Session M31: Computational Fluid Dynamics: Advanced Topics

Large-eddy simulation of the flow in downtown Oklahoma City

CFD modeling of urban canopy flow is of interest for a variety of applications, ranging from pedestrian wind comfort and air quality, to wind loading on buildings. The complexity of the flows complicates validation of simulation results, and uncertainty quantification (UQ) is indispensable to draw conclusions on the predictive capabilities of numerical tools. In previous work, we investigated inflow and turbulence model form UQ for the flow in Oklahoma City, comparing the results to field measurement data from the Joint Urban 2003 measurement campaign. In the present study, we performed a LES of the same configuration to further investigate the turbulence model form uncertainties, and determine opportunities for improving the predictions using high-fidelity simulations. Quantitative comparison of the LES results and the experimental data for mean velocity showed some local improvements compared to RANS, especially for the velocity magnitude. However, when comparing the results at all available measurement stations, a similar performance for the LES and RANS was found. The LES does capture the turbulence spectra at the measurement locations well, which is a substantial benefit over RANS for applications that need accurate predictions of the turbulence statistics. The lack of an improvement in the mean prediction with LES occurs particularly in areas that were previously shown to have a large uncertainty related to the inflow boundary condition in RANS.   

Improving urban wind flow predictions through data assimilation

Computational fluid dynamic is fundamentally important to several aspects in the design of sustainable and resilient urban environments. The prediction of the flow pattern for example can help to determine pedestrian wind comfort, air~quality, optimal building ventilation strategies, and wind loading on buildings.~ However, the significant variability and uncertainty in the boundary conditions poses a challenge when interpreting results as a basis for design decisions. To~improve our understanding of the uncertainties in the models and develop better predictive tools, we started a pilot field measurement campaign on Stanford University's campus combined with a detailed numerical prediction of the wind~flow. The experimental data is being used to investigate the potential use of data assimilation and inverse techniques to better characterize the uncertainty in the results and improve the confidence in current wind flow predictions. We~consider the incoming wind direction and magnitude as unknown parameters and perform a set of Reynolds-averaged Navier-Stokes simulations to build a polynomial chaos expansion response surface at each sensor location. We~subsequently use an inverse ensemble Kalman filter to retrieve an estimate for the probabilistic density function of the inflow parameters. Once these distributions are obtained, the forward analysis is repeated to obtain predictions for the flow field~in the entire urban canopy and the results are compared with the experimental data.   

Quantifying the influence of geometrical details on urban canopy flow simulations

Computational Fluid Dynamics (CFD) methods are frequently used to investigate urban canopy flows. Since it is not possible to represent the full complexity of these flows in a single deterministic simulation, there is a need to quantify the uncertainty in the results. In previous work, we have investigated uncertainties related to the inflow boundary conditions and the turbulence model. The results indicated that additional uncertainties are likely non-negligible, and that uncertainty in the representation of the urban canopy geometry could be an important factor.~ The objective of this study is to explore methods to quantify geometrical uncertainties in urban canopy CFD simulations. We consider a model of Stanford University's~Science and Engineering Quad, and investigate the effect of the geometry by gradually introducing features with smaller dimensions into the model, and by introducing momentum sinks to represent the presence of vegetation. The geometrical changes result in some considerable differences, such as higher wind amplification factors near the buildings around the quad. Since such differences can affect design decisions related to e.g. pedestrian wind comfort or wind loading, future work will focus on establishing a more formal framework to quantify these uncertainties.   

Incompressible flow simulations on regularized moving meshfree grids.

A moving grid meshfree solver for incompressible flows is presented. To solve for the flow field, a semi-implicit approximate projection method is directly discretized on meshfree grids using General Finite Differences (GFD) with sharp interface stencil modifications. To maintain a regular grid, an explicit shift is used to relax compressed pseudosprings connecting a star node to its cloud of neighbors. The following test cases are used for validation: the Taylor-Green vortex decay, the analytic and modified lid-driven cavities, and an oscillating cylinder enclosed in a container for a range of Reynolds number values. We demonstrate that 1) the grid regularization does not impede the second order spatial convergence rate, 2) the Courant condition can be used for time marching but the projection splitting error reduces the convergence rate to first order, and 3) moving boundaries and arbitrary grid distortions can readily be handled.   

Simulating variable-density flows with time-consistent integration of Navier-Stokes equations

In this talk, we present several features of a high-order semi-implicit variable-density low-Mach Navier-Stokes solver. A new formulation to solve pressure Poisson-like equation of variable-density flows is highlighted. With this formulation of the numerical method, we are able to solve all variables with a uniform order of accuracy in time (consistent with the time integrator being used). The solver is primarily designed to perform direct numerical simulations for turbulent premixed flames. Therefore, we also address other important elements, such as energy-stable boundary conditions, synthetic turbulence generation, and flame anchoring method. Numerical examples include classical non-reacting constant/variable-density flows, as well as turbulent premixed flames.   

A volume-fraction model for the simulation of miscible and viscous compressible fluids

Miscible multispecies compressible computations typically employ conservative equations for mass fraction transport. These equations, while simple, have a severe restriction in that they produce unphysical pressure oscillations at moving contact surfaces between gases of differing ratios of specific heats. These pressure oscillations dramatically increase the errors of the computations compared to stationary contact surfaces. Here, a new five equation model is presented which extends the volume fraction model of Allaire et al.[J. Comput. Phys. 181 (2002) 577-616] to include viscosity, diffusivity and heat conduction. It permits the computation of compressible mixing problems without producing spurious unphysical pressure oscillations. An algorithm is presented to solve the model equations at second order accuracy, demonstrating that it gives up to an order of magnitude lower errors than the mass fraction model for a given mesh resolution. Two and three-dimensional computations of the Richtmyer-Meshkov instability demonstrate that computational savings on the order of $50$-$100$ is possible for an equivalent error. The proposed model is thus very suitable for Direct Numerical Simulation and Large Eddy Simulation of compressible mixing.   

Discrete adjoint of fractional step Navier-Stokes solver in generalized coordinates

Optimization and control in transitional and turbulent flows require evaluation of gradients of the flow state with respect to the problem parameters. Using adjoint approaches, these high-dimensional gradients can be evaluated with a similar computational cost as the forward Navier-Stokes simulations. The adjoint algorithm can be obtained by discretizing the continuous adjoint Navier-Stokes equations or by deriving the adjoint to the discretized Navier-Stokes equations directly. The latter algorithm is necessary when the forward-adjoint relations must be satisfied to machine precision. In this work, our forward model is the fractional step solution to the Navier-Stokes equations in generalized coordinates, proposed by Rosenfeld, Kwak {\&} Vinokur [J. Comput. Phys \textbf{94}, 102-137 (1991)]. We derive the corresponding discrete adjoint equations. We also demonstrate the accuracy of the combined forward-adjoint model, and its application to unsteady wall-bounded flows.   

Evaluation of particle-based flow characteristics using novel Eulerian indices.

The main objective of this study is to evaluate flow characteristics in complex particle-laden flows efficiently using novel Eulerian indices. For flows with a large number of particles, a Lagrangian approach leads to accurate yet inefficient prediction in many engineering problems. We propose a technique based on Eulerian transport equation and ensemble-averaged particle properties, which enables efficient evaluation of various particle-based flow characteristics such as the residence time, accumulated travel distance, mean radial force, etc. As a verification study, we compare the developed Eulerian indices with those using Lagrangian approaches for laminar flows with and without a swirling motion and density ratio. The results show satisfactory agreement between two approaches. The accumulated travel distance is modified to analyze flow motions inside IC engines and, when applied to flow bench cases, it can predict swirling and tumbling motions successfully. For flows inside a cyclone separator, the mean radial force is applied to predict the separation of particles and is shown to have a high correlation to the separation efficiency for various working conditions. In conclusion, the proposed Eulerian indices are shown to be useful tools to analyze complex particle-based flow characteristics.   

Inferring Pre-shock Acoustic Field From Post-shock Pitot Pressure Measurement

Linear interaction analysis (LIA) and iterative ensemble Kalman method are used to convert post-shock Pitot pressure fluctuations to static pressure fluctuations in front of the shock. The LIA is used as the forward model for the transfer function associated with a homogeneous field of acoustic waves passing through a nominally normal shock wave. The iterative ensemble Kalman method is then employed to infer the spectrum of upstream acoustic waves based on the post-shock Pitot pressure measured at a single point. Several test cases with synthetic and real measurement data are used to demonstrate the merits of the proposed inference scheme. The study provides the basis for measuring tunnel freestream noise with intrusive probes in noisy supersonic wind tunnels.