载荷自适应五连杆抽油机的设计计算

介绍了新型载荷自适应五连杆抽油机的结构组成，推导出了载荷自适应五连杆抽油机的运动计算和动力计算的理论公式。以CYJZ10-4．2-53HB型载荷自适应抽油机为计算实例，论述了该五连杆抽油机的性能特点，并与偏置抽油机进行了对比。计算结果表明，在相同的条件下，载荷自适应五连杆抽油机可节电8．65％以上，连杆拉力减少44．94％，减速器峰值扭矩减少16．83％，是一种比较有发展前途的节能抽油机。

Constraine d large-e ddy simulation of turbulent flow over inhomogeneous rough surfaces

In this work we extend the method of the constrained large-eddy simulation(CLES)to simulate the tur-bulent flow over inhomogeneous rough walls.In the original concept of CLES,the subgrid-scale(SGS)stress is constrained so that the mean part and the fluctuation part of the SGS stress can be modelled separately to improve the accuracy of the simulation result.Here in the simulation of the rough-wall flows,we propose to interpret the extra stress terms in the CLES formulation as the roughness-induced stress so that the roughness inhomogeneity can be incorporated by modifying the formulation of the constrained SGS stress.This is examined with the simulations of the channel flow with the spanwise alternating high/low roughness strips.Then the CLES method is employed to investigate the temporal response of the turbulence to the change of the wall condition from rough to smooth.We demonstrate that the temporal development of the internal boundary layer is just similar to that in a spatial rough-to-smooth transition process,and the spanwise roughness inhomogeneity has little impact on the transition process.

Recent progress in compressible turbulence

In this paper, we review some recent studies on compressible turbulence conducted by the authors＇ group, which include fundamental studies on compressible isotropic turbulence （CIT） and applied studies on developing a con- strained large eddy simulation （CLES） for wall-bounded turbulence. In the first part, we begin with a newly pro- posed hybrid compact-weighted essentially nonoscillatory （WENO） scheme for a CIT simulation that has been used to construct a systematic database of CIT. Using this database various fundamental properties of compressible turbulence have been examined, including the statistics and scaling of compressible modes, the shocklet-turbulence interac- tion, the effect of local compressibility on small scales, the kinetic energy cascade, and some preliminary results from a Lagrangian point of view. In the second part, the idea and for- mulas of the CLES are reviewed, followed by the validations of CLES and some applications in compressible engineering problems.

Computing mean fields with known Reynolds stresses at steady state

With the rising of modern data science,data-driven turbulence modeling with the aid of machine learning algorithms is becoming a new promising field.Many approaches are able to achieve better Reynolds stress prediction,with much lower modeling error(∈_(M)),than traditional Reynolds-averaged Navier-Stokes(RANS)models,but they still suffer from numerical error and stability issues when the mean velocity fields are estimated by solving RANS equations with the predicted Reynolds stresses.This fact illustrates that the error of solving the RANS equations(∈_(P))is also very important for a RANS simulation.In the present work,the error∈_(P)is studied separately by using the Reynolds stresses obtained from direct numerical simulation(DNS)/highly resolved large-eddy simulation to minimize the modeling error∈_(M),and the sources of∈_(P)are derived mathematically.For the implementations with known Reynolds stresses solely,we suggest to run an auxiliary RANS simulation to make a first guess onν_(t)^(*)and S_(ij)^(0).With around 10 iterations,the error of the streamwise velocity component could be reduced by about one-order of magnitude in flow over periodic hills.The present work is not to develop a new RANS model,but to clarify the facts that obtaining mean field with known Reynolds stresses is nontrivial and that the nonlinear part of the Reynolds stresses is very important in flow problems with separations.The proposed approach to reduce∈_(P)may be very useful for the a posteriori applications of the data-driven turbulence models.

Capturing the baroclinic effect in non-Boussinesq gravity currents

Direct numerical simulations of two-dimensional gravity currents with small and medium density variations are performed using different non-Boussinesq buoyancy approximations. Taking the full low-Machnumber approximation as the reference, the accuracy of several buoyancy terms are examined. It is found that all considered buoyancy terms performed well in the cases with small density variation. In the cases with medium density variation, the classical gravitational Boussinesq’s buoyancy term showed the lack of accuracy, and a simple correction did not make any improvement. In contrast, the recently introduced second-order buoyancy term showed a significantly higher accuracy. The present results and our previous derivations indicate that simple algebraic buoyancy approximations extended from the Boussinesq’s gravitational buoyancy are unlikely to achieve an accuracy beyond first order. Instead, it seems necessary to solve at least one extra Poisson equation for buoyancy terms to capture the higher-order baroclinic effect. An approximate analysis is also provided to show the leading term of the non-Boussinesq effect corresponding to gravity.

Dissipation function in turbulent plane Poiseuille and Couette flows subject to spanwise rotations

The dissipation function in turbulent plane Poiseuille flows(PPFs) and plane Couette flows(PCFs) subject to spanwise rotations is analyzed. It is found that, in the PCFs without system rotations, the mean part is constant while the fluctuation part follows a logarithmic law, resulting in a similar logarithmic skin friction law as PPFs.However, if the flow system rotates in the spanwise direction, no obvious dependence on the rotation number can be evaluated. In the PPFs with rotations, the dissipation function shows an increase with the rotation number, while in the PCFs with rotations,when the rotation number increases, the dissipation function first decreases and then increases.

Modeling Reynolds stress anisotropy invariants via machine learning

The presentation and modeling of turbulence anisotropy are crucial for studying large-scale turbulence structures and constructing turbulence models.However,accurately capturing anisotropic Reynolds stresses often relies on expensive direct numerical simulations(DNS).Recently,a hot topic in data-driven turbulence modeling is how to acquire accurate Reynolds stresses by the Reynolds-averaged Navier-Stokes(RANS)simulation and a limited amount of data from DNS.Many existing studies use mean flow characteristics as the input features of machine learning models to predict high-fidelity Reynolds stresses,but these approaches still lack robust generalization capabilities.In this paper,a deep neural network(DNN)is employed to build a model,mapping from tensor invariants of RANS mean flow features to the anisotropy invariants of high-fidelity Reynolds stresses.From the aspects of tensor analysis and input-output feature design,we try to enhance the generalization of the model while preserving invariance.A functional framework of Reynolds stress anisotropy invariants is derived theoretically.Complete irreducible invariants are then constructed from a tensor group,serving as alternative input features for DNN.Additionally,we propose a feature selection method based on the Fourier transform of periodic flows.The results demonstrate that the data-driven model achieves a high level of accuracy in predicting turbulence anisotropy of flows over periodic hills and converging-diverging channels.Moreover,the well-trained model exhibits strong generalization capabilities concerning various shapes and higher Reynolds numbers.This approach can also provide valuable insights for feature selection and data generation for data-driven turbulence models.

Velocity transformation for compressible wall-bounded turbulence——An approach through the mixing length hypothesis

In an endeavor to establish a connection between the mean velocity profile in compressible wall-bounded turbulence and its incompressible analogue,a refined version of the Trettel and Larsson's(TL)transformation is systematically derived and rigorously assessed across diverse flow scenarios.Incorporating the recently proposed intrinsic compressibility effects and modeling the multi-layer structure of mixing lengths,the proposed transformation demonstrates exceptional performance in collapsing 57canonical flow cases,including cooled channel and pipe flows,channel flows with pseudo heat sources,as well as adiabatic and diabatic boundary layer flows.Furthermore,the transformation seamlessly extends to low Reynolds number cooled channel and pipe flows,achieving a level of accuracy unparalleled by other transformations in the current state-of-the-art.

交错扁球颗粒链在方形管道中的动态自组装行为

本文采用多松弛格子Boltzmann模型数值研究了三维方管中交错排列的扁球颗粒的动态自组装行为,着重考虑了雷诺数(Re)、平均长度分数(<L_(f>)和颗粒纵横比(AR)对整个迁移过程、分布模态和平均轴向颗粒间距(d_(i)/D)_(umi)的影响.这里颗粒AR是通过改变扁球颗粒的极轴半径来调节,相应的赤道半径保持不变.交错扁球颗粒链的整个形成过程包括向平衡位置的惯性迁移和在流向方向上的动态自组装行为.目前结果表明分布模态和交错扁球颗粒链的(d_(i)/D)_(umi)明显依赖于(L_(f))和Re.在当前研究的参数范围内,在中等(L_(f))下高Re或高(L_(f))时,颗粒链呈现连续模态.此时,所有轴向颗粒间距达到相同的值.随着<L_(f))增加,相应的(d_(i)/D)_(umi)减少.在中等(L_(f))下小Re或低(L_(f))时,颗粒链呈现间断模态。此模态下,(d_(i)/D)_(uni)主要随Re线性增加.此外,当(L_(f))=0.4时,AR从0.5变成0.75或1不会改变颗粒链的模态,即Re≤40时为间断模态,而Re≥60时为连续模态.在间断模态下,(d_(i)/D)_(umi)对AR并没有体现出明显的线性依赖关系.由于旋转直径相同,相同Re下颗粒链的面平衡位置几乎不受AR的影响.

Numerical investigation of plane Couette flow with weak spanwise rotation

Direct numerical simulation of rotating plane Couette flow(RPCF) at Re_w= 1300 and Ro = 0.02 was performed with different mesh resolutions and different sizes of computation domain. Our results showed that a grid resolution in wall units with ?x^+=8.51, ?z^+= 4.26, ?y^+|_(min)= 0.0873 and ?y^+|_(max)= 3.89 is fine enough to simulate the problem at the present parameters. The streamwise length Lxand spanwise length Lzof the computational box have different impacts on the flow statistics, where the statistics were converged if Lxis longer than 8πh, while no converged results were obtained for different Lz. More importantly,our results with very long simulation time showed that a state transition would happen if L_x≥ 8πh, from a state with four pairs of roll cells to a state with three pairs of roll cells with L_z= 6πh. Each state could survive for more than 1500 h/U_w, and the flow statistics were different.

On skin friction in wall-bounded turbulence

In this paper,we derive mathematical formulas for the skin friction coefficient in wall-bounded turbulence based on the Reynolds averaged streamwise momentum equation and the total stress.Specifically,with a theoretical or empirical relation of the total stress,the skin friction coefficient is expressed in terms of the mean velocity and the Reynolds shear stress in an arbitrary wall-normal region[h〇,h\].The formulas are validated using direct numerical simulation data of turbulent channel and boundary layer flows,and the results show that our formulas estimate the skin friction coefficient very accurately with an error less than 2%.The present integral formula can be used to determine the skin friction in turbulent channel and boundary layer flows at high Reynolds numbers where the near-wall statistics are very difficult to measure accurately.

Practical framework for data-driven RANSmodeling with data augmentation

Inspired by the iterative procedure of computing mean fields with known Reynolds stresses(Guo et al.,Theor Appl Mech Lett,2021),we proposed a way to achieve data augmentation by utilizing the intermediate mean fields after proper selections.We also proposed modifications to the Tensor Basis Neural Network(Ling et al.,J Fluid Mech,2016)model.With the modification of the learning targets and the inclusions of wall distance and logarithm of normalized eddy viscosity in the model inputs,the modified version of the model with augmented training datasets shows better performance on Reynolds stress predictions for two dimensional incompressible flow over periodic hills under different geometries.Furthermore,better propagated mean velocity fields can be achieved,showing better agreements with the direct numerical simulations(DNS)results.

Constrained Large-Eddy Simulation of Compressible Flow Past a Circular Cylinder

Compressible flow past a circular cylinder at an inflow Reynolds number of 2×105 is numerically investigated by using a constrained large-eddy simulation(CLES)technique.Numerical simulation with adiabatic wall boundary condition and at a free-stream Mach number of 0.75 is conducted to validate and verify the performance of the present CLES method in predicting separated flows.Some typical and characteristic physical quantities,such as the drag coefficient,the root-mean-square lift fluctuations,the Strouhal number,the pressure and skin friction distributions around the cylinder,etc.are calculated and compared with previously reported experimental data,finer-grid large-eddy simulation(LES)data and those obtained in the present LES and detached-eddy simulation(DES)on coarse grids.It turns out that CLES is superior to DES in predicting such separated flow and that CLES can mimic the intricate shock wave dynamics quite well.Then,the effects of Mach number on the flow patterns and parameters such as the pressure,skin friction and drag coefficients,and the cylinder surface temperature are studied,with Mach number varying from 0.1 to 0.95.Nonmonotonic behaviors of the pressure and skin friction distributions are observed with increasing Mach number and the minimum mean separation angle occurs at a subcritical Mach number of between 0.3 and 0.5.Additionally,the wall temperature effects on the thermodynamic and aerodynamic quantities are explored in a series of simulations using isothermal wall boundary conditions at three different wall temperatures.It is found that the flow separates earlier from the cylinder surface with a longer recirculation length in the wake and a higher pressure coefficient at the rear stagnation point for higher wall temperature.Moreover,the influences of different thermal wall boundary conditions on the flow field are gradually magnified from the front stagnation point to the rear stagnation point.It is inferred that the CLES approach in its current version is a useful and effective tool for simulating wall-bounded compressible turbulent flows with massive separations.

Exact mathematical formulas for wall-heat flux in compressible turbulent channel flows

In this paper,several exact expressions for the mean heat flux at the wall(qw)for the compressible turbulent channel flows are derived by using the internal energy equation or the total energy equation.Two different routes,including the FIK method and the RD method,can be applied.The direct numerical simulation data of compressible channel flows at different Reynolds and Mach numbers verify the correctness of the derived formulas.Discussions related to the different energy equations,and different routes are carried out,and we may arrive at the conclusion that most of the formulas derived in the present work are just mathematical ones and that they generally are lacking in clear physical interpretation in our opinion.They can be used to estimate qw,but might not be suitable for exploring the underlying physics.

Correction to:Practical framework for data-driven RANS modeling with data augmentation

Correction to:Acta Mechanica Sinica(2021)37(12):1750-1758 https://doi.Org/10.1007/s10409-021-01147-2 In the original publication,the last equation in Eq.(8)should be.

Effect of Oscillation Structures on Inertial-Range Intermittence and Topology in Turbulent Field

Using the incompressible isotropic turbulent fields obtained from direct numerical simulation and large-eddy simulation,we studied the statistics of oscillation structures based on local zero-crossings and their relation with inertial-range intermittency for transverse velocity and passive scalar.Our results show that for both the velocity and passive scalar,the local oscillation structures are statistically scaleinvariant at high Reynolds number,and the inertial-range intermittency of the overall flow region is determined by the most intermittent structures characterized by one local zero-crossing.Local flow patterns conditioned on the oscillation structures are characterized by the joint probability density function of the invariants of the filtered velocity gradient tensor at inertial range.We demonstrate that the most intermittent regions for longitudinal velocity tend to lay at the saddle area,while those for the transverse velocity tend to locate at the vortex-dominated area.The connection between the ramp-cliff structures in passive scalar field and the corresponding saddle regions in the velocity field is also verified by the approach of oscillation structure classification.

A CFD-Aided Galerkin Method for Global Linear Instability Analysis

Global linear instability analysis is a powerful tool for the complex flow diagnosis.However,the methods used in the past would generally suffer from some dis-advantages,either the excessive computational resources for the low-order methods or the tedious mathematical derivations for the high-order methods.The present work proposed a CFD-aided Galerkin methodology which combines the merits from both the low-order and high-order methods,where the expansion on proper basis func-tions is preserved to ensure a small matrix size,while the differentials,incompressibility constraints and boundary conditions are realized by applying the low-order linearized Navier-Stokes equation solvers on the basis functions on a fine grid.Several test cases have shown that the new method can get satisfactory results for one-dimensional,two-dimensional and three-dimensional flow problems and also for the problems with complex geometries and boundary conditions.