Zeitschriftenartikel: „Incompressible and compressible flow“

1

Crnojevic´, C., and V. D. Djordjevic´. "Correlated Compressible and Incompressible Channel Flows." Journal of Fluids Engineering 119, no. 4 (1997): 911–15. http://dx.doi.org/10.1115/1.2819516.

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Compressible flow in channels of slowly varying cross section at moderately high Reynolds numbers is treated in the paper by employing some Stewartson-type transformations that convert the problem into an incompressible one. Both adiabatic flow and isothermal flow are considered, and a Poiseuille-type incompressible solution is mapped onto compressible plane in order to generate some exact solutions of the compressible governing equations. The results show striking effects that viscosity may have upon the flow characteristics in this case, in comparison with more conventional high Reynolds number flows.

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Choi, Young-Pil. "Compressible Euler equations interacting with incompressible flow." Kinetic and Related Models 8, no. 2 (2015): 335–58. http://dx.doi.org/10.3934/krm.2015.8.335.

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3

Pretorius, J. J., A. G. Malan, and J. A. Visser. "A flow network formulation for compressible and incompressible flow." International Journal of Numerical Methods for Heat & Fluid Flow 18, no. 2 (2008): 185–201. http://dx.doi.org/10.1108/09615530810846338.

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4

Kim, Donguk, Minsoo Kim, and Seungsoo Lee. "Extension of Compressible Flow Solver to Incompressible Flow Analysis." Journal of the Korean Society for Aeronautical & Space Sciences 49, no. 6 (2021): 449–56. http://dx.doi.org/10.5139/jksas.2021.49.6.449.

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5

VON ELLENRIEDER, KARL D., and BRIAN J. CANTWELL. "Self-similar, slightly compressible, free vortices." Journal of Fluid Mechanics 423 (November 3, 2000): 293–315. http://dx.doi.org/10.1017/s0022112000001853.

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Exact and numerical similarity solutions for compressible perturbations to an incompressible, two-dimensional, axisymmetric vortex reference flow are presented. The reference flow consists of a set of two-dimensional, self-similar, incompressible vortices. Similarity variables, which give explicit expressions for the decay rates of the velocities and thermodynamic variables in the vortex flows, are used to reduce the governing partial differential equations to a set of ordinary differential equations. The ODEs are solved analytically and numerically for a Taylor vortex reference flow, and numerically for an Oseen vortex reference flow. The solutions are employed to study the dependences of the temperature, density, entropy, dissipation and radial velocity on the Prandtl number. Additionally, several integral relations, which allow one to trace the energy transfer in a slightly compressible vortex, are derived.

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6

Aboelkassem, Yasser, and Georgios H. Vatistas. "New Model for Compressible Vortices." Journal of Fluids Engineering 129, no. 8 (2007): 1073–79. http://dx.doi.org/10.1115/1.2746897.

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A new analytical solution for self-similar compressible vortices is derived in this paper. Based on the previous incompressible formulation of intense vortices, we derived a theoretical model that includes density and temperature variations. The governing equations are simplified assuming strong vortex conditions. Part of the hydrodynamic problem (mass and momentum) is shown to be analogous to the incompressible kind and as such the velocity is obtained through a straightforward variable transformation. Since all the velocity components are bounded in the radial direction, the density and pressure are then determined by standard numerical integration without the usual stringent simplification for the radial velocity. While compressibility is shown not to affect the tangential velocity, it influences only the meridional flow (radial and axial velocities). The temperature, pressure, and density are found to decrease along the converging flow direction. The traditional homentropic flow hypothesis, often employed in vortex stability and optical studies, is shown to undervalue the density and greatly overestimate the temperature. Comparable to vorticity diffusion balance for the incompressible case, the incoming flow carries the required energy to offset the contributions of conduction, viscous dissipation, and material expansion, thus keeping the temperature steady. This model is general and can be used to obtain a compressible version for all classical previous incompressible analysis from the literature such as Rankine, Burgers, Taylor, and Sullivan vortices.

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TIMMERMANS, MARY-LOUISE E., JOHN R. LISTER, and HERBERT E. HUPPERT. "Compressible particle-driven gravity currents." Journal of Fluid Mechanics 445 (October 16, 2001): 305–25. http://dx.doi.org/10.1017/s0022112001005705.

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Large-scale particle-driven gravity currents occur in the atmosphere, often in the form of pyroclastic flows that result from explosive volcanic eruptions. The behaviour of these gravity currents is analysed here and it is shown that compressibility can be important in flow of such particle-laden gases because the presence of particles greatly reduces the density scale height, so that variations in density due to compressibility are significant over the thickness of the flow. A shallow-water model of the flow is developed, which incorporates the contribution of particles to the density and thermodynamics of the flow. Analytical similarity solutions and numerical solutions of the model equations are derived. The gas–particle mixture decompresses upon gravitational collapse and such flows have faster propagation speeds than incompressible currents of the same dimensions. Once a compressible current has spread sufficiently that its thickness is less than the density scale height it can be treated as incompressible. A simple ‘box-model’ approximation is developed to determine the effects of particle settling. The major effect is that a small amount of particle settling increases the density scale height of the particle-laden mixture and leads to a more rapid decompression of the current.

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Marner, F., M. Scholle, D. Herrmann, and P. H. Gaskell. "Competing Lagrangians for incompressible and compressible viscous flow." Royal Society Open Science 6, no. 1 (2019): 181595. http://dx.doi.org/10.1098/rsos.181595.

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A recently proposed variational principle with a discontinuous Lagrangian for viscous flow is reinterpreted against the background of stochastic variational descriptions of dissipative systems, underpinning its physical basis from a different viewpoint. It is shown that additional non-classical contributions to the friction force occurring in the momentum balance vanish by time averaging. Accordingly, the discontinuous Lagrangian can alternatively be understood from the standpoint of an analogous deterministic model for irreversible processes of stochastic character. A comparison is made with established stochastic variational descriptions and an alternative deterministic approach based on a first integral of Navier–Stokes equations is undertaken. The applicability of the discontinuous Lagrangian approach for different Reynolds number regimes is discussed considering the Kolmogorov time scale. A generalization for compressible flow is elaborated and its use demonstrated for damped sound waves.

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9

Song, Charles C. S., and Mingshun Yuan. "A Weakly Compressible Flow Model and Rapid Convergence Methods." Journal of Fluids Engineering 110, no. 4 (1988): 441–45. http://dx.doi.org/10.1115/1.3243575.

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A weakly compressible flow model for small Mach number flows is applied to the computation of steady and unsteady inviscid flows. The equations of continuity and motion are decoupled from the energy equation, but, unlike the equations for incompressible fluids, these equations retain the ability to represent rapidly changing flows such as hydraulic transients and hydroacoustics. Two methods to speed up the process of convergence when an explicit method is used to calculate steady incompressible flows are proposed. The first method which is quite similar to the artificial compressiblity method is to assume an arbitrarily small sound speed (equivalent to large Mach number) to speed up the convergence. Any positive finite number may be used for M. One disadvantage of this method is the contamination of the steady flow solution by acoustic noise that may reverberate in the flow field for some time after the steady flow has been essentially established. The second method is based on the concept of valve stroking or boundary control. Certain boundary stroking functions that will unify the hydroacoustic and hydrodynamic processes can be found by using the inverse method of classical hydraulic transients. This method yields uncontaminated steady flow solution very rapidly independent of the Mach number.

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Kwon, O. Key, R. H. Pletcher, and R. A. Delaney. "Solution Procedure for Unsteady Two-Dimensional Boundary Layers." Journal of Fluids Engineering 110, no. 1 (1988): 69–75. http://dx.doi.org/10.1115/1.3243513.

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An accurate and reliable solution procedure is presented for solving the two-dimensional, compressible, unsteady boundary layer equations. The procedure solves the governing equations in a coupled manner using a fully implicit finite-difference numerical algorithm. Several unsteady compressible and incompressible laminar flows are considered. Example results for two unsteady incompressible turbulent flows are also included. An algebraic mixing length closure model is used for the turbulent flow calculations. The computed results compare favorably with experimental data and available analytical/numerical solutions.

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11

Lee, Cheong, Kim, and Kim. "Numerical Analysis and Characterization of Surface Pressure Fluctuations of High-Speed Trains Using Wavenumber–Frequency Analysis." Applied Sciences 9, no. 22 (2019): 4924. http://dx.doi.org/10.3390/app9224924.

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The high-speed train interior noise induced by the exterior flow field is one of the critical issues for product developers to consider during design. The reliable numerical prediction of noise in a passenger cabin due to exterior flow requires the decomposition of surface pressure fluctuations into the hydrodynamic (incompressible) and the acoustic (compressible) components, as well as the accurate computation of the near aeroacoustic field, since the transmission characteristics of incompressible and compressible pressure waves through the wall panel of the cabin are quite different from each other. In this paper, a systematic numerical methodology is presented to obtain separate incompressible and compressible surface pressure fields in the wavenumber–frequency and space–time domains. First, large eddy simulation techniques were employed to predict the exterior flow field, including a highly-resolved acoustic near-field, around a high-speed train running at the speed of 300 km/h in an open field. Pressure fluctuations on the train surface were then decomposed into incompressible and compressible fluctuations using the wavenumber–frequency analysis. Finally, the separated incompressible and compressible surface pressure fields were obtained from the inverse Fourier transform of the wavenumber–frequency spectrum. The current method was illustratively applied to the high-speed train HEMU-430X running at a speed of 300 km/h in an open field. The results showed that the separate incompressible and compressible surface pressure fields in the time–space domain could be obtained together with the associated aerodynamic source mechanism. The power levels due to each pressure field were also estimated, and these can be directly used for interior noise prediction.

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12

Danabasoglu, G., A. Saati, and S. Biringen. "Three-dimensional simulations of incompressible and compressible flow stability." Computer Physics Communications 65, no. 1-3 (1991): 76–83. http://dx.doi.org/10.1016/0010-4655(91)90157-g.

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13

Wang, Dehua, and Cheng Yu. "Incompressible Limit for the Compressible Flow of Liquid Crystals." Journal of Mathematical Fluid Mechanics 16, no. 4 (2014): 771–86. http://dx.doi.org/10.1007/s00021-014-0185-2.

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14

Ding, Shijin, Jinrui Huang, Huanyao Wen, and Ruizhao Zi. "Incompressible limit of the compressible nematic liquid crystal flow." Journal of Functional Analysis 264, no. 7 (2013): 1711–56. http://dx.doi.org/10.1016/j.jfa.2013.01.011.

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15

Moreira, E. A., M. D. M. Innocentini, and J. R. Coury. "Permeability of ceramic foams to compressible and incompressible flow." Journal of the European Ceramic Society 24, no. 10-11 (2004): 3209–18. http://dx.doi.org/10.1016/j.jeurceramsoc.2003.11.014.

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16

Zienkiewicz, O. C., J. Szmelter, and J. Peraire. "Compressible and incompressible flow; An algorithm for all seasons." Computer Methods in Applied Mechanics and Engineering 78, no. 1 (1990): 105–21. http://dx.doi.org/10.1016/0045-7825(90)90155-f.

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17

BENDAHMANE, MOSTAFA, ZIAD KHALIL, and MAZEN SAAD. "CONVERGENCE OF A FINITE VOLUME SCHEME FOR GAS–WATER FLOW IN A MULTI-DIMENSIONAL POROUS MEDIUM." Mathematical Models and Methods in Applied Sciences 24, no. 01 (2013): 145–85. http://dx.doi.org/10.1142/s0218202513500498.

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This paper deals with construction and convergence analysis of a finite volume scheme for compressible/incompressible (gas–water) flows in porous media. The convergence properties of finite volume schemes or finite element scheme are only known for incompressible fluids. We present a new result of convergence in a two or three dimensional porous medium and under the only consideration that the density of gas depends on global pressure. In comparison with incompressible fluid, compressible fluids requires more powerful techniques; especially the discrete energy estimates are not standard.

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18

Oggian, T., D. Drikakis, D. L. Youngs, and R. J. R. Williams. "Computing multi-mode shock-induced compressible turbulent mixing at late times." Journal of Fluid Mechanics 779 (August 19, 2015): 411–31. http://dx.doi.org/10.1017/jfm.2015.392.

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Both experiments and numerical simulations pertinent to the study of self-similarity in shock-induced turbulent mixing often do not cover sufficiently long times for the mixing layer to become developed in a fully turbulent manner. When the Mach number of the flow is sufficiently low, numerical simulations based on the compressible flow equations tend to become less accurate due to inherent numerical cancellation errors. This paper concerns a numerical study of the late-time behaviour of a single-shocked Richtmyer–Meshkov instability (RMI) and the associated compressible turbulent mixing using a new technique that addresses the above limitation. The present approach exploits the fact that the RMI is a compressible flow during the early stages of the simulation and incompressible at late times. Therefore, depending on the compressibility of the flow field, the most suitable model, compressible or incompressible, can be employed. This motivates the development of a hybrid compressible–incompressible solver that removes the low-Mach-number limitations of the compressible solvers, thus allowing numerical simulations of late-time mixing. Simulations have been performed for a multi-mode perturbation at the interface between two fluids of densities corresponding to an Atwood number of 0.5, and results are presented for the development of the instability, mixing parameters and turbulent kinetic energy spectra. The results are discussed in comparison with previous compressible simulations, theory and experiments.

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Gao, Yuan, Liuming Yang, Yang Yu, Guoxiang Hou, and Zhongbao Hou. "Improved simplified and highly stable lattice Boltzmann methods for incompressible flows." International Journal of Modern Physics C 32, no. 06 (2021): 2150077. http://dx.doi.org/10.1142/s0129183121500777.

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In this work, improved simplified and highly stable lattice Boltzmann methods (SHSLBMs) are developed for incompressible flows. The SHSLBM is a newly developed scheme within the lattice Boltzmann method (LBM) framework, which utilizes the fractional step technology to resolve the governing equations recovered from lattice Boltzmann equation (LBE) and reconstructs the equations in the Lattice Boltzmann frame. By this treatment, the SHSLBM directly tracks the macroscopic variables in the evolution process rather than the distribution functions of each grid node, which greatly saves virtual memories and simplifies the implementation of physical boundary conditions. However, the Chapman–Enskog expansion analysis reveals that the SHSLBM recover the weakly compressible Navier–Stokes equations with the low Mach number assumption. Therefore, the original SHSLBM can be regarded as an artificial compressible method and may cause some undesired errors. By modifying the evolution equation for the density distribution function, the improved SHSLBMs can eliminate the compressible effects. The incompressible SHSLBMs are compared with the original SHSLBM in terms of accuracy and stability by simulating several two-dimensional steady and unsteady incompressible flow problems, and the results demonstrate that the present SHSLBMs ensure the second order of accuracy and can reduce the compressible effects efficiently, especially for the incompressible flows with large pressure gradients. We then extended the present SHSLBMs to study the more complicated two-dimensional lid-driven flow and found that the present results are in good agreement with available benchmark results.

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Sahay, Pratap N., and Tobias M. Müller. "Diffusion in deformable porous media: Incompressible flow limit and implications for permeability estimation from microseismicity." GEOPHYSICS 85, no. 2 (2020): A13—A17. http://dx.doi.org/10.1190/geo2019-0510.1.

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Injecting fluid in a borehole often has been observed to be causally related with seismicity. The standard explanation assumes that a stress perturbation spreads out and triggers rock failure. It has been suggested that this spreading is governed by Biot’s slow P-wave, which is a diffusion process associated with compressible fluid flow. Because the diffusion constant is proportional to the permeability, the space-time evolution of seismicity is exploited to estimate the permeability. However, the more plausible scenario of incompressible fluid flow is beyond the scope of Biot’s theory. We have examined the diffusion process predicted by the de la Cruz-Spanos poroelasticity theory when the flow is incompressible. Then, the diffusion constant can be two orders of magnitude larger than the Biot diffusion constant. We have determined that seismicity-based permeability estimates strongly depend on whether the flow is compressible or incompressible. Ignoring the incompressible flow scenario might lead to an overestimation of the permeability.

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Nasu, Shoichi, and Mutsuto Kawahara. "An Analysis of Compressible Viscous Flows Around a Body Using Finite Element Method." Advanced Materials Research 403-408 (November 2011): 461–65. http://dx.doi.org/10.4028/www.scientific.net/amr.403-408.461.

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The objective of this paper is an analysis of a body in a compressible viscous flow using the finite element method. Generally, when the fluid flow is analyzed, an incompressible viscous flow is often applied. However fluids have compressibility in actual phenomena. Therefore, the compressibility should be concerned in Computational Fluid Dynamics [CFD]. In this study, two kind of equation is applied to basic equations. One is compressible Navier-stokes equation, the other is incompressible Navier-stokes equation considering density variation. These analysis results of both equations are compared.

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Brower, W. B., E. Eisler, E. J. Filkorn, J. Gonenc, C. Plati, and J. Stagnitti. "On the Compressible Flow Through an Orifice." Journal of Fluids Engineering 115, no. 4 (1993): 660–64. http://dx.doi.org/10.1115/1.2910195.

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A new theory for the compressible flow through an orifice is presented which provides a significant advance over the approach currently employed. As the flow approaches the critical regime (local sonic condition), measurements diverge from the theoretical result due to the non-one-dimensionality of the flow. Nevertheless, a straightforward correlation is available, and the measurements for different pipe/orifice geometries all appear to lie in the vicinity of a single, universal curve. As the flow approaches the incompressible condition the correlation factor (the discharge coefficient) becomes unity.

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23

Zhang, Ting, Baochang Shi, Zhenhua Chai, and Fumei Rong. "Lattice BGK Model for Incompressible Axisymmetric Flows." Communications in Computational Physics 11, no. 5 (2012): 1569–90. http://dx.doi.org/10.4208/cicp.290810.050811a.

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AbstractIn this paper, a lattice Boltzmann BGK (LBGK) model is proposed for simulating incompressible axisymmetric flows. Unlike other existing axisymmetric lattice Boltzmann models, the present LBGK model can eliminate the compressible effects only with the small Mach number limit. Furthermore the source terms of the model are simple and contain no velocity gradients. Through the Chapman-Enskog expansion, the macroscopic equations for incompressible axisymmetric flows can be exactly recovered from the present LBGK model. Numerical simulations of the Hagen-Poiseuille flow, the pulsatile Womersley flow, the flow over a sphere, and the swirling flow in a closed cylindrical cavity are performed. The results agree well with the analytic solutions and the existing numerical or experimental data reported in some previous studies.

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Yu, Qin, Chai, Huang, and Liu. "The Effect of Compressible Flow on Heat Transfer Performance of Heat Exchanger by Computational Fluid Dynamics (CFD) Simulation." Entropy 21, no. 9 (2019): 829. http://dx.doi.org/10.3390/e21090829.

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As a part of vehicle thermal management, water-cooled intercoolers play an important role in engine efficiency. The incompressible simulation model was usually applied to estimate the performance of water-cooled intercoolers. In this paper, the computational fluid dynamics (CFD) compressible model is taken to analyze more accurate prediction models. The rate of section change, heat exchange, and the surface friction coefficient are used as the comparison basis of the compressible flow model and incompressible model on the pressurized air side of the water-cooled intercooler. By comparing the simulation results of the air side, it was found that the compressible simulation is closer to the experimental value than the incompressible simulation. Compared with the experiment, the compressible model heat transfer maximum value of deviation is 6.5%, and the pressure loss maximum deviation is 7.5%. This provides guidance to optimize the design of heat exchangers, in order to save on costs and shorten development times.

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25

Tabrizi, Amir Bashirzadeh, and Binxin Wu. "The role of compressibility in computing noise generated at a cavitating orifice." International Journal of Aeroacoustics 18, no. 1 (2018): 73–91. http://dx.doi.org/10.1177/1475472x18812801.

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The computational fluid dynamics calculation can be accomplished by solving either compressible or incompressible Navier–Stokes equations to determine the flow-field variables of the noise source. The proper assumption depends on both the physical situation and the Mach number. Although in cavitating devices usually we are dealing with low Mach number flow, cavitation is an acoustic phenomenon that can be affected by compressibility. Cavitation behaves acoustically as a monopole and it is mentioned by some researchers that incompressible solution is sufficient to study the dipole sources. However, in order to study the monopole (and quadrupole) sources a compressible solution may be required. In this study, the role of compressibility in computing noise generated at a cavitating single-hole orifice was investigated using large eddy simulation and Ffowcs Williams–Hawkings formulation. The fluid zone downstream of the orifice where the cavitation occurs was evaluated as the acoustic source which generates sound. Time-accurate solutions of the flow-field variables on source surfaces were obtained from both compressible and incompressible flow simulations. Three cases of cavitation were studied and the sound pressure signals far downstream of the orifice were computed by the Ffowcs Williams–Hawkings formulation. For a developed cavitation regime at low frequencies, there is a big discrepancy between the computed values of sound pressure level from compressible and incompressible simulations, and at higher frequencies greater than 6 kHz, both simulation methods provide almost the same values for sound pressure levels. For a super cavitation regime, both compressible and incompressible simulations provide similar values for sound pressure levels at frequencies greater than 2 kHz. The results of this work demonstrate that the compressibility has a significant role in terms of computing noise generated at a cavitating orifice and cannot be ignored, especially when the noise generated by developed cavitation regimes at low frequencies is investigated.

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Park, Sunho, Woochan Seok, Sung Taek Park, et al. "Compressibility Effects on Cavity Dynamics behind a Two-Dimensional Wedge." Journal of Marine Science and Engineering 8, no. 1 (2020): 39. http://dx.doi.org/10.3390/jmse8010039.

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To understand cavity dynamics, many experimental and computational studies have been conducted for many decades. As computational methods, incompressible, isothermal compressible, and fully compressible flow solvers were used for the purpose. In the present study, to understand the compressibility effect on cavity dynamics, both incompressible and fully compressible flow solvers were developed, respectively. Experiments were also carried out in a cavitation tunnel to compare with the computational results. The cavity shedding dynamics, re-entrant jet, transition from bounded shear layer vortices to Karman vortices, and pressure and velocity contours behind the two-dimensional wedge by the two developed solvers were compared at various cavitation numbers.

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Hsu, Uzu Kuei, Chang Hsien Tai, and Chien Hsiung Tsai. "All Speed and High-Resolution Scheme Applied to Three-Dimensional Multi-Block Complex Flowfield System." Journal of Mechanics 20, no. 1 (2004): 13–25. http://dx.doi.org/10.1017/s1727719100004007.

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ABSTRACTThe improved numerical approach is implemented with preconditioned Navier-Stokes solver on arbitrary three-dimensional (3-D) structured multi-block complex flowfield. With the successful application of time-derivative preconditioning, present hybrid finite volume solver is performed to obtain the steady state solutions in compressible and incompressible flows. This solver which combined the adjective upwind splitting method (AUSM) family of low-diffusion flux-splitting scheme with an optimally smoothing multistage scheme and the time-derivative preconditioning is used to solve both the compressible and incompressible Euler and Navier-Stokes equations. In addition, a smoothing procedure is used to provide a mechanism for controlling the numerical implementation to avoid the instability at stagnation and sonic region. The effects of preconditioning on accuracy and convergence to the steady state of the numerical solutions are presented. There are two validation cases and three complex cases simulated as shown in this study. The numerical results obtained for inviscid and viscous two-dimensional flows over a NACA0012 airfoil at free stream Mach number ranging from 0.1 to 1.0E-7 indicates that efficient computations of flows with very low Mach numbers are now possible, without losing accuracy. And it is effectively to simulate 3-D complex flow phenomenon from compressible flow to incompressible by using the advanced numerical methods.

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Turgeon, E., and D. Pelletier. "Unified Formulation for Compressible-Incompressible Flow Simulation with Mesh Adaptation." AIAA Journal 39, no. 12 (2001): 2425–27. http://dx.doi.org/10.2514/2.1260.

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Turgeon, E., and D. Pelletier. "Unified formulation for compressible-incompressible flow simulation with mesh adaptation." AIAA Journal 39 (January 2001): 2425–27. http://dx.doi.org/10.2514/3.15049.

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30

Islam, Md Tajul. "Compressibility Effects in 2d Wall Heating Microchannel flow." GANIT: Journal of Bangladesh Mathematical Society 35 (June 28, 2016): 57–71. http://dx.doi.org/10.3329/ganit.v35i0.28567.

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In this article we present a numerical solution of the Navier-Stokes equations and energy equation in parallel plate microchannels with the first order slip boundary conditions on the walls, adopting control volume scheme of CFD technique. Wall heating condition was considered on the walls. Noslip boundary conditions for compressible and incompressible flows were also solved to compare the effect of slip conditions. Compressibility effects were also investigated for compressible slip and compressible noslip flow conditions. A series of simulations were performed for different heights and lengths of channels and pressure ratios. Results are presented in graphs and tables and are compared with the available analytical and experimental results. It was found that the friction constants are the highest for noslip compressible flow and lowest for the slip flow against pressure ratio and mach numbers. Friction constant decreases continuously for compressible slip flow but it approaches to an asymptotic value of 96 for compressible noslip flow for the decrease of aspect ratio.GANIT J. Bangladesh Math. Soc.Vol. 35 (2015) 57-71

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Keogh, J., G. Doig, and S. Diasinos. "Flow compressibility effects around an open-wheel racing car." Aeronautical Journal 118, no. 1210 (2014): 1409–31. http://dx.doi.org/10.1017/s0001924000010125.

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AbstractA numerical investigation has been conducted into the influence of flow compressibility effects around an open-wheeled racing car. A geometry was created to comply with 2012 F1 regulations. Incompressible and compressible CFD simulations were compared – firstly with models which maintained Reynolds number as Mach number increased, and secondly allowing Mach number and Reynolds number to increase together as they would on track. Results demonstrated significant changes to predicted aerodynamic performance even below Mach 0·15. While the full car coefficients differed by a few percent, individual components (particularly the rear wheels and the floor/diffuser area) showed discrepancies of over 10% at higher Mach numbers when compressible and incompressible predictions were compared. Components in close ground proximity were most affected due to the ground effect. The additional computational expense required for the more physically-realistic compressible simulations would therefore be an additional consideration when seeking to obtain maximum accuracy even at low freestream Mach numbers.

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Deolmi, Giulia, Wolfgang Dahmen, and Siegfried Müller. "Effective boundary conditions for compressible flows over rough boundaries." Mathematical Models and Methods in Applied Sciences 25, no. 07 (2015): 1257–97. http://dx.doi.org/10.1142/s0218202515500323.

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Simulations of a flow over a roughness are prohibitively expensive for small-scale structures. If the interest is only on some macroscale quantity it will be sufficient to model the influence of the unresolved microscale effects. Such multiscale models rely on an appropriate upscaling strategy. Here the strategy originally developed by Achdou et al. [Effective boundary conditions for laminar flows over periodic rough boundaries, J. Comput. Phys. 147 (1998) 187–218] for incompressible flows is extended to compressible high Reynolds number flow. For proof of concept a laminar flow over a flat plate with partially embedded roughness is simulated. The results are compared with computations on a rough domain.

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Blaisdell, G. A., N. N. Mansour, and W. C. Reynolds. "Compressibility effects on the growth and structure of homogeneous turbulent shear flow." Journal of Fluid Mechanics 256 (November 1993): 443–85. http://dx.doi.org/10.1017/s0022112093002848.

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Compressibility effects within decaying isotropic turbulence and homogeneous turbulent shear flow have been studied using direct numerical simulation. The objective of this work is to increase our understanding of compressible turbulence and to aid the development of turbulence models for compressible flows. The numerical simulations of compressible isotropic turbulence show that compressibility effects are highly dependent on the initial conditions. The shear flow simulations, on the other hand, show that measures of compressibility evolve to become independent of their initial values and are parameterized by the root mean square Mach number. The growth rate of the turbulence in compressible homogeneous shear flow is reduced compared to that in the incompressible case. The reduced growth rate is the result of an increase in the dissipation rate and energy transfer to internal energy by the pressure–dilatation correlation. Examination of the structure of compressible homogeneous shear flow reveals the presence of eddy shocklets, which are important for the increased dissipation rate of compressible turbulence.

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Liu, L. Q., Y. P. Shi, J. Y. Zhu, W. D. Su, S. F. Zou, and J. Z. Wu. "Longitudinal–transverse aerodynamic force in viscous compressible complex flow." Journal of Fluid Mechanics 756 (September 1, 2014): 226–51. http://dx.doi.org/10.1017/jfm.2014.403.

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AbstractWe report our systematic development of a general and exact theory for diagnosis of total force and moment exerted on a generic body moving and deforming in a calorically perfect gas. The total force and moment consist of a longitudinal part (L-force) due to compressibility and irreversible thermodynamics, and a transverse part (T-force) due to shearing. The latter exists in incompressible flow but is now modulated by the former. The theory represents a full extension of a unified incompressible diagnosis theory of the same type developed by J. Z. Wu and coworkers to compressible flow, with Mach number ranging from low-subsonic to moderate-supersonic flows. Combined with computational fluid dynamics (CFD) simulation, the theory permits quantitative identification of various complex flow structures and processes responsible for the forces, and thereby enables rational optimal configuration design and flow control. The theory is confirmed by a numerical simulation of circular-cylinder flow in the range of free-stream Mach number $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}M_{\infty }$ between 0.2 and 2.0. The L-drag and T-drag of the cylinder vary with $M_{\infty }$ in different ways, the underlying physical mechanisms of which are analysed. Moreover, each L-force and T-force integrand contains a universal factor of local Mach number $M$. Our preliminary tests suggest that the possibility of finding new similarity rules for each force constituent could be quite promising.

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Bazdidi-Tehrani, F., A. Abouata, M. Hatami, and N. Bohlooli. "Investigation of effects of compressibility, geometric and flow parameters on the simulation of a synthetic jet behaviour." Aeronautical Journal 120, no. 1225 (2016): 521–46. http://dx.doi.org/10.1017/aer.2016.8.

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ABSTRACTThe present paper focuses on a three-dimensional unsteady turbulent synthetic jet to assess the accuracy of a compressible simulation and some important parameters including the simulations of the actuator, cavity height and Reynolds number. The two-equationSST/k− ω turbulence model is used to predict the flow behaviour. Results show that the compressible simulation case is more accurate than the incompressible one and the dynamic mesh exhibits more reliable results than the mass flow inlet boundary in the compressible simulation. The compressible case displays a delay in the phase of instantaneous velocity for all three Reynolds numbers. Also, the maximum of mean velocity is less than the incompressible case. Moreover, an increase in the Reynolds number leads to an amplification of the peak of mean velocity magnitude. Finally, results demonstrate that a reduction in the cavity height regarding the compressible simulation case causes a reduction in the phase delay and rise in peak of instantaneous velocity magnitude.

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Pérez-Ràfols, F., P. Wall, and A. Almqvist. "On compressible and piezo-viscous flow in thin porous media." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 474, no. 2209 (2018): 20170601. http://dx.doi.org/10.1098/rspa.2017.0601.

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In this paper, we study flow through thin porous media as in, e.g. seals or fractures. It is often useful to know the permeability of such systems. In the context of incompressible and iso-viscous fluids, the permeability is the constant of proportionality relating the total flow through the media to the pressure drop. In this work, we show that it is also relevant to define a constant permeability when compressible and/or piezo-viscous fluids are considered. More precisely, we show that the corresponding nonlinear equation describing the flow of any compressible and piezo-viscous fluid can be transformed into a single linear equation. Indeed, this linear equation is the same as the one describing the flow of an incompressible and iso-viscous fluid. By this transformation, the total flow can be expressed as the product of the permeability and a nonlinear function of pressure, which represents a generalized pressure drop.

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Gibis, Tobias, Christoph Wenzel, Markus Kloker, and Ulrich Rist. "Self-similar compressible turbulent boundary layers with pressure gradients. Part 2. Self-similarity analysis of the outer layer." Journal of Fluid Mechanics 880 (October 9, 2019): 284–325. http://dx.doi.org/10.1017/jfm.2019.672.

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A thorough self-similarity analysis is presented to investigate the properties of self-similarity for the outer layer of compressible turbulent boundary layers. The results are validated using the compressible and quasi-incompressible direct numerical simulation (DNS) data shown and discussed in the first part of this study; see Wenzel et al. (J. Fluid Mech., vol. 880, 2019, pp. 239–283). The analysis is carried out for a general set of characteristic scales, and conditions are derived which have to be fulfilled by these sets in case of self-similarity. To evaluate the main findings derived, four sets of characteristic scales are proposed and tested. These represent compressible extensions of the incompressible edge scaling, friction scaling, Zagarola–Smits scaling and a newly defined Rotta–Clauser scaling. Their scaling success is assessed by checking the collapse of flow-field profiles extracted at various streamwise positions, being normalized by the respective scales. For a good set of scales, most conditions derived in the analysis are fulfilled. As suggested by the data investigated, approximate self-similarity can be achieved for the mean-flow distributions of the velocity, mass flux and total enthalpy and the turbulent terms. Self-similarity thus can be stated to be achievable to a very high degree in the compressible regime. Revealed by the analysis and confirmed by the DNS data, this state is predicted by the compressible pressure-gradient boundary-layer growth parameter $\unicode[STIX]{x1D6EC}_{c}$, which is similar to the incompressible one found by related incompressible studies. Using appropriate adaption, $\unicode[STIX]{x1D6EC}_{c}$ values become comparable for compressible and incompressible pressure-gradient cases with similar wall-normal shear-stress distributions. The Rotta–Clauser parameter in its traditional form $\unicode[STIX]{x1D6FD}_{K}=(\unicode[STIX]{x1D6FF}_{K}^{\ast }/\bar{\unicode[STIX]{x1D70F}}_{w})(\text{d}p_{e}/\text{d}x)$ with the kinematic (incompressible) displacement thickness $\unicode[STIX]{x1D6FF}_{K}^{\ast }$ is shown to be a valid parameter of the form $\unicode[STIX]{x1D6EC}_{c}$ and hence still is a good indicator for equilibrium flow in the compressible regime at the finite Reynolds numbers considered. Furthermore, the analysis reveals that the often neglected derivative of the length scale, $\text{d}L_{0}/\text{d}x$, can be incorporated, which was found to have an important influence on the scaling success of common ‘low-Reynolds-number’ DNS data; this holds for both incompressible and compressible flow. Especially for the scaling of the $\bar{\unicode[STIX]{x1D70C}}\widetilde{u^{\prime \prime }v^{\prime \prime }}$ stress and thus also the wall shear stress $\bar{\unicode[STIX]{x1D70F}}_{w}$, the inclusion of $\text{d}L_{0}/\text{d}x$ leads to palpable improvements.

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MANELA, A., and I. FRANKEL. "On the compressible Taylor–Couette problem." Journal of Fluid Mechanics 588 (September 24, 2007): 59–74. http://dx.doi.org/10.1017/s0022112007007422.

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We consider the linear temporal stability of a Couette flow of a Maxwell gas within the gap between a rotating inner cylinder and a concentric stationary outer cylinder both maintained at the same temperature. The neutral curve is obtained for arbitrary Mach (Ma) and arbitrarily small Knudsen (Kn) numbers by use of a ‘slip-flow’ continuum model and is verified via comparison to direct simulation Monte Carlo results. At subsonic rotation speeds we find, for the radial ratios considered here, that the neutral curve nearly coincides with the constant-Reynolds-number curve pertaining to the critical value for the onset of instability in the corresponding incompressible-flow problem. With increasing Mach number, transition is deferred to larger Reynolds numbers. It is remarkable that for a fixed Reynolds number, instability is always eventually suppressed beyond some supersonic rotation speed. To clarify this we examine the variation with increasing (Ma) of the reference Couette flow and analyse the narrow-gap limit of the compressible TC problem. The results of these suggest that, as in the incompressible problem, the onset of instability at supersonic speeds is still essentially determined through the balance of inertial and viscous-dissipative effects. Suppression of instability is brought about by increased rates of dissipation associated with the elevated bulk-fluid temperatures occurring at supersonic speeds. A useful approximation is obtained for the neutral curve throughout the entire range of Mach numbers by an adaptation of the familiar incompressible stability criteria with the critical Reynolds (or Taylor) numbers now based on average fluid properties. The narrow-gap analysis further indicates that the resulting approximate neutral curve obtained in the (Ma, Kn) plane consists of two branches: (i) the subsonic part corresponding to a constant ratio (Ma/Kn) (i.e. a constant critical Reynolds number) and (ii) a supersonic branch which at large Ma values corresponds to a constant product Ma Kn. Finally, our analysis helps to resolve some conflicting views in the literature regarding apparently destabilizing compressibility effects.

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Fannon, J. S., I. R. Moyles, and A. C. Fowler. "Application of the compressible -dependent rheology to chute and shear flow instabilities." Journal of Fluid Mechanics 864 (February 14, 2019): 1026–57. http://dx.doi.org/10.1017/jfm.2019.43.

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We consider the instability properties of dense granular flow in inclined plane and plane shear geometries as tests for the compressible inertial-dependent rheology. The model, which is a recent generalisation of the incompressible $\unicode[STIX]{x1D707}(I)$ rheology, constitutes a hydrodynamical description of dense granular flow which allows for variability in the solids volume fraction. We perform a full linear stability analysis of the model and compare its predictions to existing experimental data for glass beads on an inclined plane and discrete element simulations of plane shear in the absence of gravity. In the case of the former, we demonstrate that the compressible model can quantitatively predict the instability properties observed experimentally, and, in particular, we find that it performs better than its incompressible counterpart. For the latter, the qualitative behaviour of the plane shear instability is also well captured by the compressible model.

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Park, Sunho, and Shin Hyung Rhee. "Comparative study of incompressible and isothermal compressible flow solvers for cavitating flow dynamics." Journal of Mechanical Science and Technology 29, no. 8 (2015): 3287–96. http://dx.doi.org/10.1007/s12206-015-0727-4.

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41

Rashad, Ramy, Federico Califano, Frederic P. Schuller, and Stefano Stramigioli. "Port-Hamiltonian modeling of ideal fluid flow: Part II. Compressible and incompressible flow." Journal of Geometry and Physics 164 (June 2021): 104199. http://dx.doi.org/10.1016/j.geomphys.2021.104199.

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42

Wang, Jianchun, Yipeng Shi, Lian-Ping Wang, Zuoli Xiao, X. T. He, and Shiyi Chen. "Effect of compressibility on the small-scale structures in isotropic turbulence." Journal of Fluid Mechanics 713 (October 17, 2012): 588–631. http://dx.doi.org/10.1017/jfm.2012.474.

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AbstractUsing a simulated highly compressible isotropic turbulence field with turbulent Mach number around 1.0, we studied the effects of local compressibility on the statistical properties and structures of velocity gradients in order to assess salient small-scale features pertaining to highly compressible turbulence against existing theories for incompressible turbulence. A variety of statistics and local flow structures conditioned on the local dilatation – a measure of local flow compressibility – are studied. The overall enstrophy production is found to be enhanced by compression motions and suppressed by expansion motions. It is further revealed that most of the enstrophy production is generated along the directions tangential to the local density isosurface in both compression and expansion regions. The dilatational contribution to enstrophy production is isotropic and dominant in highly compressible regions. The emphasis is then directed to the complicated properties of the enstrophy production by the deviatoric strain rate at various dilatation levels. In the overall flow field, the most probable eigenvalue ratio for the strain rate tensor is found to be −3:1:2.5, quantitatively different from the preferred eigenvalue ratio of −4:1:3 reported in incompressible turbulence. Furthermore, the strain rate eigenvalue ratio tends to be −1:0:0 in high compression regions, implying the dominance of sheet-like structures. The joint probability distribution function of the invariants for the deviatoric velocity gradient tensor is used to characterize local flow structures conditioned on the local dilatation as well as the distribution of enstrophy production within these flow structures. We demonstrate that strong local compression motions enhance the enstrophy production by vortex stretching, while strong local expansion motions suppress enstrophy production by vortex stretching. Despite these complications, most statistical properties associated with the solenoidal component of the velocity field are found to be very similar to those in incompressible turbulence, and are insensitive to the change of local dilatation. Therefore, a good understanding of dynamics of the compressive component of the velocity field is key to an overall accurate description of highly compressible turbulence.

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Amiet, R. K. "On the second-order solution to the Sears problem for compressible flow." Journal of Fluid Mechanics 254 (September 1993): 213–28. http://dx.doi.org/10.1017/s0022112093002095.

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Significant simplifications and minor corrections are made to a previous second-order solution of Graham & Kullar for the lift on a flat-plate airfoil encountering a sinusoidal gust in compressible flow. The related cases of a skewed gust in incompressible flow, a parallel gust in compressible flow and the generalized case of a skewed gust in compressible flow are considered. In addition to the simplifications, the solutions are combined into a composite solution that is more accurate than the solutions from which it is composed, making it useful for numerical calculations.

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Abou-Haidar, N. I., and S. L. Dixon. "Measurement of Compressible Flow Pressure Losses in Wye-Junctions." Journal of Turbomachinery 116, no. 3 (1994): 535–41. http://dx.doi.org/10.1115/1.2929442.

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This paper considers the compressible flow pressure losses in sharp-cornered wye-junctions with symmetric branches under dividing and combining flow conditions. Determination of the additional total pressure losses occurring in flow through several three-leg junctions, using dry air as the working fluid, has been made experimentally. Results covering a wide speed range up to choking are presented for 30, 60, and 90 deg wye-junctions. Separate flow visualization schlieren tests detected the presence of normal shock waves, located at up to one duct diameter downstream of the junction, and therefore confirmed the choking of the flow at the vena contracta. The highest attainable Mach number (M3) of the averaged whole flow was 0.9 for one of the dividing flow geometries and 0.65 for several of the combining flow cases. These values of M3 were the maximum possible and hence represent a limiting condition dictated by choking. In general, the compressible flow loss coefficients, caused by the presence of the wye-junctions, can be expected to be higher for dividing flows and lower for combining flows than would be the case for incompressible flows because of the influence of Mach number, M3.

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Wittbrodt, M. J., and M. J. Pechersky. "A Hydrodynamic Analysis of Fluid Flow Between Meshing Spur Gear Teeth." Journal of Mechanisms, Transmissions, and Automation in Design 111, no. 3 (1989): 395–401. http://dx.doi.org/10.1115/1.3259012.

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A hydrodynamic analysis of the pumping action resulting from the meshing of spur gear teeth was performed. Both compressible (for air) and incompressible (for oil) flow cases were considered. The computed results included the velocity of the fluid at the minimum flow area between the meshing teeth. The pressure and temperature in the mesh region were also computed for the compressible flow case. The velocities were computed as a function of the mesh angle with the pitch line velocity as the normalizing parameter. The calculations required a detailed analysis of the involute geometry to compute the proper mesh region volumes and exit flow areas. For the incompressible calculations with wide face gears, it was found the peak fluid velocity could greatly exceed the pitch line velocity. For the compressible calculations, it was found that sonic conditions could be reached at the minimum flow area leading to the possibility of shock formation downstream of this region. Parametric results for both sets of calculations, including backlash, diametral pitch, and other factors, are presented.

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Xiao, Feng. "Unified formulation for compressible and incompressible flows by using multi-integrated moments I: one-dimensional inviscid compressible flow." Journal of Computational Physics 195, no. 2 (2004): 629–54. http://dx.doi.org/10.1016/j.jcp.2003.10.014.

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Mitsuya, Y., and S. Fukui. "Stokes Roughness Effects on Hydrodynamic Lubrication. Part I—Comparison Between Incompressible and Compressible Lubricating Films." Journal of Tribology 108, no. 2 (1986): 151–58. http://dx.doi.org/10.1115/1.3261153.

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A perturbation method for the Navier-Stokes equations is presented for analyzing Stokes roughness effects on hydrodynamic lubrication in both incompressible and compressible films. The solution is obtained from direct numerical calculation by using an actual rough spacing, without applying the currently accepted assumption that the roughness height should be small. The roughness wavelength and height influences on flow rate, load carrying capacity and frictional force are clarified. Secondary quantities induced by Stokes effects are found to be proportional to wavenumber n squared for sufficiently large n values, so that the amount of the Stokes effect can be determined by the spacing to wavelength squared ratio. A significant difference between incompressible and compressible films is that Stokes roughness increases the flow resistance of and then enhances the load carrying capacity of incompressible films, while it inversely affects compressible films. The compressibility with respect to secondary pressure induced by the Stokes effects can be neglected for any compressibility number, no matter how large, as long as the local compressibility number, defined by the wavelength, is small.

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Rossow, Cord-Christian. "Efficient computation of compressible and incompressible flows." Journal of Computational Physics 220, no. 2 (2007): 879–99. http://dx.doi.org/10.1016/j.jcp.2006.05.034.

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Jiang, Ning, Yi-Long Luo, and Shaojun Tang. "On well-posedness of Ericksen–Leslie’s parabolic–hyperbolic liquid crystal model in compressible flow." Mathematical Models and Methods in Applied Sciences 29, no. 01 (2019): 121–83. http://dx.doi.org/10.1142/s0218202519500052.

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We study the well-posedness of the Ericksen–Leslie’s parabolic–hyperbolic liquid crystal model in compressible flow. Inspired by our study for incompressible case [N. Jiang and Y.-L. Luo, On well-posedness of Ericsen–Leslie’s hyperbolic incompressible liquid crystal model, preprint (2017), arXiv:1709.06370v1 ] and some techniques from compressible Navier–Stokes equations, we first prove the local-in-time existence of the classical solution to the system with finite initial energy, under some natural constraints on the Leslie coefficients which ensure that the basic energy law is dissipative. Furthermore, with an additional assumption on the coefficients which provides a damping effect, and the smallness of the initial energy, the existence of global solution can be established.

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Marjanovic´, Predrag, and Vladan Djordjevic´. "On the Compressible Flow Losses Through Abrupt Enlargements and Contractions." Journal of Fluids Engineering 116, no. 4 (1994): 756–62. http://dx.doi.org/10.1115/1.2911846.

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The well-known structure of incompressible flow through abrupt enlargements and contractions is applied to the subsonic compressible flow through the same area change. Using the basic system of equations for 1-D model of flow, both cases are solved for adiabatic and isothermal conditions. The changes for all flow parameters (M, v, p, p0, T, T0, s) are obtained analytically and shown graphically. The results are compared with the available experimental data.

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