Analytical Modeling of Turbine Cascade Leading Edge Heat Transfer Using Skin Friction and Pressure Measurements

2008 ◽  
Vol 130 (2) ◽  
Author(s):  
Brian M. Holley ◽  
Lee S. Langston
Keyword(s):  
Heat Transfer ◽  
Skin Friction ◽  
Stagnation Point ◽  
Potential Flow ◽  
Leading Edge ◽  
Turbine Cascade ◽  
Stagnation Region ◽  
Stagnation Line ◽  
Point Potential ◽  
Hiemenz Flow

The flow near the leading edge stagnation line of a plane turbine cascade airfoil is analyzed using measurements, analytical modeling, and computational fluid dynamics modeling. New measurements of skin friction and pressure are used to show that the aerodynamics of the leading edge, within what we call the stagnation region, are well described by an exact analytical solution for laminar stagnation-point or Hiemenz flow. The skin friction measurements indicate the extent of the stagnation region. The same parameters that characterize Hiemenz flow also characterize stagnation-point potential flow. The thermal resistance of the laminar momentum boundary layer in Hiemenz flow is absent in the inviscid solution. Consequently, the heat transfer in stagnation-point potential flow is greater than the heat transfer in Hiemenz flow. Based on measurements from an earlier study, the highest heat transfer levels in the cascade occur along the leading edge stagnation line. Stagnation-point potential flow provides a close, upper bound for the measured heat transfer at this small but critical location within the stagnation region. This paper describes how to apply the analytical model for predicting cascade stagnation-line heat transfer using only surface pressure calculations.

Analytical Modeling of Turbine Cascade Leading Edge Heat Transfer Using Skin Friction and Pressure Measurements

2007 ◽  
Author(s):  
Brian M. Holley ◽  
Lee S. Langston
Keyword(s):  
Heat Transfer ◽  
Skin Friction ◽  
Stagnation Point ◽  
Analytical Modeling ◽  
Exact Analytical Solution ◽  
Leading Edge ◽  
Cfd Modeling ◽  
Turbine Cascade ◽  
Stagnation Line ◽  
Hiemenz Flow

The flow near the leading edge stagnation-line of a plane turbine cascade airfoil is analyzed using measurements, analytical modeling, and computational fluid dynamics (CFD) modeling. New measurements of skin friction and pressure indicate that the aerodynamics of the leading edge are well described by an exact analytical solution for stagnation-point or Hiemenz flow. The skin friction measurements indicate the extent over which the analytical model applies. Based on measurements from an earlier study, the highest heat transfer levels occur along the leading edge stagnation-line. The same parameters that characterize Hiemenz flow also characterize a stagnation-point potential flow, which is used to accurately predict the heat transfer levels along the stagnation-line. CFD analysis indicates that pressure predictions are better than skin friction predictions for characterizing the analytical modeling that is used for more accurate heat transfer evaluation. This provides an approach for predicting the peak heat transfer coefficient in a cascade based only upon surface static pressure calculations.

Stagnation Line Heat Transfer Augmentation Due to Freestream Vortical Structures and Vorticity

2002 ◽  
Vol 124 (3) ◽  
pp. 583-587 ◽  
Author(s):  
Aung N. Oo ◽  
Chan Y. Ching
Keyword(s):  
Heat Transfer ◽  
Leading Edge ◽  
Reynolds Numbers ◽  
Heat Transfer Model ◽  
Transfer Model ◽  
Freestream Turbulence ◽  
Stagnation Region ◽  
Stagnation Line ◽  
Vortical Structures ◽  
Heat Transfer Augmentation

An experimental study has been performed to investigate the effect of freestream vortical structures and vorticity on stagnation region heat transfer. A heat transfer model with a cylindrical leading edge was tested in a wind tunnel at Reynolds numbers ranging from 67,750 to 142,250 based on leading edge diameter of the model. Grids of parallel rods were placed at several locations upstream of the heat transfer model in orientations where the rods were perpendicular and parallel to the stagnation line to generate freestream turbulence with distinct vortical structures. All three components of turbulence intensity, integral length scale and the spanwise and transverse vorticity were measured to characterize the freestream turbulence. The measured heat transfer data and freestream turbulence characteristics were compared with existing empirical models for the stagnation line heat transfer. A new correlation for the stagnation line heat transfer has been developed that includes the spanwise fluctuating vorticity components.

A Study of the Relationship Between Free-Stream Turbulence and Stagnation Region Heat Transfer

1987 ◽  
Vol 109 (1) ◽  
pp. 10-15 ◽  
Author(s):  
G. J. VanFossen ◽  
R. J. Simoneau
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Free Stream ◽  
Leading Edge ◽  
Reynolds Numbers ◽  
Cylinder Surface ◽  
Nasa Lewis Research ◽  
Stagnation Region ◽  
Stagnation Line ◽  
Free Stream Turbulence

A study has been conducted at the NASA Lewis Research Center to investigate the mechanism that causes free-stream turbulence to increase heat transfer in the stagnation region of turbine vanes and blades. The work was conducted in a wind tunnel at atmospheric conditions to facilitate measurements of turbulence and heat transfer. The model size was scaled up to simulate Reynolds numbers (based on leading edge diameter) that are to be expected on a turbine blade leading edge. Reynolds numbers from 13,000 to 177,000 were run in the present tests. Spanwise averaged heat transfer measurements with high and low turbulence have been made with “rough” and smooth surface stagnation regions. Results of these measurements show that, at the Reynolds numbers tested, the boundary layer remained laminar in character even in the presence of free-stream turbulence. If roughness was added the boundary layer became transitional as evidenced by the heat transfer increase with increasing distance from the stagnation line. Hot-wire measurements near the stagnation region downstream of an array of parallel wires has shown that vorticity in the form of mean velocity gradients is amplified as flow approaches the stagnation region. Finally smoke wire flow visualization and liquid crystal surface heat transfer visualization were combined to show that, in the wake of an array of parallel wires, heat transfer was a minimum in the wire wakes where the fluctuating component of velocity (local turbulence) was the highest. Heat transfer was found to be the highest between pairs of vortices where the induced velocity was toward the cylinder surface.

Effect of Turbulence With Different Vortical Structures on Stagnation Region Heat Transfer

2001 ◽  
Vol 123 (4) ◽  
pp. 665-674 ◽  
Author(s):  
Aung N. Oo ◽  
Chan Y. Ching
Keyword(s):  
Heat Transfer ◽  
Leading Edge ◽  
Reynolds Numbers ◽  
Heat Transfer Model ◽  
Transfer Model ◽  
Stagnation Region ◽  
Stagnation Line ◽  
Vortical Structures ◽  
Transfer Data ◽  
Correlation Models

The effect of freestream turbulence with different vortical structures on the stagnation region heat transfer was experimentally studied. Reynolds numbers, based on leading edge diameter of the heat transfer model with a cylindrical leading edge, ranged from 67,750 to 142,250. Turbulence generating grids of parallel rods were placed at several positions upstream of the heat transfer model in orientations where the rods were perpendicular and parallel to the stagnation line. The turbulence intensity and ratio of integral length scale to leading edge diameter were in the range 3.93 to 11.78 percent and 0.07 to 0.70, respectively. The grids with rods perpendicular to the stagnation line, where the primary vortical structures are expected to be perpendicular to the stagnation line, result in higher heat transfer than those with rods parallel to the stagnation line. The measured heat transfer data and turbulence characteristics are compared with existing correlation models.

Influence of Freestream Vortical Structures on Stagnation Region Heat Transfer

2000 ◽  
Author(s):  
Aung N. Oo ◽  
Chan Y. Ching
Keyword(s):  
Heat Transfer ◽  
Leading Edge ◽  
Heat Transfer Model ◽  
Transfer Model ◽  
Vertical Orientation ◽  
Stagnation Region ◽  
Stagnation Line ◽  
Vortical Structures ◽  
Horizontal Orientation ◽  
The Difference

Abstract An experimental study was performed to investigate the influence of freestream vortical structures on stagnation region heat transfer. A heat transfer model with a cylindrical leading edge was tested in a low speed wind tunnel at Reynolds numbers ranging from 67,750 to 142,250 based on leading edge diameter of the model. Turbulence generating grids of parallel rods of diameter, 2.86 cm, 1.59 cm and 0.95 cm, were placed upstream of the heat transfer model in horizontal and vertical orientations to generate freestream turbulence with different orientations of vortical structures. The rods in horizontal orientation were perpendicular to the stagnation line and those in vertical orientation were parallel to the stagnation line of the heat transfer model. The distance between the grid and heat transfer model was varied from 25 to 125 rod diameters. The grids with rods in the horizontal orientation, where the primary vortical structures are expected to be perpendicular to the stagnation line, result in higher heat transfer than with the grids where the rods are in the vertical orientation. The difference in heat transfer with the two grid orientations decreases with increasing grid-to-model distance for a given rod-grid. The difference also decreases with decreasing rod size for a given normalized grid-to-model distance. For the 2.86 cm rod-grid, the difference in heat transfer augmentation between horizontal and vertical grid-orientations is highest at the stagnation line and decreases with streamwise distance. This difference, however, remains fairly constant over the whole stagnation region for the 1.59 cm and 0.95 cm rod-grids.

scholarly journals Preliminary Results of a Study of the Relationship Between Free Stream Turbulence and Stagnation Region Heat Transfer

1985 ◽  
Author(s):  
G. James VanFossen ◽  
Robert J. Simoneau
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Free Stream ◽  
Leading Edge ◽  
Reynolds Numbers ◽  
Nasa Lewis Research ◽  
Hot Wire ◽  
Stagnation Region ◽  
Stagnation Line ◽  
Free Stream Turbulence

A study is being conducted at the NASA Lewis Research Center to investigate the mechanism that causes free stream turbulence to increase heat transfer in the stagnation region of turbine vanes and blades. The work is being conducted in a wind tunnel at atmospheric conditions to facilitate measurements of turbulence and heat transfer. The model size is scaled up to simulate Reynolds numbers (based on leading edge diameter) that are to be expected on a turbine blade leading edge. Reynolds numbers from 13 000 to 177 000 were run in the present tests. Spanwise averaged heat transfer measurements with high and low turbulence have been made with “rough” and smooth surface stagnation regions. Results of these measurements show that the boundary layer remains laminar in character even in the presence of free stream turbulence at the Reynolds numbers tested. If roughness is added the boundary layer becomes transitional as evidenced by the heat transfer increase with increasing distance from the stagnation line. Hot wire measurements near the stagnation region downstream of an array of parallel wires has shown that vorticity in the form of mean velocity gradients is amplified as flow approaches the stagnation region. Circumferential traverses of a hot wire probe very near the surface of the cylinder have shown the fluctuating component of velocity changes in character depending on free stream turbulence and Reynolds number. Finally smoke wire flow visualization and liquid crystal surface heat transfer visualization have been combined to show that, in the wake of an array of parallel wires, heat transfer is a minimum in the wire wakes where the fluctuating component of velocity (local turbulence) was the highest. Heat transfer was found to be the highest between pairs of vortices where the induced velocity is toward the cylinder surface.

Turbulence and Vorticity Effects on Stagnation Region Heat Transfer

2001 ◽  
Author(s):  
Aung N. Oo ◽  
Chan Y. Ching
Keyword(s):  
Heat Transfer ◽  
Leading Edge ◽  
Reynolds Numbers ◽  
Heat Transfer Model ◽  
Transfer Model ◽  
Freestream Turbulence ◽  
Stagnation Region ◽  
Stagnation Line ◽  
Correlation Models ◽  
Low Speed Wind Tunnel

An experimental study has been performed to investigate the influences of freestream turbulence, including the vorticity field, on the stagnation region heat transfer. A heat transfer model with a cylindrical leading edge was tested in a low speed wind tunnel at Reynolds numbers ranging from 67,750 to 142,250 based on leading edge diameter of the model. Grids of parallel rods were used to generate the freestream turbulence with well-defined primary vortex lines. The grids were placed at several locations upstream of the heat transfer model in orientations where the rods were perpendicular and parallel to the stagnation line. The turbulence intensity and the ratio of integral length scale to leading edge diameter were in the range of 3.93 to 11.78 % and 0.07 to 0.7, respectively. The measured heat transfer data and freestream turbulence characteristics are compared with existing correlation models. A new correlation for the stagnation line heat transfer has been developed that includes the spanwise fluctuating vorticity components.

Wake-Induced Unsteady Stagnation-Region Heat Transfer Measurements

1994 ◽  
Vol 116 (1) ◽  
pp. 29-38 ◽  
Author(s):  
P. J. Magari ◽  
L. E. LaGraff
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Heat Transfer Rate ◽  
Transfer Rate ◽  
Edge Region ◽  
Isentropic Compression ◽  
Stagnation Region ◽  
Stagnation Line ◽  
Wide Range ◽  
Mach Numbers

An experimental investigation of wake-induced unsteady heat transfer in the stagnation region of a cylinder was conducted. The objective of the study was to create a quasi-steady representation of the stator/rotor interaction in a gas turbine using two stationary cylinders in crossflow. In this simulation, a larger cylinder, representing the leading-edge region of a rotor blade, was immersed in the wake of a smaller cylinder, representing the trailing-edge region of a stator vane. Time-averaged and time-resolved heat transfer results were obtained over a wide range of Reynolds number at two Mach numbers: one incompressible and one transonic. The tests were conducted at Reynolds numbers, Mach numbers, and gas-to-wall temperature ratios characteristic of turbine engine conditions in an isentropic compression-heated transient wind tunnel (LICH tube). The augmentation of the heat transfer in the stagnation region due to wake unsteadiness was documented by comparison with isolated cylinder tests. It was found that the time-averaged heat transfer rate at the stagnation line, expressed in terms of the Frossling number (Nu/Re), reached a maximum independent of the Reynolds number. The power spectra and cross-correlation of the heat transfer signals in the stagnation region revealed the importance of large vortical structures shed from the upstream wake generator. These structures caused large positive and negative excursions about the mean heat transfer rate in the stagnation region.

Stability analysis on the stagnation-point flow and heat transfer over a permeable stretching/shrinking sheet with heat source effect

2018 ◽  
Vol 28 (11) ◽  
pp. 2650-2663 ◽  
Author(s):  
Fatinnabila Kamal ◽  
Khairy Zaimi ◽  
Anuar Ishak ◽  
Ioan Pop
Keyword(s):  
Heat Transfer ◽  
Stability Analysis ◽  
Heat Source ◽  
Skin Friction ◽  
Stagnation Point ◽  
Stagnation Point Flow ◽  
Shrinking Sheet ◽  
Content Type ◽  
Source Effect ◽  
Flow And Heat Transfer

PurposeThis paper aims to analyze the behavior of the stagnation-point flow and heat transfer over a permeable stretching/shrinking sheet in the presence of the viscous dissipation and heat source effects.Design/methodology/approachThe governing partial differential equations are converted into ordinary differential equations by similarity transformations before being solved numerically using the bvp4c function built in Matlab software. Effects of suction/injection parameter and heat source parameter on the skin friction and heat transfer coefficients as well as the velocity and temperature profiles are presented in the forms of tables and graphs. A temporal stability analysis will be conducted to verify which solution is stable for the dual solutions exist for the shrinking case.FindingsThe analysis indicates that the skin friction coefficient and the local Nusselt number as well as the velocity and temperature were influenced by suction/injection parameter. In contrast, only the local Nusselt number, which represents heat transfer rate at the surface, was affected by heat source effect. Further, numerical results showed that dual solutions were found to exist for the certain range of shrinking case. Then, the stability analysis is performed, and it is confirmed that the first solution is linearly stable and has real physical implication, while the second solution is not.Practical implicationsIn practice, the study of the steady two-dimensional stagnation-point flow and heat transfer past a permeable stretching/shrinking sheet in the presence of heat source effect is very crucial and useful. The problems involving fluid flow over stretching or shrinking surfaces can be found in many industrial manufacturing processes such as hot rolling, paper production and spinning of fibers. Owing to the numerous applications, the study of stretching/shrinking sheet was subsequently extended by many authors to explore various aspects of skin friction coefficient and heat transfer in a fluid. Besides that, the study of suction/injection on the boundary layer flow also has important applications in the field of aerodynamics and space science.Originality/valueAlthough many studies on viscous fluid has been investigated, there is still limited discoveries found on the heat source and suction/injection effects. Indeed, this paper managed to obtain the second (dual) solutions and stability analysis is performed. The authors believe that all the results are original and have not been published elsewhere.

scholarly journals Direct numerical simulation of heat transfer from the stagnation region of a heated cylinder affected by an impinging wake

2011 ◽  
Vol 669 ◽  
pp. 64-89 ◽  
Author(s):  
JAN G. WISSINK ◽  
WOLFGANG RODI
Keyword(s):  
Heat Transfer ◽  
Free Stream ◽  
Three Dimensional ◽  
Stream Velocity ◽  
Stagnation Region ◽  
Stagnation Line ◽  
Vortical Structures ◽  
Free Stream Turbulence ◽  
Heated Cylinder ◽  
Three Dimensional Simulations

The effect of an incoming wake on the flow around and heat transfer from the stagnation region of a circular cylinder was studied using direct numerical simulations (DNSs). Four simulations were carried out at a Reynolds number (based on free-stream velocity and cylinder diameterD) ofReD= 13200: one two-dimensional (baseline) simulation and three three-dimensional simulations. The three-dimensional simulations comprised a baseline simulation with a uniform incoming velocity field, a simulation in which realistic wake data – generated in a separate precursor DNS – were introduced at the inflow plane and, finally, a simulation in which the turbulent fluctuations were removed from the incoming wake in order to study the effect of the mean velocity deficit on the heat transfer in the stagnation region. In the simulation with realistic wake data, the incoming wake still exhibited the characteristic meandering behaviour of a near-wake. When approaching the regions immediately above and below the stagnation line of the cylinder, the vortical structures from the wake were found to be significantly stretched by the strongly accelerating wall-parallel (circumferential) flow into elongated vortex tubes that became increasingly aligned with the direction of flow. As the elongated streamwise vortical structures impinge on the stagnation region, on one side they transport cool fluid towards the heated cylinder, while on the other side hot fluid is transported away from the cylinder towards the free stream, thereby increasing the heat transfer. The DNS results are compared with various semi-empirical correlations for predicting the augmentation of heat transfer due to free-stream turbulence.

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