Planar Jet Flow Research Articles

Heat and mass transfer analysis of a Maxwell-power-law fluid in a laminar planar jet flow with Cattaneo–Christov double diffusion theory

This paper focuses on the heat and mass transfer characteristics of a steady laminar planar jet flow of a Maxwell-power-law (MPL) fluid. MPL is a renowned fluid model with shear thinning and viscoelastic characteristics that can accurately exhibit the rheological features of polymer liquids. In the envisioned study, the MPL constitutive equation is introduced based on an experiment utilizing the Xanthan gum solution. The heat and mass equations are supported by the Cattaneo–Christov double diffusion (CCDD) concept with unique characteristics of thermal conductivity, mass diffusion, and chemical reaction. Thermal conductivity and mass diffusion coefficient are considered to be velocity gradient-dependent. The problem is addressed numerically by the bvp4c method in Matlab after applying the similarity transformations to the governing equations. The impacts of related parameters on velocity, temperature, and concentration are analyzed. Results show that an upsurge in the power-law index hinders momentum, energy, and mass transmission. An interesting phenomenon is that the variation in relaxation time can hinder or promote the heat and mass transfer of a Maxwell-power-law fluid jet before or after the intersection point, respectively. The study can provide a theoretical reference for engineering applications of jets.

Single cavitation bubble dynamics in a stagnation flow

Jetting of collapsing bubbles is a key aspect in cavitation-driven fluid–solid interactions as it shapes the bubble dynamics and additionally due to its direct interaction with the wall. We study experimentally and numerically the near-wall collapse and jetting of a single bubble seeded into the stagnation flow of a wall jet, i.e. a jet that impinges perpendicular onto a solid wall. High-speed imaging shows rich and rather distinct bubble dynamics for different wall jet flow velocities and bubble-to-wall stand-off distances. The simulations use a volume-of-fluid method that allows us to numerically determine the microscopic and transient pressures and shear stresses on the wall. It is shown that a wall jet at moderate flow velocities of a few metres per second already shapes the bubble ellipsoidally inducing a planar and convergent jet flow. The distinct bubble dynamics allow us to tailor the wall interaction. In particular, the shear stresses can be increased by orders of magnitude without increasing impact pressures the same way. Interestingly, at small seeding stand-offs, the bubble during the final collapse stage can lift off the wall and migrate against the flow direction of the wall jet such that the violent collapse occurs away from the wall.

Comparison of Turbulence Models in Simulation of Plane Jet Flow

Plane turbulent jets are widely used in a variety of applications. Such as jets in drying processes, air curtains for room conditioning, heating, mixing, ventilating applications etc., therefore, jet flow is a very important research topic in both experimental and analytical research.
 Depending upon the position and forces acts on the jet, jets are broadly classified as turbulent free jet and turbulent wall jet. The studies conducted herein provide the comparison between various turbulence model present Computational Fluid Dynamics(CFD). Numerical approaches were used in the present investigation. CFD technique helped to understand better the hydrodynamics of the jet flow and correlate the numerical result.
 Among the all turbulence model studied, the k-ε turbulence model performed the best. Performance of k-ω model was found to be somewhat superior to Spalart-Allmaras and Reynolds stress model.

Direct numerical simulation of planar turbulent jets: Effect of a pintle orifice

The effects of a pintle-shaped orifice on a planar turbulent jet flow at Reynolds number 4000, based on the inlet bulk mean velocity and the jet width, are studied using direct numerical simulations. Flapping of the jet along with a low-frequency modulation of the Kelvin–Helmholtz (KH) instability, in the presence of a pintle-shaped orifice, is observed. To compare the pintle-jet behavior, a free-jet is simulated as a reference case. The effects of the near-field region on the far-field flow characteristics have been investigated. In both the cases, the KH instability in the near-field influences the far-field jet, whereas the pintle-jet also exhibits a low-frequency flapping. In addition, oblique vortex pattern has been observed in the case of pintle-jet. The far-field flow statistics of the pintle-jet with a top-hat inlet interestingly agree with those of the free-jet with a hyperbolic tangent inlet. Temporal variation of the jet characteristics has been analyzed using spatiotemporal plots. In addition, the large- and small-scale turbulent motion have been studied using three anisotropic invariant maps (turbulence triangles, eigenvalue, and barycentric maps). Moreover, that the barycentric map gives a better visualization of the anisotropic behavior has been observed in the current study.

Evolution of instability modes and spreading characteristics of a planar jet flow under long-wave excitations

Switching phenomenon and parametric resonance have been identified in near field flows subjected to high-frequency controlled perturbations. This study reports the correlation between switching phenomenon, parametric resonance, and spreading characteristics caused by the instability modes after the end of the potential core of a planar jet (far field). Two periodically oscillating strips were used to control perturbations in free shear layers and three different long-wave excitations (i.e., symmetric, antisymmetric, and one-sided) were imposed at the excitation frequency (fe). The excitation frequency was fixed relative to the preferred mode frequency (fp) at fe = fp/4. To investigate the evolution of coherent structures, frequency spectral analysis and phase correlation were applied to hot-wire anemometer measurements. Under symmetric excitation, the instability mode of vortical structures is observed twice at mode switching, retaining the in-phase pattern. Jet puffing occurs when the cross correlation R12(0) is positive at the far field. These features cause vortex shedding to remain symmetric and suppresses the flapping motion of the jet. However, out-of-phase behavior reoccurs under antisymmetric and one-sided excitations and the cross correlation R12(0) becomes a negative after the end of the potential core. As a result, flapping motion is enhanced and the jet spreads wider after the end of the potential core.

Comparison of the mean skin friction with the heat transfer and the flow development in turbulent planar wall-attaching jet flows.

Measurements of the mean skin friction below turbulent planar wall-attaching offset jet flows were performed using oil-film interferometry for jets initially offset (Hs) 0.2 to 1 times the jet height (Hj) from the wall. The results were compared with turbulent flow field measurements and with previous heat transfer measurements. The profiles of the mean skin friction coefficient below the offset or preattachment region were similar when compared relative to the distance to the reattachment location (Xr). The initial recovery length of the mean skin friction downstream of the reattachment location was proportional to the reattachment length similar to the decrease in the wall pressure fluctuations in this region. The longer recovery and initial decay of the mean skin friction coefficient appeared to collapse in terms of (x-Xr)/Hj; as did the initial change in the mean static pressure, the measures of the mean flow development, and the Stanton number downstream of the reattachment point. The decay in the maximum of the turbulent stresses associated with the attached shear layer also collapsed in terms of (x-Xr)/Hj, unlike the fluctuating pressure and initial recovery of the mean skin friction. The change in the location of the minimum and zero in the turbulent shear stress as the flows transitioned to the wall jet region collapse in terms of x-Xr/Hj similar to the longer recovery and initial decay of the mean skin friction. The mean skin friction for flows with Hs of Hj and jet Reynolds numbers (Rej) of 21800 to 54500, varied as Rej-0.2 below the attaching jet, in the reattachment region, and in the downstream wall jet region.

Numerical analysis of the flow in a cylindrical container injected air from a slit nozzle

This paper describes the flow characteristics of air injected from a slit nozzle in a cylindrical container. The numerical simulation was performed by the large-eddy simulation (LES) using ANSYS Fluent 19.0 based on the finite-volume method. The non-dimensional nozzle offset distance was set to yn/D = 0.4, where D is the diameter of the cylindrical container. The Reynolds number of the plane jet flow was settled at 2,000. The velocity profiles by the numerical simulation agreed with the experimental results. The jet reached near the bottom of container, and the jet flowed out from the left side of container. Although the flow in the cylindrical container showed a three-dimensional turbulent flow structure, the mean velocity field was generated symmetrically with respect to the central cross-section of the container perpendicular to the slit nozzle. The large recirculating flow around the z-axis occurred near the central cross-section of the container by the jet. In addition, the weak recirculated flows around the y-axis were observed near the upper side wall in the container.

Reaction Engineering Approach to Turbulence Modelling—Universal Law of the Wall, Pipe Flow, and Planar Jet Flow

Although engineering turbulence modeling is a well-established field, there is room for new ideas. In the current work, the rate of Reynolds stress generation is considered the product of a probability coefficient dependent on the viscous effect over the inertia effect and an energetic parameter expressed in terms of velocity dependence. The rate of Reynolds stress dissipation is defined as a simple second-order power function; this function emphasizes the nature of the local interactions (molecular level at their origins) that are similar to those for the reaction. Hence, the current approach can be called a reaction engineering approach for turbulence. Examples analyzed with this approach are: 1) the Universal Law of the Wall; 2) diameter-wide axial velocity distribution of the circular pipe (internal flow); 3) bulk behavior of the axial velocity distribution for a turbulent planar jet (external flow); and 4) far-field axial velocity distribution for a planar jet with numerical simulations. These findings suggest the potential of this approach for future exploration.

Robust dynamic adaptation of the Smagorinsky model based on a sub-grid activity sensor

The present study deals with the application of a sub-grid activity sensor to an eddy viscosity type base model in the context of Large Eddy Simulation (LES). The coherent structure function is used to build this sensor in combination with explicit test filtering. The proposed sensor features two main advantages: First, it attenuates the sub-grid scale dissipation of the base model for transitional flows. Depending on local conditions, the sensor is essentially blending the eddy viscosity between zero and the value resulting from the standard Smagorinsky model. Second, the sensor rectifies the incorrect near-wall scaling of the standard Smagorinsky model. Application of the sensor requires no averaging (in the homogeneous direction) and is easy to implement, and the additional computational cost is insignificant. In order to assess the model, three different configurations have been examined: laminar-to-turbulent transition in the Taylor–Green vortex, wall-dominated channel flows, and a free planar jet flow including passive scalar mixing. Based on a posteriori LES, it has been found that the new sensor-enhanced Smagorinsky model often outperforms established eddy viscosity models from the literature, such as the standard Smagorinsky model and the sigma model, as well as the LES without the explicit sub-grid model.

Corrigendum to "Local similarity solution for steady laminar planar jet flow of viscoelastic FENE-P fluids" [Journal of Non-Newtonian Fluid Mechanics 279 (2020) 104265

Corrigendum to "Local similarity solution for steady laminar planar jet flow of viscoelastic FENE-P fluids" [Journal of Non-Newtonian Fluid Mechanics 279 (2020) 104265

Local similarity solution for steady laminar planar jet flow of viscoelastic FENE-P fluids

Three local self-similar solutions are obtained for the laminar planar jet flow of viscoelastic fluids, described by the FENE-P constitutive equation, through an order of magnitude simplification of the governing equations. The more general solution is shown to be more accurate than two further simplified solutions, here called the delta and the Olagunju-type solutions, at least for the profiles of conformation tensor components. In the limit of vanishing viscoelasticity, all conformation tensor components reduce to the same low elasticity asymptotic behavior, and the polymer stresses become Newtonian-like. The general solution is then used to obtain the laws of the decay of the centerline velocity and of the growth of the jet half-width and to ascertain the effects of the Weissenberg number, maximum polymer extensibility parameter and the ratio of polymer to total viscosities upon the flow characteristics. The general local self-similar solution compares well with results of numerical simulations obtained by the RheoFoam module of the freeware OpenFoam code.

Large Eddy Simulation of Planar Free Jet Flow Using the Space-Time Conservation Element/Solution Element Scheme

In order to investigate the characteristics of planar free jet flows, the Monotonically Integrated Large Eddy Simulation (MILES) method with the high-resolution space-time conservation element/solution element (CE/SE) scheme was used to simulate the two-dimensional free jet flows. For free jet flows within the Reynolds number range 35300~2200, the flow structures, averaged and instant velocity, turbulence intensity, velocity profiles of different cross-sections were examined respectively. The simulation results agree well with the experiment data. A region of constant height exists right after the jet outlet, in which the average centerline velocity and turbulence intensity maintains same with the jet outlet, and the instant fluctuation amplitudes are also small. For turbulent flows, the length of the undisturbed region is equal to the length of region of constant height. While near the laminar region, the length of undisturbed region is slightly larger than the length of zone of constant height. The vortex structures start to generate after the undisturbed region, develop coherently in the region of flow establishment, and break down gradually in the region of fully established flow region. As the Reynolds number increases, the length of zone of constant height, the length of undisturbed region and the length of potential core region all decrease correspondingly.

Assessment of Numerical Simulation Capabilities of the Fire Dynamics Simulator (FDS 6) for Planar Air Curtain Flows

Computational Fluid Dynamics (CFD) results are discussed for momentum driven planar jet flows, resembling configurations in use for air curtain in the context of smoke control in building fire. The CFD package Fire Dynamics Simulator (FDS) is used. Special focus is given to the impact of grid resolution, synthetic turbulent inflow boundary condition and sub-grid scale eddy viscosity models. The computational results are compared with summarized literature data. Investigation of different set-ups of inlet boundary conditions, including the inlet duct length, velocity profile and method of generation of turbulence at the level of the inflow, reveals that the inlet boundary condition is the most influential factor governing the flow downstream. The FDS results successfully reproduce the planar jet flows, both in terms of mean variables and second-order statistics. ‘Reference’ results have been obtained with a fully developed turbulent flow emerging from a long inlet duct. By reducing the inlet duct length and applying the Synthetic Eddy Method (SEM) at the inflow boundary condition, the ‘reference’ results have been reproduced with a reduction in the computing times of approximately 20%. However, care must be taken when choosing the parameters of SEM, in particular the number of eddies and their length scale. The impact of turbulent viscosity model is noticeable, but not of primary importance for the flow at hand, provided that a sufficiently fine computational mesh is used.

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.

Subgrid-scale scalar flux modelling based on optimal estimation theory and machine-learning procedures

ABSTRACTNew procedures are explored for the development of models in the context of large eddy simulation (LES) of a passive scalar. They rely on the combination of the optimal estimator theory with machine-learning algorithms. The concept of optimal estimator allows to identify the most accurate set of parameters to be used when deriving a model. The model itself can then be defined by training an artificial neural network (ANN) on a database derived from the filtering of direct numerical simulation (DNS) results. This procedure leads to a subgrid scale model displaying good structural performance, which allows to perform LESs very close to the filtered DNS results. However, this first procedure does not control the functional performance so that the model can fail when the flow configuration differs from the training database. Another procedure is then proposed, where the model functional form is imposed and the ANN used only to define the model coefficients. The training step is a bi-objective optimisation in order to control both structural and functional performances. The model derived from this second procedure proves to be more robust. It also provides stable LESs for a turbulent plane jet flow configuration very far from the training database but over-estimates the mixing process in that case.

Numerical study on rarefied unsteady jet flow expanding into vacuum using the Gas-Kinetic Unified Algorithm

The unsteady process of rarefied jet flows expanding into a vacuum is numerically solved by the Gas-Kinetic Unified Algorithm (GKUA) based on the Boltzmann model equations. The discrete velocity ordinate method (DVOM) is adopted to discretize the velocity space of the molecular velocity distribution function, while the corresponding numerical integral technique is developed to evaluate macroscopic flow variables, including number density, flow velocity, temperature and so on. The time-explicit finite difference scheme is constructed to capture the unsteady evolution of the discrete velocity distribution functions at each DVO point by using the unsteady time-splitting method. The multi-block docking grid technique is designed for different regions of flow field in physical space with self-adaptive adjustment. Then, the supersonic planar jet flows with the wide range of Knudsen numbers, from 100 to 0.1, are solved numerically and discussed, including startup to steady state and shutting down. The GKUA results of free-molecule jet flows are analyzed and compared with the Maxwellian analytical solutions for collisionless plume flows, in which good agreement shows the validity and accuracy of the present numerical method. When taking the collision effect into account, the unsteady jet flows with different Knudsen numbers are computed by the present GKUA method. It is shown that the collision term of the Boltzmann model equation plays an important role in this rarefied gas diffusion into the back flow when Kn ≤ 10. However, the colliding relaxation term have a little influence on the kernel region in the startup process for Kn ≥ 0.1. In general, the convective transport term of the Boltzmann model equation dominates the kernel region of the jet flow during the unsteady process of gas expanding into a vacuum. The numerical experience indicates that the present GKUA can provide a vital tool for solving unsteady flow problems covering various flow regimes by directly tracing the time evolution of the Boltzmann-type velocity distribution function.

Numerical Study of Two Dimensional Laminar Jet Flow Past a Sudden Expansion

A computational study of laminar plane jet flow past a plane symmetric sudden expansion configuration is presented. The dependence of asymmetric flow instability on the velocity profile at the expansion region has been studied. This variation in velocity profile at the expansion region is brought about by varying the length of the inlet duct. The attachment lengths of the jet for a range of Reynolds number (Re) values and aspect ratios (ratio of duct width to jet width) have been presented. An in-house two dimensional incompressible flow code has been developed for solving the problem. The Critical Reynolds Number (Recr) at which jet develops asymmetry with respect to mid-plane of the channel for a certain aspect ratio, increases as the inlet duct length is decreased. Hence, this indicates that the stability of the jet increases with the decrease in the inlet duct length. The shorter attachment length (SAL) remains nearly constant with increase in Re but longer attachment length (LAL) increases with increase in Re for various aspect ratios.

Impinging planar jet flow on a horizontal surface with slip

The flow of a planar jet (sheet) impinging onto a solid flat plate with slip is examined theoretically. The jet is assumed to spread out in a thin layer bounded by a hydraulic jump, and draining at the edge of the plate. In contrast to an adhering jet, a slipping jet does not admit a similarity solution. Taking advantage of the different scaling in each region, series expansions are used in the developing and fully viscous layers, which are matched at the transition point. We show that a slipping film exhibits a singularity in the normal stress at the leading edge of the boundary layer, as opposed to the singularity in velocity and shear stress for an adhering film. The boundary-layer and film heights are both found to decrease with slip relative to a smooth substrate, roughly like $\sqrt{30x/Re}-2S$, whereas the slip velocity intensifies like $S\sqrt{Re/30x}$ with slip. Here, $x$ is the distance along the plate, $S$ is the slip length and $Re$ is the Reynolds number (in units of the jet width). The transition is delayed by slip. Guided by the measurements of Duchesne et al. (Europhys. Lett., vol. 107, 2014, p. 54002) for a circular adhering jet, the hydraulic-jump height and location are determined for a planar jet, and are found to increase with the Froude number (flow rate) like $Fr^{1/4}$ and $Fr^{5/8}$ respectively, essentially independently of slip length.

Numerical Calculation of Interaction Between Plane Jet and Subsonic Flow

Numerical Calculation of Interaction Between Plane Jet and Subsonic Flow

Numerical investigation of a gas–solid turbulent jet flow with Reynolds number of 4500 using lattice Boltzmann method

The gas–solid two-phase turbulent plane jet flow with high Reynolds number of 4500 was numerical investigated by means of lattice Boltzmann method (LBM). The multiple relaxation time (MRT) was employed to deal with the high Reynolds number fluid flows, and the particles were traced by the Lagrangian method. The results show that the flow changes from initial symmetric mode to asymmetric mode with the development of the flow. And asymmetric pattern appears first at the position of x/d=4, where the vortex structures begin to form. The dispersion of particles at different Stokes number shows various distributions. The MRT-LBM shows its good ability in simulating turbulent flow with the high Reynolds number.