supersonic flow encounters changes in geometry, causing sudden or gradual shifts in flow properties. Understanding their behavior is key to analyzing and designing supersonic systems.
Calculating flow properties across oblique shocks and expansion waves involves specific relations and functions. The θ−β−M relation for oblique shocks and the Prandtl-Meyer function for expansion waves are essential tools. These concepts are fundamental for designing supersonic airfoils and nozzles.
Oblique Shock Waves
Oblique shocks vs expansion waves
Top images from around the web for Oblique shocks vs expansion waves
Evaluating Oblique Shock Waves Characteristics on a Double-Wedge Airfoil View original
Is this image relevant?
Evaluating Oblique Shock Waves Characteristics on a Double-Wedge Airfoil View original
Is this image relevant?
Evaluating Oblique Shock Waves Characteristics on a Double-Wedge Airfoil View original
Is this image relevant?
Evaluating Oblique Shock Waves Characteristics on a Double-Wedge Airfoil View original
Is this image relevant?
Evaluating Oblique Shock Waves Characteristics on a Double-Wedge Airfoil View original
Is this image relevant?
1 of 3
Top images from around the web for Oblique shocks vs expansion waves
Evaluating Oblique Shock Waves Characteristics on a Double-Wedge Airfoil View original
Is this image relevant?
Evaluating Oblique Shock Waves Characteristics on a Double-Wedge Airfoil View original
Is this image relevant?
Evaluating Oblique Shock Waves Characteristics on a Double-Wedge Airfoil View original
Is this image relevant?
Evaluating Oblique Shock Waves Characteristics on a Double-Wedge Airfoil View original
Is this image relevant?
Evaluating Oblique Shock Waves Characteristics on a Double-Wedge Airfoil View original
Is this image relevant?
1 of 3
Oblique shock waves form when a supersonic flow encounters a concave corner (compression ramp) causing a sudden change in flow properties across the shock
Increase in pressure, density, and temperature
Decrease in velocity
Deflect the flow towards the surface, increasing the flow angle
Expansion waves form when a supersonic flow encounters a convex corner (expansion corner) causing a gradual change in flow properties across the wave
Decrease in pressure, density, and temperature
Increase in velocity
Deflect the flow away from the surface, decreasing the flow angle
Oblique shock flow calculations
Oblique shock relations relate the upstream and downstream flow properties across an oblique shock wave depending on the upstream Mach number (M1) and the shock wave angle (β)
Calculate flow properties using the normal shock relations in conjunction with the oblique shock angle
Determine the normal component of the upstream Mach number: M1n=M1sinβ
Calculate the downstream normal Mach number (M2n) using the normal shock relations
Determine the downstream Mach number: M2=M2n/sin(β−θ), where θ is the flow deflection angle
Determine the wave angle using the θ−β−M relation: tanθ=2cotβM12(γ+cos2β)+2M12sin2β−1
Solve for β given the upstream Mach number (M1) and the flow deflection angle (θ)
Expansion Waves and Interactions
Expansion wave property determination
Prandtl-Meyer function relates the upstream and downstream flow properties across an expansion wave depending on the upstream Mach number (M1) and the flow deflection angle (θ)
Calculate flow properties using the Prandtl-Meyer function
Determine the upstream Prandtl-Meyer function value: ν1=γ−1γ+1tan−1γ+1γ−1(M12−1)−tan−1M12−1
Calculate the downstream Prandtl-Meyer function value: ν2=ν1+θ
Solve for the downstream Mach number (M2) using the inverse Prandtl-Meyer function
Wave interactions with boundaries
Reflection of oblique shock waves
Regular reflection: Incident and reflected shock waves meet at the surface, flow downstream of the reflection point is parallel to the surface
Mach reflection: Incident and reflected shock waves do not meet at the surface, a Mach stem forms perpendicular to the surface
Reflection of expansion waves
Expansion waves reflect as expansion waves from a solid boundary
Flow downstream of the reflected expansion wave is parallel to the surface
Applications in supersonic design
Supersonic airfoils designed to minimize drag and control the location of shock waves
Use a combination of compression surfaces (oblique shock waves) and expansion surfaces (expansion waves) to achieve the desired flow properties
Diamond airfoil with a sharp leading edge and a symmetric wedge shape
Supersonic nozzles designed to accelerate a flow from subsonic to supersonic speeds
Use a converging-diverging geometry to create oblique shock waves and expansion waves
De Laval nozzle with a converging section followed by a diverging section