Flow Friction Loss Research Articles

A novel oscillating flow cycle engine with characteristics of temperature glide heat addition and no regenerator for low-grade heat utilization

In oscillating flow cycle engines such as Stirling engines, nearly isothermal heat additions in heat exchangers will produce irreversibility losses during the heat transfer processes and the regenerator is indispensable and expensive. Thus, it reduces oscillating flow cycle engine’s economic attractions for low-grade heat utilization. In this work, three structures of one-way oscillating flow cycle engine are proposed for overcoming these problems. To assess the feasibility, one structure is chosen for analysis. Then, a one-dimensional computational fluid dynamic model considering various heat transfer and flow friction losses is developed. Based on the validated model, performance analysis is carried out. The temperature glide for heat absorption can reach up to 116 K and can be adjusted. The obtained maximum thermal efficiency is 7.79 %, 12 %, and 14.6 % respectively for low-grade heat’s inlet temperatures of 373 K, 423 K, and 473 K. Furthermore, the maximum specific work output for 1 kg/s hot water is 13.7 kW, 36.9 kW and 64.4 kW respectively at an inlet temperature of 373 K, 423 K, and 473 K, with corresponding maximum exergy efficiency of 42.8 %, 43.7 % and 41.1 % respectively. Thus, the results demonstrate that large temperature glide heat addition can be achieved, and a novel oscillating flow cycle engine without a regenerator is feasible and efficient.

Performance analysis of one-way oscillating flow cycle heat pump

One-way oscillating flow cycle heat pump offers potential benefits including temperature glide heat additions and high efficiency. However, effects of structural parameters on performance and the distributions of relevant losses have not been revealed because it is a novel cooling and heating technology. To address this, a one-dimensional computational fluid dynamic model with considering the heat transfer and flow friction losses is developed. At conditions of the upper cooling temperature of 243 K ∼ 273 K and heating temperature of 318 K, the simulation results reveal that the incomplete heat transfer conduction energy losses in heat exchangers are the main loss, and the losses in heat exchangers are much higher than those in regenerator. The comparisons between two novel heat pumps with temperature glide heat additions and isothermal heat additions respectively demonstrate that temperature glide heat additions can significantly reduce the incomplete heat transfer conduction energy losses in heat exchangers. The relative Carnot efficiencies of 83.27 % − 89.48 % are achieved in the novel heat pump. Analysis of effects of structural parameters on performance reveals that the cold heat exchanger’s tube diameter and the regenerator’s porosity are the main structural parameters that affects the relative Carnot efficiency. These findings offer insightful knowledge about one-way oscillating flow cycle heat pump, and demonstrate that this heat pump has huge potential as an alternative to vapor compression for cooling and heating.

Investigation on Fluid Flow Heat Transfer and Frictional Properties of Al2O3 Nanofluids Used in Shell and Tube Heat Exchanger

Nanofluids are generally utilized in providing cooling, lubrication phenomenon, and controlling the thermophysical properties of the working fluid. In this paper, nanoparticles of Al2O3 are added to the base fluid, which flows through the counterflow arrangement in a turbulent flow condition. The fluids employed are ethylbenzene and water, which have differing velocities on both the tube and the shell side of the cylinders. A shell tube-type heat exchanger is used to examine flow characteristics, friction loss, and energy transfer as they pertain to the transmission of thermal energy. The findings of the proposed method showed that the efficiency of a heat exchanger could be significantly improved by the number, direction, and spacing of baffles. With the inclusion of nanoparticles of 1% volume, the flow property, friction property, and heat transfer rate can be considerably improved. As a result, the Nusselt number and Peclet numbers have been increased to 261 and 9.14 E +5. For a mass flow rate of 0.5 kg/sec, the overall heat transfer coefficient has also been increased to a maximum value of 13464. The heat transfer rate of the present investigation with nanoparticle addition is 4.63% higher than the Dittus–Boelter correlation. The friction factor is also decreased by about 17.5% and 11.9% compared to the Gnielinski and Blasius correlation. The value of the friction factor for the present investigation was found to be 0.0376. It is hence revealed that a suitable proportion of nanoparticles along with the base fluids can make remarkable changes in heat transfer and flow behavior of the entire system.

Experimental and numerical analysis on vortex cavitation morphological characteristics in u-shape notch spool valve and the vortex cavitation coupled choked flow conditions

The u-shape notch of spool valve is usually combined with the other typical throttling notches to achieve proportional flowrate adjustments in practical hydraulic control applications. Due to the vacuum-suction nozzle-structural effect, u-shape notch is more likely for cavitation arising. Traditionally, notch throttling is based on the continuity and Bernoulli equation to explain the Harvey nuclei bubble flow from development to collapse, which is not entirely agreed with present proliferated large vapor vortex cavitation researches. In this paper, experimental and numerical analysis discuss the morphological characteristics of u-shape notch vortex cavitation and the choked flow issues caused by vortex cavitation. The large vapor vortex cavitation morphological reproduced by the Large Eddy Simulation (LES) model associated with the multi-phase cavitation model is very close to experimental observations. Further, based on the clear cavity entity obtained by simulation, it could be found that, as notch opening increases, the cavity starting position moves back and the cavity moves upward. And as pressure difference increases, the cavity length increases smoothly until critical pressure value, after which the length increases sharply and maintains in long length level. In addition, it seems that the normalized measurement manner of cavitation length could be proposed, if using local cavitation number dividing incipient cavitation as abscissa to measure the cavity length. Moreover, the cavitating flowrate equation is proposed considering the cavitation-induced serious choked flow problem. The vortex cavitation, especially its length, is assumed to represent intense enough notch vortex flow friction loss. Based on the added flow loss term, the classical flowrate equation is revised, according to which the cavitating flowrate could be predicted within the accuracy of 0.5–2.0%.

Experiments and mechanistic modeling of viscosity effect on a multistage ESP performance under viscous fluid flow

Assembled in series with multistage, Electrical Submersible Pumps (ESP) are widely used in offshore petroleum production due to the high production rate and efficiency. The hydraulic performance of ESPs is subjected to the fluid viscosity. High oil viscosity leads to the degradation of ESP boosting pressure compared to the catalog curves under water flow. In this paper, the influence of fluid viscosity on the performance of a 14-stage radial-type ESP under varying operational conditions, e.g. rotational speeds 1800–3500 r/min, viscosities 25–520 cP, was investigated. Numerical simulations were conducted on the same ESP model using a commercial Computational Fluid Dynamics (CFD) software. The simulated average pump head is comparable to the corresponding experimental data under different viscosities and rotational speeds with less than ±20% prediction error. A mechanistic model accounting for the viscosity effect on ESP boosting pressure is proposed based on the Euler head in a centrifugal pump. A conceptual best-match flowrate QBM is introduced, at which the impeller outlet flow direction matches the designed flow direction. The recirculation losses caused by the mismatch of velocity triangles and other head losses resulted from the flow direction change, friction loss and leakage flow etc., are included in the model. The comparison of model predicted pump head versus experimental measurements under viscous fluid flow conditions demonstrates good agreement. The overall prediction error is less than ±10%.

Combined APSO-ANN and APSO-ANFIS models for prediction of pressure loss in air-water two-phase slug flow in a horizontal pipeline

Abstract Prediction of air-water two-phase flow frictional pressure loss in pressurized tunnels and pipelines is essentially in the design of proper hydraulic structures and pump systems. In the present study artificial neural networks (ANN) and adaptive neuro-fuzzy inference system (ANFIS) are employed to predict pressure loss in air-water two-phase slug flow. Adaptive particle swarm optimization (APSO) is also applied to optimize the results of the ANN and ANFIS models. To predict the pressure loss in two-phase flow, the frictional pressure loss coefficient needs to be determined with respect to the effective dimensionless parameters including two-phase flow Froude and Weber numbers and the air concentration. Laboratory test results are used to determine and validate the findings of this study. The performances of the ANN-APSO and ANFIS-APSO models are compared with those of the ANN and ANFIS models. Different comparison criteria are used to evaluate the performances of developed models, suggesting that all the models successfully determine the air-water two-phase slug flow pressure loss coefficient. However, the ANFIS-APSO performs better than other models. Good agreement is obtained between estimated and measured values, indicating that the APSO with a conjugated ANFIS model successfully estimates the air-water two-phase slug flow pressure loss coefficient as a complex hydraulic problem. Results suggest that the proposed models are more accurate compared to former empirical correlations in the literature.

Valve Location Method for Evaluating Drain Efficiency in Water Transmission Pipelines

Water transmission pipelines, which transport bulk water into storage facilities, usually have a tree-type configuration with large dimensions; thus, the breakage of a pipeline may cause a catastrophic service interruption to customers. Although drain efficiency is closely related to the number of washout and control valves and their locations, there is no useful guideline. This paper proposes a valve locating method by introducing numerical analyses to enumerate drainage time and zone. A time integration method, combined with the Newton–Raphson algorithm, is suggested to resolve drainage time, while considering the friction loss in gravitational flow. A drain direction matrix, which shows drain direction and coverage, is derived using a network searching algorithm. Furthermore, a feasible practical approach is presented by introducing a critical horizontal slope, a major washout valve, drainage indices, and control valve embedment. The developed method is first applied to simple pipes to validate the drainage time module. Subsequently, the model is expanded to the CY transmission line, which is one of the BR water supply systems in South Korea currently in operation. The results reveal that three drain valve locations have been neglected, and the addition of control valves guarantees consistent drain time below the operational criteria.

General Correlations for Laminar Flow Friction Loss and Heat Transfer in Plain Rectangular Plate-Fin Cores

Abstract New generalized correlations for predicting the average fanning friction factor f and average Nusselt number Nu for laminar flow in plain plate-fin compact cores of rectangular cross section are presented. These are based on extended experimental data, as well as three-dimensional computational simulations, obtained for a broad range of fin density and geometrical attributes. The results indicate that while the fully developed forced convection scales only with the interfin channel cross-sectional ratio α (fin spacing by fin height), the entrance region hydrodynamic and thermal performance is additionally a function of the fin-core length L, flow Reynolds number Re, and fluid Prandtl number Pr. The developing flow and convection is further shown to scale as: (fRe)∼(L/dhRe)1/2, and Nu ∼(L/dhRe)1/2Pr1/3ϕ(α), where f, Re, and Nu are all based on the hydraulic diameter dh of the interfin flow channel. Generalized correlations for both (fRe) and Nu are developed by the corresponding scaling of the forced convection behavior and asymptotic matching of the entrance or developing flow (short fin-core flow length) and the fully developed flow (large fin-core flow length) region performance. Finally, the predictions from these correlations are found to be within ±15% of all available experimental data for air, water, and glycol (0.71 ≤ Pr ≤ 10), and fin cores with 0 < α ≤ 1.

Estimation of opening discharge coefficient of naturally ventilated dairy buildings by response surface methodology

The discharge coefficient (Cd) is a characteristic parameter of an opening, which represents the effect of flow contraction and frictional losses when the flow goes across the opening. It is an important parameter for the ventilation rate determination when using the orifice equation method. The objectives of this study were to investigate the relationship between Cd and its potential influencing factors, i.e. opening ratio (r), building length to width ratio (α), wind speed (U), and wind direction (θ), and to evaluate the sensitivity of each factor on the Cd for naturally ventilated dairy buildings (NVDBs). The investigations were performed using the response surface methodology together with Box-Behnken Design and Computational Fluid Dynamics simulation methods. A second-order polynomial response surface model for the estimation of the discharge coefficient was developed and verified. The results showed that the Cd was significantly affected by the individual factors of r and θ, with more sensitivity to r when r > 42.5%. By contrast, the effects from the individual factors of α and U on Cd were insignificant. In addition, the interaction effects between r and θ, and between α and θ on Cd were also identified. It was concluded that the effects from both individual factors and interactions are required to be considered in the estimation of the opening discharge coefficient for NVDBs.

Effect of molten salt properties on internal flow and disk friction loss of molten salt pump

Computational fluid dynamics is used to study the effect of temperature on flow structure and disk friction loss for different working fluids in a high temperature molten salt pump, which is used for concentrating solar power, the velocity profile and pressure distribution in the first stage of the pump model and the effect of the fluid property on the ring leakage, disk friction loss as well as the shear stress distribution on shroud are analyzed for the pure water and the molten salt with temperature 300?C and 565?C respectively. The main findings can be concluded as: the working fluids have little effect on pump performance and internal velocity distribution whereas the pressure of the flow field would increase with the fluid density, with the increase of the fluid viscosity, the shear stress inside the ring also increases and the total leakage can be eliminated evidently, the increase of the fluid density and viscosity show the significant responsibility for the disk friction loss, in which the fluid viscosity also increases the disk friction loss, and the viscosity is one of the most influential factors for the shroud shear stress and it can be observed that the shear stress on front shroud is higher than that on the rear shroud. It is believed that the present work can deep the understandings of the fluid structures inside the molten salt pump, which can provide some guidelines to improve the pump performance and optimize the pump structure.

Frictional pressure losses of Non-Newtonian fluids in helical pipes: Applications for automated rheology measurements

Frequent and accurate drilling fluid measurements are critical to optimum well construction. Proper management of drilling fluid properties such as density and rheology optimizes the fluid's hydraulic and hole cleaning ability while maintaining the fluid in its role as primary well control barrier. In current practice, these measurements are typically done only once or twice a day using the methods described by American Petroleum Institute (API) standards. Moreover, taking the measurements is labor-intensive, and the data quality and reliability are highly dependent on the practicing engineer. An automated, continuous, and practical way of measuring and monitoring drilling fluid properties is therefore needed.In this paper, we introduce a novel helical pipe viscometer system for automated and continuous drilling fluid measurements. A flow-loop was constructed to measure frictional pressure losses of aqueous solutions with various concentrations of xanthan gum in water, generating a non-Newtonian fluid that is best described by a Yield-Power Law (YPL) rheological model. Flow tests were performed simultaneously in two straight- and two helical-pipe test-sections. Flow rate, density, and temperature data were obtained using a Coriolis flow meter. Pressure loss data was obtained using side by side differential pressure measurements from each test-section.A delayed transition to turbulent flow and elevated frictional pressure losses was observed in the experiments with the curved pipes. This is attributed to secondary flow driven by centrifugal forces in the helical pipe system. The results of the experimental data were compiled and used to build an empirical correlation for friction factor predictions using the Dean number. CFD analyses were also performed to validate the accuracy of pressure loss measurements and to obtain a better understanding of the helical velocity profiles. The proposed equation was compared with theoretical equations previously reported in the literature. The results from the analyses show that the equations previously derived for Newtonian and Power Law (PL) fluids are not applicable to YPL fluids in the tested geometries.An algorithm was developed and tested using the experimental data to prove the applicability of the helical system for rheological property calculations. Good accuracy was observed in mud rheology characterization tests. The helical system, which can be fully automated, provides significant practical advantages over standard linear pipe viscometers by offering improved accuracy and smaller footprint. The results of the study are also of importance for the hydraulic design and evaluation of coiled tubing drilling and well completion operations, where the pressure loss is a limiting factor for the maximum flow rate that can be used in such operations.

Thermal-hydraulic Performance Analysis of Corrugated Plate Heat Exchanger

Plate heat exchangers (PHEs) have been getting popularity in industries due to their low cost, high heat transfer efficiency and operational flexibility. Heat transfer enhancement could be achieved by using the PHE with corrugated plate configuration, which provides additional heat transfer area and increased turbulence in fluid flow. This work explored how complex corrugated plates with different chevron angles, channel depth and pitch in multi-segmented configuration could further improve thermal-hydraulic performance of the PHE. Water was used as the heat transfer fluid. Key geometrical parameters were first identified as different chevron angles (βhigh and βlow), corrugation aspect ratio (γ) and number of plate segments (NS). Then, thermal-hydraulic models for the PHE with a wide range of corrugation geometries have been proposed and validated. These models could accurately estimate heat transfer and flow friction loss of the PHE with different plate corrugation structures and provide deep insight into the influence of the corrugation geometries. They could be applied as a guide in PHE design, operational optimization and heat transfer network retrofit in industries.

Comparison of flow field and combustion in single and double side ported rotary engine

Intake and exhaust ports have great importance on performance of the rotary engines, since flow structure of the combustion chamber is depended on position and geometry of these ports. Similar to reciprocating engines that have different in-flow patterns according to valve characteristics of the engine, the flow patterns inside the combustion chamber change according to port position, quantity and channel geometry of rotary engines. In this study, air flow inside a double-side-ported rotary engine including 4 inlet and 2 exhaust ports with ports was numerically investigated by using computational fluid dynamic techniques. Numerical flow field results were compared with experimental data presented in the literature. Change of volumetric efficiency according to engine speed and flow field data were obtained for different port combinations. The results reveal that swirl and tumble motions are together formed in one side-ported engine simulations. When double-sided-ports are used, tumble motion is prevented by opposing air flow. Results show that double side intake port configuration has highest volumetric efficiency up to 8000 rpm. Single side intake port configuration has high volumetric efficiency up to 3000 rpm and it deteriorates rapidly after 3000 rpm because of high flow frictional losses. For all configurations, it is observed that rotating flows are prevailed by rotor motion at end of compression period and almost similar flow patterns are formed when rotor reaches at top dead center. After obtaining flow field results, combustion of single and double port intake configurations were compared with each other.

Investigation of Discharge Coefficients for Single Element Lean Direct Injection Modules

Lean direct injection (LDI) combustion has a high potential as a low pollution combustion method for gas turbines. The present research aims to further investigate the discharge coefficient of an LDI module, axial swirler and convergent outlet under non-reaction and reaction conditions by theoretical, numerical and experimental methods. The functional relationship between the discharge coefficient of the LDI module, axial swirler and convergent outlet was established, and the effect of swirl angle (30°, 32°, 34°, 36°, 38°, 40°) and vane number (11, 12, 13, 14, 15, 16) on discharge coefficient was studied, and finally the differences in effective flow area of LDI combustor under different inlet conditions were analyzed. The results indicate that the flow separation on the suction side increases as the swirl angle increases, which leads to a decrease of the discharge coefficient of the axial swirler, however the discharge coefficient of the convergent outlet remains unchanged first and then decreases. As the vane number increases, the flow separation on the suction side decreases and the flow friction loss increases, so that the discharge coefficient of the axial swirler and convergent outlet will first increase with the increase of vane number and then decrease with further increases. The effective flow area of combustor changes as the conditions change, but it is approximately equal under high power conditions and normal temperature and pressure conditions.

Aerodynamics and Heat Transfer over Solid-Deflectors in Transverse, Staggered, Corrugated-Upstream and Corrugated-Downstream Patterns

Computational fluid dynamic simulations were conducted to analysis the influences of two different deflector orientations on turbulent forced-convection flow and skin friction loss of two-dimensional horizontal rectangular cross section channels with upper and lower wall-attached corrugated baffles. The governing flow equations, i.e., continuity, momentum, and energy, were numerically solved by the Finite Volume Method (FVM) using the Semi-Implicit Method for Pressure Linked Equation (SIMPLE) discretization formulation. The help of the CFD code FLUENT was employed to solve the dynamic and thermal behavior of air in the whole domain under investigation. The flow rate in terms of Reynolds number is ranged from 5,000 to 32,000. The obtained results show that augmenting the Reynolds number makes the dynamic thermo energy field redirect in the vicinity of deflector corners, and forces an augmentation in the thermal transfer rate from baffles.

Research on Annular Frictional Pressure Loss of Hydraulic-Fracturing in Buckling Coiled Tubing

Compared with conventional hydraulic fracturing, coiled tubing (CT) annular delivery sand fracturing technology is a new method to enhance the recovery ratio of low permeability reservoir. Friction pressure loss through CT has been a concern in fracturing. The small diameter of CT limits the cross-sectional area open to flow, therefore, to meet large discharge capacity, annular delivery sand technology has been gradually developed in oilfield. Friction pressure is useful for determining the required pump horsepower and fracturing construction design programs. Coiled tubing can buckle when the axial compressive load acting on the tubing is greater than critical buckling load, then the geometry shape of annular will change. Annular friction pressure loss elevates dramatically with increasing of discharge capacity, especially eccentricity and CT buckling. Despite the frequency occurrence of CT buckling in oilfield operations, traditionally annular flow frictional pressure loss considered concentric and eccentric annuli, not discussing the effects of for discharge capacity and sand ratio varying degree of CT buckling. The measured data shows that the factors mentioned above cannot be ignored in the prediction of annular pressure loss. It is necessary to carry out analysis of annulus flow pressure drop loss in coiled tubing annular with the methods of theoretical analysis and numerical simulation. Coiled tubing buckling has great influence on pressure loss of fracturing fluid. Therefore, the correlations have been developed for turbulent flow of Newtonian fluids and Two-phase flow (sand-liquid), and that improve the friction pressure loss estimation in coiled tubing operations involving a considerable level of buckling. Quartz sand evidently increases pressure loss in buckling annular, rising as high as 40%-60% more than fresh water. Meanwhile, annulus flow wetted perimeter increases with decreasing helical buckling pitch of coiled tubing, therefore, the annulus flow frictional pressure loss rapidly increases with decreasing helical buckling pitch. The research achievement provides theoretical guidance for coiled tubing annular delivery sand fracturing operation and design.

An experimental study of the characteristics of hydrostatic transmission systems

In the field of robotics, mechanical power transmission systems are fundamental and critical components. In recent years, hydrostatic transmission systems (HSTs) have begun to receive attention as power transmission systems for robotic applications. The primary goal of this study is to identify the inherent properties of HSTs. In this article, we first introduce experimental methods for determining the characteristics of HSTs and then discuss the experimental results. Our findings from the experiments suggest that the commercial external gear pump in an HST cannot entirely convert mechanical power to hydraulic power because of its internal leakage and friction behavior. These physical behaviors are mathematically modeled and experimentally identified. It is also found that a long transmission line not only results in low-pressure rise rates but also flow friction loss. We strongly believe that the results discussed in this article will provide helpful guidance for the design and control of robotic systems.

Thermodynamic Analysis of a Waste Heat Driven Vuilleumier Cycle Heat Pump

A Vuilleumier (VM) cycle heat pump is a closed gas cycle driven by heat energy. It has the highest performance among all known heat driven technologies. In this paper, two thermodynamic analyses, including energy and exergy analysis, are carried out to evaluate the application of a VM cycle heat pump for waste heat utilization. For a prototype VM cycle heat pump, equations for theoretical and actual cycles are established. Under the given conditions, the exergy efficiency for the theoretical cycle is 0.23 compared to 0.15 for the actual cycle. This is due to losses taking place in the actual cycle. Reheat losses and flow friction losses account for almost 83% of the total losses. Investigation of the effect of heat source temperature, cycle pressure and speed on the exergy efficiency indicate that the low temperature waste heat is a suitable heat source for a VM cycle heat pump. The selected cycle pressure should be higher than 100 MPa, and 200–300 rpm is the optimum speed.

Analysis on the heat transfer characteristics of a micro-channel type porous-sheets Stirling regenerator

To avoid the high flow frictional loss associated with conventional wire mesh Stirling regenerators, a micro-channel type stacked porous-sheets Stirling regenerator is investigated. An analytical solution is derived for the transient heat transfer characteristics of the fully developed reciprocating laminar flow under prescribed wall temperature profiles. The complex Nusselt number (Nu) is expressed as a function of kinetic Reynolds number (Reω) and Prandtl number (Pr). At low Reω of less than 10, the real part of Nu has an almost constant value of 6.0, approximately equal to the known real-valued Nu for the fully developed unidirectional laminar flow under constant wall heat flux, while the imaginary part is negligible, thus “scaling effect” can be utilized to enhance heat transfer. At higher Reω, both the real and imaginary parts of Nu increase with the increase of Reω and Pr, and the phase shift between the temperature difference and the heat flux gradually increases and approaches 45°. Approximate analytical solutions are also deduced for the entrance region from the integral boundary layer equations in both cases of “Thermally developing flow” and “Simultaneously developing flow”. The heat transfer is enhanced in the entrance region and the local Nu in the flow direction approaches the corresponding values of fully developed flow. The analytical results are confirmed by dynamic mesh CFD results, and the obtained Nu∼ Reω data and patterns generally agree with available analytical and experimental data from published literatures. Application of the analytical results to the design and optimization of Stirling regenerator are also shown.

Study on Low Flow Rate Operating Characteristics of Hot Waxy Crude Oil Pipelines Based on an Unsteady-State Calculation Method

Hot crude oil pipeline operated at low flow rate might work in an unstable state, where the friction loss continuously increases with the decreasing flow rate. This will lead to harmful flow stagnation and needs proper management. In this paper, the unsteady-state thermal-hydraulic behavior of the coupled pipeline-pump system is investigated by adopting an unsteady-state numerical model instead of the traditional steady-state model. The new model considers the impacts of the heating strategies, initial operating conditions, and pump characteristics on the pipeline characteristics at low flow rate. Through obtaining the transient characteristics of the flow rate and friction loss, the stable and unstable working ranges are distinguished and critical flow rate is calculated. It is shown that the transient characteristics at low flow rate can be classified into three categories. (1) The flow rate keeps constant for the initial period and then decreases continuously while the friction loss increases monotonously. (2) The flow rate is constant while the friction loss increases firstly and then stays stable. (3) The flow rate maintains constancy while the friction loss increases firstly and then decreases to a final stable level. Besides, it can be concluded that the critical flow rate calculated by the unsteady-state method is recommended with preheating before the flow rate drop.