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Topic: Compressible flow

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	Bernoulli Equation: Derivation for Compressible Flow (Site not responding. Last check: 2007-11-03)
		In nearly all elementary treatments of the Bernoulli equation, the flow is taken to be incompressible, i.e., the fluid density is taken to be a constant.
		With respect to the Bernoulli equation, the main difference between a compressible and incompressible flow is that the variations in the pressure in a compressible flow will result in compressions and expansions of the fluid blob as it moves along its own path.
		The barotropic flow assumption is tantamount to assuming that one of the commonly encountered thermodynamic variables is a constant.
	www.fluidmech.net /tutorials/bernoulli/compressible-bernoulli.htm (1666 words)

	Isentropic Flow Equations
		However, as the speed of the flow approaches the speed of sound we must consider compressibility effects on the gas.
		Considering flow through a tube, as shown in the figure, if the flow is very gradually compressed (area decreases) and then gradually expanded (area increases), the flow conditions return to their original values.
		Isentropic flows occur when the change in flow variables is small and gradual, such as the ideal flow through the nozzle shown above.
	www.grc.nasa.gov /WWW/K-12/airplane/isentrop.html (868 words)

	[No title]
		Thus the lower pressure limit on the equation is the vapour pressure of the liquid at its temperature at the throat.
		Any flow control valve has to be sufficiently far downstream (about 50 pipe diameters) so as not to disturb the flow profiles at the venturi.
		The abscissa is the ratio of the pressure difference to the upstream pressure and the values increase from 0.0 to 0.6 for nozzles, venturis and orifices and from 0.0 to 1.0 in the case of the expanders.
	www.isa.org /books/Mulley_Papers/compressible.html (2176 words)

	ME346 Gas Dynamics : University of Vermont (Site not responding. Last check: 2007-11-03)
		Compressible flow, also referred to as ‘gas dynamics’ for historical reasons, plays a vital role in a variety of engineering and physical phenomena.
		Typically compressible flow is associated with aerospace applications such as supersonic flow and rocket engines, but it also has relevance to mechanical engineering; an example of the latter is in gas turbines.
		The practical consequence is that compressible flow analyses and calculations tend to be much more complicated than their incompressible counterparts because a thermodynamic equation of state is required for the density which links it to other flow variables (e.g.
	www.uvm.edu /~dhitt/me346/?Page=ME346-S05-Syllabus.htm (1013 words)

	Compressible Flow
		Compressibility of gases leads to many interesting features such as shocks, which are absent for incompressible fluids.
		Gasdynamics is the discipline that studies the flow of compressible fluids and forms an important branch of Fluid Mechanics.
		As the flow passes through the shock its pressure increases, i.e, the flow is compressed.
	www.aeromech.usyd.edu.au /aero/gasdyn/node1.html (6882 words)

	Fluid dynamics - Wikipedia, the free encyclopedia
		Flows of liquids with pressure variations much smaller than those required to cause phase change (cavitation), or flows of gases involving speeds much lower than the isentropic sound speed are termed incompressible.
		For flow of gases, to determine whether to use compressible or incompressible fluid dynamics, the Mach number of the problem is evaluated.
		Mathematically, turbulent flow is often represented via Reynolds decomposition, in which the flow is broken down into the sum of a steady component and a perturbation component.
	en.wikipedia.org /wiki/Fluid_dynamics#Equations_of_fluid_dynamics (1541 words)

	Weymouth and Panhandle Equations for Gas Pipelines (Site not responding. Last check: 2007-11-03)
		The equations were developed from the fundamental energy equation for compressible flow, but each has a special representation of the friction factor to allow the equations to be solved analytically.
		Darcy-Weisbach incompressible flow calculation may be more accurate than the Weymouth or Panhandles for a short pipe or low flow.
		If the pressure drop is between 10% and 40%, then the density used in an incompressible flow method should be based on the average of the upstream and downstream conditions.
	www.lmnoeng.com /Flow/weymouth.htm (649 words)

	3.5 Standard solvers
		Steady-state solver for turbulent flow of compressible fluids for ventilation and heat-transfer
		Transient Solver for buoyant, turbulent flow of compressible fluids for ventilation and heat-transfer
		Steady-state solver for buoyant, turbulent flow of compressible fluids for ventilation and heat-transfer
	www.opencfd.co.uk /openfoam/doc/userse8.html (428 words)

	Solenoid Valve Selection: Don't Be Fooled by Flow Rate
		Flow rate is the quantity of a medium that passes at a given point during a given period of time.
		Another, more accurate term for gas flow is "compressible fluid flow." Compressibility refers to a gas' ability to change density with temperature and pressure changes.
		Flow rates for compressible fluids are significantly more difficult to calculate than those of incompressible fluids, simply because of their properties.
	www.chemicalprocessing.com /articles/2003/58.html (831 words)

	PIPE-FLO Compressible - fluid flow analysis software for compressible systems.
		In addition, PIPE-FLO Compressible calculates when the fluid flow in a pipeline is approaching the sonic velocity or choked flow conditions.
		The two flows handled by the program are Fanno flow (flow with friction) and simple area changes.
		Centrifugal devices are modeled by entering performance data of flow rate and discharge pressure for a range of flows.
	www.eng-software.com /products/pipeflo/compressible/faqs.aspx (1040 words)

	AERADE
		A thermodynamically-rigorous, uniform reference-mean flow is derived by extending the stagnation reservoir concept for total-state conditions in uniform flow to non-uniform flow and by requiring equality of the sectional mass flow and entropy between the non-uniform flow and the reference-mean flow, leading to logarithmic-mean definitions of the mean pressure, temperature and density.
		A thermodynamically-rigorous, uniform reference-mean flow is derived by extending the stagnation reservoir concept for total-state conditions in uniform flow to non-uniform flow and requiring equality of the sectional mass flow and entropy between the non-uniform flow and a uniform reference-mean flow, leading to rational definitions of the mean pressure, temperature and density.
		Mean values are often used to provide a simplified flow description at component interfaces and an appropriate choice is important in ensuring consistency between calculations for separate components in a system, such as a gas turbine, that may be analysed by different groups.
	aerade.cranfield.ac.uk /subject-listing/esdu/ES112.html (1117 words)

	Mass Flow Choking
		Considering the mass flow rate equation, it appears that for a given area and a fixed density, we could increase the mass flow rate indefinitely by simply increasing the velocity.
		Mach number equal to one is called a sonic condition because the velocity is equal to the speed of sound and we denote the area for the sonic condition by a special symbol "A*", pronounced "A star".
		If we have a tube with changing area, like the nozzle shown on the slide, the maximum mass flow rate through the system occurs when the flow is choked at the smallest area.
	www.grc.nasa.gov /WWW/K-12/airplane/mflchk.html (1170 words)

	Compressible hydraulic flow
		Strictly speaking all fluids are compressible to a degree.
		Request the article on Two Phase Flow of Liquefied Compressed Gases for details on the flow theory used by GSI for compressible and two-phase flow of fire fighting agents.
		During this research, it was necessary to refine the traditional approach to calculating flow of compressed gas to include compensation for continuous heat entry into the gas during the discharge.
	www.gsifire.com /compress.htm (322 words)

	Pipe Flow - a PDH Online Course for Engineers
		For turbulent flow the pipe roughness and the Reynolds number are used to evaluate the friction factor from the Colebrook equation.
		Benefits to be derived from this course include these: Awareness of the fluid properties of viscosity and compressibility, knowledge of the differences in governing equations for compressible, incompressible, isothermal, and adiabatic flow, use of the Reynolds number to determine laminar or turbulent flow, calculation of energy losses, and different methods of solving the governing equations.
		For both compressible and incompressible fluids, and for isothermal and adiabatic gases, the governing equations of continuity, momentum, and energy were presented.
	www.pdhonline.org /courses/m204/m204.htm (1130 words)

	Compressible Flow (via CobWeb/3.1 planetlab2.cs.unc.edu) (Site not responding. Last check: 2007-11-03)
		In your previous fluids classes, the working fluids (in most cases air) were treated as incompressible - a flow in which the density was considered constant.
		However, as you probably learned in earlier cases that this simplifcation (density being considered as precisely constant), does not occur in nature.
		Therefore, if the fluid flow experiences small pressure changes, then the changes in density may be small as well (i.e.
	www.cfdrl.uc.edu.cob-web.org:8888 /WebPage/Courses/comp_flow/cf_index.html (119 words)

	[No title]
		Fluid turbulence is the term used to refer to extremely complex flow which is driven by a number of fluid instabilities, such as the Kelvin-Helmholtz instability of shear flow and the Rayleigh-Taylor and Richtmyer-Meshkov instabilities of accelerated multi-fluid interfaces.
		This is a compressible flow in which an initially uniform state has been perturbed by randomly oriented, isentropic, sinusoidal sound waves.
		For these compressible flows it is not possible to untangle the flow dynamics from pictures and analysis of the vorticity alone.
	www.lcse.umn.edu /research/lanlrun/text.html (1262 words)

	Pipe Flow Modeling Software
		Powerful compressible flow pipe network flow analysis and system modeling including adiabatic, isothermal and generalized heat transfer, modeling velocities up to and including sonic choking.
		All of the powerful pipe flow system modeling capabilities of AFT Fathom coupled with an advanced optimization engine to provide the piping and ducting systems engineer with the first practical tool to truly optimize for minimum cost, size or weight.
		All of the powerful pipe flow system modeling capabilities of AFT Arrow coupled with an advanced optimization engine to provide the piping and ducting systems engineer with the first practical tool to truly optimize for minimum cost, size or weight for a wide range of gas piping and ducting systems.
	www.aft.com /products (394 words)

	Compressible Flow Modeling in a Constant Area Duct - a PDH Online Course for Engineers
		Designing a gas flowing system to supply a constant mass flow rate using sonically flow controlling devices and providing end item interface pressure depends on accurately predicting static condition either at the inlet or outlet of a pipe or duct.
		Using adiabatic flow with friction in a constant-area duct is one method for predicting pressure and temperature changes of a gas flow stream in a long insulated duct or a short uninsulated high gas velocity application where heat transfer from the surroundings to the flow stream is negligible.
		Compressible flow gases are subject to density changes based on pressure and temperature changes.
	www.pdhonline.org /courses/m198/m198.htm (730 words)

	Compressible Flow Calculator
		This type of flow turns out to be a good approximation of heat exchangers and of constant-area combustion chambers such as is typical of gas turbines.
		Typical tables of Rayleigh Flow show ratios of various thermodynamic flow quantities at a given Mach number to the value of this same quantity at a Mach number of 1.0 with the flow modified by heat transfer without friction.
		The flow ratios in terms of Mach number are straightforward codings of the equations in NACA Report 1135 or any gas dynamics textbook.
	www.pdas.com /vucalc.htm (726 words)

	Compressible flow in the automobile inlet duct
		The Matlab Simulink model previously developed that looked at the air flow in the inlet tract, made the assumption that the air flow was in-compressible.
		For a more accurate approach to this application the compressible nature of air should be considered.
		The flow is subsonic but there are three conditions that need to be satisfied as the air flow passes
	www.tech.plym.ac.uk /sme/mech331/compflow3.htm (774 words)

	Compressible Flow in Nozzle - Problem Specification (Site not responding. Last check: 2007-11-03)
		Consider air flowing at high-speed through a convergent-divergent nozzle having a circular cross-sectional area, A, that varies with axial distance from the throat, x, according to the formula
		The Reynolds number for this high-speed flow is large.
		So it is reasonable to model the flow as inviscid.
	instruct1.cit.cornell.edu /courses/fluent/nozzle/index.htm (132 words)

	Compressible Flow Results (Site not responding. Last check: 2007-11-03)
		Notable for its thoroughness and clarity, this well-written graduate-level text presents the theoretical background of fluid flow from the standpoint of the transport phenomena, relating momentum transport...
		The most extensive change is in the handling of compressible flow.
		In October 1947 a theoretical investigation of viscous effects in compressible fluids was started at GALCIT under ONR contract.
	stokes.ucsd.edu /fd_books/discipline/comflow.html (866 words)

	AME Undergraduate Courses
		An intermediate level course in the dynamics and thermodynamics of compressible flow for both internal and external geometries.
		This course will provide the student with an introduction to flows in which fluid compressibility is significant and must be taken into account.
		Be able to design devices in which compressible flow of gas is an integral component.
	www.nd.edu /~ame/undergrad/ae.360.html (233 words)

	Computer Resources for Compressible Flow Students (Site not responding. Last check: 2007-11-03)
		Here are computer-based tools which replace some of the classical tables of information for compressible flow such as the isentropic flow table, normal shock table, oblique shock table, and other analytic algebraic solutions of compressible flows.
		Compressible Flow Calculator, WEB browser-based applet, for isentropic 1-D flow plus normal and oblique shocks; author W. Devenport at Virginia Tech.
		Most of the rather spectacular images of compressible flows are obtained by Schlieren imaging, which gives particularly clear indications of shock waves.
	www.tricity.wsu.edu /~me424/cfstuff.htm (608 words)

	FlexPDE User's Forum: compressible viscous flow
		I am looking for example .pde files that deal with compressible* viscous flow in 2-dimension and conjugate heat transfer problem.
		We haven't done much with compressible flow yet, but here is a shock tube model that may provide a start.
		Just to pick one off my shelf, "Compressible Fluid Flow" by Oosterhuizen and Carscallen (ISBN 0-07-048197-0) is full of worked examples from beginning to end.
	www.pdesolutions.com /discus/messages/4/152.html?1130084330 (271 words)

	Armfield - Compressible Flow Unit - C1MKII
		The compressor is fitted with an outlet duct incorporating a throttling valve, which allows the flow to be varied.
		A pressure sensing ring tapping is provided at the inlet, at the throat and at the discharge end of the diffuser.
		This duct allows all the major concepts of compressible flow to be demonstrated.
	www.armfield.co.uk /c1mkii_datasheet.html (617 words)

	1-D Compressible Flow Calculations (Site not responding. Last check: 2007-11-03)
		This form calculates the properties of one-dimensional air flow without losses (isentropic).
		The required input is the Mach number of a point in the flow.
		The gas can be changed by entering the value of Ratio of Specific Heats (Gamma).
	www.ae.su.oz.au /aero/compressible/index.html (40 words)

	Compressible flow and gas flow modeling software for piping systems
		Compressible flow and gas flow modeling software for piping systems
		With ever increasing complexity, sizing today’s compressible flow systems for minimal cost surpasses the best traditional design methods.
		Providing the systems engineer a new technology to intelligently size the system as a whole, your compressible flow piping system can be optimally sized resulting in substantial cost savings.
	www.aft.com /products/titan (348 words)

	Compressible flow and gas flow modeling software for piping systems (via CobWeb/3.1 planetlab2.cs.unc.edu) (Site not responding. Last check: 2007-11-03)
		AFT Arrow goes beyond the boundaries of fluid flow analysis, with thermal analysis capabilities including piping heat transfer, heat exchanger modeling and varying fluid properties.
		AFT Arrow employs a robust solver using proven matrix methods to solve the governing equations of pipe flow to conduct a true and rigorous compressible flow solution.
		From the powerful drag-and-drop model building features to the fully customizable output, AFT Arrow becomes an extension of the engineer’s mind, freeing him or her to focus on their system, not the mechanics of software manipulation.
	www.aft.com.cob-web.org:8888 /products/arrow (369 words)

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