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Many waterflooding oil fields, injecting water into an oil-bearing reservoir for pressure maintenance, are in their middle to late stages of development. To explore the geological conditions and improve oilfield recovery of the most important well group of the Hu 136 block, located on the border areas of three provinces (Henan, Shandong, and Hebei), Zhongyuan Oilfield, Sinopec, central China, a 14C cross-well tracer monitoring technology was developed and applied in monitoring the development status and recognize the heterogeneity of oil reservoirs. The tracer response in the production well was tracked, and the water drive speed, swept volume of the injection fluid were obtained. Finally, the reservoir heterogeneity characteristics, such as the dilution coefficient, porosity, permeability, and average pore-throat radius, were fitted according to the mathematical model of the heterogeneous multi-layer inter-well theory. The 14C-AMS technique developed in this work is expected to be a potential analytical method for evaluating underground reservoir characteristics and providing crucial scientific guidance for the mid to late oil field recovery process.
The study of flapping-wing aerodynamics faces a large control space with different wing kinematics and deformation. The adjoint-based approach, by solving an inverse problem to obtain simultaneously the sensitivity with respect to all control parameters, has a computational cost independent of the number of control parameters and becomes an efficient tool for the study of problems with a large control space. However, the adjoint equation is typically formulated in a fixed fluid domain. In a continuous formulation, a moving boundary or morphing domain results in inconsistency in the definition of an arbitrary perturbation at the boundary, which leads to ambiguousness and difficulty in the adjoint formulation if control parameters are related to boundary changes (e.g. the control of wing kinematics and dynamic deformation). The unsteady mapping function, as a traditional way to deal with moving boundaries, can in principle be a remedy for this situation. However, the derivation is often too complex to be feasible, even for simple problems. Part of the complexity comes from the unnecessary mapping of the interior mesh, while only mapping of the boundary is needed here. Non-cylindrical calculus, on the other hand, provides a boundary mapping and considers the rest of domain as an arbitrary extension from the boundary. Using non-cylindrical calculus to handle moving boundaries makes the derivation of the adjoint formulation much easier and also provides a simpler final formulation. The new adjoint-based optimization approach is validated for accuracy and efficiency by a well-defined case where a rigid plate plunges normally to an incoming flow. Then, the approach is applied for the optimization of drag reduction and propulsive efficiency of first a rigid plate and then a flexible plate which both flap with plunging and pitching motions against an incoming flow. For the rigid plate, the phase delay between pitching and plunging is the control and considered as both a constant (i.e. a single parameter) and a time-varying function (i.e. multiple parameters). The comparison between its arbitrary initial status and the two optimal solutions (with a single parameter or multiple parameters) reveals the mechanism and control strategy to reach the maximum thrust performance or propulsive efficiency. Essentially, the control is trying to benefit from both lift-induced thrust and viscous drag (by reducing it), and the viscous drag plays a dominant role in the optimization of efficiency. For the flexible plate, the control includes the amplitude and phase delay of the pitching motion and the leading eigenmodes to characterize the deformation. It is clear that flexibility brings about substantial improvement in both thrust performance and propulsive efficiency. Finally, the adjoint-based approach is extended to a three-dimensional study of a rectangular plate in hovering motion for lift performance. Both rigid and flexible cases are considered. The adjoint-based algorithm finds an optimal hovering motion with advanced rotation which has a large leading-edge vortex and strong downwash for lift benefit, and the introduction of flexibility enhances the wake capturing mechanism and generates a stronger downwash to push the lift coefficient higher.
A methodology to achieve extremely-low-dimensional models for temporally developing shear layers is extended from incompressible flows to weakly compressible flows. The key idea is to first remove the slow variation (i.e. viscous growth of shear layers) through symmetry reduction, so that the model reduction using proper orthogonal decomposition (POD)-Galerkin projection in the symmetry-reduced space becomes more efficient. However, for the approach to work for compressible flows, thermodynamic variables need to be retained. We choose the isentropic Navier–Stokes equations for the simplicity and the availability of a well-defined inner product for total energy. To capture basic dynamics, the compressible low-dimensional model requires only two POD modes for each frequency. Thus, a two-mode model is capable of representing single-frequency dynamics such as vortex roll-up, and a four-mode model is capable of representing the nonlinear dynamics involving a fundamental frequency and its subharmonic, such as vortex pairing and merging. The compressible model shows similar behaviour and accuracy as the incompressible model. However, because of the consistency of the inner product defined for POD and for projection in the current compressible model, the orthogonality is kept and it results in simple formulation. More importantly, the inclusion of compressibility opens an entirely new avenue for the discussion of compressibility effect and possible description of aeroacoustics and thermodynamics. Finally, the model is extended to different flow parameters without additional numerical simulation. The extension of the compressible four-mode model includes different Mach numbers and Reynolds numbers. We can clearly observe the change in the nonlinear interaction of modes at two frequencies and the associated promotion or delay of vortex pairing by varying compressibility and viscosity. The dynamic response of the low-dimensional model to different flow parameters is consistent with the vortex dynamics observed in experiments and numerical simulation.
We propose a generalization of proper orthogonal decomposition (POD) for optimal flow resolution of linearly related observables. This Galerkin expansion, termed ‘observable inferred decomposition’ (OID), addresses a need in aerodynamic and aeroacoustic applications by identifying the modes contributing most to these observables. Thus, OID constitutes a building block for physical understanding, least-biased conditional sampling, state estimation and control design. From a continuum of OID versions, two variants are tailored for purposes of observer and control design, respectively. Firstly, the most probable flow state consistent with the observable is constructed by a ‘least-residual’ variant. This version constitutes a simple, easily generalizable reconstruction of the most probable hydrodynamic state to preprocess efficient observer design. Secondly, the ‘least-energetic’ variant identifies modes with the largest gain for the observable. This version is a building block for Lyapunov control design. The efficient dimension reduction of OID as compared to POD is demonstrated for several shear flows. In particular, three aerodynamic and aeroacoustic goal functionals are studied: (i) lift and drag fluctuation of a two-dimensional cylinder wake flow; (ii) aeroacoustic density fluctuations measured by a sensor array and emitted from a two-dimensional compressible mixing layer; and (iii) aeroacoustic pressure monitored by a sensor array and emitted from a three-dimensional compressible jet. The most ‘drag-related’, ‘lift-related’ and ‘loud’ structures are distilled and interpreted in terms of known physical processes.
We develop low-dimensional models for the evolution of a free shear layer in a periodic domain. The goal is to obtain models simple enough to be analysed using standard tools from dynamical systems theory, yet including enough of the physics to model nonlinear saturation and energy transfer between modes (e.g. pairing). In the present paper, two-dimensional direct numerical simulations of a spatially periodic, temporally developing shear layer are performed. Low-dimensional models for the dynamics are obtained using a modified version of proper orthogonal decomposition (POD)/Galerkin projection, in which the basis functions can scale in space as the shear layer spreads. Equations are obtained for the rate of change of the shear-layer thickness. A model with two complex modes can describe certain single-wavenumber features of the system, such as vortex roll-up, nonlinear saturation, and viscous damping. A model with four complex modes can describe interactions between two wavenumbers (vortex pairing) as well. At least two POD modes are required for each wavenumber in space to sufficiently describe the dynamics, though, for each wavenumber, more than 90% energy is captured by the first POD mode in the scaled space. The comparison of POD modes to stability eigenfunction modes seems to give a plausible explanation. We have also observed a relation between the phase difference of the first and second POD modes of the same wavenumber and the sudden turning point for shear-layer dynamics in both direct numerical simulations and model computations.
The adjoint of the perturbed and linearized compressible viscous flow equations is formulated in such a way that its solution can be used to optimize control actuation in order to reduce flow-generated sound. We apply it to a direct numerical simulation of a randomly excited two-dimensional mixing layer, with inflow vorticity-thickness Reynolds number 500 and free-stream Mach numbers 0.9 and 0.2. The control actuation is implemented as general source terms in the flow equations (body forces, mass sources, and internal energy sources) with compact support near the inflow boundary. The noise to be reduced is defined by a space-time integral of the mean-square pressure fluctuations on a line parallel to the mixing layer in the acoustic field of the low-speed stream. Both the adjoint and flow equations are solved numerically and without modelling approximations. The objective is to study the mechanics of the noise generation and its control. All controls reduce targeted noise with very little required input power, with the most effective (the internal energy control) reducing the noise intensity by 11 dB. Numerical tests confirm that the control is not by any simple acoustic cancellation mechanism but instead results from a genuine change of the flow as a source of sound. The comparison of otherwise identical flows with and without control applied shows little change of the flow's gross features: the evolution and pairings of the energetic structures, turbulence kinetic energy, spreading rate, and so on are superficially unchanged. However, decomposition of the flow into empirical eigenfunctions, as surrogates for Fourier modes in the non-periodic streamwise direction, shows that the turbulence structures advect downstream more uniformly. This change appears to be the key to reducing their acoustic efficiency, a perspective that is clarified by comparing the randomly excited mixing layer to a harmonically excited mixing layer, which is relatively quiet because it is highly ordered. Unfortunately, from the perspective of any practical implementation with actuators, the optimized control identified has a complex spatial and temporal structure, but it can be simplified. Two empirical eigenmodes were required to represent it sufficiently to reduce the targeted noise intensity by about 50%. Optimization of a simple single-degree-of-freedom control with an ad hoc spatial structure is less effective.
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