Gas Dynamics: Potential Flow Equation:

In fluid dynamics, potential flow describes the velocity field as the gradient of a scalar function: the velocity potential. As a result, a potential flow is characterized by an irrotational velocity field, which is a valid approximation for several applications. The irrotationality of a potential flow is due to the curl of the gradient of a scalar always being equal to zero.

In the case of an incompressible flow the velocity potential satisfies Laplace's equation, and potential theory is applicable. However, potential flows also have been used to describe compressible flows. The potential flow approach occurs in the modeling of both stationary as well as nonstationary flows.

Applications of potential flow are for instance: the outer flow field for aerofoils, water waves, electroosmotic flow, and groundwater flow. For flows (or parts thereof) with strong vorticity effects, the potential flow approximation is not applicable.

Gas Dynamics: Rayleigh flow

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. Click here for notes of Rayleigh Flow

Gas Dynamics: Fanno Flow

Fanno flow refers to 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.

For a flow with an upstream Mach number greater than 1.0 in a sufficiently long enough duct, deceleration occurs and the flow can become choked. On the other hand, for a flow with an upstream Mach number less than 1.0, acceleration occurs and the flow can become choked in a sufficiently long duct. It can be shown that for flow of calorically perfect gas the maximum entropy occurs at M = 1.0. Fanno flow is named after Gino Girolamo Fanno.

Refer Below Folder For Notes of Fanno Flow Click Here: Fanno Flow

Gas Dynamics: Reflection of Shocks, Intersection of Shocks

Topics covered are: 1. Reflection of shocks
2. Intersection of Shocks
2.1 Different Family(objects)
2.2 Same Family(objects)
3. Wave reflection from free Boundary

Gas Dynamics: Expansion Hodograph

Gas Dynamics: Flow over a wedge, Symmetrical wedge, Unsymmetrical wedge, Strong Shock, Weak Shock and detatched Shock

The below notes contains: Flow over a wedge, Symmetrical wedge, unsymmetrical wedge, Strong Shock, Weak Shock, Detached Shock

Gas Dynamics: Shock Polar

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.