Rarefied Flow Field Research Articles

Non-equilibrium and anisotropy in Titan atmosphere entry

Titan is the largest moon of Saturn. It is the only moon in our solar system provided with atmosphere. Therefore, exploration of Titan demands aerodynamic computations aimed at a proper design of space vehicles that will bring instruments to its surface. To this purpose, the aerodynamic computing methodologies are Computational Fluid Dynamics (CFD) for the solution of continuum flow fields and Direct Simulation Monte Carlo (DSMC) method for the solution of rarefied flow fields. The failure of the Navier-Stokes equations at high altitude is due to non-equilibrium (different translational, rotational and vibrational temperatures) and to anisotropy (different components in the x, y and z direction of the translational temperature). The limitations in using DSMC at low altitudes are due to technical limitations of the computer, i.e. memory capacity and processing speed. In the present work, non-equilibrium has been quantified by the relative differences between translational and rotational (θt-r), translational and vibrational (θt-v) temperatures. Similarly, the relative differences between the translational temperature component along x and those along y (θx-y) and z (θx-z) quantified anisotropy. For each test condition, the maximum values of θ are representative of non-equilibrium and anisotropy. Computations have been carried out considering the Huygens capsule in axial-symmetric flow, along Titan atmospheric entry in the altitude interval 100–470 km by means of the commercial codes: 1) Fluent v18.1 in the interval 100–295 km, 2) DS2V-4.5 64 bits in the interval 295–470 km. The present computations stated that in the Titan entry of a capsule of dimension comparable with that of Huygens, the altitude of about 182 km should be the limit altitude for a proper use of a CFD code.

Learning of viscosity functions in rarefied gas flows with physics-informed neural networks

The prediction of non-equilibrium transport phenomena in disordered media is a difficult problem for conventional numerical methods. An example of a challenging problem is the prediction of gas flow fields through porous media in the rarefied regime, where resolving the six-dimensional Boltzmann equation or its numerical approximations is computationally too demanding. A generalized Stokes phenomenological model using an effective viscosity function was used to recover rarefied gas flow fields: however, it is difficult to construct the effective viscosity function on first principles. Physics-informed neural networks (PINNs) show some potential for solving such an inverse problem. In this work, PINNs are employed to predict the velocity field of a rarefied gas flow in a slit at increasing Knudsen numbers according to a generalized Stokes phenomenological model using an effective viscosity function. We found that the AdamW is by far the best optimizer for this inverse problem. The design was found to be robust from Knudsen numbers ranging from 0.1 to 10. Our findings stand as a first step towards the use of PINNs to investigate the dynamics of non-equilibrium flows in complex geometries.

The Meshless Direct Simulation Monte Carlo method

A new numerical simulation method called the Meshless Direct Simulation Monte Carlo (DSMC) Method is presented in this article for solving a rarefied flow field problem. It uses a discrete points group instead of using a conventional mesh to discretize the computational domain. The meshless theory is used to solve the governing equations of the rarefied flow field. Numerical challenges related to mesh distortion and low accuracy encountered in conventional mesh technology are eliminated. The meshless technology used in the DSMC method constructs the molecular cloud structure and the virtual volume to establish the methodology of molecular fast search, molecular collision pair number calculation, and molecular cloud sampling. The numerical results of a two-dimensional flow around a cylinder, a nozzle flow, a three-dimensional flow around a sphere, and a Mars probe re-entry flow are presented to demonstrate the feasibility, accuracy, and robustness of the Meshless DSMC method. This study provides the basis for meshless technology development in the field of rarefied flow.

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.

Investigation on the Opposing Jet in the Hypersonic Rarefied Flow over a Vehicle Based on the DSMC Method

In this paper, an opposing jet is applied to the space shuttle arc leading edge and the lifting body cone leading edge in the hypersonic condition of the rarefied flow field. The DSMC numerical algorithm is used to simulate and analyze the underlying working physics of the opposing jet. The results provide a reference for designing hypersonic vehicles in near space that reduce drag and protect against heat.

High frequency AC electric glow discharge visualization technology and application in big diameter hypersonic low-density wind tunnel

In order to visualize the rarefied flow field in a Φ1m hypersonic low-density wind tunnel, an electric glow discharge technique based on high frequency excited power has been developed. Firstly, finite element simulation analysis has been carried out, and it is concluded that the breakdown voltage can be reduced by using high frequency power supply; then an electric glow discharge apparatus has been fabricated, and the discharge images were compared with simulations; besides, a clear flow field around HB-1 standard model has been observed using this technology; finally, the influence of glow discharge on the flow field, as well as the differences between direct current and high frequency electric glow discharges is discussed at the end of this paper.

Molecular dynamics simulation on the splitting of shear flow in nanochannels

With the vigorous development of micro-/nanoscience and micro-/nanotechnology, fluid flows at the micro-/nanoscale have become an important research field. The molecular dynamics simulations of Couette flow in a nanochannel are carried out in this paper. In order to evaluate the non-equilibrium effect of the rarefied flow field, a “sampling-classification” method is proposed. Through this newly developed method, we found that the rarefied gas flow in nanochannels can be regarded as the superposition of two independent shear flows with the same shear rate. A nondimensional quantity “vd” is proposed to quantificationally evaluate the degree of splitting, or more specifically, the non-equilibrium state, of the flow field. Further study shows that the growth in roughness will aggravate this rarefied non-equilibrium effect, while the increase in system temperature leads to an opposite result. The “sampling-classification” method developed in this article can provide a new analytical idea for subsequent rarefied flow researchers, and the splittable phenomenon of shear flow discovered can also be regarded as an important property of rarefied flows that is worthy of further study.

Numerical investigation of a chemically reacting and rarefied hypersonic flow field

Numerical simulations are carried out in the non-continuum flow regime to analyze flow features in the shock layer of a reentry vehicle. A new solver, rarefiedHypersonicFoam, has been developed based on the OpenFOAM platform, which can simulate the intermediate hypersonic reacting flow regime, where chemical non-equilibrium effects are imperative. The solver accommodates features to model air chemistry, multispecies transport, thermodynamic properties of high-temperature air, and non-equilibrium boundary conditions. The solver is validated with ballistic range experimental data for shock standoff distance and heat flux values over a conical reentry vehicle. Results have exhibited good agreement with the experimental data and show significant improvement when compared with the conventional high-speed compressible flow solver. The modified solver is used to analyze hypersonic flow over a bi-conic reentry capsule at different altitudes and velocities in the rarefied hypersonic flow regime. The results show that at lower altitude, chemical reactions absorb a considerable amount of heat compared to higher altitude. The rate of reaction reduces with the decrease in the flow velocity, which results in reduced heat flux values. It is observed that, if only rarefaction effects are considered in the solver, it overpredicts the heat flux values. Therefore, incorporation of chemical reactions while analyzing rarefied hypersonic flow fields is imperative.

Gas-particle two-way coupled method for simulating the interaction between a rocket plume and lunar dust

During the landing process of lunar landers, the lunar surface is eroded by the exhaust plume and a large amount of lunar dust entrained into a high-velocity spray. This high-speed lunar dust can have many adverse effects on the normal operation of both the lunar lander and any potential lunar surface facilities. It is necessary, therefore, to develop better ways to model this interaction between the plume and the lunar dust. This paper details the development of a macroscopic gas-particle two-way coupled method for simulating the interaction between the plume and the lunar dust, combining a dynamic method for simulating particle motion with the direct simulation Monte Carlo method for the rarefied plume flow field. This method considers macroscopic aerodynamic forces, convective heat transfer from the plume to the lunar dust, and the reaction of lunar particles to the plume, based on the principles of momentum and energy conservation and the interaction between the plume and its particles; it can meet the conservation conditions at each time step. A microscopic gas-particle two-way coupled method is also adopted to compare with the macroscopic method. This method considers collision behavior, momentum, and heat transfer to particles at the microscopic level, and realizes the effects of solid particles on gas by considering the behavior of gas molecules reflecting on the particle surfaces. The macroscopic simulation results show that particle size has a large influence on their spatial distribution. The results indicate that the particles decelerate as they interact with gas molecules; the particles also delay gas expansion. The results of the microscopic method differ from this method (e.g., slower particle velocities), due to its different theoretical basis. The results obtained by the macroscopic method appear to be more realistic, and this method can better demonstrate the serious impact of lunar dust on the lander and the surrounding environment.

Physical modeling and numerical studies of three-dimensional non-equilibrium multi-temperature flows

For increasingly rarefied flowfields, the Navier-Stokes (NS) equations lose accuracy partially due to the single temperature approximation. To overcome this barrier, a continuum multi-temperature model based on the Bhatnagar-Gross-Krook (BGK) equation coupled with the Landau-Teller-Jeans relaxation model has been proposed for two-dimensional hypersonic non-equilibrium multi-temperature flow computation. In recent study, a two-stage fourth-order gas-kinetic scheme (GKS) has been developed for equilibrium flows, which achieves a fourth-order accuracy in space and time as well as high efficiency and robustness. In this paper, targeting for accurate and efficient simulation of multi-temperature non-equilibrium flows, a high-order three-dimensional multi-temperature GKS is implemented under the two-stage fourth-order framework, with the fourth-order Simpson interpolation rule for the newly emerged source term. Simulations on decaying homogeneous isotropic turbulence, low-density nozzle flow, rarefied hypersonic flow over a flat plate, and type IV shock-shock interaction are used to validate the multi-temperature model through the comparison with experimental measurements. The unified gas kinetic scheme (UGKS) results, and the Direct simulation Monte Carlo (DSMC) solutions will be used as well in some cases for validation. Computational results not only confirm the high-order accuracy and quite robustness of this scheme, but also show the significant improvement on computational efficiency compared with UGKS and DSMC, especially in the near continuum flow regime.

A parallelized hybrid N-S/DSMC-IP approach based on adaptive structured/unstructured overlapping grids for hypersonic transitional flows

A new hybrid N-S/DSMC-IP approach based on adaptive structured/unstructured overlapping grids is proposed and implemented to simulate hypersonic transitional flows. This approach uses the N–S method based on structured grids and the DSMC-IP method based on unstructured grids in the simulation of continuum and rarefied flow fields. The adaptive overlapping grid method is utilized and the interface between the continuum and rarefied regions is partitioned using KnGL number. The information in the different regions is strongly coupled to the continuum/rarefied interface, and the values in the coupling cells are interpolated with the weight coefficients. Finally, an adaptive parallel strategy is proposed to further improve computational efficiency. This hybrid approach combines the advantages of the structured grid and unstructured grid methods, meaning it can investigate the various characteristics of transitional flow fields with high efficiency and accuracy, while also enhancing the approach's fitness. This hybrid approach is implemented to simulate the continuum/rarefied hypersonic transitional flows around a cylinder and a nozzle; with the results indicating that the computational speed for this hybrid approach is much higher than for the DSMC-IP method and that it can be used to investigate variation in the characteristics of continuum/rarefied regions in transitional flows. Therefore, it is an efficient algorithm for the investigation of hypersonic transitional flows.

New chemical-DSMC method in numerical simulation of axisymmetric rarefied reactive flow

The modified quantum kinetic (MQK) chemical reaction model introduced by Zakeri et al. is developed for applicable cases in axisymmetric reactive rarefied gas flows using the direct simulation Monte Carlo (DSMC) method. Although, the MQK chemical model uses some modifications in the quantum kinetic (QK) method, it also employs the general soft sphere collision model and Stockmayer potential function to properly select the collision pairs in the DSMC algorithm and capture both the attraction and repulsion intermolecular forces in rarefied gas flows. For assessment of the presented model in the simulation of more complex and applicable reacting flows, first, the air dissociation is studied in a single cell for equilibrium and non-equilibrium conditions. The MQK results agree well with the analytical and experimental data and they accurately predict the characteristics of the rarefied flowfield with chemical reaction. To investigate accuracy of the MQK chemical model in the simulation of the axisymmetric flow, air dissociation is also assessed in an axial hypersonic flow around two geometries, the sphere as a benchmark case and the blunt body (STS-2) as an applicable test case. The computed results including the transient, rotational and vibrational temperatures, species concentration in the stagnation line, and also the heat flux and pressure coefficient on the surface are compared with those of the other chemical methods like the QK and total collision energy (TCE) models and available analytical and experimental data. Generally, the MQK chemical model properly simulates the chemical reactions and predicts flowfield characteristics more accurate rather than the typical QK model. Although in some cases, results of the MQK approaches match with those of the TCE method, the main point is that the MQK does not need any experimental data or unrealistic assumption of specular boundary condition as used in the TCE method. Another advantage of the MQK model is the significant reduction of computational cost rather than the QK chemical model to reach the same accuracy because of applying more proper collision model and consequently, decrease of the particles collision number.

Aero-thermo-dynamic analysis of a low ballistic coefficient deployable capsule in Earth re-entry

The paper deals with a microsatellite and the related deployable recovery capsule. The aero-brake is folded at launch and deployed in space and is able to perform a de-orbiting controlled re-entry. This kind of capsule, with a flexible, high temperature resistant fabric, thanks to its lightness and modulating capability, can be an alternative to the current “conventional” recovery capsules. The present authors already analyzed the trajectory and the aerodynamic behavior of low ballistic coefficient capsules during Earth re-entry and Mars entry. In previous studies, aerodynamic longitudinal stability analysis and evaluation of thermal and aerodynamic loads for a possible suborbital re-entry demonstrator were carried out in both continuum and rarefied regimes. The present study is aimed at providing preliminary information about thermal and aerodynamic loads and longitudinal stability for a similar deployable capsule, as well as information about the electronic composition of the plasma sheet and its possible influence on radio communications at the altitudes where GPS black-out could occur. Since the computer tests were carried out at high altitudes, therefore in rarefied flow fields, use of Direct Simulation Monte Carlo codes was mandatory. The computations involved both global aerodynamic quantities (drag and longitudinal moment coefficients) and local aerodynamic quantities (heat flux and pressure distributions along the capsule surface). The results verified that the capsule at high altitude (150km) is self-stabilizing; it is stable around the nominal attitude or at zero angle of attack and unstable around the reverse attitude or at 180° angle of attack. The analysis also pointed out the presence of extra statically stable equilibrium trim points.

AN EMPIRICAL METHOD FOR FAST PREDICTION OF RAREFIED FLOW FIELD AROUND A VERTICAL PLATE

Numerical study is conducted to investigate the effects of free-stream Knudsen (Kn) number on rarefied flow field around a vertical plate employing an unstructured DSMC method, and an empirical method for fast prediction of flow-field structure at different Kn numbers in a given inflow velocity is proposed. First, the flow at a velocity 7500m/s is simulated using a perfect-gas model with free-stream Kn changing from 0.035 to 13.36. The flow-field characteristics in these cases with varying Kn numbers are analyzed and a linear-expansion phenomenon as a function of the square of Kn is discovered. An empirical method is proposed for fast flow-field prediction at different Kn based on the least-square-fitting method. Further, the effects of chemical reactions on flow field are investigated to verify the applicability of the empirical method in the real gas conditions. Three of the cases in perfect-gas flow are simulated again by introducing five-species air chemical module. The flow properties with and without chemical reactions are compared. In the end, the variation of chemical-reaction flow field as a function of Kn is analyzed and it is shown that the empirical method are also suitable when considering chemical reactions.

A conservative discrete ordinate method for solving semiclassical Boltzmann-BGK equation with Maxwell type wall boundary condition

A robust and efficient numerical method in phase space combining the conservative discrete ordinate method and high order spatial discretization is proposed for the semiclassical Boltzmann equation with Bhatnagar–Gross–Krook (BGK) relaxation time approximation. A general Maxwell type partially diffuse and partially specular reflection solid wall boundary condition for modeling the gas–surface interactions for semiclassical rarefied gas flows is devised. The discrete ordinate method is first applied to discretize the velocity space of the distribution function to render a set of scalar conservation laws with source term. The high order weighted essentially non-oscillatory scheme is then implemented to evolve the solution in physical space and time. The conservation property of the BGK collision integral is ensured to be fulfilled at the discrete quadrature level approximation. Both specular and diffuse reflection boundary conditions are implemented. Extensive computations of one- and two-dimensional semiclassical rarefied gas dynamical flows covering wide range of flow regimes for three statistics are presented to illustrate the method and boundary conditions treatment. The effect of accommodation coefficient on the rarefied flow field is also examined.

Asymptotic Solutions of Pressure and Heat Flux of Highly Rarefied Gas Flows in Vacuum Packaged Micro-Electro-Mechanical System Devices

This study analyzed a highly rarefied gas flow fields inside an enclosure. The enclosure is formed by four plates with two different temperatures. The plate surfaces are assumed completely diffuse; at the final steady flow stage for any point inside the enclosure or at the surface, the velocity distribution function was determined and all the macroscopic properties was determined by integrating the velocity distribution function. First, the collisionless flow solution was considered as the base solution, and then based on the Bhatnagar-Gross-Krook model, the characteristic relaxation time scale τ was used as a small parameter, and obtained general asymptotic analytical solutions for the flow fields and heat transfer expressions. To validate these asymptotic solutions, a series of numerical simulations with the direct simulation Monte Carlo method were performed and compared with the analytical results. In general, as Knudsen number decreases, the solutions for the pressure, temperature, and density fields deteriorate; the temperature fields had relatively better agreement than the density and pressure fields.

Influence of chemical models on the computation of thermo-fluid-dynamic parameters in hypersonic, rarefied flows

Four different chemical models (Bird, Fan and Shen, ‘classic’, and ‘new’ quantic) have been implemented in a direct simulation Monte Carlo (DSMC) code for comparison purpose. Computer tests simulated a hypersonic, rarefied flow field past a bluff (or flat-ended) cylinder; the working gas was nitrogen. The flow field parameters were compared with those from the advanced DS2V code. The Stanton number at the stagnation point was compared also with the experimental data. The present analysis showed that the Fan—Shen model is comparable with the widely accepted Bird model. The results from the DSMC code based on these models are close to those computed by DS2V and to the experimental data. The good comparison of the Bird and the Fan—Shen models is a very important result both from a physical point of view, because the two models rely on different approaches, and from an operative point of view, because the Fan—Shen model could be considered as a possible alternative to the Bird model. On the contrary, the quantic models appear to be not suitable.

Feasibility study on nearly-fuel-free planetary exploration with low-ballistic-coefficient aerocapture of sail-type vehicle

A novel concept of the nearly-fuel-free planetary exploration by the sail aerocapture vehicle, which uses the sail not only for the solar sailing but also for an aerodynamic decelerator at the orbit insertion, and its design methodology are presented. Considering a mission to Saturn, the trajectory analysis shows that the corridor of the entry path angle for successful aerocapture is significantly widened and that the aerodynamic heating is much reduced, thanks to the ultra-low ballistic coefficient of the sail-type vehicle. The coupled analyses of the rarefied flow field and the deformation of the sail demonstrate that the solar sail vehicle can survive under the condition of the aerodynamic heating and the stress due to the aerodynamic force. To sustain the disk-like shape of the sail during the atmospheric flight, an inflatable torus attached as a hoop support is recommended as well as a spin motion producing the centrifugal force.

Multiple temperature kinetic model and gas-kinetic method for hypersonic non-equilibrium flow computations

It is well known that for increasingly rarefied flowfields, the predictions from continuum formulation, such as the Navier–Stokes equations lose accuracy. For the high speed diatomic molecular flow in the transitional regime, the inaccuracies are partially attributed to the single temperature approximations in the Navier–Stokes equations. Here, we propose a continuum multiple temperature model based on the Bhatnagar–Gross–Krook (BGK) equation for the non-equilibrium flow computation. In the current model, the Landau–Teller–Jeans relaxation model for the rotational energy is used to evaluate the energy exchange between the translational and rotational modes. Due to the multiple temperature approximation, the second viscosity coefficient in the Navier–Stokes equations is replaced by the temperature relaxation term. In order to solve the multiple temperature kinetic model, a multiscale gas-kinetic finite volume scheme is proposed, where the gas-kinetic equation is numerically solved for the fluxes to update the macroscopic flow variables inside each control volume. Since the gas-kinetic scheme uses a continuous gas distribution function at a cell interface for the fluxes evaluation, the moments of a gas distribution function can be explicitly obtained for the multiple temperature model. Therefore, the kinetic scheme is much more efficient than the DSMC method, especially in the near continuum flow regime. For the non-equilibrium flow computations, i.e., the nozzle flow and hypersonic rarefied flow over flat plate, the computational results are validated in comparison with experimental measurements and DSMC solutions.

Multiple temperature model for near continuum flows

In the near continuum flow regime, the flow may have different translational temperatures in different directions. It is well known that for increasingly rarefied flow fields, the predictions from continuum formulation, such as the Navier-Stokes equations, lose accuracy. These inaccuracies may be partially due to the single temperature assumption in the Navier-Stokes equations. Here, based on the gas-kinetic Bhatnagar-Gross-Krook (BGK) equation, a multi-translational temperature model is proposed and used in the flow calculations. In order to fix all three translational temperatures, two constraints are additionally proposed to model the energy exchange in different directions. Based on the multiple temperature assumption, the Navier-Stokes relation between the stress and strain is replaced by the temperature relaxation term, and the Navier-Stokes assumption is recovered only in the limiting case when the flow is close to the equilibrium with the same temperature in different directions. In order to validate the current model, both the Couette and Poiseuille flows are studied in the transition flow regime.