Laura L. Pauley

The structure of two-dimensional separation

The separation of a two-dimensional laminar boundary layer under the influence of a suddenly imposed external adverse pressure gradient was studied by time-accurate numerical solutions of the Navier-Stokes equations. It was found that a strong adverse pressure gradient created periodic vortex shedding from the separation. The general features of the time-averaged results were similar to experimental results for laminar separation bubbles. Comparisons were made with the ‘steady ’ separation experiments of Gaster (1966). It was found that his ‘bursting ’ occurs under the same conditions as our periodic shedding, suggesting that bursting is actually periodic shedding which has been time-averaged. The Strouhal number based on the shedding frequency, local free-stream velocity, and boundary-layer momentum thickness at separation was independent of the Reynolds number and the pressure gradient. A criterion for onset of shedding was established. The shedding frequency was the same as that predicted for the most amplified linear inviscid instability of the separatcd shear layer.

Low-Reynolds-number separation on an airfoil

Unsteady boundary-layer separation from an Eppler 387 airfoil at low Reynolds number is studied numerically. Through a series of computations, the effects of Reynolds number and angle of attack are investigated. For all cases, vortex shedding is observed from the separated shear layer. From linear stability analysis, a KelvinHelmholtz instability is identified as causing shear layer unsteadiness. The low-turbulence wind-tunnel tests of the Eppler 387 airfoil are used to compare with the time-averaged results of the present unsteady computations. The favorable comparison between computational and experimental results strongly suggests that the unsteady largescale structure controls the low-Reynolds-number separation bubble reattachment with small-scale turbulence playing a secondary role. Nomenclature C = chord length CD - drag coefficient CL = lift coefficient Cp = pressure coefficient / = shedding frequency Re = chord Reynolds number R P - reattachment point S P = separation point Sr = Strouhal number U = velocity 9 = momentum thickness Subscripts sep = conditions at separation oo = freestream conditions

Performance Analysis of Cavitating Flow in Centrifugal Pumps Using Multiphase CFD

A multi-phase CFD method is used to analyze centrifugal pump performance under developed cavitating conditions. The differential model employed is the homogeneous two-phase Reynolds-Averaged-Navier-Stokes equations, wherein mixture momentum and volume continuity equations are solved along with vapor volume fraction continuity. Mass transfer modeling is provided for the phase change associated with sheet cavitation. Quasi-three-dimensional (Q3D) and fully-three-dimensional analyses are performed for two impeller configurations. Using Q3D analysis, steady and time-dependent analyses were performed across a wide range of flow coefficients and cavitation numbers. Characteristic performance trends associated with offdesign flow and blade cavitation are observed. The rapid drop in head coefficient at low cavitation numbers (breakdown) is captured for all flow coefficients. Local flow field solution plots elucidate the principal physical mechanisms associated with the onset of breakdown. Results are also presented which illustrate the full three dimensional capability of the method.

The unsteady structure of two‐dimensional steady laminar separation

The two‐dimensional unsteady incompressible Navier–Stokes equations, solved by a fractional time‐step method, were used to investigate separation due to the application of an adverse pressure gradient to a low‐Reynolds number boundary layer flow. The inviscid pressure distribution of Gaster [AGARD CP 4, 813 (1966)] was applied in the present computations to study the development of a laminar separation bubble. In all cases studied, periodic vortex shedding occurred from the primary separation region. The shed vortices initially lifted from the boundary layer and then returned towards the surface downstream. The shedding frequency nondimensionalized by the momentum thickness was found to be independent of Reynolds number. The value of the nondimensional Strouhal number, however, was found to differ from the results of Pauley et al. [J. Fluid Mech. 220, 397 (1990)], indicating that the shedding frequency varies with the nondimensional pressure distribution, Cp. The computational results were time averaged o...

Two- and three-dimensional large-eddy simulations of a transitional separation bubble

In the present study we use two- and three-dimensional large-eddy simulations to examine the role of small-scale turbulence within a transitional separation bubble studied experimentally by Gaster (AGARD Conference Proceedings No. 4, 1966, pp. 813–854). In addition, several large-eddy simulation parameters and models are studied to show their effect on the computations. The inclusion of a small-scale turbulence model in the two-dimensional computations leads to an increase in the time-averaged separation bubble length and a slight reduction in the peak of the pressure coefficient distribution near reattachment. Increasing the filter width or increasing the Smagorinsky coefficient reduces the peak in the pressure coefficient distribution but also decreases the pressure coefficient within the pressure plateau. The two-dimensional LES accurately predicts the time-averaged bubble length of Gaster but does not accurately describe the experimental wall pressure distribution within the bubble. Three-dimensional ...

Numerical study of the steady-state tip vortex flow over a finite-span hydrofoil

The flow over a finite-span hydrofoil creating a tip vortex was numerically studied by computing the full Navier-Stokes equations. A good agreement in pressure distribution and oil flow pattern was achieved between the numerical solution and available experimental data. The steady-state roll-up process of the tip vortex was described in detail from the numerical results. The effect of the angle of attack, the Reynolds number, and the hydrofoil planform on the tip vortex was investigated. The axial and tangential velocities within the tip-vortex core in the near-field wake region were greatly influenced by the angle of attack. A jet-like profile in the axial velocity was found within the tip-vortex core at high angle of attack, while a wake-like profile in the axial velocity was found at low angle of attack. Increasing the Reynolds number was found to increase the maximum axial velocity, but only had a slight impact on the tangential velocity. Finally, a swept hydrofoil planform was found to attenuate the strength of the tip vortex due to the low-momentum boundary layer traveling into the tip vortex on the suction side

NUMERICAL COMPUTATION OF TIP VORTEX FLOW GENERATED BY A MARINE PROPELLER

The uniform flow past a rotating marine propeller was studied using incompressible Reynolds-averaged Navier-Stokes computations with the Baldwin-Barth turbulence model. Extensive comparison with the experimental data was made to validate the numerical results. The general characteristics of the propeller flow were well predicted. The current numerical method, however, produced an overly diffusive and dissipative tip vortex core. Modification of the Baldwin-Barth model to better predict the Reynolds stress measurements also improved the prediction of the mean velocity field. A modified tip geometry was also tested to show that an appropriate cross section design can delay cavitation inception in the tip vortex without reducing the propeller performance.

Study of Tip Vortex Cavitation Inception Using Navier-Stokes Computation and Bubble Dynamics Model

The Rayleigh-Plesset bubble dynamics equation coupled with the bubble motion equation developed by Johnson and Hsieh was applied to study the real flow effects on the prediction of cavitation inception in tip vortex flows. A three-dimensional steady-state tip vortex flow obtained from a Reynolds-Averaged Navier-Stokes computation was used as a prescribed flow field through which the bubble was passively convected. A “window of opportunity” through which a candidate bubble must pass in order to be drawn into the tip-vortex core and cavitate was determined for different initial bubble sizes. It was found that bubbles with larger initial size can be entrained into the tip-vortex core from a larger window size and also had a higher cavitation inception number.

Response of Two-Dimensional Separation to Three-Dimensional Disturbances

The present study investigates the development and structure of three-dimensionality due to a three-dimensional velocity perturbation applied to the inlet of an unsteady two-dimensional separation computation. A random noise perturbation and a sine-wave perturbation are considered separately. In both cases, the spanwise variations were amplified in the separation and within the shed vortices. The vortex shedding frequency observed in the two-dimensional computation was not altered by the three dimensional of the flow field. No observable spanwise structure was produced by the random noise perturbation. The sine-wave perturbation, however, produced longitudinal Goertler vortices within the separation. Using a linear stability analysis, the presence of longitudinal vortices in a separated laminar boundary layer was predicted by Inger (1987). When the velocity field was averaged across the span, it was found that the sine-wave perturbation increased the separation length and reduced the strength of shed vortex. The span-averaged streamlines from the random noise perturbation, however, reproduced the unsteady separation of the two-dimensional computations.

Teaching the introductory computer programming course for engineers using Matlab

The introductory computer programming course for engineers is usually taught using the C++ programming language. This work describes our efforts during the past four years, as a pilot project, which can be used in an evaluation process by those departments that would like to substitute Matlab for C++. Those who would like to continue the current practice, but are looking for more challenging problems or projects involving Matlab can also use the project outcome. In order to increase student involvement in the learning process and further improve learning outcomes, the implementation plan included various hardware and software projects, not all at the same time. Robotics projects were added to illustrate an application of programming; which students can relate to and enjoy, as well as helping them improve their software and algorithm design skills for real-time applications. Software projects included the design of simple games and applications using Matlabpsilas graphical user interface (GUI) tool. A discussion of the advantages and disadvantages of conducting a computer programming course in this format, including four different course formats that we have used are included.