Mahmoud Mamou

On numerical stability analysis of double-diffusive convection in confined enclosures

The onset of thermosolutal convection and finite-amplitude flows, due to vertical gradients of heat and solute, in a horizontal rectangular enclosure are investigated analytically and numerically. Dirichlet or Neumann boundary conditions for temperature and solute concentration are applied to the two horizontal walls of the enclosure, while the two vertical ones are assumed impermeable and insulated. The cases of stress-free and non-slip horizontal boundaries are considered. The governing equations are solved numerically using a finite element method. To study the linear stability of the quiescent state and of the fully developed flows, a reliable numerical technique is implemented on the basis of Galerkin and finite element methods. The thresholds for finite-amplitude, oscillatory and monotonic convection instabilities are determined explicitly in terms of the governing parameters. In the diffusive mode (solute is stabilizing) it is demonstrated that overstability and subcritical convection may set in at a Rayleigh number well below the threshold of monotonic instability, when the thermal to solutal diffusivity ratio is greater than unity. In an infinite layer with rigid boundaries, the wavelength at the onset of overstability was found to be a function of the governing parameters. Analytical solutions, for finite-amplitude convection, are derived on the basis of a weak nonlinear perturbation theory for general cases and on the basis of the parallel flow approximation for a shallow enclosure subject to Neumann boundary conditions. The stability of the parallel flow solution is studied and the threshold for Hopf bifurcation is determined. For a relatively large aspect ratio enclosure, the numerical solution indicates horizontally travelling waves developing near the threshold of the oscillatory convection. Multiple confined steady and unsteady states are found to coexist. Finally, note that all the numerical solutions presented in this paper were found to be stable.

Closed-Loop Control Validation of a Morphing Wing Using Wind Tunnel Tests

In this paper a rectangular finite aspect ratio wing, having a wing trailing edge airfoil reference airfoil cross section, was considered. The wing upper surface was made of a flexible composite material and instrumented with Kulite pressure sensors and two smart memory alloys actuators. Unsteady pressure signals were recorded and visualized in real time while the morphing wing was being deformed to reproduce various airfoil shapes by controlling the two actuators displacements. The controlling procedure was performed using two methods which are described in the paper. Several wind-tunnel test runs were performed for various angles of attack and Reynolds numbers in the 6 × 9 foot wind tunnel at the Institute for Aerospace Research at the National Research Council Canada. The Mach number was varied from 0.2 to 0.3, the Reynolds numbers varied between 2.29 and 3.36 x 10 6 , and the angle-of-attack range was within -1 to 2 degrees. Wind-tunnel measurements are presented for airflow boundary layer transition detection using high sampling rate pressure sensors.

A hybrid fuzzy logic proportional- integral-derivative and conventional on-off controller for morphing wing actuation using shape memory alloy Part 1: Morphing system mechanisms and controller architecture design

The present paper describes the design of a hybrid actuation control concept, a fuzzy logic proportional-integral-derivative plus a conventional on-off controller, for a new morphing mechanism using smart materials as actuators, which were made from shape memory alloys (SMA). The research work described here was developed for the open loop phase of a morphing wing system, whose primary goal was to reduce the wing drag by delaying the transition (from laminar to fully turbulent flows) position toward the wing trailing edge. The designed controller drives the actuation system equipped with SMA actuators to modify the flexible upper wing skin surface. The designed controller was also included, as an internal loop, in the closed loop architecture of the morphing wing system, based on the pressure information received from the flexible skin mounted pressure sensors and on the estimation of the transition location. The controller’s purposes were established following a comprehensive presentation of the morphing wing system architecture and requirements. The strong nonlinearities of the SMA actuators’ characteristics and the system requirements led to the choice of a hybrid controller

Modal and non-modal linear stability of the plane Bingham–Poiseuille flow

The receptivity problem of plane Bingham–Poiseuille flow with respect to weak perturbations is addressed. The relevance of this study is highlighted by the linear stability analysis results (spectra and pseudospectra). The first part of the present paper thus deals with the classical normal-mode approach in which the resulting eigenvalue problem is solved using the Chebychev collocation method. Within the range of parameters considered, the Poiseuille flow of Bingham fluid is found to be linearly stable. The second part investigates the most amplified perturbations using the non-modal approach. At a very low Bingham number ( B ≪ 1), the optimal disturbance consists of almost streamwise vortices, whereas at moderate or large B the optimal disturbance becomes oblique. The evolution of the obliqueness as function of B is determined. The linear analysis presented also indicates, as a first stage of a theoretical investigation, the principal challenges of a more complete nonlinear study.

Soret effect inducing subcritical and Hopf bifurcations in a shallow enclosure filled with a clear binary fluid or a saturated porous medium: A comparative study

Soret-driven thermosolutal convection within a shallow porous or fluid layer subject to a vertical gradient of temperature is investigated analytically and numerically. The bridging between a clear fluid and Darcy porous media problems is conducted using the Brinkman–Hazen–Darcy model in its transient form. The analytical solution is derived on the basis of the parallel flow approximation, and validated numerically using a finite difference method by solving the full governing equations. The study is focused on the thermal diffusion effects on the flow intensity, and on the heat and mass transfer rates. In particular, a comparative study is made for the two limiting cases that emerge from the present investigation, namely the low porosity Darcy porous medium and the clear fluid medium. The flow behavior for both cases is qualitatively similar. The critical Rayleigh numbers for the onset of subcritical, oscillatory and stationary convection are determined explicitly as functions of the governing parameters for infinite and finite layers. At the onset of instabilities, the wavenumber is equal to zero and the oscillation frequency vanishes at the onset of Hopf bifurcation. For a finite aspect ratio enclosure, the frequency is finite and decreases as the aspect ratio increases. The codimension-2 point exists and different flow regimes are delineated. For constant heat flux boundaries, only standing oscillatory and steady waves are found to exist. The analytical and numerical results are found to be in good agreement, within the range of the governing parameters considered in the present study. The thermal diffusion effect on the flow intensity and on the heat and mass transfer is more enhanced for Darcy medium compared to the clear fluid, for which the viscous effects are significant.

Multiple solutions for double diffusive convection in a shallow porous cavity with vertical fluxes of heat and mass

Abstract The Darcy model with the Boussinesq approximation is used to study double-diffusive natural convection in a shallow porous cavity. The horizontal walls are subject to uniform fluxes of heat and mass, while the side vertical walls are exposed to a constant heat flux of intensity aq ′ , where a is a real number. Results are presented for −20⩽R T ⩽50, −20⩽R S ⩽20, 5⩽Le⩽10, 4⩽A⩽8 and −0.7⩽ a ⩽0.7, where R T , R S , Le and A correspond to thermal Rayleigh number, solutal Rayleigh number, Lewis number and aspect ratio of the enclosure, respectively. In the limit of a shallow enclosure ( A ≫1) an asymptotic analytical solution for the stream function and temperature and concentration fields is obtained by using a parallel flow assumption in the core region of the cavity and an integral form of the energy and the constituent equations. In the absence of side heating ( a =0), the solution takes the form of a standard Benard bifurcation. The asymmetry brought by the side heating ( a ≠0) to the bifurcation is investigated. For high enough Rayleigh numbers, multiple steady states near the threshold of convection are found. These states represent flows in opposite directions. In the range of the governing parameters considered in the present study, a good agreement is observed between the analytical predictions and the numerical simulations of the full governing equations.

Stability analysis of thermosolutal convection in a vertical packed porous enclosure

A linear stability theory is performed to investigate the stability of the quiescent state and fully developed thermosolutal convection within a vertical porous enclosure subject to horizontal opposing gradients of temperature and solute. The fluid motion is modeled using the unsteady form of Darcy’s law coupled with energy and species conservation equations. The effect of different thermal and solutal boundary conditions is considered. The linearized governing equations are solved numerically using a finite element method. The thresholds for oscillatory and stationary convection are determined as functions of the governing parameters. It is concluded that the porosity and the acceleration parameter of the porous medium have a strong effect on the onset of overstability for a confined enclosure and on the wave number for an infinite enclosure. The stability analysis of fully developed flows within a slender enclosure reveals that an increase in the porosity and the acceleration parameter of the porous med...

Variations in Optical Sensor Pressure Measurements due to Temperature in Wind Tunnel Testing

In this paper, wind-tunnel measurements are presented for the airflow fluctuation detection using pressure optical sensors. Twenty-one wind-tunnel test runs for various Mach numbers, angles of attack, and Reynolds numbers were performed in the 6 x 9 ft 2 wind tunnel at the Institute for Aerospace Research at the National Research Council Canada. A rectangular finite aspect ratio half-wing, having a NACA 4415 cross section, was considered with its upper surface instrumented with pressure taps, pressure optical sensors, and one Kulite transducer. The Mach number was varied from 0.1 to 0.3 and the angle of attack range was within -3 to 3 deg. Unsteady pressure signals were recorded and a thorough comparison, in terms of unsteady and mean pressure coefficients, was performed between the measurements from the three sets of pressure transducers. Temperature corrections were considered in the pressure measurements by optical sensors. Comparisons were also performed against theoretical predictions using the XFoil computational fluid dynamics code, and mean errors smaller than 10% were noticed between the measured and the predicted data.

Analytical and Numerical Study of Combined Effects of a Magnetic Field and an External Shear Stress on Soret Convection in a Horizontal Porous Enclosure

The fluid flow induced by combined actions of Soret effect and shear stress applied on the top horizontal free surface (the lower one being rigid) in a horizontal porous layer, under an external magnetic field, is studied analytically and numerically. The horizontal walls of the porous layer are subject to uniform heat fluxes. The porous layer is sparsely packed then the flow is governed by the Brinkman model assuming the Boussinesq approximation. The governing parameters are the thermal Rayleigh number, RT, the Lewis number, Le, the separation parameter, ϕ, the effective Darcy number, Da, the Hartmann number Ha, the dimensionless shear stress, τ, and the aspect ratio of the enclosure, Ar. An analytical solution is derived on the basis of the parallel flow approximation, assuming enlarge aspect ratio layer, and validated numerically using a finite-difference method. The critical Rayleigh numbers for the onset of stationary, subcritical, and oscillatory convection are determined explicitly as functions of the governing parameters for infinite layers with a zero shear stress, τ = 0. The codimension-2 point is identified and different flow behaviors are observed and discussed. The effects of the governing parameters on the fluid flow intensity and heat and mass transfer characteristics are also discussed.

SORET DRIVEN THERMOSOLUTAL CONVECTION IN A SHALLOW POROUS ENCLOSURE

We present an analytical and numerical study of the Soret effect on natural convection in a horizontal porous layer subject to uniform fluxes of heat. In the limit of a shallow enclosure, an analytical closed form solution is derived on the basis of a parallel flow approximation. The thresholds for the onset of stationary and finite amplitude parallel flow are determined analytically as a function of the Lewis number, Le, and the separation parameter, φ. There exist three regions in the plane (φ, Le) that correspond to different parallel flow regimes. The first region indicates only the possible existence of stationary convection. The second one indicates that both subcritical and stationary convection are possible. However, in the third region only subcritical flows are possible