Prediction of momentum and scalar transport in a jet-in-crossflow

Date of Award




Degree Name

Doctor of Philosophy (Ph.D.)


Mechanical Engineering

First Committee Member

Andrew T. Hsu - Committee Chair


Successful aerodynamic design of modern gas turbine combustors demands accurate predictions of velocity fields and turbulent scalar mixing in the jet-in-crossflow. In this study, the flowfield of a round jet injected normally into a confined uniform crossflow in a rectangular tunnel has been modeled and numerically simulated by using both steady and unsteady Reynolds-Averaged Navier-Stokes (RANS) equations. The standard k-3 turbulence model has been employed for turbulence closure.As a preliminary study, the assumption that the turbulent Schmidt number is constant is assessed and found inadequate in some cases of predicting the scalar mixing in the jet-in-crossflow. Under this assumption, a turbulent Schmidt number of 0.2 is found to provide a more accurate agreement with data than the commonly used value of 0.7. In order to improve the accuracy of the solution, a variable turbulent Schmidt number model is developed. In the process, a uniform micro Genetic Algorithm (GA) is employed to optimize the modeling constants. Calibration and validation of the variable Schmidt number model show that it leads to better prediction of scalar mixing in the jet-in-crossflow than the steady solution with a constant turbulent Schmidt number.Previous experimental work has found that the jet-in-crossflow is essentially unsteady and periodic. The present study has numerically verified the existence of periodic motion in the jet-in-crossflow. The unsteady solution qualitatively improved the calculated velocity profiles and accurately predicted Strouhal numbers under various Reynolds numbers and jet-to-crossflow velocity ratios.The unsteady solution for the three-dimensional jet-in-crossflow is computationally too expensive to serve as a practical design tool in engineering applications. It is found that additional correlation terms, referred to as deterministic stress and scalar flux terms, occur in the time-averaged governing equations. To avoid the calculations of unsteady governing equations, the methodology of modeling the deterministic stress and scalar flux correlations is introduced. An algebraic model of the deterministic stress tensor, based on the gradient diffusion modeling strategy, is developed to account for the unsteadiness effects. This model is established based on both experimental and numerical observations of the unsteady flowfield, and calibrated using experimental data. Validation of the present numerical procedure has been performed to demonstrate the predictive capability of the proposed model to accurately predict both velocity and scalar fields of the jet-in-crossflow.Both the variable turbulent Schmidt number model and the deterministic stress model developed in this thesis can be applied to design procedures of gas turbine combustors.Finally, the transport equations for the deterministic stress and scalar flux tensors are rigorously derived from the unsteady Reynolds-averaged governing equations. Physical meanings of the higher order correlations in the transport equations are identified.The directions for future work in this area are suggested at the end of this thesis.


Engineering, Mechanical

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