Temperature Recovery Factor Research Articles

Experimental investigation of the Eckert-Weise effect (aerodynamic cooling) of pair side-by-side circular cylinders in a compressible cross-flow

The rear surface of a thermally insulated circular cylinder placed in a subsonic high-velocity cross-flow is significantly cooled, this phenomenon is known as aerodynamic cooling or the Eckert–Weise effect. This effect is associated with the redistribution of the stagnation temperature (energy separation) in the unsteady vortex wake. Experiments show that the effect is maximal at Mach numbers of the free-stream flow of 0.5–0.7, resulting in negative values of the temperature recovery factor (the temperature of the cylinder rear surface becomes lower than the static temperature of the free-stream flow). In this case, the cooling of the rear surface can reach tens of degrees. This effect can be utilized as the basis for a novel energy separation device, as it enables heat transfer between flows with the same stagnation temperatures. As shown in a numerical study (Aleksyuk, 2021), the effect is highly sensitive to the flow interference behind side-by-side cylinders, this is especially important for its practical application. In this study, the aerodynamic cooling of a pair identical circular cylinders in side-by-side arrangement, is experimentally investigated within the Mach and Reynolds number ranges of M = 0.34–0.58 and ReD = 1.6∙105–3.1∙105. The cylinder spacing considered in this study (P/D = 1.1; 1.5; 2.0; 3.0; and 4.0, where P is the center-to-center cylinder spacing and D is the diameter) covered the key regimes of vortex interference, that is, single, bistable, and coupled vortex streets. Also, investigations were conducted for a single circular cylinder with the same diameter within the Mach and Reynolds number ranges of M = 0.34–0.68 and ReD = 1.6∙105–3.4∙105. The channel blockage ratio was found to be 8% for a single cylinder and 16% for a pair of cylinders. Consequently, this study focuses on confined flow or flow past a confined cylinder with a uniform profile of oncoming flow velocity. It is shown that the Eckert-Weise effect for the pair of cylinders can either increase or decrease depending on the interference regimes and is sensitive to the blockage ratio value.

Adiabatic wall temperature in the supersonic flow of moist air with spontaneous condensation

The expansion of moist air in supersonic nozzles is accompanied by spontaneous condensation of water vapor due to a sharp decrease in flow temperature and pressure. However, in the near-wall boundary layer due to the viscous dissipation, moist air temperature decreases slightly in comparison with initial one. This leads to the fact that the vapor remains overheated in the near-wall region and condensation does not spread to its entire depth. Droplets formed in the core flow as a result of condensation can penetrate into the near-wall region due to turbulent diffusion and evaporate due to higher temperature in the near-wall region. This process causes cooling of the near-wall gas layers and, consequently, a decrease in the adiabatic wall temperature. A decrease in the adiabatic wall temperature relative to the stagnation temperature leads to a decrease in aerodynamic heating and, consequently, in the heat flux from the gas to the body. In this paper, measurements of the adiabatic temperature of the supersonic nozzle wall for moist air flow with condensation are presented. Temperature measurements were made using an infrared thermal imager. Initial moisture content varied in the range of 1.5–20.2 g/(kg. dry air) and initial relative humidity in the range 20–90%. It is shown that in the region behind the zone of spontaneous condensation (“condensation shock”), adiabatic wall temperature depends on the initial moisture content and can be either greater or less than the value of a single-phase (dry air) flow with identical initial flow parameters. Estimates of the flow parameters behind the condensation region are obtained using one-dimensional diabatic flow equations and experimental static pressure distributions along the nozzle length. The correlation between the initial moisture content, the average droplet size and the temperature recovery factor is shown.

Experimental Study of Energy Separation in Compressible Air Cross Flow Over a Pair of Side-by-Side Circular Cylinders

The influence of the distance between two circular side-by-side cylinders in a cross flow on the surface distribution of temperature and static pressure is experimentally studied. The studies were carried out at free-stream Mach numbers M equal to 0.295 and 0.365 and Reynolds numbers ReD equal to 6.4 × 104 and 7.9 × 104, respectively. The surface distributions of the pressure coefficient and the temperature recovery factor for one of the cylinders are obtained. It is shown that, depending on the distance between the cylinders, the pressure coefficient and temperature recovery factor can be both higher and lower than the values obtained in the flow over a single cylinder with the same free-stream parameters.

Experimental and numerical study of heat transfer under laminarization condition in a small size supersonic nozzle

The present paper compares measured and calculated heat transfer parameters for a small-size slot supersonic nozzle. Heat transfer coefficient and temperature recovery factor were examined under conditions of partial laminarization of boundary layer caused by moderate flow acceleration and low Reynolds numbers. The transient heat transfer method was implemented for estimation of these values for the nozzle subsonic and supersonic parts. Maximum values of flow acceleration parameter K lied in the range 1.3 … 2.75∙10−6. Experimentally measured value was normalized to the developed turbulent boundary layer heat transfer coefficient and reached St/StRex = 0.5–0.7 and indicated partial laminarization phenomenon. It was shown that the temperature recovery factor hasn't been affected by the flow acceleration. The results are compared to numerical heat transfer predictions using sst, γ-sst and γ-Reθ-sst turbulence models. Numerical calculations and experimental data were found to be in reasonably good agreement for low acceleration level with K less than 0.75∙10−6. Nevertheless, γ-sst turbulence model made slightly conservative estimation whereas in contrast γ-Reθ-sst model overestimates quantities for the moderate flow acceleration conditions.

Temperature recovery factor for gaseous nitrogen flow in a microtube

For gas flow over a flat plate, the temperature recovery factor is defined as a fraction of free-stream total temperature rise recovered at the wall or is the ratio of the actual temperature rise at the wall to the maximum possible temperature rise in the free-stream. Its value depends on Prandtl number and is independent of Mach number. The gas velocity and temperature are determined by the temperature recovery factor using the adiabatic wall temperature. It is an important parameter to be used to evaluate the gas velocity and temperature indirectly. In the present study, for internal flow, a methodology was introduced to estimate the temperature recovery factor numerically based on the total and bulk temperature for both laminar and turbulent flow regions in a microtube. The numerical simulations are based on the arbitrary Lagrangian-Eulerian method. The compressible momentum and energy equations for an ideal gas were solved to obtain the temperature recovery factor. To further validate the temperature recovery factor from numerical results, experiments were conducted using stainless steel microtubes. Although it is not a direct comparison, the gas bulk temperature and Mach number that were determined by the temperature recovery factor were compared with the experimental results and they were in good agreement.

乱流域におけるマイクロチューブを流れるガスの温度回復係数の推定

In this paper, a temperature recovery factor defined as the ratio of the actual temperature rise at the wall to the maximum possible temperature rise were estimated from experimentally measured wall temperatures and pressures to determine the velocity and temperature of gas through an adiabatic microtube. The experiments were carried out using two pairs of stainless steel microtubes with D=528.4 and 754.2 μm. One of a pair was tested for measurements of local pressures to obtain local Mach numbers and bulk temperatures. And the other of a pair was tested for measurements of local wall temperatures. The stagnation pressure with the atmospheric back pressure was chosen in such a way that the outlet flow reached sufficiently choked. Local total and bulk temperatures were obtained with total and static enthalpies determined with the measured stagnation & local pressures, stagnation temperatures, mass flow rates by real gas manner. In order to estimate the temperature recovery factor, the measured wall temperature and the obtained total temperature were normalized by bulk temperature and represented as Mach numbers. The estimated values of the temperature recovery factor were independent of the Mach number. The present estimated temperature recovery factor was compared with numerical and experimental ones obtained with the assumption of an ideal gas.

Temperature Recovery Factor for Gas Flow in a Microtube

Temperature Recovery Factor for Gas Flow in a Microtube

Prediction of flow characteristics for micro-tube gas flow by temperature recovery factor

Prediction of flow characteristics for micro-tube gas flow by temperature recovery factor

Experimental Study on the Diagnostics of Internal Compressible Flows using Outer Surface Nozzle Temperature

Cold spray (CS) is one of the thermal spraying methods which make coatings by spraying melted minute particles on substrate surfaces. Solid particles are sprayed onto a substrate at high speed to form a coating accelerated by a supersonic gas flow using a convergent-divergent nozzle. Therefore, it is important to understand the gas flow condition inside the nozzle that accelerated the gas flow. However, diagnosing internal gas flow is almost impossible for commercial CS nozzles because the nozzle is fabricated with hard metal alloy to prevent abrasions of the nozzle. Therefore, it is impractical to drill pressure taps to the CS nozzle to diagnose the gas flow. To solve this problem, authors propose non-intrusive flow-diagnostic methods which uses outer surface temperature of the CS nozzle and temperature recovery factor of the working gas. This research shows that the accuracy of this method is improved by measuring the outer surface temperature of the entire axial direction of the nozzle, and that the temperature recovery factor of the internal flow depends on the stagnation pressure. Therefore, the temperature recovery factor of the internal flow should be treated as a function of stagnation pressure.

The influence of the supersonic nozzle length on the efficiency of energy separation of low-Prandtl gas flowing in the finned single Leontiev tube

The redistribution of the total temperature between the parts of the gas stream flowing through the Leontiev tube depends not only on the temperature recovery factor (Prandtl number) and the ratio of flows through the supersonic and subsonic channels of the tube (Mach numbers), but also on the thermal resistance of the separation wall. Earlier it has been shown that the reduction of thermal resistance due to the separation wall finning on the side of the subsonic flow leads to an increase in the efficiency of energy separation. It may be assumed that the intensification of heat exchange between channels, due to finning, reduces the length of the tube, which at the same intensity of heat exchange leads to a decrease in pressure losses and an additional increase in efficiency. This paper presents the results of numerical simulation of energy separation in Leontiev tubes with a finned separation wall and different lengths of supersonic nozzle. It is shown that the adiabatic efficiency of the energy separation in a short Leontiev tube with a finned wall increases when the outlet pressure decreases, while it does not change for smooth tubes.

Effect of freestream turbulence on recovery factor of a thermocouple probe and its consequences

The temperature recovery factor of a thermocouple probe is important when being used to measure fluid temperature of a high-speed flow. Typically, the recovery factor is assumed to be dependent on the probe geometry and Prandtl number of the fluid, and invariant with freestream turbulence. In the present study, recovery factor of a butt-joint thermocouple probe is determined for two freestream turbulence conditions (0.25% and 7%). Results show that the recovery factor decreases with an increase in the freestream turbulence, which can lead to significant errors if not taken into consideration. The consequences of not taking into account the effect of freestream turbulence on the probe recovery factor is demonstrated with an application to energy separation in the wake of a circular cylinder.

Performance Evaluation of a Rake Used for Measuring Total Pressure and Total Temperature Inside an Engine Inlet Duct

The Korea Aerospace Research Institute runs the ground-based Altitude Engine Test Facility (AETF) for simulating high-altitude environments. This facility is widely used to test the performance of gas turbine engines at ground level to high altitudes. When engine performance is tested in the AETF, total pressure and total temperature of airflow can be measured using rakes in a duct directly connected to the engine inlet. The total pressure and total temperature of airflow into an engine are the main factors affecting the thrust and specific fuel consumption rate of the engine. Furthermore, the total pressure and total temperature at the engine inlet are used as the main reference values when operating test equipment to determine the airflow rate and temperature corresponding to the performance test conditions of the engine. The performance evaluation of the rake used to measure this is crucial. Accordingly, in this study, to improve the accuracy of the total pressure and total temperature values measured using rakes, their total pressure coefficient and total temperature recovery factor are measured, and the measurement uncertainty of the total temperature recovery factor is evaluated.

Modeling a new design for extracting energy from geopressured geothermal reservoirs

Reducing geothermal energy recovery costs and environmental concerns has led to interest in modeling new borehole heat exchanger designs. These heat exchangers are environment-friendly because they inject all the geofluid back into the reservoir after harvesting its energy, resulting in zero mass withdrawal from the system. This study develops reduced-order reservoir models for quickly estimating production temperature and thermal recovery from borehole heat exchangers using inspectional analysis and predictive modeling. An inspectional analysis suggests that there are nineteen dimensionless numbers necessary to fully scale this design. These dimensionless numbers were used in the statistical modeling. A Box–Behnken experimental design was used to create the simulation runs. A rigorous sensitivity analysis was performed on these designed series of runs to identify the most important dimensionless groups in predicting the dimensionless response for different segments of time. The selected dimensionless groups along with the dimensionless production temperature and thermal recovery factor (response), were used in the regression models. The models were reduced and assessed using training and testing runs. Applications of the developed models are also presented. The approach presented in this paper is general and provides a means to interpret and develop predictive models from simulator outputs in other research areas.

The temperature recovery factor in a boundary layer on a permeable plate

A numerical investigation of the boundary layer on a permeable wall in a supersonic gas flow is performed using a differential turbulence model. Temperature recovery factors are obtained for a series of Prandtl numbers and gas suction or injection in a wide range of the permeability factor from critical injection to asymptotic suction. With the example of air injection into a supersonic air flow, two methods for determining the temperature of a heat-insulated permeable wall are considered. The first is to solve the problem with a boundary condition of zero heat flux to the wall. The second is similar to an experimental method when the temperature of the gas injected at a section along the plate length becomes equal to the wall temperature. The heat-insulated wall temperatures and temperature recovery factors obtained by these two methods for injection below the critical one are close to each other. In case of critical injection, these two methods yield different results.

Statistical modeling of geopressured geothermal reservoirs

Identifying attractive candidate reservoirs for producing geothermal energy requires predictive models. In this work, inspectional analysis and statistical modeling are used to create simple predictive models for a line drive design. Inspectional analysis on the partial differential equations governing this design yields a minimum number of fifteen dimensionless groups required to describe the physics of the system. These dimensionless groups are explained and confirmed using models with similar dimensionless groups but different dimensional parameters. This study models dimensionless production temperature and thermal recovery factor as the responses of a numerical model. These responses are obtained by a Box-Behnken experimental design. An uncertainty plot is used to segment the dimensionless time and develop a model for each segment. The important dimensionless numbers for each segment of the dimensionless time are identified using the Boosting method. These selected numbers are used in the regression models. The developed models are reduced to have a minimum number of predictors and interactions. The reduced final models are then presented and assessed using testing runs. Finally, applications of these models are offered. The presented workflow is generic and can be used to translate the output of a numerical simulator into simple predictive models in other research areas involving numerical simulation.

Investigating the Influence of Helium Based Mixtures Composition on the Temperature Recovery Factor and Prandtl Number Values

The paper studies the influence of thermo-physical and transport properties of gaseous working fluids on the efficiency of closed Brayton cycle gas turbine power plants and gas dynamic temperature stratification device (Leontiev’s tube). It is shown that using helium binary gas mixtures with low Prandtl number Pr values as working fluids instead of pure helium in closed Brayton cycle gas turbine power plants leads to significant drop in the turbo-machinery aerodynamic loading with retention of the heat transfer coefficients in heat-exchangers and with sustainable growth in the pressure losses along the power plant loop components. For the Leontiev’s tube, using the helium binary gas mixtures with low Pr values results in significant drop of the temperature recovery factor r value on the wall in supersonic flow and in rise of the available temperature difference with appropriate increase of heat flow densities and decrease of required heat transfer areas value. The paper analyses the influence of different factors on the value r . Shows that using the gas mixtures with low Pr values as working fluids, injecting gas into supersonic flow boundary layer through permeable wall and arranging regular relief on the wall surface are the most promising solutions for decreasing the value r . Examines the methodologies and correlations known from available open sources to calculate the r values depending on Pr , Reynolds number Re x and Mach number M and presents the calculation results obtained through these correlations for Pr 0,1…1, Re x 10 5 …10 9 and M up to 4. Practically, all the methodologies and correlations examined are in good agreement with experimental data obtained for air with Pr ≈ 0,7 over the intervals of Re x and M considered. However, with further reduction of Pr value the calculation results for r diverge for different methodologies and correlations with up to 35 – 40 % difference for Pr ≈ 0,2 for those which are in good agreement with the air experimental data. Thus, there is a recommendation to conduct further experimental investigations to obtain real r values for different Pr , Re x and M on the flat impermeable wall in supersonic flow for the He - Ar , He - Kr , He - Xe , He - N 2 , He - CO 2 binary gas mixtures in order to verify the methodologies and correlations examined.

Measurements of the Stack Metal Temperature During a Natural Gas Blowdown Event Through a Full-Bore Blowdown Valve

Experiments were used in conjunction with a compressible flow model to investigate the temperature recovery phenomenon along a blowdown stack during a high-pressure natural gas pipeline blowdown. The test rig involved instrumented 2 in. blowdown stacks mounted on a full-bore valve. Stacks with two wall thicknesses and stagnation pressures of approximately 3000 kPa-a and 5600 kPa-g were tested, giving a total of four test cases. Using the compressible flow model, which was calibrated using static pressure measurements, the stack-gas temperature was calculated to range from −38 °C to −18 °C for the four test cases. The respective stack wall temperatures were measured to range between −13 °C and 0 °C; thus, the temperature recovery ranged between 18 °C and 26 °C. Empirical correlations available in the literature, which were developed for aeronautical applications, were tested against the experimental results. Poor agreement was found between the measured temperature recovery factor and that predicted by five empirical correlations: the coefficient of determination (R2) between the measured and correlation-calculated recovery factor was found to be negative for all five correlations.

Experimental research of the possibility of heat transfer enhancement in gas dynamic energy separation process

Analysis of the mechanism of heat transfer enhancement in a device of machineless energy separation of flows (Leontiev tube) is presented in the paper. The main parameters that define the device's efficiency are the temperature recovery factor and heat transfer in the supersonic channel of the device. Changes in the shape and relief of the flow surface, the use of working fluids with a low Prandtl number, low-intensity shock waves and local separation areas in the supersonic channel are among the methods of heat transfer enhancement in an energy separation device. The results of experimental investigation of the influence of a supersonic separation flow on the adiabatic wall temperature and the temperature recovery factor are presented. The range of the Mach numbers analyzed is between 2 and 3.5. The Reynolds criterion along the length of the dynamic boundary layer amounts to at least 6106. Field distributions of the adiabatic wall temperature and temperature recovery factors along the plate are presented for different Mach numbers. The results indicate that local separation boundary layer regions will probably intensify heat transfer in the supersonic channel of a gas dynamic energy separation device. The research has been conducted using the experimental facilities of the Institute of Mechanics of Lomonosov Moscow State University.

Numerically Simulated Impact of Gas Prandtl Number and Flow Model on Efficiency of the Machine-less Energetic Separation Device

The presented paper regards the influence of one of similarity criteria – the Prandtl number of gas (Pr) - on the efficiency of the machine-less energetic separation device (Leontiev pipe), using numerical modeling in ANSYS software. This device, equally as Rank-Hilsch and Hartman-Schprenger pipes, is designed to separate one gas flow into two flows with different temperatures. One flow (supersonic) streams out of the pipe with a temperature higher than initial and the other (subsonic) flows out with a temperature lower than initial. This direction of energetic separation is true if the Prandtl number is less than 1 that corresponds to gases. The Prandtl number affects the efficiency of running Leontiev pipe indirectly both through a temperature difference on which a temperature recovery factor has an impact and through a thermal conductivity coefficient that shows the impact of heat transfer intensity between gas and solid wall. The Prandtl number range in the course of research was from 0.1 to 0.7. The Prandtl number value equal to 0.7 corresponds to the air or pure gases (for example, inert argon gas). The Prandtl number equal to 0.2 corresponds to the mixtures of inert gases such as helium-xenon. The numerical modeling completed for the supersonic flow with Mach number 2.0 shows that efficiency of the machine-less energetic separation device has been increased approximately 2 times with the Prandtl number decreasing from 0.7 to 0.2. Moreover, for the counter-flow scheme this effect is a little higher due to its larger heat efficiency in comparison with the straight-flow one. Also, the research shows that the main problem for the further increase of the Leontiev pipe efficiency is a small value of thermal conductivity coefficient, which requires an intensification of the heat exchange, especially in the supersonic flow. It can be obtained, for example, by using a system of oblique shock waves in the supersonic channel.

Efficiency of energy separation at compressible gas flow in a planar duct

The method of energy separation in a high-speed flow proposed by A.I. Leontyev is investigated numerically. The adiabatic compressible gas flow (of a helium-xenon mixture) with a low Prandtl number in a planar narrow duct and a flow with heat exchange in a duct partitioned by a heat-conducting wall are analysed. The temperature recovery factor on the adiabatic wall, degree of cooling the low-speed flow part, temperature efficiency, and the adiabatic efficiency in a duct with heat exchange are estimated. The data are obtained for the first time, which make it possible to compare the efficiency of energy separation in a high-speed flow with the efficiency of similar processes in vortex tubes and other setups of gas-dynamic energy separation.