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This study aims to propose an aerodynamic force decomposition which, for the first time, allows for thrust/drag bookkeeping in two-dimensional viscous and unsteady flows. Lamb vector-based far-field methods are used at the scope, and the paper starts with extending recent steady compressible formulas to the unsteady regime.

Exact vortical force formulas are derived considering inertial or non-inertial frames, viscous or inviscid flows, fixed or moving bodies. Numerical applications to a NACA0012 airfoil oscillating in pure plunging motion are illustrated, considering subsonic and transonic flow regimes. The total force accuracy and sensitivity to the control volume size is first analysed, then the axial force is decomposed and results are compared to the inviscid force (thrust) and to the steady force (drag).

Two total axial force decompositions in thrust and drag contributions are proposed, providing satisfactory results. An additional force decomposition is also formulated, which is independent of the arbitrary pole appearing in vortical formulas. Numerical inaccuracies encountered in inertial reference frames are eliminated, and the extended formulation also allows obtaining an accurate force prediction in presence of shock waves.

No thrust/drag bookkeeping methodology was actually available for oscillating airfoils in viscous and compressible flows.

The purpose of this paper is to numerically investigate the effect of guide vane unsteady passing wake on the rotor blade tip aerothermal performance with different tip clearances.

The geometry and flow conditions of the first stage of GE-E3 high-pressure turbine have been used to obtain the blade tip three-dimensional heat transfer characteristics. The first stage of GE-E3 high-pressure turbine has 46 guide vanes and 76 rotor blades, and the ratio of the vane to the blade is simplified to 38:76 to compromise the computational resources and accuracy. Namely, each computational domain comprises of one guide vane passage and two rotor blade passages. The investigations are conducted at three different tip gaps of 1.0, 1.5 and 2.0 per cent of the average blade span.

The results show that the overall discrepancy of the heat transfer coefficient between steady results and unsteady time-averaged results is quite small, but the dramatic growth of the instantaneous heat transfer coefficient along the pressure side is in excess of 20 per cent. The change of the aerothermal performance is mainly driven by turbulence-level fluctuations of the unsteady flow field within gap regions. In addition, the gap size expansion has a marginal impact on the variation ratio of tip unsteady aerothermal performances, even though it has a huge influence on the leakage flow state within the tip region.

This paper emphasizes the change ratio of unsteady instantaneous heat transfer characteristics and detailed the mechanism of blade tip unsteady heat transfer coefficient fluctuations, which provide some guidance for the future blade tip design and optimization.

The details of predicting the aerodynamic forces of maneuvering helicopter rotors are discussed in this paper. A new approach to modeling the unsteady rotor aerodynamic forces is presented based on the insight into nonuniform induced velocity distribution, inflow dynamics and unsteady airfoil behavior. For a specified maneuver, the rotor control inputs and helicopter flight attitudes during the maneuvering are first obtained using inverse solution technique, and then the unsteady rotor forces are numerically simulated by synthetically applying the vortex theory, dynamic inflow theory and unsteady airfoil aerodynamic models. Good results of the sample calculations of lateral jink and pop‐up maneuvers are obtained.

The purpose of this paper is to describe how the hydraulic performance and pressure fluctuations in the entire flow passage of a Francis turbine were predicted numerically for the highest head. The calculations are used to partition the turbine operating regions and to clarify the unsteady flow behavior in the entire flow passage including the blade channel vortex in the runner and vortex rope in the draft tube.

Three‐dimensional unsteady numerical simulations were performed for a number of operating conditions at the highest head. The unsteady Reynolds‐averaged Navier‐Stokes equations with the k‐ω based SST turbulence model were solved to model the unsteady flow within the entire flow passage of a Francis turbine.

The predicted pressure fluctuations in the draft tube agree well with the experimental results at low heads. However the peak‐to‐peak amplitudes in the spiral case are not as well predicted so the calculation domain and the inlet boundary conditions need to be improved. The unsteady simulation results are better than the steady‐state results. At the most unstable operating condition of case a0.5h1.26, the pulse in the flow passage is due to the rotor‐stator interference between the runner and the guide vanes, the blade channel vortex in the runner blade passage and the vortex rope in the draft tube.

This study investigates the characteristics of the dominant unsteady flow frequencies in different parts of the turbine for various guide vane openings at the highest head. The unsteady flow patterns in the turbine, including the blade channel vortex in the runner and the helical vortex rope in the draft tube, are classified numerically, and the turbine operating regions are partitioned to identify safe operating regions.

The purpose of this paper is to investigate and improve a new method of unstructured rotational dynamic overset grids, which can be used to simulate the unsteady flows around rotational parts of aircraft.

The computational domain is decomposed into two sub-domains, namely, the rotational sub-domain which contains the rotational boundaries, and the stationary sub-domain which contains the remainder flow field including the stationary boundaries. The artificial boundaries and restriction boundaries are used as the restriction condition to generate the entire computational grid, and then the overset grids are established according to the radius parameters of artificial boundaries set previously. The deformation of rotational boundary is treated by using the linear spring analogy method which is suitable for the dynamic unstructured grid. The unsteady Navier-Stokes/Euler equations are solved separately in the rotational sub-domain and stationary sub-domain, and data coupling is accomplished through the overlapping area. The least squares method is used to interpolate the flow variables for the artificial boundary points with a higher calculating precision. Implicit lower-upper symmetric-Gauss-Seidel (LU-SGS) time stepping scheme is implemented to accelerate the inner iteration during the unsteady simulation.

The airfoil steady flow, airfoil pitching unsteady flow, three-dimensional (3-D) rotor flow field, rotor-fuselage interaction unsteady flow field and the flutter exciting system unsteady flow field are numerically simulated, and the results have good agreements with the experimental data. It is shown that the present method is valid and efficient for the prediction of complicated unsteady problems which contain rotational dynamic boundaries.

The results are entirely based on computational fluid dynamics (CFD), and the 3D simulations are based on the Euler equations in which the viscous effect is ignored. The current work shows further applicable potential to simulate unsteady flow around rotational parts of aircraft.

The current study can be used to simulate the two-dimensional airfoil pitching, 3-D rotor flow field, rotor-fuselage interaction and the flutter exciting system unsteady flow. The work will help the aircraft designer to get the unsteady flow character around rotational parts of aircraft.

A new type of rotational dynamic overset grids is presented and validated, and the current work has a significant contribution to the development of unstructured rotational dynamic overset grids.

The purpose of this study is to propose a fast method for predicting flow fields with periodic behavior with verification in the context of a radial turbine to meet the urgent requirement to effectively capture the unsteady flow characteristics in turbomachinery. Aiming at meeting the urgent requirement to effectively capture the unsteady flow characteristics in turbomachinery, a fast method for predicting flow fields with periodic behavior is proposed here, with verification in the context of a radial turbine (RT).

Sparsity-promoting dynamic mode decomposition is used to determine the dominant coherent structures of the unsteady flow for mode selection, and for flow-field prediction, the characteristic parameters including amplitude and frequency are predicted using one-dimensional Gaussian fitting with flow rate and two-dimensional triangulation-based cubic interpolation with both flow rate and rotation speed. The flow field can be rebuilt using the predicted characteristic parameters and the chosen model.

Under single flow-rate variation conditions, the turbine flow field can be recovered using the first seven modes and fitted amplitude modulus and frequency with less than 5% error in the pressure field and less than 9.7% error in the velocity field. For the operating conditions with concurrent flow-rate and rotation-speed fluctuations, the relative error in the anticipated pressure field is likewise within an acceptable range. Compared to traditional numerical simulations, the method requires a lot less time while maintaining the accuracy of the prediction.

It would be challenging and interesting work to extend the current method to nonlinear problems.

The method presented herein provides an effective solution for the fast prediction of unsteady flow fields in the design of turbomachinery.

A flow prediction method based on sparsity-promoting dynamic mode decomposition was proposed and applied into a RT to predict the flow field under various operating conditions (both rotation speed and flow rate change) with reasonable prediction accuracy. Compared with numerical calculations or experiments, the proposed method can greatly reduce time and resource consumption for flow field visualization at design stage. Most of the physics information of the unsteady flow was maintained by reconstructing the flow modes in the prediction method, which may contribute to a deeper understanding of physical mechanisms.

The purpose of this paper is to investigate, experimentally and numerically, the pressure pulse characteristics and unsteady flow behavior in a Francis turbine runner for moderate flow heads. The pressure pulses in the runner blade passage were predicted numerically for both moderate and high heads. The calculations were used to partition the turbine operating regions and to clarify the various for the unsteady flow behavior, especially the blade channel vortex in the runner.

Experimental and numerical analyses of pressure pulse characteristics at moderate flow heads in a Francis turbine runner were then extended to high heads through numerical modeling with 3D unsteady numerical simulations performed for a number of operating conditions. The unsteady Reynolds‐averaged Navier‐Stokes equations with the k‐ω‐based shear stress transport turbulence model were used to model the unsteady flow within the entire flow passage of a Francis turbine.

The dominate frequency of the predicted pressure pulses at runner inlet agree with the experimental results in the head cover at moderate flow heads. The influence of the blade passing frequency causes the simulated peak‐to‐peak amplitudes in the runner inlet to be larger than in the head cover. The measured and predicted pressure pulses at different positions along the runner are comparable. At the most unstable operating condition of 0.5a₀ guide vane opening, the pressure pulses in the runner blade passage are due to the blade channel vortex and the rotor‐stator interference. The predictions show that the frequency of the blade channel vortex is relatively low and it changes with the operating conditions.

The paper describes a study which experimentally and numerically investigated the pressure pulses characteristics in a Francis turbine runner at moderate flow heads. The pulse characteristics and unsteady flow behavior due to the blade channel vortex in the runner at high heads were investigated numerically, with the turbine operating regions then partitioned to identify safe operating regions.

This paper seeks to develop an approach for the unsteady inverse problem of two‐dimensional oscillating airfoils based on the finite difference method (FDM) solution of the transient Euler equations.

The solution strategies are determined according to the mathematical model for the inverse‐problem of oscillating airfoils. Then the unsteady nonreflecting far field boundary condition and the permeable wall boundary condition are employed to treat the boundary conditions. The applications are carried out for the modification of an oscillating airfoil according to the design targets of the unsteady pressure distribution in an oscillating period.

The results show that the pressure distributions over the new airfoils coincide with the design objects indicating that the mathematical model and solution strategy developed in this paper is rational and reliable.

This method is limited to frictionless flow.

The paper provides a new FDM solution of unsteady inverse problem for oscillating airfoils, which can be extended to treat the multipoint problem of airfoil design.

The purpose of this paper is to use dynamic meshing to perform CFD analyses of a NACA 0012 airfoil fitted with a morphing trailing edge (TE) flap when it undergoes static and time-dependent morphing. The steady CFD predictions of the original and morphing airfoils are validated against published data. The study also investigates an airfoil with a hinged TE flap for aerodynamic performance comparison. The study further extends to an unsteady CFD analysis of a dynamically morphing TE flap for proof-of-concept and also to realise its potential for future applications.

An existing parametrization method was modified and implemented in a user-defined function (UDF) to perform dynamic meshing which is essential for morphing airfoil unsteady simulations. The results from the deformed mesh were verified to ensure the validity of the adopted mesh deformation method. ANSYS Fluent software was used to perform steady and unsteady analysis and the results were compared with computational predictions.

Steady computational results are in good agreement with those from OpenFOAM for a non-morphing airfoil and for a morphed airfoil with a maximum TE deflection equal to 5 per cent of the chord. The results obtained by ANSYS Fluent show that an average of 6.5 per cent increase in lift-to-drag ratio is achieved, compared with a hinged flap airfoil with the same TE deflection. By using dynamic meshing, unsteady transient simulations reveal that the local flow field is influenced by the morphing motion.

An airfoil parametrisation method was modified to introduce time-dependent morphing and used to drive dynamic meshing through an in-house-developed UDF. The morphed airfoil’s superior aerodynamic performance was demonstrated in comparison with traditional hinged TE flap. A methodology was developed to perform unsteady transient analysis of a morphing airfoil at high angles of attack beyond stall and to compare with published data. Unsteady predictions have shown signs of rich flow features, paving the way for further research into the effects of a dynamic flap on the flow physics.

An adaptive grid solution method is described for computing the time accurate solution of an unsteady flow problem. The solution method consists of three parts: a grid point redistribution method; an unsteady Euler equation solver; and a temporal coupling routine that links the dynamic grid to the flow solver. The grid movement technique is a direct curve by curve method containing grid controls that generate a smooth grid that resolves the severe solution gradients and the sharp transitions in the solution gradients. By design, the temporal coupling procedure provides a grid that does not lag the solution in time. The adaptive solution method is tested by computing the unsteady inviscid solutions for a one‐dimensional shock tube and a two‐dimensional shock vortex interaction. Quantitative comparisons are made between the adaptive solutions, theoretical solutions and numerical solutions computed on stationary grids. Test results demonstrate the good temporal tracking of the solution by the adaptive grid, and the ability of the adaptive method to capture an unsteady solution of comparable accuracy to that computed on a stationary grid containing significantly more grid points than used in the adaptive grid.