Sonic Eddy Model of the Turbulent Boundary Layer

The effects of Mach number on the skin friction and velocity fluctuations of the turbulent boundary layer are considered through a sonic eddy model. Originally proposed for free shear flows, the model assumes that the eddies responsible for momentum transfer have a rotation Mach number of unity, with the entrainment rate limited by acoustic signaling. Under this assumption, the model predicts that the skin friction coefficient should go as the inverse Mach number in a regime where the Mach number is larger than unity but smaller than the square root of the Reynolds number. The velocity fluctuations normalized by the friction velocity should be the inverse square root of the Mach number in the same regime. Turbulent transport is controlled by acoustic signaling. The density field adjusts itself such that the Reynolds stresses correspond to the momentum transport. In contrast, the conventional van Driest–Morkovin view is that the Mach number effects are due to density variations directly. A new experiment or simulation is proposed to test this model using different gases in an incompressible boundary layer, following the example of Brown and Roshko in the free shear layer.

Insight Into Supersonic Combustion Using High-order Simulations

High-order simulations of supersonic combustion are presented to advance understanding of the complex chemically-reacting flow processes and identify unknown mechanisms of the high-speed combustion process. We have employed 11th-order accurate implicit large-eddy simulations in conjunction with thermochemistry models comprising 20 chemical reactions. We compare the computations with available experiments and discuss the accuracy and uncertainties in both. Jets emanating from above and below the hydrogen plumes influence the combustion process and accuracy of the predictions. The simulations reveal that high temperatures are sustained for a long-distance downstream of the combustion onset. A barycentric map for the Reynolds stresses is employed to analyse the turbulent anisotropy. We correlate the axisymmetric contraction and expansion of turbulence with the interaction of reflected-shock waves with the supersonic combustion hydroxyl production regions. The physics insights presented in this study could potentially lead to more efficient supersonic combustion and scramjet technologies.

Asymptotic behaviour at the wall in compressible turbulent channels

The asymptotic behaviour of Reynolds stresses close to walls is well established in incompressible flows owing to the constraint imposed by the solenoidal nature of the velocity field. For compressible flows, thus, one may expect a different asymptotic behaviour, which has indeed been noted in the literature. However, the transition from incompressible to compressible scaling, as well as the limiting behaviour for the latter, is largely unknown. Thus, we investigate the effects of compressibility on the near-wall, asymptotic behaviour of turbulent fluxes using a large direct numerical simulation (DNS) database of turbulent channel flow at higher than usual wall-normal resolutions. We vary the Mach number at a constant friction Reynolds number to directly assess compressibility effects. We observe that the near-wall asymptotic behaviour for compressible turbulent flow is different from the corresponding incompressible flow even if the mean density variations are taken into account and semi-local scalings are used. For Mach numbers near the incompressible regimes, the near-wall asymptotic behaviour follows the well-known theoretical behaviour. When the Mach number is increased, turbulent fluxes containing wall-normal components show a decrease in the slope owing to increased dilatation effects. We observe that $R_{vv}$ approaches its high-Mach-number asymptote at a lower Mach number than that required for the other fluxes. We also introduce a transition distance from the wall at which turbulent fluxes exhibit a change in scaling exponents. Implications for wall models are briefly presented.

Entropy and Turbulence Structure

Some new perspectives are offered on the spectral and spatial structure of turbulent flows, in the context of conservation principles and entropy. In recent works, we have shown that the turbulence energy spectra are derivable from the maximum entropy principle, with good agreement with experimental data across the entire wavenumber range. Dissipation can also be attributed to the Reynolds number effect in wall-bounded turbulent flows. Within the global energy and dissipation constraints, the gradients (d/dy+ or d2/dy+2) of the Reynolds stress components neatly fold onto respective curves, so that function prescriptions (dissipation structure functions) can serve as a template to expand to other Reynolds numbers. The Reynolds stresses are fairly well prescribed by the current scaling and dynamical formalism so that the origins of the turbulence structure can be understood and quantified from the entropy perspective.

VISCOSITY IN SEAKEEPING

Application of strip theory for the prediction of ship motions in waves relies on sectional hydrodynamic coefficients; i.e. the added mass and damping coefficients. These coefficients apply to linearised problems and are normally computed for inviscid fluids. It is possible to account for viscosity but this cannot be done by the RANS equations, as in linear problems there is no room for turbulence. The hydrodynamic coefficients can include the effect of viscosity but this can be done rightly through the classic Navier–Stokes equations for laminar (non-turbulent) flows. For solving these equations commercial RANS software can be used, assuming no Reynolds stresses.

Numerical investigation of semifilled-pipe flow

This study describes turbulent flow in a semifilled pipe with a focus on its secondary currents. To the authors’ knowledge, we provide the first highly resolved data-set for semifilled-pipe flow using direct numerical simulation. The flow parameters range from $Re_\tau =115$ , just maintaining turbulence, to moderate turbulent flow at $Re_\tau =460$ . Some of the main flow characteristics are in line with previously published results from experiments, such as the velocity-dip phenomenon, the main secondary flow and the qualitative distribution of the Reynolds stresses in the core of the flow. We observe some flow phenomena which have not yet been reported in the literature so far for this type of flow. Among those is the inner secondary cell in the mixed corner between the free surface and the pipe's wall, which plays a major role in the distribution of the wall shear stress along the perimeter. We observe that the position and extension of the inner vortex scale with the wall shear stress and those of the outer vortex scale with outer variables. For the first time, we present and discuss distributions of the complete Reynolds stress tensor and its anisotropy which gives rise to the generation of mean streamwise vorticity in a small region in the mixed corners of the pipe. Mean secondary kinetic energy, however, is generated at the free surface around the stagnation point between the inner and outer vortices. This generation mechanism is in line with a vortex dynamics mechanism proposed in the literature.

Sensitivity Analysis of Turbine Fatigue and Ultimate Loads to Wind and Wake Characteristics in a Small Wind Farm

Wind turbines are designed using a set of simulations to determine the fatigue and ultimate loads, typically focused solely on unwaked wind turbine operation. These structural loads can be significantly influenced by the wind inflow conditions. When placed in the wake of upstream turbines, turbines experience altered inflow conditions, which can additionally influence the fatigue and ultimate loads. Although significant research and effort has been put into measuring and defining such parameters, limited work has been done to quantify the sensitivity of structural loads to the inevitable uncertainty in these inflow conditions, especially in a wind farm setting with waked conditions. It is therefore important to understand the impact such uncertainties have on the resulting loads of both non-waked and waked turbines. The goal of this work is to assess which wind-inflow- and wake-related parameters have the greatest influence on fatigue and ultimate loads during normal operation for turbines in a three-turbine wind farm. Twenty-eight wind inflow and wake parameters were screened using an elementary effects sensitivity analysis approach to identify the parameters that lead to the largest variation in the fatigue and ultimate loads of each turbine. This study was performed using the National Renewable Energy Laboratory 5 MW baseline wind turbine with synthetically generated inflow based on the International Electrotechnical Commission (IEC) Kaimal turbulence spectrum with IEC exponential coherence model. The focus was on sensitivity to individual parameters, though interactions between parameters were considered, and how sensitivity differs between waked and non-waked turbines. The results of this work show that for both waked and non-waked turbines, ambient turbulence in the primary wind direction and shear were the most sensitive parameters for turbine fatigue and ultimate loads. Secondary parameters of importance for all turbines were identified as yaw misalignment, u-direction integral length, and the exponent and u components of the IEC coherence model. The tertiary parameters of importance differ between waked and non-waked turbines. Tertiary effects account for up to 9.0 % of the significant events for waked turbine ultimate loads and include veer; non-streamwise components of the IEC coherence model; Reynolds stresses; wind direction; air density; and several wake calibration parameters. For fatigue loads, tertiary effects account for up to 5.4 % of the significant events and include vertical turbulence standard deviation; lateral and vertical wind integral lengths; lateral and vertical wind components of the IEC coherence model; Reynolds stresses; wind direction; and all wake calibration parameters. This information shows the increased importance of non-streamwise wind components and wake parameters in fatigue and ultimate load sensitivity of downstream turbines.

Fluid-Solid Interaction Simulation Methodology for Coriolis Flowmeter Operation Analysis

Numerical simulation is a widely used tool for Coriolis flowmeter (CFM) operation analysis. However, there is a lack of experimentally validated methodologies for the CFM simulation. Moreover, there is no consensus on suitable turbulence models and configuration simplifications. The present study intends to address these questions in a framework of a fluid-solid interaction simulation methodology by coupling the finite volume method and finite element method for fluid and solid domains, respectively. The Reynolds stresses (RSM) and eddy viscosity-based turbulence models are explored and compared for CFM simulations. The effects of different configuration simplifications are investigated. It is demonstrated that the RSM model is favorable for the CFM operation simulations. It is also shown that the configuration simplifications should not include the braces neglect or the equivalent flowmeter tube length assumption. The simulation results are validated by earlier experimental data, showing a less than 5% discrepancy. The proposed methodology will increase the confidence in CFM operation simulations and consequently provide the foundation for further studies of flowmeter usage in various fields.

Influence of pressure on the wake of a hydrophobic circular cylinder for a flow regime with Reynolds number of 2.2×105

Vortex flow structures in a turbulent wake behind a circular Teflon cylinder immersed in an incoming flow with a change in pressure for the Reynolds number Re = 2.2×105 have been experimentally studied using a two-dimensional image (2D-PIV) of particles in a closed-circuit water tunnel. The obtained results are presented in the form of time-averaged velocity fields, Reynolds stresses, and distributions of turbulent kinetic energy. The flow data showed that the size of the wake flow region, Reynolds stresses and turbulent kinetic energy change depending on the pressure in the flow. As a result of a 20% reduction in pressure, the size of the vortex zone in the wake increases by about 20%.