Large-scale structures of turbulent flows over an open cavity

Low Mach number turbulent flows over an open cavity were studied to investigate the quantitative characteristics of large-scale vortical structures responsible for self-sustained oscillations. Wind tunnel experiments with particle image velocimetry (PIV) were conducted in the range of the ratio of cavity length (L) to depth (D), 1<L/D<4, when the incoming boundary layer is turbulent at Re_θ=830 and 1810. Self-sustained oscillation modes were classified by varying the conditions of L/D and Re_θ. The oscillation modes were consistent with the number of vortical structures existing between the leading and trailing edges of the cavity. Proper orthogonal decomposition (POD) was employed to the spatial distributions of vertical velocity correlations on the lip line of cavity geometry. By examining the conditionally averaged distributions of the correlation coefficients of POD, the spatial characteristics of large-scale vortical structures for self-sustained oscillations were examined.     

Self-sustained oscillations of turbulent flows over an open cavity

The mechanism of self-sustained oscillations in laminar cavity flows has been well characterized; however, the occurrence of self-sustained oscillations in turbulent cavity flows has only previously been characterized by direct observation of flows. Here, the quantitative characteristics of vortical structures in turbulent flows over an open cavity were determined, and then statistical properties were examined for evidence of self-sustained oscillations. Specifically, instantaneous velocity fields were measured using PIV and wall pressure fluctuations were determined from microphone data. Cavity geometries of L/D = 1 and 2, where L and D are the length and depth of the cavity, respectively, were used under conditions where the incoming boundary layer was turbulent at Re _θ  = 830. Statistical analyses were applied based on the instantaneous velocity fields of PIV data. The spatial distributions of vertical velocity correlations (v–v) showed alternating patterns that reflect the organized nature of the large-scale vortical structures corresponding to the modes of N = 2 for L/D = 1 and N = 3 for L/D = 2. These values were consistent with the numbers of vortical structures obtained from a modified version of Rossiter’s equation. Furthermore the numbers of vortical structures determined in the statistical analyses were consistently observed in instantaneous distributions of the swirling strength (λ _ci). The incoming turbulent boundary layer can give rise to the formation of large-scale vortical structures responsible for self-sustained oscillations.     

A theoretical study of free convection in turbulent film boiling on a horizontal elliptical tube

The present theoretical study investigates turbulent film boiling on an isothermal elliptical tube under quiescent liquid. The effect of radiation is included in the present analysis. The results of the boiling heat transfer under the turbulent vapor show both the temperature and velocity present the non-linear distribution. Besides, under the free convection turbulent film boiling with higher Rayleigh values, the elliptical tube can get a better heat transfer efficiency than a circular tube. However, when Rayleigh values are low, the eccentricity of an elliptical tube seldom influences the heat transfer. Finally, a comparison between the results of the present study and those reported in a previous theoretical and experimental data is provided.     

A numerical study of mixed convection in a horizontal channel with a discrete heat source in an open cavity

This article aims to numerically investigate mixed convection heat transfer in a two-dimensional horizontal channel with an open cavity. A discrete heat source is considered to be located on one of the walls of the cavity. Three different heating modes are considered which relate to the location of the heat source on three different walls (left, right and bottom) of the cavity. The analysis is carried out for a range of Richardson numbers and cavity aspect ratios. The results show that there are noticeable differences among the three heating modes. When the heat source is located on the right wall, the cavity with an aspect ratio of two has the highest heat transfer rate compared to other cavity heating modes. Moreover, when the heat source is located on the bottom wall, the flow field in the cavity with an aspect ratio of two experiences a fluctuating behaviour for Richardson number of 10. The results also show that at a fixed value of Richardson number, all three different heating modes show noticeable improvements in the heat transfer mechanism as the cavity aspect ratio increases.     

Experiments on turbulent natural convection in an enclosed tall cavity

Experiments have been undertaken to investigate the natural convection of air in a tall differentially heated rectangular cavity (2.18 m high by 0.076 m wide by 0.52 m in depth). They were performed with temperature differentials between the vertical plates of 19.6°C and 39.9°C, giving Rayleigh numbers based on the width of 0.86×10⁶ and 1.43×10⁶. Under these conditions the flow in the core of the cavity is fully turbulent and property variations with temperature are comparatively small. A previously used experimental rig has been modified, by fitting partially conducting top and bottom walls and outer guard channels, to provide boundary conditions which avoid the inadequately defined sharp changes in temperature gradient and other problems associated with insufficient insulation on nominally adiabatic walls. Mean and turbulent temperature and velocity variations within the cavity have been measured, together with heat fluxes and turbulent shear stresses. The temperature and flow fields were found to be closely two-dimensional, except close to the front and back walls, and anti-symmetric across the diagonal of the cavity. The partially conducting roof and floor provide locally unstable thermal stratification in the wall jet flows there, which enhances the turbulence as the flow moves towards the temperature controlled plates. The results provide a greatly improved benchmark for the testing of turbulence models in this low turbulence Reynolds number flow.     

Experimental study of turbulent axisymmetric cavity flow

An experimental study is made of turbulent axisymmetric cavity flow. The flow configuration consists of a sudden expansion and contraction pipe joint. In using the LDV system, in an effort to minimize refraction of laser beams at the curved interface, a refraction correction formula for the Reynolds shear stress is devised. Three values of the cavity length (L = 300, 600 and 900 mm) are chosen, and the cavity height (H) is fixed at 55 mm. Both open and closed cavities are considered. Special attention is given to the critical case L = 600 mm, where the cavity length L is nearly equal to the reattachment length of the flow. The Reynolds number, based on the inlet diameter (D = 110 mm) is 73,000. Measurement data are presented for the static wall pressure, mean velocity profiles, vorticity thickness distributions, and turbulence quantities.List of symbols C _f velocity correction factor - C _p static wall pressure coefficient - D diameter of inlet pipe = 110 mm - H step height or difference in radii of two pipes = 55 mm - L cavity length = 300, 600 and 900 mm - n _a , n _w , n _f refraction indices of the medium between the transmitting lens and window, the window itself, and the working fluid - signal validation rate in LDV, Hz - P wall static pressure, Pa - P _ref wall static pressure at x = -70 mm, Pa - r radial distance from centreline, m - r _a radial position of the virtual intersection, m - r _d radial location of the dividing streamline, m - r _f radial position of the real beam intersection, m - Re Reynolds number based on the inlet diameter - R _i inner radius of the cylindrical cavity=110 mm - t thickness of the window, m - T ₁ integral time scale, s - U streamwise mean velocity, m/s - U _c centreline mean velocity, m/s - U _ref maximum upstream velocity at x= -70 mm, m/s - r.m.s. intensity of streamwise, radial and circumferential velocity fluctuations respectively, m/s - Reynolds shear stress, m²/s² - x distance in the streamwise direction, m - x _a streamwise position of virtual intersection, m - x _f streamwise position of real beam intersection, m - x _r mean reattachment length, m - x nondimensional streamwise distance - y distance normal to the wall=R–r, m Greek symbols vorticity thickness - stream function of dividing streamline      

Experimental investigation of free convection above a heated horizontal wire

Results are presented of an experimental investigation of the convective plume above a fine horizontal wire, heated by a constant current in air and in water. The temperature distribution in the plume was investigated using the IAB-451 shadow instrument in the diffraction interferometry method. The experimental results are in good agreement with laminar convection theories above a linear heat source. In the air, a comparison was made with the experimental results of other authors.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhicheskoi Fiziki, Vol. 11, No. 2, pp. 169–173, March–April, 1970.The author wishes to express his indebtedness to V. D. Zimin and N. V. Eyzhanov for their assistance with numerical solutions of Eqs. (1.3).     

Experiments in the mixed convection regime in an isothermal open cubic cavity

A detailed experimental study of the heat transfer in an open isothermal cubic cavity for mixed natural and forced convection is reported. First the experimental model with a temperature control system, the experimental procedure, and the method for determination of the convective heat losses from the experimental data are presented. After presentation of the experimental conditions for the three models of different sizes that were tested, dimensionless parameters (Gr, Re, and Nu numbers) are introduced to generalize the results. In this way, the main influence of natural convection can be separated, and, using regressional analysis, a general interdependence among Nusselt, Reynolds, and Grashof numbers can be obtained.

The local heat transfer effects are indicated by maps of local heat transfer coefficient distributions in the cavity for different orientations of the model. To reduce the effects of convective heat transfer, the influence of different types of front masks were analyzed. The usefulness of the experimental results obtained is shown by estimating the convective heat losses for the central solar receiver of the French solar power plant THEMIS.     

Experimental investigation of combined forced and free convection in horizontal and inclined tubes

Summary This investigation considers the effects of free convection on the laminar flow of water through a circular duct having essentially constant wall heat transfer rate per unit length of the duct and circumferentially uniform wall temperature. The effect of the Reynolds and Rayleigh number variations on heat transfer results has been analysed for both horizontal and inclined pipe. The experiment has covered the range of the inlet Reynolds number from 200 to 2300, and of the Rayleigh number from 6,000 to 70,000. The effect of pipe inclination has been investigated for slope angle values up to 60°, with laminar ascending flow.

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Sommario L'indagine é volta alla determinazione sperimentale dei coefficienti di scambio termico in regime di convezione mista per acqua in moto laminare entro un condotto a sezione circolare. Allo scopo di consentire il confronto dei risultati con le previsioni teoriche, l'esperienza è stata condotta cercando di approssimare le condizioni al contorno di flusso termico uniforme lungo l'asse del tubo e di temperatura uniforme in senso circonferenziale. La dipendenza dei coefficienti di scambio termico dai numeri di Reynolds e di Rayleigh è stata analizzata sia per condotto orizzontale che inclinato. La sperimentazione ha coperto il campo di valori compreso tra 200 e 2300 del numero di Reynolds all'ingresso, e tra 6000 e 70000 del numero di Rayleigh. L'influenza dell'inclinazione sullo scambio termico è stata esaminata, per moto laminare ascendente, tra 0 e 60° sull'orizzontale.

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Research supported by C.N.R., grant no. 81.002.77.07.     

Experimental analysis of unsteady free convection heat transfer from horizontal fin arrays

Experimental work has been carried out on horizontal fin arrays using the differential interferometric technique. The local variations of heat flux and temperature in the central fin of a three fin array have been studied in the transient heating and cooling regimes. The average values of heat transfer coefficients in the transient state have been calculated for three spacings of 10 mm, 15 mm and 25 mm and with two materials namely aluminum and mild steel under constant heat input to the system. The results have been compared with experimental findings in the cases of a single fin attached to a base and a vertical isothermal flat plate. Attempt has been made to explain the differences between these cases in relation to the physical mechanism of heat and fluid flow about a fin array.

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Eine experimentelle Untersuchung der Wärmeübertragung bei instationärer freier Konvektion an horizontalen Rippenanordnungen

Zusammenfassung Unter Anwendung der Differential-Interferometrie-Technik wurde eine experimentelle Arbeit auf dem Gebiet horizontaler Anordnungen von Kühlrippen durchgeführt. Die lokale Veränderung von Wärmestrom und Temperatur der mittleren Rippe einer Dreieranordnung wurde an transienten Heiz- und Kühlbereichen untersucht. Im transienten Zustand wurden die Durchschnittswerte der Wärmeübertragungskoeffizienten bei konstanter Wärmezuführ in das System für Aluminium und Flußstahl bei Zwischenräumen von 10 mm, 15 mm und 20 mm berechnet. Die Berechnungen wurden mit experimentellen Ergebnissen einer einzigen, auf einer Basis befestigten Rippe und einer vertikalen isothermen flachen Platte verglichen. Es wurde der Versuch gemacht, den Unterschied zwischen diesen Fällen, in bezug auf den physikalischen Mechanismus der Wärmeübertragung und Strömung über eine Rippenanordnung, zu erklären.

     

On the similarity solutions for free convection in a saturated porous medium adjacent to impermeable horizontal surfaces

The similarity solutions for free convection about a horizontal surface in a saturated porous medium when the wall temperature is prescribed as a power law of distance from the origin, i.e. proportional tox ^m, are considered. Solutions valid form1 are obtained. Numerical solutions are obtained which reveal that there is a valuem ₀ such that a solution of the similarity equations is possible only form>m ₀. It is shown thatm ₀=–2/5 and the nature of the singularity is discussed and an asymptotic expansion is obtained.

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Ähnlichkeitslösungen für eine freie Konvektion in einem gesättigten porösen Medium, das an eine undurchlässige, horizontale Oberfläche grenzt

Zusammenfassung Die Ähnlichkeitslösungen sind für eine freie Konvektion über eine horizontale Oberfläche in einem gesättigten porösen Medium in Betracht gezogen worden, wenn die Wandtemperatur beschrieben ist als eine Potenzfunktion des Abstandes vom Ursprung, z. B. proportional zux ^m.Gültige Lösungen sind fürm1 bestimmt. Numerische Lösungen sind bestimmt worden, die offenbaren, daß es einen Wertm ₀ geben muß, so daß eine Lösung von ähnlichen Lösungen nur fürm>m ₀ möglich ist. Es wird gezeigt, daßm ₀=–2/5 und daß die Beschaffenheit der Singularität besprochen und die asymptotische Ausdehnung bestimmt worden ist.

     

Experimental study of free convection in an elliptical annular enclosure in blunt and slender orientations

In this paper, free convection heat transfer between two elliptical cylinders having different elliptical ratios in blunt and slender situations was studied experimentally. Three pairs of elliptical cylinders having the same radius ratio of 2.0, the same surface area and different elliptical ratios of 0.662, 0.866 and 0.968 were cut using the computed numerically controlled wire-cut machining. The tests were carried out by keeping a constant heat flux on the inner cylinder while cooling the outer one to be isothermal. The effects of vertical eccentricity, lateral eccentricity, angle of attack of the inner cylinder on natural convection for both blunt and slender situations of each pair were investigated. Empirical correlation was deduced within an acceptable uncertainty for the experimental results. Compatible and satisfactory to the conscience agreement was found in the comparison among the results of present and previous works. In the vision of the comparison, it was found that; the vertical eccentricity can enhance free convection by about 15% than the concentric case, the horizontal eccentricity can enhance natural convection by about 10% than concentric case and slender situation offers about 40% enhancement in free convection than the blunt situation for the same elliptical ratio.     

Numerical and experimental study of free convection above a sinusoidal horizontal plate

A numerical and experimental analysis is performed to study the laminar free convection above a horizontal plate facing upward subjected to an uniform heat flux. The surface of the plate, in contact with the fluid, is described by a sinusoidal profile. The natural convection equations are discretized, using an implicit finite difference technique, based on the finite volume approach. The SIMPLE algorithm assumes the linkage between velocities and pressure fields. The top and the lateral boundaries of the space, where free convection is developing, are determined by using an iterative procedure. The temperature fields of the fluid, over the plate, are visualized by an experimental device, which can realize a simultaneous measurement of the temperature and the position. Qualitative information about the natural convection flow above the plate is obtained by using a laser tomography technique. The numerical results show that the flow and the heat transfer are strongly affected by the amplitude, the period of the sinusoidal profile and the type of fluid. Comparisons between numerical and experimental results show a good qualitative agreement.     

Effect of vertical heat transfer on thermocapillary convection in an open shallow rectangular cavity

In order to understand the effect of the vertical heat transfer on thermocapillary convection characteristics in a differentially heated open shallow rectangular cavity, a series of two- and three-dimensional numerical simulations were carried out by means of the finite volume method. The cavity was filled with the 1cSt silicone oil (Prandtl number Pr = 13.9) and the aspect ratio ranged from 12 to 30. Results show that thermocapillary convection is stable at a small Marangoni number. With the increase of the heat flux on the bottom surface, thermocapillary convection transits to the asymmetrical bi-cellular pattern with the opposite rotation direction. The roll near the hot wall shrinks as the Marangoni number increases. At a large Marangoni number, numerical simulations predict two types of the oscillatory thermocapillary flow. One is the hydrothermal wave, which is dominant only in a thin cavity. The other appears in a deeper cavity and is characterized by oscillating multi-cellular flow. The critical Marangoni number for the onset of the oscillatory flow increases first and then decreases with the increase of the vertical heat flux. The three-dimensional numerical simulation can predict the propagating direction of the hydrothermal wave. The velocity and temperature fields obtained by three-dimensional simulation in the meridian plane are very close to those obtained by two-dimensional simulation.     

Numerical simulation of steady-state and transient natural convection in an isothermal open cubic cavity

In this work the numeric results, of the steady-state and transient heat transfer by natural convection in a horizontal isothermal open cubic cavity are presented. The most important assumptions in the mathematical formulation are two, the flow is laminar and the Boussinesq approximation is valid. The conservation equations in primitive variables are solved using the finite volume method and the SIMPLEC algorithm. The advective terms are approximated by the SMART scheme and the diffusive terms are approximated using the central differencing scheme. The results are obtained for a Rayleigh number range from 10⁴ to 10⁷.The numerical model predicted flow instabilities and Nusselt number oscillations for high Rayleigh numbers.     

Thermal radiation effects on the natural convection flow over an isothermal horizontal plate

The natural convection boundary layer flow with conduction-radiation interaction of a viscous incompressible fluid along an isothermal horizontal surface has been studied. The equations valid in the upstream, downstream as well as in the entire regime are obtained. Solutions of the non-similar equations governing the flow for the entire regime and the downstream regime are obtained by employing an efficient implicit finite difference approximation together with the Keller box method, for a Prandtl number of 0.73. Also, the effects of the pertinent parameters, R _d, the radiation-conduction parameter and θ_w, the surface heating parameter are shown graphically in terms of the local skin-friction and the local rate of heat transfer. Comparison of the results obtained for the upstream and the downstream regimes shows good agreement over the entire regime. Effects of R _d and θ_w are also shown on the streamlines and the isotherms. Received on 15 December 1998     

Experimental study on turbulent natural convection heat transfer in water with sub-millimeter-bubble injection

Using thermocouples and a particle tracking velocimetry technique, temperature and velocity measurements are conducted to investigate flow and heat transfer characteristics of turbulent natural convection from a vertical heated plate in water with sub-millimeter-bubble injection. Hydrogen-bubbles generated by the electrolysis of water are used as the sub-millimeter-bubbles. In the turbulent region, the heat transfer deterioration occurs for a bubble flow rate Q = 33 mm³/s, while the heat transfer enhancement occurs for Q = 56 mm³/s. Temperature and velocity measurements suggest that the former is caused by a delay of the transition due to the bubble-induced upward flow. On the other hand, the latter is mainly due to two factors: one is the enhancement of the rotation of eddies in the outer layer, and the other is the increase in the gradient of the streamwise liquid velocity at the heated wall. These are caused by bubbles, which are located in the inner layer, rising at high speed.     

Experimental study of combined free and forced laminar convection in an asymmetrically heated two-dimensional aiding flow

An experimental study of mixed convection in an asymmetrically heated two-dimensional flow of water has been made. Experiments in fully developed turbulent flow (Re maximum=9000) were made initially to establish the satisfactory operation of the equipment. In the mixed convection laminar flow tests to determine local Nusselt numbers, the Reynolds number range was from about 100 to 1000 with the Rayleigh number based on heat flux varying from about 10 to 300. The data, which are presented graphically, have been compared with the results of the theoretical analyses of other workers. The effect of buoyancy in the immediate entry of the flow [(x/de)/Re Pr <.05] was found to be negligible, but at greater distances there were significant increases in the heat transfer coefficient with the larger values of Rayleigh number.