CFD Solutions Research Articles

202 数値解析結果の感度解析

202 数値解析結果の感度解析

A Coupled Free Wake - CFD Method for The Simulation of Helicopter Rotor Flow

A new coupled wake – CFD method is used to include realistic wake effects in CFD solutions for rotor flow in hover. The analytical method for predicting hovering rotor wake is described to investigate the motion of the helical tip vortex. Beginning with the generalized wake model, a semi-empirical correction for the vortex core effect on rotor wake is made. Then on the condition of circulation and wake geometry convergence, the free wake calculation is accomplished. Finally, Euler–Navier–Stokes equations are solved for transonic rotor flow employing Jameson's finite-volume explicit Runge-Kutta time-stepping scheme. The results are compared with the respective references and experimental data.

Computational-Fluid-Dynamics Based Advanced Ship-Airwake Database for Helicopter Flight Simulators

Computational e uid dynamics (CFD) is used to create an extensive aerodynamic ship-airwake database for a ship-specie c e ight simulator to train helicopter pilots for landing and takeoff from various points on a ship. The technology has been embedded into CAE’ s Merlin simulator and applied to six different ships of the Royal Navy. In achieving this, important scientie c and engineering milestones are crossed, including high geometric e delity through OEM’ s (Original Equipment Manufacturer ) CAD description of the ships, three-dimensional CFDcalculations, comparison to experimental data, and, e nally,integration, testing, and acceptance into the e ight simulator. The database is e rst built by solving the three-dimensional inviscid (Euler) e ow around the complete ship, using Finite Element Navier ‐Stokes Analysis Package, a proprietary code. And a number of wind speeds and directions, corresponding to realistic approach scenarios, are analyzed. The CFD results are then compared to a set of experiments carried out for airwakes around the Canadian Patrol Frigate and made available only after the calculations weredone. The calculationsproveto bein excellent agreement with thedata throughoutitsrange. For the purpose of integration into the simulator, the CFD solutions are interpolated onto a Cartesian grid, which is then implemented in a look-up table for the Merlin CDS, after being enhanced with turbulence models. The paper then closes with the acceptance procedure the simulator is passed through.

Combined Free Wake / CFD Methodology for Predicting Transonic Rotor Flow in Hover

A new combined wake / CFD methodology is used to include realistic wake effects in CFD solutions for the rotor flow in hover. The analytical method for predicting the hovering rotor wake is described to investigate the motion of the helical tip vortex. Beginning with the generalized wake model, a Semi-Empirical Correction for the vortex core effect on the rotor wake is made. Then on the condition of circulation and wake geometry convergence, the free wake calculation is carried out. Finally, Euler equations are solved for transonic rotor flow employing Jameson's finite-volume explicit Runge-Kutta time-stepping scheme. The results are compared with the respective references and experimental data.

Application of Model Order Reduction to Compressor Aeroelastic Models

Abstract A model order reduction technique that yields low-order models of blade row unsteady aerodynamics is introduced. The technique is applied to linearized unsteady Euler CFD solutions in such a way that the resulting blade row models can be linked to their surroundings through their boundary conditions. The technique is applied to a transonic compressor aeroelastic analysis, in which the high-fidelity CFD forced-response results are better captured than with models that use single-frequency influence coefficients. A low-speed compressor stage is also modeled to demonstrate the multistage capability of the method. These examples demonstrate how model order reduction can be used to systematically improve the versatility, fidelity, and range of applicability of the low-order aerodynamic models typically used for incorporation of CFD results into aeroelastic analyses.

2022 CFD と解析解のハイブリッド手法による円柱群の流力弾性振動解析

2022 CFD と解析解のハイブリッド手法による円柱群の流力弾性振動解析

Development and application of farfield drag extraction techniques for complex viscous flows

AbstractA new method for deriving the components of drag from the CFD solution of an aircraft flowfield, by analysis of its wake, is presented. This method is applied to viscous flow calculations. It is also applied to configurations containing powerplants. The drag values predicted by this method are compared with the values obtained using more traditional methods, and good agreement is demonstrated.

CFD modelling and experimental validation of pressure drop and flow profile in a novel structured catalytic reactor packing

Packed beds of catalyst particles are normally described using models that contain a number of empirical parameters. The development of computer technology and CFD models makes it tempting to try to (1) fully simulate the flow in packed beds to obtain a more detailed understanding of the physical phenomena that take place in the bed, and (2) to use the CFD solutions to derive ‘simple’ correlations suitable for design purposes. In this paper it is shown that a commercial CFD code (CFX-5.3) can be used to predict, with an average error of about 10%, the pressure drop characteristics of packed beds of spheres that have a tube-to-particle-diameter ratio of 1.00 to 2.00. Packed beds with these unusually low tube-to-particle-diameter ratios can be used as unit cells in a novel type of structured catalytic reactor packing, proposed in this paper, that has very favorable pressure drop characteristics. The error of 10% in the pressure drop prediction by CFD is acceptable for design purposes. The CFD model is also able to predict local velocity profiles that were measured with LDA. The CFD results have been used to fit a simple two-parameter model that describes the experimental pressure drop data with an average error of about 20%. For a grid-independent CFD solution of laminar flow in a packed bed containing only 16 particles, already three million cells are required. However, it is anticipated that within five years from now the simulation of a packed bed containing a few hundred particles will be considered a ‘standard’ problem in terms of memory and calculation time requirements.

Macro-mixing, partial segregation and 3-D selectivity fields inside a semi-batch stirred reactor

The fluid phase reaction A+ B→ R to a desired product, when accompanied by a parallel decomposition to a by-product A→ S, form a pair of reactions ideal for evaluating mixing-with-reaction tests. The reactions are typical of diazotisation in dyestuff manufacture, so that fundamental mixing studies can be linked to practical manufacturing. Earlier studies on these problems used a 2-D analysis which is approximate for some practical cases. This approach has now been extended to a full 3-D network-of-zones for a stirred vessel for single-point dip-pipe addition at any location. This is a simplified computationally tractable approach to fluid mixing, which is superior to more complex CFD solutions, because it can easily handle multiple complex reactions. The flow and mixing in the 3-D network incorporates axial and radial convection with swirling tangential flow, turbulence and flow around baffles. Computations are then tractable for long duration semi-batch addition modes of operation. Macro-mixing (in 3-D), the associated partially segregated fields of reagents A and B and the spatial-temporal evolution of the local instantaneous yields and selectivities are illustrated using solid-body AVS graphics for the Drain/ICI reactions.

Accelerating Computational Fluid Dynamics Based Aeroelastic Predictions Using System Identification

System identie cation is evaluated as an efe cient and accurate technique for modeling unsteady aerodynamic forces for use in time-domain aeroelastic analysis. In the system identie cation methodology, the constant coefe cients of a linear system model are e t to the computed response time histories from a three-dimensional, unsteady computational e uid dynamics (CFD) solver. The resulting model of the unsteady CFD solution is independent of both dynamic pressure and structural parameters. Hence, this methodology has the advantage that only one CFD e owe eld computation for each Mach number must be completed to determine the aeroelastic instability boundary. Results show that system identie cation can accurately model the unsteady aerodynamic forces for complex aerospace structures of practical interest. The methodology results in a substantial savings in computational time when predicting aeroelastic instabilities.

SWIRLING STREAMLINE-CURVATURE LAW OF THE WALL FROM A NOVEL PERTURBATION ANALYSIS

A new law of the wall for swirling axial boundary layers is derived analytically, which accounts for local streamline curvature effects. Compared to previous derivations, the new law covers a wider range of streamline curvature, y+, and the axial-to-swirl shear stress ratio. Incorporation of the local streamline curvature physics gave greatly increased mathematical difficulty. The difficulty was handled by developing a novel perturbation solution approach, which is thoroughly presented. This new solution approach allows a closed-form analytical solution to many similar nonlinear problems which heretofore required numerical techniques. To demonstrate the worst-case scenario for swirl prediction (computational fluid dynamics, CFD) improvement, the new law of the wall was implemented in the standard k-epsilon model as a wall function. The new law gives CFD solutions in closer agreement with measurements than does the classical log law.

Performance Optimization of a Supersonic Combustion Ram Accelerator Projectile

The optimization of a supersonic combustion ram projectile shape, using a computational analysis, is presented. A projectile e ying at hypersonic speed is passed through a combustible mixture. Shocks generated by a ring cowl surrounding the projectile ignite the e ow over the projectile tail, causing it to accelerate. This method could be used to accelerate projectiles to velocities in excess of 2.7 km/s. The thrust and drag forces on such a projectile are very large and are of the same order of magnitude. Small changes in the projectile design can have a large effect on the net thrust acting on the projectile. A computational analysis using an inviscid computational e uid dynamics (CFD) code, including chemical reactions, is linked to a gradient-based optimizer. The projectile is then optimized for maximum thrust at several different Mach numbers. Multiple CFD solutions are used to generate a thrust curve used in optimization for other design functions, such as maximum velocity and minimum accelerator tube length. All cone gurations are compared to determine the best cone guration for practical use. Optimized cone gurations are capable of higher velocities, but the main benee t gained is the reduction in the length required to reach that maximum velocity.

Investigation of Wedge Probe Wall Proximity Effects: Part 1—Experimental Study

Conventional three-hole wedge probes fail to measure the correct static pressure when operating in close proximity to a wall or boundary through which the probe is inserted. The free-stream pressure near the outer wall of a turbomachine may be overindicated by up to 20 percent dynamic head. This paper reports a series of experiments aimed at quantifying this so-called “wall proximity effect.” It is shown from a factorial experiment that probe wedge angle, stem design, and free-stream Mach number all have a significant influence. The yaw angle sensitivity of wedge probes is also found to depend on the proximity of the probe to the wall of introduction. Flow visualization studies on large-scale probe models are described, and a qualitative model of the probe local flow structures is developed. This model is used to explain the near-wall characteristics of the actual size wedge probes. In Part 2 of this paper, the experimental data are used to validate CFD calculations of the flow field around a wedge probe. A simple analytical model of the probe/flow interaction is developed from the CFD solutions.

Heat Transfer Predictions for Two Turbine Nozzle Geometries at High Reynolds and Mach Numbers

Predictions of turbine vane and endwall heat transfer and pressure distributions are compared with experimental measurements for two vane geometries. The differences in geometries were due to differences in the hub profile, and both geometries were derived from the design of a high rim speed turbine (HRST). The experiments were conducted in the Isentropic Light Piston Facility (ILPF) at Pyestock at a Reynolds number of 5.3 x 106, a Mach number of 1.2, and a wall-to-gas temperature ratio of 0.66. Predictions are given for two different steady-state three-dimensional Navier–Stokes computational analyses. C-type meshes were used, and algebraic models were employed to calculate the turbulent eddy viscosity. The effects of different turbulence modeling assumptions on the predicted results are examined. Comparisons are also given between predicted and measured total pressure distributions behind the vane. The combination of realistic engine geometries and flow conditions proved to be quite demanding in terms of the convergence of the CFD solutions. An appropriate method of grid generation, which resulted in consistently converged CFD solutions, was identified.

Lessons from rotor 37

NASA rotor 37 was used as a ‘blind’ test case for turbomachinery CFD by the Turbomachinery Committee of the IGTI. The rotor is a transonic compressor with a tip speed of 454 m/s (1500 ft/s) and a relatively high pressure ratio of 2.1. It was tested in isolation with a circumferentially uniform inlet flow so that the flow through it should be steady apart from any effects of passage to passage geometry variation and mechanical vibration. As such it represents the simplest possible type of test for three-dimensional turbomachinery flow solvers. However, the rotor still presents a real challenge to 3D viscous flow solvers because the shock wave-boundary layer interaction is strong and the effects of viscosity are dominant in determining the flow deviation and hence the pressure ratio. Eleven ‘blind’ solutions were submitted and in addition a ‘non-blind’ solution was used to prepare for the exercise. This paper reviews the flow in the test case and the comparisons of the CFD solutions with the test data. Lessons for both the Flow Physics in transonic fans and for the application of CFD to such machines are pointed out.

EFFECTS OF IMPLICIT PRECONDITIONERS ON SOLUTION ACCELERATION SCHEMES IN CFD

Several solution acceleration techniques, used to obtain steady state CFD solutions as quickly as possible, are applied to an implicit, upwind Euler solver to evaluate their effectiveness. The implicit system is solved using either ADI or ILU and the solution acceleration techniques evaluated are quasi-Newton iteration, Jacobian freezing, multigrid and GMRES. ILU is a better preconditioner than ADI because it can use larger time steps. Adding GMRES does not always improve the convergence. However, GMRES preconditioned with ILU and multigrid can take advantage of Jacobian freezing to produce an efficient scheme that is relatively independent of grid size and grid quality.

EFFECTS OF IMPLICIT PRECONDITIONERS ON SOLUTION ACCELERATION SCHEMES IN CFD

Several solution acceleration techniques, used to obtain steady state CFD solutions as quickly as possible, are applied to an implicit, upwind Euler solver to evaluate their effectiveness. The implicit system is solved using either ADI or ILU and the solution acceleration techniques evaluated are quasi-Newton iteration, Jacobian freezing, multigrid and GMRES. ILU is a better preconditioner than ADI because it can use larger time steps. Adding GMRES does not always improve the convergence. However, GMRES preconditioned with ILU and multigrid can take advantage of Jacobian freezing to produce an efficient scheme that is relatively independent of grid size and grid quality.

A weak statement perturbation CFD algorithm with high-order phase accuracy for hyperbolic problems

Achieving improved order of accuracy for any numerical method is a continuing quest. The discrete approximate solution error, in general, can be expressed as a truncation of a Taylor series expansion. Herein, we present a weak statement perturbation always yielding simple tridiagonal forms that can reduce, or annihilate in special cases, the Taylor series truncation error to high order. The procedure is analyzed via a von Neumann frequency analysis, and verification CFD solutions are reported in one and two dimensions. Finally, using the element specific (local) Courant number, a continuum (total) time integration procedure is derived that can directly produce a final time solution independent of mesh measure.

The Development of Fast Response Aerodynamic Probes for Flow Measurements in Turbomachinery

The advent of a new generation of transient rotating turbine simulation facilities, where engine values of Reynolds and Mach number are matched simultaneously together with the relevant rotational parameters for dimensional similitude (Dunn et al., 1988; Epstein and Guenette, 1984; Ainsworth et al., 1988), has provided the stimulus for developing improved instrumentation for investigating the aerodynamic flows in these stages. Much useful work has been conducted in the past using hot-wire and laser anemometers. However, hot-wire anemometers are prone to breakage in the high-pressure flows required for correct Reynolds numbers. Furthermore, some laser techniques require a longer run-time than these transient facilities permit, and generally yield velocity information only, giving no data on loss production. Advances in semiconductor aerodynamic probes are beginning to fulfill this perceived need. This paper describes advances made in the design, construction, and testing of two and three-dimensional fast response aerodynamic probes, where semiconductor pressure sensors are mounted directly on the surface of the probes, using techniques that have previously been successfully used on the surface of rotor blades (Ainsworth et al., 1991). These are to be used to measure Mach number and flow direction in compressible unsteady flow regimes. In the first section, a brief review is made of the sensor and associated technology that has been developed to permit a flexible design of fast response aerodynamic probe. Following this, an extensive program of testing large-scale aerodynamic models of candidate geometries for suitable semiconductor scale probes is described, and the results of these discussed. The conclusions of these experiments, conducted for turbine representative mean and unsteady flows, yielded new information for optimizing the design of the small-scale semiconductor probes, in terms of probe geometry, sensor placement, and aerodynamic performance. Details are given of a range of wedge and pyramid semiconductor probes constructed, and the procedures used in calibrating and making measurements with them. Differences in performance are discussed, allowing the experimenter to choose an appropriate probe for the particular measurement required. Finally, the application of prototype semiconductor probes in a transient rotor experiment at HP turbine representative conditions is described, and the data so obtained are compared with CFD solutions of the unsteady viscous flow-field.

THE BEHAVIOR OF SOME SOLUTION ACCELERATION TECHNIQUES IN CFD

SUMMARY Several solution acceleration techniques, used to obtain steady-state CFD solutions as quickly as possible, are applied to an upwind Euler scheme to evaluate their effectiveness. Generalized minimal residual (GMRES), multigrid (MG), and ADI are compared to a four-stage Runge-Kutta scheme using several grids. The use of different acceleration schemes combinations of produces a complementary effect: the convergence becomes relatively independent of both size and quality of the grid.