One-dimensional Compressible Flow Research Articles

Solution of the Noh problem using the universal symmetry of the gas dynamics equations

Noh’s constant-velocity shock problem is considered as a two-region solution of the one-dimensional (1D) Euler compressible flow equations, where the equation of state (EOS) closure model is included in the energy equation via an adiabatic bulk modulus. Regardless of the EOS model employed, the resulting system of equations is invariant under a universal group of scaling transformations. When combined with the required velocity field, the resulting equivalent system of ordinary differential equations coupled with the Rankine–Hugoniot shock jump conditions produces at least semi-analytic algebraic Noh solutions in 1D planar symmetry for any EOS. It is also shown for 1D curvilinear symmetries that the existence of a Noh solution is guaranteed only under more restrictive EOS conditions. In the context of this work, example Noh solutions—in some cases featuring arbitrary strength shocks—are derived for various closure models, including ideal gas, a two-parameter Clausius-like EOS, stiff gas, and a Mie–Gruneisen form. A code verification study is provided in the latter case, as an example of the application of the broader theoretical concepts.

Modeling and Computer Simulation of Centrifugal CO2 Compressors at Supercritical Pressures

The use of supercritical carbon dioxide (SC-CO2) as a working fluid in energy conversion systems has many benefits, including high efficiency, compact turbomachinery, and the abundance of CO2. A very important issue for design optimization and performance analysis of future SC Brayton cycles is concerned with the SC-CO2 flow inside high-speed compressors and turbines. The objective of this paper is to present a novel modeling approach to, and its use in numerical simulations of, SC-CO2 flow inside a high-speed compact compressor. The proposed approach capitalizes on using three different physical and mathematical formulations of one-dimensional (1D) models, i.e., compressible and incompressible flow models using actual properties of SC-CO2 and a compressible ideal gas model, as a reference to verify the predictive capabilities of a three-dimensional (3D) incompressible flow model. The incompressible model has been used to perform simulations for a complete detailed multidimensional model of an SC-CO2 high-speed compact compressor. The advantages of the new model include numerical stability, computational efficiency, and physical accuracy. In particular, it has been shown that the model's predictions are consistent with selected published technical data.

Freshwater generation from a solar chimney power plant

A modified solar chimney power plant is presented which is not only a solar thermal system able to achieve output power but also is able to extract freshwater from the air. This solar chimney power plant has no greenhouse canopy which is replaced by a collector made of black tubes around the chimney to warm the water and air. The effectiveness of this engineering structure is analyzed in comparison to natural precipitation at nine cities in China; one-dimensional compressible flow and heat transfer mathematical model has been developed to describe the moist air which cools down along the chimney and condenses above the lifting condensation level. The recovery of water is a partial duplication of natural atmospheric convection processes because of the unstable environment lapse rate. The results showed that there is often a high-strength positive correlation between the natural precipitation and the water production by this modified solar chimney power plant in those cities, Water production by the device in the conditions of the study can produce up to 37.9×106tons of water per year in Guangzhou, and 29.7×106tons of water per year in Chengdu, the correlation coefficient is even up to 0.875. Moreover, this device is more efficient in arid regions, might increase the rainfalls and enhance the regional water cycle. The amount of potable water produced by this modified solar chimney power plant is remarkable and might be able to benefit to several millions of people.

Unsteady natural gas flow within pipeline network, an analytical approach

The natural gas pipeline network (including distribution network) may be subjected to some extreme conditions such as pipeline rapture, sudden changed demand and etc. The behavior of natural gas pipeline network should be properly identified to prevent network failure and have continued pipeline operation under these extreme conditions. These conditions usually cause unsteady behavior of the pipeline network. Consequently, it is necessary to develop an unsteady state mathematical method to study natural gas pipeline network under unsteady conditions. To achieve this goal, an analytical approach has been developed to analyzed natural gas pipeline network. The governing equations derived for one-dimensional isothermal compressible viscous flow with Kirchhoff's laws have been employed to develop a method for studying the pipeline network under unsteady conditions. The proposed method has been compared with previous studies for validation purposes. The validation shows the proposed method has an average absolute present derivation (AAPD) less than 0.7%. Finally the effect of a few parameters including: friction factor, natural gas composition and decreasing and increasing demand have been studied. Results show that Weymouth and AGA equation predict highest and lowest pressure drop at the network nodes respectively. Also by increasing natural gas molar mass, the pressure at nodes will be decreased. It could be also concluded that demand rise causes pressure drop to decrease and demand fall causes pressure drop to increase.

Universal attractor for nonlinear one-dimensional compressible and radiative MHD flow

This paper is concerned with the existence of universal attractors in $H_{+}^{i}$ ( $i=1,2$ ) for one-dimensional compressible and radiative magnetohydrodynamics equations in a bounded domain $\Omega:=(0,1)$ . In this paper, the author extends the results in (Qin et al. in J. Differ. Equ. 253:1439-1488, 2012).

Accurate Radial Vaneless Diffuser One-Dimensional Model

A simplified one-dimensional model for the performance estimation of vaneless radial diffusers is presented. The starting point of such a model is that angular momentum losses occurring in vaneless diffusers are usually neglected in the most common turbomachinery textbooks: It is assumed that the angular momentum is conserved inside a vaneless diffuser, although a nonisentropic pressure transformation is considered at the same time. This means that fluid-dynamic losses are taken into account only for what concerns pressure recovery, whereas the evaluation of the outlet tangential velocity incoherently follows an ideal behavior. Several attempts were presented in the past in order to consider the loss of angular momentum, mainly solving a full set of differential equations based on the various developments of the initial work by Stanitz (1952, “One-Dimensional Compressible Flow in Vaneless Diffusers of Radial or Mixed-Flow Centrifugal Compressors, Including Effects of Friction, Heat Transfer and Area Change,” Report No. NACA TN 2610). However, such formulations are significantly more complex and are based on two empirical or calibration coefficients (skin friction coefficient and dissipation or turbulent mixing loss coefficient) which need to be properly assessed. In the present paper, a 1D model for diffuser losses computation is derived considering a single loss coefficient, and without the need of solving a set of differential equations. The model has been validated against massive industrial experimental campaigns, in which several diffuser geometries and operating conditions have been considered. The obtained results confirm the reliability of the proposed approach, able to predict the diffuser performance with negligible drop of accuracy in comparison with more sophisticated techniques. Both preliminary industrial designs and experimental evaluations of the diffusers may benefit from the proposed model.

Design of a fast diaphragmless shock tube driver

In this paper, we developed a one-dimensional compressible flow model to study the behavior of various diaphragmless drivers numerically. We determined that the diameter ratio, \(\beta _{d}\), for the discharge orifice of the back chamber controls driver actuation. Driver performance is optimized by accelerating the barrier element before breaching to minimize the opening time of the driver. Our new two-body driver outperforms various designs and exhibits opening times comparable to those of aluminum burst diaphragms. Experimental results verify the effectiveness of the new driver and show that it closely follows the pressure-Mach curve for the ideal case. Planar laser-induced fluorescence images and pressure traces confirm the consistent formation of shock waves about 41 diameters from the driver.

Keyhole collapse during high intensity beam drilling

In this study, we identify the conditions for the keyhole collapse during high power density laser and electron beam drilling processes from fundamental principles of thermal physics. Drilling with a high intensity energy beam becomes incapable and inefficient if the keyhole induced is collapsed. Drilling encounters in many diverse industrial application areas including biomedical devices, printers, flat-panel displays, semiconductors devices and telecommunications systems, and keyhole welding. The approach adapted is to probe the quasi-steady, one-dimensional compressible flow behavior of the two-phase vapor–liquid dispersion in a vertical keyhole of varying cross-section, paying particular attention to the transition between the annular and slug flows. Keyhole collapse is interpreted from balance of normal pressures between mixture gas, recoil, liquid and capillary pressures governed by the Young–Laplace equation. It shows that drilling is susceptible to collapse for higher Mach number and radius at the base, friction factor , and ratio of specific heats at constant pressure-to-constant volume, and lower the surface tension parameter, and liquid pressure at the base for a supersonic flow in the keyhole. A subsonic flow usually gives rise to collapse. Controlling the factors to enhance efficiency and quality of drilling therefore becomes achievable.

Riemann shock tube: 1D normal shocks in air, simulations and experiments

This paper presents numerical simulation of the evolution of one-dimensional normal shocks, their propagation, reflection and interaction in air using a single diaphragm Riemann shock tube and validate them using experimental results. Mathematical model is derived for one-dimensional compressible flow of viscous and conducting medium. Dimensionless form of the mathematical model is used to construct space–time finite element processes based on minimization of the space–time residual functional. The space–time local approximation functions for space–time p-version hierarchical finite elements are considered in higher order spaces that permit desired order of global differentiability of local approximations in space and time. The resulting algebraic systems from this approach yield unconditionally positive-definite coefficient matrices, hence ensure unique numerical solution. The evolution is computed for a space–time strip corresponding to a time increment Δt and then time march to obtain the evolution up to any desired value of time. Numerical studies are designed using recently invented hand-driven shock tube (Reddy tube) parameters, high/low side density and pressure values, high- and low-pressure side shock tube lengths, so that numerically computed results can be compared with actual experimental measurements.

Investigation of a high frequency pulse tube cryocooler driven by a standing wave thermoacoustic engine

In this work, a typical thermoacoustically driven pulse tube cooler as a no-moving part device has been investigated by a numerical method. A standing wave thermoacoustic engine as a prime mover in coupled with an inertance tube pulse tube cryocooler has been modeled. Nonlinear equations of unsteady one-dimensional compressible flow have been solved by the finite volume method. The model presents an important step towards the development of nonlinear simulation tools for the high amplitude thermoacoustic systems that are needed for practical use. The results of the computations show that the self-excited oscillations are well accompanied by the increasing of the pressure amplitude. The necessity of implementation of a nonlinear model to investigate such devices has been proven. The effect of APAT length as an amplifier coupler on the performance of the cooler has been investigated. Furthermore, by using Lagrangian approach, thermodynamic cycle of gas parcels has been attained.

Transient Flow in Natural Gas Pipelines Using Implicit Finite Difference Schemes

Transmission of natural gas through high pressure pipelines has been modeled by numerically solving the governing equations for one-dimensional compressible flow using implicit finite difference methods. In the first case the backward Euler method is considered using both standard first-order upwind and second-order centered differences for the spatial derivatives. The first-order upwind approximation, which is a one-sided approximation, is found to be unstable for CFL numbers less than 1, while the centered difference approximation is stable for any CFL number. In the second case a cell centered method is considered where flow values are calculated at the midpoint between grid points. This method is also stable for any CFL number. However, for a discontinuous change in inlet temperature, the method is observed to introduce unphysical oscillations in the temperature profile along the pipeline. A solution strategy where the hydraulic and thermal models are solved separately using different discretization techniques is suggested. Such a solution strategy does not introduce unphysical oscillations for discontinuous changes in inlet boundary conditions and is found to be stable for any CFL number. The one-dimensional flow model is validated using operational data from a high pressure natural gas pipeline.

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.

Investigation of hydrate formation in natural gas flow through underground transmission pipeline

A natural gas underground transmission pipeline has been simulated by solving governing equations for one-dimensional non-isothermal compressible viscous flow in steady state condition. Temperature and pressure profiles have been calculated and temperature propagation distance has been calculated for various conditions. The natural gas is considered as a real gas and effect of composition has been studied. The possibility of gas hydrate formation as an important parameter in the natural gas pipeline has been investigated. Numerical calculations have been compared with previous studies. Results show that there is less than 3% difference between current and previous studies. Results also show that natural gas composition has no effect on temperature and pressure profiles but has a big effect on natural gas hydrate temperature and temperature propagation distance. For natural gas with low molar mass, the hydrate temperature is very low and consequently, the temperature profile along the pipeline is higher than the hydrate temperature. For natural gas with a higher molar mass and consequently low hydrate formation temperature, the natural gas temperature along pipeline may fall below the hydrate temperature.

The Effects of Side Branches on Compression Waves Propagating in High-Speed Railway Tunnels

According to the theory of finite amplitude sound waves, a one-dimensional compressible unsteady non-homentropic flow model, and the method of characteristics based on the average parameter method are applied to calculate the propagation of entry compression waves in a tunnel, in which the strength of the entry compression wave mainly affects the magnitude of the micro-pressure wave. In addition, acoustical principles are used to simulate the effect of side branches in the tunnel on the sound wave to elucidate the distortion of the waveform of the compression wave. A real-world comparison shows that the programs presented correctly reveal the distortion of the compression wave in the tunnel. After validation, the effects of the number, location, and depth of the side branches are studied in detail. The results show that any change in the parameters of a single side branch has almost no effect on the distortion of the waveform of the compression wave. An increase in the number of side branches, however, does make their effect more significant. This is due to an increase in streaming and reflections which substantially reduce the pressure gradient of the compression wave arriving at the exit portal of the tunnel.

Modeling wave action effects in internal combustion engine air path systems: comparison of numerical and system dynamics approaches

The challenge of continuously improving engine fuel economy and emissions has pushed the automotive industry to adopt more efficient procedures for modeling, system simulation and model-based control. Such procedures require accurate and computationally efficient engine system simulation models that are able to predict the cylinder charge composition and the thermodynamic conditions. To this extent, reduced-order models for unsteady compressible flow systems, namely models derived from the fundamental conservation laws without over-simplifying the topology of the engine air path, are receiving considerable interest for performance simulation and control design. This paper presents a comparative study on modeling approaches for the prediction of one-dimensional unsteady compressible flow in the internal combustion engine air path system. Specifically, the paper compares a well-known second-order, shock-capturing finite-difference scheme with two novel solution methods, namely a finite-volume method and a model-order reduction method. The study aims at evaluating the ability of each method to trade-off the prediction accuracy and robustness with the computation time, in light of potential applications to real-time simulation. This is achieved by increasing the discretization length of each method, and evaluating the accuracy of the predicted response in the time and frequency domain. The characterization of the intake and exhaust flows in the manifolds of a single-cylinder engine is considered as a case study. The results are compared for the three solution methods at different discretization lengths to evaluate the ability of each model to retain accuracy and robustness. The computation times of the different methods are also evaluated. The results presented in this paper establish a clear trade-off between accuracy, stability and computation time for each solution method. This allows one to formulate considerations on the advantages and disadvantages of each method in light of potential applications to engine performance prediction, optimization and control design.

On the propagation of one-dimensional acoustic waves in liquids

Within the framework of one-dimensional unsteady compressible flow in deformable pipes, the present work proposes expressions able to represent the stress state of a “fluid-pipe” continuous system. The coefficients needed to define the friction forces are calibrated against experimental results. The proposed expressions highlight the crucial role played by the fluid compressibility on the wave resistance.

Existence and uniqueness of generalized stationary waves for viscous gas flow through a nozzle with discontinuous cross section

In this paper we study the existence and uniqueness of the generalized stationary waves for one-dimensional viscous isentropic compressible flows through a nozzle with discontinuous cross section. Following the geometric singular perturbation technique, we establish the existence and uniqueness of inviscid and viscous stationary waves for the regularized systems with mollified cross section. Then, the generalized inviscid stationary waves are classified for discontinuous and expanding or contracting nozzles by the limiting argument. Moreover, we obtain the generalized viscous stationary waves by using Hellyʼs selection principle. However, due to the choices of mollified cross section functions, there may exist multiple transonic standing shocks in the generalized stationary waves. A new entropy condition is imposed to select a unique admissible standing shock in generalized stationary wave. We show that, such admissible solution selected by the entropy condition, admits minimal total variation and has minimal enthalpy loss across the standing shock in the limiting process.

Simulation of Gas Pipelines Leakage Using Modified Characteristics Method

The process of pressure reduction and gas leakage rate (discharge characteristics) of a hole has so far been accomplished by utilizing some zero-dimensional models. In these models, the effects of complex boundaries are ignored. The major aim of this study is simulating the process of pipeline gas leakage by the aid of a modified one-dimensional characteristics model. This model, beside the possibility of modeling the impact of leakage on one-dimensional compressible flow, benefits from introducing a variety of boundary conditions to flow zone. In this approach, hole is considered as an orifice, which makes a path for gas to release in a lower pressure ambient. Also, in this study, the effects of four kinds of boundary conditions at the ends of the pipeline on gas discharge characteristics are investigated.

WENO Scheme with Subcell Resolution for Computing Nonconservative Euler Equations with Applications to One-Dimensional Compressible Two-Medium Flows

High order path-conservative schemes have been developed for solving nonconservative hyperbolic systems in (Pares, SIAM J. Numer. Anal. 44:300---321, 2006; Castro et al., Math. Comput. 75:1103---11...

Experimental–theoretical methodology for determination of inertial pressure drop distribution and pore structure properties in wall-flow diesel particulate filters (DPFs)

Wall-flow particulate filters have been placed as a standard technology for Diesel engines because of the increasing restrictions to soot emissions. The inclusion of this system within the exhaust line requires the development of computational tools to properly simulate its flow dynamics and acoustics behaviour. These aspects become the key to understand the influence on engine performance and driveability as a function of the filter placement. Since the pressure drop and the filtration process are strongly depending on the pore structure properties – permeability, porosity and pore size – a reliable definition of these characteristics is essential for model development. In this work a methodology is proposed to determine such properties based on the combination of the pressure drop rement in a steady flow test rig and two theoretical approaches. The later are a lumped model and a one-dimensional (1D) unsteady compressible flow model. The purpose is to simplify the integration of particulate filters into the global engine modelling and development processes avoiding the need to resort to specific and expensive characterisation tests. The proposed methodology was validated against measurements of the response of an uncoated diesel particulate filter (DPF) under different flow conditions as cold steady flow, impulsive flow and hot pulsating flow.