Verification and Validation (V&V) efforts focus on placing uncertainty bounds on computational models and simulations. Consult the text by Oberkampf and Roy for a detailed treatment of this field of study. In short, verification deals with quantifying the uncertainty for mathematical methods employed to solve the underlying (often differential or integral) expressions that dictate the physics of interest. One example of uncertainty in this case might be discretization (in terms of the linearized differential equations as well as the mesh that may be applied to the physical domain). Validation on the other hand includes comparison to experimental data and assessing the uncertainty between the measured and predicted parameter of interest. When properly conducted, V&V allows the engineer or scientist to assign confidence levels to their models and simulations, which becomes essential when full scale experimental studies are impractical or cost prohibitive (e.g., nuclear reactor).
This area of our research focuses on turbulent jets, which find relevance in numerous classes of applications, including power generation (e.g., high temperature gas cooled nuclear reactors) and environmental flows (e.g., wastewater discharge from pipes into lakes and rivers or natrual plumes driving atmospheric flows) to name a few. We analyze the discretized Navier-Stokes equations (isothermal studies) as well as the discretized energy equation (non-isothermal studies). The overarching goals of this work are as follows
An isothermal turbulent jet has a rich history in the literature. Some of the seminal experimental works include Wygnanski and Fiedler (W&F), Panchapakesan and Lumley (P&L), and Hussein, Capp, and George (HCG). These serve as a comparison base for the computational modeling efforts, and cover a wide range of jet Reynolds numbers. Although Large Eddy Simulation (LES) is a common approach for such a fundamental turbulent flow, our group has obtained the first result that accurately predicts the near field and far field behavior at moderately high Reynolds numbers, where the computational costs of Direct Numerical Simulation (DNS) become prohibitively high. Our result is shown below:
While others have been able to match far field conditions after results are non-dimenionalized, our model, which acccounts for the upstream flow produces centerline velocity data in excellent agreement with trusted experimental data (see below).
A more valuable contribution of this project is the insight into the transport of turbulent kinetic energy (TKE) for these high Reynolds number jets. With a fully validated computational model at multiple Reynolds numbers, we can unobtrusively quantify the various terms in the TKE budget, and asses the validity of assumptions made by previous investigators due to experimental limitations (see below).
When considering the transport of thermal energy by a turbulent jet, high quality data can be found from Mi et al. for the temperature field. The results again show excellent agreement, but only when appropriately accounting for upstream velocities and temperatures. If done properly, the spectrum of fluctuations for both quantities is reflective of the true physics.
With trusted computational models acheived, the physics can be probed in a highly detailed, unobtrusive way. This also provides a standard by which other computational results with a wide range of modeling assumptions can be gauged for accuracy. Our ongoing and future work in this area is focused on establishing a framework for quantifying uncertainty in LES for fundamental turbulent flows. This will include comparison to the energy cascade most often used to gauge the quality of data from LES.
This research was sponsored by the DOE Office of Nuclear Energy's Nuclear Energy University Programs