Navier-Stokes Simulations Of Flow Research Articles

Analysis of the aerothermal performance of modern commercial high-pressure turbine rotors using different levels of fidelity

In the field of design and optimization of sophisticated geometries such as film-cooled turbine blades of modern jet engines, Computational Fluid Dynamics (CFD) simulation is commonly employed. As the pursuit for higher turbine entry temperatures intensifies, it becomes crucial for computational analyses to offer accurate predictions of metal temperatures and heat transfer coefficients on these critical components. This study investigates the impact of key physical factors that characterize the operation of these components on the accuracy of the computational model. In particular, the effects of including the exchange of thermal energy between the fluid and solid domains, as well as modelling the unsteady interaction between the rotor and stator are studied. The research focuses on a fully featured one-and-a-half stage high-pressure turbine of a commercial jet engine, utilizing proprietary software for conducting 3D Reynolds-Averaged Navier-Stokes flow simulations. To model the fluid-solid thermal interaction, steady-state Conjugate Heat Transfer (CHT) simulations are performed. The CHT results are then compared with experimental data obtained from a thermal paint test, achieving good levels of agreement. Additionally, phase-lag simulations are executed under adiabatic-wall conditions to evaluate the influence of stator-rotor interaction on near-wall gas temperatures. This work shows that, by modelling the periodic unsteadiness at the stator-rotor interface with a phase-lag technique, the maximum near-wall gas temperature prediction is significantly increased, sometimes more than 100K, with respect to the steady-state model one. Findings from this work also suggest that simplified “strip” source terms used to model the presence of film cooling hole rows on the surface of a blade can be used with satisfactory accuracy only for nominal conditions. The mass flows delivered by each source strip should not be linearly scaled based on mainstream quantities for use in different conditions, but they should be recalculated from scratch for the new conditions.

Development and calibration of a fast flow model for solid oxide cell stack internal manifolds

Due to the commercialization of solid oxide cells (SOC) progressing at an accelerated pace, computationally inexpensive SOC models adapted to the iterative nature of the engineering process are in increasing demand. Flow simulation in the stack is especially challenging in this regard because detailed computational fluid mechanic models are computationally demanding, while simplified models rely on pressure loss coefficients and friction factors not readily available in the literature. In this study, a computationally inexpensive algebraic model of an SOC stack internal manifold is developed and calibrated for laminar flow conditions. Thereby, pressure loss coefficients and Darcy friction factors are determined for a broad range of operating conditions through symbolic regression of Navier–Stokes flow simulation results of stacks of 20 to 40 cells. The derived Darcy friction factors for the inlet and outlet manifolds prove to be of particular importance, as they deviate strongly from the expressions assumed in similar modeling studies. The predictive power of the developed model is demonstrated by providing accurate predictions of the flow distribution in the stack, even outside of the calibration window.

A generalized probabilistic learning approach for multi-fidelity uncertainty quantification in complex physical simulations

Two of the most significant challenges in uncertainty quantification pertain to the high computational cost for simulating complex physical models and the high dimension of the random inputs. In applications of practical interest, both of these problems are encountered, and standard methods either fail or are not feasible. To overcome the current limitations, we present a generalized formulation of a Bayesian multi-fidelity Monte-Carlo (BMFMC) framework that can exploit lower-fidelity model versions in a small data regime. The goal of our analysis is an efficient and accurate estimation of the complete probabilistic response for high-fidelity models. BMFMC circumvents the curse of dimensionality by learning the relationship between the outputs of a reference high-fidelity model and potentially several lower-fidelity models. While the continuous formulation is mathematically exact and independent of the low-fidelity model’s accuracy, we address challenges associated with the small data regime (i.e., only a small number of 50 to 300 high-fidelity model runs can be performed). Specifically, we complement the formulation with a set of informative input features at no extra cost. Despite the inaccurate and noisy information that some low-fidelity models provide, we demonstrate that accurate and certifiable estimates for the quantities of interest can be obtained for uncertainty quantification problems in high stochastic dimensions, with significantly fewer high-fidelity model runs than state-of-the-art methods for uncertainty quantification. We illustrate our approach by applying it to challenging numerical examples such as Navier–Stokes flow simulations and fluid–structure interaction problems.

CFD investigation on the flatback airfoil effect of 10 MW wind turbine blade

The flatback airfoil effect on the inboard region of a large wind turbine blade was investigated by numerical analysis. Complicated flow phenomena in wind turbine blade with flatback and non-flatback airfoil were captured by Reynolds-averaged Navier–Stokes flow simulation with shear stress transport turbulence model. Although both airfoil blades were designed using blade element momentum theory to produce identical shaft power, results of three-dimensional computational fluid dynamics (CFD) flow analysis indicated that at a specific location of the root area, the flatback airfoil improved the inboard force by approximately 6 % compared with the non-flatback airfoil. We were also able to confirm that by using the flatback airfoil, the overall shaft power throughout the blade increased by 1 %, thereby restraining the bending moment exerted by the thrust force on the hub by 0.5 %. Moreover, numerical analysis results indicated that the flatback airfoil blade reduced the size of the secondary vortex around the blade root area and its progress in the secondary direction in comparison with the non-flatback airfoil blade. The shape of the flatback airfoil on the trailing edge weakened the adverse pressure gradient migrating from the lower to the upper surface. Regardless of the flatback airfoils, the tip vortex core of the outboard region formed on the suction surface leading edge and strongly rolled up by the pressure surface boundary layers due to the large pressure difference between the suction and pressure surfaces in the blade tip region. This remarkable strong tip vortex developed downstream and raked up the boundary layer of the blade trailing edge with low energy.

A numerical method for the determination of flow-induced damping in hydroelectric turbines

To estimate structural fatigue, vibrational response to realistic spectrum of excitations and associated equivalent damping are of paramount importance. In this paper, an approach to quantify flow-induced damping of a relatively heavy fluid on a vibrating hydraulic turbine blade using numerical simulations is presented. First, mode shapes and frequencies of the immersed structure are obtained by modal analysis using the finite element method. Then, forced oscillatory modal motion is prescribed on the structural boundary of unsteady Reynolds-averaged Navier–Stokes flow simulations. Damping is finally computed as the normalized work done by the resulting fluid load on the structure. Validation is achieved by comparing the numerical results with available experimental data for a steel hydrofoil oscillating in flowing water. For this case, the linear increase in the damping ratio with the flow velocity is reproduced within 10% of the experimental values. Application of the method to an actual hydroelectric propeller turbine blade yields a fluid damping value of around 15% of critical damping for its first vibration mode.

CFD evaluation of added damping due to fluid flow over a hydroelectric turbine blade

To estimate structural fatigue, vibrational response to realistic spectrum of excitations and associated equivalent damping are of paramount importance. In this paper, an approach to quantify flow-induced damping of a relatively heavy fluid on a vibrating hydraulic turbine blade using numerical simulations is presented. First, mode shapes and frequencies of the immersed structure are obtained by modal analysis using the finite element method. Then, forced oscillatory modal motion is prescribed on the structural boundary of unsteady Reynolds-averaged Navier-Stokes flow simulations. Damping is finally computed as the normalized work done by the resulting fluid load on the structure. Validation is achieved by comparing the numerical results with available experimental data for a steel hydrofoil oscillating in flowing water. For this case, the linear increase in the damping ratio with the flow velocity is reproduced within 10% of the experimental values. Application of the method to an actual hydroelectric propeller turbine blade yields a fluid damping value of around 15% of critical damping for its first vibration mode.

Connected pathway relative permeability from pore-scale imaging of imbibition

Pore-scale images obtained from a synchrotron-based X-ray computed micro-tomography (µCT) imbibition experiment in sandstone rock were used to conduct Navier–Stokes flow simulations on the connected pathways of water and oil phases. The resulting relative permeability was compared with steady-state Darcy-scale imbibition experiments on 5cm large twin samples from the same outcrop sandstone material. While the relative permeability curves display a large degree of similarity, the endpoint saturations for the µCT data are 10% in saturation units higher than the experimental data. However, the two datasets match well when normalizing to the mobile saturation range. The agreement is particularly good at low water saturations, where the oil is predominantly connected. Apart from different saturation endpoints, in this particular experiment where connected pathway flow dominates, the discrepancies between pore-scale connected pathway flow simulations and Darcy-scale steady-state data are minor overall and have very little impact on fractional flow. The results also indicate that if the pore-scale fluid distributions are available and the amount of disconnected non-wetting phase is low, quasi-static flow simulations may be sufficient to compute relative permeability. When pore-scale fluid distributions are not available, fluid distributions can be obtained from a morphological approach, which approximates capillary-dominated displacement. The relative permeability obtained from the morphological approach compare well to drainage steady state whereas major discrepancies to the imbibition steady-state experimental data are observed. The morphological approach does not represent the imbibition process very well and experimental data for the spatial arrangement of the phases are required. Presumably for modeling imbibition relative permeability an approach is needed that captures moving liquid-liquid interfaces, which requires viscous and capillary forces simultaneously.

Three-dimensional flow phenomena in a wire-wrapped 37-pin fuel bundle for SFR

Abstract Three-dimensional flow phenomena in a wire-wrapped 37-pin fuel assembly mock-up of a Japanese loop-type sodium-cooled fast reactor, Monju, were investigated with a numerical analysis using a general-purpose commercial computational fluid dynamics code, CFX. Complicated and vortical flow phenomena in the wire-wrapped 37-pin fuel assembly were captured by a Reynolds-averaged Navier–Stokes flow simulation using a shear stress transport turbulence model. The main purpose of the current study is to understand the three-dimensional complex flow phenomena in a wire-wrapped fuel assembly to support the license issue for the core design. Computational fluid dynamics results show good agreement with friction factor correlation models. The secondary flow in the corner and edge subchannels is much stronger than that in an interior subchannel. The axial velocity averaged in the corner and edge subchannels is higher than that averaged in the interior subchannels. Three-dimensional multiscale vortex structures start to be formed by an interaction between secondary flows around each wire-wrapped pin. Behavior of the large-scale vortex structures in the corner and edge subchannels is closely related to the relative position between the hexagonal duct wall and the helically wrapped wire spacer. The small-scale vortex is axially developed in the interior subchannels. Furthermore, a driving force on each wire spacer surface is closely related to the relative position between the hexagonal duct wall and the wire spacer.

Effect of Spatial Resolution of Rough Surfaces on Numerically Computed Flow Fields with Application to Hydraulic Engineering

In numerical simulations of flow over rough surfaces, the roughness is often not resolved but represented by a numerical model. The validity of such an assumption is investigated in this paper by Reynolds-Averaged Navier-Stokes simulations of flow over a surface with a large roughness. The surface was created from a high-resolution laser scanning of a real rock blasted tunnel. By reducing the geometrical resolution of the roughness in two steps, the importance of an appropriate surface description could be examined. The flow fields obtained were compared to a set-up with a geometrical flat surface where the roughness was represented by a modified form of the Launder and Spalding wall-function. The flow field over the surface with the lowest resolution was substantially different from those of the two finer resolutions and rather close to the results from the set-up with the wall-function. The results also yield that the finer the resolution is the more vorticity is formed close to the rough surface and more turbulence is generated.

Effect of skewed blades on tip-clearance for different flow rates in axial fans

Tip-clearance noise induced by tip-leakage flow in axial flow fans, with the blades skewed circumferentially at angles of ±8.3°, has been investigated under off-design conditions by numerical simulation and experiments. Aerodynamic and aeroacoustic performances have been measured. Tip-leakage flow has been investigated by Navier-Stokes flow simulations at off-design conditions. The characteristics of noise sources in the tip-clearance region, obtained numerically, have been analyzed using vortex sound theory. Synergy between the tip-leakage vortex and the noise source in the tip region is discussed. Moreover, the noise source in the tip region has been measured by dynamic pressure sensors mounted in the casing wall near the blade tip and the acoustic far field has been obtained simultaneously as a function of flow rate. The frequency characteristic of the tip noise component is analyzed by measured results. The characteristics of noise source reveal that tip-clearance noise is associated with skewed blades, which are found to be effective in controlling tip-leakage flow and in eliminating the noise source in the tip-clearance region at off-design conditions. Forward-skewed blade are more effective than backward-skewed blades in reducing noise

Advanced Nonaxisymmetric Endwall Contouring for Axial Compressors by Generating an Aerodynamic Separator—Part II: Experimental and Numerical Cascade Investigation

Modern methods for axial compressor design are capable of shaping the blade surfaces in a three-dimensional way. Linking these methods with automated optimization techniques provides a major benefit to the design process. The application of nonaxisymmetric contoured endwalls is considered to be very successful in turbine rotors and vanes. Concerning axial compressors, nonaxisymmetric endwalls are still a field of research. This two-part paper presents the recent development of a novel endwall design. A vortex created by a nonaxisymmetric endwall groove acts as an aerodynamic separator, preventing the passage vortex from interacting with the suction side boundary layer. This major impact on the secondary flow results in a significant loss reduction by means of load redistribution, reduction in recirculation areas, and suppressed corner separation. Part I of this paper deals with the endwall design and its compressor application. The resulting flow phenomena and physics are described and analyzed in detail. The second paper presents the detailed experimental and numerical investigation of the developed endwall groove. The measurements carried out at the transonic cascade wind tunnel of DLR in Cologne, demonstrated a considerable influence on the cascade performance. A loss reduction and redistribution of the cascade loading were achieved at the aerodynamic design point, as well as near the stall condition of the cascade. This behavior is well predicted by the numerical simulation. The combined analysis of experimental and numerical flow patterns allows a detailed interpretation and description of the resulting flow phenomena. In this context, high fidelity 3D-Reynolds-averaged Navier–Stokes flow simulations are required to analyze the complex blade and endwall boundary layer interaction.

Experimental and numerical investigations of the tip leakage flow of axial fans with circumferential skewed blades under off-design conditions

Experimental and numerical investigations of tip leakage flow of circumferential skewed axial fans were conducted under off-design conditions. Two circumferential skewed fans, with the blade skew angles of 8.3° forward and backward, respectively, and a base fan were investigated in this study. Aerodynamic and aeroacoustic performances were measured. The Navier—Stokes flow simulations were validated experimentally and the key analysis of tip leakage flow was based on computational fluid dynamics results. The simulations show that with a decrease in flowrate, the start of the tip leakage vortex moves towards the leading edge in the chordwise direction and towards the hub in the spanwise direction. These movements are less significant for the forward-skewed blade than for the backward-skewed blade. The strength of the tip leakage vortex decreases along the vortex line. The vortex strength for the forward-skew blade is significantly less than that for the backward-skewed blade. The aeroacoustic source intensity in the tip clearance region is reduced by employing circumferential skewed blades and changes with a change in flowrate in the same manner as the measured sound pressure level. The forward-skewed blade is found to be effective in eliminating noise sources in the tip clearance region and in controlling tip leakage flow to expand the stall-free operation range under off-design conditions.

A Fast Navier Stokes Flow Simulation Tool Forimage Based CFD

The objective of this paper is to present a fast parallel incompressible Navier Stokes (NS) simulator that has enough versatility to apply to various endovascular situations with ease in medical image integration. Our long term goal is to bring NS simulation to surgeons as an additional routine image modality that can complement existing medical imaging channels. Given a medical image describing the geometry of an artery, we are able to simulate the blood flow through an artery close to clinical conditions. To achieve this goal, our interface relies on the combination of the L2 penalty method to deal with complex geometry for solving the NS equations. We present here a high performance portable domain decomposition solver based on a tuning of the fastest linear solver depending on the subdomain and the processor architecture. This paper provides a detailed proof of concept in the two dimensional case. The three dimensional results will be reported in a companion paper.

2.5D AGILD Electromagnetic Modeling and Inversion

In this paper, we propose a new 2.5D AGILD electromagnetic (EM) modeling and inversion algorithms. We derive 2.5D differential integral equations for EM field on the boundary strip and center strip Ωs with poles in cylindrical and spherical coordinate system. A 2.5D EM field Garlekin equation is derived on the remainder domain. It supposes that the electrical parameters in the rotational direction are uniform. In the cylindrical coordinate system, the EM field is function of the r, θ, and z. However, the electrical parameters are only depended on ρ and z. Upon substituting the Fourier serious of the EM field into the strip differential integral equation and Galerkin equation, we propose the 2.5D AGILD EM modeling and inversion algorithm and develop its software. The 2.5D AGILD EM modeling and inversion algorithms and software are explained in the ../files/051002183125/paper/Figs.1–6. The AGILD method has the following advantages. (1) It vanishes error on the artificial boundary; (2) It reduces the full matrix and the ill posed for inversion; (3) It resolves coordinate singularities in cylindrical and spherical coordinate system in continuous caster, geophysics, singularities in north and south poles in Earth for EM field and Navier Stokes flow simulation in atmosphere; (4) AGILD has widely applications in geophysics, atmosphere, nano-materials, caster, medical, radio, motor, etc. areas; (5) The applications show that the 2.5D AGILD and GL are fast, accurate, and have reasonable high resolution.

Anomalous Flow Phenomena Due to Breakdown of Tip Leakage Vortex in an Axial Compressor Rotor at Near-Stall Condition.

Anomalous flow phenomena in an axial compressor rotor at near-stall conditions have been investigated by unsteady three-dimensional Navier-Stokes flow simulations. The simulation show that the spiral-type breakdown of the tip leakage vortex occurs inside the rotor passage at the near-stall conditions. Downstream of the breakdown onset, the tip leakage vortex twists ant turns violently with time, thus interacting with the pressure surface of the adjacent blade. The vortex breakdown causes significant changes in the nature of the tip leakage vortex, which result in the anomalous phenomena in the tip leakage flow field at the near-stall conditions : no rolling-up of the leakage vortex downstream of the rotor, disappearance of the casing wall pressure trough corresponding to the leakage vortex, large spread of the low-energy fluid accumulating on the pressure side, and large pressure fluctuation on the blade pressure surface. As the flow rate is decreased from the near-stall conditions, the movement of the tip leakage vortex due to the vortex breakdown becomes so large that the leakage vortex interacts with the suction surface as well as the pressure one. The interaction gives rise to the three-dimensional separation of the suction surface boundary layer.

The Role of Tip Leakage Vortex Breakdown in Compressor Rotor Aerodynamics

The breakdown of tip leakage vortex has been investigated on a low-speed axial compressor rotor with moderate blade loading. Effects of the breakdown on the rotor aerodynamics are elucidated by Navier–Stokes flow simulations and visualization techniques for identifying the breakdown. The simulations show that the leakage vortex breakdown occurs inside the rotor at a lower flow rate than the peak pressure rise operating condition. The breakdown is characterized by the existence of the stagnation point followed by a bubblelike recirculation region. The onset of breakdown causes significant changes in the nature of the tip leakage vortex: large expansion of the vortex and disappearance of the streamwise vorticity concentrated in the vortex. The expansion has an extremely large blockage effect extending upstream of the leading edge. The disappearance of the concentrated vorticity results in no rolling-up of the vortex downstream of the rotor and the disappearance of the pressure trough on the casing. The leakage flow field downstream of the rotor is dominated by the outward radial flow, resulting from the contraction of the bubblelike structure of the breakdown region. It is found that the leakage vortex breakdown plays a major role in characteristic of rotor performance at near-stall conditions. As the flow rate is decreased from the peak pressure rise operating condition, the breakdown region grows rapidly in the streamwise, spanwise, and pitchwise directions. The growth of the breakdown causes the blockage and the loss to increase drastically. Then, the interaction of the breakdown region with the blade suction surface gives rise to the three-dimensional separation of the suction surface boundary layer, thus leading to a sudden drop in the total pressure rise across the rotor.

Computed Effects of Rotor-Induced Swirl on Brush Seal Performance—Part 2: Bristle Force Analysis

This paper analytically investigates the aerodynamic bristle force distributions in brush seals used in aircraft gas turbine engines. These forces are responsible for the onset of bristle tip lift-off from the rotor surface which significantly affects brush seal performance. In order to provide an enhanced understanding of the mechanisms governing the bristle force distributions, a full Navier-Stokes flow simulation is performed in a streamwise periodic module of bristles corresponding to the staggered square configuration. As is the case with a companion paper (Sharatchandra and Rhode, 1996), this study has the novel feature of considering the combined effects of axial (leakage) and tangential (swirl) flows. Specifically, the effects of intra-bristle spacing and bristle inclination angle are explored. The results indicate that the lifting bristle force increases with reduced intra-bristle spacing and increased inclination angle. It was also observed that increases in the axial or tangential flow rates increased the force component in the normal as well as the flow direction.

Code Validation for High-speed Flow Simulation Over Satellite Launch Vehicle

The development of an all-speed Euler and/or Navier-Stokes flow simulation code that uses a segregated finite volume algorithm for three-dimensional body-conforming curvilinear coordinates with a collocated variable arrangement is described. The efforts towards the physical validation of this code are the major contribution of the present work. The details of an experimental wind-tunnel investigation for pressure distribution and force measurements for the Brazilian Satellite Launch Vehicle (VLS) are also described. The computational results obtained for subsonic and supersonic flow conditions are in very good agreement with the experimental data. Transonic calculations, however, show poorer agreement with the available data for equivalent and even more refined meshes. The computational results produced by the present codes are already supplying aerodynamic information that is currently being used in the VLS design process.

Zonal Navier-Stokes methodology for flow simulation about a completeaircraft

Transonic Navier-Stokes flow simulations are presented for the F-16A fighter aircraft using a zonal grid approach. This approach subdivides the physical space about the aircraft into an ensemble of simple geometric shapes, thus mitigating many of the difficulties of generating a single grid about a complex shape, e.g., providing adequate grid refinement near all body surfaces to capture the boundary layer. Information is propagated between zones via grid overlapping and a spatial interpolation procedure. Computational Cp compare well with experimental values on the wing, horizontal and vertical tails, fuselage centerline, and the inlet/diverter region. The average y+ one grid point off the wing is 3. The experimental lift is underpredicted by 2.6%, and the experimental drag is overpredicted by 1.6%. The flexibility of the zonal approach is demonstrated by adding additional zones inside the inlet up to the compressor face to model flow spillage, and downwind of the exhaust nozzle to model power-on conditions. Computations are also presented for the F-16A in sideslip. These results demonstrate that the present zonal approach provides a flexible and viable means of simulating flowfields about complex geometries.

Cavity flow dynamics at higher Reynolds number and higher aspect ratio

A primitive variable unsteady viscous incompressible Navier-Stokes flow simulation in a higher aspect ratio ( A = depth/width = 2) driven cavity at a higher Reynold's number (Re = 10,000) exhibits dynamical features not apparent in previous studies of stationary solutions or at lower Reynold's number or in the more usual unit cavity investigations. The initial dynamics, e.g., between t = 0 sec and t = 70 sec, reveals transient bifurcations between states including two, three, and four interacting vortices in an anterior separation region. Following this, there is an intermediate interval, e.g., between t = 70 sec and t = 140 sec, characterized by a vertical oscillation of the primary vortex related to the general activities of the secondary features of the flow. The long time behavior, e.g., between t = 140 seconds and t = 360 seconds, is one of qualitative smoothing of all secondary features except a persistent oscillation indicating a Hopf bifurcation.