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Oil mist transport process in a long pipeline on turbulent flow transition region
International Journal of Multiphase Flow 87 (2016) 45–53
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Oil mist transport process in a long pipeline on turbulent flow transition region Tomoaki Takeuchi a,∗, Jumpei Ohkubo b, Norio Yonezawa b, Yoshihiko Oishi c, Ichiro Kumagai d, Yuji Tasaka b, Yuichi Murai b a
Pipeline Technology Center, Tokyo Gas Co., Ltd., 1-7-7 Suehiro-cho, Tsurumi-ku, Yokohama, 230-0045, Japan Division of Energy & Environmental Systems, Faculty of Engineering, Hokkaido University, N13W8, Sapporo 060-8628, Japan Department of Mechanical, Aerospace, and Materials Engineering, Muroran Institute of Technology, 27-1 Mizumoto-cho, Muroran, Hokkaido, 050-8585, Japan d School of Science and Engineering, Meisei University, 2-1-1, Hodokubo, Hino, Tokyo, 191-8506, Japan b c
a r t i c l e
i n f o
Article history: Available online 24 August 2016 Keywords: Pipe flow Turbulent flow transition Poiseuille flow Concentration diffusion Oil mist Pipeline
a b s t r a c t Internal gas velocity fluctuations and their effects on the mist diffusion process were examined in a long horizontal pipe to understand oil mist transportation, particularly in the laminar-to-turbulent flow transition region. Three hot-wire anemometers and aerosol concentration monitors were used to deduce these effects as the two-phase mist flow gradually developed in the stream-wise direction. We found significant axial mist diffusion at Reynolds numbers (Re) < 10 0 0 because of passive scalar transport by Poiseuille flow. However, this diffusion was restricted by the non-zero inertia of the mist at a Stokes number, O(10−5 ), relying on the Brownian motion of the mist. At Re > 2400, a sharp mist waveform was maintained by a turbulent flow with active radial mixing. New data were obtained within the range of 10 0 0 < Re < 2400, which cannot be explained by interpolation between the above-mentioned two states. The mist concentration displays multiple temporal peaks at Re < 20 0 0 owing to perturbations of localized turbulence as well as radial anisotropy as being conveyed more than 20 0 0-diameters in distance. This behavior is caused by intermittent disturbances induced by the pipe wall roughness, which sharply distorts the wall-aligned laminar mist layer left by parabolic axial stretching of local laminar flow. © 2016 Elsevier Ltd. All rights reserved.
1. Introduction The contamination of an industrial gas transport pipeline with an oil mist can lead to a range of problems. For this reason, oil mists must be purged using a clean gas and then removed by some means, such as by filtration. It is therefore important to obtain an understanding of the changes in the mist concentration within a pipeline while purging. The flow field inside pipes during the ordinary transport of a natural gas is generally turbulent. However, the flow velocities are lower than usual when conducting a purge operation since temporary interruption of the gas supply is required. This means that the mist diffusion phenomena that occur during both laminar, transitional, and turbulent flows must be clarified. The diffusion behavior subject to turbulent flow can be classified according to the associated Stokes number (St) of the mist.
∗
Corresponding author. E-mail addresses: [email protected] (T. Takeuchi), [email protected]. hokudai.ac.jp (J. Ohkubo), [email protected] (N. Yonezawa), [email protected] (Y. Oishi), [email protected] (I. Kumagai), [email protected] (Y. Tasaka), [email protected] (Y. Murai). http://dx.doi.org/10.1016/j.ijmultiphaseflow.2016.08.002 0301-9322/© 2016 Elsevier Ltd. All rights reserved.
For St 1, individual mist particles are passively transported by turbulent eddies, and the resulting diffusion is dominated by the turbulent mixing properties (Flint and Eisenklam, 1969; Ekambara and Joshi, 2003; Takeuchi and Murai, 2010). This turbulent diffusion also promotes the deposition of mist on the internal walls of the pipeline. So, the axial transport of the mist can be described by a combination of turbulent diffusion and the associated pipewall deposition rate. In this case, the mist concentration can be approximated as a symmetric Gaussian profile in the pipe axial direction, and therefore the time required for the mist purging is easily modeled by a one-dimensional advection-diffusion equation (Fick’s law). In laminar flows, mist transport results from a totally different mechanism. The mist is conveyed by a parabolic velocity profile of Poiseuille flow which has a centerline velocity that is twice the cross-sectional mean velocity. This leads to a long stretched distribution of mist in the axial direction; more importantly the stretched distribution provides a sharp gradient in the pipe’s radial direction. This consequently enhances the radial diffusion more than the axial diffusion. Similar cases for passive scalar or molecular transport were reported by Ekambara and Joshi (2004), and
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Fig. 1. Schematic representations of local turbulence.
Matas et al., (2004). The difference in behavior of the mist from the scalar or molecular scale is that mist a few micrometers in size obeys Brownian motion, associated with collisions with surrounding gas molecules (Shimada et al., 1993; Matas et al., 2004). The effective diffusion coefficient of Brownian motion is much less than that of gas diffusion, and therefore the mist is hardly diffused in the radial direction. This phenomenon could be an obstacle for an efficient purging operation in laminar flow. Theoretical predictions of transitional flow regions remain essentially impossible; this is because of the coexistence of two different stages in laminar to turbulent flow transition. One stage involves turbulent slugs intermittently appearing in ambient laminar flow. The other stage involves the appearance of turbulent puffs with specific structures independent of the pipe wall properties. These transition processes, which occur even in single phase pipe flow, has been regarded as a fundamental topic more than a century after the initial work of Reynolds (1883). The details of these transition processes have recently attracted special interest as nonlinear dynamics of sub-critical flow transition (see, for example, Hof et al., 2004, 2006; Tasaka et al., 2010; Avila et al., 2011). We will mainly focus on the transitional regime in this paper by connecting such recent knowledge on local turbulence and dispersion dynamics in dilute mist transport. Fig. 1 illustrates the internal structure of the local turbulence emerging between laminar flow sections in the transitional regime. The local turbulence is called a turbulent puff in the minimal case (Hof et al., 2004; Nishi et al., 2008; Shimazu and Kida, 2009) while it is called a turbulent slug in longer cases. The authors’ group also succeeded in visualizing the turbulent puff to reveal the threedimensional vortical structures within (Ohkubo et al., 2016). Inside the local turbulence, low-speed streaks and stream-wise vortex structures are present in proximity to the wall, where frictional stress increases locally. These structures are elongated downstream owing to high speed flow in the pipe center of the neighboring Poiseuille flow, forming a blunt boundary between the laminar and the turbulent regions. In industrial pipelines, multiple occurrences of such local turbulence should be considered as they are typically longer than 10 0 0 times the pipe diameter. At relatively large Reynolds numbers within the transition region, the overall pipeline is considered as a spatially intermittent distribution of laminar flow and turbulent slugs. This enables us to estimate the overall pressure loss (Moody, 1944) and mass diffusion coefficient (Flint and Eisenklam, 1969; Ekambara and Joshi, 2003) by finding the value between that for laminar and turbulent flows. In contrast, a specific turbulent puff structure occurs at lower Reynolds numbers, which does not give a valid estimation by taking intermediate values. A puff can be understood as the minimal elementary turbulence sustainable in the pipe flow. It propagates along the axial direction with a specific lifetime (Hof et al., 20 03, 20 06; Peixinho and Mullin, 2006; Tasaka et al., 2010). The sustainability of a puff indicates independence on the pipe wall properties; the structure will persist downstream even inside a completely smooth pipe. This phenomenon can therefore be distinguished from a turbulent slug.
Based on the above, the behavior of a mist in transitional regions can be predicted by several aspects as follows. First, mist diffusion will result from vortices that develop inside local turbulence. Second, the mist suspended in the local laminar flows will be conveyed along the center of the pipe faster than the crosssectional mean velocity, and will eventually reach the backside of slowly migrating local turbulence so as to diffuse inside the turbulence (see the lower illustration in Fig. 1). Last, rapid forward acceleration will occur in the center of the pipe at the forward side of the local turbulence because of connection to a re-laminarized velocity profile. The mist ejected from the local turbulence will subsequently experience only minimal diffusion inside the laminar domain and will migrate rapidly to reach the next downstream local turbulence. This peculiar mist behavior will lead to a complex diffusion process that cannot be explained by a state intermediate between fully laminar and fully turbulent flows. In this context, the present study was designed to address two topics. One of these is related to the industrial objectives noted above; that is, the optimization of mist purging operations. The other is the investigation of the fluid dynamics during flow transitions that affect the mist behavior. In particular, the pipe flows employed in natural gas pipelines vary from those used in the idealized experimental work referenced earlier. In-house experimentation uses smooth wall surfaces and short test lengths. In contrast, the internal surfaces of industrial pipelines often exhibit significant roughness owing to absorbed solid-state scales and gaps at pipe joints. This roughness disturbs the flow field in proximity to the wall, triggering local turbulence in the transition region. In pipes shorter than 50 times their diameter in length, this effect is rarely observed because either the laminar or turbulent state occupies the length of the pipe. For this reason, in the present study, we studied unique phenomena that becomes observable only in long pipeline systems, with lengths over 20 0 0 times their diameters. This paper begins by explaining the apparatus and measurement instruments associated with our experimental pipeline. Prior to mist injection, we measured the velocity fluctuations during the flow of clean nitrogen gas inside the pipe, using hot-wire anemometers (HWAs), so as to understand the substantial flow transition processes that take place in a very long pipe. The latter half of the paper reports the manner of the mist diffusion measured at far downstream locations, at which streamwise history of the gas phase inside the pipe affects the mist concentration characteristics especially in the earlier stages of the flow transition. 2. Measurements of internal local turbulence in a pipe 2.1. Experimental facility A schematic of the 1:1 scale test pipeline facility used to simulate a natural gas pipeline is shown in Fig. 2, while Fig. 3 presents a photograph of the overall facility. The straight test pipe section consists of multiple steel pipe sections with an inner diameter, D, of 81.0 mm. The total length of the pipe, L, is 163.3 m, such that L/D is 2016. The pipe sections are connected by welds at intervals of approximately 5 m, and the associated welding back-bead height is approximately 1 mm. The internal wall surface roughness of each pipe is approximately 10 μm. Compressed nitrogen with no humidity was used as the test fluid, and the pressure in the pipe was adjusted to 6 kPa (gauge) with a pressure regulator at the most upstream position. Various flow rates were examined and set using a flow control valve installed at the most downstream position. The pipe wall temperature was kept steady within +3°C of the gas temperature during the trials. Two HWA probes were installed at positions, x, of 5.9 m (upstream) and 158.1 m (downstream) or 5.9 m (upstream) and 82.0 m (midstream), where x = 0 is defined as the point of gas entry to the test pipe. All the test conditions
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Fig. 2. Schematic of the straight test pipeline used to simulate a natural gas pipeline. Table 1 Test conditions of the HWA measurement. Test number
Re
Mean velocity U [m/s]
Positions of installation of the HWA probe
1 2 3 4 5 6 7 8 9 10 11 12 13
10 0 0 1500 20 0 0 2200 2400 2600 2800 30 0 0 3200 3400 3600 3800 40 0 0
0.17 0.25 0.34 0.37 0.40 0.43 0.47 0.50 0.54 0.57 0.61 0.64 0.68
Upstream + Downstream, Upstream + Downstream, Upstream + Downstream, Upstream + Downstream, Upstream + Downstream, Upstream + Downstream, Upstream + Downstream, Upstream + Downstream, Upstream + Downstream, Upstream + Downstream, Upstream + Downstream, Upstream + Downstream, Upstream + Downstream,
Upstream + Midstream Upstream + Midstream Upstream + Midstream Upstream + Midstream Upstream + Midstream Upstream + Midstream Upstream + Midstream Upstream + Midstream Upstream + Midstream Upstream + Midstream Upstream + Midstream Upstream + Midstream Upstream + Midstream
Fig. 3. Photograph of the test facility at Tokyo Gas Co. Ltd.
Fig. 5. Velocity fluctuations measured by HWA at the downstream location (x/D = 1952). Fig. 4. Position of HWA probe relative to gas velocity profiles.
are listed in Table 1. The probes were inserted through the pipe wall, perpendicular to the wall. As shown in Fig. 4, the sensing part of each probe was located at approximately 10 mm from the internal wall, such that y/R = 0.25 (y: insertion length, R: inner radius of the pipe). It was controlled so to minimize disturbance to the flow from the intrusion of HWA probes: the projected area of the HWA probe was less than 0.3% compared with the internal crosssectional area of the pipe. The velocity fluctuations were measured by the HWA at a sampling rate of 1 kHz via an analogue to digital converter. Measurements were started after allowing for a flow development time, as estimated by L/U, where U is the mean gas flow velocity along the pipe cross-section. We also monitored the HWA
waveforms in real time to confirm the flow development. The 60 s data recordings were repeated three times for each flow rate. It should be noted that the HWA measurements were not conducted when the mist was injected because the adhesion of the mist to the hot wires will affect proper operation. 2.2. Flow transitions from HWA data The velocity fluctuations measured by the HWA at the most downstream measurement point, x/D = 1952, are shown in Fig. 5, in which the ordinate axis represents the velocity, u, normalized by the average velocity, u¯ , over the entire measurement period. For this data acquisition, HWA probes were installed at upstream and
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Fig. 6. Comparison of the power spectra of HWA-detected velocity fluctuations.
downstream locations but not at the midstream. As shown in the figure, the velocity remained almost constant at 10 0 0 ≤ Re ≤ 20 0 0, and so a laminar flow state was confirmed. At Re = 2200, a number of wavy velocity fluctuations took place during a recorded interval of 60 s, representing local turbulence emerging and passing by the measurement point. The smooth velocity traces between these local turbulence events are regarded as local laminar flow states. The waveforms of the local turbulence events were similar to those of a turbulent puff. That is, they exhibited gradual variation and abrupt recovery of the stream-wise velocity (Wygnansky et al., 1975). These local turbulence events occupied the entire velocity trace at Re = 2400, at which point the presence of individual puffs became difficult to discern. These data suggest the formation and development of many turbulent slugs. Upon further increasing the Reynolds number to 2600, the turbulent slug waveforms were swamped by the fully fluctuating velocity trace and were no longer seen because of fully developed turbulent flow. The transition region within the test pipeline is therefore estimated to be between Re = 220 0 and 240 0, according to the local velocity fluctuations, and has good agreement with the trend read from the pipe friction factor (Moody, 1944). Fig. 6 presents power spectra of the velocity fluctuations over the range of 10 0 0 ≤ Re ≤ 30 0 0. The ordinate axis here is the HWA output voltage squared, rather than the velocity, so that the various reasons for signal fluctuation can be carefully deduced. In the laminar flow region (Re ≤ 20 0 0), the ordinate is provided with different scales because some responses are less intense relative to others. In this region, the HWA detected several peaks with a frequency, f, of approximately 8 Hz. This is not an important phenomenon but rather resulted from weak flow oscillations transferred from the upstream pressure regulator. It is more important to consider the random peaks in the relatively higher frequency band at f > 10 Hz, observed even at Re ≤ 20 0 0. These local velocity fluctuations are believed to have been induced by inner wall roughness, including seams at the pipe-joints. These fluctuations are so feeble that they do not trigger the perturbation growth to initiate local turbulence.
However, these discrete peaks in the power spectra could potentially trigger fluid mechanical growth of turbulence at Re > 2200. Flow transition to turbulence in a circular pipe basically requires a finite disturbance in the inlet flow or at the wall (Darbyshire and Mullin, 1995; Durst and Unsal, 2006; Peixinho and Mullin, 2007). Therefore we are not allowed to ignore the relatively high frequency velocity fluctuations detected by the present HWA measurements. In fact, these have particular influences to the mist distribution distortion even at Re ≤ 20 0 0, as discussed in the next section. 2.3. Local turbulence in a long pipe Comparisons of the velocity fluctuation patterns at the upstream, midstream, and downstream locations and for Re = 2200 and 2400 are shown in Fig. 7. These data demonstrate the representative waveforms independently obtained at each position, i.e. non-synchronized recording among three locations. More in detail, these velocity data were arranged in the same 60 s, each of which was measured when HWA probes were positioned at “upstream and midstream” and at “upstream and downstream.” In the upstream region and at Re = 2200 various fluctuation spikes are observed; these then disappear midstream and reappear downstream. This result infers that at this Reynolds number, local turbulence does not persist along a long pipe over 20 0 0 diameters, but rather is generated locally with a short lifetime. At Re = 2400, local turbulence passes through in a more stable manner. The waveform of the upstream region closely resembles that of a turbulent puff. This puff is seen to grow and then couple with a slug midstream, thereby eliminating the laminar flow interval downstream. This is the single-phase scenario of flow transition to fully developed turbulence spending over a long transport distance. Based on the radial positions of the HWA probes, the passing turbulent puffs are seen by an increase in the local velocity, as shown in Fig. 7 (upstream), with large positive fluctuations. In contrast, the appearance of turbulent puffs together with turbulent
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flow transition. The disturbance caused by the HWA probe is estimated to be lower than 0.1% in kinetic energy ratio to the bulk pipe flow, considering pipe cross-sectional area and squared mean flow velocity at the tip of the probe. The probe based Reynolds number is lower than 100 in all the test cases. Therefore the probe which is inserted point wisely cannot be a major source of flow transition triggering when compared with the perturbations caused continuously by the roughness of the pipe wall. 3. Diffusion of oil mist concentration
Fig. 7. Comparison of the velocity fluctuations at upstream, midstream and downstream locations for (a) Re = 2200 and (b) Re = 2400.
slugs results in negative velocity fluctuations in the midstream and downstream regions. The reason is explained below. In laminar flow, local velocity uy obeys a parabolic velocity profile known as Poiseuille flow, given by:
uy = 2U 1 −
R − y 2 R
,
(1)
where y is the distance from the pipe inner wall. On the other hand, turbulent flow exhibits a plug-shaped velocity profile, approximated by the one-seventh power law:
uy = 1.22U
y 1 / 7 R
.
(2)
These two formulae have the same velocity at y/R = 0.30, i.e. y = 12 mm in present pipe flow. So shifting the HWA probe position from y = 12 mm enables easy detection of differences between laminar and turbulent flow states (see Fig. 4 in more detail). According to this velocity representation, the data demonstrates the generation of turbulent puffs and slugs that originate not only upstream but also midstream and downstream; this is because of surface roughness along the test pipeline, such as the joints between pipe sections. At the relatively high Reynolds numbers in the transition region, the turbulent puffs quickly grow up to turbulent slugs. The co-existence of turbulent puffs and slugs indicates the intermittent generation of turbulent puffs along the long test pipeline. Such structures are unobservable in short pipe flows; so, when the lifetime of local turbulence exceeds the transient time spent between pipe joints, it is deduced that these local turbulence comprises strings of turbulent slugs downstream. For such sensitivity to wall roughness observed in the transition region, we need to declare the influence of the HWA probe upon
Measurements of the oil mist diffusion behavior in a nitrogen gas pipe flow were conducted using the same test facility as shown in Fig. 2. The flow was categorized as a dilute dispersive twophase flow with gas-phase dominance. The procedure employed for waveform measurements of the mist concentrations was as follows. First, the target gas flow rate was obtained by opening the flow control valve installed at the most downstream position. Second, an oil mist was generated in the oil mist storage region (l = 1.82 m) between valves 1 and 2. Third, valves 1, 2 and 3 along the main pipeline were opened and, finally, the waveform of the oil mist concentration was measured upon arrival at the most downstream point. The oil mist was generated by heating an epoxy resin inside the mist storage region. The mist was assumed to be uniformly distributed inside the storage region, and was treated as a rectangular waveform in the initial condition. The distortion of the initial waveform, however, does not affect the downstream profile as it is transported over the 20 0 0 diameter distance, over which the axial profile expands by more than 50 times the initial length. This was confirmed by the repetition of mist storage experiments. The mist had a particle density, ρ P , of approximately 1.0 g/cm3 . Fig. 8 shows the mist particle size distributions before and after passing through the pipeline, as measured using a jet-cascade impactor (Andersen Sampler AN-200: Tokyo Dyrec, Japan). Most particles were less than 2.4 μm, and the peak of the particle diameter, dP , was between 0.81 and 1.4 μm. From the data, we confirmed that the particle size was mostly unchanged after passing through the pipeline. The maximum mist gas volumetric concentration at the most downstream location was O(10−7 ), which corresponds with O(10−4 ) in the maximum mass loading. Therefore, the mist was eventually diluted at downstream locations, and had little effect on the base nitrogen gas flow. The behavior of oil mist particles in a suspended flow can be characterized by the Stokes number, which is the ratio of the inertial response time of the particle to the characteristic time of the carrier phase flow. The Stokes number is defined as:
St =
ρP d P U . 18μD/2
(3)
For typical experimental conditions (U = 1.0 m/s, dP = 1.0 μm and nitrogen viscosity, μ, of 1.8 × 10−5 Pa s), the Stokes number is estimated to be approximately 8 × 10−5 , which means, theoretically, that the mist particles behave analogously to passive tracers in the nitrogen gas flow. Despite to this estimation, deposition of the mist particles on the pipe wall was significant because approximately 30–60% of the mist particles did not reach the most downstream section. The experimental fact of the mist particle size keeping own similarity infers that the deposition occurs near the wall regardless to the mist particle size on the present order of Stokes number. The mist concentration waveform as a function of time was measured by fluid-sampling nozzles attached at three points: the top (12 o’ clock), the side (3 o’ clock), and the bottom (6 o’ clock) of the pipe wall. The mist concentration was measured at 1.0 s intervals using an aerosol concentration monitor (Dust Track II
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Fig. 8. Oil mist particle size distributions before and after passing through the pipeline. Table 2 Test conditions of the mist concentration measurement. Test number 1 2 3 4 5 6 7 8 9 10 11
Re 300 800 1100 1500 1900 2300 2500 2700 2800 3900 4400
Volumetric flow rate [m3 /s(normal)] −4
3.0 × 10 6.9 × 10−4 9.7 × 10−4 1.3 × 10−3 1.6 × 10−3 2.0 × 10−3 2.2 × 10−3 2.3 × 10−3 2.4 × 10−3 3.5 × 10−3 3.8 × 10−3
Fig. 9. Relationship between the oil mist concentration waveforms and the Reynolds number. The sampling point of the oil mist was the top of the pipe.
Model 8532: TSI Inc., USA) that works on the principle of light scattering. Fig. 9 shows the arrival waveforms of the mist concentration sampled at the top of the pipe. The detailed test conditions are listed in Table 2. The abscissa represents time, t∗ , normalized by the predicted peak arrival time as conveyed by the mean gas velocity, L/U. The mist concentration, φ ∗ , plotted along the ordinate was normalized by the initial concentration, φ 0 . In this normalization, we assume a rectangular wave as the initial waveform and temporarily neglect deposition on the wall. The ignorance does not directly alter the evaluation of the oil mist diffusion process along the mainstream since mist particle-size dependency of the deposition was insignificant. To understand the interpretation of the measured data, we present several idealized examples of the mist concentration waveforms in Fig. 10 (Gill and Sankarasubramanian, 1970). For fully turbulent flows, the following one-dimensional advection-diffusion
Mean velocity U [m/s]
Predicted arrival time L/U [s]
0.057 0.13 0.19 0.25 0.32 0.38 0.41 0.45 0.46 0.66 0.73
2870 1240 880 664 518 429 394 365 354 246 223
Fig. 10. Predicted oil mist concentration waveforms derived from the onedimensional diffusion equation for turbulent flow with fully radial mixing and pure convection of the laminar flow velocity profile with no radial diffusion.
equation gives a good estimate:
∂ φ¯ ∂ φ¯ ∂ 2 φ¯ +U =Γ ∂t ∂x ∂ x2
(4)
where φ¯ is cross-sectional averaged concentration of the mist, U is cross sectional mean carrier-phase velocity, and is apparent one dimensional turbulent diffusion coefficient. The solution of Eq. (4) provides symmetric Gaussian profiles as shown in Fig. 10, dependent on the diffusion coefficient. For laminar flows, Eq. (4) does not give any valid estimate due to less diffusion in the pipe radial direction, and should be replaced with two-dimensional scalar transport equation to which a parabolic velocity profile of the carrier-phase is applied. On ultimate state with zero-molecular diffusion of the mist, laminar pipe flow conveys the initial mist distribution to the downstream as shown by red curve in Fig. 10. The curve starts with a sharp increase and leaves a long tail due to
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Fig. 11. Schematic of thin and elongated oil mist concentration distribution caused by Poiseuille flow: (∗) Initial rectangular distribution, (∗∗) Elongated distribution after long transportation of t∗ = 0.5. The mist layer at x = L/2 present around y = 12 mm with thickness of 0.16 mm and at x = L/4 present around y = 5.5 mm with thickness of 0.13 mm.
streamwise stretching of the mist. The sharp increase at t∗ = 0.5 is explained by the mist transport at the pipe center, whose velocity is twice the mean velocity in the case without turbulent diffusion. Comparing the measured data in Fig. 9 with these ideal situations, the measured data at Re ≥ 2300 generally agrees with the one-dimensional theory. Discrepancy from the theory is found to be at the concentration peak position which appears earlier than L/U, i.e. t∗ < 1. This occurs because the mist was primarily conveyed along the central region of the pipe, where the mean turbulent flow velocity is faster than the cross-sectional mean velocity. This also implies that mist deposition was active close to the wall because of near-wall turbulence. In contrast, the mist concentration in the laminar flow region (Re ≤ 20 0 0) shows the peak shifted towards the early arrival side. There were cases towards the end of the data in which the mist concentration did not fully diminish, even when t∗ exceeded 2.0, resulting in a significant elongation of the mist in the streamwise direction. These results are unsurprising when compared with the ideal laminar solutions shown in Fig. 10. The difference from the ideal situation is that the sharp front of the concentration wave disappears in laminar flow, inferring the significance of the radial diffusion of the mist. The arrival time of the wave front is also delayed from t∗ = 0.5 to t∗ > 0.6. To discuss on the discrepancy, we illustrate the mist distribution stretched in laminar flow in Fig. 11. When the mist is transported by Poiseuille parabolic base flow over a long distance, the original mist concentration is stretched in the axial direction proportionally to time elapse. It forms an extremely thin parabolic layer between the leading point and the original near-wall region. The concentration interface (or concentration gradient) of such a layer mostly faces the radial direction of the pipe, which thus results in activation of the radial diffusion. For substances with a high molecular diffusion coefficient, such a thin layer will not be formed because the layer immediately diffuses occupying the pipe cross section before reaching downstream. For mist, diffusion only relies on Brownian motion that provides a finite thickness of the layer but which is much thinner than the case of ordinary molecular diffusion process. Consequently, we have experimentally confirmed that the mist diffusion in laminar pipe flow is ultimately governed by Brownian motion (Ekambara and Joshi, 2004; Matas et al., 2004). In the region of 10 0 0 < Re < 20 0 0, over which the HWA measurements indicated that the flow kept laminar state, an irregular mist concentration waveform with multiple local maximum values was observed as shown in Fig. 12. Spatial anisotropy is also obvious in the mist concentration as compared among three sampling points (top, side and bottom of the pipe). This spiky and non-axisymmetric waveform is evidence of poor radial mixing of the mist in laminar flow, and re-attributed to the intensity level of the Brownian motion. The Brownian diffusion coefficient, γ , is generally given by the following Stokes-Einstein equation (Einstein, 1905; Shimada et al., 1993):
γ=
kT , 3 π μd P
(5)
Fig. 12. Oil mist concentration waveforms for Re = 80 0, 110 0, 150 0, 190 0 and 2300.
where k is the Botzmann constant 1.38 × 10−23 J/K. For the present experimental conditions (absolute temperature, T, of 293 K, dP = 1.0 μm and μ = 1.8 × 10−5 Pa s), the Brownian diffusion coefficient was estimated to be approximately 2 × 10−11 m2 /s. The mean square displacement of a single mist particle due to Brownian motion, < r2 >, can be estimated by the following formula (e.g., van Megan and Underwood, 1989):
r 2 =
6 · γ · t .
(6) 104
Since the test period in the longest case did not exceed s in this study, the maximum average displacement of a mist particle is estimated to be 1.1 mm. This value is sufficiently small compared with the pipe diameter of 81 mm, and explains presence of the mist layer thinner than it even at the most downstream section. Such a particular layer is never formed in gas-gas two-phase flow (Evans and Kenney, 1964; Flint and Eisenklam, 1969), and thereby the heterogeneous response of the mist concentration is regarded as one of unique phenomena taking place only in the immiscible mist-laden laminar gas flows. 4. Waveform parameterization To quantify the concentration waveform, we introduce five nondimensional evaluation parameters: the peak time (t∗ peak ), the rise time (t∗ rise ), the fall time (t∗ fall ), the “Irregularity”, and the “Anisotropy”, as well as standard deviation (σ ), skewness (Sk) and mean residence time (t∗ MRT ). The peak time is defined as the time at which the maximum concentration is observed. The rise time
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and the fall time are defined as the times at which φ ∗ > 10−4 and φ ∗ < 10−4 are achieved, respectively. The Irregularity is given by the equation:
(Irregularity ) =
∗ tfall
1 · ∗ − trise
∗ tfall
∗ trise
2 ∗ dt . φ ∗ − φSMA
(7)
particles from near the pipe wall to the pipe center. One possible driving force near the pipe wall is the local velocity fluctuation originating from the pipe roughness, as observed in the HWA data. This remains as an assumption but is supported by the fact that the measured t∗ fall decreases rather for smaller Reynolds numbers within the range of 800 < Re < 2300; further suggesting that the radial mixing due to the near-wall flow disturbance progresses for longer duration at slow flows. Finally, the irregularity and anisotropy in Fig. 13 indicate that these values increase only in the flow transition region at 10 0 0 < Re < 20 0 0. This supports that the oil mist particles behave clearly differently from those in the fully turbulent or fully laminar flow regions. Since the gas phase has no structural turbulence as long as assessed by HWA, we hereafter attempt our discussion to elaborate this phenomenon.
This formula represents the root mean square value based on the difference between the original waveform, φ ∗ , and φ ∗ SMA , the waveform derived by smoothing the concentration waveform with a central simple moving average (SMA) at a cutoff frequency, f∗ , of 10/(t∗ fall -t∗ rise ). The anisotropy is also defined in terms of the root mean square value, and is based on the differences between the concentration waveforms at the three measurement points, as in the equation below:
(Anisotropy ) =
1 · ∗ − t∗ ) 3 · (tfall rise
∗ tfall
∗ trise
2 ∗ − φ∗ d t + φtop side
∗ tfall
∗ trise
The standard deviation and skewness are defined around the weight center of the mist concentration profile: The mean residence time of the mist inside the pipe is computed by the time taken for the weight center of the mist profile to pass through the system, as described in the following equation: ∗
tfall
∗ tMRT
=
t ∗ · φ ∗ dt ∗
tfall ∗ t ∗ φ dt
∗ trise
2 ∗ ∗ − φbottom dt + φside
(9)
∗ tfall
∗ trise
2 ∗ ∗ − φtop dt φbottom
(8)
The irregularity and the anisotropy of the mist particle behavior cannot be explained solely by processes such as turbulent diffusion or Brownian motion with statistical axial symmetry. It is possibly an effect caused by the gravitational force on the mist even though it is scaled to be mostly negligible because of the low mass-loading ratio and the suite small order of Stokes number as estimated pre-
rise
Fig. 13 presents these eight parameters as functions of the Reynolds number. The graphs for σ , Sk, t∗ MRT , t∗ peak , t∗ rise , t∗ fall and irregularity values depict the mean of three locations; top, side, and bottom parts of the pipe, for each Reynolds number. Vertical bar indicates the maximum and minimum values among the three locations. The σ , Sk, t∗ MRT , t∗ peak , t∗ rise and t∗ fall values were chosen to discriminate between laminar and turbulent flows. Among these parameters, t∗ fall is the key for the purging operation because it determines the necessary time for flushing the residual mist. The irregularity and anisotropy shown at the bottom of the figure highlight well the characteristics of the mist transport in the transition region, which indicates how the mist behavior can become heterogeneous, and depart from a simple one-dimensional advectiondiffusion model. As previously explained with Fig. 10, laminar flow should have large values for σ and Sk because of distortion towards the early arrival side. This corresponds to decrease in t∗ peak , t∗ rise and increase in t∗ MRT , t∗ fall . These trends are also confirmed in the measured data in Fig. 13. For transition region between laminar and turbulent flow states, only t∗ MRT takes an intermediate value between the two states. The other parameters, σ , Sk, t∗ peak , t∗ rise and t∗ fall demonstrate that the flow structure in the transition region clearly reflects to the shape of the concentration waveform, whose changes end at Re = 2300. Concerning with the purge operation, we need to pay attention to the measured t∗ fall which has large values at Re < 2300. This proves that the purge operation works the best in the turbulent flow region. On the other hand, pure laminar flow theory tells that the gas phase in the vicinity of the pipe wall has almost no local velocity; therefore mist particles near the pipe wall are not entrained. This idea predicts t∗ fall to be infinity, however, the measured t∗ fall was a finite value even in the laminar region. It infers from the discrepancy that there is a driving force that conveys mist
Fig. 13. Parameters of the oil mist concentration waveforms as a function of the Reynolds number. The vertical bar indicates maximum and minimum value.
T. Takeuchi et al. / International Journal of Multiphase Flow 87 (2016) 45–53
viously. The gravitational force would be expected to play an important role in the laminar flow region at lower flow velocities. Another possible explanation is the intermittent and local generation of velocity fluctuations originating from the pipe joints and wall roughness. The mist concentration distribution extends parabolically with the laminar Poiseuille velocity profile, and draws a ring-shaped cross-sectional distribution. The ring exists in the center of the pipe at the most downstream location, and shifts to the wall proximity at the upstream side. In such instances, local vortices generated close to the inner surfaces of the pipe give certain distortion of the ring-shaped distribution of the mist particularly in the upstream region. This, in turn, can lead to changes in the mist concentration distribution over the pipe as the influence propagates downstream. Furthermore, these local uncontrolled disturbances have non-axisymmetric and three-dimensional structures ordinarily; this could potentially be the cause of the observed anisotropy. While the local vortices affects the mist behavior in such a way, they do not develop to organized turbulence at low Re numbers. This explains why the mist concentration is sensitively affected by the wall roughness at small Re numbers before nominal flow transition. For 20 0 0 < Re < 2400, the anisotropy of the mist distribution still remains. This is explained by appearance of turbulent puffs that have insufficient statistical axisymmetry as visualized by Hof et al., (2004) and Ohkubo et al., (2016). In summary, transition in the mist concentration behavior occurs at Reynolds numbers lower than those associated with flow transition observed in velocity fluctuations. This is because the mist distribution becomes thinner during prolonged transport along the laminar velocity profile, and becomes sensitive to the wall roughness. So, measurements of the mist concentration waveform are sensitive to flow disturbances originating from the wall structure, even if these disturbances do not develop into persistent turbulence. 5. Conclusion Experimental analyses of the oil mist diffusion process were carried out at 300 ≤ Re ≤ 4400, beyond the flow transition region between laminar and fully turbulent states. Using a model of a long industrial pipeline subject to wall roughness over the 20 0 0 diameter distance, we monitored the manner in which the mist and the carrier gas developed in the streamwise direction when the Stokes number of the mist was sufficiently low, O(10−5 ). We first measured the velocity fluctuations of mist-free nitrogen gas flow by means of hot-wire anemometers, to verify the existence of streamwise flow transitions from perfect laminar to fully developed turbulent flow. The data agreed with established understanding of pipe flow transition, such as the passage of local turbulence at 20 0 0 ≤ Re ≤ 2400 in the transition region. We also detected discrete peaks in the power spectra in the range of 10 0 0 ≤ Re ≤ 20 0 0, which were attributed to the wall roughness (including pipe joints). Secondly, we tracked the mist diffusion process in the stream-wise direction. Aerosol concentration monitors were set at the downstream outlet to detect the concentration waveforms. From these waveforms, we confirmed that, at Re < 10 0 0, the mist had a significantly diffused profile along the pipe axial direction because of parabolic transport by Poiseuille flow, which was insensitive to wall roughness. For fully turbulent flows at Re > 2400, the mist was transported sharply with less axial diffusion while rich radial mixing dominates in the cross-sectional plane. We observed the early effects of flow disturbance between 10 0 0 < Re < 20 0 0 in the mist waveform, highlighted by a front-shift in concentration, the emergence of multiple peaks, and also anisotropy across the
53
cross sectional plane. These phenomena were attributed to velocity perturbations in the proximity of the wall, which did not grow to form organized turbulence but can distort the mist layer that remained close to the wall behind the parabolic transport. This effect was observable only in a long pipeline with immiscible dispersion with the carrier gas phase. Our original objective was to optimize the purging operation; the following findings may be of use to operators and engineers: i) laminar flow causes an early arrival time of the mist wavefront, compared with the estimation via L/U, but it is always slower than that predicted by simple advection theory because of Brownian diffusion. ii) Multiple peaks of the mist concentration occur in the transition region even in straight pipe geometry. The operator needs to estimate Reynolds number to recognize the possibility of split waves from a simple Gaussian profile. iii) For industrial pipelines with wall roughness, even laminar flow can induce anisotropy in mist concentration far downstream. References Avila, K., Moxey, D., de Lozar, A., Avila, M., Barkley, D., Hof, B., 2011. The onset of turbulence in pipe flow. Science 333, 192–196. Darbyshire, A., Mullin, T., 1995. Transition to turbulence in constant-mass-flux pipe flow. J. Fluid Mech. 289, 83–114. Durst, F., Unsal, B., 2006. Forced laminar-to-turbulent transition of pipe flows. J. Fluid Mech. 560, 449–464. Einstein, A., 1905. Über die von der molekularkinetischen Theorie der Wärme geforderte Bewegung von in ruhenden Flüssigkeiten suspendierten Teilchen. Annalen der Physik. 322 (8), 549–560. Ekambara, K., Joshi, J.B., 2003. Axial mixing in pipe flows turbulent and transition regions. Chem. Eng. Sci. 58, 2715–2724. Ekambara, K., Joshi, J.B., 2004. Axial mixing in laminar pipe flows. Chem. Eng. Sci. 59, 3929–3944. Evans, E.V., Kenney, C.N., 1964. Gaseous dispersion in laminar flow through a circular tube. Proc. Roy. Soc. London. A. 284, 540–550. Flint, L.F., Eisenklam, P., 1969. Longitudinal gas dispersion in transitional and turbulent flow through a straight tube. Can. J. Chem. Eng. 47 (2), 101–106. Gill, W.N., Sankarasubramanian, R., 1970. Exact analysis of unsteady convective diffusion. Proc. Roy. Soc. Lond. A. 316, 341–350. Hof, B., Juel, A., Mullin, T., 2003. Scaling of the turbulence transition threshold in a pipe. Phys. Rev. Lett. 91, 244502. Hof, B., van Doorne, C.W.H., Westerweel, J., Nieuwstadt, F.T.M., Faiss, H., Eckhardt, B., Wedin, H., Kerswell, R.R., Waleffe, F., 2004. Experimental observation of nonlinear traveling waves in turbulent pipe flow. Science 305, 1594–1598. Hof, B., Westerweel, J., Schneider, T.M., Eckhardt, B., 2006. Finite lifetime of turbulence in shear flows. Nature 443, 59–62. Matas, J.P., Morris, J.F., Guazelli, E., 2004. Inertial migration of rigid spherical particles in Poiseuille flow. J. Fluid Mech. 515, 171–195. Moody, L.F., 1944. Friction factors for pipe flow. Trans. ASME. 66 (8), 671–684. Nishi, M., Unsal, B., Durst, F., Biswas, G., 2008. Laminar-to-turbulent transition of pipe flow through slugs and puffs. J. Fluid Mech. 614, 425–446. Ohkubo, J., Tasaka, Y., Park, H.J., Murai, Y., 2016. Extraction of 3D vortex structures from a turbulent puff in a pipe using two-color illumination and flakes. J. Visualization. doi:10.1007/s12650- 016- 0344- z. Peixinho, J., Mullin, T., 2006. Decay of turbulent in pipe flow. Phys. Rev. Lett. 96, 094501. Peixinho, J., Mullin, T., 2007. Finite-amplitude thresholds for transition in pipe flow. J. Fluid Mech. 582, 169–178. Reynolds, O., 1883. An experimental investigation of the circumstances which determine whether the motion of water shall be direct of sinuous, and the law of resistance in parallel channels. Philos. Trans. R. Soc. London, Ser. A 174, 935–982. Shimada, M., Okuyama, K., Asai, M., 1993. Deposition of submicron aerosol particles in turbulent and transitional flow. AIChE J. 39-1, 17–26. Shimizu, M., Kida, S., 2009. A driving mechanism of a turbulent puff in pipe flow. Fluid Dyn. Res. 41, 045501. Takeuchi, T., Murai, Y., 2010. Flowmetering of natural gas pipeline by tracer gas pulse injection. Meas. Sci. Technol. 21, 0154028. Tasaka, Y., Schneider, T.M., Mullin, T., 2010. Folded edge of turbulence in a pipe. Phys. Rev. Lett. 105, 174502. van Megan, W., Underwood, S.M., 1989. Tracer diffusion in colloidal dispersion. III. Mean squared displacement and self-diffusion coefficients. J. chem. Phys. 91 (1), 552–559. Wygnansky, I., Sokolov, M., Friedman, D., 1975. On transition in a pipe. Part 2. The equilibrium puff. J. Fluid Mech. 69-2, 283–304.
Contents lists available at ScienceDirect
International Journal of Multiphase Flow journal homepage: www.elsevier.com/locate/ijmulflow
Oil mist transport process in a long pipeline on turbulent flow transition region Tomoaki Takeuchi a,∗, Jumpei Ohkubo b, Norio Yonezawa b, Yoshihiko Oishi c, Ichiro Kumagai d, Yuji Tasaka b, Yuichi Murai b a
Pipeline Technology Center, Tokyo Gas Co., Ltd., 1-7-7 Suehiro-cho, Tsurumi-ku, Yokohama, 230-0045, Japan Division of Energy & Environmental Systems, Faculty of Engineering, Hokkaido University, N13W8, Sapporo 060-8628, Japan Department of Mechanical, Aerospace, and Materials Engineering, Muroran Institute of Technology, 27-1 Mizumoto-cho, Muroran, Hokkaido, 050-8585, Japan d School of Science and Engineering, Meisei University, 2-1-1, Hodokubo, Hino, Tokyo, 191-8506, Japan b c
a r t i c l e
i n f o
Article history: Available online 24 August 2016 Keywords: Pipe flow Turbulent flow transition Poiseuille flow Concentration diffusion Oil mist Pipeline
a b s t r a c t Internal gas velocity fluctuations and their effects on the mist diffusion process were examined in a long horizontal pipe to understand oil mist transportation, particularly in the laminar-to-turbulent flow transition region. Three hot-wire anemometers and aerosol concentration monitors were used to deduce these effects as the two-phase mist flow gradually developed in the stream-wise direction. We found significant axial mist diffusion at Reynolds numbers (Re) < 10 0 0 because of passive scalar transport by Poiseuille flow. However, this diffusion was restricted by the non-zero inertia of the mist at a Stokes number, O(10−5 ), relying on the Brownian motion of the mist. At Re > 2400, a sharp mist waveform was maintained by a turbulent flow with active radial mixing. New data were obtained within the range of 10 0 0 < Re < 2400, which cannot be explained by interpolation between the above-mentioned two states. The mist concentration displays multiple temporal peaks at Re < 20 0 0 owing to perturbations of localized turbulence as well as radial anisotropy as being conveyed more than 20 0 0-diameters in distance. This behavior is caused by intermittent disturbances induced by the pipe wall roughness, which sharply distorts the wall-aligned laminar mist layer left by parabolic axial stretching of local laminar flow. © 2016 Elsevier Ltd. All rights reserved.
1. Introduction The contamination of an industrial gas transport pipeline with an oil mist can lead to a range of problems. For this reason, oil mists must be purged using a clean gas and then removed by some means, such as by filtration. It is therefore important to obtain an understanding of the changes in the mist concentration within a pipeline while purging. The flow field inside pipes during the ordinary transport of a natural gas is generally turbulent. However, the flow velocities are lower than usual when conducting a purge operation since temporary interruption of the gas supply is required. This means that the mist diffusion phenomena that occur during both laminar, transitional, and turbulent flows must be clarified. The diffusion behavior subject to turbulent flow can be classified according to the associated Stokes number (St) of the mist.
∗
Corresponding author. E-mail addresses: [email protected] (T. Takeuchi), [email protected]. hokudai.ac.jp (J. Ohkubo), [email protected] (N. Yonezawa), [email protected] (Y. Oishi), [email protected] (I. Kumagai), [email protected] (Y. Tasaka), [email protected] (Y. Murai). http://dx.doi.org/10.1016/j.ijmultiphaseflow.2016.08.002 0301-9322/© 2016 Elsevier Ltd. All rights reserved.
For St 1, individual mist particles are passively transported by turbulent eddies, and the resulting diffusion is dominated by the turbulent mixing properties (Flint and Eisenklam, 1969; Ekambara and Joshi, 2003; Takeuchi and Murai, 2010). This turbulent diffusion also promotes the deposition of mist on the internal walls of the pipeline. So, the axial transport of the mist can be described by a combination of turbulent diffusion and the associated pipewall deposition rate. In this case, the mist concentration can be approximated as a symmetric Gaussian profile in the pipe axial direction, and therefore the time required for the mist purging is easily modeled by a one-dimensional advection-diffusion equation (Fick’s law). In laminar flows, mist transport results from a totally different mechanism. The mist is conveyed by a parabolic velocity profile of Poiseuille flow which has a centerline velocity that is twice the cross-sectional mean velocity. This leads to a long stretched distribution of mist in the axial direction; more importantly the stretched distribution provides a sharp gradient in the pipe’s radial direction. This consequently enhances the radial diffusion more than the axial diffusion. Similar cases for passive scalar or molecular transport were reported by Ekambara and Joshi (2004), and
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Fig. 1. Schematic representations of local turbulence.
Matas et al., (2004). The difference in behavior of the mist from the scalar or molecular scale is that mist a few micrometers in size obeys Brownian motion, associated with collisions with surrounding gas molecules (Shimada et al., 1993; Matas et al., 2004). The effective diffusion coefficient of Brownian motion is much less than that of gas diffusion, and therefore the mist is hardly diffused in the radial direction. This phenomenon could be an obstacle for an efficient purging operation in laminar flow. Theoretical predictions of transitional flow regions remain essentially impossible; this is because of the coexistence of two different stages in laminar to turbulent flow transition. One stage involves turbulent slugs intermittently appearing in ambient laminar flow. The other stage involves the appearance of turbulent puffs with specific structures independent of the pipe wall properties. These transition processes, which occur even in single phase pipe flow, has been regarded as a fundamental topic more than a century after the initial work of Reynolds (1883). The details of these transition processes have recently attracted special interest as nonlinear dynamics of sub-critical flow transition (see, for example, Hof et al., 2004, 2006; Tasaka et al., 2010; Avila et al., 2011). We will mainly focus on the transitional regime in this paper by connecting such recent knowledge on local turbulence and dispersion dynamics in dilute mist transport. Fig. 1 illustrates the internal structure of the local turbulence emerging between laminar flow sections in the transitional regime. The local turbulence is called a turbulent puff in the minimal case (Hof et al., 2004; Nishi et al., 2008; Shimazu and Kida, 2009) while it is called a turbulent slug in longer cases. The authors’ group also succeeded in visualizing the turbulent puff to reveal the threedimensional vortical structures within (Ohkubo et al., 2016). Inside the local turbulence, low-speed streaks and stream-wise vortex structures are present in proximity to the wall, where frictional stress increases locally. These structures are elongated downstream owing to high speed flow in the pipe center of the neighboring Poiseuille flow, forming a blunt boundary between the laminar and the turbulent regions. In industrial pipelines, multiple occurrences of such local turbulence should be considered as they are typically longer than 10 0 0 times the pipe diameter. At relatively large Reynolds numbers within the transition region, the overall pipeline is considered as a spatially intermittent distribution of laminar flow and turbulent slugs. This enables us to estimate the overall pressure loss (Moody, 1944) and mass diffusion coefficient (Flint and Eisenklam, 1969; Ekambara and Joshi, 2003) by finding the value between that for laminar and turbulent flows. In contrast, a specific turbulent puff structure occurs at lower Reynolds numbers, which does not give a valid estimation by taking intermediate values. A puff can be understood as the minimal elementary turbulence sustainable in the pipe flow. It propagates along the axial direction with a specific lifetime (Hof et al., 20 03, 20 06; Peixinho and Mullin, 2006; Tasaka et al., 2010). The sustainability of a puff indicates independence on the pipe wall properties; the structure will persist downstream even inside a completely smooth pipe. This phenomenon can therefore be distinguished from a turbulent slug.
Based on the above, the behavior of a mist in transitional regions can be predicted by several aspects as follows. First, mist diffusion will result from vortices that develop inside local turbulence. Second, the mist suspended in the local laminar flows will be conveyed along the center of the pipe faster than the crosssectional mean velocity, and will eventually reach the backside of slowly migrating local turbulence so as to diffuse inside the turbulence (see the lower illustration in Fig. 1). Last, rapid forward acceleration will occur in the center of the pipe at the forward side of the local turbulence because of connection to a re-laminarized velocity profile. The mist ejected from the local turbulence will subsequently experience only minimal diffusion inside the laminar domain and will migrate rapidly to reach the next downstream local turbulence. This peculiar mist behavior will lead to a complex diffusion process that cannot be explained by a state intermediate between fully laminar and fully turbulent flows. In this context, the present study was designed to address two topics. One of these is related to the industrial objectives noted above; that is, the optimization of mist purging operations. The other is the investigation of the fluid dynamics during flow transitions that affect the mist behavior. In particular, the pipe flows employed in natural gas pipelines vary from those used in the idealized experimental work referenced earlier. In-house experimentation uses smooth wall surfaces and short test lengths. In contrast, the internal surfaces of industrial pipelines often exhibit significant roughness owing to absorbed solid-state scales and gaps at pipe joints. This roughness disturbs the flow field in proximity to the wall, triggering local turbulence in the transition region. In pipes shorter than 50 times their diameter in length, this effect is rarely observed because either the laminar or turbulent state occupies the length of the pipe. For this reason, in the present study, we studied unique phenomena that becomes observable only in long pipeline systems, with lengths over 20 0 0 times their diameters. This paper begins by explaining the apparatus and measurement instruments associated with our experimental pipeline. Prior to mist injection, we measured the velocity fluctuations during the flow of clean nitrogen gas inside the pipe, using hot-wire anemometers (HWAs), so as to understand the substantial flow transition processes that take place in a very long pipe. The latter half of the paper reports the manner of the mist diffusion measured at far downstream locations, at which streamwise history of the gas phase inside the pipe affects the mist concentration characteristics especially in the earlier stages of the flow transition. 2. Measurements of internal local turbulence in a pipe 2.1. Experimental facility A schematic of the 1:1 scale test pipeline facility used to simulate a natural gas pipeline is shown in Fig. 2, while Fig. 3 presents a photograph of the overall facility. The straight test pipe section consists of multiple steel pipe sections with an inner diameter, D, of 81.0 mm. The total length of the pipe, L, is 163.3 m, such that L/D is 2016. The pipe sections are connected by welds at intervals of approximately 5 m, and the associated welding back-bead height is approximately 1 mm. The internal wall surface roughness of each pipe is approximately 10 μm. Compressed nitrogen with no humidity was used as the test fluid, and the pressure in the pipe was adjusted to 6 kPa (gauge) with a pressure regulator at the most upstream position. Various flow rates were examined and set using a flow control valve installed at the most downstream position. The pipe wall temperature was kept steady within +3°C of the gas temperature during the trials. Two HWA probes were installed at positions, x, of 5.9 m (upstream) and 158.1 m (downstream) or 5.9 m (upstream) and 82.0 m (midstream), where x = 0 is defined as the point of gas entry to the test pipe. All the test conditions
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Fig. 2. Schematic of the straight test pipeline used to simulate a natural gas pipeline. Table 1 Test conditions of the HWA measurement. Test number
Re
Mean velocity U [m/s]
Positions of installation of the HWA probe
1 2 3 4 5 6 7 8 9 10 11 12 13
10 0 0 1500 20 0 0 2200 2400 2600 2800 30 0 0 3200 3400 3600 3800 40 0 0
0.17 0.25 0.34 0.37 0.40 0.43 0.47 0.50 0.54 0.57 0.61 0.64 0.68
Upstream + Downstream, Upstream + Downstream, Upstream + Downstream, Upstream + Downstream, Upstream + Downstream, Upstream + Downstream, Upstream + Downstream, Upstream + Downstream, Upstream + Downstream, Upstream + Downstream, Upstream + Downstream, Upstream + Downstream, Upstream + Downstream,
Upstream + Midstream Upstream + Midstream Upstream + Midstream Upstream + Midstream Upstream + Midstream Upstream + Midstream Upstream + Midstream Upstream + Midstream Upstream + Midstream Upstream + Midstream Upstream + Midstream Upstream + Midstream Upstream + Midstream
Fig. 3. Photograph of the test facility at Tokyo Gas Co. Ltd.
Fig. 5. Velocity fluctuations measured by HWA at the downstream location (x/D = 1952). Fig. 4. Position of HWA probe relative to gas velocity profiles.
are listed in Table 1. The probes were inserted through the pipe wall, perpendicular to the wall. As shown in Fig. 4, the sensing part of each probe was located at approximately 10 mm from the internal wall, such that y/R = 0.25 (y: insertion length, R: inner radius of the pipe). It was controlled so to minimize disturbance to the flow from the intrusion of HWA probes: the projected area of the HWA probe was less than 0.3% compared with the internal crosssectional area of the pipe. The velocity fluctuations were measured by the HWA at a sampling rate of 1 kHz via an analogue to digital converter. Measurements were started after allowing for a flow development time, as estimated by L/U, where U is the mean gas flow velocity along the pipe cross-section. We also monitored the HWA
waveforms in real time to confirm the flow development. The 60 s data recordings were repeated three times for each flow rate. It should be noted that the HWA measurements were not conducted when the mist was injected because the adhesion of the mist to the hot wires will affect proper operation. 2.2. Flow transitions from HWA data The velocity fluctuations measured by the HWA at the most downstream measurement point, x/D = 1952, are shown in Fig. 5, in which the ordinate axis represents the velocity, u, normalized by the average velocity, u¯ , over the entire measurement period. For this data acquisition, HWA probes were installed at upstream and
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Fig. 6. Comparison of the power spectra of HWA-detected velocity fluctuations.
downstream locations but not at the midstream. As shown in the figure, the velocity remained almost constant at 10 0 0 ≤ Re ≤ 20 0 0, and so a laminar flow state was confirmed. At Re = 2200, a number of wavy velocity fluctuations took place during a recorded interval of 60 s, representing local turbulence emerging and passing by the measurement point. The smooth velocity traces between these local turbulence events are regarded as local laminar flow states. The waveforms of the local turbulence events were similar to those of a turbulent puff. That is, they exhibited gradual variation and abrupt recovery of the stream-wise velocity (Wygnansky et al., 1975). These local turbulence events occupied the entire velocity trace at Re = 2400, at which point the presence of individual puffs became difficult to discern. These data suggest the formation and development of many turbulent slugs. Upon further increasing the Reynolds number to 2600, the turbulent slug waveforms were swamped by the fully fluctuating velocity trace and were no longer seen because of fully developed turbulent flow. The transition region within the test pipeline is therefore estimated to be between Re = 220 0 and 240 0, according to the local velocity fluctuations, and has good agreement with the trend read from the pipe friction factor (Moody, 1944). Fig. 6 presents power spectra of the velocity fluctuations over the range of 10 0 0 ≤ Re ≤ 30 0 0. The ordinate axis here is the HWA output voltage squared, rather than the velocity, so that the various reasons for signal fluctuation can be carefully deduced. In the laminar flow region (Re ≤ 20 0 0), the ordinate is provided with different scales because some responses are less intense relative to others. In this region, the HWA detected several peaks with a frequency, f, of approximately 8 Hz. This is not an important phenomenon but rather resulted from weak flow oscillations transferred from the upstream pressure regulator. It is more important to consider the random peaks in the relatively higher frequency band at f > 10 Hz, observed even at Re ≤ 20 0 0. These local velocity fluctuations are believed to have been induced by inner wall roughness, including seams at the pipe-joints. These fluctuations are so feeble that they do not trigger the perturbation growth to initiate local turbulence.
However, these discrete peaks in the power spectra could potentially trigger fluid mechanical growth of turbulence at Re > 2200. Flow transition to turbulence in a circular pipe basically requires a finite disturbance in the inlet flow or at the wall (Darbyshire and Mullin, 1995; Durst and Unsal, 2006; Peixinho and Mullin, 2007). Therefore we are not allowed to ignore the relatively high frequency velocity fluctuations detected by the present HWA measurements. In fact, these have particular influences to the mist distribution distortion even at Re ≤ 20 0 0, as discussed in the next section. 2.3. Local turbulence in a long pipe Comparisons of the velocity fluctuation patterns at the upstream, midstream, and downstream locations and for Re = 2200 and 2400 are shown in Fig. 7. These data demonstrate the representative waveforms independently obtained at each position, i.e. non-synchronized recording among three locations. More in detail, these velocity data were arranged in the same 60 s, each of which was measured when HWA probes were positioned at “upstream and midstream” and at “upstream and downstream.” In the upstream region and at Re = 2200 various fluctuation spikes are observed; these then disappear midstream and reappear downstream. This result infers that at this Reynolds number, local turbulence does not persist along a long pipe over 20 0 0 diameters, but rather is generated locally with a short lifetime. At Re = 2400, local turbulence passes through in a more stable manner. The waveform of the upstream region closely resembles that of a turbulent puff. This puff is seen to grow and then couple with a slug midstream, thereby eliminating the laminar flow interval downstream. This is the single-phase scenario of flow transition to fully developed turbulence spending over a long transport distance. Based on the radial positions of the HWA probes, the passing turbulent puffs are seen by an increase in the local velocity, as shown in Fig. 7 (upstream), with large positive fluctuations. In contrast, the appearance of turbulent puffs together with turbulent
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flow transition. The disturbance caused by the HWA probe is estimated to be lower than 0.1% in kinetic energy ratio to the bulk pipe flow, considering pipe cross-sectional area and squared mean flow velocity at the tip of the probe. The probe based Reynolds number is lower than 100 in all the test cases. Therefore the probe which is inserted point wisely cannot be a major source of flow transition triggering when compared with the perturbations caused continuously by the roughness of the pipe wall. 3. Diffusion of oil mist concentration
Fig. 7. Comparison of the velocity fluctuations at upstream, midstream and downstream locations for (a) Re = 2200 and (b) Re = 2400.
slugs results in negative velocity fluctuations in the midstream and downstream regions. The reason is explained below. In laminar flow, local velocity uy obeys a parabolic velocity profile known as Poiseuille flow, given by:
uy = 2U 1 −
R − y 2 R
,
(1)
where y is the distance from the pipe inner wall. On the other hand, turbulent flow exhibits a plug-shaped velocity profile, approximated by the one-seventh power law:
uy = 1.22U
y 1 / 7 R
.
(2)
These two formulae have the same velocity at y/R = 0.30, i.e. y = 12 mm in present pipe flow. So shifting the HWA probe position from y = 12 mm enables easy detection of differences between laminar and turbulent flow states (see Fig. 4 in more detail). According to this velocity representation, the data demonstrates the generation of turbulent puffs and slugs that originate not only upstream but also midstream and downstream; this is because of surface roughness along the test pipeline, such as the joints between pipe sections. At the relatively high Reynolds numbers in the transition region, the turbulent puffs quickly grow up to turbulent slugs. The co-existence of turbulent puffs and slugs indicates the intermittent generation of turbulent puffs along the long test pipeline. Such structures are unobservable in short pipe flows; so, when the lifetime of local turbulence exceeds the transient time spent between pipe joints, it is deduced that these local turbulence comprises strings of turbulent slugs downstream. For such sensitivity to wall roughness observed in the transition region, we need to declare the influence of the HWA probe upon
Measurements of the oil mist diffusion behavior in a nitrogen gas pipe flow were conducted using the same test facility as shown in Fig. 2. The flow was categorized as a dilute dispersive twophase flow with gas-phase dominance. The procedure employed for waveform measurements of the mist concentrations was as follows. First, the target gas flow rate was obtained by opening the flow control valve installed at the most downstream position. Second, an oil mist was generated in the oil mist storage region (l = 1.82 m) between valves 1 and 2. Third, valves 1, 2 and 3 along the main pipeline were opened and, finally, the waveform of the oil mist concentration was measured upon arrival at the most downstream point. The oil mist was generated by heating an epoxy resin inside the mist storage region. The mist was assumed to be uniformly distributed inside the storage region, and was treated as a rectangular waveform in the initial condition. The distortion of the initial waveform, however, does not affect the downstream profile as it is transported over the 20 0 0 diameter distance, over which the axial profile expands by more than 50 times the initial length. This was confirmed by the repetition of mist storage experiments. The mist had a particle density, ρ P , of approximately 1.0 g/cm3 . Fig. 8 shows the mist particle size distributions before and after passing through the pipeline, as measured using a jet-cascade impactor (Andersen Sampler AN-200: Tokyo Dyrec, Japan). Most particles were less than 2.4 μm, and the peak of the particle diameter, dP , was between 0.81 and 1.4 μm. From the data, we confirmed that the particle size was mostly unchanged after passing through the pipeline. The maximum mist gas volumetric concentration at the most downstream location was O(10−7 ), which corresponds with O(10−4 ) in the maximum mass loading. Therefore, the mist was eventually diluted at downstream locations, and had little effect on the base nitrogen gas flow. The behavior of oil mist particles in a suspended flow can be characterized by the Stokes number, which is the ratio of the inertial response time of the particle to the characteristic time of the carrier phase flow. The Stokes number is defined as:
St =
ρP d P U . 18μD/2
(3)
For typical experimental conditions (U = 1.0 m/s, dP = 1.0 μm and nitrogen viscosity, μ, of 1.8 × 10−5 Pa s), the Stokes number is estimated to be approximately 8 × 10−5 , which means, theoretically, that the mist particles behave analogously to passive tracers in the nitrogen gas flow. Despite to this estimation, deposition of the mist particles on the pipe wall was significant because approximately 30–60% of the mist particles did not reach the most downstream section. The experimental fact of the mist particle size keeping own similarity infers that the deposition occurs near the wall regardless to the mist particle size on the present order of Stokes number. The mist concentration waveform as a function of time was measured by fluid-sampling nozzles attached at three points: the top (12 o’ clock), the side (3 o’ clock), and the bottom (6 o’ clock) of the pipe wall. The mist concentration was measured at 1.0 s intervals using an aerosol concentration monitor (Dust Track II
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Fig. 8. Oil mist particle size distributions before and after passing through the pipeline. Table 2 Test conditions of the mist concentration measurement. Test number 1 2 3 4 5 6 7 8 9 10 11
Re 300 800 1100 1500 1900 2300 2500 2700 2800 3900 4400
Volumetric flow rate [m3 /s(normal)] −4
3.0 × 10 6.9 × 10−4 9.7 × 10−4 1.3 × 10−3 1.6 × 10−3 2.0 × 10−3 2.2 × 10−3 2.3 × 10−3 2.4 × 10−3 3.5 × 10−3 3.8 × 10−3
Fig. 9. Relationship between the oil mist concentration waveforms and the Reynolds number. The sampling point of the oil mist was the top of the pipe.
Model 8532: TSI Inc., USA) that works on the principle of light scattering. Fig. 9 shows the arrival waveforms of the mist concentration sampled at the top of the pipe. The detailed test conditions are listed in Table 2. The abscissa represents time, t∗ , normalized by the predicted peak arrival time as conveyed by the mean gas velocity, L/U. The mist concentration, φ ∗ , plotted along the ordinate was normalized by the initial concentration, φ 0 . In this normalization, we assume a rectangular wave as the initial waveform and temporarily neglect deposition on the wall. The ignorance does not directly alter the evaluation of the oil mist diffusion process along the mainstream since mist particle-size dependency of the deposition was insignificant. To understand the interpretation of the measured data, we present several idealized examples of the mist concentration waveforms in Fig. 10 (Gill and Sankarasubramanian, 1970). For fully turbulent flows, the following one-dimensional advection-diffusion
Mean velocity U [m/s]
Predicted arrival time L/U [s]
0.057 0.13 0.19 0.25 0.32 0.38 0.41 0.45 0.46 0.66 0.73
2870 1240 880 664 518 429 394 365 354 246 223
Fig. 10. Predicted oil mist concentration waveforms derived from the onedimensional diffusion equation for turbulent flow with fully radial mixing and pure convection of the laminar flow velocity profile with no radial diffusion.
equation gives a good estimate:
∂ φ¯ ∂ φ¯ ∂ 2 φ¯ +U =Γ ∂t ∂x ∂ x2
(4)
where φ¯ is cross-sectional averaged concentration of the mist, U is cross sectional mean carrier-phase velocity, and is apparent one dimensional turbulent diffusion coefficient. The solution of Eq. (4) provides symmetric Gaussian profiles as shown in Fig. 10, dependent on the diffusion coefficient. For laminar flows, Eq. (4) does not give any valid estimate due to less diffusion in the pipe radial direction, and should be replaced with two-dimensional scalar transport equation to which a parabolic velocity profile of the carrier-phase is applied. On ultimate state with zero-molecular diffusion of the mist, laminar pipe flow conveys the initial mist distribution to the downstream as shown by red curve in Fig. 10. The curve starts with a sharp increase and leaves a long tail due to
T. Takeuchi et al. / International Journal of Multiphase Flow 87 (2016) 45–53
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Fig. 11. Schematic of thin and elongated oil mist concentration distribution caused by Poiseuille flow: (∗) Initial rectangular distribution, (∗∗) Elongated distribution after long transportation of t∗ = 0.5. The mist layer at x = L/2 present around y = 12 mm with thickness of 0.16 mm and at x = L/4 present around y = 5.5 mm with thickness of 0.13 mm.
streamwise stretching of the mist. The sharp increase at t∗ = 0.5 is explained by the mist transport at the pipe center, whose velocity is twice the mean velocity in the case without turbulent diffusion. Comparing the measured data in Fig. 9 with these ideal situations, the measured data at Re ≥ 2300 generally agrees with the one-dimensional theory. Discrepancy from the theory is found to be at the concentration peak position which appears earlier than L/U, i.e. t∗ < 1. This occurs because the mist was primarily conveyed along the central region of the pipe, where the mean turbulent flow velocity is faster than the cross-sectional mean velocity. This also implies that mist deposition was active close to the wall because of near-wall turbulence. In contrast, the mist concentration in the laminar flow region (Re ≤ 20 0 0) shows the peak shifted towards the early arrival side. There were cases towards the end of the data in which the mist concentration did not fully diminish, even when t∗ exceeded 2.0, resulting in a significant elongation of the mist in the streamwise direction. These results are unsurprising when compared with the ideal laminar solutions shown in Fig. 10. The difference from the ideal situation is that the sharp front of the concentration wave disappears in laminar flow, inferring the significance of the radial diffusion of the mist. The arrival time of the wave front is also delayed from t∗ = 0.5 to t∗ > 0.6. To discuss on the discrepancy, we illustrate the mist distribution stretched in laminar flow in Fig. 11. When the mist is transported by Poiseuille parabolic base flow over a long distance, the original mist concentration is stretched in the axial direction proportionally to time elapse. It forms an extremely thin parabolic layer between the leading point and the original near-wall region. The concentration interface (or concentration gradient) of such a layer mostly faces the radial direction of the pipe, which thus results in activation of the radial diffusion. For substances with a high molecular diffusion coefficient, such a thin layer will not be formed because the layer immediately diffuses occupying the pipe cross section before reaching downstream. For mist, diffusion only relies on Brownian motion that provides a finite thickness of the layer but which is much thinner than the case of ordinary molecular diffusion process. Consequently, we have experimentally confirmed that the mist diffusion in laminar pipe flow is ultimately governed by Brownian motion (Ekambara and Joshi, 2004; Matas et al., 2004). In the region of 10 0 0 < Re < 20 0 0, over which the HWA measurements indicated that the flow kept laminar state, an irregular mist concentration waveform with multiple local maximum values was observed as shown in Fig. 12. Spatial anisotropy is also obvious in the mist concentration as compared among three sampling points (top, side and bottom of the pipe). This spiky and non-axisymmetric waveform is evidence of poor radial mixing of the mist in laminar flow, and re-attributed to the intensity level of the Brownian motion. The Brownian diffusion coefficient, γ , is generally given by the following Stokes-Einstein equation (Einstein, 1905; Shimada et al., 1993):
γ=
kT , 3 π μd P
(5)
Fig. 12. Oil mist concentration waveforms for Re = 80 0, 110 0, 150 0, 190 0 and 2300.
where k is the Botzmann constant 1.38 × 10−23 J/K. For the present experimental conditions (absolute temperature, T, of 293 K, dP = 1.0 μm and μ = 1.8 × 10−5 Pa s), the Brownian diffusion coefficient was estimated to be approximately 2 × 10−11 m2 /s. The mean square displacement of a single mist particle due to Brownian motion, < r2 >, can be estimated by the following formula (e.g., van Megan and Underwood, 1989):
r 2 =
6 · γ · t .
(6) 104
Since the test period in the longest case did not exceed s in this study, the maximum average displacement of a mist particle is estimated to be 1.1 mm. This value is sufficiently small compared with the pipe diameter of 81 mm, and explains presence of the mist layer thinner than it even at the most downstream section. Such a particular layer is never formed in gas-gas two-phase flow (Evans and Kenney, 1964; Flint and Eisenklam, 1969), and thereby the heterogeneous response of the mist concentration is regarded as one of unique phenomena taking place only in the immiscible mist-laden laminar gas flows. 4. Waveform parameterization To quantify the concentration waveform, we introduce five nondimensional evaluation parameters: the peak time (t∗ peak ), the rise time (t∗ rise ), the fall time (t∗ fall ), the “Irregularity”, and the “Anisotropy”, as well as standard deviation (σ ), skewness (Sk) and mean residence time (t∗ MRT ). The peak time is defined as the time at which the maximum concentration is observed. The rise time
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and the fall time are defined as the times at which φ ∗ > 10−4 and φ ∗ < 10−4 are achieved, respectively. The Irregularity is given by the equation:
(Irregularity ) =
∗ tfall
1 · ∗ − trise
∗ tfall
∗ trise
2 ∗ dt . φ ∗ − φSMA
(7)
particles from near the pipe wall to the pipe center. One possible driving force near the pipe wall is the local velocity fluctuation originating from the pipe roughness, as observed in the HWA data. This remains as an assumption but is supported by the fact that the measured t∗ fall decreases rather for smaller Reynolds numbers within the range of 800 < Re < 2300; further suggesting that the radial mixing due to the near-wall flow disturbance progresses for longer duration at slow flows. Finally, the irregularity and anisotropy in Fig. 13 indicate that these values increase only in the flow transition region at 10 0 0 < Re < 20 0 0. This supports that the oil mist particles behave clearly differently from those in the fully turbulent or fully laminar flow regions. Since the gas phase has no structural turbulence as long as assessed by HWA, we hereafter attempt our discussion to elaborate this phenomenon.
This formula represents the root mean square value based on the difference between the original waveform, φ ∗ , and φ ∗ SMA , the waveform derived by smoothing the concentration waveform with a central simple moving average (SMA) at a cutoff frequency, f∗ , of 10/(t∗ fall -t∗ rise ). The anisotropy is also defined in terms of the root mean square value, and is based on the differences between the concentration waveforms at the three measurement points, as in the equation below:
(Anisotropy ) =
1 · ∗ − t∗ ) 3 · (tfall rise
∗ tfall
∗ trise
2 ∗ − φ∗ d t + φtop side
∗ tfall
∗ trise
The standard deviation and skewness are defined around the weight center of the mist concentration profile: The mean residence time of the mist inside the pipe is computed by the time taken for the weight center of the mist profile to pass through the system, as described in the following equation: ∗
tfall
∗ tMRT
=
t ∗ · φ ∗ dt ∗
tfall ∗ t ∗ φ dt
∗ trise
2 ∗ ∗ − φbottom dt + φside
(9)
∗ tfall
∗ trise
2 ∗ ∗ − φtop dt φbottom
(8)
The irregularity and the anisotropy of the mist particle behavior cannot be explained solely by processes such as turbulent diffusion or Brownian motion with statistical axial symmetry. It is possibly an effect caused by the gravitational force on the mist even though it is scaled to be mostly negligible because of the low mass-loading ratio and the suite small order of Stokes number as estimated pre-
rise
Fig. 13 presents these eight parameters as functions of the Reynolds number. The graphs for σ , Sk, t∗ MRT , t∗ peak , t∗ rise , t∗ fall and irregularity values depict the mean of three locations; top, side, and bottom parts of the pipe, for each Reynolds number. Vertical bar indicates the maximum and minimum values among the three locations. The σ , Sk, t∗ MRT , t∗ peak , t∗ rise and t∗ fall values were chosen to discriminate between laminar and turbulent flows. Among these parameters, t∗ fall is the key for the purging operation because it determines the necessary time for flushing the residual mist. The irregularity and anisotropy shown at the bottom of the figure highlight well the characteristics of the mist transport in the transition region, which indicates how the mist behavior can become heterogeneous, and depart from a simple one-dimensional advectiondiffusion model. As previously explained with Fig. 10, laminar flow should have large values for σ and Sk because of distortion towards the early arrival side. This corresponds to decrease in t∗ peak , t∗ rise and increase in t∗ MRT , t∗ fall . These trends are also confirmed in the measured data in Fig. 13. For transition region between laminar and turbulent flow states, only t∗ MRT takes an intermediate value between the two states. The other parameters, σ , Sk, t∗ peak , t∗ rise and t∗ fall demonstrate that the flow structure in the transition region clearly reflects to the shape of the concentration waveform, whose changes end at Re = 2300. Concerning with the purge operation, we need to pay attention to the measured t∗ fall which has large values at Re < 2300. This proves that the purge operation works the best in the turbulent flow region. On the other hand, pure laminar flow theory tells that the gas phase in the vicinity of the pipe wall has almost no local velocity; therefore mist particles near the pipe wall are not entrained. This idea predicts t∗ fall to be infinity, however, the measured t∗ fall was a finite value even in the laminar region. It infers from the discrepancy that there is a driving force that conveys mist
Fig. 13. Parameters of the oil mist concentration waveforms as a function of the Reynolds number. The vertical bar indicates maximum and minimum value.
T. Takeuchi et al. / International Journal of Multiphase Flow 87 (2016) 45–53
viously. The gravitational force would be expected to play an important role in the laminar flow region at lower flow velocities. Another possible explanation is the intermittent and local generation of velocity fluctuations originating from the pipe joints and wall roughness. The mist concentration distribution extends parabolically with the laminar Poiseuille velocity profile, and draws a ring-shaped cross-sectional distribution. The ring exists in the center of the pipe at the most downstream location, and shifts to the wall proximity at the upstream side. In such instances, local vortices generated close to the inner surfaces of the pipe give certain distortion of the ring-shaped distribution of the mist particularly in the upstream region. This, in turn, can lead to changes in the mist concentration distribution over the pipe as the influence propagates downstream. Furthermore, these local uncontrolled disturbances have non-axisymmetric and three-dimensional structures ordinarily; this could potentially be the cause of the observed anisotropy. While the local vortices affects the mist behavior in such a way, they do not develop to organized turbulence at low Re numbers. This explains why the mist concentration is sensitively affected by the wall roughness at small Re numbers before nominal flow transition. For 20 0 0 < Re < 2400, the anisotropy of the mist distribution still remains. This is explained by appearance of turbulent puffs that have insufficient statistical axisymmetry as visualized by Hof et al., (2004) and Ohkubo et al., (2016). In summary, transition in the mist concentration behavior occurs at Reynolds numbers lower than those associated with flow transition observed in velocity fluctuations. This is because the mist distribution becomes thinner during prolonged transport along the laminar velocity profile, and becomes sensitive to the wall roughness. So, measurements of the mist concentration waveform are sensitive to flow disturbances originating from the wall structure, even if these disturbances do not develop into persistent turbulence. 5. Conclusion Experimental analyses of the oil mist diffusion process were carried out at 300 ≤ Re ≤ 4400, beyond the flow transition region between laminar and fully turbulent states. Using a model of a long industrial pipeline subject to wall roughness over the 20 0 0 diameter distance, we monitored the manner in which the mist and the carrier gas developed in the streamwise direction when the Stokes number of the mist was sufficiently low, O(10−5 ). We first measured the velocity fluctuations of mist-free nitrogen gas flow by means of hot-wire anemometers, to verify the existence of streamwise flow transitions from perfect laminar to fully developed turbulent flow. The data agreed with established understanding of pipe flow transition, such as the passage of local turbulence at 20 0 0 ≤ Re ≤ 2400 in the transition region. We also detected discrete peaks in the power spectra in the range of 10 0 0 ≤ Re ≤ 20 0 0, which were attributed to the wall roughness (including pipe joints). Secondly, we tracked the mist diffusion process in the stream-wise direction. Aerosol concentration monitors were set at the downstream outlet to detect the concentration waveforms. From these waveforms, we confirmed that, at Re < 10 0 0, the mist had a significantly diffused profile along the pipe axial direction because of parabolic transport by Poiseuille flow, which was insensitive to wall roughness. For fully turbulent flows at Re > 2400, the mist was transported sharply with less axial diffusion while rich radial mixing dominates in the cross-sectional plane. We observed the early effects of flow disturbance between 10 0 0 < Re < 20 0 0 in the mist waveform, highlighted by a front-shift in concentration, the emergence of multiple peaks, and also anisotropy across the
53
cross sectional plane. These phenomena were attributed to velocity perturbations in the proximity of the wall, which did not grow to form organized turbulence but can distort the mist layer that remained close to the wall behind the parabolic transport. This effect was observable only in a long pipeline with immiscible dispersion with the carrier gas phase. Our original objective was to optimize the purging operation; the following findings may be of use to operators and engineers: i) laminar flow causes an early arrival time of the mist wavefront, compared with the estimation via L/U, but it is always slower than that predicted by simple advection theory because of Brownian diffusion. ii) Multiple peaks of the mist concentration occur in the transition region even in straight pipe geometry. The operator needs to estimate Reynolds number to recognize the possibility of split waves from a simple Gaussian profile. iii) For industrial pipelines with wall roughness, even laminar flow can induce anisotropy in mist concentration far downstream. References Avila, K., Moxey, D., de Lozar, A., Avila, M., Barkley, D., Hof, B., 2011. The onset of turbulence in pipe flow. Science 333, 192–196. Darbyshire, A., Mullin, T., 1995. Transition to turbulence in constant-mass-flux pipe flow. J. Fluid Mech. 289, 83–114. Durst, F., Unsal, B., 2006. Forced laminar-to-turbulent transition of pipe flows. J. Fluid Mech. 560, 449–464. Einstein, A., 1905. Über die von der molekularkinetischen Theorie der Wärme geforderte Bewegung von in ruhenden Flüssigkeiten suspendierten Teilchen. Annalen der Physik. 322 (8), 549–560. Ekambara, K., Joshi, J.B., 2003. Axial mixing in pipe flows turbulent and transition regions. Chem. Eng. Sci. 58, 2715–2724. Ekambara, K., Joshi, J.B., 2004. Axial mixing in laminar pipe flows. Chem. Eng. Sci. 59, 3929–3944. Evans, E.V., Kenney, C.N., 1964. Gaseous dispersion in laminar flow through a circular tube. Proc. Roy. Soc. London. A. 284, 540–550. Flint, L.F., Eisenklam, P., 1969. Longitudinal gas dispersion in transitional and turbulent flow through a straight tube. Can. J. Chem. Eng. 47 (2), 101–106. Gill, W.N., Sankarasubramanian, R., 1970. Exact analysis of unsteady convective diffusion. Proc. Roy. Soc. Lond. A. 316, 341–350. Hof, B., Juel, A., Mullin, T., 2003. Scaling of the turbulence transition threshold in a pipe. Phys. Rev. Lett. 91, 244502. Hof, B., van Doorne, C.W.H., Westerweel, J., Nieuwstadt, F.T.M., Faiss, H., Eckhardt, B., Wedin, H., Kerswell, R.R., Waleffe, F., 2004. Experimental observation of nonlinear traveling waves in turbulent pipe flow. Science 305, 1594–1598. Hof, B., Westerweel, J., Schneider, T.M., Eckhardt, B., 2006. Finite lifetime of turbulence in shear flows. Nature 443, 59–62. Matas, J.P., Morris, J.F., Guazelli, E., 2004. Inertial migration of rigid spherical particles in Poiseuille flow. J. Fluid Mech. 515, 171–195. Moody, L.F., 1944. Friction factors for pipe flow. Trans. ASME. 66 (8), 671–684. Nishi, M., Unsal, B., Durst, F., Biswas, G., 2008. Laminar-to-turbulent transition of pipe flow through slugs and puffs. J. Fluid Mech. 614, 425–446. Ohkubo, J., Tasaka, Y., Park, H.J., Murai, Y., 2016. Extraction of 3D vortex structures from a turbulent puff in a pipe using two-color illumination and flakes. J. Visualization. doi:10.1007/s12650- 016- 0344- z. Peixinho, J., Mullin, T., 2006. Decay of turbulent in pipe flow. Phys. Rev. Lett. 96, 094501. Peixinho, J., Mullin, T., 2007. Finite-amplitude thresholds for transition in pipe flow. J. Fluid Mech. 582, 169–178. Reynolds, O., 1883. An experimental investigation of the circumstances which determine whether the motion of water shall be direct of sinuous, and the law of resistance in parallel channels. Philos. Trans. R. Soc. London, Ser. A 174, 935–982. Shimada, M., Okuyama, K., Asai, M., 1993. Deposition of submicron aerosol particles in turbulent and transitional flow. AIChE J. 39-1, 17–26. Shimizu, M., Kida, S., 2009. A driving mechanism of a turbulent puff in pipe flow. Fluid Dyn. Res. 41, 045501. Takeuchi, T., Murai, Y., 2010. Flowmetering of natural gas pipeline by tracer gas pulse injection. Meas. Sci. Technol. 21, 0154028. Tasaka, Y., Schneider, T.M., Mullin, T., 2010. Folded edge of turbulence in a pipe. Phys. Rev. Lett. 105, 174502. van Megan, W., Underwood, S.M., 1989. Tracer diffusion in colloidal dispersion. III. Mean squared displacement and self-diffusion coefficients. J. chem. Phys. 91 (1), 552–559. Wygnansky, I., Sokolov, M., Friedman, D., 1975. On transition in a pipe. Part 2. The equilibrium puff. J. Fluid Mech. 69-2, 283–304.