Abstract Some strategies for calculating the effects of chemical reactions in large, multidimensi... more Abstract Some strategies for calculating the effects of chemical reactions in large, multidimensional finite-difference computer codes require the equilibrium gas composition as an input. Because the equilibrium problem must be solved a large number of times, it is essential that the equilibrium solver be fast and reliable. An existing solver is a variant of the Gauss-Seidel technique, and its performance can be predicted and quantified. It is relatively fast, but can be unreliable. By contrast, Newton's method is slower but more reliable. A hierarchical algorithm, in which recourse is made to Newton's method if Gauss-Seidel iteration fails, is shown to combine the speed of Gauss-Seidel and the reliability of Newton. The hierarchical solver has been incorporated into the CONCHAS computer code. The reliability of the code is improved, and there is a decrease in the amount of computer time required. The new algorithm has not failed during production runs of CONCHAS, but it has failed to find the solution of some special test problems.
This paper describes a methodology for solving chemical equilibrium systems. The methodology is e... more This paper describes a methodology for solving chemical equilibrium systems. The methodology is especially appropriate when many systems with the same structure must be solved quickly, as in finite...
A system of nonlinear equations has been used as a test case by at least two authors. This system... more A system of nonlinear equations has been used as a test case by at least two authors. This system is purported to describe the equilibrium of the products of hydrocarbon combustion. The given system does not describe the stated physical problem, a fact which invalidates it as a test of solution methods for chemical equilibrium systems. In this note, the problem is correctly stated and then solved by the method of element variables.
Computer simulations are compared with measurements of the threedimensional, unsteady scavenging ... more Computer simulations are compared with measurements of the threedimensional, unsteady scavenging flows of a motored two-stroke engine. Laser Doppler velocimetry measurements were made on a modified Suzuki DT-85 ported engine. Calculations were performed using KIVA-3, a computer program that efficiently solves the intake and exhaust port flows along with those in the cylinder. Measured and computed cylinder pressures and velcOties are compared. Pressures agree well over the cycle as do the velecities at the intake , ports. In-cylinder velocities differ in detail, but the tumbling motion in the cylinder is well replicated in a vertical plane passing through the cylinder axis. INTRODUCTION" Over the past _everal years, computational fluid dynamics (CFD) has been increasingly accepted as an adjunct to experimentation in the design and understanding of practical combustion systems. A major goal in the engine modeling effort, the calculation of three-dimensional ermine flows with spray and combustion, was realized in 1987.1, 2 Since that time, three-dimensional studies with spray and/or combustion have become commonplace in the literature. 3-9 A recent patent for a high-turbulence piston design specifically identifies threedimensional computer simulation for making the inver, tion possible. 10 Analyzing the scavenging flows of an operating two-stroke engine presents another opportunity for advancement in the sophistication and comprehensiveness of computational models and their associated verification experiments. This is a particularly challenging area in which experiment and modeling can play complementary roles in the desigrJ process, because the calculations can readily give information on scavenging that cannot be obtained experimentally. However, calculating these flows necessitates simultaneously solving for the flows in the connecting intake and exhaust channels as well as the cylinder. Flows in these channels strongly affect the scavenging process and cannot, in general, be supplied merely as boundary conditions to the in-cylinder flows. This paper presents the results of a combined theoretical and experimental study of a Suzuki DT-85 crankcase-compression, loop-scavenged, two-stroke engine operating in a motored (non-firing) mode. The purpose is to see how well
A two stroke cycle internal combustion engine is described including a cylinder having an axis an... more A two stroke cycle internal combustion engine is described including a cylinder having an axis and closed at one end, a piston reciprocable in the cylinder and having a top wall movable into closely opposed relation with the cylinder closed end, and inlet and exhaust ports in the cylinder at substantially diametrically opposite locations and controlled by reciprocating motion of the piston, the cylinder closed end including a squish portion adapted to closely confront the piston top wall at its extreme upward position and a recess extending upward from a modified delta shaped base in the squish portion to form a combustion chamber cavity with an outer wall, an inner wall and two side walls, the outer wall rising with an inward slope from an arcuate edge of the base adjacent and parallel with the cylinder portion above the inlet port, the side walls rising from opposite angled edges of the base extending laterally and angularly inward from opposite ends of the arcuate edge toward a p...
Abstract Some strategies for calculating the effects of chemical reactions in large, multidimensi... more Abstract Some strategies for calculating the effects of chemical reactions in large, multidimensional finite-difference computer codes require the equilibrium gas composition as an input. Because the equilibrium problem must be solved a large number of times, it is essential that the equilibrium solver be fast and reliable. An existing solver is a variant of the Gauss-Seidel technique, and its performance can be predicted and quantified. It is relatively fast, but can be unreliable. By contrast, Newton's method is slower but more reliable. A hierarchical algorithm, in which recourse is made to Newton's method if Gauss-Seidel iteration fails, is shown to combine the speed of Gauss-Seidel and the reliability of Newton. The hierarchical solver has been incorporated into the CONCHAS computer code. The reliability of the code is improved, and there is a decrease in the amount of computer time required. The new algorithm has not failed during production runs of CONCHAS, but it has failed to find the solution of some special test problems.
This paper describes a methodology for solving chemical equilibrium systems. The methodology is e... more This paper describes a methodology for solving chemical equilibrium systems. The methodology is especially appropriate when many systems with the same structure must be solved quickly, as in finite...
A system of nonlinear equations has been used as a test case by at least two authors. This system... more A system of nonlinear equations has been used as a test case by at least two authors. This system is purported to describe the equilibrium of the products of hydrocarbon combustion. The given system does not describe the stated physical problem, a fact which invalidates it as a test of solution methods for chemical equilibrium systems. In this note, the problem is correctly stated and then solved by the method of element variables.
... NSRDS-NBS 37, National Bureau of Standards, Washington, DC van Zeggeren, F. andStorey, SH (19... more ... NSRDS-NBS 37, National Bureau of Standards, Washington, DC van Zeggeren, F. andStorey, SH (1970). The Computation ofChemical Equilibria. Cambridge University Press, Cambridge. Watson, LT, Billups, SC and Morgan. AP (1987). ...
Abstract Some strategies for calculating the effects of chemical reactions in large, multidimensi... more Abstract Some strategies for calculating the effects of chemical reactions in large, multidimensional finite-difference computer codes require the equilibrium gas composition as an input. Because the equilibrium problem must be solved a large number of times, it is essential that the equilibrium solver be fast and reliable. An existing solver is a variant of the Gauss-Seidel technique, and its performance can be predicted and quantified. It is relatively fast, but can be unreliable. By contrast, Newton's method is slower but more reliable. A hierarchical algorithm, in which recourse is made to Newton's method if Gauss-Seidel iteration fails, is shown to combine the speed of Gauss-Seidel and the reliability of Newton. The hierarchical solver has been incorporated into the CONCHAS computer code. The reliability of the code is improved, and there is a decrease in the amount of computer time required. The new algorithm has not failed during production runs of CONCHAS, but it has failed to find the solution of some special test problems.
This paper describes a methodology for solving chemical equilibrium systems. The methodology is e... more This paper describes a methodology for solving chemical equilibrium systems. The methodology is especially appropriate when many systems with the same structure must be solved quickly, as in finite...
A system of nonlinear equations has been used as a test case by at least two authors. This system... more A system of nonlinear equations has been used as a test case by at least two authors. This system is purported to describe the equilibrium of the products of hydrocarbon combustion. The given system does not describe the stated physical problem, a fact which invalidates it as a test of solution methods for chemical equilibrium systems. In this note, the problem is correctly stated and then solved by the method of element variables.
Computer simulations are compared with measurements of the threedimensional, unsteady scavenging ... more Computer simulations are compared with measurements of the threedimensional, unsteady scavenging flows of a motored two-stroke engine. Laser Doppler velocimetry measurements were made on a modified Suzuki DT-85 ported engine. Calculations were performed using KIVA-3, a computer program that efficiently solves the intake and exhaust port flows along with those in the cylinder. Measured and computed cylinder pressures and velcOties are compared. Pressures agree well over the cycle as do the velecities at the intake , ports. In-cylinder velocities differ in detail, but the tumbling motion in the cylinder is well replicated in a vertical plane passing through the cylinder axis. INTRODUCTION" Over the past _everal years, computational fluid dynamics (CFD) has been increasingly accepted as an adjunct to experimentation in the design and understanding of practical combustion systems. A major goal in the engine modeling effort, the calculation of three-dimensional ermine flows with spray and combustion, was realized in 1987.1, 2 Since that time, three-dimensional studies with spray and/or combustion have become commonplace in the literature. 3-9 A recent patent for a high-turbulence piston design specifically identifies threedimensional computer simulation for making the inver, tion possible. 10 Analyzing the scavenging flows of an operating two-stroke engine presents another opportunity for advancement in the sophistication and comprehensiveness of computational models and their associated verification experiments. This is a particularly challenging area in which experiment and modeling can play complementary roles in the desigrJ process, because the calculations can readily give information on scavenging that cannot be obtained experimentally. However, calculating these flows necessitates simultaneously solving for the flows in the connecting intake and exhaust channels as well as the cylinder. Flows in these channels strongly affect the scavenging process and cannot, in general, be supplied merely as boundary conditions to the in-cylinder flows. This paper presents the results of a combined theoretical and experimental study of a Suzuki DT-85 crankcase-compression, loop-scavenged, two-stroke engine operating in a motored (non-firing) mode. The purpose is to see how well
A two stroke cycle internal combustion engine is described including a cylinder having an axis an... more A two stroke cycle internal combustion engine is described including a cylinder having an axis and closed at one end, a piston reciprocable in the cylinder and having a top wall movable into closely opposed relation with the cylinder closed end, and inlet and exhaust ports in the cylinder at substantially diametrically opposite locations and controlled by reciprocating motion of the piston, the cylinder closed end including a squish portion adapted to closely confront the piston top wall at its extreme upward position and a recess extending upward from a modified delta shaped base in the squish portion to form a combustion chamber cavity with an outer wall, an inner wall and two side walls, the outer wall rising with an inward slope from an arcuate edge of the base adjacent and parallel with the cylinder portion above the inlet port, the side walls rising from opposite angled edges of the base extending laterally and angularly inward from opposite ends of the arcuate edge toward a p...
Abstract Some strategies for calculating the effects of chemical reactions in large, multidimensi... more Abstract Some strategies for calculating the effects of chemical reactions in large, multidimensional finite-difference computer codes require the equilibrium gas composition as an input. Because the equilibrium problem must be solved a large number of times, it is essential that the equilibrium solver be fast and reliable. An existing solver is a variant of the Gauss-Seidel technique, and its performance can be predicted and quantified. It is relatively fast, but can be unreliable. By contrast, Newton's method is slower but more reliable. A hierarchical algorithm, in which recourse is made to Newton's method if Gauss-Seidel iteration fails, is shown to combine the speed of Gauss-Seidel and the reliability of Newton. The hierarchical solver has been incorporated into the CONCHAS computer code. The reliability of the code is improved, and there is a decrease in the amount of computer time required. The new algorithm has not failed during production runs of CONCHAS, but it has failed to find the solution of some special test problems.
This paper describes a methodology for solving chemical equilibrium systems. The methodology is e... more This paper describes a methodology for solving chemical equilibrium systems. The methodology is especially appropriate when many systems with the same structure must be solved quickly, as in finite...
A system of nonlinear equations has been used as a test case by at least two authors. This system... more A system of nonlinear equations has been used as a test case by at least two authors. This system is purported to describe the equilibrium of the products of hydrocarbon combustion. The given system does not describe the stated physical problem, a fact which invalidates it as a test of solution methods for chemical equilibrium systems. In this note, the problem is correctly stated and then solved by the method of element variables.
... NSRDS-NBS 37, National Bureau of Standards, Washington, DC van Zeggeren, F. andStorey, SH (19... more ... NSRDS-NBS 37, National Bureau of Standards, Washington, DC van Zeggeren, F. andStorey, SH (1970). The Computation ofChemical Equilibria. Cambridge University Press, Cambridge. Watson, LT, Billups, SC and Morgan. AP (1987). ...
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