Optimization of Rib Shape and Inclination in a Square Duct with Response Surface Methodology

2021 ◽  
pp. 1-34
Author(s):  
Yigang Luan ◽  
Lanyi Yan ◽  
Yue Yin ◽  
Hao Fu
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Response Surface ◽  
Navier Stokes ◽  
Internal Cooling ◽  
Square Duct ◽  
Flow And Heat Transfer ◽  
Surface Method ◽  
Geometric Factors ◽  
Parameter Ranges

Abstract The paper conducts numerical investigation coupled with Reynolds-averaged Navier Stokes method on detailed flow field and heat transfer characteristics of ribbed channel with symmetric ribs mounted on two walls. The physical domain is modeled by reference to a practical turbine blade internal cooling channel. The effects of three selected geometric factors of ribs, i.e. rib inclination angle, dimensionless rib height and dimensionless rib pitch, on the flow and heat transfer are investigated by variable-controlled simulations with the Reynolds number ranges from 5,000 to 90,000. The parameter ranges are 30°≤a≤90°, 0.5≤e/w≤1.5 and 5≤P/w≤15 with the rib width w fixed at 1mm. It is newly found that the friction factor does not follow a monotonical trend with respect to the Reynolds number under certain rib configurations. In addition, three-level numerical calculations about three geometric factors as well as the Reynolds number are conducted with the response surface method (RSM). Quadratic regression model for the targeted response, TPF, is obtained. The optimal rib shape for the goal of maximizing the channel overall thermal performance turns out to be e/w=0.5, P/w=15, a=30° as Re is fixed at 30,000.

Detached Eddy Simulation of Flow and Heat Transfer in a Stationary Internal Cooling Duct With Skewed Ribs

2005 ◽  
Author(s):  
Aroon K. Viswanathan ◽  
Danesh K. Tafti
Keyword(s):  
Heat Transfer ◽  
Secondary Flow ◽  
Navier Stokes ◽  
Internal Cooling ◽  
Detached Eddy Simulation ◽  
Square Duct ◽  
Eddy Simulation ◽  
Flow And Heat Transfer ◽  
Numerical Predictions ◽  
Flow Features

Numerical predictions of a hydrodynamic and thermally developed turbulent flow for a unit period of a stationary duct using Detached Eddy Simulation (DES) and Unsteady Reynolds Averaged Navier-Stokes (URANS) are presented. The domain under consideration is a square duct with 45° ribs on the top and bottom walls arranged in a staggered fashion. Computations are carried out for a bulk Re of 47,000. The rib height to channel hydraulic diameter (e/Dh) is 0.1 and the rib pitch to rib height (P/e) is 10. DES is applied on two grids 80 × 80 × 80 and 128 × 80 × 80 and the initial results are compared with the experimental results and LES computations. Based on this the 128 × 80 × 80 grid is chosen for the comprehensive study. DES and URANS computations are carried out on the grid. The rib geometry introduces a strong secondary flow along the rib. The presence of the secondary flow introduces a spanwise variation in the heat transfer. DES predicts flow features and heat transfer distribution which is consistent with the experimental observations and LES computations. The average friction and the augmentation ratios predicted by DES also concur with the earlier observations.

Investigating Gas Turbine Internal Cooling Using Supercritical CO2 at High Reynolds Numbers for Direct Fired Cycle Applications

2021 ◽  
Author(s):  
Matthew Searle ◽  
Arnab Roy ◽  
James Black ◽  
Doug Straub ◽  
Sridharan Ramesh
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Nusselt Number ◽  
Gas Turbines ◽  
Cfd Simulation ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
Process Conditions ◽  
Internal Cooling ◽  
Air Breathing

Abstract In this paper, experimental and numerical investigations of three variants of internal cooling configurations — dimples only, ribs only and ribs with dimples have been explored at process conditions (96°C and 207bar) with sCO2 as the coolant. The designs were chosen based on a review of advanced internal cooling features typically used for air-breathing gas turbines. The experimental study described in this paper utilizes additively manufactured square channels with the cooling features over a range of Reynolds number from 80,000 to 250,000. Nusselt number is calculated in the experiments utilizing the Wilson Plot method and three heat transfer characteristics — augmentation in Nusselt number, friction factor and overall Thermal Performance Factor (TPF) are reported. To explore the effect of surface roughness introduced due to additive manufacturing, two baseline channel flow cases are considered — a conventional smooth tube and an additively manufactured square tube. A companion computational fluid dynamics (CFD) simulation is also performed for the corresponding cooling configurations reported in the experiments using the Reynolds Averaged Navier Stokes (RANS) based turbulence model. Both experimental and computational results show increasing Nusselt number augmentation as higher Reynolds numbers are approached, whereas prior work on internal cooling of air-breathing gas turbines predict a decay in the heat transfer enhancement as Reynolds number increases. Comparing cooling features, it is observed that the “ribs only” and “ribs with dimples” configurations exhibit higher Nusselt number augmentation at all Reynolds numbers compared to the “dimples only” and the “no features” configurations. However, the frictional losses are almost an order of magnitude higher in presence of ribs.

scholarly journals Effect of Reynolds Number and Property Variation on Fluid Flow and Heat Transfer in the Entrance Region of a Turbine Blade Internal-Cooling Channel

2005 ◽  
Vol 2005 (1) ◽  
pp. 36-44 ◽  
Author(s):  
R. Ben-Mansour ◽  
L. Al-Hadhrami
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Mass Flow Rate ◽  
Heat Transfer Rate ◽  
Turbine Blade ◽  
Flow Rate ◽  
Transfer Rate ◽  
Internal Cooling ◽  
Cooling Channel ◽  
Flow And Heat Transfer

Internal cooling is one of the effective techniques to cool turbine blades from inside. This internal cooling is achieved by pumping a relatively cold fluid through the internal-cooling channels. These channels are fed through short channels placed at the root of the turbine blade, usually called entrance region channels. The entrance region at the root of the turbine blade usually has a different geometry than the internal-cooling channel of the blade. This study investigates numerically the fluid flow and heat transfer in one-pass smooth isothermally heated channel using the RNGk−εmodel. The effect of Reynolds number on the flow and heat transfer characteristics has been studied for two mass flow rate ratios (1/1and1/2) for the same cooling channel. The Reynolds number was varied between10 000and50 000. The study has shown that the cooling channel goes through hydrodynamic and thermal development which necessitates a detailed flow and heat transfer study to evaluate the pressure drop and heat transfer rates. For the case of unbalanced mass flow rate ratio, a maximum difference of8.9% in the heat transfer rate between the top and bottom surfaces occurs atRe=10 000while the total heat transfer rate from both surfaces is the same for the balanced mass flow rate case. The effect of temperature-dependent property variation showed a small change in the heat transfer rates when all properties were allowed to vary with temperature. However, individual effects can be significant such as the effect of density variation, which resulted in as much as9.6% reduction in the heat transfer rate.

scholarly journals Heat Transfer Analysis of Two Pass Cooling Channel of Gas Turbine Blade With Analytical Wall Function Turbulence Approach

2013 ◽  
Author(s):  
Hitoshi Arakawa ◽  
Shaohua Shen ◽  
Ryo S. Amano
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Heat Transfer Analysis ◽  
Computational Studies ◽  
Cooling Channel ◽  
Wall Function ◽  
Square Duct ◽  
Flow And Heat Transfer ◽  
Predicting Performance ◽  
Function Models

This paper reports experimental and computational studies of flow and heat transfer through a square duct with a sharp 180 degree turn. The main purpose of this research is to study flow and heat transfer predictions of the Analytical Wall-Function (AWF). To compare the predicting performance of the AWF, the standard Log-Law Wall-Function (LWF) and Low-Reynolds-number (LRN) k-ε model were applied. Their results were also compared with the experimental results for validation. In addition, three extended forms of the AWF were tested. Computational results showed better agreement with the experimental data, especially after the turn of the channel. It was also found that the wall-function (WF) models predicted more reasonable results as Reynolds number increased. The both wall-function models predicted similar results except for separation/reattachment regions where the LWF predicted lower Nusselt number than the other models.

A Comparative Study of DES and URANS in a Two-Pass Internal Cooling Duct With Normal Ribs

2005 ◽  
Author(s):  
Aroon K. Viswanathan ◽  
Danesh K. Tafti
Keyword(s):  
Heat Transfer ◽  
Secondary Flows ◽  
Navier Stokes ◽  
Internal Cooling ◽  
Detached Eddy Simulation ◽  
Mean Flow ◽  
Streamline Curvature ◽  
Eddy Simulation ◽  
Flow And Heat Transfer ◽  
Developing Flow

The capabilities of the Detached Eddy Simulation (DES) and the Unsteady Reynolds Averaged Navier-Stokes (URANS) versions of the 1988 κ-ω model in predicting the turbulent flow field and the heat transfer in a two-pass internal cooling duct with normal ribs is presented. The flow is dominated by the separation and reattachment of shear layers; unsteady vorticity induced secondary flows and strong streamline curvature. The techniques are evaluated in predicting the developing flow at the entrance to the duct and downstream of the 180° bend, fully-developed regime in the first pass, and in the 180° bend. Results of mean flow quantities, secondary flows, friction and heat transfer are compared to experiments and Large-Eddy Simulations (LES). DES predicts a slower flow development than LES, while URANS predicts it much earlier than LES computations and experiments. However it is observed that as fully developed conditions are established, the capability of the base model in predicting the flow and heat transfer is enhanced by switching to the DES formulation. DES accurately predicts the flow and heat transfer both in the fully-developed region as well as the 180° bend of the duct. URANS fails to predict the secondary flows in the fully-developed region of the duct and is clearly inferior to DES in the 180° bend.

Axisymmetric Stagnation-Point Flow and Heat Transfer of a Viscous Fluid on a Moving Cylinder With Time-Dependent Axial Velocity and Uniform Transpiration

2004 ◽  
Vol 126 (6) ◽  
pp. 997-1005 ◽  
Author(s):  
R. Saleh ◽  
A. B. Rahimi
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Axial Velocity ◽  
Time Dependent ◽  
Navier Stokes ◽  
Flow And Heat Transfer ◽  
Moving Cylinder ◽  
Self Similar ◽  
Suction Rate ◽  
Axial Speed

The unsteady viscous flow and heat transfer in the vicinity of an axisymmetric stagnation point of an infinite moving cylinder with time-dependent axial velocity and with uniform normal transpiration Uo are investigated. The impinging free stream is steady and with a constant strain rate k¯. An exact solution of the Navier–Stokes equations and energy equation is derived in this problem. A reduction of these equations is obtained by use of appropriate transformations for the most general case when the transpiration rate is also time-dependent but results are presented only for uniform values of this quantity. The general self-similar solution is obtained when the axial velocity of the cylinder and its wall temperature or its wall heat flux vary as specified time-dependent functions. In particular, the cylinder may move with constant speed, with exponentially increasing–decreasing axial velocity, with harmonically varying axial speed, or with accelerating–decelerating oscillatory axial speed. For self-similar flow, the surface temperature or its surface heat flux must have the same types of behavior as the cylinder motion. For completeness, sample semisimilar solutions of the unsteady Navier–Stokes and energy equations have been obtained numerically using a finite-difference scheme. Some of these solutions are presented for special cases when the time-dependent axial velocity of the cylinder is a step-function, and a ramp function. All the solutions above are presented for Reynolds numbers, Re=ka¯2/2υ, ranging from 0.1 to 100 for different values of dimensionless transpiration rate, S=Uo/ka¯, where a is cylinder radius and υ is kinematic viscosity of the fluid. Absolute value of the shear-stresses corresponding to all the cases increase with the increase of Reynolds number and suction rate. The maximum value of the shear- stress increases with increasing oscillation frequency and amplitude. An interesting result is obtained in which a cylinder moving with certain exponential axial velocity function at any particular value of Reynolds number and suction rate is axially stress-free. The heat transfer coefficient increases with the increasing suction rate, Reynolds number, Prandtl number, oscillation frequency and amplitude. Interesting means of cooling and heating processes of cylinder surface are obtained using different rates of transpiration. It is shown that a cylinder with certain type of exponential wall temperature exposed to a temperature difference has no heat transfer.

Axisymmetric Stagnation—Point Flow and Heat Transfer of a Viscous Fluid on a Rotating Cylinder With Time-Dependent Angular Velocity and Uniform Transpiration

2006 ◽  
Vol 129 (1) ◽  
pp. 106-115 ◽  
Author(s):  
A. B. Rahimi ◽  
R. Saleh
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Reynolds Number ◽  
Angular Velocity ◽  
Stokes Equations ◽  
Time Dependent ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Flow And Heat Transfer ◽  
Self Similar

The unsteady viscous flow and heat transfer in the vicinity of an axisymmetric stagnation point of an infinite rotating circular cylinder with transpiration U0 are investigated when the angular velocity and wall temperature or wall heat flux all vary arbitrarily with time. The free stream is steady and with a strain rate of Γ. An exact solution of the Navier-Stokes equations and energy equation is derived in this problem. A reduction of these equations is obtained by the use of appropriate transformations for the most general case when the transpiration rate is also time-dependent but results are presented only for uniform values of this quantity. The general self-similar solution is obtained when the angular velocity of the cylinder and its wall temperature or its wall heat flux vary as specified time-dependent functions. In particular, the cylinder may rotate with constant speed, with exponentially increasing/decreasing angular velocity, with harmonically varying rotation speed, or with accelerating/decelerating oscillatory angular speed. For self-similar flow, the surface temperature or its surface heat flux must have the same types of behavior as the cylinder motion. For completeness, sample semi-similar solutions of the unsteady Navier-Stokes equations have been obtained numerically using a finite-difference scheme. Some of these solutions are presented for special cases when the time-dependent rotation velocity of the cylinder is, for example, a step-function. All the solutions above are presented for Reynolds numbers, Re=Γa2∕2υ, ranging from 0.1 to 1000 for different values of Prandtl number and for selected values of dimensionless transpiration rate, S=U0∕Γa, where a is cylinder radius and υ is kinematic viscosity of the fluid. Dimensionless shear stresses corresponding to all the cases increase with the increase of Reynolds number and suction rate. The maximum value of the shear stress increases with increasing oscillation frequency and amplitude. An interesting result is obtained in which a cylinder rotating with certain exponential angular velocity function and at particular value of Reynolds number is azimuthally stress-free. Heat transfer is independent of cylinder rotation and its coefficient increases with the increasing suction rate, Reynolds number, and Prandtl number. Interesting means of cooling and heating processes of cylinder surface are obtained using different rates of transpiration.

Numerical investigation of fluid flow structure and heat transfer in a passage with continuous and truncated V-shaped ribs

2015 ◽  
Vol 25 (1) ◽  
pp. 171-189 ◽  
Author(s):  
Shian Li ◽  
Gongnan Xie ◽  
Bengt Sunden
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Fluid Flow ◽  
Pressure Drop ◽  
Heat Transfer Enhancement ◽  
Thermal Performance ◽  
Internal Cooling ◽  
Transfer Enhancement ◽  
Content Type ◽  
Flow And Heat Transfer

Purpose – The employment of continuous ribs in a passage involves a noticeable pressure drop penalty, while other studies have shown that truncated ribs may provide a potential to reduce the pressure drop while keeping a significant heat transfer enhancement. The purpose of this paper is to perform computer-aided simulations of turbulent flow and heat transfer of a rectangular cooling passage with continuous or truncated 45-deg V-shaped ribs on opposite walls. Design/methodology/approach – Computational fluid dynamics technique is used to study the fluid flow and heat transfer characteristics in a three-dimensional rectangular passage with continuous and truncated V-shaped ribs. Findings – The inlet Reynolds number, based on the hydraulic diameter, is ranged from 12,000 to 60,000 and a low-Re k-e model is selected for the turbulent computations. The local flow structure and heat transfer in the internal cooling passages are presented and the thermal performances of the ribbed passages are compared. It is found that the passage with truncated V-shaped ribs on opposite walls provides nearly equivalent heat transfer enhancement with a lower (about 17 percent at high Reynolds number of 60,000) pressure loss compared to a passage with continuous V-shaped ribs or continuous transversal ribs. Research limitations/implications – The fluid is incompressible with constant thermophysical properties and the flow is steady. The passage is stationary. Practical implications – New and additional data will be helpful in the design of ribbed passages to achieve a good thermal performance. Originality/value – The results imply that truncated V-shaped ribs are very effective in improving the thermal performance and thus are suggested to be applied in gas turbine blade internal cooling, especially at high velocity or Reynolds number.

scholarly journals Numerical investigation of fluid flow and heat transfer characteristics in sine, triangular, and arc-shaped channels

2007 ◽  
Vol 11 (1) ◽  
pp. 17-26 ◽  
Author(s):  
Zakir Hossain ◽  
Sadrul Islam
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Fluid Flow ◽  
Critical Reynolds Number ◽  
Navier Stokes ◽  
Heat Transfer Characteristics ◽  
Single Wave ◽  
Transfer Characteristics ◽  
Flow And Heat Transfer ◽  
Wavy Channels

Time dependent Navier-Stokes and energy equations have been solved to investigate the fluid flow and heat transfer characteristics in wavy channels. Three different types of two dimensional wavy geometries (e.g. sine-shaped, triangular, and arc-shaped) are considered. All of them are of single wave and have same geometric dimensions. Periodic boundary conditions are used to attain fully developed flow. The flow in the channels has been observed to be steady up to a critical Reynolds number, which depends on the geometric configuration. Beyond the critical Reynolds number a self-sustained oscillatory flow has been observed. As a result of this oscillation, there is increased mixing between core and the near-wall fluids, thereby increasing the heat transfer rate. For the same geometric dimensions, flow becomes unsteady at relatively lower Reynolds number in the arc-shaped channel. .

Flow and Heat Transfer in an Internally Ribbed Duct With Rotation: An Assessment of LES and URANS

2003 ◽  
Author(s):  
A. K. Saha ◽  
Sumanta Acharya
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Nusselt Number ◽  
Density Ratio ◽  
Navier Stokes ◽  
Flow And Heat Transfer ◽  
Number Ratio ◽  
Wide Range ◽  
Side Walls ◽  
Subgrid Stresses

Large Eddy Simulations (LES) and Unsteady Reynolds Averaged Navier-Stokes (URANS) simulations have been performed for flow and heat transfer in a rotating ribbed duct. The ribs are oriented normal to the flow and arranged in a staggered configuration on the leading and trailing surfaces. The LES results are based on a higher-order accurate finite difference scheme with a dynamic Smagorinsky model for the subgrid stresses. The URANS procedure utilizes a two equation k-ε model for the turbulent stresses. Both Coriolis and centrifugal buoyancy effects are included in the simulations. The URANS computations have been carried out for a wide range of Reynolds number (Re = 12,500–100,000), rotation number (Ro = 0–0.5) and density ratio (Δρ/ρ = 0–0.5), while LES results are reported for a single Reynolds number of 12,500 without and with rotation (Ro = 0.12, Δρ/ρ = 0.13). Comparison is made between the LES and URANS results, and the effects of various parameters on the flow field and surface heat transfer are explored. The LES results clearly reflect the importance of coherent structures in the flow, and the unsteady dynamics associated with these structures. The heat transfer results from both LES and URANS are found to be in reasonable agreement with measurements. LES is found to give higher heat transfer predictions (5–10% higher) than URANS. The Nusselt number ratio (Nu/Nu0) is found to decrease with increasing Reynolds number on all walls, while they increase with the density ratio along the leading and trailing walls. The Nusselt number ratio on the trailing and side walls also increases with rotation. However, the leading wall Nusselt number ratio shows an initial decrease with rotation (till Ro = 0.12) due to the stabilizing effect of rotation on the leading wall. However, beyond Ro = 0.12, the Nusselt number ratio increases with rotation due to the importance of centrifugal-buoyancy at high rotation.

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