Fluid flow compressible fluid

Flows can be classified into two major categories (a) incompressible and (b) compressible flow. Most hqnids fall into the incompressible-flow category, while most gases are compressible in nature. A perfect fluid can be defined as a flnid that is nonviscous and nonconducting. Fluid flow, compressible or incompressible, can be classified by the ratio of the inertial forces to the viscons forces. This ratio is represented by the Reynolds nnmber (Nji,). At a low Reynolds number, the flow is considered to be laminar, and at high Reynolds numbers, the... 

Equation (4.24) allows the Fanning friction factor to be found during laminar flow for both incompressible fluids and compressible fluids, i.e. liquids and gases. 

Above treatment is simplified one. However, natural system is more complicated. For instance, fluids are compressive, fluids flow under non-steady state conditions, and permeability of rocks is heterogeneously distributed. Fluids flow not only in saturated zone, but also in unsaturated zone. 

As already explained the necessity to satisfy the BB stability condition restricts the types of available elements in the modelling of incompressible flow problems by the U-V P method. To eliminate this restriction the continuity equation representing the incompressible flow is replaced by an equation corresponding to slightly compressible fluids, given as... 

Compressible Vlow. The flow of easily compressible fluids, ie, gases, exhibits features not evident in the flow of substantially incompressible fluid, ie, Hquids. These differences arise because of the ease with which gas velocities can be brought to or beyond the speed of sound and the substantial reversible exchange possible between kinetic energy and internal energy. The Mach number, the ratio of the gas velocity to the local speed of sound, plays a central role in describing such flows. 

Flows are typically considered compressible when the density varies by more than 5 to 10 percent. In practice compressible flows are normally limited to gases, supercritical fluids, and multiphase flows containing gases. Liquid flows are normally considerea incompressible, except for certain calculations involved in hydraulie transient analysis (see following) where compressibility effects are important even for nearly incompressible hquids with extremely small density variations. Textbooks on compressible gas flow include Shapiro Dynamics and Thermodynamics of Compre.ssible Fluid Flow, vol. 1 and 11, Ronald Press, New York [1953]) and Zucrow and Hofmann (G .s Dynamics, vol. 1 and 11, Wiley, New York [1976]). 

Critical (or choked) Maxinriim flow condition for compressible fluids... 

For the compressible flow cases. Regimes 1 and 3, and Regime 2 with q, > q, making use of Eq. (26-90), integration of Eq. (26-93) gives Compressible Fluid Orifice Discharge by HEM... 

Discharge Coefficients and Gas Discharge A compressible fluid, upon discharge from an orifice, accelerates from the puncture point and the cross-sec tional area contracts until it forms a minimum at the vena contracta, If flow is choked, the mass flux G, can be found at the vena contrac ta, since it is a maximum at that point, The mass flux at the orifice is related to the mass flux at the vena contracta by the discharge coefficient, which is the area contraction ratio (A at the vena contracta to Ay at the orifice) ... 

Figure 2.3. A rigid piston drives a shock wave into compressible fluid in an imaginary flow tube with unit cross-sectional area. The shock wave moves at velocity U into fluid with initial state 0, which changes discontinuously to state 1 behind the shock wave. Particle velocity u is identical to the piston velocity.

For compressible fluids one must be careful that when sonic or choking velocity is reached, further decreases in downstream pressure do not produce additional flow. This occurs at an upstream to downstream absolute pressure ratio of about 2 1. Critical flow due to sonic velocity has practically no application to liquids. The speed of sound in liquids is very liigh. See Sonic Velocity later in this chapter. 

The Lapple charts for compressible fluid flow are a good example for this operation. Assumptions of the gas obeying the ideal gas law, a horizontal pipe, and constant friction factor over the pipe length were used. Compressible flow analysis is normally used where pressure drop produces a change in density of more than 10%. 

The length of the column is also defined by the Poiseuille equation that describes the flow of a fluid through an open tube in terms of the tube radius, the pressure applied across the tube (column), the viscosity of the fluid and the linear velocity of the fluid. Thus, for a compressible fluid. 

High-pressure fluid flows into the low-pressure shell (or tube chaimel if the low-pressure fluid is on the tubeside). The low-pressure volume is represented by differential equations that determine the accumulation of high-pressure fluid within the shell or tube channel. The model determines the pressure inside the shell (or tube channel) based on the accumulation of high-pressure fluid and remaining low pressure fluid. The surrounding low-pressure system model simulates the flow/pressure relationship in the same manner used in water hammer analysis. Low-pressure fluid accumulation, fluid compressibility and pipe expansion are represented by pipe segment symbols. If a relief valve is present, the model must include the spring force and the disk mass inertia. 

The following analysis enables one to calculate the diameter of a pipeline transporting any compressible fluid. The required inputs are volumetric flow rate, the specific gravity of the gas relative to air, flow conditions, compressibility factor Z where Z is defined by nZRT = PV, the pressure at the point of origin and the destination, the pipe length, and pipe constants such as effective roughness. The working equations have been obtained from the literature. Since the friction factor... 

A compressible fluid is a fluid in which significant density variations that occur during its flow have to be considered, as is usually the case with vapors and gases. 

Shapiro, A.H, (1953). The dynamics and thermodynamics of compressible fluid flow. Ronald Press. New York. 

The flow of a compressible fluid through an orifice is limited by critical flow. Critical flow is also referred to as choked flow, sonic flow, or Mach 1. It can occur at a restriction in a line such as a relief valve orifice or a choke, where piping goes from a small branch into a larger header, where pipe size increases, or at the vent tip. The maximum flow occurs at... 

D. Givoli, J. E. Flaherty, M. S. Shephard. Parallel adaptive finite element analysis of viscous flows based on a combined compressible-incompressible formulation. Int J Numer Meth Heat and Fluid Flow 7 880, 1997. 

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