High Reynolds Number Case Research Articles

Integrated positron emission particle tracking (PEPT) and X-ray computed tomography (CT) imaging of flow phenomena in twisted tape swirl flow

A combined positron emission particle tracking (PEPT) and X-ray computed tomography (CT) technique is presented, and its utility is demonstrated through investigation of flow in a pipe with twisted tape swirl insert with varying flow conditions (diameter-based Reynolds numbers 16,300–63,300). A description of this technique is given, as well as data handling practices used to relate geometric information captured by CT to fluid flow data gathered via PEPT. It is found that the CT component is readily capable of capturing the stainless steel insert geometry in this present system, but the use of combined plastic and metal materials leads to artifacts in imaging of the plastic surface. Nonetheless, CT data are related to PEPT flow measurements, and average velocity fields are calculated via a pseudo-framing and interpolation scheme and used to visualize and interrogate key flow phenomena within the system. Radial velocity profiles of the mean flow characteristics are seen to collapse to a nearly common form across all flow conditions considered. Helical vortices are seen propagating through the flow field, generated by bypass flow around the gap between the insert and pipe wall, with additional coherent secondary flow structures seen in the higher Reynolds number cases. These findings enhance the understanding of the mixing mechanisms in these swirl flows and encourage the continued development of PEPT-CT methodologies for 3D flow measurements in optically inaccessible systems.

A Unifying Model for Turbulent Hyporheic Mass Flux Under a Wide Range of Near‐Bed Hydrodynamic Conditions

AbstractExisting models for estimating hyporheic solute mass flux often require numerous parameters related to flow, bed, and channel characteristics, which are frequently unavailable. We performed a meta‐analysis on existing data set, enhanced with high Reynolds number cases from a validated Computational Fluid Dynamics model, to identify key parameters influencing effective diffusivity at the sediment water interface. We applied multiple linear regression to generate empirical models for predicting eddy diffusivity. To simplify this, we developed two single‐parameter models using either a roughness or permeability‐based Reynolds number. These models were validated against existing models and literature data. The model using roughness Reynolds number is easy to use and can provide an estimate of the mass transfer coefficient for solutes like dissolved oxygen, particularly in scenarios where detailed bed characteristics such as permeability might not be readily available.

Numerical Investigations of Outer-Layer Turbulent Boundary Layer Control for Drag Reduction Through Micro Fluidic-Jet Actuators

Drag reduction through turbulent boundary layer control (TBLC) is an essential way to develop green aviation technologies. Compared with traditional approaches for drag reduction, turbulence drag reduction is a relatively new technology, particularly for skin friction drag reduction, and it is becoming a hotspot problem worldwide. This paper focuses on the research of micro fluidic-jet actuators used for outer-layer boundary layer control with high-performance computing (HPC). This study aims to reduce turbulent drag by reshaping the flow structure within the turbulent boundary layer. To ensure the calculation accuracy of the core region and reduce the consumption of computing resources, a zonal LES/RANS strategy and WMLES method are proposed to simulate the effects of fluidic-actuators for outer-layer boundary control, in which high-performance computing has to be involved. The studies are performed on the classical zero-gradient turbulent flat plate cases, in which three different control strategies named “W-control,” “V-control,” and “VW-control” are used and compared to study the effects of drag reduction under a low Reynolds number at Reτ = 470 and a higher Reynolds number at Reτ = 4700. The mechanism for drag reduction is analysed via a pre-multiplied spectral method and a parallel dynamic mode decomposition (DMD) method. The results show that the present approach can effectively simulate the outer-layer turbulent boundary control where the “V-control” with the fluidic-jet actuator array behaves well to achieve an average drag reduction (DR) rate of more than 5% for the high Reynolds number case of the flat plate boundary layer. The high Reynolds shear stress and turbulent kinetic energy distribution in the boundary layer region show an obvious uplift under the effects of actuators, which is the main mechanism for drag reduction.

Aerodynamic Characteristics of Flow Past Naca 0008 Airfoil at Very Low Reynolds Numbers

The flow around NACA 0008 airfoil was investigated computationally at two very low values of Reynolds numbers 2000 and 6000 and for various angles of attack 0 to 8°. The flow being laminar it was seen to separate at very small angles of attack. Due to large viscous effects the pressure recovery at the trailing edge is poorer as compared to the high Reynolds number case leading to lower values of lift coefficient Cl, higher values of drag coefficient Cd, and lower values of (Cl/Cd). The wake flow exhibits similarity behaviour similar to that in high Reynolds number flat-plate wake. The quantitative validity of the boundary layer equations in a limited range of parameters is ascertained.

LES of the T106 low-pressure turbine: Spectral proper orthogonal decomposition of the flow based on a fluctuating energy norm

This paper investigates the use of the spectral proper orthogonal decomposition (SPOD) on the flow around the T106 low-pressure turbine cascade. The chosen metric of the SPOD is based on the hydrodynamic flow disturbances for compressible flows and is used to characterize the flow structures holding large energy disturbances and synchronization processes with incoming wakes when considered. The input data for the SPOD is provided by large-eddy simulations of the T106 cascade. The Reynolds number and free-stream turbulence effects on the flow structures are studied using four operating points investigated in previous experiments and numerical simulations: Reynolds numbers of Re = 5.18 × 104 and Re = 1.48 × 105 without and with upstream wakes. The analysis of the SPOD indicates that the upstream wakes can amplify some modes of the suction side boundary layer (apparently a receptivity mechanism) and intensify the developing blade wake turbulent structures downstream of the trailing edge. This amplification happens over a reduced frequency bandwidth between Strouhal numbers equal to 7–10 for the low Reynolds number case and 20–24 for the high Reynolds number case.

Numerical Calculation of Slosh Dissipation

As part of the Sloshing Wing Dynamics H2020 EU project, an experimental campaign was conducted to study slosh-induced damping in a vertically excited tank filled with liquid water or oil and air. In this work, we simulate these experiments using two numerical approaches. First, a single-phase, weakly compressible liquid model is used, and the gas flow (air) is not modeled. For this approach, a proven Smoothed Particle Hydrodynamics (SPH) model is used. In the second approach, both phases are simulated with an incompressible liquid and weakly compressible gas model via a Finite Volume Method (FVM) using Volume-of-Fluid (VOF) to track the liquid phase. In both approaches, the energy distribution of the flow is calculated over time in two- and three-dimensional simulations. It is found that there is reasonable agreement on the energy dissipation evolution between the methods. Both approaches show converging results in 2D simulations, although the SPH simulations seem to have a faster convergence rate. In general, the SPH results tend to overpredict the total dissipation compared to the experiment, while the finite volume 2D results underpredict it. Time histories of the center of mass positions are also compared. The SPH results show a much larger vertical center of mass motion compared to the FVM results, which is more pronounced for the high Reynolds number (water) case, probably linked to the absence of the air phase. On the other hand, the limited center of mass motion of the FVM could be linked to the need for higher spatial resolutions in order to resolve the complex gas–liquid interactions, particularly in 3D.

A study on micro-step flow using a hybrid direct simulation Monte Carlo–Fokker–Planck approach

This study aimed to investigate the recirculation zone in a micro-step geometry using a hybrid molecular direct simulation Monte Carlo (DSMC) Fokker–Planck (FP) approach. As this hybrid approach benefits from the accuracy of the DSMC and reduced computational cost of FP, very low Knudsen number (Kn) and high Reynolds number (Re) cases were investigated for the first time. In particular, the role of Kn, specularity of walls, and Re was evaluated on the formation of concave and convex vortices. The Kn and Re ranges were from 0.0001 to 100 and from 0.04 to 5940, respectively. The latter considers a wide range of flow regimes from laminar to transitional flow. It is the first time that transitional flows have been treated in a micro-step using a rarefied flow solver. We demonstrated the formation of a vortex on the top wall of the micro-step geometry for low Kn conditions in the range of 0.0001 <Kn < 0.001. Extended positive pressure gradient in the geometry was found to be the cause of this secondary recirculation region. It was demonstrated that the recirculation zone lays on the vertical wall for Kn >1. It was shown that making the junction and bottom wall of the step specular did not eliminate the concave vortex but rather led to an increase in its strength. In addition, cold-to-hot transfer could be observed in all cases due to the competition between the higher-order term of the heat flux formula with the Fourier term.

Drag force on a circular cylinder in stratified flow: A two-dimensional numerical study

Using two-dimensional numerical simulations, we investigate a circular cylinder in a stratified flow with a pycnocline of a smooth density profile. We are particularly concerned about the difference between stratified flows and their homogeneous, or unstratified, counterparts in drag coefficients. It is well known that the characteristics of a stratified flow depend on the Reynolds number Re and the internal Froude number Fr. First, we change the incoming flow velocity, with the Reynolds number and the internal Froude number varying simultaneously, in the ranges of 76≤Re≤579 and 0.14≤Fr≤1.046, respectively. We find that the flow experiences a sequence of flow patterns, namely “multiple centerline structures,” “isolated mixed regions,” and “vortex shedding,” as we increase this combination, agreeing well with the previous experiments in the low Re and Fr ranges. Meanwhile, the mean drag coefficient decreases, and it drops below the value for a homogeneous state as an empirical stability parameter, k, drops below unity, indicating the transition from a lee-wave dominant wake to an unsteady, vortex shedding wake. This unique variation of drag coefficient is more clearly shown in another situation, when we fix the Reynolds number at Re = 234 while varying the Froude number within 0.094≤Fr≤4.192. In such a situation, we observe a stable “double eddy” pattern at Fr = 1.87, around which a minimum of mean drag coefficient is reached. At this critical point, we understand that the stratification in the flow inhibits lee-side separation, while the internal waves have not yet played a significant role. Although we observe turbulence-like, strong mixing regions in the far downstream wake for some specific cases, it is argued that the current two-dimensional simulations might not be able to resolve the high Reynolds number or high Froude number cases.

A Numerical Investigation Into the Heat Transfer Performance and Particle Dynamics of a Compressible, Highly Mass Loaded, High Reynolds Number, Particle Laden Flow

Abstract In this work, we study the heat transfer performance and particle dynamics of a high mass-loaded, compressible, particle-laden flow in a horizontally oriented pipe using an Eulerian–Eulerian (two-fluid) computational model. Previous experimental work by our group provides the basis for the study. Specifically, a 17 bar coflow of nitrogen gas and copper powder are modeled with inlet Reynolds numbers of 3 × 104, 4.5 × 104, and 6 × 104 and mass loadings of 0, 0.5, and 1.0. Eight binned particle sizes were modeled to represent the known powder properties. Significant settling of all particle groups is observed leading to asymmetric temperature distributions. Wall and core flow temperature distributions are observed to agree well with measurements. In high Reynolds number cases, the predictions of the multiphase computational model were satisfactorily aligned with the experimental results. Low Reynolds number model predictions were not as consistent with the experimental measurements.

Reduced order models for finite-volume simulations of turbulent flow around wind-turbine blades.

The computational cost of the design optimisation of wind turbines, as well as the optimisation of the operation and maintenance of offshore wind farms represents a limitation to the application of conventional simulation methods. New techniques such as reduced order modelling (ROM) and technologies such as hybrid-analysis methods and digital twins have increased in popularity due to their ability to deliver numerical results at a significant speed-up with reasonable accuracy. This work presents a hybrid projection-based proper orthogonal decomposition (POD) strategy applied to transient turbulent flow problems. Key feature of this work is the applicability of the methodology to high Reynolds number cases and the stabilisation of pressure in the online phase via the assembly of the so-called pressure Poisson equation. Another significant part of this work is the implementation of an interpolation scheme for the eddy viscosity field in the classical POD-Galerkin strategy. The sampling procedure and the calculation of the reduced operators in the offline phase is carried out using the finite volume method (FVM), OpenFOAM’s libraries specifically, while the construction of the reduced basis and the solution of the online phase is carried out in Python. The capability of the resulting ROM is tested using the two-dimensional flow around a NACA0015 airfoil at 17° angle of attack with Reynolds number of approximately 300 000.

The effect of static deformation on the lift loss phenomenon of an ABS downforce producing wing in ground effect

The proximity of a downforce producing wing to the ground has a significant effect on the generation of aerodynamic loads and flow structures. However, a rigid body assumption for the wing may lead to inaccuracies in the estimation of these loads. Static loosely-coupled Fluid-Structure Interaction (FSI) simulations were performed at Reynolds numbers of 4.64·105 and 6.96·105 and ground clearances ranging from 0.053 c to 0.223 c to investigate the effect of deformation in an ABS wing. Results of these simulations demonstrated that wing deflection increased the height at which lift loss occurred, as the reduced wing tip ground clearance led to an earlier main wing vortex breakdown and greater boundary layer separation. The increase in Reynolds number for a constant chord length induced larger variations in critical height: the critical height increased by 0.011 c at Re = 4.64·105 and by 0.021 c at Re = 6.96·105. The larger variation in critical height at the high Reynolds number cases was due to the increase in the magnitude of the aerodynamic loads, and larger deflections.

An adaptive plate at flapping wing’s trailing edge in promoting energy extraction performance

As is known, the maximum thickness position plays a key role in determining the energy extraction properties for flapping wing airfoils. Previous work demonstrated that the energy extraction efficiency might increase when we move the maximum thickness position towards the leading-edge direction. Inspired from this phenomenon, we propose in this work the addition of a flat plate at the tail of the flapping wings. Under two different Reynolds numbers (Re = 1100 and Re = 5×105), the effect of adding a rigid flat plate or a flexible flat plate to the trailing edge of the flapping wing on the flapping wing’s energy efficiency was investigated. The corresponding results were also compared with that of the original flapping wing. Results show that the addition of a rigid flat plate is sufficient for the amelioration of the flapping wing’s energy extraction efficiency in low Reynolds number cases. At high Reynolds number cases, the flapping wing with flexible flat plate trailing edge can maintain a relatively high energy extraction efficiency over a wide range of frequency, while the flapping wing with rigid flat plate trailing edge can only improve the energy extraction efficiency in the low frequency region. Therefore, we propose the application of flapping wings with flexible flat plate trailing edge for increasing the energy extraction efficiency under high Reynolds number conditions.

Development of a New Algorithm for Modeling Viscous Transonic Flow on Unstructured Grids at High Reynolds Numbers

Abstract This study investigates a new algorithm for modeling viscous transonic flow at high Reynolds number cases suitable for unstructured grids. The challenge of modeling viscous transonic flow around airfoils becomes intense at high Reynolds number cases due to a variety of flow regimes encountered, such as boundary layer growth and the shockwave/turbulent boundary-layer interaction, accompanied by large separation bubble. Therefore, it is highly demanded to develop robust and efficient models that can capture the shock-induced problems of turbulent flows for aircraft design purposes. The new model is essentially a hybrid algorithm to address the conflict between turbulence modeling and shock-capturing requirements. A skew-symmetric form of a collocated finite volume scheme with minimum aliasing errors was implemented to model the turbulent region in the combination of a semidiscrete, central difference scheme to capture discontinuities with adequately low numerical dissipation for the minimal effect on turbulent flows. To evaluate the effectiveness of the model, it was tested in three conventional cases. The computational results are close to measured data for predicting the shock locations. This implies that the model is able to predict the scale of the separation bubble and the main characteristics of turbulent transonic flow adequately.

Performance of Overset Mesh in Modeling the Wake of Sharp-Edge Bodies

The wake dynamics of sharp-edge rigid panels is examined using Overset Grid Assembly (OGA) utilized in OpenFOAM, an open-source platform. The OGA method is an efficient solution technique based on overlap of a single or multiple moving grids on a stationary background grid. Five test cases for a stationary panel at different angle of attack are compared with available computational data, which show a good agreement in predicting global flow variables, such as mean drag. The models also provided accurate results in predicting the main flow features and structures. The flow past a pitching square panel is also investigated at two Reynolds numbers. The study of surface pressure distribution and shear forces acting on the panel suggests that a higher streamwise pressure gradient exists for the high Reynolds number case, which leads to an increase in lift, whereas the highly viscous effects at low Reynolds number lead to an increased drag production. The wake visualizations for the stationary and pitching motion cases show that the vortex shedding and wake characteristics are captured accurately using the OGA method.

Multiple solutions and their asymptotics for laminar flows through a porous channel with different permeabilities

AbstractThe existence and multiplicity of similarity solutions for the steady, incompressible and fully developed laminar flows in a uniformly porous channel with two permeable walls are investigated. We shall focus on the so-called asymmetric case where the upper wall is with an amount of flow injection and the lower wall with a different amount of suction. The numerical results suggest that there exist three solutions designated as type $I$, type $II$ and type $III$ for the asymmetric case, type $I$ solution exists for all non-negative Reynolds number and types $II$ and $III$ solutions appear simultaneously at a common Reynolds number that depends on the value of asymmetric parameter $a$ and with the increase of $a$ the common Reynolds numbers are decreasing. We also theoretically show that there exist three solutions. The corresponding asymptotic solution for each of the multiple solutions is constructed by the method of boundary layer correction or matched asymptotic expansion for the most difficult high Reynolds number case. These asymptotic solutions are all verified by their corresponding numerical solutions.

A numerical investigation about the effects of Reynolds number on the flow around an appended axisymmetric body of revolution

Large-eddy simulations for the case of an axisymmetric body of revolution with appendages are considered. The geometry is the benchmark case of the DARPA suboff body. The paper focuses on the effects of the Reynolds number on the structure of the boundary layer in the stern area as well as the near wake. For this purpose we compare results for two Reynolds numbers (based on the length of the body, , and the free-stream velocity, ): and . Results are in good agreement with published experiments at the same Reynolds numbers. The boundary layer thickness over the stern increases substantially at both simulated Reynolds numbers, due to the adverse pressure gradient at the rear of the body. However, for the high Reynolds number case, a weaker peak of turbulent kinetic energy develops in the outer layer over the stern. Nonetheless, the associated bimodal distribution of the turbulent stresses in the wake is already very similar a few diameters downstream of the tail. First- and second-order moments demonstrate that junction vortices at the stern bring higher velocities and turbulence at the root of the appendages for both Reynolds numbers, with a more evident signature at . An azimuthal readjustment of turbulent kinetic energy occurs in the wake, becoming more axisymmetric, with increasing values in the planes aligned with the stern appendages, due to turbulence coming from both the stern boundary layer and junction vortices.

Instability of an annular liquid sheet exposed to compressible gas flows

A temporal linear stability analysis was performed for a viscous annular liquid sheet exposed to compressible gas flows. An analytical dispersion relation illustrating the disturbance growth characteristics at the gas–liquid interfaces was formulated and validated, and a parametric study was performed to explore the mechanism that affects the sheet instability. The results reflect that para-sinuous disturbances on the liquid sheet always predominate over para-varicose disturbances under the considered flow conditions. The aerodynamic interaction at the gas–liquid interfaces of the liquid sheet is the decisive factor on sheet instability. As for the main factors affecting the aerodynamic effects, the contribution of the gas–liquid velocity difference to aerodynamic interactions is more significant than that of the gas–liquid density ratio. Neglecting the gas compressibility markedly underestimates the aerodynamic effects at the gas–liquid interfaces for flow conditions of high gas Mach number, which results in decreased disturbance growth rate and dominant wave number. Moreover, both the liquid viscous force and the surface tension force hold back the disturbance growing and stabilize the liquid sheet under the considered conditions. Note that the destabilizing effect of the viscous force is limited for high liquid Reynolds number cases. In general, it is very necessary to consider the compressibility of the gas flows in the instability study of practical twin-fluid atomization.

Lattice Boltzmann Method Simulations of High Reynolds Number Flows Past Porous Obstacles

Lattice Boltzmann Method (LBM) simulations for turbulent flows over fractal and non-fractal obstacles are presented. The wake hydrodynamics are compared and discussed in terms of flow relaxation, Strouhal numbers and wake length for different Reynolds numbers. Three obstacle topologies are studied, Solid (SS), Porous Regular (PR) and Porous Fractal (FR). In particular, we observe that the oscillation present in the case of the solid square can be annihilated or only pushed downstream depending on the topology of the porous obstacle. The LBM is implemented over a range of four Reynolds numbers from 12,352 to 49,410. The suitability of LBM for these high Reynolds number cases is studied. Its results are compared to available experimental data and published literature. Compelling agreements between all three tested obstacles show a significant validation of LBM as a tool to investigate high Reynolds number flows in complex geometries. This is particularly important as the LBM method is much less time consuming than a classical Navier–Stokes equation-based computing method and high Reynolds numbers need to be achieved with enough details (i.e., resolution) to predict for example canopy flows.

A comparative study of alternating current and nanosecond plasma actuators in flow separation control

A combined numerical and experimental study is performed to elucidate the difference in flow separation control mechanisms between alternating current (ac) and nanosecond (ns) plasma actuators. The focus is on the visualization of detailed flow actuation process and establishment of relationship between flow control authority and characteristics of different actuators. Time-resolved particle image velocimetry (PIV) system is used to capture the transient separated flow over a stalled NACA 0015 airfoil at low Reynolds number (Re) of 6.3 × 104 and response of the flow to plasma actuation. Reynolds-averaged two-dimensional computation is performed for both low and high Reynolds number cases at Re = (0.063, 0.75) × 106 to complement experiment. Utilizing the elaborate Reynolds stress turbulence model in conjunction with an empirical body force model for surface ac plasma discharge and a sophisticated self-similar formulation for ns pulsed discharge, we have been able to numerically reproduce the experimentally observed intricate mechanisms, e.g. discretization of unstable shear layer into individual vortices, formation of large-scale spanwise vortex, strong entrainment effect of vortices and flow regularization procedure. Moreover, the information from simulation allows us to make a number of important observations which have no experimental counterparts. The detailed simulation shows that the convection of residual heat from ns discharge with cross flow makes ns plasma actuator more flexible in perturbing far downstream fluid in comparison with other actuators, and makes it superior to other devices in some high Re number flows. Also observed is the occurrence of strong flow resonance and frequency lock-in at a proper range of forcing frequency. In addition, the continuous ac plasma actuator appears to have complex control mechanisms, depending on flow conditions.

A computational study of two-phase viscoelastic systems in a capillary tube with a sudden contraction/expansion

Two-phase viscoelastic systems are computationally studied in a pressure-driven flow with a sudden contraction and expansion using a finite-difference/front-tracking method. The effects of viscoelasticity in drop and bulk fluids are investigated including high Weissenberg and Reynolds number cases up to Wi = 100 and Re = 100. The Finitely Extensible Non-linear Elastic–Chilcott and Rallison (FENE-CR) model is used to account for the fluid viscoelasticity. Extensive computations are performed to examine drop dynamics for a wide range of parameters. It is found that viscoelasticity interacts with drop interface in a non-monotonic and complicated way, and the two-phase viscoelastic systems exhibit very rich dynamics especially in the expansion region. At high Re, the drop undergoes large deformation in the contraction region followed by strong shape oscillations in the downstream of the expansion. For a highly viscous drop, a re-entrant cavity develops in the contraction region at the trailing edge which, in certain cases, grows and eventually causes encapsulation of ambient fluid. The re-entrant cavity formation is initiated at the entrance of the contraction and is highly influenced by the viscoelasticity. Compared to the corresponding straight channel case, the effects of viscoelasticity are reversed in the constricted channel: Viscoelasticity in drop/continuous phase hinders/enhances formation of the re-entrant cavity and entrainment of ambient fluid into main drop. Encapsulation of ambient fluid into main droplet may be another route to produce a compound droplet in microfluidic applications.