Investigation on the characteristics and mechanisms of unusual heat transfer of supercritical pressure water in vertically-upward tubes

The heat transfer characteristics of supercritical pressure water in a vertically-upward optimized internally-ribbed tube was investigated experimentally to study the mechanisms of unusual heat transfer of supercritical pressure water in the so-called large specific heat region. The experimental parameters were as follows. The pressure at the inlet of the test section ranged from 22.5 to 29.0 MPa, and the mass flux of the fluid was from 650 to 1200 kg/m² s, and the heat flux on the inside wall of the tube varied from 200 to 660 kW/m². According to experimental data, the characteristics of heat transfer enhancement and also the heat transfer deterioration of supercritical pressure water in the large specific heat region was analyzed and based on the comparison and analysis of the current major theories that were used to explain the reasons for unusual heat transfer to occur, the mechanisms of heat transfer enhancement and deterioration were discussed, respectively. The enhanced heat transfer was characterized by the gently changing wall temperature, the small temperature difference between the inside-tube-wall and the bulk fluid and the high heat transfer coefficient in comparison to the normal heat transfer. The deteriorated heat transfer could be characterized by the sharply increasing wall temperature, the large temperature difference and a sudden decrease in heat transfer coefficient in comparison to the normal heat transfer. The heat transfer enhancement of the supercritical pressure water in the large specific heat region was suggested to be a result of combined effect caused by the rapid variations of thermophysical properties of the supercritical pressure water in the large specific heat region, and the same was true of the heat transfer deterioration. The drastic changes in thermophysical properties near the pseudocritical points, especially the sudden rise in the specific heat of water at supercritical pressures, might result in the occurrence of the heat transfer enhancement, while the covering of the heat transfer surface by fluids lighter and hotter than the bulk fluid made the heat transfer deteriorated eventually and explained how this lighter fluid layer formed.     

Numerical Analysis of Jet Impingement Heat Transfer at High Jet Reynolds Number and Large Temperature Difference

Jet impingement heat transfer from a round gas jet to a flat wall was investigated numerically for a ratio of 2 between the jet inlet to wall distance and the jet inlet diameter. The influence of turbulence intensity at the jet inlet and choice of turbulence model on the wall heat transfer was investigated at a jet Reynolds number of 1.66 × 10⁵ and a temperature difference between jet inlet and wall of 1600 K. The focus was on the convective heat transfer contribution as thermal radiation was not included in the investigation. A considerable influence of the turbulence intensity at the jet inlet was observed in the stagnation region, where the wall heat flux increased by a factor of almost 3 when increasing the turbulence intensity from 1.5% to 10%. The choice of turbulence model also influenced the heat transfer predictions significantly, especially in the stagnation region, where differences of up to about 100% were observed. Furthermore, the variation in stagnation point heat transfer was examined for jet Reynolds numbers in the range from 1.10 × 10⁵ to 6.64 × 10⁵. Based on the investigations, a correlation is suggested between the stagnation point Nusselt number, the jet Reynolds number, and the turbulence intensity at the jet inlet for impinging jet flows at high jet Reynolds numbers.     

超临界压力下航空煤油在竖直管内的传热研究

对竖直上升管内超临界压力下航空煤油的传热特性进行了实验研究。分析了不同质量流量、热流密度、压力和进口温度对超临界压力下航空煤油传热特性的影响。实验结果表明,提高质量流量或进口温度均使煤油传热效果变好。而热流密度对流体传热的影响主要在于改变了流体和壁面温度,热流密度越大,传热系数越高。压力对煤油传热影响不大,一般情况下,提高压力会恶化传热。超临界状态下,煤油物性变化很大,因此对煤油的传输和热力学性质的准确计算是研究超临界压力下传热现象的关键。利用拓展的对比态法来计算煤油的密度和传输特性,如黏度、热导率等。给出了煤油在超临界压力下的传热关联式,其计算值和实验值吻合良好。     

Confined Boiling Heat Transfer,Two-Phase Flow Patterns,and Jet Impingement in a Hele-Shaw Cell

ABSTRACT

Experiments were carried out to study heat transfer and two-phase flow patterns during boiling in a Hele-Shaw cell filled with pure water vapor at atmospheric pressure and with a central inlet of a liquid jet. The Hele-Shaw cell was based on a circular copper rod surface and a polycarbonate plate permitting optical access and thus high-speed cinematography. The diameter of the heated copper rod was 10 mm, the jet diameters were 0.5 and 1 mm, and spacing was varied between 50, 100, and 200 μm. The heat was applied through 4 cartridge heaters with a maximum heat flux of 327 W/cm². Results showed how high-volume flow rates for the liquid jet led to jet impingement heat transfer while low flow rates led to a Hele-Shaw flow boiling system. The relationship between the volume flow rate and the temperature difference differed significantly between these two regimes. Different flow patterns and evaporation fronts were observed using high-speed cinematography. They strongly depended on jet properties, applied heat flux, and gap spacing. The efficiency of the Hele-Shaw flow boiling system during high heat flux levels was attributed to high interface velocities, combined with viscous fingering at the interface. This combination led to high wetting rates with substantial microlayer evaporation. Good results regarding the heat transfer and the pressure drop were obtained with the final configuration of a 10-mm copper rod diameter, a jet diameter of 1 mm, and a spacing of 0.1 mm. A rather surprising observation was the existence of a stable rotation of an evaporating liquid jet in the Hele-Shaw boiling chamber. The driving mechanism for the rotation with a frequency of 105 Hz was the rapid microlayer evaporation at the rear side of the rotating liquid jet.     

An Investigation on Heat Transfer to Supercritical Water in Inclined Upward Smooth Tubes

Within the range of pressures from 23 to 30 MPa, mass velocities from 600 to 1200 kg/(m²s), and heat fluxes from 200 to 600 kW/m², experiments have been performed for an investigation on heat transfer to supercritical water in inclined upward smooth tubes with an inner diameter of 26 mm and an inclined angle of 20° from the horizon. The results indicated that heat transfer characteristics of supercritical water are not uniform along the circumference of the inclined tube. An increase in the mass velocity of the working fluid can decrease and even eliminate the non-uniformity. Properties of supercritical fluid acutely vary with the temperature near the pseudocritical point. While the ratio of the mass velocity to the heat flux exceeded 2.16 kg/(kWs), heat transfer enhancement occurred near the pseudocritical point; conversely, heat transfer deterioration occurred while the ratio of the mass velocity to the heat flux was lower than 2.16 kg/(kWs). As the pressure increased far from the critical pressure, the amount of deterioration decreased. Correlations of heat transfer coefficients of the forced-convection heat transfer on the top and bottom of the tube have been provided, and can be used to predict heat transfer coefficient of spirally water wall in supercritical boilers.     

Experimental investigation on heat transfer characteristics of low mass flux rifled tube with upward flow

An experiment for heat transfer of water flowing in a vertical rifled tube was conducted at subcritical and supercritical pressure. The main purpose is to explore the heat transfer characteristics of the new-type rifled tube at low mass flux. Operating conditions included pressures of 12–30 MPa, mass flux of 232–1200 kg/(m² s), and wall heat fluxes of 133–719 kW/m². The heat transfer performance and wall temperature distribution at various operating conditions were captured in the experiment. In the present paper, the heat transfer mechanism of the rifled tube was analyzed, the effects of pressure, wall heat flux and mass flux on heat transfer were discussed, and corresponding empirical correlations were also presented. The experimental results exhibit that the rifled tube has an obvious enhancement in heat transfer, even at low mass flux. In comparison with a smooth tube, the rifled tube efficiently prevents Departure from Nucleate Boiling (DNB) and delays dryout at subcritical pressure, and also improves the heat transfer of supercritical water remarkably, especially near pseudo-critical point. An increase in pressure or wall heat flux impairs the heat transfer at both subcritical and supercritical pressure, whereas the increasing mass flux has a contrary effect.     

Deterioration in heat transfer of endothermal hydrocarbon fuel

Numerical studies under supercritical pressure are carried out to study the heat transfer characteristics in a single-root coolant channel of the active regenerative cooling system of the scramjet engine, using actual physical properties of pentane. The relationships between wall temperature and inlet temperature, mass flow rate, wall heat flux, inlet pressure, as well as center stream temperature are obtained. The results suggest that the heat transfer deterioration occurs when the fuel temperature approaches the pseudo-critical temperature, and the wall temperature increases rapidly and heat transfer coefficient decreases sharply. The decrease of wall heat flux, as well as the increase of mass flow rate and inlet pressure makes the starting point of the heat transfer deterioration and the peak point of the wall temperature move backward. The wall temperature increment induced by heat transfer deterioration decreases, which could reduce the severity of the heat transfer deterioration. The relational expression of the heat transfer deterioration critical heat flux derives from the relationship of the mass flow rate and the inlet pressure.     

Heat transfer and wall pressure characteristics of a twin premixed butane/air flame jets

Experimental studies were carried out to investigate the flame shape and the heat transfer and wall pressure characteristics of a pair of laminar premixed butane/air flame jets impinging vertically upon a horizontal water-cooled flat plate at jet Reynolds numbers of 800, 1000 and 1200, respectively. Equivalence ratio of the butane/air mixture was maintained constantly at unity. The flame shape, the pressure distribution on the impingement plate and the heat transfer from the flame to the plate were greatly influenced by the interference occurred between the two flame jets. This interference caused a sharp pressure peak at the between-jet midpoint and the positive pressures at the between-jet area, which led to the separation of the wall jet from the impingement plate after collision. Such interference became more significant when the non-dimensional jet-to-jet spacing (S/d) and the nozzle-to-plate distance (H/d) were reduced. Heat transfer in the interaction zone between the jets was at the lowest rate due to this interference at the smallest S/d ratio of 2.6, resulting from the separation of the high-temperature inner reaction zone of the flame from the impingement plate. On the other hand, the interference enhanced the heat transfer in the interaction zone between the jets when the S/d ratio was greater than 5, by enhancing the heat transfer coefficient. The average heat flux of the impingement plate was found to increase significantly with the increasing H/d ratio until H/d=6. The present study provided detailed information on flame shape and the heat transfer and wall pressure characteristics of a twin laminar pre-mixed impinging circular flame jets, which has rarely been reported in previous studies.     

Study on carbon dioxide gas cooler heat transfer process under supercritical pressures

In carbon dioxide transcritical air‐conditioning and heat pump systems, the high‐pressure‐side heat exchanger operating at supercritical pressures is usually called as gas cooler. The carbon dioxide gas cooler displays much difference from the traditional heat exchangers employing constant property fluids. The commonly used logarithmic mean temperature difference (LMTD) and effectiveness—heat transfer unit (ε‐NTU) fail for the gas cooler design calculation as the carbon dioxide properties change sharply near the critical or pseudo‐critical point in the heat transfer processes. The new effective heat transfer temperature difference expression for variable fluid property derived by the authors is verified by numeric simulation of the carbon dioxide gas cooler. Moreover, the available correlated models for the cooled carbon dioxide supercritical heat transfer are used to simulate the gas cooler. Detail analysis is made for the deviations among the different models, and for the distributions of local convective coefficient, heat flux, and local temperature of carbon dioxide along the flow path in the gas cooler. Copyright © 2002 John Wiley & Sons, Ltd.     

Asymmetrical Non-Uniform Heat Flux Distributions For Laminar Flow Heat Transfer With Mixed Convection In a Horizontal Circular Tube

Non-symmetric heat flux distributions in terms of gravity in solar collector tubes influence buoyancy-driven secondary flow which has an impact on the associated heat transfer and pressure drop performance. In this study the influence of the asymmetry angle (0°, 20°, 30° and 40°) with regard to gravity for non-uniform heat flux boundaries in a horizontal circular tube was investigated numerically. A stainless steel tube with an inner diameter of 62.68 mm, a wall thickness of 5.16 mm, and a length of 10 m was considered for water inlet temperatures ranging from 290 K to 360 K and inlet Reynolds numbers ranging from 130 to 2000. Conjugate heat transfer was modelled for different sinusoidal type outer surface heat flux distributions with a base-level incident heat flux intensity of 7.1 kW/m². It was found that average internal heat transfer coefficients increased with the circumferential span of the heat flux distribution. Average internal and axial local heat transfer coefficients and overall friction factors were at their highest for symmetrical heat flux cases (gravity at 0º) and lower for asymmetric cases. The internal heat transfer coefficients also increased with the inlet fluid temperature and decreased with an increase in the external heat loss transfer coefficient. Friction factors decreased with an increase in fluid inlet temperature or an increase in the external heat loss transfer coefficients of the tube model.     

An investigation into the heat transfer characteristics of spiral wall with internal rib in a supercritical sliding-pressure operation once-through boiler

Within the pressure range of 9–28 MPa, mass velocity range of 600–1 200 kg/(m²·s), and heat flux range of 200–500 kW/m², experiments were performed to investigate the heat transfer to water in the inclned upward internally ribbed tube with an inclined angle of 19.5 degrees, a maximum outer diameter of 38.1 mm, and a thickness of 7.5 mm. Based on the experiments, it was found that heat transfer enhancement of the internally ribbed tube could postpone departure from nucleate boiling at the sub-critical pressure. However, the heat transfer enhancement decreased near the critical pressure. At supercritical pressure, the temperature difference between the wall and the fluid increased near the pseudo-critical temperature, but the increase of wall temperature was less than that of departure from nucleate boiling at sub-critical pressure. When pressure is closer to the critical pressure, the temperature difference between the wall and the fluid increased greatly near the pseudo-critical temperature. Heat transfer to supercritical water in the inclined upward internally ribbed tube was enhanced or deteriorated near the pseudo-critical temperature with the variety of ratio between the mass velocity and the heat flux. Because the rotational flow of the internal groove reduced the effect of natural convection, the internal wall temperature of internally ribbed tube uniformly distributed along the circumference. The maximum internal wall temperature difference of the tube along the circumference was only 10 degrees when the fluid enthalpy exceeded 2 000 J/g. Considering the effect of acute variety of the fluid property on heat transfer, the coreelation of heat transfer coefficient on the top of the internally ribbed tube was provided. Translated from Proceedings of CSEE, 2005, 25(16): 90–95 [译自: 中国电机工程学报]     

Numerical investigation of laminar forced convection of water upwards in a narrow annulus at supercritical pressure

In the present work, convection heat transfer of water at supercritical pressure in a narrow annulus at low Reynolds numbers (less than 1500) has been investigated numerically. The continuity, momentum and energy equations have been solved simultaneously using computational fluid dynamics techniques with the inlet Reynolds number ranging from 250 to 1000, Grashof number from 2.5 × 10⁵ to 1 × 10⁶ and the inlet fluid temperature from 360 °C to 380 °C. In all of the case studies, a sub-cooled water flow at supercritical pressure (25 MPa) and a temperature close to the pseudo-critical point enters the annular channel with constant heat flux at inner wall surface and insulated at outer wall. To calculate the velocity and temperature distributions of the flow, discretized form of the governing equations in the cylindrical coordinate system are obtained by the finite volume method and solved by the SIMPLE algorithm. It has been shown that the effect of buoyancy is strong and causes extensive increase in velocity near the inner wall, and consequently an increase in the convective heat transfer, which is desirable. Besides, the effects of inlet Reynolds number, Grashof number and inlet temperature on the velocity distribution and also on the heat transfer have been investigated.     

An Experimental Study of Carbon Dioxide Condensation in Mini Channels

In this study, the local characteristics of pressure drop and heat transfer were investigated experimentally for carbon dioxide condensation in a multi-port extruded aluminum test section, which had 10 circular channels each with 1.31 mm inner diameter. The CO2 was cooled with cooling water flow inside the copper blocks that were attached at both sides of the test section. The temperatures at the outer surface of the test section were measured with 24 K-type thermocouples embedded in the upper and lower surfaces along the length. Local heat fluxes were measured with 12 heat flux sensors to estimate the local enthalpies, temperatures and heat transfer coefficients. Bulk mean temperatures of CO2 at the inlet and outlet of the test section were measured with 2 K-type thermocouples. The measurements were performed for the pressure ranged from 6.48 to 7.3 MPa, inlet temperature of CO2 from 21.63 to 31.33℃, heat flux from 1.10 to 8.12 kW/m2, mass velocity from 123.2 to 315.2 kg/m2s, and vapor quality from 0 to 1. The results indicate that pressure drop is very small along the test section, heat transfer coefficient in the two-phase region is higher than that in the single-phase, and mass velocity has important effect on condensation heat transfer characteristics. In addition, experimental data were compared with previous correlations and large discrepancies were observed.     

Confined Submerged Jet Impingement Boiling of Subcooled FC-72 over Micro-Pin-Finned Surfaces

Heat transfer characteristics of confined submerged jet impingement boiling of air-dissolved FC-72 on heated micro-pin-finned surfaces are presented. The dimension of the silicon chips is 10 × 10 × 0.5 mm³ (length × width × thickness) on micro-pin-fins with the four dimensions of 30 × 30 × 60 μm³, 50 × 50 × 60 μm³, 30 × 30 × 120 μm³, and 50 × 50 × 120 μm³ fabricated by using the dry etching technique. For comparison, experiments of jet impinging on a smooth surface were also conducted. The results have shown that submerged jet impingement boiling gives a large heat transfer enhancement compared with pool boiling, and all micro-pin-fins showed better heat transfer performance than a smooth surface. The effects of jet Reynolds number, jet inlet subcooling, micro-pin-fins, and nozzle-to-surface distance on jet impingement boiling heat transfer were explored. For micro-pin-fins, the maximum allowable heat flux increases with jet Reynolds number and subcooling. The largest value of the maximum allowable heat flux of micro-pin-fins by submerged jet impingement boiling is 157 W/cm², which is about 8.3 times as large as that for the smooth surface in pool boiling. Also, Nusselt number has a strong dependence on Reynolds number.     

Heat Transfer Characteristics of Printed Circuit Heat Exchanger with Supercritical Carbon Dioxide and Molten Salt

Molten salt and supercritical carbon dioxide (S-CO_2) are important high temperature heat transfer media,but molten salt/S-CO_2 heat exchanger has been seldom reported.In present paper,heat transfer in printed circuit heat exchanger (PCHE) with molten salt and S-CO_2 is simulated and analyzed.Since S-CO_2 can be drove along passage wall by strong buoyancy force with large density difference,its heat transfer is enhanced by natural convection.In inlet region,natural convection weakens along flow direction with decreasing Richardson number,and the thermal boundary layer becomes thicker,so local heat transfer coefficient of S-CO_2 significantly decreases.In outlet region,turbulent kinetic energy gradually increases,and then heat transfer coefficient increases for turbulent heat transfer enhancement.Compared with transcritical CO_2 with lower inlet temperature,local heat transfer coefficient of S-CO_2 near inlet is lower for smaller Richardson number,while it will be higher for larger turbulent kinetic energy near outlet.Performance of PCHE is mainly determined by the pressure drop in molten salt passage and the heat transfer resistance in S-CO_2 passage.When molten salt passage width increases,molten salt pressure drop significantly decreases,and overall heat transfer coefficient slightly changes,so the comprehensive performance of PCHE is improved.As a result,PCHE unit with three semicircular passages and one semi-elliptic passage has better performance.     

Flow characteristics and heat transfer performances of a semi-confined impinging array of jets: effect of nozzle geometry

The flow and heat transfer characteristics of confined jet array impingement with crossflow is investigated. Discrete impingement pressure measurements are used to obtain the jet orifice discharge flow coefficient. Digital particle image velocimetry (DPIV) and flow visualization are used to determine the flow characteristics. Two thermal boundary conditions at the impinging surface are presented: an isothermal surface, and a uniform heat flux, where thermocouple and thermochromic liquid crystal methods were used, respectively, to determine the local heat transfer coefficient. Two nozzle geometries are studied, circular and cusped ellipse. Based on the interaction with the jet impingement at the surface, the crossflow is shown to influence the heat transfer results. The two thermal boundary conditions differ in overall heat transfer correlation with the jet Reynolds number. Detailed velocity data show that the flow development from the cusped ellipse nozzle affects the wall region flow more than the circular nozzle, as influenced by the crossflow interactions. The overall heat transfer for the uniform heat flux boundary condition is found to increase for the cusped ellipse orifice.     

Development of a distributed-parameter model for the evaporation system in a supercritical W-shaped boiler

In this paper, a distributed parameter model of an evaporation system in a supercritical W-shaped once-through boiler is developed based on the 3-D temperature distribution. The mathematical model was formulated to predict the distributions of the heat flux and the metal-surface temperature while considering a non-uniform distribution of the surface heat transfer and the frictional resistance coefficient. The results show that the heat flux distribution on the front water wall has three high heat flux zones in the W-shaped boiler, and the peak of the heat transfer coefficient moves to the peak of the heat flux gradually with the increment of load at supercritical pressure. The maximum deviation of the metal temperature is nearly 94 °C for different loads. This distributed parameter model is fit for the in-situ operating status of the boiler, and it provides a reference for the heat transfer of a supercritical system.     

Development of a new forced convection heat transfer correlation for CO2 in both heating and cooling modes at supercritical pressures

Experimental and numerical investigations on forced convection heat transfer of carbon dioxide at supercritical pressures in a prototypic printed circuit heat exchanger under both cooling and heating conditions have been performed in this present study. The experiment test section has nine semi-circular channels with a hydraulic diameter of 1.16 mm and a length of 0.5 m. Primary operational parameters include inlet pressure of 7.5–10 MPa, mass fluxes of 326 kg/m² s and 762 kg/m² s, inlet temperatures from 10 °C to 90 °C and the average heat flux was 30 kW/m². Beyond reproducing the regular experimental cases, numerical modeling also implemented higher heat fluxes of 60 kW/m² and 90 kW/m² in order to investigate the effect of heat flux. Good agreement was found between the experiments and FLUENT simulations using an SST k–w model with the near-wall region being completely resolved. The distinctive behavior of convection heat transfer at supercritical pressures between heating and cooling modes was systematically analyzed. A more physically reasonable property-averaging technique, Probability Density Function (PDF)-based time-averaged property, was developed to account for the effect of nonlinear dependency of properties on instantaneous local temperature. Furthermore, experimental and computational data were compared to empirical predictions by the Dittus–Boelter and Jackson correlations. The results showed that Dittus–Boelter correlation has better precision for the average value of the predicted heat transfer coefficient but cannot take account of the effect of heat flux. In contrast, the Jackson correlation, with property ratio correction terms to account for the distribution of the properties in the radial direction, could predict the distinction of heat transfer characteristics under heating and cooling conditions. However, it overestimates the average value of heat transfer coefficient in the whole range of the experiment conditions. Finally, a new correlation evaluated by PDF-based time-averaged properties for forced convection heat transfer of CO₂ in both heating and cooling mode at supercritical pressures was developed. Comparison of experimental and computational data with the prediction results by the new developed correlation reveals that it works quite well; i.e., more than 90% data in either heating or cooling mode with various heat fluxes are predicted within an accuracy of ±25%.     

Evaporation Heat Transfer Coefficients of R-446A

ABSTRACT

The present study investigated the evaporation heat transfer coefficients of R-446A, as a low global warming potential alternative refrigerant to R-410A. The evaporation heat transfer coefficients were obtained by measuring the wall temperature of a straight stainless tube and refrigerant pressure. The heat transfer coefficients were measured for the quality range from 0.05 to 0.95, the mass flux from 100 to 400 kg/m²s, heat flux from 10 to 30 kW/m², and saturation temperature from 5 to 10°C. The evaporation heat transfer coefficient of R-410A was verified by comparing the measured evaporation heat transfer coefficient with the value predicted by the existing correlation. The evaporation heat transfer coefficient of R-446A was measured using a proven experimental apparatus. When the heat flux was 10 kW/m², the evaporation heat transfer coefficient of R-446A was always higher than that of R-410A. But, when the heat flux was 30 kW/m², the evaporation heat transfer coefficient of R-446A was measured to be lower than that of R-410A near the dry-out point. The effect of the tube diameter on the R-446A evaporation heat transfer coefficient was negligible. The effect of saturation pressure on the evaporation heat transfer coefficient was prominent in the low quality region where the nucleate boiling was dominant.     

CFD modeling of heat transfer of CO2 at supercritical pressures flowing vertically in porous tubes

Computational fluid dynamics (CFD) tool has been used for investigation of convective heat transfer of CO₂ in two porous tubes. Effects of some important parameters such as pressure, inlet temperature, mass flow rate, wall heat flux and porosity on temperature distribution and local heat transfer coefficients have been studied numerically. Near the supercritical conditions, these parameters are very effective on temperature gradient and local heat transfer coefficients. For example at p = 9.5 MPa, under the same conditions, the heat transfer coefficient in a tube with particle diameters of 0.1–0.12 mm is about 20–30% higher than when the particle diameter of 0.2–0.28 mm were used. The heat transfer coefficient increases with decreasing pressure and increasing mass flow rate. Also the porosity of the bed has the important role on the heat transfer. The CFD predictions have been compared to the experimental data and showed pretty good agreement.