scholarly journals Thermosolutal Convection with a Navier–Stokes–Voigt Fluid

2020 ◽  
Author(s):  
Brian Straughan
Keyword(s):  
Viscoelastic Fluid ◽  
Nonlinear Stability ◽  
Thermal Convection ◽  
Stability Limit ◽  
Thermosolutal Convection ◽  
Navier Stokes ◽  
Critical Instability ◽  
Convection Problem ◽  
Voigt Fluid ◽  
Voigt Parameter

Abstract We present a model for convection in a Navier–Stokes–Voigt fluid when the layer is heated from below and simultaneously salted from below, the thermosolutal convection problem. Instability thresholds are calculated for thermal convection with a dissolved salt field in a complex viscoelastic fluid of Navier–Stokes–Voigt type. The Kelvin–Voigt parameter is seen to play a very important role in acting as a stabilizing agent when the convection is of oscillatory type. The quantitative size of this effect is displayed. Nonlinear stability is also discussed, and it is briefly indicated how the global nonlinear stability limit may be increased, although there still remains a region of potential sub-critical instability, especially when the Kelvin–Voigt parameter increases.

scholarly journals Instability thresholds for thermal convection in a Kelvin–Voigt fluid of variable order

2021 ◽  
Author(s):  
B. Straughan
Keyword(s):  
Thermal Convection ◽  
Navier Stokes ◽  
Memory Term ◽  
Variable Order ◽  
Fading Memory ◽  
Oscillatory Convection ◽  
Numerical Techniques ◽  
Order Zero ◽  
Neutral Curves ◽  
Voigt Fluid

AbstractWe present numerical techniques for calculating instability thresholds in a model for thermal convection in a complex viscoelastic fluid of Kelvin–Voigt type. The theory presented is valid for various orders of an exponential fading memory term, and the strategy for obtaining the neutral curves and instability thresholds is discussed in the general case. Specific numerical results are presented for a fluid of order zero, also known as a Navier–Stokes–Voigt fluid, and fluids of order 1 and 2. For the latter cases it is shown that oscillatory convection may occur, and the nature of the stationary and oscillatory convection branches is investigated in detail, including where the transition from one to the other takes place.

scholarly journals Linear and nonlinear stability analysis of binary viscoelastic fluid convection

2013 ◽  
Vol 37 (16-17) ◽  
pp. 8162-8178 ◽  
Author(s):  
Mahesha Narayana ◽  
Precious Sibanda ◽  
Pradeep G. Siddheshwar ◽  
G. Jayalatha
Keyword(s):  
Stability Analysis ◽  
Viscoelastic Fluid ◽  
Nonlinear Stability ◽  
Nonlinear Stability Analysis ◽  
Fluid Convection ◽  
Linear And Nonlinear

Dynamics of a macroscopic elastic fibre in a polymeric cellular flow

2017 ◽  
Vol 817 ◽  
pp. 388-405 ◽  
Author(s):  
Qiang Yang ◽  
Lisa Fauci
Keyword(s):  
Reynolds Number ◽  
Viscoelastic Fluid ◽  
Relaxation Times ◽  
Elastic Fibre ◽  
Weissenberg Number ◽  
Navier Stokes ◽  
Immersed Boundary ◽  
Reynolds Number Flow ◽  
Number Flow ◽  
Multiple Cells

We study the dynamics and transport of an elastic fibre in a polymeric cellular flow. The macroscopic fibre is much larger than the infinitesimal immersed polymer coils distributed in the surrounding viscoelastic fluid. Here we consider low-Reynolds-number flow using the Navier–Stokes/Fene-P equations in a two-dimensional, doubly periodic domain. The macroscopic fibre supports both tensile and bending forces, and is fully coupled to the viscoelastic fluid using an immersed boundary framework. We examine the effects of fibre flexibility and polymeric relaxation times on fibre buckling and transport as well as the evolution of polymer stress. Non-dimensional control parameters include the Reynolds number, the Weissenberg number, and the elasto-viscous number of the macroscopic fibre. We find that large polymer stresses occur in the fluid near the ends of the fibre when it is compressed. In addition, we find that viscoelasticity hinders a fibre’s ability to traverse multiple cells in the domain.

Deficiencies in Turbulence Modelling for the Prediction of the Stability Boundary in Highly Loaded Compressors

2019 ◽  
Author(s):  
Jose Moreno ◽  
John Dodds ◽  
Mehdi Vahdati ◽  
Sina Stapelfeldt
Keyword(s):  
High Speed ◽  
Stability Boundary ◽  
Turbulence Models ◽  
Stability Limit ◽  
Major Effect ◽  
Navier Stokes ◽  
Tip Leakage Flow ◽  
Stall Margin ◽  
Multi Stage ◽  
The Stability

Abstract Reynolds-averaged Navier-Stokes (RANS) equations are employed for aerodynamic and aeroelastic modelling in axial compressors. Their solutions are highly dependent on the turbulence models for closure. The main objective of this work is to assess the widely used Spalart-Allmaras model’s suitability for compressor flows. For this purpose, an extensive investigation of the sources of uncertainties in a high-speed multi-stage compressor rig was carried out. The grid resolution near the casing end wall, which affects the tip leakage flow and casing boundary layer, was found to have a major effect on the stability limit prediction. Refinements in this region led to a stall margin loss prediction. It was found that this loss was exclusively due to the destruction term in the SA model.

Human Aorta Buckling Related to Dissection

2010 ◽  
Author(s):  
Kostas Karagiozis ◽  
Marco Amabili ◽  
Rosaire Mongrain ◽  
Raymond Cartier ◽  
Michael P. Pai¨doussis
Keyword(s):  
Blood Flow ◽  
Nonlinear Stability ◽  
Shell Theory ◽  
Inviscid Flow ◽  
Mechanical Stresses ◽  
Surrounding Tissue ◽  
Navier Stokes ◽  
Human Aorta ◽  
Navier Stokes Equation ◽  
Viscous Stresses

Human aortas are subjected to large mechanical stresses and loads due to blood flow pressurization and through contact with the surrounding tissue and muscle. It is essential that the aorta does not lose stability for proper functioning. The present work investigates the buckling of human aorta relating it to dissection by means of an analytical model. A full bifurcation analysis is used employing a nonlinear model to investigate the nonlinear stability of the aorta conveying blood flow. The artery is modeled as a shell by means of Donnell’s nonlinear shell theory retaining in-plane inertia, while the fluid is modelled by a Newtonian inviscid flow theory but taking into account viscous stresses via the time-averaged Navier-Stokes equation. The three shell displacements are expanded using trigonometric series that satisfy the boundary conditions exactly. A parametric study is undertaken to determine the effect of aorta length, thickness, Young’s modulus, and transmural pressure on the nonlinear stability of the aorta. As a first attempt to study dissection, a quasi-steady approach is taken, in which the flow is not pulsatile but steady. The effect of increasing flow velocity is studied, particularly where the system loses stability, exhibiting static collapse. Regions of large mechanical stresses on the artery surface are identified for collapsed arteries indicating possible ways for dissection to be initiated.

scholarly journals Darmstadt Rotor No. 2, II: Design of Leaning Rotor Blades

2003 ◽  
Vol 9 (6) ◽  
pp. 385-391
Author(s):  
Jörg Bergner ◽  
Dietmar K. Hennecke ◽  
Martin Hoeger ◽  
Karl Engel
Keyword(s):  
Mechanical Stability ◽  
Three Dimensional ◽  
Stability Limit ◽  
Operating Conditions ◽  
Rotor Blades ◽  
Navier Stokes ◽  
Structural Constraints ◽  
Transonic Compressor ◽  
Aero Engines ◽  
The Impact

For Darmstadt University of Technology's axial singlestage transonic compressor rig, a new three-dimensional aft-swept rotor was designed and manufactured at MTU Aero Engines in Munich, Germany. The application of carbon fiber–reinforced plastic made it possible to overcome structural constraints and therefore to further increase the amount of lean and sweep of the blade. The aim of the design was to improve the mechanical stability at operation that is close to stall.To avoid the hazard of rubbing at the blade tip, which is found especially at off-design operating conditions close to the stability limit of the compression system, aft-sweep was introduced together with excessive backward lean.This article reports an investigation of the impact of various amounts of lean on the aerodynamic behavior of the compressor stage on the basis of steady-state Navier-Stokes simulations. The results indicate that high backward lean promotes an undesirable redistribution of mass flow and gives rise to a basic change in the shock pattern, whereas a forward-leaning geometry results in the development of a highly back-swept shock front. However, the disadvantage is a decrease in shock strength and efficiency.

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