Free-surface Jet Research Articles

A simple hydrodynamic model of a laminar free-surface jet in horizontal or vertical flight

A useable model for laminar free-surface jet evolution during flight, for both horizontal and vertical jets, is developed through joint analytical, experimental, and simulation methods. The jet’s impingement centerline velocity, recently shown to dictate stagnation zone heat transfer, encompasses the entire flow history: from pipe-flow velocity profile development to profile relaxation and jet contraction during flight. While pipe-flow is well-known, an alternative analytic solution is presented for the centerline velocity’s viscous-driven decay. Jet-contraction is subject to influences of surface tension (We), pipe-flow profile development, in-flight viscous dissipation (Re), and gravity (Nj = Re/Fr). The effects of surface tension and emergence momentum flux (jet thrust) are incorporated analytically through a global momentum balance. Though emergence momentum is related to pipe flow development, and empirically linked to nominal pipe flow-length, it can be modified to incorporate low-Re downstream dissipation as well. Jet contraction’s gravity dependence is extended beyond existing uniform-velocity theory to cases of partially and fully developed profiles. The final jet-evolution model relies on three empirical parameters and compares well to present and previous experiments and simulations. Hence, micro-jet flight experiments were conducted to fill-in gaps in the literature: jet contraction under mild gravity-effects, and intermediate Reynolds and Weber numbers (Nj = 5–8, Re = 350–520, We = 2.8–6.2). Furthermore, two-phase direct numerical simulations provided insight beyond the experimental range: Re = 200–1800, short pipes (Z = L/d · Re ≥ 0.01), variable nozzle wettability, and cases of no surface tension and/or gravity.

Structural optimization of microjet array cooling system

The single phase heat transfer from an upward facing, horizontal copper surface to arrays of impinging water jets was experimentally investigated. Experimental configuration allows for a free-surface unconfined jets flow. Square nozzles 50×100μm arranged in four different geometries were used. Additionally, for the set of two jets array geometry was varied by adjusting the nozzle to nozzle distance. The area averaged heat transfer coefficient was found to be a strong function of working fluid mass flux and array geometrical aspect ratio. The proposed correlation agreed with the experimental data within 30% error bounds Obtained database of experimental data with analytical correlation allows the rational design of microjet modules for various industrial applications.

Numerical study on free-surface jet impingement cooling with nanoencapsulated phase-change material slurry and nanofluid

The free-surface jet impingement technique operating with two-phase advanced coolants has recently drawn much favorable attention in cooling applications. However, numerical understanding of free-surface jets along with improved realization of pros and cons associated with these advanced coolants remains a challenge. In this work, the flow and thermal performances of free-surface jet impinging on a heated copper plate are numerically investigated using water, nanoencapsulated phase-change material (NEPCM) slurry, and nanofluid as coolants. Three-dimensional continuity, momentum, and energy equations are discretized with a commercial finite volume code in accordance with a standard k-ε turbulence model. The volume of fluid multiphase technique is adopted in this study to model the free surface between the liquid jet and surrounding ambient air. A single-phase fluid approach is employed using existing models from other references to determine the effective thermophysical properties of NEPCM slurry and nanofluid. The predicted Nu and pressure drop calculations agreed well with the experimental data from references. Physical understanding of the effects of fluid jet inlet temperature, nozzle-to-target distance, and nanoparticle concentration is reported. The addition of both NEPCM and Al2O3 particles to water helps in improving the Nusselt number and decreases the stagnation point temperature with certain pressure drop penalty. The NEPCM slurry enhances the cooling performance of the system by improving its latent heat storage capability, whereas nanofluids improve the cooling performance by enhancing the effective thermal conductivity. The thermal performance can be further improved with increased particle concentration. The NEPCM slurry demonstrates performance superior to nanofluid working at the same particle loading. Overall, the proposed model can provide valuable guidelines for the use of advanced coolants in a free-surface jet impingement cooling system.

Self-similarity of heat transfer characteristics in laminar submerged and free-surface slot jet impingement

Laminar slot jet impingement of free-surface and submerged jets is investigated numerically regarding self-similar behavior in local heat transfer. Two different scaling behaviors, one for the stagnation region and one for the fully developed wall-jet region are shown, and the validity of the scaling is confirmed by fully resolved numerical simulations. Within the stagnation region, self-similarity is obtained if the relaxation process of the velocity profile is considered, which is described by the dimensionless nozzle-to-plate distance h/W·ReW as introduced in Rohlfs et al. (2014) for circular jets. Further, it is shown that the Prandtl number dependency can be well described by an analytical relationship obtained by solving the classical similarity solution of a viscous flow near stagnation point. For the wall-jet region, we first derive the scaling behavior based on the work of Watson (1964) for circular free surface jets. This analysis leads to an additional stretching of the spatial coordinate in the wall-tangential direction by the Reynolds number, e.g. x∗=x/(W·ReW).Finally, correlations for the stagnation region heat transfer are introduced for free-surface and submerged slot jets, dependent on the dimensionless nozzle-to-plate distance and constant heat flux/wall temperature, valid over a wide range of laminar flow conditions (i.e., 0.07⩽Pr≤1307,100⩽ReW⩽1000 and 4⩽h/W⩽20). Thereby, analytic Prandtl dependencies for stagnation point flows are employed and corresponding correlations for impinging slot jets are presented, valid in a very broad range (0.0005⩽Pr⩽4500).

Sensitivity of turbulent Schmidt number and turbulence model to simulations of jets in crossflow

Environmental discharges have been traditionally designed by means of cost-intensive and time-consuming experimental studies. Some extensively validated models based on an integral approach have been often employed for water quality problems, as recommended by USEPA (i.e.: CORMIX). In this study, FLOW-3D is employed for a full 3D RANS modelling of two turbulent jet-to-crossflow cases, including free surface jet impingement. Results are compared to both physical modelling and CORMIX to better assess model performance. Turbulence measurements have been collected for a better understanding of turbulent diffusion's parameter sensitivity. Although both studied models are generally able to reproduce jet trajectory, jet separation downstream of the impingement has been reproduced only by RANS modelling. Additionally, concentrations are better reproduced by FLOW-3D when the proper turbulent Schmidt number is used. This study provides a recommendation on the selection of the turbulence model and the turbulent Schmidt number for future outfall structures design studies.

Application of a two phase lattice Boltzmann model in simulation of free surface jet impingement heat transfer

In this paper a two-phase lattice Boltzmann model, capable of handling large density jumps, is used to study the free surface jet impingement cooling in the non-boiling regime. The multiple-relaxation-time (MRT) collision operator is employed to enhance the numerical stability of the model at high Reynolds numbers. The capability of the outlined two-phase LB scheme in accurate capturing of the interface shape is assessed through relevant test cases. These include the oscillating drop, Rayleigh–Taylor instability, and Kelvin–Helmholtz instability. In addition to demonstrate the validity of the model in simulation of heat transfer the predicted distribution of the Nu number on the impingement plate are compared with those of analytical results. The validated numerical solver then is employed to study a planar liquid jet emanating from a nozzle into a quiescent gas and impinging the opposite plate. The influence of the jet Re number and liquid-to-gas density ratio on the instantaneous flow field, interface shape, and heat transfer rate is also examined. This work reports for the first time the simulation of an impinging free surface liquid jet using a two phase lattice Boltzmann model.

Numerical thermal analysis and optimization of a water jet impingement cooling with VOF two-phase approach

The fluid flow and heat transfer characteristics of a free-surface liquid jet impingement cooling have been investigated numerically. The slot jet with water impinging normally on a flat plate is employed. To describe the turbulent structure, the turbulent governing equations are solved by a control-volume-based finite-difference method with a power-law scheme and the well-known turbulence model, which are associated with wall function. Numerical computations have been conducted with variations of jet exit Reynolds number (11,000≤Red≤17,000), dimensionless jet-to-surface distance (3≤H/d0≤12), dimensionless jet width (1≤B/d0≤2), and the heat flux (140kW/m2≤q″≤280kW/m2). The theoretical model developed is validated by comparing the numerical predictions with available experimental data in the literature. Under the studied ranges, the variations of local Nusselt numbers by hydraulic diameter Nud of the dimensionless jet-to-surface distance 3≤H/d0≤12 along the flat plate decrease monotonically from its maximum value at the stagnation point. In addition, the shape of the inlet area and jet-to-surface distance are optimized by using the response surface methodology (RSM) and the genetic algorithm (GA) method after solutions are carefully validated with available experimental results in the literature. Based on the optimal results, the optimum condition is in H/d0=7.86 and B/d0=2 for this physical model.

Influence of viscous flow relaxation time on self-similarity in free-surface jet impingement

Self-similar behavior in laminar free-surface jets regarding the velocity profile, its evolution, and the influence on stagnation-region heat transfer is presented. Approximate theoretical analysis shows that there are two regions with different scaling: a free-jet region where viscous relaxation dominates and an impingement region where a potential solution applies. Using the dimensionless time scale found for the first region, H/(D·Re), self-similarity is obtained for the axial velocity and its development. Fully resolved numerical simulations are performed to identify the crossover between the regions. It is further shown that the velocity profile at the cross-over point directly dictates the heat transfer distribution in the stagnation zone. The conditions under which this distribution has a central or off-center peak are found to be related to specific velocity profiles. Numerical results are used to find approximate closed-form relations tying the jet emergence velocity to the heat transfer distribution. A new comprehensive correlation is subsequently formulated for the heat transfer incorporating this new time scale, covering the range of velocity profiles emerging from pipe-type (parabolic) to orifice-type nozzles (uniform). A well-known analytical Prandtl dependency for stagnation flows is employed, yielding strong agreement with the numerical results. Agreement is observed for a very wide range of liquid and laminar flow conditions (i.e., 0.07<Pr<1307,73<Re<2000, and 4<H/D<110).

Dynamic structures of a submerged jet interacting with a free surface

The spatial structures of a submerged jet interacting with a free surface were examined experimentally. The time-resolved PIV technique was used for the quantitative measurements. Two Reynolds numbers (1920, 3480) were examined for a configuration, in which the depth of the jet beneath the free surface was fixed to H=2D. The dynamics of the flow structures were examined further using the space–time proper orthogonal decomposition (POD) analysis technique. Some common characteristics were found in both jet flows, which are believed to be the general features of the free-surface jet flows. On the other hand, the dynamic characteristics of the large-scale turbulent motions differed significantly with respect to the Reynolds number. In the low Reynolds number case, three dominant dynamic structures were found: flapping motion of the jet, very large scale vortical structure interacting with the free surface at the right side, and the transverse stretching of large scale structure due to the presence of free surface. The reconstructed fluctuating velocity fields and the swirling strength contours demonstrated that the very large scale structures began to move downward at about 10D downstream the initial interaction. In the high Reynolds number case, the first two dominant spatial modes showed the momentum exchange process between the jet flow and the free surface. The third mode displayed a vortex just below the free surface at the left side and the fourth mode showed the elongated vortex structures. The scale of vortical structures was much smaller in the high Reynolds number case than that in the low Reynolds case, and the downward motion of large scale structures was not found in the high Reynolds number case.

A Generalized Critical Heat Flux Correlation for Submerged and Free Surface Jet Impingement Boiling

A critical heat flux (CHF) correlation is developed for jet impingement boiling of a single round jet on a flat circular surface. The correlation is valid for submerged jets as well as for free surface jets with Reynolds numbers (Re) between 4000 and 60,000. Data for the correlation are obtained from an extensive experimental study of submerged jet impingement boiling performed by the authors with water at subatmospheric pressures and with FC-72 at atmospheric pressure. Additional experimental data from a free surface jet study are also incorporated to include the effect of variation in surface diameter relative to a fixed nozzle diameter, additional working fluids (water and R-113 both at atmospheric pressure), and jet configuration. The range of parameters considered include Re from 0 (pool boiling) to 60,000, jet diameter to capillary length scale ratios (dj/Lc) ranging from 0.44 to 5.50, surface diameter to capillary length scale ratios (ds/Lc) ranging from 4.47 to 38.42, and liquid-to-vapor density ratios from 119 to 8502. The proposed correlation is built on the framework of a forced convective CHF model. Using this correlation, 95% of the experimental CHF jet impingement data can be predicted within ±22% error. The corresponding average absolute error and the maximum absolute error are 8% and 36%, respectively, over the range of parameters considered.

Free-surface jet flow of a shear-thinning power-law fluid near the channel exit

AbstractThe jet flow of a shear-thinning power-law fluid is examined theoretically as it emerges from a channel at moderate Reynolds number. Poiseuille flow conditions are assumed to prevail far upstream from the exit. The problem is solved using the method of matched asymptotic expansions. A similarity solution is obtained in the inner layer near the free surface, with the outer layer extending to the jet centreline. An inner thin viscous sublayer is introduced to smooth out the singularity in viscosity at the free surface, allowing the inner algebraically decaying solutions to be matched smoothly with the solution near the free surface. A Newtonian jet is found to contract more than a shear-thinning jet. While both the inner-layer thickness and the free-surface height are $O(\mathit{Re}^{-1/3})$, and grow with downstream distance, the sublayer thickness is smaller, $O(\mathit{Re}^{-(1+n)/3})$, growing with distance for $n &lt; 0.5$, and decaying for $n &gt; 0.5$. The relaxation downstream distance for the jet is found to grow logarithmically with $\mathit{Re}$.

Numerical simulations of droplet train and free surface jet impingement

The cooling behavior of the impingement of a droplet train, and free surface jets over a heated and pre-wetted surface is explored employing an Algebraic Volume-of-Fluid methodology. The code is based on a modified version of the two-phase numerical solver interFoam (OpenFOAM) (Trujillo and Lewis, 2012). Two versions of the free surface jet are studied. The first consists of a fully-developed profile exiting the nozzle, and the second is characterized by a uniform velocity distribution. Results show that both jet configurations have higher cooling performance than the droplet train locally and globally, with the fully-developed case being the most effective of the two jet arrangements. Locally, the performance is measured by radial profiles of the boundary-layer-displacement thickness and heat transfer coefficient. Globally, the cooling effectiveness is directly proportional to the surface area that resides within the high-convection region, i.e. before the boundary layer separation point. On a temporal basis, the liquid film within the impingement region of the droplet train exhibits pronounced variations in velocity magnitude and film thickness. This is directly attributed to the nature of continuous droplet impacts affecting the impingement region, and gives rise to an unsteady cooling and heating of the fluid near the wall. In contrast for the jets, the film and the corresponding free surface are nearly steady with only minor perturbations.

Experimental investigation of free-surface jet impingement quenching process

Liquid jet impingement cooling technique is critical in many industrial processes, such as fuel bundle cooling post-loss-of-coolant-accident in nuclear reactors, heat treatment of metal parts post-hot-processing, etc. The ability of liquid jets to extract high heat flux from metal parts, with temperatures as high as 800–1000°C, at moderate flow rates has made them indispensable in these applications. The complex mechanism of flow boiling heat transfer during jet impingement cooling is not been well understood. This study presents a systematic methodology for the measurement and estimation of the temporospatial variation of heat transfer on the impingement surface during jet impingement cooling of extremely hot steel plate. The effect of jet impingement velocity and subcooling variations from 2.5 to 10m/s and 60 to 87K, respectively, on the temporospatial heat transfer variation on the impingement surface is reported.A gradually growing circular wetted region, with its periphery named as the wetting front, forms soon after the cooling starts but its velocity decreases as it grows in diameter. A local maximum in the surface heat flux closely follows the wetting front, with the local maximum heat flux reducing with distance from the stagnation point. The wetting front velocity and local maximum heat flux increase with both the jet velocity and subcooling. The enhancement in the local film velocity and subcooling result in a strong suppression of boiling activity and, resultantly, high heat transfer rates at plate surface temperatures in much excess of the critical temperature of the coolant is achieved. This observation confirms the industrial practice of using impinging jets for accelerated cooling of hot steel plates.

The effect of viscoelasticity on the dynamics of gas bubbles near free surfaces

The dynamics of bubbles immersed in a viscoelastic fluid directly beneath an initially plane free surface is modelled using the boundary integral method. The model predicts a range of dynamics that is dependent on the Deborah number, the Reynolds number and the proximity of the bubble to the free surface. The motion of the free surface jet caused by the collapse of a bubble in a viscoelastic fluid can be significantly retarded compared with the Newtonian case. The axial jet predicted in many instances in the Newtonian case is not observed when the inertial forces are sufficiently small. In this case an annular jet forms that can penetrate the bubble. At high Deborah numbers, there is a return to Newtonian-like dynamics since the effects of viscosity are abated by elasticity to such an extent that inertia is the prevailing influence on bubble dynamics.

Evaluation of the sensitivity and response of IR thermography from a transparent heater under liquid jet impingement

The feasibility of a visible/IR transparent heater and its suitability for IR thermography is experimentally examined. The most common transparent conductive coating, Indium Tin Oxide (ITO), is quite reflective and its optical properties depend on thickness and manufacturing process. Therefore, the optical properties of several thicknesses and types of ITO, coated on an IR window (BaF2), are examined. A highly transparent Cadmium Oxide (CdO) coating on a ZnS window, also examined, is found to be unusable. Transmissivity is found to increase with a decrease in coating thickness, and total emittance is relatively low. A thick ITO coating was examined for IR thermography in the challenging test case of submerged water jet impingement, where temperature differences were characteristically small and distributed. The measurements under steady state conditions were found to agree well with the literature, and the method was validated. Comparison of two IR cameras did not show the LWIR low-temperature advantage, up to the maximal acquisition rate examined, 1.3KHz. Rather the MWIR camera had a stronger signal to noise ratio, due to the higher emissivity of the heater in this range. The transient response of the transparent heater showed no time-delay, though the substrate dampens the thermal response significantly. Therefore, only qualitative transient measurements are shown for the case of pulsating free-surface jet impingement, showing that the motion of the hydraulic jump coincides with thermal measurements. From these results, recommendations are made for coating/window combination in IR thermography.

Heat transfer characteristics of submerged jet impingement boiling of saturated FC-72

Global heat transfer characteristics of submerged jet impingement boiling of a highly wetting dielectric fluid (FC-72) on a heated copper surface are presented. The effect of variation of the jet exit Reynolds number (Re) on boiling incipience, fully developed nucleate boiling, and critical heat flux (CHF) are documented. The jet exit Re is varied by variations of the jet exit velocity and the jet nozzle diameter for a fixed surface diameter. High-speed visualization is used to supplement trends observed in the heat transfer data. Scenarios of low and high incipience wall superheat are identified, corresponding to partially or fully developed nucleate boiling condition upon initiation of boiling. For the high incipience wall superheat scenario, the time of spread of boiling activity over the heated surface during temperature overshoot is found to be inversely proportional to the wall superheat temperature at boiling incipience. The incipient boiling wall superheat temperature is found to be uncorrelated with jet Re and jet diameter. A cumulative probability distribution function is used to characterize the onset of boiling with wall superheat temperature. At a fixed Re, CHF increases with increasing jet velocity and with decreasing jet diameter, indicating that the jet kinetic energy is a key parameter in CHF enhancement. The CHF data are compared with available jet impingement CHF correlations from literature on free surface and confined jets. The free surface jet CHF correlation by Monde and Katto (1978) [1] is seen to best capture the experimental data trends for Re greater than 4000.

Non‐Circular Hydraulic Jump on a Moving Surface due to an Impinging Circular Free Surface Jet of Water

AbstractLiquid jet impingement has many industrial cooling applications such as metal manufacturing and steel cooling on run‐out tables (ROT). The development of the wetting front around the impingement point of a jet is central in jet impingement cooling. In this paper, the effects of moving target surface and jet Reynolds number on wetted zone and on the formation and location of hydraulic jump (HJ) are explored through a series of industrial‐scale experiments of an impinging circular free surface long water jet with high Reynolds number of 11 000–50 000 and industrial jet parameters. The moving test surface impacts the radial evolution of circular wetted zone in all directions and alter the circular HJ at the wetting front into a non‐circular contour that depends on the jet Re number. The limited relations in the literature do not represent these measured shapes and do not appropriately predict radii of HJ in industrial scale. A new correlation for radius of non‐circular HJ has been derived in this study that compared more accurately to the experimental data. Numerical simulations of radial impingement flow on moving surface were performed using a variant of k–ε turbulent model and results are compared to the experimental data. The computational results for the wetting front were found to be close to the experimental data indicating the appropriate performance of the turbulent model.

Hydrodynamics of quenching with impinging free-surface jet

The hydrodynamics of jet impingement quenching of a stainless steel specimen has been studied experimentally. The specimen is heated to an initial temperature of about 900°C and then quenched by a subcooled free-surface water jet. High-speed imaging shows that the free-surface of the water film in the wetted region is smooth. The water film outside the wetted region is deflected away from the surface and then breaks into droplets due to surface tension and shear forces. The splashed droplet velocity is found to be low up to a wetting front radius of 6mm (r/dJ≈2), beyond which it increases rapidly before reaching a constant value at a wetting front radius of about 8 to 10mm (2.67⩽r/dJ⩽3.34). The water film velocity at the wetting front is calculated using the single-phase boundary layer model suggested by Watson [2]. At moderate subcooling, the splashed droplet velocity up to a wetting front radius of 10mm (r/dJ≈3.34) is found to be much lower than the estimated single-phase film velocity. The study shows that although the wetted region may appear devoid of any bubbles, strong two-phase flow occurs within this region.

Characteristics of a Jet in the Vicinity of a Free Surface

In this study, the characteristics of a round turbulent jet in the vicinity of a free surface are investigated. The jet issued from a nozzle located at a depth five times the nozzle diameter (d = 10 mm) below and parallel to the free surface. The jet exit velocity was 2.8 m/s and the resulting Reynolds number was 28,000. Instantaneous two-dimensional PIV measurements were obtained in the vertical central plane and in several horizontal planes at various distances (y/d = 0,±1,±2,±3± 4) from the axis of the nozzle. All fields-of-view were positioned at streamwise locations in the range of 28 &lt; x/d &lt; 62, where the jet interacts significantly with the free surface. The results reveal that the behavior of the surface jet is very similar to that of the free jet before it interacts with the free surface which occurs at about x/d = 30. Beyond this, the velocity normal to the free surface is diminished and those parallel to the free surface are enhanced in the region near the free surface. In the horizontal plane near the free surface (y/d = +4), the spreading of the surface jet is significantly greater than that of the free jet. The mean lateral flow in this region tends to be outward everywhere for the surface jet, while the opposite trend occurs in the free jet. Turbulence intensities in all three directions are reduced by the effect of the free surface confinement. Near the free surface, at y/d = +4, unlike the single peak streamwise turbulence intensity profile noticed in the case of the free jet, the off-axis double peaks reappear in the case of the surface jet. The magnitude of shear stress in the vertical central plane of the surface jet is smaller than that noticed in the free jet near the free surface. In identical horizontal planes, the shear stress (-uw¯) profiles are similar in both free jets and surface jets in regions where the interaction with the free surface is not significant (x/d ≈ 30). As the downstream distance increases near the free surface, the magnitudes of the shear stress profiles are larger compared to that of the free jet. An increase in the normal component of vorticity is observed in the horizontal planes near the free surface.

Heat transfer correlation models for electrospray evaporative cooling chambers of different geometry types

Abstract Development of future electronics for high speed computing requires a silent thermal management method capable of dissipating a broad range of heat generated from application-specific integrated circuits, while keeping the skin temperature below 45 °C. Electrospray evaporative cooling (ESEC) chambers show promise because of their ability to dissipate a broad range of heat within a relatively small size. However, the development and the optimization of ESEC chambers are currently restricted, in part due to the lack of sufficient empirical heat transfer correlations. This paper investigates empirical heat transfer correlations for ESEC chambers with three different geometry types. Since the unstable multi-jet behavior of an ESEC chamber is similar to that of a free-surface traditional impinging liquid jet, these correlations are based on the traditional impinging liquid jet’s empirical correlations, yet are modified to factor in the electric field effect. The results show that the heat transfer enhancement ratio correlations and the Nusselt number correlations for different ESEC chambers cover more than 83% of the experimental data, within ±10% deviation. The sensitivity analysis results and experimental data prove that the variation in the enhancement ratio is sensitive to that of the potential and the flow rate. It is not sensitive to the geometric factor of the same ESEC type. This paper presents a natural convection correlation for chip-scale, heated, flat surfaces when the Rayleigh number is below 3000. Further investigation is necessary to extend these heat transfer correlations to cover additional parameters for different thermal management applications.