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1. Parallel Unsteady Reynolds-Averaged Navier-Stokes (URANS) Studies of the Performance of ONR Waterjet AxWJ-2

   Stephen E. Monroe (March 2023, AIAA Region I Conference, March 2023)

   The accuracy of SimericsMP+ Unsteady Reynolds-Averaged Navier-Stokes (URANS) model is validated by studying turbulent flow past counter-rotating propellers (CRPs). Subsequently, URANS is used to study the axial flow in an Office of Naval Research (ONR) waterjet and its performance. Specifically, experimental data from Miller (1976) is employed for comparison against the URANS results. Due to the large number of degrees of freedom for both simulations, parallel computing over 80 cores is involved. For the CRP study, torque and thrust coefficients are plotted against a range of advance ratios, ensuring a Reynolds number of less than 500,000. For the waterjet, torque and head coefficients are plotted for a range of flow rates at a Reynolds number of 1.25 × 106. For both studies, two different mesh resolutions are utilized. The finer meshes of both studies contained roughly four times the total number of cells found in their respective coarse meshes. These refinements lead to minor improvements, showing good convergence. The URANS torque and thrust coefficients are found to be within 10% of that from experimental data across all advance ratios for the CRP set, showing good agreement. The torque and head coefficients for the waterjet displayed even better agreement, with the greatest error across all flow conditions remaining under 3%. It is concluded that the stator is responsible for 20% of the waterjets power production. 

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2. State Space Modeling of Viscous Unsteady Aerodynamic Loads

   https://doi.org/10.2514/6.2021-1830  

   Taha, Haitham E.; Rezaei, Amir S. (January 2021, AIAA SciTech)

   null (Ed.)

   In this paper, we started by summarizing our recently developed viscous unsteady theory based on coupling potential flow with the triple deck boundary layer theory. This approach provides a viscous extension of potential flow unsteady aerodynamics. As such, a Reynolds- number-dependence could be determined. We then developed a finite-state approximation of such a theory, presenting it in a state space model. This novel nonlinear state space model of the viscous unsteady aerodynamic loads is expected to serve aerodynamicists better than the classical Theodorsen’s model, as it captures viscous effects (i.e., Reynolds number dependence) as well as nonlinearity and additional lag in the lift dynamics; and allows simulation of arbitrary time-varying airfoil motions (not necessarily harmonic). Moreover, being in a state space form makes it quite convenient for simulation and coupling with structural dynamics to perform aeroelasticity, flight dynamics analysis, and control design. We then proceeded to develop a linearization of such a model, which enables analytical results. So, we derived an analytical representation of the viscous lift frequency response function, which is an explicit function of, not only frequency, but also Reynolds number. We also developed a state space model of the linearized response. We finally simulated the nonlinear and linear models to a non- harmonic, small-amplitude pitching maneuver at 100 , 000 Reynolds number and compared the resulting lift and pitching moment with potential flow, in reference to relatively higher fidelity computations of the Unsteady Reynolds-Averaged Navier-Stokes equations. 

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3. Viscous extension of potential-flow unsteady aerodynamics: the lift frequency response problem

   https://doi.org/10.1017/jfm.2019.159  

   Taha, Haithem; Rezaei, Amir S. (June 2019, Journal of Fluid Mechanics)

   The application of the Kutta condition to unsteady flows has been controversial over the years, with increased research activities over the 1970s and 1980s. This dissatisfaction with the Kutta condition has been recently rejuvenated with the increased interest in low-Reynolds-number, high-frequency bio-inspired flight. However, there is no convincing alternative to the Kutta condition, even though it is not mathematically derived. Realizing that the lift generation and vorticity production are essentially viscous processes, we provide a viscous extension of the classical theory of unsteady aerodynamics by relaxing the Kutta condition. We introduce a trailing-edge singularity term in the pressure distribution and determine its strength by using the triple-deck viscous boundary layer theory. Based on the extended theory, we develop (for the first time) a theoretical viscous (Reynolds-number-dependent) extension of the Theodorsen lift frequency response function. It is found that viscosity induces more phase lag to the Theodorsen function particularly at high frequencies and low Reynolds numbers. The obtained theoretical results are validated against numerical laminar simulations of Navier–Stokes equations over a sinusoidally pitching NACA 0012 at low Reynolds numbers and using Reynolds-averaged Navier–Stokes equations at relatively high Reynolds numbers. The physics behind the observed viscosity-induced lag is discussed in relation to wake viscous damping, circulation development and the Kutta condition. Also, the viscous contribution to the lift is shown to significantly decrease the virtual mass, particularly at high frequencies and Reynolds numbers. 

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4. Effect of Viscous Unsteady Aerodynamics on Flutter Calculation

   https://doi.org/10.2514/6.2019-2036  

   Taha, Haitham E.; Rezaei, Amir S. (January 2019, AIAA SciTech)

   Many studies over the 1960’s reported failure in predicting accurate flutter boundaries using the classical theory of unsteady aerodynamics even at zero angle of attack and/or lift conditions. Since the flutter phenomenon lies in the intersection between unsteady aerodynamics and structural dynamics, and because the structural dynamics of slender beams can be fairly predicted, it was inferred that the problem stems from the classical theory of unsteady aerodynamics. As a result, a research flurry occurred over the 1970’s and 1980’s investigating such a theory, with particular emphasis on the applicability of the Kutta condition to unsteady flows. There was almost a consensus that the Kutta condition must to be relaxed at high frequencies and low Reynolds numbers, which was also concluded from several recent studies of the unsteady aerodynamics of bio-inspired flight. Realizing that vorticity generation and lift development are essentially viscous processes, we develop a viscous extension of the classical theory of unsteady aerodynamics, equivalently an unsteady extension of the boundary layer theory. We rely on a special boundary layer theory that pays close attention to the details in the vicinity of the trailing edge: the triple deck theory. We use such a theory to relax the Kutta condition and determine a viscous correction to the inviscid unsteady lift. Using the developed viscous unsteady model, we develop a Reynolds-number-dependent lift frequency response (i.e., a viscous extension of Theodorsen’s). It is found that viscosity induces a significant phase lag to the lift development beyond Theodorsen’s inviscid solution, particularly at high frequencies and low Reynolds numbers. Since flutter, similar to any typical hopf bifurcation, is mainly dictated by the phase difference between the applied loads and the motion, it is expected that the viscosity-induced lag will affect the flutter boundary. To assess such an effect, we couple the developed unsteady viscous aerodynamic theory with a structural dynamic model of a typical section to perform aeroelastic simulation and analysis. We compare the flutter boundary determined using the developed viscous unsteady model to that of Theodorsen’s. 

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5. Multifidelity modeling similarity conditions for airfoil dynamic stall prediction with manifold mapping

   https://doi.org/10.1108/EC-11-2020-0650  

   Raul, Vishal; Leifsson, Leifur (September 2021, Engineering Computations)

   null (Ed.)

   Purpose The purpose of this work is to investigate the similarity requirements for the application of multifidelity modeling (MFM) for the prediction of airfoil dynamic stall using computational fluid dynamics (CFD) simulations. Design/methodology/approach Dynamic stall is modeled using the unsteady Reynolds-averaged Navier–Stokes equations and Menter's shear stress transport turbulence model. Multifidelity models are created by varying the spatial and temporal discretizations. The effectiveness of the MFM method depends on the similarity between the high- (HF) and low-fidelity (LF) models. Their similarity is tested by computing the prediction error with respect to the HF model evaluations. The proposed approach is demonstrated on three airfoil shapes under deep dynamic stall at a Mach number 0.1 and Reynolds number 135,000. Findings The results show that varying the trust-region (TR) radius (λ) significantly affects the prediction accuracy of the MFM. The HF and LF simulation models hold similarity within small (λ ≤ 0.12) to medium (0.12 ≤ λ ≤ 0.23) TR radii producing a prediction error less than 5%, whereas for large TR radii (0.23 ≤ λ ≤ 0.41), the similarity is strongly affected by the time discretization and minimally by the spatial discretization. Originality/value The findings of this work present new knowledge for the construction of accurate MFMs for dynamic stall performance prediction using LF model spatial- and temporal discretization setup and the TR radius size. The approach used in this work is general and can be used for other unsteady applications involving CFD-based MFM and optimization. 

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