Browsing by Author "Pelletier, Dominique H."

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    Finite element solution of the Navier-Stokes equations for 3-D turbulent free shear flows
    Pelletier, Dominique H. (Virginia Polytechnic Institute and State University, 1984)
    A half-equation model of turbulence has been developed to described the eddy viscosity distribution of two and three-dimensional turbulent free shear flows. The model is derived by integrating the parabolized transport equation for the turbulence kinetic energy over the cross section of the flow. The Prandtl-Kolmogrov hypothesis is used to obtain an ordinary differential equation for the eddy viscosity. The model is used in a general purpose finite element procedure using primitive variables. The penalty function method is used, in a generalized Galerkin weak formulation of the Navier-Stokes equations, to enforce the conservation of mass. In this procedure the pressure does not explicitly appear, this significantly reducing the computation time when compared to the velocity-pressure approach. Numerical solution are obtained for four problems: a round jet issuing from a wall into still surroundings, a three-dimensional square jet issuing from a wall into still surroundings, a uniform flow past a free running propeller, and a shear flow past a free running propeller. An actuator disk with variable radial distribution of thrust and torque is used to model the propeller. The numerical solution in the far field of the round jet agrees very well with the analytical similar solution. Very good agreement between prediction and experiments is observed for the square jet problem. A simplified analysis of the flow past a propeller is used to provide the initial value of the eddy viscosity. Numerical experiments on the uniform flow past a thrusting disk confirmed the validity of the analysis and illustrated the effect of the initial value of the initial value of the eddy viscosity. For both propeller flows, agreement between predictions and experiments is excellent for both the axial and swirl velocity components at two stations located at x/D = 0.025 and 0.23. The quality of the swirl prediction is a major improvement over previous analyses. Pressure predictions are obtained for the first time, and are in reasonable agreement with the experiments. The radial velocity prediction is in fair agreement with the experiments at the station x/D = 0.025 .The discrepancy between the finite element solutions and the experiments at the station x/D = 0.23, for the pressure an the radial velocity are attributed to the presence of the body housing the propeller drive train. The body is not included in the present study. The complex three-dimensional nature of the shear flow past the propeller is very well captured in the simulation.
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    New integral and differential computational procedures for incompressible wall-bounded turbulent flows
    Caillé, Jean (Virginia Tech, 1992-09-06)
    Three new computational procedures are presented for the simulation of incompressible wall-bounded turbulent flows. First, an integral method based on the strip integral method has been developed for the solution of three-dimensional turbulent boundary-layer flows. The integral equations written in a general form using non-orthogonal streamline coordinates include the turbulent shear stress at the upper limit of an inner strip inside the boundary-layer. The shear stress components are modeled using the Boussinesq assumption, and the eddy viscosity is defined explicitly as in differential methods. The turbulence modeling is not hidden in opaque empirical correlations as in conventional integral methods. A practical four-parameter velocity profile has been established based on the Johnston Law of the Wall using a triangular model for the crosswise velocity. Two strips are used to solve for the four unknowns: skin friction coefficient, wall crossflow angle, boundary-layer thickness, and location of maximum crosswise velocity. The location of maximum crosswise velocity proves to be a natural and adequate parameter in the formulation, but it is numerically sensitive and has a strong influence on the wall crossflow angle. Good results were obtained when compared to predictions of other integral or differential methods. Secondly, two computational procedures solving the Reynolds Averaged Navier-Stokes equations for 20 and 3D flows respectively have also been developed using a new treatment of the near-wall region. The flow is solved down to the wall with a slip velocity based on Clauser's idea of a pseudolaminar velocity profile. The present idea is different from the wall-function methods and does not require a multi-layer eddy viscosity model. The solution of the equations of motion is obtained by the Finite Element Method using the wall shear stress as a boundary condition along solid surfaces, and using the Clauser outer region model for the eddy viscosity. The wall shear stress distribution is updated by solving integral equations obtained from the enforcement of conservation of mass and momentum over an inner strip in the near-wall region. The Navier-Stokes solution provides the necessary information to the inner strip integral formulation in order to evaluate the skin friction coefficient for 2D flows, or the skin friction coefficient and the wall crossflow angle for 3D flows. The procedures converge to the numerically "exact" solution in a few iterations depending on the accuracy of the initial guess for the wall shear stress. A small number of nodes is required in the boundary-layer to represent adequately the physics of the flow, which proves especially useful for 3D calculations. Excellent results were obtained for the 2D simulations with a simple eddy viscosity model. 3D calculations gave good results for the turbulent boundary-layer flows considered here. The present methods were validated using well-known experiments chosen for the STANFORD conferences and EUROVISC workshop. The 2D numerical predictions are compared with the experimental measurements obtained by Wieghardt-Tillmann, Samuel-Joubert, and Schubauer-Klebanoff. For the 3D analyses, the numerical predictions obtained by the strip-integral method and the Finite Element Navier-Stokes Integral Equation procedure are validated using the Van den Berg-Elsenaar and Müller-Krause experiments.
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    A Numerical Study of Internal Flow Effects on Skin Friction Gages
    MacLean, Matthew (Virginia Tech, 2002-04-15)
    This work examines the detailed flow characteristics of direct measuring skin friction gages with computational methods. This type of device uses a small movable head mounted flush to a wall such that the head is assumed to be exposed to the same shear stress from the flow as the surrounding wall. The force caused by the action of the shear stress on the head deflects a flexure system monitored by instruments such as strain gages mounted at the base of a beam. The goal of the study was to develop an understanding of the effects that the geometric design and installation parameters of the sensor have on the surrounding flow and the ability of the sensor to reflect the undisturbed shear stress value. Disruption of the external flow due to poor design and/or improper installation of the sensor can take the form of intrusion into the flow, recession into the wall, and/or tilted alignment of the sensor such that the head is not flat in the plane of the wall, as well as flow into or out of the small gap surrounding the sensing head. Further, the performance of a direct measuring skin friction sensor in the presence of a pressure gradient has always been a concern. These effects are studied here with a three-dimensional, Navier-Stokes code based on a finite element method technique. Numerical solutions for cases in which one or more design parameters were varied are shown for a variety of flow situations. These situations include: (a) a laminar fully-developed channel flow at a low Reynolds number, (b) a turbulent flat plate boundary layer flow at a high Reynolds number, and (c) strong favorable and adverse pressure gradient turbulent boundary layer flows created by converging and diverging channels at high Reynolds number. Reported results for all cases include detailed flow visualization and stress field imagery, and total surface forces on the sensing head and gage flexure. Under ideal circumstances, these total forces should reflect as accurately as possible the average value of undisturbed shear stress times the exposed sensing head area (the friction force). Any deviation from this value was considered an "error" in the simulated measurement. The laminar channel flow case with a strong favorable pressure gradient showed the importance of proper alignment of the sensor. Protrusion or recession of the sensing head proved to be the dominant effect on resulting forces seen by the gage, changing the output by up to 15% for head protrusion and 10% for head recession for misalignments up to +/-1% of the head diameter. The thickness of the lip on the edge of the head also proved to have a significant effect on the output, with a smaller lip thickness generally showing better performance than a large one. Zero lip thickness indicated accuracy to within 1% of the desired wall shear result, since the pressure differences had little influence on the sensing head. Finally, the assumption of a linear pressure variation from the surface to the cavity along the lip as has been suggested in the past was investigated. The results indicate that the linear assumption works well only for large ratios of lip thickness to gap size, a fact which is correlated with previous experimental results. For the turbulent external flat plate case, misalignment remained the dominant effect on the sensor response. Results indicated that, in general, protrusion is more costly than the same level of recession, and a protrusion of +1% of the head diameter was shown to cause in excess of 100% error in indicated wall shear output. Both protrusion and recession produced large variations in both force and moment on the sensing flexure, but the outcome was that for protrusion the errors caused by these two effects tended to sum together, while for recession they tended to partially cancel out. The gap size played an increased role in the high Reynolds number boundary layer cases. Gap sizes of 1.67% up to 6.67% of the head diameter were studied and were shown to produce output errors between 4% and 22% (with larger errors corresponding to larger gap sizes), thus showing the importance of minimizing the gap for high Reynolds number flows. The lip was shown to have no significant effect for a flow without a pressure gradient. Finally, the favorable and adverse pressure gradient flows showed reasonable performance of the skin friction gage. Errors in output were shown to be -6% for the favorable pressure gradient case and 17% for the adverse pressure gradient case. Only the baseline gage design was studied for these situations, but the results from the two cases indicate that further reducing the lip thickness may not improve the performance of the gage. The error in output was caused almost entirely by applied moment for the adverse pressure gradient, while the applied force and applied moment had a cancellation effect in the favorable pressure gradient case. As a general result, the use of computational fluid dynamics has been shown to be an effective tool in the design and analysis of skin friction gages. Using a computational approach has the advantage of being able to resolve the small, confined gap regions of the gage, providing information that has been shown to be unavailable from previous experimental studies. This work has contributed to a much better understanding of the detailed flow over, in, and around skin friction gages. This will lead to improved gage design and reduced uncertainty in these important measurements.
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    Optimization of an airfoil's performance through moving boundary control
    Dufresne, Sophie (Virginia Tech, 1993-05-08)
    The boundary-layer behavior over an airplane's wings is of great importance in take-off and landing of the airplane. If its angle of attack is increased past a critical value, the flow separates from the lifting surface, resulting in a drastic loss of lift and a major increase in drag. In response to this phenomenon, many mechanisms have been studied to control the boundary-layer. First neglected because of implementation difficulties of its application, moving wall boundary-layer control methods have mainly relied on experimental research. The moving wall concept is principally applied as a rotating cylinder protruding into the airfoil. The purpose of this thesis is to provide a computational base to these experiments and to use mathematical tools of computational fluid dynamics and optimization to predict the optimum rotating speed of the cylinder, placed at the leading edge of the airfoil. For the sake of simplicity, we replace the airfoil by a flat plate with a wedge trailing edge. To model the incompressible viscous two-dimensional Navier-Stokes equations, the finite element method is applied on an unstructured two-dimensional mesh. An adaptive remeshing strategy utilized in conjunction with an error estimator controls the solution's accuracy. The aerodynamic forces acting on the total surface are computed from the finite element approximation. The ratio of the lift and the power required to move the flat plateairfoil and to rotate the cylinder forms the objective function to be optimized. A graph of the objective function versus the angle of attack is first constructed for several rotational speeds to provide a rough visual estimate of the optimum value for every angle of attack. Ultimately, an automatic optimization process provides the final solution. This results in the ideal rotational speed to be applied as the angle of attack varies.