Mass Flow Coefficient Research Articles

Comparison of the two-phase mass flow coefficient and the over-reading for wet gas flow metering with DP meters

A DP meter with a wet gas correlation is a widely applied technology for metering wet gas flow. The over-reading (OR) is historically the most used parameter for establishing the wet gas correlation. Recently, we proposed a new parameter termed the two-phase mass flow coefficient (K) and whereby new wet gas correlations were developed. In the present study, the comparison of K and OR is conducted. By applying the separated flow model, the basic form of the wet gas correlation based on K is derived, and meanwhile the effect of influential parameters on K is theoretically analyzed. Experiments with an orifice plate meter indicate that, compared to OR, K increases with better linearity as the Lockhart-Martinelli parameter (XLM) increases within the whole operating range and is more sensitive to the change of XLM. Experimental results also show that increasing the gas-to-liquid density ratio (ρg/ρl) results in a decrease of K, while the gas densiometric Froude number (Frg) has a minor effect. These findings coincide with our previous studies on V-cone meters and Venturi meters. The function relationship between K and its influential parameters (including XLM, ρg/ρl and Frg) is obtained through data fitting and then the specific form of the new wet gas correlation is derived. The relative error of gas mass flow rate predicted by the new correlation is within ±3.0% at the confidence level of 98.6%, superior to the existing correlations based on OR. This result is attributed to the good linearity and sensitivity of K to XLM. Note that in our previous studies on V-cone meters and Venturi meters, correlations derived from K also perform better than those derived from OR. We can therefore conclude that the two-phase mass flow coefficient provides an alternative as well as better approach to correct the liquid-induced prediction error of gas flow rate in wet gas with DP meters.

Numerical estimation of energy efficiency in cryogenic chamber with various methods of ventilation and location of test object

Various industries, including automobiles, wind power, railroads, airlines, and defense, have their own individual low-temperature test specifications. Since the performance of a test object has to be evaluated after cooling in a climate-controlled chamber, the process consumes an enormous amount of energy and a long time is needed to cool the object. Reducing energy consumption and increasing the cooling rate would offer a huge environmental and economic benefit. This study analyzed the cooling rate and energy consumption of a cryogenic chamber in terms of the ventilation methods and locations of test objects through computational fluid dynamics analysis. In order to calculate energy consumption, the study fixed the compressor power of the refrigerator and created an energy model in the form of a user-defined function that considered changes in the outlet mass flow and refrigerator coefficient of performance according to changes in outlet temperatures within the chamber; this model is used for numerical analysis. The chamber used for the upper air supply and lower exhaust method (Case A) demonstrated a faster cooling rate by 0%–32% compared to the upper air supply and lower exhaust on the opposite face method (Case B) and the upper air supply and central exhaust on the opposite face method (Case F). Case A generally consumed less energy during cooling, whereas Case F consumed the least amount of energy for 4–6 out of the 12 test object locations. Cases A, B, and F demonstrated the highest cooling rates and the lowest energy consumptions when the test object was located at P5 or P11 opposite of the air supply. The cooling rate of the test object and energy consumption should be considered in the ventilation design of a cryogenic test chamber. In the case of a pre-installed chamber, a proper location should be selected for cooling the test object for fast cooling according to the chamber ventilation method.

Determination of the mass-flow coefficient of jet-reactive turbine’s feed-in nozzle

The possibility of adjusting of the jet-reactive turbine’s head parameters through changing of mass-flow of the working body with the help of adjustable feed-in nozzle is examined. The mass-flow coefficient of the feed-in nozzle is determined experimentally.

Analysis of vortices and performance of different diffusers in a large mass flow coefficient centrifugal compressor

An appropriate diffuser following an impeller is critical to realize a high efficiency and a wide operating range for a centrifugal compressor stage. The purpose of this study is to investigate the effect of different types of vaned diffusers on a large mass flow coefficient centrifugal compressor stage performance under different operating conditions and to reveal the loss mechanisms in the vaned diffusers. Five vaned diffusers are studied. Flow fields and vortices in a conventional diffuser and a rib diffuser are first examined. Then, vortices and flow fields in three different tandem diffusers are analyzed in detail. For the three tandem diffusers, only circumferential position of first row vanes relative to the second row vanes is different. Results show that the stage with the conventional diffuser possesses the shortest operating range. The rib diffuser has less loss due to the weaker tip leakage vortex, while its static pressure recovery coefficient is lower, and the loss in the following return part is higher. Comparison results between the three tandem diffusers imply that when the trailing edge of the first row vane is close to the pressure surface of the second row vane, the stage with the tandem diffuser has a better performance. This is ascribed to the interaction of the tip leakage vortex and suction surface vortex, which decreases the total loss, especially reduces the loss induced by the suction surface vortex. When the trailing edge of the first row vanes is close to the suction surface of the second row vane, the loss is increased since the leading edge vortex has a large strength and surrounds the suction surface vortex. Therefore, the reasonable interaction of vortices in a tandem diffuser can bring a high performance of the centrifugal compressor.

Online measurement of gas and liquid flow rate in wet gas through one V-Cone throttle device

In the present study, an accurate cost-effective online system for metering both the gas flow rate and the liquid flow rate in wet gas with only one V-Cone throttle device is developed. The two-phase mass flow coefficient is employed to correct the measurement deviation of the V-Cone throttle device. The effects of the liquid densiometric Froude number, the gas densiometric Froude number and the ratio of gas density to liquid density on the two-phase mass flow coefficient are experimentally investigated. The equivalent diameter ratio of the V-Cone throttle device is 0.55. The experimental fluids are air and tap water. The operating pressure, the superficial gas velocity and superficial liquid velocity range from 0.1MPa to 0.3MPa, 4.87m/s to 25.26m/s and 0 to 0.38m/s, respectively. The results show that the two-phase mass flow coefficient linearly increases with the liquid densiometric Froude number and is affected by the gas densiometric Froude number and the ratio of gas density to liquid density. On the basis of the two-phase mass flow coefficient, the correlation for measuring the gas flow rate of the wet gas is developed. To reflect the influences of the liquid on the measurement, the pressure loss ratio of the V-Cone throttle is proposed. By incorporating the gas measurement correlation of the wet gas, the wet gas correlations to simultaneously meter the gas and liquid flow rate are concluded. In the present cases, the relative error of the gas mass flow rate predicted by the correlations is within ±5.0% and the mean absolute percentage error is 2.52%; the full scale relative error of the liquid mass flow rate is within ±5.0% and the mean absolute percentage error is 7.03%. The method proposed in this study creates a simple inexpensive wet gas metering system that can operate well in a significant range of industrial applications.

The effect of impeller–diffuser interactions on diffuser performance in a centrifugal compressor

ABSTRACTThe unsteady phenomenon abounds in centrifugal compressors and significantly affects the compressor performance. In this paper, unsteady simulations are carried out to investigate the aerodynamic performance of a process-unshrouded centrifugal compressor and the unsteady mechanism in the vaned diffuser. The predicted stage performance and pressure fluctuations at some locations are in good agreement with experimental data. The predicted main pressure fluctuation frequency spectrums at the diffuser inlet and outlet are consistent with the measured results. The results indicate that at the inlet of the diffuser there are two pressure peaks in a passage cycle. The higher pressure peak relates to the impeller wake and the lower peak is connected with the vortex generated at the diffuser’s leading edge. With a decrease in the mass flow coefficient, the vortex core region becomes larger and the lower pressure peak becomes more pronounced. The change in circumferential flow angle at the diffuser inlet is mainly responsible for the unsteadiness in the diffuser flow field, which in turn affects the inlet incidence of the diffuser vane and the vane loading distributions.

ТЕПЛОНАСОСНІ ТЕХНОЛОГІЇ ТА ЇХ ПОТЕНЦІЙНИЙ ВПЛИВ НА ПРОБЛЕМИ ЕНЕРГОЕФЕКТИВНОСТІ ТА ЗАХИСТУ НАВКОЛИШНЬОГО СЕРЕДОВИЩА В ЕНЕРГЕТИЧНОМУ СЕКТОРІ УКРАЇНИ

The increasing demand of energy sources for urban, household and industrial facilities requires strategies development for seeking new energy sources. In recent years an important problem is to have energy storage, energy production and energy consumption which fulfill the environment friendly expectations. A lot of attention is devoted to renewable energy sources. One of the most attracting among them is energy production form geothermal sources. At a few meters below the earth’s surface the underground maintains a constant temperature in an approximation through the year allowing to withdraw heat in winter for heating needs and to surrender heat during summer for air-conditioning purposes. Heat pump is a rapidly developing technology for heating and domestic hot water production. Using ground as a heat source, heat exchange is carried out with heat pumps compound to vertical ground heat exchanger tubes that allows the heating and cooling of the buildings utilizing a single unit installation. Heat pump unit provides a high degree of productivity with moderate electric power consumption. In this paper a theoretical performance study of a vapor compression heat pump system with various natural and synthetic refrigerants (HFCs) is presented. Operation mode of the heat pump unit was chosen according to European Standard EN14511-2:2007 and EN255-2. An influence of discharge temperature on system performance was evaluated at different boiling temperatures. The comparison of mass flow rate and coefficient of performance for considered refrigerants at constant cooling capacity and condensation temperature was performed.

Numerical investigation on transient flow and cavitation characteristic within nozzle during the oil drainage process for a high-pressure common-rail DI diesel engine

In the present investigation, the transient developments of flow and cavitation within an injector’s nozzle during the oil drainage process have been studied by numerical method for a high-pressure common-rail DI diesel engine, both the variation regulations of macro parameters (indicating flow characteristics and cavitation characteristics) and the distribution manners of important physical fields (indicating the cavitation evolution in the micro) have been obtained and analyzed. The obtained numerical results indicate that, during the oil drainage process, both mass flow rate and flow coefficient monotonously increase with declining variation rates, both averaged flow velocity and averaged turbulent kinetic energy also monotonously increase; however, to the curve of TKE-needle lift, there exist certain points give abrupt increase. The difference in TKE curve compared to averaged flow velocity is mainly attributed to the sudden variation of cavitation. Based upon the numerical results, the cavitation bubble will not be formed until the needle lift has been raised to a certain position due to the lower flow velocity and the lack of low (even negative) pressure zones. As needle rises, the primary bubbles are formed near the lower corner after nozzle’s entrance; but as needle further rises, the positions at where bubbles are formed have been transferred to the upper corner and then being blow downwards orifice as the increase of flow velocity.

A new correlation for wet gas flow rate measurement with Venturi meter based on two-phase mass flow coefficient

Much attention has been devoted to the study of the correlation of the wet gas flow rate measurement with a Venturi meter. However, up to now a widely-accepted correlation or model is not available. In this study, a new correlation for wet gas flow rate measurement with Venturi meter based on a two-phase mass flow coefficient was proposed. The two-phase mass flow coefficient was found to linearly increase with the Lockhart–Martinelli parameter and decrease with the increase of the gas-to-liquid density ratio. It also decreased with the gas densiometric Froude number increasing. The relationships of the two-phase mass flow coefficient with the Lockhart–Martinelli parameter, the gas densiometric Froude number and the ratio of gas to liquid density were concluded. Comparisons with the existing correlations showed that the new correlation predicted the wet gas flow rate more accurately than other correlations under the following conditions: the Lockhart–Martinelli parameter ranging from 0 to 0.3, the gas densiometric Froude number from 0.6 to 4.7, the ratio of gas to liquid density from 0.01 to 0.081 and the inlet diameter of the Venturi meter from 50 to 200mm. The present work provided an alternative approach to the study on the wet gas flow rate measurement with the Venturi meter.

Two-phase mass flow coefficient of V-Cone throttle device

The V-Cone throttle device has been paid more and more attentions on the measurement of the wet gas flow in recent years. However, it tends to over-read the gas flow rate when directly used to measure the wet gas. How to correct this over-reading and obtain an accurate yet simple wet gas correlation is still one of the challenges in the investigation on the V-Cone throttle device. In this paper, the two-phase mass flow coefficient of the V-Cone throttle device was proposed to correct the deviation of the readings produced by the device. The parameters affecting the coefficient were determined and discussed experimentally. Two V-Cone throttle devices with the respective equivalent diameter ratios of 0.65 and 0.75 were investigated under the condition of the wet gas flow. The test fluid was air and tap water. The gas-to-liquid density ratio ranged from 0.002445 to 0.006083, and the gas densiometric Froude number ranged from 0.3 to 2.0. The influencing parameters including the Lockhart–Martinelli parameter, the gas-to-liquid density ratio, the gas densiometric Froude number and the equivalent diameter ratio were studied. Then the correlations of the two-phase mass flow coefficient and the influencing parameters were proposed for the two V-Cone throttle devices and evaluated experimentally. The results show that the relative deviations of the correlations are less than ±5.0% and the average deviations of the correlations are 2.06% and 2.22% for the V-Cone throttle devices with the equivalent diameter ratio of 0.65 and 0.75, respectively. It can be concluded that the two-phase mass flow coefficient of the V-Cone throttle device is crucial for the development of the wet gas correlation.

Modeling of the double leakage and leakage spillage flows in axial flow compressors

A model to predict the double leakage and tip leakage leading edge spillage flows was developed. This model was combined by a TLV trajectory model and a TLV diameter model and formed as a function of compressor one-dimensional design parameters, i.e. the compressor massflow coefficient, ϕ and compressor loading coefficient, Ψ, and some critical blade geometrical parameters, i.e. blade solidity, σ, stagger angle, βS, blade chord length, C, and blade pitch length, S. By using this model, the double leakage and tip leakage leading edge spillage flow could be predicted even at the compressor preliminary design process. Considering the leading edge spillage flow usually indicates the inception of spike-type stall, i.e. the compressor is a tip critical design, this model could also be used as a tool to choose the critical design parameters for designers. At last, some experimental data from literature was used to validate the model and the results proved that the model was reliable.

Flow field simulation and establishment for mathematical models of flow area of spool valve with sloping U-shape notch machined by different methods

Precise function expression of the flow area for the sloping U-shape notch orifice versus the spool stroke was derived. The computational fluid dynamics was used to analyze the flow features of the sloping U-shape notch on the spool, such as mass flow rates, flow coefficients, efflux angles and steady state flow forces under different operating conditions. At last, the reliability of the mathematical model of the flow area for the sloping U-shape notch orifice on the spool was demonstrated by the comparison between the orifice area curve derived and the corresponding experimental data provided by the test. It is presented that the bottom arc of sloping U-shape notch (ABU) should not be omitted when it is required to accurately calculate the orifice area of ABU. Although the theoretical flow area of plain bottom sloping U-shape notch (PBU) is larger than that of ABU at the same opening, the simulated mass flow and experimental flow area of ABU are both larger than these of PBU at the same opening, while the simulated flow force of PBU is larger than that of ABU at the same opening. Therefore, it should be prior to adapt the ABU when designing the spool with proportional character.

Flow Control on a Thick Airfoil Using Suction Compared to Blowing

The effects of steady slot suction as a means of controlling separation on a blunt elliptical airfoil were investigated and compared to the effects of steady blowing applied to the same airfoil previously investigated. Slots whose width approaches 1% of the chord and are located downstream of the natural separation location generate the highest lift for a given dimensionless mass-flow coefficient . This holds true whether the flow separates near the leading edge due to high incidence or near the trailing edge due to the bluntness of the airfoil and is contrary to the observations made when blowing was used. Lift generated by suction through a moderately wide slot located downstream of the natural separation line depends only on , but if the slot is located upstream of the separation line it depends on Reynolds number as well. Contrary to separation control by blowing no deleterious effects were observed at low levels of suction regardless of the suction-slot location. Adding a wedge to the blunt trailing edge of this airfoil enhances the effectiveness of suction, whereas making blowing less effective at low momentum inputs thus increasing the gap between these two approaches to flow separation.

Simplified modeling analysis of mass flow characteristics in electronic expansion valve

A mass flow correlation was presented to predict mass flow coefficient in an EEV (electronic expansion valve) based on extensive experimental data for R22, R410A and R407c. Bernoulli equation for short orifice valve is modified by introducing expansion factor and the modified equation can well depict the behavior of fluid through EXV under linear, nonlinear and choked regions. Experimental analysis shows that the mass flow coefficient is dominantly influenced by EEV opening and subcooling value. Therefore, only the two parameters (EEV opening and subcooling) are used to develop the mass flow coefficient correlation. The flow coefficient predicted by polynomial fit in this paper shows a good agreement with experimental data for three datasets of R22, R410A and R407c and the relative errors are within 5% for 98% of experimental data.

Numerical and Test Investigation on an Aircraft Inlet Distortion

Subscale wind tunnel test of an aircraft vehicle is performed at different Mach number, mass-flow and angle of attack. CFD model, corrected by test results, is also presented to predict inlet performance and total pressure distortion. The result shows total pressure recovery decreases and distortion level rises when Mach number increases from subsonic to supersonic speed, AOA is negative and mass-flow value is too large or too small. Compared linear interpolation based on test result of discrete probes, numerical simulation has advantages in showing inlet flow field predicting actual surface distortion level in AIP plane. Swirl distortion is induced by vortex near the fuselage and adjustable ramp and can strengthen total pressure distortion in AIP at negative AOA. And appropriate suction mass-flow coefficient (1.7% to 3%) is beneficial for inlet performance and total pressure distortion control.

FLOW STREAMLINING FOR COOLING IMPROVEMENT IN VENTILATED BRAKE DISC USING CFD AS DESIGN TOOL

This paper presents experimental and Computational Fluids Dynamics (CFD) investigations of the flow and heat transfer in ventilated brake discs. The validation CFD model is done using the straight blade (baseline design) configuration with available experimental data. Development of an experiment rig with basic measuring devices and uncertainty calculation are discussed. Then, unidirectional racing blade configuration is then further focused on the improvement of the brake cooling using the similar numerical setting. Conventional and streamlined ventilated brake disc are simulated using commercial CFD software FLUENTTMand the parameters such as mass flow and heat transfer characteristics arecompared. The streamlined ventilated blade design shows a significant improvement in terms of the mass flow and heat transfer coefficient compared to the conventional unidirectional design. This improvement is only achieved with enhancing the aerodynamic characteristics of the internal passage blade and without any additional mass at the disc brake.

Drag minimization using active and passive flow control techniques

The objective of this paper is to appraise the practicability of weakening the shock wave and hereby reducing the wave drag in transonic flight regime using flow control devices such as two-dimensional contour bump, individual jet actuator, and also the hybrid control which includes both control devices together, and thereby to gain the desired improvements in aerodynamic performance of air-vehicle. To validate the numerical study, a natural laminar flow airfoil, Rae5243, is chosen and then comparisons with experimental data have been made before the optimization of flow control parameters. After validation study, an efficient gradient-based optimization technique is used to optimize 2D bump parameters including the length, the maximum height, the bump position via shock location, and the crest position via bump and also the jet actuation parameters such as mass flow coefficient, suction/blowing angle, actuation location over the upper surface of the airfoil. The process generally consists of using the simulation code to obtain a flow solution for given parameters and then search the optimum parameters to reduce the total drag of the airfoil via the optimizer. Most importantly, it is shown that, the optimization yields 3.94% decrease in the total drag and 5.03% increase in lift, varying the design parameters of active and passive control devices.

Optimization of Active/Passive Flow Control Parameters on Airfoils at Transonic Speeds

To improve aerodynamic performance, the active and passive flow control parameters are optimized in different combinations. The flow is simulated by solving the Navier–Stokes equations and a turbulence model. The active flow control is applied using flow suction or blowing on an airfoil, and its design variables are set to be the location and the angle of the suction/blowing port and the mass flow coefficient at this port. Airfoil surfaces are parameterized by using Bezier curves to optimize an airfoil shape in a passive way. To validate the computational methodology, successful comparisons have beenmadewith available data. A reel coded genetic algorithm is used in all optimization processes. For the demonstration problems considered herein, the best result is provided by the sequential optimization process, which results in 575.8% increment in aerodynamic performance, 183.76% increment in lift coefficient, and 68% decrease in drag coefficient.

Particle Swarm Optimization of Suction and Blowing on Airfoils at Transonic Speeds

To improve the aerodynamic performance, the control applied to the transonic flow past an airfoil is optimized. The flow is simulated by solving the Navier–Stokes equations and a turbulence model. The control is applied using flow suction or blowing on the airfoil surface. The design variables are set to be the location and the angle of the suction/blowingport and themassflowcoefficient at this port. To validate the computationalmethodology, successful comparisons have beenmadewith available experimental data. The focus of the present study is on the application of a selected design optimization methodology. Therefore, the particle swarm optimization algorithm is also validated by comparing its results with those from a more traditional approach: that is, a gradient-based method with sequential quadratic programming. It is observed that the aerodynamic performance is increased by over 20% as a result of optimizing the location, angle, and mass flow coefficient of the suction and blowing control ports on the airfoil surface at transonic speeds.

EXPERIMENTAL AND NUMERICAL INVESTIGATION OF HYPERSONIC JAWS INLET

In order to obtain the flow field characteristics and the influence of boundary layer, numerical simulations and wind tunnel tests are conducted for two streamline traced Jaws inlets at Mach number 7. The inlets are designed based on a flow field with 8-7 planar shock wave (the ramp in pitch plane is inclined at 8° to the free stream and in yaw plane is inclined at 7° to the free stream, yielding planar shocks). In the study, the static pressure distributions were measured and analyzed along the plane-symmetric centerline of the inlet with and without the boundary layer correction, respectively. Results show that boundary layer correction can obviously weaken the viscous influence to the inlet, increasing the mass flow coefficient and improving total pressure recovery.