Proceedings of the ASME 2014 4th Joint US-European Fluids Engineering Division Summer Meeting FEDSM2014 August 3-7, 2014, Chicago, Illinois, USA
FEDSM2014-21172
NUMERICAL PREDICTION OF SOLID PARTICLE EROSION FOR ELBOWS MOUNTED IN SERIES Frederic N. Felten* Halliburton Carrollton, Texas, USA ABSTRACT Erosive wear due to solid-particle impact is a complex phenomenon where different parameters are responsible for causing material removal from the metal surface. Some of the most critical parameters regarding the solid particles are the size, density, roundness, and volume concentration. The properties of the carrying fluid (density, dynamic viscosity, bulk modulus …), the geometry of the flow path (straight or deviated), and the surface material properties are also major contributors to the overall severity of the solid-particle erosion process. The intent of this paper is to focus on the impact of the flow path geometry on surface erosion for a specific carrier fluid, flow rate, sand type and sand-volume concentration. A numerical approach using the commercial CFD code FLUENT is applied to investigate the solid particle erosion in two 90 o pipe elbows mounted in series. The distance between the two elbows is varied, as is the angle between them. A total of 16 cases are analyzed numerically. The relationships between the parameters pertinent to the two elbows and the erosion pattern, erosion intensity, and location of maximum erosion are presented. Prior to the analyses for the two elbows mounted in series, an in-depth validation effort for a single elbow geometry is undertaken to determine the appropriate mesh requirement, turbulence model, and to calibrate the inputs to the erosion model. INTRODUCTION Solid particle erosion in pipes, plugged tees, valves and elbows is recognized as a significant problem in several fluidhandling industries, especially for oil and gas where multiphase flow with the presence of solids conveyed by the fluid is a common occurrence. Failure of the piping system can be expensive and dangerous, thus it is critical to know, or at least have an idea, where the failure could occur and what is the associated estimated life before an eventual puncture. Solid particle erosion is a complex phenomenon with multiple factors contributing to its severity. Among these factors, fluid and solid
mass rates, properties of the eroded material like hardness, brittleness and ductility, properties of the fluid like density and viscosity, characteristics of the solid particles like size and shape, and geometry of the flow path are recognized as major contributors. Obviously this is a non-exhaustive list and the reader is referred to Kleis et al. [1] for a more complete inventory. The purpose of this paper is to focus on the impact of the flow path geometry on surface erosion for a specific material, carrier fluid, flow rate, sand type and particle-volume concentration. Due to its simplicity, yet complex threedimensional flow patterns, the single elbow case emerges throughout the technical literature as the poster-child geometry to assess and develop models for solid particle erosion for internal flows. Shirazi et al. [2] used the single elbow geometry to develop mechanistic models for erosion prediction. In a separate study, Wang et al. [3] used a generalized methodology, involving flow simulation, particle tracking, and erosion modeling to investigate the effects of elbow radius of curvature on erosion rate. Selmer-Olsen [4] and later Mazumder et al. [5], conducted experimental studies to characterized the intensity, and location of erosion in single elbow specimens for both single phase and multiphase flows. While the single elbow case has received a lot of attention, there have been very few studies looking at elbows mounted in series, and the potential impact the flow path has to enhance or reduce solid particle erosion for a succession of elbows. Zhang et al. [6] numerically investigated the slurry flow in a U-shaped bend for a large radius of curvature. They showed that the location of maximum erosion for the first elbow is nearly the same as what is obtained in the case of a single elbow. However, no insight was offered on the harshness of the erosion for the second elbow. Deng et al. [7], using high concentrations of Olivine sand and air as the carrier fluid, conducted experiments with four bends, revealing that the puncture point location is most influenced by the bend orientations. The shortest distance between two successive elbows in the flow loop used by Deng et al. [7] was in excess of 300 times the pipe diameter, thus neglecting the
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*Corresponding author;
[email protected]
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influence of any potential flow interaction between two consecutive elbows. With this in mind, the present studies focus on numerically predicting the impact of the distance, and the orientation between two 90deg elbows mounted in series, on the potential reduction or increase of solid particle erosive wear. NOMENCLATURE D Pipe diameter R Pipe radius Rc Elbow radius of curvature Particle diameter d Averaged Particle diameter d n Roslin-Rammler model exponent m Erosion model velocity exponent V Velocity Vp Particle velocity Re Pipe Reynolds Number De Pipe Dean Number St Particle Stokes Number texp Time of exposure Erate Erosion rate θ Angle F(θ) Impact angle function L/D Normalized distance S/D Normalized curvilinear distance K Dimensionless erosion factor Tloss Thickness loss ρ Density µ Dynamic viscosity ν Kinematic viscosity k+ Dimensionless turbulent kinetic energy based on inner variables u+ Dimensionless axial velocity based on inner variables y+ Dimensionless wall distance based on inner variables
[m] [m] [m] [µm] [µm] [-] [-] [m/s] [m/s] [-] [-] [-] [s] [kg/(m2.s)] [Deg] [-] [-] [-] [-] [µm] [kg/m3] [Pa.s] [m2/s] [-]
the aluminum erosion specimen placed in the test cell. A summary of the experimental parameters is given in Table 1. The corresponding sand concentration is estimated to be 1.294% by mass or 6.059E-04% by volume. In addition, the sand particle information used for the data gathering can be modeled using the Roslin-Rammler [8] model. The Cumulative Distribution Function (CDF) for the particle size distribution is shown in Figure 2. The expression for the CDF as a function of particle diameter is given by: n CDF (d ) 1 ed d
(1)
With d 182 m and n 5
Figure 1: Schematic of Mazumder’s experimental set-up.
[-] [-]
Subscripts fluid Refers to the fluid (Air) sand Refers to the particles (Sand) material Refers to the elbow material (Aluminum) Bulk Refers to the pipe averaged velocity CFD VALIDATION FOR A SINGLE ELBOW Prior to the numerical investigation of the erosion wear for two elbows in series, it is of paramount importance to perform a preliminary validation effort in order to determine the appropriate mesh requirement, turbulence model, and to calibrate the inputs to the erosion model. The experimental work done by Mazumder et al. [5] has been chosen for this specific purpose. Erosion measurements for a 90o, 1in diameter pipe elbow are gathered for the flow of air and sand particles at ambient pressure and temperature. Figure 1 shows a schematic of the experimental set-up used by Mazumder et al. [5], with
Table 1: Experimental summary. The non-dimensional parameters associated with this study are given below: Pipe Reynolds number: Re fluid V fluid D 59,340 fluid Pipe Dean number: De Re R 34,260 Rc
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Particle Stokes number based on the averaged diameter:
St
1 sand V fluid 18 fluid fluid
d D
2 sand
3.662
The Reynolds Averaged Navier-Stokes (RANS) based K-w SST [10] turbulence model is used, in conjunction with the third-order upwind QUICK [11] scheme, to discretize the momentum and the turbulence equations. The double precision algorithm was selected and the convergence criterion for all residuals was set to 1e-08. Gravity was not included in the numerical simulations. The mesh was generated using a sweep method. Figure 4 shows the mesh on the inlet face. The mesh on the inlet face is then propagated along the length of the pipe in a uniform manner. Figure 5, shows the mesh distribution near the elbow in the symmetry plane. Inflation layers for the near-wall region were used in order to resolve the pipe boundary layer. A first cell height of y+ ≈ 0.92 is obtained for the mesh region upstream of the elbow, where the flow is turbulent and fully developed. The total mesh count is about 3.42 million elements.
Figure 2: Particle size distribution and model. CFD SET-UP FOR SINGLE ELBOW CASE The commercial CFD code FLUENT v14.5 [9] was used to perform the present numerical investigations. A steady, threedimensional model was created using an available symmetry plane in order to reduce the model size and subsequent computational requirement. Figure 3 shows the CFD domain used for the single elbow. A velocity of 34.14ft/s is imposed at the inlet, while a relative outlet pressure of 0psi is imposed at the outlet.
Figure 4: Single elbow. Mesh on inlet face (left) and mesh on symmetry plane near elbow (right). EROSION MODEL In order to model solid particle erosion, and in-light of the low sand concentration, FLUENT’s Discrete Phase Model (DPM) is used. The two-way turbulence coupling is ignored and the Discrete Random Walk method is used. An approximate total of 125,000 particles are tracked. Associated with FLUENT’s DPM, one must stipulate the inputs to the erosion rate model Erate, defined by:
Erate K V pm F
(2)
Where Vp is the particle impact velocity, m the value of the exponent, K is a non-dimensional erosion factor and F() is a dimensionless function of the impact angle and is defined as:
A 2 B F 2 2 X cos sin(W ) Y sin Z Figure 3: Single elbow. CFD domain.
The erosion model and its associated impact angle function are based on Chen et al. [12]. The empirical inputs used in the
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present study are listed below in Table 2 and are based on the work done by Wong et al. [13]. The impact angle function, obtained with the inputs from Table 2, is shown in Figure 6. The thickness loss, Tloss, associated with the predicted dimensional erosion rate Erate previously introduced in equation 2, is defined as:
texp Tloss Erate material
S/D=1.1205 (~64.2deg) and reattachment at S/D=1.9757 or 0.405 diameter downstream of the elbow.
(3)
With the following values for time of exposure texp = 60min and the density of aluminum ρmaterial = 2700 kg/m3. Constants Value A -6.500 B 5.061 K 3.58E-09 m 2.3 W -3.400 X 0.371 Y -0.836 Z 1.445 φ 24o Table 2: Inputs to the erosion model.
Figure 7: Single elbow. Representative streamlines.
Figure 6: Erosion model. Impact angle function. RESULTS FOR SINGLE ELBOW CASE Figure 7 shows representative streamlines for the flow in the elbow region. As expected, the flow is undisturbed upstream of the elbow, while it is separated, on the inner wall, downstream of the elbow. In addition, we can clearly see the mushroom shape for the velocity contours and the presence of two counter-rotating Dean vortices downstream of the elbow. The contours of velocity magnitude are presented in Figure 8 for the symmetry plane. Within the first 20 degrees past the entrance of the elbow, the flow adjusts to the transverse pressure gradient imposed by the curvature and the location of the maximum velocity is shifted toward the inner wall. About half-way through the elbow, the velocity contours show a region of high velocity gradients near the inner wall. As the flow exits the elbow and continues downstream in a straight pipe, it is no longer subjected to the transverse pressure gradient of the elbow. This results in a shift of the velocity maximum toward the outside wall. The friction coefficient along the symmetry plane for the inner wall is shown in Figure 9, predicting flow separation at
Figure 8: Single elbow. Contours of velocity magnitude.
Figure 9: Single elbow. Friction coefficient along inner wall at symmetry plane.
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The contours of Turbulence Kinetic Energy (TKE), presented in Figure 10, are consistent with those of the velocity magnitude shown in Figure 8. As expected regions of steep velocity gradients are associated with high values of velocity fluctuation thus high values of TKE.
Figure 12: Single elbow. Turbulent kinetic energy profile along line 1, in dimensionless wall units.
Figure 13: Single elbow. Normalized axial velocity profile along line 2.
Figure 10: Single elbow. TKE contours in symmetry plane. Figures 11 and 12 show the velocity and TKE profiles, respectively, plotted in wall units and compared to available experimental data [14, 15] at two diameters upstream of the elbow, along line 1. Excellent agreement is obtained for the velocity profile. The theoretical viscous sub-layer and log-layer regions are clearly captured. The TKE profile also shows also excellent agreement, especially for the near wall region. Figures 13 and 14 show the normalized velocity profiles at locations 0.3 and 1 diameter downstream of the elbow, respectively. The CFD predictions agree relatively well with the experimental data, capturing the region of high velocity shear and high TKE away from the wall, due to the flow separation in the elbow. In an effort to perform a thorough validation effort, predictions for the pressure field are also compared to available experimental data. Figure 15 shows the contours of static pressure on the surface of the elbow. As expected, from the velocity contours, the pressure decreases near the inner wall as the velocity increases, while it increases on the outer-wall, as the flow slows down locally.
Figure 14: Single elbow. Normalized axial velocity profile along line 3.
Figure 15: Single elbow. Pressure contours on elbow surface.
Figure 11: Single elbow. Profile of axial velocity along line 1, in dimensionless wall units.
Experimental data from Enayet et al. [14] and Sudo et al. [15] are included on Figure 16, where the pressure coefficient along the inside, middle and outside lines of the elbow surface, is plotted against the stream-wise location, where S/D=0.0 and S/D=3π/4 are the inlet and exit of the elbow, respectively. In order to avoid confusion regarding the values for the streamwise location, it is useful to mention that for Figure 16, S/D is
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based on the mid-line radius of curvature, Rc=1.5in, while it is based on R=1in for Figure 9, thus explaining the difference between S/D=3π/4 and S/D=π/2, for the elbow outlet. Overall, the present study agrees relatively well with the experimental data, except for the inside region of the elbow, near S/D=0.25, where it over-predicts the minimum pressure coefficient.
Figure 16: Single elbow. Pressure coefficient along inside, middle and outside lines on the elbow and pipes surfaces. The contours of erosion rate on the elbow surface are shown in Figure 17. The erosion pattern is similar to CFD predictions reported by others [12, 16]. The predicted particle tracks and particle concentrations for selected planes are shown in Figure 18. The particle concentration is uniform at the elbow inlet, and as expected, with a particle Stokes number greater than 1, the particles do not follow the streamlines. Particles inertia and centrifugal forces present in the elbow cause a segregation between the gas and the sand particles. The solid particles break-off from the fluid streamline, impinge on the outer wall surface of the elbow and form a relatively dense region referred to as a rope [17]. The rope region exhibits much higher particle concentration compared to the rest of the pipe cross-section. The location of the maximum erosion rate shown on Figure 17 occurs at the center of the elbow section which corresponds to the location of the highest particle concentration. The particle concentration at the exit of the elbow shows that there are no particles present near the inner wall. At 2 and 4 diameters downstream of the elbow, the particle concentration appears again relatively uniform, but one can notice higher particle concentration near the center of the pipe, suggesting that after impacting the elbow, the upstream uniformly distributed particles have tendency to agglomerate around the pipe centerline. Figure 19 shows the predicted thickness loss in microns for one hour of exposure time, as a function of the elbow angle, along the intersection of the elbow outer-wall and the symmetry plane. Excellent agreement with the experimental data of Mazumder et al. [5] is obtained. A maximum predicted thickness loss of 47.3 microns is obtained at the 49 o angle location. Even though the experimental data show a maximum thickness loss for the 55o position along the elbow, there are no available experimental data between 45o and 55o, thus potentially skipping the actual region of highest erosion.
Figure 17: Single elbow. Contours of erosion rate.
Figure 18: Single elbow. Particle tracks and particle concentration at selected plane locations.
Figure 19: Single elbow. Thickness loss along intersection of elbow outer surface and symmetry plane.
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A summary of the present CFD based erosion predictions for the single elbow case is presented in Table 3, below.
Case # L/D Angle Case # L/D Angle 1 0 0o 9 0 180o o 2 1 0 10 1 180o o 3 2 0 11 2 180o o 4 4 0 12 4 180o o 5 8 0 13 8 180o o 6 16 0 14 16 180o o 7 24 0 15 24 180o o 8 32 0 16 32 180o Table 4: Elbows in series. Cases investigated.
Maximum Erosion rate [kg m-2 s-1] 3.583e-05 Maximum thickness loss for 60min [micron] 47.3 Location of maximum erosion in elbow 49o -2 -1 Averaged erosion rate (elbow surface) [kg m s ] 2.608e-06 Table 3: Single elbow. Summary of CFD based erosion predictions TWO ELBOWS MOUNTED IN SERIES With the validation effort completed for the single elbow case and with a resulting acceptable CFD methodology now available, it is of interest to numerically investigate the solid particle erosion for two elbows mounted in series. The purpose of this effort is to assess if solid particle erosion will either be enhanced or reduced for the round elbow geometry, depending on specific geometrical parameters. The distance between the two elbows is varied as well as the angle between them. Figures 20 and 21 show the two geometries investigated, while Table 4 summarizes the list of the sixteen cases for which CFD was performed. The mesh density, CFD set-up and erosion model are identical to what was used for the validation effort previously discussed.
Figure 20: Elbows in series. Angle = 0o
Figure 22 shows the maximum and surface averaged erosion rate as a function of the normalized distance between the two elbows (L/D). The results are normalized by the values obtained for the single elbow case (See Table 3.) For the first elbow, the maximum and surface averaged erosion rates appear independent of both L/D and the angle between the elbows. Regarding the second elbow, the maximum and surface averaged erosion rates are lower than for the first elbow. However, solid particle erosion for the second elbow can either be enhanced or reduced depending on the combination of L/D and the angle between the two elbows. With respect to the integrity of the piping system and potential piercing of the elbow, knowledge of the maximum erosion rate is most critical. Cases 3 and 11 show the greatest increase for the maximum erosion rate for the second elbow. This suggests that regardless of the angle between the two elbows, L/D=2 must be avoided in order to retard a potential puncture of the second elbow. With respect to erosion reduction, cases 5 and 12 show the lowest maximum erosion rate for the second elbow, for 0o angle and 180o angle, respectively. It is clear that for L/D
