Inviscid Flow Solver Research Articles

Dynamic Transition of Unsteady Supersonic Flow From Mach to Regular Reflection Over a Moving Wedge

Abstract The design of supersonic and hypersonic air-breathing vehicles is influenced by the transition between the Mach reflection (MR) and regular reflection (RR) phenomena. The purpose of this study is to investigate the dynamic transition of unsteady supersonic flow from MR to RR over a two-dimensional wedge numerically. The trailing edge of the wedge moves downstream along the x-direction with a velocity, V(t) at a freestream Mach number of 3. An unsteady compressible inviscid flow solver is used to simulate the phenomenon. The Arbitrary Lagrangian–Eulerian (ALE) technique is applied to deform the mesh during the wedge motion. The dynamic transition from MR to RR is defined by two criteria, the sonic and the von Neumann. Moreover, the lag in the dynamic transition from the steady-state condition is studied using various nondimensional angular velocities, κ, in the range of [0.1-2]. The lag effect in the shock system is remarkable at the high values of κ greater than 1.5. Furthermore, the dynamic transition from MR to RR happens below the dual solution domain (DSD) because the shock is upstream curved during the wedge motion.

Vortex formation on a pitching aerofoil at high surging amplitudes

Abstract

A high-order accurate unstructured spectral difference lattice Boltzmann method for computing inviscid and viscous compressible flows

In the present work, the spectral difference lattice Boltzmann method (SDLBM) is implemented on unstructured meshes for the solution methodology to be capable of accurately simulating the compressible flows over complex geometries. Both the inviscid and viscous compressible flows are computed by applying the unstructured SDLBM. The compressible form of the discrete Boltzmann–BGK equation with the Watari model is considered and the solution of the resulting system of equations is obtained by applying the spectral difference method on arbitrary quadrilateral meshes. The accuracy and robustness of the unstructured SDLBM for simulating the compressible flows are demonstrated by simulating four problems that are steady inviscid supersonic flow past a bump, steady inviscid subsonic flow over the two-element NACA 4412-4415 airfoil with and without the ground effect, steady viscous transonic flow around the NACA 0012 airfoil and unsteady viscous subsonic flow past two side-by-side cylinders. The results obtained by applying the unstructured SDLBM are in good agreement with those of the available high-order accurate Euler/Navier-Stokes solvers and also the experimental data. The present study introduces the unstructured SDLBM as an appropriate inviscid and viscous compressible LBM flow solver for accurately simulating fluid flows over practical problems.

Concentrated energy addition for active drag reduction in hypersonic flow regime

Numerical optimization of hypersonic drag reduction technique based on concentrated energy addition is presented in this study. A reduction in wave drag is realized through concentrated energy addition in the hypersonic flowfield upstream of the blunt body. For the exhaustive optimization presented in this study, an in-house high precision inviscid flow solver has been developed. Studies focused on the identification of “optimum energy addition location” have revealed the existence of multiple minimum drag points. The wave drag coefficient is observed to drop from 0.85 to 0.45 when 50 Watts of energy is added to an energy bubble of 1 mm radius located at 74.7 mm upstream of the stagnation point. A direct proportionality has been identified between energy bubble size and wave drag coefficient. Dependence of drag coefficient on the upstream added energy magnitude is also revealed. Of the observed multiple minimum drag points, the energy deposition point (EDP) that offers minimum wave drag just after a sharp drop in drag is proposed as the most optimum energy addition location.

A spectral difference lattice Boltzmann method for solution of inviscid compressible flows on structured grids

In this work, a spectral difference lattice Boltzmann method (SDLBM) is developed and applied for an accurate simulation of two-dimensional inviscid compressible flows on structured grids. The compressible form of the discrete Boltzmann–BGK equation is used in which multiple particle speeds have to be employed to correctly model the compressibility in a thermal fluid. Here, the 2D compressible Lattice Boltzmann (LB) model proposed by Watari is applied. The spectral difference (SD) method is implemented for the solution of the LB equation in which the particle distribution function is stored at the solution points while the fluxes are computed at the flux points for calculating the particle distribution function. For time accurate solutions, the fourth-order Runge–Kutta scheme is used to discretize the temporal term in the LB equation. Note that the procedure of implementing the SD method to solve the LB equation is nearly the same as that procedure developed in the literature for the solution of the Euler equations. The accuracy and robustness of the present solution methodology are demonstrated by simulating different benchmark compressible flow problems. A sensitivity study is also conducted to evaluate the effects of the numerical parameters and the grid size/distribution on the accuracy and performance of the solution. At first, three inviscid compressible flow problems, namely, the stationary isentropic vortex, the shock tube and the shock–vortex interaction are solved by using the SDLBM to demonstrate the accuracy and robustness of the present solution methodology. Results computed for these test cases are in good agreement with the analytical and the available numerical solutions. To more assess the accuracy and robustness of the SDLBM, a third-order finite volume LBM (FVLBM) is also developed and the solutions obtained by these two methods for the test cases simulated are thoroughly compared with each other. It is demonstrated that the SDLBM is more accurate and robust compressible inviscid flow solver that can be used for evaluating the other compressible LB-based flow solvers. As the final problem, the supersonic flow past a bump is simulated to demonstrate the accuracy and robustness of the SDLBM in reaching to a steady-state solution.

GPU accelerated cell-based adaptive mesh refinement on unstructured quadrilateral grid

A GPU accelerated inviscid flow solver is developed on an unstructured quadrilateral grid in the present work. For the first time, the cell-based adaptive mesh refinement (AMR) is fully implemented on GPU for the unstructured quadrilateral grid, which greatly reduces the frequency of data exchange between GPU and CPU. Specifically, the AMR is processed with atomic operations to parallelize list operations, and null memory recycling is realized to improve the efficiency of memory utilization. It is found that results obtained by GPUs agree very well with the exact or experimental results in literature. An acceleration ratio of 4 is obtained between the parallel code running on the old GPU GT9800 and the serial code running on E3-1230 V2. With the optimization of configuring a larger L1 cache and adopting Shared Memory based atomic operations on the newer GPU C2050, an acceleration ratio of 20 is achieved. The parallelized cell-based AMR processes have achieved 2x speedup on GT9800 and 18x on Tesla C2050, which demonstrates that parallel running of the cell-based AMR method on GPU is feasible and efficient. Our results also indicate that the new development of GPU architecture benefits the fluid dynamics computing significantly.

Delusive Influence of Nondimensional Numbers in Canonical Hypersonic Nonequilibrium Flows

AbstractA finite volume–based unstructured inviscid flow solver has been developed for the study of nonequilibrium effects in high enthalpy flows. Four different inviscid flux computation schemes are tested for literature reported test cases like unsteady wave motion in a shock tube and high enthalpy flow over cylinder/sphere. During the present assessment, encouraging agreement has been noticed in capturing all the essential flow features in the reacting media. Here, the Rusanov scheme is noticed to be computationally cheaper among all the schemes with noticeable diffusion around strong gradients. Shock tube test case revealed the existence of various shock Mach numbers for a given driving pressure ratio in the presence of reactions. Similarly, freestream Mach number is found to have limitations in representing the shock standoff distance in case of high enthalpy flow over cylinder and sphere. In line with this, real gas effects are prominently observed for the case of the cylinder in comparison with the...

Numerical 3D flow simulation of attached cavitation structures at ultrasonic horn tips and statistical evaluation of flow aggressiveness via load collectives

A compressible inviscid flow solver with barotropic cavitation model is applied to two different ultrasonic horn set-ups and compared to hydrophone, shadowgraphy as well as erosion test data. The statistical analysis of single collapse events in wall-adjacent flow regions allows the determination of the flow aggressiveness via load collectives (cumulative event rate vs collapse pressure), which show an exponential decrease in agreement to studies on hydrodynamic cavitation [1]. A post-processing projection of event rate and collapse pressure on a reference grid reduces the grid dependency significantly. In order to evaluate the erosion-sensitive areas a statistical analysis of transient wall loads is utilised. Predicted erosion sensitive areas as well as temporal pressure and vapour volume evolution are in good agreement to the experimental data.

Physics-based Surrogate Optimization of Francis Turbine Runner Blades, Using Mesh Adaptive Direct Search and Evolutionary Algorithms

A robust multi-fidelity optimization methodology has been developed, focusing on efficiently handling industrial runner design of hydraulic Francis turbines. The computational task is split between low- and high-fidelity phases in order to properly balance the CFD cost and required accuracy in different design stages. In the low-fidelity phase, a physics-based surrogate optimization loop manages a large number of iterative optimization evaluations. Two derivative-free optimization methods use an inviscid flow solver as a physics-based surrogate to obtain the main characteristics of a good design in a relatively fast iterative process. The case study of a runner design for a low-head Francis turbine indicates advantages of integrating two derivative-free optimization algorithms with different local- and global search capabilities.

Multi-fidelity shape optimization of hydraulic turbine runner blades using a multi-objective mesh adaptive direct search algorithm

A robust multi-fidelity design optimization methodology has been developed to integrate advantages of high- and low-fidelity analyses, aiming to help designers reach more efficient turbine runners within reasonable computational time and cost. An inexpensive low-fidelity inviscid flow solver handles most of the computational burden by providing data to the optimizer by evaluating objective functions and constraint values in the low-fidelity phase. An open-source derivative-free optimizer, NOMAD, explores the search space, using the multi-objective mesh adaptive direct search optimization algorithm. A versatile filtering algorithm is in charge of connecting low- and high-fidelity phases by selecting among all feasible solutions a few promising solutions which are transferred to the high-fidelity phase. In the high-fidelity phase, a viscous flow solver is used outside the optimization loop to accurately evaluate filtered candidates. High-fidelity analyses results are used to recalibrate the low-fidelity optimization problem. The developed methodology has demonstrated its ability to efficiently redesign a Francis turbine blade for new operating conditions.

Excited-state kinetics and radiation transport in low-temperature plasmas

An advanced self-consistent plasma physics model including non-equilibrium vibrational kinetics, a collisional radiative model for atomic species, a Boltzmann solver for the electron energy distribution function, a radiation transport module coupled to a steady inviscid flow solver and, has been applied to study non-equilibrium in high enthalpy flows for Jupiter’s atmosphere. Two systems have been considered, a hypersonic shock tube and nozzle expansion, emphasizing the role of radiation reabsorption on macroscopic and microscopic flow properties. Large differences are found between thin and thick plasma conditions not only for the distributions, but also for the macroscopic quantities. In particular, in the nozzle expansion case, the electron energy distribution functions are characterized by a rich structure induced by superelastic collisions between excited species and cold electrons.

Multi-fidelity design optimization of Francis turbine runner blades

A robust multi-fidelity design algorithm has been developed, focusing to efficiently handle industrial hydraulic runner design considerations. The computational task is split between low- and high-fidelity phases in order to properly balance the CFD cost and required accuracy in different design stages. In the low-fidelity phase, a derivative-free optimization method employs an inviscid flow solver to obtain the major desired characteristics of a good design in a relatively fast iterative process. A limited number of candidates are selected among feasible optimization solutions by a newly developed filtering process. The main function of the filtering process is to select some promising candidates to be sent into the high-fidelity phase, which have significantly different geometries, and also are dominant in their own territories. The high-fidelity phase aims to accurately evaluate those promising candidates in order to select the one which is closest to design targets. A low-head runner case study has shown the ability of this methodology to identify an optimized blade through a relatively low computational effort, which is significantly different from the base geometry.

Numerical investigation of clocking in a two-stage gas turbine

Flow in the first two-stage of V 94.2 gas turbine is simulated numerically. In this turbine, the second stator is clocked relative to the first stator to different positions. Steady-state analysis was carried out by varying the circumferential relative position of the consecutive stator vanes to study the effects of the clocking on turbine performance. A density based compressible inviscid flow (Euler equations) solver is used for the flow simulation. The efficiency analysis and entropy generation investigation are performed and the appropriate position of the second stator is obtained. The attained efficiency improvement matches the results obtained by the entropy generation analysis.

Numerical Simulation of Free-Flight Rockets Air-Launched From a Helicopter

Numerical simulation of unsteady flows around a complete helicopter was conducted, and the effect of rotor downwash on the behavior of free-flight rockets air-launched from the helicopter and their plume was investigated. For this purpose, a three-dimensional inviscid flow solver based on unstructured meshes was developed, and an oversetmesh techniquewas adopted to handle the relativemotion of themain rotor, tail rotor, fuselage, and traveling rockets. Theflow solverwas coupledwith six-degrees-of-freedom equations ofmotion to describe the trajectory of the free-flight rockets. To validate the flow solver for simulating the plume flow from the rocket nozzle, calculations were made for a jet flow impinging on flat plates. To demonstrate the accuracy of the flow solver for predicting rotor downwash, a rotor–fuselage aerodynamic interaction flow was calculated, and the results were compared with available experimental data. The trajectory simulation of an external store released from a fixed wing was also performed to validate the present flow solver coupled with the six-degrees-of-freedom equations of motion. Then the present method was applied to the simulation of free-flight rockets air-launched from a complete helicopter configuration. It was found that rotor downwash has nonnegligible effects on the trajectory of the air-launched rockets and their plume development, which may potentially affect the safety and the reliability of other equipments installed on the mother helicopter.

헬리콥터로부터 발사된 로켓의 공력 간섭 현상에 대한 수치적 연구

Numerical simulation of air-launched rockets from a helicopter was conducted to investigate the aerodynamic interference between air-launched rocket and helicopter. For this purpose, a three-dimensional inviscid flow solver has been developed based on unstructured meshes. An overset mesh technique was used to describe the relative motion between rocket and rocket launcher. The flow solver was coupled with six degree-of-freedom equation to predict the trajectory of free-flight rockets. For the validation, calculations were made for the impinging jet with inclined plate. The rotor downwash of helicopter was calculated and applied to simulation of air-launched rocket. It is shown that the rotor downwash has non-negligible effect on the air-launched rocket and its plume development.

Optimal cross-sectional area distribution of a high-speed train nose to minimize the tunnel micro-pressure wave

Optimization of the cross-sectional area distribution of a high-speed train nose is conducted for various nose lengths in order to minimize the micro-pressure wave intensity at a tunnel exit. To this end, an inviscid compressible flow solver is adopted with an axi-symmetric patched grid system. To improve the shape of the train nose, multi-step design optimization is performed using the Broyden---Fletcher---Goldfarb---Shanno (BFGS) algorithm with a response surface model. The optimization reveals that the optimal nose shapes differ for different nose lengths. For a short nose, the shape has an extremely blunt front end, and the cross-sectional area decreases in the middle section. As the nose length increases, the nose shape flattens around the middle section. These optimal shapes divide one large compression wave into two small waves by causing a strong expansion effect between the front and rear ends. As a result, through the nose shape optimization, the intensity of the micro-pressure wave is reduced by 18---27% compared to a parabolic nose, which has a minimum variation of the cross-sectional area change. The optimized distribution of the cross-sectional area can be used as a guideline for the design of three-dimensional nose shapes of high-speed trains, further improving their aerodynamic performance.

Numerical Simulation of Rotor-Fuselage Aerodynamic Interaction Using an Unstructured Overset Mesh Technique

Numerical simulation of unsteady flows around helicopters was conducted to investigate the aerodynamic interaction of main rotor and other components such as fuselage and tail rotor. For this purpose, a three-dimensional inviscid flow solver has been developed based on unstructured meshes. An overset mesh technique was used to describe the relative motion between the main rotor, and other components. As the application of the present method, calculations were made for the rotorfuselage aerodynamic interaction of the ROBIN (ROtor Body INteraction) configuration and for a complete UH-60 helicopter configuration consisted of main rotor, fuselage, and tail rotor. Comparison of the computational results was made with measured time-averaged and instantaneous fuselage surface pressure distributions for the ROBIN configuration and thrust distribution and available experimental data for the UH-60 configuration. It is demonstrated that the present method is efficient and robust for the simulation of complete rotorcraft configurations. Key Word : Rotor fuselage interaction, Unstructured mesh, Overset mesh technique, ROBIN, UH-60

Turbine Airfoil Optimization Using Quasi-3D Analysis Codes

A new approach to optimize the geometry of a turbine airfoil by simultaneously designing multiple 2D sections of the airfoil is presented in this paper. The complexity of 3D geometry modeling is circumvented by generating multiple 2D airfoil sections and constraining their geometry in the radial direction using first- and second-order polynomials that ensure smoothness in the radial direction. The flow fields of candidate geometries obtained during optimization are evaluated using a quasi-3D, inviscid, CFD analysis code. An inviscid flow solver is used to reduce the execution time of the analysis. Multiple evaluation criteria based on the Mach number profile obtained from the analysis of each airfoil cross-section are used for computing a quality metric. A key contribution of the paper is the development of metrics that emulate the perception of the human designer in visually evaluating the Mach Number distribution. A mathematical representation of the evaluation criteria coupled with a parametric geometry generator enables the use of formal optimization techniques in the design. The proposed approach is implemented in the optimal design of a low-pressure turbine nozzle.

전투기 형상의 외부장착물이 꼬리날개에 미치는 영향에 대한 수치적 연구

본 연구에서는 삼차원 비정렬 비점성 유동 해석 코드를 이용하여 전투기 형상의 외부 장착물이 꼬리 날개에 미치는 공력 간섭효과에 대한 연구를 수행하였다. 수치적 기법으로는 격자점 중심(vertex-centered)에 기초한 유한체적법과 시간 적분을 위한 내재적인 point Gauss-Seidel 반복 계산법을 사용하였다. 해석 코드의 검증을 위해 전투기 형상에 대한 정상 유동 계산을 수행하였으며 결과를 실험 데이터와 비교하였다. 외부 장착물의 후류(wake)를 정확히 포착하기 위해 예상되는 후류 영역에 대해 국부적인 격자 조밀화를 수행하였으며 천음속 영역에서의 비정상 유동 해석을 통해 외부 장착물에서 발생하는 후류가 수평꼬리날개에 미치는 간섭효과를 확인하였다. 공력 간섭효과를 감소시키기 위한 대안으로는 뒷전 플랩 꺽임각(trailing edge flap deflection)을 고려하였으며 이에 대한 정량적인 감소효과를 제시하였다. A three-dimensional inviscid flow solver has been developed based on unstructured meshes for the investigation of the effect of the external stores on the tail surfaces of a generic fighter aircraft. The numerical method is based on a vertex-centered finite-volume discretization and an implicit point Gauss-Seidel time integration. The calculations were made for a steady flow and the computed results were compared with experimental data to validate the flow solver. An unsteady time-accurate computation of the generic fighter aircraft with external stores at transonic flight conditions showed that the external stores cause unsteady loading on the horizontal tail surface due to the mutual interference between their wake and the horizontal tail surface. It was shown that downward deflection of the trailing edge flap significantly reduces the undesirable interference effect.

Detailed Aerodynamic Analysis of a Shrouded Tail Rotor Using an Unstructured Mesh Flow Solver

The detailed aerodynamics of a shrouded tail rotor in hover has been numerically studied using a parallel inviscid flow solver on unstructured meshes. The numerical method is based on a cell-centered finite-volume discretization and an implicit Gauss-Seidel time integration. The calculation was made for a single blade by imposing a periodic boundary condition between adjacent rotor blades. The grid periodicity was also imposed at the periodic boundary planes to avoid numerical inaccuracy resulting from solution interpolation. The results were compared with available experimental data and those from a disk vortex theory for validation. It was found that realistic three-dimensional modeling is important for the prediction of detailed aerodynamics of shrouded rotors including the tip clearance gap flow.