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We present an uncertainty quantification methodology for density estimation from Background Oriented Schlieren (BOS) measurements, in order to provide local, instantaneous, a-posteriori uncertainty bounds on each density measurement in the field of view. Displacement uncertainty quantification algorithms from cross-correlation based Particle Image Velocimetry (PIV) are used to estimate the uncertainty in the dot pattern displacements obtained from cross-correlation for BOS and assess their feasibility. In order to propagate the displacement uncertainty through the density integration procedure, we also develop a novel methodology via the Poisson solver using sparse linear operators. Testing the method using synthetic images of a Gaussian density field showed agreement between the propagated density uncertainties and the true uncertainty. Subsequently the methodology is experimentally demonstrated for supersonic flow over a wedge, showing that regions with sharp changes in density lead to an increase in density uncertainty throughout the field of view, even in regions without these sharp changes. The uncertainty propagation is influenced by the density integration scheme, and for the Poisson solver the density uncertainty increases monotonically on moving away from the regions where the Dirichlet boundary conditions are specified.

A novel uncertainty-based pressure reconstruction method is proposed to evaluate the instantaneous pressure fields from velocity fields measured using particle image velocimetry (PIV) or particle tracking velocimetry (PTV). First, the pressure gradient fields are calculated from velocity fields, while the local and instantaneous pressure gradient uncertainty is estimated from the velocity uncertainty using a linear-transformation based algorithm. The pressure field is then reconstructed by solving an overdetermined linear system which involves the pressure gradients and boundary conditions. This linear system is solved with generalized least-squares (GLS) which incorporates the previously estimated variances and covariances of the pressure gradient errors as inverse weights to optimize the reconstructed pressure field. The method was validated with synthetic velocity fields of a 2D pulsatile flow and the results show significantly improved pressure accuracy with an error reduction of as much as 250% compared to the existing baseline method of solving the pressure Poisson equation (PPE). The GLS was more robust to the velocity errors and provides greater improvement with spatially correlated velocity errors. For experimental validation, the volumetric pressure fields were evaluated from a laminar pipe flow velocity field measured using 3D PTV. The GLS reduced the median absolute pressure errors by as much as 96%.

Recent applications of computational fluid dynamics (CFD) applied to the cardiovascular system have demonstrated its power in investigating the impact of hemodynamics on disease initiation, progression, and treatment outcomes. Flow metrics such as pressure distributions, wall shear stresses (WSS), and blood velocity profiles can be quantified to provide insight into observed pathologies, assist with surgical planning, or even predict disease progression. While numerous studies have performed simulations on clinical human patient data, it often lacks prediagnosis information and can be subject to large intersubject variability, limiting the generalizability of findings. Thus, animal models are often used to identify and manipulate specific factors contributing to vascular disease because they provide a more controlled environment. In this review, we explore the use of CFD in animal models in recent studies to investigate the initiating mechanisms, progression, and intervention effects of various vascular diseases. The first section provides a brief overview of the CFD theory and tools that are commonly used to study blood flow. The following sections are separated by anatomical region, with the abdominal, thoracic, and cerebral areas specifically highlighted. We discuss the associated benefits and obstacles to performing CFD modeling in each location. Finally, we highlight animal CFD studies focusing on common surgical treatments, including arteriovenous fistulas (AVF) and pulmonary artery grafts. The studies included in this review demonstrate the value of combining CFD with animal imaging and should encourage further research to optimize and expand upon these techniques for the study of vascular disease.

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Numerical simulations are carried out to study flame propagation in laminar stratified fuel-air mixtures. Studies are carried out in hydrogen-air and methane-air mixtures. A 30-species 184-step skeletal mechanism is employed for methane oxidation and a 9-species 21-step mechanism for hydrogen oxidation. The study seeks to provide an improved understanding of possible differences in the local flame speed at an equivalence ratio in the compositionally stratified mixture from the speed in a homogeneous mixture at the same equivalence ratio. Flame speed and temperature profiles are evaluated and compared with corresponding values for homogeneous mixtures. As shown in prior experimental work, the numerical results suggest that when the flame propagates from a richer mixture to a leaner mixture, the flame speed is faster than the corresponding speed of the homogeneous mixture. The flame zone thickness is observed to be thinner in the stratified mixture resulting in sharper gradients. As a result, the rate of diffusion of heat and species increases resulting in increased flame speed. The effects become more pronounced in leaner mixtures. The stratification gradient influences the results with shallower gradients showing less difference in flame speeds between stratified and homogeneous mixtures. The comparative effect of thermal diffusion and species diffusion on the differences in flame speed is studied. It is shown that the species diffusion effect is more important.

We propose an improved density integration methodology for Background Oriented Schlieren (BOS) measurements that overcomes the noise sensitivity of the commonly used Poisson solver. The method employs a weighted least-squares (WLS) optimization of the 2D integration of the density gradient field by solving an over-determined system of equations. Weights are assigned to the grid points based on density gradient uncertainties to ensure that a less reliable measurement point has less effect on the integration procedure. Synthetic image analysis with a Gaussian density field shows that WLS constrains the propagation of random error and reduces it by 80% in comparison to Poisson for the highest noise level. Using WLS with experimental BOS measurements of flow induced by a spark plasma discharge show a 30% reduction in density uncertainty in comparison to Poisson, thereby increasing the overall precision of the BOS density measurements.