First-Order Model of Free-Jet Hydrodynamic Evolution for Heat Transfer Prediction, Including Nozzle and Flow Rate Effects

2016 ◽  
Author(s):  
Ron S. Harnik ◽  
Herman D. Haustein
Keyword(s):  
Heat Transfer ◽  
Surface Tension ◽  
Free Surface ◽  
Velocity Profile ◽  
Rapid Development ◽  
Jet Impingement ◽  
Centerline Velocity ◽  
Order Model ◽  
First Order ◽  
Wide Range

Jet impingement flow is known to generate one of the highest single-phase heat transfer rates, with potential for micro-electronics cooling applications. Although free-surface jets have been studied extensively, existing models are either too complex for practical use or do not consider all relevant parameters, such as the impinging jet’s velocity profile. Recently the authors have shown that the stagnation zone heat transfer is dictated by the jet’s centerline velocity upon impingement, and that going between the limiting cases (uniform vs. parabolic profiles, laminar flow) corresponds to a two-fold increase in heat transfer. In the present study, which is motivated by cooling at micro-scales (predominantly laminar flows), this simplified analysis is extended leading to a first-order analytical approximation, which is valid not only for the limiting cases but over the entire profile range. Thereby, the development of the jet flow both in the nozzle (pipe-type) and subsequently during its flight (before impingement) is incorporated in this model over a broad range of parameters. For validation of the model, as well as for additional insight into the governing physics, direct numerical simulations were conducted. Through which it is shown that the jet’s velocity profile and its evolution during free “flight” are dependent on the level of the flow’s upstream development in the nozzle, both of which depend on a single self-similar scale: distance travelled normalized by the nozzle diameter and Reynolds number. This one-way coupling requires incorporation of both stages of development for an accurate description, as done in the present model. During pipe-flow, the first-order model employs a more-rapid development rate than during jet-flight (due to the additional pressure-driven flow) — converging to more complex, well-known models, within a few pipe diameters (for Re = 200 to 2300). During flight, the model describes velocity profile relaxation, which is dominated by viscous diffusion and assisted by jet contraction. Jet contraction is dependent on the emerging velocity profile and liquid-vapor surface tension. For most relevant conditions surface tension is negligible, under which the first-order model centerline velocity decay prediction agrees well with both present simulations and previous works. Thereby, the present work lays the foundation for a simpler, more useable model for predicting heat transfer under an impinging free-surface jet, over a wide range of conditions (various liquids, pipe-type nozzles of different lengths, flow-rates and nozzle-to-plate distances), as part of an ongoing study into micro-jet array heat transfer.

Heat Transfer Analysis of Falling Film Evaporation on a Horizontal Elliptical Tube

2012 ◽  
Vol 134 (6) ◽  
Author(s):  
Saeid Jani ◽  
Meysam Amini
Keyword(s):  
Heat Transfer ◽  
Surface Tension ◽  
Heat Transfer Coefficient ◽  
Free Surface ◽  
Transfer Coefficient ◽  
Jet Impingement ◽  
Heat Transfer Analysis ◽  
Falling Film ◽  
Transfer Coefficients ◽  
Constant Wall Temperature

Heat and mass transfer analysis of falling liquid film over a heated horizontal elliptical tube used in desalination systems are investigated. The heat transfer analysis is based on the energy integral formulation with constant wall temperature. Thermal conditions at free surface of the liquid falling film are assumed to be subcooled and saturated, and the effects of surface tension have been considered. The effects of boiling and ripple at the film free surface have been ignored. Heat transfer zoning is considered as the three distinct regions, namely, the jet impingement region, the thermal developing region, and the fully developed region. Extensive analytical study is performed on the thermal hydraulic behavior of the three above mentioned regions, and correlations for both of the film and thermal boundary layer thicknesses, as well as the local and average heat transfer coefficients, have been derived. The results show that the effects of surface tension on heat transfer coefficient is nearly negligible. Based on the presented results, it can be emphasized that the overall heat transfer coefficient increases by increasing the ellipticity of the tube, implying that the elliptical tubes possess more advantages over circular tubes in desalination systems. Comparisons of the analytical results with the existing experimental data verify the validation of the present study.

A note on the instabilities of a horizontal shear flow with a free surface

2000 ◽  
Vol 406 ◽  
pp. 337-346 ◽  
Author(s):  
L. ENGEVIK
Keyword(s):  
Surface Tension ◽  
Free Surface ◽  
Shear Flow ◽  
Velocity Profile ◽  
Froude Number ◽  
The Other ◽  
Algebraic Equations ◽  
Horizontal Shear ◽  
Analytical Treatment ◽  
Unstable Region

The instabilities of a free surface shear flow are considered, with special emphasis on the shear flow with the velocity profile U* = U*0sech2 (by*). This velocity profile, which is found to model very well the shear flow in the wake of a hydrofoil, has been focused on in previous studies, for instance by Dimas & Triantyfallou who made a purely numerical investigation of this problem, and by Longuet-Higgins who simplified the problem by approximating the velocity profile with a piecewise-linear profile to make it amenable to an analytical treatment. However, none has so far recognized that this problem in fact has a very simple solution which can be found analytically; that is, the stability boundaries, i.e. the boundaries between the stable and the unstable regions in the wavenumber (k)–Froude number (F)-plane, are given by simple algebraic equations in k and F. This applies also when surface tension is included. With no surface tension present there exist two distinct regimes of unstable waves for all values of the Froude number F > 0. If 0 < F [Lt ] 1, then one of the regimes is given by 0 < k < (1 − F2/6), the other by F−2 < k < 9F−2, which is a very extended region on the k-axis. When F [Gt ] 1 there is one small unstable region close to k = 0, i.e. 0 < k < 9/(4F2), the other unstable region being (3/2)1/2F−1 < k < 2 + 27/(8F2). When surface tension is included there may be one, two or even three distinct regimes of unstable modes depending on the value of the Froude number. For small F there is only one instability region, for intermediate values of F there are two regimes of unstable modes, and when F is large enough there are three distinct instability regions.

Effect of Temperature Ratio on Jet Impingement Heat Transfer in Active Clearance Control Systems

2019 ◽  
Vol 141 (8) ◽  
Author(s):  
Riccardo Da Soghe ◽  
Cosimo Bianchini ◽  
Jacopo D’Errico ◽  
Lorenzo Tarchi
Keyword(s):  
Heat Transfer ◽  
Jet Impingement ◽  
Effect Of Temperature ◽  
Internal Cooling ◽  
Temperature Ratio ◽  
Present Contribution ◽  
Wide Range ◽  
Depth Analysis ◽  
The Impact ◽  
Clearance Control

Impinging jet arrays are typically used to cool several gas turbine parts. Some examples of such applications can be found in the internal cooling of high-pressure turbine airfoils or in the turbine blade tip clearances control of aero-engines. The effect of the wall-to-jets temperature ratio (TR) on heat transfer is generally neglected by the correlations available in the open literature. In the present contribution, the impact of the temperature ratio on the heat transfer for a real engine active clearance control system is analyzed by means of validated computational fluid dynamics (CFD) computations. At different jets Reynolds number and considering several impingement array arrangements, a wide range of target wall-to-jets temperature ratio is accounted for. Computational results prove that both local and averaged Nusselt numbers reduce with increasing. An in-depth analysis of the numerical data shows that the last mentioned evidence is motivated by both the heat transfer incurring between the spent coolant flow and the fresh jets and the variation of gas properties with temperature through the boundary layer. A scaling procedure, based on the TR power law, was proposed to estimate the Nusselt number at different wall temperature levels necessary to correct available open-literature correlations, typically developed with small temperature differences, for real engine applications.

Application of a Simplified Velocity Profile to the Prediction of Pipe-Flow Heat Transfer

1968 ◽  
Vol 90 (2) ◽  
pp. 191-198 ◽  
Author(s):  
R. D. Haberstroh ◽  
L. V. Baldwin
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Velocity Profile ◽  
Pipe Flow ◽  
Energy Equation ◽  
Momentum Equation ◽  
Turbulent Pipe Flow ◽  
Transfer Coefficients ◽  
Constant Property ◽  
Wide Range

The temperature profiles and heat-transfer coefficients are predicted for fully developed turbulent pipe flow with constant wall heat flux for a wide range of Prandtl and Reynolds numbers. The basis for integrating the energy equation comes from a continuously differentiable velocity profile which fits the physical boundary conditions and is a rigorous (though not necessarily unique) solution of the Reynolds equations. This velocity profile is the semiempirical relation proposed by S. I. Pai, reference [12]. The assumptions are those of steady, incompressible, constant-property, fully developed, turbulent flow of Newtonian fluids in smooth, circular pipes with constant heat flux at the wall. The ratio of the turbulent thermal diffusivity to the turbulent momentum diffusivity is taken to be unity. The thermal quantities are obtained by numerical integration of the energy equation, and they are presented as curves and tables. A compact formula for the Nusselt number is given for a wide range of Reynolds and Prandtl numbers. The results degenerate identically to the case of laminar flow. The heat-transfer calculation requires neither adjustable factors nor data-fitting beyond the empirical constants in the momentum equation; thus this analysis constitutes a heat-transfer prediction to be tested against heat-transfer data.

Novel Jet Impingement Cooling Geometry for Combustor Liner Backside Cooling

2009 ◽  
Vol 1 (2) ◽  
Author(s):  
E. I. Esposito ◽  
S. V. Ekkad ◽  
Yong Kim ◽  
Partha Dutta
Keyword(s):  
Heat Transfer ◽  
Velocity Profile ◽  
Jet Impingement ◽  
Local Heat Transfer ◽  
Reynolds Numbers ◽  
Impinging Jets ◽  
Transfer Coefficients ◽  
Jet Velocity ◽  
Corrugated Wall ◽  
Combustor Liner

Impinging jets are commonly used to enhance heat transfer in modern gas turbine engines. Impinging jets used in turbine blade cooling typically operate at lower Reynolds numbers in the range of 10,000–20,000. In combustor liner cooling, the Reynolds numbers of the jets can be as high as 60,000. The present study is aimed at experimentally testing two different styles of jet impingement geometries to be used in backside combustor cooling. The higher jet Reynolds numbers lead to increased overall heat transfer characteristics, but also an increase in crossflow caused by spent air. The crossflow air has the effect of rapidly degrading the downstream jets at high jet Reynolds numbers. In an effort to increase the efficiency of the coolant air, configurations designed to reduce the harmful effects of crossflow are studied. Two main designs, a corrugated wall and extended port, are tested. Local heat transfer coefficients are obtained for each test section through a transient liquid crystal technique. Results show that both geometries reduce the crossflow induced degradation on downstream jets, but different geometries perform better at different Reynolds numbers. The extended port and corrugated wall configurations show similar benefits at the high Reynolds numbers, but at low Reynolds numbers, the extended port design increases the overall level of heat transfer. This is attributed to the developed jet velocity profile at the tube exit. The best possible explanation is that the benefit of the developed jet velocity profile diminishes as jet velocities rise and the air has lesser time to develop prior to exiting.

Predicting Heat Transfer From Unsteady Synthetic Jets

2012 ◽  
Vol 134 (8) ◽  
Author(s):  
Mehmet Arik ◽  
Tunc Icoz
Keyword(s):  
Heat Transfer ◽  
Heat Transfer Coefficient ◽  
Transfer Coefficient ◽  
Jet Impingement ◽  
Synthetic Jet ◽  
Synthetic Jets ◽  
Operating Conditions ◽  
Small Scale ◽  
Wide Range ◽  
The Heat Transfer Coefficient

Synthetic jets are piezo-driven, small-scale, pulsating devices capable of producing highly turbulent jets formed by periodic entrainment and expulsion of the fluid in which they are embedded. The compactness of these devices accompanied by high air velocities provides an exciting opportunity to significantly reduce the size of thermal management systems in electronic packages. A number of researchers have shown the implementations of synthetic jets on heat transfer applications; however, there exists no correlation to analytically predict the heat transfer coefficient for such applications. A closed form correlation was developed to predict the heat transfer coefficient as a function of jet geometry, position, and operating conditions for impinging flow based on experimental data. The proposed correlation was shown to predict the synthetic jet impingement heat transfer within 25% accuracy for a wide range of operating conditions and geometrical variables.

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