Acoustic streaming in Maxwell fluids generated by standing waves in two-dimensional microchannels

In this work, a semianalytic solution for the acoustic streaming phenomenon, generated by standing waves in Maxwell fluids through a two-dimensional microchannel (resonator), is derived. The mathematical model is non-dimensionalized and several dimensionless parameters that characterize the phenomenon arise: the ratio between the oscillation amplitude of the resonator and the half-wavelength ( $\eta =2A/\lambda _{a}$ ); the product of the fluid relaxation time times the angular frequency known as the Deborah number ( $De=\lambda _{1}\omega$ ); the aspect ratio between the microchannel height and the wavelength ( $\epsilon =2 H_{0}/\lambda _{a}$ ); and the ratio between half the height of the microchannel and the thickness of the viscous boundary layer ( $\alpha =H_{0}/\delta _{\nu }$ ). In the limit when $\eta \ll 1$ , we obtain the hydrodynamic behaviour of the system using a regular perturbation method. In the present work, we show that the acoustic streaming speed is proportional to $\alpha ^{2.65}De^{1.9}$ , and the acoustic pressure varies as $\alpha ^{6/5}De^{1/2}$ . Also, we have found that the growth of inner vortex is due to convective terms in the Maxwell rheological equation. Furthermore, the velocity antinodes show a high dependency on the Deborah number, highlighting the fluid's viscoelastic properties and the appearance of resonance points. Due to the limitations of perturbation methods, we will only analyse narrow microchannels.

Pulsating Flow of a Viscous Fluid over a Cavity Containing a Compressible Gas Bubble

A two-dimensional pulsating flow of a viscous fluid in a plane channel whose wall has rectangular microcavities partially or completely filled with a compressible gas is investigated. This problem formulation can clarify the friction reduction mechanism in a laminar sublayer of a turbulent viscous boundary layer flow over a textured stripped superhydrophobic surface containing periodically arranged rectangular micro-cavities filled with gas. It is assumed that the dimensions of the cavities are much smaller than the channel thickness. On the macroscale, the problem of one-dimensional unsteady viscous flow in a plane channel with no-slip conditions on the walls and a harmonic variation of the pressure difference is solved. The solution obtained in this way is used for formulating non-stationary in time and periodic in space boundary conditions for the flow on the scale of a chosen cavity (microscale), with the instantaneous volume of the gas bubble in the cavity depending on the instantaneous pressure over the cavity. The flow on the microscale near a cavity with a gas bubble occurs in the Stokes regime. The numerical solution is obtained using an original version of the boundary element method. A parametric numerical study of the flow field in a pulsating shear flow over a cavity with a compressible gas bubble is performed. The averaged parameters characterizing the effective ‘velocity slip’ of viscous fluid and the friction reduction in a pulsating flow over a stripped superhydrophobic surface are calculated.

A model of an inflatable elastic aerofoil

A novel method is presented to calculate the deformation of a simple elastic aerofoil with a view to determining its aerodynamic viability. The aerofoil is modelled as a thin two-dimensional elastic sheet whose ends are joined together to form a corner of prescribed angle, with a simple support included to constrain the shape to resemble that of a classical aerofoil. The weight of the aerofoil is counterbalanced exactly by the lift force due to a circulation set according to the Kutta condition. An iterative process based on a boundary integral method is used to compute the deformation of the aerofoil in response to an inviscid fluid flow, and a range of flow speeds is determined for which the aerofoil maintains an aerodynamic shape. As the flow speed is increased the aerofoil deforms significantly around its trailing edge, resulting in a negative camber and a loss of lift. The loss of lift is ameliorated by increasing the inflation pressure but at the expense of an increase in drag as the aerofoil bulges into a less aerodynamic shape. Boundary layer calculations and nonlinear unsteady viscous simulations are used to analyse the aerodynamic characteristics of the deformed aerofoil in a viscous flow. By tailoring the internal support the viscous boundary layer separation can be delayed and the lift-to-drag ratio of the aerofoil can be substantially increased.

Effect of the Backward-Facing Step Location on the Aerodynamics of a Morphing Wing

Over the last decade, aircraft morphing technology has drawn a lot of attention in the aerospace community, because it is likely to improve the aerodynamic performance and the versatility of aircraft at different flight regimes. With the fast paced advancements in this field, a parallel stream of research is studying different materials and designs to develop reliable morphing skins. A promising candidate for a viable morphing skin is the sliding skin, where two or more rigid surfaces remain in contact and slide against each other during morphing. The overlapping between each two panels create a backward-facing step on the airfoil surface which has a critical effect on the aerodynamics of the wing. This paper presents a numerical study of the effect of employing a backward-facing step on the suction side of a National Advisory Committee for Aeronautics (NACA) 2412 airfoil at a high Reynolds number of 5.9 × 106. The effects of the step location on the lift coefficient, drag coefficient and critical angle of attack are studied to find a favorable location for the step along the chord-wise direction. Results showed that employing a step on the suction side of the NACA 2412 airfoil can adversely affect the aforementioned aerodynamic properties. A drop of 21.1% in value of the lift coefficient and an increase of 120.8% in the drag coefficient were observed in case of a step located at 25% of the chord length. However, these effects are mitigated by shifting the step location towards the trailing edge. Introducing a step on the airfoil caused the airfoil’s thickness to change, which in turn has affected the transition point of the viscous boundary layer from laminar to turbulent. The location of the step, prior or post the transition point, has a noteworthy effect on the pressure and shear stress distribution, and consequently on the values of the lift and drag coefficients.

One-equation turbulence models applied to practical scramjet inlet

Reynolds-averaged Navier–Stokes equations are used to simulate a practical scramjet inlet geometry using the shock-unsteadiness modified Spalart–Allmaras (SA) turbulence model. The geometry consists of fore-body ramps, expansion corners, and inlet ducts. The focus is to study the impingement of the cowl shock on the opposite wall boundary-layer. The resulting separation bubble can lead to blockage and inlet unstarts. The shock-unsteadiness correction is employed and is found to improve the computational fluid dynamics (CFD) prediction of flow separation in shock/boundary-layer interactions. The shock-unsteadiness parameter is calibrated against available experimental data of canonical flows, and the predicted flow-field is analyzed in detail. A large separation bubble size normalized to the upstream boundary-layer thickness of 4.6 is observed in the interaction region. Across the reattachment region in the interaction region, a peak value of wall pressure is observed. The inlet performance parameters are also calculated. The total pressure losses of 62% are observed across different shock waves, with an additional loss of 15% due to viscous boundary-layer effects.

Development of an Aerostructural Analysis Tool for a Low-Sweep Parametric Wing

An aerostructural analysis program was developed to predict the aerodynamic performance of a non-rigid, low-sweep wing. The wing planform was geometrically defined to have a rectangular section, and a trapezoidal section. The cross-section was further set to an airfoil shape which was consistent across the entire wingspan. Furthermore, to enable the inclusion of this multidisciplinary analysis module into an optimization scheme, the wing geometry was defined by a series of parameters: root chord, taper ratio, leading-edge sweep, semi-span length, and the kink location. Aerodynamic analysis was implemented through the quasi-three-dimensional approach, including a three-dimensional inviscid solution and a sectional two-dimensional viscous solution. The inviscid analysis was provided through the implementation of the vortex ring lifting surface method, which modelled the wing about its mean camber surface. The viscous aerodynamic solution was implemented through a sectional slicing of the wing. For each section, the effective angle of attack was determined and provided as an input to a two-dimensional airfoil solver. This airfoil solution was comprised of two subcomponents: a linear-strength vortex method inviscid solution, and a direct-method viscous boundary layer computation. The converged airfoil solution was developed by adjusting the effective airfoil geometry to account for the boundary layer displacement thickness, which in itself required the inviscid tangential speeds to compute. The structural solution was implemented through classical beam theory, with a torsion and bending calculator included. The torque and bending moment distribution along the wing were computed from the lift distribution, neglecting the effects of drag, and used to compute the twist and deflection of the wing. Interdisciplinary coupling was achieved through an iterative scheme. With the developed implementation, the inviscid lift loads were used to compute the deformation of the wing. This deformation was used to update the wing mesh, and the inviscid analysis was run again. This iteration was continued until the lift variation between computations was below 0.1%. Once the solution was converged upon by the inviscid and structural solutions, the viscous calculator was run to develop the parasitic drag forces. Once computation had completed, the aerodynamic lift and drag forces were output to mark the completion of execution.

Effect of the Backward-Facing Step Location on the Aerodynamics of a Morphing Wing

Over the last decade, aircraft morphing technology has drawn a lot of attention in the aerospace community, because it is likely to improve the aerodynamic performance and the versatility of aircraft at different flight regimes. With the fast paced advancements in this field, a parallel stream of research is studying different materials and designs to develop reliable morphing skins. A promising candidate for a viable morphing skin is the sliding skin, where two or more rigid surfaces remain in contact and slide against each other during morphing. The overlapping between each two panels create a backward-facing step on the airfoil surface which has a critical effect on the aerodynamics of the wing. This paper presents a numerical study of the effect of employing a backward-facing step on the suction side of a National Advisory Committee for Aeronautics (NACA) 2412 airfoil at a high Reynolds number of 5.9 × 106. The effects of the step location on the lift coefficient, drag coefficient and critical angle of attack are studied to find a favorable location for the step along the chord-wise direction. Results showed that employing a step on the suction side of the NACA 2412 airfoil can adversely affect the aforementioned aerodynamic properties. A drop of 21.1% in value of the lift coefficient and an increase of 120.8% in the drag coefficient were observed in case of a step located at 25% of the chord length. However, these effects are mitigated by shifting the step location towards the trailing edge. Introducing a step on the airfoil caused the airfoil’s thickness to change, which in turn has affected the transition point of the viscous boundary layer from laminar to turbulent. The location of the step, prior or post the transition point, has a noteworthy effect on the pressure and shear stress distribution, and consequently on the values of the lift and drag coefficients.

Effect of the Backward-Facing Step Location on the Aerodynamics of a Morphing Wing

Over the last decade, aircraft morphing technology has drawn a lot of attention in the aerospace community, because it is likely to improve the aerodynamic performance and the versatility of aircraft at different flight regimes. With the fast paced advancements in this field, a parallel stream of research is studying different materials and designs to develop reliable morphing skins. A promising candidate for a viable morphing skin is the sliding skin, where two or more rigid surfaces remain in contact and slide against each other during morphing. The overlapping between each two panels create a backward-facing step on the airfoil surface which has a critical effect on the aerodynamics of the wing. This paper presents a numerical study of the effect of employing a backward-facing step on the suction side of a National Advisory Committee for Aeronautics (NACA) 2412 airfoil at a high Reynolds number of 5.9 × 106. The effects of the step location on the lift coefficient, drag coefficient and critical angle of attack are studied to find a favorable location for the step along the chord-wise direction. Results showed that employing a step on the suction side of the NACA 2412 airfoil can adversely affect the aforementioned aerodynamic properties. A drop of 21.1% in value of the lift coefficient and an increase of 120.8% in the drag coefficient were observed in case of a step located at 25% of the chord length. However, these effects are mitigated by shifting the step location towards the trailing edge. Introducing a step on the airfoil caused the airfoil’s thickness to change, which in turn has affected the transition point of the viscous boundary layer from laminar to turbulent. The location of the step, prior or post the transition point, has a noteworthy effect on the pressure and shear stress distribution, and consequently on the values of the lift and drag coefficients.

Development of an Aerostructural Analysis Tool for a Low-Sweep Parametric Wing

An aerostructural analysis program was developed to predict the aerodynamic performance of a non-rigid, low-sweep wing. The wing planform was geometrically defined to have a rectangular section, and a trapezoidal section. The cross-section was further set to an airfoil shape which was consistent across the entire wingspan. Furthermore, to enable the inclusion of this multidisciplinary analysis module into an optimization scheme, the wing geometry was defined by a series of parameters: root chord, taper ratio, leading-edge sweep, semi-span length, and the kink location. Aerodynamic analysis was implemented through the quasi-three-dimensional approach, including a three-dimensional inviscid solution and a sectional two-dimensional viscous solution. The inviscid analysis was provided through the implementation of the vortex ring lifting surface method, which modelled the wing about its mean camber surface. The viscous aerodynamic solution was implemented through a sectional slicing of the wing. For each section, the effective angle of attack was determined and provided as an input to a two-dimensional airfoil solver. This airfoil solution was comprised of two subcomponents: a linear-strength vortex method inviscid solution, and a direct-method viscous boundary layer computation. The converged airfoil solution was developed by adjusting the effective airfoil geometry to account for the boundary layer displacement thickness, which in itself required the inviscid tangential speeds to compute. The structural solution was implemented through classical beam theory, with a torsion and bending calculator included. The torque and bending moment distribution along the wing were computed from the lift distribution, neglecting the effects of drag, and used to compute the twist and deflection of the wing. Interdisciplinary coupling was achieved through an iterative scheme. With the developed implementation, the inviscid lift loads were used to compute the deformation of the wing. This deformation was used to update the wing mesh, and the inviscid analysis was run again. This iteration was continued until the lift variation between computations was below 0.1%. Once the solution was converged upon by the inviscid and structural solutions, the viscous calculator was run to develop the parasitic drag forces. Once computation had completed, the aerodynamic lift and drag forces were output to mark the completion of execution.