Instantaneous Heat Transfer Coefficient Research Articles

CFD simulation of the inundation effect for saturated propane vapor condensation on the surface of a horizontal tube using the volume of fluid method

The inundation of the lower tubes in a tube bundle with condensate formed on the upper tubes is among the major causes of reduced condensation rate. Experimental methods can hardly be used to get detailed information on the inundation effect, since each factor that controls the condensation process should be considered individually. However, CFD modelling using direct interface-tracking methods is an effective tool for analyzing such processes. This paper reports the results of simulation of the saturated propane vapor condensation on the surface of a horizontal tube using the Volume of Fluid method with the modified Lee model. The study presents, for the first time, the characteristics of saturated vapor condensation including the effect of inundation predicted using a 3D model. The interphase surface and the distribution of instantaneous heat transfer coefficients over the surface of the inundated pipe are presented. It has been shown that increasing the temperature of the condensate flow can substantially affect the distribution of the heat transfer rate over the tube surface due to the formation of a thermal entrance region. These results may become a starting point for modelling condensation in a tube bundle that enjoys current interest in practice.

Experimental analysis of convective drying of paper and board

Conventional multi-cylinder drying of paper and board involves a mixture of conductive drying from steam-heated dryer cylinders and convective drying by the flow of heated air over the surface of the paper web in the pockets. Pocket ventilation is a critical component in assisting heat and mass transfer during the drying process but is the primary contributor toward removing evaporated water from the web. Air temperature, velocity, and humidity are critical parameters involved in the convective drying process. This paper covers an experimental study involving the design and development of a small lab-scale setup for convective drying of various grades of paper and board, monitoring multiple parameters like paper temperature, moisture content, air humidity, temperature, and velocity measured in situ as the drying proceeds with continuous and accurate sampling capabilities for all parameters in the sample and the system. Instantaneous drying rates, heat, and mass transfer coefficients were also deduced for every time step till the paper completely dried. Furthermore, the coefficients obtained were also reported in the form of dimensionless correlations, and the results were compared against traditional correlations used in the modeling of paper drying. This data will be useful in process development, modeling, design, and the paper drying process simulation.

Numerical simulation study on heat transfer and fluid performance of novel calcium carbide heat collection system

This article proposes a novel recovery system for the substantial waste heat from the hot calcium carbide (CA). The study employs numerical simulation to investigate the heat transfer performance of the heat collection system (HCS). The research explores the effects of outlet position, inlet velocity, and inlet temperature on the operational characteristics and heat transfer performance of the HCS. The results indicate that optimal heat transfer performance is achieved when the outlet position is at the center of the collector. Instantaneous efficiency (IE), exergy loss (EL), pressure drop (PD), and heat transfer coefficient (HTC) increase with the velocity, while effectiveness decreases with the velocity. The peak values for IE, effectiveness, and HTC are 28.22%, 29.69%, and 1212.45 W/(m2*K), respectively. The heat transfer performance of the HCS is highest when the inlet temperature is 280K. The proposed CA HCS holds significant importance for recovering waste heat from electric stone production, providing a theoretical basis for subsequent experimental work.

Experimental study of steam condensation heat transfer characteristics in a horizontal tube under rolling motion

As an efficient heat transfer method, in-tube condensation heat transfer is widely used in various fields, including passive residual heat removal systems (PRHRS) of floating power plants under ocean conditions. The experimental investigation aimed to study the condensation heat transfer characteristics of steam in a 25 mm inner diameter horizontal tube with a heat transfer length of 1050 mm under rolling motion. The study used a mass flux of 30 kg/(m2·s) and investigated average vapor qualities, rolling amplitude, and rolling period ranging from 0.32 to 0.79, 0 °–20°, and 10 s–20 s, respectively. The experimental results show that the condensation flow patterns under rolling conditions are more complex than those under non-rolling motion due to the influence of the rolling period and rolling amplitude. The instantaneous heat transfer coefficient (IHTC) changes periodically due to the rolling motion and has the same change period. The pulsation amplitude of the IHTC increases with increasing rolling amplitude but weakens as the vapor quality increases. The effect of the rolling period on the IHTC is much less than that of the rolling amplitude. At low vapor quality, the time-averaged heat transfer coefficient (THTC) under the rolling motion condition increases with the rolling amplitude and period, and the maximum enhancement of THTC is 44%. As the vapor quality increases, the THTC under rolling conditions is the same as that under non-rolling conditions. These findings provide important insights into the condensation heat transfer characteristics of vapor in a horizontal tube under rolling motion, which can help improve the design and operation of in-tube condensation heat transfer systems in various fields.

Instantaneous Heat Transfer Coefficient of Droplets Impinged on Heated Surfaces

Droplet impingement is one of the phase change techniques used for equipment cooling because of the proper utilization of sensible and latent heat. This study analyzes droplet evaporation on aluminum and copper substrate. The instantaneous heat transfer coefficient (HTC) during evaporation of 100 µl de-ionized water is studied. The infrared camera is used to visualize and analyze the evaporation mechanism. The effect of substrate and fluid temperature on droplet evaporation is analyzed. The surface temperatures of both substrates are varied from 105 °C to 165 °C. The test fluid is maintained at temperatures of 30 °C, 50 °C, 75 °C, and 99.4 °C. The droplets exhibited Leidenfrost behavior for temperatures beyond 145 °C with copper and 150 °C with aluminum surface. It is observed that the evaporation rate is higher for copper than aluminum. A user-friendly interface is developed for determining the instantaneous surface area of an evaporating droplet. The apparent peak in the area in copper is higher than aluminum for all cases due to surface tension gradient and Marangoni flow. HTC increases with the temperature of droplet evaporating on a given substrate and is higher for copper. When substrate temperature increases for a given droplet temperature, the instantaneous HTC increases.

Oil jets piston cooling: A numerical methodology for the estimation of heat transfer coefficients and optimization of the piston temperature field through a genetic algorithm

High-efficiency internal combustion engines need specific methodologies to be developed for the design improvement of the components. Predicting and reducing the thermal loadings on the parts are critical tasks to be addressed. This contribution focuses on the thermal management of the piston through oil jets. The operating temperature of the piston deeply affects its thermo-mechanical behavior, thus possibly jeopardizing the structural integrity of the component. The design of piston cooling jets is usually addressed through Computational Fluid Dynamics, which can guarantee accurate results, usually at a high computational cost. In this contribution, a faster tool is derived to grasp the effect of the cooling jets on the temperature of the piston. Empirical correlations are applied to predict the instantaneous heat transfer coefficients on the piston. The reciprocating motion of the piston is considered since it affects the interaction between the surface and the oil jets. Instantaneous coefficients are cycle-averaged and used to estimate the temperature of the piston through a Finite Element thermal analysis. Finally, an optimization code is developed to find the best jet configuration capable to minimize the temperature of the piston. This methodology is a powerful tool to select the optimal oil jet nozzles for piston cooling.

Derivation and validation of heat transfer model for Spark-Ignition engine cylinder head

The valve train is located in the engine cylinder head, which has various operational heat transfer mechanisms to accommodate the combustion process. Most heat transfer studies in this area have only addressed medium-to high-power vehicles at a single running speed. In this study, a model of an air-cooled underbone motorcycle valve, valve seat, and engine cylinder head was tested to determine the thermal characteristics using actual engine operating conditions at low, medium, and high engine speeds. One-dimensional thermal simulation analyses were conducted to obtain the instantaneous heat-transfer coefficients of an actual engine. The average thermal value was determined as the boundary condition in the three-dimensional thermal analysis. A three-dimensional model was prepared using the ANSYS commercial computational fluid dynamics software package. The results show that as the engine speed increases, so does the thermal load toward the component in the engine cylinder head. The strongest temperature regions were concentrated around the combustion face. The exhaust valve held most of the heat, with the valve neck recording the highest temperature. For the intake valve, the combustion face registered the majority of the heat. The heat flux intensity was gathered in the contact surface area between the valve and its seat, between the valve stem and guide, and between the stem guide and tip section. A thermal survey was used to validate the three modelling results for two separate engine datasets. The cumulative relative errors for intake and exhaust valve seats for low engine speeds were 3.73% and 0.17%, respectively. The intake and exhaust valve seats had cumulative relative errors of 4.12% and 0.70%, respectively, at intermediate speeds. This methodology provides valuable information for analysing the heat characterisation of air-cooled engines. It can also be a useful blueprint for the automotive industry and other researchers involved in thermal measurements.

Effect of a Triangular Configuration of Heat Exchanging Tubes on Local Heat Transfer Coefficient in Bubble Column Reactor

The effect of a triangular configuration of heat exchanging tubes (HETs) on the instantaneous and local heat transfer coefficient (LHTC) has been investigated and quantified in an air-water bubble column (BC) utilising an advanced heat transfer technique. The bundle of heat exchange tubes was designed to cover 25% of the column's cross-sectional area (CSA) to simulate the heat exchanger tubes used in the industrial Fischer Tropsch (FT) process. The local heat flux, surface temperature, bulk temperature, and heat transfer coefficient (HTC) were investigated instantaneously in a Plexiglass BC under a wide range of superficial gas velocity (5-45 cm/s). The obtained results reveal that the presence of a bundle of (HETs) and their arrangement effect the (HTC) in the bubble column, where unsymmetrical profiles for (HTC) were obtained with triangular tube pitch arrangement. Additionally, steeper (HTC) profiles notice were when the triangular tube pitch arrangement was utilized. High (HTC) values were obtained at the core region of the column relative to the wall region under all the studied operating conditions. It was discovered that the local and (HTC) increase as superficial gas velocity increases despite the fact that the bubble column is heavily packed with a bundle of (HETs). The rise in HTCs was higher at the core than at the wall region of the column. For example, at a superficial gas velocity of 45 cm/s and at an axial height of 65 cm (Z/D=5), compared to the wall, the HTC in the core of the column increased by 131 %.

Coarsening‐induced disappearing droplets contribute to condensation

AbstractCondensation heat transfer is widely used in water and energy systems. Despite being extensively studied, since 1973, the models for dropwise condensation have strongly relied on the droplet size distribution. In this study, we report that the classical models underestimate the heat transfer performance of dropwise condensation on a hydrophilic liquid‐infused surface, on which the meniscus‐mediated coarsening droplets lead to a previously unachieved droplet coverage ratio down to 30%. We found that the time‐averaged classical models have overlooked the coarsening‐induced disappearing droplets. Moreover, these models cannot be used to determine the instantaneous heat transfer coefficient on the shedding‐induced water‐free surface under steam condensation. Thus, a dynamic model is developed for dropwise condensation by considering the disappearing droplets induced by both coarsening and shedding, which shows good agreement with the experimental validation. Such a dynamic model provides a theoretical foundation to design surfaces for condensation, giving rise to an advanced design guideline for water and energy systems.

Mechanistic chamber models: A review of geometry, mass flow, valve, and heat transfer sub-models

The evolution of computer resources paved the way for numerical models to substitute extensive experimental campaigns to develop and optimize compressors for the HVAC&R industry. A particular class of compressor models referred to as mechanistic (or deterministic) chamber model is well-known to be computationally efficient and has reasonable model fidelity for performance prediction and extrapolation. The overall model architecture requires inputs from various sub-models, including the mass flow, heat transfer and valve models. The accuracy of the overall model depends on the fidelity and accuracy of the individual sub-models. This article provides a comprehensive review of the different approaches available in literature which were used to model the geometry, mass flow, valves, and heat transfer processes in the compressor. The article aims to help researchers identify suitable approaches for their analysis. Additionally, it was found that there are opportunities for additional research to develop analytical correlations for discharge coefficients for the mass flow model, explore solubility in leakage gaps, develop effective flow/force area estimation for valve models, and develop instantaneous heat transfer coefficients for specific compressor architectures and thermal conductance models for multi-lumped network models.

Approach to enhance the heat transfer of valve seats through thermal analysis

The valve seat insert is a component of the engine cylinder head, whose primary function is to seal the combustion chamber and absorb the valve's heat, releasing it to the engine cylinder head. The valves experience high temperatures owing to high thermal loading and low heat absorption in the valve seat, which can potentially damage the engine. Therefore, the thermal characteristics of the valve seat must be optimised to increase the heat transmission between the valve and its seat. Here, three copper alloy valve seats, brass, beryllium copper, and bronze copper, were tested against the existing sintered iron valve seat, and their temperature maps were determined using actual engine operation conditions. The instantaneous heat transfer coefficients of the valves, seats, and engine cylinder head during the four-stroke cycle were evaluated using a one-dimensional thermal simulation analysis. The values obtained were used to assess the finite-element model using a three-dimensional thermal simulation in the Ansys software. The results show that the brass, beryllium-, and bronze-copper valve seats increased the overall heat flux by 4.46%, 4.16%, and 2.06%, respectively, compared to those for sintered iron. Thus, the results are essential to improve the thermal characteristics of the copper alloy valve seat imposed on the cylinder head. For validation, an experimental engine thermal survey and uncertainty magnification factors were used to validate the model. The results indicate that the maximum difference between the simulation and experimental values is 8.42%. Therefore, this approach offers a direct and comprehensible application for evaluating the temperature distribution, heat gradient, and heat flux of the cylinder head of air-cooled spark-ignition moped motorcycle engines using copper alloy valve seat materials at intermediate engine speeds. Furthermore, this method is applicable as a platform for the automotive industry to improve the heat transfer of the structural parts of internal combustion engines.

Study of heat transfer to supercritical pressure water across a wide range of parameters in pulse heating experiments

• Controlled pulse heating of supercritical pressure water was performed. • Unexpected response to the short-term release of high-power heat was revealed. • It is consistent with the character of the density change over supercritical isobars. • Reduced heat transfer coefficient exhibits a minimum at pseudocritical temperature. • We attribute this minimum to the suppression of fluctuations in short-term experiment. From experimental data on pulse heating of a thin wire probe in water pre-compressed to supercritical pressures at room temperature, the instantaneous heat transfer coefficient has been calculated over a wide temperature range from 250 °C to 700 °C. The pressure, being the parameter of the experiment, has been varied from the near-supercritical value (22.1 MPa) to 100 MPa. The heat flux density across the probe surface reached 10 MW/m 2 at a characteristic heating time of 20 ms. Under conditions of powerful heat release and small temporal and spatial scales, heat transfer is carried out mainly due to the heat conduction mode, which is the most physically determined mechanism of heat transfer. It has been revealed that the reduced heat transfer coefficient exhibits a minimum in the region of pseudocritical temperatures; this minimum becomes deeper, as the pressure value approaches the critical one. The obtained data can be useful in the design of heat exchange devices, the operation of which may include powerful local heat release, as well as in the simulation of emergencies associated with a sharp jump in reactivity in nuclear power units.

Numerical investigation on the effects of spatial angle on oscillating flow and heat transfer characteristics of piston cooling galleries

• The SOCR and SHTC of gallery are affected by the inlet/outlet position. • The ICOR and IHTC in groups A and B are different at the same crank angle. • The spatial angle has a non-negligible influence on the piston cooling performance. • The results provide reference for piston improvement design of multi-cylinder diesel. The oscillating cooling method is currently one of the most efficient cooling solutions for highly reinforced pistons. Previous studies only focused on the piston galleries with the reciprocating motion along a specified direction relative to the direction of the gravity force, e.g., the vertical direction in inline multi-cylinder engines. There are strong needs to study the cooling performance of the pistons that are designed to have reciprocating motions with different directions relative to gravity. In this paper, a concept of spatial angle is introduced to describe the design angle between the direction of the piston reciprocating motion and the direction of the gravity force in a coordinate system. When the spatial angle is changed, the gravity components of the piston are changed along the direction of the piston axial motion and its perpendicular direction. Moreover, with a given spatial angle, different piston designs can be achieved to obtain different relative positions of the cooling oil inlet and outlet passages, being higher or lower relative to each other. Because both the spatial angle and the relative positions of the oil passages affect flow and cooling performance, several simulation models are established to cover five spatial angles including −90°, −45°, 0°, 45°, and 90° as well as two groups of relative positions, i.e., groups A and B. The CFD simulation is validated by experimental testing. The results show that the flow and heat transfer performance of group B is more stable than that of group A because the inlet and outlet of the cooling passages of group B are at the same height. It is found that the steady-state oil charge ratio and steady-state heat transfer coefficient of group A gradually decrease with the increase of the spatial angle. The fluctuation patterns of the instantaneous oil charge ratios and heat transfer coefficients of groups A and B are very similar, but their spatial distribution values are different at the same crank angle (CA). The maximum difference in the instantaneous heat transfer coefficients between A1 and A3 reaches 23.27% at 303° CA. Moreover, it is found that when the piston moves between 150° CA and 300° CA, a phenomenon of liquid plug attenuates with the increase of the spatial angle. These findings can support the cooling performance analysis and optimization design of the piston galleries of the V-type, W-type, and horizontal opposed-piston diesel engines.

Aerothermal and aerodynamic performance of turbine blade squealer tip under the influence of guide vane passing wake

In this paper, the performance of the turbine blade squealer tip has been studied detailed aimed to highlight the impact of the upstream guide vane passing wake. The first stage of GE-E3 high-pressure turbine has been employed to perform the three-dimensional simulation and the computational domain has been scaled based on the domain scaling method. Boundary conditions are consistent with operating conditions of the annular cascade testing. Circumferential averaged and realistic non-uniform interface conditions have been used to obtain steady and unsteady characteristics respectively. The validation of the turbulent model and mesh independent test has been conducted detailed in previous work. Three squealer tips, including two widths and heights, have been designed and investigated to understand its influence. Results show that the aerothermal performance of the squealer tip is remarkably influenced by the upstream passing wake. Although steady and time-averaged results have a good agreement, the variation of instantaneous heat transfer coefficient (HTC) would be over 30%, especially on the Cavity Floor region. Changing the geometry of the squealer also has different impacts on both steady and unsteady performance. The unsteady aerodynamic has relatively small fluctuation within 10%, and the distribution of steady and time-averaged leakage flow as well as total pressure loss coefficient still have a satisfactory agreement.

Tomography-based investigation of flow and heat transfer inside reticulated porous ceramics

This study investigates the flow and heat transfer within reticulated porous ceramics, with the aim of enhancing the understanding of phenomena occurring at the pore scale in order to extract useful information for the optimisation of heat sinks or other reticulated porous devices in engineering applications. In this study, X-ray computed tomography is used to reconstruct the reticulated porous ceramic. From the voxel mesh, the real geometry of the foam sample can be obtained, and an unstructured mesh is generated using ICEM. Then, a fully coupled heat transfer model is established. Based on this model, the transient conjugate heat transfer between the airstream and the porous matrix is solved using FLUENT software. The numerical results show that the pressure drop vs. the superficial velocity follows the Darcy–Forchheimer equation, and the border-affected region is only 1–2 times the mean cell size. Moreover, a local thermal equilibrium lasting for 7–10 s is found in the transient coupled flow and heat transfer process in this study. Additionally, the local convective heat transfer coefficient, which mainly depends on the velocity, is constant along the flow direction, and the instantaneous volumetric heat transfer coefficient increases monotonically with time. The obtained results are important theoretical supplements for understanding the flow and heat transfer in porous materials, and are crucial for enhancing the heat transfer in applications of reticulated porous ceramic materials.

Heat and mass transport analysis of the drying of freshwater fishes by a forced convective air‐dryer

AbstractThe drying behavior of different freshwater fishes (with/without scales) is investigated using a simple convective heated air dryer. Drying processes are analyzed to study the kinetics of drying, shrinkage dependent variable effective diffusivity, convective heat and mass transport, and the energy aspect of drying. Among the drying kinetic models, Hasibuan–Daud and Haghi–Angiz‐I models produce the best fit for fishes with scales and Hii model produces the best fit for fish without scales. Diffusion analysis performed based on simplified solution of Fick's diffusion equation shows higher effective diffusivity for fish without scales, proving additional barrier from scales (for fish with scales) that need to be considered during dryer design. Calculated instantaneous heat and mass transfer coefficients (different for fish with or without scales) also agree with this observation, accentuating the difference based on scales. Drying process for all fishes obeys the heat‐mass transfer correlation. Estimated parameters such as effective diffusivity (0.2–1 × 10−9 m2/s) and convective heat and mass transfer coefficients (7–14 W/m2/K and 2.8–4.5 × 10−6 m/s, respectively) can be utilized in designing different fish drying systems. Average and instantaneous total energy consumption, specific moisture extraction ratio, and specific energy consumption are evaluated in order to provide a comprehensive picture of the drying process.Practical ApplicationsFresh‐ and salt‐water fishes account for major sources of protein‐rich food for substantial parts of the population in underdeveloped and developing nations. To circumvent the wastage associated with microbial contaminations during prolific seasons, fish drying has been widely employed as a way of preserving this perishable food. Convective drying of agricultural products as well as marine foods is a commonly employed drying method for food preservation. This study investigates the drying behavior of three different freshwater fishes using an in‐house constructed forced convective air dryer. The experimental drying characteristics and estimated parameters by model fitting during fish drying will be particularly applicable in the wide field of fish drying. The outcome of this study can also be utilized for more effectively designing and evaluating low‐cost convective fish dryers.

Two-phase flow-based numerical investigation of the temperature maps of sodium-cooled exhaust valves in a turbocharged engine

Valves at the outlet of the combustion chamber in modern combustion engines must withstand very high temperature and acceleration. Such valves are subject to thermal loading to have to tolerate the limit of material temperature. The present study constitutes a contribution to predict the temperature maps of the sodium-cooled exhaust valves considering the real conditions of an engine operation. An adequate subdivision of the valve is used to better assess the effect of each part of the cylinder head. Therefore, the instantaneous heat transfer coefficient and adiabatic wall temperature for each subdivision are evaluated. To survey the two-phase flow phenomenon, the valve motion was modeled by a dynamic mesh method, and the sodium sloshing was modeled by the volume of fluid multiphase model. The average values of these parameters are calculated and introduced as boundary conditions in a finite element model implemented in the commercial code ANSYS to extract the temperature map. The results indicated that the maximum temperature errors between the simulated and the test results were 45.5 °C and 37.2 °C in the axial and radial directions of the valve, respectively, and their maximum relative errors were not more than 8%. As an application, this methodology is used to highlight the temperature maps and to show the region of extreme temperature in the aim of avoiding any damage.

Effect of rolling motion on heat transfer characteristics of narrow rectangular channel with high subcooled boiling

In this paper, the effects of vertical and rolling motion conditions on high subcooled boiling heat transfer in narrow rectangular channels of natural circulation system are investigated experimentally. To analyze the error of instantaneous heat transfer coefficient better, a calculation error method based on temperature difference is proposed. The results show that the error between the predicted heat transfer coefficient of Yan’s formula and the experimental value is less than 30% under vertical and rolling motion conditions.

Numerical investigations of unsteady passing wake effects on turbine blade tip aerothermal performance with different tip clearances

Purpose The purpose of this paper is to numerically investigate the effect of guide vane unsteady passing wake on the rotor blade tip aerothermal performance with different tip clearances. Design/methodology/approach The geometry and flow conditions of the first stage of GE-E3 high-pressure turbine have been used to obtain the blade tip three-dimensional heat transfer characteristics. The first stage of GE-E3 high-pressure turbine has 46 guide vanes and 76 rotor blades, and the ratio of the vane to the blade is simplified to 38:76 to compromise the computational resources and accuracy. Namely, each computational domain comprises of one guide vane passage and two rotor blade passages. The investigations are conducted at three different tip gaps of 1.0, 1.5 and 2.0 per cent of the average blade span. Findings The results show that the overall discrepancy of the heat transfer coefficient between steady results and unsteady time-averaged results is quite small, but the dramatic growth of the instantaneous heat transfer coefficient along the pressure side is in excess of 20 per cent. The change of the aerothermal performance is mainly driven by turbulence-level fluctuations of the unsteady flow field within gap regions. In addition, the gap size expansion has a marginal impact on the variation ratio of tip unsteady aerothermal performances, even though it has a huge influence on the leakage flow state within the tip region. Originality/value This paper emphasizes the change ratio of unsteady instantaneous heat transfer characteristics and detailed the mechanism of blade tip unsteady heat transfer coefficient fluctuations, which provide some guidance for the future blade tip design and optimization.

Thermomechanical Analysis of Purging Plugs by Applying Fluid–Solid Conjugate Heat Transfer Modeling

Purging plugs are important functional units in advanced steel‐making processes, which experience extreme heat exchange and temperature changes during the purging procedure. Fluid–solid conjugate heat transfer modeling is conducted to determine the inconstant and instantaneous heat transfer coefficients at slit walls. Further thermomechanical simulations are performed on the purging plug by assuming elastic material behavior. Dimensionless temperature change and stress analysis indicate that transverse tensile failure is highly likely at the area close to 0.323 m from the base of the frustum purging plug. A comparison with practical observations proves that thermomechanical modeling coupled with the fluid–solid conjugate heat transfer method is a useful approach for investigating purging plugs under practical service conditions, as well as other cases involving fluid–solid interactions.