Effects of Adverse Pressure Gradient on Heat Transfer Mechanism in Thermal Boundary Layer

2005 ◽  
pp. 793-802
Author(s):  
T. Houra ◽  
Y. Nagano
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Pressure Gradient ◽  
Thermal Boundary Layer ◽  
Adverse Pressure Gradient ◽  
Transfer Mechanism ◽  
Heat Transfer Mechanism

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.

scholarly journals Effects of Pressure Gradient on Convective Heat Transfer in a Boundary Layer Flow of a Maxwell Fluid Past a Stretching Sheet

2021 ◽  
Vol 26 (3) ◽  
pp. 104-118
Author(s):  
A.N. Kashif ◽  
F. Salah ◽  
D.S. Sankar ◽  
M.D.N. Izyan ◽  
K.K. Viswanathan
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Pressure Gradient ◽  
Boundary Layer Thickness ◽  
Thermal Boundary Layer ◽  
Stretching Sheet ◽  
Maxwell Fluid ◽  
Gradient Term ◽  
Pressure Gradient Term ◽  
Layer Flow

Abstract The pressure gradient term plays a vital role in convective heat transfer in the boundary layer flow of a Maxwell fluid over a stretching sheet. The importance of the effects of the term can be monitored by developing Maxwell’s equation of momentum and energy with the pressure gradient term. To achieve this goal, an approximation technique, i.e. Homotopy Perturbation Method (HPM) is employed with an application of algorithms of Adams Method (AM) and Gear Method (GM). With this approximation method we can study the effects of the pressure gradient (m), Deborah number (β), the ratio of the free stream velocity parameter to the stretching sheet parameter (ɛ) and Prandtl number (Pr) on both the momentum and thermal boundary layer thicknesses. The results have been compared in the absence and presence of the pressure gradient term m . It has an impact of thinning of the momentum and boundary layer thickness for non-zero values of the pressure gradient. The convergence of the system has been taken into account for the stretching sheet parameter ɛ. The result of the system indicates the significant thinning of the momentum and thermal boundary layer thickness in velocity and temperature profiles. On the other hand, some results show negative values of f '(η) and θ (η) which indicates the case of fluid cooling.

The Effects of Adverse Pressure Gradients on Momentum and Thermal Structures in Transitional Boundary Layers: Part 1 — Mean Quantities

1995 ◽  
Author(s):  
Scott P. Mislevy ◽  
Ting Wang
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Pressure Gradient ◽  
Temperature Profile ◽  
Adverse Pressure Gradient ◽  
Surface Heat ◽  
Pressure Gradients ◽  
Surface Heat Transfer ◽  
Mean Temperature ◽  
The Mean

The effects of adverse pressure gradients on the thermal and momentum characteristics of a heated transitional boundary layer were investigated with free-stream turbulence ranging from 0.3 to 0.6%. The acceleration parameter, K=vU¯∞2dU¯∞dx, was kept constant along the test section. Both surface heat transfer and boundary layer measurements were conducted. The boundary layer measurements were conducted with a three-wire probe (two velocity wires and one temperature wire) for two representative cases, K1=−0.51 × 10−6 and K2=−1.05 × 10−6. The surface heat transfer measurements were conducted for K values ranging from −0.045 × 10−6 to −1.44 × 10−6 over five divergent wall angles. The Stanton numbers of the cases with adverse pressure gradients were greater than that of the zero-pressure-gradient turbulent correlation in the low-Reynolds number turbulent flow, and the difference increased as the adverse pressure gradient was increased. The adverse pressure gradient caused earlier transition onset and shorter transition length based on Rex, Reδ*, and Reθ in comparison to zero-pressure-gradient conditions. As expected, there was a reduction in skin friction as the adverse pressure gradient increased. In the U+-Y+ coordinates, the adverse pressure gradients had a significant effect on the mean velocity profiles in the near-wall region for the late-laminar and early transition stations. The mean temperature profile was observed to precede the velocity profile in starting and ending the transition process, opposite to what occurred in favorable pressure gradient cases in previous studies. A curve fit of the turbulent temperature profile in the log-linear region for the K2 case gave a conduction layer thickness of Y+=9.8 and an average Prt=0.71. In addition, the wake region of the turbulent mean temperature profile was significantly suppressed.

The Effects of Adverse Pressure Gradients on Momentum and Thermal Structures in Transitional Boundary Layers: Part 1—Mean Quantities

1996 ◽  
Vol 118 (4) ◽  
pp. 717-727 ◽  
Author(s):  
S. P. Mislevy ◽  
T. Wang
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Pressure Gradient ◽  
Temperature Profile ◽  
Adverse Pressure Gradient ◽  
Surface Heat ◽  
Pressure Gradients ◽  
Surface Heat Transfer ◽  
Mean Temperature ◽  
The Mean

The effects of adverse pressure gradients on the thermal and momentum characteristics of a heated transitional boundary layer were investigated with free-stream turbulence ranging from 0.3 to 0.6 percent. The acceleration parameter, K, was kept constant along the test section. Both surface heat transfer and boundary layer measurements were conducted. The boundary layer measurements were conducted with a three-wire probe (two velocity wires and one temperature wire) for two representative cases, K1 = −0.51 × 10−6 and K2 = −1.05 × 10−6. The surface heat transfer measurements were conducted for K values ranging from −0.045 × 10−6 to −1.44 × 10−6 over five divergent wall angles. The Stanton numbers of the cases with adverse pressure gradients were greater than that of the zero-pressure-gradient turbulent correlation in the low-Reynolds-number turbulent flow, and the difference increased as the adverse pressure gradient was increased. The adverse pressure gradient caused earlier transition onset and shorter transition length based on Rex, Reδ*, and Reθ in comparison to zero-pressure-gradient conditions. As expected, there was a reduction in skin friction as the adverse pressure gradient increased. In the U+−Y+ coordinates, the adverse pressure gradients had a significant effect on the mean velocity profiles in the near-wall region for the late-laminar and early transition stations. The mean temperature profile was observed to precede the velocity profile in starting and ending the transition process, opposite to what occurred in favorable pressure gradient cases in previous studies. A curve fit of the turbulent temperature profile in the log-linear region for the K2 case gave a conduction layer thickness of Y+ = 9.8 and an average Prt = 0.71. In addition, the wake region of the turbulent mean temperature profile was significantly suppressed.

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.

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