by Dave Dewees, Zumao Chen and L. Magnus Gustafsson
This 2-part blog deals with CFD modeling of a mixing tee that is often found in industry. Traditional simulation is validated against experiment, as well as a new commercially available method that offers the possibility of substantial solution time reduction. In fact, the new method is shown to give accurate results in a much shorter computer time than the traditional analysis, allowing much more rapid turnaround of difficult problems such as the turbulent mixing behavior of industrial mixing tees.
When there is a large temperature difference between two fluid streams, large temperature fluctuations can occur, which can lead to thermal fatigue of the piping system, even at “steady-state” bulk flow conditions. Advanced CFD modeling is capable of predicting these fluid temperature fluctuations at the mix point, as well as characterizing the corresponding temperature variations in the pipe wall itself. Specifically, large eddy simulation (LES) is required to capture the time-varying turbulent behavior at the mix point, which is significantly more time and resource intensive than traditional two-parameter (e.g. k-e and k-w) Reynolds Averaged Navier-Stokes (RANS) simulation which is the workhorse of most industrial CFD simulation. In the first part of this twin blog, both the traditional LES approach and a new hybrid RANS-LES method are used to predict the mixing of the two fluid streams and the results are compared with test data reported in the literature for validation purposes. The new hybrid model is termed stress-blended eddy simulation (SBES) and has recently been included in the commercial software ANSYS/Fluent. SBES retains most of the fidelity of the traditional LES approach in a fraction of the time for typical problems. The SBES approach is then used in Part 2 as part of an actual industrial application to predict temperature fluctuations in a mixing tee. The simulation is used to determine the length of thermal sleeve required to protect the pipe from thermal fatigue.
The test data utilized here is from an experiment specifically designed to investigate thermal mixing in a T-junction . The data has been used to validate different turbulence scale-resolving simulation models, such as LES, scale-adaptive simulation (SAS) and delayed detached eddy simulation (DDES) [2, 3]. In this blog, the data is used to (re-)validate the traditional LES approach, as well as the new SBES approach. The model consists of a horizontal pipe with an inner diameter of 0.14 m (D) for a cold-water (19°C) flow rate of 9 liters/s and a vertical pipe with an inner diameter of 0.10 m (D0) for a hot water (36°C) flow rate of 6 liters/s. The inlets are located at 3.1D0 and 3.0D upstream of the junction for the hot and cold water, respectively. The inlet velocity distributions are based on measurements. The water physical properties, such as the density, viscosity, specific heat and thermal conductivity, are treated as functions of the local water temperature.
Turbulence is characterized by eddies with different space and time scales. In LES, large eddies are resolved directly, while small eddies are modeled using a subgrid model. LES requires significantly finer meshes and a smaller time step than those for a RANS model. SBES is a hybrid RANS-LES turbulence model, in which the boundary layer is modeled using an unsteady RANS model, while the LES model is applied to the core turbulent region where large turbulence scales play a dominant role. As such, SBES allows a coarser mesh and a larger time step than LES does.
Figure 1 shows unsteady flow structures as predicted by the SBES model (iso-surfaces of Q-criterion colored by time-averaged temperature). The results indicate the formation of unsteady turbulence structures emanating from the initial mixing of the two streams, forming a so-called “horseshoe vortex”. In the mixing zone, additional turbulence is formed which then dominates the downstream mixing process. Figure 2 shows the instantaneous velocity and temperature as well as time-averaged velocity and temperature based on the SBES model. The velocity field indicates the presence of a large recirculation region extending approximately 1D downstream of the junction. The results show that the SBES approach can resolve the turbulent eddies generated by shear layer instabilities where the hot and cold streams meet. The instantaneous temperature field shows that the thermal mixing is highly turbulent.
Figure 1: Iso-surfaces of Q-Criterion Colored by Time-Averaged Temperature
Figure 2: Time-Averaged and Instantaneous Velocity and Temperature on Vertical Plane
Both the LES and SBES simulations are carried out for 10.32 seconds of flow time using 16 processors. The LES model contains twice the computational cells of the SBES model and requires slightly more than three times the computational time (wall-clock time) for the SBES analysis. The SBES model is also run for a total of 37.3 seconds of flow time. The results for a longer flow time are very similar to those with 10.32 seconds of flow time and are not presented here.
Figures 3 through 7 compare the modeling results (labeled LES and SBES) with test data (labeled Exp.) obtained in different locations downstream of the junction. The model predictions of the time-averaged water temperature (approximately 1 mm away from the inner wall of the pipe) are in good agreement with the test data at both the bottom and the top of the pipe. The predicted temperature fluctuations compare favorably with the test data as shown in Figure 4 where the root-mean-square-error (RMSE) temperatures are plotted as a function of the axial distance from the junction.
The predicted time-averaged axial velocity component (u) and vertical velocity component (v) compare satisfactorily with the test data. The predicted fluctuations of the velocity components are also in good agreement with the measurements for both the LES and SBES simulations. It is whorth noting that the SBES simulation takes a much shorter time to solve than the LES simulation for the same basic results.
Figure 3: Modeling Results and Experimental Data for Time-Averaged Dimensionless Temperatures along Horizontal Pipe
Figure 4: Modeling Results and Experimental Data for Temperature Fluctuations along Horizontal Pipe
Figure 5: Modeling Results and Experimental Data for Time-Averaged Axial Velocity Components along the z-Axis
Figure 6: Modeling Results and Experimental Data for Time-Averaged Axial and Vertical Velocity Components along the y-axis at x = 1.6D
Figure 7: Modeling Results and Experimental Data for Fluctuations of Velocity Components along the y-axis
The model predictions show that the results from both the LES and SBES models are in excellent agreement with the measurements of the time-averaged and RMSE temperature and velocity components of the flow in a mixing tee. The SBES model can predict turbulent flow structures in the thermal mixing process. Since the SBES model requires a much lower computational cost and provides a faster turn-around of difficult problems than the LES model does, this approach will be used in Part 2 to predict temperature fluctuations in a mixing tee, which blends light gas oil with a recycled gas, to determine the length of a thermal sleeve which is used to protect the pressure boundary piping.
Read Part 2 - CFD Modeling of a Mixing Tee
 Smith B.L., Mahaffy J.H., Angele K. and Westin J., Report of the OECD/NEA-Vattenfall T-junction benchmark exercise, NEA/CSNI/R(2011)5, 2011.
 Gritskevich M.S., Garbaruk A.V., Frank Th. and Menter F.R., Investigation of the thermal mixing in a T-junction flow with different SRS approaches, Nuclear Engineering and Design, 279, 83-90, 2014.
 Kuczaj A.K., Komen E.M.J. and Loginov M.S., Large-eddy simulation study of turbulent mixing in a T-junction, Nuclear Engineering and Design, 240, 2116-2122, 2010.
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Dave has worked in the petrochemical, nuclear and power industries over the last 16 years. Dave’s specialties include finite element analysis (FEA - heat transfer/thermal-stress, creep, fracture and shock and vibration), fatigue, fracture and creep modeling, as well as computational fluid dynamics (CFD) and multiphysics problems.
He is a long time member of ASME (Sections I, III and VIII) and API committees, as well as AWS (weld residual stress modeling). Dave lives in the Cleveland, Ohio area. where he works out of the Medina, Ohio office.
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