Stephen Jordan - Academia.edu (original) (raw)
Papers by Stephen Jordan
During the American Revolution Patriots and Tories alike knew the Americans could not win the war... more During the American Revolution Patriots and Tories alike knew the Americans could not win the war without foreign aid. In 1776 Benjamin Franklin had been sent to France to negotiate a mutual defense treaty. In February 1778, the treaty was signed and Admiral d’Estaing and the Toulon fleet were dispatched to help the Patriot’s. Plans were made for a campaign – comprised of 10,000 Americans under the command of Major General John Sullivan along with d’Estaing’s squadron and 4,000 French troops to retake Newport, Rhode Island, a significant port held by the British since 1776. It was the first joint military operation of the newly formed alliance. Just as the allies took action, circumstances changed and a sudden and violent storm hit the area. The hurricane battered and badly damaged the French fleet, which had left Newport Harbor in pursuit of the British, causing d’Estaing to insist on retreating to Boston for repairs. Positioned initially at the top of the Aquidneck Island, followi...
Thesis Virginia Polytechnic Institute and State University 1994 Source Dissertation Abstracts International Volume 56 01 Section B Page 0305, 1994
Journal of Fluids Engineering-transactions of The Asme, 2005
Current suggestions for estimating the numerical uncertainty in solutions by the Large-Eddy Simul... more Current suggestions for estimating the numerical uncertainty in solutions by the Large-Eddy Simulation (LES) methodology require either a posteriori input or reflect global assessments. In most practical applications, this approach is rather costly for the user and especially time consuming due to the CPU effort needed to reach the statistical steady state. Herein, we demonstrate two alternate a priori graphical exercises. An evaluation of the numerical uncertainty uses the turbulent quantities given by the area under the wave number spectra profiles. These profiles are easily constructed along any grid line in the flow domain prior to the collection of the turbulent statistics. One exercise involves a completion of the spectrum profile beyond the cutoff wave number to the inverse of Kolmorgorov’s length scale by a model of isotropic turbulence. The other extends Richardson Extrapolation acting on multiple solutions. Sample test cases of both LES solutions and direct numerical simulations as well as published experimental data show excellent agreement between the integrated matched spectra and the respective turbulent statistics. Thus, the resultant uncertainties themselves provide a useful measure of accumulated statistical error in the resolved turbulent properties.
Volume 1: Symposia, Parts A and B, 2006
Journal of Fluids Engineering, 2014
Even after several decades of experimental and numerical testing, our present-day knowledge of th... more Even after several decades of experimental and numerical testing, our present-day knowledge of the axisymmetric turbulent boundary layer (TBL) along long thin circular cylinders still lacks a clear picture of many fundamental characteristics. The main issues causing this reside in the experimental testing complexities and the numerical simplifications. An important characteristic that is crucial for routine scaling is the boundary layer length scales, but the downstream growth of these scales (boundary layer, displacement, and momentum thicknesses) is largely unknown from the leading to trailing edges. Herein, we combine pertinent datasets with many complementary numerical computations (large-eddy simulations) to address this shortfall. We are particularly interested in expressing the length scales in terms of the radius-based and axial-based Reynolds numbers (Rea and Rex). Although the composite dataset gave an averaged shape factor H = 1.09 that is substantially lower than the pla...
Journal of Fluids Engineering, 2001
The dynamic eddy-viscosity relationship is a suitable choice for modeling the subgrid-scales (SGS... more The dynamic eddy-viscosity relationship is a suitable choice for modeling the subgrid-scales (SGS) in a large-eddy simulation (LES) of complex turbulent flows in irregular domains. This algebraic relationship is easy to implement and its dynamic coefficient will give negligible turbulent viscosity contributions in the flow regions that are irrotational or laminar. Its fine-scale turbulence predictions can be qualitatively reasonable if the local grid resolution maintains the SGS field predominantly within the equilibrium range of turbulent energy spectra. This performance is given herein by two curvilinear coordinate forms of the dynamic Smagorinsky model that are formally derived and a-priori tested using the resolved physics of the cylinder wake. The conservative form evaluates the dynamic coefficient in the computational (transformed) space whereas its non-conservative counterpart operates in the physical domain. Although both forms equally captured the real normal SGS stress rea...
Journal of Fluids Engineering, 1998
The formation and the downstream transport of the Strouhal vortices in the near wake of a circula... more The formation and the downstream transport of the Strouhal vortices in the near wake of a circular cylinder are investigated using the large-eddy simulation (LES) method. The governing equations are formulated in curvilinear coordinates to accommodate a nonorthogonal grid with formal development of a dynamic model to account for the subgrid turbulent scales. Results were produced with and without use of the model. The focus of the investigation is at a subcritical Reynolds number of 5600. Using the dynamic model, the LES results compared best to the published experimental data in terms of both the global and local wake characteristics such as the drag and base pressure coefficients, shedding and detection frequencies, peak vorticity, and the downstream mean velocity-defect and Reynolds stresses. The results further showed streamwise filaments that connect subsequent Strouhal vortices. Qualitatively, the time-averaged Reynolds stresses of the formation region revealed similar symmetr...
Journal of Fluids Engineering, 2003
Resolving the turbulent statistics of bluff-body wakes is a challenging task. Frequently, the str... more Resolving the turbulent statistics of bluff-body wakes is a challenging task. Frequently, the streamwise grid point spacing approaching the vortex exit boundary is sacrificed to gain near full resolution of the turbulent scales neighboring the body surface. This choice favors the solution strategies of direct numerical and large-eddy simulations (DNS and LES) that house spectral-like resolving characteristics with inherent dissipation. Herein, two differencing stencils are tested for approximating four forms of the convective derivative in the DNS and LES formulations for incompressible flows. The wake spectral characteristics and conventional parameters are computed for Reynolds numbers Re=200 (laminar wake) and Re=3900. These tests demonstrated reliable stability and spectral-like accuracy of compact fifth-order upwinding for the advective derivative and fourth-order cell-centered Pade´ (with fourth-order upwinding interpolation) for the Arakawa form of the convective derivative. ...
Journal of Fluids Engineering, 2004
Flow past cavities covered by perforated lids pose a challenging problem for design engineers. Ke... more Flow past cavities covered by perforated lids pose a challenging problem for design engineers. Kelvin–Helmholtz waves appear early in the separated shear layers above the perforations that quickly mature into large-scale coherent structures far downstream. This evolution is sustained by a hydrodynamic feedback mechanism within the cavity even when its aft wall is far removed from the lid. Herein, the results from large-eddy simulations show analogous fundamental characteristics between open and perforated-cover cavities. Both adequately scale the fundamental frequency of the large-scale disturbance using the freestream velocity and the cavity width (or lid length). Moreover, the dimensionless frequencies jump to higher modes at equivalent length scales. Unlike the open cavity, one can invoke certain conditions that instigate the instability above the perforations but not a simultaneous long-term feedback mechanism necessary to fully sustain the periodic oscillation. The lid itself o...
Journal of Fluids Engineering, 1994
The three-dimensional shear-driven cavity flow is numerically investigated at Reynolds numbers of... more The three-dimensional shear-driven cavity flow is numerically investigated at Reynolds numbers of 5000 and 10000. This investigation focuses on the unsteadiness and turbulent characteristics of the flow. At the moderate Reynolds number (Re = 5000) where the cavity flow is fully laminar, a direct numerical simulation (DNS) is used whereas large-eddy simulation (LES) methodology is adopted to predict the cavity flow at the higher Reynolds number (Re = 10000). Establishing a suitable form for the subgrid scale (SGS) turbulence model in this complex flow is guided by the DNS results at Re = 5000. Additionally, the SGS model is verified against DNS results at Re = 7500 where the cavity flow is known through experimentation to be locally transitional. The LES results verify the published experimental evidence as well as uncover new flow features within the cavity.
Journal of Fluids Engineering, 2012
After three decades of accumulated experimental and numerical results, a comprehensive understand... more After three decades of accumulated experimental and numerical results, a comprehensive understanding of the spatial evolution of axisymmetric turbulent boundary layers (ATBL) along long thin cylinders still eludes both scientists and engineers. While experimentalists dealt with axial alignment complexities, computationalists lacked proper inflow boundary conditions. Herein, we correct this latter deficiency and initiate an investigation of the thin cylinder turbulence under low Reynolds numbers and high transverse curvatures (boundary layer thicknesses to radius). Using the large-eddy simulation (LES) methodology, we are particularly interested in the radial propagation of the transverse curvature on the ATBL statistics. A ten-simulation matrix was constructed to examine these effects with validation against the experimental evidence. These tests investigated the ATBL maturity up to transverse curvatures approaching 2 orders of magnitude. A recently developed turbulent inflow proced...
Journal of Fluids Engineering, 2012
Generating acceptable inflow conditions for the turbulent boundary layer (TBL) growth along long ... more Generating acceptable inflow conditions for the turbulent boundary layer (TBL) growth along long thin cylinders is a challenging task. Previous production methods such as rescale/recycling, artificial turbulence, and antecedent databases are difficult to implement because the downstream physics do not conform to consistent scaling laws. An alternate inflow approach that involves only recycling the fluctuating elements coupled with a dynamic form of Spalding’s relationship for assigning the mean quantities shows promise for spatially resolving the axisymmetric turbulence along the thin cylinder. Applying this inflow technique for resolving the turbulent scales along a flat plate at a tested momentum-based Reynolds number of Reθ = 670 showed excellent agreement with the experimental data as well as the analytical results from the momentum-integral method. A minor adjustment length of approximately two inflow TBL thicknesses was necessary to attain consistent streamwise growth of the b...
Journal of Fluids Engineering, 2009
Parameter optimization is an excellent path for easily raising the resolution efficiency of compa... more Parameter optimization is an excellent path for easily raising the resolution efficiency of compact finite differencing schemes. Their low-resolution errors are attractive for resolving the fine-scale turbulent physics even in complex flow domains with difficult boundary conditions. Most schemes require optimizing closure stencils at and adjacent to the domain boundaries. But these constituents can potentially degrade the local resolution errors and destabilize the final solution scheme. Current practices optimize and analyze each participating stencil separately, which incorrectly quantifies their local resolution errors. The proposed process optimizes each participant simultaneously. The result is a composite template that owns consistent spatial resolution properties throughout the entire computational domain. Additionally, the optimization technique leads to templates that are numerically stable as understood by an eigenvalue analysis. Finally, the predictive accuracy of the opt...
Journal of Fluids Engineering, 2008
When establishing the spatial resolution character of a composite compact finite differencing tem... more When establishing the spatial resolution character of a composite compact finite differencing template for high-order field solutions, the stencils selected at nonperiodic boundaries are commonly treated independent of the interior scheme. This position quantifies a false influence of the boundary scheme on the resultant interior dispersive and dissipative consequences of the compound template. Of the three ingredients inherent in the composite template, only its numerical accuracy and global stability have been properly treated in a coupled fashion. Herein, we present a companion means for quantifying the resultant spatial resolution properties that lead to improved predictions of the salient problem physics. Compact boundary stencils with free parameters to minimize the field dispersion (or phase error) and dissipation are included in the procedure. Application of the coupled templates for resolving the viscous Burgers wave and two-dimensional acoustic scattering reveal significan...
During the American Revolution Patriots and Tories alike knew the Americans could not win the war... more During the American Revolution Patriots and Tories alike knew the Americans could not win the war without foreign aid. In 1776 Benjamin Franklin had been sent to France to negotiate a mutual defense treaty. In February 1778, the treaty was signed and Admiral d’Estaing and the Toulon fleet were dispatched to help the Patriot’s. Plans were made for a campaign – comprised of 10,000 Americans under the command of Major General John Sullivan along with d’Estaing’s squadron and 4,000 French troops to retake Newport, Rhode Island, a significant port held by the British since 1776. It was the first joint military operation of the newly formed alliance. Just as the allies took action, circumstances changed and a sudden and violent storm hit the area. The hurricane battered and badly damaged the French fleet, which had left Newport Harbor in pursuit of the British, causing d’Estaing to insist on retreating to Boston for repairs. Positioned initially at the top of the Aquidneck Island, followi...
Thesis Virginia Polytechnic Institute and State University 1994 Source Dissertation Abstracts International Volume 56 01 Section B Page 0305, 1994
Journal of Fluids Engineering-transactions of The Asme, 2005
Current suggestions for estimating the numerical uncertainty in solutions by the Large-Eddy Simul... more Current suggestions for estimating the numerical uncertainty in solutions by the Large-Eddy Simulation (LES) methodology require either a posteriori input or reflect global assessments. In most practical applications, this approach is rather costly for the user and especially time consuming due to the CPU effort needed to reach the statistical steady state. Herein, we demonstrate two alternate a priori graphical exercises. An evaluation of the numerical uncertainty uses the turbulent quantities given by the area under the wave number spectra profiles. These profiles are easily constructed along any grid line in the flow domain prior to the collection of the turbulent statistics. One exercise involves a completion of the spectrum profile beyond the cutoff wave number to the inverse of Kolmorgorov’s length scale by a model of isotropic turbulence. The other extends Richardson Extrapolation acting on multiple solutions. Sample test cases of both LES solutions and direct numerical simulations as well as published experimental data show excellent agreement between the integrated matched spectra and the respective turbulent statistics. Thus, the resultant uncertainties themselves provide a useful measure of accumulated statistical error in the resolved turbulent properties.
Volume 1: Symposia, Parts A and B, 2006
Journal of Fluids Engineering, 2014
Even after several decades of experimental and numerical testing, our present-day knowledge of th... more Even after several decades of experimental and numerical testing, our present-day knowledge of the axisymmetric turbulent boundary layer (TBL) along long thin circular cylinders still lacks a clear picture of many fundamental characteristics. The main issues causing this reside in the experimental testing complexities and the numerical simplifications. An important characteristic that is crucial for routine scaling is the boundary layer length scales, but the downstream growth of these scales (boundary layer, displacement, and momentum thicknesses) is largely unknown from the leading to trailing edges. Herein, we combine pertinent datasets with many complementary numerical computations (large-eddy simulations) to address this shortfall. We are particularly interested in expressing the length scales in terms of the radius-based and axial-based Reynolds numbers (Rea and Rex). Although the composite dataset gave an averaged shape factor H = 1.09 that is substantially lower than the pla...
Journal of Fluids Engineering, 2001
The dynamic eddy-viscosity relationship is a suitable choice for modeling the subgrid-scales (SGS... more The dynamic eddy-viscosity relationship is a suitable choice for modeling the subgrid-scales (SGS) in a large-eddy simulation (LES) of complex turbulent flows in irregular domains. This algebraic relationship is easy to implement and its dynamic coefficient will give negligible turbulent viscosity contributions in the flow regions that are irrotational or laminar. Its fine-scale turbulence predictions can be qualitatively reasonable if the local grid resolution maintains the SGS field predominantly within the equilibrium range of turbulent energy spectra. This performance is given herein by two curvilinear coordinate forms of the dynamic Smagorinsky model that are formally derived and a-priori tested using the resolved physics of the cylinder wake. The conservative form evaluates the dynamic coefficient in the computational (transformed) space whereas its non-conservative counterpart operates in the physical domain. Although both forms equally captured the real normal SGS stress rea...
Journal of Fluids Engineering, 1998
The formation and the downstream transport of the Strouhal vortices in the near wake of a circula... more The formation and the downstream transport of the Strouhal vortices in the near wake of a circular cylinder are investigated using the large-eddy simulation (LES) method. The governing equations are formulated in curvilinear coordinates to accommodate a nonorthogonal grid with formal development of a dynamic model to account for the subgrid turbulent scales. Results were produced with and without use of the model. The focus of the investigation is at a subcritical Reynolds number of 5600. Using the dynamic model, the LES results compared best to the published experimental data in terms of both the global and local wake characteristics such as the drag and base pressure coefficients, shedding and detection frequencies, peak vorticity, and the downstream mean velocity-defect and Reynolds stresses. The results further showed streamwise filaments that connect subsequent Strouhal vortices. Qualitatively, the time-averaged Reynolds stresses of the formation region revealed similar symmetr...
Journal of Fluids Engineering, 2003
Resolving the turbulent statistics of bluff-body wakes is a challenging task. Frequently, the str... more Resolving the turbulent statistics of bluff-body wakes is a challenging task. Frequently, the streamwise grid point spacing approaching the vortex exit boundary is sacrificed to gain near full resolution of the turbulent scales neighboring the body surface. This choice favors the solution strategies of direct numerical and large-eddy simulations (DNS and LES) that house spectral-like resolving characteristics with inherent dissipation. Herein, two differencing stencils are tested for approximating four forms of the convective derivative in the DNS and LES formulations for incompressible flows. The wake spectral characteristics and conventional parameters are computed for Reynolds numbers Re=200 (laminar wake) and Re=3900. These tests demonstrated reliable stability and spectral-like accuracy of compact fifth-order upwinding for the advective derivative and fourth-order cell-centered Pade´ (with fourth-order upwinding interpolation) for the Arakawa form of the convective derivative. ...
Journal of Fluids Engineering, 2004
Flow past cavities covered by perforated lids pose a challenging problem for design engineers. Ke... more Flow past cavities covered by perforated lids pose a challenging problem for design engineers. Kelvin–Helmholtz waves appear early in the separated shear layers above the perforations that quickly mature into large-scale coherent structures far downstream. This evolution is sustained by a hydrodynamic feedback mechanism within the cavity even when its aft wall is far removed from the lid. Herein, the results from large-eddy simulations show analogous fundamental characteristics between open and perforated-cover cavities. Both adequately scale the fundamental frequency of the large-scale disturbance using the freestream velocity and the cavity width (or lid length). Moreover, the dimensionless frequencies jump to higher modes at equivalent length scales. Unlike the open cavity, one can invoke certain conditions that instigate the instability above the perforations but not a simultaneous long-term feedback mechanism necessary to fully sustain the periodic oscillation. The lid itself o...
Journal of Fluids Engineering, 1994
The three-dimensional shear-driven cavity flow is numerically investigated at Reynolds numbers of... more The three-dimensional shear-driven cavity flow is numerically investigated at Reynolds numbers of 5000 and 10000. This investigation focuses on the unsteadiness and turbulent characteristics of the flow. At the moderate Reynolds number (Re = 5000) where the cavity flow is fully laminar, a direct numerical simulation (DNS) is used whereas large-eddy simulation (LES) methodology is adopted to predict the cavity flow at the higher Reynolds number (Re = 10000). Establishing a suitable form for the subgrid scale (SGS) turbulence model in this complex flow is guided by the DNS results at Re = 5000. Additionally, the SGS model is verified against DNS results at Re = 7500 where the cavity flow is known through experimentation to be locally transitional. The LES results verify the published experimental evidence as well as uncover new flow features within the cavity.
Journal of Fluids Engineering, 2012
After three decades of accumulated experimental and numerical results, a comprehensive understand... more After three decades of accumulated experimental and numerical results, a comprehensive understanding of the spatial evolution of axisymmetric turbulent boundary layers (ATBL) along long thin cylinders still eludes both scientists and engineers. While experimentalists dealt with axial alignment complexities, computationalists lacked proper inflow boundary conditions. Herein, we correct this latter deficiency and initiate an investigation of the thin cylinder turbulence under low Reynolds numbers and high transverse curvatures (boundary layer thicknesses to radius). Using the large-eddy simulation (LES) methodology, we are particularly interested in the radial propagation of the transverse curvature on the ATBL statistics. A ten-simulation matrix was constructed to examine these effects with validation against the experimental evidence. These tests investigated the ATBL maturity up to transverse curvatures approaching 2 orders of magnitude. A recently developed turbulent inflow proced...
Journal of Fluids Engineering, 2012
Generating acceptable inflow conditions for the turbulent boundary layer (TBL) growth along long ... more Generating acceptable inflow conditions for the turbulent boundary layer (TBL) growth along long thin cylinders is a challenging task. Previous production methods such as rescale/recycling, artificial turbulence, and antecedent databases are difficult to implement because the downstream physics do not conform to consistent scaling laws. An alternate inflow approach that involves only recycling the fluctuating elements coupled with a dynamic form of Spalding’s relationship for assigning the mean quantities shows promise for spatially resolving the axisymmetric turbulence along the thin cylinder. Applying this inflow technique for resolving the turbulent scales along a flat plate at a tested momentum-based Reynolds number of Reθ = 670 showed excellent agreement with the experimental data as well as the analytical results from the momentum-integral method. A minor adjustment length of approximately two inflow TBL thicknesses was necessary to attain consistent streamwise growth of the b...
Journal of Fluids Engineering, 2009
Parameter optimization is an excellent path for easily raising the resolution efficiency of compa... more Parameter optimization is an excellent path for easily raising the resolution efficiency of compact finite differencing schemes. Their low-resolution errors are attractive for resolving the fine-scale turbulent physics even in complex flow domains with difficult boundary conditions. Most schemes require optimizing closure stencils at and adjacent to the domain boundaries. But these constituents can potentially degrade the local resolution errors and destabilize the final solution scheme. Current practices optimize and analyze each participating stencil separately, which incorrectly quantifies their local resolution errors. The proposed process optimizes each participant simultaneously. The result is a composite template that owns consistent spatial resolution properties throughout the entire computational domain. Additionally, the optimization technique leads to templates that are numerically stable as understood by an eigenvalue analysis. Finally, the predictive accuracy of the opt...
Journal of Fluids Engineering, 2008
When establishing the spatial resolution character of a composite compact finite differencing tem... more When establishing the spatial resolution character of a composite compact finite differencing template for high-order field solutions, the stencils selected at nonperiodic boundaries are commonly treated independent of the interior scheme. This position quantifies a false influence of the boundary scheme on the resultant interior dispersive and dissipative consequences of the compound template. Of the three ingredients inherent in the composite template, only its numerical accuracy and global stability have been properly treated in a coupled fashion. Herein, we present a companion means for quantifying the resultant spatial resolution properties that lead to improved predictions of the salient problem physics. Compact boundary stencils with free parameters to minimize the field dispersion (or phase error) and dissipation are included in the procedure. Application of the coupled templates for resolving the viscous Burgers wave and two-dimensional acoustic scattering reveal significan...