Effects of Selected Gas Stream Parameters and Coolant Properties on Liquid Film Cooling

1964 ◽  
Vol 86 (2) ◽  
pp. 271-278 ◽  
Author(s):  
C. F. Warner ◽  
D. L. Emmons
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Liquid Film ◽  
Film Cooling ◽  
Boundary Layer Theory ◽  
Simple Analysis ◽  
Flow Rates ◽  
Hot Gas ◽  
Pipe Flows ◽  
Temperature Distributions

Experimental determinations were made of the effects of changes in the temperature, pressure, and Reynolds number of a hot gas stream upon the required flow rate of a single liquid (water) used for film cooling different lengths (4, 5, 6, 7, and 8 in.) of a cylindrical rocket motor combustion chamber. Experiments were also conducted with other coolants, such as anhydrous ammonia, ethyl alcohol, and Freon-113 for determining the effects of the physical properties of those liquids on the required film-coolant flow rates for a single condition of gas stream temperature, pressure, and Reynolds number. Determinations were also made of the heat flux and wall temperature distributions downstream from the terminus of the liquid film; that is, in the region where there is considerable vaporized film coolant in the vicinity of the chamber wall. The experimental results are correlated by means of a simple analysis based on turbulent boundary-layer theory applicable in pipe flows.

Linear Spatial Evolution Formulation of Two-Dimensional Waves on Liquid Films Under Evaporating/Isothermal/Condensing Conditions

2002 ◽  
Author(s):  
Xuemin Ye ◽  
Chunxi Li ◽  
Weiping Yan
Keyword(s):  
Boundary Layer ◽  
Surface Tension ◽  
Reynolds Number ◽  
Evolution Equation ◽  
Film Thickness ◽  
Boundary Conditions ◽  
Liquid Films ◽  
Boundary Layer Theory ◽  
Spatial Evolution ◽  
Two Dimensional

The linear spatial evolution formulation of the two-dimensional waves of the evaporating or isothermal or condensing liquid films falling down an inclined wall is established for the film thickness with the collocation method based on the boundary layer theory and complete boundary conditions. The evolution equation indicates that there are two different modes of waves in spatial evolution. And the flow stability is highly dependent on the evaporation or condensation, thermocapillarity, surface tension, inclination angle and Reynolds number.

Linear Stability of Two-Dimensional Stationary Waves on Evaporating or Condensing Liquid Films

2003 ◽  
Author(s):  
Xuemin Ye ◽  
Weiping Yan
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Film Thickness ◽  
Boundary Conditions ◽  
Liquid Films ◽  
Boundary Layer Theory ◽  
Stationary Waves ◽  
Two Dimensional ◽  
Stability Equation ◽  
Liquid Property

The linear spatial stability equation of the two-dimensional stationary waves of evaporating or isothermal or condensing liquid films falling down an inclined wall is established for the film thickness with the collocation method based on the boundary layer theory and complete boundary conditions. This model includes the effects of Reynolds number, thermocapillarity, inclination angle, liquid property, evaporation, isothermal or condensation. The stabilities characteristics of stationary waves are fully indicated in theory for evaporating or condensing films.

scholarly journals The Effect of Bulk Flow Pulsations on Film Cooling From Two Rows of Holes

1997 ◽  
Author(s):  
Dong Kee Sohn ◽  
Joon Sik Lee
Keyword(s):  
Boundary Layer ◽  
Film Cooling ◽  
Free Stream ◽  
Bulk Flow ◽  
Phase Lag ◽  
Cooling Effectiveness ◽  
Freestream Velocity ◽  
Film Cooling Effectiveness ◽  
Temperature Distributions ◽  
Flow Pulsations

Effect of bulk flow pulsations on film cooling from two rows of holes with inline and staggered arrangements is experimentally investigated. As a baseline study, a single row injection is also tested. Two-row injection is important because the phase lag between the two rows may cause changes in the film coolant coverage. Potential flow pulsations are generated by the rotating shutter mechanism attached downstream of the test section. Free-stream Strouhal number based on the boundary layer thickness is in the range of 0.033–0.33, and the amplitude of the phase-averaged freestream velocity due to static pressure variation about 10–20% Both the time-averaged and phase-averaged temperature distributions in the cross-sectional plane of the boundary layer are presented for four different pulsation frequencies of 0, 4, 20 and 40 Hz. Film cooling effectiveness is evaluated from the adiabatic wall temperature distributions, with time-averaged temperature measurements showing rapid diffusion of the injectant due to the free-stream pulsations. Effect of the phase lag between two rows is evidenced from the phase-averaged measurements, particularly in the case of staggered hole arrangement. All film cooling effectiveness distributions are reduced compared to no-pulsation case. Effect of pulsations appears dominantly in the case of the two-row staggered arrangement which shows more than 35% reduction in the film cooling effectiveness.

Flow and Heat Transfer in Convectively Cooled Underground Electric Cable Systems: Part 2—Temperature Distributions and Heat Transfer Correlations

1978 ◽  
Vol 100 (1) ◽  
pp. 36-40 ◽  
Author(s):  
R. S. Abdulhadi ◽  
J. C. Chato
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Reynolds Number ◽  
Cross Section ◽  
Thermal Boundary Layer ◽  
Electric Cable ◽  
Nusselt Numbers ◽  
Temperature Distributions ◽  
Cable Systems ◽  
Heat Transfer Correlations

Temperature distributions and heat transfer correlations have been obtained experimentally for a wide range of physical, flow and thermal parameters in three models of oil-cooled underground electric cable systems. The results show that in the laminar range, with the oils used, the thermal boundary layer thickness around the heated cables is only of the order of 2–3 mm over the entire length of the test section. Consequently, the best correlation of the heat transfer results is obtained if the Nusselt number, based on the cable diameter, is plotted against Re·Pr0.4, where the Reynolds number is based on the overall hydraulic diameter of the cross section of the flow. For laminar flows, the oil temperatures in the restricted flow channels between three cables or two cables and the pipe wall are about 11°C higher than corresponding bulk temperatures. As the flow becomes turbulent, the thermal boundary layer tends to vanish and the oil temperature becomes uniform over the entire flow cross section. Laminar Nusselt numbers are independent of the skid wire roughness ratio and the flow Reynolds number, but increase with increasing Rayleigh number and axial distance from the inlet, indicating significant natural convection effect. The range of laminar Nusselt numbers was 5–16. Turbulent Nusselt numbers increase with increasing roughness ratios. The Nusselt numbers at Re = 3000 are 30 and 60 for roughness ratios of 0.0216 and 0.0293, respectively.

scholarly journals Swirl boundary layer and flow separation at the inlet of a rotating pipe

2016 ◽  
Vol 811 ◽  
pp. 350-371 ◽  
Author(s):  
F.-J. Cloos ◽  
D. Stapp ◽  
P. F. Pelz
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Flow Separation ◽  
Momentum Equation ◽  
Layer Growth ◽  
Boundary Layer Theory ◽  
Critical Flow ◽  
Flow Number ◽  
The Impact ◽  
Momentum Boundary Layer

When a fluid enters a rotating circular pipe, an angular momentum or swirl boundary layer appears at the wall and interacts with the axial momentum boundary layer. In the centre of the pipe, the fluid is free of swirl and is accelerated due to boundary layer growth. Below a critical flow number, defined as the ratio of average axial velocity to circumferential velocity of the pipe, there is flow separation, known in the turbomachinery context as part load recirculation. To describe this phenomenon analytically, we extended boundary layer theory to a swirl boundary layer interacting with the axial momentum boundary layer. The solution of the resulting generalized von Kármán momentum equation takes into account the influence of the Reynolds number and flow number. We show the impact of swirl on the axial boundary layer and conduct experiments in which we vary Reynolds number, flow number and surface roughness to validate the analytical results. The extended boundary layer theory predicts a critical flow number which is analytically derived and validated. Below this critical flow number, separation is expected.

Effects of Orientation Angles on Film Cooling Over a Flat Plate: Boundary Layer Temperature Distributions and Adiabatic Film Cooling Effectiveness

1999 ◽  
Vol 122 (1) ◽  
pp. 153-160 ◽  
Author(s):  
In Sung Jung ◽  
Joon Sik Lee
Keyword(s):  
Boundary Layer ◽  
Film Cooling ◽  
Plate Boundary ◽  
Orientation Angle ◽  
Thermochromic Liquid Crystal ◽  
Test Plate ◽  
Cooling Effectiveness ◽  
Film Cooling Effectiveness ◽  
Temperature Distributions ◽  
Film Cooling Holes

Presented are experimental results describing the effects of orientation angle of film cooling holes on boundary layer temperature distributions and film cooling effectiveness. Film flow data were obtained from a row of five film cooling holes on a flat test plate. The inclination angle of the hole was fixed at 35 deg and four orientation angles of 0, 30, 60, and 90 deg were investigated. The velocity ratios surveyed were 0.5, 1.0, and 2.0. The boundary layer temperature distributions were measured at three downstream locations using 1μm platinum wire. Detailed adiabatic film cooling effectiveness distributions were measured using thermochromic liquid crystal. Results show that the increased lateral momentum in the case of large orientation angle injection strongly affects boundary layer temperature distributions. Temperature distribution characteristics are, in general, explained in the context of the interactions between injectant and free-stream fluid and between injectants issuing from adjacent holes. The adiabatic film cooling effectiveness distributions are discussed in connection with the boundary layer temperature distributions. Spanwise-averaged effectiveness distributions and space-averaged effectiveness distributions are also presented with respect to the velocity ratios and the orientation angles. [S0889-504X(00)01701-3]

The Flow of a Laminar, Incompressible Jet Along a Parabola

1972 ◽  
Vol 39 (1) ◽  
pp. 13-17 ◽  
Author(s):  
A. Plotkin
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
External Flow ◽  
Boundary Layer Theory ◽  
Second Order ◽  
Wall Jet ◽  
Governing Equations ◽  
Displacement Effect ◽  
First Order ◽  
External Stream

The flow of a laminar, incompressible jet along a parabola in the absence of an external stream is analyzed using the techniques of second-order boundary-layer theory. The first-order solution is the Glauert wall-jet solution. Second-order corrections in the jet due to the effects of curvature and displacement are obtained numerically after the external flow is corrected to account for the displacement effect. The shear stress at the wall is calculated and it appears that for values of the Reynolds number at which the governing equations are valid the jet does not separate from the parabola.

Streakline Flow Visualization of Discrete Hole Film Cooling for Gas Turbine Applications

1976 ◽  
Vol 98 (2) ◽  
pp. 245-250 ◽  
Author(s):  
R. S. Colladay ◽  
L. M. Russell
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Flow Field ◽  
Gas Turbine ◽  
Layer Thickness ◽  
Turbulent Mixing ◽  
Film Cooling ◽  
Boundary Layer Thickness ◽  
Hole Diameter ◽  
Neutrally Buoyant

Film injection from discrete holes in a three row staggered array with 5-dia spacing was studied for three hole angles: (1) normal, (2) slanted 30 deg to the surface in the direction of the mainstream, and (3) slanted 30 deg to the surface and 45 deg laterally to the mainstream. The ratio of the boundary layer thickness-to-hole diameter and the Reynolds number were typical of gas turbine film cooling applications. Results from two different injection locations are presented to show the effect of boundary layer thickness on film penetration and mixing. Detailed streaklines showing the turbulent motion of the injected air were obtained by photographing very small neutrally-buoyant helium filled “soap” bubbles which follow the flow field. Unlike smoke, which diffuses rapidly in the high turbulent mixing region associated with discrete hole blowing, the bubble streaklines passing downstream injection locations are clearly identifiable and can be traced back to their point of ejection.

A Theoretical Investigation of the Maximum-Lift Coefficient

1935 ◽  
Vol 2 (1) ◽  
pp. A21-A27
Author(s):  
Th. von Kármán ◽  
Clark B. Millikan
Keyword(s):  
Boundary Layer ◽  
Experimental Investigation ◽  
Reynolds Number ◽  
Velocity Distribution ◽  
Theoretical Investigation ◽  
Laminar Boundary Layer ◽  
Lift Coefficient ◽  
Boundary Layer Theory ◽  
First Approximation ◽  
Transition Points

Abstract In the present paper the application of a laminar boundary-layer theory, previously developed by the authors, to the problem of the maximum-lift coefficient of airfoils is discussed. The calculations are carried through in detail for a first approximation, called a single-roof profile, to the potential velocity distribution over the upper surface of an airfoil. The results indicate a large variation in Clmax with turbulence but the quantitative dependence on Reynolds’ number and turbulence is not satisfactory. The calculations are then repeated for a so-called double-roof profile which approximates to the flow over the upper surface of an N.A.C.A. 2412 airfoil. These results are compared with those obtained from an experimental investigation on the same airfoil. The agreement is considered to indicate that for moderate values of R and Clmax the phenomenon of the maximum-lift coefficient is controlled by a contest between the separation and transition points of the laminar boundary layer over the nose of the airfoil. The difficulties involved in extending the theory to larger values of R, or to airfoils whose Cl vs. α curves are not approximately linear up to the stall, are mentioned.

Stability of two-dimensional collapsible-channel flow at high Reynolds number

2012 ◽  
Vol 705 ◽  
pp. 371-386 ◽  
Author(s):  
Ramesh B. Kudenatti ◽  
N. M. Bujurke ◽  
T. J. Pedley
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Poiseuille Flow ◽  
Pressure Difference ◽  
High Reynolds Number ◽  
Boundary Layer Theory ◽  
Unexpected Finding ◽  
Two Dimensional ◽  
High Reynolds ◽  
The Stability

AbstractWe study the linear stability of two-dimensional high-Reynolds-number flow in a rigid parallel-sided channel, of which part of one wall has been replaced by a flexible membrane under longitudinal tension ${T}^{\ensuremath{\ast} } $. Far upstream the flow is parallel Poiseuille flow at Reynolds number $\mathit{Re}$; the width of the channel is $a$ and the length of the membrane is $\lambda a$, where $1\ll {\mathit{Re}}^{1/ 7} \lesssim \lambda \ll \mathit{Re}$. Steady flow was studied using interactive boundary-layer theory by Guneratne & Pedley (J. Fluid Mech., vol. 569, 2006, pp. 151–184) for various values of the pressure difference ${P}_{e} $ across the membrane at its upstream end. Here unsteady interactive boundary-layer theory is used to investigate the stability of the trivial steady solution for ${P}_{e} = 0$. An unexpected finding is that the flow is always unstable, with a growth rate that increases with ${T}^{\ensuremath{\ast} } $. In other words, the stability problem is ill-posed. However, when the pressure difference is held fixed (${= }0$) at the downstream end of the membrane, or a little further downstream, the problem is well-posed and all solutions are stable. The physical mechanisms underlying these findings are explored using a simple inviscid model; the crucial factor in the fluid dynamics is the vorticity gradient across the incoming Poiseuille flow.

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