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Register a new userNumerical simulation of turbulent duct flows with constant power input
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The numerical simulation of a flow through a duct requires an externally specified forcing that makes the fluid flow against viscous friction. To this aim, it is customary to enforce a constant value for either the flow rate (CFR) or the pressure gradient (CPG). When comparing a laminar duct flow before and after a geometrical modification that induces a change of the viscous drag, both approaches (CFR and CPG) lead to a change of the power input across the comparison. Similarly, when carrying out the (DNS and LES) numerical simulation of unsteady turbulent flows, the power input is not constant over time. Carrying out a simulation at constant power input (CPI) is thus a further physically sound option, that becomes particularly appealing in the context of flow control, where a comparison between control-on and control-off conditions has to be made. We describe how to carry out a CPI simulation, and start with defining a new power-related Reynolds number, whose velocity scale is the bulk flow that can be attained with a given pumping power in the laminar regime. Under the CPI condition, we derive a relation that is equivalent to the Fukagata--Iwamoto--Kasagi relation valid for CFR (and to its extension valid for CPG), that presents the additional advantage of natively including the required control power. The implementation of the CPI approach is then exemplified in the standard case of a plane turbulent channel flow, and then further applied to a flow control case, where the spanwise-oscillating wall is used for skin friction drag reduction. For this low-Reynolds number flow, using 90% of the available power for the pumping system and the remaining 10% for the control system is found to be the optimum share that yields the largest increase of the flow rate above the reference case, where 100% of the power goes to the pump.
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Parameter extension simulation (PES) as a mathematical method for simulating turbulent flows has been proposed in the study. It is defined as a calculation of the turbulent flow for the desired parameter values with the help of a reference solution. A typical PES calculation is composed of three consecutive steps: Set up the asymptotic relationship between the desired solution and the reference solution; Calculate the reference solution and the necessary asymptotic coefficients; Extend the reference solution to the desired parameter values. A controlled eddy simulation (CES) method has been developed to calculate the reference solution and the asymptotic coefficients. The CES method is a special type of large eddy simulation (LES) method in which a weight coefficient and an artificial force distribution are used to model part of the turbulent motions. The artificial force distribution is modeled based on the eddy viscosity assumption. The reference weight coefficient and the asymptotic coefficients can be determined through a weight coefficient convergence study. The proposed PES/CES method has been used to simulate four types of turbulent flows. They are decaying homogeneous and isotropic turbulence, smooth wall channel flows, rough wall channel flows, and compressor blade cascade flows. The numerical results show that the 0-order PES solution (or the reference CES solution) has a similar accuracy as a traditional LES solution, while its computational cost is much lower. A higher order PES method has an even higher model accuracy.
The turbulent boundary layer over a Gaussian shaped bump is computed by direct numerical simulation (DNS) of the incompressible Navier-Stokes equations. The two-dimensional bump causes a series of strong pressure gradients alternating in rapid succession. At the inflow, the momentum thickness Reynolds number is approximately 1,000 and the boundary layer thickness is 1/8 of the bump height. DNS results show that the strong favorable pressure gradient (FPG) causes the boundary layer to enter a relaminarization process. The near-wall turbulence is significantly weakened and becomes intermittent, however relaminarization does not complete. The streamwise velocity profiles deviate above the standard logarithmic law and the Reynolds shear stress is reduced. The strong acceleration also suppresses the wall-shear normalized turbulent kinetic energy production rate. At the bump peak, where the FPG switches to an adverse gradient (APG), the near-wall turbulence is suddenly enhanced through a partial retransition process. This results in a new highly energized internal layer which is more resilient to the strong APG and only produces incipient flow separation on the downstream side. In the strong FPG and APG regions, the inner and outer layers become largely independent of each other. The near-wall region responds to the pressure gradients and determines the skin friction. The outer layer behaves similarly to a free-shear layer subject to pressure gradients and mean streamline curvature effects. Results from a RANS simulation of the bump are also discussed and clearly show the lack of predictive capacity of the near-wall pressure gradient effects on the mean flow.
The aim of the present work is to investigate the role of coherent structures in the generation of the secondary flow in a turbulent square duct. The coherent structures are defined as connected regions of flow where the product of the instantaneous fluctuations of two velocity components is higher than a threshold based on the long-time turbulence statistics, in the spirit of the three-dimensional quadrant analysis proposed by Lozano-Duran et al. (J. Fluid Mech., vol. 694, 2012, pp. 100-130). We consider both the direct contribution of the structures to the mean in-plane velocity components and their geometrical properties. The instantaneous phenomena taking place in the turbulent duct are compared with turbulent channel flow at Reynolds numbers of $Re_tau=180$ and $360$, based on friction velocity at the center-plane and channel half height. In the core region of the duct, the fractional contribution of intense events to the wall-normal component of the mean velocity is in very good agreement with that in the channel, despite the presence of the secondary flow in the former. Additionally, the shapes of the three-dimensional objects do not differ significantly in both flows. On the other hand, in the corner region of the duct, the proximity of the walls affects both the geometrical properties of the coherent structures and the contribution to the mean component of the vertical velocity, which is less relevant than that of the complementary portion of the flow not included in such objects. Our results show however that strong Reynolds shear-stress events, despite the differences observed between channel and duct, do not contribute directly to the secondary motion, and thus other phenomena need to be considered instead.
Most fluid flow problems that are vital in engineering applications involve at least one of the following features: turbulence, shocks, and/or material interfaces. While seemingly different phenomena, these flows all share continuous generation of high wavenumber modes, which we term the $k_infty$ irregularity. In this work, an inviscid regularization technique called observable regularization is proposed for the simulation of two-phase compressible flows. The proposed approach regularizes the equations at the level of the partial differential equation and as a result, any numerical method can be used to solve the system of equations. The regularization is accomplished by introducing an observability limit that represents the length scale below which one cannot properly model or continue to resolve flow structures. An observable volume fraction equation is derived for capturing the material interface, which satisfies the pressure equilibrium at the interface. The efficacy of the observable regularization method is demonstrated using several test cases, including a one-dimensional material interface tracking, one-dimensional shock-tube and shock-bubble problems, and two-dimensional simulations of a shock interacting with a cylindrical bubble. The results show favorable agreement, both qualitatively and quantitatively, with available exact solutions or numerical and experimental data from the literature. The computational saving by using the current method is estimated to be about one order of magnitude in two-dimensional computations and significantly higher in three-dimensional computations. Lastly, the effect of the observability limit and best practices to choose its value are discussed.
The efficient mixing of fluids is key in many applications, such as chemical reactions and nanoparticle precipitation. Detailed experimental measurements of the mixing dynamics are however difficult to obtain, and so predictive numerical tools are helpful in designing and optimizing many processes. If two different fluids are considered, the viscosity and density of the mixture depend often nonlinearly on the composition, which makes the modeling of the mixing process particularly challenging. Hence water-water mixtures in simple geometries such as T-mixers have been intensively investigated, but little is known about the dynamics of more complex mixtures, especially in the turbulent regime. We here present a numerical method allowing the accurate simulation of two-fluid mixtures. Using a high-performance implementation of this method we perform direct numerical simulations resolving the spatial and temporal dynamics of water-ethanol flows for Reynolds numbers from 100 to 2000. The flows states encountered during turbulence transition and their mixing properties are discussed in detail and compared to water-water mixtures.
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