During drilling, the mud column sustains a slightly higher pressure than the formation to maintain the stability of the well wall, which causes the mud filtrate to penetrate into formation pores and displace in-situ fluids. The invasion depth is affected by reservoir properties, especially the reservoir permeability. Therefore, it is possible to estimate the reservoir permeability if the invasion depth can be measured. A numerical study was conducted to investigate the feasibility of evaluating reservoir permeability with array induction logging. A mud invasion model was built up by coupling mud cake growth with multiple-phase fluid flow ,and an array induction logging model was established based on the Born geometric factor theory. Joint forward simulations of mud invasion and array induction logging indicated that the responses of array induction logging can reflect the effect of mud invasion on the formation resistivity. Inversion based on the damped least square method revealed that the invasion depth can be acquired from array induction logging data. We investigated the association between reservoir permeability and invasion depth, and found that in a reservoir with a permeability of 1 to 100mD(1 mD= 0.987×10-3μm～2),the reservoir permeability governs the invasion depth, and thus the permeability can be evaluated according to invasion depth. A two-dimensional numerical simulation showed that the inversed invasion depth curve had a similar fluctuation to the permeability variation. For a layered formation, a series of interpretation charts can be produced to evaluate the permeability of every layer with tolerable errors. The numerical investigation proves the feasibility of estimating reservoir permeability with array induction logging.@en

We investigate the shock-induced turbulent mixing between a light and a heavy gas, where a Richtmyer-Meshkov instability (RMI) is initiated by a shock wave with Mach number Ma = 1.5. The prescribed initial conditions define a deterministic multimode interface perturbation between the gases, which can be imposed exactly for different simulation codes and resolutions to allow for quantitative comparison. Wellresolved large-eddy simulations are performed using two different and independently developed numerical methods with the objective of assessing turbulence structures, prediction uncertainties and convergence behaviour. The two numerical methods differ fundamentally with respect to the employed subgrid-scale regularisation, each representing state-of-the-art approaches to RMI. Unlike previous studies, the focus of the present investigation is to quantify the uncertainties introduced by the numerical method, as there is strong evidence that subgrid-scale regularisation and truncation errors may have a significant effect on the linear and nonlinear stages of the RMI evolution. Fourier diagnostics reveal that the larger energy-containing scales converge rapidly with increasing mesh resolution and thus are in excellent agreement for the two numerical methods. Spectra of gradient-dependent quantities, such as enstrophy and scalar dissipation rate, show stronger dependences on the small-scale flow field structures as a consequence of truncation error effects, which for one numerical method are dominantly dissipative and for the other dominantly dispersive. Additionally, the study reveals details of various stages of RMI, as the flow transitions from large-scale nonlinear entrainment to fully developed turbulent mixing. The growth rates of the mixing zone widths as obtained by the two numerical methods are ~t^7/12 before re-shock and ~(t - t₀)^2/7 long after re-shock. The decay rate of turbulence kinetic energy is consistently ~(t-t₀)^-10/7 at late times, where the molecular mixing fraction approaches an asymptotic limit ≈ 0.85. The anisotropy measure.

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We quantify initial-data uncertainties on a shock accelerated heavy-gas cylinder by two-dimensional well-resolved direct numerical simulations. A high-resolution compressible multicomponent flow simulation model is coupled with a polynomial chaos expansion to propagate the initial-data uncertainties to the output quantities of interest. The initial flow configuration follows previous experimental and numerical works of the shock accelerated heavy-gas cylinder.We investigate three main initialdata uncertainties, (i) shock Mach number, (ii) contamination of SF₆ with acetone, and (iii) initial deviations of the heavy-gas region from a perfect cylindrical shape. The impact of initial-data uncertainties on the mixing process is examined. The results suggest that the mixing process is highly sensitive to input variations of shock Mach number and acetone contamination. Additionally, our results indicate that the measured shock Mach number in the experiment of Tomkins et al. ["An experimental investigation of mixing mechanisms in shock-accelerated flow," J. Fluid. Mech. 611, 131 (2008)] and the estimated contamination of the SF₆ region with acetone [S. K. Shankar, S. Kawai, and S. K. Lele, "Two-dimensional viscous flow simulation of a shock accelerated heavy gas cylinder," Phys. Fluids 23, 024102 (2011)] exhibit deviations from those that lead to best agreement between our simulations and the experiment in terms of overall flow evolution.

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We present results of well-resolved direct numerical simulations (DNS) of the turbulent flow evolving from Richtmyer-Meshkov instability (RMI) in a shock-tube with square cross section. The RMI occurs at the interface between a mixture of O2 and N2 (light gas) and SF6 and acetone (heavy gas). The interface between the light and heavy gas is accelerated by a Ma = 1.5 planar shock wave. RMI is triggered by a well-defined multimodal initial disturbance at the interface. The DNS exhibit grid-resolution independent statistical quantities and support the existence of a Kolmogorov-like inertial range with a k-5/3 scaling unlike previous simulations found in the literature. The results are in excellent agreement with the experimental data of Weber et al. ["Turbulent mixing measurements in the Richtmyer-Meshkov instability," Phys. Fluids24, 074105 (2012)]10.1063/1.4733447.

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Two-dimensional simulations of the single-mode Richtmyer-Meshkov instability (RMI) are conducted and compared to experimental results of Jacobs and Krivets (2005 Phys. Fluids 17 034105). The employed adaptive central-upwind sixth-order weighted essentially non-oscillatory (WENO) scheme (Hu et al 2010 J. Comput. Phys. 229 8952-65) introduces only very small numerical dissipation while preserving the good shock-capturing properties of other standard WENO schemes. Hence, it is well suited for simulations with both small-scale features and strong gradients. A generalized Roe average is proposed to make the multicomponent model of Shyue (1998 J. Comput. Phys. 142 208-42) suitable for high-order accurate reconstruction schemes. A first sequence of single-fluid simulations is conducted and compared to the experiment. We find that the WENO-CU6 method better resolves small-scale structures, leading to earlier symmetry breaking and increased mixing. The first simulation, however, fails to correctly predict the global characteristic structures of the RMI. This is due to a mismatch of the post-shock parameters in single-fluid simulations when the pre-shock states are matched with the experiment. When the post-shock parameters are matched, much better agreement with the experimental data is achieved. In a sequence of multifluid simulations, the uncertainty in the density gradient associated with transition between the fluids is assessed. Thereby the multifluid simulations show a considerable improvement over the single-fluid simulations.@en

In most technical applications involving cavitation, vapor bubbles occur in clouds, and their collapse is affected by the interaction with neighboring bubbles. One approach to study the influence of these interactions is the investigation of the collapse of cavity arrays in water under shock wave loading. We describe in detail the collapse mechanisms during the collapse of a horizontal cavity array, with particular consideration of maximum pressures. As general trend, we find a pressure amplification in consecutive cavity collapses. However, by increasing the number of cavities, we are able to demonstrate that the amplification is not monotonic. A parameter study of the bubble separation distance in horizontal arrays shows that a smaller distance generally, but not necessarily, results in larger collapse pressure. Exceptions from the general trend are due to the very complex shock and expansion-wave interactions and demonstrate the importance of using state-of-the-art numerical methods. By varying boundary conditions, we illustrate the significance of large test sections in experimental investigations, as the expansion wave emitted at a free surface has a large effect on the collapse dynamics.

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In this paper, we investigate the high-speed dynamics of symmetric and asymmetric cavitation bubble-collapse. For this purpose, a sharp-interface numerical model is employed, that includes a numerically efficient evaporation/condensation model. The underlying assumption is that phase change occurs in thermal non-equilibrium and that the associated timescale is much larger than that of the wave-dynamics described by the interfacial Riemann problem. The sharp-interface model allows for an accurate tracking of the interface evolution throughout collapse and rebound. With a first set of simulations, we investigate the influence of the non-equilibrium on the relaxation behaviour of an oscillating vapour bubble. We observe that a good prediction of the phase-change rate is essential. Of high practical interest is the collapse of cavitation bubbles near walls under high ambient-pressure conditions. We investigate the differences in collapse evolution for detached and attached bubbles. It is shown that the maximum wall pressure strongly depends on the symmetry of the collapse mechanisms, and regions with a high probability of bubble rebound are identified. Asymmetric attached bubbles lead to significantly different topology changes during collapse than symmetric bubbles but exhibit roughly the same range of maximum pressures.

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We propose a conservative, second-order accurate immersed interface method for representing incompressible fluid flows over complex three dimensional solid obstacles on a staggered Cartesian grid. The method is based on a finite-volume discretization of the incompressible Navier-Stokes equations which is modified locally in cells that are cut by the interface in such a way that accuracy and conservativity are maintained. A level-set technique is used for description and tracking of the interface geometry, so that an extension of the method to moving boundaries and flexible walls is straightforward. Numerical stability is ensured for small cells by a conservative mixing procedure. Discrete conservation and sharp representation of the fluid-solid interface render the method particularly suitable for Large-Eddy Simulations of high-Reynolds number flows. Accuracy, second-order grid convergence and robustness of the method is demonstrated for several test cases: inclined channel flow at Re= 20, flow over a square cylinder at Re= 100, flow over a circular cylinder at Re= 40, Re= 100 and Re= 3900, as well as turbulent channel flow with periodic constrictions at Re= 10,595.

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This work presents an immersed interface method for representing complex boundaries in Implicit Large-Eddy Simulation on three-dimensional, staggered Cartesian Grids. The immersed obstacle in the fluid domain is characterized by a levelset field. Initial flux calculations are carried out for the entire domain in the same way. Cells intersected by the immersed interface then undergo a special treatment: only the fluid part is considered, no-slip condition and no-through-flux condition are imposed by changing the flux balance and a homogeneous Neumann condition for pressure is enforced in the pressure projection. To deal with the small cell problem a cell-mixing procedure is applied. The approach is fully conservative and we demonstrate the method is second-order accurate. The validation and the performance of the approach are done with some numerical examples of 2D and 3D flow configurations.@en