Numerical Simulation of Isothermal Cruciform Jet Flow

Results from Large Eddy Simulation (LES) of fully developed flow in a ribbed duct are presented with rib pitch-to-height ratio (P/e) is 10 and a rib height to hydraulic diameter ratio (e/Dh) is 0.1. Computations are carried out on a square duct with 45° ribs on the top and bottom walls arranged in a staggered fashion. The ribs have a rounded cross-section and are skewed at 45° to the main flow. The Reynolds number based on bulk velocity is 25,000. Mean flow and turbulent quantities, together with heat transfer and friction augmentation results are presented for a stationary case. The flow is characterized by a helical vortex behind each rib and a complementary cross-sectional secondary flow, both of which result from the angle of the rib with respect to the mean flow and result in a spanwise variation of the heat transfer. The mean flow, the turbulent quantities and the heat transfer in the duct show similar trends as in the duct with square cross-section ribs. However the results show that there is lesser friction in the ducts with rounded ribs. The overall heat transfer on the ribbed wall was augmented by 2.85 times that of a smooth duct, at the cost of friction which increases by a factor of 10. The computed values compare well with the experimental values.

Experimental validation of large eddy simulations of flow and heat transfer in a stationary ribbed duct

In this work, the modelling of horizontal two-phase flows within the two-fluid Euler–Euler approach is investigated. A modified formulation of the morphology detection functions within the Algebraic Interfacial Area Density (AIAD) model is presented in combination with different models for the drag force acting on a sheared gas–liquid interface. In the case of free surface flows, those closure laws are often based on experimental correlations whose applicability is limited to certain flow regimes. It is investigated here whether the implementation of the modified blending functions in ANSYS CFX avoids this limitation. The influence of the new functions on the prediction of turbulence parameters in free surface flows is also examined quantitatively for the k-ω and k-ε two-equation turbulence models. Transient simulations of the WENKA counter-current stratified two-phase flow experiment were performed for validation. A prediction of the correct flow pattern as observed in the experiment improved dramatically when a turbulence damping term was included in the standard two-equation models. Using the k-ω and a modified k-ε turbulence model with damping terms close to the interface, better agreement with the experimental data was achieved. The morphology detection mechanism of the unified blending functions within the AIAD is seen as an improvement with respect to the detection of sharp interfaces. Satisfactory quantitative agreement is achieved for the modified free surface drag. Furthermore, it is demonstrated that turbulence dampening has to be accounted for in both turbulence models to qualitatively reproduce the mean flow and turbulence quantities from the experiment.

Predicting rocker shoe parameters for reducing plantar pressure using machine learning methods

Experimental measurements were carried out in an incompressible three-dimensional turbulent shear layer in the vicinity of an appendage mounted perpendicular to a flat plate. The thickness of the turbulent boundary layer as it approached the appendage leading edge was 76 mm or 1.07 times the maximum thickness of the appendage. As the oncoming boundary layer passed around the appendage, a strong secondary flow was formed which was dominated by a horseshoe root vortex. This secondary flow had a major effect in redistributing both the mean flow and turbulence quantities throughout the shear layer, and this effect persisted to a significant degree up to at least three chord lengths downstream of the appendage leading edge.

This paper reports on experimental study of turbulent flows over straight and inclined transverse ribs of square and triangular cross sections attached to the bottom and top walls of an asymmetric converging channel. The pitch-to-height ratio of the ribs was 10. A particle image velocimetry technique was used to conduct extensive velocity measurements at channel midspan and in planes close to the leading and trailing edges of the inclined ribs. From these measurements, spatial averaged profiles of the mean velocity and higher order statistics were obtained to study the effects of rib geometry, pressure gradient, spanwise plane, and rib inclination on the flow characteristics. The results show that rib geometry has no significant effects on the mean flow and turbulent quantities. The roughness effects produced by the straight ribs outweighed pressure gradient effects in the inner region of the flow. As a result, the skin friction coefficient is nearly independent of pressure gradient. The Reynolds shear stress and turbulent transport of the shear stress are also independent of pressure gradient. On the contrary, favorable pressure gradient decreased the Reynolds normal stresses in the outer region and increased the magnitudes of the triple velocity correlations and transport of turbulent kinetic energy (TKE). The three-dimensional secondary motion produced by the inclined ribs distorted the mean flow pattern and substantially diminished the ribs’ effectiveness to augment skin friction and turbulence. For example, the skin friction over the inclined ribs is only 50%–70% of the value measured over the straight ribs. Furthermore, the size of equivalent sand grain required to produce the same amount of drag is one-tenth to one-third of the rib height for the inclined ribs compared to two- to fourfold for the straight ribs. The inclined ribs also reduced the level of the Reynolds stresses, triple velocity correlations, and transport of both the turbulent kinetic energy and Reynolds shear stress compared to the straight ribs. The skewness factors showed that important structural differences exist between flows over straight and inclined ribs.

A Reynolds-Averaged Navier-Stokes (RANS) method has been developed in conjunction with a chimera domain decomposition technique for timedomain simulation of transient flow induced by practical 3D ships approaching a berthing structure. The method solves the mean flow and turbulence quantities on embedded, overlapped, and/or matched grids. The chimera domain decomposition approach was employed to accommodate the relative motions between different grid blocks. Calculations have been performed for a 3D barge and a DDG-51 ship hull in lateral motions to demonstrate the capability of the chimera RANS approach for time-domain simulation of the hydrodynamic coupling between the ship and berthing structures. The numerical solutions successfully captured many important features of the transient flow around berthing ships including the underkeel flow acceleration, wake flow separation, water cushion between the ship and harbor quaywall, and the complex interaction among bow, shoulder and stem wave systems.

Detached eddy simulation of flow around two wall-mounted cubes in tandem

The scale-similarity model in large-eddy simulation (LES) leads to an attractive, functionally simple expression for the subgrid-scale (SGS) stress tensor. It is well known, however, that the similarity model fails to accurately predict some of the most fundamental quantities in turbulent flows, perhaps the most important being the global energy transfer and the associated subgrid-scale dissipation. To address this, additional dissipative terms are usually added to the similarity model to improve its performance. In the present paper, considerations of interscale energy transfer have been used to identify sources of the observed deficiencies of the similarity model, specifically its inadequate balancing of terms contributing energy to the smallest scales and its duplication of terms producing effects in the largest scales. These considerations provide guidance in the development of a new model, which shows more favorable characteristics of energy transfer while preserving the functional simplicity of the scale-similarity model. Partial nonlinear terms are used to decompose the nonlinear transfer present in LES and to formulate a model expression capable of balancing small-scale production terms depositing energy near the LES cutoff. The proposed model is formulated in the same vein as the scale-similarity model, consisting of test filtered velocities and their products, but offers clear improvements in predictions of mean flow quantities and the global energy flux from the resolved to subgrid scales without the need for additional terms to augment subgrid-scale energy dissipation. The application of the new interscale transfer model in LES of wall-bounded flows leads to predictions of mean and RMS flow quantities comparable to those obtained for other, established SGS models.

Modeling swirling wakes is of considerable interest to wind farm designers. The present work is an attempt to develop a computational tool to understand free, far-wake development behind a single rotating wind turbine. Besides the standard momentum and continuity equations from the boundary layer theory in two dimensions, an additional equation for the conservation of angular momentum is introduced to study axisymmetric swirl effects on wake growth. Turbulence is simulated with two options: the standard <TEX>${\kappa}-{\varepsilon}$</TEX> model and the Reynolds Stress transport model. A finite volume method is used to discretize the governing equations for mean flow and turbulence quantities. A marching algorithm of expanding grids is employed to enclose the growing far-wake and to solve the equations implicitly at every axial step. Axisymmetric far-wakes with/without swirl are studied at different Reynolds numbers and swirl numbers. Wake characteristics such as wake width, half radius, velocity profiles and pressure profiles are computed. Compared with the results obtained under similar flow conditions using the computational software, FLUENT, this far-wake model shows simplicity with acceptable accuracy, covering large wake regions in far-wake study.

Measurement of the local skin friction coefficient and re-examination of the Reynolds-number-effect on the mean flow quantities were made in a zero-pressure gradient, smooth wall, turbulent boundary layer. In order to do this fairly, the two-dimensionality of the flow field was carefully adjusted. And, the wall shear stress τω was determined by direct measurement using a floating element device. The Reynolds number based on the momentum thickness Rθ=U1θ / ν ranges from 840 to 6 220. The present experimental results of cf propose a new empirical formula which well represents the present experimental data and confirms that the Karman constant χ=0.41, which implies a slope of the logarithmic linear layer, is independent of Rθ down to Rθ=860, whereas the additive constant varies with Rθ. The magnitude of the wake parameter takes an asymptotic value of 0.62 if the Reynolds number is sufficiently high. The effect of Rθ on all the turbulent intensities is evident even within the viscous sublayer. The constant stress layer does exist in the Reynolds shear stress profiles despite that the constant value varies with Rθ.

A Large Eddy Simulation of the flow around a NACA 0012 airfoil at a Reynolds number of 500,000 is presented. At this Reynolds number, the boundary layers transition from an initially laminar state to a turbulent state before reaching the trailing edge. Results obtained in this LES show a well-placed transition zone, and turbulence levels in good agreement with experimental data. Furthermore, the radiated acoustic field is computed directly in the same computation, which should allow future detailed examinations of the noise radiated by such a flow configuration. Recent rapid advances in Computational Aeroacoustics (CAA) have greatly increased the scope of problems that can be tackled by numerical methods. This is particularly true of Direct Noise Computations (DNC), in which the sound waves generated by turbulent flows are obtained directly from an unsteady compressible simulation of the Navier-Stokes equations. Indeed, high-Reynolds-number flows are now increasingly attainable, thanks to the development of high-order LES simulations that manage to preserve the large-scale small-amplitude acoustic perturbations alongside the small-scale large-amplitude aerodynamic fluctuations. The field of jet aeroacoustics has been particularly active in the advancement of these techniques, and a number of high-Reynolds-number jet flow simulations can be found in the literature. 2, 5, 6, 29 More recently, work on high-accuracy computations around curved geometries has shown that these methods are not restricted to Cartesian simulations. 21, 22, 26, 27, 30 A small number of time-accurate numerical studies has been performed around airfoils, generally placed at a small angle of attack to the flow, using an acoustic analogy to obtain far-field sound characteristics. 17, 21, 25, 31 The current work describes the use of a parallel curvilinear solver, based on high-order methods, to study the compressible flow around a 3-D NACA 0012 airfoil at a chord-based Reynolds number of 500,000, placed parallel to the upstream flow. It focuses on showing that realistic boundary layer transition is captured without needing to trigger the transition artificially, even when the airfoil is parallel to the upstream flow. Both mean flow quantities as well as fluctuation statistics compare well with experimental data. The acoustic field generated by the airfoil is also examined.

The tonal and broadband noise of an ultrahigh-bypass-ratio fan stage, which has been developed at École Centrale de Lyon, is studied using large-eddy simulations (LES). Wall-modeled LES of a periodic sector and a 360-deg full fan stage have been performed at approach conditions, which is a relevant operating point for aircraft noise certifications. The fan noise is directly obtained from the fully compressible LES, using a well-refined unstructured mesh, and compared with state-of-the-art analytical models. The impact of the periodic boundary conditions, which are often used for high-fidelity simulations of turbofan engines, is assessed. The results from the 360-deg and periodic-sector LES are compared from aerodynamic and acoustic perspectives, including an analysis of the mean and turbulent flow quantities and sound-pressure spectra. Aerodynamic parameters show similar results for both configurations. However, the fan blade loading is slightly reduced in the 360-deg- LES near the blade tip. Acoustically, lower sound power levels at the intake and exhaust sections of the fan stage are obtained in the 360-deg LES, when compared to the periodic sector LES, particularly at low and middle frequencies. This can be associated with lower coherence levels in the fan wakes and smaller spanwise correlation lengths at the trailing edge of the blades. The modal content of the acoustic field has also been analyzed in detail and shows that the periodic sector LES cannot correctly simulate the modal content of the fan noise.

Experimental investigations in an atmospheric boundary layer wind tunnel were carried out in order to study the influence of the windward forest edge structure on the flow characteristics above the canopy. Two different types of forest edges were used: abstracted edges, made of highly porous foam, and more realistic edges, consisting of individual model trees. The taper angle of the edge was varied three times for both edge types and all edges were combined with both dense and sparse forest stands. Time‐averaged mean and turbulent flow quantities were measured by means of a two‐dimensional laser Doppler anemometer system (LDA) and are presented in form of horizontal profiles near the canopy top.

Low Reynolds number axisymmetric turbulent boundary layer on a cylinder