2,517 research outputs found
Optimal transient growth in an incompressible flow past a backward-slanted step
With the aim of providing a first step in the quest for a reduction of the
aerodynamic drag on the rear-end of a car, we study the phenomena of separation
and reattachment of an incompressible flow focusing on a specific aerodynamic
geometry, namely a backward-slanted step at 25 degrees of inclination. The
ensuing recirculation bubble provides the basis for an analytical and numerical
investigation of streamwise-streak generation, lift-up effect, and
turbulent-wake and Kelvin-Helmholtz instabilities. A linear stability analysis
is performed, and an optimal control problem with a steady volumic forcing is
tackled by means of variational formulation, adjoint method, penalization
scheme and orthogonalization algorithm. Dealing with the transient growth of
spanwise-periodic perturbations and inspired by the need of
physically-realizable disturbances, we finally provide a procedure attaining a
kinetic-energy maximal gain of the order of one million with respect to the
power introduced by the external forcing.Comment: 17 figure
Boosting the accuracy of SPH techniques: Newtonian and special-relativistic tests
We study the impact of different discretization choices on the accuracy of
SPH and we explore them in a large number of Newtonian and special-relativistic
benchmark tests. As a first improvement, we explore a gradient prescription
that requires the (analytical) inversion of a small matrix. For a regular
particle distribution this improves gradient accuracies by approximately ten
orders of magnitude and the SPH formulations with this gradient outperform the
standard approach in all benchmark tests. Second, we demonstrate that a simple
change of the kernel function can substantially increase the accuracy of an SPH
scheme. While the "standard" cubic spline kernel generally performs poorly, the
best overall performance is found for a high-order Wendland kernel which allows
for only very little velocity noise and enforces a very regular particle
distribution, even in highly dynamical tests. Third, we explore new SPH volume
elements that enhance the treatment of fluid instabilities and, last, but not
least, we design new dissipation triggers. They switch on near shocks and in
regions where the flow --without dissipation-- starts to become noisy. The
resulting new SPH formulation yields excellent results even in challenging
tests where standard techniques fail completely.Comment: accepted for publication in MNRA
Lift-up, Kelvin-Helmholtz and Orr mechanisms in turbulent jets
Three amplification mechanisms present in turbulent jets, namely lift-up, Kelvin–Helmholtz and Orr, are characterized via global resolvent analysis and spectral proper orthogonal decomposition (SPOD) over a range of Mach numbers. The lift-up mechanism was recently identified in turbulent jets via local analysis by Nogueira et al. (J. Fluid Mech., vol. 873, 2019, pp. 211–237) at low Strouhal number ( St ) and non-zero azimuthal wavenumbers ( m ). In these limits, a global SPOD analysis of data from high-fidelity simulations reveals streamwise vortices and streaks similar to those found in turbulent wall-bounded flows. These structures are in qualitative agreement with the global resolvent analysis, which shows that they are a response to upstream forcing of streamwise vorticity near the nozzle exit. Analysis of mode shapes, component-wise amplitudes and sensitivity analysis distinguishes the three mechanisms and the regions of frequency–wavenumber space where each dominates, finding lift-up to be dominant as St/m→0 . Finally, SPOD and resolvent analyses of localized regions show that the lift-up mechanism is present throughout the jet, with a dominant azimuthal wavenumber inversely proportional to streamwise distance from the nozzle, with streaks of azimuthal wavenumber exceeding five near the nozzle, and wavenumbers one and two most energetic far downstream of the potential core
Constraint-consistent Runge-Kutta methods for one-dimensional incompressible multiphase flow
New time integration methods are proposed for simulating incompressible
multiphase flow in pipelines described by the one-dimensional two-fluid model.
The methodology is based on 'half-explicit' Runge-Kutta methods, being explicit
for the mass and momentum equations and implicit for the volume constraint.
These half-explicit methods are constraint-consistent, i.e., they satisfy the
hidden constraints of the two-fluid model, namely the volumetric flow
(incompressibility) constraint and the Poisson equation for the pressure. A
novel analysis shows that these hidden constraints are present in the
continuous, semi-discrete, and fully discrete equations.
Next to constraint-consistency, the new methods are conservative: the
original mass and momentum equations are solved, and the proper shock
conditions are satisfied; efficient: the implicit constraint is rewritten into
a pressure Poisson equation, and the time step for the explicit part is
restricted by a CFL condition based on the convective wave speeds; and
accurate: achieving high order temporal accuracy for all solution components
(masses, velocities, and pressure). High-order accuracy is obtained by
constructing a new third order Runge-Kutta method that satisfies the additional
order conditions arising from the presence of the constraint in combination
with time-dependent boundary conditions.
Two test cases (Kelvin-Helmholtz instabilities in a pipeline and liquid
sloshing in a cylindrical tank) show that for time-independent boundary
conditions the half-explicit formulation with a classic fourth-order
Runge-Kutta method accurately integrates the two-fluid model equations in time
while preserving all constraints. A third test case (ramp-up of gas production
in a multiphase pipeline) shows that our new third order method is preferred
for cases featuring time-dependent boundary conditions
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Linear and nonlinear dynamics in stratified shear flows
Stably stratified shear flows, in which a less dense layer of fluid lies above and moves counter to a more dense layer below, are ubiquitous in geophysical fluid dynamics. These are often found to be unstable if the non-dimensional Richardson number Ri, quantifying the strength of stratification to shear, is sufficiently low. This is of particular importance in oceanography, where shear instabilities are conjectured to be important in the generation of turbulence in the deep ocean, an area of huge uncertainty in contemporary climate models. The Miles-Howard theorem tells us that for a steady, inviscid, parallel shear flow, if the local Richardson number is everywhere greater than one quarter, the flow is stable to infinitesimal perturbations. Though an important result, the strong restrictions in the applicability of this theorem mean care must be used when applying the criterion of Ri > 1/4 for stability. This thesis explores some of these limitations, beginning with an overview in chapter 1.
Chapter 2 explores the infinitesimal restriction of the Miles-Howard theorem, by asking whether finite-amplitude perturbations could lead to significant nonlinear behaviour, in a so-called subcritical instability. It is found that while the classical Kelvin-Helmholtz instability does indeed exhibit subcriticality, nonlinear steady states are found only just above Ri = 1/4.
Chapter 3 investigates in detail a hitherto unknown linear instability, which was discovered in chapter 2. Behaving similarly to the classic Holmboe instability, it exists for Ri > 1/4 when viscosity is introduced, and reveals new insights into the possible physical interpretations of stratified shear
instability.
Chapter 4 revisits the results of chapter 2 but considers two cases of the Prandtl number Pr, the ratio of diffusivity of the momentum to density. When Pr = 0.7, as is approximately the case for air, a simple supercritical instability is found. However, for Pr = 7, corresponding approximately to water, strong subcritical behaviour is observed, and it is demonstrated that finite-amplitude perturbations can trigger Kelvin-Helmholtz-like behaviour well above Ri = 1/4.
Chapter 5 considers the time-varying, non-parallel flow of an oblique internal gravity wave incident on a shear layer. Using direct-adjoint looping, it is shown that the disturbances which maximise energy after a certain time, so-called linear optimal perturbations, can be convective-like rolls in the spanwise direction, rather than a shear instability, calling into question the relevance of the classical shear instabilities in oceanography.
Chapter 6 concludes the thesis with a discussion of the implications of the results
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