Compressible Pipe Flow Research Articles

Linear stability analysis of compressible pipe flow

Linear stability analysis of compressible pipe flow

Compressible Pipe Flow with Friction and Gravity

A viscous one-dimensional compressible pipe flow under gravity effect is studied analytically. The compressible one-dimensional pipe flow with friction is called Fanno flow and the solution is given by analytical formula. In gas dynamics, the gravity effect is minimal and it is not included in the equations. However, it was shown by the present author that the elevation of a pipe could change the flow conditions in a one-dimensional compressible potential flow under gravity. The sonic condition is reached at the maximum height for an inviscid pipe flow. In this paper, the gravity effect is extended to the viscous one- dimensional pipe flow. Subsonic–supersonic transition is also possible by up and down of the pipe as in the inviscid flow, and it is found that the sonic condition deviates from the peak position of the pipe.

Numerical Modeling of Gas-Liquid Compressible Pipe Flow Based on the Theory of Thermodynamically Compatible Systems

Based on the theory of thermodynamically compatible systems, we formulate the governing equations of a gas-liquid compressible pipe flow and develop the Runge–Kutta–TVD and Runge–Kutta–WENO high accuracy methods. The computational model is used to solve a series of test cases demonstrating its efficiency and capability to be applied to slug flows modeling.

Mixing and evaporation analysis of a high-pressure SCR system using a hybrid LES-RANS approach

A hybrid Large Eddy Simulation (LES) – Reynolds-Averaged Navier-Stokes (RANS) method (HLR) has been applied to simulate an engine related selective catalytic reduction (SCR) system. Typical SCR systems utilize low pressure urea injection together with a mixer for vapor field homogenization. Simultaneously, it is also desirable to reduce spray-wall interaction to avoid urea crystallization. The present study considers an SCR system where a high pressure (150 bar) urea spray is injected towards hot exhaust gases in exhaust pipe. The system has been shown to work well in a previous experimental study but detailed characterization of the system is missing. The novelty of the present study rises from: 1) the creation of phase diagrams with single droplet simulations that predict the optimum operation regions for the SCR system, 2) validation of the HLR method in a high Reynolds number (Re=49,900) compressible pipe flow, 3) the use of HLR simulations in an engine SCR system for the first time, and 4) the detailed characterization of the present SCR system. As a result of the study, new non-dimensional timescale ratios are proposed to link the droplet size and liquid injection velocity to the exhaust pipe dimensions in future SCR systems.

Validation of 1D flow model for high pressure offshore natural gas pipelines

Transportation of natural gas through high pressure large diameter offshore pipelines is modeled by numerically solving the governing equations for one-dimensional compressible pipe flow using an implicit finite difference method. The pipelines considered have a diameter of 1 m and length of approximately 650 km. The influence of different physical parameters which enter into the model are investigated in detail. These include the friction factor, equation of state and heat transfer model. For high pressure pipelines it is shown that the selection of the equation of state can have a considerable effect on the simulated flow results, with the recently developed GERG 2004 being compared to the more traditional SRK, Peng–Robinson and BWRS equations of state. Also, including heat accumulation in the ground is important in order to model the correct temperature at the outlet of the pipeline. The flow model is validated by comparing computed results to measured values for an offshore natural gas pipeline.

DNS of compressible pipe flow exiting into a coflow

Direct numerical simulations were conducted of a fully turbulent canonical nozzle/jet configuration. For all cases, the target Reynolds number, based on the jet velocity and diameter, was specified as 7500 and the jet Mach number and coflow Mach number were varied. Turbulence statistics at the nozzle exit are shown to collapse with fully developed turbulent pipe flow profiles when using the wall shear-stress, and in the case of higher Mach number cases also the wall density, from the fully developed flow region upstream in the nozzle. Predictions of flow variables in the near-nozzle region obtained from asymptotic theory are found to agree qualitatively with Direct Numerical Simulation data. The data from the different cases are shown to collapse in the potential core region when scaling with the appropriate mixing layer parameter while further downstream the appropriate parameter is the non-dimensional local velocity excess. For all scalings investigated, including virtual-origin correction of the streamwise axis, the case with the highest coflow magnitude did not agree well with the other cases implying that self-similarity of coflowing jets is restricted to low coflow values. Finally, it is shown that the acoustic field is resolved by the simulations making the data suitable for subsequent aeroacoustic analysis.

A Novel Model of Turbulent Convective Heat Transfer in Round Tubes at Supercritical Pressures

In the present study, a novel model was established to investigate the enhanced heat transfer to turbulent pipe flow of supercritical pressure fluids. The governing equations for the steady turbulent compressible pipe flow were simplified into the one-dimensional nondimensionalized forms based on the boundary layer theory. A conventional mixing length turbulence model for constant-property pipe flows was modified by introducing the effect of density fluctuations into the equations of turbulent transport, and the modified turbulence model was applicable to both constant-property and variable-property pipe flows. With the suggested model, which was a combination of the nondimensional governing equations and the modified turbulence model, the numerical calculations were carried out for the turbulent convective heat transfer of water in round tubes at supercritical pressures. The results showed that the present model can provide a relatively precise prediction about the effect of pressure, mass flux, and wall heat flux on heat transfer for supercritical fluid flows and greatly reduce the calculation workload. The modified turbulence model showed a much better agreement with the experimental results than the original turbulence model.

Simulation of compressible flow in high pressure buried gas pipelines

The aim of this work is to analyze the gas flow in high pressure buried pipelines subjected to wall friction and heat transfer. The governing equations for one-dimensional compressible pipe flow are derived and solved numerically. The effects of friction, heat transfer from the wall and inlet temperature on various parameters such as pressure, temperature, Mach number and mass flow rate of the gas are investigated. The numerical scheme and numerical solution was confirmed by some previous numerical studies and available experimental data. The results show that the rate of heat transfer has not a considerable effect on inflow Mach number, but it can reduce the choking length in larger f DL / D values. The temperature loss will also increase in this case, if smaller pressure drop is desired along the pipe. The results also indicate that for f DL / D = 150, decreasing the rate of heat transfer from the pipe wall, indicated here by Biot number from 100 to 0.001, will cause an increase of about 7% in the rate of mass flow carried by the pipeline, while for f DL / D = 50, the change in the rate of mass flow has not a considerable effect. Furthermore, the mass flow rate of choked flow could be increased if the gas flow is cooled before entrance to the pipe.

Numerical simulation of turbulent unsteady compressible pipe flow with heat transfer in the entrance region

In this paper, the compressible gas flow through a pipe subjected to wall heat flux in unsteady condition in the entrance region is investigated numerically. The coupled conservation equations governing turbulent compressible viscous flow in the developing region of a pipe are solved numerically under different thermal boundary conditions. The numerical procedure is a finite-volume-based finite-element method applied to unstructured grids. The convection terms are discretized by the well-defined Roe method, whereas the diffusion terms are discretized by a Galerkin finite-element formulation. The temporal terms are evaluated based on an explicit fourth-order Runge–Kutta scheme. The effect of different thermal conditions on the pressure loss of unsteady flow is investigated. The results show that increase in the inflow temperature or pipe-wall heat flux increases the pressure drop or decreases the mass flow rate in the pipe.

Numerical solutions of the unsteady Fanno model for compressible pipe flow

This paper presents numerical results on the evolution of the solutions of the Fanno model for compressible pipe flow. The principal results concern the large-time behaviour when nonlinear effects are appreciable throughout the evolution. Our computations show that compression waves can be expected to evolve into travelling waves for large times whereas expansion waves cannot.

Technically oriented algorithms for unsteady pipe flow: Comput. Meth. in Applied Mechanics and Eng. Vol 2 No 3 (July/Aug 1973) pp 279–303

Abstract The two best-known integration methods for nonlinear hyperbolic systems of partial differential equations, i.e. the method of characteristics and the explicit difference method, are examined with respect to systematic calculation of complicated technical problems of instationary compressible pipe flow, especially with regard to their adaptability to computer solution. Although difference methods are much easier to program than characteristic methods, they generally tend to produce unpredictable errors, at least in their current form. Therefore, it is the aim of this paper to develop and test difference algorithms for some of the most usual boundary conditions of technical pipe flow, including such essentially two-dimensional configurations as the flow through bends and branches.

Technically oriented algorithms for unsteady pipe flow

The two best-known integration methods for nonlinear hyperbolic systems of partial differential equations, i.e. the method of characteristics and the explicit difference method, are examined with respect to systematic calculation of complicated technical problems of instationary compressible pipe flow, especially with regard to their adaptability to computer solution. Although difference methods are much easier to program than characteristic methods, they generally tend to produce unpredictable errors, at least in their current form. Therefore, it is the aim of this paper to develop and test difference algorithms for some of the most usual boundary conditions of technical pipe flow, including such essentially two-dimensional configurations as the flow through bends and branches.