Rolf Verberg

Rheology of particle suspensions with low to moderate fluid inertia at finite particle inertia

The lattice Boltzmann method is applied to simulate the rheology of particle suspensions with low-to-moderate fluid inertia and a wide range of particle inertia. The viscous dissipation in a suspension of particles with a Maxwellian velocity distribution is shown to have a linear dependence on the Reynolds number similar to the Ergun correlation for the drag in a fixed bed of particles. Dynamic simulations of the flow of a suspension of elastic particles being sheared between two rough walls are used to determine the range of Reynolds and Stokes numbers for which a treatment of a homogeneous, sheared suspension based on kinetic theory and the simulated viscous dissipation can accurately describe the particle-phase kinetic energy and effective viscosity of the suspension. The dependence of the particle-phase slip velocity and the depletion of particles near the boundaries on the particle volume fraction and Stokes number is determined.

Reduced-order Model for NASA Space Launch System Liftoff Aerodynamics

Reduced-order aerodynamic models have been developed for the lift-off phase of NASA’s Space Launch System (SLS), using physics-based modeling technology that serves several purposes. Conventional aerodynamic models establish relationships between operational variables and the forces and moments acting on the airframe—often in the form of response surfaces and “look-up” tables. The physics-based modeling technology provides more information than conventional aerodynamic models: spatially distributed surface properties in addition to integrated forces and moments. The capability enables tighter coupling of the engineering disciplines, integrating aerodynamics, structural dynamics, and flight control at all stages of the system development process. The modeling technology also facilitates accurate and efficient assimilation of heterogeneous data from computational simulations of varying fidelity and computational expense, from ground tests, and from flight tests. The computationally efficient aerodynamic models enable fast-turnaround conceptual design trade studies, flight simulations, and detailed system development with data fusion. Construction of the SLS lift-off aerodynamic model utilized two sets of computational fluid dynamics (CFD) solutions, one based on Reynolds-averaged Navier-Stokes (RANS) simulations and the other on detached eddy simulations (DES). These data were assimilated with wind tunnel measurements of six-degrees-of-freedom forces and moments and surface pressures. The model was evaluated through comparisons between model predictions of forces, moments, and pressures and wind tunnel and CFD values.

A Reduced-Order Model of an Aeroelastic Wing Exhibiting a Sub-Critical Hopf Bifurcation

Reduced-order aeroelastic models have been formulated for an AGARD 445.6 wing that exhibits limit cycle oscillations and a sub-critical Hopf bifurcation. The nonlinear aeroelastic behavior and sensitivity to initial conditions requires a nonlinear model. The flow dynamics are approximated with a low-dimensional set of eigenmodes, utilizing the method of proper orthogonal decomposition. The reduced-order flow model is coupled to a modal representation of the structural dynamics, forming a small set of nonlinear ordinary differential equations that comprise the aeroelastic model. The physics-based, reduced-order model is constructed with data from a subset of aeroelastic CFD simulations. The method is evaluated by comparing predictions of bifurcating responses (stability or limit cycle oscillations) from a much larger set of aeroelastic CFD simulations that includes on-design conditions used to construct the model and off-design conditions that were not used for model construction. The reduced-order model correctly predicts the sensitivity to initial perturbations and is four orders of magnitude smaller than the aeroelastic CFD model with a commensurate reduction in computational overhead.

Flutter Predictions with a Reduced-Order Aeroelastic Model

Reduced-order aeroelastic models have been formulated to approximate the flow dynamics with a low-dimensional set of eigenmodes, utilizing the method of proper orthogonal decomposition. The reduced-order flow model is coupled to a modal representation of the structural dynamics, forming a small set of ordinary differential equations that comprise the aeroelastic model. The eigenvalues of the system of linear equations determine aeroelastic response. The physics-based, reduced-order model is constructed with data from a relatively small set aeroelastic CFD simulations. The method was evaluated by comparing predictions of the flutter boundary of an AGARD 445.6 wing to a boundary computed with data from much larger sets of aeroelastic CFD simulations that include the on-design runs used to construct the model and off-design runs that were not used during model construction. The correspondence between each reduced-order model and its high-dimensional, parent model is reasonably close, and the difference in size between the two is four orders of magnitude with a commensurate reduction in computational overhead.

Dense, bounded shear flows of agitated solid spheres in a gas at intermediate Stokes and finite Reynolds numbers

We consider moderately dense bounded shear flows of agitated homogeneous inelastic frictionless solid spheres colliding in a gas between two parallel bumpy walls at finite particle Reynolds numbers, volume fractions between 0.1 and 0.4, and Stokes numbers large enough for collisions to determine the velocity distribution of the spheres. We adopt a continuum model in which constitutive relations and boundary conditions for the granular phase are derived from kinetic theory, and in which the gas contributes a viscous dissipation term to the fluctuation energy of the grains. We compare its predictions to recent lattice-Boltzmann (LB) simulations. The theory underscores the role played by the walls in the balances of momentum and fluctuation energy. When particle inertia is large, the solid volume fraction is nearly uniform, thus allowing us to treat the rheology using unbounded flow theory with an effective shear rate, while predicting slip velocities at the walls. When particle inertia decreases or fluid inertia increases, the solid volume fraction becomes increasingly heterogeneous. In this case, the theory captures the profiles of volume fraction, mean and fluctuation velocities between the walls. Comparisons with LB simulations allow us to delimit the range of parameters within which the theory is applicable.

Aeroservoelastic modeling with proper orthogonal decomposition

A physics-based, reduced-order, aeroservoelastic model of an F-18 aircraft has been developed using the method of proper orthogonal decomposition (POD), introduced to the field of fluid mechanics by Lumley. The model is constructed with data from high-dimensional, high-fidelity aeroservoelastic computational fluid dynamics (CFD-ASE) simulations that couple equations of motion of the flow to a modal model of the aircraft structure. Through POD modes, the reduced-order model (ROM) predicts both the structural dynamics and the coupled flow dynamics, offering much more information than typically employed, low-dimensional models based on system identification are capable of providing. ROM accuracy is evaluated through direct comparisons between predictions of the flow and structural dynamics with predictions from the parent, the CFD-ASE model. The computational overhead of the ROM is six orders of magnitude lower than that of the CFD-ASE model—accurately predicting the coupled dynamics from simulations of an F...

Active Flow Control of a Pitching Turret Flow Field Using Closed-Loop Feedback Control

Experimental testing of an active ow control system on a three-dimensional, nonconformal turret has been performed at a diameter based Reynolds number of 2:0 10. Active ow control was achieved using dynamic suction and various open and closed-loop feedback control algorithms in an e ort to determine the most e ective and e cient control scheme for reducing aero-optic distortions in the vicinity of the turret aperture. Dynamic surface pressure and PIV measurements have been used to better characterize and understand the ow eld in order to evaluate the active control system. From this research, it has been shown that dynamic suction has the ability to manipulate the separated ow above the turret aperture and can signi cantly alter the characteristics of the aperture ow eld. Open-loop control was shown to be the most e cient form of control when set to the proper suction levels, but the merit of closed-loop feedback control has also been shown, especially for cases where the aperture of the turret is dynamically pitching. Generally, open-loop control systems require scheduling of the active control system during pitching where a closed-loop control system would not due to the sensing capabilities.

Mulitple-Input-Multiple-Output Aerodynamic Control

Multiple-input-multiple-output (MIMO), closed-loop control systems have been developed and tested for tracking prescribed values of aerodynamic forces on a NACA 4412 airfoil. Control actuation (inputs) consists of two surface jets located on the suction and pressure sides of the airfoil tail. The system includes a measurement-based estimator that utilizes a low-dimensional model of the perturbation flow—based on the method of proper orthogonal decomposition—and stochastic correlations between the measurements and the state estimates. The system also includes approximations of the performance outputs, defined as total lift and drag on the airfoil. The control objective is to reduce or eliminate oscillations in the two force components that are generated by unsteady vortex shedding in the wake of the airfoil. Control-in-the-loop CFD simulations were performed using a Proportional-Integral (PI) regulator with CFD-computed forces in the loop, a PI regulator with a measurement-based estimator and low-dimensional approximations of the forces in the loop, and a Linear Quadratic Regulator (LQR) with measurement-based estimator and force approximations. Using computationally intensive CFD-based models in controllers on deployed aircraft is not practicable; however, the simulation with CFD-computed forces in the loop serves as a benchmark in evaluating the low-dimensional controllers. The dimension of the plant (CFD model) is approximately 2 × 10 5 . With four states and eight pressure sensors, the measurement-based estimator reduces the size by four orders of magnitude, providing a controller of viable size. Lift and drag oscillations are reduced by 93% and 95% in the benchmark simulation with CFD-computed forces in the loop. The PI regulator with a measurement-based estimator reduces lift and drag oscillations by 70% and 53%. The LQR reduces oscillations by 85% and 69%. Inclusion of an output error integral term in simulations with the measurement-based estimator in the loop—using both the PI regulator and a LQR—lead to eventual failure of the controller. Exclusion of the term produces biases in the tracked outputs, particularly in the tracked value of drag. The LQR controller reduces actuation requirements by imposing a penalty on large jet amplitudes.