Case Of Turbulent Flow Research Articles

Slip velocity of rigid fibers in turbulent channel flow

In this study, the slip velocity between rigid fibers and a viscous carrier fluid is investigated for the reference case of turbulent channel flow. The statistical moments of the slip velocity are evaluated modelling fibers as prolate spheroids with Stokes number, St, ranging from 1 to 100 and aspect ratio, λ, ranging from 3 to 50. Statistics are compared one-to-one with those obtained for spherical particles (λ = 1) to highlight effects due to fiber elongation. Comparison is also made at different Reynolds numbers (Reτ =150, 180, and 300 based on the fluid shear velocity) to discuss effects due to an increase of turbulent fluctuations. Results show that elongation has a quantitative effect on slip velocity statistics, particularly evident for fibers with small St. As St increases, differences due to the aspect ratio tend to vanish and the relative translational motion between individual fibers and surrounding fluid is controlled by fiber inertia through preferential concentration. A clear manifestation of inertial effects is the different distribution of slip velocities for fibers trapped in sweep/ejection events and for fibers segregated in near-wall fluid streaks. The corresponding conditional probability distribution functions, shown here for the streamwise and wall-normal slip velocity components, are found to be non-Gaussian, thus suggesting that fiber motion relative to the fluid in high-shear flow regions may not be modelled as a pure diffusion process with constant diffusion coefficient. For the range of simulation parameters investigated, no significant Reynolds number effects are observed, indicating that fiber dynamics exhibit a scaling behavior with respect to the shear velocity up to Reτ =300.

Turbulent drag reduction through oscillating discs

AbstractThe changes in a turbulent channel flow subjected to sinusoidal oscillations of wall flush-mounted rigid discs are studied by means of direct numerical simulations (DNS). The Reynolds number is ${Re}_{\tau }=180$, based on the friction velocity of the stationary-wall case and the half-channel height. The primary effect of the wall forcing is the sustained reduction of wall-shear stress, which reaches a maximum of 20 %. A parametric study on the disc diameter, maximum tip velocity, and oscillation period is presented, with the aim of identifying the optimal parameters which guarantee maximum drag reduction and maximum net energy saving, the latter computed by taking into account the power spent to actuate the discs. This may be positive and reaches 6 %. The Rosenblat viscous pump flow, namely the laminar flow induced by sinusoidal in-plane oscillations of an infinite disc beneath a quiescent fluid, is used to predict accurately the power spent for disc motion in the fully developed turbulent channel flow case and to estimate localized and transient regions over the disc surface subjected to the turbulent regenerative braking effect, for which the wall turbulence exerts work on the discs. The Fukagata–Iwamoto–Kasagi identity is employed effectively to show that the wall-friction reduction is due to two distinguished effects. One effect is linked to the direct shearing action of the near-wall oscillating-disc boundary layer on the wall turbulence, which causes the attenuation of the turbulent Reynolds stresses. The other effect is due to the additional disc-flow Reynolds stresses produced by the streamwise-elongated structures which form between discs and modulate slowly in time. The contribution to drag reduction due to turbulent Reynolds stress attenuation depends on the penetration thickness of the disc-flow boundary layer, while the contribution due to the elongated structures scales linearly with a simple function of the maximum tip velocity and oscillation period for the largest disc diameter tested, a result suggested by the Rosenblat flow solution. A brief discussion on the future applicability of the oscillating-disc technique is also presented.

Particle tracking in LES flow fields: conditional Lagrangian statistics of filtering error

In this paper, we examine the conditional Lagrangian statistics of the pure filtering error, which affects particle tracking in large-eddy simulations of wall-bounded turbulence. A-priori tests are performed for the reference case of turbulent channel flow, and statistics are computed along the trajectory of many particles with different inertia, initially released in near-wall regions where either a sweep event or an ejection event is taking place. It is shown that the Lagrangian probability density function (PDF) of the filtering error is, in general, different from the Eulerian one, computed at fixed grid points. Lagrangian and Eulerian PDFs become similar only in the long-time limit, when the filtering error distribution is strongly non-Gaussian and intermittent. Results also show that the distribution of the short-time error in the homogeneous directions can be approximated by a Gaussian function. Due to flow anisotropy effects, which are particularly significant for small-inertia particles, such approximation does not hold in the wall-normal direction.

Numerical Heat Transfer Analysis in Vertical Rectangular Channels in the Core of a Typical Nuclear Research Reactor

Numerical Heat Transfer Analysis in Vertical Rectangular Channels in the Core of a Typical Nuclear Research Reactor The heat transfer characteristics for the case of turbulent forced and mixed convection flow of water through narrow vertical rectangular heated channel simulating a cooling channel of a typical material testing reactor (MTR) have been analysed and numerically investigated. Numerical solutions are performed on demineralized water as coolant passing under atmospheric pressure through narrow rectangular channel of 80 cm length, 7 cm width, and 2.7 mm gap thickness under different heat fluxes that covers almost all possible heat fluxes in the single-phase liquid. Qualitative results are presented for the normalized temperature and velocity profiles in the transverse direction with a comparison between the forced and mixed convection flow for the cases of upward directions. The effect of the axial locations and the parameter Gr/Re on the variation of the normalized temperature profiles in the transverse direction for both the regions of forced and mixed convection and for the upward and downward flow directions are obtained. The normalized velocity profiles in the transverse directions are also determined at different inlet velocities and heat fluxes for the previous cases. A Computational Fluid Dynamics (CFD) study will bring much understanding of the phenomena for the different situations.

Rotation statistics of fibers in wall shear turbulence

In this paper, the rotation of rigid fibers is investigated for the reference case of turbulent channel flow. The aim of the study is to examine the effect of local shear and turbulence anisotropy on the rotational dynamics of fibers with different elongation and inertia. To this aim, statistics of the fiber angular velocity, Ω, are extracted from direct numerical simulation of turbulence at shear Reynolds number Reτ = 150 coupled with Lagrangian tracking of prolate ellipsoidal fibers with Stokes number, St, ranging from 3 to 100 and aspect ratio, λ, ranging from 1 to 50. Accordingly, the fiber-to-fluid density ratio ranges from \({S \simeq 7}\) (for St = 1, λ = 50) to \({S \simeq 3, 470}\) (for St = 100, λ = 1). Statistics are compared one to one with those obtained for spherical particles to highlight effects due to elongation. Results for mean and fluctuating angular velocities show that elongation is important for fibers with small inertia (St ≤ 5 in the present flow-fiber combination). For fibers with larger inertia, elongation has an impact on fiber rotation only in the streamwise and wall-normal directions, where mean values of Ω are zero. It is also shown that, in the center of the channel, the Lagrangian autocorrelation coefficients of Ω and corresponding rotational turbulent diffusivities match the exponential behavior predicted by the theory of homogeneous dispersion. In this region of the channel, the probability density function of fiber angular velocities is generally close to Gaussian, indicating that particle rotation away from solid walls can be modeled as a diffusion process of the Ornstein–Uhlenbeck type at stationary state. In the strong shear region (comprised within a distance of 50 viscous units from the wall in the present simulations), fiber anisotropy adds to flow anisotropy to induce strong deviations on fiber rotational dynamics with respect to spherical particles. The database produced in this study is available to all interested users at https://www.fp1005.cism.it.

A finite-volume gas-kinetic method for the solution of the Navier-Stokes equations

AbstractGas-kinetic theory is also valid in the continuum regime: the Euler and Navier-Stokes equations can be obtained as projection of the Boltzmann equation on to the physical space (x,t). The numerical schemes derived from gas-kinetic theory are computationally more expensive than Navier-Stokes based ones, but offer advantages which have been attracting a growing level of attention: they can (i) accommodate discontinuities at cells interface, (ii) provide high-resolution fluxes, (iii) provide advantages in the simulation of turbulence, (iv) handle hypersonic and/or rarefied flows. This study extends the validation of gas-kinetic schemes investigating a few turbulent flow cases. At a slightly higher computational cost, gas-kinetic schemes provide results comparable to those obtained with well-validated Navier-Stokes schemes using the same turbulence model, grid and reconstruction order. In the case of shock-separated flows, the results obtained with the gas-kinetic scheme are even closer to experimental data. These findings are consistent with the idea that gas-kinetic theory is a physically more consistent framework for investigating the mechanics of fluids.

Direct numerical simulations of local and global torque in Taylor–Couette flow up to Re = 30 000

AbstractThe torque in turbulent Taylor–Couette flows for shear Reynolds numbers $R{e}_{S} $ up to $3\times 1{0}^{4} $ at various mean rotations is studied by means of direct numerical simulations for a radius ratio of $\eta = 0. 71$. Convergence of simulations is tested using three criteria of which the agreement of dissipation values estimated from the torque and from the volume dissipation rate turns out to be most demanding. We evaluate the influence of Taylor vortex heights on the torque for a stationary outer cylinder and select a value of the aspect ratio of $\Gamma = 2$, close to the torque maximum. The local transport resulting in the torque is investigated via the transverse current ${J}^{\omega } $ which measures the transport of angular momentum and can be computed from the velocity field. The typical spatial distribution of the individual convective and viscous contributions to the local torque is analysed for a turbulent flow case. To characterize the turbulent statistics of the transport, probability density functions (p.d.f.s) of local current fluctuations are compared with experimental wall shear stress measurements. P.d.f.s of instantaneous torques reveal a fluctuation enhancement in the outer region for strong counter-rotation. Moreover, we find for simulations realizing the same shear $R{e}_{S} \geq 2\times 1{0}^{4} $ the formation of a torque maximum for moderate counter-rotation with angular velocities ${\omega }_{o} \approx - 0. 4\hspace{0.167em} {\omega }_{i} $. In contrast, for $R{e}_{S} \leq 4\times 1{0}^{3} $ the torque features a maximum for a stationary outer cylinder. In addition, the effective torque scaling exponent is shown to also depend on the mean rotation state. Finally, we evaluate a close connection between boundary-layer thicknesses and the torque.

Discrete Tracer Point Method to Evaluate Turbulent Diffusion in Circular Pipe Flow

Diffusion of a solute in turbulent flows through a circular pipe or tunnel is an important aspect of environmental safety. In this study, the diffusion coefficient of turbulent flow in circular pipe has been simulated by the Discrete Tracer Point Method (DTPM). The DTPM is a Lagrangian numerical method by a number of imaginary point displacement which satisfy turbulent mixing by velocity fluctuations, Reynolds stress, average velocity profile and a turbulent stochastic model. Numerical simulation results of points’ distribution by DTPM have been compared with the analytical solution for turbulent plug-flow. For the case of turbulent circular pipe flow, the appropriate DTPM calculation time step has been investigated using a constantβ, which represents the ratio between average mixing lengths over diameter of circular pipe. The evaluated values of diffusion coefficient by DTPM have been found to be in good agreement with Taylor’s analytical equation for turbulent circular pipe flow by givingβ=0.04 to 0.045. Further, history matching of experimental tracer gas measurement through turbulent smooth-straight pipe flow has been presented and the results showed good agreement.

Statistical description of turbulent dispersion

We derive a comprehensive statistical model for dispersion of passive or almost passive admixture particles such as fine particulate matter, aerosols, smoke, and fumes in turbulent flow. The model rests on the Markov limit for particle velocity. It is in accordance with the asymptotic structure of turbulence at large Reynolds number as described by Kolmogorov. The model consists of Langevin and diffusion equations in which the damping and diffusivity are expressed by expansions in powers of the reciprocal Kolmogorov constant C_{0}. We derive solutions of O(C_{0}^{0}) and O(C_{0}^{-1}). We truncate at O(C_{0}^{-2}) which is shown to result in an error of a few percentages in predicted dispersion statistics for representative cases of turbulent flow. We reveal analogies and remarkable differences between the solutions of classical statistical mechanics and those of statistical turbulence.

Numerical Simulation of a Turbulent Flow Over a Backward Facing Step With Heated Wall: Effect of Pulsating Velocity and Oscillating Wall

An accurate prediction of the flow and the thermal boundary layer is required to properly simulate gas to wall heat transfer in a turbulent flow. This is studied with a view to application to gas turbine combustors. A typical gas turbine combustion chamber flow presents similarities with the well-studied case of turbulent flow over a backward facing step, especially in the near-wall regions where the heat transfer phenomena take place. However, the combustion flow in a gas turbine engine is often of a dynamic nature and enclosed by a vibrating liner. Therefore apart from steady state situations, cases with an oscillatory inlet flow and vibrating walls are investigated. Results of steady state and transient calculations for the flow field, friction coefficient, and heat transfer coefficient, with the use of various turbulence models, are compared with literature data. It has been observed that the variations in the excitation frequency of the inlet flow and wall vibrations have an influence on the instantaneous heat transfer coefficient profile. However, significant effect on the time mean value and position of the heat transfer peak is only visible for the inlet velocity profile fluctuations with frequency approximately equal to the turbulence bursting frequency.

Convective heat transfer equation for turbulent flow in tubes applied to internal combustion engines operated under motored conditions

An equation developed for the case of turbulent flow in tubes was applied for the study of convective heat transfer in internal combustion engines. Calculated average heat flux values under motored conditions were compared to measurements, results available in the literature obtained by using a computational fluid dynamics (CFD) code and the correlations of Woschni and Annand. Cumulative heat flux values for the four models were also compared to measurements at the end of the compression stroke and start of expansion. Average heat transfer rates were found to be predicted with reasonable accuracy by the proposed model. The major advantage of this equation compared to the correlations of Woschni and Annand is that it does not require any corrections for specific engine characteristics or working conditions. The proposed model was found to correctly predict higher heat transfer rates as engine speed, load and compression ratio were increased. Accuracy at the end of the compression stroke was found to be within acceptable limits for the cumulative heat flux, comparable to that of the CFD code, except for one case of the seven different engines investigated. Therefore, this model can be used to predict spatial average convective heat flux values with fairly good accuracy under motored conditions, when limited information on engine geometry is available, or when computing resources are required to be minimal.

Gear Dynamics Analysis With Turbulent Journal Bearings Under Quadratic Damping and Nonlinear Suspension—Bifurcation and Chaos

This study performs a systematic analysis of the dynamic behavior of the gear for the gear-bearing system with the turbulent flow effect, quadratic damping effect, nonlinear suspension effect, nonlinear oil-film force, and complicated gear mesh force. The dynamic orbits of the system are observed using bifurcation diagrams plotted using the dimensionless unbalance coefficient and the dimensionless rotational speed ratio as control parameters. The onset of chaotic motion is identified from the phase diagrams, power spectra, Poincaré maps, Lyapunov exponents, and fractal dimension of the gear-bearing system. The ignorance of quadratic damping effect for turbomachineries especially in turbulent cases may cause significant errors. The proposed simulation model and theory may provide some useful information for engineers in designing or controlling some turbomachineries particularly in turbulent flow cases.

Turbulence and internal waves in stably-stratified channel flow with temperature-dependent fluid properties

AbstractDirect numerical simulation (DNS) is used to study the behaviour of stably-stratified turbulent channel flow with temperature-dependent fluid properties: specifically, viscosity ($\ensuremath{\mu} $) and thermal expansion coefficient ($\ensuremath{\beta} $). The governing equations are solved using a pseudo-spectral method for the case of turbulent water flow in a channel. A systematic campaign of simulations is performed in the shear Richardson number parameter space (${\mathit{Ri}}_{\tau } = \mathit{Gr}/ {\mathit{Re}}_{\tau } $, where $\mathit{Gr}$ is the Grashof number and ${\mathit{Re}}_{\tau } $ the shear Reynolds number), imposing constant-temperature boundary conditions. Variations of ${\mathit{Ri}}_{\tau } $ are obtained by changing ${\mathit{Re}}_{\tau } $ and keeping $\mathit{Gr}$ constant. Independently of the value of ${\mathit{Ri}}_{\tau } $, all cases exhibit an initial transition from turbulent to laminar flow. A return transition to turbulence is observed only if ${\mathit{Ri}}_{\tau } $ is below a threshold value (which depends also on the flow Reynolds number). After the transient evolution of the flow, a statistically-stationary condition occurs, in which active turbulence and internal gravity waves (IGW) coexist. In this condition, the transport efficiency of momentum and heat is reduced considerably compared to the condition of non-stratified turbulence. The crucial role of temperature-dependent viscosity and thermal expansion coefficient is directly demonstrated. The most striking feature produced by the temperature dependence of viscosity is flow relaminarization in the cold side of the channel (where viscosity is higher). The opposite behaviour, with flow relaminarization occurring in the hot side of the channel, is observed when a temperature-dependent thermal expansion coefficient is considered. We observe qualitative and quantitative modifications of structure and wall-normal position of internal waves compared to previous results obtained for uniform or quasi-uniform fluid properties. From the trend we observe in the investigated low-Reynolds-number range, we can hypothesize that, whereas the effects of temperature-dependent viscosity may be masked at higher Reynolds number, the effects of temperature-dependent thermal expansion coefficient will persist.

A simple procedure for calculating the mean and maximum bed stress under wave and current conditions for rough turbulent flow based on method

In the marine environment, particularly on continental shelves, the processes of wave dissipation and sediment transport depend crucially on the bed shear stress. When waves and currents are superimposed the bed shear stress exhibits non-linear behaviour such that it is insufficient to simply sum vectorially the wave-alone and current-alone stress components. Soulsby and Clarke (2005) [Bed shear-stresses under combined waves and currents on smooth and rough beds. Report TR 137. HR Wallingford, Wallingford, UK, 22 pp.] developed a simple analytical, non-iterative method for calculating the mean and maximum bed shear stress in combined wave and current flows. For rough turbulent flow their method produces non-linearities in the mean and maximum bed stress that are consistent with those measured, while it under-predicts the non-linearities in the bed stresses in comparison with model predictions. Here their method is generalised such that it may be used to predict non-linearities in the bed stresses that are consistent with either the measurements or the models, for the case of rough turbulent flow. Also the Soulsby and Clarke method relies on the fact that the depth-averaged current is already known. However, in the field it is often the case that the current at a particular height above the bed is measured, so here their method is reposed in terms of a current measured at a particular height. A MATLAB script is provided for this modified Soulsby and Clarke method, such that either strong or weak non-linearity can be included in the wave–current interaction and the current can be input at a particular height or as a depth average.

Derivation from the Field Equation of the Mean Consumption Velocity for Front Propagation in Homogeneous Turbulent Flow

Based on purely geometrical considerations of the level sets of the scalar G(x, t) satisfying the field equation ( G - equation), A. Kerstein, T. Ashurst and F. Williams [Phys. Rev. A, 37, 2728, (1988)] derived the expression for the mean flame consumption velocity in a 1D premixed turbulent flame in a homogeneous flow of uniform density in terms of the volume average of |▽ G(x, t)| for a particular choice of the initial condition G(x, t = 0). In the present study we develop further the KAW work in two directions. First, in section 2, in contrast with the KAW approach, we consider the G - equation immediately and, using ensemble averaging, obtain the expression for the mean flame consumption velocity in terms of ensemble averages equivalent to the KAW result. Then, in section 3 the developed approach is applied to the case of homogeneous turbulent flow with a uniform mean strain rate field depending only on time.

Extension of the momentum transfer model to time-dependent pipe turbulence

We analyze a possible extension of Gioia and Chakraborty's momentum transfer model of friction in steady turbulent pipe flows [Phys. Rev. Lett. 96, 044502 (2006)] to the case of time- and/or space-dependent turbulent flows. The end result is an expression for the stress at the wall as the sum of a steady and a dynamic component. The steady part is obtained by using the instantaneous velocity in the expression for the stress at the wall of a stationary flow. The unsteady part is a weighted average over the history of the flow acceleration, with a weighting function similar to that proposed by Vardy and Brown [J. Sound Vibr. 259, 1011 (2003); J. Sound Vibr. 270, 233 (2004)], but naturally including the effect of spatial derivatives of the mean flow, as in the Brunone model [Brunone et al., J. Water Res. Plan. Manage. 126, 236 (2000)].

The effect of conceptual and contextual familiarity on transfer performance

Applying a previously learned concept to a novel problem is an important but difficult process called transfer. It is suggested that a commonsense analogy aids in transfer by linking novel concepts to familiar ones. How the context of practice affects transfer when learning using analogies is still unclear. This study investigated the effect of a commonsense analogy and context familiarity for transfer of physiological concepts. First year psychology students (n = 24) learned three concepts: Starling's law, Laplace's law, and laminar-turbulent flow. The control group saw standard explanations while the intervention group saw an additional commonsense analogy. The context of learning was the organ system used for two practice clinical cases which differed for all concepts. Testing consisted of 12 new clinical cases. Starling's law cases used the organ system from practice while the other concepts presented in both novel and familiar organ systems. Half of the sample repeated testing after 1 week delay. The outcome was ratings of explanations of cases on a 0-3 scale. The effect of analogy was significant (Mean = 1.24 with, 0.86 without, F(1,22) = 4.26, p < 0.05) but not after delay (means of 1.08 and 0.75 respectively, F = (1,10), p = 0.06) There was significant effect for familiar context (Same = 1.23 (Starling), different = 0.68 (Laplace) and 0.73 (laminar-turbulent flow) (F(2,44) = 5.14, p < 0.01). Laplace's law and laminar turbulent flow cases in the familiar organ system had means of 1.65 and 1.77 respectively compared to novel cases with means of 0.74 and 0.68 (F(1,22) = 35.64, p < 0.0001). Similar effects were observed after delay. There was significant decay in performance after delay for all participants (immediate = 1.17, delayed = 0.91, F = 11.9 (1,10) p < 0.01). Common analogies aid conceptual understanding necessary for transfer. Despite conceptual aids, solving transfer problems is difficult.

The Design of Heat Exchangers

A relation between heat transferred and energy loss, for turbulent flow. In different tube arrangements, is made. The conditions are determined which decide the dimensions and velocities for a heat exchanger. Also, a reference to the economic dimensioning of heat exchangers is presented. In this study, the conditions which a heat exchanger must satisfy represent the best balance between the amounts of material employed. The investigation is restricted to the case of turbulent flow.

Computation of the Turbulent Flow in a Square Duct Using a Cubic Low-Reynolds Stress Model

The aim of this work is to predict numerically the turbulent flow through a straight square duct using a nonlinear stress-strain model. The paper considers the application of the Craft et al.'s model [Craft, Launder, and Suga (1996)] to the case of turbulent incompressible flow in a straight square duct. In order to handle wall proximity effects, damping functions are introduced. Using a priori and a posteriori investigations, we show the performance of this model to predict such flows. The analysis of the flow anisotropy is made using the anisotropy-invariant map proposed by Lumley and Newman [Lumley and Newman (1977)]. This map shows the various possible states of the turbulence. The mean flow field and the turbulent statistics are compared with existing numerical and experimental data for square and rectangular duct flows. Overall, the model performance is shown to be satisfactory. In particular, the mean secondary velocity field and the streamwise vorticity are well predicted.

Impact of location and flow rate oscillation of the pilot jet on the flow structures in swirling premixed flames

The paper investigates the swirling flow structures in an unconfined coannular swirl burner under different conditions, namely, with or without heat release, two locations of the pilot jet, and constant or pulsating mass flow rate in the pilot jet. Six turbulent premixed swirling flames as well as two isothermal turbulent swirling flow cases for reference are studied with the aid of large-eddy simulation. Detailed comparisons with experimental data are performed for velocity statistics, and generally good agreement is achieved. Furthermore, coherent structures are analyzed, and local power spectra are computed. In the nonreactive case with retracted pilot jet, a very strong precessing vortex core (PVC) is observed in both the numerical result and the experiment. The PVC is weak in the nonretracted case. In the reactive cases in which the whole central recirculation zone is enclosed in the high-temperature postflame region, the PVC is almost completely suppressed. In pulsating reactive jets, the vortex str...