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Viewing 121 to 150 of 24523
2017-03-28
Technical Paper
2017-01-1725
Tanawat Tessathan, Chutiphon Thammasiri, Prabhath De Silva, Rehan Hussain, Nuksit Noomwongs
Abstract It is common for users of commuting passenger cars in Thailand to use the vehicle’s HVAC (Heating, Ventilating and Air Conditioning) system predominantly in recirculation (REC) mode. This minimizes the compressor work, thereby saving fuel, and reduces dust and odor infiltration into the vehicle cabin. The car windows are rarely opened for ventilation purposes, except for exchanges at service stations such as garage entrances and tollway booths. As such, there are few opportunities for fresh air to enter the cabin with the consequent accumulation of CO2 in vehicle cabins due to occupants’ exhalations being well documented. Field experiments conducted showed that the in-vehicle CO2 concentrations could reach up to 15 times that of the ambient concentration level during typical city commutes. Preliminary experiments were also conducted to quantify the air exchanges between the cabin and the ambient when the doors are opened for occupant egression.
2017-03-28
Technical Paper
2017-01-1721
Ho Teng, Ruigang Miao, Liming Cao, Xuwei Luo, Tingjun Hu, Min Wu
Abstract In order to improve low speed torques, turbocharged gasoline direct injection (TGDI) engines often employ scavenging with a help of variable valve timing (VVT) controlled by the cam phasers. Scavenging improves the compressor performance at low flows and boosts low-speed-end torques of the engines. Characteristics of the engine combustion in the scavenging zone were studied with a highly-boosted 1.5L TGDI engine experimentally. It was found that the scavenging zone was associated with the highest blowby rates on the engine map. The blowby recirculation was with heavy oil loading, causing considerable hydrocarbon fouling on the intake ports as well as on the stem and the back of the intake valves after the engine was operated in this zone for a certain period of time. The low-speed pre-ignition (LSPI) events observed in the engine tests fell mainly in the scavenging zone.
2017-03-28
Technical Paper
2017-01-0382
Oscar Hernandez Cervantes, Antonio Espiritu Santo Rincon
Abstract The development of an automatic control system for a towing dynamometer used for testing is described in this paper. The process involved the deployment of new power electronics circuit boards, a TELMA retarder, instrumentation and a human machine interface (HMI) achieved through an open source platform. The purpose of this platform is to have a low cost system that allows further function development, data acquisition and communication with other devices. This system is intended as a novel solution that will allow closed loop and automated tests integrated with PCM data for engine calibration. It is projected to be part of a flexible calibration system with direct communication to the interfaces used during development (ATI, ETAS), which will be used to achieve lean test and development schedules.
2017-03-28
Journal Article
2017-01-0647
Bradley Denton, Christopher Chadwell, Raphael Gukelberger, Terrence Alger
Abstract The Dedicated EGR (D-EGR®) engine has shown improved efficiency and emissions while minimizing the challenges of traditional cooled EGR. The concept combines the benefits of cooled EGR with additional improvements resulting from in-cylinder fuel reformation. The fuel reformation takes place in the dedicated cylinder, which is also responsible for producing the diluents for the engine (EGR). The D-EGR system does present its own set of challenges. Because only one out of four cylinders is providing all of the dilution and reformate for the engine, there are three “missing” EGR pulses and problems with EGR distribution to all 4 cylinders exist. In testing, distribution problems were realized which led to poor engine operation. To address these spatial and temporal mixing challenges, a distribution mixer was developed and tested which improved cylinder-to-cylinder and cycle-to-cycle variation of EGR rate through improved EGR distribution.
2017-03-28
Journal Article
2017-01-0648
Dennis Robertson, Christopher Chadwell, Terrence Alger, Jacob Zuehl, Raphael Gukelberger, Bradley Denton, Ian Smith
Abstract Dedicated EGR (D-EGR) is an EGR strategy that uses in-cylinder reformation to improve fuel economy and reduce emissions. The entire exhaust of a sub-group of power cylinders (dedicated cylinders) is routed directly into the intake. These cylinders are run fuel-rich, producing H2 and CO (reformate), with the potential to improve combustion stability, knock tolerance and burn duration. A 2.0 L turbocharged D-EGR engine was packaged into a 2012 Buick Regal and evaluated on drive cycle performance. City and highway fuel consumption were reduced by 13% and 9%, respectively. NOx + NMOG were 31 mg/mile, well below the Tier 2 Bin 5 limit and just outside the Tier 3 Bin 30 limit (30 mg/mile).
2017-03-28
Journal Article
2017-01-0052
Andre Kohn, Rolf Schneider, Antonio Vilela, Udo Dannebaum, Andreas Herkersdorf
Abstract A main challenge when developing next generation architectures for automated driving ECUs is to guarantee reliable functionality. Today’s fail safe systems will not be able to handle electronic failures due to the missing “mechanical” fallback or the intervening driver. This means, fail operational based on redundancy is an essential part for improving the functional safety, especially in safety-related braking and steering systems. The 2-out-of-2 Diagnostic Fail Safe (2oo2DFS) system is a promising approach to realize redundancy with manageable costs. In this contribution, we evaluate the reliability of this concept for a symmetric and an asymmetric Electronic Power Steering (EPS) ECU. For this, we use a Markov chain model as a typical method for analyzing the reliability and Mean Time To Failure (MTTF) in majority redundancy approaches. As a basis, the failure rates of the used components and the microcontroller are considered.
2017-03-28
Journal Article
2017-01-0246
Sentao Miao, Xiuli Chao, Michael Tamor, Yan Fu, Margaret Strumolo
Abstract Over half of the greenhouse gas (GHG) emissions in the United States come from the transportation and electricity generation sectors. To analyze the potential impact of cross-sector cooperation in reducing these emissions, we formulate a bi-level optimization model where the transportation sector can purchase renewable energy certificates (REC) from the electricity generation sector. These RECs are used to offset emissions from transportation in lieu of deploying high-cost fuel efficient technologies. The electricity generation sector creates RECs by producing additional energy from renewable sources. This additional renewable capacity is financed by the transportation sector and it does not impose additional cost on the electricity generation sector. Our results show that such a REC purchasing regime significantly reduces the cost to society of reducing GHG emissions. Additionally, our results indicate that a REC purchasing policy can create electricity beyond actual demand.
2017-03-28
Technical Paper
2017-01-0179
Saravanan Sambandan, Manuel Valencia, Sathish Kumar S
Abstract In an automotive air-conditioning (AC) system, the heater system plays a major role during winter condition to provide passenger comforts as well as to clear windshield defogging and defrost. In order to meet the customer satisfaction the heater system shall be tested physically in severe cold conditions to meet the objective performance in wind tunnel and also subjective performance in cold weather regions by conducting on road trials. This performance test is conducted in later stage of the program development, since the prototype or tooled up parts will not be available at initial program stage. The significance of conducting the virtual simulation is to predict the performance of the HVAC (Heating ventilating air-conditioning) system at early design stage. In this paper the development of 1D (One dimensional) model with floor duct systems and vehicle cabin model is studied to predict the performance. Analysis is carried out using commercial 1D simulation tool KULI®.
2017-03-28
Technical Paper
2017-01-0169
Ward J. Atkinson, William Raymond Hill, Gursaran D. Mathur
Abstract The EPA has issued regulations in the Final Rulemaking for 2017-2025 Light-Duty Vehicle Greenhouse Gas Emission Standards and Corporate Average Fuel Economy Standards (420r12901-3). This document provides credits against the fuel economy regulations for various Air Conditioning technologies. One of these credits is associated with increased use of recirculation air mode, when the ambient is over 24°C (75°F.). The authors want to communicate the experiences in their careers that highlighted issues with air quality in the interior of the vehicle cabin. Cabin contamination sources may result in safety and health issues for both younger and older drivers. Alertness concerns may hinder their ability to operate a vehicle safely.
2017-03-28
Technical Paper
2017-01-0163
Gursaran D. Mathur
The author has developed a model that can be used to predict build-up of cabin carbon dioxide levels for automobiles based on many variables. There are a number of parameters including number of occupants that dictates generation of CO2 within the control volume, cabin leakage (infiltration or exfiltration) characteristics, cabin volume, blower position or airflow rate; vehicle age, etc. Details of the analysis is presented in the paper. Finally, the developed model has been validated with experimental data. The simulated data follows the same trend and matches fairly well with the experimental data.
2017-03-28
Technical Paper
2017-01-0160
Longjie Xiao, Tianming He, Gangfeng Tan, Bo Huang, Xianyao Ping
Abstract While the car ownership increasing all over the world, the unutilized thermal energy in automobile exhaust system is gradually being realized and valued by researchers around the world for better driving energy efficiency. For the unexpected urban traffic, the frequent start and stop processes as well as the acceleration and deceleration lead to the temperature fluctuation of the exhaust gas, which means the unstable hot-end temperature of the thermoelectric module generator (TEG). By arranging the heat conduction oil circulation at the hot end, the hot-end temperature’s fluctuation of the TEG can be effectively reduced, at the expense of larger system size and additional energy supply for the circulation. This research improves the TEG hot-end temperature stability by installing solid heat capacity material(SHCM) to the area between the outer wall of the exhaust pipe and the TEG, which has the merits of simple structure, none energy consumption and light weight.
2017-03-28
Technical Paper
2017-01-0154
Sudhi Uppuluri, Hemant R Khalane, Ajay Naiknaware
Abstract With the upcoming regulations for fuel economy and emissions, there is a significant interest among vehicle OEMs and fleet managers in developing computational methodologies to help understand the influence and interactions of various key parameters on Fuel Economy and carbon dioxide emissions. The analysis of the vehicle as a complete system enables designers to understand the local and global effects of various technologies that can be employed for fuel economy and emission improvement. In addition, there is a particular interest in not only quantifying the benefit over standard duty-cycles but also for real world driving conditions. The present study investigates impact of exhaust heat recovery system (EHRS) on a typical 1.2L naturally aspirated gasoline engine passenger car representative of the India market.
2017-03-28
Technical Paper
2017-01-0141
Ray Host, Peter Moilanen, Marcus Fried, Bhageerath Bogi
Abstract Future vehicle North American emissions standards (e.g., North American Tier 3 Bin 30 or LEVIII SULEV 30) require the exhaust catalyst to be greater than 80% efficient by 20 seconds after the engine has been started in the Federal Test Procedure. Turbocharged engines are especially challenged to deliver fast catalyst light-off since the presence of the turbocharger in the exhaust flow path significantly increases exhaust system heat losses. A solution to delivering cost effective SULEV 30 emissions in turbocharged engines is to achieve fast catalyst light-off by reducing exhaust system heat losses in cold start, without increasing catalyst thermal degradation during high load operation. A CAE methodology to assess the thermal performance of exhaust system hardware options, from the exhaust port to the catalyst brick face is described, which enables compliance with future emissions regulations.
2017-03-28
Technical Paper
2017-01-0135
Jose Grande, Julio Abraham Carrera, Manuel Dieguez Sr
Abstract Exhaust Gas Recirculation (EGR) is an effective technique for reducing NOx emissions in order to achieve the ever more stringent emissions standards. This system is widely used in commercial vehicle engines in which thermal loads and durability are a critical issue. In addition, the development deadlines of the new engine generations are being considerably reduced, especially for validation test phase in which customers usually require robust parts for engine validation in the first stages of the project. Some of the most critical issues in this initial phases of program development are heavy boiling and thermal fatigue. Consequently it has been necessary to develop a procedure for designing EGR coolers that are sufficiently robust against heavy boiling and thermal fatigue in a short period of time, even when the engine calibration is not finished and the working conditions of the EGR system are not completely defined.
2017-03-28
Technical Paper
2017-01-0123
Saiful Bari
Abstract In general, diesel engines have an efficiency of about 35% and hence, a considerable amount of energy is expelled to the ambient air. In water-cooled engines, about 25%, 33% and 7% of the input energy are wasted in the coolant, exhaust gas, and friction, respectively. The heat from the exhaust gas of diesel engines can be an important heat source to provide additional power and improve overall engine efficiency. Studies related to the application of recoverable heat to produce additional power in medium capacity diesel engines (< 100 kW) using separate Rankine cycle are scarce. To recover heat from the exhaust of the engine, an efficient heat exchanger is necessary. For this type of application, the heat exchangers are needed to be designed in such a way that it can handle the heat load with reasonable size, weight and pressure drop. This paper describes the study of a diesel generator-set attached with an exhaust heat recovery system.
2017-03-28
Technical Paper
2017-01-0127
Norimitsu Matsudaira, Mitsuru Iwasaki, Junichiro Hara, Tomohiko Furuhata, Tatsuya Arai, Yasuo Moriyoshi, Naohiro Hasegawa
Abstract Among the emerging technologies in order to meet ever stringent emission and fuel consumption regulations, Exhaust Gas Recirculation (EGR) system is becoming one of the prerequisites particularly for diesel engines. Although EGR cooler is considered to be an effective measure for further performance enhancement, exhaust gas soot deposition may cause degradation of the cooling. To address this issue, the authors studied the visualization of the soot deposition and removal phenomena to understand its behavior. Based on thermophoresis theory, which indicates that the effect of thermophoresis depends on the temperature difference between the gas and the wall surface exposed to the gas, a visualization method using a heated glass window was developed. By using glass with the transparent conductive oxide: tin-doped indium oxide, temperature of the heated glass surface is raised.
2017-03-28
Technical Paper
2017-01-0091
Songyao Zhou, Gangfeng Tan, Kangping Ji, Renjie Zhou, Hao Liu
Abstract The mountainous roads are rugged and complex, so that the driver can not make accurate judgments on dangerous road conditions. In addition, most heavy vehicles have characteristics of large weight and high center of gravity. The two factors above have caused most of the car accidents in mountain areas. A research shows that 90% of car accidents can be avoided if drivers can respond within 2-3 seconds before the accidents happen. This paper proposes a speed warning scheme for heavy-duty vehicle over the horizon in mountainous area, which can give the drivers enough time to respond to the danger. In the early warning aspect, this system combines the front road information, the vehicle characteristics and real-time information obtained from the vehicle, calculates and forecasts the danger that may happen over the horizon ahead of time, and prompts the driver to control the vehicle speed.
2017-03-28
Technical Paper
2017-01-0084
Jiantao Wang, Bo Yang, Jialiang Liu, Kangping Ji, Qilu Wang
Abstract Studies show that driving in foggy environment is a security risk, and when driving in foggy environment, the drivers are easy to accelerate unconsciously. The safety information prompted to the driver is mainly from fog lights, road warning signs and the traffic radio. In order to increase the quality of the safety tips to prevent drivers from unintended acceleration and ensure the security of driving in foggy environment, the study proposes a safety speed assessment method for driving in foggy environment, combining the information of driving environment, vehicle’s speed and the multimedia system. The method uses camera which is installed on the front windshield pillar to collect the image about the environment, and uses the dark channel prior theory to calculate the visibility. And by using the environment visibility, the safety speed can be calculated based on the kinematics theory. And it is appropriate for vehicles which have different braking performance.
2017-03-28
Technical Paper
2017-01-0447
Zhe Li, Mike Dong, Dennis Harrigan, Michael Gardner
In gasoline Powertrain systems, the evaporative emission control (EVAP) system canister purge valve (CPV) can be actuated by pulse-width modulated (PWM) signals. The CPV is an electronically actuated solenoid. The PWM controlled CPV, when actuated, creates pressure pulsations in the system. This pulsation is sent back to the rest of the EVAP system. Given the right conditions, the fill limit vent valve (FLVV) inside the fuel tank can be excited. The FLVV internal components can be excited and produce noise. This noise can be objectionable to the occupants. Additional components within the EVAP system may also be excited in a similar way. This paper presents a bench test method using parts from vehicle’s EVAP system and other key fuel system components.
2017-03-28
Journal Article
2017-01-1639
Gerard W. Malaczynski, Gregory Roth
Abstract Onboard diagnostic regulations require performance monitoring of diesel particulate filters used in vehicle aftertreatment systems. Delphi has developed a particulate matter (PM) sensor to perform this function. The objective of this sensor is to monitor the soot (PM) concentration in the exhaust downstream of the diesel particulate filter which provides a means to calculate filter efficiency. The particulate matter sensor monitors the deposition of soot on its internal sensing element by measuring the resistance of the deposit. Correlations are established between the soot resistance and soot mass deposited on the sensing element. Currently, the sensor provides the time interval between sensor regeneration cycles, which, with the knowledge of the exhaust gas flow parameters, is correlated to the average soot concentration.
2017-03-28
Technical Paper
2017-01-1400
Keyu Qian, Gangfeng Tan, Renjie Zhou, Binyu Mei, Wanyang XIA
Abstract Downhill mountain roads are the accident prone sections because of their complexity and variety. Drivers rely more on driving experience and it is very easy to cause traffic accidents due to the negligence or the judgment failure. Traditional active safety systems, such as ABS, having subjecting to the driver's visual feedback, can’t fully guarantee the downhill driving safety in complex terrain environments. To enhance the safety of vehicles in the downhill, this study combines the characteristics of vehicle dynamics and the geographic information. Thus, through which the drivers could obtain the safety speed specified for his/her vehicle in the given downhill terrains and operate in advance to reduce traffic accidents due to driver's judgment failure and avoid the brake overheating and enhance the safety of vehicles in the downhill.
2017-03-28
Technical Paper
2017-01-1444
Mitali Chakrabarti, Alfredo Perez Montiel, Israel Corrilo, Jing He, Angelo Patti, James Gebbie, Loren Lohmeyer, Bernd Dienhart, Klaus Schuermanns
CO2 is an alternative to replace the conventional refrigerant (R134a) for the air-conditioning system, due to the high Global Warming Potential (GWP) of R134a. There are concerns with the use of CO2 as a refrigerant due to health risks associated with exposure to CO2, if the concentration of CO2 is over the acceptable threshold. For applications with CO2 as the refrigerant, the risk of CO2 exposure is increased due to the possibility of CO2 leakage into the cabin through the duct system; this CO2 is in addition to the CO2 generated from the respiration of the occupants. The initiation of the leak could be due to a crash event or a malfunction of the refrigerant system. In an automobile, where the interior cabin is a closed volume (with minimal venting), the increase in concentration can be detrimental to the customer but is hard to detect.
2017-03-28
Technical Paper
2017-01-0975
Pankaj Kumar, Imad Makki
Abstract A three-way catalytic converter (TWC) is an emissions control device, used to treat the exhaust gases in a gasoline engine. The conversion efficiency of the catalyst, however, drops with age or customer usage and needs to be monitored on-line to meet the on board diagnostics (OBD II) regulations. In this work, a non-intrusive catalyst monitor is developed to diagnose the track the remaining useful life of the catalyst based on measured in-vehicle signals. Using air mass and the air-fuel ratio (A/F) at the front (upstream) and rear (downstream) of the catalyst, the catalyst oxygen storage capacity is estimated. The catalyst capacity and operating exhaust temperature are used as an input features for developing a Support Vector Machine (SVM) algorithm based classifier to identify a threshold catalyst. In addition, the distance of the data points in hyperspace from the calibrated threshold plane is used to compute the remaining useful life left.
2017-03-28
Technical Paper
2017-01-0976
Seun Olowojebutu, Thomas Steffen
Abstract The integration of selective catalytic reduction catalysts (SCR) into diesel particulate filters (DPF) as a way to treat nitrogen oxides (NOx) and particulate matter (PM) emission is an emerging technology in diesel exhaust aftertreatment. This is driven by ever-tightening limits on NOx and PM emission. In an integrated SCR-in-DPF (also known as SCRF®, SCR-on-DPF, SDPF, or SCR coated filter), the SCR catalyst is impregnated within the porous walls of the DPF. The compact, low weight/volume of the integrated unit provides improvement in the diesel engine cold start emission performance. Experimental investigations have shown comparable performance with standard SCR and DPF units for NOx conversion and PM control, respectively. The modelling of the integrated unit is complicated.
2017-03-28
Journal Article
2017-01-0978
Andrew Auld, Andrew Ward, Kenan Mustafa, Benjamin Hansen
Abstract Since previous publications, Ricardo have continued to investigate the development of advanced after-treatment technologies through model based system simulation using an integrated model based development (IMBD) approach. This paper presents the results of the evaluation of after-treatment systems and management strategies for a range of diesel passenger cars. The targets of this study are applicable to Real Driving Emissions (RDE) legislation, but now targeting emissions levels beyond Euro 6d. The work was carried out as part of the EC Horizon 2020 co-funded REWARD (Real World Advanced technologies foR Diesel engines) project. Owing to the wide variation in feed-gas properties expected over an RDE cycle, the results seen for current production system architectures such as Lean NOX traps (LNT) or actively dosed Selective Catalytic Reduction (aSCR) systems highlight the challenge to adhere to emissions limitations for RDE legislation whilst fulfilling stringent CO2 targets.
2017-03-28
Technical Paper
2017-01-0979
Changpu Zhao, Yayong Zhu, Yaohui Wang, Sirui Huang
Abstract Although diesel engines have higher output torque, lower fuel consumption, and lower HC pollutant emissions, larger amounts of NOx and PM are emitted, compared with equivalent gasoline engines. The diesel particulate filters (DPF) have proved one of the most promising aftertreatment technologies due to the more stringent particulate matters (PM) regulations. In this study, the computational fluid dynamics (CFD) model of DPF was built by utilizing AVL-Fire software code. The main objective of this paper was to investigate the pressure drop and soot regeneration characteristics of hexagonal and conventional square cell DPFs with various inlet mass flow rates, inlet temperatures, cell densities, soot loads and ash loads. Different cell geometry shapes of DPF were evaluated under various ash distribution types.
2017-03-28
Technical Paper
2017-01-0971
Uladzimir Budziankou, Thomas Lauer, Xuehai Yu, Brian M Schmidt, Nam Cho
Experimental studies have shown that knitted wiremesh mixers reduce the formation of solid deposits and improve ammonia homogenization in automotive SCR systems. However, their implementation in CFD models remains a major challenge due to the complex WM geometry. It was the aim of the current study to investigate droplet WM interaction. Essential processes, such as secondary droplet generation, wall film formation, and heat exchange, were analyzed in detail and a numerical model was set up. A box with heat resisting glass was used to study urea-water solution spray impingement on a WM under a wide range of operating conditions. High speed videography was used to identify the impingement regimes. Infrared thermography was applied to investigate WM cooling. In order to determine the impact of the WM on the spray characteristics, the droplet spectrum was measured both upstream and downstream of the WM using the laser diffraction method.
2017-03-28
Technical Paper
2017-01-0972
Jiri Figura, Jaroslav Pekar, Pavel Krejza, David Mracek, Dirk von Wissel, Tianran Zhang
Abstract Many control approaches for selective catalytic reduction (SCR) systems require knowledge of ammonia storage (NH3 storage) to dose urea accurately. Currently there are no technologies to directly measure internal NH3 storage in a vehicle, so it can only be inferred from hardware sensors located upstream, downstream, or in the catalyst. This paper describes an application of extended Kalman filter (EKF) state estimator used as a virtual sensor for urea injection control of a multi-brick aftertreatment system. The proposed estimator combines mean-value physics-based models of combined SCR and diesel particulate filter (SCR/DPF), SCR and clean-up catalyst (CUC). It uses hardware sensors at the inlet and outlet of the aftertreatment system, and includes no sensors between the catalysts. Performance of the proposed estimator was validated in simulations against a high-fidelity model of the aftertreatment system.
2017-03-28
Technical Paper
2017-01-0973
Naoko Uchiumi, Hiroshi Hirabayashi, Shinya Sato, Takafumi Yamauchi
Abstract Urea-SCR(selective catalytic reduction) system is widely used as a technology of NOx(Nitrogen Oxides) reduction from diesel engine exhaust gases. Emission regulations have becoming stricter all over the world, and high NOx reduction performance is necessary to meet the emission regulations. To get higher NOx reduction performance of the Urea-SCR system, it is important to understand detailed chemical reaction mechanisms of Urea-SCR catalysts. In this study, we focused on elucidation of the reaction mechanism of the Urea-SCR catalyst by numerical simulation approach. The chemical reaction models with detail chemical reactions were built for both Fe-catalyst and Cu-catalyst. Both of the catalytic reaction models can predict difference of the catalytic reaction performance between the Fe-catalyst and the Cu-catalyst. In addition, rate-determining reaction step of the Cu-catalyst was successfully identified by the numerical simulation results.
2017-03-28
Journal Article
2017-01-0974
Timothy C. Watling, Maya R. Ravenscroft, Jason P.E. Cleeton, Ian D. Rees, David A.R. Wilkins
Abstract The development of a one-dimensional model for the prediction of backpressure across a gasoline or diesel particulate filter (PF) is presented. The model makes two innovations: Firstly, the term for momentum convection in the gas momentum balance equations includes the loss (or gain) of axial momentum in the direction perpendicular to the channels; neglecting this results in the momentum convection term being too large. Secondly, equations for the pressure change due to the abrupt contraction at the PF entrance and for abrupt expansion at the exit are derived which take into account the fact that the velocity profile across the channels is not flat; often workers have used equations appropriate for high Reynolds numbers which assume flat velocity profiles. The model has been calibrated/tested against cold flow data for more than one length of PF. The use of more than one length allows along-filter pressure losses to be separated from entrance and exit effects.
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