Swirling Boundary Layer Research Articles

Experimental Investigation of the Swirl Development at the Inlet of a Coaxial Rotating Diffuser or Nozzle

When a fluid enters a rotating pipe, a swirl boundary layer with thickness of δ̃S appears at the wall and interacts with the axial momentum boundary layer with thickness of δ̃. The swirl is produced by the wall shear stress and not due to kinematic reasons as by a turbomachine. In the center of the pipe, the fluid is swirl-free and is accelerated due to axial boundary layer growth. Below a critical flow number φ < φc, there is flow separation, known in the turbomachinery context as part load recirculation. The previous work analyzes the flow at the inlet of a coaxial rotating circular pipe (R̃=R̃0). For a systematic approach to a turbomachine, the influence of the turbine's and pump's function, schematically fulfilled by a diffuser and a nozzle, on the evolution of the swirl and flow separation is to analyze. The radius of the rotating pipe depends linearly on the axial coordinate, yielding a rotating circular diffuser or nozzle. The swirl evolution depends on the Reynolds number, flow number, axial coordinate, and apex angle. The influence of the latter is the paper's main task. The circumferential velocity component is measured applying one-dimensional laser Doppler anemometry (LDA) to investigate the swirl evolution.

Developing Swirl Boundary Layer and Flow Separation at the Inlet of a Coaxial Rotating Diffuser or Nozzle

When an axial flow enters a rotating diffuser or nozzle, a swirl boundary layer appears at the wall and interacts with the axial boundary layer. Below a critical flow number φc, there is a flow separation, known in the turbomachinery context as part load recirculation. This paper extends the previous work for a cylindrical coaxial rotating pipe still considering the influence of the centrifugal force by varying the pipe's radius, yielding a coaxial rotating circular diffuser or nozzle. The integral method of boundary layer theory is used to describe the flow at the inlet of a rotating circular diffuser or nozzle, obtaining a generalized von Kármán momentum equation. This work conducts experiments to validate the analytical results and shows the influence of Reynolds number, flow number, apex angle, and surface roughness on the boundary layers evolution. By doing so, a critical flow number for incipient flow separation is analytically derived, resulting in a stability map for part load recirculation depending on Reynolds number and apex angle. Hereby, positive apex angles (diffuser) and negative apex angles (nozzle) are considered.

Swirl boundary layer and flow separation at the inlet of a rotating pipe

When a fluid enters a rotating circular pipe, an angular momentum or swirl boundary layer appears at the wall and interacts with the axial momentum boundary layer. In the centre of the pipe, the fluid is free of swirl and is accelerated due to boundary layer growth. Below a critical flow number, defined as the ratio of average axial velocity to circumferential velocity of the pipe, there is flow separation, known in the turbomachinery context as part load recirculation. To describe this phenomenon analytically, we extended boundary layer theory to a swirl boundary layer interacting with the axial momentum boundary layer. The solution of the resulting generalized von Kármán momentum equation takes into account the influence of the Reynolds number and flow number. We show the impact of swirl on the axial boundary layer and conduct experiments in which we vary Reynolds number, flow number and surface roughness to validate the analytical results. The extended boundary layer theory predicts a critical flow number which is analytically derived and validated. Below this critical flow number, separation is expected.

Two turbulent flow regimes at the inlet of a rotating pipe

▪ When a fluid enters a rotating circular pipe a swirl boundary layer with thickness of δ̃S appears at the wall and interacts with the axial momentum boundary layer with thickness of δ̃. We investigate the turbulent flow applying Laser-Doppler-Anemometry to measure the circumferential velocity profile at the inlet of a rotating pipe. The measured swirl boundary layer thickness follows a power law taking Reynolds number and flow number into account. A critical combination of Reynolds number, flow number and axial position causes a transition of the swirl boundary layer development in the turbulent regime. At this critical combination, the swirl boundary layer thickness as well as the turbulence intensity increase and the latter yields a self-similarity. The circumferential velocity profile changes to a new presented self-similarity. A method is established to define the transition inlet length, when the transition appears and a stability map for two regimes is given.

Parametric studying of low-profile vortex generators flow control in an aggressive inter-turbine duct

This paper presents a study of low-profile vortex generators flow control on the effect of casing boundary layer separation in an aggressive inter-turbine duct. Counter-rotating and co-rotating vortex generators configurations were tested parametrically to obtain the optimum low-profile vortex generators’ setup within the aggressive inter-turbine duct, in terms of the axial location, height, angle of attack and streamwise vortices per swirl vane pitch. Surface oil flow visualization was used to qualitatively examine the low-profile vortex generators eliminating the casing separation and subsequently the detailed seven-hole probe measurements were carried out to evaluate the loss reduction quantitatively. The inter-turbine duct examined for this study was more aggressive compared with the geometries found in the most current modern engine designs. Measurements were made inside the aggressive inter-turbine duct annulus at Reynolds number of 150,000. The flow structures within the aggressive inter-turbine duct were found to be dominated by counter-rotating vortices evolved by the swirl vanes and boundary layer separation in both casing and hub regions. A massive casing boundary layer separation extending from the duct first bend to the second bend was found within the aggressive inter-turbine duct. The primary source of pressure loss in the aggressive inter-turbine ducts was the result of the extensive casing boundary layer separation. Flow control by utilizing the low-profile vortex generators installed on the casing was conducted to eliminate the casing separation. Regardless of the vortex generator mitigating the casing separation associated with consequential loss reduction, a pair of casing counter-rotating vortices was always evident at the duct second bend in all cases. Among the tested low-profile vortex generator configurations, two of the most effective low-profile vortex generator configurations, one counter-rotating and one co-rotating low-profile vortex generator configurations, were acquired as a result of successfully eliminating the casing separation. Despite that the inter-turbine duct is aggressively designed, it is concluded that this duct associated with proper flow control techniques is considered as a potential candidate for weight saving in a high bypass ratio engine.

On the Use of Doppler Radar–Derived Wind Fields to Diagnose the Secondary Circulations of Tornadoes

Abstract A number of studies in recent years have used wind fields derived from portable Doppler radars in combination with the ground-based velocity track display (GBVTD) technique to diagnose the primary (tangential) and secondary (radial and vertical) circulations in tornadoes. These analyses indicate very strong vertical motions in the vortex core, in some cases with updrafts and downdrafts exceeding 100 m s−1. In addition, many of the analyses indicate strong radial outflow at low levels and in the vicinity of the low-level tangential wind maximum. This paper shows that strong outward motion at this location cannot be consistent with a tornado circulation that lasts more than a few minutes. In addition, using data from numerical simulations as truth, it is shown that using observed radial velocities to diagnose vertical velocities greatly overestimates the intensity of downward motion in the core for two reasons: neglect of the mass flux into the core through the swirling boundary layer, and the likely positive bias in low-level radial velocities due to the centrifuging of debris. Possible methods for accounting for these errors are briefly discussed.

Passive Control of Supersonic Rectangular Jets through Boundary Layer Swirl

Mixing characteristics of under-expanded supersonic jets emerging from plane and notched rectangular nozzles are computationally studied using nozzle exit boundary layer swirl as a mean of passive flow control. The coupling of the rectangular jet instability modes, such as flapping, and the swirl is investigated. A three-dimensional unsteady Reynolds-Averaged Navier-Stokes (RANS) code with shock adaptive grids is utilized. For plane rectangular nozzle with boundary layer swirl, the flapping and spanwise oscillations are captured in the jet’s small and large dimensions at twice the frequencies of the nozzles without swirl. A symmetrical oscillatory mode is also observed in the jet with double the frequency of spanwise oscillation mode. For the notched rectangular nozzle with boundary layer swirl, the flapping oscillation in the small jet dimension and the spanwise oscillation in the large jet dimension are observed at the same frequency as those without boundary layer swirl. The mass flow rates in jets at 11 and 8 nozzle heights downstream of the nozzles increased by nearly 25% and 41% for the plane and notched rectangular nozzles respectively, due to swirl. The axial gross thrust penalty due to induced swirl was 5.1% for the plane and 4.9% for the notched rectangular nozzle.

Purely analytic solutions of magnetohydrodynamic swirling boundary layer flow over a porous rotating disk

The prime objective of the present study is to derive analytical expressions for the solution of steady, laminar, incompressible, viscous and electrically conducting fluid of the boundary layer flow due to a rotating disk subjected to a uniform suction and injection through the wall in the presence of a uniform transverse magnetic field. To serve this purpose, the recently popular homotopy analysis method is employed to obtain the exact solutions, in contrast to the numerically evaluated ones in the literature. It is shown here that such a technique is extremely powerful in gaining magnetohydrodynamic solutions in terms of the purely exponential and decaying functions if a special care is taken into account. This makes it possible to obtain explicitly analytic solutions particularly in coincident with the Ackroyd’s solutions in (Ackroyd, 1978) [1] and with the solutions in (Ariel, 2001) [2]. The method is further shown to be capable of overcoming the difficulties existed in calculating Ackroyd’s solutions for high values of injection. Using the homotopy analysis method, electrically conducting mean velocity profiles corresponding to a wide range of suction and injection velocities can be readily computed non-iteratively and analytically. Explicit formulas are also derived for some parameters of physical significance.

Instabilities in hurricane-like boundary layers

Recent advances in observational technology have led to a more detailed knowledge of the low-level flow in hurricanes. In particular, quasi-streamwise rolls on a variety of scales have been observed. Some of these rolls have radial wavelengths of 4–10 km, which is comparable to rolls associated with instabilities inherent to Ekman-type boundary layers. The evolution and stability of the swirling boundary layer underneath a hurricane-like vortex is studied using both a nonlinear model and linearized stability analysis. The nonlinear model is an axisymmetric model of incompressible fluid flow, which is used to simulate the development of boundary layers underneath vortices with hurricane-like wind profiles. Axisymmetric rolls appear in these boundary layers, which have some similarities to the observed rolls in hurricanes. The axisymmetric flow is also used as the basic-state for a linearized stability analysis. The analysis technique allows for arbitrary variation in the radial and vertical directions for both the basic-state flow and the perturbations. Thus, the strong radial variations and curvature effects common to strong vortices are part of the analysis. The analysis finds both symmetric and asymmetric instabilities that are similar to those in the nonlinear simulations and in observations. The instabilities acquire some of their energy from the vertical shear associated with a reversal of the radial inflow at the top of the boundary layer, and some of their energy from vertical shear of the azimuthal flow. The radial flow energy conversion tends to increase for flows with less inertial stability and for modes oriented across the low-level shear; the azimuthal flow conversion increases for larger inertial stability and for modes aligned with the low-level shear.

Effect of boundary layer swirl on supersonic jet instabilities and thrust

This paper reports the effects of nozzle exit boundary layer swirl on the instability modes of underexpanded supersonic jets emerging from plane rectangular nozzles. The effects of boundary layer swirl at the nozzle exit on thrust and mixing of supersonic rectangular jets are also considered. The previous study was performed with a 30° boundary layer swirl (S=0.41) in a plane rectangular nozzle exit. At this study, a 45° boundary layer swirl (S=1.0) is applied in a plane rectangular nozzle exit. A three-dimensional unsteady compressible Reynolds-Averaged Navier-Stokes code with Baldwin-Lomax and Chien’sk-e two-equation turbulence models was used for numerical simulation. A shock adaptive grid system was applied to enhance shock resolution. The nozzle aspect ratio used in this study was 5.0, and the fully-expanded jet Mach number was 1.526. The “flapping” and “pumping” oscillations were observed in the jet’s small dimension at frequencies of about 3,900Hz and 7,800Hz, respectively. In the jefs large dimension, “spanwise” oscillations at the same frequency as the small dimension’s “flapping“ oscillations were captured. As reported before with a 30° nozzle exit boundary layer swirl, the induction of 45° swirl to the nozzle exit boundary layer also strongly enhances jet mixing with the reduction of thrust by 10%.

Free Waves on Barotropic Vortices. Part I: Eigenmode Structure

To understand the nature of coupling between a hurricane vortex and asymmetries in its near-core region, it is first necessary to have an understanding of the spectrum of free waves on barotropic vortices. As foundation for upcoming work examining the nonaxisymmetric initial-value problem in inviscid and swirling boundary layer vortex flows, the complete spectrum of free waves on barotropic vortices is examined here. For a variety of circular vortices in gradient balance the linearized momentum and continuity equations are solved as a matrix eigenvalue problem for perturbation height and wind fields. Vortex eigensolutions are found to fall into two continuum classes. Eigenmodes with frequencies greater than the advective frequency for azimuthal wavenumber n are modified gravity–inertia waves possessing nonzero potential vorticity in the near-core region. Eigenmodes whose frequencies scale with the advective frequency comprise both gravity–inertia waves and Rossby–shear waves. Linearly superposing the Rossby–shear waves approximates the sheared disturbance solutions. For wavenumbers greater than a minimum number, Rossby–shear waves exhibit gravity wave characteristics in the near-vortex region. Although such eigenstructure changes are not anticipated by traditional scaling analyses using solely external flow parameters, a criterion extending Rossby’s characterization of “balanced” and “unbalanced” flow to that of azimuthal waves on a circular vortex is developed that correctly predicts the observed behavior from incipient vortices to hurricane-like vortices. The criterion is consistent with asymmetric balance theory. Possible applications of these results to the wave-mean-flow dynamics of geophysical vortex flows are briefly discussed.

Measurements of a swirling turbulent boundary layer developing in a conical diffuser

Measurements were made of the swirling boundary layer developing in a conical diffuser with a 20° included angle and an area ratio of 2.84. The inlet swirl was close to solid-body rotation and was of sufficient magnitude to prevent boundary layer separation but just insufficient to cause recirculation in the core flow. A single hot-wire was traversed from the wall to the centerline to determine the mean velocities. All six Reynolds stresses were measured within the boundary layer using a rotatable X-probe. The discussion concentrates on the complex response of the turbulence to the numerous perturbations imposed by the swirl and the geometry, of which the dominant ones appear to be the axial pressure gradient and the streamline curvature.

Experimental investigation of a swirling, axisymmetric, turbulent boundary layer with pressure gradient

The results of an experimental investigation designed to document data on both mean and turbulence quantities in the axisymmetric, swirling boundary layer (with and without a pressure gradient) flowing over a stationary cylinder downstream of a spinning cylindrical section are discussed. The pressure gradient was introduced into the flow field by a 25.4-mm-high, forward-facing circular step mounted on the stationary cylinder, the step height being nearly equal to the approaching boundary-layer thickness. All the measurements were made at upstream reference velocity of 36-37 m/sec, with the rotation of the spinner set to make its peripheral speed equal to the reference velocity. The data reported include measurements of surface pressure and the mean surface-shear-stress vector (using a miniature directional surface-fence gage) and oil-flow visualization studies of the stationary cylinder. The data indicate that the streamwise pressure gradient controls the development of the streamwise component of wall shear but leaves the peripheral component of wall shear practically unaffected.

Application of the Dorodnitsyn finite element method to swirling boundary layer flow

AbstractThe Dorodnitsyn finite element method for turbulent boundary layer flow with surface mass transfer is extended to include axisymmetric swirling internal boundary layer flow. Turbulence effects are represented by the two‐layer eddy viscosity model of Cebeci and Smith1 with extensions to allow for the effect of swirl. The method is applied to duct entry flow and a 10 degree included‐angle conical diffuser, and produces results in close agreement with experimental measurements with only 11 grid points across the boundary layer. The introduction of swirl (we/ue = 0.4) is found to have little effect on the axial skin friction in either a slightly favourable or adverse pressure gradient, but does cause an increase in the displacement area for an adverse pressure gradient. Surface mass transfer (blowing or suction) causes a substantial reduction (blowing) in axial skin friction and an increase in the displacement area. Both suction and the adverse pressure gradient have little influence on the circumferential velocity and shear stress components. Consequently in an adverse pressure gradient the flow direction adjacent to the wall is expected to approach the circumferential direction at some downstream location.

Vorticity dynamics of a convective swirling boundary layer

The vorticity dynamics of a convective swirling boundary layer are studied from the viewpoint of steady, inviscid fluid-dynamics theory. Attention is confined to the region of flow lying directly below and within a circularly shaped updraft. Fluid enters the updraft region without vorticity save for that in the boundary layer upstream of the updraft radius. Solutions of the equation \[ r\eta = r^2\frac{dH}{d\psi}-\frac{d}{d\psi}\bigg(\frac{\Gamma^2}{2}\bigg) \] (e.g. Batchelor 1967, p. 545) are presented. By the nature of this approach it allows one to compute the ‘outer’ flow together with the outer boundary-layer structure and hence side-step the interaction problem. A drawback is that the inner viscous structure is not captured. These solutions are compared to some numerical solutions of the time-dependent, viscous axisymmetric Navier-Stokes equations which are reported elsewhere (Rotunno 1979). Although the agreement is not perfect, model results are close enough whereby a number of useful deductions concerning the effects of viscous diffusion and time-dependence may be made.

Boundary-layer separation at a free streamline. Part 3. Axisymmetric flow and the flow downstream of separation

The results of Ackerberg (1970, 1971a), on the two-dimensional boundary-layer separation at a sharp trailing edge where a free streamline is attached, are extended to the axisymmetric case, with and without swirl. When the flow has swirl, the boundary-layer swirl velocity close to the wall may be opposite to that in the external flow; this may help explain the ‘bathtub vortex paradox’ observed by Sibulkin (1962). The solutions for the detached shear layers downstream of separation for two-dimensional and axisymmetric flows, with and without swirl, have been obtained. Some misprints in parts 1 and 2 are corrected in the appendix.

An inverse solution procedure for turbulent swirling boundary layer combustion flow

A detailed description is presented of the mathematical and computational aspects of the general inverse solution procedure developed for turbulent swirling boundary layer combustion flow. The situation is that a nonrecirculating swirling turbulent flame in which experimental time-mean measurements of the axial and swirl velocities ν z and ν θ , temperature T and chemical species concentrations m j have been made. The problem is to calculate the distributions of the significant turbulent momentum, enthalpy and chemical species' flux components ( τ rz , τ rθ , ( J h ) r and ( J i ) r ) and associated exchange coefficients, Prandtl and Schmidt numbers. A solution is provided by the inverse solution TEXCO code; it provides a link between mean measurements and certain correlations of turbulent fluctuation components and throws light on the appropriateness or otherwise of any given turbulence model for the flow under consideration. The method is applied to both isothermal and chemically reacting flows, and calculations show that previous assumptions of isotropy of the turbulent stress tensor and constancy of Prandtl-Schmidt numbers are not generally valid. The exchange coefficients are shown to be functions of the degree of swirl and position in the flowfield. For the isothermal case, it is shown that the assumption of an isotropic uniform mixing length parameter distribution is quite feasible for weak swirl but is progressively less valid as the degree of swirl increases. For the flame case, similar results are obtained and the turbulent viscosity is found to be highly nonisotropic.