Thermoelastic Deflection Research Articles

Predictions of the thermo elastic deformation of dry gas seal rings in the hydrodynamic lubrication regime

Dry gas seals represent a significant advancement in turbo machinery due to their ability to handle high pressures and speeds without the use of external sealing fluids, such as oil or water, thus reducing contamination and increasing reliability. Despite their widespread use, internal working mechanisms are not fully understood to date, in particular regarding fluid film thickness prediction, which is an essential component of the seal design. The axial deflection of the rotating and stationary rings in a dry gas seal affects the development of the fluid film formed between the ring faces of the seal, influencing the performance of the seal during its operation, as well as leakage of the seal when it is at rest. The hydrodynamic and hydrostatic pressure fields of the fluid film, together with temperature gradients in the rings, induce axial deflection of these components. This in turn modifies the pressure field developed in the film. This paper focuses on establishing a methodology to couple the deformation field and the dynamic behavior of the fluid film (pressure and temperature fields) through numerical computations. Analytical relationships are employed to obtain the thermo-elastic deflection of the seal rings in the axial direction and this distortion is used in the numerical methodology to accelerate the prediction of the seal behavior. The coupled seal ring-fluid film dynamic system with 11° and 15° spiral angle is stable because the axial deflection calculated from numerical analysis produces a converging radial taper in the direction of the flow (producing a net opening force). An important result of this work is that the predicted magnitude of the axial deflection (as a result of pressure and temperature effects) under thermal and pressure loads on the stationary and rotating rings is smaller but of the same order of magnitude as the fluid film thickness.

Modified DPL Green–Naghdi theory for thermoelastic vibration of temperature-dependent nanobeams

A unified multi-dual-phase-lag thermoelasticity theory is presented to study the vibration of a temperature-dependent nanobeam subjected to a ramp-type heating. The nonlocal thermoelasticity theory based on Euler-Bernoulli hypothesis is applied. Laplace transform domain is adopted to solve the governing partial differential equations using the state space approach. Numerical computations are carried out using the inverse of Laplace transforms. The present heat conduction and constitutive equations are covering at least five models of the generalized thermoelasticity. Comparison between the classical thermoelasticity (CTE), the Lord–Shulman (L–S), the Green–Lindsay (G–L), and the simple and refined-phase-lag models are made. The effects of nonlocal, ramp-type heating, and temperature-dependent parameters on all quantities have been discussed and presented graphically. It is found that the ramp-type heating parameter has significant effects on all quantities. However, the thermoelastic deflection, axial displacement, dilatation, and bending moment have strong dependencies on the nonlocal and temperature-dependent parameters.

Nonlinear finite element solutions of thermoelastic deflection and stress responses of internally damaged curved panel structure

• A novel numerical model is developed to study the deflection and stress values of the pre-damaged composite structure. • The internal damage has been modeled via sub-laminate approach including two kinematic theories. • The nonlinear FEM solutions are obtained under the combined thermomechanical loading. • The numerical solutions (deflection and stress) are evaluated for different panel geometries via the derived models. Thermoelastic deflection and corresponding stresses of the pre-damaged layered panel structure are investigated numerically in this article including the large deformation kinematics under the linearly varying temperature field. The composite structural deformation kinematics is derived using two different polynomial type of kinematic theories including the through-thickness stretching effect. The inter-laminar separation between the adjacent layers is incurred via the sub-laminate approach and Green–Lagrange strain to count the total structural deformation. Also, the intermittent displacement continuity conditions are imposed in the current mathematical model to establish the displacement continuity between the separated layers. The variational principle is adopted for the evaluation of the nonlinear structural equilibrium equations and solved via total Lagrangian approach . The convergence and the corresponding validity of the currently derived nonlinear finite element solutions are checked by solving different sets of numerical examples. Additionally, the comprehensive inferences are drawn from various numerical examples for the well-defined important input parameter including the size, position, and location of delamination .

Thermo-elastic response of SUS316-Al2O3 functionally graded beams under various heat loads

Geometric nonlinearity and temperature dependent material properties are accounted for in the theoretical analysis of time dependent thermo-elastic response of thin functionally graded material (FGM) SUS316-Al2O3 beam subjected to various heat loads. A two dimensional Lagrangian rectangular finite element is used to obtain the temperature distribution on the transverse plane of the beam. Nonlinear thermo-elastic deflection and thermal stresses are evaluated for various structural and thermal boundary conditions. Thermo-elastic oscillations are observed in case of beams subjected to step, concentrated line and shock heat load whereas thermo-elastic deflection is observed for beams subjected to moving heat load. As the thermal load increases, the nonlinear thermal deflection of FGM beam are higher compared to linear analysis. In general, temperature dependency of material properties influence the amplitude of thermal oscillations. High thermal stresses are induced in beams with pin-pin and clamp-pin boundary condition as compared to hinge-hinge beam.

Nonlinear thermoelastic deflection of temperature-dependent FGM curved shallow shell under nonlinear thermal loading

ABSTRACTThe geometrically nonlinear thermomechanical transverse deflection responses of the functionally graded curved structure under the influence of nonlinear thermal field are reported in this article. For the numerical analysis, a nonlinear mathematical model is derived using the higher-order shear deformation theory and Green–Lagrange nonlinear strains. The current model includes all of the nonlinear higher-order terms to achieve the true flexure of the structure under the combined action of loads. It is assumed that the panel structure is exposed to nonuniform temperature field combined with the transversely distributed mechanical load. Additionally, the properties of material constituents are assumed to vary with the nonuniform temperature load and corresponding properties are evaluated considering dependency and independence of temperature. Furthermore, the panel material grading has been obtained mathematically with the help of Voigt’s micromechanical rule together with the power-law distribution. The system of equations is obtained using the variational principle and solved numerically using the finite element steps in association with the direct iterative method. The stability of the present numerical model has been established through the convergence test and compared with the benchmark results to show the validity. Finally, numerical experimentations have been carried out for different parameters and discussed in detail.

Analytical Modelling of Temperature Distribution Using Potential Theory by Reference to Broaching of Nickel-Based Alloys

Knowledge of temperature fields and heat flow evolving during metal cutting processes is of significant importance for ensuring and predicting the product`s quality. Furthermore, this knowledge enables an improved usage of resources, such as machine tools and tool deployment. The strength of the heat sources as a result of the process and the distribution of the temperature in the material directly influence the tool wear mechanisms, wear rate, thermo-elastic deflection of the tool centre point and the amount of heat flowing into the newly generated work piece surface. Especially the latter effect is of crucial importance when it comes to safety critical components as they are employed in aero-engines. In aviation industry, the surface integrity is used as a complex quality measure summarising several aspects at the machined surface and sub-surface out of which many issues are predominantly thermal issues (e.g. temperature driven hardening of the work piece material, re-cast and white etching layers as well as residual stress profiles).

Spring-Supported Thrust Bearings Used in Hydroelectric Generators: Comparison of Experimental Data with Numerical Predictions

Laboratory experiments that simulate the conditions acting on large spring-supported thrust bearings in hydroelectric generators were performed and film thicknesses, temperatures and pressures were measured. A software package provided theoretical predictions of the experimental results. This software used a control volume, numerical formulation to model the three dimensional flow of mass, momentum and energy in the thrust bearing and included thermoelastic deflection of the pad and flow of oil in the groove between the pads. A detailed comparison of the experimental data with the numerical predictions showed quite good overall agreement, particularly with the deformed shape and temperatures of the pad. The agreement provided evidence of the fidelity of the software package and supported its continued use in analysis and design. Presented as a Society of Tribologists and Lubrication Engineers paper at the ASME/STLE Tribology Conference in Toronto, Ontario, Canada, October 26–28, 1998