A circular duct passes 8. The entry pressure temperature are 3. If the Mach number at entry is 0. The diameter of the duct, II. Length of the duct, III. Pressure and temperature at the exit, IV.
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Equation 1 may be used for representing Rayleigh line on the h- s diagram, as illustrated in fig shown in below. In general, most of the fluids in practical use have Rayleigh curves of the general form shown in fig. An entropy increases due to heat addition and entropy decreases due to heat rejection. Therefore, the Mach number is increased by heating and decreased by cooling at subsonic speeds.
On the other hand, the Mach number is decreased by heating and increased by cooling at supersonic speeds. Therefore, like friction, heat addition also tends to make the Mach number in the duct approach unity. Cooling causes the Mach number to change in the direction away from unity. Rayleigh Flow Rayleigh flow refers to adiabetic 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. Rayleigh flow is named after John Strutt, 3rd Baron Rayleigh. Theory The Rayleigh flow model begins with a differential equation that relates the change in Mach number with the change in stagnation temperature, T0.
The differential equation is shown below. Fundamental Equations The following fundamental equations will be used to determine the variation of flow parameters in Rayleigh flows.
FANNO AND RAYLEIGH LINES PDF
The Rayleigh flow model has many analytical uses, most notably involving aircraft engines. For instance, the combustion chambers inside turbojet engines usually have a constant area and the fuel mass addition is negligible. These properties make the Rayleigh flow model applicable for heat addition to the flow through combustion, assuming the heat addition does not result in dissociation of the air-fuel mixture. 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.