The purpose of this paper is to present a rigorous analysis of streamline patterns and their bifurcation to a viscoplastic Bingham fluid model that involves heat and mass transfer in an electroosmotic flow through a complex wavy microchannel. The Bingham fluid act as a solid medium in the core layer, which divides the channel into three distinct sections utilized to model the problem as a switched dynamical system between these zones. To track multiple steady states (stagnation points) and related trapping phenomena, we perform both analytical and numerical bifurcation analysis of each subsystem with respect to different physical effects such as electrical double layer thickness and Helmholtz-Smoluchowski velocity. The key feature of the technique presented here is its ability to reveal the peristaltic transport characteristics of the Bingham fluid model in the presence or absence of symmetric flow properties. The primary novelty here is the ability to regulate the location and stability of the equilibrium points in the domain of interest. This leads to the detection of global bifurcations that reflect important dynamic elements of the model. Our results highlighted a new category of complex behavior that controls transitions between qualitatively different transport mechanisms, as well as a class of non-classical trapping phenomena. Both blood pumps and heart-lung devices operate on a similar premise7.The use of bio-inspired materials has been increasingly prevalent in modern engineering model improvements. In order to update traditional engineering systems and attain previously unheard-of levels of endurance and performance, a number of intricate processes have been developed using biological systems. One such process is peristaltic movement. The contraction and expansion of a fluid-filled, flexible, tubular structure is known as peristalsis. Peristalsis has a wide variety of uses, and there are numerous researches regarding it in the literature8.Boosting heat transfer inside a channel is crucial to create more compact heat exchangers, which are used in a variety of engineering applications like cooling for electronic devices, air conditioning equipment, and ocean thermal energy conversion technologies. For scientists and engineers, the creation of these technologies is of the utmost importance11. The field of electrokinetic transfer has seen a boom in modern fluid mechanics. The interaction of electrolytic fluids with external electric fields, either static or alternating, is explored experimentally and analytically. Charge distributions, wetted surfaces, zeta potentials, and electric double layers are just a few of the fascinating phenomena it exhibits. Electrokinetic encompasses a wide range of phenomena, including electroosmosis, electrophoresis, and diffusiophoresis . Electroosmosis in narrow micro-vessels12. Diversified bio microfluidics systems13.Microchannel procedures produce electroosmotic fluxes, and chemical separation is used in a variety of biotechnology applications16. electro-magneto-hydrodynamics17. Heat and mass transfer in complicated, wavy microchannels of microvascular blood flow18, and some literatures were found24.Complex peristaltic pumping or complex boundary wall wavy patterns are two more significant peristaltic pumping occurrences. In industry, complicated pumping phenomena are employed to increase the effectiveness of micro and nano pumps, particularly in the medical field. Electroosmotic flow of pseudoplastic nano liquids via peristaltic pumping biomimetic propulsion is causing complex wavy, curving surfaces to be studied. Complex wavy channel with MHD effects25. Numerous engineering applications, including petroleum engineering, the discharge of groundwater into aquifers, and MHD generators, require a thorough understanding of Bingham fluid flow28.A branch of non-Newtonian fluids known as viscoplastic materials has a yield stress threshold for the applied stress. The material deforms as a viscous fluid for applied stresses greater than the yield stress; for applied forces less than the yield stress, the material behaves as a rigid solid. The phrase “viscoplastic materials” in this context often refers to substances that solely have viscous and plastic qualities. The first and simplest model is the Bingham fluid32. With the help of this method, you may identify the dynamics of fluid physical events and gain a better knowledge of the behaviour of the system as a whole. Regarding this, stability and bifurcation theory for streamline patterns has recently been created in order to offer critical insights for regulating and recognizing fluid transport mechanisms in specific classes of fluid-mechanical systems34. There have been several attempts to discuss the structural bifurcations and associated stagnation spots for two-dimensional incompressible flow, with the flow supposedly being explicitly represented by a polynomial form36. The streamline patterns and bifurcations around the stagnation (equilibrium) regions of peristaltic flow of various biological fluids are explored39, they determined the important qualitative aspects of the peristaltic flow, such as “bolus” (or “trap”) on the assumption that the flow motion shape was produced by a uniform channel.When parameters are altered or when variables and processes interact, dynamic systems theory outlines methods for analysing stability and changes in a system’s overall structureIn this paper, we focus on the topology of streamlines in a viscoplastic Bingham fluid model that includes heat and mass transfer in an electroosmotic flow through a complex wavy microchannel, especially on issues about bifurcations and stability, which are used to predict flow phenomena in streamline patterns when physical parameters are changed. The Bingham fluid  channel has one plug region and two distinct non-plug regions in the wave frame. Because the flow behavior in the plug region is constant, the nonlinear switched dynamical system is formed by connecting the obtained expression of the stream function with velocity fields in two distinct non-plug regions. The equilibrium points of each subsystem are calculated analytically and numerically, and a bifurcation analysis of these points is performed to show how topological characteristics change as one or more physical parameters are changed. The equilibrium point is classified as admissible or virtual depending on whether it is within or outside the domain of validity. The transition of virtual to admissible equilibrium points and the possibility of bifurcation in each domain independently are obtained. A heteroclinic connection is formed when a streamline connects two or more saddle-points. The use of heteroclinic connections in a subsystem or a full system has the advantage of completely trapping the flow between the orbits of the connection. If a heteroclinic connection exists, the distance between two saddle points is used to determine the minimum (or maximum) trapping zone limits. The bifurcation results are used to explain the effect of various physical parameters on fluid flow behaviors, such as flow rate, plug region size, electrical double layer thickness, and Helmholtz-Smoluchowski velocity.The paper is structured as follows: Sect. “18 is shown below.The electroosmosis peristaltic transport flow is described using a complex wavy two-dimensional microchannel. An externally supplied electric field is used through this channel to adjust the electroosmotic flow of an aqueous ionic solution in a non-Newtonian fluid (Bingham viscoplastic fluid), see Fig. Bingham fluid is a viscoplastic fluid, a type of non-Newtonian fluid in which the flow field is divided into two regions: an un-yielded zone in which the fluid is at rest or undergoes stiff motion, and a yielded zone in which the fluid flows like a viscous liquid. In the un-yielded zone, the second invariant of the extra stress tensor is less than or equal to the yield stress and a constitutive relation is undefined. In the yielded region, this invariant exceeds the yield stress and a constitutive relation exists for the extra stress tensor. Thus, the location and shape of the yield surface(s), i.e. the interface between these two sets, is also a part of the solution of flow problems of such fluids. Viscoplastic fluids occur in various chemical, metal, and food industries, e.g., margarine, mayonnaise and ketchup. The constitutive equation of an incompressible Bingham fluid is based on the assumption that the fluid remains at rest or moves as a rigid body if the second invariant of the extra stress tensor 25 that is required to describe a Bingham model is:The constitutive equation40. In this context, most lava flows are obvious applications of Bingham fluids. additionally, Bingham Fluid can be designed as the interaction of blood’s non-Newtonian nature and its flow through arteries, such as microvascular blood flow through a complex wavy microchannel, see18.The hypothetical viscous fluid has a yield strength that needs to be exceeded before it may flow. A lava channel, for example, is defined as a stream of flowing lava contained within zones of static  lava or lava levees. Levees may not exist in the original channel until the parental flow settles over what forms the channel and produces natural levees. Therefore, lava behaves as a multiphase non-Newtonian fluid, for example see18 are given by:12, which can be expressed as:The governing equations that serve as guiding principles for electroosmotic fluid flowIn this context, the Nernst-Planck equation for ionic number distribution is utilized to assess potential distribution as follows:We introduce the following set of non-dimensional variables and parameters to help get explicit analytical solutions to the governing equations.Debye-Huckel modifies the Poisson equation as follows:antities  allow foSolving the above equation with the associated conditions  for  for 7) f18:Physical boundary conditions for temperature, concentration, and velocity are imposed asThe axial velocity is determined by solving the Eq.  with bouThe solution for the normalized temperature distribution is found by solving Eq.  and usinFurther solving Eq.  with theUpper region of non-plug flow Plug flow region Lower region of no-plug flow Thus, for the vector d-dimensional parameter space and The main goal of this section is to describe and control the nonlinear behavior of all flow modes using dynamical system theory and state space simulations. The equations of motion of individual fluid particles in a two-dimensional flow can be written in classical form, with the stream function acting as the Hamiltonian switched dynamical system. The following regions are defined based on the problem formulation and stage configuration flow. The equilibrium points (or stagnation points) are the solution points If If If Assume that e system , then IfSwitches between distinct types of dynamical behavior may be performed by describing the transition of virtual to admissible equilibrium points, as well as the possibility of bifurcation in each domain independently.It is beneficial to consider a specific situation in order to fully comprehend the basic flow motion through the wavy channel. Hence, we consider the flow mode when l system  is identThe identification of equilibrium points and the study of their stability is an important step in the analysis of fluid dynamics. The equilibrium points of the vector fields  can be dFor instance, let Note that if function  explicitentclass1pt{minimaThe linearization of generalized system  at the pn system  iff \docThe configuration of the possible bifurcation of the above explicit formulas of equilibrium point is sufficient to report the most of the significant different flow behavior that may occur in this situation. It is clear in Fig. In general situation, We are unable to proceed with the explicit bifurcation analysis of the above vector fields due to their high level of nonlinearity. Therefore, in the following section, we will extend our analysis of bifurcation using an efficient numerical technique.Numerical analysis is an important tool in dealing with nonlinear bifurcation problems in various biological and physical systems. One of the main advantage of this approach is that it is used to measure the steady-state curves for an undetermined system of equations.The solutions to the following piecewise nonlinear system are helpful in determining all potentially admissible, virtual, boundary, and degenerate equilibrium points, as well as their bifurcation.A nonlinear system 39).It should be noted that there is no equilibrium point for the system e system  can be le system . Then tho system  independo system  are consIn this section, we discuss the impact of different physical parameters on fluid flow behaviors using numerical bifurcation analysis.Trapping phenomenon: Based on a dynamical examination of flow behavior around equilibrium points, this phenomenon can be discovered in two scenarios, namely local and global modes of system behavior. The flow is trapped in terms of local mode when the system  has centThe plug flow region By taking the Debye length x-axis. In addition, depending on whether the Helmholtz-Smoluchowski velocity parameter is negative or positive, the electrical field acts in the positive axial direction or is oriented in the reverse x-direction. The maximum trapping zone is shown in Fig. x-axis, see Fig. Following that, we show how different Helmholtz-Smoluchowski velocity Temperature fields in Analytical and numerical bifurcation analysis is used to systematically identify dynamic behavior and characterize fluid flow to reveal associated physical phenomena.Our results indicate that heteroclinic connections to saddle points are the primary cause of the trapping phenomenon in two scenarios, namely the presence or absence of symmetric flow.The non-uniform geometry caused by the plug region and varying amplitude ratio parameters has a significant impact on the trapping phenomenon.We assert that the trapping zone does not exist with a large Debye length The impact of Helmholtz-Smoluchowski velocity A parametric study is carried out to evaluate the effect of the Joule heating term, chemical reaction, and the Brinkman and Schmidt numbers on the temperature field contour across the microchannel and fluid concentration behavior.The qualitative aspects of an electroosmotic peristaltic Bingham fluid model, specifically geometrical properties of flow fields such as bifurcation and the stability of its streamline patterns, are investigated. This model simulates the effect of heat and mass transfer on Bingham fluid flow through a complex wavy microchannel influenced by electroosmosis. The following are the key results of the current study:


The structural condition of hydroelectric tunnels is important to the overall performance, safety, and longevity of generating stations. Significant effort is required to inspect, monitor, and maintain these tunnels. Photogrammetry is an effective method of collecting highly accurate visual and spatial data. However, it also presents the complex challenge of positioning a camera at thousands of difficult-to-reach locations throughout the large and varying-diameter tunnels. A semi-automated robotic camera positioning system was developed to enhance the collection of images within hydroelectric tunnels for photogrammetric inspections. A continuous spiral image network was developed to optimize the collection speed within the bounds of photography and capture-in-motion constraints. The positioning system and image network optimization reduce the time and effort required while providing the ability to adapt to different and varying tunnel diameters. To demonstrate, over 28,000 images were captured at a ground sampling distance of 0.4 mm in the 822 m long concrete-lined section of the Grand Falls Generating Station intake tunnel. High-resolution visual and spatial models are enhancing traditional methods of inspecting large-scale structures. Data collection for these models can be accomplished with lidar; however, photogrammetry can produce very high-resolution RGB point clouds at high speeds that can be inspected visually. These improved models overcome the inaccuracy and uncertainty of traditional inspection methods and enable a better understanding of infrastructure condition and deterioration trends.Typical hydroelectric generating stations have multiple penstocks and often include additional associated tunnels. These tunnels are often kilometers long and upwards of 10 m in diameter and beyond; the Grand Falls Generating Station  intake tunnel is 7.5 m in diameter, and the concrete-lined section is 822 m long, for example. The current methods of collecting photogrammetric data at the quality and resolution desired for inspection consist primarily of manual tasks that demand great labor efforts, especially in large tunnels. This process is time intensive and takes longer than a traditional walk-through inspection by an inspector. With individual generating stations having different diameter tunnels or multiple different stations being inspected by the same equipment, tunnel-specific image capture methods are inefficient, costly and require substantial modifications to capture unique locations. Station shutdowns come at a significant expense as replacement electricity must be outsourced during the downtime. The Mactaquac Generating Station (Mactaquac), a generating station near Grand Falls, has a 670 MW capacity, whereas Grand Falls has a capacity of 66 MW. For example, the cost of replacement electricity for the smaller Grand Falls station was estimated to be $38,000 per day during the 2017 shutdown, which lasted for 10 days in 2017 , the  the GSD . This veEquation  defines © Photo Equipment Co. The product manual documentation lists the number of flash actions that will activate over-temperature protection for a particular output power; at an output power of In addition to the direct limitations on the physical motion speed of the cameras, constraints are placed on the image capture rate due to aspects of the photography equipment. As each camera has a set of two flashes that operate at close to full power to provide sufficient lighting for the images, image capture frequency significantly affects the power consumption and the rate at which the flash can take successive images: the flash refresh rate (FRR). As the frequency of image capture increases, the risk of overheating increases as well. If a fast flash rate is sustained for an extended period, the FRR will be automatically reduced or completely halted for a period to cool-down. The flashes used were the AD400Pro from GODOX flashes . HoweverThe Equation . The resEquation .(20)ωFRConsideration of both of these limitations is key to ensuring effective capture, but only one will be the critical factor at a given time (Equation ):(22)ICRThe powerhouse at the Grand Falls in New Brunswick houses four Francis turbines with a total capacity of 66 MW. Water is diverted to this station from the Saint John River through an intake tunnel running under the town center. This tunnel is approximately 920 m in length, consisting primarily of an 822 m long concrete lined section.Visual walkthrough inspections have been the primary method of inspection for decades and continue to be conducted to identify current defects and areas for caution or immediate repair. The first photogrammetric scan of this tunnel was completed by BE in 2017 [The total image acquisition process spanned just over four working days, each being a scheduled 10 h work day (7:00 a.m.–5:00 p.m.); however, the general tailboard meetings, safety discussions, and uncontrollable time spent waiting for entrance to the tunnel allowed for approximately seven working hours in the tunnel per day, which were broken into two sessions. Actual scanning time was further reduced due to the daily set up and tear down of the camera equipment and the preparation of the ATI.The ability to bring and set up equipment in the tunnel through the main access port, which involved transporting through a small porthole and the use of a rope hoist, simplified the process compared to the special treatment that was required to transport TIA into the tunnel in 2017, validating a benefit of the new modular design of the ATI. As this was the first time setting up and operating within the actual tunnel environment, its behavior on the muddy, slippery, and rough tunnel surface was thoroughly tested before confidently beginning the actual scanning process. Complete scanning began and proceeded steadily for approximately four and a half working days. Much of this process was smooth, and minimal interjections or interrupts were experienced; however, some locations within the tunnel required additional attention. A number of locations along the tunnel had hose-sized sprays coming from the top or sides of the tunnel, which were to be avoided if possible to protect the camera equipment. In many cases, risk of water contact with photography equipment could be mitigated by using extended umbrellas to divert the sprays away, while other cases required alteration to the spiral scan sequence to ensure as many images were captured around these locations as possible with sufficient OL, while still mitigating water contact with the cameras.In addition to the presence of water, rough terrain at the invert of the tunnel required cautious attention throughout, as there were a collection of defects, grooves and potholes of up to ten centimeters deep that a wheel could fall into. For the most part, these were avoided if noticed; however, it was not uncommon for a wheel to slip into one of these, which may have caused some slight jerking or skewing of the ATI but did not cause a significant interference. It was slightly offset from the center of the invert and was rectangular in shape, measuring approximately 2.5 m long, 0.75 m wide, and over 0.5 m deep. Scenarios like this are a prime example of the extreme complexity of fully automating the motion of the ATI in these types of environments.Since the first scan in 2017, the abilities of the photogrammetric analysis performed by BE have steadily improved from the former methods and technologies, which now allow for images to be captured at a resolution of 0.4 mm for these tunnels. This requires a camera–surface distance of 2 m. This camera offset, combined with the desired 80%/60% image OL and other properties of the photography system, resulted in the choice of 52 images per rotation. The ICR, as defined in Using a dual camera system allows for twice the linear advance to be made during one complete rotation, as same-angle images will be captured by opposing cameras every half rotation. Synchronizing the linear advance (40%) with the timing of the rotation sets the linear speed of the ATI to 0.67 m/min. At this rate, the 822 m section of the tunnel was estimated to require approximately 23 h of scanning time, assuming perfect efficiency; this turned out to be a reasonably accurate estimation, considering the delays and interference with the ability to scan that slowed the overall process at times. A similar estimation for the ATI to perform a scan of similar quality and resolution to the scan conducted in 2017 shows a total required capture time of 7 h. While this assumes ideal efficiency and does not include the time for set up and interruption, a drastic improvement in automation, control, and image capture over the approach taken in 2017 is evident.As discussed, a semi-automated camera positioning system, referred to as the ATI, was designed and developed to address a set of limitations identified in the data acquisition process of photogrammetric inspections in hydroelectric tunnels. ATI utilizes a variety of electromechanical components and advanced predictive control techniques to drive and automate elements of the image collection process. The ATI design is capable of automatically adapting to tunnel diameters between 4.5 m and 9 m and maintaining consistent image capture parameters at any variation. Modification of the camera-to-surface distance can be used to vary the image resolution and alter the total scan procedure. The ATI allows for complete driven mobility, including pure translation or rotation for effective reorientation and alignment within the tunnel environment.The model quality constraints, photography equipment properties, and photogrammetric parameters formed the basis for the required image capture parameters throughout the tunnel. A unique spiral image network was developed that allows the full potential of the ATI to be utilized by facilitating continuous image capture while rotating and driving along the tunnel. This sequence eliminated any idle time that creates inefficiencies in the process that had been observed in the previous, more incremental capture sequences. The rate of capture limits were quantified based on the motion limit to avoid blur in the images, the refresh rate of the flashes, and the time required to change orientation, all of which vary depending on tunnel and photogrammetric parameters. This analysis optimizes the rate of capture of the continuous approach and promotes efficiency in the collection process. In the process of the development and implementation of the ATI, advanced closed-loop control techniques, including various PI-based and model predictive control schemes, have been formulated and assessed in a unique and challenging environment on this large scale robotic system.While the direct goal of this work is to make significant improvements to a semi-automated system, this work can serve as a foundational element for future research in the pursuit of an autonomous ATI.Further research into localization within GNSS-denied, dark, featureless environments should be conducted to improve the accuracy and consistency of real-time localization within a tunnel to identify the complete pose of a vehicle in these challenging environments. This area of research is foundational for other automation-related applications.Maintaining alignment of the ATI while moving throughout the tunnel required frequent steering adjustment, and although fully automating this was outside of this project’s scope, it stands as an aspect for significantly reducing the efforts and attention required of the operator. The self-navigation of a three-wheeled vehicle in a generally cylindrical tunnel with the goal of maintaining centricity, alignment, and velocity would be a significant advancement in this aspect. This would include maneuvering in dynamic environments, and involving object avoidance methods would be a key element to this.The control systems for each portion of the ATI were created as different configurations of SISO systems. Further research into the system identification of MIMO systems would formulate a more optimal control scheme, particularly in the case of the model predictive control of the drive system.Elements of this work are included in currently pursued patents.


Different techniques are used to analyze annular flow, but the more interesting ones are those techniques that do not perturb the flow and provide enough resolution to clearly distinguish the interfacial phenomena that take place at the interface, especially the disturbance waves (DW) and the ripple waves (DW). The understanding of these events is important because it influences the heat and mass transfer taking place through the thin film formed near the walls in this flow regime. The laser-induced fluorescence (LIF) and the three-electrode conductance probe are two commonly used techniques to study experimentally annular flow phenomena. In this paper, a set of experiments at different temperatures of 20 °C, 30 °C and 40 °C and different liquid Reynolds numbers have been performed in the annular flow regime, the characteristic of the DW and RW as average height and frequency of these waves has been measured by both techniques LIF and conductance probes. In addition, we also measured the mean film thickness. It was found that the mean film thickness and the DW height are practically the same when measured by both techniques; however, the height of the RW is smaller when measured by the conductance probe and this difference diminishes when the temperature increases. Annular flow is one of the most important two-phase flow regimes because it is the dominant regime for heat transfer in refrigeration equipment, boiling water reactors (BWR), passive safety systems as the passive containment cooling condensers in the simplified BWR and some types of small modular reactors (SMR) ,2,3,4. AThe annular flow is characterized by the presence of several types of waves at the interface between the phases, which enhance the heat transfer between the phases. The most important ones are the disturbance waves (DW) and the ripple waves (RW) ,8. The fAmong the main methods used at present times that perform localized measurements at a given space position to obtain the time evolution are the electrical and optical procedures. These methods can give details on interfacial phenomena over remarkable time scales. Their extended use is due to their no-trouble implementation and utilization for many different applications. Employment of these techniques facilitates obtaining reasonably localized measurements, with good spatial resolutions generally of the order of millimeters. Sometimes the measurement position can be changed by displacing the probe or replicating the measurement system at different positions in the facility ,10,11,12Among the most popular localized-time evolution methods that produce a minimum distortion on the film characteristics to describe the annular flow properties are the electric methods. The most popular are the capacitance methods and the conductance ones. The first one uses capacitance probes. This technique relies on the difference between the dielectric permittivity of the liquid and the gas phases, so the capacitance value obtained by placing two electrodes will be bigger or smaller relative to the thickness of the liquid layer .printed circuit board) capable of taking the same shape through which the liquid layer displaces. Each electrode couple can give a spatial resolution for the measurement of the order of millimeters [The conductance probes are based on the difference in electrical conductance of the liquid and gas phases ,16. Therlimeters . The maiRecently, Liu et al.  used a mThe other set of methods that allow us to obtain localized and spatial distributed results and their evolution with time are the optical methods. These methods generally use high-speed advanced cameras; the most advanced ones have high spatial resolution and can perform a high number of frames per second to obtain the thickness of the liquid film in annular flow. These methods emerge as an evolution of localized techniques and attain at present times a high level of development. The use of optical methods is the most common one due to their simplicity compared with other kinds of methods and they have the additional advantage of providing a large amount of information in their measurements. However, when applied to annular flow they present some drawbacks, as the distortion caused by light total reflection at the irregular interface between the two phases that are not uniform and contain many waves. In addition, the pipe wall distorts the film images. Xue et al. ,11,12 anThe technique of light absorption by photography involves obtaining the quantity of light coming from a light LED source that is attenuated by the liquid layer and the wall as displayed in Within the optical method, one of the most used at present times is laser-induced fluorescence (LIF). This method and its different techniques are very widespread nowadays. To perform the measurements with this technique, it is required to dye the liquid phase with a fluorescent substance, commonly Rhodamine B or 6G, which is then illuminated by a laser plane beam in the measurement region. The Rhodamine B is a fluorescent organic compound with an excitation wavelength of Subsequently, a high-speed camera is employed to capture images of the liquid film. This water layer is discernible by the fluorescence emitted by the contained dye. The technique planar laser-induced fluorescence (PLIF) utilizes a planar sheet beam created by a series of lenses, generating a green-colored laser sheet as illustrated in Zadrazil et al. ,29,30 usIn addition to the previous findings, Zadrazil et al. ,29,30 alAs with the rest of the methods previously discussed, LIF has also some inconveniences. The main disadvantage that is common to all optical methods is the error produced by the light refraction as it passes from one medium to another. The annular flow is characterized by having two phases contained generally inside a curved pipe. The main error types occurring because of the refraction phenomenon have been explained by Charogiannis et al.  and are The error source displayed in x and y being the longitudinal and transverse coordinates, K the interfacial reflection index between phases, equal to 0.02 for moderate interface slopes, and, finally, To avoid these errors, the LIF method has been ameliorated in recent years by two different approaches. The first one of these procedures is the brightness-based laser-induced fluorescence (BBLIF) technique developed by Alekseenko et al. , which ignitudes :(1)I method displayed in Recently Xue et al. ,11,12 haThis paper compares two measurement methods, one electric  and one optic (PLIF40 method with subpixel correction), used to measure the film thickness in the GEPELON and CAPELON facilities located at the thermal-hydraulics laboratory of the IEE institute at the Technical University of Valencia (UPV), the first one was used to perform the comparative measurements, while the second one was used to develop the method for optical measurements.The paper organization is as follows, In this section, we first explain the characteristics of the GEPELON facility used to perform both the conductance probe measurements and the optical measurements with all the instrumentation used to measure the mass flow rates of gas and liquid, the pressure and the temperature, respectively. In addition, we describe all the instrumentation used to perform both the conductance probe measurements and the PLIF optical measurements. In the case of the PLIF optical measurements, we analyze the optical corrections by refraction and reflection that are necessary to achieve the correct value of the thickness, the subpixel correction of the interfacial edge ,33,34, aThe GEPELON experimental flow facility (GEneración de PELícula ONdulatoria or translate to English Wavy Film Generation) is an installation designed to generate an annular two-phase flow. This equipment has been designed to generate a layer of liquid sliding on the pipe walls while the air mass remains in the core part of the pipe, either quiescent or moving in co-current flow, i.e., GEPELON produces a downward annular air-liquid flow moving downward through the vertical test section of the facility. The expected phenomena to occur will be like the ones of the passive cooling systems in third-generation reactors or small modular reactors (SMR), or like the ones occurring in steam generator tubes during some accidental scenarios, but only in their hydraulic performance. In this phase of the facility, there is no incorporation of heated fluids, meaning that it does not account for heat transfer between the fluids or the wall. However, it should be noted that a recent upgrade has been implemented to enable the system to accommodate heated fluids. In the present study, we will display the results obtained with water as fluid at three temperatures 20 °C, 30 °C and 40 °C, the temperature control system of GEPELON allows us to control the temperature in the circuit with very high precision. The facility configuration is displayed in The water used in all experimental data sets is carefully managed before being supplied to the loop. Its properties are adequately prepared using filters, temperature controller and PH controller to have the appropriate conductivity without impurities.Along its path from the feed water tank to the injector, the liquid goes through several devices to control and measure its properties. In particular, the conductivity calibration sensor, displayed in In the free-fall configuration, a water pump, capable of exerting a maximum pumping pressure of 4.2 bar, moves the water along the system close loop. The pump conveys the water to the upper section of the standpipe via a custom-designed pressurized water injection system . Being tThe facility configuration for co-current experiments is the same one as for free fall experiments being the only difference in the air injection system. The air stream is filtered, de-dusted and demisted prior to its injection into the upper part of the facility, as displayed in Conductance probes are based on the conductance value measured between the emitter and receiver electrodes at high frequencies, which depends on the liquid film thickness ,17,19,36quencies .The conductance probes work because there is a proportionality between the liquid layer thickness located between the electrodes and the current transmitted between them; the reason is that the conductivity of the liquid is much higher than the gas conductivity. The conductance probe comprises three electrodes that are integrated into the wall, positioned in parallel or perpendicular alignment to the direction of fluid flow. The emitting electrode, situated at one extremity of the device, sends a sinusoidal signal with a frequency of 100 kHz and an amplitude of 5 Vpp coming from a signal generator. One of the electrodes is connected to the ground normally the central one, while the position of the receiver electrode is at the other end of the device. This last electrode receives the signal and sends it to the filtering and processing device. The way the conductance probe works is as follows: the first electrode emits an electrical AC signal, which is then transmitted through the thin liquid film, and finally captured by the receiver electrode, resulting in a direct correlation between the received signal and the thickness of the liquid layer. The mission of the ground electrode is to collect the parasitic currents.The port design of the conductance probes has been built by 3D impression because it guarantees the perfect alignment of the conductance probes and the distance among them. The first ones were manufactured mechanically but this procedure was discarded because we do have not in our laboratory the necessary precision to manufacture the sensor with the required accuracy for small electrodes and the distance between them. The electronic circuit associated with the conductance probe remains consistent with the one employed in previous publications . The eleA signal generator displayed in ocessing . The uniThe calibration procedure was performed in two steps: in the first step, we obtained the calibration curves at different temperatures and for several film thicknesses using the same method used by Rivera et al ,9 to cheb and scaled denote the base calibration values and the scaled calibration values, respectively.Based on this idea, the calibration voltage for a given thickness for each temperature run has been carried out by measuring the saturation voltage Finally, to finish this section, we discuss the calibration procedure performed for all conductance probes. The device employed consists of the following parts: an electronic precision positioning system; a flatness optical table; and several dielectric cylinders of different diameters. The positioning system places each cylinder of known diameter at the central position of the inner side of the conductance probe port. Then, a high-precision positioning system allows us to know the exact placement of the cylinders, so that the exterior side of the cylinder and the interior side of the probe have a constant known gap in their entire circumference. This gap is then filled with treated water. Then, the calibration procedure includes the following steps: The signal generator sends a specific signal, which excites the probe’s emitting electrode. The electrical signal passes through the known liquid layer thickness, and the correspondent signal is received by the probe’s receiving electrode. This electrical signal is then collected by the DAQ. Subsequently, the relationship between the voltage of the electrical signal and the liquid film thickness can be obtained, as the liquid thickness is known, and the signal voltage is being measured. This process is then replicated for all-dielectric cylinders to acquire a sufficient number of calibration points that establish the correlation between signal voltage and liquid film thickness for each probe. In addition, the GEPELON facility has a temperature control unit to maintain the temperature of the circuit at a constant fixed value. By using this system, GEPELON achieves high-temperature stability, and it is observed that the conductivity does not vary once the facility attains stable temperature conditions.As commented in the introduction section, in the method of planar laser-induced fluorescence (PLIF), a small concentration of a fluorescent dye (Rhodamine) is added to the water causing the liquid film to appear as bright regions on the images once exposed to laser light with a wavelength equal to the excitation wavelength of the rhodamine. These images are then processed to locate the edge of the bright region, asserted to be a gas–liquid interface. The main difficulty arises because there are different types of errors as total reflection at the interface and refraction in the tube wall that can cause misleading film thickness measurements. Xue, Li, and Zhang  recentlyOne of the problems we found is the reflection and the refraction of the laser light in the tube walls making it very difficult to find the interface between the tube wall and the liquid. This problem is easily solved because when the laser photons interact with the dye, the wavelength changes from 532 nm to 610 nm. This means that if we place an optical filter in front of the camera lens, we can remove the laser’s base wavelength and keep only the wavelength of interest. In theory, this would allow us to observe only the liquid, completely solving one of the problems: determining the location of the inner tube wall.In addition, to mitigate the challenges posed by refraction when measuring annular flow within a pipe, many researchers employ the liquid box technique . This teTo establish a meaningful relationship between Here, To relate all the angles, we need to consider their relationships as shown in Consequently, the angles From Equations (9) and (10), it follows:It is possible to generalize the previous expression to the entire system:Similarly, as carried out for angles The only missing term gives the relation of the angles With this set of equations, it becomes possible to iterate and derive the true film thickness value  was obtained by fitting the data of the true values computed with the algorithm with a polynomial function in terms of the measured values. The determination coefficient was practically 1 and the data and the fit curve are displayed in Based on the experiments of previous authors  and afteSub-pixel detection is a widely used method for object detection and computer vision. This method is much more accurate than pixelated contour detection (the method used previously). For this study, we will use a detection operator called Sobel operator used in artificial vision for edge detection ,34. SobeHorizontal changes. First, it performs the convolution of the image with the horizontal Sobel kernel, i.e., it performs the following operation:Vertical changes. Second, it performs the convolution of the image with the vertical Sobel kernel, i.e., it performs the operation:If Horizontal filter operator of Sobel:Vertical filter operator of Sobel:G), combines the strengths of both the horizontal and vertical gradients [Therefore, the operators radients : (24)G=GG represents the overall strength of the gradient at each pixel. By comparing this gradient strength to a predefined threshold, we can classify a pixel as an edge pixel, with the threshold influencing the sensitivity of the edge detection process. Additionally, we can determine the direction of edges θ to provide the orientation of the detected edge, distinguishing between horizontal and vertical edges. Comparing magnitudes of If If Applying the previous algorithm to each experimental snapshot, it is possible to identify the film thickness with better accuracy compared with the traditional pixelated contour detection, accurately indicating the liquid evolution.In conclusion, the action of the Sobel operator on the image can be seen as a two-dimensional mapping of the gradient on each image point, where the regions with high gradients represent the edges and the rest is the background.The implementation of the sub-pixel detection algorithm produced the image displayed in Finally, to convert the number of pixels of the recorded images into length (mm), we locate a reference length rule with an imprinted length scale in the position of the laser sheet and we count the number of pixels located between two marks, obtaining the equivalence in mm between pixels and length. The result was that 1 mm is equivalent to 30 pixels.x-axis and the shorter distance y-axis. So, the x coordinates will be in the axial direction and the y coordinates in the radial direction. In our images we take the x coordinates in the normal direction to the pipe wall and name it as x′ and the y coordinates in the direction of the pipe axis and denote it y′ so we perform the change:Normally in the Sobel algorithm, the larger distance is denoted as the So, the values of z-axis) at different positions (y′-axis) versus the time (frame number) for the measurements performed in annular flow with subpixel edge detection. The position along the y′ axis was expressed in pixels (30 pixels is 1 mm), the time was expressed in frames and the CMOS camera worked at 1940.1 Hz or frames per second. It is observed that the disturbance waves (DW) propagate all with the same celerity given by the slope of the straight lines displayed in Next, we display in To effectively extract the crucial characteristics defining the behavior of the film under study, the development of a rigorous signal postprocessing methodology becomes imperative. This methodology must not only ensure the accurate analysis of the film but also guarantee consistency in handling data obtained from different measurement approaches. As the primary objective of this research is to compare the outcomes derived from both the conductance probe and PLIF methodologies, it is essential to establish a methodology that harmonizes the data processing for both techniques, considering the unique aspects of each measurement approach.For the PLIF snapshots, we have previously explained the algorithm employed to extract the interface, and, consequently, the film thickness. However, the subsequent step demands the generation of a comprehensive data set including all the images acquired during each experimental run. One notable advantage of the PLIF system relies on its capability to capture the spatiotemporal measurements, enabling the assessment of the film’s evolution from both spatial and temporal perspectives. In contrast, the conductance probe measurements offer insights solely into the temporal evolution of film thickness at a specific location within the test section. To facilitate a meaningful comparison between these two instrumentation types, we initially process the PLIF measurements to extract the temporal evolution in a similar way as the conductance probes. This involves calculating the average film thickness within a 7.5 mm window for each snapshot and aggregating these values over the entire run. The choice of a 7.5 mm window aligns with the physical separation of the probe electrodes (emitter and receiver), providing a basis for equitable comparison. At this point, both sets of measurements are rendered equivalent, and the treatment for extracting the primary film variables has been standardized across the two methodologies.The mean film thickness, denoted as a et al. , ensurink) until the minimum of Equation (27) is achieved. This operation can be expressed mathematically as:x-pixel at time x-pixel at time As previously mentioned, the spatial evolution of the film thickness can be analyzed using PLIF measurements. This method involves detecting the overlap between the film shape in two consecutive snapshots, allowing for the extraction of additional information in each new frame. The process of determining this overlap consists of minimizing the differences in film thickness between two consecutive snapshots by shifting the pixels of the new frame pixel by pixel (varying x (expressed in number of pixels), you need to know where this same film height will be in the next snapshot at time k by minimizing Equation (27).The explanation is simple; if you have a film height The different equipment employed that contribute to experimental conditions uncertainties include the water flow meter  and the T-type thermocouples copper–constantan . The total error of the measurements usually entails an analysis of systematic error and accidental error. For the conductance probes, different devices contribute to the deviation due to systematic errors including the data acquisition system, the fitting error between the calibration curve and calibration points, and the positioning error during the calibration process. An extensive analysis in this regard has been carried out in previous experimental studies carried out by the group ,9. AccidThe precise error assessment for PLIF techniques remains a topic with many open questions for the research community. The main errors are described in  and compThis section of this study presents a comprehensive analysis of the experimental data obtained from the two distinct measurement techniques, PLIF and conductance probes, used to investigate annular two-phase flow. These techniques have been widely employed to study annular flow phenomena; however, a systematic comparison between them has been lacking in the literature. In this section, we provide a detailed examination of key parameters characterizing the liquid film, disturbance waves, and their temporal evolution, shedding light on the differences and similarities between the two measurement methods. Additionally, we discuss the implications of these findings and their significance in the context of annular flow characterization and engineering applications.Several kinds of results have been obtained in the GEPELON facility when measuring the film thickness in the free-fall configuration for several Reynolds numbers of the downward water film and at three different temperatures 20 °C, 30 °C, and 40 °C. The measurements were performed using the conductance probe explained previously, with the three electrodes oriented perpendicularly to the flow direction as shown in Before comparing the PLIF and conductance probe, we analyzed the differences in the temporal evolution of the film thickness using the PLIF methodology. To determine the waveform, a minimum of one pixel resolution can be considered to generate the total evolution of the film thickness during the measured time. Nevertheless, to reduce the noise introduced by the binarization during the pre-processing of the images, a moving average filter with a window of 15 pixels has been applied. Therefore, the spatial resolution is slightly increased from 1 pixel (or 0.033 mm approximately) to 15 pixels, equivalent to 0.5 mm. The conversion relation is 1 mm equivalent to 30 pixels as explained in the previous section.x-axis in the spatial evolution representation is not a direct reflection of the physical length of the tube. Instead, it serves as a composite extension, if both the film thickness and the waves remain unchanged over time. This abstraction allows for a focused examination of the evolving patterns and behavior of the liquid film. Upon closer examination of the comparison between the two techniques, it becomes evident that both consistently identify the waveform. They exhibit similar trends, although subtle discrepancies manifest in most of the waves. Notably, the temporal evolution analysis showcases a more uniform pattern, while the spatial evolution analysis excels in detecting the rugosity present at the liquid–gas interface. Differences in the disturbance wave height are also detected. The first explanation for these differences is that the snapshots were performed at a rate of 1940.1 Hz, so the difference in time between snapshots was Next, the results obtained from the analysis of the spatial and temporal evolution of the liquid film thickness in annular two-phase flow are presented. As discussed earlier, the spatial evolution methodology for the data gathered using PLIF differs from the temporal evolution. To compare the measurements between both techniques, the temporal evolution has been taken as a reference. It is important to underscore that the measurements conducted through the PLIF (planar laser-induced fluorescence) technique, and the conductivity probe were executed in not identical close regions, with a separation distance of approximately 100 mm. The measurement region using PLIF is, therefore, slightly anterior to the ROI of the probe. D the pipe diameter equal to 30 mm, and The experimental measurements using both methods were performed with the same boundary conditions, i.e., three different superficial velocities for the liquid Several magnitudes were calculated from the measurements in this paper and then compared for both types of measurement techniques, the average thickness of the liquid film To facilitate a fair evaluation, first, the PLIF results obtained have been compared between temporal measurements using the 7.5 mm average and the 0.5 mm average. It is important to remember that the measurements are the same, but the methodology used to capture the interface varies depending on the specific temporal average considered.In The final goal of this study is to analyze the differences observed in all the variables under investigation when comparing PLIF40 and the conductance probe. Building on the preceding discussion concerning the spatial resolution of PLIF40, we have employed a 7.5 mm spatial processing approach for the purpose of comparison. This approach ensures that we consider the spatial average affecting the conductance probes, specifically spanning the 7.5 mm distance between the extremities of the emitter and receiver electrodes.The disturbance wave height comparison is depicted in Finally, we need to discuss the differences found in the ripple wave height. As shown in In this paper, the GEPELON facility was employed to conduct a study of air-water annular two-phase flow. The primary objective was to investigate the behavior of this flow using different techniques under varying conditions, specifically focusing on film thickness measurement in a free-fall configuration. This study included a range of Reynolds numbers for the downward water film and was conducted at three distinct temperatures: 20 °C, 30 °C and 40 °C. The two measurement techniques employed are the conductance probe, featuring three electrodes oriented perpendicularly to the flow direction, and the PLIF40 method, employing a laser sheet and a high-speed camera. The test measurements were performed in regions close to each other but not identical, with a separation of 100 mm being the PLIF measurements before, as displayed in For conductance probe measurements, we employ a method based on the current between emitter and receiver electrodes at high frequencies located flush mounted to the wall. This approach allows for precise measurement of temporal variations in film thickness with a high sampling rate and high recording times. The technique relies on the difference in conductivity between liquid and gas, employing three electrodes embedded in the wall to measure the liquid film thickness. In PLIF optical measurements, a fluorescent dye is added to the water, making the liquid film emit light under a laser sheet. However, challenges arise due to errors caused by refraction and total reflection at the gas–liquid interface. To address this, we employ optical corrections involving taking the measurements with an angle of 40°, the use of optical filters and a correction algorithm based on known refractive indices of the media. Sub-pixel edge detection is utilized to precisely locate the gas–liquid interface in PLIF measurements. The Sobel operator is employed for edge detection, enhancing the accuracy of the measurements.To analyze the temporal evolution of film thickness, data processing techniques are applied to both conductance probe and PLIF measurements. For PLIF, this involves calculating the temporal evolution of the film thickness within different windows and identifying waves in the signal. A standardized approach is adopted to make comparisons between the two measurement techniques meaningful. Furthermore, spatial evolution analysis of film thickness in PLIF measurements is conducted by an algorithm able to systematically compare consecutive snapshots and detect changes between them. This process enables a detailed understanding of how the film thickness evolves over time with a very high spatial resolution.The comparative analysis of results begins with an examination of the differences in the temporal evolution of film thickness using the PLIF methodology. The spatial resolution of PLIF was found to impact the accuracy of waveform reproduction. A 0.5 mm spatial resolution offered higher precision but introduced subtle errors in interface rugosity. Conversely, a 7.5 mm spatial resolution provided a more uniform representation but dampened the visualization of smaller ripple waves.Subsequently, a study of the experiments conducted with PLIF40 at different Reynolds numbers and temperatures is shown in The final goal of the study was to compare results obtained using the conductance probe and PLIF40 techniques. A 7.5 mm spatial processing approach was applied to PLIF40 to match the spatial averaging effect of the conductance probe. The comparison included the same main key film characteristics. For mean film thickness, both techniques produced consistent trends across various liquid Reynolds numbers and temperatures, with minor differences at 30 °C. As the Reynolds number of the liquid film increases, a growth in the mean film thickness is observed at all temperatures. However, when the temperature rises, the average film thickness diminishes for all Reynolds numbers. Additionally, the differences in average thickness measured by both methods diminished when the temperature rose, ultimately converging at the highest Reynolds number and temperature. This convergence highlights the conductance technique’s heightened sensitivity to temperature variations due to changes in water conductivity.Furthermore, disturbance waves, being large and coherent, were not significantly affected by spatial averaging, and both methods yielded similar wave height results. Both techniques also showcased a decrease in disturbance wave height with rising temperatures. However, this reduction was more pronounced when using the conductance probe, primarily due to the strong dependence of conductivity on temperature. In contrast, ripple waves, characterized by their smaller size and interface roughness, showed more substantial differences, with a maximum of 28% deviation between techniques. Disturbance wave frequency also showed deviations, primarily due to the wave detection algorithm and the short PLIF40 total time of each run, limiting its capacity for transient statistics.This research provides insights into annular two-phase flow behavior measurement techniques. Both PLIF40 and the conductance probe prove valuable for studying film characteristics, each with its unique strengths and limitations. The choice between these two techniques relies on the specific aspects of the liquid film under investigation. PLIF40, with a 0.5 mm spatial resolution or less, excels in capturing interface rugosity and studying smaller ripple waves. In contrast, the conductance probe offers consistent and reliable results, especially for averaged parameters such as mean film thickness and disturbance wave height and frequency. These findings contribute to a deeper understanding of annular two-phase flow dynamics and offer researchers valuable options for measurement techniques, adapted to their research objectives and desired level of detail.


Accurate forecasting of hospital bed demand is crucial during infectious disease epidemics to avoid overwhelming healthcare facilities. To address this, we developed an intuitive online tool for individual hospitals to forecast COVID-19 bed demand. The tool utilizes local data, including incidence, vaccination, and bed occupancy data, at customizable geographical resolutions. Users can specify their hospital’s catchment area and adjust the initial number of COVID-19 occupied beds. We assessed the model’s performance by forecasting ICU bed occupancy for several university hospitals and regions in Germany. The model achieves optimal results when the selected catchment area aligns with the hospital’s local catchment. While expanding the catchment area reduces accuracy, it improves precision. However, forecasting performance diminishes during epidemic turning points. Incorporating variants of concern slightly decreases precision around turning points but does not significantly impact overall bed occupancy results. Our study highlights the significance of using local data for epidemic forecasts. Forecasts based on the hospital’s specific catchment area outperform those relying on national or state-level data, striking a better balance between accuracy and precision. These hospital-specific bed demand forecasts offer valuable insights for hospital planning, such as adjusting elective surgeries to create additional bed capacity promptly. Hospital beds are usually in limited supply, because most hospitals run at near-full capacity under normal circumstances. This sudden increase in admissions, in combination with a potential long length of stay of patients in hospital, can put sudden pressure on the limited number of beds available2.The speed of community transmission of virulent pathogens during epidemics or pandemics has the potential to overwhelm healthcare systemsForecasting of bed demand is therefore essential to hospitals in order to prevent them from becoming overwhelmed by incoming patients. The capacity of hospitals to admit COVID-19 patients is not static, and available beds, as well as nursing staff, doctors, and personal protective equipment can, to a certain degree, be steered. For instance, cancellation of elective surgeries can free up resources needed to cater for an increasing number of admitted COVID-19 patients. However, this can’t be done overnight, and a preparation period needs to be considered. Forecasting models help bridge the gap between the current situation and the situation after the preparation period, thus forming a critical part of the decision process.4. One prominent example is the Johns Hopkins University dashboard which mostly focuses on the visualisation of data at the country, region, or city level5. Some online accessible dashboards additionally offer forecasts of the hospital bed demand7. However, many forecasting models focus on large geographical areas, such as entire countries, states, or provinces, for their predictions6. This creates a problem for the hospitals trying to interpret what these predictions entail for their own hospital planning, as the proportion of the nationally required beds that should be freed up locally is largely unknown. Furthermore, local epidemic dynamics may deviate substantially from the national trend8, causing the national level forecast to over- or underestimate the local epidemic growth, and consequently the local future bed demand.Several online dashboards which provide critical information such as the number of cases, hospitalizations, etc. have been established to facilitate access to COVID-19 related data10. Some of these transfers could be avoided if the local bed supply is updated reacting to the local trends and forecasts.Relying only on national-level models to produce forecasts of the total bed demand may result in an excessive transfer of patients when local bed demand does not align with the local bed supply. This can happen when certain localities experience sudden increases in incidence that were absent elsewhere, for instance after super-spreading events. Such patient transfers have happened on a regular basis during the COVID-19 pandemic, sometimes over large distances and across country bordersHowever, local forecasting comes with a unique set of challenges. Because numbers are lower, actual bed occupancy in a single hospital is strongly influenced by stochastic events. The discharge of a couple of patients from an Intensive Care Unit (ICU) matters a lot for the bed supply of a single hospital. Uncertainty about future numbers of beds is therefore greater when looking at a single hospital compared to an entire country. To be widely applicable, the model needs to be able to produce bespoke forecasts for each hospital in a country for which basic levels of data are available. This capability requires a flexible forecasting system because of the vast number of potential combinations of parameter choices for all individual hospitals, in particular concerning the possible choices for catchment areas per hospital, the number of currently occupied beds, and patients’ lengths of stay on various wards. Such a variety of parameters enables the extreme forecast flexibility required to produce ad-hoc reports and forecasts for all situations of specific hospitals.We made the use of this model accessible for non-technical users by creating an online interactive dashboard. To our knowledge, this is the first online accessible tool for predicting the bed demand on a regional level for Germany. Our platform allows individual users  to enter the data and parameters related to their specific context and requirements and produce ad-hoc bed occupancy estimates and predictions. End user-specific forecasting of bed demand is a unique concept, as on-request forecasting is often avoided because of the computational challenges of multiple concurrent user modelling platforms.Here we show how some of these computational challenges can be solved. Careful streamlining of the model and its technical implementation can help produce epidemic forecasts in a reasonable time, allowing users to explore the potential future epidemic trajectory without being restricted to the developer’s viewpoint.We will first discuss the forecast model itself, its data and parameter requirements, as well as the different modules it contains. Each module is designed to guide the user through the steps and assumptions needed to produce the forecast. Then we will discuss the technical implementation of the online dashboard and the technologies that ensure usability for multiple concurrent users. Finally, we investigate the forecasting performance of this tool for several hospitals during the COVID-19 pandemic in Germany. In particular, we focus on the influence of the choice to use local, regional, or national COVID-19 incidence data on the precision and accuracy of the forecast.https://github.com/QUPI-IUK/Bed-demand-forecast/releases/tag/v.0.5.6.The code used to implement the dashboard, in the version used to prepare this manuscript, is available at: The complete forecast model consists of 5 main pieces of code, referred to as modules: 1) Data loading and nowcasting, (2) Reproduction number estimates, (3) Vaccination coverage forecasting, (4) Incidence model, and (5) Care path model. The calculations done in modules 2 and 3 rely only on the loaded data and user input, while modules 4 and 5 also build further on the results of each previous module 12, the model can be applied to any country that has the following data available : Incidence, Administered vaccinations, Bed occupancy on general wards (GW) where t denotes the time in days since a reference date before the start of the pandemic, g denotes a geographical subdivision , and d denotes the dose of vaccine administered . Incidence and vaccination data are needed for each day of the period of reference, while merely the value at the start date of the forecast is needed for bed occupancy.The model needs data on infection incidence, vaccine doses, bed occupancy in general wards and intensive care units, and a simulation window for which a forecast is required. Although we developed this model for hospitals in Germany, based on data provided by the Robert Koch InstituteL; the last forecasted date is therefore given as N being the population size.The user defines the catchment area of interest, selecting geographical areas from the available list , and the model uses discrete time steps, we need to discretise the parameter distributions. For each continuous distribution, with probability density function (PDF) User input for all distributions is given in terms of the mean The model can take the effect of emerging Variants of Concern (VoCs) into account, based on user input on the VoC proportion and increased transmissibility. For a full description of the implementation of VoC in the model see Supplementary Text The vaccination model consists of two parts. In the first, we forecast the number of people vaccinated over the length of the forecast for each of the doses , while in the second part we convert these administered vaccinations into population-level protection against transmission.The first doses  on the development of the In order to inform the transmission process part of the incidence model, we need to forecast the reproduction number of the pathogen over the model timeframe. This forecast is based on the observed time-varying effective reproduction number (14 as implemented in the EpiEstim R package (version 2.2-4), with a given non-parametric Serial Interval (SI). This SI distribution denotes the number of days between equal disease events  of directly connected cases. The default SI is assumed to be Gamma distributed with a mean of 5 days and a standard deviation of 4.9. These values were chosen to reflect estimates of mean SI from multiple studies15 with a relatively high standard deviation.We estimate the time-varying effective reproduction number t, defined as S(t):By keeping track of the cumulative number of infected individuals, as well as the previously calculated population protection  model, which has additive errors (A), additive trend (A) and no seasonality (N); We use a To produce a dynamic forecast of S(t)) to infection and of infection pressure (P(t)) exerted by all those currently infectious, and the total population size (N). The size of the components is given as absolute numbers of individuals; thus The incidence forecast model is based on a stochastic implementation of a Susceptible-Infected-Recovered (SIR) model. The model describes the number of new cases as a function of the population still susceptible . Conversely, the model converts into a two-strain model if a VoC is defined, keeping track of the infected individuals for either variant as well as the total number of individuals susceptible to either variant.S(t) is then given as the weighted number of infected individuals in the preceding serial interval,H(i) is the serial interval distribution, defined as the probability that the proportion of cases causing new cases i days after they were reported themselves. These are thus all past cases that are able to cause new cases on the current day t, weighted by the serial interval distribution. Given the current P(t), the expected mean total number of newly infected individuals on day t+1 is The size of the susceptible class is determined by both the cumulative number of infected individuals and the population level protection through vaccination, as defined before,The transmission rate per infected individual , is given as t is then calculated asP(t)) can be simplified to The infection pressure exerted on each individual within the population at time 16. Then we join this model with the predicted incidence to forecast the hospital admission rate and the bed occupancy.To forecast bed occupancy in the hospital, the main endpoint of this work, we first simulate the path of each single patient admitted to the hospital through the general ward, ICU, and step-down units (care path model), as described in Donker et al.Length of stay (LoS) distribution on general wards (GW),LoS distribution on intensive care units (ICU),LoS distribution on step-down units (SDU),Proportion of patients being transferred from GW to ICU,Proportion of patients being transferred from ICU to SDU.It is possible to add the proportion of patients directly admitted to ICU .To estimate the proportion of reported cases being admitted to hospital, we need to compare the incidence of reported cases to the total number of patients in hospital at a given moment . This can be achieved by taking the length of stay of admitted patients into account. We create a complete Length of Stay distribution The same method delivers the distribution of admitted patients on the GW The admission rate can also be calculated for the separate wards,This admission rate then determines the number of individuals admitted to the hospital, entering the care path model, pulled from the binomial distributionHowever, the care path model needs to determine the lengths of stays for the patients already in hospital at We then select all patients present in the GW or ICU at 17) as an R-Shiny18 (version 1.6) app running using shiny-server on an 8-core, 16GB ram, Ubuntu (version 20.04.3) VM server. An IP-hashed load balancer divides traffic over eight separate instances of shiny-server, reducing the number of concurrent users per shiny-server. We measure the performance of the model based on this infrastructure.The main backbone of the model is written in R 20 to allow communication between the Julia and R code bases. One of the drawbacks of Julia is that the functions require just-in-time compilation the first time they are used; the overhead related to compilation time exceeds the running time of the entire care path model. To address this issue, we generated a fully compiled version of the model code21, virtually eliminating loading time. Once the main server is started, a concurrent Julia session is created and is shared between all shiny-server sessions. For a detailed dashboard performance benchmarking, see Supplementary Information Section The most computationally demanding part of the care path model was written in the Julia programming languageThe user interface of the dashboard is shown in Fig. R, showing the time-varying R estimation based on the EpiEstim package. This tab also includes the option to use the ETS model and the option to include a variant of concern (VoC), together with the needed VoC parameters. (4) Incidence forecast, showing the results of the incidence model, with the option to include the reporting pattern related to the weekdays. (5) Bed forecast, reporting the results of the within-hospital care path model. The model is run using data on the current number of occupied beds in the hospital of interest, inputted either manually or by uploading a specifically structured file. (6) Parameter choices. This tab includes all parameters included as default values in the other tabs, which should only be changed by users with more advanced knowledge of the underlying model.Tabs are ordered as follows: (1) Incidence, showing the daily reported number of cases with and without the nowcast. (2) Vaccination, showing the cumulative number of vaccine doses administered, as well as the forecast of vaccinations. It also includes the option to change the assumptions on the future vaccinations . (3) Effective d  of the median of each set of forecast simulations corresponding to its start date for the given time period for the university hospital of Freiburg. MASE of the 23. One possible explanation is the use of a static We show the importance of employing local data rather than national data when producing epidemic forecasts. Forecasts of bed demand produced based on the incidence in the specific catchment area of the hospital of interest, better predicted the local future bed demand than those based on the incidence of the entire country or state. Such hospital-specific bed demand forecasts can help inform hospital planning, e.g. by cancellation of elective surgeries. This has the potential to reduce the need to transfer critically ill patients between hospitals, because the local bed capacity can be better adjusted to the local bed demand. Ideally, the forecast horizon is far enough for the adjustments to take effect but near enough to still be accurate and precise enough to be informative. We observe a clear trade-off between the accuracy and precision of the forecast, governed by the size of the selected catchment area: larger catchment sizes generally produce more precise results at the expense of their accuracy, while smaller catchments result in more accurate but less precise forecasts. This is probably caused by a reduction of the stochastic variation in the underlying data. Basing the time-varying reproduction number  and general risk perception in the community. Likely, a high incidence situation will trigger behavioural changes that reduce the peak size of the epidemic, or conversely, low incidence may trigger relaxation of NPIs. Because the model doesn’t take these changes into account, it is often inaccurate around the inflection points of the epidemic curve. Furthermore, local forecasts are by design less precise than those based on national-level data, because the predictions are based on both lower case numbers and smaller base population sizes. This means that estimates of reproduction numbers have wider confidence bounds, and incidence, admission rates, and lengths of stays are stronger influenced by stochastic variation in the model. This sometimes results in forecasts that predict anything between an empty and fully overwhelmed hospital. Although these predictions may seem useless, they avoid a false sense of security and echo the true uncertainty of the situation (i.e. anything can happen). However, for most of the time, the forecasts show a clear trend that can form the basis for further strategic planning, such as cancellation of elective surgeries or opening of designated COVID-19 wards.The dashboard was successfully used by local healthcare providers, hospitals, and healthcare policymakers to evaluate incidence and hospital bed occupancy in Germany during the 2020-2022 COVID-19 pandemic. We argue that on-request forecasts are much more helpful in informing stakeholders at a local level where health management decisions, such as cancelling elective surgeries, directly affect the bed capacity. This way, the pandemic or epidemic response can be driven in near real-time on the level where it matters most.Supplementary Information.