Technique for producing wind-tunnel heat-transfer models

Inexpensive thin skinned wind tunnel models with thermocouples on certain surface areas were fabricated. Thermocouples were designed for measuring aerodynamic heat transfer in wind tunnels

A high order compact scheme for hypersonic aerothermodynamics

A novel high order compact scheme for solving the compressible Navier-Stokes equations has been developed. The scheme is an extension of a method originally proposed for solving the Euler equations, and combines several techniques for the solution of compressible flowfields, such as upwinding, limiting and flux vector splitting, with the excellent properties of high order compact schemes. Extending the method to the Navier-Stokes equations is achieved via a Kinetic Flux Vector Splitting technique, which represents an unusual and attractive way to include viscous effects. This approach offers a more accurate and less computationally expensive technique than discretizations based on more conventional operator splitting. The Euler solver has been validated against several inviscid test cases, and results for several viscous test cases are also presented. The results confirm that the method is stable, accurate and has excellent shock-capturing capabilities for both viscous and inviscid flows

On well-balanced schemes for non-equilibrium flow with stiff source terms

In the modeling of unsteady reactive problems, the interaction of turbulence with finiterate chemistry introduces a wide range of space and time scales, leading to additional numerical difficulties. A main difficulty stems from the fact that most numerical algorithms used in reacting flows were originally designed to solve non-reacting fluids. As a result, spatial stiffness due to reacting source terms and turbulence/chemistry interaction are major stumbling blocks to numerical algorithm development. One of the important numerical issues is the proper numerical treatment of a system of highly coupled stiff non-linear source terms, which will result in possible spurious steady state numerical solutions (see Lafon & Yee 1996). It was shown in LeVeque (1998) that a well-balanced scheme, which can preserve the steady state solution exactly, may solve this spurious numerical behavior. The goal of this work is to consider a simple 1-D model with one temperature and three species as studied by Gnoffo, Gupta & Shinn (1989) and to study the well-balanced property of various popular linear and non-linear numerical schemes in the literature. The different behaviors of those numerical schemes in preserving steady states and in resolving small perturbations of such states will be shown

On spurious numerics in solving reactive equations

1. Motivation and objectives Consider 3D reactive Euler equations of the form Ut + F(U)x + G(U)y + H(U)z = S(U), (1.1) where U, F(U), G(U), H(U) and S(U) are vectors. Here, the source term S(U) is restricted to be homogeneous in U; that is, (x, y, z) and t do not appear explicitly in S(U). If physical viscosities are present, viscous flux derivative should be added. If the time scale of the ordinary differential equation (ODE) Ut = S(U) for the source term is orders of magnitude smaller than the time scale of the homogeneous conservation law Ut +F(U)x +G(U)y +H(U)z = 0, then the problem is said to be stiff due to the source terms. In combustion or high speed chemical reacting flows the source term represents the chemical reactions which may be much faster than the gas flow, leading to problems of numerical stiffness. Insufficient spatial/temporal resolution may cause an incorrect propagation speed of discontinuities and nonphysical states for standard numerical methods that were developed for non-reacting flows. See Wang et al. (2012) for a comprehensive overview of the last two decades of development. Schemes designed to improve the prediction of propagation speed of discontinuities for systems of stiff reacting flows remain a challenge for algorithm development (Wang et al. 2012). Wang et al. also proposed a new high order finite difference method with subcell resolution for advection equations with stiff source terms for a single reaction for (1.1) to overcome this difficulty. Research for multi-species (or more species and multi-reactions) is forthcoming. The objective of this study is to gain a deeper understanding of the behavior of high order shock-capturing schemes for problems with stiff source terms and discontinuities and on corresponding numerical prediction strategies. The studies by Yee et al. (2012) and Wang et al. (2012) focus only on solving the reactive system by the fractional step method using the Strang splitting (Strang 1968). It is a common practice by developers in computational physics and engineering simulations to include a cut off safeguard if densities are outside the permissible range. Here we compare the spurious behavior of the same schemes by solving the fully coupled reactive system without the Strang splitting vs. using the Strang splitting. Comparison between the two procedures and the effects of a cut off safeguard is the focus the present study. The comparison of the performance of these schemes is largely based on the degree to which each method captures the correct location of the reaction front for coarse grids. Here “coarse grids” means standard mesh density requirement for accurate simulation of typical non-reacting flows of similar problem setup. It is remarked that, in order to resolve the sharp reaction front, local refinement beyond standard mesh density is still needed. For reacting flows there are different ways in formulating (1.1). The present study considers the following two commonly used formulations. These are using all the species variables vs. using the total density and Ns − 1 number of species variables (Ns is the total number of species)

High Order Finite Difference Methods with Subcell Resolution for 2D Detonation Waves

In simulating hyperbolic conservation laws in conjunction with an inhomogeneous stiff source term, if the solution is discontinuous, spurious numerical results may be produced due to different time scales of the transport part and the source term. This numerical issue often arises in combustion and high speed chemical reacting flows

Variable high-order multiblock overlapping grid methods for mixed steady and unsteady multiscale viscous flows, part II: hypersonic nonequilibrium flows

The variable high-order multiblock overlapping (overset) grids method of Sjogreen & Yee (CiCP, Vol.5, 2008) for a perfect gas has been extended to nonequilibrium flows. This work makes use of the recently developed high-order well-balanced shock-capturing schemes and their filter counterparts (Wang et al., J. Comput. Phys., 2009, 2010) that exactly preserve certain non-trivial steady state solutions of the chemical nonequilibrium governing equations. Multiscale turbulence with strong shocks and flows containing both steady and unsteady components is best treated by mixing of numerical methods and switching on the appropriate scheme in the appropriate subdomains of the flow fields, even under the multiblock grid or adaptive grid refinement framework. While low dissipative sixth- or higher-order shock-capturing filter methods are appropriate for unsteady turbulence with shocklets, second- and third-order shock-capturing methods are more effective for strong steady or nearly steady shocks in terms of convergence. It is anticipated that our variable high-order overset grid framework capability with its highly modular design will allow an optimum synthesis of these new algorithms in such a way that the most appropriate spatial discretizations can be tailored for each particular region of the flow. In this paper some of the latest developments in single block high-order filter schemes for chemical nonequilibrium flows are applied to overset grid geometries. The numerical approach is validated on a number of test cases characterized by hypersonic conditions with strong shocks, including the reentry flow surrounding a 3D Apollo-like NASA Crew Exploration Vehicle that might contain mixed steady and unsteady components, depending on the flow conditions

Star Formation in Cluster Galaxies at 0.2<z<0.55

The rest frame equivalent width of the [OII]3727 emission line, W(OII), has been measured for cluster and field galaxies in the CNOC redshift survey of rich clusters at 0.2<z<0.55. Emission lines of any strength in cluster galaxies at all distances from the cluster centre, out to 2R_{200}, are less common than in field galaxies. The mean W(OII) in cluster galaxies more luminous than M_r^k<-18.5 + 5\log h (q_o=0.1) is 3.8 \pm 0.3 A (where the uncertainty is the 1 sigma error in the mean), significantly less than the field galaxy mean of 11.2 \pm 0.3 A. For the innermost cluster members (R<0.3R_{200}), the mean W(OII) is only 0.3 \pm 0.4 A. Thus, it appears that neither the infall process nor internal tides in the cluster induce detectable excess star formation in cluster galaxies relative to the field. The colour-radius relation of the sample is unable to fully account for the lack of cluster galaxies with W(OII)>10 A, as expected in a model of cluster formation in which star formation is truncated upon infall. Evidence of supressed star formation relative to the field is present in the whole cluster sample, out to 2 R_{200}, so the mechanism responsible for the differential evolution must be acting at a large distance from the cluster centre, and not just in the core. The mean star formation rate in the cluster galaxies with the strongest emission corresponds to an increase in the total stellar mass of less than about 4% if the star formation is due to a secondary burst lasting 0.1 Gyr.Comment: aasms4 latex, 3 postscript figures, accepted for publication in ApJ Letters. Also available at http://astrowww.phys.uvic.ca/~balogh

Exoplanet Detection Techniques

We are still in the early days of exoplanet discovery. Astronomers are beginning to model the atmospheres and interiors of exoplanets and have developed a deeper understanding of processes of planet formation and evolution. However, we have yet to map out the full complexity of multi-planet architectures or to detect Earth analogues around nearby stars. Reaching these ambitious goals will require further improvements in instrumentation and new analysis tools. In this chapter, we provide an overview of five observational techniques that are currently employed in the detection of exoplanets: optical and IR Doppler measurements, transit photometry, direct imaging, microlensing, and astrometry. We provide a basic description of how each of these techniques works and discuss forefront developments that will result in new discoveries. We also highlight the observational limitations and synergies of each method and their connections to future space missions.Comment: 24 pages, 19 figures, PPVI proceedings. Appears as 2014, Protostars and Planets VI, Henrik Beuther, Ralf S. Klessen, Cornelis P. Dullemond, and Thomas Henning (eds.), University of Arizona Press, Tucson, 914 pp., p.715-73