Numerical Analysis of Heat Transfer from a Moving Surface Due to Impingement of Slot Jets

Heat transfer from a moving surface with uniform wall temperature due to impingement of series of slot jets has been investigated numerically. In the present paper, transition–shear stress transport model has been used for numerical simulations, which can predict the heat transfer in laminar as well as turbulent flows. This model is adopted here to study the transport phenomenon and predict the transition from laminar to turbulent flow seamlessly under different surface velocities. The present model with stationary surface is validated with the correlation given by Martin for series of slot jets. It has also shown good agreement with existing data for both laminar and turbulent slot jets, and is further studied to understand the heat transfer under wide range of flow conditions and the effect of surface velocity on flow regime. The range of Reynolds number is from 100 to 5,000, whereas surface velocity varied up to six times the jet velocity at the nozzle exit. It has been observed that at high surface velocities the heat transfer from the moving wall is more than stationary case. The transition from laminar to turbulent regime is found to be starting at a Reynolds number of 400 and turns completely turbulent at a Reynolds number of 3,000. Q-criterion is used to confirm the transition zone by observing the breaking of vortices at higher Reynolds number.     

Numerical solution of three-dimensional rectangular submerged jets with the evidence of the undisturbed region of flow

ABSTRACT

The evolution of turbulent rectangular submerged free jets has been investigated numerically with a two-dimensional (2D) approach by the present authors and, by using the large eddy simulations (LES) at several Reynolds numbers. The average numerical results confirmed the presence of the undisturbed region of flow (URF) located between the slot exit and the beginning of the potential core region (PCR) previously observed experimentally at the University of Rome “Tor Vergata” by Gori and coworkers. The 2D study of the present authors carried out under the conditions previously investigated in the literature, showed that the URF has a self-similar behavior, and proposed a new law for the evolution of the momentum. The present paper extends the LES to three-dimensional (3D) rectangular submerged free jets, in the range from Re = 5,000 to Re = 40,000, showing that the self-similar behavior of URF is also present in the 3D numerical simulations, as well as in the PCR and in the fully developed region (FDR).     

Mean Flow and Thermal Characteristics of a Turbulent Dual Jet Consisting of a Plane Wall Jet and a Parallel Offset Jet

The standard high-Reynolds number two-equation k ? ? model is used to study the flow and thermal characteristics of a dual jet consisting of a plain wall turbulent jet and a parallel turbulent offset jet (hereafter, dual jet). The flow and thermal characteristics are presented in the form of streamlines, mean velocity vector, turbulent kinetic energy, dissipation of turbulent energy, Reynolds stresses, and isothermal contour plots. The variation in local heat flux and local Nusselt number on the bottom wall is also presented. The finite-volume-method-based SIMPLE algorithm is utilized for understanding the complex nature of flow arising due to a dual jet. The convective flux is discretized using the power-law upwind scheme, while the diffusive term is discretized using the central difference scheme. To study the effect of offset ratio, which is defined as the ratio of height of the jet from the horizontal wall to the width of the jet (nozzle), it is varied between 3 and 15 at an interval of 2. It is noted that the presence of a wall jet in addition to the parallel offset jet has a significant effect on flow and thermal characteristics.     

Heat transfer characteristics of a slot jet impinging on a semi-circular convex surface

Surface heat transfer characteristics of a heated slot jet impinging on a semi-circular convex surface have been investigated by using the transient heating liquid crystal technique. Free jet velocity, turbulence and temperature characteristics have been determined by using a combination of an X-wire and a cold wire anemometry. The parametric effects of jet Reynolds number (Re_W) ranging from 5600 to 13,200 and the dimensionless slot nozzle-to-impingement surface distance (Y/W) ranges from 2 to 10 on the local circumferential heat transfer have been studied. Local circumferential Nusselt number (Nu_S) decreases with increasing the dimensionless circumferential distance (S/W) from its maximum value at the stagnation point up to S/W=3.1. The transition in the wall jet from laminar to turbulent flow was completed by about 3.3?S/W?4.2 which coincided with a secondary peak in heat transfer. Correlations of local and average Nusselt numbers with Re_W, Y/W and S/W have been established for the stagnation point and the circumferential distribution. The rate of decay of average circumferential Nusselt numbers around the semi-circular convex surface is much faster than that which occurs laterally along the flat surface. As Y/W increases, the effect of surface curvature becomes apparent and the difference between the flat surface correlation and the convex surface becomes more pronounced.     

Experimental investigation and modelling of a buoyant attached plane jet in a room

Buoyant attached jets are widely used in various types of supply air devices especially in office buildings. This study focuses on a two-dimensional cooled attached jet characteristic, including mean flow field structure, specification of the jet regions and maximum velocity decay. A new superimposing model is derived to predict the maximum velocity decay and validated by measurement results. The measurement results demonstrate that the intermediate region of a buoyant jet does exist when an inner layer extends downstream of the jet slot. In addition, by assuming that the buoyant force is the main extra force on the jet flow in the acceleration process, the superimposing model predicted the maximum velocity decay with precise accuracy in a Reynolds number range of 667–4000, based on slot heights of 20 and 30 mm and slot velocities of 0.50, 1.00 and 2.00 m/s. At a distance of 1000 mm from the slot, the velocity profile displays a self similarity character like an isothermal turbulent jet. In the final region, where the buoyancy flux completely dominates the jet, the jet behaved like a plume with an unstable flow field.     

Local heat transfer distribution on a smooth flat plate impinged by a slot jet

Experimental investigation of local heat transfer distribution on a smooth flat plate impinged by a normal slot jet is conducted. Present study concentrates on the influence of jet-to-plate spacing (z/b) and Reynolds number on the fluid flow and heat transfer distribution. A single slot jet with an aspect ratio (l/b) of about 50 is chosen to get the fully developed flow at the nozzle exit. Reynolds number based on slot width is varied from 4200 to 12,000 and jet-to-plate spacing (z/b) is varied from 0.5 to 12. The local heat transfer coefficients are estimated from the thermal images obtained from infrared thermal imaging camera. Measurement for the static wall pressure is carried out for various jet-to-plate spacings at a Reynolds number of 12,000. Normalized value of turbulence and velocity are measured using hot wire anemometer along the streamwise direction (x/b) for jet-to-plate spacings (z/b) of 1, 2, 4, 6, 8, 10 and 12. The entire flow field is divided into three regimes namely stagnation region (laminar boundary layer associated with favorable pressure gradient), transition region (associated with increase in turbulence intensities and heat transfer) and turbulent wall jet region. Semi-empirical correlation for the Nusselt number in the stagnation region is proposed. Heat transfer characteristics in the transition region are explained based on the fluid dynamic behavior from the hot wire measurements. Semi-empirical correlation for the Nusselt number in the wall jet region is presented using the velocity profile obtained from the hot wire measurements.     

Nonlinear flow and heat transfer dynamics of a slot jet impinging on a slightly curved concave surface

The nonlinear flow and heat transfer characteristics for a slot jet impinging on a slightly curved concave surface are experimentally studied here. The effects of jet Reynolds number on the jet velocity distribution and circumferential Nusselt numbers are examined. The nozzle geometry is a rectangular slot and the dimensionless nozzle-to-surface distance equals to L^⁎ = 8. The constant heat fluxes are accordingly applied to the surface to obtain an impingement cooling by the air jet at ambient temperature. The measurements are made for the jet Reynolds numbers of 8617, 13 350 and 15 415. New correlations for local, stagnation point, and average Nusselt numbers as a function of jet Reynolds number and dimensionless circumferential distance are reported.     

Turbulent impinging jet heat transfer enhancement due to intermittent pulsation

A numerical study was carried out of heat transfer under a pulsating turbulent slot impinging jet. The jet velocity was varied in an intermittent (on–off) fashion. The effects of the time-mean jet Reynolds number, temperature difference between the jet flow and the impinging surface, nozzle-to-target distance as well as the frequency on heat and mass transfer were examined. The numerical results indicate significant heat transfer enhancement due to intermittent pulsation of the jet flow over a wide range of conditions for both cooling and heating cases. Simulations of the flow and temperature fields show that the instantaneous heat transfer rate on the target surface is highly dependent on the hydrodynamic and thermal boundary layer development with time.     

Numerical Study of Pulsed Turbulent Plane Wall Jet by Low-Reynolds-Number k–ε Model

The present study reports on the numerical characterization of the influence of an initial perturbation in the development of turbulent plane two-dimensional wall jets. At the nozzle exit, the pulsation is imposed by a vertical component velocity: u = u ₀[1 + Asin(ω t)]. In the configuration investigated, the jet may be either isothermal or submitted to various wall thermal boundary conditions: uniform temperature in mixed-convection regime or uniform heat flux in forced-convection regime. Numerical modeling of the pulsed wall jet is performed using a low-Reynolds number k–ε model. A finite-difference method, sing a staggered grid, is employed to solve the coupled governing equations associated to the inlet and boundary conditions. The effects of the parameters characterizing the pulsation, such as the amplitude and the frequency, on the dynamic, turbulent, and thermal characteristics of the turbulent wall jets are investigated in detail.     

3D Numerical study on the flow topology and heat transfer characteristics of turbulent forced convection in spirally corrugated tube

ABSTRACT

This paper presents a numerical analysis on flow configurations and heat transfer characteristics of turbulent forced convection in spirally corrugated tubes. The influences of corrugation depth (DR = 0.02–0.16), pitch ratio (PR = 0.10–1.00), and Reynolds number (Re = 5,000–20,000) on flow structure and heat transfer characteristics are described. Comparisons between the full length and periodic domains are also reported. The results show that spirally corrugated tubes induced vortex flows which helped to increase heat transfer due to enhanced fluid mixing. The maximum thermal enhancement factor of 1.16 was obtained by using the spirally corrugated tube with DR = 0.06, PR = 0.25 at Re = 5,000.     

Numerical simulation and optimization of turbulent fluids in a three-dimensional angled ribbed channel

ABSTRACT

In this study, numerical simulations of turbulent steam forced convection in a three-dimensional angled ribbed channel with constant heat flux are investigated. The elliptical, coupled, steady-state, and three-dimensional governing partial differential equations for turbulent forced convection are solved numerically using the finite volume approach. The standard k?? turbulence model is applied to solve the turbulent governing equations. Numerical results are first validated using reference’s data reported in the literature and the maximum discrepancy between them is 3%. The effects of Reynolds number, angled rib height ratio, angled rib pitch ratio, and rib angle on the friction factor ratio and averaged Nusselt number are investigated. Numerical results show that the increase in heat transfer is accompanied by an increase in the friction factor ratio of the steam, the minimum friction factor ratio occurs at θ = 30^○ and the maximum friction factor ratio is found at θ = 60^○. In addition, after the validation of the numerical results, the numerical optimization of this problem is also presented by using the response surface methodology coupled with computational fluid dynamic method.     

Nonlinear flow and heat transfer dynamics of impinging jets onto slightly-curved surfaces

The nonlinear flow and heat transfer characteristics for a slot-jet impinging on slightly-curved surfaces are experimentally studied here. The effects of curved surface geometry and jet Reynolds number on the jet velocity distribution and circumferential Nusselt numbers are examined. Two different slightly-curved surface geometries of convex and concave are used as target surfaces. The nozzle geometry is a rectangular slot, and the dimensionless nozzle-to-surface distance equals to L¹ = 8. The constant heat fluxes are accordingly applied to the surfaces to obtain an impingement cooling by the air jet at ambient temperature. The measurements are made for the jet Reynolds numbers of Re = 8617, Re = 13 350 and Re = 15 415 for both curved surfaces. The velocity distributions of issuing jet from the nozzle exit to the target surface are obtained by a highly sensitive hot-wire anemometer. The T-type thermocouples are used to measure local temperatures of both the air jet and the plates. Two-dimensional velocity measurements show that the surfaces are remained out of the potential core region for all Re tested here. New correlations for local, stagnation point, and average Nusselt numbers as a function of jet Reynolds number and dimensionless circumferential distance are reported. The correlations reveal that the impinging cooling rate is higher with the concave surface and increase with increasing Re.     

Evaluation of Turbulence Models in the Prediction of Heat Transfer Due to Slot Jet Impingement on Plane and Concave Surfaces

The performance of several turbulence models in the prediction of convective heat transfer due to slot jet impingement onto flat and concave cylindrical surfaces is evaluated against available experimental data. The candidate models for evaluation are (1) the standard k – ε model, (2) the RNG k – ε model, (3) the realizable k – ε model, (4) the SST k – ω model, and (5) the LRR Reynolds stress transport model. Various near-wall treatments such as equilibrium wall function and two-layer enhanced wall treatment are used in combination with these turbulence models. The computations are performed using the commercial computational fluid dynamics (CFD) code Fluent. From the validation exercises, it is found that when the impingement surface is outside the potential core of the jet, most of the turbulence models predict reasonably accurate thermal data (local Nusselt number variation along the impingement surface). When the impingement surface is within the potential core of the jet, the turbulence models grossly overpredict the Nusselt number in the impingement region, but in the wall jet region the Nusselt number prediction is fairly accurate. Overall, the RNG k – ε model with the enhanced wall treatment and the SST k – ω model predict the Nusselt number distribution better than the other models for the flat plate as well as for the concave surface impingement cases. However, the hydrodynamic data such as the mean velocity profiles are not accurately predicted by the SST k – ω model for the concave surface impingement case, whereas the RNG k – ε model predictions of the velocity profiles agree very well with the experiment. The Reynolds stress model does not show any distinctive advantage over the other eddy viscosity models.     

A numerical study of the unsteady flow and heat transfer in a transitional confined slot jet impinging on an isothermal surface

A numerical finite-difference approach was used to compute the steady and unsteady flow and heat transfer due to a confined two-dimensional slot jet impinging on an isothermal plate. The jet Reynolds number was varied from Re=250 to 750 for a Prandtl number of 0.7 and a fixed jet-to-plate spacing of H/W=5. The flow was found to become unsteady at a Reynolds number between 585 and 610. In the steady regime, the stagnation Nusselt number increased monotonically with Reynolds number, and the distribution of heat transfer in the wall jet region was influenced by flow separation caused by re-entrainment of the spent flow back into the jet. At a supercritical Reynolds number of 750 the flow was unsteady and the net effect in the time mean was that the area-averaged heat transfer coefficient was higher compared to what it would have been in the absence of jet unsteady effects. The unsteady jet exhibited a dominant frequency that corresponded to the formation of shear layer vortices at the jet exit. Asymmetry in the formation of the vortex sheets caused deformation or buckling of the jet that induced a low-frequency lateral jet “flapping” instability. The heat transfer responds to both effects and leads to a broadening of the cooled area.     

Study of the heat transfer characteristics in turbulent combined wall and offset jet flows

The heat transfer study of a combined wall jet and offset jet flow with different wall jet and offset jet flow velocities are considered. The flow is considered two-dimensional, steady, incompressible, turbulent at high Reynolds number with negligible body forces. The streamline curvature modification of the standard k–ε model is used to carry out the turbulence modeling. The Reynolds number is varied from 10⁴ to 4 × 10⁴ and Pr = 0.71 is taken for all computations. Constant wall temperature and constant wall heat flux boundary conditions are considered. The results are presented in the form of local Nusselt number, local heat flux, surface temperature in case of constant heat flux condition, average Nusselt number and total heat transfer.     

CFD and correlations of the heat transfer from a wall at constant temperature to an impinging swirling jet

Numerical simulations of the impingement of a swirling jet against a heated solid wall at a prescribed temperature are presented in order to propose correlations of the heat transfer coefficients along the heated wall as a function of the jet Reynolds number Re, jet swirl intensity S_i, jet average turbulent intensity I_avg, and jet to wall spacing H. The swirling jet used as boundary condition of the numerical simulations is the one described by Ortega-Casanova et al. [1]. It is created by a experimental nozzle (whose exit diameter is D) and with the swirl given to the jet by moving swirl blades: different blade orientations give jets with different swirl intensities. In Ortega-Casanova et al. [1], the jet velocity components (measured by means of a LDA system) just at the nozzle exit and their mathematical models are also presented for seven Reynolds numbers and each nozzle configuration. The LDA measurements show the jet is axisymmetric and highly turbulent. For those reasons, axisymmetric flow and turbulent models are used in the simulations. The same seven Reynolds numbers and three nozzle-to-wall distances are simulated numerically in this work. Taking into account the blade orientations, the Reynolds numbers and the nozzle-to-wall distances, a total of 63 different simulations have been carried out. From them, correlations of the area-weighted average Nusselt number Nu_avg and the stagnation point Nusselt number Nu₀ as a function of the dimensionless parameter Re (ranging from around 7000 to 20 000), S_i (ranging from around 0.015 to 0.45), I_avg (ranging from around 10 to 40%), and H/D (=5, 10 and 30), are proposed. The results presented in Ortega-Casanova [2], where the heat transfer when other blade orientation is studied, have been also taken into account to obtain some of the proposed correlations.     

Wall-Resolved LES and Zonal LES of Round Jet Impingement Heat Transfer on a Flat Plate

Numerical large-eddy simulation (NLES) is performed for a round jet impinging on a flat surface at a Reynolds number of Re = 23,000 for nozzle-to-plate spacings of H/D = 6 and 2, where H is the distance from the nozzle to the plate and D is the jet diameter. The Reynolds number has been set to match the experiments of Cooper et al. (Int J. Heat Mass Transfer, vol. 36, pp. 2675–2684, 1993). Two numerical large-eddy simulation approaches are examined. The first quasi-direct numerical simulation (DNS) approach resolves streaklike structures using fine near-wall grids; the second is the zonal approach of Tucker (Int J. Heat Fluid Flow, vol. 25, pp. 625–635, 2004), which uses the Wolfshtein k–l (Int J. Heat Mass Transfer, vol. 12, pp. 301–318, 1969) Reynolds-averaged Navier-Stokes (RANS) model near the walls and NLES elsewhere. A Hamilton-Jacobi equation is used to match the RANS region to the NLES zone. The use of a Spalart-Allmaras model leads to low levels of turbulent viscosity in the near-wall region. This is also observed when using detached-eddy (DES) when using a volume-based filter. The use of the standard DES filter based on maximum grid spacing prevents jet shear-layer transition. The k–l near-wall model maintains RANS levels of turbulent viscosity in the boundary layer. The results of both the near-wall quasi-DNS and hybrid RANS-NLES methods are generally encouraging.     

Heat Transfer Enhancement by Jet Impingement on a Flat Surface with Detached-Ribs under Cross-flow Conditions

In this article, the heat transfer augmentation on a flat surface with jet impingement on axisymmetric detached ribs is numerically investigated. Both single and multiple jet impingement with and without crossflow interaction is investigated. Numerical simulations are done using Reynold-averaged Navier–Stokes (RANS) equations with a shear stress transport (SST) model with the commercial CFD code ANSYS-CFX. The influence of jet Reynolds number (7000 ≤ Re _j  ≤ 78,000), blowing ratio (5.8 ≤ M ≤ 11.5), and jet-outlet-to-target wall distance (2 ≤ H/D ≤ 6) are examined. Results show that the heat transfer is enhanced on the target wall with detached ribs in single and multiple jet impingement at moderate crossflow speeds.     

Numerical study of transient conjugate heat transfer of a turbulent impinging jet

This study presents the numerical study of transient conjugate heat transfer in a high turbulence air jet impinging over a flat circular disk. The numerical simulation of transient, two-dimensional cylindrical coordinate, turbulent flow and heat transfer is adopted to test the accuracy of the theoretical model. The turbulent governing equations are resolved by the control-volume based finite-difference method with a power-low scheme, and the well-known low-Re κ–ω turbulence model to describe the turbulent structure. The SIMPLE algorithm is adopted to solve the pressure–velocity coupling. The parameters studied include turbulent flow Reynolds number (Re = 16,100–29,600), heated temperature of a circular disk (T_h = 373 K) or heat flux (q″ = 63–189 kW/m²), and orifice to heat-source spacing (H/D = 4–10). The numerical results of the transient impinging process indicate that the jet Reynolds number has a significant effect on the hydrodynamics and heat transfer, particularly in the stagnation region of an impinging jet. High turbulence values lead to greater heat transfer coefficients in the stagnation region and cause a bypass of the laminar-to-turbulent transition region in the wall jet region. Induced turbulence from the environment around the jet also influences the variation of the stagnation heat transfer. The modeling approach used here effectively captures both the stagnation region behavior and the transition to turbulence, thus forming the basis of a reliable turbulence model.