A robust and accurate numerical method for transcritical turbulent flows at supercritical pressure with an arbitrary equation of state

Kawai, Soshi; Terashima, Hiroshi; Negishi, Hideyo

doi:10.1016/j.jcp.2015.07.047

Cited by 50 publications

(33 citation statements)

References 47 publications

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“…Recently, researchers have studied how non-ideal gas effects influence turbulence and heat transfer. For example, Kawai et al (2015); Kawai (2016) studied turbulent boundary layers with supercritical pressures and transcritical temperatures. They found that the mean velocity profiles (with density weighted Van Driest transformation) coincide with the same log-law as seen in an ideal gas.…”

Section: Introductionmentioning

confidence: 99%

Linear instability of Poiseuille flows with highly non-ideal fluids

Ren

Pečnik

2018

J. Fluid Mech.

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The objective of this work is to investigate linear modal and algebraic instability in Poiseuille flows with fluids close to their vapour-liquid critical point. Close to this critical point, the ideal gas assumption does not hold and large non-ideal fluid behaviours occur. As a representative non-ideal fluid, we consider supercritical carbon dioxide (CO 2 ) at pressure of 80 bar, which is above its critical pressure of 73.9 bar. The Poiseuille flow is characterized by the Reynolds number (Re = ρ * w u * r h * /µ * w ), the product of Prandtl (Pr = µ * w C * pw /κ * w ) and Eckert number (Ec = u * 2 r /C * pw T * w ), and the wall temperature that in addition to pressure determines the thermodynamic reference condition. For low Eckert numbers, the flow is essentially isothermal and no difference with the well-known stability behaviour of incompressible flows is observed. However, if the Eckert number increases, the viscous heating causes gradients of thermodynamic and transport properties, and non-ideal gas effects become significant. Three regimes of the laminar base flow can be considered, subcritical (temperature in the channel is entirely below its pseudo-critical value), transcritical, and supercritical temperature regime. If compared to the linear stability of an ideal gas Poiseuille flow, we show that the base flow is more unstable in the subcritical regime, inviscid unstable in the transcritical regime, while significantly more stable in the supercritical regime. Following the corresponding states principle, we expect that qualitatively similar results will be obtained for other fluids at equivalent thermodynamic states.

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Section: Introductionmentioning

confidence: 99%

Linear instability of Poiseuille flows with highly non-ideal fluids

Ren

Pečnik

2018

J. Fluid Mech.

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“…A review of the turbulent flows of supercritical fluids was conducted by [7] in order to study various effects like buoyancy, flow acceleration and heat transfer deterioration in supercritical fluid flows. A numerical method has however been provided by [8] for conducting high fidelity simulations for supercritical fluids involving trans-critical transition. [9] has investigated developing turbulent flows of supercritical CO 2 in a pipe geometry involving forced and mixed convection.…”

Section: Introductionmentioning

confidence: 99%

Fully Compressible Low-Mach Number Simulations of Carbon-dioxide at Supercritical Pressures and Trans-critical Temperatures

Sengupta

Nemati

Boersma

et al. 2017

Flow Turbulence Combust

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This work investigates fully developed turbulent flows of carbon-dioxide close to its vapour-liquid critical point in a channel with a hot and a cold wall. Two direct numerical simulations are performed at low Mach numbers, with the trans-critical transition near the channel centre and the cold wall, respectively. An additional simulation with constant transport properties is used to selectively investigate the effect of the non-linear equation of state on turbulence. Compared to the case where the pseudo-critical transition occurs in the channel center, the case with the pseudo-critical transition close to the cold wall reveals that compressibility effects can exist in the near-wall region even at low Mach numbers. An analysis of the velocity streaks near the hot and the cold walls also indicates a greater degree of streak coherence near the cold wall. A comparison between the constant and variable viscosity cases at the same Reynolds number, Mach number and having the same isothermal wall boundary conditions reveals that variable viscosity increases turbulence near the cold wall and also causes higher velocity gradients near the hot wall. We also show that the extended van Driest transformation results in a better agreement of the velocity profile with the log-law of the wall compared to the standard van Driest transformation. The semi-locally scaled turbulent velocity fluctuations and the turbulent kinetic energy budgets on the hot and the cold sides of the channel collapse on top of each other, thereby establishing the validity of Morkovin’s hypothesis.

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“…The objective of this work is to pursue and assess discontinuous Galerkin (DG) solutions of the modified Navier‐Stokes (NS) equations in which the energy equation is written in the pressure form. The NS equations of such form (also Euler equations at the inviscid limit) have applications in the context of a variety of complex flow problems, especially those related to variable thermodynamic properties or real‐fluid equations of state (EoS) . The motivation of solving for pressure (a primitive variable) instead of total energy (a conservative variable) is the presence of spurious pressure oscillations from the fully conservative calculations of thermodynamically varying flows.…”

Section: Introductionmentioning

confidence: 99%

“…These studies commonly utilized quasi‐ or nonconservative formulations as a relaxation of energy conservation, which enforces mechanical equilibrium across material interfaces and thermal‐property varying regions. Solving the pressure equation was shown to be an appealing relaxation method that can completely eliminates the solution spuriousness and effectively mitigates the strong nonlinearity associated with the stiff EoS . Although such a nonconservative formulation might not be well behaved in the vicinity of discontinuities, it has unique advantages to conveniently incorporate a number of complex flow physics, such as turbulence, arbitrary EoS, chemical reaction, multiphase, nonlinear acoustics, etc.…”

Section: Introductionmentioning

confidence: 99%

“…Because of the unique advantages offered by the pressure‐based nonconservative flow models, there have been particular interests in developing numerical methods for such a problem formulation, for example, based on finite‐volume (FV) and high‐order finite‐difference (FD) schemes. These conventional schemes, although made reasonable success, introduce significant limitations, such as slow convergence and application to geometrically complex configurations.…”

Section: Introductionmentioning

confidence: 99%

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Development of a nonconservative discontinuous Galerkin formulation for simulations of unsteady and turbulent flows

2019

Numerical Methods in Fluids

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Summary In this paper, discontinuous Galerkin (DG) discretization schemes for Navier‐Stokes equations of a nonconservative form was proposed, in which the constitutional equation for energy conservation is written in terms of pressure. The primary focus is to address the treatment of nonconservative products in the pressure equation, for which we formulate four different scheme variants by using the path‐conservative scheme or solely regarding the nonconservative products as source terms. In addition to the complete description of the discretization formulations, we highlight the positivity‐preserving properties of the proposed nonconservative DG schemes. The performance of the four schemes are thoroughly assessed and tested with the consideration of a series of classical flow configurations that involve steady/unsteady, inviscid/viscous, and laminar/turbulence flow physics. It is found that two out of the four schemes are able to provide the optimal convergence and similar accuracies as the fully conservative formulation. The nonconservative formulations provide an alternative way to model fluid flows with substantial thermodynamic and compositional complexities. The present work aims to lay the theoretical foundation for further algorithmic extensions to simulations of such fluid flows of practical relevance.

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A robust and accurate numerical method for transcritical turbulent flows at supercritical pressure with an arbitrary equation of state

Cited by 50 publications

References 47 publications

Linear instability of Poiseuille flows with highly non-ideal fluids

Linear instability of Poiseuille flows with highly non-ideal fluids

Fully Compressible Low-Mach Number Simulations of Carbon-dioxide at Supercritical Pressures and Trans-critical Temperatures

Development of a nonconservative discontinuous Galerkin formulation for simulations of unsteady and turbulent flows

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