Turbulent Normal Stresses Research Articles

Experimental study on flow and turbulence characteristics of jet impinging on cylinder using three-dimensional Lagrangian particle tracking velocimetry

When a round jet impinges on a convex cylindrical surface, complex three-dimensional (3D) flow structures occur, accompanied by the Coanda effect. To characterize the flow and turbulence properties of the general system, ensemble averages of 3D Lagrangian particle tracking velocimetry measurements were taken. The radial bin-averaging method was used in post-processing the tracked particles and corresponding instantaneous velocity vectors to generate appropriate ensemble-averaged statistics. Two impinging angles were selected, and at a fixed Reynolds number, the ensemble-averaged volumetric velocity field and turbulent stress tensor components were measured. The flow and turbulence characteristics of the impinging jet on the cylinder were notably different based on the impinging angle, especially in the downstream region. Surprisingly, the attached wall jet with a half-elliptic shape was abruptly thickened in the wall-normal direction, similar to the axis switching phenomenon observed in elliptic jets in the case of oblique impingement. In the jet-impinging region, the flow spread in all directions with high mean vorticity values. With the development of a 3D curved wall jet, both the Coanda effect and centrifugal force played a significant role in the flow behavior. A notable feature of the self-preserving region was the similarity of mean velocity profiles with scaling by the maximum velocity and the jet half-width for both impinging angle cases. Local isotropy of turbulent normal stresses was observed in this region, supporting the existence of self-preservation in the 3D curved wall jet. The volumetric ensemble-averaged Reynolds stress tensor revealed strong inhomogeneous turbulence in the boundary layer region and the curvature effect on the Reynolds shear stress in the free shear layer.

Unsteady Motion of Shock Wave for a Supersonic Compression Ramp Flow Based on Large Eddy Simulation

A large eddy simulation (LES) is conducted to investigate shock wave/turbulent boundary layer interaction in a 24° compression ramp at a high inlet Mach number of Ma=2.9. The recycling/rescaling Method is used as the inflow turbulence generation technique. The shock wave structure and boundary layer flow in the interaction region are studied by flow visualization methods, such as vortex recognition and numerical schlieren. The distributions of turbulent kinetic energy and Reynolds normal stresses at different streamwise locations are analyzed. The results show that a strong anisotropy turbulent flow appears in the reattached boundary layer after the interaction of the shock wave. The large-scale unsteady motion of the separation shock wave is analyzed by using the intermittent factor and power spectrum. It is found that the shock moves around the averaged separation position, and the length scale is equal to 72% of the inlet boundary layer thickness. The power spectrum analysis reveals the existence of low-frequency instability in the separation region.

Reynolds stress turbulence modelling of surf zone breaking waves

Computational fluid dynamics is increasingly used to investigate the inherently complicated phenomenon of wave breaking. To date, however, no single model has proved capable of accurately simulating the breaking process across the entirety of the surf zone for both spilling and plunging breakers. The present study newly considers the Reynolds stress–$\omega$turbulence closure model for this purpose, where$\omega$is the specific dissipation rate. Novel stability analysis proves that, unlike two-equation closures (at least in their standard forms), the stress–$\omega$model is neutrally stable in the idealized potential flow region beneath surface waves. It thus naturally avoids unphysical exponential growth of turbulence prior to breaking, which has plagued numerous prior studies. The analysis is confirmed through simulation of a progressive surface wave train. The stress–$\omega$model is then applied to simulate a turbulent wave boundary layer, demonstrating superior accuracy relative to a two-equation model, especially during flow deceleration. Finally, the stress–$\omega$model is employed to simulate spilling and plunging breaking waves, with seemingly unprecedented accuracy. Specifically, the present work marks the first time that a single turbulence closure model collectively: (1) avoids turbulence over-production prior to breaking, (2) accurately predicts the breaking point, (3) provides reasonable evolution of turbulent normal stresses, while also (4) yielding accurate evolution of undertow velocity structure and magnitude across the surf zone, for both spilling and plunging cases. Differences in the predicted Reynolds shear stresses (hence flow resistance) are identified as key to the improved inner surf zone performance, relative to a state-of-the-art two-equation model.

A Comparative Study of the Buoyancy-Opposed Wall Jet using Different Turbulent Models

A comparative study of the buoyancy-opposed wall jet has been carried out using RANS methods (including RNG model, Realizable k-ε model, and two low Reynolds number k-ε models) and LES methods (including the subgrid scale model developed by Smagorinsky et al.(1963), Germano et al. (1991) and Kim et al. (1997)). The capability of each turbulence model to predict the flow field and temperature field in mixing stage was investigated. The results show that the k-ε series model can accurately predict the velocity distribution of flow field under isothermal case. However, in the case of buoyancy, due to the assumption of turbulent normal stress isotropy, the trend of temperature change in the mixing region and transition position existed an obvious deviation with experimental data. The LES methods, solved directly the large scale vortices, take into account the influence of turbulence stress anisotropy in the mixing region on the temperature change and capture the temperature change trend over the whole domain accurately. Due to the application of the subgrid kinetic energy transport equation, KET model has certain advantages in numerical simulation of similar engineering flow phenomenon.

Forced Turbulent Convection Along Heated and Cooled Walls With Variable Fluid Properties

Abstract The effect of temperature depending material properties on heat and momentum transfer along heated/cooled walls in turbulent pipe flow was investigated using direct numerical simulations (DNS). For the considered thermal wall conditions, always associated with a molecular Prandtl number well over unity Prw = 10, the significantly dampened/enhanced turbulent motion caused by the increase/decrease of the viscosity with distance to the heated/cooled wall turned out to clearly dominate over the opposite trend of the enthalpy fluctuations. The Nusselt number and, quantitatively less pronounced, the wall friction coefficient are accordingly decreased/increased for the heated/cooled case. A comparison against a well-established Nu-correlation unveils the limits of the generally applied approach, which is essentially based on uniform bulk flow conditions and subsequently modified accounting for material property variation, when applied to heated and cooled conditions. An enhanced disparity of the turbulent normal stresses is observed inside the inertial subrange for the heated case, indicating a stronger deviation from isotropic turbulence, which possibly challenges mostly isotropic standard turbulence models.

Bubble refinement by non-invasive rotating flow

Gas–liquid flow widely exists in industrial processes. Bubble refinement is of importance because smaller bubbles lead to higher efficiency of the gas–liquid interaction. Here, the novel rotating flow is designed for bubble refinement without using invasive parts. The drag force along the flow direction and the additional shear-lift force applied on the mother bubble allow it to detach from the orifice more easily with smaller size. In addition, the non-invasive rotating flow generates a large velocity gradient in both the shear and normal directions, resulting in turbulent shear and normal stress, causing the rising mother bubbles to break up in either the shear or normal direction. As a result, the number of bubbles increases to 408 compared to 9 under the static condition. Approximately 50% of the bubbles in the liquid are less than 3.60 mm in size and the Sauter mean bubble diameter is reduced from 10.45 to 4.77 mm, a decrease of 54.41%. The bubble refinement mechanism in the non-invasive rotating flow applies to other occasions where no invasive parts are needed.

Study of the detailed catalyst hydrodynamics using radioactive particle tracking technique in a mimicked Fischer-Tropsch slurry bubble column

Slurry bubble column reactor (SBCR) is the preferred choice of reactor for Fischer – Tropsch (FT) synthesis. However, the understanding of the catalyst flow dynamics in FT-SBCR is still lacking. In this work, hydrodynamics of the FT catalyst were studied using computer aided radioactive particle tracking (CARPT) technique at the mimicked conditions of FT synthesis for the first time. Solids ensemble averaged velocity, turbulent kinetic energy, Reynolds normal and shear stresses were experimentally obtained. Effect of operating conditions on the velocity flow field were investigated. Further, studies were conducted to quantify the difference in flow field due to the change in the liquid and solid phases. It was found that the change of solids turbulence is insignificant with pressure and solids loading at the studied operating conditions. Further, it was found that the surface tension of the fluid and the solid properties plays a dominant role on the turbulence.

Hydrodynamics of the steam-water two-phase flows behind a pair of bluff cylinderical bodies inside and around the wake region

A significant number of natural and industrial phenomena exist, where steam-water, two-phase flows face resistance due to the cylindrical shaped bodies. It is useful to explore such flows for their direct relevance to the steam driven industrial processes having Direct Contact Condensation (DCC) as the core phenomena for heat, mass, and momentum transfer. An experimental setup has been fabricated to study the influence of twin, different sized cylinders with a gap between them on the formation of wake region as the steam-water flow past the cylinders. Hot and cold wire sensors were used to measure the fluctuations in the velocity and temperature respectively of the flow within the wake and the region surrounding wake. The diameter of the smaller cylinder was fixed as 0.5 cm and the dimensions of the larger cylinder was varied from 1, 1.5 and 2.0 cm. Values for the fluctuating velocity were measure for all the cases and based on these measurements, the turbulent normal stresses and Reynolds shear stresses were determined. The asymmetry of the wake region increases by raising the gap between the two cylinders as the wake region aligned to the smaller cylinder has been deflected larger than the wake aligned to the larger cylinder. The wake asymmetry signified the possible effect of buoyancy on the thermal and momentum diffusivities, which was emphasized here through the measured values of turbulent normal and Reynolds stresses.

Flow and heat transfer in a rotating cavity with de-swirl nozzles: An LES study

Large eddy simulation was applied for studying the flow and heat transfer characteristics in the rotating cavity with de-swirl nozzles. Simulations were performed at the rotational Reynolds number of 1.4 × 105 and nondimensional flow rate of 4040. Compared with vertical nozzle, de-swirl nozzle generates lower swirl ratio, pressure loss and Nusselt number. Distributions of radial velocity show that de-swirl nozzle generates lower velocity in the Ekman boundary layer, but higher velocity in the core region. In the corner region of shroud and jet, the ‘dead zone’ of coherent vortices exists for vertical nozzle. However, for de-swirl nozzle, the ‘dead zone’ disappears due to the impact of inclined injection, and accordingly, the scale of time-averaged counter-rotating vortex pair is reduced effectively. In the middle and lower sections of cavity, plenty of vortex stripes are formed both for vertical and de-swirl nozzles; however, in the Ekman layer, turbulent kinetic energy and Reynolds normal stress for vertical nozzle is much higher than de-swirl nozzle. The distributions of turbulent energy spectrum and energy integral length scale show that, for de-swirl nozzle, large-scale eddies take the dominant role in middle section, while small-scale eddies dominate the flow fields in upper and lower sections of cavity.

Budgets of Turbulent Kinetic Energy and Reynolds Normal Stresses in Coaxial Jets with and Without Swirl: A Numerical Study

Budgets of Turbulent Kinetic Energy and Reynolds Normal Stresses in Coaxial Jets with and Without Swirl: A Numerical Study

Prediction of Reynolds stresses in high-Mach-number turbulent boundary layers using physics-informed machine learning

Modeled Reynolds stress is a major source of model-form uncertainties in Reynolds-averaged Navier-Stokes (RANS) simulations. Recently, a physics-informed machine-learning (PIML) approach has been proposed for reconstructing the discrepancies in RANS-modeled Reynolds stresses. The merits of the PIML framework has been demonstrated in several canonical incompressible flows. However, its performance on high-Mach-number flows is still not clear. In this work we use the PIML approach to predict the discrepancies in RANS modeled Reynolds stresses in high-Mach-number flat-plate turbulent boundary layers by using an existing DNS database. Specifically, the discrepancy function is first constructed using a DNS training flow and then used to correct RANS-predicted Reynolds stresses under flow conditions different from the DNS. The machine-learning technique is shown to significantly improve RANS-modeled turbulent normal stresses, the turbulent kinetic energy, and the Reynolds-stress anisotropy. Improvements are consistently observed when different training datasets are used. Moreover, a high-dimensional visualization technique and distance metrics are used to provide a priori assessment of prediction confidence based only on RANS simulations. This study demonstrates that the PIML approach is a computationally affordable technique for improving the accuracy of RANS-modeled Reynolds stresses for high-Mach-number turbulent flows when there is a lack of experiments and high-fidelity simulations.

Unsteady boundary layer development on a wind turbine blade: an experimental study of a surrogate problem

Wind turbines with thick blade profiles experience turbulent, periodic approach flow, leading to unsteady blade loading and large torque fluctuations on the turbine drive shaft. Presented here is an experimental study of a surrogate problem representing some key aspects of the wind turbine unsteady fluid mechanics. This experiment has been designed through joint consideration by experiment and computation, with the ultimate goal of numerical model development for aerodynamics in unsteady and turbulent flows. A cylinder at diameter Reynolds number of 65,000 and Strouhal number of 0.184 is placed 10.67 diameters upstream of a NACA 63215b airfoil with chord Reynolds number of 170,000 and chord-reduced frequency of $$k=2\pi f\frac{c}{2}/V=1.5$$ . Extensive flow field measurements using particle image velocimetry provide a number of insights about this flow, as well as data for model validation and development. Velocity contours on the airfoil suction side in the presence of the upstream cylinder indicate a redistribution of turbulent normal stresses from transverse to streamwise, consistent with rapid distortion theory predictions. A study of the boundary layer over the suction side of the airfoil reveals very low Reynolds number turbulent mean streamwise velocity profiles. The dominance of the high amplitude large eddy passages results in a phase lag in streamwise velocity as a function of distance from the wall. The results and accompanying description provide a new test case incorporating moderate-reduced frequency inflow for computational model validation and development.

Two-point similarity in turbulent planar jet flows

A similarity analysis was performed using the governing equations for the two-point velocity correlations and for the second order structures functions in the far field of a turbulent planar jet. The equilibrium of the large- and small-scale motions was ensured by requiring that the turbulent transfer terms are in equilibrium throughout the flow. The results show that the equations for the two-point velocity correlations at large separation distances admit similarity solutions where the dissipation rate is proportional to uo3/lo when the growth rate of the flow is constant and proportional to Uouo2/δ or uo3/lo(dδ/dx1)−12 when the growth rate decreases as the flow evolves. The turbulent normal stresses decay at x1−1 in all solutions suggesting that the change in dissipation rate is associated with a change in the development of the mean flow. The analysis for the structure functions show that these equations admit similarity solutions for the inertial range with a length scale proportional to the Taylor microscale λ. The scale for the third order structures function is proportional to ϵλ or uo3/Reλ in all cases, but the velocity scale for the second order structure functions is proportional to uoReλ−(1−ns)/(3−ns) where ns ≤ 1. The velocity scale is uo when ns is 1 but previous measurements in high Reynolds number planar jets (Pearson and Antonia, 2001, J. of Fluid Mech., 444, 343-382), indicate that ns ≲ 0.

Afterbody Effects on Axisymmetric Base Flows

The influence of an afterbody on an axisymmetric wake flow is investigated with two-component particle image velocimetry at a Reynolds number of based on the model diameter. The reattachment distance is found to vary from two to four step heights as the afterbody diameter is increased. Measurements performed on equivalent planar backward-facing step geometries reveal that the reattachment length scales similarly to a planar backward-facing step when the afterbody to main-body diameter ratio approaches unity. The distribution of turbulent normal and shear stresses reveals a progressive inhibition of the radial fluctuations for increasing afterbody diameter, whereas a proper orthogonal decomposition analysis highlights a concurrent weakening of the shear-layer flapping mode. For , the frequency spectrum of the time coefficient of the first proper orthogonal decomposition mode appears associated with the wake flapping motion and peaks in the range of . This frequency is associated with the recirculating flow unsteadiness observed in the azimuthal plane of the wake. The configuration without afterbody features an additional contribution at , which is associated with vortex shedding. The current results reveal the dependence of low-frequency unsteadiness upon changes in the afterbody diameter.

Turbulent flow structures in alluvial channels with curved cross‐sections under conditions of downward seepage

AbstractExperimental investigations have been done to analyze turbulent structures in curved sand bed channels with and without seepage. Measures of turbulent statistics such as time‐averaged near‐bed velocities, Reynolds stresses, thickness of roughness sublayer and shear velocities were found to increase with application of downward seepage. Turbulent kinetic energy and Reynolds normal stresses are increased in the streamwise direction under the action of downward seepage, causing bed particles to move rapidly. Analysis of bursting events shows that the relative contributions of all events (ejections, sweeps and interactions) increase throughout the boundary layer, and the thickness of the zone of dominance of sweep events, which are responsible for the bed material movement, increases in the case of downward seepage. The increased sediment transport rate due to downward seepage deforms the cross‐sectional geometry of the channel made of erodible boundaries, which is caused by an increase in flow turbulence and an associated decrease in turbulent kinetic energy dissipation and turbulent diffusion.

Experimental measurements of the drag force and the near-wake flow patterns of a longitudinally grooved cylinder

Flow around a smooth cylinder and a longitudinally grooved cylinder was investigated experimentally at Reynolds numbers ranged from 7.4×103 to 1.8×104. This study aims to establish a better understanding of the effects of grooved surface on the drag coefficient and flow characteristics of the cylinder. The force measurement results showed that grooved surface significantly reduces the mean drag coefficient, say about 20% with reference to that of the smooth cylinder at the same Reynolds number. Distributions of the ensemble-averaged mean velocities, turbulent kinetic energy, Reynolds normal and shear stresses were obtained by using the particle image velocimetry (PIV) technique. The PIV measurement results showed that the shear layers emanated from the grooved cylinder are relatively lower in magnitude and smaller in size as compared to those from a smooth cylinder. Vortex shedding from the cylinder is weakened due to the presence of grooved surface.

Modeling the Spatial Evolution of Roll Waves with Diffusive Saint Venant Equations

AbstractIn this paper, modeling the spatial evolution of roll waves with diffusive Saint Venant equations is examined. A momentum diffusion term is added to the equations to describe turbulent normal stress occurring in extremely nonuniform roll waves. Roll-wave flows with the same hydraulic conditions as in Brock’s experiment are simulated so as to obtain time-averaged wave crest and trough depths. The magnitude of the diffusion effect is found to have significant influence on the spatial growth rate of the wave amplitude. Simulated wave crest and trough depths along the channel agree with experimental data only when the proper turbulent viscosity value is selected. This study indicates that the nondiffusive Saint Venant equations are unable to describe roll-wave flows because the wave amplitude is largely overestimated. The Saint Venant–type model should incorporate comprehensive turbulent stresses and appropriate closure approaches for predicting the spatial evolution of roll waves.

Numerical study of turbulent wall jet over multiple-inclined flat surface

In the present work flow field of a turbulent oblique wall jet with multiple flat inclined wall has been numerically investigated. The Reynolds averaged Navier–Stokes (RANS) equations for incompressible flow are solved in transformed geometry using boundary-fitted coordinate system. The aim of the work is to investigate the influence of three inlet conditions: uniform, parabolic and trapezoidal inlet velocity profiles, on the mean flow and turbulent characteristics of the jet flowing tangentially along a multiple inclined solid wall. The results show that the inlet conditions affect the flow in the vicinity of the nozzle exit area and also the far field region. Mean flow has been presented in terms of evolution of mean velocity profiles, jet spread, decay of streamwise maximum velocity, distribution of wall pressure and skin friction coefficients, and streamwise variations of integrated momentum and energy fluxes. Discontinuities in the boundary slope of the segmented wall produces oscillations in distribution of skin friction and pressure coefficients. Reduced pressure in the region of wall discontinuity appeared to be causing the deflected jet to remain attached to the wall. The growth of the inner layer of the jet is relatively high with uniform inlet velocity profiles in the near-field region, but in the far-field region the inner layer grows with higher rate for the trapezoidal and the parabolic profiles. The rate of decay of maximum streamwise velocity for oblique wall jet on segmented wall is higher than that of plane wall jet. The jet with parabolic and trapezoidal inlet profiles show higher rate of decay than that with a uniform inlet profile. Similarity of streamwise velocity and velocity component parallel to the oblique wall has been observed in the developed region of flow. The volume flow rate of the jet varies linearly along the flow direction due to entrainment of the fluid from the surrounding. Sudden change in slope of the wall causes a sharp rise in entrained volume of fluid. The distribution of near wall velocity in the inner coordinates of the boundary layer is grossly altered and the profiles do not conform to the universal velocity profiles in the form of the law of the wall. Relatively higher position of defect law data signifies comparatively lower turbulence in the outer mixing layer. Cross-stream distribution of Reynolds stresses shows that the effect of inlet velocity profiles is more pronounced in the near field region of flow. Self-similarity is observed in the normalized turbulent shear stress profiles whereas considerable scatter can be noticed in the profiles of turbulent normal stresses for all the inlet velocity conditions. Two distinct peaks in the normalized turbulent kinetic energy profiles characterize the two shear layers of the jet and shifting of the outer peak toward the wall suggests a strong interaction of the outer layer with the inner layer as the jet develops.

Turbulent flow computation in a circular U-Bend

Turbulent flows through a circular 180° curved bend with a curvature ratio of 3.375, defined as the the bend mean radius to pipe diameter is investigated numerically for a Reynolds number of 4.45×10 4 . The computation is performed for a U-Bend with full long pipes at the entrance and at the exit. The commercial ANSYS FLUENT is used to solve the steady Reynolds-Averaged Navier-Stokes (RANS) equations. The performances of standard k-e and the second moment closure RSM models are evaluated by comparing their numerical results against experimental data and testing their capabilities to capture the formation and extend this turbulence driven vortex. It is found that the secondary flows occur in the cross-stream half-plane of such configurations and primarily induced by high anisotropy of the cross-stream turbulent normal stresses near the outer bend.

Nonlinear eddy viscosity modeling and experimental study of jet spreading rates

Indoor airflow pattern is strongly influenced by turbulent shear and turbulent normal stresses that are responsible for entrainment effects and turbulence-driven secondary motion. Therefore, an accurate prediction of room airflows requires reliable modeling of these turbulent quantities. The most widely used turbulence models include RANS-based models that provide quick solutions but are known to fail in turbulent free shear and wall-affected flows. In order to cope with this deficiency, this study presents a nonlinear k-ε turbulence model and evaluates it along with linear k-ε models for an indoor isothermal linear diffuser jet flow measured in two model rooms using PIV. The results show that the flow contains a free jet near the inlet region and a wall-affected region downstream where the jet is pushed toward the ceiling by entrainment through the well-known Coanda effect. The CFD results show that an accurate prediction of the entrainment process is very important and that the nonlinear eddy viscosity model is able to predict the turbulence-driven secondary motions. Furthermore, turbulence models that are calibrated for high Reynolds free shear layer flows were not able to reproduce the measured velocity distributions, and it is suggested that the model constants of turbulence models should be adjusted before they are used for room airflow simulations.