Rarefied gas effects on hypersonic flow over a transpiration-cooled flat plate

This paper investigates the impact of transpiration on a hypersonic flow over a cylinder, considering different degrees of rarefaction. The study analyzes the interaction between freestream argon gas flow at Mach 5 and transpiring argon gas at the fluid–solid interface at a velocity of 10 m/s. Freestream Knudsen numbers considered are 0.002, 0.01, 0.05, and 0.25, spanning from a continuum to rarefied regime. Flow simulations utilize the open-source direct simulation Monte Carlo solver, Stochastic PArallel Rarefied-gas Time-accurate Analyzer. The influence of transpiration on flow and surface properties is examined by comparing non-transpiration and transpiration cases. At all regimes, transpiration increases the normal shock stand-off distance, while a comparison of flow properties along the stagnation line reveals a reduction in the velocity and an increase in the post-shock temperature with transpiration. Surface heat flux comparison indicates that transpiring gas reduces heat flux on the cylinder's upstream-facing front surface at all Knudsen numbers. However, at Kn∞ = 0.25, a shift occurs, and surface heat flux starts increasing locally from the top/bottom point on the cylinder surface through the rear face of the cylinder. Furthermore, a test for the validity of the continuum-based blowing correction correlation function reveals the failure of the empirical model, even in the continuum regime at Kn∞ = 0.002, casting doubt on its applicability to vehicles with curvilinear blunt-body shapes. Additionally, a sensitivity analysis demonstrates that transpiring gas with a number density an order of magnitude higher than the freestream reduces stagnation peak heat flux by nearly 30%, while transpiring gas with a temperature two times higher than the freestream shows a ∼13% reduction.

Recently, as aerodynamics was applied to flying vehicles with very high speed and flying at high altitude, the numerical simulation based on the Navier–Stokes (NS) equations was found that cannot correctly predict certain aero-thermo-dynamic properties in a certain range of velocity and altitude while the Knudsen number indicates that the flow is still in the continuum regime. As first noted by Zhou and Zhang (Science in China, 2015), the invalidity of NS equations for such flows might be attributed to an non-equilibrium effect originating from the combined effects of gas rarefaction and strong shear in the boundary-layer flows. In this paper, we present the scope, physical concept, mathematical model of this shear non-equilibrium effect in hypersonic flows, as well as the way of considering this effect in conventional computational fluid mechanics (CFD) for engineering applications. Several hypersonic flows over sharp bodies and blunt bodies are analyzed by the proposed new continuum model, named direct simulation Monte Carlo (DSMC) data-improved Navier–Stokes (DiNS) model. Recently, as aerodynamics was applied to flying vehicles with very high speed and flying at high altitude, the numerical simulation based on the Navier–Stokes (NS) equations was found that cannot correctly predict certain aero-thermo-dynamic properties in a certain range of velocity and altitude while the Knudsen number indicates that the flow is still in the continuum regime. As first noted by Zhou and Zhang (Science in China, 2015), the invalidity of NS equations for such flows might be attributed to an non-equilibrium effect originating from the combined effects of gas rarefaction and strong shear in the boundary-layer flows. In this paper, we present the scope, physical concept, mathematical model of this shear non-equilibrium effect in hypersonic flows, as well as the way of considering this effect in conventional computational fluid mechanics (CFD) for engineering applications. Several hypersonic flows over sharp bodies and blunt bodies are analyzed by the proposed new continuum model, named direct simulation Monte Carlo (DSMC) data-improved Navier–Stokes (DiNS) model..

This paper demonstrates the newly developed particle method in the Direct Simulation Monte Carlo (DSMC) framework, and we refer to it as the Maxwellian–DSMC (M–DSMC) method. The M–DSMC solver is utilized for various fluid flow problems with different length scales varied from continuum to transitional regime. The hypersonic flow of argon over a cylinder simulation is carried out using M–DSMC and the same simulation results are compared with the regular DSMC method. The present work shows that the M–DSMC results are quite a good match with the DSMC results. The computational cost is significantly reduced by using M–DSMC method and the same is compared with regular DSMC method.

Direct Simulation Monte Carlo (DSMC) solves the Boltzmann equation with large Knudsen number. The Boltzmann equation generally consists of three terms: the force term, the diffusion term and the collision term. While the first two terms of the Boltzmann equation can be discretized by numerical methods such as the finite volume method, the third term can be approximated by DSMC, and DSMC simulates the physical behaviors of gas molecules. However, because of the low sampling efficiency of Monte Carlo Simulation in DSMC, this part usually occupies large portion of computational costs to solve the Boltzmann equation. In this paper, by Markov Chain Monte Carlo (MCMC) and multicore programming, we develop Direct Simulation Multi-Chain Markov Chain Monte Carlo (DSMC3): a fast solver to calculate the numerical solution for the Boltzmann equation. Computational results show that DSMC3 is significantly faster than the conventional method DSMC.

Tsien summarized the similarity in hypersonic flows, and related Knudsen number to Mach number and Reynolds number. Recently, a path-based problem, aero-optical effect, arises in hypersonic flows, and it concerns about the compressibility and the Knudsen number of the gas flows, which differs from the Tsien’s focus to some extent. In this paper, the similarity of hypersonic aero optics is theoretically studied, and both flow fields and induced aero-optical effect after flows pass through a cylinder are predicted by a well-accepted particle-based method, direct simulation Monte-Carlo (DSMC) method. The results show that the optical distortions are inversely proportional to the Knudsen number, while the compressibility plays an important role in the optical degradations. Hence, it is confirmed that the effects of Mach number and Knudsen number on the aero-optical effect induced by hypersonic flows are of great significance. Besides, since the Knudsen number is defined straightforwardly based on the optically active region, the physics is clearer than any other similarity criteria.

Hypersonic flow over Stardust Re-entry Capsule using ab-initio based chemical reaction model

Numerical simulations have been carried out to explore the expansion ratio effects on the hypersonic rarefied flow past a forward-facing step using the Direct Simulation Monte Carlo (DSMC) method. An open source solver named dsmcFoam has been used for this purpose. The solver has been validated with well-established results from the literature and good agreement is found among them. Simulations have been carried out for expansion ratios (ER) of 2,4,6,8,10 in the transition regime. The different flow field properties have been studied. The profiles have found to be influenced by the compressibility and rarefaction effects. Limiting case of ER=8 and above has no influence on the flow field properties.

For computation of hypersonic flowfields about space vehicles in low earth orbits, where the local Knudsen numbers (Kri) lie in the continuum-transition regime, a set of extended three-dimensional hydrodynamic equations are required which are more accurate than the NavierStokes equations and computationally more efficient than the Direct Simulation Monte Carlo (DSMC) computations. One such set is the Burnett equations which are obtained from the Chapman-Enskog expansion of the Boltzmann equation (with Knudsen number (Kri) as a small parameter) to O(Kn). In this paper, the threedimensional augmented Burnett equations are derived from the Chapman-Enskog expansion of the Boltzmann equation to O(Kn) and adding the augmented terms (linear third-order super Burnett terms with coefficients determined from linearized stability analysis to ensure stability of the augmented Burnett equations to small wavelength disturbances). The equations are solved using an explicit time-stepping scheme with Steger-Warming flux-vector splitting algorithm for the convective flux terms and second-order central differencing for the stress and heat flux terms. Maxwell-Smoluchowski slip boundary conditions are employed at the wall. 3-D augmented Burnett equations solver is developed both in FORTRAN?? and object-oriented JAVA. Both the FORTRAN and JAVA codes are applied to compute the three-dimensional hypersonic blunt-body flows for various range of Knudsen numbers and Mach numbers producing identical results. The focus of this paper is on development of a JAVA code for a very complex set of equations and its application to 3-D complex configurations. x Graduate Research Assistant * Bloomfield Distinguished Professor and Executive Director, Fellow AIAA Copyright © by authors. Published by the American Institute of Aeronautics and Astronautics, Inc. with permission. NOMENCLATURE et total energy per unit mass E total flux vector in x direction Ej convective flux vector in x direction EV viscous flux vector in x direction F total flux vector in y direction F! convective flux vector in y direction Fv viscous flux vector in y direction G total flux vector in z direction GI convective flux vector in z direction GV viscous flux vector in z direction Kn Knudsen number L reference length M Mach number Pr Prandtl number P pressure qt heat flux terms Q unknown vector in physical domain rn nose radius Re Reynolds number R gas constant T temperature Tw wall temperature u velocity components in x direction v velocity components in y direction w velocity components in z direction a accommodation coefficient for wall surface a/, P/ coefficients of stress terms in augmented Burnett equations y/ coefficients of heat flux terms in augmented Burnett equations K thermal conductivity K mean free path of gas molecules ILI viscosity 0, coefficients of heat flux terms in augmented Burnett equations p density a,y stress tensor a reflection coefficient for wall surface Y specific heat ratio co, coefficients of stress terms in augmented Burnett equations w circular frequency of perturbation American Institute of Aeronautics and Astronautics

The Bhatnagar-Gross-Krook (BGK) model and its extensions (ellipsoidal statistical BGK, Shakhov BGK, and unified BGK) are used in particle-based fluid dynamics and compared with the Direct Simulation Monte Carlo (DSMC) method. To this end, different methods are investigated that allow efficient sampling of the Shakhov and the unified target distribution functions. As a consequence, particle simulations based on the Shakhov BGK and unified BGK models are possible in an efficient way. Furthermore, different energy conservation schemes are tested for the BGK models. It is shown that the choice of the energy conservation scheme has a major impact on the quality of the results for each model. The models are verified with a Couette flow problem at different Knudsen numbers and wall velocities. Furthermore, the models are compared with the DSMC results of a hypersonic flow around a 70° blunted cone. It is shown that the unified BGK model is able to reproduce rarefied gas phenomena. Furthermore, it is shown that the difference in the reproduction of the shock structure is not significant between the ellipsoidal statistical BGK and Shakhov BGK models for the flow around a 70° blunted cone and significantly depends on the energy conservation method. The choice of the energy conservation method is especially crucial for the Shakhov model whereas the ellipsoidal statistical BGK model is much more robust concerning the energy conservation scheme. Additionally, a computational time study is performed to show the efficiency of BGK-based simulations for low Knudsen number flows compared with DSMC.

The Direct Simulation Monte Carlo (DSMC) method was widely used to simulate low density gas flows with large Knudsen numbers. However, DSMC encounters limitations in the regime of lower Knudsen numbers (Kn<0.05). In such cases, approaches from classical computational fluid dynamics (CFD) relying on the continuum assumption are preferred, offering accurate solutions at acceptable computational costs. In experiments aimed at imaging aerosolized nanoparticles in vacuo a wide range of Knudsen numbers occur, which motivated the present study on the analysis of the advantages and drawbacks of DSMC and CFD simulations of rarefied flows in terms of accuracy and computational effort. Furthermore, the potential of hybrid methods is evaluated. For this purpose, DSMC and CFD simulations of the flow inside a convergent–divergent nozzle (internal expanding flow) and the flow around a conical body (external shock generating flow) were carried out. CFD simulations utilize the software OpenFOAM and the DSMC solution is obtained using the software SPARTA. The results of these simulation techniques are evaluated by comparing them with experimental data (1), evaluating the time-to-solution (2) and the energy consumption (3), and assessing the feasibility of hybrid CFD-DSMC approaches (4).

Flows of gas through nozzles with abrupt changes in cross-sectional area are often encountered in practice. In our case such nozzles are used as short length diffuser for producing a layer of organic light-emitting diodes. A hybrid Navier- Stokes/Direct Simulation Monte Carlo simulation is necessary here due to the strong decrease in pressure in the system related to an increase in the Knudsen number. Two popular software tools were coupled. For the domain, where the continuum theory is valid, ANSYS Fluent was chosen, which is one of the world wide leading simulation software for Navier-Stokes simulations. The open source CFD toolbox OpenFOAM includes a widely used Direct Simulation Monte Carlo (DSMC) solver. We coupled both solvers doing a one-shot NS-simulation in the whole domain and defined the boundary to the DSMC subdomain manually. Data are exchanged using Dirichlet-Dirichlet type boundary conditions. Our implementation was validated by comparing the results with two experiments. In this paper we describe our implementation and the test scenarios. It is shown that we get a very good agreement between the simulation and the experimental results.

Establishment of particle motion model and study of particle volume fraction distribution in the turbo air classifier based on DSMC

Rarefied flow conditions can have an impact on performance and radiation characterization at not only high-altitudes conditions but also for separated flow regions either behind blunt bodies or around divert jets at high continuum altitudes. Under rarefied flow conditions, standard continuum CFD methodologies fall short. More appropriate are Direct Simulation Monte Carlo (DSMC) techniques. However, DSMC techniques can quickly become intractable for flows that are either primarily rarefied and have small continuum regions, or, that are primarily continuum with regions of rarefied flow. The solution is to partition the flow into continuum and non-continuum regimes separated by an interface surface. Unfortunately, the interface surface can be quite complex leading to a substantial amount of ‘man-in-the-loop’ effort to obtain a surface that is both well-posed and compatible with the DSMC solver. An automated Arbitrary Breakdown Surface Generation procedure is developed to address this situation. This automated procedure not only reduces the amount of ‘man-in-the-loop’ effort but is also general enough to apply to a wide variety of continuum/non-continuum coupling problems. Particulates (from solid motors) are also of interest for high-altitude plume flowfields. Past efforts to simulate particles within the rarefied regime have decoupled the particulate simulation from the rarefied gas simulation. This inefficient process is eliminated by implementing particle integration directly into the DAC97 DSMC solver. Some generic straightback plume flow field simulations and divert jet studies serve to demonstrate the capabilities of these new procedures.

An airfoil, equipped with a curved-channel ABLE, is a good alternative to increase the lift-to-drag ratio. For this purpose, a curved-channel artificial blunted leading edge (ABLE) was applied to several supersonic/hypersonic symmetrical airfoils to analyse the aerodynamic performance in low-altitude supersonic continuous flow and high-altitude hypersonic rarefied flow during the process of re-entry into the atmosphere. The compressible Navier–Stokes equations were solved using the finite volume method to analyse the aerodynamic performance and determine the optimal curved-channel ABLE airfoil for supersonic continuous flow. Thereafter, the drag reduction and lift increment efficiency of the optimal ABLE airfoil were analysed in the hypersonic rarefied flow. The variation in the aerodynamic performance of the ABLE airfoil with the Knudsen number and freestream Mach number was determined using the direct simulation Monte Carlo (DSMC) method. The results showed that with suitable ABLE configuration and parameter values, the concept of ABLE can help reduce the drag coefficient, improve the lift coefficient, and obtain a better lift-to-drag ratio in both continuous and rarefied flows without considerable aerothermal penalty. However, the drag reduction effect of the curved-channel airfoil in the rarefied flow is much lower than that in the continuous flow, because of the lower proportion of the wave drag in the total drag, and the overall aerodynamic performance is significantly deteriorated because of the rarefaction effect of the atmosphere.

A hybrid particle scheme, which is based on the direct simulation Monte Carlo (DSMC) method and incorporates a low diffusion particle method for continuum flow simulation, is extended for improved efficiency and wider applicability. The hybrid scheme is intended for simulation of gas flows involving a wide range of Knudsen number regimes, where strong coupling is desired between calculations in rarefied and continuum flowfield regions. A series of modifications are presented for cell-based numerical weight and time step adaptation, diffusive transport of nonequilibrium internal energy modes, and decreased sensitivity to DSMC cell size. Proposed modifications are employed in a hybrid simulation of a Mach 20 flow around a cylinder with a global Knudsen number of 0.002, for which a factor of 2.6 efficiency increase relative to full DSMC computation is demonstrated. I. Introduction n a variety of gas flow problems, portions of the flowfield exhibit large translational nonequilibrium effects and require relatively expensive simulation techniques based on the Boltzmann equation, while other regions are within low Knudsen number (Kn) continuum flow regimes and can be prohibitively expensive to simulate using such Boltzmann equation techniques. These “multiscale” flow problems include flows around atmospheric entry vehicles and hypersonic aircraft, where local Kn values based on gradient length scales may be very small through much of the flowfield but become large within shock, forebody boundary layer and wake regions. Other examples include rocket exhaust plumes and fuel venting flows at high altitude, where the mean free path may differ by several orders of magnitude between nearfield and farfield regions. A. Simulation Methods for Multiscale Gas Flows Accurate simulations may be performed for some of these flows using a two step, one-way coupled approach. 1-3 In this type of approach, continuum and rarefied regions are considered independently and different simulation techniques are applied in each region. In general, however, effects of two-way coupling between rarefied and continuum regions must be considered, and a single simulation employing a coupled hybrid algorithm is required. In one popular type of hybrid algorithm, a computational fluid dynamics (CFD) technique based on the Navier-Stokes equations is used in low-Kn continuum regions, the direct simulation Monte Carlo (DSMC) method is employed in rarefied regions, and additional procedures are used for evaluation of continuum breakdown and two-way information transfer between CFD and DSMC calculations.