A previously presented overset mesh enabled hybridizable discontinuous Galerkin (HDG) finite element method is extended in this work to an isentropic compressible (pseudo-compressible) fluid. This formulation is a first-principles approach, and is complementary to the augmented Lagrangian approach that was utilized in previous HDG incompressible Navier-Stokes formulations which eliminate the global pressure field. \hl{This is the first original presentation combining overset meshes, HDG, and fluid flow, specifically isentropic flow for low mach number applications.} Verification of the code implementation of the proposed overset-HDG formulation is performed via the method of manufactured solutions on a successively refined overset mesh configuration containing five meshes, and for order $k=1,\ldots,4$ Lagrange polynomial elements in both two- and three-dimensions. Optimal order convergence, $k+1$, can be observed in all fields for both the two- and three-dimensional simulations\hl{, for each mesh}. A two-dimensional benchmark problem is also presented, to enable code-to-code comparison as a preliminary validation exercise.

Tip clearance is a crucial aspect of turbomachines in terms of aerodynamic and thermal performance. A gap between the blade tip surface and the stationary casing must be maintained to allow the relative motion of the blade. The leakage flow through the tip gap measurably reduces turbine performance and causes high thermal loads near the blade tip region. Several studies focused on the tip leakage flow to clarify the flow-physics in the past. The "squealer" design is one of the most common designs to reduce the adverse effects of tip leakage flow. In this paper, a genetic-algorithm-based optimization approach was applied to the conventional squeal tip design to enhance aerothermal performance. A multi-objective optimization method integrated with a meta-model was utilized to determine the optimum squealer geometry. Squealer height and width represent the design parameters which are aimed to be optimized. The objective functions for the genetic-algorithm-based optimization are the total pressure loss coefficient and Nusselt number calculated over the blade tip surface. The initial database is then enlarged iteratively using a coarse-to-fine approach to improve the prediction capability of the meta-models used. The procedure ends once the prediction errors are smaller than a prescribed level. The present study indicates that squealer height and width have complex effects on the aerothermal performance, and optimization study allows to determine the optimum squealer dimensions.

This paper introduces a general methodology for determining the uncertainty of the solution to implicit systems of equations. Equation systems of this type arise from many practical applications, including the analysis of pipe networks, and in the implementation of complex numerical (finite difference or finite element) solution algorithms. The procedure is applicable to either linear or nonlinear equation systems, and does not require any specific algorithm for solution to the equation system itself. A general sensitivity matrix is constructed from an implicit sensitivity analysis of the equation system. This overall sensitivity matrix is expressed in terms of input and output sensitivity matrices, which represents the sensitivity of the equation system to changes in the independent (parameters) and dependent (calculated) variables, respectively. A vector representing the rms uncertainty of the solution variables in the equation system is then given as a function of the given uncertainty in the input parameters. Two specific examples are presented to illustrate the practical application of the technique: (1) An example from fluid mechanics evaluating the Uncertainty in solutions to a Pipe Network Problem, and (2) An example evaluating the Uncertainty of a Thermistor Calibration and Measurement Problem.

The effects of a laser beam propagating through atmospheric turbulence are investigated using the phase screen approach. Turbulence effects are modeled by the Kolmogorov description of the energy cascade theory, and outer scale effect is implemented by the von Kármán refractive power spectral density. In this study, we analyze a plane wave propagating through varying atmospheric horizontal paths. An important consideration for the laser beam propagation of long distances is the random variations in the refractive index due to atmospheric turbulence. To characterize the random behavior, statistical analysis of the phase data and related metrics are examined at the output signal. We train three different machine learning algorithms in tensorflow library with the data at varying propagation lengths, outer scale lengths, and levels of turbulence intensity to predict statistical parameters that describe the atmospheric turbulence effects on laser propagation. tensorflow is an interface for demonstrating machine learning algorithms and an implementation for executing such algorithms on a wide variety of heterogeneous systems, ranging from mobile devices such as phones and tablets to large-scale distributed systems and thousands of computational devices such as GPU cards. The library contains a wide variety of algorithms including training and inference algorithms for deep neural network models. Therefore, it has been used for deploying machine learning systems in many fields including speech recognition, computer vision, natural language processing, and text mining.

Particle image velocimetry (PIV) data processing time can constrain data set size and limit the types of statistical analyses performed. General purpose graphics processing unit (GPGPU) computing can accelerate PIV data processing allowing for larger datasets and accompanying higher order statistical analyses. However, this has not been widespread likely due to limited accessibility to the GPU-PIV hardware and software. Most GPU-PIV software is platform dependent and proprietary, which restricts the computing systems that can be used and makes the details of the algorithm unknown. This work highlights the development of an open-source, cross-platform, GPU-accelerated, PIV algorithm. Validation of the algorithm is done using both synthetic and experimental images. The algorithm was found to accurately resolve the time-averaged flow, instantaneous velocity fluctuations, and vortices. All data processing was done on a GPU supercomputing cluster and notably outperformed the central processing unit version of the software by a factor of 175. The algorithm is freely available and included in the OpenPIV distribution.

Numerical problems are usually solved using heuristic algorithms, due to their simplicity and easy understanding. Nevertheless, most of these methods have calibration parameters that do not count with selection premises oriented to obtain the best performance for the algorithm. This paper introduces an iterative technique that deals with this problem, searching for the calibration parameters that improve the Differential Evolution (DE) algorithm. The application of the proposed technique is illustrated on a real burst location problem in a pipeline prototype. The obtained results show the good performance of the methodology proposed for the burst location task, including the mapping of the calibration parameters that ameliorate the searching process.

The choked mass flux density and the choked momentum flux density for the nonideal fluids methane and nitrogen have been calculated using the Soave–Redlich–Kwong equation of state (EoS). For the computation a steady, one-dimensional (1D), isenthalpic and isentropic flow is assumed. The developed algorithm for the calculation of the choked flow properties includes a bounded multidimensional Newton method. A possible second phase emerging in the critical nozzle area is excluded using the saturation properties of the considered fluids. The critical ratios of pressure, density, temperature, and speed of sound are discussed and compared to other publications. Formulations of the choked mass flux density and the choked momentum flux density explicit in T r , p r , and Z r are given valid for different reduced pressures and temperatures depending on the fluid. Additional computational fluid dynamics (CFD) simulations are carried out in order to validate the findings of the algorithm and the proposed correlations.

We present three algorithms for robust and efficient geometric calculations in the context of immersed boundary method (IBM), including classification of mesh cells as inside/outside of a closed surface, projection of points onto a surface, and accurate calculation of the solid volume fraction field created by a closed surface overlapping with a background Cartesian mesh. The algorithms use the signed distance field (SDF) to represent the surface and remove the intersection tests, which are usually required by other algorithms developed before, no matter the surface is described in analytic or discrete form. The errors of the algorithms are analyzed. We also develop an approximate method on efficient SDF field calculation for complex geometries. We demonstrate how the algorithms can be implemented within the framework of IBM with a volume-average discrete-forcing scheme and applied to simulate fluid–structure interaction problems.

In this study, a second-order accurate Godunov-type finite volume method is used for the solution of the two-dimensional (2D) water hammer problem. The numerical scheme applied here is well balanced and is able to treat the unsteady friction terms, together with the convective terms, within the differences between fluxes of neighboring computational cells. In order to consider the effect of unsteady friction terms during the water hammer process, k − ε and k − ω turbulence models are employed. The performance of the proposed method with the choice of different turbulence models is evaluated using experimental data obtained from one low and one high Reynolds-number turbulent test cases. In addition to velocity and pressure distributions, the turbulence characteristics of each variant of the model, including eddy viscosity, dissipation rate, and turbulent kinetic energy during the water hammer process are fully analyzed. It is found that the inclusion of the convective inertia terms leads to more accurate pressure profiles. The results also show that using a relatively high Courant–Friedrichs–Lewy (CFL) number close to unity, the introduced numerical solver with both choices of turbulence models provides reasonable and acceptable predictions for the studied flows.

Simulations of oscillatory motion in partially filled rectangular tanks with different tank geometries, fullness ratios, and motion frequencies are presented. Smoothed particle hydrodynamics (SPH) method is used to discretize the governing equations together with new velocity variance-based free surface (VFS) and artificial particle displacement (APD) algorithms to enhance the robustness and the accuracy of the numerical scheme. Two-dimensional (2D) oscillatory motion is investigated for three different scenarios where the first one scrutinizes the kinematic characteristics in resonance conditions, the second one covers a wave response analysis in a wide range of enforced motion frequencies, and the last one examines the dynamic properties of the fluid motion in detail. The simulations are carried on for at least 50 periods in the wave response analysis. It is shown that numerical results of the proposed SPH scheme are in match with experimental and numerical findings of the literature.

To provide porous media substrates that are quick to generate and characterize for lattice Boltzmann analysis, we propose a straightforward algorithm. The method leverages the benefits of the lattice Boltzmann method (LBM), and is extensible to multiphysics flows. Several parameters allow for simple customization. The generation algorithm and LBM are reviewed, and suggested implementation covered. Additionally, results are discussed and interpreted to evaluate the approach. Several verification tools are employed such as Darcy's law, the Ergun equation, the Koponen correlation, a newly proposed correlation, and experimental data. Agreement and repeatability are found to be excellent, suggesting this relatively simple method is a good option for engineering studies.

In the boundary element method (BEM), the Galerkin weighting technique allows to obtain numerical solutions of a boundary integral equation (BIE), giving the Galerkin boundary element method (GBEM). In three-dimensional (3D) spatial domains, the nested double surface integration of GBEM leads to a significantly larger computational time for assembling the linear system than with the standard collocation method. In practice, the computational time is roughly an order of magnitude larger, thus limiting the use of GBEM in 3D engineering problems. The standard approach for reducing the computational time of the linear system assembling is to skip integrations whenever possible. In this work, a modified assembling algorithm for the element matrices in GBEM is proposed for solving integral kernels that depend on the exterior unit normal. This algorithm is based on kernels symmetries at the element level and not on the flow nor in the mesh. It is applied to a BIE that models external creeping flows around 3D closed bodies using second-order kernels, and it is implemented using OpenMP. For these BIEs, the modified algorithm is on average 32% faster than the original one.

This paper deals with rotating effects simulation of steady flows in turbomachinery. To take into account the rotating nature of the flow, the frozen rotor approach is one of the widely used approaches. This technique, known in a more general context as a multiple rotating frame (MRF), consists on building axisymmetric interfaces around the rotating parts and solves for the flow in different frames (static and rotating). This paper aimed to revisit this technique and propose a new algorithm referred to it by a virtual multiple rotating frame (VMRF). The goal is to replace the geometrical interfaces (part of the computer-aided design (CAD)) that separate the rotating parts replaced by the virtual ones created at the solver level by a simple user input of few point locations and/or parameters of basic shapes. The new algorithm renders the MRF method easy to implement, especially for edge-based numerical schemes, and very simple to use. Moreover, it allows avoiding any remeshing (required by the MRF approach) when one needs to change the interface position, shape, or simply remove or add a new one, which frequently happened in practice. Consequently, the new algorithm sensibly reduces the overall computations cost of a simulation. This work is an extension of a first version published in an ASME conference, and the main new contributions are the detailed description of the new algorithm in the context of cell-vertex finite volume method and the validation of the method for viscous flows and the three-dimensional (3D) case which is of significant importance to the method to be attractive for real and industrial applications.

An algorithm to prevent or delay bubble coalescence for the level set (LS) method is presented. This novel algorithm uses the LS method field to detect when bubbles are in close proximity, indicating a potential coalescence event, and applies a repellent force to simulate the unresolved liquid drainage force. The model is introduced by locally modifying the surface tension force near the liquid film drainage area. The algorithm can also simulate the liquid drainage time of the thin film by controlling the length of time the increased surface tension has been applied. Thus, a new method of modeling bubble coalescence has been developed. Several test cases were designed to demonstrate the capabilities of the algorithm. The simulations, including a mesh study, confirmed the abilities to identify and prevent coalescence as well as implement the time tracking portion, with an additional 10–25% computational cost. Ongoing tests aim to verify the algorithm's functionality for simulations with different flow conditions, a ranging number of bubbles, and both structured and unstructured computational mesh types. Specifically, a bubble rising toward a free surface provides a test of performance and demonstrates the ability to consistently prevent coalescence. In addition, a two bubble case and a seven bubble case provide a more complex demonstration of how the algorithm performs for larger simulations. These cases are compared to much more expensive simulations capable of resolving the liquid film drainage (through very high local mesh resolution) to investigate how the algorithm replicates the liquid film drainage process.

Unlike the Navier boundary condition, this paper deals with the case when the slip of a fluid along the wall may occur only when the shear stress attains certain bound which is given a priori and does not depend on the solution itself. The mathematical model of the velocity–pressure formulation with this type of threshold slip boundary condition is given by the so-called variational inequality of the second kind. For its discretization, we use P1-bubble/P1 mixed finite elements. The resulting algebraic problem leads to the minimization of a nondifferentiable energy function subject to linear equality constraints representing the discrete impermeability and incompressibility condition. To release the former one and to regularize the nonsmooth term characterizing the stick–slip behavior of the algebraic formulation, two additional vectors of Lagrange multipliers are introduced. Further, the velocity vector is eliminated, and the resulting minimization problem for a quadratic function depending on the dual variables (the discrete pressure and the normal and shear stress) is solved by the interior point type method which is briefly described. To justify the threshold model and to illustrate the efficiency of the proposed approach, three physically realistic problems are solved and the results are compared with the ones solving the Stokes problem with the Navier boundary condition.

A new simplified approach for modeling and simulating pressure transients resulting from the rapid acceleration or deceleration of turbulent flow in smooth-walled fluid lines is introduced. In contrast to previous approaches for modeling turbulence by modifying the head loss terms in the momentum partial differential equation, this approach is achieved by coupling the frequency domain analytical solution to the laminar flow version of the partial differential equations in series with a lumped resistance that has been sized so that the steady flow resistance for the line is equivalent to an empirical turbulent steady flow resistance. The model provides normalized pressure and flow transients that have good agreement with experimental data and with method-of-characteristics (MOC) solutions associated with previously validated turbulence models. The motivation for this research is based on the need for a practical means to simulate the effects of fluid transients in lines that are internal components within a total engineering system without the need to understand the different unsteady turbulence one- and two-dimensional (1D/2D) friction models and also be proficient with the complexities of nonlinear interaction of friction and interpolation errors encountered using MOC. This modeling approach utilizes a preprogramed inverse frequency algorithm, commonly used for system identification, which generates “equivalent” high-order normalized linear ordinary differential equations that can be coupled with models for other fluid power components and easily solved in the time domain using preprogramed numerical algorithms for ordinary differential equations.

Current simulations of swirling flows in pipes are limited to relatively low Reynolds number flows (Re < 6000); however, the characteristic Reynolds number is much higher (Re > 20,000) in most of engineering applications. To address this difficulty, this paper presents a numerical simulation algorithm of the dynamics of incompressible, inviscid-limit, axisymmetric swirling flows in a pipe, including the vortex breakdown process. It is based on an explicit, first-order difference scheme in time and an upwind, second-order difference scheme in space for the time integration of the circulation and azimuthal vorticity. A second-order Poisson equation solver for the spatial integration of the stream function in terms of azimuthal vorticity is used. In addition, when reversed flow zones appear, an averaging step of properties is applied at designated time steps. This adds slight artificial viscosity to the algorithm and prevents growth of localized high-frequency numerical noise inside the breakdown zone that is related to the expected singularity that must appear in any flow simulation based on the Euler equations. Mesh refinement studies show agreement of computations for various mesh sizes. Computed examples of flow dynamics demonstrate agreement with linear and nonlinear stability theories of vortex flows in a finite-length pipe. Agreement is also found with theoretically predicted steady axisymmetric breakdown states in a pipe as flow evolves to a time-asymptotic state. These findings indicate that the present algorithm provides an accurate prediction of the inviscid-limit, axisymmetric breakdown process. Also, the numerical results support the theoretical predictions and shed light on vortex dynamics at high Re.

Flow behavior in complex three-dimensional (3D) microscale domains is the key in the development of microcirculatory pathologies and the design of 3D microfluidics. While numerical simulations are common practice for the derivation of velocity fields in such domains, they are limited to known geometries. Current experimental methods such as micron-scale particle tracing comprise of intricate algorithmic approaches for the accurate tracing of numerous particles in a dense moving liquid suspension and are fundamentally limited in resolution to the finite size of the interrogated steps. Here, we introduce 3D streamlines image velocimetry (3D-SIV), a method to derive fluid velocity fields in arbitrary resolution for fully developed laminar flow in 3D geometries. Our approach utilizes 3D geometrical fitting and superimposed Delaunay triangulation to reconstruct streamtubes and to trace their volumetric changes. Our algorithm has applications in out-of-plane velocimetries, which we demonstrate in a 3D dilated curved geometry and in an ascending aorta. The 3D-SIV can be applied for high-resolution derivation of velocity fields in microcirculatory pathologies and to 3D microfluidic circuits, extending the potential of out-of-plane velocimetries to complex geometries and arbitrary resolution.

A simple variant of recycling and rescaling method to generate inflow turbulence using unstructured grid computational fluid dynamics (CFD) codes is presented. The method has been validated on large eddy simulation (LES) of spatially developing flat plate turbulent boundary layer. The proposed rescaling algorithm is based on the momentum thickness which is more robust and essentially obviates the need of finding the edge of the turbulent boundary layer in unstructured grid codes. Extension of this algorithm to hybrid Reynolds-Averaged Navier-Stokes (RANS) LES type of approaches and for wall-bounded turbomachinery flows is also discussed. Results from annular diffuser with different inflow boundary layer characteristics are presented as an example application to show the utility of such an algorithm.

A robust modified weakly compressible smoothed particle hydrodynamics (WCSPH) method based on a predictive corrective scheme is introduced to model the fluid flows engaged with stationary and moving boundary. In this paper, this model is explained and practically verified in three distinct laminar incompressible flow cases; the first case involves the lid driven cavity flow for two Reynolds numbers 400 and 1000. The second case is a flow generated by a moving block in the initially stationary fluid. The third case is flow around the stationary and transversely oscillating circular cylinder confined in a channel. These results in comparison with the standard benchmarks also confirm the good accuracy of the present solution algorithm.