Wind tunnel flow generation section

A flow generation section for a wind tunnel test facility is described which provides a uniform flow for the wind tunnel test section over a range of different flow velocities. The throat of the flow generation section includes a pair of opposed boundary walls which are porous to the flowing medium in order to provide an increase of velocity by expansion. A plenum chamber is associated with the exterior side of each of such porous walls to separate the same from ambient pressure. A suction manifold is connected by suction lines with each one of the chambers. Valves are positioned in each of the lines to enable the suction manifold to be independently varied

Connecting microstructural attributes and permeability from 3D tomographic images of in situ shear-enhanced compaction bands using multiscale computations

Tomographic images taken inside and outside a compaction band in a field specimen of Aztec sandstone are analyzed by using numerical methods such as graph theory, level sets, and hybrid lattice Boltzmann/finite element techniques. The results reveal approximately an order of magnitude permeability reduction within the compaction band. This is less than the several orders of magnitude reduction measured from hydraulic experiments on compaction bands formed in laboratory experiments and about one order of magnitude less than inferences from two-dimensional images of Aztec sandstone. Geometrical analysis concludes that the elimination of connected pore space and increased tortuosities due to the porosity decrease are the major factors contributing to the permeability reduction. In addition, the multiscale flow simulations also indicate that permeability is fairly isotropic inside and outside the compaction band

On the lifespan of classical solutions to a non-local porous medium problem with nonlinear boundary conditions

In this paper we analyze the porous medium equation \begin{equation}\label{ProblemAbstract} \tag{$\Diamond$} %\begin{cases} u_t=\Delta u^m + a\io u^p-b u^q -c\lvert\nabla\sqrt{u}\rvert^2 \quad \textrm{in}\quad \Omega \times I,%\\ %u_\nu-g(u)=0 & \textrm{on}\; \partial \Omega, t>0,\\ %u({\bf x},0)=u_0({\bf x})&{\bf x} \in \Omega,\\ %\end{cases} \end{equation} where $\Omega$ is a bounded and smooth domain of $\R^N$, with $N\geq 1$, and $I= [0,t^*)$ is the maximal interval of existence for $u$. The constants $a,b,c$ are positive, $m,p,q$ proper real numbers larger than 1 and the equation is complemented with nonlinear boundary conditions involving the outward normal derivative of $u$. Under some hypothesis on the data, including intrinsic relations between $m,p$ and $q$, and assuming that for some positive and sufficiently regular function u_0(\nx) the Initial Boundary Value Problem (IBVP) associated to \eqref{ProblemAbstract} possesses a positive classical solution u=u(\nx,t) on $\Omega \times I$: \begin{itemize} \item [$\triangleright$] when $p>q$ and in 2- and 3-dimensional domains, we determine a \textit{lower bound of} $t^*$ for those $u$ becoming unbounded in $L^{m(p-1)}(\Omega)$ at such $t^*$; \item [$\triangleright$] when $p<q$ and in $N$-dimensional settings, we establish a \textit{global existence criterion} for $u$. \end{itemize

Flow stabilization with active hydrodynamic cloaks

We demonstrate that fluid flow cloaking solutions based on active hydrodynamic metamaterials exist for two-dimensional flows past a cylinder in a wide range of Reynolds numbers, up to approximately 200. Within the framework of the classical Brinkman equation for homogenized porous flow, we demonstrate using two different methods that such cloaked flows can be dynamically stable for $Re$ in the range 5-119. The first, highly efficient, method is based on a linearization of the Brinkman-Navier-Stokes equation and finding the eigenfrequencies of the least stable eigen-perturbations; the second method is a direct, numerical integration in the time domain. We show that, by suppressing the Karman vortex street in the weekly turbulent wake, porous flow cloaks can raise the critical Reynolds number up to about 120, or five times greater than for a bare, uncloaked cylinder.Comment: 5 pages, 3 figure

Flow of non-Newtonian Fluids in Converging-Diverging Rigid Tubes

A residual-based lubrication method is used in this paper to find the flow rate and pressure field in converging-diverging rigid tubes for the flow of time-independent category of non-Newtonian fluids. Five converging-diverging prototype geometries were used in this investigation in conjunction with two fluid models: Ellis and Herschel-Bulkley. The method was validated by convergence behavior sensibility tests, convergence to analytical solutions for the straight tubes as special cases for the converging-diverging tubes, convergence to analytical solutions found earlier for the flow in converging-diverging tubes of Newtonian fluids as special cases for non-Newtonian, and convergence to analytical solutions found earlier for the flow of power-law fluids in converging-diverging tubes. A brief investigation was also conducted on a sample of diverging-converging geometries. The method can in principle be extended to the flow of viscoelastic and thixotropic/rheopectic fluid categories. The method can also be extended to geometries varying in size and shape in the flow direction, other than the perfect cylindrically-symmetric converging-diverging ones, as long as characteristic flow relations correlating the flow rate to the pressure drop on the discretized elements of the lubrication approximation can be found. These relations can be analytical, empirical and even numerical and hence the method has a wide applicability range.Comment: 36 pages, 14 figures, 5 table

Finite and infinite speed of propagation for porous medium equations with fractional pressure

We study a porous medium equation with fractional potential pressure: $$\partial_t u= \nabla \cdot (u^{m-1} \nabla p), \quad p=(-\Delta)^{-s}u,$$ for $m>1$, $0<s<1$ and $u(x,t)\ge 0$. To be specific, the problem is posed for $x\in \mathbb{R}^N$, $N\geq 1$, and $t>0$. The initial data $u(x,0)$ is assumed to be a bounded function with compact support or fast decay at infinity. We establish existence of a class of weak solutions for which we determine whether, depending on the parameter $m$, the property of compact support is conserved in time or not, starting from the result of finite propagation known for $m=2$. We find that when $m\in [1,2)$ the problem has infinite speed of propagation, while for $m\in [2,\infty)$ it has finite speed of propagation. Comparison is made with other nonlinear diffusion models where the results are widely different.Comment: 6 pages, 1 figur