## Doctoral Dissertations

Winter 2016

Dissertation

#### Program or Major

Mechanical Engineering

#### Degree Name

Doctor of Philosophy

Christopher M White

Gregory Chini

Yves Dubief

#### Abstract

Transport of momentum and heat in non-equilibrium wall-bounded flows is studied analytically and experimentally to better understand the underlying physics, transition dynamics, and appropriate flow scaling in non-equilibrium flows. Non-equilibrium flows, in which the mean flow time scales are comparable to turbulent flow time scales, do not exhibit universal behaviors and cannot be characterized only in terms of local parameters. Pressure gradients, fast transients and complex geometries are among the sources that can perturb a flow from an equilibrium state to a non-equilibrium state. Since all or some of these perturbation sources are present in many engineering application relevant flow systems and geophysical flows, understanding and predicting the non-equilibrium flow dynamics is essential to reliably analyze and control such flows.

Reynolds-averaged Navier-Stokes (RANS) simulations are extensively used to model and predict fluid transport across a wide range of disciplines. The shortcoming is that most turbulence models used in RANS simulations use almost exclusively wall-models based on equilibrium boundary layer behaviors, despite the fact that many basic assumptions required of equilibrium boundary layers are not satisfied in the majority of the flow systems in which RANS simulations are used. In particular, pressure gradients, dynamic walls, roughness, and large-scale flow obstacles produce boundary layers that are strongly non-equilibrium in nature. Often the prediction of RANS simulations in complex engineering systems (with perturbations that induce non-equilibrium flow behaviors) fail spectacularly primarily owing to the fact that the turbulence models do not incorporate the correct physics to accurately capture the transport behaviors in non-equilibrium boundary layers. These failures result in over-engineered and hence, less efficient designs. This lack of efficiency manifests in higher economic and environmental costs. The broad objective of this dissertation work is to develop analytical and experimental tools needed to better understand the underlying transport physics in non-equilibrium boundary layers.

The key scaling parameter in wall-bounded flows is the wall flux of momentum and heat. It follows that an accurate determination of the wall fluxes is essential to study the dynamics of non-equilibrium wall-bounded flows. As part of this dissertation research, an integral method to evaluate wall heat flux suitable for experimental data is developed. The method is exact and does not require any streamwise gradient measurements. The integral method is validated using simulation and experimental data. Complications owing to experimental limitations and measurement error in determining wall heat flux from the method are presented, and mitigating strategies are described. In addition to the ability to evaluate the wall heat flux, the method provides a means to connect transport properties at the wall to the mean flow dynamics.

The integral method is further developed to formulate a novel and robust validation technique of Reynolds-averaged Navier-Stokes (RANS) turbulence models. Validation of the turbulence models employed in RANS simulations is a critical part of model development and application. The integral based validation technique is used to evaluate the performance of two low-Reynolds-number and two high-Reynolds number RANS turbulence models of reciprocating channel flow, and results are compared to the so-called standard validation technique. While the standard validation technique indicates that the low-Reynolds-number models predict the wall heat flux well, the integral validation technique shows that the models do not accurately capture the correct physics of thermal transport in reciprocating channel flow. Moreover, it shows that the correct prediction of the wall heat flux by the models is owed to the serendipitous cancellation of model errors.

One of the identified failures of the RANS simulations of reciprocating channel flow is the inability to accurately predict the flow dynamics during the laminar-turbulence transition. The development of improved RANS turbulence models, therefore requires an improved understanding of the underlying laminar-turbulent transition mechanisms. As part of this dissertation work, the balance of the leading order terms in the phase-averaged mean momentum equation are used to study the transition mechanism in a reciprocating channel flow. It is concluded that the emergence of an internal layer in the late acceleration phase of the cycle triggers the flow to transition from a self-sustaining transitional regime to an intermittently turbulent regime. In the absence of this internal layer, the flow remains transitional throughout the cycle.

Lastly, since experimental studies of heat transfer in non-equilibrium wall-bounded flows are very limited, a unique experimental facility was developed to study non-equilibrium boundary layers with heat transfer. The facility consists of boundary layer wind tunnel that nominally measures 303x135mm cross-section and 2.7m in length. A freestream heater and a thermal wall-plate are used to maintain the desired outer and inner thermal boundary conditions, respectively. A rotor-stator assembly is fabricated to generate a periodic pressure gradient used to produce pulsatile boundary layer flow. The facility is first validated for equilibrium flow conditions, and then used to study the transport of momentum in a pulsatile boundary layer (PBL). The results show that although the PBL flow at each phase departs from equilibrium, the time-average profiles, except for the streamwise turbulent intensity $\overline{u'^2}$, appears similar to steady-state, zero-pressure-gradient boundary layer flow. Using $\overline{u'^2}$ as a metric for departure of the time mean flow from equilibrium, a critical frequency range $0.014<\omega_c^+<0.020$ was identified, where $\omega^+ = \frac{\omega}{u_\tau^2/\nu}$, $\omega$ is the angular frequency of the pressure gradient modulation, $u_\tau$ is the friction velocity and $\nu$ is the fluid viscosity. For $\omega^+>\omega_c^+$, $\overline{u'^2}$ does not exhibit significant difference from ZPG boundary layer flow. For $\omega^+<\omega_c^+$, however, $\overline{u'^2}$ has a higher value compared to ZPG boundary layer flow where magnitude of the differences is inversely proportional to flow frequency. The wall shear stress modulation is investigated to study the perturbation field in PBL. The perturbation wall shear stress of the two lower frequency cases is in phase with the freestream and the amplitude of modulation matches the Stokes' boundary layer solution. For the highest frequency case, however, the perturbation wall shear stress leads the freestream and the amplitude of modulation is slightly larger than the Stokes' boundary layer solution. It is, therefore, concluded that the perturbation flow of the highest frequency case is non-equilibrium and eddy-viscosity model (EVM) simulation models fail to predict the perturbation field accurately.

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