Mach number is a dimensionless quantity in fluid dynamics representing the ratio of flow velocity past a boundary to the local speed of sound.
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.
The Rankine–Hugoniot conditions, also referred to as Rankine–Hugoniot jump conditions or Rankine–Hugoniot relations, describe the relationship between the states on both sides of a shock wave or a combustion wave in a one-dimensional flow in fluids or a one-dimensional deformation in solids. They are named in recognition of the work carried out by Scottish engineer and physicist William John Macquorn Rankine and French engineer Pierre Henri Hugoniot.
The pressure coefficient is a dimensionless number which describes the relative pressures throughout a flow field in fluid dynamics. The pressure coefficient is used in aerodynamics and hydrodynamics. Every point in a fluid flow field has its own unique pressure coefficient, .
In thermal physics and thermodynamics, the heat capacity ratio, also known as the adiabatic index, the ratio of specific heats, or Laplace's coefficient, is the ratio of the heat capacity at constant pressure to heat capacity at constant volume. It is sometimes also known as the isentropic expansion factor and is denoted by γ (gamma) for an ideal gas or κ (kappa), the isentropic exponent for a real gas. The symbol γ is used by aerospace and chemical engineers.
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.
Rayleigh flow refers to frictionless, non-adiabatic flow through a constant area duct where the effect of heat addition or rejection is considered. Compressibility effects often come into consideration, although the Rayleigh flow model certainly also applies to incompressible flow. For this model, the duct area remains constant and no mass is added within the duct. Therefore, unlike Fanno flow, the stagnation temperature is a variable. The heat addition causes a decrease in stagnation pressure, which is known as the Rayleigh effect and is critical in the design of combustion systems. Heat addition will cause both supersonic and subsonic Mach numbers to approach Mach 1, resulting in choked flow. Conversely, heat rejection decreases a subsonic Mach number and increases a supersonic Mach number along the duct. It can be shown that for calorically perfect flows the maximum entropy occurs at M = 1. Rayleigh flow is named after John Strutt, 3rd Baron Rayleigh.
In fluid dynamics, stagnation pressure is the static pressure at a stagnation point in a fluid flow. At a stagnation point the fluid velocity is zero. In an incompressible flow, stagnation pressure is equal to the sum of the free-stream static pressure and the free-stream dynamic pressure.
Choked flow is a compressible flow effect. The parameter that becomes "choked" or "limited" is the fluid velocity.
The Chapman–Jouguet condition holds approximately in detonation waves in high explosives. It states that the detonation propagates at a velocity at which the reacting gases just reach sonic velocity as the reaction ceases.
In incompressible fluid dynamics dynamic pressure is the quantity defined by:
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.
In fluid dynamics, a moving shock is a shock wave that is travelling through a fluid medium with a velocity relative to the velocity of the fluid already making up the medium. As such, the normal shock relations require modification to calculate the properties before and after the moving shock. A knowledge of moving shocks is important for studying the phenomena surrounding detonation, among other applications.
Fanno flow is the adiabatic flow through a constant area duct where the effect of friction is considered. Compressibility effects often come into consideration, although the Fanno flow model certainly also applies to incompressible flow. For this model, the duct area remains constant, the flow is assumed to be steady and one-dimensional, and no mass is added within the duct. The Fanno flow model is considered an irreversible process due to viscous effects. The viscous friction causes the flow properties to change along the duct. The frictional effect is modeled as a shear stress at the wall acting on the fluid with uniform properties over any cross section of the duct.
Shock is an abrupt discontinuity in the flow field and it occurs in flows when the local flow speed exceeds the local sound speed. More specifically, it is a flow whose Mach number exceeds 1.
The Sod shock tube problem, named after Gary A. Sod, is a common test for the accuracy of computational fluid codes, like Riemann solvers, and was heavily investigated by Sod in 1978. The test consists of a one-dimensional Riemann problem with the following parameters, for left and right states of an ideal gas.
Isentropic nozzle flow describes the movement of a gas or fluid through a narrowing opening without an increase or decrease in entropy.
Taylor–von Neumann–Sedov blast wave refers to a blast wave induced by a strong explosion. The blast wave was described by a self-similar solution independently by G. I. Taylor, John von Neumann and Leonid Sedov during World War II.
A high pressure jet is a stream of pressurized fluid that is released from an environment at a significantly higher pressure than ambient pressure from a nozzle or orifice, due to operational or accidental release. In the field of safety engineering, the release of toxic and flammable gases has been the subject of many R&D studies because of the major risk that they pose to the health and safety of workers, equipment and environment. Intentional or accidental release may occur in an industrial settings like natural gas processing plants, oil refineries and hydrogen storage facilities.
