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A term-by-term comparison has been conducted between the residuals of the continuous and discrete adjoint methods for quasi-1D flow equations. This comparison is done to identify the origin of numerical instabilities near boundaries of the discrete adjoint method. The results show that there is one-to-one correspondence between the terms of the two residuals. Furthermore, the adjoint boundary conditions are rigorously analyzed. It turns out that improvement can be achieved by replacing some of the terms of the discrete adjoint residual with the counterparts in the continuous adjoint method.

Unsteady turbulent flow simulations were performed based on the Reynolds-averaged Navier–Stokes (RANS) equations to investigate flow oscillation due to three-dimensional (3D) configuration of a Mach 1.5 supersonic open cavity flow with a length-to-depth ratio of 3. Two-dimensional (2D) and 3D unsteady simulation results were analyzed and compared with experimental data and Rossiter’s empirical prediction data. The three-dimensional cavity width-to-depth ratio (W/D) was 1, 3.8 and 7.6. Computational results indicated that pressure oscillation in the 2D flow was generated by a single-flow structure, whereas a multiple-flow structure generated multiple oscillation peaks in the 3D flow. The flow structure in the 3D cavity was investigated. For the 2D flow case, the cavity internal pressure wave was directly synchronized with the free shear layer. In the 3D flow case, an unstable spanwise flow due to the sidewall was observed. This spanwise fluctuation produced additional pressure oscillations coupled with the streamwise internal pressure wave. The numerical results indicate that the spanwise flow reduces the propagation speed of the internal pressure waves and the intensity of the corresponding pressure fluctuation.

Flapping wing micro-air vehicles are biologically inspired by nature flyers, specifically insects and birds. Specifically, insect wings generally consist of veins and membrane components. In this study, a structural analysis considering the vein/membrane components of an insect-like flapping wing is presented. Co-rotational (CR) finite elements are adopted in order to consider the complex wing configuration including both vein and membrane. The CR beam elements with warping degrees of freedom are employed for veins and CR shell elements for the wing membrane. The present structural analysis is verified against the analytical results obtained by an existing software, and it is validated by comparison to existing results from the literature. A fluid–structure interaction analysis is then performed. In the procedure, an aerodynamic analysis based on three-dimensional preconditioned Navier–Stokes equations is employed. Finally, a comparative study with respect to the structural characteristics is conducted. As a result, an efficiency of the present structural analysis is confirmed by comparing with the existing software. It is found that the present FSI results are in good agreement with the existing experimental and numerical results. Moreover, the passive wing twist may have a significant influence on the hover performance.

In this paper, we present a computational aeroelastic analysis of flexible flapping wings in the vicinity of solid walls. The wall effects change the aerodynamic forces and moments of the wings, and thus the aeroelastic behavior. The numerical simulation is carried out using a fluid–structure interaction framework by coupling the computational fluid dynamics and computational structural dynamics. A preconditioned Navier–Stokes solver based on a finite volume method is used for the aerodynamic analysis. The structural analysis is performed using a nonlinear structural model based on a geometrically exact beam formulation. The method is validated using previous numerical and experimental results. The aeroelastic characteristics of the flexible wings with and without the walls are computed and compared.

This paper presents numerical analyses of lateral jets in supersonic cross flows on a flat plate and on a generic missile. The freestream Mach number is 4 for the flat plate and 3 for the missile, and the jets are sonic for both cases. The numerical results are validated with wind tunnel data such as Schlieren images and surface pressure distributions. The flow structure due to the jet interaction with the supersonic free-stream is examined in terms of the vortex structure. A 3-dimensional compressible RANS solver is used for the study. To describe the effects of high temperature, a thermally perfect gas is assumed. When high temperature is applied, the shock structure changes, which affects the separation region and recirculation zone. Next, the effects of turbulence models on the jet interaction flow are investigated. The Spalart–Allmaras, Menter's shear-stress transport k–ω, Huang and Coakley's k–e, and Coakley's q–ω models are used to analyze the flows. The differences in pressure distribution among the turbulence models are larger in the case of the flat plate than the missile. In addition, several numerical flux functions are compared to investigate their effects on the jet interaction: the Roe scheme with Sanders's H-correction, RoeM scheme, and the HLLE scheme. Although the HLLE scheme shows a little difference at the indent of the barrel shock, the three numerical flux schemes give similar C P distributions on the wall.

Wing flexibility affects the flight performance of flapping-wing micro air vehicles. In this paper, we present a computational approach for the aeroelastic analysis of realistic insect-like flexible flapping wings with hovering and forward-flight modes. A three-dimensional preconditioned Navier–Stokes solver is used with a deforming mesh technique for the aerodynamic analysis of a flapping wing. For the structural analysis, co-rotational (CR) finite elements and CR shell elements are used. As seen from the numerical analysis, wing flexibility leads to thrust increments with the increasing flapping frequency. The advance ratio, however, is the cause of the thrust decrease for flexible flapping wings with high flapping-frequency motions.

The RANS equations are widely used to analyze complex flows over aircraft. The equations require a turbulence model for turbulent flow analyses. A suitable turbulence must be selected for accurate predictions of aircraft aerodynamic characteristics. In this study, numerical analyses of three-dimensional aircraft are performed to compare the results of various turbulence models for the prediction of aircraft aerodynamic characteristics. A 3-D RANS solver, MSAPv, is used for the aerodynamic analysis. The four turbulence models compared are the Sparlart–Allmaras (SA) model, Coakley’s $$q-\omega $$ model, Huang and Coakley’s $$k-\varepsilon $$ model, and Menter’s $$k-\omega $$ SST model. Four aircrafts are considered: an ARA-M100, DLR-F6 wing–body, DLR-F6 wing–body–nacelle–pylon from the second drag prediction workshop, and a high wing aircraft with nacelles. The CFD results are compared with experimental data and other published computational results. The details of separation patterns, shock positions, and $$C_{p}$$ distributions are discussed to find the characteristics of the turbulence models.

During the past few decades, various fluid–structure interaction (FSI) analysis approaches have been developed and applied to understand the physical processes related to a flexible flappin...

Recent advance in flapping-wing MAVs has led to greater attention being paid to the interaction between the structural dynamics of the wing and its aerodynamics, both of which are closely related to the performance of a flapping wing. In this paper, an improved computational framework to simulate a flapping wing is developed. This framework is established by coupling a preconditioned Navier–Stokes solution and a co-rotational beam analysis with a restrained warping degree of freedom. Validation of the present framework is performed by a comparison with examples from either earlier analyses or experiments. Further, a numerical analysis of a wing under simultaneous pitching and plunging motion is examined. The results are compared with those obtained with a wing under pure plunging motion, in order to assess the additional motion effect within a spanwise flexible wing. The comparison shows different aerodynamic characteristics induced by the flexibility of the wing, which can be beneficial.

In this paper, a triangular planar element is developed for a geometrically nonlinear structural analysis, which includes the drilling degrees of freedom using a corotational framework. Based on the assumptions of a small degree of strain and large displacement, the corotational framework allows an accurate geometrically nonlinear structural analysis. The presently improved corotational framework accommodates in-plane rotational behavior (that is, the drilling degrees of freedom) by using the corotational framework corresponding to a solidlike planar element. It focuses on triangular planar elements that will be useful for three-dimensional analysis using a reduced number of degrees while targeting a structure with a complex geometry, such as a flapping wing. Regarding the present analysis, validation by solving both static and time-transient problems is conducted. The fluid–structure interaction framework is then developed by using the present structural analysis. During this validation procedure, the pr...

Realistic computations of flows induced by synthetic jets in multiple flow conditions are studied with an unsteady preconditioned Reynolds-averaged Navier–Stokes solver with deforming meshes. Deforming meshes suitable for structured grid systems are used to simulate the motion of diaphragms driven at a given frequency.With deforming meshes, a boundary-conditionmodel is not necessary for synthetic jet calculations. To obtain time-accurate solutions with a grid system under deformation, the geometric conservation law is employed. Numerical calculations of three cases of the Langley Research Center Workshop Computational Fluid Dynamics Validation of Synthetic Jets and Turbulent Separation Control workshop are carried out, and the computational results are compared with the experimental data. The results indicate the effectiveness of the current method in synthetic jet flow computations.

In this study, fairing configurations for an aircraft are designed and the aerodynamic analyses of the fairings are performed to find the best choice for the aircraft. Fairings considered are wing-tip fairing and wing-body fairing. Wing alone analyses are done for the wing-tip faring selection, while wing-body-tail analyses are done for the wing-body fairing selection. A 3-D RANS solver with Menter`s SST turbulence model are used for the aerodynamic analyses. The effects on the drag of the aircraft are examined by comparing the analysis results with and without the farings.

Luxury sound is one of the most important sound qualities in a premium passenger car. Previous work has shown that, because of the effects of many different interior sounds, it is difficult to evaluate the luxury sound objectively by using only the A-weighted sound pressure level. The characteristics of such sound were systematically investigated and a new objective evaluation was proposed of the luxury sound quality index. This was developed by the systematic combination of the seven major interior sound quality indices based on path analysis. These sounds inside a passenger car were evaluated by the members of a luxury automotive club. Then, by using sound metrics (psychoacoustic parameters) and multiple regression, seven major interior sound quality indexes were developed. Multiple regression was used to model the correlation between objective and subjective evaluation. The newly developed luxury sound quality index can be applied to the objective evaluation of the seven premium passenger cars in a pilot car stage based on the customer preference.

A soft recovery system (SRS) is a device that stops a high speed projectile without damaging the projectile. The SRS is necessary to verify the shock resistant requirements of microelectronics and electro-optic sensors in smart munitions, where the projectiles experience over 20,000 g acceleration inside the barrel. In this study, a computer code for the performance evaluation of a SRS based on ballistic compression decelerator concept has been developed. It consists of a time accurate compressible one-dimensional Euler code with use of deforming grid and a projectile motion analysis code. The Euler code employs Roe’s approximate Riemann solver with a total variation diminishing (TVD) method. A fully implicit dual time stepping method is used to advance the solution in time. In addition, the geometric conservation law (GCL) is applied to predict the solutions accurately on the deforming mesh. The equation of motion for the projectile is solved with the four-stage Runge-Kutta time integration method. A small scale SRS to catch a 20 mm bullet fired at 500 m/s within 1,600 g-limit has been designed with the proposed method.

A new fully automated store-trajectory simulation code has been developed. The method couples a highly robust computational fluid dynamics method and a cut-paste algorithm for Chimera domain decomposition to enhance the efficiency of store-trajectory simulation. The time-step size limitation caused by grid movement is relaxed with the interpolation of solutions in the previous time step. A treatment for orphan cells is also devised to improve the robustness of the method

A new systemized procedure for chimera-domain decomposition is presented. This procedure consists of a new cut-paste algorithm for optimal mesh interface and a two-step search method for donor cell identification. It is fully automated and requires minimal user input. The cut-paste algorithm is based on the advancing front technique in which the fronts are iteratively determined from the initial fronts, which are a collection of fringe points obtained from conventional Chimera hole cutting. The final fronts are determined iteratively in such a way that the overlapping region is minimized. With this method, interpolation points are located away from solid walls where flow gradient is high. We also can reduce the error that may arise from interpolation in stiff gradient regions. Two- and three-dimensional examples are chosen to demonstrate the effectiveness of this new procedure

Numerical simulations of flows around Nagashima et al.'s supersonic inlet with three exit configurations are performed to determine the effects of exit configurations on inlet buzz. Two exits are axisymmetric configurations with different locations, and the other is a 3-D configuration exit with several holes. The supersonic inlet used in the simulations is an external compression type, and axisymmetric except the exit. Three-dimensional simulations are carried out using a Reynolds-averaged Navier-Stokes (RANS) solver with the SpalartAlmaras turbulence model. Results with two axisymmetric exit configurations indicate that the amplitude of the pressure oscillation and the dominant frequency are larger than those of the experimental data. On the other hand, the result with the 3-D configuration exit shows that both the pressure history and the dominant frequency are good agreement with experimental data.

Numerical simulations of 3D aircraft configurations are performed in order to understand the effects that turbulence models have on the aerodynamic characteristics of an aircraft. An in-house CFD code that solves 3D RANS equations and 2-equation turbulence model equations is used for the study. The code applies Roe’s approximated Riemann solver and an AF-ADI scheme. Furthermore van Leer’s MUSCL extrapolation with van Albada’s limiter is adopted. Various versions of Menter’s k-omega SST turbulence models as well as Coakley’s q-omega model are incorporated into the CFD code. Menter’s k-omega SST models include the standard model, the 2003 model, the model incorporating the vorticity source term, and the model containing controlled decay. Turbulent flows over a wing are simulated in order to validate the turbulence models contained in the CFD code. The results from these simulations are then compared to computational results of the 3rd AIAA CFD Drag Prediction Workshop. Moreover, numerical simulations of the DLR-F6 wing-body and wing-body-nacelle-pylon configurations are conducted and compared to computational results of the 2nd AIAA CFD Drag Prediction Workshop. Especially, the aerodynamic characteristics as well as flow features with respect to the turbulence models are scrutinized. The results obtained from each simulation incorporating Menter’s k-omega SST turbulence model variations are compared with one another.Copyright © 2011 by KSME

of the grid size). The solution is considered converged when the maximum absolute residual is one order of magnitude smaller than the truncation error. The convergence history for the stream-function vorticity formulation is similar. The residual of the linear Poisson equation for the stream function is always of machine accuracy and the residual of the vorticity transport equation reduces quadratically; convergence is obtained after six iterations. For the biharmonic equation, convergence takes six iterations and is also quadratic. The solutions in terms of the wall skin-friction distribution are presented in Fig. 2. The results for the three formulations are in excellent agreement and correlate well with the skin-friction distribution presented by Briley. 8 Next, the model problem of a separated flow in a symmetrical diffuser, introduced by Inoue, 9 is examined. The diffuser problem is solved using the stream-function vorticity and the biharmonic formulation. The inlet and outlet boundary of the diffuser are at x = - 1.0 and x = 3.0, respectively. The shape factor of the diffuser wall A = -0.089. The centerline is located at.y = 1.0 and the Reynolds number based on this reference length and the free-stream velocity is R = 6250. The inflow conditions provide the initial conditions for the entire flowfield. Convergence is quadratic and machine zero is reached in 6-7 iterations. The solutions in terms of the wall skin-friction distribution are shown in Fig. 3. The results for the two formulations are in excellent agreement and correlate well with Inoue's results, except for the outflow conditions. In Fig. 3 the solution for the higher Reynolds number, R - 12500, with a larger separation region is also presented. The biharmonic equation is the most efficient of the three formulations in terms of CPU time and storage requirements. The biharmonic program is more than two-times faster and requires more than a factor two less memory than the streamfunction vorticity program. The primitive variable method is the slowest among the three formulations and it puts severe demands on the computer storage requirements. In this case the bandwidth is 0(67V) and this coupled with the increase in the number of variables results in more than a four-fold increase in storage and CPU time as compared to the biharmonic program. Conclusions Three formulations of the two-dimensional Navier-Stokes equations are solved numerically using Newton's method and a direct solution routine for banded matrices. The fully implicit solution techniques use second-order central differencing for all the terms and are shown to be reliable and to provide quadratic convergence. The biharmonic formulation is most efficient in terms of CPU time and memory without loss of accuracy. Finally, while it is well known that iterative methods (line overrelaxation or ADI) for biharmonic equations have very slow rates of convergence, the present study, using direct solvers, indicates that the biharmonic formulation is the most recommended.