Turbulent boundary layers with secondary flow

An experimental analysis of the boundary layer on a plane wall, along which the flow occurs, whose potential flow lines are curved in plane parallel to the wall is discussed. According to the equation frequently applied to boundary layers in a plane flow, which is usually obtained by using the pulse law, a generalization is derived which is valid for boundary layers with spatial flow. The wall shear stresses were calculated with this equation

Heaping, Secondary Flows and Broken Symmetry in Flows of Elongated Granular Particles

In this paper we report experiments where we shear granular rods in split-bottom geometries, and find that a significant heap of height of least 40% of the filling height can form at the particle surface. We show that heaping is caused by a significant secondary flow, absent for spherical particles. Flow reversal transiently reverses the secondary flow, leading to a quick collapse and slower regeneration of the heap. We present a symmetry argument and experimental data that show that the generation of the secondary flow is driven by a misalignment of the mean particle orientation with the streamlines of the flow. This general mechanism is expected to be important in all flows of sufficiently anisometric grains.Comment: Accepted for Soft Matte

A simple laminar boundary layer with secondary flow

The incompressible laminar boundary layer over a flat plate is studied for the simple case where the stream lines in the free flow have a parabolic shape. An exact solution of the boundary layer equations is derived. No separation occurs, even when there is a strong adverse pressure gradient along the stream lines, so that in this instance the secondary flow has a favorable influence. Because of the variation of total pressure from one stream line to another in the free stream, the total pressure within the boundary layer at a given point can exceed that of the corresponding free stream

Influence of pressure driven secondary flows on the behavior of turbofan forced mixers

A finite difference procedure was developed to analyze the three dimensional subsonic turbulent flows in turbofan forced mixer nozzles. The method is based on a decomposition of the velocity field into primary and secondary flow components which are determined by solution of the equations governing primary momentum, secondary vorticity, thermal energy, and continuity. Experimentally, a strong secondary flow pattern was identified which is associated with the radial inflow and outflow characteristics of the core and fan streams and forms a very strong vortex system aligned with the radial interface between the core and fan regions. A procedure was developed to generate a similar generic secondary flow pattern in terms of two constants representing the average radial outflow or inflow in the core and fan streams as a percentage of the local streamwise velocity. This description of the initial secondary flow gave excellent agreement with experimental data. By identifying the nature of large scale secondary flow structure and associating it with characteristic mixer nozzle behavior, it is felt that the cause and effect relationship between lobe design and nozzle performance can be understood

Axial compressor middle stage secondary flow study

This report describes an experimental investigation of the secondary flow within and aft of an axial compressor model with thick endwall boundary layers. The objective of the study was to obtain detailed aerodynamic and trace gas concentration traverse data aft of a well documented isolated rotor for the ultimate purpose of improving the design phases of compressor development based on an improved physical understanding of secondary flow. It was determined from the flow visualization, aerodynamic, and trace gas concentration results that the relative unloading of the midspan region of the airfoil inhibitied a fullspan separation at high loading preventing the massive radial displacement of the hub corner stall to the tip. Radial distribution of high and low total pressure fluid influenced the magnitude of the spanwise distribution of loss, such that, there was a general decreases in loss near the hub to the extent that for the least loaded case a negative loss (increase in total pressure) was observed. The ability to determine the spanwise distribution of blockage was demonstrated. Large blockage was present in the endwall regions due to the corner stall and tip leakage with little blockage in the core flow region. Hub blockage was found to increase rapidly with loading

A semi-direct solver for compressible 3-dimensional rotational flow

An iterative procedure is presented for solving steady inviscid 3-D subsonic rotational flow problems. The procedure combines concepts from classical secondary flow theory with an extension to 3-D of a novel semi-direct Cauchy-Riemann solver. It is developed for generalized coordinates and can be exercised using standard finite difference procedures. The stability criterion of the iterative procedure is discussed along with its ability to capture the evolution of inviscid secondary flow in a turning channel

Controlling secondary flow in Taylor-Couette turbulence through spanwise-varying roughness

Highly turbulent Taylor-Couette flow with spanwise-varying roughness is investigated experimentally and numerically (direct numerical simulations (DNS) with an immersed boundary method (IBM)) to determine the effects of the spacing and axial width $s$ of the spanwise varying roughness on the total drag and {on} the flow structures. We apply sandgrain roughness, in the form of alternating {rough and smooth} bands to the inner cylinder. Numerically, the Taylor number is $\mathcal{O}(10^9)$ and the roughness width is varied between $0.47\leq \tilde{s}=s/d \leq 1.23$, where $d$ is the gap width. Experimentally, we explore $\text{Ta}=\mathcal{O}(10^{12})$ and $0.61\leq \tilde s \leq 3.74$. For both approaches the radius ratio is fixed at $\eta=r_i/r_o = 0.716$, with $r_i$ and $r_o$ the radius of the inner and outer cylinder respectively. We present how the global transport properties and the local flow structures depend on the boundary conditions set by the roughness spacing $\tilde{s}$. Both numerically and experimentally, we find a maximum in the angular momentum transport as function of $\tilde s$. This can be atributed to the re-arrangement of the large-scale structures triggered by the presence of the rough stripes, leading to correspondingly large-scale turbulent vortices.Comment: 20 pages, 7 figures, draft for JF

Numerical simulation of flows in curved diffusers with cross-sectional transitioning using a three-dimensional viscous analysis

A three dimensional analysis for fully viscous, subsonic, compressible flow is evaluated. An approximate form of the Navier Stokes equations is solved by an implicit spatial marching technique. Calculations were made for flow in a circular S duct and in the F 16 inlet duct. The computed total pressure contours and secondary flow velocity vectors are presented. Qualitative comparisons with experiment are shown for both ducts. The analysis is used to show how the cross section transitioning in the F 16 inlet suppresses the development of a secondary flow vortex

Drag reduction within radial turbine rotor passages using riblets

In this paper, reducing the friction losses in a radial inflow turbine rotor surface by adding engineered features (riblets) is explored. Initially, computational fluid dynamics analysis was used to study the operating mechanism of riblets and to test their ability to reduce drag within the rotor passage when running the turbine at the design point. Thereafter, riblets with different heights and spacing have been implemented at the rotor hub to study the effect of riblets geometry and arrangement on the drag reduction, which leads to determine the riblet geometry where the maximum benefit on turbine performance can be achieved. The effect of riblets on boundary layer development and on the secondary flow generation within the rotor passage has been examined. It was found that the introduction of riblets could reduce the wall shear stress at the hub surface, and on the other hand, they contribute to increasing the stream-wise vorticity within the rotor passage. The maximum wall shear reduction was achieved with riblet with relative height hrel = 2.5% equivalent to 19.3 wall units, while the maximum performance happens when using riblets with hrel = 1.5% equivalent to 11.8 wall units as the later contributes less in secondary flow generation within the passage. For riblets with height more than 19.3 wall units, the overall effect is negative, as they cause an increase in drag and give rise to secondary flow leading to lower turbine performance

Travelling-waves consistent with turbulence-driven secondary flow in a square duct

We present numerically determined travelling-wave solutions for pressure-driven flow through a straight duct with a square cross-section. This family of solutions represents typical coherent structures (a staggered array of counter-rotating streamwise vortices and an associated low-speed streak) on each wall. Their streamwise average flow in the cross-sectional plane corresponds to an eight vortex pattern much alike the secondary flow found in the turbulent regime