Entropy-Based Drag-Error Estimation and Mesh Adaptation in Two Dimensions

An experimental and numerical investigation has been performed to study the evolution of shock waves undergoing a sudden expansion in one direction while restricted in the second. Experimental data are gathered and studied for shock waves undergoing the sudden 4:l area expansion in air for Mach numbers of 1.5 and 2.0. Detailed, time-accurate measurements of the shock wave and vortex core location as well as wall pressure data are presented. In addition, the evolving flow structure through the time-accurate flowfield imagery is also presented. The results of these experiments are compared to twodimensional numerical simulations specific to the Mach 1.5 and 2.0 initial conditions and geometry. The direct comparisons of the experimental work and numerical simulations provide insight into flowfield phenomena such as viscous dissipation and sh&&/vortex interaction. The data presented in this effort further elucidates key modeling questions by providing time-accurate flow visualization and pressure data of a two-dimensional shock wave undergoing a sudden expansion in a confined chamber. * Aerospace Engineer, Senior Member AIAA ’ Senior Principal Consultant, Associate Fellow AIAA ’ Research Engineer, Member AIAA ’ Professor & Department Chairman, Associate Fellow AIAA ‘I Associate Professor ’ Associate Professor, Senior Member AIAA ‘* Assistant Professor This paper is declared a work of the U.S. Government and is not subject to copyright protection in the United States. Background Gas dynamics of fast, transient characteristics includes issues such as shock wave reflections, vorticity production, shock-vortex interaction, energy exchange between shock and turbulence, and shock focusing (Chang and Kim, 1995). Figure 1 illustrates the sudden area expansion of a shock wave within a confined domain indicating these interesting fluid dynamic phenomena. These phenomena occur at time scales ranging from microseconds to milliseconds. This paper presents a focused look at sudden shock wave expansion within a confined chamber and the interaction of that shock wave with other fluid dynamic features. Both experimental and numerical tools have been adopted. Recent investigations of this type of gas dynamic flow, given by Jiang et al. (1997), present experimental and numerical simulations of a circular shock tube generated flow undergoing a sudden expansion. Figure 1 highlights the salient flow features of such a sudden expansion. Here it is seen that as the initial shock wave travels down the shock tube (Figure 1) it will undergo a sudden area expansion into a confined area (Figure lb-d), the flowfield gives rise to two important features. First, a “starting jet”, characterized by the formation of a vortex ring, Mach disk, and shear layer’ appear. Second, this precursor shock reflects off the confining walls of the expansion chamber and interacts with the starting jet flowfield. It is clearly seen in Figure 1 that this reflected shock splits once it interacts with the primary vortex ring, which gives rise to secondary shock waves. This shock/vortex/shear layer interaction is also shown in Figure 1. Here the reflected shock splits when it interacts with the primary vortex ring. It was also American Institute of Aeronautics and Astronautics (c)2000 American Institute of Aeronautics & Astronautics or published with permission of author(s) and/or author(s)’ sponsoring organization. observed by Jiang et al. (1997) that once the reflected shock wave passes through the developing shear layer that the shear layer splits, it is moved into the jet flow, and it is convected downstream. This allows another shear layer to form from the jet exit forming another weaker vortex ring. This is referred to as shear layer splitting and is largely an inviscid phenomenon (Jiang et al., 1997) Another phenomenon noted by Jiang et al. (1997) is the shock/shear layer interactions. It is noted that a vortex ring in the shear layer induced a shock wave and the shock wave separated the vortex ring from the shear layer. This is most often noted in strongly expanded free jets. Due to the strong influence of vortex dynamics and compressibility, the turbulence structure can be fruitfully assessed via an evaluation of viscous dissipation.

Numerical simulations and optimisation methods, such as mesh adaptation, rely on the accurate and inexpensive use of error estimation methods. Adjoint-based error estimation is the most accurate method, and generally the most costly. A strong contributor to this cost is the need to compute a higher resolution adjoint solution. Here, it is proposed to use super-resolution neural networks to super-resolve a fine adjoint solution from a lower-cost coarse adjoint solution: a superAdjoint. The method is compared to reference error estimators on an unsteady Burgers’ equation using the method of manufactured solutions. Two forms of the superAdjoint were implemented, a twice and a four times refining super-resolution neural network. These were used to demonstrate both the computational cost reduction and the potential for the reduction of the storage footprint of the primal problem. The first, referred to as 2×CNN, was able to reconstruct the spatially enriched adjoint solution, thus providing a robust and inexpensive local output error. The second, the 4×CNN, was able to demonstrate the reconstruction ability of super-resolution neural networks for higher upscaling factors. This was leveraged in order to subsample the primal solution in space, thus reducing substantially the storage footprint of the discrete primal solution. Both superAdjoints could achieve the desired level of accuracy when compared to the reconstruction of the refined adjoint-based error estimate. Moreover, superAdjoint was shown to be able to generalise to a new QoI that was untrained for. This gives great confidence in the use of super-resolution neural networks for the reduction of both computational cost and storage requirements of adjoint-based error estimation, and goal-oriented mesh adaptation.

Optimal configuration of oblique air curtains for heat loss suppression from vertical solar-thermal receiver surfaces

Two-dimensional computational fluid dynamics simulation of nitrogen and sulfur oxides emissions in a circulating fluidized bed combustor

The prediction of airloads and the corresponding structural response in high-speed forward flight of rotors poses a significant challenge to predictive rotorcraft aeromechanics methods. One of the issues identified in the flight test data of the Puma and Black Hawk aircraft is the phase difference between the minimum lift coefficient and the minimum of the blade pitch on the advancing side of the rotor during high-speed forward flight. This is commonly referred to as the advancing-side lift-phase delay. In the present work, the unsteady three-dimensional flowfield on the advancing side of a helicopter rotor is analyzed using computational fluid dynamics in an attempt to quantify contributions to the preceding effect. Time-dependent two-dimensional computational fluid dynamics simulations of blade sections with combined pitch/freestream Mach number oscillation were carried out to isolate the contribution to the phase difference of pitch angle and Mach number variations in the absence of the complex rotor-induced flowfield, sideslip, and rotor blade dynamics. The results for the freestream Mach number oscillations show that the lift coefficient lags the Mach changes at outboard stations, but this effect is reduced for combined pitch/Mach number oscillations. Finite span and sideslip contributions to the phasing were quantified by investigating the chordwise extent of supersonic flow on the advancing side for two nonlifting rotors in high-speed flight. Finally, the UH-60A rotor in high-speed forward flight was considered. By comparing results for rigid blades with results for a prescribed blade torsional deflection, the contribution of the blade torsion to the advancing-blade lift phasing was also quantified. Furthermore, rigid-blade simulations with different flapping schedules demonstrated the sensitivity of the lift phasing to trim-state variations. It was found that Mach number effects are dominant and the lift phasing depends primarily on the encountered Mach number and pitch schedule. Further, the elastic torsional deflection of the blades effectively changes the pitch schedule of the blade sections and also plays a role in the phasing of the lift and pitching moment coefficients.

PurposeNowadays flaps and winglets are one of the main mechanisms to increase airfoil efficiency. This study aims to investigate the power performance of vertical axis wind turbines (VAWT) that are equipped with diverse gurney flaps. This study could play a crucial role in the design of the VAWT in the future.Design/methodology/approachIn this paper, the two-dimensional computational fluid dynamics simulation is used. The second-order finite volume method is used for the discretization of the governing equations.FindingsThe results show that the gurney flap enhances the power coefficient at the low range of tip speed ratio (TSR). When an angled and standard gurney flap case has the same aerodynamic performance, an angled gurney flap case has a lower hinge moment on the junction of airfoil and gurney flap which shows the structural excellence of this case. In all gurney flap cases, the power coefficient increases by an average of 20% at the TSR range of 0.6 to 1.8. The gurney flap cases do not perform well at the high TSR range and the results show a lower amount of power coefficient compare to the clean airfoil.Originality/valueThe angled gurney flap which has the structural advantage and is deployed to the pressure side of the airfoil improves the efficiency of VAWT at the low and medium range of TSR. This study recommends using a controllable gurney flap which could be deployed at a certain amount of TSR.

Endothelial cell (EC) responsiveness to shear stress is essential for vasoregulation and plays a role in atherogenesis. Although blood is a non-Newtonian fluid, EC flow studies in vitro are typically performed using Newtonian fluids. The goal of the present study was to determine the impact of non-Newtonian behavior on the flow field within a model flow chamber capable of producing flow disturbance and whose dimensions permit Reynolds and Womersley numbers comparable to those present in vivo. We performed two-dimensional computational fluid dynamic simulations of steady and pulsatile laminar flow of Newtonian and non-Newtonian fluids over a backward facing step. In the non-Newtonian simulations, the fluid was modeled as a shear-thinning Carreau fluid. Steady flow results demonstrate that for Re in the range 50–400, the flow recirculation zone downstream of the step is 22–63% larger for the Newtonian fluid than for the non-Newtonian fluid, while spatial gradients of shear stress are larger for the non-Newtonian fluid. In pulsatile flow, the temporal gradients of shear stress within the flow recirculation zone are significantly larger for the Newtonian fluid than for the non-Newtonian fluid. These findings raise the possibility that in regions of flow disturbance, EC mechanotransduction pathways stimulated by Newtonian and non-Newtonian fluids may be different.

A numerical and experimental investigation on the performance of a low-flux direct absorption solar collector (DASC) using graphite, magnetite and silver nanofluids

Periprosthetic wear particle migration and distribution modelling and the implication for osteolysis in cementless total hip replacement

This work presents a mesh refinement indicator based on entropy variables, with an application to the compressible Navier–Stokes equations. The entropy variables are shown to satisfy an adjoint equation, an observation that allows recent work in adjoint-based error estimation to be leveraged in constructing a relatively cheap but effective adaptive indicator. The output associated with the entropy-variable adjoint is shown to be the entropy production in the computational domain, including physical viscous dissipation when present, minus entropy transport out of the domain. Adaptation using entropy variables, which is equivalent to adapting on the integrated residual of the entropy transport equation, thus targets areas of the domain responsible for numerical, or spurious, entropy production. Adaptive results for inviscid and viscous aerodynamic examples in two and three dimensions demonstrate performance efficiency on par with output-based adaptation, as measured by errors in various engineering quantities of interest, with the comparative advantage of the proposed approach that no adjoint equations need to be solved.

The effects of an arc discharge to create an Air-Spike in a hypersonic flow are currently being studied in the Rensselaer Polytechnic Institute 24-inch Hypersonic Shock Tunnel (RPI HST), modeled computationally, and compared to existing theory. The arc is a high current car battery array-driven, 75kilowatt peak, self-sustaining electrical discharge in a Mach 10, 260 psia stagnation pressure, and 560 K stagnation temperature flow. In this low enthalpy, ideal gas, condition, schlieren photographs are taken of the apparatus with and without a downstream blunt body, with varying arc powers. Blunt body drag measurements are also made with both hanging and sliding models with fast-response accelerometers, with and without the arc to establish a correlation between arc power and body drag. The computational effort employs the Euler gasdynamic equations to represent a heat source in flow conditions and geometries identical to those tested in the RPI HST. These two results are then compared to early Air-Spike theoretical predictions to qualitatively validate the CFD code and gain a better perspective on the loss mechanisms involved in the experiment. INTRODUCTION Among the most critical factors in the design of a hypersonic vehicle are aerodynamic drag and heating. To design for low aerodynamic drag would leave the body with sharp edges and a high fineness ratio. Heat transfer concerns would lead the design to a blunt body with a very low fineness ratio, which leads to a substantial increase in wave drag. It has been suggested by several authors (Myrabo, 1978, Tidman, 1990, Myrabo, et a/., 1994, Head, 1994, Seo, 1994, Gurijanov, et al.9 1996, and Co vault 1999) that both the drag and heating of a hypersonic Trans-Atmospheric Vehicle (TAV) could be greatly reduced by adding energy to the air ahead of the craft. This energy addition could be accomplished through the focusing of beamed electromagnetic radiation from a laser or microwave source. Figure 1 shows a diagram of this concept of focusing a laser beam to support the Directed-Energy Air-Spike (DEAS). Marsh, et al, (1996), have experimentally demonstrated that the strong bow shock wave normally produced by a blunt body would become a more benign conical shock wave when an electric arc torch is fired ahead of the body. Figure 2 is a schlieren photo from these tests. * Graduate Student, AIAA Student Member f Associate Professor of Engineering Physics, AIAA Senior Member : Active Professor Emeritus of Aeronautical Engineering, AIAA Fellow 5 Graduate Student, AIAA Student Member * Researcher, AIAA Member Copyright ©2001 by R.M. Bracken and L.N. Myrabo. Published by the American Institute of Aeronautics and Astronautics, Inc, with permission. $Annular inlet t Air Flow Shock Wave

As the complexity of spacecraft and space systems increases, there is an ever increasing need for more accurate and robust estimators to track the system. While the demand placed on an individual spacecraft is increasing, the spacecraft itself is being pushed towards smaller, independent pieces of hardware which may have limited power and/or computational abilities. One such initiative is often refereed to as Operational Responsive Space (ORS). The primary goal of ORS systems is acceleration of the mission conception-to-launch timeline of spacecraft by means of utilizing off-the-shelf type modular components for construction of the spacecraft. With such modular systems, customized interfacing and software necessary to direct all data to a central processor may not be possible given the accelerated timeline, the unfortunate result of which would be degradation of the estimates due to missing data. Graduate Student, Department of Mechanical & Aerospace Engineering. E-mail: ckn@buffalo.edu. Student Member AIAA. Professor, Department of Mechanical & Aerospace Engineering. E-mail: johnc@buffalo.edu. Associate Fellow AIAA. Senior Professional Staff I, SEG, Space Department. Email: adam.fosbury@jhuapl.edu. Member AIAA. Assistant Professor, Department of Aerospace Engineering. Email: cheng@ae.msstate.edu, Senior Member AIAA.

Measurement of unsteady fluid dynamic phenomena: edited by B. E. Richards Hemisphere/McGraw-Hill, New York (1977). Price $35.00

This paper develops the discrete adjoint equations for a turbomachinery RANS solver and proposes a framework for fully-automatic gradient-based constrained aerodynamic shape optimization in a multistage turbomachinery environment. The systematic approach for the development of the discrete adjoint solver is discussed. Special emphasis is put on the development of the turbomachinery specific features of the adjoint solver, i.e. on the derivation of flow-consistent adjoint inlet/outlet boundary conditions and, to allow for a concurrent rotor/stator optimization and stage coupling, on the development of an exact adjoint counterpart to the non-reflective, conservative mixing-plane formulation used in the flow solver. The adjoint solver is validated by comparing its sensitivities with finite difference gradients obtained from the flow solver. A sequential quadratic programming algorithm is utilized to determine an improved blade shape based on the objective function gradient provided by the adjoint solution. The functionality of the proposed optimization method is demonstrated by the redesign of a single-stage transonic compressor. The objective is to maximize the isentropic efficiency while constraining the mass flow rate and the total pressure ratio.

An experimental study of the breakdown of leading-edge vortices on diamond, cropped, delta, and double delta wings during dynamic pitching