Direct numerical simulation (DNS) of a turbulent boundary layer over the Gaussian (Boeing) bump is performed. This boundary layer exhibits a series of adverse and favourable pressure gradients and convex and concave curvature effects before separating. These effects on turbulent boundary layers are characterised and compared with a lower-Reynolds-number flow over the same geometry. The momentum budgets are analysed in the streamline-aligned coordinate system upstream of the separation region. These momentum budgets allow the simplification of equations to facilitate an integral analysis. Integral-analysis-based approximations for Reynolds stresses in the inner and outer regions of the boundary layer are also formulated. The shear and wall-normal Reynolds stress profiles normalised by these approximations exhibit a better collapse compared with friction velocity and Zagarola–Smits normalisations in the strong favourable pressure gradient region and in the mild adverse pressure region that precedes it in this flow. Simplification of these Reynolds stress approximations along with results from the DNS are used to obtain semi-empirical approximations that are able to provide stress closure in terms of wall solution fields for the turbulent boundary layer under consideration.

A pair of Direct Numerical Simulations is used to investigate curvature and pressure effects. One has a Gaussian test bump and a straight opposite wall, while the other has a straight test wall and a blowing/suction distribution on an opposite porous boundary, adjusted to produce the same pressure distribution. The calculation of the transpiration distribution is made in potential flow, ignoring the boundary layer. This problem of specifying a pressure distribution is known to be ill-posed for short waves. We address this issue by considering a pressure distribution that is very smooth compared with the distance from wall to opposite boundary. It is also ill-posed once separation occurs. The pressure distribution of the viscous flow nevertheless ended up very close to the specified one, upstream of separation, and comparisons are confined to that region. In the entry region the boundary layers have essentially the same thicknesses and are well-developed turbulence-wise, which is essential for a valid comparison. The focus is on the attached flow in the favorable and adverse gradients. The convex curvature is strong enough compared with the boundary-layer thickness to make the strain-rate tensor drop to near zero over the top of the bump. An intense internal layer forms in the favorable gradient, an order of magnitude thinner than the incoming boundary layer. The effect of curvature follows expectations: concave curvature moderately raises the skin friction, although without creating Gortler vortices, and convex curvature reduces it. The pressure gradient still dominates the physics. Common turbulence models unfortunately over-predict the skin friction in both flows near its peak, and under-predict the curvature effect even when curvature corrections are included.

This paper aims to introduce developments within the PHASTA flow solver that are needed for applications in hypersonic CFD research. The PHASTA formulation is described and unit tests are performed that serve to validate new features that enable the simulation of thermochemical nonequilibrium. These features include a multi-species reacting flow module, a two-temperature formulation that includes a model for vibrational temperature, a model for mass diffusion, and the Spalart-Allmaras RANS turbulence model. The code accurately predicts the physics for simple problems but requires further development for more complex flows that represent real-world engineering problems.

The convective nature of unsteady gusts in open test section wind tunnels offer distinct testing advantages in contrast to closed test sections where the disturbances travel at the speed of sound. Matching such configurations in computational studies brings specific challenges in terms of domain, boundary conditions, and the scales that must be resolved. This study focuses on the validation of a high-fidelity simulation of an open test section low-speed unsteady wind tunnel facility and analysis of the resulting flow physics. Results from a Delayed Detached Eddy Simulation matching the entire wind tunnel facility are compared to experimental measurements at steady and unsteady conditions. After validating the computational setup, further analysis of the behaviors of the velocity fields and shear layer dynamics in the wind tunnel setup are investigated which are impractical to measure experimentally. The simulation results allow for a more complete understanding of the overall setup, including the physical effects which need to be taken into account when testing in unsteady conditions and the coupling of velocity fluctuations in the jet core to structures in the shear layers.

We present a new approach for constructing data-driven subgrid stress models for large eddy simulation of turbulent flows using anisotropic grids. The key to our approach is a Galilean, rotationally, reflectionally and unit invariant model form that also embeds filter anisotropy in such a way that an important subgrid stress identity is satisfied. We use this model form to train a data-driven subgrid stress model using only a small amount of anisotropically filtered DNS data and a simple and inexpensive neural network architecture. A priori and a posteriori tests indicate that the trained data-driven model generalizes well to filter anisotropy ratios, Reynolds numbers and flow physics outside the training dataset.

The current study analyzes the dynamic response of a NACA 0015 finite-span wing to a time-varying freestream in an unsteady wind tunnel at a mean Reynolds number of [Formula: see text]. The aerodynamic response of the wing can be categorized based on the angle of attack and the degree of flow separation on the suction side of the wing. When the suction side is dominated by separated flow, either at low angles of attack with long laminar separation bubbles or at high, poststall, angles of attack, the lift is enhanced by the favorable pressure gradient during freestream acceleration and decremented by the adverse pressure gradient during freestream deceleration. In these cases, the sectional lift coefficient is shown to oscillate by as much as [Formula: see text] due to the unsteady pressure gradient. Comparatively, regions of attached flow on the wing surface remain largely unaffected by the time-varying conditions, regardless of the reduced frequency. Discrepancies between the measured lift and the estimated response from Isaacs’s theory demonstrate that the coupling between the viscous flow separation and the unsteady conditions dominates the unsteady aerodynamic response.

Abdominal aortic aneurysm can exhibit transitional flow characteristics in laminar flow regimes. To report transitional flow characteristics, we examined the convergence of phase-averaged solutions by executing blood flow simulations of a patient-specific abdominal aortic aneurysmal model for 257 cardiac cycles with periodic, pulsatile boundary conditions. The phase-averaged solutions were computed by averaging the solutions over various numbers of cardiac cycles and compared against the ones averaged over 124 cycles. The phase-averaged solutions reported small differences when they were averaged over a large number of cardiac cycles. The instantaneous solutions, however, failed to exhibit fluctuations reported in the phase-averaged solutions. To study transitional blood flows in the aneurysmal region, we need to report phase-averaged solutions as they exhibit nonperiodic, disturbed flow characteristics. Additionally, when reporting phase-averaged solutions, it is preferred to compute an average over a large number of cardiac cycles to be able to represent flow structures of the converged phase-averaged solutions.

Recent years have seen many successful applications of machine learning (ML) to facilitate fluid dynamic computations. As simulations grow, generating new training datasets for traditional offline learning creates I/O and storage bottlenecks. Additionally, performing inference at runtime requires non-trivial coupling of ML framework libraries with simulation codes. This work offers a solution to both limitations by simplifying this coupling and enabling in situ training and inference workflows on heterogeneous clusters. Leveraging SmartSim, the presented framework deploys a database to store data and ML models in memory, thus circumventing the file system. On the Polaris supercomputer, we demonstrate perfect scaling efficiency to the full machine size of the data transfer and inference costs thanks to a novel co-located deployment of the database. Moreover, we train an autoencoder in situ from a turbulent flow simulation, showing that the framework overhead is negligible relative to a solver time step and training epoch.

Wall-resolved and wall-modeled simulations for turbulent flows over complex geometries require anisotropic grids to avoid prohibitive computational cost. However, subgrid stress models based on eddy viscosity models often employ anisotropic length scale definitions that are inadequate for modeling the influence of subgrid eddies on the resolved eddies for such grids. This motivates the need to extend existing well-established models to anisotropic resolutions. We take a step in this direction by proposing a natural extension of the commonly used Smagorinsky model to anisotropic resolutions. The main ingredients in our approach are the construction of a mapping from physical space with an anisotropic filter kernel to a parent space with an isotropic filter kernel and then defining the Smagorinsky model in the parent space. We refer to this model as the anisotropic Smagorinsky model. A priori and a posteriori tests on forced homogeneous and isotropic turbulence indicate that the model performs better than several common anisotropic length scale definitions for the classical Smagorinsky model. We also formulate a dynamic version of the anisotropic Smagorinsky model. For turbulent channel flow, the performance of both the static and dynamic versions of the anisotropic Smagorinsky model is very similar to that of the dynamic Smagorinsky model. These results indicate that the anisotropic Smagorinsky model is a promising method to account for the grid anisotropy.

Direct numerical simulation (DNS) of a turbulent boundary layer over the Gaussian (Boeing) bump is performed. This boundary layer exhibits a series of adverse and favorable pressure gradients and convex and concave curvature effects before separating. These effects on turbulent boundary layers are characterized and compared to a lower Reynolds number flow over the same geometry. The momentum budgets are analyzed in the streamline-aligned coordinate system upstream of the separation region. These momentum budgets allow the simplification of equations to facilitate an integral analysis. Integral analysis-based scalings for Reynolds stresses in the inner and outer regions of the boundary layer are also formulated. These proposed scalings exhibit a better collapse of Reynolds stress profiles compared to friction velocity scaling and Zagarola-Smits scaling in the strong favorable pressure gradient region and in the mild adverse pressure region that precedes it in this flow.

Abstract Unsteady flows threaten the performance and efficiency of systems operating in gusty environments. The impact of an unsteady freestream, generated in a closed test-section unsteady wind tunnel, on the flow separation and aerodynamic performance of a wing at a post-stall angle of attack is examined within the current study. Synchronized two-dimensional, high-speed particle image velocimetry and integrated surface pressure measurements were collected for a finite-span wing in a time-varying, spatially uniform freestream. Freestream accelerations impose additional unsteady pressure gradients within the wind tunnel that alter the behavior of shed vortical structures within the separated flow above the wing. Freestream acceleration and conservation of circulation determine the orientation and interaction of shed vortical structures, which alter the magnitude of the fluctuations in the lift force and pitching moment experienced by the wing. Specifically, fluctuations in the sectional lift and pitching moment coefficients are amplified during deceleration and attenuated during acceleration.

A novel shock capturing technique using an artificial diffusion-based shock sensor is introduced. The compressible branch of the finite-element PHASTA CFD solver is verified via a mesh refinement study and validated via comparison to previous research at turbulent supersonic conditions. Shock stand-off distance and turbulent supersonic boundary layer parameters are estimated in a single simulation of a diamond-shaped 2D fin, showing good agreement with previous research.

View Video Presentation: https://doi.org/10.2514/6.2023-1231.vid The aerodynamic response of two finite-span wings with sweep angles of 0° and 30° was studied under the impact of a convectively unsteady freestream. To assess the aerodynamic response, the unsteady total lift and pitching moment measurements were collected and analyzed, along with time-resolved pressure distributions at select locations across the wingspan. The convective nature of the unsteady freestream generates a streamwise velocity that varies both temporally and spatially over the wing surface, generating spatial velocity gradients that are acceleration dependent. The total lift coefficient response was found to be similar for the unswept and swept wings, while the hysteresis in the total pitching moment coefficient is magnified with increased sweep angle.

Data-driven turbulence modeling is currently a popular approach in constructing new RANS models with improved performance. Even though data-driven models have generally failed to extrapolate outside training cases well, they harbor potential in design-space exploration. Currently the most popular data-driven models typically employ a corrective approach, where a Reynolds stress correction improves upon an existing precursor RANS simulation without coupling with the RANS solver. Corrective models are trained on data from a RANS simulation and thus are limited in predictive capability and accuracy. On the other hand, the rarely used iterative models utilize DNS data for training and completely couple with the solver, and thus they have the potential to provide more accuracy. In this article, we propose the use of model derived turbulence variables to train iterative data-driven models. The model derived variables are arrived at by freezing the flow variables on the grid and solving turbulent transport equations to convergence. A model form is arrived that is Galilean invariant, frame invariant and unit invariant for a particular design space in consideration. A dense feed-forward neural network is used as a surrogate model for the functional mapping in the model. Numerical results for the popular periodic hills benchmark problem are presented to demonstrate the effectiveness of iterative models for design space exploration.

Finite element methods provide very low dissipation, higher order accurate discretizations for use in scale resolving simulations of turbulence. Their ability to use unstructured grids to match grid resolution to the local needs of the scale resolving simulation makes them particularly attractive and efficient for complex geometry flows and more fundamental flows with a large spatial variation in the smallest required scale that must be resolved. This chapter provides the background for the basis functions that will be used with the finite element method to convert partial differential equation into ordinary differential equations which are then integrated in time by either explicit or implicit methods. The chapter also provides a contrast of classical and newer approaches to equation formation, assembly, and solution that accounts for emerging hardware and closes with a demonstration of the method's application to flow over a vertical tail rudder assembly where the methods ability to support grid adaptivity provides additional computational efficiency.

Structural subgrid stress models for large-eddy simulation often allow for backscatter of energy from unresolved to resolved turbulent scales, but excessive model backscatter can eventually result in numerical instability. A commonly employed strategy to overcome this issue is to set predicted subgrid stresses to zero in regions of model backscatter. This clipping procedure improves the stability of structural models, however, at the cost of reduced correlation between the predicted subgrid stresses and the exact subgrid stresses. In this paper, we propose an alternative strategy that removes model backscatter from model predictions through the solution of a constrained minimization problem. This procedure, which we refer to as optimal clipping, results in a parameter-free mixed model, and it yields predicted subgrid stresses in higher correlation with the exact subgrid stresses as compared with those attained with the traditional clipping procedure. We perform a series of a priori and a posteriori tests to investigate the impact of applying the traditional and optimal clipping procedures to Clark's gradient subgrid stress model, and we observe that optimal clipping leads to a significant improvement in model predictions as compared to the traditional clipping procedure.

Despite their well-known limitations, Reynolds averaged Navier-Stokes (RANS) models remain the most commonly employed tool for modeling turbulent flows in engineering practice. RANS models are predicated on the solution of the RANS equations, but the RANS equations involve an unclosed term, the Reynolds stress tensor, which must be modeled. The Reynolds stress tensor is often modeled as an algebraic function of mean flow field variables and turbulence variables. This, however, introduces a discrepancy between the Reynolds stress tensor predicted by the Reynolds stress model and the exact Reynolds stress tensor. This discrepancy can result in inaccurate mean flow field predictions for complex flows of industrial relevance. In this paper, we introduce a data-informed approach for arriving at Reynolds stress models with improved predictive performance. Our approach relies on learning the components of the Reynolds stress discrepancy tensor associated with a given Reynolds stress model in the mean strain-rate tensor eigenframe. These components are typically smooth and hence simple to learn using state-of-the-art machine learning strategies and regression techniques. Our approach automatically yields Reynolds stress models that are symmetric, and it yields Reynolds stress models that are both Galilean and frame invariant provided the inputs are themselves Galilean and frame invariant. To arrive at computable models of the discrepancy tensor, we employ feed-forward neural networks and an input space spanning the integrity basis of the mean strain-rate tensor, the mean rotation-rate tensor, the mean pressure gradient, and the turbulent kinetic energy gradient, and we introduce a framework for dimensional reduction of the input space to further reduce computational cost. Numerical results illustrate the effectiveness of the proposed approach for data-informed Reynolds stress closure for a suite of turbulent flow problems of increasing complexity. • A new data-driven approach to modeling Reynolds stress discrepancy is proposed. • Reynolds stress discrepancy is represented in terms of components in strain-rate eigenframe. • Strain-rate eigenframe discrepancy components are approximated with neural networks. • The approach yields Galilean, frame, and scale invariant Reynolds stress models. • A framework is introduced for input space dimension reduction to reduce computational cost.