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Steven W. Armfield - One of the best experts on this subject based on the ideXlab platform.
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Direct simulation of impinging plane fountains in a Homogeneous Fluid
Jets, 2020Co-Authors: N. Srinarayana, G. D. Mcbain, Steven W. ArmfieldAbstract:In this paper we present the behaviour of plane fountains, injected into a Homogeneous Fluid of lower density, impinging on a ceiling. The transient behaviour of the impinging fountain with Reynolds number 100 ≤ Re ≤ 1000, Prandtl number Pr=7, and Froude number Fr = 4 and 5 is studied by direct numerical simulation using a fractional-step solution of the Navier–Stokes equations. When a vertical fountain impinges on a ceiling it spreads until gravity forces it to fall. The results show that the spreading distance is dependent on the source Froude number and independent of Reynolds number for range studied.
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Numerical Simulation of Free-fountains in a Homogeneous Fluid
2020Co-Authors: N. Srinarayana, Steven W. ArmfieldAbstract:The behaviour of plane fountains, resulting from the injection of dense Fluid upwards into a large container of Homogeneous Fluid of lower density, is investigated. The transient behaviour of fountains with parabolic inlet velocity profile and Reynolds numbers, 50 ≤ Re ≤ 150, Prandtl numbers, Pr=7, 300 and 700, and Froude numbers, Fr = 0.25 to 10.0 are studied numerically. The fountain behaviour falls into three distinct regimes; steady and symmetric; unsteady and periodic flapping; unsteady and aperiodic. The analytical scaling of nondimensional fountain height, zm, with Fr and Re is zm ∼ Fr4/3−2γ/3Re −γ. The constant γ is found empirically for each of the regimes. The fountain height decreases with increase in Reynolds number in the steady region but increases with Reynolds number in the unsteady regimes. However, the fountain height increases with Froude number in all regimes. Numerical results and the analytical scaling show that zm is independent of Prandtl number in the range considered. The fountain exhibits periodic lateral oscillations, i.e., periodic flapping for intermediate Froude numbers ranging from 1.25 ≤ Fr ≤ 2.25.
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Interaction behavior of triple transitional round fountains in a Homogeneous Fluid
International Journal of Heat and Fluid Flow, 2016Co-Authors: Hasan Mahmud, Steven W. Armfield, Yinghe HeAbstract:Abstract In this study, the PIV and flow visualization techniques and three-dimensional direct numerical simulation are used to investigate the behavior of triple transitional round fountains, which are aligned along a straight line, interacting with each other in a Homogeneous Fluid over the ranges of 1 ≤ Fr ≤ 10 and 100 ≤ Re ≤ 1000, at a fixed spacing of D / X 0 = 6 , where Re and Fr are the Reynolds and Froude numbers, D is the spacing between the two neighbouring fountain sources, and X0 is the radius of orifices at the fountain source, respectively. The results show that the interaction behavior of triple transitional round fountains, over the ranges of Re and Fr studied, is dominated by the bobbing and flapping motions, and is either steady, or unsteady weakly multi-modal, or unsteady strongly multi-modal. In a steady interaction, the bobbing-flapping motions are only present in its initial development stage and the interaction will attain a steady state in the later stage in which the bobbing-flapping motions are no longer present. In contrast, in an unsteady interaction, the interaction remains unsteady all the time and the bobbing-flapping motions are present at all stages. Among all cases considered, a steady interaction occurs at Re ≤ 300 with F r = 1 and at R e = 100 with Fr ≤ 5; an unsteady weakly multi-modal interaction occurs at R e = 100 with 6 ≤ Fr ≤ 10, at 200 ≤ Re ≤ 300 with 2 ≤ Fr ≤ 10, and at R e = 400 with F r = 1 ; and an unsteady strongly multi-modal interaction occurs at 600 ≤ Re ≤ 1000 with F r = 1 and at 400 ≤ Re ≤ 1000 with 2 ≤ Fr ≤ 10. Such interaction behavior is found to be similar to that of twin transitional round fountains over comparable ranges of Re and Fr, as discovered by us in an earlier study. It is also found that the two interaction regions formed by the three fountains have essentially symmetrical behavior about the middle fountain for all cases considered. Furthermore, the maximum fountain penetration heights and the maximum thicknesses of the interaction regions of the triple transitional round fountains are quantified with the experimental and numerical results and compared to the available scalings for single fountains at comparable Fr and Re values. Several scaling relations are then developed for these parameters over the ranges of Fr and Re considered.
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Behavior of the interaction between twin transitional round fountains in a Homogeneous Fluid, Part 2: Numerical study
International Journal of Heat and Mass Transfer, 2015Co-Authors: Hasan Mahmud, Steven W. Armfield, Yinghe HeAbstract:This paper is the second part of our study on the behavior of the interaction between twin transitional round fountains with equal power in a Homogeneous Fluid. In the first part (Mahmud et al., 2015), an experimental study using PIV techniques and flow visualization was carried out over the ranges 1⩽Fr⩽5 and 25⩽Re⩽400, where Re and Fr are the Reynolds and Froude numbers, respectively. In the current paper, this work is extended to wider ranges, i.e., 1⩽Fr⩽10 and 25⩽Re⩽1000, by a series of three-dimensional direct numerical simulation (DNS). In addition, a preliminary study on the effect of the distance between the two fountain sources is also carried out for three representative cases. The DNS results are found to capture all the major features of the steady, and unsteady weakly multi-modal and strongly multi-modal interaction behavior, which is dominated by bobbing and flapping motions, as found by the experimental study (Mahmud et al., 2015), but over wider ranges of Fr and Re. Furthermore, the maximum fountain penetration height and the maximum thickness of the interaction region, obtained with the DNS, together with the experimental results of (Mahmud et al., 2015), are quantified and compared to the available scalings for single fountains in a Homogeneous Fluid at comparable Fr and Re values, and several scaling relations are then developed for these parameters over the ranges of Fr and Re considered in the current study.
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PIV Study on the Interaction of Triple Transitional Round Fountains in a Homogeneous Fluid
2012Co-Authors: Hasan Mahmud, Yinghe He, B. Hill, Steven W. ArmfieldAbstract:This paper investigates experimentally the transient behavior of the interaction of triple transitional fountains injected from three round sources into a Homogeneous Fluid using the PIV technique over the Reynolds and Froude numbers in the ranges 100
S W Armfield - One of the best experts on this subject based on the ideXlab platform.
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Behavior of the interaction between twin transitional round fountains in a Homogeneous Fluid, Part 1: Experimental study
International Journal of Heat and Mass Transfer, 2020Co-Authors: Hasan Mahmud, B. Hill, S W Armfield, Yinghe HeAbstract:The interaction of multiple sourced fountains is very common in many applications such as computers and electronic instruments, discharge of waste water from power plants to marine environments, displacement ventilation and air conditioning of large building spaces. But the understanding of such an interaction is currently scarce. This paper is the first part of the study on the behavior of the interaction between twin transitional round fountains with equal power in a Homogeneous Fluid. In this paper, the interaction behavior is investigated experimentally using a noninvasive PIV technique and flow visualization over the ranges 25⩽Re⩽400 and 1⩽Fr⩽5 at the fixed spacing of D/X0=10, where Re and Fr are the Reynolds and Froude numbers, D is the spacing between the two fountain sources, and X0 is the radius of orifices at the fountain source. The interaction behavior is observed to be dominated by bobbing and flapping motions and is either steady, or unsteady and weakly multi-modal or strongly multi-modal, depending on the specific values of Re and Fr. In a steady interaction, 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, zi , becomes constant. In an unsteady interaction, the interaction remains unsteady all the time and the bobbing–flapping motions are present at all development stages. The unsteady interaction is characterized by a finite number of discrete modes, with the time averaged zi approximately constant. Among all cases considered, the steady interaction behavior is observed for the cases of Re⩽100 with all Fr values considered and of Fr⩽1 with all Re values considered, except Re= 400; the unsteady weakly multi-modal interaction behavior is observed for 150⩽Re⩽300 with 1:5⩽Fr⩽5 and Fr = 1 with Re= 400; and the unsteady strongly multi-modal interaction behavior is found for Re= 400 with 1 < Fr ⩽5. Dimensional analysis and the experimental results are also used to develop an empirical scaling relation between zi, which is the time-averaged dimensionless maximum interaction height at full development, and Re and Fr, i.e., zi= 0.194Fr^(7/4)Re^(1/4) over the ranges 25⩽Re⩽400 and 1⩽Fr⩽5, at the fixed spacing of D/X0= 10
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Height and stability of laminar plane fountains in a Homogeneous Fluid
International Journal of Heat and Mass Transfer, 2020Co-Authors: N. Srinarayana, G. D. Mcbain, S W ArmfieldAbstract:The behaviour of plane fountains, resulting from the injection of a denser Fluid upwards into a large body of a lighter Homogeneous\ud Fluid, is investigated numerically. The transient behaviour of fountains with a uniform inlet velocity, Reynolds number Re = 100, Prandtl\ud number Pr = 7, and Froude number 0.25 6 Fr 6 10.0 is studied numerically. In the present case, the density variation is as a result of\ud temperature difference between the fountain and the ambient Fluids. Three distinct regimes are identified; steady and symmetric fountains\ud for 0.25 6 Fr 6 2.0, unsteady fountains with periodic lateral oscillation for 2.25 6 Fr 6 3.0, and unsteady fountains with aperiodic lateral\ud oscillations for Fr P4.0. It is found empirically that the non-dimensional fountain height, zm, scales differently with Froude number\ud in each of these regimes; in the steady and symmetric region zm Fr, in the unsteady and periodic lateral oscillation region zm Fr1:15 and\ud in the unsteady and aperiodic lateral oscillation region zm Fr4=3. The results are compared with previous numerical and experimental\ud results, where available and are consistent.\ud 2008 Elsevier Ltd. All rights reserved
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behaviour of laminar plane fountains with a parabolic inlet velocity profile in a Homogeneous Fluid
International Journal of Thermal Sciences, 2013Co-Authors: N. Srinarayana, S W ArmfieldAbstract:Abstract The behaviour of plane laminar fountains with parabolic velocity inlet profile is studied using numerical simulation over the parametric range 0.25 ≤ Fr ≤ 10.0, 50 ≤ Re ≤ 150 and Pr = 7, 300, 700. The behaviour of the flow is most strongly affected by the Froude number and to a lesser extent by the Reynolds number, particularly for weak fountains at low Reynolds numbers. Behaviour is independent of the Prandtl number over the parametric range investigated. Three distinct regimes are observed: a steady symmetric pattern at low Froude numbers (Fr
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height and stability of laminar plane fountains in a Homogeneous Fluid
International Journal of Heat and Mass Transfer, 2008Co-Authors: N. Srinarayana, G. D. Mcbain, S W ArmfieldAbstract:Abstract The behaviour of plane fountains, resulting from the injection of a denser Fluid upwards into a large body of a lighter Homogeneous Fluid, is investigated numerically. The transient behaviour of fountains with a uniform inlet velocity, Reynolds number Re = 100, Prandtl number Pr = 7, and Froude number 0.25 ⩽ Fr ⩽ 10.0 is studied numerically. In the present case, the density variation is as a result of temperature difference between the fountain and the ambient Fluids. Three distinct regimes are identified; steady and symmetric fountains for 0.25 ⩽ Fr ⩽ 2.0, unsteady fountains with periodic lateral oscillation for 2.25 ⩽ Fr ⩽ 3.0, and unsteady fountains with aperiodic lateral oscillations for Fr ⩾ 4.0. It is found empirically that the non-dimensional fountain height, zm, scales differently with Froude number in each of these regimes; in the steady and symmetric region z m ∼ Fr , in the unsteady and periodic lateral oscillation region z m ∼ Fr 1.15 and in the unsteady and aperiodic lateral oscillation region z m ∼ Fr 4 / 3 . The results are compared with previous numerical and experimental results, where available and are consistent.
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direct simulation of weak axisymmetric fountains in a Homogeneous Fluid
Journal of Fluid Mechanics, 2000Co-Authors: S W ArmfieldAbstract:The weak axisymmetric fountain that results from the injection of a dense Fluid upwards into a large container of Homogeneous Fluid of lower density is studied numerically. Using a time-accurate finite volume code, the behaviour of fountains with both a uniform and a parabolic profile of the discharge velocity at the source have been investigated. The evolution of the transient fountain flow has been analysed and two distinct stages of evolution have been identified. The time series of the passage of the fountain front has been presented and the initial, temporary and final characteristic fountain heights have been determined and scaled with the Froude number at the source. At steady state, the final fountain height and the fountain width are found to be the height and horizontal length scales which provide the full parameterization of the fountain flow in the fountain core. The vertical velocity and temperature on the symmetry axis have been scaled with the height scale and an explicit correlation is also obtained for the former. The radial distributions of both the vertical and horizontal velocities in the zone of self similarity in the fountain core at steady state have been scaled with the two length scales and empirical correlations have been obtained.
Alberto J Ochoatapia - One of the best experts on this subject based on the ideXlab platform.
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diffusive mass transfer between a microporous medium and an Homogeneous Fluid jump boundary conditions
Chemical Engineering Science, 2006Co-Authors: Francisco J Valdesparada, Benoiˆt Goyeau, Alberto J OchoatapiaAbstract:Abstract The method of volume averaging is used to derive the diffusive mass transfer boundary conditions for transport between the micro-pores ( ω -region) and the Fluid in the macro-pores ( η -region) in a catalyst pellet. In this configuration, the mass jump boundary condition between the Homogeneous regions takes the form - n η ω · ( D γ ∇ 〈 c A γ 〉 η γ ) + n η ω · ( e γ D ω · ∇ 〈 c A γ 〉 ω γ ) = K eff 〈 c A γ 〉 ω γ , where K eff is the effective reaction rate coefficient at the inter-region. In this study, a closure is derived in order to predict this average jump coefficient as a function of the microstructure of the porous layer and the Thiele modulus. The jump coefficient predicted for three inter-region structures is presented.
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heat transfer at the boundary between a porous medium and a Homogeneous Fluid
International Journal of Heat and Mass Transfer, 1997Co-Authors: Alberto J Ochoatapia, Stephen WhitakerAbstract:The heat transfer conditions that apply at the boundary between a porous medium and a Homogeneous Fluid are developed as flux jump conditions based on the non-local form of the volume averaged thermal energy equations for both the Fluid and the solid. These jump conditions take the form of surface transport equations that contain excess surface accumulation, convection, and conduction, in addition to a term representing the excess surface heat exchange. It would appear that this latter term controls the manner in which the flux from the porous medium to the Homogeneous Fluid is distributed between the solid and Fluid phases that make up the porous medium.
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momentum transfer at the boundary between a porous medium and a Homogeneous Fluid i theoretical development
International Journal of Heat and Mass Transfer, 1995Co-Authors: Alberto J Ochoatapia, Stephen WhitakerAbstract:Abstract The momentum transfer condition that applies at the boundary between a porous medium and a Homogeneous Fluid is developed as a jump condition based on the non-local form of the volume averaged momentum equation. Outside the boundary region this non-local form reduces to the classic transport equations, i.e. Darcy's law and Stokes' equations. The structure of the theory is comparable to that used to develop jump conditions at phase interfaces, thus experimental measurements are required to determine the coefficient that appears in the jump condition. The development presented in this work differs from previous studies in that the jump condition is constructed to join Darcy's law with the Brinkman correction to Stokos' equations. This approach produces a jump in the stress but not in the velocity, and this has important consequences for heat transfer processes since it allows the convective transport to be continuous at the boundary between a porous medium and a Homogeneous Fluid.
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momentum transfer at the boundary between a porous medium and a Homogeneous Fluid ii comparison with experiment
International Journal of Heat and Mass Transfer, 1995Co-Authors: Alberto J Ochoatapia, Stephen WhitakerAbstract:Abstract In Part I of this paper a stress jump condition was developed based on the non-local form of the volume averaged Stokes' equations. The excess stress terms that appeared in the jump condition were represented in a manner that led to a tangential stress boundary condition containing a single adjustable coefficient of order one. In this paper we compare the theory with the experimental studies of Beavers and Joseph [J. Fluid Mech. 30, 197–207 (1967)], and we explore the use of a variable porosity model as a substitute for the jump condition. The latter approach does not lead to a successful representation of all the experimental data, but it does provide some insight into the complexities of the boundary region between a porous medium and a homogenous Fluid.
Stephen Whitaker - One of the best experts on this subject based on the ideXlab platform.
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heat transfer at the boundary between a porous medium and a Homogeneous Fluid
International Journal of Heat and Mass Transfer, 1997Co-Authors: Alberto J Ochoatapia, Stephen WhitakerAbstract:The heat transfer conditions that apply at the boundary between a porous medium and a Homogeneous Fluid are developed as flux jump conditions based on the non-local form of the volume averaged thermal energy equations for both the Fluid and the solid. These jump conditions take the form of surface transport equations that contain excess surface accumulation, convection, and conduction, in addition to a term representing the excess surface heat exchange. It would appear that this latter term controls the manner in which the flux from the porous medium to the Homogeneous Fluid is distributed between the solid and Fluid phases that make up the porous medium.
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momentum transfer at the boundary between a porous medium and a Homogeneous Fluid i theoretical development
International Journal of Heat and Mass Transfer, 1995Co-Authors: Alberto J Ochoatapia, Stephen WhitakerAbstract:Abstract The momentum transfer condition that applies at the boundary between a porous medium and a Homogeneous Fluid is developed as a jump condition based on the non-local form of the volume averaged momentum equation. Outside the boundary region this non-local form reduces to the classic transport equations, i.e. Darcy's law and Stokes' equations. The structure of the theory is comparable to that used to develop jump conditions at phase interfaces, thus experimental measurements are required to determine the coefficient that appears in the jump condition. The development presented in this work differs from previous studies in that the jump condition is constructed to join Darcy's law with the Brinkman correction to Stokos' equations. This approach produces a jump in the stress but not in the velocity, and this has important consequences for heat transfer processes since it allows the convective transport to be continuous at the boundary between a porous medium and a Homogeneous Fluid.
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momentum transfer at the boundary between a porous medium and a Homogeneous Fluid ii comparison with experiment
International Journal of Heat and Mass Transfer, 1995Co-Authors: Alberto J Ochoatapia, Stephen WhitakerAbstract:Abstract In Part I of this paper a stress jump condition was developed based on the non-local form of the volume averaged Stokes' equations. The excess stress terms that appeared in the jump condition were represented in a manner that led to a tangential stress boundary condition containing a single adjustable coefficient of order one. In this paper we compare the theory with the experimental studies of Beavers and Joseph [J. Fluid Mech. 30, 197–207 (1967)], and we explore the use of a variable porosity model as a substitute for the jump condition. The latter approach does not lead to a successful representation of all the experimental data, but it does provide some insight into the complexities of the boundary region between a porous medium and a homogenous Fluid.
N. Srinarayana - One of the best experts on this subject based on the ideXlab platform.
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Direct simulation of impinging plane fountains in a Homogeneous Fluid
Jets, 2020Co-Authors: N. Srinarayana, G. D. Mcbain, Steven W. ArmfieldAbstract:In this paper we present the behaviour of plane fountains, injected into a Homogeneous Fluid of lower density, impinging on a ceiling. The transient behaviour of the impinging fountain with Reynolds number 100 ≤ Re ≤ 1000, Prandtl number Pr=7, and Froude number Fr = 4 and 5 is studied by direct numerical simulation using a fractional-step solution of the Navier–Stokes equations. When a vertical fountain impinges on a ceiling it spreads until gravity forces it to fall. The results show that the spreading distance is dependent on the source Froude number and independent of Reynolds number for range studied.
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Numerical Simulation of Free-fountains in a Homogeneous Fluid
2020Co-Authors: N. Srinarayana, Steven W. ArmfieldAbstract:The behaviour of plane fountains, resulting from the injection of dense Fluid upwards into a large container of Homogeneous Fluid of lower density, is investigated. The transient behaviour of fountains with parabolic inlet velocity profile and Reynolds numbers, 50 ≤ Re ≤ 150, Prandtl numbers, Pr=7, 300 and 700, and Froude numbers, Fr = 0.25 to 10.0 are studied numerically. The fountain behaviour falls into three distinct regimes; steady and symmetric; unsteady and periodic flapping; unsteady and aperiodic. The analytical scaling of nondimensional fountain height, zm, with Fr and Re is zm ∼ Fr4/3−2γ/3Re −γ. The constant γ is found empirically for each of the regimes. The fountain height decreases with increase in Reynolds number in the steady region but increases with Reynolds number in the unsteady regimes. However, the fountain height increases with Froude number in all regimes. Numerical results and the analytical scaling show that zm is independent of Prandtl number in the range considered. The fountain exhibits periodic lateral oscillations, i.e., periodic flapping for intermediate Froude numbers ranging from 1.25 ≤ Fr ≤ 2.25.
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Height and stability of laminar plane fountains in a Homogeneous Fluid
International Journal of Heat and Mass Transfer, 2020Co-Authors: N. Srinarayana, G. D. Mcbain, S W ArmfieldAbstract:The behaviour of plane fountains, resulting from the injection of a denser Fluid upwards into a large body of a lighter Homogeneous\ud Fluid, is investigated numerically. The transient behaviour of fountains with a uniform inlet velocity, Reynolds number Re = 100, Prandtl\ud number Pr = 7, and Froude number 0.25 6 Fr 6 10.0 is studied numerically. In the present case, the density variation is as a result of\ud temperature difference between the fountain and the ambient Fluids. Three distinct regimes are identified; steady and symmetric fountains\ud for 0.25 6 Fr 6 2.0, unsteady fountains with periodic lateral oscillation for 2.25 6 Fr 6 3.0, and unsteady fountains with aperiodic lateral\ud oscillations for Fr P4.0. It is found empirically that the non-dimensional fountain height, zm, scales differently with Froude number\ud in each of these regimes; in the steady and symmetric region zm Fr, in the unsteady and periodic lateral oscillation region zm Fr1:15 and\ud in the unsteady and aperiodic lateral oscillation region zm Fr4=3. The results are compared with previous numerical and experimental\ud results, where available and are consistent.\ud 2008 Elsevier Ltd. All rights reserved
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behaviour of laminar plane fountains with a parabolic inlet velocity profile in a Homogeneous Fluid
International Journal of Thermal Sciences, 2013Co-Authors: N. Srinarayana, S W ArmfieldAbstract:Abstract The behaviour of plane laminar fountains with parabolic velocity inlet profile is studied using numerical simulation over the parametric range 0.25 ≤ Fr ≤ 10.0, 50 ≤ Re ≤ 150 and Pr = 7, 300, 700. The behaviour of the flow is most strongly affected by the Froude number and to a lesser extent by the Reynolds number, particularly for weak fountains at low Reynolds numbers. Behaviour is independent of the Prandtl number over the parametric range investigated. Three distinct regimes are observed: a steady symmetric pattern at low Froude numbers (Fr
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Impinging plane fountains in a Homogeneous Fluid
International Journal of Heat and Mass Transfer, 2009Co-Authors: N. Srinarayana, Steven W. ArmfieldAbstract:Abstract The transient behaviour of plane fountains with a uniform inlet velocity, injected upwards into a quiescent Homogeneous Fluid of lower density to impinge on a solid flat ceiling, is investigated. The Reynolds number, the Froude number and the Prandtl number of these impinging fountains have the values in the ranges of 50 ⩽ Re ⩽ 1000 , 8 ⩽ Fr ⩽ 20 and 7 ⩽ Pr ⩽ 700 , and the height of the solid ceiling away from the fountain source is varied in the range of 10 X in ⩽ H ⩽ 30 X in , where X in is the half-width of the planar fountain source slot. A scaling is found by dimensional analysis for the augmented spreading distance ( H + X d , where X d is the spreading distance of the impinging fountain), which shows that ( H + X d ) / X in ∼ Fr 4 3 - 2 3 ( γ + η + 2 ϕ ) Re - ( γ + η ) Pr - η ( H / X in ) ϕ , where the powers γ , η and ϕ can be determined empirically. The direct numerical simulation results show that after the fountain impinges upwards on the ceiling it spreads outwards along the ceiling until gravity forces it to fall. Two different scenarios are identified. In the first scenario, a nearly constant measurable spreading distance is obtained at full development. In the second scenario, however, the fountain floods the whole computational domain and no spreading distance exists at full development. The numerical results further show that in the first scenario the augmented spreading distance ( H + X d ) has the reduced scaling of ( H + X d ) / X in ∼ Fr 2 / 3 ( H / X in ) 1 / 2 for the plane impinging fountains with the parameter values in the ranges of 50 ⩽ Re 125 , 8 ⩽ Fr ⩽ 20 and 7 ⩽ Pr ⩽ 700 .