Prediction of wall-pressure fluctuation in turbulent flows with an immersed boundary method

The objective of this paper is to assess the accuracy and efficiency of the immersed boundary (IB) method to predict the wall pressure fluctuations in turbulent flows, where the flow dynamics in the near-wall region is fundamental to correctly predict the overall flow. The present approach achieves sufficient accuracy at the immersed boundary and overcomes deficiencies in previous IB methods by introducing additional constraints – a compatibility for the interpolated velocity boundary condition related to mass conservation and the formal decoupling of the pressure on this surfaces. The immersed boundary-approximated domain method (IB-ADM) developed in the present study satisfies these conditions with an inexpensive computational overhead. The IB-ADM correctly predicts the near-wall velocity, pressure and scalar fields in several example problems, including flows around a very thin solid object for which incorrect results were obtained with previous IB methods. In order to have sufficient near-wall mesh resolution for LES and DNS computations, the present approach uses local mesh refinement. The present method has been also successfully applied to computation of the wall-pressure space–time correlation in DNS of turbulent channel flow on grids not aligned with the boundaries. When applied to a turbulent flow around an airfoil, the computed flow statistics – the mean/RMS flow field and power spectra of the wall pressure – are in good agreement with experiment.     

近壁区湍流脉动压力相关项的理论模型

提出在湍流边界层近壁区采用三维波的理论模型描述湍流相干结构,根据理论模型计算了Ｒｅｙｎｏｌｄｓ应力输运方程中的脉动速度与脉动压力梯度的相关项,理论计算结果与直接数值模拟（ＤＮＳ）符合很好。表明该理论方法不仅有益于对湍流机制的了解,而且可能为湍流的近壁模型化开辟一条新的途径。     

Flame/flow dynamics at the piston surface of an IC engine measured by high-speed PLIF and PTV

Resolving fluid transport at engine surfaces is required to predict transient heat loss, which is becoming increasingly important for the development of high-efficiency internal combustion engines (ICE). The limited number of available investigations have focused on non-reacting flows near engine surfaces, while this work focuses on the near-wall flow-field dynamics in response to a propagating flame front. Flow-field and flame distributions were measured simultaneously at kHz repetition rates using particle tracking velocimetry (PTV) and planar laser induced fluorescence (PLIF) of sulfur dioxide (SO₂). Measurements were performed near the piston surface of an optically accessible engine operating at 800?rpm with homogeneous, stoichiometric isooctane-air mixtures. High-speed measurements reveal a strong interdependency between near-wall flow and flame development which also influences subsequent combustion. A conditional analysis is performed to analyze flame/flow dynamics at the piston surface for cycles with ‘weak’ and ‘strong’ flow velocities parallel to the surface. Faster flame propagation associated with higher velocities before ignition demonstrates a stronger flow acceleration ahead of the flame. Flow acceleration associated with an advancing flame front is a transient feature that strongly influences boundary layer development. The distance from the wall to 75% maximum velocity (δ₇₅) is analyzed to compare boundary layer development between fired and motored datasets. Decreases in δ₇₅ are strongly related to flow acceleration produced by an approaching flame front. Measurements reveal strong deviations of the boundary layer flow between fired and motored datasets, emphasizing the need to consider transient flow behavior when modeling boundary layer physics for reacting flows.     

平板湍流边界层瞬时摩擦阻力的光学测量和统计分析

采用近壁粒子图像测速（particle image velocimetry,PIV）技术实现了中低Reynolds数光滑平板湍流边界层瞬时摩擦阻力的测量.发展了单行互相关算法和迭代拟合技术估算瞬时摩擦阻力,其法向空间分辨率可达到2~4 pixel.作为对比,同时分析了相似Reynolds数范围的直接数值模拟数据.统计结果表明:摩擦阻力的脉动强度随Reynolds数升高呈现对数增长趋势,证实了外区大/超大尺度结构对壁面的影响.谱分析结果表明近壁区的低速条带结构主导着摩擦阻力的多尺度脉动特性,外区大/超大尺度结构对摩擦阻力的印迹作用较小,其主要通过调制作用实现对摩擦阻力的影响,这一结论可以从瞬时摩擦阻力的偏度以及概率密度函数曲线具有Reynolds数不变性得到进一步证实.      

近壁区理论耗散率k-ε模型的研究

提出在湍流边界层近壁区采用共振三波的理论模型描述湍流相干结构,根据理论模型计算了ε的分布。并且在传统k-ε模式基础上依照理论ε值计算了平均速度分布。在粘性作用层理论值与直接数值模拟符合很好。表明该理论方法不仅有益于对湍流机制的了解,而且可能为湍流的近壁模型化开辟一条新的途径。     

Turbulent boundary layer on a body of revolution with periodic blowing/suction

The effect of periodic blowing/suction on characteristics of a turbulent boundary layer formed on an axisymmetric body of revolution in a nominally gradientless incompressible flow is studied experimentally. The Reynolds number based on the momentum thickness at the location of an annular slot for blowing/suction is 1176. The dimensionless slot width in the wall units is 68. It is demonstrated that blowing/suction aimed at controlling the boundary-layer flow is a fairly effective method for controlling the near-wall turbulence structure and ensures a certain gain in friction drag over the initial configuration (the maximum gain reaches 25–30 %).     

Effect of surface roughness element on near wall turbulence with zero-pressure gradient

In the present paper,we present an investigation on the effect of roughness elements onto near-wall kinematics of a zeropressure-gradient turbulent boundary layer.An array of spanwisely-aligned cylindrical roughness elements was attached to the wall surface to regulate the near-wall low-speed streaky structures.With both qualitative visualization and quantitative measurement,we found that the regularization only occurs in the region below the height of the roughness elements.Statistical analysis on the probability distribution of the streak spanwise spacing showed that the mean spanwise streak spacing is dominated by the roughness elements;however,the latter's effect is in competition with the intrinsic streak generation mechanisms of smooth wall turbulence.Below the top of the roughness elements,local streamwise turbulent fluctuation intensity can be reduced by about 10%.We used POD analysis to depict such regularization effect in terms of near-wall structure modulation.We further found that if the spanwise spacing of roughness elements increased to be larger than the mean streak spacing in the smooth wall turbulence,there is no streak-regularization effect in the buffer region,so that the near-wall streamwise turbulent fluctuation intensity doesn't reduce.     

Head-on quenching of laminar premixed methane flames diluted with hot combustion products

Transient head-on quenching of laminar premixed methane flames diluted with hot combustion products is analyzed using full-chemistry 1D DNS. The impact of the dilution level, pressure and wall temperature on carbon monoxide (CO) emissions is investigated. Increasing dilution level and pressure reduce peak average near-wall CO concentrations, and reduce the near-wall CO reduction rate. However, the peak average near-wall CO and near-wall CO reduction rate increase with increasing wall temperature. Analysis of the species transport budget for CO near the wall before, during and after quenching indicates that there are conditions where diffusion is the dominant transport term. As a consequence, it may be possible to model the near-wall CO using only the integrated diffusion term within certain spatial regions. Dilution increases the size of these regions, whereas increasing pressure reduces this size.     

High-order non-uniform grid schemes for numerical simulation of hypersonic boundary-layer stability and transition

The direct numerical simulation of receptivity, instability and transition of hypersonic boundary layers requires high-order accurate schemes because lower-order schemes do not have an adequate accuracy level to compute the large range of time and length scales in such flow fields. The main limiting factor in the application of high-order schemes to practical boundary-layer flow problems is the numerical instability of high-order boundary closure schemes on the wall. This paper presents a family of high-order non-uniform grid finite difference schemes with stable boundary closures for the direct numerical simulation of hypersonic boundary-layer transition. By using an appropriate grid stretching, and clustering grid points near the boundary, high-order schemes with stable boundary closures can be obtained. The order of the schemes ranges from first-order at the lowest, to the global spectral collocation method at the highest. The accuracy and stability of the new high-order numerical schemes is tested by numerical simulations of the linear wave equation and two-dimensional incompressible flat plate boundary layer flows. The high-order non-uniform-grid schemes (up to the 11th-order) are subsequently applied for the simulation of the receptivity of a hypersonic boundary layer to free stream disturbances over a blunt leading edge. The steady and unsteady results show that the new high-order schemes are stable and are able to produce high accuracy for computations of the nonlinear two-dimensional Navier–Stokes equations for the wall bounded supersonic flow.     

Effects of low-temperature chemistry on the wall heat flux in HCCI combustion

Direct numerical simulations of homogeneous charge compression ignition combustion are performed to investigate the behaviour of the wall heat flux, Φ, under engine relevant conditions. In laminar conditions, there are four distinctive stages where Φ evolution is affected by low-temperature chemistry (LTC), resulting in multiple local maxima with a lagged maximum value in Φ evolution. These effects are also observed in turbulence conditions locally. However, they no longer appear in the mean Φ evolution clearly, although some weak non-monotonicity in Φ due to the LTC are observed. The locality of the LTC effects may need to be addressed for near-wall pollutant prediction in future.     

Simulation of viscous flows with undulatory boundaries. Part I: Basic solver

A numerical method for the simulation of viscous flows with undulatory walls and free surfaces is presented. The simulation domain is discretized by a boundary-fitted and time-dependent grid. The Navier–Stokes equations, subject to fully nonlinear kinematic and dynamic boundary conditions at the free surface and no-slip boundary condition at the wall, are simulated by a hybrid pseudo-spectral and finite difference method in space and a semi-implicit fractional-step method in time. The performance of the method is demonstrated by a series of test cases including flows over wavy boundaries, various surface waves, and interaction between vortices and free surfaces. Validation by convergence test and extensive comparisons with previous theoretical, experimental, and numerical studies indicate the accuracy and efficiency of the method. Finally, a simulation example of turbulence and free surface interaction is presented. Results show that the rich features of the free surface such as surface waves, splats, anti-splats, dimples, and scars are captured accurately. Characteristic vortical structures and variation of turbulence statistics in the near-surface region are also elucidated.     

Development of an algebraic wall heat transfer model for LES in IC engines using DNS data

This paper presents a novel algebraic wall-modeled large-eddy simulation (WMLES) approach for wall heat transfer (WHT) in internal combustion engines (ICE) using recent high-fidelity simulation data from two real ICE and a flame-wall interaction (FWI) setup. The model formulation is based on intuitive arguments rather than simplified forms of near-wall governing equations. Input information from the two wall-normal wall-adjacent nodes is used, facilitating the interpretation of the local state of the thermal boundary layer (TBL). With filtered direct numerical simulation (DNS) data (i.e. a ‘perfect’ LES), model performance is evaluated locally at different near-wall resolutions. The proposed model is compared to a widely used wall function (WF) approach and to a data-driven model.     

Frequency Response of Near-Wall Coherent Structures to Localized Periodic Blowing and Suction in Turbulent Boundary Layer

We experimentally investigate the frequency response of near-wall coherent structures to localized periodic blow- ing and suction through a spanwise slot in a turbulent boundary layer by changing the frequency of periodic disturbance at similar velocities of free stream. The effects of blowing and suction disturbance on energy redistri- bution, turbulent intensity U^＋ rums over y^＋ and waveforms of phase-averaged velocity during sweeping process are respectively discussed under three frequencies of periodic blowing and suction in near-wall region of turbulent boundary layer, compared with those in a standard turbulent boundary layer. The most effective disturbance frequency is figured out in this system.     

Error analysis and correction for Lattice Boltzmann simulated flow conductance in capillaries of different shapes and alignments

We study the relative error in conductance calculations, for simulated flow of a single component single phase fluid through a capillary in three dimensions, by the Lattice Boltzmann (LB) method with bounce-back boundary conditions. The relative error with respect to analytical results for capillary cross-sections of circular, triangular and square shapes are calculated as a function of the cross-section diameter, a, and for different alignment of the cross-section relative to the underlying lattice grid. It is shown, when the shapes are not aligned perfectly to the lattice, that the relative error decreases systematically with the size, a, as ～1/a when a is evaluated by mapping the computed cross-sectional area, in terms of the enclosed number of grid points, to the respective geometrical shapes concerned. For perfectly aligned geometries, viz. the square capillary aligned to the LB lattice grid or rotated with its side along the diagonal of the LB grid, the relative error decreases as ～1/a². A simple method is suggested to locate the boundary wall depending on its orientation relative to the grid, such that the exact conductance of the new shape matches the LB computed conductance.     

A representation of curved boundaries for the solution of the Navier–Stokes equations on a staggered three-dimensional Cartesian grid

A method is presented for representing curved boundaries for the solution of the Navier–Stokes equations on a non-uniform, staggered, three-dimensional Cartesian grid. The approach involves truncating the Cartesian cells at the boundary surface to create new cells which conform to the shape of the surface. We discuss in some detail the problems unique to the development of a cut cell method on a staggered grid. Methods for calculating the fluxes through the boundary cell faces, for representing pressure forces and for calculating the wall shear stress are derived and it is verified that the new scheme retains second-order accuracy in space. In addition, a novel “cell-linking” method is developed which overcomes problems associated with the creation of small cells while avoiding the complexities involved with other cell-merging approaches. Techniques are presented for generating the geometric information required for the scheme based on the representation of the boundaries as quadric surfaces. The new method is tested for flow through a channel placed oblique to the grid and flow past a cylinder at Re=40 and is shown to give significant improvement over a staircase boundary formulation. Finally, it is used to calculate unsteady flow past a hemispheric protuberance on a plate at a Reynolds number of 800. Good agreement is obtained with experimental results for this flow.     

嵌套网格技术中的Collar网格和虚拟网格方法

针对嵌套网格技术中的结合部问题,提出了Collar网格和虚拟网格方法.用双曲型微分方程生成的处于结合部的有两个边界分别处于不同固定曲面上的Collar网格,在保证计算网格的生成方便快捷而且网格质量高的前提下,解决了为物体结合部的内外边界点提供有效插值单元的问题.虚拟网格为紧贴物面的面网格,它的作用是将物面边界条件传递给其它网格的边界面,而其本身不作流场计算.计算实践表明,将Collar网格和虚拟网格结合起来应用在嵌套网格技术中能保证几何外形不发生变化,有效地处理各种复杂组合体外形的结合部问题.     

Generalized wall functions for turbulent flows with strong adverse pressure gradient

The generalized wall functions for turbulent flows with strong adverse pressure gradients are derived on the basis of the asymptotic theory of near-wall turbulence. The generalized wall functions have a correct asymptotic behavior in the limit of zero friction velocity and can be applied to computations of flows under a strong adverse pressure gradient and with separation or reattachment. Calculations of a turbulent boundary layer in a strong adverse pressure gradient with the aid of the developed modified k-ɛ model of turbulence and comparison with the experimental data validate the advantages of the generalized wall functions over traditional wall functions based on the logarithmic law of the wall.     

Accurate measurement of wall skin friction by single-pixel ensemble correlation

The present work deals with accurately estimating wall-skin friction from near-wall mean velocity by means of PIV measurement.The estimation accuracy relies on the spatial resolution and the precision of the resolved velocity profile inside the viscous sublayer,which is a big challenge for conventional window-based correlation method(K?hler C J,et al.Exp Fluids,2012,52:1641–1656).With the help of single-pixel ensemble correlation,the ensemble-averaged velocity vector can be resolved at significant spatial resolution,thus improving the measurement accuracy.To demonstrate the feasibility of this single-pixel ensemble correlation method,we first study the velocity estimation precision in a case of steady near-wall flow.Synthetic particle images are used to investigate the effect of different image parameters.It is found that the velocity RMS-uncertainty level of the single-pixel ensemble correlation method can be equivalent to the conventional window correlation method once the effective particle number used for the ensemble correlation is large enough.Furthermore,a canonical turbulent boundary layer is synthetically simulated based on velocity statistics resolved by previous Direct Numerical Simulation(DNS)work(Schlatter P,et al.J Fluid Mech,2010,659:116–126).The relative error of wall skin friction coefficient is shown to be one-order smaller than that of the window correlation method.And the optimization strategy to further minimize the measurement uncertainty is discussed in the last part.     

Near-wall conductivity effect under a space-charge-saturated sheath in the Hall thruster

In this paper, we adopt the modified Morozov secondary electron emission model to investigate the influence of the characteristic of a space-charge-saturated sheath near the insulated wall of the Hall thruster on the near-wall conductivity, by the method of two-dimensional (2D) particle simulation (2D+3V). The results show that due to the sharp increase of collision frequency between the electrons and the wall under the space-charge-saturated sheath, the near-wall transport current under this sheath is remarkably higher than that under a classical sheath, and equals the near-wall transport current under a spatially oscillating sheath in order of magnitude. However, the transport currents under a space-charge-saturated sheath and a spatially oscillating sheath are different in mechanism, causing different current density distributions under the above two sheaths, and a great influence of channel width on the near-wall transport current under a space-charge-saturated sheath.     

边界条件对对流扩散方程数值稳定性的影响

本文利用数值计算方法对采用均分网格的一维线性无源的对流－扩散方程在各种边界条件下的稳定性进行了分析,燕求出了不同边界条件下一维问题的中心差分和ＱＵＩＣＫ格式的临界网格Ｐｅｃｌｅｔ数。指出按现有方法得出的临界网格Ｐｅｃｌｅｔ数是判别差分格式对流数值稳定性的最苛刻的要求。对中心差分和ＱＵＩＣＫ格式,除两点边值问题以外的其它边界条件下的稳定性范围均不小于或远远大于两点边值问题的稳定性范围。通过计算还得出了格式的数值稳定性主要取决于计算区域下游侧的边界条件类型而与计算区域上游侧的边界条件类型无关的结论。