Behavior of multiple transitional round fountains interacting in homogeneous and stratified fluids

Mahmud, Hasan (2014) Behavior of multiple transitional round fountains interacting in homogeneous and stratified fluids. PhD thesis, James Cook University.

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Abstract

Fountain flows are present in many industrial and environmental settings, such as in natural ventilation, volcanic eruptions, cumulus clouds, displacement ventilation and air-conditioning, to name a few. There have been extensive experimental, analytical and numerical studies on single fountain flows, including very weak, weak and turbulent fountains, both in homogeneous fluids and in stratified fluids. However, the interaction between multiple fountains, which are also frequently found in nature and in many industrial and environmental applications, is currently lacking, which motivates this thesis project.

In this thesis, the transient flow behavior of the interactions between twin and triple transitional round fountains in homogeneous fluid is explored using cutting-edge Particle Image Velocimetry (PIV) experimental techniques, direct numerical simulations and scaling analysis. Furthermore, transient flow behavior of the interactions between twin fountains in linearlystratified fluids is also explored using direct numerical simulation and scaling analysis. A rectangular and a cylindrical configuration have been considered for twin and triple transitional round fountains respectively.

A High Framing Rate Stereo PIV (HFR-SPIV) system from Dantec Dynamics was used to capture and analyse the transient flow patterns to validate numerically simulated results and quantify the scaling relations obtained by dimensional analysis. The PIV system used two Redlake high speed HG-100K cameras and a Lee LDP-100MQG laser. Although the system is able to produce three-dimensional velocities in the flow field, only two-dimensional version (by using only a single CCD) was used in all the PIV experiments in this thesis.

In this thesis, Ansys CFX13 is used to solve the continuity, momentum and energy equation for fluid flow which is discretized in space by adopting finite element based finite volume method with a co-located or staggered variable arrangement. To solve continuity equation, a second order central differencing approximation is used. The transient terms in all equations are discretized using a second order Euler scheme. The advective terms are discretized using a high resolution scheme. For time discretization schemes, second order backward Euler scheme which is completely an implicit time-stepping scheme, is used.

The behavior of the interaction between twin transitional round fountains with equal power in a homogeneous fluid over the ranges 25 ≤ Re ≤ 1000 and 1 ≤ Fr ≤ 10 with D/X₀ = 10 (where D is the distance between the centers of the twin fountain sources and X₀ is the jet nozzle radius) was studied experimentally using a noninvasive PIV technique and flow visualization and direct simulation. The study found that the interaction is dominated by bobbing and flapping motions which is either unsteady or steady, depending on the specific values of Re and Fr. The major difference between a steady and an unsteady interaction is that, in the steady case the bobbing-flapping motions are only present in its initial development stage and the interaction will attain a steady state in the later development stage in which the bobbing-flapping motions are no longer present and the maximum interaction height becomes constant. In the unsteady case the interaction remains unsteady all the time and the bobbing-flapping motions are present at all development stages, and the interaction can only attain a quasi-steady state, in a time-averaged perspective, in which the time-averaged bobbing and flapping motions are negligible and the time-averaged maximum interaction height becomes almost constant. The study further revealed that the unsteady interaction has four distinct sub-regimes: a BFUS-A (bobbing-flapping unsteady Type A) is found to occur at 1.5 ≤ Fr ≤ 10 with 150 ≤ Re ≤ 300 and 7 ≤ Fr ≤ 10 with Re = 100, a BFUS-B (bobbing-flapping unsteady Type B) occurs at 400 ≤ Re ≤ 1000 with Fr = 1, a BFUS-C (bobbing-flapping unsteady circling) occurs at 2 ≤ Fr ≤ 5 with Re = 400 and 500 and BFUS-T (bobbing-flapping unsteady turbulent) interaction occurs at high Re/Fr values, i.e., at 2 ≤ Fr ≤ 10 with 600 ≤ Re ≤ 1000, as well as 8 ≤ Fr ≤ 10 with Re = 400 and 5.5 ≤ Fr ≤ 10 with Re = 500. The major differences between the first two types are that in Type B the bobbing motions are broadbanded and chaotic whereas in Type A the bobbing motions are single-modal, and in Type B the flapping motions are dominated by a single dominant frequency with two secondary dominant frequencies while in Type A the flapping motions are dominated by two dominant frequencies. Although the circling type interaction possesses a similar bobbing-flapping behavior to that observed for the other two types of unsteady interactions, its flapping behavior is more broadbanded and chaotic. Another major difference is that at the later development stage of the circling interaction, a noticeable rotation (circling) of the core of the interaction region is present, which is not observed in any other interactions studied in the work. Flapping and bobbing motions in BFUS-T interactions are more aperiodic, broadbanded, and chaotic, represented by many dominant frequencies over a wider ranges. On the other hand, a steady interaction was found to occur at Re ≤ 100 with all Fr considered and at Fr ≤ 1 with all Re considered, except Re = 400. There is much stronger unsteadiness in the fountain flow and associated interaction and increased mixing with the ambient have been seen for the higher Fr with low Re cases. Empirical scaling relation between the time-averaged maximum interaction height at the steady or quasi-steady state and Re and Fr was also developed by the study using a dimensional analysis, experimental results and numerical data over the ranges of Re and Fr mentioned above, which includes zᵢ = 0.172Fr¹.⁷⁸⁸Re⁰.²⁶ and zᵢ = 1.249Fr¹.⁰²⁸Re⁰.⁰⁷⁹² over the ranges of 1 ≤ Fr ≤ 5.5; 5.5 ≤ Fr ≤ 10; respectively. This study significantly extended by a series of three-dimensional direct numerical simulation to over the ranges 25 ≤ Re ≤ 1000 and 1 ≤ Fr ≤ 10, with several cases varying D/X₀ in the range 5 ≤ D/X₀ ≤ 40 for improved understanding of the behavior of the interaction of twin transitional round fountains in a homogeneous fluid, which is shown that the effect of D/X₀ on z(m) is not significant, but noticeable effect on zᵢ is observed. In the meanwhile, experimental results agrees well with DNS results.

The behavior of the interaction among triple transitional round fountains with equal power in a homogeneous fluid over the ranges of 100 ≤ Re ≤ 1000, 1 ≤ Fr ≤ 10 at D/X₀ = 6 respectively, was studied experimentally using a noninvasive PIV technique and flow visualization with series of direct numerical simulation. The DNS code was benchmarked against PIV results. Similar to above, this study found that the interaction is dominated by bobbing and flapping motions which is either unsteady or steady, depending on the specific values of Re and Fr. The major difference between a steady and an unsteady interaction is that in the steady case the bobbing-flapping motions are only present in its initial development stage and the interaction will attain a steady state in the later development stage in which the bobbing-flapping motions are no longer present and the maximum interaction height becomes constant, whereas in the unsteady case the interaction remains unsteady all the time and the bobbing-flapping motions are present at all development stages, and the interaction can only attain a quasi-steady state, in a time-averaged perspective, in which the time-averaged bobbing and flapping motions are negligible and the time-averaged maximum interaction height becomes almost constant. Among all cases considered in this study, it is found that a steady interaction behavior occurs for the cases of 1 ≤ Fr ≤ 5 with Re ≤ 100 and Fr ≤ 1 with all Re < 400. The remaining cases possess unsteady interaction behavior, which can be divided into three different types, i.e., BFUS-A (bobbing-flapping unsteady Type A), BFUS-B (bobbing-flapping unsteady Type B), and BFUS-T (bobbing-flapping unsteady turbulent), same as those observed for the twin transitional round fountains interacting in a homogeneous fluid at comparable Re/Fr values. The results further demonstrate that the interaction of the triple transitional fountains, similar to that of the twin transitional fountains, does not have any significant effect on the scalings for the time-averaged maximum fountain penetration height. Two separate scaling relations which incorporate the Re and Fr effect are obtained for maximum time average interaction height zᵢ, i.e., zᵢ = 0.161Fr¹.⁷⁹Re⁰.²⁶⁵ for 1 ≤ Fr ≤ 5.5 and zᵢ = 1.249Fr¹.⁰²⁸Re⁰.⁰⁷⁹ for 5.5 ≤ Fr ≤ 10, respectively. A study on the effect of the distance between the twin fountain source, D/X₀, on the maximum fountain penetration heights and the maximum thicknesses of the interaction regions is also carried out for triple interacting fountains in three representative cases, which shows that in general D/X₀ has a negligible effect on the maximum fountain penetration heights, but a noticeable effect on the maximum thicknesses of the interaction regions.

When the receiving fluid is stably stratified, twin transitional round fountains are also subject to the influence of the stratification of the ambient fluid, which is characterized by s, the non-dimensional temperature stratification number. The behavior of interactions of twin transitional round fountains in a stratified fluid has been investigated using three dimensional direct numerical simulation over the ranges of 100 ≤ Re ≤ 1000, 1 ≤ Fr ≤ 10 with s = 0.04 and D/X₀ = 10. Observed behavior of interaction in here is found strongly depend on both the Fr, Re and s. Re = 200, Fr = 2 and s = 0.04 with D/X₀ = 10 case demonstrated a BFUS-A like behavior but its flow pattern/characteristics changed and bobbing-flapping signal is dominated with varying frequency whenever s value increased upto 0.12. z(m) shows nearly an inversely proportional relationship with s but the variations of zᵢ with respect to s is significant at the cases of Re = 200, Fr = 2, Re = 500, Fr = 5 and Re = 1000, Fr = 10. The results further demonstrate that the interaction of the twin transitional round fountains in a stratified fluid at specific s, similar to that of the twin and triple transitional fountains in homogeneous fluid does not have any significant effect on the scalings for the time-averaged maximum fountain penetration height, z(m). Two separate scaling relations which incorporate the momentum as well as buoyancy effect are obtained for zᵢ, i.e., zᵢ = 0.08Fr¹.⁸³Re⁰.³² for 1 ≤ Fr ≤ 5.5 and zᵢ = 0.773Fr¹.⁰⁵Re⁰.⁰⁸⁹ for 5.5 ≤ Fr ≤ 10, respectively. A comparison of these scaling relations to those obtained for the twin and triple transitional round fountains in homogeneous fluid shows that these scaling relations are essentially the same, with negligible differences of the constants of proportionality and the exponents in Fr or Re. The results further show that the gradual decrease of the exponent in Re in these scaling relations when Fr increases confirms that the fountains under consideration in this study are of the transitional nature, and the decreasing dependence of the behavior of the fountains on Re. When a study on the effect of the distance between the twin fountains on the maximum fountain penetration heights and the maximum thicknesses of the interaction regions is carried out for twin interacting fountains in stratified fluid, it shows that in general D/X₀ has a negligible effect on the maximum fountain penetration heights, but a noticeable effect on the maximum thicknesses of the interaction regions.

Item ID: 41014
Item Type: Thesis (PhD)
Keywords: bobbing; direct numerical simulation; flapping; flow chemistry; flow visualisation; fluid dynamics; interaction behavior; interaction behaviour; particle image velocimetry; PIV; transitional flow; transitional round fountain; twin fountains; unsteady flow
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Publications arising from this thesis are available from the Related URLs field. The publications are:

Mahmud, Hasan, Lin, Wenxian, Gao, Wenfeng, Armfield, St.W., and He, Yinghe (2015) Behavior of the interaction between twin transitional round fountains in a homogeneous fluid, Part 2: numerical study. International Journal of Heat and Mass Transfer, 86. pp. 973-991.

Mahmud, Hasan, Lin, Wenxian, Gao, Wenfeng, Hill, Blair, Armfield, S.W., and He, Yinghe (2015) Behavior of the interaction between twin transitional round fountains in a homogeneous fluid, Part 1: experimental study. International Journal of Heat and Mass Transfer, 86. pp. 957-972.

Mahmud, H., Hill, B., Gao, W., Lin, W., He, Y., and Armfield, S.W. (2012) PIV study on the interaction of triple transitional round fountains in a homogeneous fluid. In: Proceedings of the 18th Australasian Fluid Mechanics Conference, pp. 1-4. From: 18th Australasian Fluid Mechanics Conference, 3-7 December 2012, Launceston, Tasmania, Australia.

Mahmud, H., Lin, Wenxian, Gao, Wenfeng, He, Yinghe, and Armfield, S.W. (2012) Direct numerical simulation of interaction of twin transitional fountains in a homogeneous fluid. In: Proceedings of the 4th International Conference on Computational Methods (ICCM 2012), pp. 1-8. From: 4th International Conference on Computational Methods (ICCM 2012), 25-28 NOV 2012, Gold Coast, Australia.

Mahmud, Hasan, Hill, Blair, Gao, Wenfeng, Lin, Wenxian, He, Yinghe, and Armfield, Steven (2012) PIV Study of behavior of interaction of twin fountains in homogenous fluid. In: Proceedings of the 23rd International Congress of Theoretical and Applied Mechanics, pp. 1-2. From: ICTAM 2012: 23rd International Congress of Theoretical and Applied Mechanics, 19-24 August 2012, Beijing, China.

Date Deposited: 29 Oct 2015 02:34
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