Thermodynamics and compressible flow spring 2015 1 fanno flow thermodynamics steady, 1d. Figure 3 shows the rayleigh and fanno lines intersecting with each other for initial conditions of s i 0 and m i 3. Rayleigh flow 1 ae3450 school of aerospace engineering. The typical questions that are raised in rayleigh flow are related to the maximum heat that can be transferred to gas reaction heat and to the maximum flow rate. The critical rayleigh number for turbulent flow induced by a horizontal heated plate is ra c 2. Fundamentals of fluid mechanics chapter 11 analysis of. 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. Several observations can be made in regards to the stagnation temperature. Incompressible flow can be mainly classified into isentropic flow, fanno flow and rayleigh flow according to 3 factors.
On hs diagram, can draw fanno line line connecting points with same ho and. The rayleigh flow model is also used extensively with the fanno flow model. Variation in the cross sectional area of the duct heat transfer friction the above parameters contribute to changes the ow properties. I know i originally learned it from oosthuizen and carscallen, but you can find it in other books. May 22, 2014 mod01 lec10 rayleigh flow fanno flow nptelhrd. Fanno flow thermodynamics steady, 1d, constant area, adiabatic flow with no external work but with friction conserved quantities since adiabatic, no work. How can i sketch the ts diagram for a flow in a duct with constant area through a fanno, normal shock, rayleigh with heating and fanno conditions, respectively. 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 rayleigh flow model certainly also applies to incompressible flow.
Modeling of compressible flow with friction and heat transfer. A pulse detonation engine, or pde, is a type of propulsion system that uses detonation waves to combust the fuel and oxidizer mixture. This concise and wellorganised text covers a wide range of interesting topics such as isentropic flow, fanno flow, rayleigh flow, simple flow with mass addition, waves in supersonic flow and measurement techniques in gas dynamics. May 28, 2019 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. Compressible flow variable density, and equation of state is. Fanno flow provides an analytical solution of compressible flow in a long slender pipe where incoming subsonic flow can be choked due to friction. When dealing with the mathematics and science of compressible flow, the text is unbiased. Rayleigh flow fanno flow tutorial of gas dynamics and propulsion course by prof v. The aim of this note is to obtain a flow rate equation for subsonic fanno flow, which has a form similar to the flow rate equation for isothermal flow.
Fundamentals of compressible flow mechanics open textbook. Okay in the previous class, we completed our discussion of flow with heat addition. The area and mass flow rate are held constant for rayleigh flow. Woods department of mechanical engineering, queen mary and westfield college, university of london, london, u k this article introduces a model fluid that has ideal liquid and perfect gas phases and a homogeneous. Like rayleigh curve, hs diagram for fanno flow shown in fig. It is helpful to know the derivations of things such as the isentropic flow relations before attempting rayleigh flow or fanno flow. Chan school of mechanical and production engineering, nanyang technological university, singapore w. Schematic diagram for flow through a convergingdiverging section and then a constant area duct. Qualitative analysis of flow in onvergingdiverging ducts and nozzles, flow downstream of a cd nozzle, rocket nozzle design lecture 09 notes lecture 10 notes lecture 11 notes youtube video overexpanded supersonic jet with shock diamonds jet comes out of a soda bottle. Because mach is the default of mtype, mtype is optional when this array is. The t w o exit states can b e represen ted on the t s diagram as follo ws.
Pdf on apr 1, 2019, shaswat anurag saincher and others published lecture 4 rayleigh flow find, read and cite all the research you need. At section 1 flow can be either subsonic or supersonic. Aug, 2019 the bleed flow will be studied under two cases. However, the entropy values for each model are not equal at the sonic state. An ideal flow used to study the flow of fluids in long pipes. Hence, the mass rate is a function of the mach number. For this model, the duct area remains constant and no mass is added within the duct. On rayleigh and fanno flows of homogeneous equilibrium twophase fluids s. When possible, these functions assume perfect gas environments. Apr 23, 2015 not sure how far you went on understanding, but they both describe different types of compressible flow through a constant area channel. The maximum temperature is not at mach equal to one. Each function has an mtype argument that lets you specify the inputs for the flow.
The flow after the inlet is divided into two sections. Calculate flow relations for fanno lines, isentropic, normal shock, prandtlmeyer functions, and rayleigh lines. Lecture notes compressible fluid dynamics mechanical. In each of these flows,one factor changes and effect of other 2 are neglected or absent.
Pdf fanno flow and rayleigh flow calculations for bleed flow. Therefore, the momentum equation, eqn 8 must be placed in differential form before it can be modified further. Fanno curve for various mass flow rat conditions is given in fig. Fanno flow and rayleigh flow fundamentals duration. Therefore, unlike fanno flow, the stagnation temperature is a variable. What is the difference between fanno flow and rayleigh flow. The mach number is indeed a function of the pressure ratio but mass flow rate is a function of pressure ratio only through mach number. Applied gas dynamics, john with no external work, is called fanno line flow. More examples of fanno flow engineering libretexts. Woods department of mechanical engineering, queen mary and westfield college, university of london, london, u k this article introduces a model fluid that has ideal liquid and perfect gas phases and a. In the case of an isothermal compressible flow, the. Show that the maximum static temperature in rayleigh flow occurs when the mach. On the other hand, raleigh flow provides analytical solution of frictionless compressible flow with heat transfer where incoming subsonic. The rayleigh number ranges from less than 1 for heptanol to 23,000 for pentane.
You can find these equations derived in many compressible flow books. Compared to rayleigh flow, fanno flow accounts for friction but neglects heat transfer effects, whereas rayleigh flow accounts for heat transfer but. The fanno flow model is often used in the design and analysis of nozzles. A key to understanding fanno flow is that the shear stress is a function of velocity and density of the gas, so, as the state of the flow changes under the action of the shear force, the magnitude of the shear force itself changes. Gas dynamics simple frictional ow fanno flow adiabatic frictional ow in a constantarea duct the flow of a compressible uid in a duct is always accompanied by. Yet the maximum enetropy accurs at mach equal to one. Dec 22, 2019 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. Introduction zcompressible flow variable density, and equation of state is important zideal gas equation of statesimple yet representative of actual gases at pressures and temperatures of interest zenergy equation is important, due to the significant variation of temperature. Unit 1 rayleigh and fanno flow free download as powerpoint presentation. Unit 1rayleigh and fanno flow compressible flow fluid. Download gas dynamics for engineers by balachandran, p.
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. Ts diagram for 1d, adiabatic, flow of ideal gas with friction in a constant area. The ratios for the pressure, density, static temperature, velocity and stagnation pressure are shown below, respectively. Spc 407 sheet 6 solution compressible flow fanno flow solution.
In the main compressible flow chapters normal and oblique shocks, prandtlmeyer expansion, rayleigh and fanno flow, variable area flow, isentropic flow, the chapters are more polished and accurate. What is the difference between fanno flow and rayleigh. Powers department of aerospace and mechanical engineering university of notre dame notre dame, indiana 465565637. Sep 30, 2019 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. Modeling of compressible flow with friction and heat. A flow rate equation for subsonic fanno flow request pdf. The conditions across a normal shock a lie at the intersection of the fanno and rayleigh lines for the flow. Not sure how far you went on understanding, but they both describe different types of compressible flow through a constant area channel. Let us examine the momen tum ux e v 2 e a p e r t e for b oth cases. Fanno flow article about fanno flow by the free dictionary. These two models intersect at points on the enthalpyentropy and mach numberentropy diagrams, which is meaningful for many applications. Jan 27, 2018 fanno flow and rayleigh flow fundamentals sri eshwar college of engneering mechanical dept. In the case of short molecules, the motion of the vapor.
Fanno flow and the other involving heat addition i. A read is counted each time someone views a publication summary such as the title, abstract, and list of authors, clicks on a figure, or views or downloads the fulltext. 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. This workbook implements the 1d, compressible flow functions for a perfect gas. Spreadsheet for 1d compressible flow of an ideal gas. Learn vocabulary, terms, and more with flashcards, games, and other study tools. Spc 407 sheet 6 solution compressible flow fanno flow.
Rayleigh line flow stagnation temperature change in the absence of friction and area change. Fanno flow thermodynamics steady, 1d, constant area, adiabatic. Show that the maximum static temperature in rayleigh flow occurs when the mach number is 3. Unit 1rayleigh and fanno flow free download as powerpoint presentation. Therefore, the rayleigh flow model is critical for an initial design of the duct geometry and combustion temperature for an engine. Pdf fanno flow and rayleigh flow calculations for bleed. Heat addition will cause both supersonic and subsonic mach numbers to approach mach 1, resulting in choked flow. On rayleigh and fanno flows of homogeneous equilibrium two.
This video lecture is for exams like gate ese ies ias and for any university course on gas dynamics or compressible flow. Find materials for this course in the pages linked along the left. Ae 312 exam 2 compressible flow flashcards quizlet. The fanno flow model is also used extensively with the rayleigh flow model. Brodkey pub these equations are shown fqnno for fanno and rayleigh flow, ane. Compressibility effects often come into consideration, although the fanno flow model certainly also applies to incompressible flow. Explanation for fanno curve for various mass flow rates can be obtained on similar line as it has been obtained for rayleigh flow for various mass flow rates. Aug 18, 2019 equally important to the fanno flow model is the dimensionless ratio of the change in entropy over the heat capacity at constant pressure, c p. Equally important to the fanno flow model is the dimensionless ratio of the change in entropy over the heat capacity at constant pressure, c p. Flod rayleigh flow model has many analytical uses, most notably involving aircraft engines. Because mach is the default of mtype, mtype is optional when this array is the input mode. Flow with heat addition rayleigh flow governing equations. These equations are shown below for fanno and rayleigh flow, respectively. Fanno flow curve analysis homework help, assignment help.
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