Maximum Turbulent Kinetic Energy Research Articles

Numerical studies on air flow around a cube

In this paper, air approach flow moving towards a cube will be studied using computational fluid dynamics (CFD). The Reynolds Averaging of Navier–Stokes (RANS) equation types of k – ε turbulence model are used. Some RANS predicted results are compared with different upstream air speeds. Flow separation at the corner above the top of the cube, level of separation and reattachment are investigated. Reference is made to the experimental data on wind tunnels reported in the literature. A method similar to ‘recirculation bubble promoter’ is used for different approach flow speed distributions. Problems encountered in numerical simulations due to the sharp corner are discussed with a view to obtaining better prediction on recirculation flow in regions above the top of the cube. Correlations between the turbulent kinetic energy above the cube and the recirculation bubble size are derived for different distributions of approach flow speed. By limiting the longitudinal velocities in the first cell adjacent to the sharp edge of the cube or rib, and making good use of the wall functions at the intersection cells of the velocity components, positions of maximum turbulent kinetic energy and the flow separation and reattachment can be predicted by a standard k – ε model. The results agree with those obtained in the experiments.

Turbulence Structure of Hydraulic Jumps of Low Froude Numbers

Turbulence characteristics of hydraulic jumps with Froude numbers of 2.0, 2.5, and 3.32 are presented. A Micro Acoustic Doppler velocimeter was used to obtain measurements of the velocities, turbulence intensities, Reynolds stresses, and power spectra. The maximum turbulence intensities and Reynolds stress at any section were found to decrease rapidly from the toe of the jump towards downstream within the jump and then gradually level off in the transition region from the end of the jump to the friction dominated open channel flow downstream. The maximum turbulence kinetic energy at each section decreases linearly with the longitudinal distance within the jump and gradually levels off in the transition region. The Reynolds stress and turbulence intensities within the jump show some degree of similarity. The dissipative eddy size was estimated to vary from 0.04 mm within the jump to 0.15 mm at the end of the transition region. The dominant frequency is in the range from 0 to 4 Hz for both horizontal and vertical velocity components.

Coupled radiation and turbulent multiphase flow in an aluminised solid propellant rocket engine

We present in this paper numerical simulations of coupled radiative transfer and turbulent flows at high temperature and pressure, typical of multiphase flows encountered in aluminised solid propellant rocket engines. The radiating medium is constituted of gases and of liquid or solid particles of oxidised aluminum. The turbulent flow of the gaseous phase is treated by using a four equation, low Reynolds number, boundary-layer-type turbulence model. The distributions of concentrations, temperatures, and temperature fluctuation variances of particles are calculated from a Lagrangian approach and a turbulence dispersion model. Thermal and mechanical non-equilibrium between the gas and different classes of particles is allowed. A locally one dimensional, iteratively based, radiative transfer solver is developed to compute wall fluxes and radiative source terms. It is shown that the thermal boundary layer attenuates significantly the radiative fluxes coming from the outer regions. Particle radiation is found to be much more important than gas radiation. Turbulent dispersion of particles in the boundary layer induces a decrease of particle concentration in the region of maximum turbulent kinetic energy, and then, decreases the attenuation effect of wall fluxes due to the boundary layer. The effects of turbulent temperature fluctuations are found to be small in the problem under consideration.

Some aspects of the effect of surface friction on flows over mountains

AbstractThe effect of surface friction on flow over mountains in stratified fluids is investigated using a two‐dimensional version of the Naval Research Laboratory's non‐hydrostatic Coupled Ocean/Atmosphere Mesoscale Prediction System (COAMPS). Without surface friction, flow over a mountain attains a maximum speed at the surface on the lee slope. With surface friction, the flow speed vanishes at the surface and reaches a maximum near the top of the boundary layer (BL). Corresponding to this wind distribution is a shallow layer of very large vertical wind shear beneath the jet maximum and a weaker but deeper sheared layer elsewhere. This strong shear generates maximum turbulent kinetic energy (TKE) at the jet maximum region. Meanwhile, the buoyancy effect associated with the mountain gravity wave inhibits the production of the TKE above the jet maximum region. The combined effects of shear and buoyancy lead to a very shallow BL on the lee slope. In general, surface friction reduces the amplitude of mountain gravity waves. Comparison of the flow fields with the outline of the BL height indicates that flow characteristics correspond closely to the distribution of the BL height. It is hypothesized that the reduction in mountain‐wave amplitude in the presence of surface friction is due to the reduction in the slope of the BL height as compared to the terrain height. For narrower and/or higher mountains, the BL height exhibits a secondary peak on the lee side that further modifies the wave. Simulations using the BL height as a solid mountain without surface friction confirm that characteristics of flow over the mountain are associated with the distribution of BL height rather than the terrain height field. As the non‐dimensional mountain height increases, the magnitude of the effect of surface friction decreases due to decreasing BL depth on the lee side, with the result that the BL height profile becomes closer to the terrain height field.The effect of surface friction on asymmetric mountains is also investigated. Without surface friction, the pressure drag shows distinctive reduction with a secondary peak on the downstream side, but the effect is less when the secondary peak is on the upstream side. With surface friction, all three mountains have similar pressure drag, corresponding to their similar BL height profiles. Copyright © 2003 Royal Meteorological Society

Flow structure around a 3-D rectangular prism in a turbulent boundary layer

Flow around a three-dimensional (3-D) rectangular prism has been investigated by using a particle image velocimetry technique. The prism was immersed in a thick turbulent boundary layer. The ratio of the boundary layer thickness and the model height was about 0.06. Measurements were made at Reynolds number of 7.9×10 3 which is based on free stream velocity and model height. Detailed flow structures and characteristics including three circulation zones were obtained by averaging over a large number of instantaneous velocity maps. The 3-D structure in a wake zone is clearly seen from mean flow streamline topology. Turbulent kinetic energy distribution is also obtained approximately. Maximum turbulent kinetic energy was found at the separated layer in the upper boundary of the separation bubble near the leading edge of a roof. The magnitude of the maximum energy is about 2.5 times that in the wake region.

Justifying the WKB approximation in pure katabatic flows

Pure katabatic flow is studied with a Prandtl-type model allowing eddy diffusivity/conductivity to varywith height. Recently we obtained an asymptotic solution to the katabatic flow assuming the validity ofthe WKB method, which solves the fourth-order governing equation coupling the momentum and heat transfer. The WKB approximation requires that eddy diffusivity may vary only gradually compared to the calculated quantities, i.e., potential temperature and wind speed. This means that the scale heightfor eddy diffusivity must be higher than that for the calculated potential temperature and wind speed. The ratio between the maximum versus the mean eddy diffusivity should be less than that for the scale heights of the diffusivity versus the calculated quantities (temperature and wind). Here we justify(a posteriori) the WKB method independently based on two arguments: (i) a scaling argument and (ii )a philosophy behind a higher-order closure turbulence modeling. Both the eddy diffusivity maximum and the level of the relevant maximum turbulent kinetic energy are above the strongest part of the near surface inversion and the low-level jet which is required for the WKB validity. Thus, the numerical modeling perspective lends credibility to the simple WKB modeling. This justification is important before other data sets are analyzed and a parameterization scheme written.

On the evolution of maximum turbulent kinetic energy production in a channel flow

The Reynolds number effects on turbulent kinetic energy production and mean transport terms in near-wall turbulent channel flow are investigated analytically and with the help of direct numerical simulations (DNS). Using the momentum equation for turbulent channel flow, an analytical expression for the envelope of turbulent kinetic energy production curves is derived. It is shown that this envelope coincides with the wall-normal position at which the turbulent and viscous shear stress are equal. The DNS results carried out corroborate this finding and assess other quantitative details, namely the evolution of the peak of kinetic energy production and of its wall-normal position in terms of the Reynolds number. Empirical relations for the envelopes of the mean momentum transport terms and for their extrema position are also derived.

Justifying the WKB approximation in pure katabatic flows

Pure katabatic flow is studied with a Prandtl-type model allowing eddy diffusivity/conductivity to varywith height. Recently we obtained an asymptotic solution to the katabatic flow assuming the validity ofthe WKB method, which solves the fourth-order governing equation coupling the momentum and heattransfer. The WKB approximation requires that eddy diffusivity may vary only gradually compared tothe calculated quantities, i.e., potential temperature and wind speed. This means that the scale heightfor eddy diffusivity must be higher than that for the calculated potential temperature and wind speed. The ratio between the maximum versus the mean eddy diffusivity should be less than that for thescale heights of the diffusivity versus the calculated quantities (temperature and wind). Here we justify(a posteriori) the WKB method independently based on two arguments: (i) a scaling argument and (ii )a philosophy behind a higher-order closure turbulence modeling. Both the eddy diffusivity maximumand the level of the relevant maximum turbulent kinetic energy are above the strongest part of the nearsurfaceinversion and the low-level jet which is required for the WKB validity. Thus, the numericalmodeling perspective lends credibility to the simple WKB modeling. This justification is importantbefore other data sets are analyzed and a parameterization scheme written.

The Atmospheric Boundary-Layer Structure Within A Cold Air Outbreak: Comparison Of In Situ, Lidar And Satellite Measurements With Three-Dimensional Simulations

A cold-air outbreak over the Mediterranean, associated with a Tramontane event, has been simulated with the atmospheric non-hydrostatic model Meso-NH using a horizontal resolution of 2 km. Results are compared with in situ aircraft, airborne lidar and satellite measurements. On average, the mean and turbulent parameters simulated in the surface layer and mixed layer compared well with in situ measurements. The model was able to reproduce accurately the Foehn effect in the wake of Cape Creus, as well as the occurence of rolls in the coastal region in connection with cloud streets observed with AVHRR. Over the sea, the threshold value of turbulent kinetic energy defining the height of the atmospheric boundary-layer top in the model (defined as 25% of the maximum turbulent kinetic energy in the profile) enables the simulated atmospheric boundary-layer height to match the one retrieved from lidar measurements. Nevertheless, the model did not handle very well the abrupt gradients of all meteorological parameters observed at the top of the atmospheric boundary-layer. Reasons for this are investigated.

Computational fluid dynamics modelling of boundary roughness in gravel‐bed rivers: an investigation of the effects of random variability in bed elevation

AbstractResults from a series of numerical simulations of two‐dimensional open‐channel flow, conducted using the computational fluid dynamics (CFD) code FLUENT, are compared with data quantifying the mean and turbulent characteristics of open‐channel flow over two contrasting gravel beds. Boundary roughness effects are represented using both the conventional wall function approach and a random elevation model that simulates the effects of supra‐grid‐scale roughness elements (e.g. particle clusters and small bedforms). Results obtained using the random elevation model are characterized by a peak in turbulent kinetic energy located well above the bed (typically at y/h = 0·1–0·3). This is consistent with the field data and in contrast to the results obtained using the wall function approach for which maximum turbulent kinetic energy levels occur at the bed. Use of the random elevation model to represent supra‐grid‐scale roughness also allows a reduction in the height of the near‐bed mesh cell and therefore offers some potential to overcome problems experienced by the wall function approach in flows characterized by high relative roughness. Despite these benefits, the results of simulations conducted using the random elevation model are sensitive to the horizontal and vertical mesh resolution. Increasing the horizontal mesh resolution results in an increase in the near‐bed velocity gradient and turbulent kinetic energy, effectively roughening the bed. Varying the vertical resolution of the mesh has little effect on simulated mean velocity profiles, but results in substantial changes to the shape of the turbulent kinetic energy profile. These findings have significant implications for the application of CFD within natural gravel‐bed channels, particularly with regard to issues of topographic data collection, roughness parameterization and the derivation of mesh‐independent solutions. Copyright © 2001 John Wiley & Sons, Ltd.

Turbulent flow in stirred vessels agitated by a single, low-clearance hyperboloid impeller

Detailed angle-resolved measurements of the mean and rms of the three components of the velocity vector were carried out by laser-Doppler anemometry in a stirred vessel mechanically agitated by a ribbed, low power consumption hyperboloid impeller at a Reynolds number of 50,000. Due to the small clearance of the agitator the flow pattern in the vessel was typical of that encountered when using an axial turbine although the flow in the vicinity of the impeller was alike that in a radial device with the mean flow discharge following a λ- type pattern. In most of the vessel the flow was gentle with mean velocities of the order of 5% of the tip velocity, increasing to about 20% V imp towards the tip of the impeller because of the ribs. Their small size limited the extent of periodic flow to a region delimited by the bottom and z/ R=0.2 in the vertical direction, and r/ R=0.85–1.4 in the radial direction, plus the volume below the impeller. In these regions the turbulence was not isotropic and reached the highest values so that the maximum turbulence kinetic energy was 65% higher than for the corresponding hyperboloid flow in the absence of shear ribs.

Modifying a reattaching shear layer using a rotating cylinder

The interaction between an incompressible turbulent reattaching flow over a 2D backward facing step and a rotating cylinder mounted after the step was investigated numerically. The flow field was solved using the finite element numerical method and the RNG turbulence model. The effects of the cylinder rotational speed and position on the reattachment length and normalized maximum turbulent kinetic energy are reported and discussed. The rotating cylinder could be used to control the flow field, both locally and globally.

Modified Reattaching Shear Layer Using a Stationary Cylinder

The problem of an incompressible turbulent reattaching flow over a 2-D backward facing step with a cylinder mounted after the step was investigated numerically. The flow field was solved using the finite element numerical method with the RNG turbulence model. The effects of the cylinder diameter and position on the reattachment length, recirculation velocity, maximum axial velocity, and normalized maximum turbulent kinetic energy are reported and discussed. The cylinder could be used to modify the flow field.

Reattachment of Turbulent Shear Layer over a Backward Facing Step with Isotropic Porous Floor Segments

The incompressible turbulent reattaching flow over a 2-D backward facing step with different length porous floor segments was solved numerically using the finite element numerical method. The accuracy of the numerical solution was established by comparing the numerical results to experimental measurements reported in the literature. Three different floor configurations with different normalized length isotropic porous segments, Xp = 4, 8, and 12, were studied. The porosity of each segment was varied over a wide range by changing the value of the pressure loss coefficient (KP). The variation of the normalized reattachment length (Xr), normalized maximum recirculation velocity (Urec), and normalized maximum turbulent kinetic energy (TKE) are reported and discussed for all configurations. The results show that, depending on the length and loss coefficient of the segments, a floor with porous segments can significantly change the values of Xr, Urcc, and TKE.

Incompressible Turbulent Reattaching Shear Layer Flow Over a Backward Facing Step with Orthotropic Porous Floor Segments

The incompressible turbulent reattaching flow over a 2-D backward facing step with different length porous floor segments was investigated numerically. The flow field was solved using the finite element numerical method and the RNG turbulence model. The porous segment can be used to model solid fuel being entrained by the incoming flow in a combustor. The effect of the porous segment length, depth, and anisotropic and orthotropic pressure loss coefficient on the normalized reattachment length (Xr), normalized maximum recirculation velocity (Urec), and normalized maximum turbulent kinetic energy (TKE) are reported and discussed. Depending on the combination of segment length, depth, pressure loss coefficient, and orthotropicity, a floor with porous segments can be used to change the location and magnitude Xr, Urec, and TKE.

Large eddy simulation of longitudinal stationary vortices

The response of longitudinal stationary vortices when subjected to random perturbations is investigated using temporal large-eddy simulation. Simulations are obtained for high Reynolds numbers and at a low subsonic Mach number. The subgrid-scale stress tensor is modeled using the dynamic eddy-viscosity model. The generation of large-scale structures due to centrifugal instability and their subsequent breakdown to turbulence is studied. The following events are observed. Initially, ring-shaped structures appear around the vortex core. These structures are counter-rotating vortices similar to the donut-shaped structures observed in a Taylor–Couette flow between rotating cylinders. These structures subsequently interact with the vortex core resulting in a rapid decay of the vortex. The turbulent kinetic energy increases rapidly until saturation, and then a period of slow decay prevails. During the period of maximum turbulent kinetic energy, the normalized mean circulation profile exhibits a logarithmic region, in agreement with the universal inner profile of Hoffman and Joubert [J. Fluid Mech. 16, 395 (1963)].

The Flow Inside a Model Gas Turbine Combustor: Calculations

The present study assesses the ability of the k-ε turbulence model to calculate the flow inside gas turbine combustors. Results of calculations using a cylindrical system of coordinates, hybrid differencing, and a mesh with about 40,000 nodes are compared with velocity measurements of the flow inside a perspex model of can-type gas turbine combustor. The larger discrepancies between measurements and predictions were found in the primary region. The complexity of the flow near the primary jet impingement led to underprediction of the maximum negative axial velocity and turbulence kinetic energy by about 35 and 20 percent, respectively. The calculated results exhibited higher levels of momentum diffusion compared to the experiments and did not show the two contrarotating vortices created between the primary jets; no qualitative agreement with the azimuthal velocity downstream of the primary jets could be achieved. Despite these deficiencies, the model gave acceptable results in other regions of the combustor and correct prediction of the main features of the combustor flow was possible.

LDV Measurements of Periodic Fully Developed Main and Secondary Flows in a Channel With Rib-Disturbed Walls

Laser-Doppler velocimeter measurements of mean velocities, turbulence intensities, and Reynolds stresses are presented for periodic fully developed flows in a channel with square rib-disturbed walls on two opposite sides. Quantities such as the vorticity thickness and turbulent kinetic energy are used to characterize the flow. The investigated flow was periodic in space. The Reynolds number based on the channel hydraulic diameter was 3.3×104. The ratios of pitch to rib-height and rib-height to chamber-height were 10 and 0.133, respectively. Regions where maximum and minimum Reynolds stress and turbulent kinetic energy occurred were identified from the results. The growth rate of the shear layers of the present study was compared with that of a backward-facing step. The measured turbulence anisotropy and structure parameter distribution were used to examine the basic assumptions embedded in the k–ε and k–ε–A models. For a given axial station, the peak axial mean-velocity was found not to occur at the center point. The secondary flow was determined to be Prandtl’s secondary flow of the second kind according to the measured streamwise mean vorticity and its production term.

Mean flow and turbulence measurements in a half-delta wing vortex

A subsonic experimental study has been conducted to examine the mean and turbulent properties of a single longitudinal vortex generated by a half-delta wing. Measurements were made on fine cross-plane grids at seven streamwise locations using hot cross-wires. The evaluated streamwise vorticity contours indicated that the initially distorted vortex at a streamwise station equivalent to a half wing height became round by about three wing heights. In this initial "transition" region, where the vortex was still rolling-up, the peak vorticity dropped by about 50% following a X-1/2 decay. In this region, the generator wake remained distinct from the region of maximum vorticity, although the two regions were seen to slowly merge together. The Reynolds stress contours were also distorted initially with the maximum values occurring in the generator wake region, rather than in the vortex core, but these also decayed rapidly. Downstream of the transition region, the vortex appeared to reach an equilibrium state with the regions of maximum vorticity and turbulent kinetic energy coincident and the levels approximately constant with increasing streamwise distance. Comparison with previous data on vortices produced by double-branched generators further confirmed that the present vortex had achieved a fully developed state, and in a relatively short streamwise distance.

Velocity characteristics in the turbulent near wakes of confined axisymmetric bluff bodies

Measurements of the velocity characteristics and wall pressure are reported for the axisymmetric turbulent flow downstream of three bluff bodies (disks of 25% and 50% area blockage and a cone of 25% blockage) confined by a long pipe. The dimensions of the recirculation regions were found from the mean-velocity components, which were determined by a laser-Doppler velocimeter: the corresponding components of Reynolds stress were also recorded. The lengths and maximum widths of the recirculation bubbles (in bluff-body diameters), recirculating mass-flow rates (normalized by the average velocity in the plane of the baffle, U0, and the baffle diameter) and maximum turbulent kinetic energy (normalized by U02) were as follows: cone 1.55, 0.55, 0.19, 0.11; disk (25% blockage) 1.75, 0.62, 0.31, 0.19; disk (50% blockage) 2.20, 0.55, 0.26, 0.16. The increase in recirculation length with blockage is opposite to the trend in unconfined, annular jets. The distribution of Reynolds stresses is strongly dependent on blockage: for the smaller blockage both the disk and the cone have the maximum value of kinetic energy near the rear stagnation point. It is proposed that this is because the generation of turbulence by normal stresses is more important in the flow consequent on the smaller blockage.The measurements include profiles of the velocity characteristics at, as well as upstream of, the trailing edges of the baffles for use as boundary conditions in numerical solutions of the equations of motion.