Mach reflection

Last updated

Mach reflection is a supersonic fluid dynamics effect, named for Ernst Mach, and is a shock wave reflection pattern involving three shocks.

Contents

Introduction

Mach reflection can exist in steady, pseudo-steady and unsteady flows. When a shock wave, which is moving with a constant velocity, propagates over a solid wedge, the flow generated by the shock impinges on the wedge thus generating a second reflected shock, which ensures that the velocity of the flow is parallel to the wedge surface. Viewed in the frame of the reflection point, this flow is locally steady, and the flow is referred to as pseudosteady. When the angle between the wedge and the primary shock is sufficiently large, a single reflected shock is not able to turn the flow to a direction parallel to the wall and a transition to Mach reflection occurs. [1]

In a steady flow situation, if a wedge is placed into a steady supersonic flow in such a way that its oblique attached shock impinges on a flat wall parallel to the free stream, the shock turns the flow toward the wall and a reflected shock is required to turn the flow back to a direction parallel to the wall. When the shock angle exceeds a certain value, the deflection achievable by a single reflected shock is insufficient to turn the flow back to a direction parallel to the wall and transition to Mach reflection is observed. [1]

Mach reflection consists of three shocks, namely the incident shock, the reflected shock and a Mach stem, as well as a slip plane. The point where the three shocks meet is known as the 'triple point' in two dimensions, or a shock-shock in three dimensions. [2]

Types of Mach reflection

The only type of Mach reflection possible in steady flow is direct-Mach reflection, in which the Mach stem is convex away from the oncoming flow, and the slip plane slopes towards the reflecting surface.

By new results [3] [4] [5] there is a new configuration of shock waves - configuration with a negative angle of reflection in steady flow. Numerical simulations demonstrate two forms of this configuration - one with a kinked reflected shock wave, and an unstable double Mach configuration, depending on the transition path.

In pseudo-steady flows, the triple point moves away from the reflecting surface and the reflection is a direct-Mach reflection. In unsteady flows, it is also possible that the triple point remains stationary relative to the reflecting surface (stationary-Mach reflection), or moves toward the reflecting surface (inverse-Mach reflection). In inverse Mach reflection, the Mach stem is convex toward the oncoming flow, and the slip plane curves away from the reflecting surface. Each one of these configurations can assume one of the following three possibilities: single-Mach reflection, transitional-Mach reflection and double-Mach reflection. [2]

See also

Related Research Articles

<span class="mw-page-title-main">Mach number</span> Ratio of speed of an object moving through fluid and local speed of sound

The Mach number, often only Mach, is a dimensionless quantity in fluid dynamics representing the ratio of flow velocity past a boundary to the local speed of sound. It is named after the Austrian physicist and philosopher Ernst Mach.

<span class="mw-page-title-main">Hypersonic speed</span> Speed that exceeds five times the speed of sound (Mach 5 and above)

In aerodynamics, a hypersonic speed is one that exceeds five times the speed of sound, often stated as starting at speeds of Mach 5 and above.

<span class="mw-page-title-main">Shock wave</span> Propagating disturbance

In physics, a shock wave, or shock, is a type of propagating disturbance that moves faster than the local speed of sound in the medium. Like an ordinary wave, a shock wave carries energy and can propagate through a medium but is characterized by an abrupt, nearly discontinuous, change in pressure, temperature, and density of the medium.

Compressible flow is the branch of fluid mechanics that deals with flows having significant changes in fluid density. While all flows are compressible, flows are usually treated as being incompressible when the Mach number is smaller than 0.3. The study of compressible flow is relevant to high-speed aircraft, jet engines, rocket motors, high-speed entry into a planetary atmosphere, gas pipelines, commercial applications such as abrasive blasting, and many other fields.

<span class="mw-page-title-main">Waverider</span> Hypersonic aircraft design

A waverider is a hypersonic aircraft design that improves its supersonic lift-to-drag ratio by using the shock waves being generated by its own flight as a lifting surface, a phenomenon known as compression lift.

<span class="mw-page-title-main">Transonic</span> Flight condition in which airflow speeds are concurrently above and below the speed of sound

Transonic flow is air flowing around an object at a speed that generates regions of both subsonic and supersonic airflow around that object. The exact range of speeds depends on the object's critical Mach number, but transonic flow is seen at flight speeds close to the speed of sound, typically between Mach 0.8 and 1.2.

<span class="mw-page-title-main">Mach wave</span> Pressure wave

In fluid dynamics, a Mach wave is a pressure wave traveling with the speed of sound caused by a slight change of pressure added to a compressible flow. These weak waves can combine in supersonic flow to become a shock wave if sufficient Mach waves are present at any location. Such a shock wave is called a Mach stem or Mach front. Thus, it is possible to have shockless compression or expansion in a supersonic flow by having the production of Mach waves sufficiently spaced. A Mach wave is the weak limit of an oblique shock wave where time averages of flow quantities don't change. If the size of the object moving at the speed of sound is near 0, then this domain of influence of the wave is called a Mach cone.

<span class="mw-page-title-main">Specular reflection</span> Mirror-like wave reflection

Specular reflection, or regular reflection, is the mirror-like reflection of waves, such as light, from a surface.

<span class="mw-page-title-main">Inlet cone</span> Supersonic aircraft component

Inlet cones are a component of some supersonic aircraft and missiles. They are primarily used on ramjets, such as the D-21 Tagboard and Lockheed X-7. Some turbojet aircraft including the Su-7, MiG-21, English Electric Lightning, and SR-71 also use an inlet cone.

<span class="mw-page-title-main">Busemann biplane</span>

The Busemann biplane is a theoretical aircraft configuration invented by Adolf Busemann, which avoids the formation of N-type shock waves and thus does not create a sonic boom or the associated wave drag. However in its original form it does not generate lift either. A Busemann biplane concept, which provides adequate lift, and which can reduce the wave intensity and drag but not eliminate them, has been studied for a "boomless" supersonic transport.

<span class="mw-page-title-main">Oblique shock</span> Shock wave that is inclined with respect to the incident upstream flow direction

An oblique shock wave is a shock wave that, unlike a normal shock, is inclined with respect to the incident upstream flow direction. It will occur when a supersonic flow encounters a corner that effectively turns the flow into itself and compresses. The upstream streamlines are uniformly deflected after the shock wave. The most common way to produce an oblique shock wave is to place a wedge into supersonic, compressible flow. Similar to a normal shock wave, the oblique shock wave consists of a very thin region across which nearly discontinuous changes in the thermodynamic properties of a gas occur. While the upstream and downstream flow directions are unchanged across a normal shock, they are different for flow across an oblique shock wave.

Choked flow is a compressible flow effect. The parameter that becomes "choked" or "limited" is the fluid velocity.

<span class="mw-page-title-main">Shock diamond</span> Visible wave pattern in a supersonic exhaust plume

Shock diamonds are a formation of standing wave patterns that appear in the supersonic exhaust plume of an aerospace propulsion system, such as a supersonic jet engine, rocket, ramjet, or scramjet, when it is operated in an atmosphere. The "diamonds" are actually a complex flow field made visible by abrupt changes in local density and pressure as the exhaust passes through a series of standing shock waves and expansion fans. Mach diamonds are named after Ernst Mach, the physicist who first described them.

<span class="mw-page-title-main">Ludwieg tube</span>

A Ludwieg tube is a cheap and efficient way of producing supersonic flow. Mach numbers up to 4 in air are easily obtained without any additional heating of the flow. With heating, Mach numbers of up to 11 can be reached.

<span class="mw-page-title-main">Prandtl–Meyer expansion fan</span> Phenomenon in fluid dynamics

A supersonic expansion fan, technically known as Prandtl–Meyer expansion fan, a two-dimensional simple wave, is a centered expansion process that occurs when a supersonic flow turns around a convex corner. The fan consists of an infinite number of Mach waves, diverging from a sharp corner. When a flow turns around a smooth and circular corner, these waves can be extended backwards to meet at a point.

<span class="mw-page-title-main">Unstart</span> Breakdown of supersonic airflow in an engine intake

In supersonic aerodynamics, an unstart refers to a generally violent breakdown of the supersonic airflow. The phenomenon occurs when mass flow rate changes significantly within a duct. Avoiding unstarts is a key objective in the design of the engine air intakes of supersonic aircraft that cruise at speeds in excess of Mach 2.2.

<span class="mw-page-title-main">Components of jet engines</span> Brief description of components needed for jet engines

This article briefly describes the components and systems found in jet engines.

<span class="mw-page-title-main">Laminar–turbulent transition</span> Process of fluid flow becoming turbulent

In fluid dynamics, the process of a laminar flow becoming turbulent is known as laminar–turbulent transition. The main parameter characterizing transition is the Reynolds number.

The term shock polar is generally used with the graphical representation of the Rankine–Hugoniot equations in either the hodograph plane or the pressure ratio-flow deflection angle plane. The polar itself is the locus of all possible states after an oblique shock.

A supersonic airfoil is a cross-section geometry designed to generate lift efficiently at supersonic speeds. The need for such a design arises when an aircraft is required to operate consistently in the supersonic flight regime.

References