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Compressible Flows

Mach 3 Flow Past a Forward Facing Step

--Benkirk 10:53, 26 Jul 2005 (PDT)

Space Shuttle Orbiter Reentry Configuration at Wind Tunnel Conditions

Hypersonic Shockwave/Boundary Layer and Shock/Shock Interaction

The following are two experimental investigations cocnducted by Holden et al. at the CUBRC hypersonic test facility in Buffalo, NY. These experimental data, including measurements of surface pressure and heat transfer, are available as part of a large experimental database which is useful for code validation (AIAA-2003-1137). The presented results, obtained with a finite element formulation of the compressible Navier-Stokes equations, are in excellent agreement with previous analyses by MacLean using two separate finite volume flow solvers (AIAA 2004-0529).

Shockwave/Boundary Layer Interaction for a Hollow Cylinder/Flare

In this problem Mach 10.3 flow of laminar Nitrogen over an axisymmetric hollow cylinder with conical flare is considered. The adverse pressure gradient caused by the conical flare feeds upstream through the subsonic portion of the boundary layer, inducing flow separation and recirculation. A separation shock is produced and interacts with the reattachment region on the conical flare. Three images depict the external flowfield:

The computed and measured values are in good agreement as shown in the next image.

--Benkirk 09:46, 4 May 2006 (PDT)

Shock/Shock Interaction for a Blunt Double Cone

In this problem Mach 12.4 flow of laminar Nitrogen over an axisymmetric blunt double cone is considered. The adverse pressure gradient caused by the conical flare feeds upstream through the subsonic portion of the boundary layer, inducing flow separation and recirculation. A separation shock is produced and interacts with the detached bow shock caused by the second conical section. Three images depict the external flowfield:

The magnitude of the density gradient yields a schlieren-like image which provides insight into the flow structure:

Experimental measurements of surface pressure and heat transfer were made at the CUBRC facility by Holden et al. The computed and measured values are in good agreement as shown in the next image.

--Benkirk 20:07, 9 May 2006 (PDT)

Type IV Shock-Shock Interaction

Of the six distinct shock-shock interaction patterns identified by Edney the most severe is the type IV. This pattern occurs when an external shock impinges inside a bow shock's sonic lines. A very complex flowfield results which features a supersonic jet that terminates very close to the surface, resulting in elevated pressure and heat flux. In this simulation a shock generator was used to interact with the bow shock of a cylinder.

The following figures present comparisons with experimental data.

--Benkirk 11:40, 14 June 2006 (PDT)

Mach 10 Blunt-Body Flow

The following images combine experimental and computational results for the case of a blunt reentry vehicle at angle of attack. The freestream Mach number and Reynolds number (based on diameter) are 10 and 2.8 million, respectively. Surface pressure and pitch-plane properties are overlaid on top of experimental schlieren images.

The computational domain consists only of the heatshield portion of the vehicle. It is clear from the sonic line location that the outflow of the computational domain is supersonic.

--Benkirk 07:27, 6 August 2007 (PDT)

Hook'Em! Mach 5 Flow Past a Longhorn Head

Images by Benkirk.

Combined Buoyant Surface-Tension Driven Flows

Triangular Prism Container

Surface-tension driven flow is solved in a triangular prismatic container with aspect ratio 22. The aspect ratio is defined as the square root of the surface area divided by the container height. This simulation was inspired by the experiments of Koschmieder and Prahl, who treated square and round containers as well. In this case, the aspect ratio of 22 is relatively large, and therefore hexagonal convection cells are expected to develop. In smaller aspect ratio cases, other geometries (such as squares and pentagons) are possible for the convection cells. These simulations found that the configurations of the convection cells were, to a large extent, independent of the Rayleigh and Marangoni numbers, and instead depended strongly on the container aspect ratio.

--Jwpeterson 10:13, 28 Jun 2005 (PDT)

Sound Radiation

Analysis of Tire Rolling Noise

A physically motivated modeling process for the prediction of noise radiated from rolling tires has been developed. The simulation procedure is based on a decomposition in the non-linear stationary rolling case, the eigenvalue analysis in the deformed state, and the calculation of the noise radiation including a modal superposition approach with an excitation by deterministic functions. The computations for the acoustic part of the overall model are based on a combined finite/infinite element approach.

--Spetersen 03:28, 30 November 2005 (PST)

Nonlinear Water Waves

Solitary Wave Interaction

The interaction of a plane second order solitary wave with an array of four vertical cylinders in shallow water is investigated. The fluid is assumed to be incompressible and inviscid. The diffraction analysis assumes irrotationality, which allows for the use of Boussinesq equations. A simultaneous expansion in a small nonlinearity parameter (wave amplitude/depth) and a small dispersion parameter (depth/horizontal scale) is performed. Boussinesq models, which describe weakly nonlinear and weakly dispersive long waves, are characterized by the assumption that the nonlinearity and dispersion are both small and of the same order. An incident plane second order solitary wave is the Laitone solution of Boussinesq equations. The representation of variables as a series of small nonlinearity parameters leads to the sequence of linear boundary value problems of increasing order. The first order approximation can be determined as a solution of homogeneous differential equations and the second order approximation follows as a solution of non-homogeneous differential equations, where the right hand sides can be computed from the first order solution.

--Spetersen 01:57, 28 February 2006 (PST)

Material Science

Cahn-Hilliard Phase Decomposition

The separation of material phases from small perturbations in an initially homogeneous binary mixture is investigated using the Cahn-Hilliard equation, a fourth order model of the competing interaction between the thermodynamics of interfacial free energy and configurational free energy in the materials. In this example, a faint spatially varying bias in the configurational free energy is amplified by the anti-diffusive properties of the phase separation process to produce sharp material patterns. Isosurface plots show the interface between the two phases.

--Roystgnr 11:31, 7 June 2007 (PDT)

Carbon Dioxide Aquifer Transport

CO2 transport, from A Process Oriented Toolbox for Numerical Analysis of CO2 Disposal in Aquifers.

- contributed by M. A. Sbai, July 2008.

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