Vivanco Gutowski Sells 497k Team Project

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  • PENN STATE UNIVERSITY

    NucE 497K: Thermal Hydraulics of Two-Phase

    Flow Team Project

    Dan Sells

    Ricky Vivanco Tom Gutowski

  • 497K Team Project 4/1/2014

    Problem Statement An engineer performs separate-effect experiments to study the geometric effects of a 45-degree elbow in air-water bubbly two-phase flow through a horizontal pipe. A simplified schematic diagram of the test facility is shown in Figure 1. A round pipe with inner diameter of 50.3 mm is employed as a test section, along which a 45-degree elbow with (L/D)elbow=23.3 is installed at L/D = 156.5 from the two-phase mixture inlet. In total, 15 different flow conditions, all in bubbly flow regime, are examined under room temperature. The local static pressures are measured at four axial locations at L/D = 0, 145, 169 and 224 from the two-phase mixture inlet. In addition, a local double sensor conductivity probe is used to measure various local two-phase flow parameters by traversing the probe along the vertical direction of the pipe cross-section radius (or rv in Fig. 1). The data acquired in the experiments are summarized in two ways; one in an area-averaged form in the Avg_Data.xls file, and another in local form in Local_Data.xls file. Your job is to analyze the data and discuss observed geometric effects stemming from the 45-degree elbow on two-phase flow transport.

    Figure 1: Schematic of Flow Test (top view)

  • 497K Team Project 4/1/2014

    1) (a) Plot local gage pressure (ploc) along the axial direction of the flow. Discuss the significance of the results.

    Figure 2: Local Gage Pressure along Axial Direction

    From the graph it is apparent that in all runs the elbow bend in the pipe contributes to more rapid decrease in pressure than flow along the straight sections of pipe. Total pressure drop is comprised of three factors which are friction, acceleration, and gravity. Friction is increased during the bend due to increased rotation in the flow which is proportional to the Reynolds Number and the frictional loss, as well as the minor loss due to the flow restriction at the elbow. The bend sees a significant effect from acceleration pressure drop due to changing direction. Because flow is in the horizontal direction the gravitational pressure drop is uniform along the pipe. As flow rates were increased, the bend has a greater effect on pressure drop in the pipe.

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  • 497K Team Project 4/1/2014

    (b) Plot evolution of area-averaged void fraction , interfacial area concentration , and Sauter-mean diameter along the axial direction. Discuss the significance of the results.

    Figure 3: Area-Averaged Void Fraction along Axial Direction

    At all points during the experiment, the flow remains in the bubbly regime because the void fraction remains below 0.30. With increasing gas flow rate, the void fraction rises due to increased gas volume in the flow. In higher gas flow rate conditions, the void fraction is more sensitive to changes in the liquid flow rate as shown in Figure 3. As gas flow rate increases the effect of the pipe bend on void fraction has a greater effect. The liquid having more mass and velocity carries more momentum going into the bend. There is a significant increase in bubble interactions due to the bend.

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  • 497K Team Project 4/1/2014

    Figure 4: Area-Averaged Interfacial Area Concentration along Axial Direction

    Figure 4 shows a very interesting correlation between the change in interfacial area concentration and the varying flow rates for the gas and liquid. It appears that in most runs, the bubbles in the flow coalesce around the bend. The runs with the higher gas flow rates (Runs 13-15) displayed a much larger change in interfacial area concentration than the lower gas flow rate runs (Runs 1-3). An interesting phenomena occurs in Runs 4, 5, 6, and 9, the interfacial area concentration decreases over the length of the bend. This may be due to a particular condition where the gas is transitioning from laminar to turbulent flow.

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    Area-Averaged Interfacial Area Concentration along Axial Direction

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  • 497K Team Project 4/1/2014

    Figure 5: Area-Averaged Sauter Mean Diameter along Axial Direction

    The trend in the Sauter mean diameter for each run can be related to the interfacial area concentration trends. It is clear that Sauter mean diameter decreases and increases as the interfacial area concentration increases and decreases. This can be explained by the equation for Sauter mean diameter:

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  • 497K Team Project 4/1/2014

    (c) Plot versus for all test conditions in one graph. Discuss the significance of the results.

    Figure 6: vs.

    From Figure 6, two distinct groupings of flow conditions dominate the various trends between interfacial area concentration and void fraction. In the first group (Runs 1-6), the changes over the bend are minimal and erratic. The second group (Runs 7-15), the trend shows an increase in both interfacial area concentration and void fraction over the bend. However, Run 9 seems to be an aberration because it shows a conversely decreasing along the elbow. Increasing the gas flow rate increases the effect the bend has on both interfacial area concentration and void fraction. However, as the gas flow rate increases the bend has a greater effect on interfacial area concentration than on void fraction. Also, as the velocity of the gas approaches the velocity of the liquid, the changes in interfacial area concentration and void fraction are more uniform.

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  • 497K Team Project 4/1/2014

    (d) Use the data and determine the distribution parameter (C0) and the drift velocity () of the drift flux model via graphical method. Discuss the significance of the results.

    Figure 7: Drift Flux Model

    Figure 7 shows a vaguely linear trend in the relationship between and . The results show a distribution parameter (C0) of 1.4326 which would suggest a parabolic distribution along the radial direction of the pipe. The negative value of -1.9602 for is interesting because this can only occur in horizontal flow. The negative suggests that the gas is moving slower than the liquid resulting in a negative relative velocity between the two phases. The slower moving gas is caused by the drag incurred on the bubbles while the buoyancy force is pushing the bubbles to the upper half of the pipe causing a pile-up.

    y = 1.4326x - 1.9602 R = 0.7336

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  • 497K Team Project 4/1/2014

    (e)

    Part I: Use the pressure data between the inlet and exit and determine the parameter C that fits the data best.

    Figure 8: Pressure Drop Across the Entire Section

    Part II: Use the pressure data across the elbow, and compare the results with the values

    predicted by the Lockhard-Martinelli correlation with the C value determined in Part I.

    Figure 9: Pressure Drop Across the Elbow

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  • 497K Team Project 4/1/2014

    Part III: Discuss the significance of the results observed in both Part I and Part II.

    Across the whole section, the C value is ~40-45 which is higher than the conventional

    value of C=20 for turbulent flow. This is due to the Lockhart Martinelli correlation not taking into account the minor loss due to the elbow.

    There is a significant difference between the Martinelli parameters of the pressure drop across the whole section and across the bend. This is primarily due to the fact that the pressure drop over the elbow is dominated by the minor loss due to the flow restriction, whereas the pressure drop over the entire test section is dominated by the frictional loss in the liquid phase. This resulted in a Martinelli parameter over the elbow that is approximately 4x higher than the entire test section.

    2) (a) Fill in the column for the bubble Sauter-mean diameter (in millimeter unit). Discuss the results.

    Table 1 Part 2 Data

    r/RV ai [1/m]

    Dsm [mm]

    ai [1/m]

    Dsm [mm]

    ai [1/m]

    Dsm [mm]

    0.9707 0.404 705.04 3.44 0.024 50.27 2.90 0.266 378.40 4.22 0.9495 0.434 672.38 3.88 0.028 56.27 2.96 0.317 387.00 4.91 0.9243 0.461 651.35 4.24 0.032 61.28 3.10 0.339 347.41 5.86 0.8990 0.489 657.28 4.46 0.035 65.55 3.23 0.372 332.44 6.72 0.8485 0.504 637.18 4.75 0.040 73.89 3.22 0.398 291.66 8.20 0.7980 0.454 585.18 4.66 0.046 81.61 3.41 0.383 263.72 8.71 0.6970 0.369 497.52 4.45 0.059 98.51 3.59 0.311 205.51 9.07 0.5960 0.232 351.64 3.96 0.066 104.56 3.79 0.213 147.30 8.69 0.4950 0.115 192.23 3.60 0.064 101.59 3.80 0.130 93.98 8.28 0.3940 0.044 76.88 3.44 0.055 87.04 3.80 0.072 53.62 8.06 0.2930 0.016 30.04 3.24 0.038 66.57 3.41 0.039 29.96 7.81 0.1920 0.005 8.48 3.18 0.022 42.55 3.10 0.015 14.12 6.25 0.0911 0.000 0.00 0.013 25.82 3.07 0.006 5.82 6.39 -0.0099 0.000 0.00 0.012 21.21 3.48 0.000 0.00 -0.1109 0.000 0.00 0.022 29.09 4.48 0.000 0.00 -0.2119 0.000 0.00 0.061 66.15 5.55 0.000 0.00 -0.3129 0.000 0.00 0.154 141.42 6.54 0.000 0.00 -0.4139 0.000 0.00 0.271 197.47 8.24 0.000 0.00 -0.5149 0.000 0.00 0.335 210.34 9.54 0.000 0.00 -0.6159 0.000 0.00 0.298 182.43 9.79 0.000 0.00 -0.7169 0.000 0.00 0.186 139.53 7.99 0.000 0.00 -0.8179 0.000 0.00 0.059 59.64 5.98 0.000 0.00 -0.8684 0.000 0.00 0.022 24.98 5.16 0.000 0.00 -0.9189 0.000 0.00 0.000 0.00 0.000 0.00

  • 497K Team Project 4/1/2014

    The bubbly flow consists of small bubbles before the bend at the top of the pipe. The bend varies the location of the bubbles and some of them are significantly larger. This means coalescence took place between smaller bubbles due to turbulent collisions. Downstream it is clear that the bubbles do not break up and so the large bubbles created by the bend continue down the pipe. This is shown in Table 1. (b) Plot profiles of local time-averaged void fraction (), interfacial area concentration (ai) and bubble velocity (ug) with respect to the dimensionless vertical radius (r/Rv) for three different measurement ports.

    Figure 10: Local Time-Averaged Void Fraction ()

    Figure 11: Interfacial Area Concentration (ai)

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  • 497K Team Project 4/1/2014

    Figure 12: Bubble Velocity

    (c) Discuss the significance of the results observed in Part (b) for each parameter. During the long straights the void fraction is higher at the top of the pipe because gravity keeps the gas at the top of the pipe. However, the bend causes a turbulence that spreads the bubbles out. The void fraction actually peaks in the lower half on the pipe for a brief time after the bend before gravity takes over again and the bubbles rise back to the top of the pipe. Interfacial area concentration undergoes the most drastic change in this experiment. The bend makes the bubbles in the flow interact and coalesce. Because there were many smaller bubbles that combined into fewer big bubbles the interfacial area concentration is dramatically reduced. Bubble velocity undergoes some interesting changes. Mostly, the bubble velocity has an even profile across the spectrum and bubble velocity drops off on the edge of its spectrum due to the no slip condition. The bubbles only undergo a slight increase in velocity when they first go around the bend but speed up significantly going downstream.

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