Prediction Of Flow Field Research Articles

Performance analysis of a horizontal axis ocean current turbine with spanwise microgrooved surface

The design of turbine blade is a vital issue in the performance of horizontal axis ocean current turbine (HAOCT). The purpose of this paper is to conduct the performance analysis for HAOCT blade with spanwise microgrooved surface, including hydrodynamic analysis and hydrodynamic noise analysis. To recognize the flow around the blades, and to obtain the radiated noise of the turbines, four turbines with different configurations of microgrooved surface are tested through computational fluid dynamics (CFD) method. The hydrodynamic characteristics are obtained based on large eddy simulation (LES), then Ffowcs Williams-Hawkings (FW-H) analogy is used to predict the rotating noise generated by the HAOCT. The accuracy of the numerical predictions of flow field is checked against existing experimental data, with good agreement achieved. The results indicated that the rational design of spanwise microgrooved surface could help to reduce the annoying hydrodynamic noise. Moreover, it is shown that the microgrooved surface in blade tip region has better noise reduction effect than that in blade root region. Nevertheless, the noise reduction effect is obtained at the cost of weakening the thrust and torque at a certain degree.

WakeNet 0.1 - A Simple Three-dimensional Wake Model Based on Convolutional Neural Networks

Deep convolutional neural networks are a promising machine learning approach for computationally efficient predictions of flow fields. In this work we present a simple modelling framework for the prediction of the time-averaged three-dimensional flow field of wind turbine wakes. The proposed model requires the mean inflow upstream of the turbine, aerodynamic data of the turbine and the tip-speed ratio as input data. The output comprises all three mean velocity components as well as the turbulence intensity. The model is trained with the flow statistics of 900 actuator line large-eddy simulations of a single turbine in various inflow and operating conditions. The model is found to accurately predict the characteristic features of the wake flow. The overall accuracy and efficiency of the model render it as a promising approach for future wind turbine wake predictions.

Linear and weakly nonlinear dominant dynamics in a boundary layer flow

The aim of this paper is to investigate the linear and weakly nonlinear dynamics in flow over a flat-plate with leading edge. Linear optimal and suboptimal inflow perturbations are obtained using a Lagrangian multiplier technique. In particular, the suboptimal inflow conditions and the corresponding downstream responses are investigated in detail for the first time. Unlike the suboptimal dynamics reported in other canonical cases such as the backward-facing step flow, the growth rate of the suboptimal perturbation is in the same order as the optimal one, and both of them depend on the lift-up mechanism even though they are orthogonal. The suboptimal mode has an additional layer of vorticity that penetrates into the boundary layer farther downstream, generating a second patch of high- and low-speed streaks. The farther suboptimal ones spread to the free-stream without entering the boundary layer. The weakly nonlinear dynamics are examined by decomposing the flow field into multiple orders of perturbations using the Volterra series. Small structures in the higher order perturbations mainly concentrate in the region farther away from wall, suggesting a mechanism of outward perturbation developments, which is opposite with the well reported inward development of perturbations, i.e., from free-stream to boundary layer. The significance of these modes is then demonstrated through a prediction of flow field from the inflow condition by exploiting the orthogonality of the modes.

Prediction model of temperature field in dual-mode combustors based on wall pressure

Effective acquisition of the complex flow fields in dual-mode combustors is valuable in improving dual-mode combustor performance. Introducing deep learning methods for fast flow field prediction is an effective way to provide high-quality temperature fields in a dual-mode combustor. A data-driven model to obtain temperature fields based on wall pressure of a dual-mode combustor is proposed in this paper. The temperature fields in dual-mode combustors depend on the combustor geometry, incoming flow condition, and equivalent ratio. The prediction model takes convolutional neural network as the main framework and includes multiple branches. The trained temperature field prediction model can effectively output the temperature distribution of the combustor with the input of wall pressure. The temperature field prediction accuracy has been discussed in depth. From the analysis results, the effectiveness and accuracy of the approach have been demonstrated under the current dataset.

PINN-Based Method for Predicting Flow Field Distribution of the Tight Reservoir after Fracturing

The physical-informed neural network (PINN) model can greatly improve the ability to fit nonlinear data with the incorporation of prior knowledge, which endows traditional neural networks with interpretability. Considering the seepage law in the tight reservoir after hydraulic fracturing, a model based on PINN and two-dimensional seepage physical equations was proposed, which can effectively predict the flow field distribution of the tight reservoir after fracturing. Firstly, the dataset was obtained based on physical and numerical models of the tight reservoirs developed by volume fracturing. Furthermore, coupling the neural networks and the two-dimensional unsteady seepage equation, a PINN model was developed to predict the flow field distribution of the tight reservoir. Finally, a systematic study was performed concerning the noise corruption levels, training iterations, and training sample size that affect the prediction results of PINN models. Besides, a comparison between PINN and traditional deep neural networks (DNN) was presented. The results show that the DNN model was not only sensitive to noisy data but also more vulnerable to overfitting as the training iterations increase. In addition, the prediction accuracy cannot be guaranteed when the samples are inadequate (<500). In contrast, the PINN model was less affected by noise and training iterations and thus indicates greater stability. Moreover, the PINN model outperforms the DNN model in the case of inadequate samples attributing to prior knowledge. This study confirms that the adopted PINN model can provide algorithmic support for the accurate prediction of flow field distribution of the tight reservoirs.

Computational modelling of turbulent Taylor–Couette flow for bearing chamber applications: A comparison of unsteady Reynolds-averaged Navier–Stokes models

The capability to accurately model fluid flow within rotating Taylor–Couette systems has a primary role in informing computational investigations of rotating machinery. There is considerable uncertainty regarding selection of modelling approach, including a suitable turbulence model, that can accurately resolve turbulence within such complex flows while remaining computationally feasible for industrially relevant applications. This paper presents a numerical comparison of axisymmetric and three-dimensional unsteady Reynolds-averaged Navier–Stokes (URANS) turbulence models within ANSYS Fluent. The CFD geometries are representative of ones for which there are published experimental measurements. For the Taylor–Couette study, investigation into inner cylinder start-up procedure, based on previous published findings, confirmed that the final state of the flow is highly dependent on the initial conditions and acceleration rate. Once Taylor vortices form and stabilise, they are not disrupted by small steps in inner cylinder speed, allowing computationally efficient accelerations. Investigations into applying rotational periodicity were unsuccessful, resulting in a significantly reduced core velocity. Axisymmetric predictions provided reasonable agreement with experimental data only at low rotation rates. A good prediction of the velocity flow field was obtained for three-dimensional simulations of the full 360° domain with differences of less than 5% for radial velocities. Among the URANS models, the standard k-ω model and baseline Reynolds stress model (BSL-RSM) provided the closest agreement to published experimental data. In the paper, the developed Taylor–Couette turbulence modelling methodology is extended to a bearing chamber geometry. Analysis of the secondary vortex flow field is compared both qualitatively and quantitatively to published bearing chamber experimental measurements. Overall, whilst a good agreement is still found using the standard k-ω turbulence model, discrepancies arise with the BSL-RSM. However, for this more complex bearing chamber environment compared to a Taylor–Couette flow, the shear stress transport k-ω turbulence model provided the closest agreement and is recommended for future bearing chamber modelling.

A deep learning approach to predicting permeability of porous media

In this work, a data-driven surrogate to high-fidelity numerical simulations is developed to replace the numerical simulations of porous media., This model can accurately predict flow fields for new sets of simulation runs by learning the communications among grid cells in the numerical domain. Because of the many possible random arrangements of particles and their orientation to each other, generalization of permeability with high accuracy is not trivial — nor is it practical using conventional means. Furthermore, building a comprehensive database for different grain/pore arrangements is impossible because of the cost of running numerical simulations to generate the database that represents all possible arrangements. The objective is to predict grid-level flow fields in porous media as a priori to determine the permeability of porous media. This work is a continuation of our previous research. The rationale is that once the detailed grid-level dynamics can be accurately predicted using a data-driven approach, for any configuration/topology of the porous media, the detailed dynamics could be predicted without any need for new expensive new numerical simulation runs. In this work, we improved previous work by accurately predicting permeability of the porous media, irrespective of the grain density, pore/grain shape, with a significant reduction in computational time as opposed to previous work, which was limited to a unique grain shape/size. The surrogate model is developed by employing a deep learning technique using high-fidelity numerical simulations for two-dimensional porous media consisting of circular grains, generated by varying the number and size of the circular solid grains. The robustness of the developed model is then tested for numerous variations of porous media – generated by changing the number and size of the solid grain angularity and elongation – which have not been used for developing the model. The deep convolutional neural network employed in this work combines deep U-Net and ResNet structures to capture context and enable precise localization while avoiding issues in training caused by vanishing gradients.

Finite volume method network for the acceleration of unsteady computational fluid dynamics: Non‐reacting and reacting flows

Despite rapid improvements in the performance of the central processing unit (CPU), the calculation cost of simulating chemically reacting flow using CFD remains infeasible in many cases. The application of the convolutional neural networks (CNNs) specialized in image processing in flow field prediction has been studied, but the need to develop a neural network design fitted for CFD has recently emerged. In this study, a neural network model introducing the finite volume method (FVM) with unique network architecture and physics-informed loss function was developed to accelerate CFD simulations. The developed network model, considering the nature of the CFD flow field where the identical governing equations are applied to all grids, can predict the future fields with only two previous fields unlike the CNNs requiring many field images (>10 000). The performance of this baseline model was evaluated using CFD time series data from non-reacting flow and reacting flow simulation; counterflow and hydrogen flame with 20 detailed chemistries. Consequently, we demonstrated that (a) the FVM-based network architecture provided significantly improved accuracy of multistep time series prediction compared to the previous MLP model (b) the physic-informed loss function prevented non-physical overfitting problem and ultimately reduced the error in time series prediction (c) observing the calculated residuals in an unsupervised manner could monitor the network accuracy. Additionally, under the reacting flow dataset, the computational speed of this network model was measured to be about 10 times faster than that of the CFD solver.

Accurate prediction of the particle image velocimetry flow field and rotor thrust using deep learning

With particle image velocimetry (PIV), cross-correlation and optical flow methods have been mainly adopted to obtain the velocity field from particle images. In this study, a novel artificial intelligence (AI) architecture is proposed to predict an accurate flow field and drone rotor thrust from high-resolution particle images. As the ground truth, the flow fields past a high-speed drone rotor obtained from a fast Fourier transform-based cross-correlation algorithm were used along with the thrusts measured by a load cell. Two deep-learning models were developed, and for instantaneous flow-field prediction, a generative adversarial network (GAN) was employed for the first time. It is a spectral-norm-based residual conditional GAN translator that provides a stable adversarial training and high-quality flow generation. Its prediction accuracy is 97.21 % (coefficient of determination, or R2). Subsequently, a deep convolutional neural network was trained to predict the instantaneous rotor thrust from the flow field, and the model is the first AI architecture to predict the thrust. Based on an input of the generated flow field, the network had an R2 accuracy of 94.57 %. To understand the prediction pathways, the internal part of the model was investigated using a class activation map. The results showed that the model recognized the area receiving kinetic energy from the rotor and successfully made a prediction. The proposed architecture is accurate and nearly 600 times faster than the cross-correlation PIV method for real-world complex turbulent flows. In this study, the rotor thrust was calculated directly from the flow field using deep learning for the first time.

Unsteady flow prediction from sparse measurements by compressed sensing reduced order modeling

Prediction of complex fluid flows from sparse and noisy sensor measurements is widely applied to many engineering fields. In the present study, a novel compressed sensing reduced-order modeling framework has been proposed to predict unsteady flow fields from sparse and noisy sensor observations, which includes offline learning and online forecasting. In the offline learning stage, the Long Short Term Memory (LSTM) model is used for modeling the dynamic evolution of the sensor signals. Moreover, the sparsity-promoting Dynamic Mode Decomposition (DMD) algorithm is applied to extract spatio-temporal coherent structures from high-dimensional fluid dynamic system and choose optimal DMD modes for flow reconstruction. In order to establish the correlation between sensor space and feature-based coherent structures space, the Deep Neural Network (DNN) is employed. In the online forecasting stage, the trained framework is applied to predict the flow fields from limited sensor measurements in the actual experiment setup. In the current work, the proposed framework is applied in two numerical examples, including the flow past a circle cylinder at Re=100 characterized by laminar flow and at Re=3900 characterized by turbulent flow. It is shown that the proposed framework performs accurately and robustly in both prediction of sensor measurements and unsteady flow fields. Especially, the important physical features and quantities can be well maintained for both laminar and turbulent flow, even if high level noise is involved. Therefore, the proposed framework is a promising tool for sparse representation from complex flow fields in realistic experiments.

Unsteady physics-based reduced order modeling for large-scale compressible aerodynamic applications

A physics-based reduced order model is presented as a viable approach to accurately predict unsteady flowfield solutions at a fraction of the computational time that is required by high fidelity computational fluid dynamics solvers. Such a model could be useful during the preliminary phases of the aircraft design process when an accurate prediction of unsteady loads is crucial to reduce the uncertainty of design choices. This paper extends the formulation of a previously defined technique to unsteady aerodynamic problems involving motion excitation in both subsonic and transonic conditions. In particular, the proposed unsteady-residual-based model defines a reduced solution space by applying proper orthogonal decomposition to a set of snapshots collected from the unsteady high fidelity simulations. Approximate flow solutions for unseen motion signals is then obtained in a time-marching fashion where, at each time step, the prediction coefficients are computed via L2-norm minimization of the unsteady residual vector as provided from the underlying flow solver. As suggested by previous studies, a further reduction of computational complexity is attempted by including a hyperreduction node selection, specifically the missing point estimation routine, in the prediction framework. Different model reduction and hyperreduction levels for the flowfield prediction of harmonic pitching motion of a 2D airfoil and a 3D aircraft in both subsonic and transonic conditions are investigated to determine their influence on the solution accuracy as well as on the required computational cost. Results show that the proposed technique accurately predicts unsteady solutions (maximum prediction error of about 3%) with a computational cost that is around 10% of the time needed to perform the equivalent high fidelity simulations. This performance achievement substantiates the idea that a reduced order model based on unsteady residual minimization is viable replacement for expensive flow solver evaluations in various applications where the computational budget is constrained.

Laminar Mixing in Corotating Disk Processors

Abstract Qualitative and quantitative studies of laminar mixing in a corotating disk processor chamber were carried out experimentally and theoretically. Theoretical study of the flow field in a parallel chamber indicates the presence of an orthogonal circulation flow pattern with a double circulation pattern at constant radii. A color tracer was used for studying experimentally the laminar mixing. The experiments verified the theoretically predicted flow fields and showed that the two orthogonal flow patterns bring about a composition randomization throughout the volume. Quantitative measurement of interfacial area evolution helped in characterizing the laminar mixing behaviour of such a configuration.

Three-dimensional deep learning-based reduced order model for unsteady flow dynamics with variable Reynolds number

In this article, we present a deep learning-based reduced order model (DL-ROM) for predicting the fluid forces and unsteady vortex shedding patterns. We consider the flow past a sphere to examine the accuracy of our DL-ROM predictions. The proposed DL-ROM methodology relies on a three-dimensional convolutional recurrent autoencoder network (3D CRAN) to extract the low-dimensional flow features from the full-order snapshots in an unsupervised manner. The low-dimensional features are evolved in time using a long short-term memory-based recurrent neural network and reconstructed back to the full-order as flow voxels. These flow voxels are introduced as static and uniform query probes in the point cloud domain to reduce the unstructured mesh complexity while providing convenience in the 3D CRAN training. We introduce a novel procedure to recover the interface description and the instantaneous force quantities from these 3D flow voxels. To evaluate the 3D flow reconstruction and inference, the 3D CRAN methodology is first applied to an external flow past a static sphere at the single Reynolds number of Re = 300. We provide an assessment of the computing requirements in terms of the memory usage, training, and testing cost of the 3D CRAN framework. Subsequently, variable Re-based flow information is infused in one 3D CRAN to learn a symmetry-breaking flow regime (280 ≤ Re ≤ 460) for the flow past a sphere. Effects of transfer learning are analyzed for training this complex 3D flow regime on a relatively smaller time series dataset. The 3D CRAN framework learns the flow regime nearly 20 times faster than the parallel full-order model and predicts this flow regime in time with a reasonable accuracy. Based on the predicted flow fields, the network demonstrates an R2 accuracy of 98.58% for the drag and 76.43% for the lift over the sphere in this flow regime. The proposed framework aligns with the development of a digital twin for 3D unsteady flow field and instantaneous force predictions with variable Re-based effects.

Modeling total drag force exerted on particles in dense swarm from experimental measurements using an inline image-based method

• A procedure from measurements is developed to establish the total drag model. • The new model is applicable from dilute to dense suspensions. • It predicts the holdup distributions with higher precision. • This procedure is also applicable to other multiphase systems. It is of significance but still a great challenge to model drag force exerted on particles in dense systems directly from experimental measurements. In this work, a new procedure using inline experimental measurements is developed to establish a total drag model. Specifically, local flow characteristics including slip velocity, particle holdup and particle acceleration are measured simultaneously using an inline vision probe. Then, the total drag coefficient exerted on particles in suspension is calculated using the inline data with the unsteady motion of particles taken into account. At last, the total drag coefficient versus five dimensionless numbers including all important factors are correlated as C D = 3.55 × 10 - 2 ρ r - 1.82 A r 0.53 Re l 0.45 Re - 1.79 α P - 0.49 . Systematically evaluated using the image-based results in this work and PEPT data in the reference as well as Tang model, Gidaspow model and Brucato model popularly used in suspensions, the newly developed model shows some excellent characteristics. (i) It can predict flow field and solid holdup distributions with sufficient accuracy in a wider range of holdups from dilute to dense systems. (ii) Especially, the prediction precision is significantly higher (with deviation of 5.6%) in the holdup distribution compared to Gidaspow model, Brucato model and Tang model. (iii) Furthermore, better mass conservation is always kept during the simulation process compared to the other three models. It is preliminarily inferred that some particles are not fully suspended due to the smaller drag force in the case of Gidaspow model. More studies are still needed to explain quantitatively the above evaluation results.

Inverse Design and Optimization of Low Specific Speed Centrifugal Pump Blade Based on Adaptive POD Hybrid Model

To improve the prediction accuracy of the surrogate model and reduce the calculation cost for hydraulic optimization design of centrifugal pump impeller, an inverse design and optimization method based on adaptive proper orthogonal decomposition (APOD) hybrid model was proposed. Initial samples were designed by perturbing blade control parameters of the original model. The samples were classified using the K-means clustering algorithm, and the adaptive samples were selected according to the category of the objective sample. The snapshot set is composed of blade shape parameters and the CFD flow field data in impeller, which is decomposed into a linear combination of orthogonal bases by the proper orthogonal decomposition (POD) method to predict the objective parameters. According to the objective load distribution, the low specific speed centrifugal pump was inversely designed by using the APOD model, and its initial blade was obtained. And then, the flow field corresponding to disturbed blade shape was predicted using the APOD method, so as to evaluate the gradient of the objective function to design variables. Finally, the initial blade was optimized by the gradient descent method. The results show that the APOD hybrid model method can be employed to accomplish the blade inverse design and the flow field prediction in the optimization design of centrifugal impeller, which significantly reduces the numerical calculation cost and improves the accuracy of the flow field prediction.

Multifidelity aerodynamic flow field prediction using random forest-based machine learning

In this paper, a novel random forest (RF)-based multifidelity machine learning (ML) algorithm to predict the high-fidelity Reynolds-averaged Navier-Stokes (RANS) flow field is proposed. The RF ML algorithm is used to increase the fidelity of a low-fidelity potential flow field. Three cases are studied, the first two consist of a flow past a backward-facing step, and the third, a subsonic flow around an airfoil. In the first case, the data is generated using ten different inlet velocities, in the second using six different step heights, and in the third using 20 different airfoil shapes parameterized using B-spline curves. Input parameters to RF are case dependent. For the first case, the x and y cell-center locations and the corresponding x and y potential flow velocities, along with the specified inlet velocity, are used. For the second, the cell-center values are nondimensionalized using the step height, and the step height is used in place of the inlet velocity. The remaining two input features used are the same as in the previous case. For the third case, the potential flow stream function and velocity potential along with the B-spline control point values are used as input variables. The outputs of the RF algorithm are the same for all the cases and include the RANS velocities, pressures, and turbulent viscosities. The results in this study are compared to those generated using the tensorFlowFoam (TFF) and from directly solving the RANS equations. To quantify the errors, the absolute error and relative L2 norm error metrics are used. The results show that for the first two cases, RF consistently has two to 30 times lower relative L2 norm compared to TFF, with the only exception being the turbulent viscosities for the second case. For the third case, RF is better at predicting the pressure and skin friction coefficients for the RAE 2822 airfoil compared to the NACA 0012 airfoil. The relative L2 norm error is 1.67 and 1.19 times lower for the pressure and skin friction coefficients, respectively.

Evaluation of machine learning algorithms for predictive Reynolds stress transport modeling

The application of machine learning (ML) algorithms to turbulence modeling has shown promise over the last few years, but their application has been restricted to eddy viscosity based closure approaches. In this article, we discuss the rationale for the application of machine learning with high-fidelity turbulence data to develop models at the level of Reynolds stress transport modeling. Based on these rationales, we compare different machine learning algorithms to determine their efficacy and robustness at modeling the different transport processes in the Reynolds stress transport equations. Those data-driven algorithms include Random forests, gradient boosted trees, and neural networks. The direct numerical simulation (DNS) data for flow in channels are used both as training and testing of the ML models. The optimal hyper-parameters of the ML algorithms are determined using Bayesian optimization. The efficacy of the above-mentioned algorithms is assessed in the modeling and prediction of the terms in the Reynolds stress transport equations. It was observed that all three algorithms predict the turbulence parameters with an acceptable level of accuracy. These ML models are then applied for the prediction of the pressure strain correlation of flow cases that are different from the flows used for training, to assess their robustness and generalizability. This explores the assertion that ML-based data-driven turbulence models can overcome the modeling limitations associated with the traditional turbulence models and ML models trained with large amounts of data with different classes of flows can predict flow field with reasonable accuracy for unknown flows with similar flow physics. In addition to this verification, we carry out validation for the final ML models by assessing the importance of different input features for prediction.

Modeling Transport of SARS-CoV-2 Inside a Charlotte Area Transit System (CATS) Bus

We present in this paper a model of the transport of human respiratory particles on a Charlotte Area Transit System (CATS) bus to examine the efficacy of interventions to limit exposure to SARS-CoV-2, the virus that causes COVID-19. The methods discussed here utilize a commercial Navier–Stokes flow solver, RavenCFD, using a massively parallel supercomputer to model the flow of air through the bus under varying conditions, such as windows being open or the HVAC flow settings. Lagrangian particles are injected into the RavenCFD predicted flow fields to simulate the respiratory droplets from speaking, coughing, or sneezing. These particles are then traced over time and space until they interact with a surface or are removed via the HVAC system. Finally, a volumetric Viral Mean Exposure Time (VMET) is computed to quantify the risk of exposure to the SARS-CoV-2 under various environmental and occupancy scenarios. Comparing the VMET under varying conditions should help identify viable methods to reduce the risk of viral exposure of CATS bus passengers during the COVID-19 pandemic.

Quantitation of the uncertainty in the prediction of flow fields induced by the spatial variation of the fracture aperture

The problem of fluid flow in a single fracture with variable aperture is analyzed from a stochastic point of view. The spatially distributed fracture aperture is treated as a random variable and the random aperture process can be characterized as a zero-order intrinsic random process (nonstationary random process with homogeneous increments), resulting in nonstationary flow fields. To characterize the stochastic behavior of the flow process, the general solutions for the mean values of and variances of the pressure head and the integrated flux in the mean flow direction are derived. These derivations are performed using the Fourier-Stieltjes representation approach. The mean is an unbiased estimator and the variance can be used to characterize the uncertainty of the mean model. The theory is applied to the case where the process of random aperture can be described as fractal Brownian motion. The analysis shows that the larger the parameter H, the greater the variance of pressure head and integrated flux. The transfer function helps smooth out much of the small-scale variation caused by the random aperture field. The variance (uncertainty) of the integrated flux in x-direction around the mean flux (or the classical deterministic model solution) increases with distance. Estimation of total flux through a natural fractured system is often evaluated for the purpose of rational management of groundwater resources. The proposed stochastic theory for flow prediction under uncertainty under the natural field conditions as input to the flow model for a fractured system should provide useful information for regional groundwater resource management. To our knowledge, the subject of fluid flow in nonstationary random flow fields has not yet been addressed in fracture. Our findings will be useful for the interpretation of real field data and as a stimulus for further research in this area.

Transonic small disturbance unsteady potential flow over very high aspect ratio wings

AbstractIn this paper, the prediction of the unsteady flow field over typical high aspect ratio (AR) wings in the transonic flow regime but below the sonic Mach number is of interest. The methodology adopted is a computational approach based on the transonic small disturbance unsteady potential equation. It is shown that the higher AR wings generally have a higher lift coefficient as well as a higher lift-to-drag ratio. With NASA’s common research model (CRM) wing, there is an increase in maximum lift with increasing AR while the induced drag is almost the same. There is also an optimum sweep angle, which is different for each angle-of-attack so that variable sweep lifting surfaces may be designed to provide optimum solutions. The computed flutter speeds indicate an expected reduction with increasing AR.