The boundary layer equations for plane, incompressible, and steady flow are 

$$\matrix{ {u{{\partial u} \over {\partial x}} + v{{\partial u} \over {\partial y}} = - {1 \over \varrho }{{\partial p} \over {\partial x}} + v{{{\partial ^2}u} \over {\partial {y^2}}},} \cr {0 = {{\partial p} \over {\partial y}},} \cr {{{\partial u} \over {\partial x}} + {{\partial v} \over {\partial y}} = 0.} \cr }$$

Boundary Layer Theory

A hybrid RANS-LES approach with delayed-DES and wall-modelled LES capabilities

Strategies for turbulence modelling and simulations

The numerical simulation of high Reynolds number flows is hampered by model accuracy if the Reynolds-averaged Navier–Stokes (RANS) equations are used, and by computational cost if direct or large-eddy simulations (LES) that resolve the near-wall layer are employed. The cost of a calculation scales like the Reynolds number to the power 3 for direct numerical simulations, or 2.4 for LES, making the resolution of the wall layer at high Reynolds number infeasible even with the most advanced computers. In LES, an attractive alternative to compute high-Re flows is the use of wall-layer models, in which only the outer layer is resolved, while the near-wall region is modeled. Three broad classes of approaches are presently used: bypassing this region altogether using wall functions, solving a separate set of equations in the near-wall region, weakly coupled to the outer flow, or simulating the near-wall region in a global, Reynolds-averaged, sense. These approaches are discussed and their ranges of applicability are highlighted. Various unresolved issues in wall-layer modeling are presented.

Wall-layer models for large-eddy simulations

The Structure of Turbulent Shear Flow By Dr. A. A. Townsend. Pp. xii + 315. 8¾ in. × 5½ in. (Cambridge: At the University Press.) 40s.

/pdf/the-structure-of-turbulent-shear-flow-2yf3szhaqb.pdf

The Structure of Turbulent Shear Flow

This paper analyses the properties of viscous swirling flow in a pipe. The analysis is based on the time-averaged quasi-cylindrical Navier-Stokes equations and is applicable to steady, unsteady and turbulent swirling flow. A method is developed to determine the critical level of swirl (vortex breakdown) for an arbitrary vortex. The method can also be used for an estimation of the radial velocity profile if the other components are given or measured along a single radial line. The quasi-cylindrical equations are rearranged to yield a single ordinary differential equation for the radial distribution of the radial velocity component. The equation is singular for certain levels of swirl. It is shown that the lowest swirl level at which the equation is singular corresponds exactly to the sufficient condition for axisymmetric vortex breakdown as derived by Wang and Rusak [J. Fluid Mech. {340}, 177-223 (1997)] and Rusak et al. [AIAA J. {36}, 1848-1853 (1998)]. In narrow regions around the critical levels of swirl, the solution violates the quasi-cylindrical assumptions and the flow must undergo a drastic change of structure. The critical swirl level is determined by the sign change of the smallest eigenvalue of the discrete linear operator which relates the radial velocities to effects of viscosity and turbulence. It is shown that neither viscosity nor turbulence directly alters the critical level of swirl.

On the failure of the quasicylindrical approximation and the connection to vortex breakdown in turbulent swirling flow

The Rotary bell spray applicator technique is commonly used in the automotive industry for paint application because of its high transfer efficiency and high-quality result. The bell spins rapidly around its axis with a tangential velocity at the edge in the order of 100 m/s. The paint falls off the edge and enters the air with a large relative velocity, driving the atomization into small droplets where the resulting size distribution depends on the process conditions. Especially the rotation speed of the bell is an important parameter governing the size distribution. The main research question in this work is to investigate if the Taylor Analogy Breakup (TAB) model can be used to predict the resulting droplet size distributions in spray painting. As the paint is a viscous fluid a modification of the TAB model taking non-linear effects of large viscosity into account is proposed. The parameters in the breakup model are tuned by optimization to match droplet size distributions obtained in CFD simulations with measured ones. Results are presented for three cases with rotation speeds from 30 to 50 thousand RPM where the full droplet size distributions are compared with measurements. Good results are obtained for all three cases where the simulated size distributions compare well to measurements over a wide range of droplet sizes. The TAB method is able to quantitatively predict the result of the breakup process and can be used in a preprocessing stage of a full spray painting simulation, thereby reducing the need for costly and cumbersome measurements.

A Modified TAB Model for Simulation of Atomization in Rotary Bell Spray Painting

An acoustic analogy applied to the laminar upstream flow over an open 2D cavity

Accurately predicting both average flow quantities and acoustic sources at the front window of today's ground vehicles are still a considerable challenge to automotive companies worldwide. One of the most important aspects in terms of obtaining not only trustworthy results but also the most tedious one and therefore perhaps overlooked, is the control and outcome of the mesh generation process. Generating unstructured volume meshes suitable for large eddy simulations with high level representation of geometrical details is both a time consuming and an extremely computer demanding activity. This work investigates two different mesh generation processes with its main aim to evaluate their outcome with respect to the prediction of the two dominating dipole sources in a temporal form of the Curle's equation. Only a handful of papers exists that report a high level representation of the vehicle geometry and the aim of predicting the fluctuating exterior noise sources. To the author's knowledge no studies have been conducted in which both these source terms are evaluated quantitatively against measurements. The current paper investigates the degree to which the amplitude of these two source terms can be predicted by using the traditional law-of-the-wall and hex-dominant meshes with isotropic resolution boxes for a detailed ground vehicle geometry. For this purpose, the unstructured segregated commercial FLUENT finite volume method code is used. The flow field is treated as incompressible and the Smagorinsky-Lilly model is used to compute the subgrid stresses. Mean flow quantities are measured with a 14 hole probe for 14 rakes downstream of the side mirror. The dynamic pressure sensors are distributed at 16 different positions over the side window to capture the fluctuating pressure signals. All measurements in this work were conducted at Ford's acoustic wind tunnel in Cologne. All three simulations accurately predict the velocity magnitude closest to the window and downstream of the mirror head recirculation zone. Some variations in the size and shape of this recirculation zone are found between the different meshes, most probably caused by differences in the detachment of the mirror head boundary layer. The Strouhal number of the shortest simulation was computed from the fundamental frequency of the drag force coefficient. The computed Strouhal number agrees well with the corresponding results from similar objects and gives an indication of an acceptable simulation time. The dynamic pressure sensors at 16 different locations at the vehicle side window were also used to capture the levels of the two dipole source terms. These results are compared with the three simulations. With the exception of three positions, at least one of the three simulations accurately captures the levels of both source terms up to about 1000 Hz. The three positions with less agreement as compared with measurements were found to be in regions sensitive to small changes in the local flow direction. [DOI: 10.1115/1.4001340]

Flow and Dipole Source Evaluation of a Generic SUV

/pdf/room-airflows-with-low-reynolds-number-effects-499t64s76t.pdf

Lars Davidson

Papers

On the failure of the quasicylindrical approximation and the connection to vortex breakdown in turbulent swirling flow

A Modified TAB Model for Simulation of Atomization in Rotary Bell Spray Painting

An acoustic analogy applied to the laminar upstream flow over an open 2D cavity

Flow and Dipole Source Evaluation of a Generic SUV

Room Airflows with Low Reynolds Number Effects