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Abstract Image-based computational fluid dynamics (CFD) has become a new capability for determining wall stresses of pulsatile flows. However, a computational platform that directly connects image information to pulsatile wall stresses is lacking. Prevailing methods rely on manual crafting of a hodgepodge of multidisciplinary software packages, which is usually laborious and error-prone. We present a new computational platform, to compute wall stresses in image-based pulsatile flows using the volumetric lattice Boltzmann method (VLBM). The novelty includes: (1) a unique image processing to extract flow domain and local wall normality, (2) a seamless connection between image extraction and VLBM, (3) an en-route calculation of strain-rate tensor, and (4) GPU acceleration (not included here). We first generalize the streaming operation in the VLBM and then conduct application studies to demonstrate its reliability and applicability. A benchmark study is for laminar and turbulent pulsatile flows in an image-based pipe (Reynolds number: 10 to 5000). The computed pulsatile velocity and shear stress are in good agreements with Womersley's analytical solutions for laminar pulsatile flows and concurrent laboratory measurements for turbulent pulsatile flows. An application study is to quantify the pulsatile hemodynamics in image-based human vertebral and carotid arteries including velocity vector, pressure, and wall-shear stress. The computed velocity vector fields are in reasonably well agreement with MRA (magnetic resonance angiography) measured ones. This computational platform is good for image-based CFD with medical applications and pore-scale porous media flows in various natural and engineering systems. 

Computational fluid dynamics (CFD) and its uncertainty quantification are computationally expensive. We use Gaussian Process (GP) methods to demonstrate that machine learning can build efficient and accurate surrogate models to replace CFD simulations with significantly reduced computational cost without compromising the physical accuracy. We also demonstrate that both epistemic uncertainty (machine learning model uncertainty) and aleatory uncertainty (randomness in the inputs of CFD) can be accommodated when the machine learning model is used to reveal fluid dynamics. The demonstration is performed by applying simulation of Hagen-Poiseuille and Womersley flows that involve spatial and spatial-tempo responses, respectively. Training points are generated by using the analytical solutions with evenly discretized spatial or spatial-temporal variables. Then GP surrogate models are built using supervised machine learning regression. The error of the GP model is quantified by the estimated epistemic uncertainty. The results are compared with those from GPU-accelerated volumetric lattice Boltzmann simulations. The results indicate that surrogate models can produce accurate fluid dynamics (without CFD simulations) with quantified uncertainty when both epistemic and aleatory uncertainties exist. 

We have derived a 3-D kinetic-based discrete dynamic system (DDS) from the lattice Boltzmann equation (LBE) for incompressible flows through a Galerkin procedure. Expressed by a poor-man lattice Boltzmann equation (PMLBE), it involves five bifurcation parameters including relaxation time from the LBE, splitting factor of large and sub-grid motion scales, and wavevector components from the Fourier space. Numerical experiments have shown that the DDS can capture laminar behaviors of periodic, subharmonic, n-period, and quasi-periodic and turbulent behaviors of noisy periodic with harmonic, noisy subharmonic, noisy quasi-periodic, and broadband power spectra. In this work, we investigated the effects of bifurcation parameters on the capturing of the laminar and turbulent flows in terms of the convergence of time series and the pattern of power spectra. We have found that the 2nd order and 3rd order PMLBEs are both able to capture laminar and turbulent flow behaviors but the 2nd order DDS performs better with lower computation cost and more flow behaviors captured. With the specified ranges of the bifurcation parameters, we have identified two optimal bifurcation parameter sets for laminar and turbulent behaviors. Beyond this work, we are exploring the regime maps for a deeper understanding of the contributions of the bifurcation parameters to the capturing of laminar and turbulent behaviors. Surrogate models (to replace the PMLBE) are being developed using deep learning techniques to overcome the overwhelming computation cost for the regime maps. Meanwhile, the DDS is being employed in the large eddy simulation of turbulent pulsatile flows to provide dynamic sub-grid scale information. 

Inlet and outlet boundary conditions (BCs) play an important role in newly emerged image-based computational hemodynamics for blood flows in human arteries anatomically extracted from medical images. We developed physiological inlet and outlet BCs based on patients’ medical data and integrated them into the volumetric lattice Boltzmann method. The inlet BC is a pulsatile paraboloidal velocity profile, which fits the real arterial shape, constructed from the Doppler velocity waveform. The BC of each outlet is a pulsatile pressure calculated from the three-element Windkessel model, in which three physiological parameters are tuned by the corresponding Doppler velocity waveform. Both velocity and pressure BCs are introduced into the lattice Boltzmann equations through Guo’s non-equilibrium extrapolation scheme. Meanwhile, we performed uncertainty quantification for the impact of uncertainties on the computation results. An application study was conducted for six human aortorenal arterial systems. The computed pressure waveforms have good agreement with the medical measurement data. A systematic uncertainty quantification analysis demonstrates the reliability of the computed pressure with associated uncertainties in the Windkessel model. With the developed physiological BCs, the image-based computation hemodynamics is expected to provide a computation potential for the noninvasive evaluation of hemodynamic abnormalities in diseased human vessels. 

The instability and transition to turbulence and its evolution in pulsatile flows, which involve reverse flows and unsteady flow separations, is the primary focus of this experimental work. A piston driven by a programmable DC servo motor was used to set-up a water flow system and provide the pulsation characteristics. Time-resolved particle image velocimetry data were acquired in a refractive index matching set-up by using a continuous wave laser and a high-frame-rate digital camera. The position of the piston was continuously recorded by a laser proximity sensor. Five different experiments were carried out with Reynolds numbers in the range of 535–4825 and Womersley numbers from 11.91 to 23.82. The non-stationarity of the data was addressed by incorporating trend removal methods involving low- and high-pass filtering of the data, and using empirical mode decomposition together with the relevant Hilbert–Huang transform to determine the intrinsic mode functions. This latter method is more appropriate for nonlinear and non-stationary cases, for which traditional analysis involving classical Fourier decomposition is not directly applicable. It was found that transition to turbulence is a spontaneous event covering the whole near-wall region. The instantaneous vorticity profiles show the development of a large-scale ring-like attached wall vortical layer (WVL) with smaller vortices of higher frequencies than the pulsation frequency superimposed, which point to a shear layer Kelvin–Helmholtz (K–H) type of instability. Inflectional instability leads to flow separation and the formation of a major roll-up structure with the K–H vortices superimposed. This structure breaks down in the azimuthal direction into smaller turbulence patches with vortical content, which appears to be the prevailing structural content of the flow at each investigated Reynolds number ( Re ). At higher Re numbers, the strength and extent of the vortices are larger and substantial disturbances appear in the free stream region of the flow, which are typical of pipe flows at transitional Re numbers. Turbulence appears to be produced at the locations of maximum or minimum vorticity within the attached WVL, in the ridges between the K–H vortices around the separated WVL and the upstream side of the secondary vortex where the flow impinges on the wall. This wall turbulence breaks away into the middle section of the pipe, at approximately $Re \ge 2200$ , by strong eruptions of the K–H vortices.