Streamline Tracing Research Articles

Optimal aerodynamic design of hypersonic inlets by using streamline-tracing techniques

Rectangular-to-Ellipse Shape Transition (REST) inlets are a class of inward turning inlets designed for hypersonic flight. The aerodynamic design of REST inlets involves very complex flows and shock-wave patterns. These inlets are used in highly integrated propulsive systems. Often the design of these inlets may require many geometrical constraints at different cross-section. In present work a design approach for hypersonic inward-turning inlets, adapted for REST inlets, is coupled with a multi-objective optimization procedure. The automated procedure iterates on the parametric representation and on the numerical solution of a base flow from which the REST inlet is generated by using streamline tracing and shape transition algorithms. The typical design problem of optimizing the total pressure recovery and mass flow capture of the inlet is solved by the proposed procedure. The accuracy of the optimal solutions found is discussed and the performances of the designed REST inlets are investigated by means of fully 3-D Euler and 3-D RANS analyses.

Performance of wavecatcher intakes at angles of attack and sideslip

A wavecatcher type scramjet intake, that reduces the Mach number number from 4 to 1.552, is used as the basis for a study of flow starting/unstarting as affected by freestream angles of attack and sideslip. The intake design is based on a morphed streamtube consisting of two conical flow streamlines using streamline tracing and osculating axisymmetric design theory. Intake flow and performance is modeled using the numerical CFD code and the k-ε turbulence model. The intake unstarts at a sideslip angle of 2°, a positive angle of attack of 1°. Both positive angle of attack and sideslip angle have an adverse effect on the startability of the MBus intake. At negative angles, the intake initially unstarts at −5° angle of attack, due to the thickened shear layer induced by the streamwise vortex. Then it re-starts at −8° angle of attack, mainly due to the expansion fan formed at the leading edge, causing the shock wave structures inside the intake to be re-established.

A Vector Field Texture Generation Method without Convolution Calculation

In the LIC algorithm process, symmetrical streamline tracing is used to symmetrically convolve the original values of all the primitive values that pass by to obtain the resulting texture. In this process, streamline tracking and convolution consume a lot of computing resources. To generate more expressive textures for vector fields with less time consumption, a novel method named random increment streamline (RIS) is put forward, which can generate streamline textures without convolution calculations. First, the mesh unit filling preprocessing (MUFP) method is presented to transform an undressed irregular grid into a special kind of regular grid named a “texture pixel”, and the point location and interpolation processes of all sampling points in the texture pixels are calculated before streamline tracking. Second, the random increment streamline method is used to generate line integral convolution style textures without any convolution calculations, thus greatly reducing the algorithm’s time consumption. Third, the vector directions at each point in the static vector field are clearly expressed using the periodic cyclic animation method. Finally, several simplifications of the RIS algorithm are discussed, which help to achieve a better visual effect with faster speed. The programming results show that the method is faster and more applicable than the traditional LIC method and provides clearer expression of the vector field.

Application of Flow Diagnostics to Rapid Production Data Integration in Complex Grids and Dual-Permeability Models

SummaryStreamline-based methods, as repeatedly demonstrated in multiple applications, offer a robust and elegant framework for reconciling high-resolution geologic models with observed field responses. However, significant challenges persist with the application of streamline-based methods in complex grids and dual-permeability media due to the difficulty with streamline tracing in these systems. In this work, we propose a novel and efficient framework that circumvents these challenges by avoiding explicit tracing of streamlines but exploits the inherent desirable features of streamline-based production data integration in high-resolution geologic models.Our approach features the application of flow diagnostics to inverse problems involving the integration of multiphase production data in reservoir models. Here, time-of-flight as well as numerical tracer concentrations for each well, on the basis of a defined flux field, are computed on the native finite-volume grid. The information embedded in these metrics are used in the dynamic definition of stream-bundles and, eventually, in the computation of analytical water arrival-time sensitivities with respect to model properties. This calculation mimics the streamline-derived analytical sensitivity computation used in the well-established generalized travel-time inversion (GTTI) technique but precludes explicit streamline tracing. The reservoir model property field is updated iteratively by solving the LSQR (sparse least-squares with QR factorization) system composed of the computed analytical sensitivity and the optimal water travel-time shift, augmented with regularization and smoothness constraints.The power and efficacy of our approach are demonstrated using synthetic model and field applications. We first validate our approach by benchmarking with the streamline-based GTTI algorithm involving a single-permeability medium. The flow-diagnostics-derived analytical sensitivities were observed to show good agreement with the streamline-derived sensitivities in terms of correctly capturing relevant spatiotemporal trends. Furthermore, the desirable quasilinear behavior characteristic of the traditional streamline-based GTTI technique was preserved. The flow-diagnostics-based inversion technique is then applied to a field-scale problem involving the integration of multiphase production data into a dual-permeability model of a large naturally fractured reservoir. The results clearly demonstrate the effectiveness of the proposed approach in overcoming the limitations of classical streamline-based methods with dual-permeability systems. By construction, this approach finds direct application in single/multicontinuum models with generic grid designs, both in structured and fully unstructured formats, thereby aiding well-level history matching and high-resolution updates of modern geologic models.This work presents, for the first time, an application of the GTTI to dual-permeability models of naturally fractured reservoirs. This is facilitated by a simplified, yet effective approach to travel-time sensitivity computations directly on finite-volume grids. The proposed approach can be easily applied to subsurface models at levels of complexity identified as challenging for classical streamline-based methods.

Streamline tracing and applications in embedded discrete fracture models

Fractures play important role in unconventional resources by influencing the fluid flow pattern underground. Streamline-based flow diagnostic is important to the history matching or operational optimization process of fractured reservoirs. This paper presents a robust streamline tracing framework for use in the Embedded Discrete Fracture Models (EDFM) and several applications including flow visualization, flow diagnostics, and rate allocation optimization. The proposed streamline tracing framework is based on a boundary layer method that can honor the flux communications between the matrix and fractures or between fracture and fracture. The proposed method is benchmarked with a semi-analytical solution and its robustness is illustrated by a series of numerical examples encompassing different levels of geologic and geometrical complexity. Streamlines in complex fracture networks provide flow diagnostics such as sweep efficiency and connectivity of wells and fractures. The streamlines are then utilized to develop a workflow for rate allocation optimization for waterflood in naturally fractured reservoirs. We apply a streamline-based gradient free algorithm whereby both injection and production rates are adjusted under realistic operational constraints to a field scale fractured reservoir. This approach only requires a few forward simulations and therefore offers significant advantage in terms of computational efficiency. It is confirmed that the optimized schedule provides improvements in oil recovery and sweep efficiency compared to the base scenario with uniform injection and production rates.

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.

Mesh-independent streamline tracing

Following the theory of R-functions, a mesh cell of any type can be implicitly described by one single operator constructed from several distance-like functions which, combined with the transfinite interpolation technique and Darcy's velocities specified at the grid nodes, allows us to compute a velocity vector everywhere in the domain, producing a globally continuous vector field with locally performed calculations. Then, knowing a particle's initial position and using these velocities, one can compute its trajectory, obtaining simple equations to determine the exit point of the particle from a given cell. This alternative approach differs from standard schemes in that there is little dependence on the Eulerian topology for tracing the paths and all computations can be made directly at the physical space for any kind of mesh. Numerical experiments show the applicability of our method for streamline modeling on problems with hybrid grids, domains with non-trivial inner structures, and highly variating flows, among others.

Deficiencies of streamline tracing techniques for designing hypersonic inlets and potential solutions

This work focuses on streamline tracing techniques for designing hypersonic inlets, and two deficiencies were discovered. Firstly, constriction ratios of stream-traced inlets are unpredictable and uncontrollable, which may affect the integration with airframes and combustors. Secondly, stream-traced inlets cannot exactly inherit properties from a basic flowfield through which they are traced. Then flow mechanisms underneath these phenomena were clarified. It was made clearly that properties of flow tubes captured by an inlet are what essentially determines constriction ratios as well as performances of inlets. Based on flow mechanisms, the method of calculating along streamlines (MCS) was proposed, which makes it possible to evaluate inlet performances directly. At last, optimization design methodologies were introduced to make inlet constriction ratios controllable, and simultaneously improve inlet performances as much as possible.

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.

Design and Applications of Preliminary Evaluation Platform of Aerodynamic Forces for Supersonic/Hypersonic Vehicles

Rapid evaluation of aerodynamic forces is a key technology in conceptual and preliminary performance assessment and design optimization for supersonic/hypersonic vehicles, which is expected to achieve a balance between accuracy and time. In this paper, the preliminary evaluation platform of aerodynamic forces is built based on the physical theories and engineering methods. This platform computes the local velocity vector by using the streamline tracing technology, and extracts the pressure and friction coefficients by calling methods in method database. Furthermore, an example based on HL-20 is brought out. A good agreement is obtained by comparing the calculated results via CFD with the experimental. Also, a good angle of attack compatibility of streamline tracing technology is concluded. This platform has a computation time less than that via CFD and an flight range greater than that via wind tunnel. Finally, the simple flight dynamics simulation is taken out and the synergetic process is verified.

Bundle-specific tractography with incorporated anatomical and orientational priors

Anatomical white matter bundles vary in shape, size, length, and complexity, making diffusion MRI tractography reconstruction of some bundles more difficult than others. As a result, bundles reconstruction often suffers from a poor spatial extent recovery. To fill-up the white matter volume as much and as best as possible, millions of streamlines can be generated and filtering techniques applied to address this issue. However, well-known problems and biases are introduced such as the creation of a large number of false positives and over-representation of easy-to-track parts of bundles and under-representation of hard-to-track.To address these challenges, we developed a Bundle-Specific Tractography (BST) algorithm. It incorporates anatomical and orientational prior knowledge during the process of streamline tracing to increase reproducibility, sensitivity, specificity and efficiency when reconstructing certain bundles of interest. BST outperforms classical deterministic, probabilistic, and global tractography methods. The increase in anatomically plausible streamlines, with larger spatial coverage, helps to accurately represent the full shape of bundles, which could greatly enhance and robustify tract-based and connectivity-based neuroimaging studies.

Streamline Tracing Methods Based on Piecewise Polynomial Pressure Approximations

AbstractIn this paper, a unified approach for developing streamline tracing method is proposed based on piecewise polynomial pressure approximation functions. It is designed for the numerical schemes that solve the pressure solution at grid blocks while the interior velocity field remains unknown. The suitable velocity approximation functions are derived through analytical differentiation of pressure functions. They better represent the relationship between velocity field and pressure distribution in reality, satisfy the Laplace equation everywhere in a grid block, and ensure local mass conservation and normal flux continuity. Based on different polynomial pressure functions, the Trilinear/Bilinear and Cubic streamline tracing methods are developed. Additionally, a piecewise parabolic velocity reconstruction method is proposed to extend the application of the Cubic method to first‐order numerical schemes. The accuracy and efficiency of the newly proposed methods are evaluated through comparing it with the Pollock and the high‐order method in terms of velocity approximations and computational cost in numerical cases. Comparison results indicate that the Cubic method delivers the most accurate results at the same computational cost.

Optimization design for shape-transition curved isolator with controllable cross-sectional area

In order to obtain a type of variable cross-section curved isolator, a generic method was developed to design a supersonic curved isolator with controllable cross-sectional area by streamline tracing technique based on parameterizing and optimizing basic flow field. Firstly, traditional streamline tracing technique was conducted to design curved isolator. Analysis shows that the traced flow passage presents serious areal throats, which would be detrimental to the unstart performance of inlet and ability of stabilizing shock trains. It is unacceptable in practical applications. Then, the reason, which caused cross-sectional area changing non-monotonously, was analyzed and an improved method was proposed by introducing cross-sectional area constraints in the optimization process. What's more, two parameters, including total pressure recovery coefficient of basic flow field at the exit and maximum area deviation of traced area and designed area, are chosen as the optimization target. Finally, the basic flow field was optimized through modified method and the traced three-dimensional flow path was analyzed. The results show that the cross-sectional area can be controlled within a certain deviation range through the improving optimization method. And combining the blending function, the rectangular-to-circular isolator is designed and analyzed in the paper. It shows that the three-dimensional shape-transition curved isolator, which has well total pressure recovery performance, can be obtained through the method in this paper.

Point cloud movement for fully Lagrangian meshfree methods

In Lagrangian meshfree methods, the underlying spatial discretization, referred to as a point cloud or a particle cloud, moves with the flow velocity. In this paper, we consider different numerical methods of performing this movement of points or particles. The movement is most commonly done by a first order method, which assumes the velocity to be constant within a time step. We show that this method is very inaccurate and that it introduces volume and mass conservation errors. We further propose new methods for the same which prescribe an additional ODE system that describes the characteristic velocity. Movement is then performed along this characteristic velocity. The first new way of moving points is an extension of mesh-based streamline tracing ideas to meshfree methods. In the second way, the movement is done based on the difference in approximated streamlines between two time levels, which approximates the pathlines in unsteady flow. Numerical comparisons show these method to be vastly superior to the conventionally used first order method.

4D multi-scale imaging of reactive flow in carbonates: Assessing the impact of heterogeneity on dissolution regimes using streamlines at multiple length scales

Abstract We have experimentally investigated the impact of heterogeneity on the dissolution of two limestones, characterised by distinct degrees of flow heterogeneity at both the pore and core scales. The two rocks were reacted with reservoir-condition CO2-saturated brine at both scales and scanned dynamically during dissolution. First, 1 cm long 4 mm diameter cores were scanned during reactive flow with a 4 μm voxel size between 10 and 71 times using 4D X-ray micro-tomography (μ-CT) over the course of 90 min. Second, 3.8 cm diameter, 8 cm long cores were reacted at the same conditions inside a reservoir-condition flow apparatus and imaged using a medical-grade X-ray computed tomography scanner (XCT). Each sample was imaged ~13 times over the course of 90 min at a 250 × 250 × 500 μm resolution. These larger cores were then scanned inside a μ-CT at a 27 μm voxel size to assess the alteration pore-space heterogeneity after reaction. Both rock types exhibited channel widening at the mm scale and progressive high porosity pathway dissolution at the cm scale. In the more heterogeneous rock, dissolution was more focussed and progressed along the direction of flow. Additionally, the dissolution pathways contained a distinct microstructure captured with the μ-CT that was not visible at the resolution of the XCT, where the reactive fluid had not completely dissolved the internal pore-structure. This microstructure was further analyzed by performing a direct simulation of the flow field and streamline tracing on the image voxels. We found that at the larger scales the interplay between flow and reaction significantly affects flow in the unreacted regions of the core. When flow is focussed in large reacted channels, this focusing is carried through to the unreacted parts of the rock where flow continues to be confined to preferential pathways after passing the reaction front. This focussing effect is greater with increasing pore space heterogeneity indicating that the representative elementary volume (REV) for dissolution is far greater than the dissolution front itself. This study of scale dependence using in situ 4D tomography provides insight into the mechanisms that control local reaction rates at the mm and cm scales. Furthermore, this work suggests that under these conditions at larger scales it is likely to be structural heterogeneity that dominates the pattern of dissolution and therefore the evolution of high permeability pathways.

Waterflood Management Using Hybrid Approach of Streamline‐Based Interwell Flux Information and Finite Volume Reservoir Simulation

In this work, we implement new software for improved waterflood management by combining classical finite volume reservoir simulation together with streamline tracing and corresponding interwell flux evaluations to optimize waterflood performance. We have introduced two basic modules here: a commercial reservoir simulator and our own streamline tracing and waterflood management program. Waterflood simulation is performed for a certain time span until simulation is paused, and the streamline tracing program is called to calculate interwell fluxes and adjust new well rates for better waterflood performance. The simulation continues afterwards until the next tracing and adjustment point is reached. The two modules work iteratively. The streamline tracing program is designed to trace streamlines on a compressible velocity field and a general corner point grid system with nonneighboring connections. The new injection rates are adjusted according to each well′s injection efficiency calculated from interwell multi‐phase fluxes. Streamline tracing is performed successfully not only on simple geometry corner point grid cases, but also on heavily faulted realistic reservoirs under waterflood. After readjusting injection rates multiple times during the simulation, we typically observe a reduction in field water cut of up to 5% and an increase in oil recovery in our test cases. Interwell flux information serves as effective diagnostic tools to identify injector‐producer pairs with large amount of water cycling. All simulations conducted here are rigorously finite volume based, which takes into account the full physics of nonadvective processes such as gravity and capillary effects. In conclusion, we have implemented a streamline‐based waterflood management program which works iteratively and cooperatively with a commercial reservoir simulator, without switching to streamline simulation. It provides an effective solution for improving oil recovery in brown fields by combining the rigorous mathematical nature of finite volume simulation and the power of streamline‐based flood management.

Design of a three-dimensional scramjet nozzle considering lateral expansion and geometric constraints

A new method based on quasi two-dimensional supersonic flow and maximum thrust theory to design a three-dimensional nozzle while considering lateral expansion and geometric constraints is presented in this paper. To generate the configuration of the three-dimensional nozzle, the inviscid flowfield is calculated through the method of characteristics, and the reference temperature method is applied to correct the boundary layer thickness. The computational fluid dynamics approach is used to obtain the aerodynamic performance of the nozzle. Results show that the initial arc radius slightly influences the axial thrust coefficient, whereas the variations in the lateral expansion contour, the length and initial expansion angle of the lower cowl significantly affect the axial thrust coefficient. The three-dimensional nozzle designed by streamline tracing technique is also investigated for comparison to verify the superiority of the new method. The proposed nozzle shows increases in the axial thrust coefficient, lift, and pitching moment of 6.86%, 203.15%, and 642.86%, respectively, at the design point, compared with the nozzle designed by streamline tracing approach. In addition, the lateral expansion accounts for 22.46% of the entire axial thrust, while it has no contribution to the lift and pitching moment in the proposed nozzle.

Design and analysis on three-dimensional scramjet nozzles with shape transition

A trimming method to optimize the configuration of a three-dimensional asymmetric nozzle with shape transition, which aims to obtain good aerodynamic performance and to save weight at the same time, is presented in this paper. Then the effects of the entry shape on the performance of the three-dimensional nozzle are investigated. The streamline tracing involved in an axisymmetric flowfield with optimal thrust is employed to obtain the inviscid contour of the three-dimensional nozzle with shape transition, and the reference temperature method is applied to correct the thickness of the boundary layer. The performance of the designed nozzle is obtained by using computational fluid dynamics. The calculated results show that the trimmed nozzle gains increases in the lift and pitching moment by 427.00% and 10.80%, respectively, with only a 0.76% decrease in the axial thrust coefficient, while the weight can be reduced by as much as 37.51%. For the nozzles with elliptical entrances, as the axial ratio ranges from 1.0 to 2.0, the axial thrust coefficient is increased by 5.38%, while the lift is decreased by 67.74%. When considering the nozzles with rectangular entrances, as the aspect ratio ranges 1.0 to 2.0, the axial thrust coefficient is increased by 3.58%, while the lift and pitching moment are decreased by 82.09% and 16.43%, respectively. Most of the axial thrust is produced on the upper-wall and side-walls in all nozzles, and the contribution of the expansion flow along the side-walls on the thrust generation is pronounced in the nozzle with a relatively smaller entry ratio. However, the majority of the lift and pitching moment are generated on the upper-wall and lower-wall. Besides, the viscosity loss and weight can be reduced by applying the elliptical cross-section in the propulsion system.

Design and experimental study of a practical Osculating Inward Cone Waverider Inlet

A design method based on tip to tail streamline tracing and osculating inward cone methods is discussed for designing the integrated Osculating Inward Cone Waverider Inlet (OICWI). A practical geometrical constrained experimental model of OICWI is designed based on the validated design method. It has a total contraction ratio of 4.61 and inner contraction ratio is 2.0. Wind-tunnel tests have been conducted for the OICWI model at free stream Mach number (Ma∞) of 4.0, 3.5 and 3.0 respectively. The experimental results show that the OICWI has high flow capture ratio and compression abilities. It can self-start at Ma∞=3.5 and 4.0 and its flow capture ratio is 0.73 at Ma∞=4.0, and Angle of Attack (AOA) 0°. The research results show that the OICWI has advantages of inward cone waverider and streamline tracing inlet. Present OICWI is a novel approach for waverider inlet integration studies and it will promote the use of waverider inlet integration configuration in the studies of airbreathing hypersonic vehicles.

A conceptual design of shock-eliminating clover combustor for large scale scramjet engine

A new concept of shock-eliminating clover combustor is proposed for large scale scramjet engine to fulfill the requirements of fuel penetration, total pressure recovery and cooling. To generate the circular-to-clover transition shape of the combustor, the streamline tracing technique is used based on an axisymmetric expansion parent flowfield calculated using the method of characteristics. The combustor is examined using inviscid and viscous numerical simulations and a pure circular shape is calculated for comparison. The results showed that the combustor avoids the shock wave generation and produces low total pressure losses in a wide range of flight condition with various Mach number. The flameholding device for this combustor is briefly discussed.