The well-known Fanno-line process deals with a perfect gas flowing in a duct of constant cross-sectional area with friction in which there is no heat transfer to or. Show that the maximum (static) temperature in Rayleigh flow occurs when the a T –s diagram for the system, showing the complete Fanno and Rayleigh lines. It is possible to obtain physical picture of the flow through a normal shock by employing some of the ideas of Fanno line and Rayleigh line Flows. Flow through a.
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If initial values of s i and M i are defined, a new equation for dimensionless entropy versus Mach number can be defined for each model.
Conversely, adding heat to a duct with an upstream, supersonic Mach number will cause the Mach number to decrease until the flow chokes.
The characteristic aspect of Rayleigh flow is its involvement of heat transfer. Choking Due To Friction The theory here predicts that for adiabatic frictional flow in a constant area duct, no matter what the inlet Mach number M1 is. For this model, the duct area remains constant and no mass is added within the duct. 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, the flow is assumed to be steady and one-dimensional, and no mass is added within fwnno duct.
This page was last edited on 23 Julyat Conversely, the Mach number of a supersonic flow will decrease until the flow is choked. What do the intersection points of these two curves represent? The Fanno flow model is also used extensively with the Rayleigh flow model. Conversely, heat rejection decreases a subsonic Mach number and increases a supersonic Mach number along the duct.
This page was last edited on 3 Augustat These equations are shown below for Fanno and Rayleigh flow, respectively. Differential equations can also be linea and solved to describe Fanno flow property ratios with respect to the values at the choking location. Heat addition will cause both supersonic and subsonic Mach numbers to approach Mach 1, resulting in choked flow.
They are represented graphically along with the Fanno parameter. Mass and Energy Analysis of Control Volumes. Cooling produces the opposite result for each of those two cases.
Point 3 labels the end of the nozzle where the flow transitions from isentropic to Fanno.
Shock waves and expansion waves Rayleigh flow Fanno flow Assignment
My presentations Profile Feedback Log out. Oblique shocks occur when a gas flowing at supersonic speeds strikes a flat or inclined surface. The Fanno line curve does not satisfy Eq. The main assumptions associated with Fanno flow are: The characteristic aspect of Fanno flow is its consideration of friction.
Fanno flow is named after Gino Girolamo Fanno. The average friction factor for the duct is estimated to be if the Ma number at the duct exit is 0.
We know normal shock should satisfy all the six equations stated above. Registration Forgot your password?
Additionally, the stagnation temperature remains constant. If initial values of s i and M i are defined, a new equation for dimensionless entropy versus Mach number can be defined for each model.
The Rayleigh flow model has many analytical uses, most notably involving aircraft engines. This is also consistent with directional principle indicated by the second law of thermodynamics, i. In other projects Wikimedia Commons.
Commons category link from Wikidata. The heat addition causes a decrease in stagnation pressurewhich is known as the Rayleigh effect and is critical in the design of combustion systems.
Download ppt “Shock waves and expansion waves Rayleigh flow Fanno flow Assignment”. Retrieved from ” https: Each point on the Fanno line corresponds with a different Mach number, and the movement to choked flow is shown in the diagram. The area and mass flow rate are held constant for Rayleigh flow. Views Read Edit View history. Share buttons are a little bit lower. The Fanno line defines the possible states for a gas when the mass flow rate and total enthalpy are held constant, but the momentum varies.
Normal shock waves are perpendicular to flow whereas inclined shock waves, as the name implies, are typically inclined relative to the flow direction. The Fanno flow model is considered an irreversible process due to viscous effects.
These values are significant in the design of combustion systems. These two models intersect at points on the enthalpy-entropy and Mach number-entropy diagrams, which is meaningful for many applications.
Also, normal shocks form a straight line whereas oblique shocks can be straight or curved, depending llnes the surface geometry.
Control volume for flow across a normal shock wave. Air stagnation conditions are Compute. For a flow with an upstream Mach number greater than 1.