Fanno Flow
Fanno flow means adiabatic flow through a stable region duct where the effect of friction is considered. Compressibility effects frequently arrive into consideration in spite of the fanno flow model definitely applies to compressible flow. Here the duct region stays constant the flow is assumed to be stable and one dimensional and no mass is added inside the duct. The fanno flow is considered an irreversible process because of viscous effects. The viscous friction creates the flow properties to modify along the duct. The frictional effect is modeled as a shear stress at the wall acting on the fluid with standardized properties over any cross section of the duct.
Deceleration and maximum entropy
Deceleration happens and the flow is choked when a flow has upstream Mach number greater than 1.0 in a sufficiently long duct. On the contrary, for a flow with an upstream Mach number less than 1.0, acceleration happens and the flow is choked in a sufficiently long duct. It can be exhibited that for flow of calorically proper gas the maximum entropy happens at M = 1.0. In the name of Gino Girolamo Fanno this has been known as Fanno flow.
This model starts with a differential equation that relates the change in Mach number with respect to the length of the duct, dM/dx. Other terms in the differential equation are the heat capacity ratio, y, the fanning friction factor, f, and the hydraulic diameter, Dh:
Differential Equation
Supposing the fanning friction factor is a constant along the duct wall the differential equation can be solved simply. Nevertheless, the value of the fanning friction factor can be complex to decide for supersonic and particularly hypersonic flow velocities. The outcome reaction is exhibited below where L is the needed duct length to choke the flow assuming the upstream Mach number is supersonic. The left hand side is referred as the fanno parameter.
The fanno flow model is widely used in the design and analysis of nozzles. In a nozzle, the meeting or departing area is modeled with isentropic flow, while the constant area section afterwards is modeled with fanno flow. With adequate high primary pressure supersonic flow can be maintained through the constant area duct similar to the desired performance of a blow down type supersonic wind tunnel. Nevertheless these figures exhibit the shock wave before it has moved completely through the duct. If the shock wave exists the flow transitions from the supersonic portion of the fanno line to the subsonic portion before continuing towards M=1.
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