Therefore, the momentum equation, eqn 8 must be placed in differential form before it can be modified further. In the diagram, the fanno line reaches maximum entropy at h 0. Variable area flow, choked flow, subsonic and supersonic nozzles, restrictors. For long lines, you can break up the line into segments that each have a pressure drop that keeps the change in density to under 10%, but you have to be serious about it. John anderson, 2nd edition, is a generally comprehensive and factual textbook, but i found the treatment. Schematic ts diagram fanno flow line for a constant area duct t p po. 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. Thermo ideal gases steady isentropic flow, stagnation state.
Ducts with area change 1 onedimensional, isentropic flow model a useful engineering model can be obtained by neglecting heat transfer, friction, and other irreversible e. On the other hand, raleigh flow provides analytical solution of frictionless compressible flow with heat transfer where incoming subsonic. A wide range of unsteady compressible flow phenonema exist and these are covered in the works of glass and sislian 1994 and kentfield. Energy equation entropy equation flow with fricton, fanno line. Dec 10, 2017 for the love of physics walter lewin may 16, 2011 duration. Thermodynamics of compressible flow, perfect gas, general effect.
The main assumptions associated with fanno flow are. The characteristic aspect of fanno flow is its consideration of friction. Fanno flow,detailed derivation of fanno flow relationships. Compared to rayleigh flow, fanno flow accounts for friction but neglects.
Fanno flow fanno flow is compressible flow that ideal gas flows through a duct having constant cross section area with friction in adiabatic process with the following assumption. Fundamentals of fluid mechanics chapter 11 analysis of. In the area of compressible flow, it was commonly believed and taught that there is only. Computes and plots, as a function of mach number, errors in fanno calculations. Iv flow in a constant area duct with friction fanno flow governing equations fanno line on h s and p v diagram fanno relation for a perfect gas chocking due to friction working tables for fanno flow isothermal flow elementary treatment only 615% second internal exam v flow through constant area duct with heat. Introduction to fluid mechanics chapter compressible flow. The proposed correlations, thus, allow to tackle the open question of the compressibility effects in microflows. Anderson, modern compressible flow with historical perspective, mcgrawhill 2nd edition, 1990. A steady onedimensional flow in a constant area duct with friction in the absence of work and heat transfer is known as, fanno flow. Thermodynamics and compressible flow spring 2015 1 fanno flow thermodynamics steady, 1d. Applied gas dynamics, john with no external work, is called fanno line flow. Rayleigh line flow stagnation temperature change in the absence of friction and area change.
Thus the operator of the system will lose the capability of knowing the exact flow rate based on the orifice upstream pressure, temperature, and orifice cd. Spc 407 sheet 6 solution compressible flow fanno flow solution. Thermodynamics and compressible flow spring 2015 1 fanno flow thermodynamics steady, 1d, constant area, adiabatic flow with no external work but with friction conserved quantities since adiabatic, no work. As a rough guide, compressible effects can be ignored at mach numbers below approximately 0.
Method of characteristics, supersonics nozzle design 6 suggested books. Pdf the fanno model for turbulent compressible flow. Fannoline flow, rayleigh pipe flow, natural gas flow in pipelines 3 compressible potential flow. At section 1 flow can be either subsonic or supersonic. Compressible flow variable density, and equation of state is. According to the second law of thermodynamics, entropy must always increase for fanno flow. The flow does act as a compressible fluid of low speed of sound and exhibits shock structure.
Fanno line flow, rayleigh pipe flow, natural gas flow in pipelines 3 compressible potential flow. Compressible gas flow generally represents a flow that the downstream density is less than 90% of the upstream density. The flows in gas turbine engine components are generally compressible. Isothermal compressible flow is the flow at constant temperature. Compressible flow continuity equation the continuity equation is obtained by applying the principle of conservation of mass to flow through a control volume. The model holds under the assumptions of adiabatic flow and constant crosssection channel. Point \a\ is the choking point for the supersonic branch in which the exit mach number reaches to one. In this study of compressibility effects, we mainly consider the steady, onedimensional, constant including zero viscosity, compressible flow of. Variation in the cross sectional area of the duct heat transfer friction the above parameters contribute to changes the ow properties. The equation above can be used to plot the fanno line, which represents a locus of states for given fanno flow conditions on an h. In this study of compressibility effects, we mainly consider the steady, onedimensional, constant including zero viscosity, compressible flow of an ideal gas.
Property changes for 1d, adiabatic, flow of ideal gas with friction in constant area pipe. Fanno flow provides an analytical solution of compressible flow in a long slender pipe where incoming subsonic flow can be choked due to friction. Compressible flow or gas dynamics is the branch of fluid mechanics that deals with flows having significant changes in fluid density. In this case we will consider the flow to be adiabatic also, that is, with no heat transfer. 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.
Mass conservation, eulers equation sound speed, mach number. Fundamentals of compressible flow stanford university. Ts diagram for 1d, adiabatic, flow of ideal gas with friction in a constant area pipe showing fanno line and flow path from section 1 to section 2 shown in figure 1. A mach line a is a curve which is everywhere perpendicular to the stream lines in a subsonic flow b is a wave which is perpendicular to the stream lines in a supersonic flow c is perpendicular to the stream lines when the flow is sonic d has the same slope as an arbitrary oblique shock wave x. There are several transitional points that change the pattern of the flow. Unit 1rayleigh and fanno flow free download as powerpoint presentation.
Pdf the paper considers the derivation and properties of the fanno model for nearly unidirectional turbulent flow of gas in a tube. Lecture notes compressible fluid dynamics mechanical. Unit 1rayleigh and fanno flow compressible flow fluid. Contents vii 12 evacuating semirigid chambers 225 12. Other relation between pressure and specific volume are called polytrophic and interpretation for each individual case is almost impossible. Spc 407 sheet 6 solution compressible flow fanno flow. Anderson, modern compressible flow with historical perspective, mcgrawhill 2nd edition, 1990 s m yahya, fundamentals of. We will frame our description of fanno flow on the lines usually. Consider a flow of air in conduct with a fuel injected into the flow as shown in figure 11. Compressible flow variable density, and equation of state is fanno flow adiabatic flow with friction.
The density of a gas changes significantly along a streamline compressible flow definition of compressibility. Onedimensional compressible flow isentropic flow of an ideal gas area variation flow in a constant area duct with friction frictionless flow in a constantarea duct with heat exchange normal shocks supersonic channel flow with shocks oblique shocks and expansion waves. Variation in the cross sectional area of the duct heat transfer friction the above. While all flows are compressible, flows are usually treated as being incompressible when the mach number the ratio of the speed of the flow to the speed of sound is less than 0. Modeling of compressible flow with friction and heat. Fanno line flow functions for onedimensional flow of an ideal gas. Aug 19, 2016 a steady onedimensional flow in a constant area duct with friction in the absence of work and heat transfer is known as, fanno flow. The fanno model for turbulent compressible flow article pdf available in journal of fluid mechanics 445. The vertical line is representative of flow between the stagnation state and any. One of the reason that rayleigh flow model was invented is to be analyzed the flow in a combustion chamber. Isothermal compressible flow often more closer to fact in piping transportation systems like in natural gas lines.
The enhanced fanno flow model has been validated over additional cfd simulations providing extremely good matchings for all the flow characteristics predicted when compared to a standard fanno flow onedimensional model. Although written in bad english, the op intends to state. Pdf fanno flow adiabatic flow in a constant area duct. Department of bioindustrial mechatronics engineering. Introduction to compressible flow mechanical engineering. Fanno theory provides an analytical model for onedimensional confined viscous compressible flows. Many aircraft fly fast enough to involve a compressible flow field. Does one use the units nm 3 hr or actual m 3 hr one can use mass flow rate kghr, standard or normal volumetric flow rate, or the actual volumetric flow rate it all depends on which flow equation one employs. Me409 compressible fluid flow ktu notes ktu cff notes ktu students note textbook syllabus question papers ktu cff notes ktu s7 mechanical syllabus ktu s7 mechanical notes ktu s7 mechanical question paper ktu s7 mechatronics notes ktu s7 mechanical university question paper ktu s7 mech syllabus ktu s7 mechanical subject code ktu s7 mechatronics question paper ktu s7 mechanical model. Fanno flow thermodynamics steady, 1d, constant area, adiabatic flow with no external work but with friction conserved quantities since adiabatic, no work. Lets go on to apply the knowledge of entropy to the flow of compressible fluids starting with isentropic flow. Onedimensional compressible flow second law of thermodynamics first law of thermodynamics.
Before to develop compressible flow equation, we need to become more familiar. Powers department of aerospace and mechanical engineering university of notre dame notre dame, indiana 465565637. Fundamentals of compressible fluid mechanics aeronautical. A given flow with a constant duct area can switch between the rayleigh and fanno models at these points. Fanno flow supersonic branch engineering libretexts. The fanno model for turbulent compressible flow core. Fanno flow adiabatic flow in a constant area duct with friction for incompressible flow in pipes or duct, the effect of friction is mainly reduced the pressure because of friction viscosity. On hs diagram, can draw fanno line line connecting points with same ho and. Fanno flow thermodynamics steady, 1d, constant area, adiabatic.
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