On the suppression of shock-induced separation 
in Bethe–Zel'dovich–Thompson fluids

Cramer, M. S.; Park, S.

doi:10.1017/s0022112099005479

Cited by 24 publications

(12 citation statements)

References 32 publications

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“…The fluid viscosity and thermal conductivity are evaluated by means of the generalized laws derived by Chung et al (1988), which contain a correction term that takes into account the strong density dependence of the transport properties in the dense-gas region. These laws, extensively used in previous works (Cramer & Tarkenton 1992;Cramer & Park 1999), are described in appendix A. In the modelling, the bulk viscosity µ b = λ + 2µ/3 is set to zero, assuming a Stokesian fluid.…”

Section: Governing Equationsmentioning

confidence: 99%

Direct numerical simulations of supersonic turbulent channel flows of dense gases

2017

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The influence of dense-gas effects on compressible wall-bounded turbulence is investigated by means of direct numerical simulations of supersonic turbulent channel flows. Results are obtained for PP11, a heavy fluorocarbon representative of dense gases, the thermophysics properties of which are described by using a fifth-order virial equation of state and advanced models for the transport properties. In the dense-gas regime, the speed of sound varies non-monotonically in small perturbations and the dependency of the transport properties on the fluid density (in addition to the temperature) is no longer negligible. A parametric study is carried out by varying the bulk Mach and Reynolds numbers, and results are compared to those obtained for a perfect gas, namely air. Dense-gas flow exhibits almost negligible friction heating effects, since the high specific heat of the fluids leads to a loose coupling between thermal and kinetic fields, even at high Mach numbers. Despite negligible temperature variations across the channel, the mean viscosity tends to decrease from the channel walls to the centreline (liquid-like behaviour), due to its complex dependency on fluid density. On the other hand, strong density fluctuations are present, but due to the non-standard sound speed variation (opposite to the mean density evolution across the channel), the amplitude is maximal close to the channel wall, i.e. in the viscous sublayer instead of the buffer layer like in perfect gases. As a consequence, these fluctuations do not alter the turbulence structure significantly, and Morkovin’s hypothesis is well respected at any Mach number considered in the study. The preceding features make high Mach wall-bounded flows of dense gases similar to incompressible flows with variable properties, despite the significant fluctuations of density and speed of sound. Indeed, the semi-local scaling of Patel et al. (Phys. Fluids, vol. 27 (9), 2015, 095101) or Trettel & Larsson (Phys. Fluids, vol. 28 (2), 2016, 026102) is shown to be well adapted to compare results from existing surveys and with the well-documented incompressible limit. Additionally, for a dense gas the isothermal channel flow is also almost adiabatic, and the Van Driest transformation also performs reasonably well. The present observations open the way to the development of suitable models for dense-gas turbulent flows.

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Section: Governing Equationsmentioning

confidence: 99%

Direct numerical simulations of supersonic turbulent channel flows of dense gases

2017

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“…Non-classical effects of progressively increasing interest for practical applications have been demonstrated, e.g. a shock-compression-strength limitation induced by an inviscid shock-splitting effect (Cramer 1989), a suppression of separation in viscous-inviscid shock boundary layer interactions (Cramer & Park 1999) and a shock-free turbine blade in ORC turbines (Brown & Argrow 2000). Theoretical studies of the viscous shock structure also revealed strong non-classical effects close to Γ = 0, e.g.…”

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confidence: 99%

One-dimensional refraction properties of compression shocks in non-ideal gases

Alferez

Touber

2017

J. Fluid Mech.

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Non-ideal gases refer to deformable substances in which the speed of sound can decrease following an isentropic compression. This may occur near a phase transition such as the liquid-vapour critical point due to long-range molecular interactions. Isentropes can then become locally concave in the pressure/specific-volume phase diagram (e.g. Bethe-Zel'dovich-Thompson (BZT) gases). Following the pioneering work of Bethe (Tech. Rep. 545, Office of Scientific Research and Development, 1942) on shocks in non-ideal gases, this paper explores the refraction properties of stable compression shocks in non-reacting but arbitrary substances featuring a positive isobaric volume expansivity. A small-perturbation analysis is carried out to obtain analytical expressions for the thermo-acoustic properties of the refracted field normal to the shock front. Three new regimes are discovered: (i) an extensive but selective (in upstream Mach numbers) amplification of the entropy mode (hundreds of times larger than those of a corresponding ideal gas); (ii) discontinuous (in upstream Mach numbers) refraction properties following the appearance of non-admissible portions of the shock adiabats; (iii) the emergence of a phase shift for the generated acoustic modes and therefore the existence of conditions for which the perturbed shock does not produce any acoustic field (i.e. 'quiet' shocks, to contrast with the spontaneous D'yakov-Kontorovich acoustic emission expected in 2D or 3D). In the context of multidimensional flows, and compressible turbulence in particular, these results demonstrate a variety of pathways by which a supplied amount of energy (in the form of an entropy, vortical or acoustic mode) can be redistributed in the form of other entropy, acoustic and vortical modes in a manner that is simply not achievable in ideal gases. These findings are relevant for turbines and compressors operating close to the liquid-vapour critical point (e.g. organic Rankine cycle expanders, supercritical CO 2 compressors), astrophysical flows modelled as continuum media with exotic equations of state (e.g. the early Universe) or Bose-Einstein condensates with small but finite temperature effects.

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“…Such a model has been extensively used in previous works on dense gases (e.g. [24,25]) and is considered to be a reasonably accurate semi-theoretical model for calculating the viscosity based on the knowledge of a few thermophysical input parameters (see [26] for more details). A full description of the model equations is given in [9], Appendix A.…”

Section: Governing Equations and Numerical Methodsmentioning

confidence: 99%

A Priori Tests of RANS Models for Turbulent Channel Flows of a Dense Gas

Sciacovelli

Cinnella

Gloerfelt

2018

Flow Turbulence Combust

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Dense gas effects, encountered in many engineering applications, lead to unconventional variations of the thermodynamic and transport properties in the supersonic flow regime, which in turn are responsible for considerable modifications of turbulent flow behavior with respect to perfect gases. The most striking differences for wall-bounded turbulence are the decoupling of dynamic and thermal effects for gases with high specific heats, the liquid-like behavior of the viscosity and thermal conductivity, which tend to decrease away from the wall, and the increase of density fluctuations in the near wall region. The present work represents a first attempt of quantifying the influence of such dense gas effects on modeling assumptions employed for the closure of the Reynolds-averaged Navier-Stokes equations, with focus on the eddy viscosity and turbulent Prandtl number models. For that purpose, we use recent direct numerical simulation results for supersonic turbulent channel flows of PP11 (a heavy fluorocarbon representative of dense gases) at various bulk Mach and Reynolds numbers to carry out a priori tests of the validity of some currently-used models for the turbulent stresses and heat flux. More specifically, we examine the behavior of the modeled eddy viscosity for some low-Reynolds variants of the k − ε model and compare the results with those found for a perfect gas at similar conditions. We also investigate the behavior of the turbulent Prandtl number in dense gas flow and compare the results with the predictions of two well-established turbulent Prandtl number models.

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On the suppression of shock-induced separation in Bethe–Zel'dovich–Thompson fluids

Cited by 24 publications

References 32 publications

Direct numerical simulations of supersonic turbulent channel flows of dense gases

Direct numerical simulations of supersonic turbulent channel flows of dense gases

One-dimensional refraction properties of compression shocks in non-ideal gases

A Priori Tests of RANS Models for Turbulent Channel Flows of a Dense Gas

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