Part 1 of this two-part paper presents a comprehensive approach to verification and validation methodology and procedures for CFD simulations from an already developed CFD code applied without requiring availability of the source code for specified objectives, geometry, conditions, and available benchmark information. Concepts, definitions, and equations derived for simulation errors and uncertainties provide the overall mathematical framework. Verification is defined as a process for assessing simulation numerical uncertainty and, when conditions permit, estimating the sign and magnitude of the numerical error itself and the uncertainty in that error estimate. The approach for estimating errors and uncertainties includes (1) the option of treating the numerical error as deterministic or stochastic, (2) the use of generalized Richardson extrapolation for J input parameters, and (3) the concept of correction factors based on analytical benchmarks, which provides a quantitative metric to determine proximity of the solutions to the asymptotic range, accounts for the effects of higher-order terms, and are used for defining and estimating errors and uncertainties. Validation is defined as a process for assessing simulation modeling uncertainty by using benchmark experimental data and, when conditions permit, estimating the sign and magnitude of the modeling error itself. The approach properly takes into account the uncertainties in both the simulation and experimental data in assessing the level of validation. Interpretation of results of validation efforts both where the numerical error is treated as deterministic and stochastic are discussed. Part 2 provides an example for RANS simulations for a cargo/container ship where issues with regard to practical application of the methodology and procedures and interpretation of verification and validation results are discussed.

Reynolds-averaged Navier-Stokes (RANS) equations are widely used in engineering turbulent flow simulations. However, RANS predictions may have large discrepancies due to the uncertainties in modeled Reynolds stresses. Recently, Wang et al. demonstrated that machine learning can be used to improve the RANS modeled Reynolds stresses by leveraging data from high fidelity simulations (Physics informed machine learning approach for reconstructing Reynolds stress modeling discrepancies based on DNS data. Physical Review Fluids. 2, 034603, 2017). However, solving for mean flows from the improved Reynolds stresses still poses significant challenges due to potential ill-conditioning of RANS equations with Reynolds stress closures. Enabling improved predictions of mean velocities are of profound practical importance, because often the velocity and its derived quantities (QoIs, e.g., drag, lift, surface friction), and not the Reynolds stress itself, are of ultimate interest in RANS simulations. To this end, we present a comprehensive framework for augmenting turbulence models with physics-informed machine learning, illustrating a complete workflow from identification of input features to final prediction of mean velocities. This work has two innovations. First, we demonstrate a systematic procedure to generate mean flow features based on the integrity basis for mean flow tensors. Second, we propose using machine learning to predict linear and nonlinear parts of the Reynolds stress tensor separately. Inspired by the finite polynomial representation of tensors in classical turbulence modeling, such a decomposition is instrumental in overcoming the ill-conditioning of RANS equations.Numerical tests demonstrated merits of the proposed framework.

The canine nasal cavity contains hundreds of millions of sensory neurons, located in the olfactory epithelium that lines convoluted nasal turbinates recessed in the rear of the nose. Traditional explanations for canine olfactory acuity, which include large sensory organ size and receptor gene repertoire, overlook the fluid dynamics of odorant transport during sniffing. But odorant transport to the sensory part of the nose is the first critical step in olfaction. Here we report new experimental data on canine sniffing and demonstrate allometric scaling of sniff frequency, inspiratory airflow rate and tidal volume with body mass. Next, a computational fluid dynamics simulation of airflow in an anatomically accurate three-dimensional model of the canine nasal cavity, reconstructed from high-resolution magnetic resonance imaging scans, reveals that, during sniffing, spatially separate odour samples are acquired by each nostril that may be used for bilateral stimulus intensity comparison and odour source localization. Inside the nose, the computation shows that a unique nasal airflow pattern develops during sniffing, which is optimized for odorant transport to the olfactory part of the nose. These results contrast sharply with nasal airflow in the human. We propose that mammalian olfactory function and acuity may largely depend on odorant transport by nasal airflow patterns resulting from either the presence of a highly developed olfactory recess (in macrosmats such as the canine) or the lack of one (in microsmats including humans).

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The canine nasal airway is an impressively complex anatomical structure, having many functional roles. The complicated branching and intricate scrollwork of the nasal conchae provide large surface area for heat, moisture, and odorant transfer. Of the previous anatomical studies of the canine nasal airway, none have included a detailed rendering of the maxilloturbinate and ethmoidal regions of the nose. Here, we present a high-resolution view of the nasal airway of a large dog, using magnetic resonance imaging scans. Representative airway sections are shown, and a three-dimensional surface model of the airway is reconstructed from the image data. The resulting anatomic structure and detailed morphometric data of the airway provide insight into the functional nature of canine olfaction. A complex airway network is revealed, wherein the branched maxilloturbinate and ethmoturbinate scrolls appear structurally distinct. This is quantitatively confirmed by considering the fractal dimension of each airway, which shows that the maxilloturbinate airways are more highly contorted than the ethmoidal airways. Furthermore, surface areas of the maxilloturbinate and ethmoidal airways are shown to be much different, despite having analogous physiological functions. Functionally, the dorsal meatus of the canine nasal airway is shown to be a bypass for odorant-bearing inspired air around the complicated maxilloturbinate during sniffing for olfaction. Finally, nondimensional analysis is used to show that the airflow within both the maxilloturbinate and ethmoturbinate regions must be laminar. This work has direct relevance to biomimetic sniffer design, chemical trace detector development, intranasal drug delivery, and inhalation toxicology.

This study is part of a FDA-sponsored project to evaluate the use and limitations of computational fluid dynamics (CFD) in assessing blood flow parameters related to medical device safety. In an interlaboratory study, fluid velocities and pressures were measured in a nozzle model to provide experimental validation for a companion round-robin CFD study. The simple benchmark nozzle model, which mimicked the flow fields in several medical devices, consisted of a gradual flow constriction, a narrow throat region, and a sudden expansion region where a fluid jet exited the center of the nozzle with recirculation zones near the model walls. Measurements of mean velocity and turbulent flow quantities were made in the benchmark device at three independent laboratories using particle image velocimetry (PIV). Flow measurements were performed over a range of nozzle throat Reynolds numbers (Re(throat)) from 500 to 6500, covering the laminar, transitional, and turbulent flow regimes. A standard operating procedure was developed for performing experiments under controlled temperature and flow conditions and for minimizing systematic errors during PIV image acquisition and processing. For laminar (Re(throat)=500) and turbulent flow conditions (Re(throat)≥3500), the velocities measured by the three laboratories were similar with an interlaboratory uncertainty of ∼10% at most of the locations. However, for the transitional flow case (Re(throat)=2000), the uncertainty in the size and the velocity of the jet at the nozzle exit increased to ∼60% and was very sensitive to the flow conditions. An error analysis showed that by minimizing the variability in the experimental parameters such as flow rate and fluid viscosity to less than 5% and by matching the inlet turbulence level between the laboratories, the uncertainties in the velocities of the transitional flow case could be reduced to ∼15%. The experimental procedure and flow results from this interlaboratory study (available at http://fdacfd.nci.nih.gov) will be useful in validating CFD simulations of the benchmark nozzle model and in performing PIV studies on other medical device models.

Olfaction begins when an animal draws odorant-laden air into its nasal cavity by sniffing, thus transporting odorant molecules from the external environment to olfactory receptor neurons (ORNs) in the sensory region of the nose. In the dog and other macrosmatic mammals, ORNs are relegated to a recess in the rear of the nasal cavity that is comprised of a labyrinth of scroll-like airways. Evidence from recent studies suggests that nasal airflow patterns enhance olfactory sensitivity by efficiently delivering odorant molecules to the olfactory recess. Here, we simulate odorant transport and deposition during steady inspiration in an anatomically correct reconstructed model of the canine nasal cavity. Our simulations show that highly soluble odorants are deposited in the front of the olfactory recess along the dorsal meatus and nasal septum, whereas moderately soluble and insoluble odorants are more uniformly deposited throughout the entire olfactory recess. These results demonstrate that odorant deposition patterns correspond with the anatomical organization of ORNs in the olfactory recess. Specifically, ORNs that are sensitive to a particular class of odorants are located in regions where that class of odorants is deposited. The correlation of odorant deposition patterns with the anatomical organization of ORNs may partially explain macrosmia in the dog and other keen-scented species.

The canine nasal cavity contains a complex airway labyrinth, dedicated to respiratory air conditioning, filtering of inspired contaminants, and olfaction. The small and contorted anatomical structure of the nasal turbinates has, to date, precluded a proper study of nasal airflow in the dog. This study describes the development of a high-fidelity computational fluid dynamics (CFD) model of the canine nasal airway from a three-dimensional reconstruction of high-resolution magnetic resonance imaging scans of the canine anatomy. Unstructured hexahedral grids are generated, with large grid sizes ((10-100) x 10(6) computational cells) required to capture the details of the nasal airways. High-fidelity CFD solutions of the nasal airflow for steady inspiration and expiration are computed over a range of physiological airflow rates. A rigorous grid refinement study is performed, which also illustrates a methodology for verification of CFD calculations on complex unstructured grids in tortuous airways. In general, the qualitative characteristics of the computed solutions for the different grid resolutions are fairly well preserved. However, quantitative results such as the overall pressure drop and even the regional distribution of airflow in the nasal cavity are moderately grid dependent. These quantities tend to converge monotonically with grid refinement. Lastly, transient computations of canine sniffing were carried out as part of a time-step study, demonstrating that high temporal accuracy is achievable using small time steps consisting of 160 steps per sniff period. Here we demonstrate that acceptable numerical accuracy (between approximately 1% and 15%) is achievable with practical levels of grid resolution (approximately 100 x 10(6) computational cells). Given the popularity of CFD as a tool for studying flow in the upper airways of humans and animals, based on this work we recommend the necessity of a grid dependence study and quantification of numerical error when presenting CFD results in complicated airways.