The Formula of Discharge Coefficient of the Cooling Hole in the Combustion Chamber for a Uniform Penetration Boundary Method

2020 ◽  
Author(s):  
Sen Wang ◽  
Donghai Jin ◽  
Xingmin Gui ◽  
Xiaoheng Liu
Keyword(s):  
Numerical Simulation ◽  
Mach Number ◽  
Combustion Chamber ◽  
Discharge Coefficient ◽  
Pressure Ratio ◽  
Diameter Ratio ◽  
Geometric Parameters ◽  
Cooling Flow ◽  
Cooling Hole ◽  
Aerodynamic Parameters

Abstract At present, researches on the discharge coefficient of the combustion chamber cooling holes are mostly based on the experimental study of the porous plates considering various geometric structures under different flow conditions. In this method, the average discharge coefficients of multiple holes are obtained. Since the discharge coefficient will be applied to the numerical simulation, it is important to obtain an accurate formula for each cooling hole. Therefore, the discharge coefficient will be associated with some local aerodynamic parameters around the cooling holes and geometric parameters of the cooling holes. In this paper, the geometric parameters consist of length-to-diameter ratio (L/d) and inclination angle (α). The aerodynamic parameters cover the Mach number of cooling flow and mainstream (Mac, Mam), characterizing the flow feature, and the pressure ratio (π) which associates the cooling flow with the mainstream. The purpose of this paper is to study the discharge coefficient of a single circular hole with variable geometries under a cold condition of a combustion chamber, which has low crossflow and low-pressure ratio on both sides of the hole. In this environment, according to the research results, the discharge coefficient is sensitive to the cooling flow Mach number, length-to-diameter ratio and pressure ratio (π ≈ 1.05). Discharge coefficient decreases with L/d linearly, conforms the quadratic function with Mac and changes complexly at π ≈ 1.05. Other parameters have little effect on the discharge coefficient. The data for discharge coefficient of the cylindrical hole considering different parameters is obtained through numerical simulation and the correlations summarized by these data are valid for the following ranges: L/d = 3∼12, α = 20°∼45°, Mac = 0.05∼0.15, Mam = 0∼0.1, π = 1.05∼1.15. Compared with the CFD data, the prediction formula has a maximum error of less than 3% and a mean absolute error of 0.78%.

Discharge Coefficient Measurements of Film-Cooling Holes With Expanded Exits

1998 ◽  
Vol 120 (3) ◽  
pp. 557-563 ◽  
Author(s):  
M. Gritsch ◽  
A. Schulz ◽  
S. Wittig
Keyword(s):  
Mach Number ◽  
Film Cooling ◽  
Discharge Coefficient ◽  
Pressure Ratio ◽  
Cylindrical Hole ◽  
Flow Conditions ◽  
Wide Range ◽  
Cooling Hole ◽  
Shaped Hole ◽  
Film Cooling Holes

This paper presents the discharge coefficients of three film-cooling hole geometries tested over a wide range of flow conditions. The hole geometries include a cylindrical hole and two holes with a diffuser-shaped exit portion (i.e., a fan-shaped and a laidback fan-shaped hole). The flow conditions considered were the crossflow Mach number at the hole entrance side (up to 0.6), the crossflow Mach number at the hole exit side (up to 1.2), and the pressure ratio across the hole (up to 2). The results show that the discharge coefficient for all geometries tested strongly depends on the flow conditions (crossflows at hole inlet and exit, and pressure ratio). The discharge coefficient of both expanded holes was found to be higher than of the cylindrical hole, particularly at low pressure ratios and with a hole entrance side crossflow applied. The effect of the additional layback on the discharge coefficient is negligible.

scholarly journals Discharge Coefficient Measurements of Film-Cooling Holes With Expanded Exits

1997 ◽  
Author(s):  
M. Gritsch ◽  
A. Schulz ◽  
S. Wittig
Keyword(s):  
Mach Number ◽  
Film Cooling ◽  
Discharge Coefficient ◽  
Pressure Ratio ◽  
Cylindrical Hole ◽  
Flow Conditions ◽  
Discharge Coefficients ◽  
Wide Range ◽  
Cooling Hole ◽  
Film Cooling Holes

This paper presents the discharge coefficients of three film-cooling hole geometries tested over a wide range of flow conditions. The hole geometries include a cylindrical hole and two holes with a diffuser shaped exit portion (i.e. a fanshaped and a laidback fanshaped hole). The flow conditions considered were the crossflow Mach number at the hole entrance side (up to 0.6), the crossflow Mach number at the hole exit side (up to 1.2), and the pressure ratio across the hole (up to 2). The results show that the discharge coefficient for all geometries tested strongly depends on the flow conditions (crossflows at hole inlet and exit, and pressure ratio). The discharge coefficient of both expanded holes was found to be higher than of the cylindrical hole, particularly at low pressure ratios and with a hole entrance side crossflow applied. The effect of the additional layback on the discharge coefficient is negligible.

Numerical Simulation of Supersonic Jet Control by Tabs with Slanted Perforation

2019 ◽  
Vol 0 (0) ◽  
Author(s):  
G. Ezhilmaran ◽  
Suresh Chandra Khandai ◽  
Yogesh Kumar Sinha ◽  
S. Thanigaiarasu
Keyword(s):  
Numerical Simulation ◽  
Mach Number ◽  
Near Field ◽  
Pressure Ratio ◽  
Supersonic Jet ◽  
Pressure Gradients ◽  
Nozzle Pressure Ratio ◽  
Nozzle Pressure ◽  
Jet Control ◽  
Different Diameters

Abstract This paper presents the numerical simulation of Mach 1.5 supersonic jet with perforated tabs. The jet with straight perforation tab was compared with jets having slanted perforated tabs of different diameters. The perforation angles were kept as 0° and 10° with respect to the axis of the nozzle. The blockage areas of the tabs were 4.9 %, 4.9 % and 2.4 % for straight perforation, 10° slanted perforation ( {{{\Phi }}_{\ }} = 1.3 mm) and 10° slanted perforation ( {{{\Phi }}_{\ }} = 1.65 mm) respectively. The 3-D numerical simulations were carried out using the software. The mixing enhancements caused by these tabs were studied in the presence of adverse and favourable pressure gradients, corresponding to nozzle pressure ratio (NPR) of 3, 3.7 and 5. For Mach number 1.5 jet, NPR 3 corresponds to 18.92 % adverse pressure gradients and NPR 5 corresponds to 35.13 % favourable pressure gradients. The centerline Mach number of the jet with slanted perforations is found to decay at a faster rate than uncontrolled nozzle and jet with straight perforation tab. Mach number plots were obtained at both near-field and far field downstream locations. There is 25 % and 65 % reduction in jet core length were observed for the 0° and 10° perforated tabs respectively in comparison to uncontrolled jet.

Experimental Study on Pressure Losses in Circular Orifices With Inlet Cross Flow

2018 ◽  
Vol 140 (7) ◽  
Author(s):  
Daniel Feseker ◽  
Mats Kinell ◽  
Matthias Neef
Keyword(s):  
Experimental Study ◽  
Film Cooling ◽  
Gas Turbines ◽  
Discharge Coefficient ◽  
Pressure Ratio ◽  
Cross Flow ◽  
Pressure Losses ◽  
Wide Range ◽  
Cooling Hole ◽  
Secondary Air

The ability to understand and predict the pressure losses of orifices is important in order to improve the air flow within the secondary air system. This experimental study investigates the behavior of the discharge coefficient for circular orifices with inlet cross flow which is a common flow case in gas turbines. Examples of this are at the inlet of a film cooling hole or the feeding of air to a blade through an orifice in a rotor disk. Measurements were conducted for a total number of 38 orifices, covering a wide range of length-to-diameter ratios, including short and long orifices with varying inlet geometries. Up to five different chamfer-to-diameter and radius-to-diameter ratios were tested per orifice length. Furthermore, the static pressure ratio across the orifice was varied between 1.05 and 1.6 for all examined orifices. The results of this comprehensive investigation demonstrate the beneficial influence of rounded inlet geometries and the ability to decrease pressure losses, which is especially true for higher cross flow ratios where the reduction of the pressure loss in comparison to sharp-edged holes can be as high as 54%. With some exceptions, the chamfered orifices show a similar behavior as the rounded ones but with generally lower discharge coefficients. Nevertheless, a chamfered inlet yields lower pressure losses than a sharp-edged inlet. The obtained experimental data were used to develop two correlations for the discharge coefficient as a function of geometrical as well as flow properties.

CFD Predicted Discharge Coefficients of a Single Cylindrical Hole With Compressible External Cross-Flow

2009 ◽  
Author(s):  
L. Guo ◽  
Y. Y. Yan ◽  
J. D. Maltson
Keyword(s):  
Mach Number ◽  
Pressure Distribution ◽  
Inclination Angle ◽  
Film Cooling ◽  
Discharge Coefficient ◽  
Static Pressure ◽  
Pressure Ratio ◽  
Cylindrical Hole ◽  
Static Pressure Distribution ◽  
Mainstream Flow

A computational investigation on discharge coefficient (Cd) of a single cylindrical hole is presented in this paper. The numerical calculations are carried out on a 3-D compressible model. The Shear-Stress Transport (SST) k–ω model is used to simulate the turbulence in the flow. The inclination angle (α) of the film cooling hole varies from 20° to 30°, 45° and 90°, respectively. The diameter of the hole is fixed at 10mm, but different coolant to mainstream pressure ratios (ptc/pm) are examined. The coolant Mach number (Mac) is set at a constant value of 0.3 and the mainstream flow Mach number (Mam) varies from 0.3 to 1.4. The effects of Mam and α on the Cd value as well as the static pressure distribution at the jet exit are investigated. The numerical results show an acceptable agreement in the trend of the Cd variation compare with the available experimental data. It has been predicted that the static pressure distribution in the vicinity of the jet exit is influenced by a number of factors including the mainstream flow Mach number, shock wave, jet inclination angle and the pressure ratio of the coolant to the mainstream flow. And then the static pressure field near the hole can further give strong influence on the discharge coefficient.

scholarly journals Numerical Characterization of Pressure Drop Across the Manifold of Turbine Casing Cooling System

2012 ◽  
Author(s):  
Riccardo Da Soghe ◽  
Antonio Andreini
Keyword(s):  
Discharge Coefficient ◽  
Cooling System ◽  
Pressure Ratio ◽  
Turbine Blades ◽  
Diameter Ratio ◽  
Data Set ◽  
Wide Range ◽  
Depth Analysis ◽  
Length To Diameter Ratio

Array of jets is an arrangement typically used to cool several gas turbine parts. Some examples of such applications can be found in the impingement cooling systems of turbine blades and vanes or in the turbine blade tip clearances control of large aeroengines. In order to correctly evaluate the impinging jet mass flow rate, the characterization of holes discharge coefficient is a compulsory activity. In a previous work the authors have performed an aerodynamic analysis of different arrays of jets for active clearance control; the aim was the definition of a correlation for the discharge coefficient (Cd) of a generic hole of the array. The developed empirical correlation expresses the Cd of each hole as a function of the ratio between the hole and the manifold mass velocity and the local value of the pressure ratio. In its original form, the correlation does not take in to account the effect of the hole length to diameter ratio (t/d) so, in the present contribution, the authors report a study with the aim of evaluating the influence of such parameter on the discharge coefficient distribution. The data were taken from a set of CFD RANS simulations, in which the behaviour of the cooling system was investigated over a wide range of fluid-dynamics conditions (Pressure-Ratio = 1.01–1.6, t/d = 0.25–3). To point out the reliability of the CFD analysis, some comparisons with experimental data were drawn. An in depth analysis of the numerical data set has led to an improved correlation with a new term function of the hole length to diameter ratio.

The Compressible Discharge Coefficient of a Borda Pipe and other Nozzles

1964 ◽  
Vol 68 (641) ◽  
pp. 346-349 ◽  
Author(s):  
T. H. Frost
Keyword(s):  
Mach Number ◽  
Discharge Coefficient ◽  
Pressure Ratio ◽  
Applied Pressure ◽  
Back Pressure ◽  
Theoretical Treatment ◽  
Flow Conditions ◽  
Vena Contracta ◽  
A Value ◽  
Shaped Nozzle

Bragg, in ref. 1, gives a theoretical treatment for the variation of the discharge coefficient in compressible flow of any shaped nozzle with applied pressure ratio given one set of values. This shows that the discharge coefficient of any nozzle with a value less than unity at a pressure ratio approaching unity, rises continuously as the pressure ratio increases and reaches the maximum at a pressure ratio of infinity (zero back pressure). This is based on the assumption that the flow conditions at the Vena contracta are uniform and at unity Mach number once the applied pressure ratio is equal to/ or above the critical (sonic) value.

Effect of Internal Coolant Crossflow Orientation on the Discharge Coefficient of Shaped Film Cooling Holes

1999 ◽  
Author(s):  
Michael Gritsch ◽  
Christian Saumweber ◽  
Achmed Schulz ◽  
Sigmar Wittig ◽  
Edwin Sharp
Keyword(s):  
Mach Number ◽  
Film Cooling ◽  
Gas Flow ◽  
Flow Direction ◽  
Pressure Ratio ◽  
Strong Impact ◽  
Hot Gas ◽  
Discharge Coefficients ◽  
Wide Range ◽  
Cooling Hole

Discharge coefficients of three film-cooling hole geometries are presented over a wide range of engine like conditions. The hole geometries comprise a cylindrical hole and two holes with a diffuser shaped exit portion (a fanshaped and a laidback fanshaped hole). For all three hole geometries the hole axis was inclined 30° with respect to the direction of the external (hot gas) flow. The flow conditions considered were the hot gas crossflow Mach number (up to 0.6), the coolant crossflow Mach number (up to 0.6) and the pressure ratio across the hole (up to 2). The effect of internal crossflow approach direction, perpendicular or parallel to the main flow direction, is particularly addressed in the present study. Comparison is made of the results for a parallel and perpendicular orientation, showing that the coolant crossflow orientation has a strong impact on the discharge behavior of the different hole geometries. The discharge coefficients were found to strongly depend on both hole geometry and crossflow conditions. Furthermore, the effects of internal and external crossflow on the discharge coefficients were described by means of correlations used to derive a predicting scheme for discharge coefficients. A comparison between predictions and measurements reveals the capability of the method proposed.

Experimental evaluation and numerical simulation of performance of the bypass dual throat nozzle

2020 ◽  
pp. 095441002095988
Author(s):  
Mohammad Hadi Hamedi-Estakhrsar ◽  
Hossein Mahdavy-Moghaddam
Keyword(s):  
Numerical Simulation ◽  
Discharge Coefficient ◽  
Deflection Angle ◽  
Pressure Ratio ◽  
Modern Concept ◽  
Thrust Coefficient ◽  
Thrust Vector Control ◽  
Nozzle Pressure ◽  
Thrust Vector ◽  
Turbulent Air Flow

Bypass dual throat nozzle (BDTN) is a modern concept of fluidic thrust vector control. This method able to solve the problem of thrust loss without need the secondary mass flow from other part of engine. Internal nozzle performance and thrust vector angles have been measured in the BDTN experimentally and numerically. A new simple approach is proposed to detect the thrust deflection angle. Numerical simulation of 3-D turbulent air flow is carried out by using the RNG k-e turbulence model. The obtained results of thrust coefficient, discharge coefficient and thrust deflection angle have been validated by comparing with measured experimental data. The results show that for nozzle pressure ratio of 1–4 the tested nozzle able to deflect the thrust vector of 26.5°-19°. By increasing NPR from 2 up to 4, the thrust coefficient values will change in the range of 0.85-0.93. Also the effect of different positions of the bypass channel on the BDTN performance parameters has been investigated numerically. The predicted results show that the BDTN configuration with bypass duct on the first nozzle throat has the highest value of thrust deflection angle over the range of NPRs.

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