Streamline Tracing Method Research Articles

Stress field-aware infill toolpath generation for additive manufacturing of continuous fiber reinforced polymer composites

The infill toolpath utilized in continuous fiber reinforced polymer composites via additive manufacturing (CFRPCs-AM) significantly influences the mechanical performance of printed structures. However, existing infill toolpath for CFRPCs-AM are primarily designed for 2D planar structures and do not account for 3D shell structures with complex shapes or load path dependent characteristics. To address these limitations, this paper proposes an explicit streamline tracing method to convert the stress field into adaptive infill toolpaths for CFRPCs-AM. The method leverages principal stress direction and value fields to control toolpath density and distribution while considering the minimum allowable bead width constraint. Additionally, the geodesic distance is employed to precisely represent the distance between adjacent infill toolpaths on shell structures. Experimental validation on 2D and 3D complex structures under varying conditions demonstrates the effectiveness of the proposed method, which significantly improves stiffness and strength by 200–300% compared to traditional uniform toolpaths for CFRPCs-AM.

Hybrid Mimetic Finite Difference and Streamline Methods for Numerical Simulation of Two-phase Flow in Fractured Reservoirs

In this work, we present a novel numerical formulation for efficiently modeling two-phase flow in fractured reservoirs. The novel formulation is developed by hybridizing mimetic finite difference and streamline (MFD-SL) methods, in which mimetic finite difference (MFD) is employed to discretize the pressure equation, and the streamline (SL) method is adopted to solve the saturation equation along 1D streamlines. The hybrid formulation is implemented on discrete fracture model (DFM) and is operated in an IMPES-like manner. A simple and practical streamline tracing method is developed on 2D triangular and 3D tetrahedral grids that are commonly implemented in the DFM framework. We benchmark the hybrid MFD-SL formulation with others using various cases with different complexity. Results show the proposed approach could achieve promising results yet with lower computation costs compared to other classical formulations. These achievements benefit from utilizing streamline tracing, which significantly alleviates the numerical diffusion error and improves the computation efficiency. This work, for the first time, incorporates hybrid MFD-SL formulation into DFM in case of triangular and tetrahedral grids and has great potential to be deployed on reservoir-scale simulation workflow.

An integration method based on a novel combined flow for aerodynamic configuration of strutjet engine

In this paper a novel design method of aerodynamic configuration is proposed to integrate forebody, strut and inlet for strutjet engine, and a model at design point of Mach number 6 is generated to investigate the aerodynamic performance by both simulations and experiments. The basic flow field employed by proposed method is a combined flow named IBB, which is combined by Internal Conical Flow A (ICFA), truncated Busemann flow I (BI) for external section, and truncated Busemann flow II (BII) for internal section. The model configuration is generated by streamline tracing method from basic flow field, in which the forebody section is traced from ICFA and BI flows, and the inlet as well as strut section is traced from BII flow. The simulations in Mach number 4, 5, and 6 demonstrate uniform starting flow fields with relatively high total pressure recovery, which agree well with experiments in wind tunnel. Additionally, in low Mach number cases, this inlet could start at Mach number 3 while it is unstarted at Mach number 2.7; in high Mach number cases, a uniform flow could still exist in Mach number 6.5 while a relatively strong shock wave boundary layer interaction is found in cowl area of Mach number 7 case, indicating the inlet designed by proposed method works in a relatively wide Mach number range.

High-order streamline simulation and macro-scale visualization experimental studies on waterflooding under given pressure boundaries

In this paper, a new high-order streamline simulation method with a known pressure boundary is proposed. It extends the Riemann approach along streamlines from constant flow rate boundaries to given pressure boundaries. This method computes the varied flow resistance of streamtube directly by using the velocity and time-of-flight of its central streamline, and improves the simulation accuracy by applying a high-order streamline tracing method. Simultaneously, a series of macro-model visualization experiments are performed to study waterflooding processes under given pressure boundaries. The new streamline method is independently validated by history matching and direct modelling of the experiments. Finally, the capillary effects at the water front are quantified as a function of time and space with the assists of streamline simulations.

Three-Dimensional Streamline Tracing Method over Tetrahedral Domains

Getting a clear understanding of the fluid velocity field in underground porous media is critical to various engineering applications, such as oil/gas reservoirs, CO2 sequestration, groundwater, etc. As an effective visualization tool and efficient transport behaviors solution algorithm, the streamline-based method was improved significantly by numerous studies conducted in the last couple of decades. However, the implementation of streamline simulation is still challenging while working with Finite Element Method (FEM) over 3D tetrahedral domains, where the mass conservation is not guaranteed. Considering the increased computational cost to enforce mass conservation in FEM and additional complexity, a new three-dimensional streamline tracing algorithm is presented that only relies on the velocity vector of a flow field on each vertex of a tetrahedron in a 3D unstructured mesh system. Owning to the shape functions and transformation equations between the master element and actual element, the exit coordinate leaving a tetrahedral element can be determined effectively. As a result, Time of Flight (TOF), the coordinate variable along each streamline, can be calculated accurately and efficiently because that the analytical solution depicting the trajectory in Master Element is deduced. The presented streamline-based method is tested under FEniCS, a programming framework for FEM, which eases the implementation and further development of the presented method.

Novel integration methodology for an inward turning waverider forebody/inlet

In this study, an inward turning waverider forebody/inlet axisymmetric reference flow model with a conical leading-edge shock wave was designed based on the method of characteristics. The design eliminates the lip shock wave at the shoulder point. Based on the reference flow model, a novel integrated design method for an inward turning waverider forebody/inlet is proposed. The streamline tracing method and related technologies were used to generate the integrated configuration in the reference flow model. During the design process, the inward turning inlet was divided into an upper and a lower surface. After the formation of these surfaces, the front external surface and the lip external surface were simultaneously generated. Finally, an integrated configuration was formed with these four generated surfaces and a base plane. An analysis of the formed configuration was carried out using numerical simulation software, which verified the correctness and feasibility of the method. The conclusions drawn from the research indicate that the integrated design method is feasible and effective.

An airframe/inlet integrated full-waverider vehicle design using as upgraded aerodynamic method

ABSTRACTWith the aims of overcoming the limitations of the existing basic flow model derived from an axisymmetric generating body and extending the aerodynamic design method of the airframe/inlet integrated waverider vehicle, this study develops an upgraded basic flow model derived from an axisymmetric shock wave. It then upgrades the design method for airframe/inlet integration of an air-breathing hypersonic waverider vehicle, which is termed the ‘full-waverider vehicle’ in this study. In this paper, first, the design principle and method for the upgraded full-waverider vehicle derived from an axisymmetric basic shock wave are described in detail. Second, an upgraded basic flow model that accounts for both internal and external flows is derived from an axisymmetric basic shock wave by use of both the streamline tracing method and the method of characteristics (MOC). Third, the upgraded full-waverider vehicle is developed from the upgraded basic flow model by the streamline tracing method. Fourth, the design theories and methodologies of both the upgraded basic flow model and the upgraded full-waverider vehicle are validated by a numerical computation method. Finally, the aerodynamic performances and viscous effects of both the upgraded basic flow model and the upgraded full-waverider vehicle are analysed by numerical computation. The obtained results show that the upgraded basic flow model and aerodynamic design method are effective for the design of the airframe/inlet integration of an air-breathing hypersonic waverider vehicle.

Comparison between Methods of Generation of Waveriders Derived from Streamline Tracing and Simplified Method

Waverider with a high lift-to-drag ratio has drawn an ever increasing attention. Usually, waverider is obtained by tracing streamline. A simplified generation method of waverider is introduced in the present paper named geometric relations method. Three groups of cone-derived waverider configuration, respectively, based on the geometric relations method and the streamline tracing method are generated for the comparisons of the shape factors, inviscid aerodynamic characteristics, and flow field structures by investigating the numerical simulation results. The results show that the effect of the Mach number and the shock angle on the differences caused by the two methods are not significantly different. While the volumetric efficiency of the waverider configuration based on the geometric relations method is larger than those based on the streamline tracing, the inviscid lift-to-drag ratio of the former is less than the latter. Although the geometric relations method is much easier than the streamline tracing method, the simplified method reduces the aerodynamic performance of the waverider configuration.

Strain gradient plasticity based finite element analysis of ultra-fine wire drawing process

Steady-state rigid-plastic finite element analysis coupled with strain gradient plasticity theory has been performed to examine the size effect of material on its plastic deformation behavior and find an optimal semi-cone angle of die which minimizes the drawing energy in the ultra-fine wire drawing process. A stream-line tracing method was adopted to calculate strain component at each element and a strain surface function was introduced to compute the equivalent strain gradient of each element. Introduction of this function enables us to use an established FE code without renewal of its main structure. Hence, the constitutive equation in FE formulation is changed to couple the strain gradient plasticity. A series of FE simulation reveals that significant differences in drawing stress are observed when material size approaches its intrinsic material length. When the strain gradient plasticity theory is reflected on the steady-state FE analysis, the optimal semi-cone angle of the die is reduced by 30%. The variation of optimal semi-cone angle is attributable to considerable increment of homogeneous deformation when the material size reaches its intrinsic material length.

Tracing Streamlines on Unstructured Grids From Finite Volume Discretizations

Summary The accuracy of streamline reservoir simulations depends strongly on the quality of the velocity field and the accuracy of the streamline tracing method. For problems described on complex grids (e.g., corner-point geometry or fully unstructured grids) with full-tensor permeabilities, advanced discretization methods, such as the family of multipoint flux approximation (MPFA) schemes, are necessary to obtain an accurate representation of the fluxes across control volume faces. These fluxes are then interpolated to define the velocity field within each control volume, which is then used to trace the streamlines. Existing methods for the interpolation of the velocity field and integration of the streamlines do not preserve the accuracy of the fluxes computed by MPFA discretizations. Here we propose a method for the reconstruction of the velocity field with high-order accuracy from the fluxes provided by MPFA discretization schemes. This reconstruction relies on a correspondence between the MPFA fluxes and the degrees of freedom of a mixed finite-element method (MFEM) based on the first-order Brezzi-Douglas-Marini space. This link between the finite-volume and finite-element methods allows the use of flux reconstruction and streamline tracing techniques developed previously by the authors for mixed finite elements. After a detailed description of our streamline tracing method, we study its accuracy and efficiency using challenging test cases.

Robust streamline tracing for the simulation of porous media flow on general triangular and quadrilateral grids

Streamline methods for subsurface-flow simulation have received renewed attention as fast alternatives to traditional finite volume or finite element methods. Key aspects of streamline simulation are the accurate tracing of streamlines and the computation of travel time along individual streamlines. In this paper, we propose a new streamline tracing framework that enables the extension of streamline methods to unstructured grids composed of triangular or quadrilateral elements and populated with heterogeneous full-tensor coefficients. The proposed method is based on the mathematical framework of mixed finite element methods, which provides approximations of the velocity field that are especially suitable for streamline tracing. We identify and implement two classes of velocity spaces: the lowest-order Raviart–Thomas space (low-order tracing) and the Brezzi–Douglas–Marini space of order one (high-order tracing), both on triangles and quadrilaterals. We discuss the implementation of the streamline tracing method in detail, and we investigate the performance of the proposed tracing strategy by means of carefully designed test cases. We conclude that, for the same computational cost, high-order tracing is more accurate (smaller error in the time-of-flight) and robust (less sensitive to grid distortion) than low-order tracing.