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The basic numerical techniques used for the direct simulation of transition to turbulence are described. Applications are presented for the computation of finite amplitude, two-dimensional steady states, the simulation of the secondary instability of channels and boundary-layers, and the simulation of the breakdown of detached shear layers.
Measurements of Pitot pressure and flow angle were made in the plume of a nozzle flowing nitrogen and exhausting to a vacuum. The measurements were compared to results from a numerical simulation of the flow that was based on kinetic theory and used the direct-simulation Monte Carlo (DSMC) method. Numerical results were compared with measurements made in the plume at various axial and radial stations. Total pressure measurements were made with Pitot tubes sized for specific regions of the plume. Flow angle measurements were made with a conical probe. The measurement area for flow angle extended to 160 mm (5 exit diameters) downstream of the nozzle exit plane and radially to 60 mm (1.9 exit diameters) from the plume axis. The total pressure measurements extended 480 mm (16 exit diameters) downstream and radially to 60 mm. Comparisons of computed results from the DSMC method with measurements of flow angle displayed improved agreement with increasing distance from the exit plane. Pitot pressures computed from the DSMC method were in reasonably good agreement with experimental results over the entire measurement area.
Physical processes that form the spectra of saturated absorption and magnetic scanning resonances on an atomic transition with level momentum J = 1 in the field of unidirectional waves of arbitrary intensity under variation in their polarization directions are investigated by numerical simulation and analytically. It is shown that anomalies in nonlinear resonance spectra are determined by the polarization of the waves and the degree of openness of the atomic transition, while anomalies in the experimentally observed magnetic scanning spectra are attributed to the magnetic coherence induced by the fields directly on the levels of the lower state, rather than to its transfer from the excited states, as was assumed earlier.
Numerical results obtained with the direct simulation Monte Carlo (DSMC) method are presented for Mach 20 nitrogen flow about a 70-deg blunted cone. The flow conditions simulated are those that can be obtained in existing low-density hypersonic wind tunnels. Three sets of flow conditions are simulated with freestream Knudsen numbers ranging from 0.03 to 0.001. The focus is to characterize the wake flow under rarefied conditions. This is accomplished by calculating the influence of rarefaction on wake structure along with the impact that an afterbody has on flow features. This data report presents extensive information concerning flowfield features and surface quantities.
Using classical nucleation theory we consider transient nucleation occurring in a one-component, condensed system under isothermal conditions. We obtain an exact closed-form expression for the time dependent cluster populations. In addition, a more versatile approach is developed: a numerical simulation technique which models directly the reactions by which clusters are produced. This simulation demonstrates the evolution of cluster populations and nucleation rate in the transient regime. Results from the simulation are verified by comparison with exact analytical solutions for the steady state. Experimental methods for measuring transient nucleation are assessed, and it is demonstrated that the observed behavior depends on the method used. The effect of preexisting cluster distributions is studied. Previous analytical and numerical treatments of transient nucleation are compared to the solutions obtained from the simulation. The simple expressions of Kashchiev are shown to give good descriptions of the nucleation behavior.
Computational fluid dynamics (CFD) has made great strides in the detailed simulation of complex fluid flows, including some of those not before understood. It is now being routinely applied to some rather complicated problems and starting to affect the design cycle of aerospace flight vehicles and their components. It is being used to complement, and is being complemented by, experimental studies. Several examples are presented in the paper to illustrate the current state of the art. Included is a discussion of the barriers to accomplishing the basic objective of numerical simulation. In addition, the directions for the future in the discipline of computational fluid dynamics are addressed.
Turbulent flows that exhibit inhomogeneities in the streamwise direction pose a particular challenge to numerical simulation approaches due to the need to prescribe time-dependent turbulent inflow conditions. In most cases the flow downstream is more or less 'driven' by the conditions at the inlet, making it necessary to specify realistic turbulent fluctuations that are in equilibrium with the assumed mean flow. This requirement often dictates that the inflow data should satisfy the Navier-Stokes equations, which in turn implies that an independent simulation be used to generate them. Detailed simulations for the purpose of creating inflow conditions can be costly and thus certain levels of approximation are desirable. In this paper we shall focus on an approximate yet accurate method for generating inflow conditions for spatially-developing boundary layer simulations. The proposed method is essentially a simplification of the method of Spalart and Leonard (1985), who devised an ingenious transformation that allows for the calculation of spatially evolving boundary layers in conjunction with periodic boundary conditions applied in the streamwise direction. While this method is elegant and highly accurate, it is more complicated than is necessary for the purpose of generating inflow data. A few key approximations are used in this work to arrive at a 'modified Spalart method' that is very easy to implement and efficient to use. The new method is shown to yield results that compare well with the computations of Spalart (1988). When used as a means of generating inflow data, the modified Spalart method is shown to be superior to existing approaches.
Physics-based numerical simulation codes are widely used in science and engineering to model complex systems that would be infeasible to study otherwise. While such codes may provide the highest- fidelity representation of system behavior, they are often so slow to run that insight into the system is limited. Trying to understand the effects of inputs on outputs by conducting an exhaustive grid-based sweep over the input parameter space is simply too time-consuming. An alternative approach called "directed exploration" has been developed to harvest information from numerical simulators more efficiently. The basic idea is to employ active learning and supervised machine learning to choose cleverly at each step which simulation trials to run next based on the results of previous trials. SIM_EXPLORE is a new computer program that uses directed exploration to explore efficiently complex systems represented by numerical simulations. The software sequentially identifies and runs simulation trials that it believes will be most informative given the results of previous trials. The results of new trials are incorporated into the software's model of the system behavior. The updated model is then used to pick the next round of new trials. This process, implemented as a closed-loop system wrapped around existing simulation code, provides a means to improve the speed and efficiency with which a set of simulations can yield scientifically useful results. The software focuses on the case in which the feedback from the simulation trials is binary-valued, i.e., the learner is only informed of the success or failure of the simulation trial to produce a desired output. The software offers a number of choices for the supervised learning algorithm (the method used to model the system behavior given the results so far) and a number of choices for the active learning strategy (the method used to choose which new simulation trials to run given the current behavior model). The software also makes use of the LEGION distributed computing framework to leverage the power of a set of compute nodes. The approach has been demonstrated on a planetary science application in which numerical simulations are used to study the formation of asteroid families.
Crack growth under coupled creep-fatigue strongly influences service life of metallic components operating at high temperatures. However, there lack numerical models that enable direct simulations of crack growth and plasticity development under coupled creep-fatigue. Here, in this study, a unified phase-field model is developed for simulating crack growth under fatigue, creep, and coupled creep-fatigue. This model is able to reproduce the Paris laws for both brittle and ductile materials in pure fatigue mode, which shows that the degradation rate due to cyclic stress in ductile materials is generally larger than that in brittle materials. Fatigue simulations with different yield strengths demonstrate that plasticity facilitates crack growth in typical ductile materials. High-throughput simulations are performed under coupled creep-fatigue conditions, with varying hold-stress levels and hold-time. By analyzing crack growth rate under different hold-time, a creep-fatigue interaction term is obtained. Simulation results demonstrate that the creep-fatigue interaction is caused by smaller stress gradient and enhanced degradation rate ahead of the crack tips under coupled creep-fatigue, compared to the situation of pure fatigue. This work reveals the origin of different Paris-law exponents in brittle and ductile materials and demonstrates how the interplay between creep and fatigue affects crack growth.
The linear dispersion relation for collisionless kinetic tearing instabilities is calculated for the Harris equilibrium. In contrast to the conventional 2D geometry, which considers only modes at the center of the current sheet, modes can span the current sheet in 3D. Modes at each resonant surface have a unique angle with respect to the guide field direction. Both kinetic simulations and numerical eigenmode solutions of the linearized Vlasov-Maxwell equations have recently revealed that standard analytic theories vastly overestimate the growth rate of oblique modes. In this paper, we find that this stabilization is associated with the density-gradient-driven diamagnetic drift. The analytic theories miss this drift stabilization because the inner tearing layer broadens at oblique angles sufficiently far that the assumption of scale separation between the inner and outer regions of boundary-layer theory breaks down. The dispersion relation obtained by numerically solving a single second order differential equation is found to approximately capture the drift stabilization predicted by solutions of the full integro-differential eigenvalue problem. Finally, a simple analytic estimate for the stability criterion is provided.
Efficient thermal management of power electronics systems is crucial for higher reliability. With the miniaturization of systems, high-loss-density electronics require cooling systems that can extract a large amount of heat. This study explored a liquid-jet-impingement-based direct substrate cooling system for single-sided and double-sided cooling to improve heat extraction efficiency and improve the power density by reducing the volume and mass. The cooling system was implemented for a SiC-based direct bonded copper substrate. Numerical simulations were performed to determine the effects of nozzle diameter, the number of nozzles, and nozzle array orientation on single-sided cooling and thermal performance gain over double-sided cooling. A novel manifold design was proposed that reduced the volume and mass of the manifold and still achieved the target power density. The performance of the proposed design was compared with the pin-fin-based cooling system used in the BMW I3 module, and a comparative analysis was done.
This paper extends the finite element scheme to handle the highly nonlinear interfacial fields generated in the fluid filled annulli of squeeze film and journal bearings so as to model the transient response of rotor-bearing-stator systems. Since such simulations are highly nonlinear, direct numerical integration schemes are employed to generate the overall response. In this context, the paper gives consideration to such items as (1) numerical efficiency/stability, (2) comparison of implicit and explicit schemes, (3) determines extent of response nonlinearity as well as (4) extensively benchmarks the overall concept/methodologies.
Presented are the results of numerical simulations of hypersonic flow about blunt cones and hemispherical nose configurations for reentry velocities of 7.5 and 10 km/s. Cone half angles 0, 5, and 10 deg are considered at zero angle of incidence; however, the focus is for the 5 deg cone. The body size and altitude ranges considered (70 to 110 km) are such that the flow is in the transitional regime. Translational, thermodynamic, and chemical nonequilibrium effects are considered in the numerical simulation by utilizing the direct simulation Monte Carlo (DSMC) method of Bird. The DSMC results are compared with those obtained with viscous shock-layer and Navier-Stokes methods. Comparisons between the DSMC and continuum calculations show the altitude range where differences in flowfield structure and surface quantities become significant. The current calculations show that the binary scaling similitude provides a means of correlating the blunt body surface quantities in the hypersonic, transitional regime. Furthermore, for the higher velocity entry conditions, the results highlight some of the concerns in the application of multitemperature continuum formulations, particularly the use of some proposed functional relations for the chemical rate constants under thermodynamic nonequilibrium conditions.
Results of a numerical study using the direct simulation Monte Carlo (DSMC) method are presented for the transitional flow about a flat plate at 40 deg incidence. The plate has zero thickness and a length of 1.0 m. The flow conditions simulated are those experienced by the Shuttle Orbiter during reentry at 7.5 km/s. The range of freestream conditions are such that the freestream Knudsen number values are between 0.02 and 8.4, i.e., conditions that encompass most of the transitional flow regime. The DSMC simulations show that transitional effects are evident when compared with free molecule results for all cases considered. The calculated results demonstrate clearly the necessity of having a means of identifying the effects of transitional flow when making aerodynamic flight measurements as are currently being made with the Space Shuttle Orbiter vehicles. Previous flight data analyses have relied exclusively on adjustments in the gas-surface interaction models without accounting for the transitional effect which can be comparable in magnitude. The present calculations show that the transitional effect at 175 km would increase the Space Shuttle Orbiter lift-drag ratio by 90 percent over the free molecule value.
Results of a numerical study using the direct simulation Monte Carlo (DSMC) method are presented for the transitional flow about a flat plate at 40 deg incidence. The plate has zero thickness and a length of 1.0 m. The flow conditions simulated are those experienced by the Shuttle Orbiter during reentry at 7.5 km/s. The range of freestream conditions are such that the freestream Knudsen number values are between 0.02 and 8.4, i.e., conditions that encompass most of the transitional flow regime. The DSMC simulations show that transitional effects are evident when compared with free molecule results for all cases considered. The calculated results demonstrate clearly the necessity of having a means of identifying the effects of transitional flow when making aerodynamic flight measurements as are currently being made with the Space Shuttle Orbiter vehicles. Previous flight data analyses have relied exclusively on adjustments in the gas-surface interaction models without accounting for the transitional effect which can be comparable in magnitude. The present calculations show that the transitional effect at 175 km would increase the Space Shuttle Orbiter lift-drag ratio by 90 percent over the free molecule value.
The interaction of an oblique, overdriven detonation wave with a vorticity disturbance is investigated by a direct two-dimensional numerical simulation using a multi-domain, finite-difference solution of the compressible Euler equations. The results are compared to those of linear theory, which predict that the effect of exothermicity on the interaction is relatively small except possibly near a critical angle where linear theory no longer holds. It is found that the steady-state computational results agree with the results of linear theory. However, for cases with incident angle near the critical angle, moderate disturbance amplitudes, and/or sudden transient encounter with a disturbance, the effects of exothermicity are more pronounced than predicted by linear theory. Finally, it is found that linear theory correctly determines the critical angle.
A computational method is given for the prediction of local pressure and viscous shear stress on windward surfaces of bluff, convex, axisymmetric or quasi-axisymmetric, hypersonic bodies in the transitional, rarefied flow regime. Overall aerodynamic forces and moments are computed by integration of the local quantities. The method is based upon a correlation of local pressure and shear stress computed by the direct simulation Monte Carlo (DSMC) numerical technique for cold wall, real gas conditions and some supplemental data from low-density, hypersonic wind tunnels. The relative simplicity of the method makes it feasible to do the necessary calculations with a personal computer. Two-dimensional shapes and leeward surfaces are not included in the scope of the method as it is presented here. Results are compared with DSMC computations for both local and overall coefficients. The latter includes sphere and blunt cone drag as well as lift and pitching moment coefficients for the NASA AFE vehicle at various angles of attack. Very satisfactory agreement is shown.
Results of a numerical study using the direct simulation Monte Carlo (DSMC) method are presented for hypersonic rarefied flow about a 1.6-m-diameter sphere. The flow conditions considered are those experienced by a typical satellite in orbit or by a space vehicle during entry. The altitude range considered is that from 90 to 200 km, which encompasses the near continuum, transitional and free-molecular flow regimes. A freestream velocity of 7.5 km/s is assumed in the simulations. The results show that transitional effects are significant at all altitudes below 200 km, but at 200 km the flow about the sphere attains the free-molecular limit. Very little chemical activity is present above 120 km. Both the stagnation point heat transfer and the sphere drag approach their respective free molecule values at 200 km. Results highlight the thermal and chemical nonequilibrium nature of the flowfield. Nonequilibrium effects on the surface heating and body drag are also investigated.