Abstract

Entrainment characteristics of a pure jet and buoyant jets in a stably-stratified ambient are compared with the help of laboratory experiments employing simultaneous particle image velocimetry and planar laser induced fluorescence techniques. For the buoyant jet, two cases of background stratification are considered, N = 0.4 s\(^{-1}\) and 0.6 s\(^{-1}\), where N is the buoyancy frequency. Evolution of volume flux, Q, momentum flux, M, buoyancy flux, F, characteristic velocity, \(w_m\), width, \(d_m\), and buoyancy, \(b_m\) with axial distance is quantified that helps in understanding the mean flow characteristics. Subsequently, two different methods are used for computing the entrainment coefficient, \(\alpha\); namely the standard entrainment hypothesis based on the mass conservation equation and energy-consistent entrainment relation proposed by van Reeuwijk and Craske (J Fluid Mech 782:333–355, 2015). It is observed that entrainment coefficient is constant for the pure jet (\(\alpha _{pj}\approx\) 0.1) up until the point where the upper horizontal boundary starts to influence the flow. The entrainment coefficient for buoyant jets, \(\alpha _{bj}\), is not constant and varies with axial location before starting to detrain near the neutral layer. Near the source, \(\alpha _{bj}\approx\) 0.12 for both the values of N, while away from the source, N = 0.6 s\(^{-1}\) exhibits a higher value of \(\alpha _{bj}\approx\) 0.15 in comparison to \(\alpha _{bj}\approx\) 0.13 for N = 0.4 s\(^{-1}\). During detrainment near the neutral layer, \(\alpha _{bj}\approx\) – 0.2 for N = 0.4 \({\mathrm{s}}^{-1}\) and \(\alpha _{bj}\approx\) – 0.3 for N = 0.6 \({\mathrm{s}}^{-1}\). Importantly, close to the source, \(\alpha\) from standard entrainment hypothesis and energy-consistent relation are in reasonable match for pure jet and buoyant jets. However, far away from the source, the energy-consistent relation is ineffective in quantifying the entrainment coefficient in the pure jet and detrainment in buoyant jets. We propose ways in which the energy-consistent relation could be reconciled with standard entrainment hypothesis in the far-field region.

Article Highlights

• Entrainment coefficient stays invariant for jets till the finite size of the domain in the axial direction disrupts this feature.

• Entrainment coefficient for buoyant jets evolving in a stratified ambient varies with axial distance followed by detrainment beyond the neutral layer.

• The existing entrainment relation performs reasonably well in the momentum dominated region but performs poorly when the finite size of the domain affects the flow for pure jet and when the flow is buoyancy dominated for the case of buoyant jets.

中文翻译：

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稳定分层环境中浮力射流的夹带动力学

摘要

借助采用同时粒子图像测速和平面激光诱导荧光技术的实验室实验，比较了稳定分层环境中纯射流和浮力射流的夹带特性。对于浮力射流，考虑两种背景分层情况，N  = 0.4 s \(^{-1}\)和 0.6 s \(^{-1}\)，其中N是浮力频率。体积通量Q、动量通量M、浮力通量F、特征速度\(w_m\)、宽度\ (d_m\)和浮力\(b_m\) 的演变轴向距离被量化，有助于理解平均流量特性。随后，使用两种不同的方法来计算夹带系数\(\alpha\)；即 van Reeuwijk 和 Craske 提出的基于质量守恒方程和能量一致的夹带关系的标准夹带假设 (J Fluid Mech 782:333–355, 2015)。可以观察到，纯射流的夹带系数是恒定的（\(\alpha_{pj}\approx\) 0.1），直到上水平边界开始影响流动的点。浮力射流的夹带系数\(\alpha _{bj}\)不是恒定的，并且在开始在中性层附近脱轨之前随轴向位置而变化。靠近源头，\(\alpha _{bj}\approx\)对于N的两个值都为 0.12 ，而远离源，N = 0.6 s \(^{-1}\)表现出更高的\(\alpha _{ bj}\approx\) 0.15 与\(\alpha _{bj}\approx\) 0.13相比N = 0.4 s \(^{-1}\)。在中性层附近的去训练期间，\(\alpha _{bj}\approx\) – 0.2 for N = 0.4 \({\mathrm{s}}^{-1}\)和\(\alpha _{bj} \approx\) – N = 0.6 \({\mathrm{s}}^{-1}\)时为 0.3 。重要的是，靠近源头，\(\alpha\)从标准夹带假设和能量一致关系来看，纯射流和浮力射流是合理匹配的。然而，在远离源头的地方，能量一致关系在量化纯射流中的夹带系数和浮力射流中的脱附方面是无效的。我们提出了使能量一致关系与远场区域中的标准夹带假设相协调的方法。

文章重点

• 夹带系数对于射流保持不变，直到轴向域的有限尺寸破坏了这一特征。

• 在分层环境中演化的浮力射流的夹带系数随轴向距离而变化，然后是中性层之外的夹带。

• 现有的夹带关系在动量主导区域表现得相当好，但当域的有限尺寸影响纯射流的流动以及在浮力射流的情况下流动以浮力为主时表现不佳。