Uncertainty Estimation for Numerical Solutions of Wall Bounded Turbulent Flows

In this study numerical solutions are presented for a steady state, incompressible, 2-D turbulent flow near a wall. For this specific problem a manufactured (exact) solution was provided by the organizers of the 2006 Lisbon Workshop [6]. With the help of manufactured solution, assessment of the true error and other relevant uncertainty measures are possible. The calculations were performed using the commercial flow solver FLUENT along with some user defined functions to define source terms and velocity profiles at boundaries. Though the flow regime is turbulent; the numerical solution is carried out for pseudo-laminar flow. This was done in order to avoid the errors implicit in turbulence models. The transformation from turbulent to laminar flow was done by defining a momentum source term which precludes the pressure gradient term. A detailed grid convergence analysis was performed. Using three-grid triplets the limiting values of the variables solved as the grid size tends to zero were calculated using different extrapolations. The L2 norms of the true error obtained from various extrapolations are assessed. These results exhibit solution convergence as the grid size decreases. It was also shown that cubic spline extrapolation perform the best among the methods considered.

Analysis of the Motion and Deformation of a Bubble Rising in a Viscoelastic Fluid

A finite element code based on the level set method is developed for performing two and three dimensional direct numerical simulations (DNS) of viscoelastic two-phase flow problems. The Oldroyd-B constitutive equation is used to model the viscoelastic liquid and both transient and steady state shapes of bubbles in viscoelastic buoyancy driven flows are studied. The influence of the governing dimensionless parameters, namely the Capillary number (Ca), the Deborah Number (De) and the polymer concentration parameter c, on the deformation of the bubble is also analyzed. Our simulations demonstrate that the rise velocity oscillates before reaching a steady value. The shape of the bubble, the magnitude of velocity overshoot and the amount of damping depend mainly on the parameter c and the bubble radius. Simulations also show that there is a critical bubble volume at which there is a sharp increase in the bubble terminal velocity as the increasing bubble volume increases, similar to the behavior observed in experiments. The structure of the wake of a bubble rising in a Newtonian fluid is strikingly different from that of a bubble rising in a viscoelastic fluid. In addition to the two recirculation zones at the equator of the bubble rising in a Newtonian fluid, two more recirculation zones exist in the wake of a bubble rising in viscoelastic fluids which influence the shape of a rising bubble. Interestingly, the direction of motion of the fluid a short distance below the trailing edge of a bubble rising in a viscoelastic fluid is in the opposite direction to the direction of the motion of the bubble, thus creating a “negative wake”. In this paper, the velocity field in the wake of the bubble, the effect of the parameters on the velocity field and their influence on the shape of the bubble are also investigated.

Experimental Modeling of Air Temperature and Velocity Distribution in an Engine Compartment

Investigation of air distribution and wind effect on a vehicle body from the point of view of underhood heat transfer effect and proper positioning of vehicle elements such cooler, condenser and engine configuration is an important area for engine researchers and manufacturers as well. In this research, the effect of air velocity distribution and wind effect around a vehicle is simulated and temperature and velocity distribution around engine block which is influenced by the wind effect is investigated. Thermal investigation of the engine compartment components is performed using results of underhood air temperature and velocity distribution. The heat transfer from engine surface is calculated from the engine energy balance in which their input data are obtained from a comprehensive experimental study on a four cylinder gasoline engine.

Numerical Simulation of the Unsteady Flow Patterns in a Small Squirrel-Cage Fan

In this work, a numerical simulation on the main flow features in a squirrel-cage fan, used in automotive air conditioning units, has been carried out. A 3D unsteady model has been developed for the entire machine. The flow in this geometrical model has been solved using the commercial code FLUENT®. Some of the analyzed features are the performance curves, the flow distribution over the different aspiration sections, the pressure and velocity distributions in selected surfaces, and the forces on the blades and on the whole impeller. The numerical results have been compared with the available experimental data, showing a reasonable good agreement.

Smooth and Rough Turbulent Boundary Layers: A Look at Skin Friction, Pressure Gradient and Roughness

The skin friction for a turbulent boundary layer can be measured and calculated in several ways with varying degrees of accuracy. In particular, the methods of the velocity gradient at the wall, the integrated boundary layer equation and the momentum integral equation are evaluated for both smooth and rough surface boundary layers. These methods are compared to the oil film interferometry technique measurements for the case of smooth surface flows. The integrated boundary layer equation is found to be relatively reliable, and the values computed with this technique are used to investigate the effect of increasing external favorable pressure gradient for both smooth and rough surfaces, and increasing roughness parameter for the rough surfaces.

Visualization of the Heat Transfer Enhancement During Condensation in a Microfin Tube

Microfins tubes are largely used in refrigeration industry for in-tube refrigerant condensation, because of the heat transfer enhancement when compared to equivalent smooth tubes under the same operating conditions. But not much evidence about the effect of microfins on the condensation flow patterns is available in the open literature. There is agreement in the open literature that the mechanisms of heat transfer are intimately linked with the prevailing two-phase flow regime. The present authors have recently measured the heat transfer coefficient during condensation of R410A in a microfin tube. The heat transfer enhancement in this tube can be experimentally evaluated by comparing those coefficients to the ones measured by Cavallini et al. (2001) in a plain tube, at the same operating conditions. The same operative conditions (saturation temperature, vapor quality and mass flux), occurring during the heat transfer measurements, were reproduced in a different section for visualization of flow patterns during condensation of R410A. The flow visualization has been carried out both in the plain tube and in the microfin tube. The objective of the present paper is to present the heat transfer enhancement during condensation of R410A and to show the flow visualized at the same operating condition for both the smooth and the microfin tube, aiming to link the heat transfer enhancement to the flow pattern variation.

Comparison of the Unsteady Loads of an Airfoil in the Pitching and Plunging Motions

A series of experiments were conducted on an oscillating airfoil in subsonic flow. The model was oscillated in two types of motions, pitch and plunge, at different velocities, and reduced frequencies. In addition, steady data were acquired and examined to furnish a baseline for analysis and comparison. The imposed variables of the experiment were reduced frequency, mean incident angle, amplitude of motion, and free stream velocity as well as the surface grit roughness. The unsteady aerodynamic loads were calculated using surface pressure measurements, 64 ports, along the chord for both upper and lower surfaces of the model. Particular emphases were placed on the effects of different type of motion on the unsteady aerodynamic loads of the airfoil at pre-stall, near stall, and post stall conditions. Variations of the aerodynamic coefficients with equivalent angle of attack for both pitching and plunging motions showed strong sensitivity to the reduced frequency, oscillation amplitude, Reynolds number, and mean angles of attack.

Discrete Bubble Modeling of Unsteady Cavitating Flow

A discrete vapor bubble model is developed to simulate the unsteady cavitating flows. The mixed vapor-liquid mixture is modeled as a system of pure phase domains (vapor and liquid) separated by free interfaces. On the phase boundary, a numerical solution for the phase transition is developed for compressible flows.

Spatio-Temporal Development of Supercavitation Over an Impulsively Launched Projectile

Supercavitation inception and formation was studied over blunt projectiles. The projectiles were fired using a gas gun method. In this method, projectiles are launched under the action of expanding detonation gases. Both qualitative and quantitative optical flow diagnostics using high speed digital imaging were used to analyze the spatio-temporal development of the supercavitating flow. For the first time, quantification of the supercavitation was achieved using Time Resolved Digital Particle Image Velocimetry (TRDPIV) detailing the two phase flow field surrounding the translating projectiles and the gas vapor bubble. Experimental results indicate that the supercavity forms at the aft end of the projectile and travels forward along the direction of projectile travel. The impulsive start of the projectile generates two asymmetric vortices which are shed from the blunt nose of the projectile. The vortices interact with the moving cavity and subsequently deform. This interaction is believed to directly contribute to the instabilities in the flight path.

Growth and Dissolution of Encapsulated Microbubble Used in Ultrasound Contrast Imaging

Steady dissolution of a bubble with two gases and a permeable shell has been modeled. At first the shell is modeled without elasticity. Factors such as permeability of the shell, surface tension, mole fraction of the osmotic agent, gas concentration in the bulk have been varied to study the growth and the time scale for dissolution of the bubble. It has been found that the inclusion of shell elasticity also plays a vital role in the growth and dissolution of the bubble.