Three-dimensional Wall Jet Research Articles

Effects of oscillated wall on the turbulent structure and heat transfer of three-dimensional wall jet

Effects of oscillated wall on the turbulent structure and heat transfer of three-dimensional wall jet

Budgets of Reynolds stresses in film cooling with fan-shaped and cylindrical holes

The compressible budget terms in the transport equations of Reynolds stresses are examined from the large eddy simulation (LES) result of the film cooling. The capability of LES and the statistical post-processing procedure were first validated. The compressible Reynolds stress budget terms are then analyzed for both fan-shaped and cylindrical cooling films. The balance of all budget terms is shown. The effect of the blowing ratio on each budget term is examined. The mechanisms by which energy is extracted from the mean flow and distributed among the normal Reynolds stresses are highlighted. The sources of anisotropy in the Reynolds stress distributions are examined in detail, and their relation to the flow patterns of the mean and instantaneous flow is explored. The downstream development of the Reynolds stress budgets is studied, and it is shown that the jets of both fan-shaped and cylindrical films can be split into a near field and a far field with different properties. Far downstream of the cooling films, the Reynolds stress budgets near the wall present similarities with the Reynolds stress budgets in a boundary layer, while the Reynolds stress budgets further away from the wall resemble budgets in a free-shear flow. It is shown that the budgets of the Reynolds stress in the three-dimensional wall jets object of this study obey approximate similarity laws. These laws are based on easily obtained integral scales but need to be modified by suitable powers of the distance from the orifice producing the jet.

Scaling and similarity laws in three-dimensional wall jets

Wall jets appear in many situations of technological and scientific interest. In gas turbines, flows produced by the film as well as impingement cooling devices are three-dimensional wall jets. High-lift devices produce flows that can easily be represented by two-dimensional wall jets. It has been known for a long time that wall jets in both stagnant and moving environments display a layered structure and only partially obey similarity laws. In this paper, we derive scaling laws and obtain self-similar velocity defect and Reynolds stress profiles for the outer part of three-dimensional wall jets in the high-Reynolds-number limit. The scaling laws are derived from prime principles under realistic assumptions about the behavior of the flow. We show that the leading term in an expansion of the turbulent kinetic energy (TKE) as a series of powers of the distance from the source must scale like the transversal velocity causing the jet to spread laterally. Only the second term in the TKE expansion is shown to scale like the square of the velocity defect. The scaling laws are tested on numerical and experimental data representing two commonly used film cooling devices.

Scaling laws for two- and three-dimensional wall jet scour based on the phenomenological theory of turbulence

The scour induced by wall jets may cause serious bed erosion and thus damage to hydraulic structures. Previous studies are largely empirical, providing only correlations of experimental data. At present, it is not clear what difference exists in the physical mechanisms of two-dimensional (2D) and three-dimensional (3D) wall jet scour. This study first summarizes previous efforts for predicting wall jet scour depths. Then, a scaling analysis is presented for investigating scour depths by applying the phenomenological theory of turbulence. It is shown that for wall jet cases, the dimensionless equilibrium scour depth can generally be expressed as a power function of the densimetric Froude number and relative roughness height, with the power index depending on jet configurations. The predictions of scour depth using the resulting formulas agree well with published data. The present analysis provides new insights into the understanding of the underlying physical mechanisms of wall jet scour as well as the difference between 2D and 3D configurations.

Flow Structure of a Three-Dimensional Turbulent Wall Jet

A numerical simulation is conducted to study the flow of a three-dimensional incompressible wall jet. The study is aimed to determine the flow structure and to compare the propagation mechanisms of turbulent and laminar wall jets. The numerical solution of the Navier–Stokes equations in the turbulent case is obtained using the wall-resolved large eddy simulation. The simulation results are compared with experimental data.

Influence of sidewalls on three-dimensional turbulent wall jet: An experimental and numerical approach

In this study, with the help of with and without sidewall configurations, experimental and numerical approaches are utilised to investigate the sidewall influence on a three-dimensional turbulent wall jet. The mean flow profile of the three-dimensional turbulent wall jet is measured through experimental method and compared with the numerical results. In addition, the numerical method is used to characterise the turbulence characteristics of the wall jet for both the configurations. A 200 mm square nozzle (height h=20 ± 0.5 mm) is used to generate the developing jet exit profile for the experimental results. The Reynolds number based on the jet exit velocity and nozzle height is 25,000. The numerical results are obtained by solving the Reynolds Average Navier stokes (RANS) equations with low Reynolds number k−ε turbulence models proposed by Yang and Shih and Launder and Sharma. The experimental results are obtained by a single probe hotwire anemometer and a K-type thermocouple. It is observed that the sidewall affects the temperature distribution just after the potential core region x/h=5 whereas the velocity distribution is affected in the fully developed region after the downstream location x/h=22.5. Sidewalls drastically influenced the thermal and velocity decay in wall-normal and lateral directions. It is found from the numerical simulation that the decay of maximum streamwise velocity is increased by 9%, whereas centerline temperature decay is decreased by 25% in sidewall configuration as compared to without sidewall configuration. The contour plots of temperature and velocity also exhibit the sidewall effect on the whole domain. The Reynolds shear stress <u′v′> dominates in the vertical jet centerline plane atz=0, whereas <u′w′> dominates in the lateral direction at ymax plane in both the configurations. On the vertical jet centerline plane at z=0, Reynolds shear stress <u′v′> is nearly increased by 10% in the presence of sidewall compared to without sidewall configuration. The entrainment of the ambient fluid initially decreases, but after the downstream location x/h=22.4, it increases for the case of the sidewall compared to the corresponding case without the sidewall. This happens owing to an increase in maximum turbulent kinetic energy generation inside the flow domain by 10%. The turbulent heat flux <T′V′> dominates in lateral and wall-normal shear layers in both the configurations. The correlations of decay of temperature and velocity are also suggested through numerical techniques.

Dependence of wall jet phenomenology on inlet conditions and near-field flow development

In this paper, the three-dimensional turbulent wall jet flow is investigated for three different developing initial velocity profiles. The developing initial velocity profiles at the nozzle exit are generated by three different lengths (, 50 and 90) of the square nozzle . The velocity profiles at the nozzle exit are measured with the single probe hot-wire anemometer. The Reynolds number based on the bulk mean velocity and nozzle height is 25,000 for all the cases. The measured velocity profiles at the nozzle exit are used as the inlet conditions for the numerical simulations. The results show that the initial velocity profile affects the flow field of the wall jet in near and far-field regions. It is found that the contours of streamwise velocity and turbulent kinetic energy exhibit the effect of initial conditions in the near field. The Reynolds shear stress component dominates in the vertical jet centreline plane, and it increases with a decrease in the nozzle length. The Reynolds shear stress component dominates in the lateral plane, and also exhibit the dependency on initial conditions.

Far Field of a Three-Dimensional Laminar Wall Jet

We consider a steady submerged laminar jet of viscous incompressible fluid flowing out of a tube and propagating along a solid plane surface. The numerical solution of Navier–Stokes equations is obtained in the stationary three-dimensional formulation. The hypothesis that at large distances from the tube exit the flowfield is described by the self-similar solution of the parabolized Navier–Stokes equations is confirmed. The asymptotic expansions of the self-similar solution are obtained for small and large values of the coordinate in the jet cross-section. Using the numerical solution the self-similarity exponent is determined. An explicit dependence of the self-similar solution on the Reynolds number and the conditions in the jet source is determined.

Experimental Study of the Sidewall Effect on Three-Dimensional Turbulent Wall Jet

Abstract An experimental study on the effect of sidewalls on the flow characteristics of a three-dimensional turbulent square wall jet is carried out at a Reynolds number of 25,000. The sidewalls are defined as the two parallel plates along the vertical jet centerline. Four different sizes of sidewall enclosure (here after referred to as ‘SWE’) are placed at the lateral positions (z) of ±3.5h, ±4h,±4.5h, and ±5h from the vertical jet centerline plane, where h is the height of square jet. The mean characteristics of fluid flow in wall normal (y) and lateral (z) directions at different downstream locations (x/h=0.2−45) are measured using a hotwire anemometer. The velocity measurements are also performed in the z – y lateral plane at four downstream locations (x/h=30, 35, 40, and 45). Results indicate that the mean velocity profile in lateral and wall normal directions behaves differently depending on the size of SWEs. The decay rate of the maximum mean velocity increases with decrease in size of SWEs after the downstream location (x/h≥20). The decay rate of the maximum mean velocity increases about 5.6% in 140 mm SWE as compared to 200 mm SWE. It is noted that spread of the jet in wall normal and lateral directions increases with decrease in size of SWEs after the attachment of the flow stream on the sidewalls. In the far-field location of the present case, the smaller size of SWE (140 mm SWE) has 10.7% and 23.1% higher spread rate as compared to larger size of SWE (200 mm SWE) in wall-normal and lateral directions, respectively. It is also seen that the self-similar profile gets delayed in wall-normal direction as compared to lateral direction for all the cases. The wall-normal self-similar profile is obtained early with increase in the size of SWEs and it is obtained at x/h=30, 27, 24, and 20 for 140 mm, 160 mm, 180 mm, and 200 mm SWEs, respectively. The flow stream seems to climb the sidewall and this tendency increases with increase in size of SWEs.

Flow and thermal characteristics of three-dimensional turbulent wall jet

In the present work, a three-dimensional turbulent wall jet is simulated using large-eddy simulation to characterize its flow and thermal characteristics. The solver is first validated for streamwise velocity decay, wall-normal and spanwise spread rates, and mean and second-order flow statistics using reference experimental data from the literature. The mean vorticity transport equation for the streamwise component is analyzed to identify the dominant terms that contribute to the large spanwise spread of the jet. The terms that contain Reynolds normal stresses are identified as major contributors to a large mean streamwise component of vorticity. The mean streamwise and wall-normal components of vorticity are studied for their evolution and contribution to the spanwise spread. It was found that both these components together aid in the large spanwise spread of the jet. The heat transfer characteristics are studied for the jet flow on a heated isothermal wall. The profiles of mean and fluctuating temperatures, the evolution of the Nusselt number, and turbulent heat flux characteristics are studied. The streamwise evolution of Nusselt number behavior is explained using instantaneous vortical structures. A significant drop in heat transfer is observed in the potential core region. Further, the turbulent heat flux contours show that the transport of heat in the streamwise direction is different from that of the plane wall jet. A peculiar turbulent heat transport was found in the analysis of the spanwise heat flux. The heat transfer characteristics noted for the three-dimensional wall jet may help in the design and analysis of film-cooling applications.

A comparative study of heat transfer characteristics of wall jet with boundary layer transition using six low-Reynolds number k–ε models

A Low-Reynolds Number (LRN) k–ε model can well simulate the transition characteristics of the momentum boundary layer, but so far, there are few studies on the influence of boundary layer transition on heat transfer characteristics by using the LRN k–ε model. Due to the larger degree of flexibility and controllability of flow parameters than the conventional boundary layer, a wall jet is an ideal flow configuration to research the transition of the boundary layer. To investigate the performance of the LRN k–ε model in simulating the heat transfer characteristics of the wall jet with boundary layer transition, six versions of LRN k–ε models are used to simulate a three-dimensional wall jet with boundary layer transition and the computational results were compared with experimental data. It is found that the Abe–Kondoh–Nagano (AKN) and Yang–Shih (YS) models can accurately simulate the flow field and heat transfer of the laminar boundary layer due to the use of the Kolmogorov scale in the developing region. Compared with the YS model, the AKN model is capable of predicting the influence of boundary layer transition on the heat transfer process in good agreement with experimental results over the whole domain. From the calculation results, it is found that Abid and Change and Hsieh and Chen models are more appropriate for simulating the heat transfer in the fully turbulent region of the wall jet. The damping function fµ of the Lam–Bremhorst and Launder–Sharma models approaches a constant value near the wall, which does not meet the wall limiting conditions and leads to a negative impact on the simulation of heat transfer near the wall.

Coherent Streamwise Vortex Structure of a Three-Dimensional Wall Jet

The dynamics of the coherent structures in a turbulent three-dimensional wall jet with an exit Reynolds number of 250,000 were investigated using the Snapshot Proper Orthogonal Decomposition (POD). A low-dimensional reconstruction using the first 10 POD modes indicates that the turbulent flow is dominated by streamwise vortex structures that grow in size and relative strength, and that are often accompanied by strong lateral sweeps of fluid across the wall. This causes an increase in the bulging and distortions of streamwise velocity contours as the flow evolves downstream. The instantaneous streamwise vorticity computed from the reconstructed instantaneous velocities has a high level of vorticity associated with these outer streamwise vortex structures, but often has a persistent pair of counter-rotating regions located close to the wall on either side of the jet centerline. A model of the coherent structures in the wall jet is presented. In this model, streamwise vortex structures are produced in the near-field by the breakdown of vortex rings formed at the jet outlet. Separate structures are associated with the near-wall streamwise vorticity. As the flow evolves downstream, the inner near-wall structures tilt outward, while the outer streamwise structures amalgamate to form larger streamwise asymmetric structures. In all cases, these streamwise vortex structures tend to cause large lateral velocity sweeps in the intermediate and far-field regions of the three-dimensional wall jet. Further, these structures meander laterally across the jet, causing a strongly intermittent jet flow.

Attached and Attaching Three-Dimensional Jets From Circular Nozzles: Analytical Model

Abstract Here we consider velocity profiles of three dimensional attaching and attached jets emerging from circular nozzles. Like their well-studied two-dimensional counterparts, these wall jets lose momentum due to interactions with nearby surfaces. Unlike their two-dimensional counterparts, simple and quantitative expressions for the velocity profiles of three-dimensional wall jets remain elusive. Here we present a quantitative analytical model of the three-dimensional velocity profiles of attached jets inclusive of a local skin coefficient of friction. We compare these expressions to experimental velocity profiles at moderate and high nozzle Reynolds numbers to find reasonable quantitative agreement. This work has implications for a variety of industries including nuclear waste processing, where jet flows in mixing vessels suspend solids and gases trapped in radioactive waste tanks.

Measurement of three-dimensional flow structure and transient heat transfer on curved surface impinged by round jet

In this study, the transient heat transfer characteristics of a circular cylinder surface cooled by an impinging air jet were measured through thermographic phosphor thermometry. Time-resolved surface temperature fields were visualized under constant heat flux conditions. After the jet impingement on the circular cylinder, the curved three-dimensional (3D) wall jet developed toward both spanwise and streamwise directions, followed by most of the fluid moving along the curved surface due to the Coanda effect. Therefore, the high heat transfer region was elongated toward the streamwise direction. The impinging angle was established to be a dominant factor in heat transfer characteristics. The heat transfer was improved with an increase in the impinging angle, as the cooling area expanded toward the streamwise direction. To discuss the transient heat transfer characteristics, time-resolved two-dimensional Nusselt number distributions were obtained according to the varied impinging angles and Reynolds numbers. The secondary peak of heat transfer was not clearly observed due to the stabilizing effect of curvature on the wall jet. To understand the heat transfer phenomenon, the 3D flow structures of the jet on the curved surface were obtained using time-resolved volumetric particle tracking velocimetry (PTV). The velocity vectors and streamwise vortices were visualized according to the impinging angle and analyzed in three-dimensions. The 3D curved wall jet possessed a big counter-rotating streamwise vortex structure in the upper region of the attached wall jet on the cylinder wall. With an increase in the impingement angle, the streamwise vortex developed longer at the same Reynolds number. The 3D flow structure and heat transfer distribution were found to demonstrate similar tendencies.

Heat transfer from a single and row of three dimensional wall jets - A combined experimental and numerical study

This paper reports the results of experimental and numerical studies to understand the heat transfer characteristics of three-dimensional wall jets exiting from a single and a row of circular jet openings over an unheated flat plate. Infrared thermography is employed to obtain the temperature distribution over the target surface, and the semi-infinite approximation methodology is used to estimate the heat transfer coefficients. Single wire constant temperature hot-wire anemometer is used to measure the flow characteristics. Additionally, computational studies have been performed to select a suitable low Reynolds number turbulence closure models among the following models, namely (i) Spalart Almaras (SA) (ii) Realizable k-ε with enhanced wall treatment (RKE-ewt) (iii) k-ω SST and (iv) Reynolds Stress Model with enhanced wall treatment (RSM-ewt) that predicts the experimentally obtained results for heat transfer characteristics accurately. Based on the investigations carried out, it is observed that RKE-ewt turbulence closure model is not only accurate but also faster in the prediction of heat transfer coefficient. Further, it is also seen that for a fixed mass flow rate, and at a given diameter of the jet opening, widely spaced jets show higher heat transfer coefficients. Furthermore, for a row of three-dimensional wall jets correlations based on the numerical results are developed for the Nusselt number for a Reynolds number range of 5000 to 15000.

Low-order estimation of the velocity, hydrodynamic pressure, and acoustic radiation for a three-dimensional turbulent wall jet

A method for the experimental characterization of the velocity, hydrodynamic pressure, and acoustic generation in a subsonic (ReH=25,500), three-dimensional, turbulent wall jet is presented. An acoustic analogy formulated for the turbulent wall jet shows that the far-field acoustics relate to the Reynolds stress fluctuations of the velocity field or the product of the hydrodynamic pressure fluctuations and the rate-of-strain field. As these quantities cannot be measured directly with sufficient resolution, low-order reconstructions of the velocity field based on the use of the Proper Orthogonal Decomposition and Stochastic Estimation are developed. Reconstruction of the three-dimensional field is accomplished using spanwise-aligned, stereoscopic particle image velocimetry measurements, obtained at 16 streamwise locations synchronously with an array of 32 surface pressure transducers. The velocity field reconstruction is then used to calculate the fluctuating pressure field (via Poisson’s equation) allowing for the evaluation of coupled pressure-velocity terms in addition to an acoustic analogy for the acoustic far-field. Application of these methods show that the large-scale motion throughout the shear layer is captured by the velocity and hydrodynamic pressure field estimates and features of the acoustic far-field are recovered.

Study on Mechanism of Series-Flow of Pollutants between Consecutive Tunnels by Numerical Simulation

The characteristics of series-flow between two consecutive tunnels with distance ranging from 20 m to 250 m are explored by computational fluid dynamics (CFD) parametric simulations of structure and operation parameters. The research indicates that series-flow can be considered the three-dimensional wall jet diffusion of upstream tunnel pollutants under the effects of the negative pressure area of the downstream tunnel entrance. The jet characteristics are primarily related to the tunnel distance between upstream and downstream tunnels and hydraulic diameters, and only influenced by the negative pressure in the area very close to downstream entrance where the tunnel air velocity ratio, i.e., the velocity of upstream tunnel air divided by the velocity of downstream tunnel air, decides the degree of the influence. If ignoring the effects of ambient wind and traffic flow, the series-flow ratio decreases with the increasing of parameters of the normalized tunnel distance, i.e., the tunnel distance divided by tunnel hydraulic diameter, and the tunnel air velocity ratio. Based on the three-dimensional wall jet theory, a series-flow model covering all jet characteristic sections is built. The experiment results indicate that the model applies to consecutive tunnels with any spacing and exhibits higher prediction accuracy.

Effect of the Inlet Geometry on the Flow and Heat Transfer Characteristics of Three-Dimensional Wall Jets

AbstractIn this work, fluid flow and heat transfer characteristics of three-dimensional (3D) wall jets exiting from a circular and square opening are presented based on experimental investigations. Two hydraulic diameters, namely, 2.5 and 7.5 mm and a Reynolds number range of 5000–20,000 have been considered. Mean velocity and turbulence intensity distribution in the walljet are quantified using a hot wire anemometry. Measurements are done both along the streamwise and spanwise directions. Transient infrared thermography is used for mapping the temperatures over the surface, and the heat transfer coefficients are estimated using a semi-infinite approximation methodology. Results show that, for circular jets, the effect of the jet diameter on the local and the spanwise-averaged Nusselt number is most pronounced near the jet exit. Further, it is also observed that circular jets have an edge over square jets. A correlation with a high correlation coefficient of 0.95 has been developed for spanwise average Nusselt number as a function of the Reynolds number and the dimensionless streamwise distance.

Evaluation of candidate strategies for the estimation of local heat transfer coefficient from wall jets

ABSTRACTThis paper reports results of experimental investigations on planar and three-dimensional wall jets over a flat surface. The local heat transfer coefficient is estimated at transient conditions with a semi-infinite approximation and at steady state conditions with a uniform wall heat flux boundary. Liquid crystal thermography and infrared thermography are used to map the surface temperatures. Experiments are performed for 2000 Re 8000 and 0 x/L 80. Results show that transient infrared thermography with semi-infinite approximation is a better candidate for the estimation of the heat transfer coefficient from wall jets.

Experimental Investigation on Mean Flow Development of a Three-Dimensional Wall Jet Confined by a Vertical Baffle

Three-dimensional (3D) confined wall jets have various engineering applications related to efficient energy dissipation. This paper presents experimental measurements of mean flow development for a 3D rectangular wall jet confined by a vertical baffle with a fixed distance (400 mm) from its surface to the nozzle. Experiments were performed at three different Reynolds numbers of 8333, 10,000 and 11,666 based on jet exit velocity and square root of jet exit area (named as B), with water depth of 100 mm. Detailed measurements of current jet were taken using a particle image velocimetry technique. The results indicate that the confined jet seems to behave like an undisturbed jet until 16B downstream. Beyond this position, however, the mean flow development starts to be gradually affected by the baffle confinement. The baffle increases the decay and spreading of the mean flow from 16B to 23B. The decay rate of 1.11 as well as vertical and lateral growth rates of 0.04 and 0.19, respectively, were obtained for the present study, and also fell well within the range of values which correspond to the results in the radial decay region for the unconfined case. In addition, the measurements of the velocity profiles, spreading rates and velocity decay were also found to be independent of Reynolds number. Therefore, the flow field in this region appears to have fully developed at least 4B earlier than the unconfined case. Further downstream (after 23B), the confinement becomes more pronounced. The vertical spreading of current jet shows a distinct increase, while the lateral growth was found to be decreased significantly. It can be also observed that the maximum mean velocity decreases sharply close to the baffle.