Ziemowit Ostrowski

Solving inverse heat conduction problems using trained POD-RBF network inverse method

The article presents advances in the approach aiming to solve inverse problems of steady state and transient heat conduction. The regularization of ill-posed problem comes from the proper orthogonal decomposition (POD). The idea is to expand the direct problem solution into a sequence of orthonormal basis vectors, describing the most significant features of spatial and time variation of the temperature field. Due to the optimality of proposed expansion, the majority of the basis vectors can be discarded practically without accuracy loss. The amplitudes of this low-order expansion are expressed as a linear combination of radial basis functions (RBF) depending on both retrieved parameters and time. This approximation, further referred as trained POD-RBF network is then used to retrieve the sought-for parameters. This is done by resorting to least square fit of the network and measurements. Numerical examples show the robustness and numerical stability of the scheme.

CFD Two-Scale Model of a Wet Natural Draft Cooling Tower

A 2-D axisymmetric model of multiphase heat, mass, and momentum transfer phenomena in natural draft cooling tower is developed using a CFD code Fluent. The fill of the tower is modeled as a porous medium. The energy and mass sources in this zone are evaluated solving a separate 1-D model of mass and heat exchange. The spatial dependence of the sources is accounted for by dividing the fill into a set of vertical channels. The CFD solver produces boundary conditions for each channel, while the model of the channel exports the heat and mass sources to the CFD solver. To accelerate the calculations, an original technique known as the proper orthogonal decomposition (POD) is applied. This approach produces a reduced dimensionality model resulting in significant time economy and accuracy loss lower than 2%. The Euler-Euler multiphase model is used in the rain zone. The simulation results have been validated against experimental data coming from field measurements of a large industrial installation.

Coupling BEM, FEM and analytic solutions in steady-state potential problems

Problems solved by using different steady-state solution techniques in adjacent subregions are discussed. The computational domain typically consists of two subregions, with a linear boundary value problem in one of them. BEM or analytical methods are used to solve the problem in this subregion. Static condensation of the off-interfacial degrees of freedom in this subdomain produces a linear set of equations linking nodal potentials and fluxes on the interface. This set of equations is generated by solving a sequence of boundary value problems in the linear subregion. Access to the source version of the software used to solve these boundary value problems is not required. Thus, the condensation can be accomplished using any commercial BEM code. The resulting set of equation is then treated as a boundary condition attached to the second subregion. In the latter, any numerical technique can be used and both linear and nonlinear problems may be considered. The paper addresses coupling of BEM and FEM, BEM and BEM and analytical solutions with BEM and FEM. Numerical examples are included.

Application of the Proper Orthogonal Decomposition in Steady State Inverse Problems

A novel inverse analysis technique for retrieving unknown boundary conditions has been developed. The first step of the approach is to solve a sequence of forward problems made unique by defining the missing boundary condition as a function of some unknown parameters. Taking several combinations of values of these parameters produces a sequence of solutions (snapshots) which are then sampled at a predefined set of points. Proper Orthogonal Decomposition (POD) is used to produce a truncated sequence of orthogonal basis functions, being appropriately chosen linear combinations of the snapshots. The solution of the forward problem is then written as a linear combination of the basis vectors. The unknown coefficients of this combination are evaluated by minimizing the discrepancy between the measurements and the POD approximation of the field. Two numerical examples show the robustness and numerical stability of the proposed scheme.

An inverse POD-RBF network approach to parameter estimation in mechanics

An inverse approach is formulated using proper orthogonal decomposition (POD) integrated with a trained radial basis function (RBF) network to estimate various physical parameters of a specimen with little prior knowledge of the system. To generate the truncated POD-RBF network utilized in the inverse problem, a series of direct solutions based on the finite element method, the boundary element method or exact analytical solutions are used to generate a data set of temperatures or deformations within the system or body, each produced for a unique set of physical parameters. The data set is then transformed via POD to generate an orthonormal basis to accurately solve for the desired material characteristics using the Levenberg-Marquardt algorithm to minimize the objective least-squares functional. While the POD-RBF inverse approach outlined in this article focuses primarily in application to conduction heat transfer, elasticity and fracture mechanics, this technique is designed to be directly applicable to other realistic conditions and/or relevant industrial problems.

Absorption line black body distribution function evaluated with proper orthogonal decomposition for mixture of CO2 and H2O

Purpose – The purpose of this paper is to present a new approach of evaluation of the absorption line black body distribution function (ALBDF) for a mixture of gases. Currently published correlations, which are used to reproduce the ALBDF, treat only single gases. Design/methodology/approach – A discrete form of the ALBDF is generated using line by line (LBL) calculations. The latest spectroscopic database HITEMP 2010 is used for the generation of the absorption coefficient histogram, which is cumulated later in order to produce a tabulated form of the ALBDF. The proper orthogonal decomposition (POD) statistical method is employed for the reproduction of the ALBDF. Interpolation property of the POD allows to reproduce the ALBDF for arbitrary gas mixture parameters. Findings – POD proved to possess optimal interpolation properties. Results obtained by using POD are in very good agreement with LBL integration. Research limitations/implications – One have to be aware that the model generated with the POD met...

CFD analysis of multiphase blood flow within aorta and its thoracic branches of patient with coarctation of aorta using multiphase Euler - Euler approach

In the research a numerical Computational Fluid Dynamics (CFD) model of the pulsatile blood flow was created and analyzed. A real geometry of aorta and its thoracic branches of 8-year old patient diagnosed with a congenital heart defect - coarctation of aorta was used. The inlet boundary condition were implemented as the User Define Function according to measured values of volumetric blood flow. The blood flow was treated as multiphase: plasma, set as the primary fluid phase, was dominant with volume fraction of 0.585 and morphological elements of blood were treated in Euler-Euler approach as dispersed phases (with 90% Red Blood Cells and White Blood Cells as remaining solid volume fraction).

Virtual Therapy Simulation for Patient with Coarctation of Aorta Using CFD Blood Flow Modelling

The paper presents a numerical method of blood flow simulation in two geometries. The first geometry covered the ascending and descending parts of aorta and its main branches in patient with a congenital heart disease - coarctation of aorta (inborn narrowing of the descendent aorta). The second geometry used in the flow field analysis mimicked the state of the vessel after a successful percutaneous intervention and thus without pathological narrowing (virtual therapy). The blood was treated as a non-Newtonian fluid. The pulsating flow was set at the inlet to ascending aorta. The lumped model based on electrical analogy using three-element-Windkessel model was created to calculate pressure at the outlets. In the publication the fields of velocity and pressure were presented. The obtained outflow streams were modified after virtual therapy.

Retrieving thermal conductivity of the solid sample using reduced order model inverse approach

Purpose Prompted by the reliability and robustness of the previously proposed method of non-destructive measurement of thermal conductivity (TC) for anisotropic materials, the enhanced approach is presented in this study. The main improvement lies in the substitution of the analytic solution of direct problem solver with a numerical one. This solver, used during the inverse procedure that fits measurement data into simulated ones, is proposed to be a numerical one (finite volume method). Moreover, the purpose of this study is to show the applicability of the reduce order model for retrieving thermal conductivity of solid body. Design/methodology/approach In the proposed methodology, both the laser heat source and temperature measurements are performed on the same side of the sample material, which is the main difference with respect to the classic Parker flash method. To speed up the computational time, the full numerical model used in the course of inverse solution is replaced by the proper orthogonal decomposition (POD)-radial basis function (RBF) reduced order model, which is fast and accurate. Findings The TCs measured using the proposed methodology are in good agreement with the well established (but destructive) measurement methods. The advantage of the proposed approach lies in the optimal approximation properties of the POD approximation basis used in reduced order model, as well as in its regularization properties. Practical implications The proposed technique has high application potential in the design of novel apparatus for non-destructive measurement of TCs for both isotropic and anisotropic materials. Originality/value This is the first time when the POD-RBF reduced order model is used in the procedure of non-destructive TC measurement for anisotropic bodies.

Dry heat loses of newborn baby in infant care bed: use of a thermal manikin

The energy balance and heat exchange for newborn baby in infant care bed environment (radiant warmer) are considered. The present study was performed to assess the body dry heat loss from an infant in radiant warmer, using copper cast anthropomorphic thermal manikin and controlled climate chamber laboratory setup. The total body dry heat losses were measured for varying manikin surface temperatures (nine levels between 32.5oC and 40.1oC) and ambient air temperatures (five levels between 23.5oC and 29.7oC). Radiant heat losses were estimated based on measured climate chamber wall temperatures. After subtracting radiant part, resulting convective heat loses are compared with computed ones, based on Nu correlations for common geometries. Simplified geometry of newborn baby was represented as: (a) single cylinder and (b) weighted sum of 5 cylinders and sphere. The computed values are significantly overestimated relative to measured ones by: 28.8% (23.5%) for (a) and 40.9% (25.2%) for (b). This shows that use of adopted general purpose correlations for approximation of convective heat losses of newborn baby can lead to substantial errors, hence approximation formula is proposed. The thermal manikin appears to provide a precise method for the noninvasive assessment of thermal conditions in neonatal care.