Gas-liquid Two-phase Flow Patterns Research Articles

Simulation of non-Newtonian fluid flow in a horizontal pipe

Microchannel reactors exhibit distinct gas-liquid two-phase flow behaviors compared to macro-scale channels, offering advantages like efficient heat and mass transfer, compact size, and low energy consumption. Sodium carboxymethyl cellulose (CMC) emerges as a potent stabilizer, enhancing mixing, homogenization and pipeline transport. Its judicious application reduces equipment strain, amplifies homogenization efficiency and finds diverse utility in food processing and beyond. However, incorrect employment bears the risk of compromised outcomes, potentially leading to product wastage. Consequently, investigating N2-CMC solution flow in microchannels holds paramount significance for elevating efficacy, minimizing usage, refining product quality and bolstering yield. In this study, we simulated the N2-CMC solution flow dynamics within an interleaved T-shaped microchannel using FLUENT which is a numerical simulation software. The simulation delved into alterations in gas-liquid two-phase flow patterns and pressure drops. We examined the impacts of liquid concentration and gas-liquid flow rate ratio on flow patterns, pressure drops and bubble lengths. The simulation results exhibited congruence with experimental data. Notably, elevated liquid concentrations correlated with higher pressure drops and elongated bubble lengths. Conversely, augmenting the gas-liquid flow rate ratio led to diminished pressure drops while elongating bubble lengths. These findings furnish insights into flow patterns and pressure drop behaviors for gas-non-Newtonian fluids within microchannels, forming a pivotal reference for microfluidic system design.

Experimental and numerical study on the pressure drop and flow pattern of liquid foam in a foam generator

In the present study, a comprehensive analysis of the pressure drop, flow pattern, and foam structural properties of vertical upward two-phase flow in a Kenics static foam generator of a compressed air foam system was carried out. A liquid with an extremely low surface tension (16.5 mN/m) was used for making the foam. The effects of the number of elements (number of individual elements combined into the mixer), aspect ratio (the ratio of length to diameter of each element), and transition angle (transition angle between elements) of the Kenics mixers on the pressure loss during foam generation were studied in detail over a wide range of Reynolds numbers through experiments and numerical simulation. A new pressure drop correlation was successfully obtained by scaling analysis and the modified Lockhart–Martinelli correlation was proposed to describe the pressure drop during foam generation. Furthermore, the experimental results validated the proposed correlation and exhibited good reliability and predictive accuracy. Finally, four flow patterns for foam generation in vertical pipes that were different from the classical gas–liquid two-phase flow patterns were proposed, and the relationships among the pressure drop, flow pattern, and foam structural properties were explored. This research expands the study of foam generation in vertical tubes containing a built-in spiral structure with low flow resistance. It provides new insights and guidance for developing continuous foam manufacturing.

The identification of gas–liquid two-phase flow patterns in a centrifugal pump with an imbalanced sample and variable rotational speeds

Due to the effects of the working medium and external conditions, centrifugal pumps often produce complex gas–liquid two-phase flows during operation. The entrainment of gas can lead to a significant decrease in the pressure head of the centrifugal pump and a serious reduction in conveyance efficiency. Therefore, in the absence of visualization or noninvasive techniques, the question of how to predict and model the flow status inside the pump is a key issue that needs to be urgently addressed. Using experimental data for gas–liquid two-phase flows in centrifugal pumps, this paper proposes a flow pattern identification model based on one-dimensional pressure increment signals. This deep learning model consists of convolutional neural networks and bidirectional gated recurrent units. Bayesian optimization is used for automatic hyperparameter tuning, and under the premise of balanced data distribution, the model achieves an identification rate of 0.98 on the test set. Subsequently, addressing the issue of the uneven sample distribution in centrifugal pumps due to their poor gas-carrying capacity, a data augmentation model based on the conditional Wasserstein generative adversarial network with gradient penalty approach is proposed based on the predictive model. Finally, to establish a flow pattern identification method with good extrapolation capability, a transfer learning strategy that accounts for the domain adaptation problem is introduced to the dataset with variable speeds based on the previous two studies. This method achieves knowledge transfer from the source domain to the target domain with a recognition rate of over 0.988 without hyperparameter optimization.

Analysis of abnormal operation of condenser water chamber evacuation system in nuclear power plants

During the operation of a nuclear power plant, there was no level indication in some of the condenser outlet water chamber, the level of the vacuum control tank upstream of the water chamber evacuation pump was rising frequently and unintentionally. To find out the causes of the above phenomena, a phenomenological analysis was first carried out. The cause analysis is then carried out in conjunction with the internal pressure of the condenser, the calculation of the air volume inside the condenser water chamber, and the flow pattern of the medium inside the water chamber evacuation pipeline. The final analysis concludes that a low junction point between the inlet water chamber's evacuation pipeline and the outlet can lead to the formation of an airlock at the top of the condenser's outlet water chamber. When there is a leak in the evacuation pipeline of the condenser's outlet water chamber, the increased air intake, in conjunction with gas-liquid two-phase flow, causes the liquid level in the vacuum control tank to rise unexpectedly and frequently. Thus, the factor of higher pressure at the inlet water chamber evacuation point and the influence of gas-liquid two-phase flow pattern should be taken into account when designing the evacuation pipeline.

Features selection for recognition of severe slugging in a long pipeline with an S-shaped riser by decision tree

In deep-sea oil and gas, S-shaped riser is the key equipment to transport the multiphase working substance produced underwater to the surface platform. The occurrence of severe slugging will seriously threaten the safe production of offshore oil and gas fields. Therefore, accurate and rapid recognition of hazardous flow patterns such as severe slugging is an urgent need to ensure the safety of multiphase flow in deep-sea long-distance pipelines. This paper has built a set of long S-shaped riser with industrial parameters, including 1687 m horizontal and downward inclined pipelines and 16.7 m S-shaped riser. The gas-liquid two-phase flow patterns, including severe slugging, oscillating flow and stable flow, are studied in this system. The pressure and differential pressure features of different signals are extracted from different positions along the pipeline, and a more comprehensive and reasonable evaluation criterion of signal performance is established. Making use of the advantages of visualization of the structure of decision tree, a new method to evaluate the recognition effect of features is proposed based on its classification principle. The original signal is decomposed into components of different scales through wavelet multi-scale analysis, and then the statistical features with good flow pattern differentiation ability are calculated. It is found that the mean of wavelet approximate component has the best recognition effect among all features. On the basis of feature correlation analysis, 7 features with high recognition rate applicable to 22 signals along the pipeline are optimally selected from 13 original features. For the water differential pressure signal DP13, the recognition rate obtained by using its 4 optimal features is 91.4 %, and the error between the recognition rate obtained by using all features is only 0.2 %. The overall recognition rate of the signal is the highest and the practicability is the best. When the sample duration is 6.2s, the recognition rate using the optimal feature reaches 90.8 %, thus ensuring the real-time recognition of the flow pattern while obtaining a high recognition rate.

Convolutional Neural Networks and Feature Fusion for Flow Pattern Identification of the Subsea Jumper

The gas–liquid two-phase flow patterns of subsea jumpers are identified in this work using a multi-sensor information fusion technique, simultaneously collecting vibration signals and electrical capacitance tomography of stratified flow, slug flow, annular flow, and bubbly flow. The samples are then processed to obtain the data set. Additionally, the samples are trained and learned using the convolutional neural network (CNN) and feature fusion model, which are built based on experimental data. Finally, the four kinds of flow pattern samples are identified. The overall identification accuracy of the model is 95.3% for four patterns of gas–liquid two-phase flow in the jumper. Through the research of flow profile identification, the disadvantages of single sensor testing angle and incomplete information are dramatically improved, which has a great significance on the subsea jumper’s operation safety.

Analysis and identification of gas-liquid two-phase flow pattern based on multi-scale power spectral entropy and pseudo-image encoding

Gas-liquid two-phase flow is closely related to the production and transportation of energy industries. A flow pattern analysis and identification method based on multi-scale power spectral entropy (MPSE) with pseudo-image encoding (PIE) is proposed. The resistance sensor array is used to collect gas-liquid two-phase flow information from the vertical upward pipeline, and the data is dimensionally reduced to simplify analysis. The MPSE is derived from the power spectrum of reduced-dimensional sequences to characterize the frequency domain complexity of the flow system at different scales. The optimal scale for spectral entropy analysis is further calculated to investigate the transition mechanism of gas-liquid two-phase flow patterns. In addition, the PIE algorithm is used to map the power spectrum into two-dimensional grayscale images to visualize the differences in frequency domain features of flow patterns. Combined with the deep learning model ResNeXt, the flow patterns are classified and compared with the traditional identification scheme. Results show that the proposed method can reveal the dynamic evolution behavior of gas-liquid two-phase flow from the frequency domain and achieve accurate identification of the flow patterns.

Simulation Experiment and Mathematical Model of Liquid Carrying in the Entire Wellbore of Shale Gas Horizontal Wells

Shale gas is mostly produced using horizontal wells, since shale gas reservoirs have low porosity and permeability. It is challenging to predict a horizontal well’s critical liquid-carrying gas flow rate because horizontal wells have more complicated well structures and gas–liquid two-phase pipe flows than vertical wells. In addition, there are significant differences between shale gas reservoirs and conventional natural gas reservoirs as well as dynamic changes in the liquid production rate. The majority of critical liquid-carrying models currently in use in engineering are based on the force analysis of droplets in the gas stream or liquid film on the pipe wall in annular-mist flow in the vertical wellbore. However, they do not take into account the impact of changes to the entire wellbore structure and dynamic changes in the liquid production rate on gas–liquid two-phase flow patterns and liquid carrying in the wellbore. In order to perform the critical gas velocity test for liquid carrying in the entire wellbore of horizontal wells, a visual liquid-carrying simulation experimental device for the entire wellbore of horizontal wells and a high-speed camera were used in this study. The onset of liquid accumulation was analyzed comprehensively according to the overall increase of the wellbore liquid and the change of the system pressure. A modified K–H wave theory liquid-carrying model was developed by taking into account the impacts of liquid production rate and well inclination angle based on the experimental data, the K–H wave theory, the cross-section actual gas velocity, and the angle correction correlation formula. The improved liquid-carrying model is in good accordance with the test findings, according to the experimental results. In Shunan Gas Mine, Sichuan, China, there are eight deep shale gas wells, which produced a total of 25 sets of tests. The modified model was used to forecast and diagnose the liquid-carrying capacity in the entire wellbore of these wells. The diagnosis results are in good agreement with the actual production situation, and the coincidence rate is 92%.

High-accuracy recognition of gas–liquid two-phase flow patterns: A Flow–Hilbert–CNN hybrid model

In multiphase flow pipelines, the timely and precise identification of flow pattern characteristics is crucial to guide industrial production, assess pipeline safety, and facilitate early risk warnings. Current research highlights that the combined application of flow imagery and convolutional neural networks (CNNs) can yield high accuracy flow pattern recognition. However, in the industrial sector, conveniently measurable signals such as pressure and flow rate present as one-dimensional signals rather than two-dimensional signals such as images and matrices, which CNNs are equipped to process. Therefore, the selection of a suitable data encapsulation type to convert one-dimensional signals into matrix or image form is vital to the successful application of CNNs in this field and to the precise identification of flow patterns in industrial production. In this research, we propose a Flow–Hilbert–CNN hybrid model, which integrates the one-dimensional liquid holdup signal, the Hilbert curve technique, and CNNs. The experimental data from multiphase flow in an undulating pipeline with low liquid holdup demonstrates that this hybrid model provides excellent classification accuracy, the model effectively identified four flow patterns—slug flow, pseudo-slug flow, wavy-stratified flow, and smooth-stratified flow—with recognition accuracies of 100.0%, 90.38%, 93.07%, and 100.0%, respectively, from a 16,384-length data source. Compared to models that employ standard data encapsulation methods (Space Folding (SF) and Fast Fourier Transform (FFT)) combination with CNNs, this hybrid model exhibits remarkable recognition accuracy and superior adaptability to data source scales. Notably, in the case of small-scale datasets, the accuracy improvement was 43.24% and 35.89% in comparison with SF- and FFT-based models, respectively. Moreover, the recognition accuracy of the hybrid model shows significant improvement when compared to results from traditional machine learning models and deep neural networks combined with the liquid holdup signal. The hybrid model, when used with different CNNs—MobileNetV2, Resnet18, and VGG16—yields recognition accuracies of 95.87%, 97.76%, and 96.64%, respectively, while the accuracies of machine learning models—deep neural network, k-nearest neighbors algorithm, and support vector machine—stand at 91.35%, 74.12%, and 90.57%, respectively. These results convincingly demonstrate the universality of combining the Hilbert curve with CNNs in the hybrid model, as well as the model's reliability and superiority in industrial application. This hybrid model can facilitate online, high-precision monitoring of flow patterns in the industrial sector and aid in preventing risk accidents within the production process.

Interconnected ordinal pattern complex network for characterizing the spatial coupling behavior of gas-liquid two-phase flow.

The complex phase interactions of the two-phase flow are a key factor in understanding the flow pattern evolutional mechanisms, yet these complex flow behaviors have not been well understood. In this paper, we employ a series of gas-liquid two-phase flow multivariate fluctuation signals as observations and propose a novel interconnected ordinal pattern network to investigate the spatial coupling behaviors of the gas-liquid two-phase flow patterns. In addition, we use two network indices, which are the global subnetwork mutual information (I) and the global subnetwork clustering coefficient (C), to quantitatively measure the spatial coupling strength of different gas-liquid flow patterns. The gas-liquid two-phase flow pattern evolutionary behaviors are further characterized by calculating the two proposed coupling indices under different flow conditions. The proposed interconnected ordinal pattern network provides a novel tool for a deeper understanding of the evolutional mechanisms of the multi-phase flow system, and it can also be used to investigate the coupling behaviors of other complex systems with multiple observations.

Two-Phase Flow Pattern Identification by Embedding Double Attention Mechanisms into a Convolutional Neural Network

There are inevitable multiphase flow problems in the process of subsea oil-gas acquisition and transportation, of which the two-phase flow involving gas and liquid is given much attention. The performance of pipelines and equipment in subsea systems is greatly affected by various flow patterns. As a result, correctly and efficiently identifying the flow pattern in a pipeline is critical for the oil and gas industry. In this study, two attention modules, the convolutional block attention module (CBAM) and efficient channel attention (ECA), are introduced into a convolutional neural network (ResNet50) to develop a gas–liquid two-phase flow pattern identification model, which is named CBAM-ECA-ResNet50. To verify the accuracy and efficiency of the proposed model, a collection of gas–liquid two-phase flow pattern images in a vertical pipeline is selected as the dataset, and data augmentation is employed on the training set data to enhance the generalization capability and comprehensive performance of the model. Then, comparison models similar to the proposed model are obtained by adjusting the order and number of the two attention modules in the two positions and by inserting other different attention modules. Afterward, ResNet50 and all proposed models are applied to classify and identify gas–liquid two-phase flow pattern images. As a result, the identification accuracy of the proposed CBAM-ECA-ResNet50 is observed to be the highest (99.62%). In addition, the robustness and complexity of the proposed CBAM-ECA-ResNet50 are satisfactory.

Experimental study on gas–liquid flow patterns and bubble size in a high-speed rotating impeller of a three-stage centrifugal pump

Head degradation and performance failure will occur when centrifugal pumps work under high gas volume fraction. The gas–liquid two-phase flow patterns and bubble size in a rotating impeller were experimentally studied by high-speed photography technology in a three-stage centrifugal pump. A new impeller was designed with double rings and a transparent shroud, overcoming the speed limitation below 1500 rpm in current studies and reaching the maximum speed of 3500 rpm. Four gas–liquid flow patterns are observed, which are discrete bubble flow, bubble flow, gas pocket flow and stratified flow. The result shows that the transition from bubble flow to gas pocket flow is the critical condition for the severe head degradation. Reducing inlet gas volume fraction, increasing rotational speed and reducing liquid flow rate lower than design value cause the transition from gas pocket flow to bubble flow and the delay of head degradation. By image processing technique, the probability density function (PDF) of bubble diameter in impeller is found to follow a lognormal distribution. Moreover, bubble Sauter diameter dSa has a linear relationship with inlet gas volume fraction λ, rotational speed n−0.75 and liquid flow rate Qw−0.6, respectively. A new correlation is established for predicting bubble Sauter diameter in impeller under high rotational speeds (1500–3500 rpm). The strong relationship between flow pattern transition and head degradation is revealed. Based on the same head performances of three booster stages in pump, the conclusions driven from the visual impeller in the first stage can also be extended to other stages.

Gas/Liquid Two-Phase Flow Pattern Identification Method Using Gramian Angular Field and Densely Connected Network

Accurate identification of flow patterns is of great importance for industrial production. A flow pattern identification method based on Gramian angular field (GAF) and densely connected network (DenseNet) was proposed. Experimental data of gas–liquid two-phase flow in a vertical upward pipeline were collected using a resistance sensor array, and the multivariate measurement data were downscaled into univariate time series for feature reduction. Then, the data were encoded into 2-D images using the Gramian angular summation field (GASF) and Gramian angular difference field (GADF) to highlight the characteristic differences between flow patterns, and the evolutionary behavior of flow patterns was further analyzed based on the images. A DenseNet model was established, and the GAF images were used as model inputs for training and testing to achieve the flow pattern identification. The results show that the GAF images can effectively reflect the characteristics of different flow patterns; in particular, the combination of GADF and DenseNet has the best recognition effect, and the average flow pattern identification accuracy reaches 98.3%. This method provides a new perspective for distinguishing complex gas–liquid two-phase flow patterns.

Identifying Flow Patterns in a Narrow Channel via Feature Extraction of Conductivity Measurements with a Support Vector Machine.

In this work, a visualization experiment for rectangular channels was carried out to explore gas-liquid two-phase flow characteristics. Typical flow patterns, including bubble, elastic and mixed flows, were captured by direct imaging technology and the corresponding measurements with fluctuation characteristics were recorded by using an electrical conductivity sensor. Time-domain and frequency-domain characteristics of the corresponding electrical conductivity measurements of each flow pattern were analyzed with a probability density function and a power spectral density curve. The results showed that the feature vectors can be constructed to reflect the time-frequency characteristics of conductivity measurements successfully by introducing the quantized characteristic parameters, including the maximum power of the frequency, the standard deviation of the power spectral density, and the range of the power distribution. Furthermore, the overall recognition rate of the four flow patterns measured by the method was 93.33% based on the support vector machine, and the intelligent two-phase flow-pattern identification method can provide a new technical support for the online recognition of gas-liquid two-phase flow patterns in rectangular channels. It may thus be concluded that this method should be of great significance to ensure the safe and efficient operation of relevant industrial production systems.

Symbolic transition network for characterizing the dynamics behaviors of gas–liquid​ two-phase flow patterns

Gas–liquid two-phase flows are widely encountered in many industrial applications, and the evolutionary dynamics of the flow patterns are fundamental knowledge for the establishment of the two-phase controlling system. In this work, we propose a symbolic complex network-based method for identifying the evolutionary dynamics of the gas–liquid​ two-phase flow system. First, we establish a series of symbolic networks with the derived gas–liquid two-phase flow symbolic series. Then we suggest a symbolic network index, which is the number of enumerated elementary cycles, to reveal the periodic oscillation properties of various gas–liquid flow patterns. In addition, we estimate the symbolic network average degree C and average shortest path length L to reveal the evolutionary dynamics of the flow patterns. The results suggest that our developed method is efficient for detecting the dynamics of the two-phase flow system, which can be further applied to other complex fluid systems.

Two-phase flow pattern identification in horizontal gas–liquid swirling pipe flow by machine learning method

Gas–liquid two-phase swirling flow has been widely used in nuclear industry. Its flow pattern is fundamental to investigate the two-phase flow. Although flow patterns of non-swirling flow in a horizontal pipe have been investigated for a long history, flow patterns of swirling flow in the pipe are rarely reported. In this paper, gas–liquid two-phase flow patterns of swirling flow generated by a vane-type swirler inside a horizontal pipe were investigated by a visualization experiment. Five swirling flow patterns were observed and recorded by the backlight imaging method. Then image processing method was used to obtain void fraction, and the statistical analysis (CDF and PDF) of void fraction for each swirling flow patterns was performed. Owing to the distinguished and stable feature of PDF signals, four parameters describing the characteristics of PDF signals have been proposed as the indicator of machine learning method. Finally, five algorithms of machine learning method have been used to identify the swirling flow patterns, and RUSBoost tree algorithm performs best with an accuracy of 97.4%.

Gas–liquid two-phase flow patterns and pressure drop of decaying swirling flow inside a horizontal pipe

Gas–liquid two phase swirling flow has been widely used in industry. Its flow pattern is fundamental to investigate the two-phase flow. In this paper, two-phase air–water flow patterns and pressure drop of decaying swirling flow generated by vane-type swirler inside a horizontal pipe have been systematically investigated by visualization experiment. The range of superficial gas phase Reynolds number is 17–23902, while superficial liquid phase Reynolds number is 12–37871, and gauge pressure is 0.003–0.17 MPa. The five typical flow patterns in a horizontal swirling flow were characterized based on flow visualizations and fluctuation characteristics of pressure drop signals. Then swirling flow regime map nearby the swirler outlet was proposed. As flow patterns altered along the streamwise direction due to swirl decay, flow pattern maps at different positions were proposed, which indicated the swirling flow patterns gradually transformed to non-swirling flow patterns. Finally, a new model to predict frictional pressure drop of air–water swirling flow inside a horizontal pipe containing vane-type swirler was proposed. This correlation performed well on predicting the frictional pressure drop.

Mathematical Model for Predicting the Development of Two-Phase Flow in a Horizontal Pipe

Prediction of the flow pattern is a central problms in multi-phase flow analysis. It is a vital point for researchers to accurately predict which flow pattern category types will occur at different flow rates. For this purpose, a mathematical model using the MATLAB (R2017b) computer program is developed for the prediction of gas-liquid two-phase flow patterns in a horizontal pipe with an inner diameter of 30mm under standard conditions. The properties of the air-water two-phase, the pipe geometry, and the flow rates of phases are defined to initiate the operating conditions. The mass flow rates of air and water changed from 0.002 to 0.004 kg/s and 0.672 to 1.334 kg/s, respectively. The impact of properties of the fluid and pipe diameters on two-phase flow configuration is considered to predict the impact of fluid properties on the flow pattern. The findings indicate that as the mass flux increases, the pipe diameters decrease, affecting the configuration of the flow pattern types. The mathematical model�s predicted results are validated by comparing with previous studies. In addition, good agreement is obtained when the predicted results are compared to the ongoing experiment of this research.

Lattice Boltzmann Method simulation of wellbore gas–liquid​ phase transition

Whenever the drilling wellbore is at the state of gas–liquid two-phase flow, gas slips and migrates along the drilling fluid. Due to the decreased wellbore temperature and pressure during gas migration, gas volume will gradually increase. When the temperature and pressure reach the critical value of gas–liquid phase, phase change occurs. The volume of natural gas expands suddenly, and a large amount of gas is generated. It easily leads to a well blowout, which is a great challenge to well control. Therefore, analyzing the gas–liquid phase changes in drilling wellbore has important practical significance for realizing well control safety. In this paper, Lattice Boltzmann Method (LBM) is applied to simulate phase transition of wellbore gas–liquid​ two-phase system. Research results show that gas–liquid distribution after phase transition is closely related to the system original density. Compared to the critical density of gas–liquid phase change, when the system original density is lower, continuous gas forms in wellbore. While the system original density is higher, gas phase breaks out into small bubbles and migrates along the wellbore. Phase distribution directly determines gas–liquid two-phase flow pattern in wellbore, which is crucial to wellbore pressure accurate prediction. Some valuable attempts are conducted to investigate gas–liquid two-phase flow in wellbore by using LBM in this research.

Numerical simulation and experimental study of gas–liquid two-phase flow pattern of hydrodynamic retarder

The internal flow of hydrodynamic retarder is a three-dimensional, complex, viscous, and unstable gas–liquid two-phase flow. The importance of numerical simulation of a hydrodynamic retarder has been paid attention to, but the research on the two-phase flow pattern of the retarder is rarely. Flow pattern diagnosis plays an important role in the study of two-phase flow because the premise of establishing the mathematical model of the two-phase flow is to accurately determine the flow structure of the flow system. Based on the numerical simulation and experimental research, this study found the corresponding relationship between the two-phase flow distribution inside the hydrodynamic retarder and the filling rate (expressed as “q”). The result shows that, when q = 0.1–0.2, the liquid in the working chamber is less. Under the action of centrifugal force, the liquid mainly gets distributed in the outer ring of the circulating circle, forming a laminar flow. When q = 0.3–0.4, the flow pattern of the gas–liquid two-phase flow changes from the laminar flow to slug flow. When q = 0.5–0.9, with a further increase in the filling ratio, the flow becomes a dispersed bubble flow. This paper provides an effective method for the analysis and identification of the two-phase flow pattern of a hydrodynamic retarder.