Turbulent Velocity Profiles Research Articles

Computational analysis of convective heat transfer properties of turbulent slot jet impingement

PurposeConvective heat transfer features of a turbulent slot jet impingement are comprehensively studied using two different computational approaches, namely, URANS (unsteady Reynolds-averaged Navier–Stokes equations) and SAS (scale-adaptive simulation). Turbulent slot jet impingement heat transfer is used where a considerable heat transfer enhancement is required, and computationally, it is a quite challenging flow configuration.Design/methodology/approachCustomized OpenFOAM 4.1, an open-access computational fluid dynamics (CFD) code, is used for SAS (SST-SAS k-ω) and URANS (standard k-ε and SST k-ω) computations. A low-Re version of the standard k-ε model is used, and other models are formulated for good wall-refined calculations. Three turbulence models are formulated in OpenFOAM 4.1 with second-order accurate discretization schemes.FindingsIt is observed that the profiles of the streamwise turbulence are under-predicted at all the streamwise locations by SST k-ω and SST SAS k-ω models, but follow similar trends as in the reported results. The standard k-ε model shows improvements in the predictions of the streamwise turbulence and mean streamwise velocity profiles in the zone of outer wall jet. Computed profiles of Nusselt number by SST k-ω and SST-SAS k-ω models are nearly identical and match well with the reported experimental results. However, the standard k-ε model does not provide a reasonable profile or quantification of the local Nusselt number.Originality/valueHybrid turbulence model is suitable for efficient CFD computations for the complex flow problems. This paper deals with a detailed comparison of the SAS model with URANS and LES for the first time in the literature. A thorough assessment of the computations is performed against the results reported using experimental and large eddy simulations techniques followed by a detailed discussion on flow physics. The present results are beneficial for scientists working with hybrid turbulence models and in industries working with high-efficiency cooling/heating system computations.

Investigation on Incompressible Turbulent Boundary Layer with Maximum Deceleration.(Dept.M)

Incompressible turbulent boundary layer problems are solved based on certain assumed boundary conditions, by integrating Prandtl integral equation. Representing the velocity profile parameter as a function of dimensionless similarity number of turbulent boundary layers, a separation criteria can be achieved. This helps in solving the attached boundary layers with max mum deceleration. The obtained theoretical results are compared with previous available experimental data obtained for radial diffuser. Moreover, this investigation contains relation between the turbulent velocity profile and shear stress profile in a parametric form for equilibrium boundary layers and agree well with that obtained from Mellor-Gibson theory.

Analytical Formula for the Mean Velocity Profile in a Pipe Derived on the Basis of a Spatial Polynomial Vorticity Distribution

The derivation of the mean velocity profile for a given vorticity distribution over the pipe cross-section is presented in this paper1. The velocity profile and the vorticity distribution are axisymmetric, which means that the radius is the only variable. The importance of the vortex field for the flow analysis is discussed in the paper. The polynomial function with four free parameters is chosen for the vorticity distribution. Free parameters of this function are determined using boundary conditions. There are also two free exponents in the polynomial. These exponents are determined based on the comparison of this analytical formula with experimental data. Experimental data are taken from the Princeton superpipe data which consist of 26 velocity profiles for a wide range of Reynolds numbers (Re). This analytical formula for the mean velocity profile is more precise than the previous one and it is possible to use it for the wide range of Reynolds number <31,577; 35,259,000>. This formula is easy to use, to integrate, or to derivate. The empirical formulas for the profile parameters as a function of Re are also included in this paper. All information for the mean velocity profile prediction in the mentioned Re range are in the paper. It means that it is necessary to know the average velocity v(av), the pipe radius R, and Re to be able to predict the turbulent mean velocity profile in a pipe.

Simplified Transition and Turbulence Modeling for Oscillatory Pipe Flows

One-dimensional unsteady Reynolds-averaged Navier–Stokes computations were performed for oscillatory transitional and turbulent pipe flows and the results were validated against existing experimental data for a wide variety of oscillatory Reynolds and Womersley numbers. An unsteady version of the Johnson–King model was implemented with optional near-wall modification to account for temporal pressure gradient variations, and the predictions were compared with those of the Spalart–Allmaras and k–ε turbulence models. Transition and relaminarization were based on empirical Womersley number correlations and assumed to occur instantaneously: in the former case, this assumption was valid, but in the latter case, deviations between data and predictions were observed. In flows where the oscillatory Reynolds numbers are substantially higher than the commonly accepted steady critical value (~2000), fully or continuously turbulent models produced the best correspondence with experimental data. Critically and conditionally turbulent models produced slightly inferior correspondence, and no significant benefit was observed when near-wall pressure gradient effects were implemented or when common one- and two-equation turbulence models were employed. The turbulent velocity profiles were mainly unaffected by the oscillations and this was explained by noting that the turbulent viscosity is significantly higher than its laminar counterpart. Thus, a turbulent Womersley number was proposed for the analysis and categorization of oscillatory pipe flows.

MODIFICATION OF THE GEOMETRY OF THE FLOW CONDITIONER

MODIFICATION OF THE GEOMETRY OF THE FLOW CONDITIONER

On the generation of turbulent inflow for hybrid RANS/LES jet flow simulations

The present work is devoted to the assessment of a low-noise turbulence generation methodology used to produce boundary layer with three-dimensional resolved turbulence at the exit of a jet nozzle to reproduce experimental conditions. The method relies on the use of roughness elements introduced in the computational domain with Immersed Boundary Conditions and ZDES mode 3 (Wall Modelled LES branch of ZDES). The simulation of a round jet at M = 0.9 and Reynold number 106 with turbulence generation is compared to a simulation with no resolved turbulence in the nozzle boundary layer using ZDES mode 2. The behaviour of the boundary layer downstream of the roughness elements inside the nozzle is scrutinized using two grids. The turbulence generation method combined with ZDES mode 3 produces satisfying levels of resolved turbulence at the nozzle exit. The early stages of the shear layer development are modified by the ZDES mode 3 simulations providing an initially turbulent shear layer. On the other hand, the ZDES mode 2 simulations, with a turbulent mean exit velocity profile but no resolved turbulence, display a short area of strong shear layer instabilities leading to the quick development of three-dimensional turbulence in the mixing layer. The present results give insights on the level of turbulent modelling of the nozzle boundary layer needed depending on the purposes of the jet flow simulations considered.

Investigation of shock wave control by suction in a supersonic cascade

The numerical simulation of suction control on a supersonic cascade is presented in this paper. The purpose of this study is to enhance the resistance backpressure characteristics of a flow field by suction control and demonstrate the evolution of shock structures and parameter distributions in the flow field controlled by suction. The study is based on the SAV21 supersonic cascade designed by the German Aerospace Centre and operated under an incoming Mach number of 2.4 and a flow turning angle of 45°. The three-dimensional Reynolds-averaged Navier-Stokes (RANS) equations in a Cartesian coordinate system are successfully applied to the cascade flow. The two-equation shear-stress transport (SST) k-ω turbulence model of Menter is employed to model the turbulent velocity profile. The results show that when the backpressure is greater than the critical backpressure, the shock train leading edge crosses the throat, causing a decrease in the mass-capturing coefficient and the occurrence of stall. To control supersonic cascade by suction, the most effective location is at the interaction of the shock train leading edge and the suction surface boundary layer. By applying suction control at the key position, the shock train is stabilized at the downstream boundary of the suction slot with a small loss of suction mass flow. At mild backpressure ratio range, the increased backpressure is compensated by the local enhanced barrier wave. By increasing the pressure gradient downstream of the barrier wave, the maximum backpressure is improved by suction control. By using the improved combined suction scheme with one spanwise slot on the suction surface and one streamwise slot on the endwall, the maximum backpressure can be improved by 20% under a suction mass flow of 8% of the capture mass.

Calculation of the mean velocity profile for strongly turbulent Taylor–Couette flow at arbitrary radius ratios

Abstract

Large eddy simulation of turbulent pulp flow in a channel

Large eddy simulation (LES) of turbulent flow of concentrated fiber suspension or pulp is carried out to investigate the flow and turbulence structures in a channel. The simulations are carried out for the turbulent flow of Eucalyptus pulp suspension using OpenFOAM for three fiber concentrations (c = 1.5, 2.0 and 2.5) and six different Reynolds numbers (6 ≤Res≤ 16,600). It is observed that the variation in flow regime is similar in the two lower fiber concentrations while the flow regime is highly affected by fiber concentration for c = 2.5. Visualizations of vortical structures for different Reynolds numbers and fiber concentrations are used to investigate different flow regimes. Variation of apparent viscosity with Reynolds number and fiber concentration is also presented to show its effect on the turbulent properties of fiber suspension flow. It is shown that the deviation of turbulent velocity profile from that of a Newtonian flow increases with an increase in Reynolds number and fiber concentration. Also, the extend of buffer layer increases at higher Re. Using the calculated turbulent velocity profile, the values of constant in logarithmic velocity profile is proposed for fiber suspension. Finally, a discussion is presented on the variation of turbulent intensities and Reynolds stress with Reynolds number and fiber concentration.

Streamwise-constant large-scale structures in Couette and Poiseuille flows

The linear amplification mechanisms leading to streamwise-constant large-scale structures in laminar and turbulent channel flows are considered. A key feature of the analysis is that the Orr--Sommerfeld and Squire operators are each considered separately. Physically this corresponds to considering two separate processes: (i) the response of wall-normal velocity fluctuations to external forcing; and (ii) the response of streamwise velocity fluctuations to wall-normal velocity fluctuations. In this way we exploit the fact that, for streamwise-constant fluctuations, the dynamics governing the wall-normal velocity are independent of the mean velocity profile (and therefore the mean shear). The analysis is performed for both plane Couette flow and plane Poiseuille flow; and for each we consider linear amplification mechanisms about both the laminar and turbulent mean velocity profiles. The analysis reveals two things. First, that the most amplified structures (with a spanwise spacing of approximately $4h$, where $h$ is the channel half height) are to a great extent encoded in the Orr-Sommerfeld operator alone, thus helping to explain their prevalence. Second---and consistent with numerical and experimental observations---that Couette flow is significantly more efficient than Poiseuille flow in leveraging wall-normal velocity fluctuations to produce large-scale streamwise streaks.

Resolvent analysis of turbulent channel flow with manipulated mean velocity profile

Using the resolvent analysis, we investigate how the near-wall mode primarily responsible for the friction drag is amplified or suppressed depending on the shape of the mean velocity profile of a turbulent channel flow. Following the recent finding by Kuhnen et al. (2018), who modified the mean velocity profile to be flatter and attained¨ significant drag reduction, we introduce two types of artificially flattened turbulent mean velocity profiles: one is based on the turbulent viscosity model proposed by Reynolds and Tiederman (1967), and the other is based on the mean velocity profile of laminar flow. A special care is taken so that both the bulk and friction Reynolds numbers are unchanged, whereby only the effect of change in the mean velocity profile can be studied. These mean velocity profiles are used as the base flow in the resolvent analysis, and the response of the wavenumber-frequency mode corresponding to the near-wall coherent structure is assessed via the change in the singular value (i.e., amplification rate). The flatness of the modified mean velocity profiles is quantified by three different measures. In general, the flatter mean velocity profiles are found to result in significant suppression of near-wall mode. Further, increasing the mean velocity gradient in the very vicinity of the wall is found to have a significant importance for the suppression of near-wall mode through mitigation of the critical layer.

Numerical Simulation of Flow between Two Parallel Co-Rotating Discs

The study of fluid flow between two rotating discs aims to predict flow characteristics. In this paper numerical simulation is used to investigate axisymmetric swirling flow between two parallel co-rotating discs. Methodology entails, firstly, inputing parameters from CFD software are into previos study developed dimensionless radial velocity model for flow between two discs to obtain dimensional radial velocity of the model. Secondly, previous study parameters are used to perform numerical simulation on laminar and turbulent flows between two parallel co-rotating discs. The numerical simulation results are compared to previous study results. Then comparative numerical simulations was carried out on laminar and turbulent flows using CFD software. Results obtained showed that for the this study dimensional radial velocity and previous study dimensionless radial velocity, radial velocity distribution increase proportionately from the disc surface at 0m/s to 2208.00m/s and 0 to 0.0002396 respectively, at the domain centre. And both results satisfy initial inlet and boundary conditions with resultant parabolic profiles. In the study, it is shown that turbulent flow radial velocity profile is smoother than for laminar flow. The radial velocity increases from 0 at the walls to 0.15m/s before decreasing to - 0.2m/s at the mid-centre for laminar flow while for turbulent flow the radial velocity intitially increases from 0 at the walls to 0.15m/s before decreasing to -0.06m/s at the discs centre; while for laminar flow, swirl velocity decrease from approximately 2.55m/s to 0.55m/s and for turbulent flow the swirl velocity decrease from approximately 2.84m/s to 1.62m/s. The turbulent flow swirl velocity profile seen to be smoother than for laminar flow around the discs centre. The study further showed that for fluid near the discs surfaces radial velocity net momentum is radially towards the outlet with flow laminar in the boundary layer region and the velocity turbulent towards the domain centre. For static pressure, laminar flow maximum and minimum static pressure 2.48pa and -0.033pa respectively, while for turbulent flow maximum and minimum static pressure were 0.00 and -0.0024pa. The developed previous study model can therefore be used to predict radial velocity distribution between steady axisymmetric flow between two parallel co-rotating discs.

Improved roughness model for turbulent flow in 2D viscous‐inviscid panel methods

AbstractThe present study presents a modified expression for the turbulent skin friction coefficient (Cf) in 2D viscous‐inviscid panel methods. The modified Cf expression includes surface roughness effects and is therefore believed to be an improvement to the modelling of leading edge roughness (LER) effects on airfoils. The basis for the study is the two‐equation viscous formulation used in 2D viscous‐inviscid panel methods, where the standard integral momentum and kinetic energy shape parameter equations are solved together with a number of turbulent closures. One of the closures relates the skin friction coefficient with the shape parameter and the momentum thickness Reynolds number. The relation is derived from Coles' law of the wake, which reasonably accurately describes any 2D turbulent boundary layer velocity profile. This is used to derive a new Cf‐expression with the Prandtl‐Schlichting sand grain roughness effect included, which is implemented in the Q3UIC code. Simulations on a NACA63‐418 profile with sand grain roughness on the forward part are compared with measurements and show an improved agreement with the measurements.

Turbulent Drag Reduction Characteristics of Bionic Nonsmooth Surfaces with Jets

Aiming at aerodynamic drag reduction for transportation systems, a new active surface is proposed that combines a bionic nonsmooth surface with a jet. Simulations were performed in the computational fluid dynamics software STAR-CCM+ to investigate the flow characteristics and drag reduction efficiency. The SST K-Omega model was used to enclose the equations. The simulation results showed that when the active surface simultaneously reduced the skin friction and overcame the sharp increase of pressure drag caused by a common nonsmooth surface, the total net drag decreased. The maximum drag reduction ratio reached 19.35% when the jet velocity was 11 m/s. Analyses of the turbulent kinetic energy, pressure distribution, and velocity profile variations showed that the active surface reduced the peak pressure on the windward side of the nonsmooth unit cell, thereby reducing the total pressure drag. Moreover, the recirculation formed in the unit cell transformed the fluid–wall sliding friction into fluid–fluid rolling friction like a rolling bearing, thereby reducing the skin friction. This study provides a new efficient way for turbulent drag reduction to work.

Effect of the wing trailing-edge flaps and spoilers position on the jet-vortex wake behind an aircraft during takeoff and landing run

The large-scale vortex structure of flow in the near wake behind an aircraft during its run on a runway is investigated numerically. The geometrical aircraft configuration was taken close to a mid-range commercial aircraft like Boeing 737-300. It included all essential elements: a body (fuselage), wings with winglets, horizontal and vertical stabilizers, engine nacelles, nacelle pylons, inboard flap track fairings, leading-edge and trailing-edge flaps, and spoilers. The position of flaps and spoilers corresponded to the takeoff and landing run conditions. Computational simulation was based on solving the Reynolds averaged Navier–Stokes equations closed with the Menter Shear Stress Transport turbulence model. Patterns of streamlines, fields of the axial vorticity and the turbulent intensity, vertical and horizontal velocity profiles in the wake are compared and discussed for both run regimes. The flow model was preliminary tested for validity by comparison of the calculated velocity profiles behind a reduced-scale aircraft model with those obtained in special wind tunnel experiments.

Characteristics of the pressure fluctuations generated in turbulent boundary layers over rough surfaces

Experiments were carried out in high Reynolds number turbulent boundary layers over rough surfaces of diverse geometries. Roughness configurations varied in element height, distribution (random versus ordered), shape and spacing. Rough surfaces comprising of two superposed element geometries were also tested. All flows were free of transitional effects with upwards of 40 000 and ratios above 73. The wall-pressure spectrum and turbulent velocity profiles revealed that the roughness element spacing has the greatest impact on the turbulent structures in the boundary layer. The high-frequency scaling on shear friction velocity, , (Meyers et al.J. Fluid Mech., vol. 768, 2015, pp. 261–293) was validated and was shown to be the viscous contribution to the overall surface drag. An empirical formula for the pressure drag on roughness elements was developed to reflect the finding that the pressure drag is a function of only two variables: sparseness ratio and roughness Reynolds number . Results also suggest that the viscous contribution to drag approaches a constant non-zero value at high Reynolds numbers, and ‘fully rough-wall flow’ may occur at higher than previously thought.

Numerical study of air-water two-phase flow in a two-dimensional vertical helical channel

In this study, air-water two-phase flow patterns in a two-dimensional vertical helical channel are investigated. The simulations are performed using OpenFOAM software. The single-fluid method and Eulerian−Eulerian approach are used to solve the governing equations. The paper focuses on different flow patterns based on the change in the apparent velocity of water and air, and the influence of volume fraction of the air at the entrance of the channel. The variations of turbulent kinetic energy, volume fraction and velocity profile are presented. The range of air and water apparent velocities at the channel entrance is 0.05–10 m s−1 and 0.1–1.5 m s−1, respectively. According to the results, four flow patterns including bubbly, churn, turbulent, and annular are observed. It is demonstrated that for the bubbly regime, the values of volume fraction of phases are close to unity. When the air inlet velocity is very high, the two-phase flow forms the annular flow pattern.

Saddle-node bifurcations of traveling waves in the asymptotic suction boundary layer flow

Finite-amplitude traveling wave solutions in the asymptotic suction boundary layer are computed for different wall permeabilities. The permeability has negligible effect on the Reynolds number at which they emerge, but it affects their shape and amplitude and the turbulent flow velocity profile.

Self-similar hierarchies and attached eddies

It is demonstrated that time-evolving coherent structures with features consistent with Townsend's attached eddies and the developments associated with the reconstruction of flow statistics using the attached eddy hypothesis can be obtained from analysis of the (linear) resolvent operator associated with the Navier-Stokes equations. A discrete number of members of a single self-similar hierarchy, chosen by assuming a constant ratio of critical layer heights between neighboring members with overlapping wall-normal footprints, produces a geometrically self-similar, fractal-like structure of the spatial distribution of the velocity field and an associated signature of uniform momentum zones. The range of convection velocities associated with the hierarchy gives rise to time evolution of the velocity. The scaling of the streamwise wave number on a hierarchy can be reconciled with Townsend's distance-from-the-wall scaling for self-similar, attached eddies, at least conceptually, by considering coherent spatial structures in the velocity field and thus enforcing an exact equivalence between compared features. It has been shown previously that both the linear and nonlinear terms in the resolvent framework have self-similar representations in the logarithmic overlap region of the turbulent mean velocity profile. The conditions under which self-sustaining self-similar behavior may be obtained from self-similar hierarchical members in this region are elaborated and some similarities with other results and theories associated with self-similarity in this region are identified.

Diameter Effect on the Wall Temperature Behaviors During Supercritical Water Heat Transfer Deterioration in Circular Tubes and Annular Channels

Diameter effect on heat transfer deterioration (HTD) was numerically studied for supercritical water flowing upward in circular tubes and annular channels at high heat flux and low mass flux based on validated turbulence model. When the same boundary conditions were applied, i.e. heat flux, mass flux, and inlet temperature, it was found that in circular tubes the first wall temperature peak moves upstream and the magnitude of the peak increases first and then decreases with the increase of tube diameter, the second peak moves downstream with the increase of tube diameter. Whereas in annular channels with a fixed inner diameter, HTD is suppressed when the outer diameter is small and HTD occurs gradually with the increase of outer diameter. These phenomena are consistent with previous experimental results. The mechanism was analyzed based on fully developed turbulent velocity profile at the inlet of the heated sections. Increasing inner diameter for circular tubes or outer diameter for annular channels will result in the decrease of maximum velocity and velocity gradient in the near wall region, which makes velocity profile in this region much easier to be flattened by the buoyancy. Then an M-shaped velocity profile is formed, which will significantly decrease the Reynolds shear stress and turbulent kinetic energy and hence impair the heat transfer and cause HTD. For the same flow conditions, HTD is much easier to occur in circular tubes than in annular channels with the same hydraulic diameters.