Heat flux evaluation in high temperature ring-on-ring contacts

A comprehensive methodology to investigate heat flux in a ring-on-ring tribometer is presented. Thermal fluxes under high contact pressures and temperature differences were evaluated through an experimental campaign and by a numerical procedure of inverse analysis applied to surface temperature measurements. An approximation of a two-dimensional time-dependent analytical solution for the temperature distribution was first developed and subsequently adapted to mimic the specific testing configuration characteristics; the problem was finally simplified to enable further inverse analysis. Experiments were performed using an innovative high temperature ring-on-ring tribometer. The evaluated contact heat transfer rates were reported as a function of normal load and temperature difference between the discs under steady-state conditions; the results reported here show that, in the present test configuration, the temperature difference has stronger influence than the applied load in terms of heat transfer induced by contact

Direct and inverse heat conduction in rock materials using the finite element method

A finite element method is presented for solution of direct and inverse heat conduction problems in rock materials. Finite element programs for direct and inverse heat conduction problems were developed and demonstrated. Flow charts are given for the finite element programs. The direct finite element heat conduction program changes material properties with temperature to approximate the temperature dependent properties of rock materials. An example problem was solved by the finite element method and also using Kirchoff\u27s transformation. The finite element solution compared quite well with the Kirchoff transformation solution. The inverse method utilizes the direct finite element heat conduction program to iterate for the inverse solution. Data to test the inverse finite element program was generated with the direct finite element program of this research. The inverse program solved these generated problems very accurately. Internal temperature and fracture time measurements are presented on a series of hollow Dresser Basalt cylinders heated by a Kanthal wire heater. The internal temperature measurements were used in conjunction with the inverse method to obtain surface temperatures. The surface temperatures were used for thermal stress calculations to obtain time to fracture for an infinite cylinder --Abstract, page ii

Thermal analysis of anti-icing systems in aeronautical velocity sensors and structures

This work reviews theoretical–experimental studies undertaken at COPPE/UFRJ on conjugated heat transfer problems associated with the transient thermal behavior of heated aeronautical Pitot tubes and wing sections with anti-icing systems. One of the main objectives is to demonstrate the importance of accounting for the conduction–convection conjugation in more complex models that attempt to predict the thermal behavior of the anti-icing system under adverse atmospheric conditions. The experimental analysis includes flight tests validation of a Pitot tube thermal behavior with the military aircraft A4 Skyhawk (Brazilian Navy) and wind tunnel runs (INMETRO and NIDF/COPPE/UFRJ, both in Brazil), including the measurement of spatial and temporal variations of surface temperatures along the probe through infrared thermography. The theoretical analysis first involves the proposition of an improved lumped-differential model for heat conduction along a Pitot probe, approximating the radial temperature gradients within the metallic and ceramic (electrical insulator) walls. The convective heat transfer problem in the external fluid is solved using the boundary layer equations for compressible flow, applying the Illingsworth variables transformation considering a locally similar flow. The nonlinear partial differential equations are solved using the Generalized Integral Transform Technique in the Mathematica platform. In addition, a fully local differential conjugated problem model was proposed, including both the dynamic and thermal boundary layer equations for laminar, transitional, and turbulent flow, coupled to the heat conduction equation at the sensor or wing section walls. With the aid of a single-domain reformulation of the problem, which is rewritten as one set of equations for the whole spatial domain, through space variable physical properties and coefficients, the GITT is again invoked to provide hybrid numerical–analytical solutions to the velocity and temperature fields within both the fluid and solid regions. Then, a modified Messinger model is adopted to predict ice formation on either wing sections or Pitot tubes, which allows for critical comparisons between the simulation and the actual thermal response of the sensor or structure. Finally, an inverse heat transfer problem is formulated aimed at estimating the heat transfer coefficient at the leading edge of Pitot tubes, in order to detect ice accretion, and estimating the relative air speed in the lack of a reliable dynamic pressure reading. Due to the intrinsic dynamical behavior of the present inverse problem, it is solved within the Bayesian framework by using particle filter.Indisponível

The method of fundamental solutions for some direct and inverse problems

We propose and investigate applications of the method of fundamental solutions (MFS) to several parabolic time-dependent direct and inverse heat conduction problems (IHCP). In particular, the two-dimensional heat conduction problem, the backward heat conduction problem (BHCP), the two-dimensional Cauchy problem, radially symmetric and axisymmetric BHCPs, the radially symmetric IHCP, inverse one and two-phase linear Stefan problems, the inverse Cauchy-Stefan problem, and the inverse two-phase one-dimensional nonlinear Stefan problem. The MFS is a collocation method therefore it does not require mesh generation or integration over the solution boundary, making it suitable for solving inverse problems, like the BHCP, an ill-posed problem. We extend the MFS proposed in Johansson and Lesnic (2008) for the direct one-dimensional heat equation, and Johansson and Lesnic (2009) for the direct one-phase one-dimensional Stefan problem, with source points placed outside the space domain of interest and in time. Theoretical properties, including linear independence and denseness, the placement of source points, and numerical investigations are included showing that accurate results can be efficiently obtained with small computational cost. Regularization techniques, in particular, Tikhonov regularization, in conjunction with the L-curve criterion, are used to solve the illconditioned systems generated by this method. In Chapters 6 and 8, investigating the linear and nonlinear Stefan problems, the MATLAB toolbox lsqnonlin, which is designed to minimize a sum of squares, is used

Third International Conference on Inverse Design Concepts and Optimization in Engineering Sciences (ICIDES-3)

Papers from the Third International Conference on Inverse Design Concepts and Optimization in Engineering Sciences (ICIDES) are presented. The papers discuss current research in the general field of inverse, semi-inverse, and direct design and optimization in engineering sciences. The rapid growth of this relatively new field is due to the availability of faster and larger computing machines

The CQDRNG8 - a quadratic, isoparametric, axisymmetric finite element for the NASTRAN computer program

The development of an axisymmetric ring finite element is presented and FORTRAN subroutines for implementing the capability into the MSC/NASTRAN finite element program are given. The element is an eightnoded isoparametric quadrilateral of quadratic order. The following matrices and capabilities are developed: 1. stiffness matrix for homogeneous isotropic materials, 2. thermal conductance matrix for homogeneous isotropic materials, 3. calculation of equivalent nodal forces due to temperature loads, 4. calculation of stresses, and 5. plotting of undeformed and deformed structures. Several classical thermal and structural problems are solved to demonstrate these capabilities. In all cases, the element results compare well with theory. Comparisons are made to existing MSC/NASTRAN axisymmetric finite elements. The new element shows increased accuracy compared to the existing elements. Convergence of the element is shown

Solution of Physics-based Bayesian Inverse Problems with Deep Generative Priors

Inverse problems are notoriously difficult to solve because they can have no solutions, multiple solutions, or have solutions that vary significantly in response to small perturbations in measurements. Bayesian inference, which poses an inverse problem as a stochastic inference problem, addresses these difficulties and provides quantitative estimates of the inferred field and the associated uncertainty. However, it is difficult to employ when inferring vectors of large dimensions, and/or when prior information is available through previously acquired samples. In this paper, we describe how deep generative adversarial networks can be used to represent the prior distribution in Bayesian inference and overcome these challenges. We apply these ideas to inverse problems that are diverse in terms of the governing physical principles, sources of prior knowledge, type of measurement, and the extent of available information about measurement noise. In each case we apply the proposed approach to infer the most likely solution and quantitative estimates of uncertainty.Comment: Paper: 18 pages, 5 figures. Supplementary: 9 pages, 6 Figures, 2 Table

A finite element solution algorithm for the Navier-Stokes equations

A finite element solution algorithm is established for the two-dimensional Navier-Stokes equations governing the steady-state kinematics and thermodynamics of a variable viscosity, compressible multiple-species fluid. For an incompressible fluid, the motion may be transient as well. The primitive dependent variables are replaced by a vorticity-streamfunction description valid in domains spanned by rectangular, cylindrical and spherical coordinate systems. Use of derived variables provides a uniformly elliptic partial differential equation description for the Navier-Stokes system, and for which the finite element algorithm is established. Explicit non-linearity is accepted by the theory, since no psuedo-variational principles are employed, and there is no requirement for either computational mesh or solution domain closure regularity. Boundary condition constraints on the normal flux and tangential distribution of all computational variables, as well as velocity, are routinely piecewise enforceable on domain closure segments arbitrarily oriented with respect to a global reference frame