Direct Numerical Simulation of Real-gas Effects within Turbulent Boundary Layers for Fully-developed Channel Flows

Abstract

Real-gas effects have a significant impact on compressible turbulent flows of dense gases, especially when flow properties are in proximity of the saturation line and/or the thermodynamic critical point. Understanding of these effects is key for the analysis and improvement of performance for many industrial components, including expanders and heat exchangers in organic Rankine cycle systems. This work analyzes the real-gas effect on the turbulent boundary layer of fully developed channel flow of two organic gases, R1233zd(E) and MDM - two candidate working fluids for ORC systems. Compressible direct numerical simulations (DNS) with real-gas equations of state are used in this research. Three cases are set up for each organic vapour, representing thermodynamic states far from, close to and inside the supercritical region, and these cases refer to weak, normal and strong real-gas effect in each fluid. The results within this work show that the real-gas effect can significantly influence the profile of averaged thermodynamic properties, relative to an air baseline case. This effect has a reverse impact on the distribution of averaged temperature and density. As the real-gas effect gets stronger, the averaged centre-to-wall temperature ratio decreases but the density drop increases. In a strong real-gas effect case, the dynamic viscosity at the channel center point can be lower than at channel wall. This phenomenon can not be found in a perfect gas flow. The real-gas effect increases the normal Reynolds stress in the wall-normal direction by 7–20% and in the spanwise direction by 10–21%, which is caused by its impact on the viscosity profile. It also increases the Reynolds shear stress by 5–8%. The real-gas effect increases the turbulence kinetic energy dissipation in the viscous sublayer and buffer sublayer <inline-formula><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"><mml:mo stretchy="false">(</mml:mo><mml:msup><mml:mi>y</mml:mi><mml:mo>∗</mml:mo></mml:msup><mml:mo><</mml:mo><mml:mn>30</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:math></inline-formula> but not in the outer layer. The turbulent viscosity hypthesis is checked in these two fluids, and the result shows that the standard two-function RANS model (<inline-formula><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"><mml:mi>k</mml:mi><mml:mo>−</mml:mo><mml:mi>ϵ</mml:mi></mml:math></inline-formula> and <inline-formula><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"><mml:mi>k</mml:mi><mml:mo>−</mml:mo><mml:mi>ω</mml:mi></mml:math></inline-formula>) with a constant <inline-formula><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"><mml:msub><mml:mi>C</mml:mi><mml:mi>μ</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mn>0.09</mml:mn></mml:math></inline-formula> is still suitable in the outer layer <inline-formula><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"><mml:mo stretchy="false">(</mml:mo><mml:msup><mml:mi>y</mml:mi><mml:mo>∗</mml:mo></mml:msup><mml:mo>></mml:mo><mml:mn>70</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:math></inline-formula>, with an error in ±10%.

High-subsonic boundary-layer flows of an organic vapour

“…The profile of Wenzel et al (2018) obtained in air at M = 0.85 and for a smaller Reynolds number shows lower values than those encountered in Novec649 at the highest Reynolds number, suggesting that the fluctuations in Mach number are even greater for Novec649. Such a result was also obtained by Sciacovelli et al (2017) and Chen et al (2021) for turbulent channel flows of dense gases. The levels of dilatation fluctuations can be inferred by the acoustic field radiated by the turbulent boundary layer, which can be directly obtained in our DNS (figure 23b).…”

“…(2017) and Chen et al. (2021) for turbulent channel flows of dense gases. The levels of dilatation fluctuations can be inferred by the acoustic field radiated by the turbulent boundary layer, which can be directly obtained in our DNS (figure 23 b ).…”

“…If the modelled eddy viscosity behaves in the same manner as for air flows at similar conditions, the agreement with turbulent Prandtl number models is less conclusive due to the reduced thermal boundary layer. More recently, Chen et al (2021) performed DNS of turbulent channel flow for two organic gases, R1233zd(E) and MDM, two candidate working fluids for ORC systems, at conditions close to the supercritical region. The results show that real-gas effects can significantly affect the profiles of averaged thermodynamic properties, and the viscosity has a liquid-like profile, in contrast to a perfect gas flow.…”

“…More recently, Chen et al. (2021) performed DNS of turbulent channel flow for two organic gases, R1233zd(E) and MDM, two candidate working fluids for ORC systems, at conditions close to the supercritical region. The results show that real-gas effects can significantly affect the profiles of averaged thermodynamic properties, and the viscosity has a liquid-like profile, in contrast to a perfect gas flow.…”