Rarefied Conditions Research Articles

Surrogate multi-objective optimization of missile RCS performance in hypersonic rarefied flow of the near space

This study focuses on optimizing the lateral jet efficiency of THAAD-like (Terminal High Altitude Area Defense) missiles operating under hypersonic rarefied flow conditions. We employ the DSMC-QK algorithm to simulate the three-dimensional lateral jet flow field, accounting for thermochemical non-equilibrium effects. The analysis investigates how the force/momentum amplification coefficient varies with the angle of attack, jet pressure ratio, jet Mach number, and jet gas composition. Subsequently, we develop an artificial neural network (ANN) proxy model using the pyrenn toolbox, achieving an average prediction error of 0.866% and a maximum error of 1.60%. Utilizing this ANN model, we perform single- and multi-objective optimizations with a genetic algorithm to determine the optimal jet parameters. The results reveal that in multi-objective optimization, the proportion of helium in the jet gas composition increases, leading to a slight reduction in the force amplification coefficient but a substantial 61.4% decrease in the mass flow rate. This demonstrates that a judicious selection of jet gas composition can significantly reduce mass flow while maintaining high jet efficiency, thus achieving efficient lateral jet control.

Modeling drag coefficients of spheroidal particles in rarefied flow conditions

Transport of particles in flows is often modeled in a combined Eulerian–Lagrangian framework. The flow is evaluated on an Eulerian grid, while particles are modeled as Lagrangian points whose positions and velocities are evolved in time, resulting in particle trajectories embedded in the time-dependent flow field. The method essentially resolves the flow field in complex geometries in detail but uses a closure model for the particle dynamics aimed at including the essential particle–fluid interactions at the cost of detailed small-scale physics. Rarefaction effects are usually included through the phenomenological Cunningham correction on the drag force experienced by the particles. In this Lagrangian point-particle approach, any explicit reference to the finite size and the shape of the particles, and their local orientation in the flow field, is typically ignored. In this work we aim to address this gap by deriving, from fully-resolved Direct Simulation Monte Carlo (DSMC) studies, heuristic or closure models for the drag force acting on prolate and oblate spheroidal particles with different aspect ratios, and a fixed orientation, in uniform ambient rarefied flows covering the transition regime between the continuum and free-molecular limits. These closure models predict the drag in the transition regime for all considered parameter settings (validated with DSMC data). The continuum limit is enforced a priori and we retrieve the free-molecular limit with reasonable accuracy (based on comparisons with literature data). We also include in the models the capability to predict effects related to basic gas-surface interactions via the tangential momentum accommodation coefficient. We furthermore assess the validity of the proposed closure model for particle dynamics in proximity to solid walls. This investigation extends our previous work, which focused on small aspect ratio spheroids with exclusively diffusive gas-surface interactions [see Livi et al. (2022)]. The derived models are obtained for isothermal, subsonic flows relevant for particle contamination control in semiconductor manufacturing.

A statistical boundary for 3D rarefied flows through meshes: implementation to a new version of dsmcFoam+ and wind tunnel validation

AbstractThe Direct Simulation Monte Carlo (DSMC) method has become a standard tool for rarefied aerodynamics and microchannel flows. However, the performance benefits of DSMC, such as adaptive grid sizes and number of particles, are constrained by the need to resolve small geometric details of mesh applications within relatively large simulation volumes. The requirement for a sufficient number of particles in even the smallest cells imposes a significant computational burden. A novel set of cyclic statistical boundary conditions is proposed to address the computational bottleneck associated with simulating micrometre-scale structures prevalent in atmospheric and space research under rarefied flow conditions. These conditions account for the geometric parameters of a geometric mesh and the angular dependency of impacting particles, aiming to alleviate the computational challenges posed by conventional approaches. Validation against wind tunnel measurements demonstrates excellent agreement for one of the implemented boundaries, able to simulate fine meshes for conditions of rocket soundings in the Mesosphere. The newly developed boundary conditions are implemented within the advanced DSMC solver, dsmcFoam+ framework. For this study, the solver is ported from OpenFOAM® version 2.4.0 to the OpenFOAM® version v2306 to leverage recent code developments, particularly in dynamic meshes, load balancing, and barycentric particle tracking. This advancement enhances the capabilities of DSMC simulations, offering improved fidelity and accuracy in capturing rarefied flow phenomena.

Interaction between lateral jet and hypersonic rarefied flow

Reaction control systems (RCS) are commonly utilized in a variety of air vehicles, and they give rise to complex flow phenomena. For flows dominated by shock waves and expansion, such as lateral jets, a significant gradient is formed in the local region of the flow field, resulting in a high local Knudsen number, and the continuum hypothesis is no longer applicable, even if the freestream belongs to near-continuum flow. As a result, multi-scale simulation approaches should be used to capture the interactions between these multi-scale structures and appropriately determine aerodynamic forces. Our earlier work, which used the conserved discrete unified gas kinetic scheme (CDUGKS) for monatomic gas, studied the flow field features of lateral jets and aerodynamic forces on blunt bodies under various rarefied freestream conditions. In this research, the Rykov model is used to expand the CDUGKS suit for diatomic gas flow while taking into account the excitation of molecular rotational energy. The impact on the flow field and aerodynamic forces from four parameters, namely freestream Mach number, jet Mach number, jet pressure ratio, and nozzle position, is thoroughly investigated. The results show that even if the incoming Mach number is different, the flow field structure and aerodynamic properties don't change much when the jet momentum ratio stays the same. The solid wall stagnation point value and local peak also show some linear relationships. The jet pressure ratio mainly affects the expansion characteristics of the jet, such as the influence range on the solid wall. In addition, with an increase in the distance between the nozzle position and the torque reference point, higher control efficiency can be obtained. The study of these aspects will help us comprehend lateral jet flow and provide reference for the design of an air vehicle's RCS.

Thin-airfoil aerodynamics in a rarefied gas wind tunnel: A theoretical study

We study the steady aerodynamic field and loadings about a thin flat plate placed in a wind tunnel under non-continuum conditions. Considering a two-dimensional straight tunnel configuration, the flow is driven by either density or temperature differences between the inlet and outlet tunnel reservoirs, producing a pressure gradient across the channel. Focusing on highly rarefied conditions, we derive a semi-analytic description for the gas flow field in the free-molecular limit for diffuse- and specular-wall configurations. The solution is valid at arbitrary differences between the inlet and outlet reservoirs as well as plate angles of attack α. The results are compared with direct simulation Monte Carlo calculations, indicating that the free-molecular description is valid through O(1) plate-size-based Knudsen numbers. The aerodynamic lift and drag forces are evaluated and their variations with α, reservoir conditions, and tunnel size are analyzed. At a fixed pressure ratio between the outlet and inlet reservoirs, the density-driven flow generates higher aerodynamic loads compared with its counterpart temperature-driven configuration, in line with the associated larger mass flow rate in the former. The results are discussed in light of the existing rarefied-gas description of the free-stream (non-confined) problem.

Study of the spike-aerodisk-opposing jet on heat protection to both the spike-aerodisk and the blunt body and overall drag reduction in rarefied hypersonic flow in near space

The Direct Simulation Monte Carlo method (DSMC) is utilized in this study to investigate the flowfield surrounding the spike-aerodisk without and with an opposing jet under rarefied hypersonic conditions within near space (altitudes of 60∼90 km and Mach numbers 7∼20). As the flight altitude increases, the incoming flow gradually becomes rarefied, weakening the drag reduction effect of the spike-aerodisk model. At altitudes reaching 90 km, the spike-aerodisk loses its drag reduction effect due to the increasing proportion of the viscous drag coefficient. At a flight altitude of 70 km, as flight Mach numbers increase, the drag reduction and thermal protection performance of the spike-aerodisk remains unchanged, mainly demonstrating the excellent performance of the spike-aerodisk model at high Mach numbers. However, the peak wall heat flux coefficient on the aerodisk can be 4.8 times higher than on the blunt body. Therefore, an opposing jet is introduced to protect the spike-aerodisk from overheating and further improve the spike-aerodisk's drag and heat reduction efficiency. Within the investigated parameter range, when the opposing-jet pressure ratio is 0.02, the peak wall heat flux coefficient of the aerodisk can decrease from 0.58 to a level similar to that of the blunt body, approximately 0.12. To make the aerodisk more certain from overheating, choosing the opposing-jet pressure ratio of 0.08 can improve drag reduction and heat prevention on the blunt body by 60.9 % and 59.7 %, respectively, compared to the spike-aerodisk model without an opposing jet.

Measurement of binary diffusion at elevated Knudsen numbers using laser absorption spectroscopy

Mass diffusion coefficients of gas mixtures have been measured for more than 100 years. However, the experimental data for the mass diffusion coefficient of gas mixtures in the rarefied gas regimes at Knudsen numbers (Kn) above 0.01 are few and remain uncertain due to the inherent precision limitations of the available state-of-the-art measurement techniques. The increased frequency of gas-wall collision, wall-friction, and surface-diffusion over the wall surface at Kn > 0.01 increases the uncertainty of the diffusive mass transport processes for internal gas flow in microcapillaries. Due to the growing interest in microfluidic applications at rarefied gas conditions, accurate diffusion coefficient measurements are needed to inform theoretical predictions and empirical relations in rarefied gas regimes. Thus, this article introduces a new experiment methodology consisting of a two-bulb (TB) diffusion configuration accompanied by a tunable diode laser absorption spectroscopy (TDLAS) detection technique that uses the measured time history of path-integrated absorbance to provide a non-intrusive, species-specific, in situ measurement of mass diffusion for a He–CO2 binary gas mixture at Kn > 0.01. To demonstrate the TB-TDLAS method's capability, the effective diffusion coefficient for a He–CO2 binary gas mixture was measured in the transition gas regime at Knudsen numbers relative to the tube radius in the range 0.1 < Kn < 5.4, and the results are compared against the Bosanquet empirical relation.

Multiscale modeling of lubrication flows under rarefied gas conditions

We present a multiscale method for simulating non-equilibrium lubrication flows. The effect of low pressure or tiny lubricating geometries that gives rise to rarefied gas effects means that standard Navier–Stokes solutions are invalid, while the large lateral size of the systems that need to be investigated is computationally prohibitive for Boltzmann solutions, such as the direct simulation Monte Carlo method (DSMC). The multiscale method we propose is applicable to time-varying, low-speed, rarefied gas flows in quasi-3D geometries that are now becoming important in various applications, such as next-generation microprocessor chip manufacturing, aerospace, sealing technologies and MEMS devices. Our multiscale simulation method provides accurate solutions, with errors of less than 1% compared to the DSMC benchmark results when all modeling conditions are met. It also shows computational gains over DSMC that increase when the lateral size of the systems increases, reaching 2–3 orders of magnitude even for relatively small systems, making it an effective tool for simulation-based design.

A numerical analysis study on the characteristics of evaporation in liquid hydrogen tank with vacuum layer according to changes in heat flux and vacuum pressure

Recently, many studies have been conducted on hydrogen, one of the new energy sources, because of environmental pollution and energy depletion. In the case of liquid hydrogen, since it is necessary to maximize insulation performance to maintain a cryogenic (20 K) environment, high-pressure gas hydrogen is currently applied that simply increases pressure and increases density. However, liquid hydrogen compared to gas hydrogen has the advantage of compressing the volume by 800 times and compared to high-pressure hydrogen gas (70.0 MPa high-pressure hydrogen gas), it can secure a density of about 10 times, which is advantageous in terms of storage/transportation. Therefore, in order to convert its form from high-pressure hydrogen to liquid hydrogen in the transport and storage of hydrogen energy, study on storage tanks with insulation performance that can maintain liquid hydrogen is needed. This work presents a numerical simulation study on characteristics of evaporation in liquid hydrogen tank related to heat flux and vacuum pressure by using verified numerical method. To study this characteristics of evaporation in liquid hydrogen tank, first, data of a prior study with numerical analysis data was compared to verify the numerical method. In this step, the coefficient values for the evaporation model was presented. Second, the heat conduction value according to the degree of vacuum was calculated by using rarefied gas condition and set on the outer wall of the liquid hydrogen tank to confirm the insulation performance according to the increase in the degree of vacuum. As a result, the mass transfer time relaxation parameter of the Lee model applied for evaporation simulation was derived as about 0.0035 1/s by trial and error. In addition, as a result of research from the perspective of thermal conductivity according to the pressure reduction of the vacuum layer, it was confirmed that the vacuum degree should be maintained below 0.001 to 0.0001 torr and the insulation performance effect was insignificant due to the decrease in vacuum layer pressure.

Inversion in binary gas mixtures in rarefied flow conditions: Direct simulation Monte Carlo solution and comparison with the analytical solutions at free molecular regime

This paper analyzes the mixing of gases in a plane channel at rarefied conditions. The direct simulation Monte Carlo method is employed to simulate gas mixing in parallel mixers working at different Knudsen numbers and having different values of wall accommodation coefficient. Results show that the normal-to-wall component of the mole fraction gradient may have the same sign as the corresponding component of the diffusive mass flux vector near the diffuse solid walls in contrast to the predictions of Fick's law for continuum conditions. This non-continuum behavior, which is called “inversion” in the present study, will become more pronounced at higher Knudsen numbers, whereas it will become less evident for smaller wall accommodation coefficients. To confirm that the observed phenomenon is consistent with the basic physical laws governing the rarefied gas dynamics and it is not an artifact of the numerical method, a new analytical model based on the kinetic theory of gases is developed for the parallel mixers that have diffuse walls and are working in the free-molecular regime. Excellent agreement is observed between the analytical and direct simulation Monte Carlo results in the free molecular flow regime. Both methods predict the occurrence of inversion near the diffuse walls at highly rarefied flow conditions.

Crystal cluster forming process under rarefied gas and low temperature environment

Aerospace engine plume flow under high altitude environment generates crystal due to low atmosphere temperature, thus causing variation on flow field and radiation properties. In order to gain better understanding on crystal generation and growth process, this article fundamentally establishes thermal motion phase change (TMPC) model based on molecular thermal motion. Direct calculation on molecular motion in phase change process takes influence of large scaled molecular free path caused by rarefied environment into consideration. The effect of temperature, H2O vapor number density, and characteristic length on phase change process is studied. According to the results, characteristic length determines non-continuum degree quantitatively under rarefied gas condition. Increasing characteristic length decreases phase change time before reaching steady state. Crystal number density decreases when working condition is near saturation condition, while crystal radius shows contrary trend. The effect of characteristic length on crystal cluster quantity and radius variation is prominent under low vapor number density condition, for increasing vacuum effect caused by decreasing gas molecules quantity. Existence of other gas components contamination obstructs H2O vapor molecules thermal motion, thus decreasing non-continuum effect on phase change process, where variation of characteristic length shows relatively limited influence on crystal cluster properties and phase change time.

Full continuum approach for simulating plume-surface interaction in planetary landings

A high-fidelity computational framework for predicting the interaction of a rocket plume with a dust blanket in an almost vacuum ambient that represents the descent/ascend phase of planetary landing is developed. Compared to the existing continuum frameworks, the developed tool benefits from nonlinear-coupled constitutive relationships obtained using a method of moments approach to tackle the non-equilibrium effects in the rarefied condition. The two-phase flow is modeled in an Eulerian framework that allows for the simulation of a wider range of solid regimes compared to the Lagrangian counterpart. Simulations were conducted to analyze the cratering phenomena and regolith ejecta dynamics. Moreover, the vorticity growth rates were analyzed using a new vorticity transport equation (VTE) by including the bulk viscosity and multiphase terms to demonstrate the contribution of each term to the formation of counterintuitive festooned patterns on the surface owing to jet impingement. This analysis identified a new contributing mechanism responsible for the scour patterns. Although all the investigated terms in the VTE contribute to such patterns, the viscous term has more effect during the entire investigation period. Furthermore, studies on particulate loading, particle diameter, and bed height were conducted to highlight the role of these parameters on brownout phenomena and scour formation patterns. The simulation results depict that the generated vortex core beneath the nozzle is highly dependent on the diameter of the particles as well as the bed height: an increase in the height of the bed and particle diameter can lead to a more favorable brownout status.

Critical assessment of various particle Fokker–Planck models for monatomic rarefied gas flows

In the past decade, the particle-based Fokker–Planck (FP) method has been extensively studied to reduce the computational costs of the direct simulation Monte Carlo method for near-continuum flows. The FP equation describes a continuous stochastic process through the combined effects of systematic forces and random fluctuations. A few different FP models have been proposed to fulfill consistency with the Boltzmann equation, but a comprehensive comparative study is needed to assess their performance. The present paper investigates the accuracy and efficiency of four different FP models—Cubic-FP, ellipsoidal-statistical FP (ES-FP), and quadratic entropic FP (Quad-EFP)—under rarefied conditions. The numerical test cases include one-dimensional Couette and Fourier flows and an argon flow past a cylinder at supersonic and hypersonic velocities. It is found that the Quad-EFP model gives the best accuracy in low-Mach internal flows, whereas the ES-FP model performs best at predicting shock waves. In terms of numerical efficiency, the Linear-FP and ES-FP models run faster than the Cubic-FP and Quad-EFP models due to their simple algebraic nature. However, it is observed that the computational advantages of the FP models diminish as the spatiotemporal resolution becomes smaller than the collisional scales. In order to take advantage of their numerical efficiency, high-order joint velocity-position integration schemes need to be devised to ensure the accuracy of FP models with very coarse resolution.

Density estimation of an ultrahigh-speed rarefied flow field based on force analysis of a pendulum sphere

The similarity criterion for high speed or high enthalpy rarefied reaction flows is the binary scaling law, one of which is the product of the incoming flow density and the characteristic scale of the test model in a rarefied wind tunnel should be equal to that under the flight condition. This is to ensure that the ratio between the characteristic distance of the relaxation process and the characteristic length of the body is equal. However, in a rarefied wind tunnel, it is difficult to directly measure the flow density below 10−5 kg/m3 using common methods due to the relatively high rarefied degree, an indirect density estimation method based on force analysis of a pendulum sphere was proposed in this study. The oscillation trajectory of the pendulum sphere under ultrahigh-speed rarefied flow conditions was recorded and the corresponding aerodynamic drag force acted on the sphere along the trajectory was analyzed, based on which the density distribution of the flow was then estimated combined with DSMC simulations. The obtained results show that in the present study, the flow is in under-expanded condition and the measured density sharply decreased from 10−6 kg/m3 to 10−7 kg/m3 at 140–170 mm from the nozzle outlet.

Machine Learning based reduced models for the aerothermodynamic and aerodynamic wall quantities in hypersonic rarefied conditions

Since their development at the end of the 50s, panel methods were widely used for the fast simulation of aerospace objects reentry. Although improvements were proposed for the continuum regime formulations, the bridging functions usually employed in the transitional regime did not go through major changes since then. With the current interest in designing Very Low Earth Orbit satellites and more efficient reentry vehicles, a greater level of preciseness is now required for the fast computation of the aerodynamic and aerothermodynamic wall quantities in rarefied regime. In this context, this paper presents a new approach to build Machine Learning based surrogates going from the choice of the design variables and the Design of Experiments, to the models training and evaluation. Hence, kriging and Artificial Neural Networks are respectively trained to predict the pressure and heat flux stagnation coefficients, and the pressure, friction and heat flux coefficient distributions in the rarefied portion of any aerodynamic shape’s reentry.

Validation of inhomogeneous chamber states in rotary positive displacement vacuum pumps

Chamber model simulation is a common approach to simulate rotary positive displacement vacuum pumps. Therefore the pump is abstracted into working chambers and connecting clearances, whereby the clearance leakages can be identified as the major loss mechanism in such machines. The clearance mass flow rates are calculated with respect to the thermodynamic states in the adjacent chambers, which are inhomogeneous for rarefied gases due to the movement of the rotors which causes a pressure gradient within the chamber. This effect increases with higher Knudsen numbers, because of the increasingly dominant friction. These inhomogeneous chamber states are assumed to be quasi-static in case that the chamber volume is constant with time. Therefore the chamber must not have a connection to the suction or discharge port. This can be modelled with a one-dimensional approach for geometrically abstracted chambers. In order to validate the one-dimensional characteristics in circumferential direction three-dimensional steady state simulations of a working chamber are performed using a Computational Fluid Dynamics (CFD) solver. To improve the accuracy for rarefied gases Maxwell velocity slip boundary conditions are applied. It is shown, that the inhomogeneous chamber states can be approximated by a regression analysis of a dimensionless number. Furthermore the housing clearance and the radial clearance mass flow rates for given boundary conditions are geometrically abstracted and calculated using a one-dimensional model. The new clearance models and the inhomogeneous chamber states are implemented in a chamber model simulation software and results of a test machine are compared to measurements and to previous simulations.

Correlation between waverider shock waves and aerodynamic forces in supersonic rarefied flow, experimental investigation in the wind tunnel MARHy

This paper presents an experimental study of the influence of viscous flows on the aerodynamic behaviour of waveriders. This investigation was carried out in the MARHy facility, under supersonic and rarefied flow conditions. Three supersonic and low density flow conditions were tested operating at Mach 2 and 4 with free stream pressures of 8 Pa and 2.67 Pa giving slip regime flows. Knudsen numbers associated with these flow conditions and this test model are between 2.79 × 10-3 and 7.33 × 10-4. In terms of pressure, these conditions are similar at altitudes between 50 km and 80 km. The studied waverider has a geometry proposed in the literature and optimised for a Mach 10 flow and an altitude of 50 km. The purpose of this work is to experimentally analyse how viscous effects will affect the aerodynamic performances of the waverider in off-design conditions. This work is based on the analysis of the upper and lower shock wave angles obtained from glow discharge imaging technique for different angles of attack and the three operating conditions. Results showed that the evolution of shock wave angles are Mach number dependent, as predicted by the inviscid shock relations, but also strongly depends on the flow pressure. From these experimental results, fitting equations have been established to predict the variation of upper and lower shock angles with the flow density, Mach number as a function of the angle of attack in continuum and especially in slip regime. Shock wave angles behaviour are compared to measured Lift-to-Drag ratio. Comparison presents a similar behaviour with flows conditions and shows that viscous layers appearing at low densities have a great influence on aerodynamic forces.

Drag and lift coefficients of ellipsoidal particles under rarefied flow conditions.

The capability to simulate a two-way coupled interaction between a rarefied gas and an arbitrary-shaped colloidal particle is important for many practical applications, such as aerospace engineering, lung drug delivery, and semiconductor manufacturing. By means of numerical simulations based on the direct-simulation Monte Carlo (DSMC) method, we investigate the influence of the orientation of the particle and rarefaction on the drag and lift coefficients, in the case of prolate and oblate ellipsoidal particles immersed in a uniform ambient flow. This is done by modeling the solid particles using a cut-cell algorithm embedded within our DSMC solver. In this approach, the surface of the particle is described by its analytical expression and the microscopic gas-solid interactions are computed exactly using a ray-tracing technique. The measured drag and lift coefficients are used to extend the correlations, based on the sine-squared drag law, available in the continuum regime to the rarefied regime, focusing on the transitional and free-molecular regimes. The functional forms of the correlations for the ellipsoidal particles are chosen as a generalization from the spherical case. We show that the fits over the data from numerical simulations can be extended to regimes outside the simulated range of Kn. Our approach allows to achieve a higher precision when compared with existing predictive models from the literature. Finally, we underline the importance of this work in providing correlations for nonspherical particles that can be used for point-particle Euler-Lagrangian simulations to address the problem of contamination from finite-size particles in high-tech mechanical systems.

Flow characteristics of low pressure chemical vapor deposition in the micro-channel

Chemical vapor deposition is a method of producing thin films by chemical reactions on the substrate surface. The preparation of semiconductor devices, graphene fiber materials, carbon nanotubes, and other materials by this method involves the reaction of the rarefied gas flows. In this paper, the flow characteristics of two-component dilute gases containing methane and hydrogen are studied by numerical simulation, which also provides an explanation for the experimental phenomena of graphene growth in rarefied conditions. To reveal the reaction mechanism from the perspective of molecular collision effects, the competitive mechanism between the collision effects in the bulk region and on the substrate surface is studied over a wide range of Kn. It is found that the collisions in the bulk region dominate at moderate Kn (0.1–5), while the surface collisions are prevailing at large Kn (Kn > 5). Furthermore, the influence of inlet gas temperature, Kn, and aspect ratio of a single channel on system temperature distribution is also studied. The results show that the temperature distribution is symmetrical for a rarefied system, while it is asymmetric when the system is in the near continuum regime. Furthermore, the change in aspect ratio has little effect on the temperature distribution.

Derivation of a Closed Form Expression for Estimating the Reduced Flow Rate for Pressure Driven Rarefied Gas Flow Through Circular Nano/Micro Pores

In this paper, a new model to predict the gas flow rate through short tubes under rarefied condition based on the sigmoidal bahaviour of gas reduced flow rate (W) versus the rarefaction parameter (d) under rarefied condition was developed. The data produced by Varoutis et al. via Direct Simulation Monte Carlo (DSMC) method were utilised to obtain the model coefficients as functions of tube length to radius (w) and pressure ratio (Pr). Then, the model was tested against the published experimental data.There was a high degree of agreement between the model predictions and the experimental data. Moreover, the new model was capable to predict the reduced flow rate of rarefied systems, not only at free molecular region and hydrodynamic region, but also at transition region, hence covering all the Knudsen number domain within the utilised data. Therefore, the proposed model was capable to make predictions as well as meet all the criteria of the rarefied gas flow within the following conditions: 0<Pr<0.9, 0.01<d<1000 and 0.0<w<20. Thus, the proposed model provides a useful tool to make a valid prediction of the rarefied gas flow behavior in a wide range of gas transport regime.