Rho-Shin Myong

Velocity slip in microscale cylindrical Couette flow: The Langmuir model

The velocity slip on the solid surfaces of microscale cylindrical Couette flow is investigated using the Langmuir adsorption model for the gas-surface molecular interaction. The accommodation coefficient in the Maxwell model, which is a free parameter based on the concept of diffusive reflection, is replaced by a physical parameter of heat adsorption in the Langmuir model. The phenomenon of velocity inversion is then clearly explained by introducing a velocity polar on the hodograph plane. It is also shown that the quantity used to determine the momentum slip in a concentric cylindrical geometry should be based upon the angular velocity, not the velocity itself. Finally, and despite their totally independent considerations of the gas-surface molecular interaction, the Maxwell and Langmuir slip models are shown to be in qualitative agreement with direct simulation Monte Carlo data in capturing the general features of the flow field.

THERMODYNAMICALLY CONSISTENT HYDRODYNAMIC COMPUTATIONAL MODELS FOR HIGH-KNUDSEN-NUMBER GAS FLOWS

In high-Knudsen-number flows nonequilibrium effects become dominant and the use of Navier–Stokes–Fourier equations becomes questionable since they are based on small deviation from local thermodynamic equilibrium. In this paper new hydrodynamic computational models are proposed for modeling gases in the transition regime. They are based on Eu’s generalized hydrodynamic equations and it turns out that they apply in all Mach numbers and satisfy the second law of thermodynamics to every order of approximation. In order to learn more about the new equations a model equation similar to the Burgers’ equation is studied. From this analysis new insight into constitutive relations of various hydrodynamic equations has been gained. In addition, a convergent iterative method for solving the highly nonlinear constitutive equations is developed. Finally, the shock structure and slip flow problems are computed by using high resolution numerical schemes and issues of extending the one-dimensional solver to multidimensio...

Gaseous slip models based on the Langmuir adsorption isotherm

On the basis of Langmuir’s theory of adsorption of gases on solids, a robust gaseous slip model is presented. The concept of accommodation coefficient and the difference of gas particles are explained within the new framework. It turned out that the Langmuir model recovers the Maxwell model in the first-order approximation in the case of the microchannel gas flow. In order to validate the new approach, the model is applied to problems of technical interests: pressure-driven microchannel gas flow and low Reynolds number gas flow past a sphere. With the help of previous theoretical and experimental results it is shown that with an adjustable parameter the model in low-speed creeping regime with moderate Knudsen numbers yields a prediction in qualitative agreement with the data.

A full analytical solution for the force-driven compressible Poiseuille gas flow based on a nonlinear coupled constitutive relation

The compressible Poiseuille gas flow driven by a uniform force is analytically investigated using a phenomenological nonlinear coupled constitutive relation model. A new fully analytical solution in compact tangent (or hyperbolic tangent in the case of diatomic gases) functional form explains the origin behind the central temperature minimum and a heat transfer from the cold region to the hot region. The solution is not only proven to satisfy the conservation laws exactly but also well-defined for all physical conditions (the Knudsen number and a force-related dimensionless parameter). It is also shown that the non-Fourier law associated with the coupling of force and viscous shear stress in the constitutive relation is responsible for the existence of the central temperature minimum, while a kinematic constraint on viscous shear and normal stresses identified in the velocity shear flow is the main source of the nonuniform pressure distribution. In addition, the convex pressure profile with a maximum at t...

A triangular discontinuous Galerkin method for non-Newtonian implicit constitutive models of rarefied and microscale gases

The discontinuous Galerkin (DG) method has been popular as a numerical technique for solving the conservation laws of gas dynamics. In the present study, we develop an explicit modal DG scheme for multi-dimensional conservation laws on unstructured triangular meshes in conjunction with non-Newtonian implicit nonlinear coupled constitutive relations (NCCR). Special attention is given to how to treat the complex non-Newtonian type constitutive relations arising from the high degree of thermal nonequilibrium in multi-dimensional gas flows within the Galerkin framework. The Langmuir velocity slip and temperature jump conditions are also implemented into the two-dimensional DG scheme for high Knudsen number flows. As a canonical scalar case, Newtonian and non-Newtonian convection-diffusion Burgers equations are studied to develop the basic building blocks for the scheme. In order to verify and validate the scheme, we applied the scheme to a stiff problem of the shock wave structure for all Mach numbers and to the two-dimensional hypersonic rarefied and low-speed microscale gas flows past a circular cylinder. The computational results show that the NCCR model yields the solutions in better agreement with the direct simulation Monte Carlo (DSMC) data than the Newtonian linear Navier-Stokes-Fourier (NSF) results in all cases of the problem studied.

Downstream flow condition effects on the RR → MR transition of asymmetric shock waves in steady flows

In this paper, the regular reflection (RR) to Mach reflection (MR) transition of asymmetric shock waves is theoretically studied by employing the classical two- and three-shock theories. Computations are conducted to evaluate the effects of expansion fans, which are inherent flow structures in asymmetric reflection of shock waves, on the RR → MR transition. Comparison shows good agreement among the theoretical, numerical and experimental results. Some discrepancies between experiment and theory reported in previous studies are also explained based on the present theoretical analysis. The advanced RR → MR transition triggered by a transverse wave is also discussed for the interaction of a hypersonic flow and a double-wedge-like geometry.

On the high Mach number shock structure singularity caused by overreach of Maxwellian molecules

The high Mach number shock structure singularity arising in moment equations of the Boltzmann equation was investigated. The source of the singularity is shown to be the unbalanced treatment between two high order kinematic and dissipation terms caused by the overreach of Maxwellian molecule assumption. In compressive gaseous flow, the high order stress-strain coupling term of quadratic nature will grow far faster than the strain term, resulting in an imbalance with the linear dissipation term and eventually a blow-up singularity in high thermal nonequilibrium. On the other hand, the singularity arising from unbalanced treatment does not occur in the case of velocity shear and expansion flows, since the high order effects are cancelled under the constraint of the free-molecular asymptotic behavior. As an alternative method to achieve the balanced treatment, Eus generalized hydrodynamics, consistent with the second law of thermodynamics, was revisited. After introducing the canonical distribution function...

Microscopic molecular dynamics characterization of the second-order non-Navier-Fourier constitutive laws in the Poiseuille gas flow

The second-order non-Navier-Fourier constitutive laws, expressed in a compact algebraic mathematical form, were validated for the force-driven Poiseuille gas flow by the deterministic atomic-level microscopic molecular dynamics (MD). Emphasis is placed on how completely different methods (a second-order continuum macroscopic theory based on the kinetic Boltzmann equation, the probabilistic mesoscopic direct simulation Monte Carlo, and, in particular, the deterministic microscopic MD) describe the non-classical physics, and whether the second-order non-Navier-Fourier constitutive laws derived from the continuum theory can be validated using MD solutions for the viscous stress and heat flux calculated directly from the molecular data using the statistical method. Peculiar behaviors (non-uniform tangent pressure profile and exotic instantaneous heat conduction from cold to hot [R. S. Myong, “A full analytical solution for the force-driven compressible Poiseuille gas flow based on a nonlinear coupled constitutive relation,” Phys. Fluids 23(1), 012002 (2011)]) were re-examined using atomic-level MD results. It was shown that all three results were in strong qualitative agreement with each other, implying that the second-order non-Navier-Fourier laws are indeed physically legitimate in the transition regime. Furthermore, it was shown that the non-Navier-Fourier constitutive laws are essential for describing non-zero normal stress and tangential heat flux, while the classical and non-classical laws remain similar for shear stress and normal heat flux.

Theoretical description of the gaseous Knudsen layer in Couette flow based on the second-order constitutive and slip-jump models

The Knudsen layer, found in the region of gas flow very close (in order of a few mean free paths) to the solid surfaces, plays a critical role in accurately modeling rarefied and micro-scale gases. In various previous investigations, abnormal behaviors at high Knudsen numbers such as nonlinear velocity profile, velocity gradient singularity, and pronounced thermal effect are identified to exist in the Knudsen layer. However, some behaviors, in particular, the velocity gradient singularity near the surface and higher temperature, remain elusive in the continuum framework. In this study, based on the second-order macroscopic constitutive equation recently derived from the kinetic Boltzmann equation via the balanced closure and cumulant expansion [R. S. Myong, “On the high Mach number shock structure singularity caused by overreach of Maxwellian molecules,” Phys. Fluids 26(5), 056102 (2014)], the macroscopic second-order constitutive and slip-jump models that are able to explain qualitatively all the known non-classical and non-isothermal behaviors are proposed. As a result, new analytical solutions to the Knudsen layer in Couette flow, in conjunction with the algebraic nonlinearly coupled second-order constitutive and Maxwell velocity slip and Smoluchowski temperature jump models, are derived. It was shown that the velocity gradient singularity in the Knudsen layer can be explained within the continuum framework, when the nonlinearity of the constitutive model is morphed into the determination of the velocity slip in the nonlinear slip and jump model. Also, the smaller velocity slip and shear stress are shown to be caused by the shear-thinning property of the second-order constitutive model, that is, vanishing effective viscosity at high Knudsen number.

Numerical and Experimental Investigation of Ice Accretion on Rotorcraft Engine Air Intake

Ice accretion on the surface of an electrothermal anti-icing system around a rotorcraft engine air intake was investigated on the basis of computational and experimental methods. A compressible Navier–Stokes–Fourier computational fluid dynamics code was used to determine the fully three-dimensional flowfield around the inlet of the engine and the environment control system. Three-dimensional droplet trajectory and ice accretion codes based on the Eulerian approach, DROP3D and ICE3D modules of FENSAP-ICE, were used to calculate the collection efficiency and ice shape on the surface of an engine air intake. Furthermore, an experimental study using an icing wind tunnel was conducted to validate the computational predictions of ice accretion on the surface of the electrothermal anti-icing system in heat-off and heat-on modes. It is shown that the general shape and range of ice accretion obtained by numerical calculations are in close agreement with experimental observation. In particular, two features of glaz...