On linear instability mechanisms in incompressible open cavity flow

A theoretical study of linear global instability of incompressible flow over a rectangular spanwise-periodic open cavity in an unconfined domain is presented. Comparisons with the limited number of results available in the literature are shown. Subsequently, the parameter space is scanned in a systematic manner, varying Reynolds number, incoming boundary-layer thickness and length-to-depth aspect ratio. This permits documenting the neutral curves and leading eigenmode characteristics of this flow. Correlations constructed using the results obtained collapse all available theoretical data on the three-dimensional instabilities.

Analysis of Meshfree Methods for Lagrangian Fluid-Structure Interaction

In this dissertation a new numerical method for solving Fluid-Structure Interaction (FSI) problems in a Lagrangian framework is developed, where solids of different constitutive laws can suffer very large deformations and fluids are considered to be newtonian and incompressible. For that, we first introduce a meshless discretization based on local maximum-entropy interpolants. This allows to discretize a spatial domain with no need of tessellation, avoiding the mesh limitations. Later, the Stokes flow problem is studied. The Galerkin meshless method based on a max-ent scheme for this problem suffers from instabilities, and therefore stabilization techniques are discussed and analyzed. An unconditionally stable method is finally formulated based on a Douglas-Wang stabilization. Then, a Langrangian expression for fluid mechanics is derived. This allows us to establish a common framework for fluid and solid domains, such that interaction can be naturally accounted. The resulting equations are also in the need of stabilization, what is corrected with an analogous technique as for the Stokes problem. The fully Lagrangian framework for fluid/solid interaction is completed with simple point-to-point and point-to-surface contact algorithms. The method is finally validated, and some numerical examples show the potential scope of applications.

Quasi-cylindrical approximation to the swirling flow in an atomizer chamber

A quasi-cylindrical approximation is used to analyse the axisymmetric swirling flow of a liquid with a hollow air core in the chamber of a pressure swirl atomizer. The liquid is injected into the chamber with an azimuthal velocity component through a number of slots at the periphery of one end of the chamber, and flows out as an anular sheet through a central orifice at the other end, following a conical convergence of the chamber wall. An effective inlet condition is used to model the effects of the slots and the boundary layer that develops at the nearby endwall of the chamber. An analysis is presented of the structure of the liquid sheet at the end of the exit orifice, where the flow becomes critical in the sense that upstream propagation of long-wave perturbations ceases to be possible. This nalysis leads to a boundary condition at the end of the orifice that is an extension of the condition of maximum flux used with irrotational models of the flow. As is well known, the radial pressure gradient induced by the swirling flow in the bulk of the chamber causes the overpressure that drives the liquid towards the exit orifice, and also leads to Ekman pumping in the boundary layers of reduced azimuthal velocity at the convergent wall of the chamber and at the wall opposite to the exit orifice. The numerical results confirm the important role played by the boundary layers. They make the thickness of the liquid sheet at the end of the orifice larger than predicted by rrotational models, and at the same time tend to decrease the overpressure required to pass a given flow rate through the chamber, because the large axial velocity in the boundary layers takes care of part of the flow rate. The thickness of the boundary layers increases when the atomizer constant (the inverse of a swirl number, proportional to the flow rate scaled with the radius of the exit orifice and the circulation around the air core) decreases. A minimum value of this parameter is found below which the layer of reduced azimuthal velocity around the air core prevents the pressure from increasing and steadily driving the flow through the exit orifice. The effects of other parameters not accounted for by irrotational models are also analysed in terms of their influence on the boundary layers.

Influence of gravity on heavy particle statistics in turbulent channel and pipe flow at matched Kàrmàn number

In this work, we use large eddy simulations (LES) and Lagrangian tracking to study the influence of gravity on particle statistics in a fully developed turbulent upward/downward flow in a vertical channel and pipe at matched Kàrmàn number. Only drag and gravity are considered in the equation of motion for solid particles, which are assumed to have no influence on the flow field. Particle interactions with the wall are fully elastic. Our findings obtained from the particle statistics confirm that: (i) the gravity seems to modify both the quantitative and qualitative behavior of the particle distribution and statistics of the particle velocity in wall normal direction; (ii) however, only the quantitative behavior of velocity particle in streamwise direction and the root mean square of velocity components is modified; (iii) the statistics of fluid and particles coincide very well near the wall in channel and pipe flow with equal Kàrmàn number; (iv) pipe curvature seems to have quantitative and qualitative influence on the particle velocity and on the particle concentration in wall normal direction.

On the role of global flow instability analysis in closed loop flow control

Control of linear flow instabilities has been demonstrated to be an effective theoretical flow control methodology, capable of modifying transitional flows on canonical geometries such as the plane channel and the flat-plate boundary layer. Extending the well-developed theoretical flow control techniques to flows over or through complex geometries requires addressing the issue of efficient capturing of the leading members of the global eigenspectrum pertinent to such flows. The present contribution describes state-of-the-art modal global instability analysis methodologies recently developed in our group, based on matrix formation and time-stepping, respectively. The relative performance of these algorithms is assessed on the recovery of BiGlobal and TriGlobal eigenspectra in the spanwise periodic and the cubic lid-driven cavity, respectively; the adjoint eigenspectrum in the latter flow is recovered for the first time. For three-dimensional flows without any homogeneous spatial direction, the time-stepping methodology was found to outperform the matrix-forming approach and permit recovering the leading TriGlobal eigenmodes in an three-dimensional open cavity of aspect ratio L : D : W = 5 : 1 : 1; theoretical flow control of this configuration is underway.

Numerical issues in Lagrangian tracking and topological evolution of fluid particles in wallbounded turbulent flows

The determination of the local Lagrangian evolution of the flow topology in wall-bounded turbulence, and of the Lagrangian evolution associated with entrainment across the turbulent / non-turbulent interface into a turbulent boundary layer, require accurate tracking of a fluid particle and its local velocity gradients. This paper addresses the implementation of fluid-particle tracking in both a turbulent boundary layer direct numerical simulation and in a fully developed channel flow simulation. Determination of the sub-grid particle velocity is performed using both cubic B-spline, four-point Hermite spline and higher-order Hermite spline interpolation. Both wall-bounded flows show similar oscillations in the Lagrangian tracers of both velocity and velocity gradients, corresponding to the movement of particles across the boundaries of computational cells. While these oscillation in the particle velocity are relatively small and have negligible effect on the particle trajectories for time-steps of the order of CFL = 0.1, they appear to be the cause of significant oscillations in the evolution of the invariants of the velocity gradient tensor.

On the role of global flow instability analysis in closed loop flow control

Control of linear flow instabilities has been demonstrated to be an effective theoretical flow control methodology, capable of modifying transitional flow on canonical geometries such as the plane channel and the flat-plate boundary layer.

Global Stability Analysis of a Compressible Turbulent Flow around a High-Lift Configuration

The purpose of this work is to analyze a complex high lift configuration for which significant regions of separated flow are present. Current state of the art methods have some diffculty to predict the origin and the progression of this separated flow when increasing the angle of attack. The mechanisms responsible for the maximum lift limit on multi-element wing con?gurations are not clear; this stability analysis could help to understand the physics behind the phenomenon and to find a relation between the flow separation and the instability onset. The methodology presented herein consists in the computation of a steady base flow solution based on a finite volume discretization and a proposal of the solution for a generalized eigenvalue problem corresponding to the perturbed and linearized problem. The eigenvalue problem has been solved with the Arnoldi iterative method, one of the Krylov subspace projection methods. The described methodology was applied to the NACA0012 test case in subsonic and in transonic conditions and, finally, for the first time to the authors knowledge, on an industrial multi-component geometry, such as the A310 airfoil, in order to identify low frequency instabilities related to the separation. One important conclusion is that for all the analyzed geometries, one unstable mode related to flow separation appears for an angle of attack greater than the one correspondent to the maximum lift coe?cient condition. Finally, an adjoint study was carried out in order to evaluate the receptivity and the structural sensitivity of the geometries, giving an indication of the domain region that could be modified resulting in the biggest change of the flowfield.

Analysis of air flow past and through the 2415-3S airfoil for an unmanned aerial vehicle with internal propulsion system

This paper deals with the prediction of velocity fields on the 2415-3S airfoil which will be used for an unmanned aerial vehicle with internal propulsion system and in this way analyze the air flow through an internal duct of the airfoil using computational fluid dynamics. The main objective is to evaluate the effect of the internal air flow past the airfoil and how this affects the aerodynamic performance by means of lift and drag forces. For this purpose, three different designs of the internal duct were studied; starting from the base 2415-3S airfoil developed in previous investigation, basing on the hypothesis of decreasing the flow separation produced when the propulsive airflow merges the external flow, and in this way obtaining the best configuration. For that purpose, an exhaustive study of the mesh sensitivity was performed. It was used a non-structured mesh since the computational domain is three-dimensional and complex. The selected mesh contains approximately 12.5 million elements. Both the computational domain and the numerical solution were made with commercial CAD and CFD software, respectively. Air, incompressible and steady was analyzed. The boundary conditions are in concordance with experimental setup in the AF 6109 wind tunnel. The k-e model is utilized to describe the turbulent flow process as followed in references. Results allowed obtaining velocity contours as well as lift and drag coefficients and also the location of separation and reattachment regions in some cases for zero degrees of angle of attack on the internal and external surfaces of the airfoil. Finally, the selection of the configuration with the best aerodynamic performance was made, selecting the option without curved baffles.

Numerical analysis of air flow past the 2415-3S airfoil for an unmanned aerial vehicle with internal propulsion system

This paper deals with the prediction of pressure and velocity fields on the 2415-3S airfoil which will be used for and unmanned aerial vehicle with internal propulsion system and in this way analyze the air flow through an internal duct of the airfoil using computational fluid dynamics. The main objective is to evaluate the effect of the internal air flow past the airfoil and how this affects the aerodynamic performance by means of lift and drag forces. For this purpose, three different designs of the internal duct were studied; starting from the base 2415-3S airfoil developed in previous investigation, basing on the hypothesis of decreasing the flow separation produced when the propulsive airflow merges the external flow, and in this way obtaining the best configuration. For that purpose, an exhaustive study of the mesh sensitivity was performed. It was used a non-structured mesh since the computational domain is tridimensional and complex. The selected mesh contains approximately 12.5 million elements. Both the computational domain and the numerical solution were made with commercial CAD and CFD software respectively. Air, incompressible and steady was analyzed. The boundary conditions are in concordance with experimental setup in the AF 6109 wind tunnel. The k-ε model is utilized to describe the turbulent flow process as followed in references. Results allowed obtaining pressure and velocity contours as well as lift and drag coefficients and also the location of separation and reattachment regions in some cases for zero degrees of angle of attack on the internal and external surfaces of the airfoil. Finally, the selection of the configuration with the best aerodynamic performance was made, selecting the option without curved baffles.

Pulsatile blood flow interaction with arterial walls of aorta : autoregulation and impedance pressure boundary condition and its biomedical applications

Para las decisiones urgentes sobre intervenciones quirúrgicas en el sistema cardiovascular se necesitan simulaciones computacionales con resultados fiables y que consuman un tiempo de cálculo razonable. Durante años los investigadores han trabajado en diversos métodos numéricos de cálculo que resulten atractivos para los cirujanos. Estos métodos, precisos pero costosos desde el punto de vista del coste computacional, crean un desajuste entre la oferta de los ingenieros que realizan las simulaciones y los médicos que operan en el quirófano. Por otra parte, los métodos de cálculo más simplificados reducen el tiempo de cálculo pero pueden proporcionar resultados no realistas. El objetivo de esta tesis es combinar los conceptos de autorregulación e impedancia del sistema circulatorio, la interacción flujo sanguíneo-pared arterial y modelos geométricos idealizados tridimensionales de las arterias pero sin pérdida de realismo, con objeto de proponer una metodología de simulación que proporcione resultados correctos y completos, con tiempos de cálculo moderados. En las simulaciones numéricas, las condiciones de contorno basadas en historias de presión presentan inconvenientes por ser difícil conocerlas con detalle, y porque los resultados son muy sensibles ante pequeñas variaciones de dichas historias. La metodología propuesta se basa en los conceptos de autorregulación, para imponer la demanda de flujo aguas abajo del modelo en el ciclo cardiaco, y la impedancia, para representar el efecto que ejerce el flujo en el resto del sistema circulatorio sobre las arterias modeladas. De este modo las historias de presión en el contorno son resultados del cálculo, que se obtienen de manera iterativa. El método propuesto se aplica en una geometría idealizada del arco aórtico sin patologías y en otra geometría correspondiente a una disección Stanford de tipo A, considerando la interacción del flujo pulsátil con las paredes arteriales. El efecto de los tejidos circundantes también se incorpora en los modelos. También se hacen aplicaciones considerando la interacción en una geometría especifica de un paciente anciano que proviene de una tomografía computarizada. Finalmente se analiza una disección Stanford tipo B con tres modelos que incluyen la fenestración del saco. Clinicians demand fast and reliable numerical results of cardiovascular biomechanic simulations for their urgent pre-surgery decissions. Researchers during many years have work on different numerical methods in order to attract the clinicians' confidence to their colorful contours. Though precise but expensive and time-consuming methodologies create a gap between numerical biomechanics and hospital personnel. On the other hand, simulation simplifications with the aim of reduction in computational time may cause in production of unrealistic outcomes. The main objective of the current investigation is to combine ideas such as autoregulation, impedance, fluid-solid interaction and idealized geometries in order to propose a computationally cheap methodology without excessive or unrealistic simplifications. The pressure boundary conditions are critical and polemic in numerical simulations of cardiovascular system, in which a specific arterial site is of interest and the rest of the netwrok is neglected but represented by a boundary condition. The proposed methodology is a pressure boundary condition which takes advantage of numerical simplicity of application of an imposed pressure boundary condition on outlets, while it includes more sophisticated concepts such as autoregulation and impedance to gain more realistic results. Incorporation of autoregulation and impedance converts the pressure boundary conditions to an active and dynamic boundary conditions, receiving feedback from the results during the numerical calculations and comparing them with the physiological requirements. On the other hand, the impedance boundary condition defines the shapes of the pressure history curves applied at outlets. The applications of the proposed method are seen on idealized geometry of the healthy arotic arch as well as idealized Stanford type A dissection, considering the interaction of the arterial walls with the pulsatile blood flow. The effect of surrounding tissues is incorporated and studied in the models. The simulations continue with FSI analysis of a patient-specific CT scanned geometry of an old individual. Finally, inspiring of the statistic results of mortality rates in Stanford type B dissection, three models of fenestrated dissection sac is studied and discussed. Applying the developed boundary condition, an alternative hypothesis is proposed by the author with respect to the decrease in mortality rates in patients with fenestrations.

Effect of the pulse trajectory on ultrasonic fluid velocity measurement

In a general situation a non-uniform velocity field gives rise to a shift of the otherwise straight acoustic pulse trajectory between the transmitter and receiver transducers of a sonic anemometer. The aim of this paper is to determine the effects of trajectory shifts on the velocity as measured by the sonic anemometer. This determination has been accomplished by developing a mathematical model of the measuring process carried out by sonic anemometers; a model which includes the non-straight trajectory effect. The problem is solved by small perturbation techniques, based on the relevant small parameter of the problem, the Mach number of the reference flow, M. As part of the solution, a general analytical expression for the deviations of the computed measured speed from the nominal speed has been obtained. The correction terms of both the transit time and of the measured speed are of M 2 order in rotational velocity field. The method has been applied to three simple, paradigmatic flows: one-directional horizontal and vertical shear flows, and mixed with a uniform horizontal flow.

Discrete linear stability and sensitivity analysis of fluid flows

Este trabajo presenta un método discreto para el cálculo de estabilidad hidrodinámica y análisis de sensibilidad a perturbaciones externas para ecuaciones diferenciales y en particular para las ecuaciones de Navier-Stokes compressible. Se utiliza una aproximación con variable compleja para obtener una precisión analítica en la evaluación de la matriz Jacobiana. Además, mapas de sensibilidad para la sensibilidad a las modificaciones del flujo de base y a una fuerza constante permiten identificar las regiones del campo fluido donde una modificacin (ej. fuerza puntual) tiene un efecto estabilizador del flujo. Se presentan cuatro casos de prueba: (1) un caso analítico para comprobar la derivación discreta, (2) una cavidad cerrada a bajo Reynolds para mostrar la mayor precisión en el cálculo de los valores propios con la aproximación de paso complejo, (3) flujo 2D en un cilindro circular para validar la metodología, y (4) flujo en un cavidad abierta, presentado para validar el método en casos de inestabilidades convectivamente inestables. Los tres últimos casos mencionados (2-4) se resolvieron con las ecuaciones de Navier-Stokes compresibles, utilizando un método Discontinuous Galerkin Spectral Element Method. Se obtuvo una buena concordancia para el caso de validación (3), cuando se comparó el nuevo método con resultados de la literatura. Además, este trabajo muestra que para el cálculo de los modos propios directos y adjuntos, así como para los mapas de sensibilidad, el uso de variables complejas es de suprema importancia para obtener una predicción precisa. El método descrito es aplicado al análisis para la estabilización de la estela generada por un disco actuador, que representa un modelo sencillo para hélices, rotores de helicópteros o turbinas eólicas. Se explora la primera bifurcación del flujo para un disco actuador, y se sugiere que está asociada a una inestabilidad de tipo Kelvin-Helmholtz, cuya estabilidad se controla con en el número de Reynolds y en la resistencia del disco actuador (o fuerza resistente). En primer lugar, se verifica que la disminución de la resistencia del disco tiene un efecto estabilizador parecido a una disminución del Reynolds. En segundo lugar, el análisis hidrodinmico discreto identifica dos regiones para la colocación de una fuerza puntual que controle las inestabilidades, una cerca del disco y otra en una zona aguas abajo. En tercer lugar, se muestra que la inclusión de un forzamiento localizado cerca del actuador produce una estabilización más eficiente que al forzar aguas abajo. El análisis de los campos de flujo controlados confirma que modificando el gradiente de velocidad cerca del actuador es más eficiente para estabilizar la estela. Estos resultados podrían proporcionar nuevas directrices para la estabilización de la estela de turbinas de viento o de marea cuando estén instaladas en un parque eólico y minimizar las interacciones no estacionarias entre turbinas. ABSTRACT A discrete framework for computing the global stability and sensitivity analysis to external perturbations for any set of partial differential equations is presented. In particular, a complex-step approximation is used to achieve near analytical accuracy for the evaluation of the Jacobian matrix. Sensitivity maps for the sensitivity to base flow modifications and to a steady force are computed to identify regions of the flow field where an input could have a stabilising effect. Four test cases are presented: (1) an analytical test case to prove the theory of the discrete framework, (2) a lid-driven cavity at low Reynolds case to show the improved accuracy in the calculation of the eigenvalues when using the complex-step approximation, (3) the 2D flow past a circular cylinder at just below the critical Reynolds number is used to validate the methodology, and finally, (4) the flow past an open cavity is presented to give an example of the discrete method applied to a convectively unstable case. The latter three (2–4) of the aforementioned cases were solved with the 2D compressible Navier–Stokes equations using a Discontinuous Galerkin Spectral Element Method. Good agreement was obtained for the validation test case, (3), with appropriate results in the literature. Furthermore, it is shown that for the calculation of the direct and adjoint eigenmodes and their sensitivity maps to external perturbations, the use of complex variables is paramount for obtaining an accurate prediction. An analysis for stabilising the wake past an actuator disc, which represents a simple model for propellers, helicopter rotors or wind turbines is also presented. We explore the first flow bifurcation for an actuator disc and it suggests that it is associated to a Kelvin- Helmholtz type instability whose stability relies on the Reynolds number and the flow resistance applied through the disc (or actuator forcing). First, we report that decreasing the disc resistance has a similar stabilising effect to an decrease in the Reynolds number. Second, a discrete sensitivity analysis identifies two regions for suitable placement of flow control forcing, one close to the disc and one far downstream where the instability originates. Third, we show that adding a localised forcing close to the actuator provides more stabilisation that forcing far downstream. The analysis of the controlled flow fields, confirms that modifying the velocity gradient close to the actuator is more efficient to stabilise the wake than controlling the sheared flow far downstream. An interesting application of these results is to provide guidelines for stabilising the wake of wind or tidal turbines when placed in an energy farm to minimise unsteady interactions.

Fluid-solid interaction in arteries incorporating the autoregulation concept in boundary conditions

In pre-surgery decisions in hospital emergency cases, fast and reliable results of the solid and fluid mechanics problems are of great interest to clinicians. In the current investigation, an iterative process based on a pressure-type boundary condition is proposed in order to reduce the computational costs of blood flow simulations in arteries, without losing control of the important clinical parameters. The incorporation of cardiovascular autoregulation, together with the well-known impedance boundary condition, forms the basis of the proposed methodology. With autoregulation, the instabilities associated with conventional pressure-type or impedance boundary conditions are avoided without an excessive increase in computational costs. The general behaviour of pulsatile blood flow in arteries, which is important from the clinical point of view, is well reproduced through this new methodology. In addition, the interaction between the blood and the arterial walls occurs via a modified weak coupling, which makes the simulation more stable and computationally efficient. Based on in vitro experiments, the hyperelastic behaviour of the wall is characterised and modelled. The applications and benefits of the proposed pressure-type boundary condition are shown in a model of an idealised aortic arch with and without an ascending aorta dissection, which is a common cardiovascular disorder.

Vascular MADs: Two novel MAD-related genes selectively inducible by flow in human vascular endothelium

Vascular endothelium is an important transducer and integrator of both humoral and biomechanical stimuli within the cardiovascular system. Utilizing a differential display approach, we have identified two genes, Smad6 and Smad7, encoding members of the MAD-related family of molecules, selectively induced in cultured human vascular endothelial cells by steady laminar shear stress, a physiologic fluid mechanical stimulus. MAD-related proteins are a recently identified family of intracellular proteins that are thought to be essential components in the signaling pathways of the serine/threonine kinase receptors of the transforming growth factor β superfamily. Smad6 and Smad7 possess unique structural features (compared with previously described MADs), and they can physically interact with each other, and, in the case of Smad6, with other known human MAD species, in endothelial cells. Transient expression of Smad6 or Smad7 in vascular endothelial cells inhibits the activation of a transfected reporter gene in response to both TGF-β and fluid mechanical stimulation. Both Smad6 and Smad7 exhibit a selective pattern of expression in human vascular endothelium in vivo as detected by immunohistochemistry and in situ hybridization. Thus, Smad6 and Smad7 constitute a novel class of MAD-related proteins, termed vascular MADs, that are induced by fluid mechanical forces and can modulate gene expression in response to both humoral and biomechanical stimulation in vascular endothelium.