Computational Fluid Dynamics Solutions Research Articles

Interpolation-based reduced-order modelling for steady transonic flows via manifold learning

This paper presents a parametric reduced-order model (ROM) based on manifold learning (ML) for use in steady transonic aerodynamic applications. The main objective of this work is to derive an efficient ROM that exploits the low-dimensional nonlinear solution manifold to ensure an improved treatment of the nonlinearities involved in varying the inflow conditions to obtain an accurate prediction of shocks. The reduced-order representation of the data is derived using the Isomap ML method, which is applied to a set of sampled computational fluid dynamics (CFD) data. In order to develop a ROM that has the ability to predict approximate CFD solutions at untried parameter combinations, Isomap is coupled with an interpolation method to capture the variations in parameters like the angle of attack or the Mach number. Furthermore, an approximate local inverse mapping from the reduced-order representation to the full CFD solution space is introduced. The proposed ROM, called Isomap+I, is applied to the two-dimensional NACA 64A010 airfoil and to the 3D LANN wing. The results are compared to those obtained by proper orthogonal decomposition plus interpolation (POD+I) and to the full-order CFD model.

Similitude and scaling laws for the rotating flow between concentric discs

In this article, a systematic dimensional analysis and similitude study for the three-dimensional rotating flow within the narrow spacing (usually of the order of 100 µm) of multiple concentric discs is presented. An engineering application of this flow configuration is the Tesla disc turbine, and the dimensional analysis leads to proper scaling laws for such machines. Using the Buckingham Pi theorem, the list of non-dimensional numbers necessary for describing the incompressible flow through the concentric discs has been formulated and physical interpretation of the non-dimensional numbers has been provided. The complete criteria for achieving geometric, kinematic and dynamic similarity between a model and the prototype have been established. Computational fluid dynamics (CFD) solutions have been obtained for various geometries, fluid properties and flow conditions to demonstrate the validity of the similitude criteria developed. The CFD results show that, when the present similitude criteria are fulfilled, the values of all non-dimensional output parameters such as the power and pressure-drop coefficients remain unchanged for various combinations of input variables. What is more striking is that the three-dimensional variations of non-dimensional z component of velocity Uz (whose non-zero values are computed by the CFD solver even though the only physical boundary condition applied is [Formula: see text] at the inlet and on disc surfaces) are superposed on one another for all models and the prototype. Systematic methods for arriving at simplified conservation equations are discussed and it is shown how the corresponding list of non-dimensional numbers and similitude criteria evolve with such simplification of the conservation equations.

Dealing with numerical noise in CFD-based design optimization

Numerical noise is an inevitable by-product of Computational Fluid Dynamics (CFD) simulations which can lead to challenges in finding optimum designs. This article draws attention to the issue, illustrating the difficulties it can cause for road vehicle aerodynamics simulations. Firstly a benchmark problem is used to assess a range of turbulence models and grid types. Large noise amplitudes up to 22% are evident for solutions computed on unstructured tetrahedral grids whereas computations on hexahedral and polyhedral grid structures exhibit substantially less noise. The Spalart Allmaras turbulence model is shown to be far less susceptible to noise levels than two other commonly-used models for this application. Secondly, multi-objective aerodynamic shape optimization is applied to a fairing for a practical road vehicle which is parameterised in terms of three design variables. Moving Least Squares (MLS) metamodels are constructed from 50 high-fidelity CFD solutions for two objective functions. Subsequent optimization is successful for the first objective, however numerical noise levels in excess of 7% give rise to difficulties for the second one. A revision to the problem leads to success and the construction of a small Pareto front. Further analysis underlines the inherent capability of MLS metamodels in dealing with noisy CFD responses.

Velocity pick-up and discharge coefficient for round orifices with cross flow at inlet

This study investigates the flow through round orifices with cross flow at the inlet. Emphasis is placed on the change in tangential velocity component for orifices with low L/ D. A definition of velocity pick-up is developed based on the orifice exit to cross-flow tangential velocity ratio. Steady, incompressible, and 3D computational fluid dynamics models with the SST [Formula: see text] turbulent model are employed to calculate orifice flows with different geometrical and flow conditions. Stationary orifices and axial orifices in a rotating disk are considered. Computational fluid dynamics solutions are compared with experimental results and published correlations for discharge coefficients, and good agreement is generally demonstrated. It is found that the non-dimensional velocity pick-up depends strongly on the ratio of characteristic times for flow to travel across the orifice in the tangential direction and that for the flow to pass through the orifice. A correlation of velocity pick-up as a function of this ratio is given.

Integration of Off-Track Sonic Boom Analysis for Supersonic Aircraft Conceptual Design

A highly desired capability for aircraft conceptual design is the ability to rapidly and accurately evaluate new concepts to avoid adverse trade decisions that may hinder the development process in the later stages of design. Evaluating the robustness of new low-boom concepts is important for the conceptual design of supersonic aircraft. Here, robustness means that the aircraft configuration has a low-boom ground signature at both under- and off-track locations. An integrated process for under- and off-track sonic boom analysis is developed to facilitate the design of robust low-boom supersonic aircraft. The key enabler for sonic boom analysis is accurate computational fluid dynamics solutions for off-body pressure distributions. To ensure the numerical accuracy of the off-body pressure distributions, a mesh study is performed with Cart3D (an inviscid computational fluid dynamics solver) to determine the mesh requirements for off-body computational fluid dynamics analysis. Comparisons are made between the sonic boom analysis results conducted with the Cart3D and USM3D inviscid computational fluid dynamics solvers. The variation in the ground signature that results from changes in the location of the computational fluid dynamics off-body pressure distribution is also examined. Finally, a complete under- and off-track sonic boom analysis is presented for two distinct supersonic concepts to demonstrate the capability of the integrated analysis process.

Feasibility of utilizing numerical viscosity from coarse grid CFD for fast turbulence modeling of indoor environments

Computational fluid dynamics (CFD) is a useful tool in building indoor environment study. However, the notorious computational effort of CFD is a significant drawback that restricts its applications in many areas and stages. Factors such as grid resolution and turbulence modeling are the main reasons that lead to large computing cost of this method. This study investigates the feasibility of utilizing inherent numerical viscosity induced by coarse CFD grid, coupled with simplest turbulence model, to greatly reduce the computational cost while maintaining reasonable modeling accuracy of CFD. Numerical viscosity introduced from space discretization in a carefully specified coarse grid resolution may have similar magnitude as turbulence viscosity for typical indoor airflows. This presents potentials of substituting sophisticated turbulence models with inherent numerical viscosity models from coarse grid CFD that are often used in fast CFD analysis. Case studies were conducted to validate the analytical findings, by comparing the coarse grid CFD predictions with the grid-independent CFD solutions as well as experimental data obtained from literature. The study shows that a uniform coarse grid can be applied, along with a constant turbulence viscosity model, to reasonably predict general airflow patterns in typical indoor environments. Although such predictions may not be as precise as fine-grid CFDs with well validated complex turbulence models, the accuracy is acceptable for indoor environment study, especially at an early stage of a project. The computing speed is about 100 times faster than a fine-grid CFD, which makes it possible to simulate a complicated 3-dimensional building in real-time (or near real-time) with personal computer.

Mind the Gap: Impact of Computational Fluid Dynamics Solution Strategy on Prediction of Intracranial Aneurysm Hemodynamics and Rupture Status Indicators

Computational fluid dynamics has become a popular tool for studying intracranial aneurysm hemodynamics, demonstrating success for retrospectively discriminating rupture status; however, recent highly refined simulations suggest potential deficiencies in solution strategies normally used in the aneurysm computational fluid dynamics literature. The purpose of the present study was to determine the impact of this gap. Pulsatile flow in 12 realistic MCA aneurysms was simulated by using both high-resolution and normal-resolution strategies. Velocity fields were compared at selected instants via domain-averaged error. We also compared wall shear stress fields and various reduced hemodynamic indices: cycle-averaged mean and maximum wall shear stress, oscillatory shear index, low shear area, viscous dissipation ratio, and kinetic energy ratio. Instantaneous differences in flow and wall shear stress patterns were appreciable, especially for bifurcation aneurysms. Linear regressions revealed strong correlations (R(2) > 0.9) between high-resolution and normal-resolution solutions for all indices except kinetic energy ratio (R(2) = 0.25) and oscillatory shear index (R(2) = 0.23); however, for most indices, the slopes were significantly <1, reflecting a pronounced underestimation by the normal-resolution simulations. Some high-resolution simulations were highly unstable, with fluctuating wall shear stresses reflected by the poor oscillatory shear index correlation. Typical computational fluid dynamics solution strategies may ultimately be adequate for augmenting rupture risk assessment on the basis of certain highly reduced indices; however, they cannot be relied on for predicting the magnitude and character of the complex biomechanical stimuli to which the aneurysm wall may be exposed. This impact of the computational fluid dynamics solution strategy is likely greater than that for other modeling assumptions or uncertainties.

Comparison of Harmonic and Time Marching Unsteady Computational Fluid Dynamics Solutions With Measurements for a Single-Stage High-Pressure Turbine

The unsteady aerodynamics of a single-stage high-pressure turbine has been the subject of a study involving detailed measurements and computations. Data and predictions for this experiment have been presented previously, but the current study compares predictions obtained using the nonlinear harmonic simulation method to results obtained using a time-marching simulation with phase-lag boundary conditions. The experimental configuration consisted of a single-stage high-pressure turbine (HPT) and the adjacent, downstream, low-pressure turbine nozzle row (LPV) with an aerodynamic design that is typical to that of a commercial high-pressure ratio HPT and LPV. The flow path geometry was equivalent to engine hardware and operated at the proper design-corrected conditions to match cruise conditions. The high-pressure vane and blade were uncooled for these comparisons. All three blade rows are instrumented with flush-mounted, high-frequency response pressure transducers on the airfoil surfaces and the inner and outer flow path surfaces, which include the rotating blade platform and the stationary shroud above the rotating blade. Predictions of the time-dependent flow field for the turbine flow path were obtained using a three-dimensional, Reynolds-averaged Navier–Stokes computational fluid dynamics (CFD) code. Using a two blade row computational model of the turbine flow path, the unsteady surface pressure for the high-pressure vane and rotor was calculated using both unsteady methods. The two sets of predictions are then compared to the measurements looking at both time-averaged and time-accurate results, which show good correlation between the two methods and the measurements. This paper concentrates on the similarities and differences between the two unsteady methods, and how the predictions compare with the measurements since the faster harmonic solution could allow turbomachinery designers to incorporate unsteady calculations in the design process without sacrificing accuracy when compared to the phase-lag method.

Analytical and computational solutions for three-dimensional flow-field and relative pathlines for the rotating flow in a Tesla disc turbine

The three-dimensional flow field and the flow pathlines within a Tesla disc turbine have been investigated analytically and computationally. The description of the flow field includes the three-dimensional variation of the radial velocity, tangential velocity and pressure of the fluid in the flow passages within the rotating discs. A detailed comparison between the results obtained from the analytical theory and computational fluid dynamic (CFD) solutions of Navier–Stokes equations is presented in order to establish the reliability of the simplified mathematical model. The present work reveals the dependence of the shape, size and orientation of the pathlines on various operating parameters (such as tangential speed ratio, radial pressure drop, inlet nozzle angle, and position of the exit) and local balance of various forces (viz. inertial, viscous, centrifugal and Coriolis). The relative merits of two possible ways of representing the pathlines in the absolute and relative frame of reference are discussed that provide physical understanding of subtle flow features.

On the analysis of aerostatic thrust bearings with the differential quadrature method

This paper presents a numerical approach to analyze the performance of aerostatic thrust bearings based on the differential quadrature method. The Reynolds equation of aerostatic thrust bearings is firstly discretized as a series of algebraic equations by the differential quadrature method and the pressure distribution is calculated with the discretized equations invoking the boundary conditions. Analytical approximation of Heaviside step function and a multi-domain technique are then introduced to resolve the discontinuous problem of grooved aerostatic bearings. Numerical solutions are obtained for two types of aerostatic thrust bearings. The mass flow rate, load capacity, and stiffness predicted by these solutions are further compared with corresponding analytical, finite difference method and computational fluid dynamics solutions. It is demonstrated that the differential quadrature method has high efficiency and accuracy for the solution of aerostatic thrust bearings.

Effects of mesh refinement, time step size and numerical scheme on the computational modeling of temperature evolution during natural-convection heating

A computational fluid dynamics (CFD) analysis includes creating geometry, dividing it into elements, discretizing governing equations and solving with suitable numerical schemes. Refining mesh and lowering time step size increase accuracy. However, this may not always give the best result since convergence depends upon parameters of time step size, mesh resolution and numerical scheme. Therefore, the objective of this study was to determine the effects of these on the accuracy of a CFD solution. For this purpose, canning example was used, and results obtained with ANSYS CFX (v12.1.) were experimentally validated. Effects of time step size, mesh resolution and numerical scheme on temperature and velocity field evolution were determined. Mesh refinement affected temperature distribution significantly and surprisingly led to less accuracy. The reasons for this behavior were presented and explained comprehensively.

Far-Field Drag Decomposition Applied to the Drag Prediction Workshop 5 Cases

A far-field drag prediction and decomposition method has been applied to the results of the AIAA Drag Prediction Workshop 5 held in Louisiana during the summer of 2012. The method has two principal advantages: it allows the removal of spurious drag inherent to computational fluid dynamics solutions, and it allows the decomposition of drag into viscous, wave, and induced physical drag components. This research shows that accurate drag coefficients can be predicted on coarse grids when the spurious drag is extracted with the far-field method and that these results are closer to experimental values than drag coefficients computed on finer meshes when spurious drag is not extracted. The research also investigated the reasons behind the lift and drag losses found by some participants in the workshop. It is shown that the lift loss is caused by the boundary-layer separation at the wing root, inducing a reduction of 20% of the shock wave drag and a significant change in the wing loading. The initiation of buffet is also analyzed. The study shows that mesh refinement is critical to capture the physical effects of the flow, such as its separation, and provides an explanation of the discrepancies in results observed at the Drag Prediction Workshop 5.

Measuring the coefficient of restitution of high speed microparticle impacts using a PTV and CFD hybrid technique**This is a revised and expanded version of a paper originally presented at the ASME conference Turbo Expo held in Copenhagen in June 2012.

A novel particle tracking velocimetry (PTV)/computational fluid dynamics (CFD) hybrid method for measuring coefficient of restitution (COR) has been developed which is relatively simple, cost-effective, and robust. A laser and camera system is used in the Virginia Tech Aerothermal Rig to measure velocity trajectories of microparticles. The method solves for particle impact velocity at the impact surface using a CFD solution and Lagrangian particle tracking. The methodology presented here attempts to characterize a difficult problem by a combination of established techniques, PTV and CFD, which have not been used in this capacity before. Erosion and deposition are functions of particle/wall interactions and COR is a fundamental property of these interactions. COR depends on impact velocity, angle of impact, temperature, particle composition, and wall material. Two sizes of Arizona road dust and one size of glass beads are impacted on to a 304 stainless steel coupon. The particles are entrained into a free jet of 27 m s−1 at room temperature. Impact angle was varied from 85° to 25° depending on particle. Mean results collected using this new technique compare favorably with trends established in literature. The utilization of this technique to measure COR of microparticle sand will help develop a computational model and serve as a baseline for further measurements at elevated air and wall temperatures.

Simulation of mass flux measurement based on tunable diode laser absorption spectroscopy in non-uniform flows

This work combines the computational fluid dynamics (CFD) solutions and laser absorption spectroscopy technology to simulate the process of the mass flux measurement in supersonic scramjet inlet/isolator. The effects of non-uniform flows on the absorption line shape were analyzed in detail. Using an optimal line selection, the accuracy of the mass flux measurement with tunable diode laser absorption spectroscopy (TDLAS) has been improved. Simulated results indicated that the TDLAS-based mass flux had a good performance with error of less than 2% at the isolator where 6% of path length contains the boundary layers. In contrast, large deviation appeared between the simulation data and CFD results when the sensor location was near the cowl lip of the inlet, due to the large gradient of temperature, pressure and velocity in y direction.

Quasi-Steady Modeling of Ice Accretion on a Helicopter Fuselage in Forward Flight

Computational modeling of ice accretion on a rotorcraft is an alternative and/or a complement for flight test in icing certification and ice protection system design. Although computational fluid dynamics solutions of helicopter flow have advanced in the last few years, icing simulations are rare and, to the best of the authors’ knowledge, none has modeled helicopter icing completely. In this work, a three-dimensional simulation of long-term in-flight ice accretion, accounting for rotor-fuselage quasi-steady interaction, is performed. For flow solution, the three-dimensional compressible turbulent Navier–Stokes equations are solved, with the rotor modeled as an actuator disk that imparts radial and azimuthal distributions of pressure rise and swirl to the flow field. The authors’ code FENSAP-ICE is used to solve the three-dimensional flow, impingement, and ice accretion. The flow solutions for a test case, at two forward speeds, are obtained and validated against published experimental results and then used to illustrate icing on the helicopter’s fuselage. Also, in this work, the effects of different parameters (such as forward speed, ambient temperature, droplet diameter, and liquid water content) on droplet impact, ice accretion, and the aerodynamic degradation of helicopter fuselage, were studied.

Numerical analysis of multiple, thin-sail geometries based on Prandtl’s lifting-line theory

Solutions obtained from a numerical method based on Prandtl’s lifting-line theory, valid for multiple lifting surfaces with arbitrary sweep, are obtained for a number of rigid wing and sail geometries. The results are compared against solutions obtained using established vortex-lattice methods, and computational fluid dynamics solutions to the Euler equations. For the case of an untwisted, rectangular wing, numerical lifting-line, vortex-lattice, and Euler solutions were all in reasonable agreement. However, the numerical lifting-line method was the only method to predict the constant ratio of induced-drag coefficient to lift coefficient squared, which has been predicted from the analytic solution and confirmed by well established experimental data. Results are also presented for a forward-swept, tapered wing. Additional results are presented in terms of lift and induced-drag coefficients for an isolated mainsail, and mainsail/jib combinations with sails representative of both a standard and tall rig Catalina 27. The influence of the nonlinear terms in the lifting-line solution appears minimal, with the exception of mainsail results when considering jib/mainsail combinations.

Time-accurate CFD conjugate analysis of transient measurements of the heat-transfer coefficient in a channel with pin fins

Heat-transfer coefficients (HTC) on surfaces exposed to convection environments are often measured by transient techniques such as thermochromic liquid crystal (TLC) or infrared thermography. In these techniques, the surface temperature is measured as a function of time, and that measurement is used with the exact solution for unsteady, zero-dimensional (0-D) or one-dimensional (1-D) heat conduction into a solid to calculate the local HTC. When using the 0-D or 1-D exact solutions, the transient techniques assume the HTC and the free-stream or bulk temperature characterizing the convection environment to be constants in addition to assuming the conduction into the solid to be 0-D or 1-D. In this study, computational fluid dynamics (CFD) conjugate analyses were performed to examine the errors that might be invoked by these assumptions for a problem, where the free-stream/bulk temperature and the heat-transfer coefficient vary appreciably along the surface and where conduction into the solid may not be 0-D or 1-D. The problem selected to assess these errors is flow and heat transfer in a channel lined with a staggered array of pin fins. This conjugate study uses three-dimensional (3-D) unsteady Reynolds-averaged Navier–Stokes (RANS) closed by the shear-stress transport (SST) turbulence model for the gas phase (wall functions not used) and the Fourier law for the solid phase. The errors in the transient techniques are assessed by comparing the HTC predicted by the time-accurate conjugate CFD with those predicted by the 0-D and 1-D exact solutions, where the surface temperatures needed by the exact solutions are taken from the time-accurate conjugate CFD solution. Results obtained show that the use of the 1-D exact solution for the semi-infinite wall to give reasonably accurate “transient” HTC (less than 5% relative error). Transient techniques that use the 0-D exact solution for the pin fins were found to produce large errors (up to 160% relative error) because the HTC varies appreciably about each pin fin. This study also showed that HTC measured by transient techniques could differ considerably from the HTC obtained under steady-state conditions with isothermal walls.

Variability of Computational Fluid Dynamics Solutions for Pressure and Flow in a Giant Aneurysm: The ASME 2012 Summer Bioengineering Conference CFD Challenge

Stimulated by a recent controversy regarding pressure drops predicted in a giant aneurysm with a proximal stenosis, the present study sought to assess variability in the prediction of pressures and flow by a wide variety of research groups. In phase I, lumen geometry, flow rates, and fluid properties were specified, leaving each research group to choose their solver, discretization, and solution strategies. Variability was assessed by having each group interpolate their results onto a standardized mesh and centerline. For phase II, a physical model of the geometry was constructed, from which pressure and flow rates were measured. Groups repeated their simulations using a geometry reconstructed from a micro-computed tomography (CT) scan of the physical model with the measured flow rates and fluid properties. Phase I results from 25 groups demonstrated remarkable consistency in the pressure patterns, with the majority predicting peak systolic pressure drops within 8% of each other. Aneurysm sac flow patterns were more variable with only a few groups reporting peak systolic flow instabilities owing to their use of high temporal resolutions. Variability for phase II was comparable, and the median predicted pressure drops were within a few millimeters of mercury of the measured values but only after accounting for submillimeter errors in the reconstruction of the life-sized flow model from micro-CT. In summary, pressure can be predicted with consistency by CFD across a wide range of solvers and solution strategies, but this may not hold true for specific flow patterns or derived quantities. Future challenges are needed and should focus on hemodynamic quantities thought to be of clinical interest.

Modeling of aerosol spray characteristics for synthesis of sensor thin film from solution

A model is developed of aerosol spray for synthesis of sensor film from solution. The synthesis technique considered involves atomization of a solution of mixed salts in methanol, spraying of solution droplets, droplet deposition on a heated substrate, evaporation and chemical reaction to produce mixed oxides, and subsequent film growth. The precise control of oxide nanoparticle size distribution and inter-particle spacing in the film is crucial to achieving high sensitivity. These in turn largely depend on the droplet characteristics prior to impingement on the substrate. This paper focuses on the development of a model to describe the atomization and spray processes prior to the film growth. Specifically, a mathematical model is developed utilizing computational fluid dynamics solution of the equations governing the transport of atomized droplets from the nozzle to the substrate in order to predict droplet characteristics in flight. The predictions include spatial distribution of droplet size and concentration, and the effect on these characteristics of swirling inlet flow at the spray nozzle.

Influence of Porosity on the Performance of a Pulse Tube Refrigerator: A CFD Study

Abstract This research article illustrates a numerical study of single stage coaxial as well as inline Inertance-Type Pulse Tube Refrigerator (ITPTR), which performance is mostly depending upon a regenerator. Regenerator is the significant component of a pulse tube refrigerator which has a great importance of producing cooling effect. In this present work a computational fluid dynamic (CFD) solution approach has been chosen for numerical purpose. The detail analysis of cool down behaviour, heat transfer at the cold end and pressure variation inside the whole system has been carried out by using the computational fluid dynamic software package FLUENT. A number of cases have been solved by changing the porosity of the regenerator from 0.5 to 0.9 and rest of parameter are remains unchanged. The operating frequency for all case is 34 Hz, pulse tube diameter 5 mm and length is 125 mm not changed for all cases. The result shows that porosity value of 0.6 produce a better cooling effect on the cold end of pulse tube refrigerator. The variation of pressure inside the pulse tube refrigerator during the process also analysed. To get an optimum parameter experimentally is a very tedious for iterance tube pulse tube refrigerator job so the CFD approach gives a better solution which is the main purpose of the present work.