Shaaban Abdallah

Numerical solutions for the pressure poisson equation with Neumann boundary conditions using a non-staggered grid, 1

Abstract Numerical solutions are obtained for the pressure Poisson equation with Neumann boundary conditions using a non-staggered grid. The existence of a solution for this equation requires the satisfaction of a compatibility condition which relates the source of the Poisson equation and the Neumann boundary conditions. This compatibility condition is not automatically satisfied on non-staggered grids. Failure to satisfy the compatibility condition leads to non-convergent iterative solutions. Consistent finite-difference approximations for the pressure equation with Neumann boundary conditions are developed to satisfy the compatibility condition on non-staggered grids. The method is applied to calculate the pressure coefficient in a driven cavity when given the velocity field. The velocity is computed from the stream function-vorticity formulation of the Navier-Stokes equations.

The discrete continuity equation in primitive variable solutions of incompressible flow

Abstract The use of a non-staggered computational grid for the numerical solutions of the incompressible flow equations has many advantages over the use of a staggered grid. A penalty, however, is inherent in the finite-difference approximations of the governing equations on non-staggered grids. In the primitive-variable solutions, the penalty is that the discrete continuity equation does not converge to machine accuracy. Rather it converges to a source term which is proportional to the fourth-order derivative of the pressure, the time increment, and the square of the grid spacing. An approach which minimizes the error in the discrete continuity equation is developed. Numerical results obtained for the driven cavity problem confirm the analytical developments.

Numerical solutions for the incompressible Navier-Stokes equations in primitive variables using a non-staggered grid, 11

Abstract In Part I of this study, a method was developed for the solution of the pressure Poisson equation, with Neumann boundary conditions, on a non-staggered grid. This method was used to determine the pressure when given the velocity field from a stream function-vorticity solution. In Part II, the pressure equation is solved iteratively with the momentum (Navier-Stokes) equations on a non-staggered grid. In this case, the solution of the pressure equation not only provides the pressure, but also serves to indirectly satisfy the continuity equation. This primitive variables formulation has a major advantage over the stream function-vorticity method in its applicability for three-dimensional flow. Numerical results are obtained and compared with the stream function-vorticity results for the driven cavity of Part I.

A primitive variable method for the solution of three-dimensional incompressible viscous flows

Abstract In this paper we present a new primitive variable method for the solution of the three-dimensional, incompressible, Reynolds averaged Navier-Stokes equations in generalized curvilinear coordinates. The governing equations are discretized on a non-staggered grid and the discrete continuity equation is replaced by a discrete pressure-Poisson equation. The discrete pressure equation is designed in such a way that: (i) the compatibility condition for the Poisson-Neumann problem is automatically satisfied, and (ii) the discrete incompresibility constraint is satisfied to, at least, truncation error accuracy while the computed pressure is smooth. The momentum equations are integrated in time using the four-stage Runge-Kutta algorithm while the pressure equation is solved using the point-successive relaxation technique. The method is applied to calculate the turbulent flow field over a ship model. The computed results are in very good agreement with the experimental data.

Cumulative spinal loading exposure methods for manual material handling tasks. Part 2: methodological issues and applicability for use in epidemiological studies

Objective: The goal of this paper is to review and discuss methodological issues related to cumulative spinal loading exposure assessment methods. Background: Research has indicated that there likely is an association between integrated spinal loading and lower back pain. A number of studies have been conducted to evaluate cumulative load; however, comparisons between studies is difficult due to the use of different methods for the assessment of cumulative spinal loading. Methods: A comprehensive electronic search was conducted to locate articles dealing with methods of cumulative spinal loading estimation. The articles were evaluated with respect to methods for obtaining postural data, methods for estimating spinal loads, methods for integrating loads over time and spinal load parameters to be measured. Results: Thirteen articles were located. A summary of the methods used to estimate cumulative spinal load is described and evaluated. Conclusions: There is a pressing need for integrated spinal loading methods that are reliable, valid and practical for use in large occupational epidemiological studies. A number of research needs were outlined aimed at improving the ability to use cumulative load to predict risk of low back disorders due to manual material handling.

Coupled fully implicit solution procedure for the steady incompressible Navier-Stokes equations

Abstract This paper presents a new fully implicit procedure for the solution of the steady incompressible Navier-Stokes equations in primitive variables. The momentum equations are coupled with a Poisson-type equation for the pressure and solved using the Beam and Warming approximate factorization method. The present formulation does not require the iterative solution of the pressure equation at each time step. Thus, the major drawback of the pressure-Poisson approach, which made it prohibitively expensive for complex three-dimensional applications, is eliminated. Numerical solutions for the problem of the two-dimensional driven cavity are obtained using a non-staggered grid at Re = 100, 400, and 1000. All the computed results are obtained without any artificial dissipation. This feature of the present procedure demonstrates its excellent convergence and stability characteristics. Those characteristics result from the coupling of the pressure equation, which is elliptic in space, with the momentum equations.

Use of XFOIL in design of camber-controlled morphing UAVs

The standard curriculum for Aerospace Engineering students at the University of Cincinnati includes AEEM361 Integrated Aircraft Engineering. The goal of this course is to instruct students in the tools and methodology of aircraft design. The integrated aspects of aircraft design are underscored by introducing pre‐junior (between sophomore and junior) students to the state‐of‐the‐art morphing technology, inspired by bat and bird flight, which can enable an aircraft to adapt its shape to best suit the flight condition thereby enhancing mission performance. In this article, we present the development of unique software tools, which provide undergraduates an opportunity to design airfoils for morphing aircraft. Morphing is introduced in the form of “on demand” camber as well as sweep change with the aim of improving aerodynamic efficiency for a multi‐objective (several design points) mission profile. The Global Hawk UAV mission in general and its LRN1015 airfoil in particular is in focus due to the relative long mission times spent at the two different flight conditions, namely high‐speed dash and low‐speed loiter. We are using several tools to virtually simulate a morphing wing including XFOIL to perform fast and relatively accurate two‐dimensional steady‐flow simulations of different morphed configurations using a camber‐controlled morphed wing to maneuver. In this article we detail AeroMorph, the educational MATLAB‐based tool developed for design of a camber‐controlled morphing of airfoils with the aim of improving aerodynamic efficiency and exploration of the basic relationships between flap deflection and airfoil morphing based on a camber change.

Camber Controlled Airfoil Design for Morphing UAV

Morphing technology, inspired by bat and bird flight, can enable an aircraft to adapt its shape to best suit the flight condition thereby enhancing mission performance. In this paper, we propose a camber change for the morphing of airfoils with the aim of improving aerodynamic efficiency. The Global Hawk UAV mission in general and its LRN1015 airfoil in particular is in focus due to the relative long mission times spent at the two different flight conditions, namely high-speed dash and low speed loiter. Specifically, we are in search of the basic relationships between flap deflection and airfoil morphing based on a camber change. We are using several tools to virtually simulate a morphing wing including XFOIL to perform fast and relatively accurate two-dimensional steady-flow simulations of different morphed configurations using a camber controlled morphed wing to maneuver. Results show that for the LRN1015 airfoil, we can achieve the lift differential required to perform a maneuver while maintaining higher efficiency than an aircraft using flaps to perform the same maneuver.

Effectiveness of 2D Path Planning in Real Time using Fuzzy Logic

The effectiveness of 2D path planning of a UAV using fuzzy logic for the purpose of decision making in real time is explored in this paper. Previous work has shown that by using a fuzzy inference system, an agent can navigate an unknown environment. It does this by taking information about obstacles (if within the agent’s sensing range) and target location, and outputting a change in heading angle and speed. Often there are scenarios in which it is desirable for an aircraft to redirect its path midflight. These situations can involve threats, changing mission objectives, and/ or be very complex; with multiple and moving obstacles. A system that can handle these varying conditions rapidly and efficiently is imperative to the future of autonomous aircraft. A fuzzy logic approach is used here for its ability to imitate human heuristics and simplicity to implement. The effectiveness of this methodology is analyzed by comparing it to an optimal path planning approach. While the optimal path will give either the shortest path (or time to a target), control algorithms are incapable of being re-tasked. Presented here is a fuzzy inference system (FIS) for path planning with obstacle avoidance. This FIS has been tweaked and tested for robustness by comparing it to other 2D path planning methods on numerous obstacle environments.

Path Planning of a Fire-Fighting Aircraft using Fuzzy Logic

The effectiveness of path planning of a fire-fighting aircraft using fuzzy logic for the purpose of fighting forest fires is explored in this paper. Using previous work on path tracking and obstacle avoidance with fuzzy logic as a starting point, the effort has been expanded to include logic for continuously changing target location and verification of results for moving obstacles. When combating wildfires, situations can change rapidly due to fluctuating environmental conditions (wind, fuel, terrain, etc) that can affect the target location. A system that can handle these varying conditions rapidly and efficiently is imperative to these situations. Presented here is a fuzzy inference system that takes information about obstacles (if within the agent’s sensing range) and target location and outputs a change in heading angle and speed accordingly. The agent’s objective is to take the shortest path to the target area while also avoiding obstacles. These obstacles could be mountains, no-fly zones, areas in which it is too dangerous to fly, or other agents. Presented here is a path planning with obstacle avoidance fuzzy inference system and verification on a simplified fire growth model.