An Entropic Minimization Technique for Turbine Blade Profiles

2002 ◽  
Author(s):  
Ed Walsh ◽  
Mark Davies ◽  
Roy Myose
Keyword(s):  
Boundary Layer ◽  
Velocity Distribution ◽  
Boundary Layers ◽  
Turbine Blade ◽  
Entropy Generation ◽  
Incompressible Flows ◽  
Generation Rate ◽  
Entropy Generation Rate ◽  
Minimization Technique ◽  
Boundary Layer Edge

The optimization of the boundary layer edge velocity distribution may hold the key to the minimization of entropy generation in the boundary layers of turbomachinery blades. A preliminary optimization analysis in the laminar region of a non film cooled turbine blade is presented, which demonstrates the concept of how the entropy generation rate may be reduced by varying the boundary layer edge velocity distribution along the suction surface, whilst holding the work done by the blade constant. In the laminar region the analytical technique developed by Pohlhausen and others to predict the boundary layer momentum thickness in the presence of pressure gradients has been adopted to predict the entropy generated as described in other papers by the same authors. The result gives an expression for the entropy generation rate in terms of the boundary layer edge velocity distribution for incompressible flows. The boundary layer edge velocity distribution may then be represented as a polynomial with undefined variables. This allows a minimization technique to be used to minimize the entropy generation rate on these variables. Constraints are included to keep the work output constant and the diffusion low to avoid separation. In this analysis it is only the laminar region that is considered for minimization, thus it is necessary to ensure that the modified boundary layer edge velocity distribution does not undergo transition earlier than the baseline boundary layer edge velocity distribution. This is accomplished by considering transition and separation criteria available in the literature. The result of this analysis indicates that the entropy generation rate may be reduced in the laminar boundary layers by using this technique.

Predicting Entropy Generation Rates in Transitional Boundary Layers Based on Intermittency

2006 ◽  
Author(s):  
Kevin P. Nolan ◽  
Edmond J. Walsh ◽  
Donald M. McEligot ◽  
Ralph J. Volino
Keyword(s):  
Boundary Layer ◽  
Pressure Gradient ◽  
Transition Region ◽  
Boundary Layers ◽  
Entropy Generation ◽  
Generation Rate ◽  
Entropy Generation Rate ◽  
Time Averaging ◽  
Laminar And Turbulent Flow ◽  
Intermittency Factor

Prediction of thermodynamic loss in transitional boundary layers is typically based on time averaged data only. This approach effectively ignores the intermittent nature of the transition region. In this work laminar and turbulent conditionally-sampled boundary layer data for zero pressure gradient and accelerating transitional boundary layers have been analyzed to calculate the entropy generation rate in the transition region. By weighting the non-dimensional dissipation coefficient for the laminar conditioned data and turbulent conditioned data with the intermittency factor, the entropy generation rate in the transition region can be determined and compared to the time averaged data and correlations for laminar and turbulent flow. It is demonstrated that this method provides an accurate and detailed picture of the entropy generation rate during transition in contrast with simple time averaging. The data used in this paper have been taken from conditionally-sampled boundary layer measurements available in the literature for favorable pressure gradient flows. Based on these measurements a semi-empirical technique is developed to predict the entropy generation rate in a transitional boundary layer with promising results.

Turbine Blade Entropy Generation Rate: Part II — The Measured Loss

2000 ◽  
Author(s):  
F. K. O’Donnell ◽  
M. R. D. Davies
Keyword(s):  
Boundary Layer ◽  
Turbine Blade ◽  
Entropy Generation ◽  
Generation Rate ◽  
Entropy Generation Rate ◽  
Local Entropy ◽  
Suction Surface ◽  
Layer Velocity ◽  
Local Entropy Generation ◽  
Profile Loss

Using detailed boundary layer velocity measurements the profile loss, expressed in terms of local entropy generation rate, is evaluated at discrete locations along the suction surface of a turbine blade in a subsonic linear cascade at a chord Reynolds number of 1.8 × 103 under adiabatic test conditions. The distribution of loss through the entire boundary layer is thus established with particular attention given to the comparison of the relative contributions from the laminar, transitional and turbulent regions. It is found that 75% of the entropy generation occurs in the laminar region of the blade, with transition being one of the key features of the overall loss distribution. Traditional correlation methods are considered and shown to give accurate results when compared to the experimental measurements within both the laminar and turbulent regions, the application of such correlations is however dependant upon knowledge of the onset and extent of transition. Finally it is demonstrated that an existing method for the evaluation of local entropy generation rate from measurements of wall shear stress in laminar flow, may be adapted for use in turbulent flow and hence the possibility is presented for the measurement of loss from surface mounted sensors.

Predicting Entropy Generation Rates in Transitional Boundary Layers Based on Intermittency

2006 ◽  
Vol 129 (3) ◽  
pp. 512-517 ◽  
Author(s):  
Kevin P. Nolan ◽  
Edmond J. Walsh ◽  
Donald M. McEligot ◽  
Ralph J. Volino
Keyword(s):  
Boundary Layer ◽  
Pressure Gradient ◽  
Transition Region ◽  
Boundary Layers ◽  
Entropy Generation ◽  
Generation Rate ◽  
Entropy Generation Rate ◽  
Time Averaging ◽  
Laminar And Turbulent Flow ◽  
Intermittency Factor

Prediction of thermodynamic loss in transitional boundary layers is typically based on time-averaged data only. This approach effectively ignores the intermittent nature of the transition region. In this work laminar and turbulent conditionally sampled boundary layer data for zero pressure gradient and accelerating transitional boundary layers have been analyzed to calculate the entropy generation rate in the transition region. By weighting the nondimensional dissipation coefficient for the laminar conditioned data and turbulent conditioned data with the intermittency factor, the entropy generation rate in the transition region can be determined and compared to the time-averaged data and correlations for laminar and turbulent flow. It is demonstrated that this method provides an accurate and detailed picture of the entropy generation rate during transition in contrast with simple time averaging. The data used in this paper have been taken from conditionally sampled boundary layer measurements available in the literature for favorable pressure gradient flows. Based on these measurements, a semi-empirical technique is developed to predict the entropy generation rate in a transitional boundary layer with promising results.

Choice of the Pseudo-Optimal Configuration of a Cooled Gas-Turbine Blade Based on a Constrained Minimization of the Global Entropy Production Rate

1996 ◽  
Author(s):  
Gianni Natalini ◽  
Enrico Sciubba
Keyword(s):  
Gas Turbine ◽  
Turbine Blade ◽  
Entropy Generation ◽  
Optimization Procedure ◽  
Optimal Configuration ◽  
Generation Rate ◽  
Maximum Temperature ◽  
Entropy Generation Rate ◽  
Gas Turbine Blade ◽  
Blade Profile

The problem of determining the optimal configuration of a cooled gas-turbine blade is approached by an entropy minimization technique proposed in previous works by the same authors. The present paper describes the application of the same line of thought to a more complex (and realistic) pseudo-optimization procedure, in which the objective function is again the global entropy generation rate, but two integral constraints are added to the original formulation: the maximum blade temperature (weak constraint) and the overall enthalpy drop of the working fluid in the blade passage (strong constraint). The discontinuous optimization procedure is presented here in an application which resembles a trial-and-error technique, but can be rigorously and formally described and implemented [12]. As a “zero configuration”, a realistic 2-D geometry is considered, and the thermo-fluiddynamic field around it is computed via a standard finite-element code. Then, the entropy generation rates in the blade/fluid system are calculated, and the value of the overall enthalpy drop of the gas as well as the value and location of the maximum blade temperature are recorded. Keeping all other parameters fixed (in particular, maintaining the same cooling air flowrate), the geometry of the blade is slightly “perturbed”, by introducing arbitrary modifications in the blade profile, the number and location of cooling holes, etc. Again, the velocity and temperature fields are computed, and inlet conditions are tuned so that the overall enthalpy drop remains approximately constant and the blade maximum temperature does not exceed a certain assigned value. An “optimal” configuration is found, which is affected by the minimal entropy generation rate, while abiding to the imposed constraints. The procedure is demonstrated on a realistic blade profile, and is shown to produce a better performing cascade, at least in this 2-D simulation. The extension to 3-D problems is — in principle — straightforward (but see Section 3 for further comments).

A Prediction Method for the Local Entropy Generation Rate in a Transitional Boundary Layer With a Free Stream Pressure Gradient

2002 ◽  
Author(s):  
Ed Walsh ◽  
Roy Myose ◽  
Mark Davies
Keyword(s):  
Boundary Layer ◽  
Entropy Generation ◽  
Prediction Method ◽  
Accurate Method ◽  
Generation Rate ◽  
Entropy Generation Rate ◽  
Suction Surface ◽  
Turbulent Region ◽  
Percentage Difference ◽  
Moderate Reynolds Number

To design an aerodynamically efficient blade the distribution of entropy generation on the blade surface should be known. Having only knowledge of the integrated loss, makes the task of improving the efficiency of a blade extremely difficult. A method to predict the entropy generation rate in steady, two-dimensional, incompressible, adiabatic boundary layer flows is presented, which gives both the distribution and magnitude of the entropy generation rate. This prediction method is based upon five correlations which are used to determine the: 1. entropy generated in the laminar region; 2. entropy generated in the turbulent region; 3. location of transition; 4. length of transition; 5. entropy generated in the transition region. These are then used to predict the entropy generation rate on the suction surface of a turbine rotor blade at a moderate Reynolds number; comparisons are then drawn with past measurements. The aim is to develop a quick, simple and relatively accurate method for the prediction of entropy in the boundary layers of turbomachines, although the method is not confined to this application. The only information required to implement this prediction method is the boundary layer edge velocity distribution and the turbulence intensity. A benefit of this method is that it does not rely upon dissipative CFD predictions, which are both slow to use in a design process and not yet sufficiently trustworthy. The dissipation coefficient and entropy generation rate predicted for this test case compare well to experimental measurements, with the percentage difference between the integrated entropy measured and predicted being approximately 13%. However, the difference in the turbulent region is found to be as high as 30%.

Entropy Generation in the Viscous Parts of Turbulent Boundary Layers

2008 ◽  
Vol 130 (6) ◽  
Author(s):  
Donald M. McEligot ◽  
Edmond J. Walsh ◽  
Eckart Laurien ◽  
Philippe R. Spalart
Keyword(s):  
Pressure Gradient ◽  
Boundary Layers ◽  
Entropy Generation ◽  
Turbulent Boundary Layers ◽  
Generation Rate ◽  
Entropy Generation Rate ◽  
Unit Surface Area ◽  
Pressure Gradients ◽  
Viscous Layer ◽  
Flat Plates

The local (pointwise) entropy generation rate per unit volume S‴ is a key to improving many energy processes and applications. Consequently, in the present study, the objectives are to examine the effects of Reynolds number and favorable streamwise pressure gradients on entropy generation rates across turbulent boundary layers on flat plates and—secondarily—to assess a popular approximate technique for their evaluation. About two-thirds or more of the entropy generation occurs in the viscous part, known as the viscous layer. Fundamental new results for entropy generation in turbulent boundary layers are provided by extending available direct numerical simulations. It was found that, with negligible pressure gradients, results presented in wall coordinates are predicted to be near “universal” in the viscous layer. This apparent universality disappears when a significant pressure gradient is applied; increasing the pressure gradient decreases the entropy generation rate. Within the viscous layer, the approximate evaluation of S‴ differs significantly from the “proper” value but its integral, the entropy generation rate per unit surface area Sap″, agrees within 5% at its edge.

The Effect of Reynolds Number, Compressibility and Free Stream Turbulence on Profile Entropy Generation Rate

2002 ◽  
Author(s):  
Philip C. Griffin ◽  
Mark R. D. Davies ◽  
Francis K. O’Donnell ◽  
Ed Walsh
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Laminar Boundary Layer ◽  
Entropy Generation ◽  
Free Stream ◽  
Generation Rate ◽  
Entropy Generation Rate ◽  
Suction Surface ◽  
Free Stream Turbulence ◽  
Layer Velocity

Detailed aerodynamic data from the suction surface boundary layer on a turbine blade arranged in a linear subsonic cascade was acquired under high free stream turbulence conditions (∼ 5.2%) generated using a perforated plate placed upstream of the cascade. In addition, data was also obtained from a transonic turbine cascade utilizing the same blade profile but of much smaller chord at free stream turbulence levels of 3.5%. Velocity profiles from the laminar, transitional and turbulent boundary layers were measured at various locations along the airfoil suction surface for the incompressible regime at ReC of 76,000. For the compressible test cases, boundary layer velocity profiles were measured at two locations towards the aft section of the blade at ReC of 163,000 and MEx of 0.37 respectively. For both cases the boundary layer velocity profiles were acquired by traversing a single normal hot wire probe normal to the blade surface. In addition the extent of the transition region over the blade surface was determined for both compressible and incompressible regimes by the use of an array of heated thin film sensors over a range of Reynolds and exit Mach numbers. It was observed that an earlier transition ensued at high free stream turbulence conditions in comparison to a previous investigation at comparable ReC and lower turbulence level (0.8% Tu). In addition comparisons were made to existing incompressible data at ReC = 185,000 and 0.8% free stream turbulence intensity. One of the primary observations resulting from an earlier transition was a thicker turbulent boundary layer, but in addition it was also noted that shear strain rates in the laminar boundary layer were significantly higher than those obtained at the 0.8% turbulence intensity. Further analyses also elucidated the presence of fluctuating components of velocity in the laminar boundary layer and were attributed to the effects of the free stream turbulence. This leads to the notion of a hybrid boundary layer, possessing both laminar and turbulent characteristics. These findings have implications regarding the profile loss of the blade, that is the loss generated in blade boundary layers and wakes normally associated with phenomena such as viscous shear, Reynolds stress production, shock wave formation and heat transfer across temperature differences and can be quantified in terms of the amount of entropy generated. For the purposes of this study entropy creation is solely restricted to that arising due to fluid dynamic phenomena, thereby assuming an adiabatic and quasi-isothermal flow. The entropy generation rate per unit volume is obtained directly from the boundary layer velocity profile; further integration gives rise to the entropy generation rate over the boundary layer at a point or over the entire suction surface length. Even though the number of quantitative measurement points on the transonic cascade was limited due to the very thin boundary layer present, no effects attributable to compressibility were observed on the entropy generation rate at the Mach number in question. Increased free stream turbulence had a greater effect on the generated entropy due to increased viscous shear in the laminar boundary layer and increased Reynolds stress production. In contrast, free stream turbulence did not have any significant effect on the turbulent boundary layer in the context of this study, as it was observed that the amount of entropy generated in the turbulent boundary layer was approximately equivalent for both turbulence levels at comparable Reynolds number.

Turbine Blade Entropy Generation Rate: Part I — The Boundary Layer Defined

2000 ◽  
Author(s):  
M. R. D. Davies ◽  
F. K. O’Donnell ◽  
A. J. Niven
Keyword(s):  
Boundary Layer ◽  
Turbine Blade ◽  
Entropy Generation ◽  
Leading Edge ◽  
Stress Generation ◽  
Entropy Generation Rate ◽  
Suction Surface ◽  
Viscous Shear ◽  
Layer Flow ◽  
Hot Film

The profile loss of a gas turbine blade is normally associated with the entropy increase due to the boundary layer phenomena of viscous shear, Reynolds stress generation and heat transfer. To establish the relative contributions of laminar, transitional and turbulent adiabatic boundary layer flow, to the overall entropy generation (as described in part two of this paper), detailed hot film and hot wire measurements have been made over the suction surface of a turbine blade mounted within a subsonic linear cascade. At a Reynolds number of 185 × 103, a natural transition region was found between 53 and 70% suction surface length, followed by a slowly relaxing turbulent boundary layer. The wall shear stress distribution indicated a peak in the leading edge region, dropping to a minimum value prior to transition, with a sharp rise over the transitional length before decreasing within the turbulent portion. The measurements were compared with predictions obtained from a commercial computational fluid dynamics code, which utilised the renormalisation group theory (RNG) turbulence model.

scholarly journals Analysis of entropy generation with heat generation in time dependent hydromagnetic flow of nanofluid in an oscillatory  semi- porous curved channel

2021 ◽  
Author(s):  
Muhammad Imran ◽  
Zaheer Abbas ◽  
Muhammad Naveed
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Brownian Motion ◽  
Entropy Generation ◽  
Heat Production ◽  
Time Dependent ◽  
Generation Rate ◽  
Entropy Generation Rate ◽  
Radius Of Curvature ◽  
Curved Channel

The present study focusses on the investigation of thermodynamic optimization of hydromagnetic time dependent boundary layer nanofluid flow by employing entropy generation method (EMG) in semi- permeable oscillatory curved channel. We used Buongiorno model for nanofluid to address the impact of the parameters of Brownian motion and thermophoresis. The consequences of heat production are also taken into consideration in energy the equation. The mathematical form of boundary layer equations is accomplished by following the curvilinear coordinates scheme for the considered flow problem. The analytical convergent solution of the determined nonlinear PDEs is achieved through the process of homotopy analysis (HAM). A detailed analysis is conducted out to analyze the consequences of dissimilar variables concerned, such as non-dimensional radius of curvature, Lewis number, magnetic parameter, relation of wall oscillation frequency to its parameter of velocity, Reynolds number, Prandtl number, heat production and thermophoresis parameters, entropy generation rate, Brownian motion parameter and Brickman number, concentration and temperature difference parameters on temperature, velocity profile, concentration, pressure, drag surface force, Bejan number, entropy generation, rate of mass and heat transport are addressed in detail via tables and graphs. It is noted that, the magnitude of heat transmission rate (local Nusselt number) steadily decays for advanced values of radius of curvature variable and Reynolds number.

Sign in / Sign up

Export Citation Format

Share Document