For dry air at 20 c with d75and mmol d29g mol1, the sound speed comes to c0 d343m s1 d1235km h1. Modeling and simulation of steadystate pipeline networks, m. An explicit method for the analysis of transient compressible. The university of texas at austin, 2015 supervisor. We must remember that cf depends on the reynolds number. Systems of equations describing steady flow in pipe networks. P age transient analysis of gas flow in pipeline was. Comprehensive simulation of onedimensional unsteady pipe network. Pipe fractional flow through branching conduits jeffrey robert stewart, m. The purpose of this paper is to describe the structure of a simulator developed for the prediction of the steadystate behavior of pipeline networks with compressible fluids.
The work presented in this thesis studies acoustic perturbations in slowly varying pipes. Steadystate modeling and simulation of pipeline networks for. Compressible flow has often been an undereducated aspect of chemical engineering, but is important to many different careers in which piping systems are used. Computational fluid dynamicscomputational fluid dynamics lecture 6. In this case we would need to think about recalculating cf every time we change the flow. Introduction to compressible flow me 322 lecture slides, winter 2007 gerald recktenwald.
The objective of the course note is to provide a survey of a wide variety of topics in fluid mechanics, including a rigorous derivation of the compressible navierstokes equations, vorticity dynamics, compressible flow, potential flow, and viscous laminar flow. Analysis of complex pipe networks with multiple loops and inlets and outlets the techniques described previously for analysis of pipe flow are satisfactory if the pipe system is simple, consisting of one pipe or a combination of pipes in which the flow directions are all known unambiguously. An implicit method for transient gas flows in pipe networks. Losses of fittings and valves are express as 10 % from pipe length. An explicit method for the analysis of transient compressible flow in pipe networks. The equation gives for a known pipe, the maximum pressure rise given any closure time. January 28, 2007 this document describes a collection of matlab programs for pipe. In partial fulfillment of the requirements for the degree of.
Compressible flow or gas dynamics is the branch of fluid mechanics that deals with flows having significant changes in fluid density. Turbulent and laminar pulsating flows in a straight smooth pipe are compared at identical frequencies and reynolds numbers. While straightforward in terms of the onedimensional nature of pipe networks, the. Comprehensive simulation of onedimensional unsteady pipe network hydraulics. The pressure loss depends on the type of flow of the fluid in the network, pipe material, and the fluid flowing through the pipe. Unsteady and transient flow of compressible fluids in.
Logically, fluid flow waves must also occur in saturated pipe networks and, by extension, in porous media, provided the interstitial fluid is compressible andor the porous medium is deformable. This thesis deals with the development of an explicit pipe network analysis code for the benchmarking of flownet. Associate professor, mechanical and materials engineering department portland state university, portland, oregon. Pressure loss or pressure change over any section is decreased. The slow variation is introduced in the form of a small parameter. Shows a gas flow through a control volume of a pipe. Unlike liquids, gases are compressible, and the change in the conditions of the fluid as it moves down the pipe must be considered in these calculations.
The stochastic analysis consists in estimation of the pdf of the network. Sharma in the field of multiphase flow, the socalled phase splitting problem is a recurrent topic of discussion. Pdf wave propagation in pipes of slowlyvarying radius. Technical documents about pipe flow and pressure drops. Compressible fluid flow calculation methods article pdf available in chemical engineering new york mcgraw hill incorporated then chemical week publishing llc 1212. Part of the civil and environmental engineering commons, and the water resource management commons recommended citation. Isothermal flow is considered throughout this thesis as this work represents the first.
The limits of the darcy weisbach equation pertaining to compressible fluids are covered on page 18 of the method of solution for pipe flo and elsewhere in this knowledge base. Compressible flow refresher in production plants, there are many situations where pressure drops of process vapors and gases need to be calculated. Gordon livesey the nature of gas flow in pipes and ducts changes with the gas pressure and its. Changes in piping pressure, flow rate, gas density and velocity all effect the pressure drop across the pipe and without careful consideration can cause. Compressible flow modeling in a constant area pipe neil hicks pe course content figure 1 shows a system that is designed to power a gearbox through the use of a turbine by expansion of a constant mass flow rate helium gas. Note that the h l, pipe contributions are usually computed by assuming that the. Understanding compressible flow fluid flow articles.
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. Lastly, the manual calculation of the network analysis is compare with fortran. This method is based on the successive addition of flow rate corrections in each branch, in order to achieve satisfaction of energy conservation along every path in the network. The pipe flow expert and pipe flow wizard software programs use the darcyweisbach method to calculate friction loss in pipes since it is generally accepted that this equation, together with the friction factor obtained from use of the colebrookwhite equation, gives the most accurate solution for non compressible fluids and works well for. Flow through pipes in a typical plant where line lengths are short, or the pipe is well insulated can be considered adiabatic. The modelica fluid and media library for modeling of incompressible and compressible thermofluid pipe networks conference paper pdf available january 2006 with 606 reads how we measure reads. Using these functions it is relatively easy to perform head loss calculations, solve.
For compressible flow simulations it is quite common to see the use of eulers equation instead of navierstokes. Become familiar with a compressible flow visualization technique, namely the schlieren optical technique. Comprehensive simulation of onedimensional unsteady pipe. Thus, density change is decreased too density can be considered as a constant value for each pipe segment only. Using an incompressible flow darcy weibach is not an option for me since we have to divide the pipe to many small segments. Tiley the mathematical modelling of highly compressible unsteady flows has been of interest for some years. It used by engineers in over 75 countries worldwide, to model pipe systems where the flow rates, pressure losses, and pumping requirements of the system need to. Pipelines and pipe networks ii series, parallel and branch piping 3. It is frequently used to obtain the pressure distribution of. Implementation of the hardycross method for the solution. I am trying to estimate decompression time for fuselage with multiple chambers connected in serial and parallel network.
The compressible flow equations calculate a gas flow rate for a difference in pressure between two points. These systems may have freesurface, pressurized, or mixed flow conditions. In this system the designer wants to control the mass flow rate using a regulator and a sonic orifice. Which pipe diameter is necessary for required flow rate. Usually extremes are considered like adiabatic and isothermal flow. Compressibility factor function of temperature and pressure was considered. This thesis investigates the choking condition for compressible gas flow in a single microscopic pore. A thesis submitted in fulfillment of the requirements for the. These pressures normally refer to values in perhaps notional plenums at the entrance and exit of a duct or a system fitting such as a valve.
Fluid statics, kinematics of fluid, conservation equations and analysis of finite control volume, equations of motion and mechanical energy, principles of physical similarity and dimensional analysis, flow of ideal fluids viscous incompressible flows, laminar boundary layers, turbulent flow, applications of viscous flows. Most measurements were made at a mean reynolds number of 4000, but the influence of re was checked for 2900 thesis, the development of outflow models to simulate the fullbore rupture of horizontal pipelines is presented. High speed compressible flow through pipe cfd online. However, the literature on rigorous pipe network simulation with compressible fluids is scarce. Ejectors in a compressible network for gas turbine. Changes in piping pressure, flow rate, gas density and velocity all effect the pressure drop across the pipe.
Compressible fluid flow through an orifice by herschel nathaniel waller, jr. The incompressible steady flow energy equation, including friction loss, would generalise to 22 12,1,2 2212 mm f ppuu zzh gg g g. Compressible flow modeling in pipe networks is a challenging technical application because of the coupled nature of the governing equations and the large number of parameters involved. Flow chokes at resriction in pipe flow chokes at expansion in pipe area 0. Modelling and control of aircraft environmental control systems. In a branching conduit, it is of practical importance to know a priori how the phases split. Modeling of compressible flow with friction and heat. Fluid flow in tjunction of pipes the topic of this masters thesis was approved by the department council of the department of information technology on 16 january 2007.
For single pipe systems engineers can frequently perform a rough compressible flow calculation for prediction of pressure drop. The purpose of this work is to derive a flow wave propagation model for a single pipe and use it to investigate flow waves through pipe networks. This allows an asymptotic approach and the wkb method is used to solve the subsequent mathematical problems. However, the literature on rigorous pipe network simulation with compressible fluids is scarce greyvenstein and laurie, 1994. Consider fully developed flow through a constantarea pipe between section 1 and 2 in figure 3. The suffix o refers to the initial conditions when the head behind the valve and is equal to the gross supply head if the friction in the pipe is neglected and is the inertia head at a time. Pdf the modelica fluid and media library for modeling of. Improved formulations and adaptive hybrid modeling johnathan d.
Modeling a flow meter with compressible flow pipe flo professional has certain limitations concerning the use of compressible fluids in a piping network. What drives the flow in a pipe is only as a first approximation the total to static pressure ratio. Nault doctor of philosophy department of civil engineering university of toronto 2017 abstract from municipal water supply to wastewater collection, pressurized pipe networks form the. The purpose of this paper is to describe the equations which govern the flow of compressible fluids through pipes. Conduct experiments to illustrate phenomena that are unique to compressible flow, such as choking and shock waves. Any of these piping configurations can result in sonic choking a crosssectional flow area of a pipe d diameter of a pipe e pipe wall roughness f friction factor ff, g. The hapn application for flow pressure analyses of low pressure gas pipe networks is completely designed in objectoriented programming technology. The present computer implementation is primarily intended for academic. Pulsating flow in a pipe journal of fluid mechanics. L, pipe is the viscous loss in a straight section of pipe and h l,minor is a minor loss due to a. 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. The flow through short straight pipes iii a compressible viscous stream j. On the other hand, raleigh flow provides analytical solution of frictionless compressible flow with heat transfer where incoming subsonic flow can be choked at the outlet boundary with heat addition to the control volume. Can we use pipe flow network model for this kind of compressible flow analysis.
For simplicity, we will examine perfect gases, which have the equation of state. Eulers equation is obtained by dropping the viscous term of the navierstokes equation, which makes it a first order pde. For laminar flow n 1 and cf 16re basically we are saying hf. The flow through short straight pipes in a compressible.
Compressible flow is the area of fluid mechanics that deals with fluids in which the fluid density varies significantly in response to a change in pressure. In order to investigate the effectiveness of an orifice system in producing pressure drops and the effect of compressibility on the pressure drop, computations using the massaveraged implicit navierstokes equations were applied to the axisymmetric pipe flows with the operating pressure ratio from 1. Isentropicflow d cm v m s t given t c p t kpa 2 250 20 500. In terms of flow rate q hf r qn r or often k is the fluid resistance. Library for modeling of incompressible and compressible thermo fluid pipe networks. Since the temperature of the homentropic atmosphere falls linearly with height according to eq. Adiabatic flow of a compressible fluid through a conduit. Pipe flow analysis with matlab computer action team. Chapter 1 governing equations of fluid flow and heat transfer. In the design of mall models of aircraft or tolssiles for testing in supersonic tunnels, it may be desrred to represent jet engine nacelles by means of simple hollow pipes. Compressible flow equation industrial professionals. A typical situation is a pipe into which gas enters at a given pressure and temperature and flows at a rate determined by the length and diameter of the pipe and. The algorithm for solving the finitedifference equations of a pipe is based on the newtonraphson method.
One dimensional isentropic flow compressible pipe flow. Content laaaadubue ominar and turbulent flow entrance region flow in a pipe channels of nonchannels of noncircular crosscircular crosssection. Analysis of complex pipe networks with multiple loops and. Modeling a flow meter with compressible flow engineered. Compressible flow in pipe, adiabatic, isothermal flow, specific volume, pressure drop in compressible flow, exact relation between pressure and specific volume is required, but it is not easily determined in each specific problem. Summary gas turbines are generally optimized to work at full load condition.
The pipe flow expert software first solves the compressible network using non compressible flow equations to find an approximate solution and then it employs the compressible flow engine to converge this to an accurate solution. Feb 16, 2011 compressible flow equation posted in industrial professionals. The use of pipe flow network analysis techniques as a special case of flow in ducts and pipes is commonly applied in engineering studies for the modelling of gas and water distribution. Fluent compressible flow in a nozzle simcafe dashboard. A thesis in mathematics submitted to the graduate faculty of texas tech university in partial fulfillment of the requirements for the degree of master of science chairmarr of the committee accepted deanof the i graduateschool may, 1973. Compressibility effects are typically considered significant if the mach number of the flow exceeds 0. Compressible gas flow experiment and assisted comsol modeling. Pressure drop control using multiple orifice system in. Dear all, i have just learned to use compressible flow on my recent incoming project. Fundamentals 0f flow in pipelines compressible flows. When any fluid flows through a pipe, the velocity adjacent to the pipe wall is zero and the velocity gradually increases from the wall. Fundamentals of compressible flow mechanics pdf 376p. In the following two sections well provide differential forms of the governing equations used to study compressible and incompressible flows.
Viscosity is the fluid resistance to flow, which reveals itself as a shearing stress within a flowing fluid and between a flowing fluid and its container. Compressible flow compressible flow study 1 2 n p assume a pipeline 1n is divided into sections12, 23, 34, etc. Nozzles and diffusers and converging diverging nozzles 2. Fluid flow in tjunction of pipes university of vermont.
Pressure drop for valves and fittings is accounted for as equivalent length of pipe. In the former case, the analysis is carried out on the basis of mass flow. The equations, which describe the physical flow pressure conditions. Except for the discussion of adiabatic compressible flow, it is generally assumed throughout this chapter that isothermal conditions apply. Therefore im now looking for compressible flow articles or books whose content are simple and have been acknowledged. Incompressible flow water hammer pipes fluid mechanics. Colebrook eqn 110 equivalent length of valves and fittings. Particular emphasis is placed on those used within the natural gas industry in hopes that engineers within that industry can make knowledgeable decisions on how to model pipes. Flownet is a generalpurpose thermalfluid network analysis code used as a tool in the design of the pebble bed modular reactor. Steadystate modeling and simulation of pipeline networks.
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