John Steinhoff - Academia.edu (original) (raw)
Papers by John Steinhoff
WORLD SCIENTIFIC eBooks, Dec 1, 2001
A technique, "Vorticity Confinement", is described that represents a very effective, un... more A technique, "Vorticity Confinement", is described that represents a very effective, unified way of treating complex, high Reynolds number separated flows with thin convecting vortices, as well as complex solid bodies with thin attached boundary layers. Vorticity Confinement involves, essentially, treating vortical regions as nonlinear solitary waves that "live" on the grid lattice. The basic assumptions mainly involve using the solitary wave structure as a model for the vortical region. At high Reynolds number, this then represents a fundamentally discrete turbulence model since these regions are then typically turbulent. First, drawbacks of conventional Eulerian computational methods particularly for treating thin, convecting vortices are described. Then, how Vorticity Confinement, which is also Eulerian, eliminates these problems. The basic assumptions in Vorticity Confinement are then reviewed and some details of the method are described. Following the description, a sequence of results are presented: First, 2-D results for convecting vortices and flow over a cylinder are presented. These describe the salient features of the method for convecting vortices and for flow over solid surfaces, embedded in a uniform Cartesian grid. Then, 3-D results for flow over complex bodies, including rotorcraft, are presented.
National Computer Conference, 1978
In the last several years, minicomputer based systems have been considered or used for an increas... more In the last several years, minicomputer based systems have been considered or used for an increasing number of scientific computing tasks. For example, Kottler and McGilP used a minicomputer system to solve a series of problems, including a partial differential equation for pollutant dispersal. Also, in 1973, Steven Orszag compared a minicomputer system to large general purpose machines for solving some time dependent hydrodynamics codes. The conclusions were that minicomputers could be more cost effective than the large machines. In particular, Orszag concluded that the minicomputer was more cost effective than a CDC 7600 but less than a CDC STAR for moderate resolution hydrodynamics codes. For these problems, the data bases are large and the system is essentially a disk based one, where data flows from a large data base on the disk to the computer. When these studies were done, disk speed was not a restriction and the limiting factor was the computational speed of the minicomputer. In the last several years, improvements in LSI technology have made it possible to assemble reliable computational devices with a much lower cost per computation than mini"' computers. These devices, ranging from moderately priced (-$100,000) fast systems with tightly coupled multiple functional units to very inexpensive simple units can be very cost effective when used with a minicomputer as host. They have had a large impact on the signal processing field, 3 in some cases proving to be faster than large machines such as the CDC 7600. They can also be effective for real-time simulation, as described in Reference 4. In this paper we will describe a study that was done on the effectiveness of a minicomputer based system with moving head disk and peripheral processor for a class of fluid flow problems. It is easy to see that a moderately priced system can be assembled that would have a (disk) data capacity and contiguous block throughput and a (peripheral) computational speed of a large multi-million dollar machine. The extent to which this potential can be realized for our problem depends on, among other things;
WORLD SCIENTIFIC eBooks, 2003
AHS International Forum 60, Jun 7, 2004
A method is described to compute flow over llelicopter ,rotor blades. The method utilizes a compr... more A method is described to compute flow over llelicopter ,rotor blades. The method utilizes a compressible potential flow field with embedded vortex sheets. It is fully compressible, with the ability to capture shocks in transonic cases, and is able to treat the wake as free with no external inputs. Also, the wake is treated in a general, unified way as a surface that moves through the flow field with no constraints imposed by the computation .. The method is quite different from others being developed. In other approaches the wake is typically treated as a collection of separate filaments. Also, other compressible approaches typically break the computational region into a set of small regions near each blade where the compressible flow equations are solved, and an outer region where the wake is computed. These approaches do not appear to be adequate for modern rotor blades because the physical wake from each blade usually does not break up into a set of well-defined vortex filaments, and also because it can approach quite close to other blades. The vortex embedding technique has been implemented in a computer code, HELIX I. In validation studies involving comparisons between results computed with HELIX I and experiments there has been very good agreement for the prediction of pressure distributions on blade surfaces, even in transonic cases with significant shocks. Also, the rotor wake geometry was also well predicted, for both two and four blade rotors. Successful prediction of the initial tip vortex descent rate (ki) is especially notable because previous methods have difficulty doing so.
A new computational technique, Wave Confinement (WC), is ext ended here to account for sound diff... more A new computational technique, Wave Confinement (WC), is ext ended here to account for sound diffraction around arbitrary terrain. While diffraction around elementary sc attering objects, such as a knife edge, single slit, disc, sp here, etc. has been studied for several decades, realistic enviro nments still pose significant problems. This new technique is first validated against Sommerfeld’s classical problem o f diffraction due to a knife edge. This is followed by comparisons with diffraction over three-dimensional smoo th bstacles, such as a disc and Gaussian hill. Finally, comparisons with flight test acoustics data measured behind a hill are also shown. Comparison between experiment and Wave Confinement prediction demonstrates that a Poisson spot occurred behind the isolated hill, resulting in significantly increased sound intensity near the center of t he shadowed region.
Physical review, Nov 15, 1971
A self-consistent model of asymptotic high-energy hadron-hadron scattering determining the t depe... more A self-consistent model of asymptotic high-energy hadron-hadron scattering determining the t dependence a t small angles i s formulated and compared with available experimental results. This model takes the Pomeranchuk singularity a s a fixed pole, self-generating through unitarity in the s channel. The production mechanisms assumed to be most important in the elastic-scattering unitarity sum a r e those involving essentially the Pomeranchukon; they a r e "diffraction dissociation," o r "strong bremsstrahlung" with the pion (as the lightest hadron) mass determining the scale f o r t dependences. In addition to pion propagators, a form factor which i s required in the production model may be determined self-consistently by postulating a certain universality and the Chou-Yang hypothesis. Specific predictions for diffractionpeak widths a t asymptotic energies a r e given and a r e in qualitative agreement with presently available data.
Ia REPORTSECURITY CILASSIFICATION 1 aSECURITY CLASSIFICATION AUTHORITY ' J3 DISTRIBUTION/AVAILI.l... more Ia REPORTSECURITY CILASSIFICATION 1 aSECURITY CLASSIFICATION AUTHORITY ' J3 DISTRIBUTION/AVAILI.liUTY OF REPORT 2b. ECLSIIFICTIOIDONI3ADI Approved for public release; b. DECLASSIFICATION/DOWNGRADIN distribution unlimited. PEFRMN ORGAIZATION REPORT NUMDER(S) S. MONITORING ORGANIZATION REPORT NUMBER(S)-Ago ,20Yo '-54 NAME OF PERFORMING ORGANIZATION 6b. OFFICE SYMBOL 7a. NAME OF MONITORING ORGANIZATION
In this paper a method is described for predicting the compressible, free-wake, flow about a lift... more In this paper a method is described for predicting the compressible, free-wake, flow about a lifting rotor-body configuration. The method is an extension of a unique vorticity embedded full-potential method used to calculate f n c d e rotor hover performance. An unusual feature of this method is that it obviates the requirement for multiple grids to treat the rotor-body problem. The approach used to treat the body is similar to that used to include the rotor wake in the full potential calculation. The body is modeled M a structured circulation sheet and the strength of this sheet is determined in an iterative manner. Initially the method is tested to compute the flow past simple isolated bodies like cylindem and spheres. After a comparison of these simple computations with exact solutions this proeedure is included into the HELIX-I, free-wake rotor code, to compute the flow around a rotor mounted on a large whirl toner. The cfTects of the tower on rotor wake geometry and load distribution are presented. v
30th Aerospace Sciences Meeting and Exhibit, Jan 6, 1992
A new, simple method is described for measuring and visualizing air flows. The method involves pr... more A new, simple method is described for measuring and visualizing air flows. The method involves projecting a small heated metal pellet through the air at a speed greater than the flow. The pellet burns as it moves through the air and leaves a wake of very fine, visible, metal oxide particles. The position of this visible smoke trail is then photographed at a sequence of times. The displacement of the trail can be used to provide a plot of the normal component of velocity as a function of distance. Examples are given for very low speed thermal convection (less than about 1 m/sec) and low speed flow over airfoils and cylinders (less than about 10 m/sec). Comparisons of the method to pulsed smoke-wire, spark-tracer and laser fluorescence methods, which give similar information, are discussed.
40th AIAA Aerospace Sciences Meeting & Exhibit, Jan 14, 2002
Many flows of interest are characterized by large regions of concentrated (and turbulent) vortica... more Many flows of interest are characterized by large regions of concentrated (and turbulent) vortical structures that persist and can convect over long distances. Flows of this nature include those associated with aircraft, but also include flows associated with ships, automobiles, bridges, and buildings. Conventional CFD methods tend to dissipate vortical structures, degrading the overall accuracy of the computed flow. This dissipation can be reduced through the use of fine grids, but at the expense of greatly increased computational demands. In addition, no conventional CFD method produces the unsteady chaotic flow associated with turbulence except on extremely fine grids and in very small regions. The vorticity confinement method prevents ~ Senior Research Scientist 0 Research Scientist *Professor Copyright © 2002 by Flow Analysis, Inc. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission. the dissipation of vortical structures on coarse grids, and approximately produces the unsteady small-scale features (down to grid-cell scale) associated with physical turbulence. In this paper, vorticity confinement is used to model a turbulent wake behind a cylinder. Comparisons with data demonstrate the potential of vorticity confinement to predict mean wake flow and Reynolds stresses accurately and efficiently, even on a coarse grid. In addition, computations are performed on a realistic ship configuration; the resulting velocity field and bow vortex trajectory are shown to agree well with wind tunnel measurements.
A technique, "Vorticity Confinement", is described that represents a very effective, un... more A technique, "Vorticity Confinement", is described that represents a very effective, unified way of treating complex, high Reynolds number separated flows with thin convecting vortices, as well as complex solid bodies with thin attached boundary layers. Vorticity Confinement involves, essentially, treating vortical regions as nonlinear solitary waves that "live" on the grid lattice. The basic assumptions mainly involve using the solitary wave structure as a model for the vortical region. At high Reynolds number, this then represents a fundamentally discrete turbulence model since these regions are then typically turbulent. First, drawbacks of conventional Eulerian computational methods particularly for treating thin, convecting vortices are described. Then, how Vorticity Confinement, which is also Eulerian, eliminates these problems. The basic assumptions in Vorticity Confinement are then reviewed and some details of the method are described. Following the description, a sequence of results are presented: First, 2-D results for convecting vortices and flow over a cylinder are presented. These describe the salient features of the method for convecting vortices and for flow over solid surfaces, embedded in a uniform Cartesian grid. Then, 3-D results for flow over complex bodies, including rotorcraft, are presented.
13th Computational Fluid Dynamics Conference, Jun 29, 1997
Many features of high Reynolds number flows are thin and have at least one dimension that is smal... more Many features of high Reynolds number flows are thin and have at least one dimension that is small. These include shocks, boundary layers, free shear layers, interfaces between different fluids and short acoustic pulses. In many flows the internal structure of these features may not significantly affect the overall outer solution. We describe a simple method to efficiently solve for these flows which involves treating the features as "solitary waves". These involve functions which are defined only on a fixed Eulerian computational grid and which obey a non-linear discrete evolution equation, such that their internal structure remains fixed and thin - confined to a region about the feature only 2-4 grid cells wide, over arbitrarily long times or distances. These solitary waves represent the feature, which may be much thinner than a grid cell, and carry only minimal information about it such as an integral and the centroid location at each point along the feature. Solitary waves have been applied to represent convecting vortices, boundary layers on surfaces in a non-body-fitted cartesian grid, fluid interfaces and acoustic pulses. They can 'be symmetric about the feature as for concentrated vortex sheets, or they can pass through each other, as for acoustic pulses. As such, they can be thought of as generalizations of "level set" schemes which involve a signed distance function. On the other hand, they involve a nonlinear negative diffusion-like term that is added to the evolution equations and, as such, represent a generalization of "Artificial Compression" schemes or recently developed "Vorticity Confinement" methods.
Physics Letters B, Jul 1, 1973
ABSTRACT
38th Aerospace Sciences Meeting and Exhibit, Jan 10, 2000
ABSTRACT It is well known that modern computational fluid dynamics codes based on Eulerian descri... more ABSTRACT It is well known that modern computational fluid dynamics codes based on Eulerian descriptions do not adequately handle flows involving the convection of thin vortical layers. These layers often remain very thin and persist long distances without significant dissipation. Over the past decade, Steinhoff has introduced a class of methods, generally known as "vorticity confinement," which have been used successfully to predict complex flows, particularly involving helicopter rotors. These methods have involved an incompressible finite difference formulation. We extend vorticity confinement to compressible flows by noting that the confinement term added to the momentum equation in Steinhoff's formulation may be interpreted as a body force. We can then extend the approach to compressible flows by adding the contribution of this body force to the integral conservation laws. The development of a finite volume compressible vorticity confinement scheme then follows directly. We have implemented the scheme with a matrix artificial dissipation and a new matrix confinement term. Results are presented for supersonic shear layers, vortices moving in a uniform stream, and vortex separation on the leeward surface of a flat plate delta wing at supersonic speed.
14th Computational Fluid Dynamics Conference, Aug 22, 1999
Ducted propellers and turbines operating in a square closed wind tunnel test section are analyzed... more Ducted propellers and turbines operating in a square closed wind tunnel test section are analyzed. A multiple image method is used to account for tunnel wall interference effects and a detailed method of singularities model is used for the ducted rotor. The size of the rotor wake is computed, taking into account the tunnel walls. Several ducted rotor model/wind tunnel dimension ratios are examined, ranging between 0.02 and 0.50. In addition, ducted rotor disk loading coefficients, CT , between - 30 and 0.89 are considered (the negative values correspond to the rotor acting as a propeller; the positive values indicate that the rotor is a turbine). Values of ideal propeller thrust are reduced by over 30% at the highest value of propeller disk loading (CT = — 30). The tunnel wall effect for a ducted turbine is less than for a ducted propeller and is opposite in direction. For the nearoptimum condition CT. =0.89, the ideal turbine power is increased by about 8% for the largest model/tunnel ratio considered. Nomenclature CP. = ideal thrust power coefficient for DAP (diffuseraugmented propeller) or ideal power coefficient for DAWT (diffuser-augmented wind turbine) CT() = disk loading coefficient based on freestream dynamic head D = dimension of wind tunnel test section E = complete elliptic integral, Eq. (5) K = complete elliptic integral, Eq. (4) kn = function of ring vortex coordinates and field point coordinates, Eq. (3) TV = the number of images along the side of a square image array q = velocity in r direction r = radial coordinate rp = ideal power augmentation ratio R = diffuser radius at a particular value of z S = the number of vortex rings used to represent the diffuser surface T = total number of vortices used to represent both the diffuser and the wake u = velocity in x direction U0 = freestream velocity, dimensional v = velocity in y direction w = velocity in z direction (axial direction) x = lateral coordinate in plane perpendicular to mean flow y = vertical coordinate in plane perpendicular to mean
WORLD SCIENTIFIC eBooks, Dec 1, 2001
A technique, "Vorticity Confinement", is described that represents a very effective, un... more A technique, "Vorticity Confinement", is described that represents a very effective, unified way of treating complex, high Reynolds number separated flows with thin convecting vortices, as well as complex solid bodies with thin attached boundary layers. Vorticity Confinement involves, essentially, treating vortical regions as nonlinear solitary waves that "live" on the grid lattice. The basic assumptions mainly involve using the solitary wave structure as a model for the vortical region. At high Reynolds number, this then represents a fundamentally discrete turbulence model since these regions are then typically turbulent. First, drawbacks of conventional Eulerian computational methods particularly for treating thin, convecting vortices are described. Then, how Vorticity Confinement, which is also Eulerian, eliminates these problems. The basic assumptions in Vorticity Confinement are then reviewed and some details of the method are described. Following the description, a sequence of results are presented: First, 2-D results for convecting vortices and flow over a cylinder are presented. These describe the salient features of the method for convecting vortices and for flow over solid surfaces, embedded in a uniform Cartesian grid. Then, 3-D results for flow over complex bodies, including rotorcraft, are presented.
National Computer Conference, 1978
In the last several years, minicomputer based systems have been considered or used for an increas... more In the last several years, minicomputer based systems have been considered or used for an increasing number of scientific computing tasks. For example, Kottler and McGilP used a minicomputer system to solve a series of problems, including a partial differential equation for pollutant dispersal. Also, in 1973, Steven Orszag compared a minicomputer system to large general purpose machines for solving some time dependent hydrodynamics codes. The conclusions were that minicomputers could be more cost effective than the large machines. In particular, Orszag concluded that the minicomputer was more cost effective than a CDC 7600 but less than a CDC STAR for moderate resolution hydrodynamics codes. For these problems, the data bases are large and the system is essentially a disk based one, where data flows from a large data base on the disk to the computer. When these studies were done, disk speed was not a restriction and the limiting factor was the computational speed of the minicomputer. In the last several years, improvements in LSI technology have made it possible to assemble reliable computational devices with a much lower cost per computation than mini"' computers. These devices, ranging from moderately priced (-$100,000) fast systems with tightly coupled multiple functional units to very inexpensive simple units can be very cost effective when used with a minicomputer as host. They have had a large impact on the signal processing field, 3 in some cases proving to be faster than large machines such as the CDC 7600. They can also be effective for real-time simulation, as described in Reference 4. In this paper we will describe a study that was done on the effectiveness of a minicomputer based system with moving head disk and peripheral processor for a class of fluid flow problems. It is easy to see that a moderately priced system can be assembled that would have a (disk) data capacity and contiguous block throughput and a (peripheral) computational speed of a large multi-million dollar machine. The extent to which this potential can be realized for our problem depends on, among other things;
WORLD SCIENTIFIC eBooks, 2003
AHS International Forum 60, Jun 7, 2004
A method is described to compute flow over llelicopter ,rotor blades. The method utilizes a compr... more A method is described to compute flow over llelicopter ,rotor blades. The method utilizes a compressible potential flow field with embedded vortex sheets. It is fully compressible, with the ability to capture shocks in transonic cases, and is able to treat the wake as free with no external inputs. Also, the wake is treated in a general, unified way as a surface that moves through the flow field with no constraints imposed by the computation .. The method is quite different from others being developed. In other approaches the wake is typically treated as a collection of separate filaments. Also, other compressible approaches typically break the computational region into a set of small regions near each blade where the compressible flow equations are solved, and an outer region where the wake is computed. These approaches do not appear to be adequate for modern rotor blades because the physical wake from each blade usually does not break up into a set of well-defined vortex filaments, and also because it can approach quite close to other blades. The vortex embedding technique has been implemented in a computer code, HELIX I. In validation studies involving comparisons between results computed with HELIX I and experiments there has been very good agreement for the prediction of pressure distributions on blade surfaces, even in transonic cases with significant shocks. Also, the rotor wake geometry was also well predicted, for both two and four blade rotors. Successful prediction of the initial tip vortex descent rate (ki) is especially notable because previous methods have difficulty doing so.
A new computational technique, Wave Confinement (WC), is ext ended here to account for sound diff... more A new computational technique, Wave Confinement (WC), is ext ended here to account for sound diffraction around arbitrary terrain. While diffraction around elementary sc attering objects, such as a knife edge, single slit, disc, sp here, etc. has been studied for several decades, realistic enviro nments still pose significant problems. This new technique is first validated against Sommerfeld’s classical problem o f diffraction due to a knife edge. This is followed by comparisons with diffraction over three-dimensional smoo th bstacles, such as a disc and Gaussian hill. Finally, comparisons with flight test acoustics data measured behind a hill are also shown. Comparison between experiment and Wave Confinement prediction demonstrates that a Poisson spot occurred behind the isolated hill, resulting in significantly increased sound intensity near the center of t he shadowed region.
Physical review, Nov 15, 1971
A self-consistent model of asymptotic high-energy hadron-hadron scattering determining the t depe... more A self-consistent model of asymptotic high-energy hadron-hadron scattering determining the t dependence a t small angles i s formulated and compared with available experimental results. This model takes the Pomeranchuk singularity a s a fixed pole, self-generating through unitarity in the s channel. The production mechanisms assumed to be most important in the elastic-scattering unitarity sum a r e those involving essentially the Pomeranchukon; they a r e "diffraction dissociation," o r "strong bremsstrahlung" with the pion (as the lightest hadron) mass determining the scale f o r t dependences. In addition to pion propagators, a form factor which i s required in the production model may be determined self-consistently by postulating a certain universality and the Chou-Yang hypothesis. Specific predictions for diffractionpeak widths a t asymptotic energies a r e given and a r e in qualitative agreement with presently available data.
Ia REPORTSECURITY CILASSIFICATION 1 aSECURITY CLASSIFICATION AUTHORITY ' J3 DISTRIBUTION/AVAILI.l... more Ia REPORTSECURITY CILASSIFICATION 1 aSECURITY CLASSIFICATION AUTHORITY ' J3 DISTRIBUTION/AVAILI.liUTY OF REPORT 2b. ECLSIIFICTIOIDONI3ADI Approved for public release; b. DECLASSIFICATION/DOWNGRADIN distribution unlimited. PEFRMN ORGAIZATION REPORT NUMDER(S) S. MONITORING ORGANIZATION REPORT NUMBER(S)-Ago ,20Yo '-54 NAME OF PERFORMING ORGANIZATION 6b. OFFICE SYMBOL 7a. NAME OF MONITORING ORGANIZATION
In this paper a method is described for predicting the compressible, free-wake, flow about a lift... more In this paper a method is described for predicting the compressible, free-wake, flow about a lifting rotor-body configuration. The method is an extension of a unique vorticity embedded full-potential method used to calculate f n c d e rotor hover performance. An unusual feature of this method is that it obviates the requirement for multiple grids to treat the rotor-body problem. The approach used to treat the body is similar to that used to include the rotor wake in the full potential calculation. The body is modeled M a structured circulation sheet and the strength of this sheet is determined in an iterative manner. Initially the method is tested to compute the flow past simple isolated bodies like cylindem and spheres. After a comparison of these simple computations with exact solutions this proeedure is included into the HELIX-I, free-wake rotor code, to compute the flow around a rotor mounted on a large whirl toner. The cfTects of the tower on rotor wake geometry and load distribution are presented. v
30th Aerospace Sciences Meeting and Exhibit, Jan 6, 1992
A new, simple method is described for measuring and visualizing air flows. The method involves pr... more A new, simple method is described for measuring and visualizing air flows. The method involves projecting a small heated metal pellet through the air at a speed greater than the flow. The pellet burns as it moves through the air and leaves a wake of very fine, visible, metal oxide particles. The position of this visible smoke trail is then photographed at a sequence of times. The displacement of the trail can be used to provide a plot of the normal component of velocity as a function of distance. Examples are given for very low speed thermal convection (less than about 1 m/sec) and low speed flow over airfoils and cylinders (less than about 10 m/sec). Comparisons of the method to pulsed smoke-wire, spark-tracer and laser fluorescence methods, which give similar information, are discussed.
40th AIAA Aerospace Sciences Meeting & Exhibit, Jan 14, 2002
Many flows of interest are characterized by large regions of concentrated (and turbulent) vortica... more Many flows of interest are characterized by large regions of concentrated (and turbulent) vortical structures that persist and can convect over long distances. Flows of this nature include those associated with aircraft, but also include flows associated with ships, automobiles, bridges, and buildings. Conventional CFD methods tend to dissipate vortical structures, degrading the overall accuracy of the computed flow. This dissipation can be reduced through the use of fine grids, but at the expense of greatly increased computational demands. In addition, no conventional CFD method produces the unsteady chaotic flow associated with turbulence except on extremely fine grids and in very small regions. The vorticity confinement method prevents ~ Senior Research Scientist 0 Research Scientist *Professor Copyright © 2002 by Flow Analysis, Inc. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission. the dissipation of vortical structures on coarse grids, and approximately produces the unsteady small-scale features (down to grid-cell scale) associated with physical turbulence. In this paper, vorticity confinement is used to model a turbulent wake behind a cylinder. Comparisons with data demonstrate the potential of vorticity confinement to predict mean wake flow and Reynolds stresses accurately and efficiently, even on a coarse grid. In addition, computations are performed on a realistic ship configuration; the resulting velocity field and bow vortex trajectory are shown to agree well with wind tunnel measurements.
A technique, "Vorticity Confinement", is described that represents a very effective, un... more A technique, "Vorticity Confinement", is described that represents a very effective, unified way of treating complex, high Reynolds number separated flows with thin convecting vortices, as well as complex solid bodies with thin attached boundary layers. Vorticity Confinement involves, essentially, treating vortical regions as nonlinear solitary waves that "live" on the grid lattice. The basic assumptions mainly involve using the solitary wave structure as a model for the vortical region. At high Reynolds number, this then represents a fundamentally discrete turbulence model since these regions are then typically turbulent. First, drawbacks of conventional Eulerian computational methods particularly for treating thin, convecting vortices are described. Then, how Vorticity Confinement, which is also Eulerian, eliminates these problems. The basic assumptions in Vorticity Confinement are then reviewed and some details of the method are described. Following the description, a sequence of results are presented: First, 2-D results for convecting vortices and flow over a cylinder are presented. These describe the salient features of the method for convecting vortices and for flow over solid surfaces, embedded in a uniform Cartesian grid. Then, 3-D results for flow over complex bodies, including rotorcraft, are presented.
13th Computational Fluid Dynamics Conference, Jun 29, 1997
Many features of high Reynolds number flows are thin and have at least one dimension that is smal... more Many features of high Reynolds number flows are thin and have at least one dimension that is small. These include shocks, boundary layers, free shear layers, interfaces between different fluids and short acoustic pulses. In many flows the internal structure of these features may not significantly affect the overall outer solution. We describe a simple method to efficiently solve for these flows which involves treating the features as "solitary waves". These involve functions which are defined only on a fixed Eulerian computational grid and which obey a non-linear discrete evolution equation, such that their internal structure remains fixed and thin - confined to a region about the feature only 2-4 grid cells wide, over arbitrarily long times or distances. These solitary waves represent the feature, which may be much thinner than a grid cell, and carry only minimal information about it such as an integral and the centroid location at each point along the feature. Solitary waves have been applied to represent convecting vortices, boundary layers on surfaces in a non-body-fitted cartesian grid, fluid interfaces and acoustic pulses. They can 'be symmetric about the feature as for concentrated vortex sheets, or they can pass through each other, as for acoustic pulses. As such, they can be thought of as generalizations of "level set" schemes which involve a signed distance function. On the other hand, they involve a nonlinear negative diffusion-like term that is added to the evolution equations and, as such, represent a generalization of "Artificial Compression" schemes or recently developed "Vorticity Confinement" methods.
Physics Letters B, Jul 1, 1973
ABSTRACT
38th Aerospace Sciences Meeting and Exhibit, Jan 10, 2000
ABSTRACT It is well known that modern computational fluid dynamics codes based on Eulerian descri... more ABSTRACT It is well known that modern computational fluid dynamics codes based on Eulerian descriptions do not adequately handle flows involving the convection of thin vortical layers. These layers often remain very thin and persist long distances without significant dissipation. Over the past decade, Steinhoff has introduced a class of methods, generally known as "vorticity confinement," which have been used successfully to predict complex flows, particularly involving helicopter rotors. These methods have involved an incompressible finite difference formulation. We extend vorticity confinement to compressible flows by noting that the confinement term added to the momentum equation in Steinhoff's formulation may be interpreted as a body force. We can then extend the approach to compressible flows by adding the contribution of this body force to the integral conservation laws. The development of a finite volume compressible vorticity confinement scheme then follows directly. We have implemented the scheme with a matrix artificial dissipation and a new matrix confinement term. Results are presented for supersonic shear layers, vortices moving in a uniform stream, and vortex separation on the leeward surface of a flat plate delta wing at supersonic speed.
14th Computational Fluid Dynamics Conference, Aug 22, 1999
Ducted propellers and turbines operating in a square closed wind tunnel test section are analyzed... more Ducted propellers and turbines operating in a square closed wind tunnel test section are analyzed. A multiple image method is used to account for tunnel wall interference effects and a detailed method of singularities model is used for the ducted rotor. The size of the rotor wake is computed, taking into account the tunnel walls. Several ducted rotor model/wind tunnel dimension ratios are examined, ranging between 0.02 and 0.50. In addition, ducted rotor disk loading coefficients, CT , between - 30 and 0.89 are considered (the negative values correspond to the rotor acting as a propeller; the positive values indicate that the rotor is a turbine). Values of ideal propeller thrust are reduced by over 30% at the highest value of propeller disk loading (CT = — 30). The tunnel wall effect for a ducted turbine is less than for a ducted propeller and is opposite in direction. For the nearoptimum condition CT. =0.89, the ideal turbine power is increased by about 8% for the largest model/tunnel ratio considered. Nomenclature CP. = ideal thrust power coefficient for DAP (diffuseraugmented propeller) or ideal power coefficient for DAWT (diffuser-augmented wind turbine) CT() = disk loading coefficient based on freestream dynamic head D = dimension of wind tunnel test section E = complete elliptic integral, Eq. (5) K = complete elliptic integral, Eq. (4) kn = function of ring vortex coordinates and field point coordinates, Eq. (3) TV = the number of images along the side of a square image array q = velocity in r direction r = radial coordinate rp = ideal power augmentation ratio R = diffuser radius at a particular value of z S = the number of vortex rings used to represent the diffuser surface T = total number of vortices used to represent both the diffuser and the wake u = velocity in x direction U0 = freestream velocity, dimensional v = velocity in y direction w = velocity in z direction (axial direction) x = lateral coordinate in plane perpendicular to mean flow y = vertical coordinate in plane perpendicular to mean