A further investigation of effects of jet-disk separation distance on steady mixed convective vortex flow resulting from a confined impinging air jet

We extend our previous study [J.C. Hsieh, T.F. Lin, Effects of jet-to-disk separation distance on the characteristics of mixed convective vortex flow in an impinging air jet confined in a cylindrical chamber, Int. J. Heat Mass Transfer 48 (2005) 511–525] here to further investigate how the jet-disk separation distance H affects the mixed convective vortex flow resulting from a round air jet impinging onto a heated horizontal circular disk confined in a vertical cylindrical chamber. The experiment is conducted for the jet-disk separation distance varying from 40.0 to 60.0 mm and the jet flow rate is varied from 0 to 12.0 slpm (standard liter per minute) for the jet Reynolds number Re_j ranging from 0 to 1623. The temperature difference between the disk and the air injected into the chamber is varied from 0 to 25.0 °C for the Rayleigh number Ra ranging from 0 to 507,348. The data from the present study for the ratio H/D_j = 4–6 are compared with our previous study for H/D_j = 1–3. The results indicate that the critical jet Reynolds numbers for the onsets of the secondary and tertiary inertia-driven rolls and for the onset of the buoyancy-driven roll vary nonmonotonically with the jet-disk separation distance due to the complicate changes of the vortex flow structure with H. In the steady vortex flow, both the primary inertia-driven roll and the buoyancy-driven roll get larger at increasing jet-disk separation distance before they contact with each other for H/D_j = 1 and 2. But for H/D_j ≧ 3 the primary roll and buoyancy roll do not always grow at increasing H. Finally, empirical correlations are proposed for the critical conditions leading to the onsets of the inertia- and buoyancy-driven vortex rolls.     

Unstable vortex flow and new inertia-driven vortex rolls resulting from an air jet impinging onto a confined heated horizontal disk

An experiment combining flow visualization and temperature measurement is carried out here to investigate the possible presence of new inertia-driven vortex rolls and some unique characteristics of the time-dependent mixed convective vortex flow in a high-speed round air jet impinging onto a heated horizontal circular disk confined in a vertical cylindrical chamber. How the jet Reynolds and Rayleigh numbers and jet-to-disk separation distance affect the unique vortex flow characteristics is examined in detail. Specifically, the experiment is conducted for the jet Reynolds number varying from 0 to 1623 and Rayleigh number from 0 to 63,420 for the jet-to-disk separation distance fixed at 10.0, 20.0 and 30.0 mm. The results indicate that at sufficiently high Re_j the inertia-driven tertiary and quaternary rolls can be induced aside from the primary and secondary rolls. At an even higher Re_j the vortex flow becomes unstable due to the inertia-driven flow instability. Only for H = 20.0 mm the flow is also subjected to the buoyancy-driven instability for the ranges of the parameters covered here. Because of the simultaneous presence of the inertia- and buoyancy-driven flow instabilities, a reverse flow transition can take place in the chamber with H = 20.0 mm. At the large H of 30.0 mm the flow unsteadiness results from the mutual pushing and squeezing of the inertia- and buoyancy-driven rolls since they are relatively large and contact with each other. It is also noted that the critical Re_j for the onset of unsteady flow increases with ΔT for H = 10.0 and 20.0 mm. But for H = 30.0 mm the opposite is true and raising ΔT can destabilize the vortex flow. Based on the present data, flow regime maps delineating the temporal state of the flow are provided and correlating equations for the boundaries separating various flow regimes are proposed.     

Structure of mixed convective longitudinal vortex air flow driven by a heated circular plate embedded in the bottom of a horizontal flat duct

In this study experimental flow visualization combined with transient temperature measurement are conducted to investigate the structure of the buoyancy driven longitudinal vortex rolls in low Reynolds number mixed convective air flow through a horizontal flat duct with an isothermally heated circular disk embedded in the bottom plate of the duct for the Reynolds number ranging from 15.1 to 99.2 and Rayleigh number from 3506 to 29,493. How the circular geometry of the heated surface affects the longitudinal vortex flow characteristics is investigated in detail. The results indicate that the longitudinal vortex rolls (L-rolls) in the duct core are induced at more upstream locations than those near the duct sides, which is completely opposite to those induced in a duct with a uniformly heated bottom. Besides, the thermals driven by the circular heated surface are not evenly spaced in the spanwise direction and are slightly asymmetric. It is of interest to note that at a given Rayleigh number Ra the thermals are unstable at high Reynolds numbers, suggesting the existence of the inertia driven instability. Thus the L-rolls evolved from these thermals are also unstable with the presence of nonperiodic generation and disappearance of new L-rolls. But at slightly lower Re the thermals and L-rolls are steady and regular. The vortex flow becomes unstable and irregular for a further reduction in the Reynolds number, which obviously results from the buoyancy driven instability. The simultaneous presence of these two instability mechanisms explains the appearance of the reverse steady-unsteady transition in the vortex flow.Based on the present data, a flow regime map is given to delineate various L-roll patterns driven by the circular heated plate. In addition, the boundaries separating these patterns are empirically correlated. Empirical correlations for the onset points of the L-rolls are also provided.     

Visualization of mixed convective vortex rolls in an impinging jet flow of air through a cylindrical chamber

In this study a combined buoyancy and inertia driven vortex flow in an air jet impinging onto a heated circular plate confined in a cylindrical chamber simulating that in a vertical single-wafer rapid thermal processor for semiconductor manufacturing is investigated experimentally by flow visualization. A copper plate is used here to simulate the wafer for its better uniformity of the surface temperature and air is used to replace the inert gases. We concentrate on how the inlet gas flow rate, temperature difference between the wafer and air jet, and chamber pressure affect the vortex flow. The results show that typically the flow in the chamber is in the form of two-roll structure characterized by a circular vortex roll around the air jet along with another circular roll near the side wall of the chamber. Both rolls are somewhat deformed. The rolls are generated by the reflection of the jet from the wafer and by the deflection of the wall boundary layer flow along the wafer surface by the upward buoyancy due to the heated wafer. At low buoyancy and inertia the vortex rolls are steady and axisymmetric. At increasing buoyancy associated with the higher temperature difference and chamber pressure, the inner roll becomes slightly smaller and the outer roll becomes correspondingly bigger. Moreover, at a higher gas flow rate the inner roll is substantially bigger. Based on the present data, a correlation equation is provided to predict the location where the two rolls contact each other, providing the approximate size of the rolls. Moreover, at high buoyancy and inertia the flow becomes time dependent and does not evolve to a steady state.     

Stationary transverse rolls and U-rolls in limiting low Reynolds number mixed convective air flow near the convective threshold in a horizontal flat duct

Combined experimental flow visualization and temperature measurement are carried out in the present study to explore the buoyancy driven vortex flow patterns in a limiting low Reynolds number mixed convective air flow through a bottom heated horizontal flat duct. In Particular, attention is paid to the flow approaching the natural convection limit (Re=0) for Re=1.0 and 2.0 with the Rayleigh number near the critical level for the onset of convection for 1200?Ra?4000. Results from the flow visualization have revealed two unfamiliar vortex flow patterns which were not seen in our earlier study [Int. J. Heat Mass Transfer 44 (4) (2001) 705]. One is characterized by the stable stationary transverse rolls in the duct entry and stable longitudinal rolls in the downstream. Another is in the form of U-rolls. The relations of these two patterns with those reported in the literature from analytical, numerical and experimental studies are discussed. Moreover, stable longitudinal rolls along with nonperiodic traversing waves, and mixed longitudinal and transverse rolls as well as irregular cells which appear in the higher Reynolds number for 3.0?Re?5.0 are also noted here. The temporal and spatial characteristics of the unfamiliar vortex flows are inspected in detail. In addition, the flow formation processes leading to the two unfamiliar vortex flow structures are also examined carefully. During the flow formation we noted merging of longitudinal and transverse rolls to form U-rolls, splitting of rolls into cells and the reverse process of cell integration into rolls, aside from the generation of the longitudinal and transverse rolls. Finally, a flow regime map is provided to delineate various vortex flow structures observed in this study and in the previous study (cf. the above-mentioned reference) driven by the slightly supercritical and subcritical buoyancies for 1.0?Re?5.0.     

Mixed convection on jet impingement cooling of a constant heat flux horizontal porous layer

In the present study, numerical investigation of jet impingement cooling of a constant heat flux horizontal surface immersed in a confined porous channel is performed under mixed convection conditions, and the Darcian and non-Darcian effects are evaluated. The unsteady stream function-vorticity formulation is used to solve the governing equations. The results are presented in the mixed convection regime with wide ranges of the governing parameters: Reynolds number (1 ≤ Re ≤ 1000), modified Grashof number (10 ≤ Gr¹ ≤ 100), half jet width (0.1 ≤ D ≤ 1.0), Darcy number (1 × 10^?6 ≤ Da ≤ 1 × 10^?2), and the distance between the jet and the heated portion (0.1 ≤ H ≤ 1.0). It is found that the average Nusselt number (Nu_avg) increases with increase in either modified Grashof number or jet width for high values of Reynolds number. The average Nusselt number also increases with decrease in the distance between the jet and the heated portion. The average Nusselt number decreases with the increase in Da for the non-Darcy regime when Re is low whereas Nu_avg increases when Re is high. It is shown that mixed convection mode can cause minimum heat transfer unfavorably due to counteraction of jet flow against buoyancy driven flow. Minimum Nu_avg occurs more obviously at higher values of H. Hence the design of jet impingement cooling through porous medium should be carefully considered in the mixed convection regimes.     

Electrochemical mass transfer between an impinging jet and a rotating disk in a confined system

This paper presents the mass transfer results from an impinging liquid jet to a rotating disk. The mass transfer coefficients were measured using the electrochemical limiting diffusion current technique (ELDCT). Rotational Reynolds number (Re_r) in the range of 3.4 × 10⁴–1.2 × 10⁵, jet Reynolds number (Re_j) 1.7 × 10⁴–5.3 × 10⁴ and non-dimensional jet-to-disk spacing (H/d) 2–8 were taken into consideration as parameters. It was found that the jet impingement resulted in a substantial enhancement in the mass transfer compared to the case of the rotating disk without jet.     

Laser schlieren measurement of vertical flow past a heated horizontal circular cylinder

Flow past a heated horizontal circular cylinder in the vertically upward direction has been experimentally studied using a monochrome schlieren technique. Both free convection ((Gr)^1/3Re)=0 and mixed convection ((Gr)^1/3Re)=1011, 1055, 1095 and 1133 cases have been studied. The Reynolds number based on the cylinder diameter is set at 102 for the mixed convection, and four heating levels have been utilized with Grashof numbers of Gr=975, 1105, 1240 and 1370. The temperature distribution of the plume, the Strouhal number and the schlieren images have been reported. The vortex shedding frequency decreases with increasing Grashof number and a complete suppression of vortex shedding takes place at Grashof number of 1370. The wake is seen to become visibly narrow during the suppression of vortex shedding. The nondimensional temperature profile inside the plume is a strong function of Grashof number for free convection in comparison to that of mixed convection.     

Heat transfer study in a rotor–stator system air-gap with an axial inflow

Discoidal rotor–stator systems are nowadays sometimes used in electrical wind generator. The cooling of such a system is a major problem due to the fact that high electrical losses are dissipated for relatively low rotational speed, responsible of the cooling. A new cooling solution is then investigated in this paper. So, this paper presents an experimental study of the local heat transfers on the rotor surface in the air-gap of a discoidal rotor–stator system, in which an air jet comes through the stator and impinges the rotor. To determine the surface temperatures, measurements were taken on the rotor, using an experimental technique based on infrared thermography. A thermal balance equation was used to identify the local convective heat transfer coefficient. The influence of the axial Reynolds number Re_j and the rotational Reynolds number Re was measured and compared with the data available in the literature. Local convective heat transfer coefficients were obtained for an inter-disk dimensionless spacing interval G ranging from 0.01 to 0.16 for Re_j between 0 and 41,666 and for Re between 20,000 and 516,000. The rotating disk can thus be divided into zones: one dominated by the air jet near the center of the rotor and one affected by both the air jet and rotation. Even though these two zones are not located in the same place on the disk, the heat transfers with non-zero impinging jets appear to be continuously improved compared to those with no jets. Critical radii over the rotor surface are identified and correlations are given.     

Heat transfer in a small gap between co-axial rotating cylinders

This paper investigates the local heat transfer of a co-axial rotating cylinder. In the inner flow field of the rotating cylinder, the dimensionless parameters include the rotational Reynolds number (Re_Ω) and buoyancy parameter (Gr). The test rig is designed to make the rotating in the inner cylinder and stationary in the outer cylinder. The local temperature distributions of the inner and outer cylinder on axial direction were measured. Under the experimental condition, whereas the ranges of the rotational Reynolds number are 2400 ≤ Re_Ω ≤ 45,000. Experimental results reveal that the rotational Reynolds number's increase is with the heat transfer coefficient distributions increase types. Finally, the local heat transfer rate on the wall are correlated and compared with that in the existing literature.     

Oscillatory double-diffusive mixed convection in a two-dimensional ventilated enclosure

By starting from a steady flow configuration based on the work of Deng et al. [Qi-Hong Deng, Jiemin Zhou, Chi Mei, Yong-Ming Shen, Fluid, heat and contaminant transport structures of laminar double-diffusive mixed convection in a two-dimensional ventilated enclosure, Int. J. Heat Mass Transfer 47 (2004) 5257–5269], a numerical investigation was conducted to analyse the unsteady double-diffusive mixed convection in two-dimensional ventilated room due to heat and contaminant sources. Owing to the large number of parameters, the results are reported only for a constant buoyancy ratio N equal to 1. The flow is found to be oscillatory for a fixed Reynolds number (700 ⩽ Re ⩽ 1000) when the Grashof number is varied in a wide range (10³ ⩽ Gr ⩽ 10⁶). Results of the simulations show that the onset of the oscillatory indoor airflow occurs for couples (Re, Gr) values that can be correlated as Re = aGr^b.     

Laminar mixed convection boundary layers induced by a linearly stretching permeable surface

The boundary layer flow on a linearly moving permeable vertical surface is studied when the buoyancy force assists or opposes the flow. Similarity and local similarity solutions are obtained for the boundary layer equations subject to power law temperature and velocity variation. The effect of various governing parameters, such as Prandtl number Pr, injection parameter d, and the mixed convection parameter λ=Gr_x/Re_x², which determine the velocity and temperature distributions, the heat transfer coefficient, and the shear stress at the surface are studied. The heat transfer coefficient increases as λ assisting the flow for all d for uniformly or linearly heated surface and as Pr increases it becomes almost independent of λ. However, as the temperature inversely proportional to the distance up the surface, the buoyancy has no effects on the heat transfer coefficient. Critical buoyancy parameter values are obtained for vanished shear stress and for predominate natural convection. Critical values are also presented for predominate buoyancy shear stress at the surface for assisting or opposing flow. A closed form analytical solution is also presented as a special case of the energy equation.     

Conjugated heat transfer on leading edge of a wedge-shaped concave wall internally impinged by hot jets from corrugated orifice plate

An experimental and numerical investigation is conducted to study the conjugated heat transfer performance on the leading edge of a wedge-shaped concave wall subjected to external cold flow and internal hot jets impingement. A corrugated impinging plate with an extended front-extended port inside the concave cavity is proposed for the purpose of heat transfer enhancement. The effects of corrugation length-to-diameter ratio (H_j/d) ranging from 5 to 11 and width-to-diameter ratio (W_j/d) ranging from 2.5 to 6 on the conjugated heat transfer performance are examined under some representative jet Reynolds numbers (Re_j) in the range of 7900–31,700. The results show that the corrugated impinging plate has a significant impact on improving the conjugated heat transfer performance in the vicinity of concave wall leading edge. The presence of corrugation plays two roles by reducing the jet impinging distance on one hand and aggravating the jet confinement on the other hand. Therefore, it produces more complicated jet impinging flow and convective heat transfer behaviors than the baseline case without corrugation. According to the tested results, the specified area-averaged heating effectiveness is increased approximately 6.3%–18.8% under Re_j = 7900 and 2.5%–9.4% Under Re_j = 31,700 respectively by increasing the corrugation length when W_j/d is fixed as 2.5. The specified area-averaged heating effectiveness is increased approximately 16.1%–22.1% under Re_j = 7900 and 7.7%–12.7% under Re_j = 31,700 respectively by increasing the corrugation width when H_j/d is fixed as 9. In general, the corrugation with larger length and width seems to perform the better heating effectiveness over the entire concave surface. The enhancement of heating effectiveness related to the baseline case behaves more significantly under a smaller jet Reynolds number.     

Local turbulent opposing mixed convection heat transfer in inclined flat channel for stably stratified airflow

Local turbulent mixed convection heat transfer in inclined flat channels (?=20-90° from horizontal position) for opposing flows was investigated for the case when only upper wall is heated (under stably stratified flow conditions). Wide ranges of airflow parameters are covered: Re=4 × 10³-4 × 10⁴, Gr_q=1.7 × 10⁸-1.4 × 10¹⁰, pressures; p=0.2; 0.4; 0.6; 0.8 MPa. Based on analysis of local heat transfer data and existing information in the literature three characteristic regions in the buoyancy parameter range investigated were identified: region without buoyancy instabilities, transition region and region with buoyancy instabilities in whole heated section. For the region without buoyancy instabilities correlation for calculation of heat transfer in inclined flat channels was suggested.     

Low Reynolds number mixed convection in vertical tubes with uniform wall heat flux

Upward mixed convection of air in a long, vertical tube with uniform wall heat flux has been studied numerically for Re=1000, Re=1500 and Gr?10⁸ using a low Reynolds number k-ε model. The results for the fully developed region identify two critical Grashof numbers for each Reynolds number, which correspond to laminar-turbulent transition and relaminarization of the flow. They also distinguish the Re-Gr combinations that result in a pressure decrease over the tube length from those resulting in a pressure increase. A correlation expressing the fully developed Nusselt number in terms of the Grashof and Reynolds numbers is proposed. It is valid for laminar and turbulent flows in the range 1000?Re?1500, Gr?5×10⁷.     

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.     

Fluid flow and heat transfer of mixed convection adjacent to vertical heated plates placed in uniform horizontal flow of air

Experiments have been carried out for mixed convective flows of air adjacent to the vertical heated plates in uniform horizontal forced flows to investigate relationships between the flow and the heat transfer. The experiments cover the ranges of the Reynolds and modified Rayleigh numbers: Re_L = 160 to 2300 and Ra_L^* = 4.3 × 10⁵ to 2.0 × 10⁸. The flow fields over the plates are visualized with particles and smoke. The results show that a stagnation point moves downward away from the center of the plate when the surface heat flux is beyond a critical value. The condition where the stagnation point begins to move is expressed with non‐dimensional parameters as: Gr_L^*/Re_L^2.5 = 0.15. Profiles of measured local heat transfer coefficients are smooth even at the stagnation points in all the cases examined. When buoyancy effect is sufficiently weak, the coefficients agree well with those of the wedge flow. With increasing the surface heat flux, the coefficients are augmented to approach asymptotically the boundary layer solution of natural convection along a vertical heated plate. Finally, forced, mixed, and natural convection regimes are classified by the non‐dimensional parameter (Gr_L^*/Re_L^2.5). © 2009 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.20256     

Vortex shedding and heat transfer dependence on effective Reynolds number for mixed convection around a cylinder in cross flow

The influence of surface heating of a circular cylinder on the wake structure and heat transfer in the range of Reynolds number (Re) for which parallel vortex shedding occurs, is investigated numerically for different values of the buoyancy parameter, Gr. The role of buoyancy induced baroclinic vorticity on the wake formation is addressed in the present study. The variation of Strouhal number and Nusselt number with the ’effective Reynolds number’, is analyzed for different values of cylinder to free stream temperature ratio. Both Strouhal number and the rate of heat transfer increases monotonically with the increase of the effective Reynolds number. The validity of the correlations, which have been established by several authors, between the effective Reynolds number and Strouhal/ Nusselt number for forced convection, is examined in the mixed convection regime. The curves between the effective Reynolds number and the computed data for Strouhal number and Nusselt number do not collapse for the range of temperature ratio considered here. The flow field is found to be asymmetric and the cylinder experiences a negative lift. The drag coefficient increases steadily with the rise of surface temperature.     

Heat transfer from a spinning disk during semi-confined axial impingement from a rotating nozzle

Conjugate heat transfer from a uniformly heated spinning solid disk of finite thickness and radius during a semi-confined liquid jet impingement from a rotating nozzle is studied. The model covers the entire fluid region including the impinging jet on a flat circular disk and flow spreading out downstream under the spinning confinement plate and free surface flow after exposure to the ambient gaseous medium. The model examines how the heat transfer is affected by adding a secondary rotational flow under semi-confined jet impingement. The solution is made under steady state and laminar conditions. The study considered various plate materials such as aluminum, copper, silver, constantan and silicon. Ammonia, water, flouroinert FC-77 and MIL-7808 oil were used as working fluids. The range of parameters covered included Reynolds number (220–900), Ekman number (7.08 × 10^?5–∞), nozzle-to-target spacing (β = 0.25–1.0), disk thicknesses to nozzle diameter ratio (b/d_n = 0.25–1.67), Prandtl number (1.29–124.44) and solid to fluid thermal conductivity ratio (36.91–2222). It was found that a higher Reynolds number increased local heat transfer coefficient reducing the interface temperature difference over the entire disk surface. The rotational rate also increased local heat transfer coefficient under most conditions. An engineering correlation relating the Nusselt number with other dimensionless parameters was developed for the prediction of the system performance.