Date of Award

Winter 2020

Degree Type

Restricted to Claremont Colleges Dissertation

Degree Name

Engineering and Industrial Applied Mathematics Joint PhD with California State University Long Beach, PhD


Institute of Mathematical Sciences

Advisor/Supervisor/Committee Chair

Hamid R. Rahai

Dissertation or Thesis Committee Member

Ali Nadim

Dissertation or Thesis Committee Member

Marina Chugunova

Dissertation or Thesis Committee Member

Praveen Shankar

Terms of Use & License Information

Terms of Use for work posted in Scholarship@Claremont.

Rights Information

© 2019 Saeid Janani


The objective of this study was to numerically investigate the mixing characteristics of two and three confined jets in crossflow (JICF) at supercritical pressure using K-ℇ and K-ꞷ turbulence models as well as the Large Eddy Simulation (LES) method using Siemens CCM+ software. The JICF has many applications such as in gas turbine film cooling system, fuel atomization for scramjet engine, vertical takeoff and landing of an aircraft, and core fluid of liquid rocket engine pre-burner. The Reynolds Averaged Navier Stokes (RANS) equations were solved using k-ε and k-ꞷ turbulence models for two and three confined perpendicular jets at 180 and 120 degrees respectively from each other, injecting liquid nitrogen into crossflow gaseous nitrogen. The gaseous nitrogen was at 293.3K and the liquid nitrogen was at 83.3K at an operating pressure of 5.5 MPa. The results from using k-ε and k-ꞷ turbulence models; which are steady Eulerian methods; are compared with each other. Comparisons of the corresponding results for the mean velocity, pressure, temperature and density show that with the k-ε turbulence model, the injecting fluid penetrates less into the crossflow and density gradient is mostly confined to the tube circumference, while with the k-ꞷ turbulence model, higher jet penetration and mixing is observed. Also, increased vorticity near the tube mid-section is seen, working as the mechanism for higher mixing and the spread of the cold fluid into the crossflow and further cooling near the tube wall. However, the axial circulation variation for the k-ε downstream of the two injecting jets implies that the circulation starts increasing from x/D=0.1 and reaches its peak at x/D=0.2.

The maximum circulation zone is from x/D=0.1 to 0.6 and the minimum circulation zone is from x/D=0.6 to 1.2. On the other hand, the corresponding axial circulation variation using k-ω model indicates that the maximum and minimum circulation zones of k-ω is very similar to k-ε except the magnitude of peak circulation for the k-ω model is about 5% larger than the peak circulation obtained using the k-ε model. Investigating the counter rotating vortices (CVP) for three jets show that, further downstream, the existence of three pairs of CVP; one pair for each jet; for both models. However, with the k-ℇ model, the CVPs are larger and oriented toward the tube wall. Both models predict that there are regions of high temperature near the wall downstream of where the two jets mix. Higher mixing is observed with the k-ꞷ model. Increased vorticity near the tube mid-section is seen as the mechanism for higher mixing and spread of the cold fluid into the crossflow and further cooling near the tube wall. Furthermore, since the LES is an unsteady Lagrangian method and provides the transient characteristics of the large eddy structure, the LES results were tracked at different time steps. Variations of where the maximum and minimum mixing zones were identified by four different methods. The first method was assessment of mixing enhancement using circulation at different locations downstream. The LES results indicate that the maximum circulation zone extends from the immediate wake of the jets to about x/D=0.35, whereas the minimum circulation zone extends to almost x/D=0.95. The second method was by identifying the constant density zones, and therefore uniform flow zones downstream which is the sign of enhanced mixing. The plots of percent differences in density and temperature versus x/D identified the zones where density becomes nearly constant. The results indicated that at x/D=4.5 nearly constant density was achieved and assumed to be the beginning of well-mixed zone. The third method was by

identifying the mixing enhancement zones using image processing and method of Spatial Unmixedness. This technique provides a measure of unmixedness based on the variance of the concentration distribution which is defined as “spatial unmixedness, Us “. Having an Us = 0 corresponds to a perfectly mixed system, and Us= 1 indicates a perfectly segregated system. The results indicated that at x/D = 0 which is at the mid-section of injecting jets; the mixing process starts and the spatial unmixedness value is equal to 1, indicating there was no mixing. At about x/D=0.35 the unmixedness value approaches about 0.08 with a very steep slope which means from x/D=0 to x/D=0.35 the mixing process is occurring rapidly. From about x/D=0.35 to 5D the unmixedness value approaches zero with a slope of about 0.02 indicating the start of a relatively fully mixed zone which could typically extend from 5D to further downstream locations. The fourth method was by analyzing the orientation of the counter rotating vortex pairs (CVPs) at different x/Ds in order to identify the center position of the CVPs as well as their extended boundary with respect to the tube’s wall. The quantified results from the three jets show that the CVPs are about 0.30D closer to the core flow centerline using RANS with the k-ꞷ model as compared to the corresponding results using the k-ℇ model. The results of the LES for the two jets at the solution time of 0.01245 s and time step of 1239 which corresponded to the end of the simulation, revealed that the CVPs are apparent at 0.25D where they have been oriented very close to the core-flow centerline. The outer boundary of these vortices was about 0.17D closer to the centerline. This indicated more mixing has taken place around the centerline, as compare to the wall side. In pursuit of visualizing the Lagrangian particle tracking and further investigate the mixing characteristics of the gaseous and liquid nitrogen, a single particle of one-micron laden carbon has been injected into one jet in the two-jet configuration, using the LES. Via the use of

history feature of the StarCCM+ software, the path and position of the injected particle from the injection time until t=0.0014 s has been tracked. This segment of the solutions reveals the effect of the initial interaction of the gaseous and liquid nitrogen on the injected particle’s path. Once the particle enters into the core flow in a straight path, its velocity increases due to the influence of higher velocity of the core-flow. At about 0.2D along -y axis, the acting force of the core-flow causes the particle to tilt in the direction of the core-flow along the x axis towards the centerline and due to increasing axial velocity, the particle’s velocity magnitude decreases. The slip velocity of the particle in this segment is about 2 m/s which is the difference between the particle’s velocity magnitude and the flow velocity magnitude. Once the particle reaches the centerline of the core-flow, it aligns itself with the centerline. Further downstream The motion of the particle is aligned with trajectory of the CVP as they evolve downstream.