Variable Viscosity Effect on the Laminar Water Boundary Layer on Heated Cones

1978 ◽  
Vol 45 (3) ◽  
pp. 481-486 ◽  
Author(s):  
L.-S. Yao
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Shear Stress ◽  
Pressure Gradient ◽  
Variable Viscosity ◽  
Fluid Flows ◽  
Temperature Dependent ◽  
Viscosity Effect ◽  
Favorable Pressure Gradient ◽  
Half Angle

Heat transfer and shear stress may be significantly affected by buoyancy-forced and associated free-convection motions in many forced-convection flows. A crossflow is induced when a uniform, horizontal stream passes along a heated, axisymmetric slender body. The crossflow effects on heat transfer and shear stress grow as the fluid flows downstream, and eventually become one of the dominant mechanisms even for a moderate-speed forced-convection flow. Early study of the longitudinal cylinder flow showed that the crossflow may destabilize the boundary layer and degrade the heat transfer over the upper half of the body. On the other hand, heating can be used to stabilize the water boundary layer due to its temperature-dependent viscosity, since (dμ/dT) of water is negative. However, the influences of the pressure gradient on the destabilizing crossflow effect and on the stabilizing variable-viscosity effect have never been studied before. It is important to know the interaction of the buoyancy-force effect and the variable-viscosity effect under the non-zero pressure gradient conditions in stabilizing the boundary layer by heating. In this paper a similarity solution is presented for a three-dimensional boundary layer on a heated cone to stimulate the water flow past the forward part of an axisymmetric slender body. The numerical solutions of the ordinary differential equations reduced by the similarity transformation are presented in the region near the vertex of the cone. The results indicate that the crossflow grows as the fluid flows downstream for the cone of its half angle less than 66.25°. For a cone of its half angle larger than 66.25°, the magnitude of the crossflow is about the same order as that of the axial flow in the neighborhood of the cone vertex and is suppressed by the favorable pressure gradient as the fluid moves downstream. The effect of the temperature-dependent water viscosity has been shown to enhance the favorable pressure-gradient effects and to counterbalance the crossflow effects.

The Effect of Real Turbine Roughness With Pressure Gradient on Heat Transfer

2003 ◽  
Author(s):  
Jeffrey P. Bons ◽  
Stephen T. McClain
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Pressure Gradient ◽  
Adverse Pressure Gradient ◽  
Combined Effects ◽  
Pressure Gradients ◽  
Smooth Wall ◽  
Reynolds Analogy ◽  
Integral Boundary ◽  
Favorable Pressure Gradient

Experimental measurements of heat transfer (St) are reported for low speed flow over scaled turbine roughness models at three different freestream pressure gradients: adverse, zero (nominally), and favorable. The roughness models were scaled from surface measurements taken on actual, in-service land-based turbine hardware and include samples of fuel deposits, TBC spallation, erosion, and pitting as well as a smooth control surface. All St measurements were made in a developing turbulent boundary layer at the same value of Reynolds number (Rex≅900,000). An integral boundary layer method used to estimate cf for the smooth wall cases allowed the calculation of the Reynolds analogy (2St/cf). Results indicate that for a smooth wall, Reynolds analogy varies appreciably with pressure gradient. Smooth surface heat transfer is considerably less sensitive to pressure gradients than skin friction. For the rough surfaces with adverse pressure gradient, St is less sensitive to roughness than with zero or favorable pressure gradient. Roughness-induced Stanton number increases at zero pressure gradient range from 16–44% (depending on roughness type), while increases with adverse pressure gradient are 7% less on average for the same roughness type. Hot-wire measurements show a corresponding drop in roughness-induced momentum deficit and streamwise turbulent kinetic energy generation in the adverse pressure gradient boundary layer compared with the other pressure gradient conditions. The combined effects of roughness and pressure gradient are different than their individual effects added together. Specifically, for adverse pressure gradient the combined effect on heat transfer is 9% less than that estimated by adding their separate effects. For favorable pressure gradient, the additive estimate is 6% lower than the result with combined effects. Identical measurements on a “simulated” roughness surface composed of cones in an ordered array show a behavior unlike that of the scaled “real” roughness models. St calculations made using a discrete-element roughness model show promising agreement with the experimental data. Predictions and data combine to underline the importance of accounting for pressure gradient and surface roughness effects simultaneously rather than independently for accurate performance calculations in turbines.

On the Momentum and Thermal Structures of Turbulent Spots in a Favorable Pressure Gradient

2005 ◽  
Vol 128 (4) ◽  
pp. 689-698 ◽  
Author(s):  
T. P. Chong ◽  
S. Zhong
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Pressure Gradient ◽  
Velocity Component ◽  
Thermal Boundary Layer ◽  
Temperature Fluctuations ◽  
Turbulent Spots ◽  
Zone Length ◽  
Favorable Pressure Gradient ◽  
The Difference

This paper represents the results from an experimental investigation of the flow physics behind the difference in the transition zone length indicated by the momentum boundary layer and thermal boundary layer parameters observed on the suction surfaces of gas turbine blades. The experiments were carried out on turbulent spots created artificially in an otherwise laminar boundary layer developing over a heated flat plate in a zero pressure gradient and a favorable pressure gradient. A specially designed miniature triple wire probe was used to measure the streamwise velocity component U, transverse velocity component V and temperature T simultaneously during the passage of the spots. In this paper, the general characteristics of the ensemble-averaged velocity and temperature perturbations, rms fluctuations, and the second moment turbulent quantities are discussed and the influence of favorable pressure gradient on these parameters is examined. When a favorable pressure gradient is present, unlike in the velocity boundary layer where significant velocity fluctuations and Reynolds shear stress occur both on the plane of symmetry and the spanwise periphery, high temperature fluctuations (and turbulent heat fluxes) are confined in the plane of symmetry. The difference in the levels of velocity/temperature fluctuations at these two locations gives an indication of the effectiveness of momentum/heat transfer across the span of the spots. The results of this study indicate that the heat transfer within a spot is inhibited more than that of the momentum transfer at the presence of a favorable pressure gradient. This phenomenon is expected to slow down the development of a transitional thermal boundary layer, leading to a longer transitional zone length indicated by the heat transfer parameters as reported in the literature.

The Effect of Real Turbine Roughness With Pressure Gradient on Heat Transfer

2004 ◽  
Vol 126 (3) ◽  
pp. 385-394 ◽  
Author(s):  
Jeffrey P. Bons ◽  
Stephen T. McClain
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Pressure Gradient ◽  
Adverse Pressure Gradient ◽  
Combined Effects ◽  
Pressure Gradients ◽  
Smooth Wall ◽  
Reynolds Analogy ◽  
Integral Boundary ◽  
Favorable Pressure Gradient

Experimental measurements of heat transfer (St) are reported for low speed flow over scaled turbine roughness models at three different freestream pressure gradients: adverse, zero (nominally), and favorable. The roughness models were scaled from surface measurements taken on actual, in-service land-based turbine hardware and include samples of fuel deposits, TBC spallation, erosion, and pitting as well as a smooth control surface. All St measurements were made in a developing turbulent boundary layer at the same value of Reynolds number Rex≅900,000. An integral boundary layer method used to estimate cf for the smooth wall cases allowed the calculation of the Reynolds analogy 2St/cf. Results indicate that for a smooth wall, Reynolds analogy varies appreciably with pressure gradient. Smooth surface heat transfer is considerably less sensitive to pressure gradients than skin friction. For the rough surfaces with adverse pressure gradient, St is less sensitive to roughness than with zero or favorable pressure gradient. Roughness-induced Stanton number increases at zero pressure gradient range from 16–44% (depending on roughness type), while increases with adverse pressure gradient are 7% less on average for the same roughness type. Hot-wire measurements show a corresponding drop in roughness-induced momentum deficit and streamwise turbulent kinetic energy generation in the adverse pressure gradient boundary layer compared with the other pressure gradient conditions. The combined effects of roughness and pressure gradient are different than their individual effects added together. Specifically, for adverse pressure gradient the combined effect on heat transfer is 9% less than that estimated by adding their separate effects. For favorable pressure gradient, the additive estimate is 6% lower than the result with combined effects. Identical measurements on a “simulated” roughness surface composed of cones in an ordered array show a behavior unlike that of the scaled “real” roughness models. St calculations made using a discrete-element roughness model show promising agreement with the experimental data. Predictions and data combine to underline the importance of accounting for pressure gradient and surface roughness effects simultaneously rather than independently for accurate performance calculations in turbines.

Effects of the Condition of the Approach Boundary Layer and of Mainstream Pressure Gradients on the Heat Transfer Coefficient on Film-Cooled Surfaces

1985 ◽  
Vol 107 (1) ◽  
pp. 99-104 ◽  
Author(s):  
N. Hay ◽  
D. Lampard ◽  
C. L. Saluja
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Mass Transfer ◽  
Heat Transfer Coefficient ◽  
Pressure Gradient ◽  
Transfer Coefficient ◽  
Adverse Pressure Gradient ◽  
Pressure Gradients ◽  
Favorable Pressure Gradient ◽  
The Heat Transfer Coefficient

This paper describes an investigation of the sensitivity of the heat transfer coefficient under the film to the state of the approach boundary layer for injection through a row of holes on a flat plate. The investigation is done for a range of blowing parameters using a heat-mass transfer analogy. Injection angles of 35 deg and 90 deg are covered. Additionally, for the same injection geometries, the effect of injection in the presence of mild adverse, mild favorable, and strong favorable mainstream pressure gradients is investigated. The results indicate that the heat transfer coefficient under the film is sensitive neither to the condition of the approach boundary layer nor to the presence of a mild adverse pressure gradient, but it is significantly lowered by a favorable pressure gradient, particularly at low blowing parameters.

scholarly journals Laminar Boundary Layer Flow and Heat Transfer With Favorable Pressure Gradient at Constant K Values

1992 ◽  
Author(s):  
Dadong Zhou ◽  
Ting Wang
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Friction Coefficient ◽  
Pressure Gradient ◽  
Leading Edge ◽  
Skin Friction Coefficient ◽  
Convergent Channel ◽  
Flow And Heat Transfer ◽  
Favorable Pressure Gradient ◽  
Layer Flow

Approximate algebraic correlations for the two-dimensional laminar boundary layer flow and heat transfer with favorable pressure gradient at constant K (≡vUe2dUedx) values were found by using Pohlhausen’s integral method. Two thermal boundary conditions were considered: constant wall heat flux and constant wall temperature. These correlations were tabulated and compared in the limits KRex → 0 and KRex → ∞ with the similarity solutions of the Blasius flow and the convergent-channel flow. The comparisons between these correlations and those obtained numerically from the STAN5 code were excellent. The results showed that the momentum boundary layer grows at the leading edge with an initial rate like the Blasius flow to a maximum value, then decreases and asymptotically approaches the behavior of a convergent-channel flow. As KRex increases, the skin friction coefficient decreases and approaches a constant; the Pohlhausen’s pressure gradient parameter (Λ≡δ2vdUedx) increases from zero at the leading edge and approaches a constant. While hydrodynamically asymptotical solutions were obtained, no asymptotical thermal similarity was found. Skin friction coefficient and various integral parameters could be collapsed into a corresponding single curve when suitable normalization factors were chosen. The effects of Prandtl number and unheated starting length were also analyzed.

Effects of Free-Stream Turbulence and Pressure Gradient on Flat-Plate Boundary-Layer Velocity Profiles and on Heat Transfer

1967 ◽  
Vol 89 (2) ◽  
pp. 169-175 ◽  
Author(s):  
G. H. Junkhan ◽  
G. K. Serovy
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Nusselt Number ◽  
Pressure Gradient ◽  
Flat Plate ◽  
Turbulence Intensity ◽  
Free Stream ◽  
Free Stream Turbulence ◽  
Favorable Pressure Gradient ◽  
Layer Velocity

Experimental data indicating some effects of free-stream turbulence intensity on time-average boundary-layer velocity profiles and on heat transfer from a constant-temperature flat plate with a favorable pressure gradient are presented for local Reynolds numbers ranging from 4 × 104 to 4 × 105 and for free-stream turbulence intensities from 0.4 to 8.3 percent. It is concluded that, for the range of variables covered by the experiments: (a) The effect of free-stream turbulence intensity on heat transfer through the laminar boundary layer with a zero pressure gradient is negligible; (b) for a given Reynolds number, the local Nusselt number increases with increasing free-stream turbulence intensity when a pressure gradient is present, the boundary-layer profiles for these conditions changing with a variation in free-stream turbulence intensity; and (c) no increase in Nusselt number with increase in free-stream turbulence intensity occurs for turbulent boundary layers with a favorable pressure gradient.

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