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.     

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.     

Experimental and numerical investigation of natural convection effects on confined impinging jet heat transfer

The influence of natural convection on the local and average heat transfer at increasing temperature differences between the jet and the target plate from confined impinging jets has been experimentally and numerically investigated. Local Nusselt numbers were obtained numerically for jet Reynolds numbers in the range of 250–1000, and jet to target spacings of 2, 4, 8, 12 jet diameters at various modified Grashof numbers, to determine the effect of buoyancy induced natural convection. To determine the overall effect of natural convection on the average heat transfer, experiments have been conducted for Re numbers in the range 250–5000 and dimensionless jet to target spacing 2, 4, 6, 8, and 12 at increasing modified Grashof numbers. It has been determined that buoyancy induced natural convection might have opposing or assisting influence on local heat transfer at different locations of the target plate. It has also been shown that especially at low jet inlet velocities the average heat transfer coefficient at the highest modified Grashof number, where the natural convection is effective, is higher than the value corresponding to the lowest Grashof number at which buoyancy effects are negligible, by as much as 37%.     

Characteristics of vortex flow in a low speed air jet impinging onto a heated disk in a vertical cylindrical chamber

An experiment combining flow visualization and transient temperature measurement is carried out to investigate the characteristics of the mixed convective vortex flow resulting from a low speed air jet impinging onto a heated horizontal circular disk confined in a vertical adiabatic cylindrical chamber. Attention is focused on the conditions leading to the onset of the inertia and buoyancy driven vortex rolls and the effects of governing nondimensional groups on the steady and time dependent vortex flow. More specifically, experiments are conducted for the jet Reynolds number varied from 0 to 1082 and Rayleigh number from 0 to 18,790 for two different injection pipes. The results show that typically the steady vortex flow in the processing chamber consists of two inertia-driven and one buoyancy-driven circular vortex rolls. The secondary inertia-driven roll only appears at high jet Reynolds numbers. At low buoyancy-to-inertia ratio Gr/Re_j² the vortex rolls are steady and axisymmetric. But at certain high Gr/Re_j² the vortex flow becomes unstable and the vortex rolls are somewhat deformed. Besides, new vortex rolls can be induced by the additional thermal rising from the heated disk and the splitting of the primary inertia-driven roll. The temporal characteristics of the time periodic vortex flows are examined in detail. In the region dominated by the new rolls the flow oscillates significantly. Finally, empirical equations are proposed to correlate the oscillation frequency of the time periodic flow, and the size and location of the vortex rolls. Furthermore, the conditions for the onset of the buoyancy driven rolls are given. A flow regime map is provided to delineate the temporal state of the vortex flow.     

A Study of Under-expanded Moist Air Jet Impinging on a Flat Plate

When a gas expands through a convergent nozzle in which the ratio of the ambient to the stagnation pressures is higher than that of the critical one, the issuing jet from the nozzle is under-expanded. If a flat plate is placed normal to the jet at a certain distance from the nozzle, a detached shock wave is formed at a region between the nozzle exit and the plate. In general, supersonic moist air jet technologies with non-equilibrium condensation are very often applied to industrial manufacturing processes. In spite of the importance in major characteristics of the supersonic moist air jets impinging to a solid body, its qualitative characteristics are not known satisfactorily. In the present study, the effect of the non-equilibrium condensation on the under-expanded air jet impinging on a vertical flat plate is investigated numerically in the case with non-equilibrium condensation, frequency of oscillation for the flow field becomes larger than that without the non-equilibrium condensation, and amplitudes of static pressure become small compared with those of dry air. Furthermore, the numerical results are compared with experimental ones.     

Effect of jet-jet spacing on convective heat transfer to confined, impinging arrays of axisymmetric air jets

The effects of jet-jet spacing (X_n/D), low nozzle-plate spacings (H/D = 0.25, 1.0 and 6.0) and spent air exits located between the jet orifices were studied on the magnitude and uniformity of the convective heat transfer coefficients for confined 3 × 3 square arrays of isothermal axisymmetric air jets impinging normally to a heated surface. Local and average Nusselt numbers are presented for Reynolds number range of 3500–20 400. The local Nusselt numbers illustrate the (non)uniformity of the heat transfer and aid in understanding the variations in the average Nusselt number. The jet-jet spacing affects the convective coefficient by varying the influence of the adjacent jet interference and fraction of the impingement surface covered by the wall jet. The addition of spent air exits increased the convective coefficient and influenced the location of the optimum separation distance. In addition, significant enhancement of the uniformity and the convective coefficients was observed at H/D = 0.25 and 1.0 when compared to H/D = 6.0.     

Effects of jet plate size and plate spacing on the stagnation Nusselt number for a confined circular air jet impinging on a flat surface

This work deals with the effects of jet plate size and plate spacing (jet height) on the heat transfer characteristics for a confined circular air jet vertically impinging on a flat plate. The jet after impingement was restricted to flow in two opposite directions. A constant surface heat flux of 1000 W/m² was arranged. Totally 88 experiments were performed. Jet orifices individually with diameter of 1.5, 3, 6 and 9 mm were adopted. Jet Reynolds number (Re) was in the range 10,000–30,000 and plate spacing-to-jet diameter ratio (H/d) was in the range 1–6. Eleven jet plate width-to-jet diameter ratios (W/d = 4.17–41.7) and seven jet plate length-to-jet diameter ratios (L/d = 5.5–166.7) were individually considered. The measured data were correlated into a simple equation. It was found that the stagnation Nusselt number is proportional to the 0.638 power of the Re and inversely proportional to the 0.3 power of the H/d. The stagnation Nusselt number was also found to be a function of exp[−0.044(W/d) − 0.011(L/d)]. Through comparisons among the present obtained data and documented results, it may infer that, for a jet impingement, the impingement-plate heating condition and flow arrangement of the jet after impingement are two important factors affecting the dependence of the stagnation Nusselt number on H/d.     

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.     

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.     

A numerical investigation on the fluid flow and heat transfer in the confined impinging slot jet in the low Reynolds number region for different channel heights

The numerical solution is obtained for unsteady two-dimensional fluid flow and heat transfer in a confined impinging slot jet using the finite volume method. In order to consider the effect of Reynolds number and height ratio on the flow and temperature fields in the channel, the numerical simulations were performed for different Reynolds numbers of 50–500 and different height ratios of 2–5. The critical Reynolds number, beyond which the flow and thermal fields change their state from steady to unsteady, depends on the Reynolds number and height ratio. The unsteadiness gives a big impact on the flow and temperature fields and as a result the pressure coefficient, skin friction coefficient and Nusselt number in the unsteady region show different characteristics from those in the steady region.     

Hydrodynamics of a turbulent slot jet flow impinging on a concave surface

This study investigates hydrodynamic characteristics of a slot jet flow impinging on a concave surface experimentally and numerically. Six different concave plates with varying surface curvature and a flat plate are used. Air is used as the impinging coolant. In the experimental work, the slot nozzle used was specially designed with a sixth degree polynomial in order to provide a uniform velocity profile at its exit. The experiments were carried out for the jet Reynolds numbers in the range of 3000 < Re < 12500, the dimensionless nozzle-to-surface distance range of 1 ≤ H/W ≤ 14 for dimensionless value of the curvature of impinging surfaces in the range of R/L = 0.5, 0.5125, 0.566, 0.725, and 1.3. The pressure coefficient, C_p, for each test case was obtained across dimensionless arc length, s/W. Numerical computations were performed by using the k-ε turbulence model with enhanced wall functions for the concave plate with R/L = 0.725 and for the flat plate. The numerical results showed a reasonable agreement with the experimental data.     

Experimental investigation on controlled cooling by coupling of thermoelectric and an air impinging jet for CPU

In this study, experimental tests have been carried out on the coupling thermoelectric cooling module with minichannel heatsink subjected to impinging airflow for cooling desktop central processing unit (CPU). A controlled thermoelectric-forced test system was designed for this purpose. This was designed using electronic Arduino card. The proposed hybrid cooling system was compared with the conventional forced air-cooling technique. Three power of heat source (CPU) were adopted, investigated, and compared, namely 60, 87, and 95 W. Performance of controlled thermoelectric cooling with three preset temperature were experimentally examined. The effects of air velocity and thermoelectric input current on the case temperature (T_case), thermal resistance, and heat transfer coefficient were analyzed. Results showed that the T_case increases with the increase of its input power. In addition, increasing air jet velocity and thermoelectric input current improve CPU cooling significantly. For a CPU power of 95 W, the recorded T_case temperature was 57°C with the conventional system. While it was maintained below 50°C in the hybrid system. The thermoelectric cooler has had a major effect on CPU cooling, having 15% improvement over conventional forced air-cooling. However, this was accompanied by an increase in energy consumption in the range of 45 W.     

Experimental determination of mixed convective heat transfer from a sphere to air

Experimental data for mixed convection heat loss from spheres was collected over a range of angles between forced and natural convection flows. The results indicate that opposing flow must be treated differently from cross and aiding flows. A hypothetical explanation is given for the general results.     

Hall and ion-slip effects on steady MHD free convective flow through a porous medium in a vertical microchannel

We have considered the steady fully developed magnetohydrodynamic free convection flow through a porous medium in a microchannel bounded by two infinite vertical parallel plates due to asymmetric heating of plates taking Hall and ion-slip effects into account. Effects of velocity slip and temperature jump have been considered on the microchannel surfaces, and the exact solutions have been obtained for momentum and energy equations under relevant boundary conditions. The influence of governing parameters on flow formation is discussed with the aid of graphs. The significant result from the study is that an increase in the value of rarefaction parameter leads to enhancement in volume flow rate. Furthermore, it is evident that the volume flow rate is found to be an increasing function of the Hall current parameter.     

A numerical study of mixed convection in a vertical channel flow impinging on a horizontal surface

In this study, mixed convection in a vertical channel flow discharging over a horizontal isotherm surface is investigated numerically using a finite difference method based on projection algorithm. The governing equations are discretized by a second order central difference in space and first order in time. The average Nusselt number is calculated on the horizontal surface in various vertical channels of varying areas considering non-dimensional parameters consisting of Reynolds and Richardson (or Grashof) numbers. Analysis of the results shows that there is an optimum gap to have a maximum heat transfer rate over the surface. The optimum gap value varies with Grashof and Reynolds numbers and inlet length of the channel but for high Richardson numbers, Nu has an increasing trend with reduction of gap size. By increasing the Re, Gr and Ri numbers, Nu number increases but in Ri of 0.1 and 0.01 the variations are approximately similar to each other. In addition, a divergent channel is usually more efficient than convergent one concerning heat transfer over the horizontal surface. Effects of Prandtl number and asymmetricity in channel are investigated in detail too.     

Estimation of heat flux on the surface of an initially hot cylinder cooled by a laminar confined impinging jet

In this study, an inverse algorithm based on the conjugate gradient method and the discrepancy principle is applied to estimate the unknown space-and time-dependent heat flux at the surface of an initially hot cylinder cooled by a laminar confined slot impinging jet from the knowledge of temperature measurements taken on the cylinder’s surface. It is assumed that no prior information is available on the functional form of the unknown heat flux; hence the procedure is classified as the function estimation in inverse calculation. The temperature data obtained from the direct problem are used to simulate the temperature measurements, and the effect of the errors in these measurements upon the precision of the estimated results is also considered. The results show that an excellent estimation on the space-and time-dependent heat flux can be obtained even the distributions of thermal properties inside the cylinder is unknown.     

Buoyancy driven vortex flow and its stability in mixed convection of air through a blocked horizontal flat duct heated from below

Experimental flow visualization combined with transient temperature measurement are carried out here to explore the possible stabilization of the buoyancy drive vortex flow in mixed convection of air in a bottom heated horizontal flat duct by placing a rectangular solid block on the duct bottom. Two acrylic blocks having dimensions 40 × 20 × 5 mm³ (block A) and 40 × 20 × 10 mm³ (block B) are tested. The blocks are placed on the longitudinal centerline of the duct bottom at selected locations. How the location and orientation of the rectangular block affect the stability of the regular vortex flow is investigated in detail. Experiments are conducted for the Reynolds number varying from 3 to 30 and Rayleigh number from 3000 to 6000, covering a wide range of the buoyancy-to-inertia ratio. For longitudinal vortex flow, the presence of either block near the duct entry causes the onset points of the longitudinal rolls to move significantly upstream especially for the roll pair directly behind the block. Besides, the longitudinal vortex flow in the exit portion of the duct is destabilized by the block. The transverse vortex flow is found to be only slightly affected by the block when it is placed in the exit half of the duct. Significant deformation of the transverse rolls is noted as they pass over the block. However, they restore to their regular shape in a short distance. Substantial decay in the transient flow oscillation results in the region right behind the block. Elsewhere the flow oscillates at nearly the same frequency and amplitude as that in the unblocked duct. When the block is placed near the duct entry, stabilization of the vortex flow behind the block is more pronounced. This flow stabilization is more prominent for block B with its height being twice of block A. Placing the block with its long sides normal to the forced flow direction can also enhance the flow stabilization. For the mixed longitudinal and transverse vortex flow, placing the block near the duct inlet causes the transverse rolls to change to regular or deformed longitudinal rolls in the duct depending on the buoyancy-to-inertia ratio and orientation of the block. The flow stabilization by the block is substantial. Again the stabilization of the mixed vortex flow can be enhanced by increasing the block height and length and by placing the block with its long sides normal to the forced flow direction.