Aerothermal Boundary Layer Computation Including Strong Viscous-Inviscid Flow Interaction

1990 ◽  
Author(s):  
P. Kulisa ◽  
F. Leboeuf ◽  
P. Klinger ◽  
J. Bernard
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Film Cooling ◽  
Turbine Blades ◽  
Flow Characteristics ◽  
Inviscid Flow ◽  
Advanced Materials ◽  
Pressure Gradients ◽  
Flat Plates ◽  
Boundary Layer Equations

The high temperature level reached at the exit of combustion chambers of modern aircraft engines and the practical limitations of advanced materials, demand efficient cooling of turbine blades. Optimization of the cooling requires an accurate prediction of aerodynamic losses and heat transfer on turbine blades. A new two-dimensional compressible, aerothermal boundary layer code has been developed. The formulation includes strong viscous-inviscid interaction, which enhances the stability properties of the code. The boundary layer equations associated with the energy equation are solved with an implicit Keller-box scheme. Viscous-inviscid flow coupling is performed by adding an interaction equation which has an elliptic character. The complete system of equations is solved by a multi-pass procedure. This technique contributes to the stabilization of the method and allows the computation of regions with strong adverse pressure gradients, separation bubbles and injections in case of film cooling. Comparisons between experimental and theoretical results are provided. Flow characteristics including heat transfer were computed for several cases such as flat plates with strong pressure gradients, and turbine blade boundary layers. Good agreement between computation and experiment is observed, demonstrating the high accuracy and robustness of the code.

Prediction of Film Cooling by a Row of Holes With a Two-Dimensional Boundary-Layer Procedure

1987 ◽  
Vol 109 (4) ◽  
pp. 579-587 ◽  
Author(s):  
B. Scho¨nung ◽  
W. Rodi
Keyword(s):  
Boundary Layer ◽  
Film Cooling ◽  
Turbine Blades ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Flat Plates ◽  
Specific Flow ◽  
Boundary Layer Equations ◽  
Dimensional Boundary ◽  
Dispersion Terms

The present paper describes predictions of film cooling by a row of holes. The calculations have been performed by a two-dimensional boundary-layer code with special modifications that account for the basically three-dimensional, elliptic nature of the flow after injection. The elliptic reverse-flow region near the injection is leapt over and new boundary-layer profiles are set up after the blowing region. They take into account the oncoming boundary layer as well as the characteristics of the injected jets. The three dimensionality of the flow, which is very strong near the injection and decreases further downstream, is modeled by so-called dispersion terms, which are added to the two-dimensional boundary-layer equations. These terms describe additional mixing by the laterally nonuniform flow. Information on the modeling of the profiles after injection and of the dispersion terms has been extracted from three-dimensional fully elliptic calculations for specific flow configurations. The modified two-dimensional boundary-layer equations are solved by a forward-marching finite-volume method. A coordinate system is used that stretches with the growth of the boundary layer. The turbulent stresses and heat fluxes are obtained from the k-ε turbulence model. Results are given for flows over flat plates as well as for flows over gas turbine blades for different injection angles, relative spacings, blowing rates, and injection temperatures. The predicted cooling effectiveness and heat transfer coefficients are compared with experimental data and show generally fairly good agreement.

Laminar and Transitional Boundary Layer Structures in Accelerating Flow With Heat Transfer

1986 ◽  
Vol 108 (1) ◽  
pp. 116-123 ◽  
Author(s):  
K. Rued ◽  
S. Wittig
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Gas Turbine ◽  
Turbine Blades ◽  
Pressure Gradients ◽  
Transfer Coefficients ◽  
Gas Turbine Blades ◽  
Heat Transfer Coefficients ◽  
Layer Structures ◽  
Flow Heat

The accurate prediction of heat transfer coefficients on cooled gas turbine blades requires consideration of various influence parameters. The present study continues previous work with special efforts to determine the separate effects of each of several parameters important in turbine flow. Heat transfer and boundary layer measurements were performed along a cooled flat plate with various freestream turbulence levels (Tu = 1.6−11 percent), pressure gradients (k = 0−6 × 10−6), and cooling intensities (Tw/T∞ = 1.0−0.53). Whereas the majority of previously available results were obtained from adiabatic or only slightly heated surfaces, the present study is directed mainly toward application on highly cooled surfaces as found in gas turbine engines.

Boundary Layer Calculation Including the Prediction of Transition and Curvature Effects

1989 ◽  
Author(s):  
B. Guyon ◽  
T. Arts
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Boundary Layers ◽  
Convex Surface ◽  
Turbine Blades ◽  
Operating Conditions ◽  
Detailed Knowledge ◽  
Flat Plates ◽  
Transfer Rates ◽  
Curvature Effects

The calculation of surface temperature on gas turbine blades in severe operating conditions requires a detailed knowledge of boundary layers behaviour. The prediction of laminar to turbulent transition as to existence and location, as well as the evaluation of heat transfer rates are major concerns. The program developed by SNECMA for this purpose is presented, in which models are introduced to take into account the main effects occuring on blades without film-cooling. The algorithm and discretisation scheme for boundary layer equations is Patankar and Spalding’s, with profiles initialization by Pohlhausen’s method. The turbulence and transition model, after Mc Donald and Fish, was improved in search for more stability and to have a better detection of the beginning of the transition. Adams and Johnston’s model for curvature, including propagation effects, was adapted to a transitional boundary layer. The validation tests of this program are described, which are based on numerous experimental data taken from a bibliography of tests over flat plates and blades. Other tests use heat transfer rate measurements conducted by SNECMA, together with VKI, on vanes and blades in non-rotating grids. The calculation results are further compared to the STAN5 program results; they show a superiority in predicting the transfer rates on a convex surface and for transitional boundary layers.

scholarly journals The Effects of Upstream Mass Injection on Downstream Heat Transfer

1970 ◽  
Vol 92 (3) ◽  
pp. 385-392 ◽  
Author(s):  
W. R. Wolfram ◽  
W. F. Walker
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Laminar Boundary Layer ◽  
Flat Plates ◽  
Transfer Rates ◽  
Boundary Layer Equations ◽  
Mass Injection ◽  
Complete Set ◽  
Injection Region ◽  
Body Heat

The present study was performed in order to determine the effects of upstream mass injection on downstream heat transfer in a reacting laminar boundary layer. The study differs from numerous previous investigations in that no similarity assumptions have been made. The complete set of coupled reacting laminar boundary layer equations with discontinuous mass injection was solved for this problem using an integral-matrix technique. The effects of mass injection on heat transfer to both sharp and blunt-nosed isothermal flat plates were studied for a Mach 2 freestream. The amount of injection and the length of the injected region were varied for each body. Heat transfer rates were found to decrease markedly in the injected region. A sharp rise in heat transfer was found immediately downstream of the region of injection followed by an asymptotic approach to the heat transfer rates calculated for the case of no injection. An insulating effect was found to persist for a considerable distance downstream from the injection region. The distance required for this insulating effect to die out was found to depend on the length of the injection region as well as the rate of injection.

A simple derivation of Lighthill's heat transfer formula

1958 ◽  
Vol 3 (4) ◽  
pp. 357-360 ◽  
Author(s):  
H. W. Liepmann
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Pressure Gradients ◽  
Simple Derivation ◽  
Simple Argument ◽  
Boundary Layer Equations ◽  
Permit Application ◽  
Von Mises ◽  
Separating Flows ◽  
Operational Methods

In the following it will be shown that a simple argument based on the use of the energy integral equation of the laminar boundary layer permits the derivation of a heat transfer formula valid for non-uniform temperature distribution and non-zero pressure gradients. The formula is then shown to be identical in structure with Lighthill's (1950) well-known results. Lighthill obtained his formula by solving the boundary layer equations in the von Mises form using operational methods. An elegant way to obtain the same results using exact similarity consideration was given by Lagerstrom (not yet published). The derivation given here is probably the most simple-minded one and the method may be useful for other applications as well. Furthermore, it is shown that the approach can be slightly modified to permit application of the formula to flow near separation. The latter result is applied to the Falkner-Skan solution for just separating flows and is found to be in excellent agreement with the exact solutions.

Computation of a Wall Boundary Layer With Discrete Jet Injections

1992 ◽  
Vol 114 (4) ◽  
pp. 756-764 ◽  
Author(s):  
P. Kulisa ◽  
F. Leboeuf ◽  
G. Perrin
Keyword(s):  
Boundary Layer ◽  
Turbine Blades ◽  
Three Dimensional ◽  
Inviscid Flow ◽  
Conservation Equations ◽  
Boundary Layer Equations ◽  
Keller Box Method ◽  
Wall Boundary Layer ◽  
Wall Boundary ◽  
Jet Interactions

Cooling of turbine blades is often achieved with cold discrete jets introduced at the wall. In this paper, a new method for computation of a wall boundary layer with discrete jet interactions is presented. The jets are assumed to be arranged in rows and the flow is assumed locally periodic in the row direction. The conservation equations are spatially averaged between two jet orifices. The resulting equations look like two-dimensional boundary layer equations, but with three-dimensional jet source terms. The numerical method solves the boundary layer equations with a Keller box method. A strong interaction with inviscid flow is also introduced in order to avoid numerical difficulty in the jet region. Three-dimensional jet conservation equations are solved with an integral method, under the boundary layer influence. A coupling of the two methods is performed. Comparisons with low-speed experimental data are presented, particularly near the jet orifices. It is shown that the agreement between the results of computation and the experiments depends on the jet behavior very near the jet exit.

Comparison of Conjugate Heat Transfer Analysis of Flat Plate Film Cooling Arrays Against Experimental Data

2015 ◽  
Author(s):  
William Humber ◽  
Ron-Ho Ni ◽  
Jamie Johnson ◽  
John Clark ◽  
Paul King
Keyword(s):  
Heat Transfer ◽  
Experimental Data ◽  
Film Cooling ◽  
Conjugate Heat Transfer ◽  
Flow Characteristics ◽  
Heat Transfer Analysis ◽  
Pressure Side ◽  
Flat Plates ◽  
Cooling Effectiveness ◽  
Cooling Hole

Conjugate heat transfer (CHT) simulations were conducted for five film-cooled flat plates designed to model the pressure side of the High Impact Technologies Research Turbine First Vane (HIT RT1V). The numerical results of the CHT analysis were compared against experimental data. The five test cases consist of one baseline geometry and four different cooling hole geometries applied to a film-cooling hole arrangement that was optimized to achieve a more uniform cooling effectiveness. This optimized film-cooling hole configuration was designed by coupling a genetic algorithm with a Navier-Stokes fluid solver, using source terms to model film holes, starting from a baseline cooling configuration. All five plates were manufactured, and surface temperature measurements were taken using infrared thermography while the plates were exposed to flow conditions similar to the pressure side of the HIT RT1V. CHT simulations were carried out using unstructured meshes for both fluid and solid with all film holes fully resolved. Comparison of experimental data and simulations shows a consistent trend between the optimized configurations as well as correct predictions of the flow characteristics of each hole geometry although the absolute temperatures are underpredicted by the CHT. Both experimental measurements and CHT predictions show the optimized geometry with mini-trenched-shaped holes to give the best cooling effectiveness.

An Analytical Study of Laminar Film Condensation: Part 1—Flat Plates

1961 ◽  
Vol 83 (1) ◽  
pp. 48-54 ◽  
Author(s):  
Michael Ming Chen
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Velocity Gradient ◽  
Film Condensation ◽  
Transfer Coefficients ◽  
Flat Plates ◽  
Integral Boundary ◽  
Boundary Layer Equations ◽  
Laminar Film ◽  
Laminar Film Condensation

The boundary-layer equations of momentum and energy are written in a modified integral form and solved for the case of laminar film condensation along a vertical flat plate. The analysis differs from previous works by employing the more realistic boundary condition of stationary vapor at large distances instead of zero velocity gradient at the interface. Solutions for both the liquid film and vapor boundary layer are given for the case μvρv ≪ μρ. Velocity and temperature profiles are obtained using perturbation method and the modified integral boundary-layer equations. The results show a significant negative velocity gradient at the interface as a result of vapor drag except for small values of kΔt/μλ. Theoretical heat-transfer coefficients are computed and found to be lower than previous theories, especially for low Prandtl numbers. Comparison with experimental heat-transfer data is given. The heat-transfer results are also presented in the form of an approximate formula for ease of application.

scholarly journals Computation of a Wall Boundary Layer With Discrete Jet Injections

1991 ◽  
Author(s):  
P. Kulisa ◽  
F. Leboeuf ◽  
G. Perrin
Keyword(s):  
Boundary Layer ◽  
Turbine Blades ◽  
Three Dimensional ◽  
Inviscid Flow ◽  
Conservation Equations ◽  
Boundary Layer Equations ◽  
Keller Box Method ◽  
Wall Boundary Layer ◽  
Wall Boundary ◽  
Jet Interactions

Cooling of turbine blades is often achieved with cold discrete jets introduced at the wall. In this paper, a new method for computation of a wall boundary layer with discrete jet interactions is presented. The jets are assumed to be arranged in rows and the flow is assumed locally periodic in the row direction. The conservation equations are spatially averaged between two jet orifices. The resulting equations look like two-dimensional boundary layer equations, but with three-dimensional jet source terms. The numerical method solves the boundary layer equations with a Keller box method. A strong interaction with inviscid flow is also introduced in order to avoid numerical difficulty in the jet region. Three-dimensional jet conservation equations are solved with an integral method, under the boundary layer influence. A coupling of the two methods is performed. Comparisons with low speed experimental data are presented, particularly near the jet orifices. It is shown that the agreement between the results of computation and the experiments depends on the jet behaviour very near to the jet exit.

Film Cooling in the Presence of Mainstream Pressure Gradients

1990 ◽  
Author(s):  
A. J. H. Teekaram ◽  
C. J. P. Forth ◽  
T. V. Jones
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Pressure Gradient ◽  
Film Cooling ◽  
Gas Turbines ◽  
Pressure Gradients ◽  
Superposition Model ◽  
Single Row ◽  
Unit Reynolds Number ◽  
High Mach

Film-cooling in the presence of mainstream pressure gradients typical of gas turbines has been studied experimentally on a flat plate This paper describes, measurements of the spanwise averaged effectiveness and heat transfer coefficient for an inclined slot and a single row of holes in the presence of favourable, zero and adverse pressure gradients. Acceleration parameters of K = 2.62×10−6 and - 0.22 × 10−6 were achieved at the point of injection where the freestream unit Reynolds number was held constant at Re/m = 2.7 × 107. The flow was accelerated to high Mach number and results are analysed using a superposition model of film-cooling which included the effects of viscous energy dissipation. The experimental results show the effects of pressure gradient differ between the geometries and a discussion of these results is included. The unblown turbulent boundary layer with pressure gradient were also studied. Experiments were performed using the Isentropic Light Piston Tunnel, a transient facility which enables conditions representative of those in the engine to be attained.

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