Introduction Increasing the efficiency of modern gas turbine engines and units for virtually any purpose (aircraft, transport, marine, stationary, power generation, etc.) is closely linked to the need to increase the temperature of the working fluid upstream of the turbine. This, in turn, requires special attention to ensuring the operability of components operating in high-temperature parts, which cannot be achieved without the use of reliable calculation methods that allow for the reliably determination of heat transfer parameters for calculating the thermal state of the components. In the design of virtually any modern gas turbine engine, one of the most important systems is the cooling system, designed to cool engine components operating at high temperatures.These cooled components can include turbine components (cases, disks, blades), as well as combustion chamber components such as liners, transition pieces, etc. There are a wide variety of cooling methods for components operating in high-temperature zones, but one of the most important is the jet cooling method, which combines high efficiency and relative ease of implementation.For modern gas turbines, temperatures of 1 350-1 500 K behind the combustion chamber are well established. Almost all of them, such as the NK-14ST gas turbines series, or the NK-14E manufactured by UEC, the T-32 (MS5002E) manufactured by JSC REPH, and many others, have identical or even higher working gas temperatures before of the turbine. At these temperature levels, the operability of the unit's components can only be ensured with a sufficiently efficient cooling system.Therefore, this article is not narrowly focused on marine applications. The information provided below can be considered by engineers working in the design of any high-temperature gas turbine units, regardless of their purpose, power output, shaft speed, etc. The jet cooling method for turbine components is perhaps one of the most widely used in practice. The large number of different criterion equations and the wide variety of experimental methods used to obtain these criterion equations make it worthwhile to attempt a general comparison of the results obtained by various, well-known researchers.Currently, a significant number of papers have been published containing experimental data, in which the authors have derived various criterion equations for calculating heat transfer parameters using the jet cooling method.This paper presents a general comparative analysis of the calculated heat transfer coefficients for air cooling a flat surface using the jet cooling method.Jet cooling method has been studied in numerous works by foreign [1-8] and domestic [9-11] authors. The data discussed in this paper are based on the results described in detail in [1-9]. Designation of the options under considerationFor ease of description and notation in the figures, the numerical notation system for the criterion equations of various authors is used, as shown in column 2 of Table 1. To perform a comparative analysis, subroutines were developed to calculate the main heat transfer characteristics using the criterion equations. The software modules are developed in C#. Table 1Numerical notation system for the criterion equations of various authors Author Designation in the textand in the figuresNoteL. W. Florschuetz, D. E. Metzger,C. R. Truman, i.e. [1-6]В-1, В-2B-1 – equation (10a) [5];B-2 – equation (11a) [5]J. L. Chance [8]В-3–D. M. Kercher, W. Tabakoff [7]В-4–L. M. Zysina-Molozhen, L. V. Zysin, M. P. Poliak [9]В-5–A. F. Slitenko [10]В-6–  A system of geometric notations describing the main parameters of the jet cooling system componentsCooling air jets are formed in holes of diameter d in the jet plate and strike the blown surface located at a distance Z from this plate. The flow, as a crossflow (relative to the jets), is directed along the blown plate toward the outlet section. The holes can be arranged transversely in either a corridor or a staggered pattern. A pressure differential exists between the cavity in front of the jet plate and the outlet section, causing the air flow under study (flow rate mc, Fig. 1). The location of the measuring probe for changing the pressure in the channel between the jet plate and the blown surface is shown in Fig. 2.  Fig. 1. Basic test model geometry and nomenclature  Fig. 2. Pressure measurement diagram The criteria dependencies for the Nu number as a function of the Reynolds flow number in the jet for the considered series of orifices Rej used:1) relative crossflow velocity Gc / Gj;2) three geometric parameters related to the orifice diameter:– streamwise jet hole spacing xn / d;– spanwise jet hole spacing yn / d;– channel height z / d.In this paper these parameters were varied in the following ranges (to meet requirements B-1 and B-2):– Rej = 2.5 ∙ 103 / 7 ∙ 104; – Gc / Gj = 0 / 0.8;– streamwise jet hole spacing xn / d = 5/15   for an inline pattern;– streamwise jet hole spacing xn / d = 5/10   for a staggered pattern;– spanwise jet hole spacing yn / d = 4/8; – channel height z / d = 1/3.The criteria dependencies for B-1–B-6 were used to develop the calculation software module written in C#. Initial data for the software module and the results obtainedBelow (Table 2) is a list of the initial data used to calculate the parameters of the jet cooling system. The list of results data obtained during the calculations is given in Table 3. Table 2Input data listParameter NoteAir flow rate at the compressor inletUsed to estimate air rate for coolingCooling air temperature–Cooling air pressure–Pressure drop at the end of the jet plateAs a percentage of the air pressure supplied for coolingThe type of hole arrangement on the jet platInline/staggeredThe diameter of the hole in the jet plate–Streamwise jet hole spacingxn / d = 5/15 for an inline pattern;xn / d = 5/10 for a staggered patternSpanwise jet hole spacingyn / d = 4/8Relative height of the channelz / d = 1/3Number of holes in the streamwise direction–Number of rows of jet holes in the spanwise direction–Heat transfer coefficient on the gas side–Temperature of the gas from the side of the thermobarrier coating–Type of thermobarrier coatingSelected from the database of thermobarrier coatings included in the software moduleThickness of thermobarrier coating–Material of the metal (cooled) surfaceSelected from the database of metalls included in the software moduleThickness of the metal (cooled) surface–Date of calculationUsed to organize calculation result filesResults file name–Table 3List of data obtained during the calculationsCalculated parameterNoteSurface temperature of thermobarrier coating on the gas sideDistribution in streamwise directionTemperature between thermobarrier coating and metalDistribution in streamwise directionMetal temperature on the cooling air sideDistribution in streamwise directionMean metal temperature–Cooling air temperatureDistribution in streamwise directionTotal increase in cooling air temperature–Heat transfer coefficient of the cooling airDistribution in streamwise directionCooling air rateFor each of the rows in the spanwise direction  Comparison of calculation results using criterial equations from different authorsThe comparison of calculation results using criteria equations from different authors was performed using the same initial data, described below. Calculations were performed for three jet cooling variants of a gas turbine combustion chamber transition pipe section made of 5 mm thickness Nimonic-263.The number of parameters that can be varied is quite large; however, for this case, we will limit ourselves to considering the calculation results for only one parameter: z / d – the channel height, i.e., the distance between the jet plate and the cooled surface (Table 4). Table 4Designation scheme for the calculated variantsStreamwise size x / dSpanwise size y / dRelative channel heightz / dDesignation of design options in figuresand in the text106110-6-1106210-6-2106310-6-3  On the gas side, the surface of the transition piece is coated with a thermobarrier coating with a thermal conductivity coefficient of k = 1.15 W/(m·K). The surface is blown by a gas flow at a temperature of 1 500 K with a heat transfer coefficient on the gas side ∝g = 1 500 W/(m2·K).To provide jet cooling for the transition pipe, a screen with ny = 5 rows of nx = 15 holes with a diameter of d = 2 mm, spaced x / d = 10 along the flow, is installed at a distance of Z (Fig. 1). The rows of holes spanwise the flow are spaced y / d = 6 apart. The order of the holes on the jet screen is inline. For ease of analysis of the results, a coding system for the jet cooling design variants is adopted, as described in Table 4.Cooling air is supplied from the compressor discharge cavity at a temperature of 731.6 K. Cooling air pressure at the compressor discharge corresponding to the pressure before the jet plate, is 15.72 bar. The pressure drop at the end of the last downstream row of holes in the jet plate is 1.5% of the pressure at the compressor discharge.Thus, the total area of the transition piece surface fragment cooled by jet cooling is Figures 3-5 show the results of comparative calculations.   Fig. 3. Pressure drop across the jet plate holes As can be seen from the data in Fig. 3, the distance from the jet plate to the cooled surface, all other parameters being equal, significantly affects the pressure drop across the jet plate, which leads to significant changes in cooling air flow rate, jet velocities, etc.As test calculations for variants 10-6-1, 10-6-2, and 10-6-3 show, the heat transfer coefficients for B-6 are significantly (2.5-3 times) higher than those obtained from the data of the other five authors. Thus, the data from [10] differ significantly from those of the other authors, which, in general, correlate well with each other. Only the calculation results from the nine literature sources [1-9] (Table 1), with the exception of B-6, are discussed below.a b cFig. 4. Heat transfer coefficients distribution: a – for 10-6-1; b – for 10-6-2; c – for 10-6-3 a bFig. 5. Heat transfer coefficients for different z / d: a – calculated by B-1; b – calculated by B-5 Overall, good agreement can be noted between the calculated heat transfer coefficient data obtained from various literary sources. Obviously, the thermal state calculation data based on these criteria equations will be very close. Conclusion 1. The heat transfer coefficients calculated using data from [10] for B-6 are significantly (2.5-3 times) higher than those obtained using data from other authors [1-9].2. The heat transfer coefficients calculated using data from five different sources for B-1–B-5 correlate well with each other (Fig. 4), and the temperature state of the cooled surfaces calculated using the jet method from these sources will differ only slightly. Higher values are obtained for B-5. 3. Increasing the distance between the jet plate and the cooled surface significantly increases the pressure drop across the first rows of holes (Fig. 3), which leads to an increase in the jet flow velocity through them and increases the cooling intensity under the first rows of holes (see left arrows in Fig. 5). 4. Due to the increase in the speed of the jet flow through the first rows of holes with an increase in the distance between the jet plate and the cooled surface, the flow rate (and speed) of the cross-flow of air along the flow increases, which reduces the efficiency of the jet effect for subsequent rows and reduces the heat transfer coefficients under them (see right arrows in Fig. 5).