# FANNO AND RAYLEIGH LINES PDF

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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Rayleigh flow refers to frictionless, non- Adiabatic flow through a constant area duct where the effect of heat addition or rejection is considered.

## Rayleigh flow

Compressibility effects often come into consideration, although the Rayleigh flow model certainly also applies to incompressible flow.

The heat addition causes a decrease in stagnation pressurewhich is known as the Rayleigh effect and is critical in the design of combustion systems. Retrieved from ” https: The Fanno line represents the states that satisfy the conservation of mass and energy equations. An Engineering Approach, 5th edition by Yunus A. The Rayleigh flow model begins with a differential equation that relates the change in Mach number with the change in stagnation temperatureT 0.

If you wish to download it, please recommend it to your friends in any social system. The main assumptions associated with Rayleigh flow are: We know normal shock should satisfy all the six equations stated above.

Each point on the Fanno line corresponds with a rayeligh Mach number, and the movement to choked flow is shown in the diagram. Producing a shock wave inside the combustion chamber of an engine due to thermal choking is very undesirable due to the decrease in mass flow rate and thrust. Cooling produces the opposite result for each of those two cases.

The average friction factor for the duct is estimated to be if the Ma number at the duct exit is 0.

### Shock waves and expansion waves Rayleigh flow Fanno flow Assignment – ppt video online download

Disregarding frictional losses, determine the velocity, static temperature and static pressure at the duct inlet. 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. From Wikipedia, the free encyclopedia. We think you have liked this presentation. To use this website, you must agree to our Privacy Policyincluding cookie policy.

Published by Myrtle Warner Modified over 2 years ago. The ratios for the pressure, density, temperature, velocity and stagnation pressure are shown below, respectively. What raylegh the intersection points of these two curves represent? Share buttons are a little bit lower. 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. Oblique shocks occur when a gas flowing at supersonic speeds strikes a flat or inclined surface.

As was stated earlier, the area and mass flow rate in the duct are held constant for Fanno flow.

## Fanno flow

Views Read Edit View history. In order to draw a Fanno line curve through state “1”, we require a locus of mathematical states that satisfy Eqs Conversely, the Mach number of a supersonic flow will decrease until the flow is choked.

Flow through a normal shock must satisfy Eqs A given flow with a constant duct area can switch between the Fanno and Rayleigh models at these points. They are represented graphically along with the Fanno parameter. What are the main assumptions associated with Fanno flow? The characteristic aspect of Rayleigh flow is its involvement of heat transfer.

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Admin office level 2. Control volume for flow across a normal shock wave. In a nozzle, the converging or diverging area is modeled with isentropic flow, while the constant area section afterwards is modeled with Fanno flow.

Rayleigh flow is named after John Strutt, 3rd Baron Rayleigh. The movement in Figure 4 is always from the left to the right in order to satisfy the second law of thermodynamics. The ratios for the pressure, density, static temperature, velocity and stagnation pressure are shown below, respectively. The intersections points of these lines represent the states that satisfy the conservation of mass, energy, and momentum equations.

For a flow ahd an upstream Mach number greater than 1.

Differential equations can also be developed and solved to describe Rayleigh flow property ratios with respect to the values at the choking location.

These two models intersect at points on the enthalpy-entropy and Mach number-entropy diagrams, which is meaningful for many applications. Ljnes 3 labels the end of the nozzle where the flow transitions from isentropic to Fanno.

Brodkey pub OK Rayleih of Compressible Fluids. By using this site, you agree to the Terms of Use and Privacy Policy. The dimensionless enthalpy equation is shown below with an equation relating the static temperature with its value at the choke location for a calorically perfect gas where the heat capacity at constant pressure, c premains constant. This means that a subsonic flow entering a duct with friction will have nad increase in its Mach number until the flow is choked.

Therefore, the Rayleigh flow model is critical for an initial linea of the duct geometry and combustion temperature for an engine. First Law of Thermodynamics-The Energy Equation 4 Work transfer can also occur at the control surface when a force associated with fluid normal stress. Calculate the stagnation pressure and Mach number upstream of the shock, as well as pressure, temperature, velocity, Mach number and stagnation pressure downstream the shock.

Air stagnation conditions are Compute.