José A. Camberos

Entropy-based design and analysis of fluids engineering systems

Introduction Introduction Governing Equations of Fluid Flow and Heat Transfer Mathematical Properties of Entropy and Exergy Governing Equations of Entropy and the Second Law Formulation of Entropy Production and Exergy Destruction Statistical and Numerical Formulations of the Second Law Introduction Conservation Laws as Moments of the Boltzmann Equation Extended Probability Distributions Selected Multivariate Probability Distribution Functions Concave Entropy Functions Statistical Formulation of the Second Law Numerical Formulation of the Second Law Predicted Irreversibilities of Incompressible Flows Introduction Entropy Transport Equation for Incompressible Flows Formulation of Loss Coefficients with Entropy Production Upper Entropy Bounds in Closed Systems Case Study of Automotive Fuel Cell Design Case Study of Fluid Machinery Design Measured Irreversibilities of Incompressible Flows Introduction Experimental Techniques of Irreversibility Measurement Case Study of Magnetic Stirring Tank Design Case Study of Natural Convection in Cavities Measurement Uncertainties Entropy Production in Microfluidic Systems Introduction Pressure-Driven Flow in Microchannels Applied Electric Field in Microchannels Micropatterned Surfaces with Open Microchannels Numerical Error Indicators and the Second Law Introduction Discretization Errors of Numerical Convection Schemes Physical Plausibility of Numerical Results Entropy Difference in Residual Error Indicators Numerical Stability and the Second Law Introduction Stability Norms Entropy Stability of Finite Difference Schemes Stability of Shock Capturing Methods Entropy Transport with Phase Change Heat Transfer Introduction Entropy Transport Equations for Solidification and Melting Heat and Entropy Analogies in Phase Change Processes Numerical Stability of Phase Change Computations Thermal Control of Phase Change with Inverse Methods Entropy Production with Film Condensation Entropy Production in Turbulent Flows Introduction Reynolds Averaged Entropy Transport Equations Eddy Viscosity Models of Mean Entropy Production Turbulence Modeling with the Second Law

Active Control of Transpiration Boundary Conditions for Drag Minimization with an Euler CFD Solver

The induced drag on wings is reduced at off-design cruise conditions with simulated active conformal control surface deflections modeled through transpiration boundary conditions with an Euler CFD program, the Air Vehicles Unstructured Solver (AVUS). An inverse optimization technique is used to manipulate the spanwise lift distribution resulting in the minimization of the induced drag. The method is demonstrated on a high aspect ratio rectangular wing at a subsonic and transonic flight conditions. The control surfaces deflections are calibrated to determine the extent to which their effect can be matched by a transpiration boundary condition. The CoNstrained MiNimization(CONMIN) program is used to minimize a squared error objective function. It is determined that the use of transpiration boundary conditions can drastically reduce the grid requirements and complexity associated with grid motion and deformation.

Numerical integration techniques for discontinuous manufactured solutions

When applying the method of manufactured solutions (MMS) on computational fluid dynamic software, determining the exact solutions and source terms for finite volume codes where the stored value is an integrated average over the control volume is non-trivial and not frequently discussed. MMS with discontinuities further complicates the problem of determining these values. In an effort to adapt the standard MMS procedure to solutions that contain discontinuities we show that Newton-Cotes and Gauss quadrature numerical integration methods exhibit high error, first order limitations. We propose a new method for determining the exact solutions and source terms on a uniform structured grid containing shock discontinuities by performing linearly and quadratically exact transformations on split cells. Transformations are performed on triangular and quadrilateral elements of a systematically divided discontinuous cell. Using a quadratic transformation in conjunction with a nine point Gauss quadrature method, a minimum of 4th order accuracy is achieved for fully general solutions and shock shapes. A linear approximation of curved shocks is also experimentally shown to be 2nd order accurate. The numerical integration method is then applied to a CFD code using simple discontinuous manufactured solutions which return consistent 1st order convergence values. The result is an important step towards being able to use MMS to verify solutions with discontinuities. This work also highlights the use of higher order numerical integration techniques for continuous and discontinuous solutions that are required for MMS on higher order finite volume codes.

Aeroelastic Analysis with Transpiration Enabled Euler Flow Solver

A static aeroelastic analysis is conducted using a transpiration boundary condition enabled Euler flow solver and a finite element analysis tool. The transpiration boundary condition eliminates the need for CFD grid deformation algorithms, this lead to an efficient technique to incorporate high fidelity analysis in the design environment. In a preliminary investigation, the results from the coupled finite element inviscid fluid solver analysis are compared and validated against solutions obtained from ASTROS linear aeroelastic flow solver. Nomenclature 4 ∇ = Biharmonic operator θ = Angular polar coordinate θ = Angle of the camber line slope γ = Ratio of specific heats ρ = Density ∀ = Volume υ = Poisson ratio A = Undetermined coefficient a = Speed of sound i a = Undetermined coefficient B = System dampening B = Undetermined coefficient a

Computation of Induced Drag for 3D Wing with Volume Integral (Trefftz Plane) Technique

distribution over a finite wing throughout a typical aircraft mission for minimizing lift – induced drag. Our ultimate goal requires extracting accurate and robust calculations of induced drag from the numerical solutio ns. We compare computational fluid dynamics numerical results for an untwisted, finite rectangular wing (NACA 00 12 , AR = 6.7 ) using no flap deflections against theoretical lifting line results. A comparison of the numerical and lifting -line lift distributi ons, under flow conditions representing Mach 0.3 – 0.7 subsonic and transonic flows at small angle s of attack, shows good agreement with a maximum deviation of only 2.4% over the wing span. The i naccuracies associated with the common surface integral meth od of calculating drag and the inability to isolate induced drag from other drag components prompted our approach of us ing a wake integral method. The numerical solution of the Euler equations demonstrate s successful implementation of the wake integral met hod via a Trefftz Plane analysis of the induced drag. We also present an initial effort to identify and to quantify the numerical uncertainties associated with the simulation .

Feature extraction from massive, dynamic computational data based on proper orthogonal decomposition and feature mining

Proper orthogonal decomposition (POD) has been widely used to extract dominant modes and structures from massive dynamic computational data to improve the understanding and discovery of the phenomena as well as to guide experimental design and control. This paper presents a framework and data mining technique that directly identifies the region of interest (ROI) from the POD modes and determines relevant feature for targeted visualization and learning. Two key elements in the procedure are described, including (1) POD to reduce data dimensions and to decouple the time-averaged and time-varying flow structures in high-fidelity Computational Fluid Dynamics (CFD) data with non-uniform grids, and (2) feature mining, including clustering-based data mining and filtering to detect both mean and unsteady flow features in the ROI. The rationale and benefits of our POD-compatible feature detection for fast scalable feature extraction are discussed. Case studies of vortex extraction are undertaken to validate the present approach. The POD accurately captures the characteristic flow structures and provides useful insight into the underlying flow phenomena. The feature mining module is capable of identifying key features in the ROI (3–10xa0% of the original data) for focused visualization, discovery, and learning.Graphical Abstract

A Flow feature detection framework for large-scale computational data based on incremental proper orthogonal decomposition and data mining

ABSTRACT A framework based on incremental proper orthogonal decomposition (iPOD) and data mining to perform large-scale computational data analysis is presented. It includes iPOD to incrementally reduce data dimensions and decouple dynamic flow structures in massive CFD data; data mining to classify and identify candidate global regions of interest (ROIs) for focused analysis; feature detection to capture key flow features and ultimate ROIs (UROIs); and targeted data storage and visualisation. Quantitative results show that iPOD is able to process large datasets that overwhelm the batch-POD, leading to 4–16× data reduction in the temporal domain. Data mining and feature detection algorithms, respectively, identify 50–70% of the spatial domain with high probability of flow feature occurrence and only 2–30% containing key flow features. The UROI and associated data can be selectively stored and visualised. In contrast to batch-POD, iPOD reduces memory usage by more than 10× and time by up to 75%.

Zero-Lift Drag Prediction Including Aeroelastic Effects

One of the aerospace design engineer’s goals aims to reduce drag for increased aircraft performance, in terms of range, endurance, or speed in the various flight regimes. To accomplish this the designer must have rapid and accurate techniques for computing drag. At subsonic Mach numbers drag is primarily a sum of lift-induced drag and zero-lift drag. While lift-induced drag is easily and efficiently determined by a far field method, using the Trefftz plane analysis, the same cannot be said of zero-lift drag. Zero-lift drag (CD,0) usually requires consideration of the Navier-Stokes equations, the solution of which is as yet unknown except by using approximate numerical techniques with computational fluid dynamics (CFD). The approximate calculation of zero-lift drag from CFD is normally computed with so-called near-field techniques, which can be inaccurate and too time consuming for consideration in the design environment. This paper presents a technique to calculate zero-lift drag in the subsonic regime that includes aeroelastic effects and is suitable for the design environment. The technique loosely couples a two-dimensional airfoil boundary layer model with a 3-D aeroelastic solver to compute zero-lift drag. We show results for a rectangular wing (baseline), a swept wing, and a tapered wing. Then compare with a rectangular wing with variable thickness and camber, thinning out from the root to tip (spanwise direction), thus demonstrating the practicality of the technique and its utility for rapid conceptual design.

Uncertainty Estimation in Induced Drag by Virtual Surface Deflection and Trefftz Plane Analysis

We examine the errors in predicting the induced drag using a Trefftz plane analysis and using trailing edge “virtual flaps” to control the span-wise lift distribution over a finite wing. An uncertainty analysis is used to quantify the several errors known to the numerical model. We compare Euler code results of an untwisted, finite rectangular wing (NACA 0012, AR = 40/6) with trailing edge flap deflections against a transpiration boundary condition. A comparison of the numerical and theoretical lift distributions, under flow conditions representing Mach 0.3 at small angle of attack, shows good agreement with a quantifiable uncertainty. We study the potential of a far-field (Trefftz plane) analysis to delineate between induced drag and irreversible artificial diffusion in order to obtain a better estimate of the uncertainty in the error in the induced drag prediction.