Analysis of a parallelized nonlinear elliptic boundary value problem solver with application to reacting flows

A parallelized finite difference code based on the Newton method for systems of nonlinear elliptic boundary value problems in two dimensions is analyzed in terms of computational complexity and parallel efficiency. An approximate cost function depending on 15 dimensionless parameters is derived for algorithms based on stripwise and boxwise decompositions of the domain and a one-to-one assignment of the strip or box subdomains to processors. The sensitivity of the cost functions to the parameters is explored in regions of parameter space corresponding to model small-order systems with inexpensive function evaluations and also a coupled system of nineteen equations with very expensive function evaluations. The algorithm was implemented on the Intel Hypercube, and some experimental results for the model problems with stripwise decompositions are presented and compared with the theory. In the context of computational combustion problems, multiprocessors of either message-passing or shared-memory type may be employed with stripwise decompositions to realize speedup of O(n), where n is mesh resolution in one direction, for reasonable n

Medical treatment of Cushing’s disease: Overview and recent findings

Cushing’s disease, due to pituitary adrenocorticotropic hormone (ACTH) hypersecretion, is the most common etiology of spontaneous excess cortisol production. The majority of pituitary tumors causing Cushing’s disease measure <1 cm and the excess morbidity associated with these tumors is mostly due to the effects of elevated, nonsuppressible, ACTH levels leading to adrenal steroid hypersecretion. Elevated circulating cortisol levels lead to abnormal fat deposition, hypertension, diabetes, coronary artery disease, osteoporosis, muscle weakness and psychological disturbances. At experienced centers, initial surgical remission rate via transnasal, transphenoidal resection approaches 80% for tumors less than 1 cm, but may be as low as 30% for larger lesions and long-term recurrence in all groups approaches 25%. Residual disease may be managed with more radical surgery, pituitary-directed radiation, bilateral adrenalectomy, or medical therapy. This paper addresses current and novel therapies in various stages of development for Cushing’s disease

Numerical modeling of flame-balls in fuel-air mixtures

At low gravity, when buoyancy effects are small, flame-balls can be generated. These are stationary spherical structures whose existence appears to require a near-limit mixture, a small Lewis number and heat losses from radiation. It is our goal to combine computational modeling with existing experimental and theoretical studies (NASA) of these structures so that an improved understanding of flammability limits and near-limit phenomena will occur. The question of flammability limits is of fundamental importance and has long been examined. It is of great practical importance to predict, from first principles, a limit mixture strength that agrees with experimental values for the configuration at hand. Flame-balls provide an excellent configuration in which convective losses can be eliminated and the resulting stable solutions are produced from a diffusive, reactive and radiative balance. Although analytical modeling provides convincing evidence that the key physical ingredients of flame-balls have been identified, quantitative confirmation can only come from detailed numerical simulations. Our goal is to predict theoretically the mass fractions of the species and the temperature as functions of the independent coordinate r

A comparison of computational and experimental lift-off heights of coflow laminar diffusion flames

As a sensitive marker of changes in flame structure, the number densities of excited-state CH (denoted CH*), and excited-state OH (denoted OH*) are imaged in coflow laminar diffusion flames. Measurements are made both in normal gravity and on the NASA KC-135 reduced-gravity aircraft. The spatial distribution of these radicals provides information about flame structure and lift-off heights that can be directly compared with computational predictions. Measurements and computations are compared over a range of buoyancy and fuel dilution levels. Results indicate that the lift-off heights and flame shapes predicted by the computations are in excellent agreement with measurement for both normal gravity (1g) and reduced gravity flames at low dilution levels. As the fuel mixture is increasingly diluted, however, the 1g lift-off heights become underpredicted. This trend continues until the computations predict stable flames at highly dilute fuel mixtures beyond the 1g experimental blow-off limit. To better understand this behavior, an analysis was performed, which indicates that the lift-off height is sensitive to the laminar flame speed of the corresponding premixed mixture at the flame edge. By varying the rates of two key "flame speed" controlling reactions, we were able to modify the predicted lift-off heights so as to be in closer agreement with the experiments. The results indicate that reaction sets that work well in low dilution systems may need to be modified to accommodate high dilution flames

Efficient computation of high index Sturm-Liouville eigenvalues for problems in physics

Finding the eigenvalues of a Sturm-Liouville problem can be a computationally challenging task, especially when a large set of eigenvalues is computed, or just when particularly large eigenvalues are sought. This is a consequence of the highly oscillatory behaviour of the solutions corresponding to high eigenvalues, which forces a naive integrator to take increasingly smaller steps. We will discuss some techniques that yield uniform approximation over the whole eigenvalue spectrum and can take large steps even for high eigenvalues. In particular, we will focus on methods based on coefficient approximation which replace the coefficient functions of the Sturm-Liouville problem by simpler approximations and then solve the approximating problem. The use of (modified) Magnus or Neumann integrators allows to extend the coefficient approximation idea to higher order methods

A Computational and Experimental Study of Coflow Laminar Methane/Air Diffusion Flames: Effects of Fuel Dilution, Inlet Velocity, and Gravity

The influences of fuel dilution, inlet velocity, and gravity on the shape and structure of laminar coflow CH4-air diffusion flames were investigated computationally and experimentally. A series of nitrogen-diluted flames measured in the Structure and Liftoff in Combustion Experiment (SLICE) on board the International Space Station was assessed numerically under microgravity (mu g) and normal gravity (1g) conditions with CH4 mole fraction ranging from 0.4 to 1.0 and average inlet velocity ranging from 23 to 90 cm/s. Computationally, the MC-Smooth vorticity-velocity formulation was employed to describe the reactive gaseous mixture, and soot evolution was modeled by sectional aerosol equations. The governing equations and boundary conditions were discretized on a two-dimensional computational domain by finite differences, and the resulting set of fully coupled, strongly nonlinear equations was solved simultaneously at all points using a damped, modified Newton's method. Experimentally, flame shape and soot temperature were determined by flame emission images recorded by a digital color camera. Very good agreement between computation and measurement was obtained, and the conclusions were as follows. (1) Buoyant and nonbuoyant luminous flame lengths are proportional to the mass flow rate of the fuel mixture; computed and measured nonbuoyant flames are noticeably longer than their 1g counterparts; the effect of fuel dilution on flame shape (i.e., flame length and flame radius) is negligible when the flame shape is normalized by the methane flow rate. (2) Buoyancy-induced reduction of the flame radius through radially inward convection near the flame front is demonstrated. (3) Buoyant and nonbuoyant flame structure is mainly controlled by the fuel mass flow rate, and the effects from fuel dilution and inlet velocity are secondary

Analysis of turbulent flame propagation in equivalence ratio-stratified flow

Equivalence ratio-stratified combustion is an important technology for achieving stable low-emission operation in internal combustion engines and gas turbines. This study examines how equivalence ratio stratification affects the physics of turbulent flame propagation using Direct Numerical Simulation. Three-dimensional simulations of a turbulent slot-Bunsen flame configuration are performed with accurate multi-step kinetic modelling for methane-air combustion. We compare one perfectly-premixed and three equivalence ratio-stratified cases with the mean equivalence ratio gradient aligned with, tangential to or opposed to the mean flame brush. The simulation results are analysed in terms of flame surface area and the burning intensity. The local effects of stratification are then investigated further by examining statistics of the displacement speed conditioned on the flame-normal equivalence ratio gradient. The local burning intensity is found to depend on the orientation of the stratification with respect to the flame front, so that burning intensity is enhanced when the flame speed in the products is faster than in the reactants. This effect of alignment between equivalence ratio gradients and flame fronts has been observed previously in laminar flames and it is found here that it also affects the global behaviour of turbulent flames. The flame surface area is also influenced by equivalence ratio stratification and this may be explained by differences in the surface-averaged consumption speed and differential propagation effects due to flame speed variations associated with equivalence ratio fluctuations

A Numerical and Experimental Study of Coflow Laminar Diffusion Flames: Effects of Gravity and Inlet Velocity

In this work, the influence of gravity, fuel dilution, and inlet velocity on the structure, stabilization, and sooting behavior of laminar coflow methane-air diffusion flames was investigated both computationally and experimentally. A series of flames measured in the Structure and Liftoff in Combustion Experiment (SLICE) was assessed numerically under microgravity and normal gravity conditions with the fuel stream CH4 mole fraction ranging from 0.4 to 1.0. Computationally, the MC-Smooth vorticity-velocity formulation of the governing equations was employed to describe the reactive gaseous mixture; the soot evolution process was considered as a classical aerosol dynamics problem and was represented by the sectional aerosol equations. Since each flame is axisymmetric, a two-dimensional computational domain was employed, where the grid on the axisymmetric domain was a nonuniform tensor product mesh. The governing equations and boundary conditions were discretized on the mesh by a nine-point finite difference stencil, with the convective terms approximated by a monotonic upwind scheme and all other derivatives approximated by centered differences. The resulting set of fully coupled, strongly nonlinear equations was solved simultaneously using a damped, modified Newton's method and a nested Bi-CGSTAB linear algebra solver. Experimentally, the flame shape, size, lift-off height, and soot temperature were determined by flame emission images recorded by a digital camera, and the soot volume fraction was quantified through an absolute light calibration using a thermocouple. For a broad spectrum of flames in microgravity and normal gravity, the computed and measured flame quantities (e.g., temperature profile, flame shape, lift-off height, and soot volume fraction) were first compared to assess the accuracy of the numerical model. After its validity was established, the influence of gravity, fuel dilution, and inlet velocity on the structure, stabilization, and sooting tendency of laminar coflow methane-air diffusion flames was explored further by examining quantities derived from the computational results

An Experimental and Computational Study on Soot Formation in a Coflow Jet Flame Under Microgravity and Normal Gravity

Upon the completion of the Structure and Liftoff in Combustion Experiment (SLICE) in March 2012, a comprehensive and unique set of microgravity coflow diffusion flame data was obtained. This data covers a range of conditions from weak flames near extinction to strong, highly sooting flames, and enabled the study of gravitational effects on phenomena such as liftoff, blowout and soot formation. The microgravity experiment was carried out in the Microgravity Science Glovebox (MSG) on board the International Space Station (ISS), while the normal gravity experiment was performed at Yale utilizing a copy of the flight hardware. Computational simulations of microgravity and normal gravity flames were also carried out to facilitate understanding of the experimental observations. This paper focuses on the different sooting behaviors of CH4 coflow jet flames in microgravity and normal gravity. The unique set of data serves as an excellent test case for developing more accurate computational models.Experimentally, the flame shape and size, lift-off height, and soot temperature were determined from line-of-sight flame emission images taken with a color digital camera. Soot volume fraction was determined by performing an absolute light calibration using the incandescence from a flame-heated thermocouple. Computationally, the MC-Smooth vorticity-velocity formulation was employed to describe the chemically reacting flow, and the soot evolution was modeled by the sectional aerosol equations. The governing equations and boundary conditions were discretized on an axisymmetric computational domain by finite differences, and the resulting system of fully coupled, highly nonlinear equations was solved by a damped, modified Newtons method. The microgravity sooting flames were found to have lower soot temperatures and higher volume fraction than their normal gravity counterparts. The soot distribution tends to shift from the centerline of the flame to the wings from normal gravity to microgravity