No description available.

One of the biggest unsolved problems of modern physics is the turbulence phenomena in fluid flow. The appearance of turbulence in a flow system is regularly determined by velocity and length scales of the system. If those scales are small the motion of the fluid is laminar, but at larger scales, disturbances appear and grow, leading the flow field to transition to a fully turbulent state. The prediction of transitional flow is critical for many complex fluid flow applications, such as aeronautical, aerospace, biomedical, automotive, chemical processing, heating and cooling systems, and meteorology. For example, in some cases the flow may remain laminar throughout a significant portion of a given domain, and fully turbulent simulations may produce results that can lead to inaccurate conclusions or inefficient design, due to an inability to resolve the details of the transition process. This work aims to develop, implement, and test a new model concept for the prediction of transitional flows using a linear eddy-viscosity RANS approach. The effects of transition are included through one additional transport equation for v2 as an alternative to the Laminar Kinetic Energy (LKE) framework. Here v2 is interpreted as the energy of fully turbulent, three-dimensional velocity fluctuations. This dissertation presents two new single-point, physics-based turbulence models based on the transitional methodology mentioned above. The first one uses an existing transitional model as a baseline which is modified to accurately capture the physics of fully turbulent free shear flows. The model formulation was tested over several boundary layer and free shear flow test cases. The simulations show accurate results, qualitatively equal to the baseline model on transitional boundary layer test cases, and substantially improved over the baseline model for free shear flows. The second model uses the SST k-w fully turbulent model and again the effects of transition are included through one additional transport equation for v2. An initial version of the model is presented here. Simplicity of the formulation and ease of extension to other baseline models are two potential advantages of the new method.

In dilute polymer solution, polymers are able to change the flow structures and suppress the intensity of turbulence, resulting in a considerable friction drag reduction (DR). Despite the extraordinary progress made in the past few decades, some critical questions remain unanswered. This dissertation will try to address two fundamental questions in dilute polymeric turbulence: (I) interactions between polymers and turbulent motions during the qualitative low-extent to high-extent drag reduction (LDR and HDR) transition in inertia-driven turbulence, (II) roles of the inertia- and elasticity-driven turbulent motions in the dynamics of high elasticity polymeric flows. Many studies in the area of DR turbulence have been focused on the onset of DR and the maximum drag rection (MDR) asymptote. Between these two distinct stages, polymeric turbulent flows can also be classified into the qualitative LDR and HDR stages. Understanding the polymer-turbulence interactions during the drastic LDR-HDR transition is of vital importance for the development of efficient flow control technology. However, knowledge regarding this qualitative transition is still limited. In our DNS (direct numerical simulation) study, differences between the LDR and HDR stages are presented by a number of sharp changes in flow structures and statistics. Drag reduction in the flows is thus governed by two different mechanisms. The first is introduced at the onset of DR, which has been well explained by the indiscriminate suppression of turbulent fluctuations during the coil-stretch transition of polymers. The second mechanism starts at the LDR-HDR transition but its physical origin is not clear. Based on instantaneous observations and indirect statistical evidence, we proposed that polymers, after the LDR-HDR transition, could suppress the lift-up process of the near-wall vortices and modify the turbulent regeneration cycles. However, direct evidence to support this hypothesis is not available without a statistical analysis of the vortex configurations. Therefore, a new vortex tracking algorithm -- VATIP (vortex axis tracking by iterative propagation) -- is developed to analyze statistically the configurations and distribution of vortices. Implementing this method in the polymeric turbulence demonstrates that the lift-up process of streamwise vortices in the buffer layer is restrained at HDR, while the generation of hairpins and other three-dimensional vortices is suppressed. In addition, the characteristic lifting angle of conditional eddies extracted by a conditional sampling method is found to be larger in HDR than in the Newtonian turbulence. These observations all support our hypothesis about the mechanism of LDR-HDR transition. Research on the low elasticity turbulence usually considered the flow motions to be Newtonian-like. Turbulence here is driven by the inertial force (and hence called ``inertia-driven'' turbulence (IDT)) while polymers are responsible for dissipating turbulent kinetic energy. In the high elasticity turbulence, recent studies found a completely different turbulent flow type in which turbulence is driven by the elastic force and polymers could also feed energy to the flow. The behaviors of this ``elasticity-driven'' turbulence (EDT) are of significant interest in this area because of its potential connection to the MDR asymptote. However, EDT is difficult to capture by the traditional pseudo-spectral DNS scheme (SM) as a global artificial diffusion (GAD) term is involved in the polymer constitutive equation to stabilize the simulation. In our study, a new hybrid pseudo-spectral/finite-difference scheme is developed to simulate the polymeric turbulence without requiring a GAD. All of the spatial derivative terms are still discretized by the Fourier-Chebyshev-Fourier pseudo-spectral projection except for the convection term in the constitutive equation which is discretized using a conservative second-order upwind TVD (total variation diminishing) finite difference scheme. The numerical study using the hybrid scheme suggests that turbulent flows can be either driven by the inertial or the elastic forces and respectively result in the IDT and EDT flows. A dynamical flow state is also found in the high elasticity flow regime in which IDT and EDT can be sustained alternatively. / Thesis / Doctor of Philosophy (PhD) / Turbulence is known to consume kinetic energy in a fluid system. To enhance the efficiency of fluid transportation, various techniques are developed. Especially, it was found that a small amount of polymers in turbulent flows can significantly suppress turbulent activity and cause considerable friction drag reduction (DR). Extraordinary progress has been made to study this phenomenon, however, some questions still remain elusive. This dissertation tries to address some fundamental questions that relate to the two typical polymeric turbulent motions: the inertia- (IDT) and elasticity-driven turbulence (EDT). In IDT, mechanisms of transitions between the intermediate stages are investigated from the perspective of vortex dynamics. The different effects of polymers at each stage of the flow lead to different flow behaviors. Particularly, starting from the low- to high-extent DR transition, the lift-up process of vortices is suppressed by polymers. The regeneration cycles of turbulence are thus modified, which results in qualitative changes of flow statistics. Numerical study on EDT is enabled by a newly developed hybrid pseudo-spectral/finite-difference scheme. A systematic investigation of the parameter space indicates that EDT is one self-contain turbulence driven purely by the elastic force. It can also interact with IDT and lead to a dynamical flow state in which EDT and IDT can alternatively occur.

No description available.

An experimental program is designed to study the salient features of separated and reattached flows in pressure gradients generated in asymmetric diverging and converging channels. The channels comprised a straight flat floor and a curved roof that was preceded and followed by straight parallel walls. Reference measurements were also made in a parallel-wall channel to facilitate the interpretation of the pressure gradient flows. A transverse square rib located at the start of convergence/divergence was used to create separation inside the channels. In order to simplify the interpretation of the relatively complex separated and reattached flows in the asymmetric converging and diverging channels, measurements were made in the plain converging and diverging channel without the rib on the channel wall. All the measurements were obtained using a high resolution particle image velocimetry technique. The experiments without the ribs were conducted in the diverging channel at Reynolds number based on half channel depth (Reh) of 27050 and 12450 and in the converging channel at Reh = 19280. For each of these three test conditions, a high resolution particle image velocimetry technique (PIV) was used to conduct detailed velocity measurements in the upstream parallel section, within the converging and diverging section, and downstream of the converging and diverging sections. From these measurements, the boundary layer parameters and profiles of the mean velocities, turbulent quantities as well as terms in the transport equations for turbulent kinetic energy and Reynolds stresses were obtained to document the effects of pressure gradient on the flow. In the adverse pressure gradient case, the turbulent quantities were enhanced more significantly in the lower boundary layer than the upper boundary layer. On the other hand, favorable pressure gradient attenuated the turbulence levels and the effect was found to be similar on both the upper and the lower boundary layers. For the separated and reattached flows in the converging, diverging and parallel-wall channels at Reh = 19440, 12420 and 15350, respectively. The Reynolds number based on the approach velocity and rib height was Rek  2700. From these measurements, profiles of the mean velocities, turbulent quantities and the various terms in the transport equations for turbulent kinetic energy and Reynolds stresses were also obtained. The flow dynamics in the upper boundary layer in the separated region and the early stages of flow redevelopment were observed to be insensitive to the pressure gradients. In the lower boundary layer, however, the flow dynamics were entirely dominated by the separated shear layer in the separated region as well as the early region of flow redevelopment. The effects of the separated shear layer diminished in the redevelopment region so that the dynamics of the flow were dictated by the pressure gradients. The proper orthogonal decomposition (POD) was applied to educe the dominant large scale structures in the separated and reattached flows. These dominant scales were used to document structural differences between the canonical upstream flow and the flow field within the separated and redeveloping region. The contributions of these dominant structures to the dynamics of the Reynolds normal and shear stresses are also presented and discussed. It was observed that the POD recovers Reynolds shear stress more efficiently than the turbulent kinetic energy. The reconstruction reveals that large scales contribute more to the Reynolds shear stress than the turbulent kinetic energy. / February 2009

A novel computational approach, Two Level Simulation (TLS), was developed based on the explicit reconstruction of the small-scale velocity by solving the small-scale governing equations on the domain with reduced dimension representing a collection of one-dimensional lines embedded in the three-dimensional flow domain. A coupled system of equations, that is not based on an eddy-viscosity hypothesis, was derived based on the decomposition of flow variables into the large-scale and the small-scale components without introducing the concept of filtering. Simplified treatment of the small-scale equations was proposed based on modeling of the small-scale advective derivatives and the small-scale dissipative terms in the directions orthogonal to the lines. TLS approach was tested to simulate benchmark cases of turbulent flows, including forced isotropic turbulence, mixing layers and well-developed channel flow, and demonstrated good capabilities to capture turbulent flow features using relatively coarse grids.

Optimal large eddy simulation (OLES) is an approach to LES sub-grid modeling that requires multi-point correlation data as input. Until now, this has been obtained by analyzing DNS statistics. In the finite-volume OLES formulation studied here, under the assumption of small-scale homogeneity and isotropy, these correlations can be theoretically determined from Kolmogorov inertial-range theory, small-scale isotropy, along with the quasi-normal approximation. These models are expressed as generalized quadratic and linear finite volume operators that represent the convective momentum flux. These finite volume operators have been analyzed to determine their characteristics as numerical approximation operators and as models of small-scale effects. In addition, the dependence of the model operators on the anisotropy of the grid and on the size of the stencils is analyzed to develop idealized general operators that can be used on general grids. The finite volume turbulence operators developed here will be applicable in a wide range of LES problems. / text

The increase in the availability and power of computational resources over the last fifteen years has contributed to the development of many different types of numerical optimization methods and created a large area of research focussed on numerical aerodynamic shape optimization and, more recently, high-fidelity multidisciplinary optimization. Numerical optimization provides dramatic savings when designing new aerodynamic configurations, as it allows the designer to focus more on the development of a well-posed design problem rather than on performing an exhaustive search of the design space via the traditional cut-and-try approach, which is expensive and time-consuming. It also reduces the dependence on the designer’s experience and intuition, which can potentially lead to more optimal designs. Numerical optimization methods are particularly attractive when designing novel, unconventional aircraft for which the designer has no pre-existing studies or experiences from which to draw; these methods have the potential to discover new designs that might never have been arrived at without optimization. This work presents an extension of an efficient gradient-based numerical aerodynamic shape optimization algorithm to enable optimization in turbulent flow. The algorithm includes an integrated geometry parameterization and mesh movement scheme, an efficient parallel Newton-Krylov-Schur algorithm for solving the Reynolds-Averaged Navier-Stokes (RANS) equations, which are fully coupled with the one-equation Spalart-Allmaras turbulence model, and a discrete-adjoint gradient evaluation. In order to develop an efficient methodology for optimization in turbulent flows, the viscous and turbulent terms in the ii governing equations were linearized by hand. Additionally, a set of mesh refinement tools was introduced in order to obtain both an acceptable control volume mesh and a sufficiently refined computational mesh from an initial coarse mesh. A series of drag minimization studies was carried out which show that the algorithm is able to maintain robustness in the mesh movement and flow analysis in the presence of large shape changes, an important requirement for performing exploratory optimizations aiming to discover novel configurations and for multidisciplinary optimization. Additionally, the algorithm is able to find incremental improvements when given well-designed initial planar and nonplanar geometries. A comparison of Euler-based and RANS-based optimizations highlights the importance of considering viscous and turbulent effects. A multi-point optimization demonstrates that the algorithm is able to address practical aerodynamic design problems.

The increase in the availability and power of computational resources over the last fifteen years has contributed to the development of many different types of numerical optimization methods and created a large area of research focussed on numerical aerodynamic shape optimization and, more recently, high-fidelity multidisciplinary optimization. Numerical optimization provides dramatic savings when designing new aerodynamic configurations, as it allows the designer to focus more on the development of a well-posed design problem rather than on performing an exhaustive search of the design space via the traditional cut-and-try approach, which is expensive and time-consuming. It also reduces the dependence on the designer’s experience and intuition, which can potentially lead to more optimal designs. Numerical optimization methods are particularly attractive when designing novel, unconventional aircraft for which the designer has no pre-existing studies or experiences from which to draw; these methods have the potential to discover new designs that might never have been arrived at without optimization. This work presents an extension of an efficient gradient-based numerical aerodynamic shape optimization algorithm to enable optimization in turbulent flow. The algorithm includes an integrated geometry parameterization and mesh movement scheme, an efficient parallel Newton-Krylov-Schur algorithm for solving the Reynolds-Averaged Navier-Stokes (RANS) equations, which are fully coupled with the one-equation Spalart-Allmaras turbulence model, and a discrete-adjoint gradient evaluation. In order to develop an efficient methodology for optimization in turbulent flows, the viscous and turbulent terms in the ii governing equations were linearized by hand. Additionally, a set of mesh refinement tools was introduced in order to obtain both an acceptable control volume mesh and a sufficiently refined computational mesh from an initial coarse mesh. A series of drag minimization studies was carried out which show that the algorithm is able to maintain robustness in the mesh movement and flow analysis in the presence of large shape changes, an important requirement for performing exploratory optimizations aiming to discover novel configurations and for multidisciplinary optimization. Additionally, the algorithm is able to find incremental improvements when given well-designed initial planar and nonplanar geometries. A comparison of Euler-based and RANS-based optimizations highlights the importance of considering viscous and turbulent effects. A multi-point optimization demonstrates that the algorithm is able to address practical aerodynamic design problems.

An experimental program is designed to study the salient features of separated and reattached flows in pressure gradients generated in asymmetric diverging and converging channels. The channels comprised a straight flat floor and a curved roof that was preceded and followed by straight parallel walls. Reference measurements were also made in a parallel-wall channel to facilitate the interpretation of the pressure gradient flows. A transverse square rib located at the start of convergence/divergence was used to create separation inside the channels. In order to simplify the interpretation of the relatively complex separated and reattached flows in the asymmetric converging and diverging channels, measurements were made in the plain converging and diverging channel without the rib on the channel wall. All the measurements were obtained using a high resolution particle image velocimetry technique. The experiments without the ribs were conducted in the diverging channel at Reynolds number based on half channel depth (Reh) of 27050 and 12450 and in the converging channel at Reh = 19280. For each of these three test conditions, a high resolution particle image velocimetry technique (PIV) was used to conduct detailed velocity measurements in the upstream parallel section, within the converging and diverging section, and downstream of the converging and diverging sections. From these measurements, the boundary layer parameters and profiles of the mean velocities, turbulent quantities as well as terms in the transport equations for turbulent kinetic energy and Reynolds stresses were obtained to document the effects of pressure gradient on the flow. In the adverse pressure gradient case, the turbulent quantities were enhanced more significantly in the lower boundary layer than the upper boundary layer. On the other hand, favorable pressure gradient attenuated the turbulence levels and the effect was found to be similar on both the upper and the lower boundary layers. For the separated and reattached flows in the converging, diverging and parallel-wall channels at Reh = 19440, 12420 and 15350, respectively. The Reynolds number based on the approach velocity and rib height was Rek  2700. From these measurements, profiles of the mean velocities, turbulent quantities and the various terms in the transport equations for turbulent kinetic energy and Reynolds stresses were also obtained. The flow dynamics in the upper boundary layer in the separated region and the early stages of flow redevelopment were observed to be insensitive to the pressure gradients. In the lower boundary layer, however, the flow dynamics were entirely dominated by the separated shear layer in the separated region as well as the early region of flow redevelopment. The effects of the separated shear layer diminished in the redevelopment region so that the dynamics of the flow were dictated by the pressure gradients. The proper orthogonal decomposition (POD) was applied to educe the dominant large scale structures in the separated and reattached flows. These dominant scales were used to document structural differences between the canonical upstream flow and the flow field within the separated and redeveloping region. The contributions of these dominant structures to the dynamics of the Reynolds normal and shear stresses are also presented and discussed. It was observed that the POD recovers Reynolds shear stress more efficiently than the turbulent kinetic energy. The reconstruction reveals that large scales contribute more to the Reynolds shear stress than the turbulent kinetic energy.