Transition regime analytical solution to gas mass flow rate in a rectangular micro channel

We present an analytical model predicting the experimentally observed gas mass flow rate in rectangular micro channels over slip and transition regimes without the use of any fitting parameter. Previously, Sone [1] reported a class of pure continuum regime flows that requires terms of Burnett order in constitutive equations of shear stress to be predicted appropriately. The corrective terms to the conventional Navier-Stokes equation were named the ghost effect. We demonstrate in this paper similarity between Sone ghost effect model and newly so-called ‘volume diffusion hydrodynamic model’. A generic analytical solution to gas mass flow rate in a rectangular micro channel is then obtained. It is shown that the volume diffusion hydrodynamics allows to accurately predict the gas mass flow rate up to Knudsen number of 5. This can be achieved without necessitating the use of any adjustable parameters in boundary conditions or parametric scaling laws for constitutive relations. The present model predicts the non-linear variation of pressure profile along the axial direction and also captures the change in curvature with increase in rarefaction

Molecular free path distribution in rarefied gases

We present the results of investigations into the distribution of molecular free paths in rarefied gases using molecular dynamics simulations. Our tests on a range of different gas densities and confinements (unbounded, single bounding wall and parallel bounding walls) indicate that the molecules perform Lévy-type flights, irrespective of the presence of a bounding wall. The free paths most closely follow a power-law distribution. Simulations of gases confined by planar surfaces indicate that the local molecular mean free path varies sharply close to a solid surface. These results may yield new insight into diffusive transport in rarefied gases, in particular, the constitutive behaviour of gas flows in micro- and nanoscale devices

Modeling of Knudsen layer effects in micro/nanoscale gas flows

We propose a power-law based effective mean free path (MFP) model so that the Navier-Stokes-Fourier equations can be employed for the transition-regime flows typical of gas micro/nanodevices. The effective MFP model is derived for a system with planar wall confinement by taking into account the boundary limiting effects on the molecular free paths. Our model is validated against molecular dynamics simulation data and compared with other theoretical models. As gas transport properties can be related to the mean free path through kinetic theory, the Navier-Stokes-Fourier constitutive relations are then modified in order to better capture the flow behavior in the Knudsen layers close to surfaces. Our model is applied to fully developed isothermal pressure-driven (Poiseuille) and thermal creep gas flows in microchannels. The results show that our approach greatly improves the near-wall accuracy of the Navier-Stokes-Fourier equations, well beyond the slip-flow regime

Behaviour of microscale gas flows based on a power-law free path distribution function

We investigate a power-law form for the probability distribution function of free paths of dilute gas molecules in a confined region. A geometry-dependent effective molecular mean free path (MFP) model is then derived for a planar wall confinement, by taking into account the boundary limiting effects on the molecular paths. The power-law based effective MFP is validated against molecular dynamics simulation data and compared with exponential effective MFP models. The Navier-Stokes constitutive relations are then modified according to the kinetic theory of gases i.e. transport properties can be described in terms of the free paths which the molecules describe between collisions. Results for isothermal pressure-driven Poiseuille gas flows in micro-channels are reported, and we compare results with conventional hydrodynamic models, solutions of the Boltzmann equation and experimental data

Molecular dynamics studies of anomalous transport in rarefied gas flows

We investigate the thermodynamically non-equilibrium gas dynamics by measuring molecular free path distribution functions, inter-molecular collision rates and wall dependent mean free path (MFP) profiles using the molecular dynamics (MD) method. The simulations cover a wide range of fluid densities for single-wall case, parallel walls cases and a cube with all periodic walls. The simulations are validated by deducing the theoretical unconfined MFP values at standardpressure and temperature conditions. The free path MD measurements of individual molecules convey that conventional exponential distribution function is not valid under rarefied conditions and molecules follow L´evy type flights, irrespective of the presence of a wall. MFP profile measurements for confined planar surfaces in the transition flow regime show sharp gradients close to the wall, while theoretical models predict shallower gradients. As gas transport properties can be related to the MFP through kinetic theory, our MD data may help to modify the constitutive relationships, which may then be fed into the Navier-Stokes equations for better effective modeling of micro gas flows in the transition flow regime

The importance of mean free path in determining gas micro flow behaviour

We investigate whether a power-law form of probability distribution function better describes the free paths of dilute gas molecules in a confined system. An effective molecular mean free path model is derived, which allows the mean free path to vary close to bounding surfaces. Our model is compared with molecular dynamics simulation data, and also other classical mean free path models. As gas transport properties can be related to the mean free path through kinetic theory, the Navier-Stokes constitutive relations are then modified and applied to various benchmark test cases. Results for isothermal pressure-driven Poiseuille flows in micro-channels are reported, and we compare our results with conventional hydrodynamic models, solutions of the Boltzmann equation, and experimental data. Our new approach provides good results for mean free path and cross-sectional flow velocity profiles up to Knudsen numbers around 1, and for integral flow parameters such as flow rate and friction factor up to Knudsen number of 10. We discuss some limitations of our power-law model, and point to the way forward for further development

EFFECT OF CHEMICAL NON-EQUILIBRIUM ON FLOW PARAMETERS IN THE INTERMEDIATE HYPERSONIC REGIME

The new solver hypersonicIithFoam has been developed in the OpenFOAM framework. OpenFOAM has rhoCentralFoam which is a density based N-S solver, is used as a base solver. Additional features are incorporated to model reacting flows, variable multi-species diffusion and thermodynamic proper- ties of high-temperature air. The solver is implemented to model the transport properties based on a kinetic theory for its widespread applicability. Viscosity and Thermal conductivity are obtained using the model based on Lennard-Jones potential, and Chapman-Enskog diffusivity model is used to compute binary dif- fusion coefficient. Multicomponent mixture properties are calcu- lated based on a mole fraction. All species are assumed to be in thermodynamic equilibrium, so the state of the gas is governed by single equilibrium temperature. The solver is tested with the available experimental data for Heat flux and coefficient of pres- sure Cp distribution over a surface of ELECTRE article. The hy- personic solver is shown significant improvement over a conven- tional compressible solver. Simulations are carried out for the flow over a sphere at different altitudes using both the conven- tional and the hypersonic solver for qualitative and quantitative comparisons. Post shock temperature and peak heat flux values are remarkably reduces due to the implementation of real gas ef- fects and air chemistry. Rarefaction effects become significant from 70 km

Multi response optimization of Inconel 625 wire arc deposition for development of additive manufactured components using Grey relational analysis (GRA)

The paper investigates the multi response optimization of single bead deposition characteristics which affects the additive manufactured structures in later stages of multi layered depositions. Inconel 625 single beads were deposited using the cold metal transfer (CMT) based on Wire Arc Additive Manufacturing (WAAM). The bead width, bead height, penetration depth as well as microhardness of the fusion region are considered for the decision criteria models. Grey relational analysis (GRA) is used to solve the multi criteria optimization problem. Analysis of variance has been performed to quantify the parameters effects on grey relational grade (GRG). From the GRA, it is observed that at parameter setting of 110 Amps current, 0.4 mm/sec weld speed, and 4 mm standoff distance gives minimum bead width, minimum bead height, maximum penetration depth, and maximum microhardness