A Bi-Fidelity Approach for Uncertainty Quantification of Heat Transfer in a Rectangular Ribbed Channel

2016 ◽  
Author(s):  
Alireza Doostan ◽  
Gianluca Geraci ◽  
Gianluca Iaccarino
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Temperature Distribution ◽  
Rectangular Channel ◽  
Numerical Test ◽  
Computational Cost ◽  
High Fidelity ◽  
Reduced Basis ◽  
Ribbed Channel ◽  
Fidelity Model

This paper presents a bi-fidelity simulation approach to quantify the effect of uncertainty in the thermal boundary condition on the heat transfer in a ribbed channel. A numerical test case is designed where a random heat flux at the wall of a rectangular channel is applied to mimic the unknown temperature distribution in a realistic application. To predict the temperature distribution and the associated uncertainty over the channel wall, the fluid flow is simulated using 2D periodic steady Reynolds-Averaged Navier-Stokes (RANS) equations. The goal of this study is then to illustrate that the cost of propagating the heat flux uncertainty may be significantly reduced when two RANS models with different levels of fidelity, one low (cheap to simulate) and one high (expensive to evaluate), are used. The low-fidelity model is employed to learn a reduced basis and an interpolation rule that can be used, along with a small number of high-fidelity model evaluations, to approximate the high-fidelity solution at arbitrary samples of heat flux. Here, the low- and high-fidelity models are, respectively, the one-equation Spalart-Allmaras and the two-equation shear stress transport k–ω models. To further reduce the computational cost, the Spalart-Allmaras model is simulated on a coarser spatial grid and the non-linear solver is terminated prior to the solution convergence. It is illustrated that the proposed bi-fidelity strategy accurately approximates the target high-fidelity solution at randomly selected samples of the uncertain heat flux.

Heat Transfer Analysis of Laminar Pulsating Flow in a Rectangular Channel Using Infrared Thermography

2021 ◽  
Author(s):  
Richard Blythman ◽  
Sajad Alimohammadi ◽  
Nicholas Jeffers ◽  
Darina B. Murray ◽  
Tim Persoons
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Analytical Solution ◽  
Local Time ◽  
Rectangular Channel ◽  
Pulsating Flow ◽  
Time Dependent ◽  
Heat Transfer Analysis ◽  
Flux Boundary Condition ◽  
Hydrodynamic Behaviour

Abstract While numerous applied studies have successfully demonstrated the feasibility of unsteady cooling solutions, a consensus has yet to be reached on the local instantaneous conditions that result in heat transfer enhancement. The current work aims to experimentally validate a recent analytical solution (on a local time-dependent basis) for the common flow condition of a fully-developed incompressible pulsating flow in a uniformly-heated vessel. The experimental setup is found to approximate the ideal constant heat flux boundary condition well, especially for the decoupled unsteady scenario where the amplitude of the most significant secondary contributions (capacitance and lateral conduction) amounts to 1.2% and 0.2% of the generated heat flux, respectively. Overall, the experimental measurements for temperature and heat flux oscillations are found to coincide well with a recent analytical solution to the energy equation by the authors. Furthermore, local time-dependent heat flux enhancements and degradations are observed to be qualitatively similar to those of wall shear stress from a previous study, suggesting that the thermal performance is indeed influenced by hydrodynamic behaviour.

The effect of single-sided ribs on heat transfer and pressure drop within a trailing edge internal channel of a gas turbine blade

2021 ◽  
pp. 1-43
Author(s):  
Suhyun Kim ◽  
Seungwon Suh ◽  
Seungchan Baek ◽  
Wontae Hwang
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Pressure Drop ◽  
Secondary Flow ◽  
Gas Turbine ◽  
Turbine Blade ◽  
Sharp Corner ◽  
Trailing Edge ◽  
Edge Channel ◽  
Ribbed Channel

Abstract Convective cooling in a gas turbine blade internal trailing edge channel is often insufficient at the sharp trailing edge. This study examines convective heat transfer and pressure drop within a simplified trailing edge channel. The internal passage has been modeled as a right triangular channel with a 9° angle sharp corner. Smooth baseline and ribbed copper plates were heated from underneath via a uniform heat flux heater and examined via infrared thermography. Non-uniformity in the heat flux due to conduction is corrected by a RANS conjugate heat transfer calculation, which was validated by the mean velocity, friction factor, and temperature fields from experiments and LES simulations. Nusselt number distributions illustrate that surface heat transfer is increased considerably with ribs, and coupled with the vortices in the flow. Heat transfer at the sharp corner is increased by more than twofold due to ribs placed at the center of the channel, due to secondary flow. The present partially ribbed channel utilizes secondary flow toward the corner, and is presumed to have better thermal performance than a fully ribbed channel. Thus, it is important to set the appropriate rib length within the channel.

Enabling efficient uncertainty quantification for seismic modeling via projection-based model reduction

2021 ◽  
Author(s):  
Francesco Rizzi ◽  
Eric Parish ◽  
Patrick Blonigan ◽  
John Tencer
Keyword(s):  
Uncertainty Quantification ◽  
Shear Waves ◽  
Computational Cost ◽  
Memory Bandwidth ◽  
High Fidelity ◽  
Seismic Modeling ◽  
Order Model ◽  
Rank 2 ◽  
Many Core ◽  
Fidelity Model

<p>This talk focuses on the application of projection-based reduced-order models (pROMs) to seismic elastic shear waves. Specifically, we present a method to efficiently propagate parametric uncertainties through the system using a novel formulation of the Galerkin ROM that exploits modern many-core computing nodes.</p><p>Seismic modeling and simulation is an active field of research because of its importance in understanding the generation, propagation and effects of earthquakes as well as artificial explosions. We stress two main challenges involved: (a) physical models contain a large number of parameters (e.g., anisotropic material properties, signal forms and parametrizations); and (b) simulating these systems at global scale with high-accuracy requires a large computational cost, often requiring days or weeks on a supercomputer. Advancements in computing platforms have enabled researchers to exploit high-fidelity computational models, such as highly-resolved seismic simulations, for certain types of analyses. Unfortunately, for analyses requiring many evaluations of the forward model (e.g., uncertainty quantification, engineering design), the use of high-fidelity models often remains impractical due to their high computational cost. Consequently, analysts often rely on lower-cost, lower-fidelity surrogate models for such problems.</p><p>Broadly speaking, surrogate models fall under three categories, namely (a) data fits, which construct an explicit mapping (e.g., using polynomials, Gaussian processes) from the system's parameters to the system response of interest, (b) lower-fidelity models, which simplify the high-fidelity model (e.g., by coarsening the mesh, employing a lower finite-element order, or neglecting physics), and (c) pROMs which reduce the number of degrees of freedom in the high-fidelity model by a projection process of the full-order model onto a subspace identified from high-fidelity data. The main advantage of pROMs is that they apply a projection process directly to the equations governing the high-fidelity model, thus enabling stronger guarantees (e.g., of structure preservation or of accuracy) and more accurate a posteriori error bounds.</p><p>State-of-the-art Galerkin ROM formulations express the state as a rank-1 tensor (i.e., a vector), leading to computational kernels that are memory bandwidth bound and, therefore, ill-suited for scalable performance on modern many-core and hybrid computing nodes. In this work, we introduce a reformulation, called rank-2 Galerkin, of the Galerkin ROM for linear time-invariant (LTI) dynamical systems which converts the nature of the ROM problem from memory bandwidth to compute bound, and apply it to elastic seismic shear waves in an axisymmetric domain. Specifically, we present an end-to-end demonstration of using the rank-2 Galerkin ROM in a Monte Carlo sampling study, showing that the rank-2 Galerkin ROM is 970 times more efficient than the full order model, while maintaining excellent accuracy in both the mean and statistics of the field.</p>

A parallel multi-fidelity optimization approach in induction hardening

2019 ◽  
Vol 39 (1) ◽  
pp. 133-143
Author(s):  
Marco Baldan ◽  
Alexander Nikanorov ◽  
Bernard Nacke
Keyword(s):  
Parallel Computing ◽  
Optimization Technique ◽  
Computational Cost ◽  
Induction Hardening ◽  
Computational Time ◽  
High Fidelity ◽  
Optimization Approach ◽  
Content Type ◽  
Fidelity Model ◽  
Hardening System

Purpose Reliable modeling of induction hardening requires a multi-physical approach, which makes it time-consuming. In designing an induction hardening system, combining such model with an optimization technique allows managing a high number of design variables. However, this could lead to a tremendous overall computational cost. This paper aims to reduce the computational time of an optimal design problem by making use of multi-fidelity modeling and parallel computing. Design/methodology/approach In the multi-fidelity framework, the “high-fidelity” model couples the electromagnetic, thermal and metallurgical fields. It predicts the phase transformations during both the heating and cooling stages. The “low-fidelity” model is instead limited to the heating step. Its inaccuracy is counterbalanced by its cheapness, which makes it suitable for exploring the design space in optimization. Then, the use of co-Kriging allows merging information from different fidelity models and predicting good design candidates. Field evaluations of both models occur in parallel. Findings In the design of an induction heating system, the synergy between the “high-fidelity” and “low-fidelity” model, together with use of surrogates and parallel computing could reduce up to one order of magnitude the overall computational cost. Practical implications On one hand, multi-physical modeling of induction hardening implies a better understanding of the process, resulting in further potential process improvements. On the other hand, the optimization technique could be applied to many other computationally intensive real-life problems. Originality/value This paper highlights how parallel multi-fidelity optimization could be used in designing an induction hardening system.

Variable Fidelity Modeling in Closed Loop Dynamical Systems

2014 ◽  
Author(s):  
Matthew A. Williams ◽  
Andrew G. Alleyne
Keyword(s):  
Dynamical Systems ◽  
Closed Loop ◽  
System Development ◽  
Computational Cost ◽  
Computational Effort ◽  
High Fidelity ◽  
Vapor Compression System ◽  
Variable Fidelity ◽  
Time Required ◽  
Fidelity Model

In the early stages of control system development, designers often require multiple iterations for purposes of validating control designs in simulation. This has the potential to make high fidelity models undesirable due to increased computational complexity and time required for simulation. As a solution, lower fidelity or simplified models are used for initial designs before controllers are tested on higher fidelity models. In the event that unmodeled dynamics cause the controller to fail when applied on a higher fidelity model, an iterative approach involving designing and validating a controller’s performance may be required. In this paper, a switched-fidelity modeling formulation for closed loop dynamical systems is proposed to reduce computational effort while maintaining elevated accuracy levels of system outputs and control inputs. The effects on computational effort and accuracy are investigated by applying the formulation to a traditional vapor compression system with high and low fidelity models of the evaporator and condenser. This sample case showed the ability of the switched fidelity framework to closely match the outputs and inputs of the high fidelity model while decreasing computational cost by 32% from the high fidelity model. For contrast, the low fidelity model decreases computational cost by 48% relative to the high fidelity model.

Time-Resolved Heat Transfer Measurements on the Tip Wall of a Ribbed Channel Using a Novel Heat Flux Sensor: Part II — Heat Transfer Results

2006 ◽  
Author(s):  
Sean Jenkins ◽  
Jens von Wolfersdorf ◽  
Bernhard Weigand ◽  
Tim Roediger ◽  
Helmut Knauss ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Heat Flux Sensor ◽  
Internal Cooling ◽  
Time Resolved ◽  
Mean Values ◽  
Cooling Channels ◽  
Ribbed Channel ◽  
Detailed Surface ◽  
Flux Sensor

Measurements using a novel heat flux sensor were performed in an internal ribbed channel representing the internal cooling passages of a gas turbine blade. These measurements allowed for the characterization of heat transfer turbulence levels and unsteadiness not previously available for internal cooling channels. In the study of heat transfer, often the fluctuations can be equally as important as the mean values for understanding the heat loads in a system. In this study comparisons are made between the time-averaged values obtained using this sensor and detailed surface measurements using the transient thermal liquid crystal technique. The time-averaged heat flux sensor and transient TLC results showed very good agreement, validating both methods. Time-resolved measurements were also corroborated with hot film measurements at the wall at the location of the sensor to better clarify the influence of unsteadiness in the velocity field at the wall on fluctuations in the heat flux. These measurements resulted in turbulence intensities of the velocity and heat flux of about 20%. The velocity and heat flux integral length scales were about 60% and 35% of the channel width respectively, resulting in a turbulent Prandtl number of about 1.7 at the wall.

Heat Transfer in Rotating Multi-Pass Rectangular Ribbed Channel With and Without a Turning Vane

2012 ◽  
Author(s):  
Jiang Lei ◽  
Shiou-Jiuan Li ◽  
Je-Chin Han ◽  
Luzeng Zhang ◽  
Hee-Koo Moon
Keyword(s):  
Heat Transfer ◽  
Rectangular Channel ◽  
Transfer Coefficients ◽  
Heat Transfer Coefficients ◽  
The Third ◽  
Ribbed Channel ◽  
Rotation Numbers ◽  
Loss Coefficients ◽  
Channel Loss ◽  
Turn Region

This paper experimentally investigates the effect of turning vane on hub region heat transfer in a multi-pass rectangular channel with rib-roughed wall at high rotation numbers. The experimental data were taken in the second and the third passages (Aspect Ratio = 2:1) connected by 180° U-bend. The flow was radial inward in the second passage and was radial outward after the 180° U-bend in the third passage. The square-edged ribs with P/e = 8, e/Dh = 0.1, and α = 45° were applied on the leading and trailing surfaces of the second and third passages. Results showed that rotation increases heat transfer on the leading surface but decreases it on the trailing surface in the second passage. In the third passage, rotation decreases heat transfer on the leading surface but increases it on the trailing surface. Without a turning vane, rotation reduces heat transfer on the trailing surface and increases it on the leading surface in the hub 180° turn region. After adding a half-circle-shaped turning vane, heat transfer coefficients do not change in the second passage before-turn while they are different in the turn region and after-turn region in the third passage. Regional heat transfer coefficients and channel loss coefficients are correlated with rotation numbers for multi-pass rectangular ribbed channel with and without a turning vane.

Heat Transfer Augmentation in a Rectangular Channel With Slit Rib-Turbulators on Two Opposite Walls

1997 ◽  
Vol 119 (3) ◽  
pp. 617-623 ◽  
Author(s):  
Jenn-Jiang Hwang ◽  
Tong-Miin Liou
Keyword(s):  
Heat Transfer ◽  
Rectangular Channel ◽  
Local Heat Transfer ◽  
Local Heat ◽  
Open Area ◽  
Transfer Coefficients ◽  
Turbine Blade Cooling ◽  
Heat Transfer Coefficients ◽  
Ribbed Channel ◽  
Rib Turbulators

The effect of slit ribs on heat transfer and friction in a rectangular channel is investigated experimentally. The slit ribs are arranged in-line on two opposite walls of the channel. Three rib open-area ratios (β = 24, 37, and 46 percent), three rib pitch-to-height ratios (Pi/H = 10, 20, and 30), and two rib height-to-channel hydraulic diameter ratios (H/De = 0.081, and 0.162) are examined. The Reynolds number ranges from 10,000 to 50,000. Laser holographic interferometry is employed to measure the local heat transfer coefficients of the ribbed wall quantitatively, and observe the flow over the ribbed wall qualitatively. The results show that the slit rib has an advantage of avoiding “hot spots.” In addition, the heat transfer performance of the slit-ribbed channel is much better than that of the solid-ribbed channel. Semi-empirical correlations for friction and heat transfer are developed to account for rib spacings and open-area ratios. These correlations may be used in the design of turbine blade cooling passages.

Research on the Inversion of Equivalent Surface Heat Transfer Coefficient of Mass Concrete by Calculating its Heat Flux

2012 ◽  
Vol 188 ◽  
pp. 264-269
Author(s):  
Li Xin Qu ◽  
Yi Hong Zhou ◽  
Yao Ying Huang ◽  
Guo Qing Tang ◽  
Shao Wu Zhou
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Heat Transfer Coefficient ◽  
Temperature Distribution ◽  
Optical Fiber ◽  
Transfer Coefficient ◽  
Surface Heat ◽  
Mass Concrete ◽  
Surface Heat Transfer Coefficient ◽  
The Heat Transfer Coefficient

Most of the cracks on concrete dam are external ones, while external heat preservation is an important measure to prevent cracking. In order to obtain the actual thermal parameters, according to thermal conduction theory and the temperature distribution conditions of optical fiber on concrete surface, the surface temperature distribution of concrete pouring deck was real-time monitored by setting optical fiber in different depths; then the surface heat flux of mass concrete was calculated, thereby the equivalent surface heat transfer coefficient, which varied as time goes, was inversed. It is indicated that the inversion process is relatively simple and reliable, and the heat transfer coefficient obtained can well reflect the real performance of the insulation materials. Meanwhile, it is also indicated that the heat transfer coefficient of equivalent surface varies as time goes, which can contribute to back analysis calculation and actual engineering practice.

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