The particle-in-cell method has been used to obtain numerically the full, time-dependent development of the plane or cylindrical wake behind the flat base of a projectile moving with supersonic speed through air. Viscous and real-gas effects were neglected, but it is indicated how they could be incorporated into the calculation. Particular attention is paid to the case of Mach 1.89, arising from the passage of a very strong shock over a projectile at rest. Many features are shown of the transient build-up to statistically steady state, as well as of the late-time flow behavior. Comparisons between plane and cylindrical projectiles reveal a number of differences. Effects at higher Mach numbers are discussed briefly. I. Introduction H IGH-SPEED photographs of the flow of air about a supersonic projectile usually show the prominent structure indicated in Fig. 1. From these and other visible features, a number of details about the flow can be calculated or inferred, especially in the region outside of the wake. Within the wake itself, however, the behavior is less easily amenable to precise experimental analysis. Such properties as the timeaveraged fields of velocity, temperature, and density are difficult to obtain. Recent experimental papers1 ~3 show some of the techniques that have been successfully tried and include references to much of the earlier work. Other authors have introduced idealized models of the wake flow whose properties could be examined numerically,4 or analytically.57 The advantage of such an approach is that the achievement of agreement with some of the measured flow properties tends to confirm the physical basis of the model and to strengthen faith in the prediction of unmeasurables. The disadvantage of most models is that the restrictions required for analytical tractability are too stringent to reveal some of the most interesting flow features. Models for which numerical solution is accomplished by high-speed computer may not be so restricted, and it is the purpose of the present paper to show that such a model can be quite detailed in its presentation of the time-dependent flow throughout the entire near-wake region. We have used the particle-in-cell (PIC) method for numerical, multidimensional, time-dependent fluid dynamic studies to calculate several typical wake-flow problems. Transient effects were investigated for those examples in which flow was initiated by the diffraction of a shock about the projectile base. In those and higher Mach-number flows, the late-time statistically steady state was analyzed in detail. The calculations were performed without the inclusion of viscous or real-gas effects, but it is shown that one of the great advantages of the numerical model is that these effects are almost trivially simple to include. Use has been made of the symmetry of both the plane and cylindrical flows to reduce the number of spatial variables to two. The PIC method is well suited to hydrodynamic calculations in which multidimensional compressible flow involves large fluid distortions. We made use of a PIC code called VALLE which was written for the IBM 7030 (Stretch) Data Processing System. The computing method has been described in detail in previous literature811; thus, only a brief description will be given here. , The differential equations on which the computing method is based are those of mass, momentum, and energy conservation (dp/5*) + (u-V) P = -pV-u p(5u/50 + p(u-V) u = -Vp P(57/50 -f P(U-V)/ = -pV-u in which all symbols have their usual meanings. In the version of the method reported here, the effects of true viscosity and heat conduction have been neglected. The calculational system is based upon a rectangular mesh of fixed Eulerian cells through which the fluid moves. The fluid is represented by Lagrangian mass points called particles, each of which carries a fixed mass of fluid. The mass of each cell is represented by the sum of the particle masses within that cell. The calculation proceeds through a sequence of finite time steps in which the field variables are changed as follows: first, cell pressures are calculated from cellwise values of mass, volume, and specific internal energy. (For this problem we chose the simple gas equation of state with a fixed specific heat ratio.) From the gradients of these pressures, tentative new values of the two components of velocity are calculated, each of which is compared with a maximum allowable value. If the new value is too large, the calculation would become unstable, and so the time cycle interval is cut and the velocity calculation is restarted. Tentative new values of specific internal energy are also computed. In both cases, the values are tentative because o'f omission of transport

Equations are derived for multicomponent fuel evaporation of airborne fuel droplets and wall films, and are implemented as a multicomponent fuel model into KIVA-3V. Temporal and spatial variations in liquid droplet composition and temperature are not modeled but solved for by discretizing the interior of the droplet in an implicit and computationally efficient way. We find that an interior discretization is necessary to compute the evolution of the droplet composition correctly. This is because an interior discretization gives significantly improved results for the evolution of droplet compositions and temperatures over the alternatives of using infinite diffusivities or of using correlations based on the differences between surface and average values. Numerical simulations of the evaporation of single droplets, axisymmetric sprays, and sprays in 3-D engine geometries demonstrate the need for interior discretization and for using a multicomponent fuel model in gasoline spray simulations.

We derive equations for multicomponent fuel evaporation in airborne fuel droplets and wall films, and implement the model into KIVA-3V. Temporal and spatial variations in liquid droplet composition and temperature are not modelled but solved for by discretizing the interior of the droplet in an implicit and computationally efficient way. We find that an interior discretization is necessary to correctly compute the evolution of the droplet composition. The details of the one-dimensional numerical algorithm are described. Numerical simulations of multicomponent evaporation are performed for single droplets and compared to experimental data.

A new numerical technique is presented that has many advantages for obtaining solutions to a wide variety of time-dependent multidimensional fluid dynamics problems. The method uses a finite difference mesh with vertices that may be moved with the fluid (Lagrangian), be held fixed (Eulerian), or be moved in any other prescribed manner, as in the Arbitrary Lagrangian-Eulerian (ALE) technique. In addition, it employs an implicit formulation similar to that of the Implicit Continuous-fluid Eulerian (ICE) technique, making it applicable to flows at all speeds.This paper describes the basic methodology, presents finite difference approximations, and discusses such matters as stability, accuracy, and zoning. In addition, illustrations are included from a number of representative calculations. (C) 1974 Academic Press.

This report describes an extended version of KIVA-3, known as KIVA-3V, that can model any number of vertical or canted valves in the cylinder head of an internal combustion (IC) engine. The valves are treated as solid objects that move through the mesh using the familiar snapper technique used for piston motion in KIVA-3. Because the valve motion is modeled exactly, and the valve shapes are as exact as the grid resolution will allow, the accuracy of the valve model is commensurate with that of the rest of the program. Other new features in KIVA-3V include a particle-based liquid wall film model, a new sorting subroutine that is linear in the number of nodes and preserves the original storage sequence, a mixing-controlled turbulent combustion model, and an optional RNG {kappa}-{epsilon} turbulence model. All features and capabilities of the original KIVA-3 have been retained. The grid generator, K3PREP, has been expanded to support the generation of grids with valves, along with the shaping of valve ports and runners. Graphics output options have also been expanded. The report discusses the new features, and includes four examples of grids with vertical and canted valves that are representative of IC engines in use today.

The planned use of hydrogen as the energy carrier of the future introduces new challenges and opportunities, especially to the engine design community. Hydrogen is a bio-friendly fuel that can be produced from renewable resources and has no carbon dioxide combustion products; and in a properly designed ICE, almost zero NO{sub x} and hydrocarbon emissions can be achieved. Because of the unique properties of hydrogen combustion - in particular the highly wrinkled nature of the laminar flame front due to the preferential diffusion instability - modeling approaches for hydrocarbon gaseous fuels are not generally applicable to hydrogen combustion. This paper reports on the current progress to develop a engine design capability based on KIVA family of codes for hydrogen-fueled, spark-ignited engines in support of the National Hydrogen Program. A turbulent combustion model, based on a modified eddy-turnover model in conjunction with an intake flow valve model, is found to describe well the efficiency and NO{sub x} emissions of this engine satisfy the Equivalent Zero Emission Vehicle (EZEV) standard established by the California Resource Board. 26 refs., 10 figs., 1 tab.

To help predict hydrocarbon emissions during cold-start conditions the authors are developing a numerical model for the dynamics and vaporization of the liquid wall films formed in port-injected spark-ignition engines and incorporating this model in the KIVA-3 code for complex geometries. This paper summarizes the current status of the project and presents illustrative example calculations. The dynamics of the wall film is influenced by interactions with the impinging spray, the wall, and the gas flow near the wall. The spray influences the film through mass, tangential momentum, and energy addition. The wall affects the film through the no-slip boundary condition and heat transfer. The gas alters film dynamics through tangential stresses and heat and mass transfer in the gas boundary layers above the films. New wall functions are given to predict transport in the boundary layers above the vaporizing films. It is assumed the films are sufficiently thin that film flow is laminar and that liquid inertial forces are negligible. Because liquid Prandtl numbers are typically about then, unsteady heating of the film should be important and is accounted for by the model. The thin film approximation breaks down near sharp corners, where an inertial separation criterion is used. A particle numerical method is used for the wall film. This has the advantages of compatibility with the KIVA-3 spray model and of very accurate calculation of convective transport of the film. The authors have incorporated the wall film model into KIVA-3, and the resulting combined model can be used to simulate the coupled port and cylinder flows in modern spark-ignition engines. They give examples by comparing computed fuel distributions with closed- and open-valve injection during the intake and compression strokes of a generic two-valve engine.

We have significantly increased our computational modeling capability by the addition of a vertical valve model in KIVA-3, code used internationally for engine design. In this report the implementation and application of the valve model is described. The model is shown to reproduce the experimentally verified intake flow problem examined by Hessel. Furthermore, the sensitivity and performance of the model is examined for the geometry and conditions of the hydrogen-fueled Onan engine in development at Sandia National Laboratory. Overall the valve model is shown to have comparable accuracy as the general flow simulation capability in KIVA-3, which has been well validated by past comparisons to experiments. In the exploratory simulations of the Onan engine, the standard use of the single kinetic reaction for hydrogen oxidation was found to be inadequate for modeling the hydrogen combustion because of its inability to describe both the observed laminar flame speed and the absence of autoignition in the Onan engine. We propose a temporary solution that inhibits the autoignition without sacrificing the ability to model spark ignition. In the absence of experimental data on the Onan engine, a computational investigation was undertaken to evaluate the importance of modeling the intake flow on the combustionmore » and NO{sub x} emissions. A simulation that began with the compression of a quiescent hydrogen-air mixture was compared to a simulation of the full induction process with resolved opening and closing of the intake valve. Although minor differences were observed in the cylinder-averaged pressure, temperature, bulk-flow kinetic energy and turbulent kinetic energy, large differences where observed in the hydrogen combustion rate and NO{sub x} emissions. The flow state at combustion is highly heterogeneous and sensitive to the details of the bulk and turbulent flow and that an accurate simulation of the Onan engine must include the modeling of the air-fuel induction.« less

The design considerations and computational fluid dynamics (CFD) modeling of a high efficiency, low emissions, hydrogen-fueled engine for use as the prime mover of a series hybrid automobile is described. The series hybrid automobile uses the engine to generate electrical energy via a lightweight generator, the electrical energy is stored in a power peaking device (like a flywheel or ultracapacitor) and used as required to meet the tractive drive requirements (plus accessory loads) through an electrical motor. The engine/generator is stopped whenever the energy storage device is fully charged. Engine power output required was determined with a vehicle simulation code to be 15 to 20 kW steady state with peak output of 40 to 45 kW for hill climb. Combustion chamber and engine geometry were determined from a critical review of the hydrogen engine experiments in the literature combined with a simplified global engine model. Two different engine models are employed to guide engine design. The models are a simplified global engine performance model that relies strongly on correlations with literature data for heat transfer and friction losses, and a state-of-the-art CFD combustion model, KIVA-3, to elucidate fluid mechanics and combustion details through full three-dimensional modeling. Both intake and exhaust processes as well as hydrogen combustion chemistry and thermal NO{sub x} production are simulated. Ultimately, a comparison between the simulation and experimental results will lead to improved modeling and will give guidance to changes required in the next generation engine to achieve the goal of 45% brake thermal efficiency.

KIVA-3 is the latest version of a 3-D Finite Difference CFD code developed by Amsden for combustion engine simulations. A distributed-memory implementation has many advantages for problems that hardly fit affordable existing memory banks. Previous attempts to parallelize KIVA-2 by Yasar, et al. were focused mostly on diffusion solvers because of their heavy time consumption during execution. The study suggested a complete parallelization of the code, including advection and spray dynamics, along with the use of a block-wise decomposition scheme to assure an efficient load balancing and a low communication/computation ratio. Here, the authors report rather a general analysis of the issues involved in such a distributed implementation for the latest version of the code, KIVA-3, on MIMD parallel systems. A more detailed analysis of the code and corresponding algorithms have already been implemented by Yasar and will be published soon.

The authors discuss a case history of technology transfer from a government laboratory to industry, to other laboratories, and to universities. The technology transferred is a computer program named KIVA that simulates air flow, fuel sprays, and combustion in practical combustion devices such as a automobile and truck engines, gas turbines that power jet aircraft, and industrial furnaces, heaters,...