Steady-state Assumption Research Articles

A NUMERICAL STUDY ON THE REDUCTION OF GREENHOUSE GASEOUS COMPONENT (CO2) DUE TO THE ADDITION OF H2 IN THE FUEL STREAM OF THE COUNTERFLOW CH4/AIR DIFFUSION FLAME

In this study, a series of 1-D and steady-state numerical simulations have been performed for the prediction of the effect of the addition of H2 on the characteristics of a non-sooting counterflow CH4/Air diffusion flame using detailed chemical reaction model, which is composed of 325 elementary chemical reactions and 53 chemical species. Under the steady-state assumption, a set of one-dimensional transport equations of mass, momentum, species, and energy along with the equation of state has been solved numerically at the atmospheric conditions over the counterflow configuration by exploiting an efficient numerical code, OPPDIF (a Fortran Program for Computing Opposed-Flow Diffusion Flames). The grid adaption technique has been used to achieve better convergence as well as to ensure the maximum accuracy of the simulated results. It is found that the flame temperature is increased due to the addition of H2 with CH4, which is injected into the fuel stream. The elevation in the temperature is caused by the augmentation of the integrated heat release rate of the elementary reactions supported by the active radicals (H, O, and OH), which are generated by the higher reactivity of H2. Besides, it is found that the mole fractions of H2O are increased as the percentage of H2 in the loading fuel (CH4) is increased and also, it is identified that the chain propagating reaction, OH + H2 => H2O + H is dominating one which produces highest amount of H2O. Furthermore, it is noticed that the indirect greenhouse gas or precursor, CO is reduced when H2 is added to CH4. Consequently, the mole fraction of the principle greenhouse gas, CO2 is decreased significantly when the fuel, CH4 percentage is modified by the higher percentage of H2. The sensitivity analysis of elementary reactions reveals the fact that the chemical reaction: OH + CO => H + CO2 is a dominating reaction in producing a lower amount of CO2 when the volume fraction of H2 is increased in the fuel (CH4) stream. In the presence of 75 % H2 in CH4, the pressure-dependent reaction, O + CO (+M) => CO2 (+M) appears as another chemical route that also generates greenhouse gas, CO2 but its contribution is negligibly small.

Systematic construction of combustion reaction model for large hydrocarbon fuels based on a two-step reaction scheme

Understanding the combustion chemistry of large hydrocarbons in practical gasoline, diesel and jet fuels is critical for the reduction of pollutant emissions and increase of fuel and engine efficiencies. The primary objective of the present study is to illustrate the methodology and application of a simplified modeling approach based on a two-step reaction scheme (TSRS) for describing the combustion chemistry of large hydrocarbon fuels under engine-relevant high-temperature conditions. Under such conditions, the combustion process of large hydrocarbons consists of two distinct subsequent reaction steps: the first step is the prompt fuel decomposition, converting the parent fuel to critical intermediate products; the second step is the oxidation reactions of the intermediates. Particularly, the second step is slower, thus rate-limiting, controlling the heat release and formation of final combustion products of the entire combustion reaction process. A systematic analysis by mathematical methods was performed to obtain a unified treatment for hydrocarbons with different molecular sizes. Based on the analysis of characteristic time scale of elementary reaction and steady-state assumption, TSRS used a fuel decomposition submodel to describe the fuel molecule decompose into critical intermediate species, including ethene, propene, butenes and methane for n-alkanes, and used a detailed foundational fuel chemistry mechanism to describe the oxidation reaction of the intermediates. The entire TSRS reaction model for large hydrocarbons is compact, consisting ∼110 species and ∼800 reactions, which can be further reduced. It was shown in the present study that, by revealing the relationship between the functional group composition of linear alkanes and the distribution of intermediates, and in combination with the rate criterion, the fuel decomposition submodel can be systematically generated to facilitate the automatic construction of compact kinetic models. One unified TSRS combustion reaction model was created and demonstrated for several large hydrocarbons ranging from C8 to C16, which was validated by comprehensive datasets, including speciation, ignition delay times and laminar flame speeds.

Time-dependent Dynamics of the Corona

We present in this Letter the first global comparison between traditional line-tied steady-state magnetohydrodynamic models and a new, fully time-dependent thermodynamic magnetohydrodynamic simulation of the global corona. To approximate surface magnetic field distributions and magnitudes around solar minimum, we use the Lockheed Evolving Surface-Flux Assimilation Model to obtain input maps that incorporate flux emergence and surface flows over a full solar rotation, including differential rotation and meridional flows. Each time step evolves the previous state of the plasma with a new magnetic field input boundary condition, mimicking photospheric driving on the Sun. We find that this method produces a qualitatively different corona compared to steady-state models. The magnetic energy levels are higher in the time-dependent model, and coronal holes evolve more along the following edge than they do in steady-state models. Coronal changes, as illustrated with forward-modeled emission maps, evolve on longer timescales with time-dependent driving. We discuss implications for active and quiet Sun scenarios, solar wind formation, and widely used steady-state assumptions like potential field source surface calculations.

Evaluation of four calving laws for Antarctic ice shelves

Abstract. Many floating ice shelves in Antarctica buttress the ice streams feeding them, thereby reducing the discharge of icebergs into the ocean. The rate at which ice shelves calve icebergs and how fast they flow determine whether they advance, retreat, or remain stable, exerting a first-order control on ice discharge. To parameterize calving within ice sheet models, several empirical and physical calving “laws” have been proposed in the past few decades. Such laws emphasize dissimilar features, including along- and across-flow strain rates (the eigencalving law), a fracture yield criterion (the von Mises law), longitudinal stretching (the crevasse depth law), and a simple ice thickness threshold (the minimum thickness law), among others. Despite the multitude of established calving laws, these laws remain largely unvalidated for the Antarctic Ice Sheet, rendering it difficult to assess the broad applicability of any given law in Antarctica. We address this shortcoming through a set of numerical experiments that evaluate existing calving laws for 10 ice shelves around the Antarctic Ice Sheet. We utilize the Ice-sheet and Sea-level System Model (ISSM) and implement four calving laws under constant external forcing, calibrating the free parameter of each of these calving laws for each ice shelf by assuming that the current position of the ice front is in steady state and finding the set of parameters that best achieves this position over a simulation of 200 years. We find that, in general, the eigencalving and von Mises laws best reproduce observed calving front positions under the steady-state position assumption. These results will streamline future modeling efforts of Antarctic ice shelves by better informing the relevant physics of Antarctic-style calving on a shelf-by-shelf basis.

Constraining the power-function complementary relationship with a steady-state Budyko equation for predicting terrestrial evapotranspiration globally

The power-function complementary relationship (CR) represents the latest advancement in definitive CR models, offering enhanced predictions of terrestrial evapotranspiration (E), all while elucidating the physical interpretations of its associated parameters. In this study, we introduced practical approaches to integrate the traditional Budyko framework into the novel CR model for global-scale E prediction. Under a steady-state assumption, the power-function CR was equated with the Turc-Mezentsev equation, thereby introducing an additional constraint for determining key parameters. We presented two illustrative cases where the aridity index and land-specific parameter constrain the exponent and the Priestley-Taylor coefficient of the CR, respectively. Compared to its calibration-free counterpart, the CR model constrained by the Budyko framework demonstrated improved performance in capturing spatial and temporal variations of E in point locations, mesoscale catchments, and large river basins. This improvement was not only from considering long-term precipitation partitioning, but also from the ability of the combined framework to rectify biases in input data. While the calibration-free methods exhibited poorer performance, they hold potential for superior results with higher-quality forcing inputs. By merging the Turc-Mezentsev equation with the power-function CR, this study provides insights into refining E predictions, accounting for climatic conditions and input data quality.

Cosmogenic (un-)steadiness revealed by paired-nuclide catchment-wide denudation rates in the formerly half-glaciated Vosges Mountains (NE France)

Although catchment-wide denudation rates inferred from in situ cosmogenic nuclide concentrations measured in stream sediments has represented a ground-breaking progress in geomorphology over the last three decades, most of these studies rely on 10Be concentrations only. It seems that this current and routine one-nuclide approach to infer catchment-wide denudation rates has somehow overshadowed two key assumptions that are cosmogenic steady-state and short sediment transit time at the catchment scale. Although a paired-nuclide approach allow testing these assumptions, it is rarely performed on stream sediments and this can become highly problematic in slow-eroding, formerly glaciated contexts. In this study, we thus measure both 10Be and 26Al in stream sediments pertaining to twenty-one rivers draining an entire low mountain range: the Vosges Massif (NE France). The latter exhibits a sharp gradient between its southern and northern part in terms of lithology, morphometry and climate. Moreover, if its northern part remained void of glacial cover during Quaternary cold stages, its southern part was significantly and repeatedly glaciated. We aim to assess the factors that control the denudation of the Vosges Mountains and to quantitatively explore the impact of both repeated glacial cover and storage of glacially derived sediments on 26Al/10Be ratios, hence cosmogenic (un-)steadiness in modern river samples. Our results first show that elevation, slope, channel steepness and precipitation are primarily organised along a N-S increasing trend. 10Be- and 26Al-derived catchment-wide denudation rates accordingly range from 34 ± 1 to 66 ± 2, and 41 ± 3 to 73 ± 7 mm/ka, respectively, in thirteen investigated catchments that are in cosmogenic equilibrium. Lithological contrasts may control the pattern of denudation with a higher erodibility of the sandstone-dominated catchment to the north compared to the crystalline-dominated catchments to the south.Our results also show that catchments in strong cosmogenic disequilibrium (26Al/10Be ratios from 1.4 to 5.2) spatially cluster in the SW part of the Vosges Mountains that was the most intensively glaciated during Quaternary cold stages. If this precludes any conclusion about controlling factors at the whole massif scale, this study is the first to quantify the impact of past glaciations on cosmogenic (un-)steadiness measured in stream sediments. A statistically significant relationship between the degree of depletion of the 26Al/10Be ratios and the spatial pattern of glaciation is found: the larger the former glacial cover in each catchment, the lower the 26Al/10Be ratio. Equally important is the significant correlation reported between the degree of depletion of the 26Al/10Be ratios and the proportion of glacial and fluvio-glacial deposits within each catchment. These two relationships underline the link between cosmogenic unsteadiness in the stream cosmogenic signal and long-lasting and repetitive ice shielding, and complex sediment routing systems in glacial environments, respectively. We thus argue to systematically measure 26Al in complement to 10Be and to test the steady-state assumption when it comes to infer catchment-wide denudation rates from modern stream sediments, especially in slow eroding, formerly glaciated landscapes.

Density profile of a self-gravitating polytropic turbulent fluid in a rotating disc near to the cloud core

ABSTRACT We obtain two equations (following from two different approaches) for the density profile in a self-gravitating polytropic cylindrically symmetric and rotating turbulent gas disc. The adopted physical picture is appropriate to describe the conditions near to the cloud core where the equation of state of the gas changes from isothermal (in the outer cloud layers) to one of ‘hard polytrope’, and the symmetry changes from spherical to cylindrical. On the assumption of steady state, as the accreting matter passes through all spatial scales, we show that the total energy per unit mass is an invariant with respect to the fluid flow. The obtained equation describes the balance of the kinetic, thermal, and gravitational energy of a fluid element. We also introduce a method for approximating density profile solutions (in a power-law form), leading to the emergence of three different regimes. We apply, as well, dynamical analysis of the motion of a fluid element. Only one of the regimes is in accordance with the two approaches (energy and force balance). It corresponds to a density profile of a slope −2, polytropic exponent 3/2, and sub-Keplerian rotation of the disc, when the gravity is balanced by the thermal pressure. It also matches with some observations and numerical works and, in particular, leads to a second power-law tail (of a slope ∼−1) of the density distribution function in dense, self-gravitating cloud regions.

Couette-Poiseuille flow in a fluid overlying an anisotropic porous layer

In this study, Couette-Poiseuille flow inside a channel partially filled with a porous medium is treated. Considering the applicability to the practical scenarios, we assume that the porous medium is anisotropic in nature. More precisely, the model under steady-state assumption is described by the coupling of Brinkman-Forchheimer and Stokes equations. We develop the existence and uniqueness results corresponding to this two-dimensional Stokes-Brinkman-Forchheimer coupled system using the Browder-Minty theorem. For this we restrict the permeability to a diagonal matrix. The coupled system involves a non-linear term due to the Brinkman-Forchheimer equation. We propose an algorithm based on shooting and searching techniques to develop a numerical solution for this system, however, for an arbitrary anisotropic permeability matrix. The robustness of the presented numerical solution is established by comparing it with asymptotic solutions corresponding to small and large Darcy numbers. For the case of a large Darcy number, the problem of interest is a regular perturbation while the same is a singular perturbation problem for the case of a small Darcy number, which is dealt with using Prandtl's matching principle. With the velocity distribution determined, we have presented a comparative analysis of the shear stress distribution at the liquid-porous interface and at the bottom plate, which is of interest to analyze the stress distribution on the arterial wall. The asymptotic results are found to be in good agreement with those obtained numerically.

On the Incompatibility of Steady-State Assumption and Abnormal Grain Growth in the Presence of Homogenous Pinning

On the Incompatibility of Steady-State Assumption and Abnormal Grain Growth in the Presence of Homogenous Pinning

Implications of the steady-state assumption for the global vegetation carbon turnover

Vegetation carbon turnover time (τ) is a central ecosystem property to quantify the global vegetation carbon dynamics. However, our understanding of vegetation dynamics is hampered by the lack of long-term observations of the changes in vegetation biomass. Here we challenge the steady state assumption of τ by using annual changes in vegetation biomass that derived from remote-sensing observations. We evaluate the changes in magnitude, spatial patterns, and uncertainties in vegetation carbon turnover times from 1992 to 2016. We found the robustness in the steady state assumption for forest ecosystems at large spatial scales, contrasting with local larger differences at the grid cell level between τ under steady state and τ under non-steady state conditions. The observation that terrestrial ecosystems are not in a steady state locally is deemed crucial when studying vegetation dynamics and the potential response of biomass to disturbance and climatic changes.

Novel experimental technique to evaluate soil thermal conductivity in a transient state

novel experimental technique to evaluate soil thermal conductivity in a transient state

Dynamical charging of interstellar dust particles in the heliosphere

Interstellar dust (ISD) particles penetrate the solar system due to the relative motion of the Sun and the local interstellar cloud. Before entering the heliosphere, they pass through the heliospheric interface – the region of the solar wind interaction with the interstellar plasma. The size distribution and number density of dust grains are modified in the interface essentially. The modification depends on the charging of the dust particles along their trajectories. In this paper, we present modeling results of the charging of ISD particles passing through the heliospheric interface. The main physical processes responsible for the charging within the heliospheric conditions are the sticking of primary plasma particles, secondary electron emission, photoemission, and the effects of cosmic ray electrons. We consider two methods to calculate the electric charge of ISD particles based on (1) the classic steady-state assumption that the charge depends only on local plasma and radiation conditions and (2) the dynamical computation of charge along the particle trajectory. We demonstrate that the steady-state assumption is quite justified to model trajectories and number density distributions of relatively big ISD grains (radius of 100 nm and larger) penetrating the heliosphere. The estimates show that ISD grains of these sizes require less than 0.25 years (distance of ≈1 au) after transition from the LISM into the heliosphere to reach an equilibrium. For small particles ( radius of 10 nm), the dynamical computation of charge influences the trajectories and modifies the number density substantially. The dust density accumulations are distributed within a more elongated region along the heliopause in case of dynamically changed charge as compared with the use of a steady-state charge approximation. As a result, the magnitudes of number density at the points of density features differ several times between the results obtained by the two considered approaches.

Transient thrust behavior of low‐aspect‐ratio rocket propulsion systems**

AbstractIn this work, the transient thrust force of the solid propellant rocket motor is numerically computed to illustrate the shortcomings of the common thrust formula in transient periods of operation. The internal ballistics of the solid rocket motor is simulated using the quasi one‐dimensional governing equations in which the finite volume method and the Roe′s scheme are utilized in calculation procedure. This is demonstrated that in transient operation of the propulsion systems, the common thrust formula may ignore some parts of physical phenomena because it has been derived based on steady state assumption, but there are some moving waves in transient operation in the combustion chamber which induce the fluctuations on the thrust force. So, the thrust‐time history must be computed by pressure force integration over the whole solid boundaries of the motor at any instant. The results show that such transient thrust behavior is more intense in low aspect ratio propulsion systems like small space thrusters.

The impact of dust evolution on the dead zone outer edge in magnetized protoplanetary disks

Context. The dead zone outer edge corresponds to the transition from the magnetically dead to the magnetorotational instability (MRI) active regions in the outer protoplanetary disk midplane. It has been previously hypothesized to be a prime location for dust particle trapping. A more consistent approach to access such an idea has yet to be developed, since the interplay between dust evolution and MRI-driven accretion over millions of years has been poorly understood. Aims. We provide an important step toward a better understanding of the MRI–dust coevolution in protoplanetary disks. In this pilot study, we present a proof of concept that dust evolution ultimately plays a crucial role in the MRI activity. Methods. First, we study how a fixed power-law dust size distribution with varying parameters impacts the MRI activity, especially the steady-state MRI-driven accretion, by employing and improving our previous 1+1D MRI-driven turbulence model. Second, we relax the steady-state accretion assumption in this disk accretion model, and partially couple it to a dust evolution model in order to investigate how the evolution of dust (dynamics and grain growth processes combined) and MRI-driven accretion are intertwined on million-year timescales, from a more sophisticated modeling of the gas ionization degree. Results. Dust coagulation and settling lead to a higher gas ionization degree in the protoplanetary disk, resulting in stronger MRI-driven turbulence as well as a more compact dead zone. On the other hand, fragmentation has an opposite effect because it replenishes the disk in small dust particles which are very efficient at sweeping up free electrons and ions from the gas phase. Since the dust content of the disk decreases over millions of years of evolution due to radial drift, the MRI-driven turbulence overall becomes stronger and the dead zone more compact until the disk dust-gas mixture eventually behaves as a grain-free plasma. Furthermore, our results show that dust evolution alone does not lead to a complete reactivation of the dead zone. For typical T-Tauri stars, we find that the dead zone outer edge is expected to be located roughly between 10 au and 50 au during the disk lifetime for our choice of the magnetic field strength and configuration. Finally, the MRI activity evolution is expected to be crucially sensitive to the choice made for the minimum grain size of the dust distribution. Conclusions. The MRI activity evolution (hence the temporal evolution of the MRI-induced α parameter) is controlled by dust evolution and occurs on a timescale of local dust growth, as long as there are enough dust particles in the disk to dominate the recombination process for the ionization chemistry. Once that is no longer the case, the MRI activity evolution is expected to be controlled by gas evolution and occurs on a viscous evolution timescale.

A coupled NS-DSMC method applied to supersonic molecular beam and experimental validation

In this paper, experimental and numerical studies are conducted on supersonic molecular beam injection (SMBI) for fusion devices based on steady-state assumption. To explore the characteristics of SMBI from continuous to rarefied flow, the flow information is predicted by solving the Navier-Stokes (NS) equation based CFD method and direct simulation Monte Carlo (DSMC) method. To verify the coupled NS-DSMC method, a flow measurement apparatus platform is designed and constructed. A moveable full-range vacuum gauge with Pitot probe in the vacuum chamber is employed to measure the spatial distribution of the beam pressure signal. The simulation results are converted into Pitot pressure, corrected for rarefaction effect and compared with the experimental data. It is observed that the experimental results are consistent with the simulation results. This study provides technical support for the accurate prediction of SMBI flow characteristics and optimization of the SMBI systems.

Assessing the impact of growth on estimates of fishing mortality — An illustration with Indian Ocean bigeye tuna

Growth is a crucial biological feature and a key component in quantitative fish population stock assessments. Regional tuna fisheries management organizations have conducted extensive sampling programs to measure the growth of tuna species more accurately over the last decades. Although research improved growth estimates in most cases, competing or conflicting estimates of growth characteristics due to differences in sampling coverage, aging techniques, and modeling methodologies can introduce significant bias and uncertainty in the stock assessment. In the Indian Ocean, the recently determined growth curve for the bigeye tuna stock differs significantly from the length-at-age relationship now used in stock assessment. This study looked at how new growth affected estimation of fishing mortality for bigeye tuna caught with longline. Under steady-state assumption, the analytical method derives the fishing mortality and selectivity parameters from the longline length frequency dataset, conditioned on the growth and natural mortality factors. Simple simulations were used to validate the estimator’s performance. According to the estimates, the annual fishing mortality rates under the new growth curve will be 100%–200% higher than those under the current growth curve. The findings were also supported by an integrated Stock Synthesis model that was derived and simplified from the current bigeye tuna assessment model, as well as the length-based spawning potential ratio method, which used the same length frequency dataset as input. We emphasize that using a basic model to analyze the impact of alternative or competing growth scenarios on key management quantities can help decision makers easily understand the outcomes of more complex models, increasing the transparency of the stock assessment process.

A framework for modelling single slug horizontal pneumatic conveying

The complexity of dense phase flows generally results in a reliance on empirical or qualitative analysis, which lacks reliability and limits the adoption of these desirable low-velocity flows in practice. Within horizontal slug flow, an additional challenge has been relating the highly dynamic properties of individual slugs to steady feed rates of solids and gas — with the result being the widespread application of steady-state assumptions on slug properties. This paper attempts to address these gaps through the development of a numerical framework for modelling single slugs founded on the authors’ recent research on slug dynamics and stability. Based on a finite difference approximation, the developed framework provides a much-needed fundamental and quantitative tool for analysing slug dynamics and a foundation for research beyond single slug conveying.

Performance enhancement and parametric optimization of a sky radiative and thermoelectric hybrid cooling system for water harvesting from humid air

The aim of this study is to deepen into the study and analysis of energetic performance of a novel RSC-TEC hybrid cooling system for water harvesting by combining thermoelectric and radiative sky cooling mechanisms. The main contents of this study are to propose the thermodynamic model of the novel hybrid system considering main losses and steady-state assumption, solve the operating temperatures of the thermoelectric cooler by energy balance equations, discuss the influences of multiple system variables including air flow rate, electric current of the thermoelectric cooler, ambient relative humidity, and ambient temperature on effectiveness and water production rate, and, evaluate and compare the performances of the whole system and the thermoelectric cooler. The main novelties are to provide the parametric optimum selection criteria of some key parameters of the overall system operating at optimum states. Results show that the maximum effectiveness and water production rate of the hybrid system can reach 1.93×10- 6 kg J−1 (amount to 6.95×103 ml of water by consuming 1 kWh of electrical energy) and 1.51×10- 5 kg s−1 (amount to 54.4 ml of water within 1 h) at 0.75 relative humidity and the ambient temperature of 298 K. In addition, the system is capable of producing about 140 ml of water within 1 h from the air with high relative humidity, which is more efficient than other different existing air water generators. The optimized effectiveness (coefficient of performance) of the hybrid system is much better than that of a separate (subsystem) thermoelectric cooler operating at the same ambient condition. The results obtained reveal the advantages of the present hybrid system. Complementary perspectives on compromise performance regimes are also displayed from Pareto front yielded from numerical multi-parametric and multi-objective methods.

Concurrent Shape Optimization of the Part and Scanning Path for Powder Bed Fusion Additive Manufacturing

This paper investigates the concurrent path planning optimization and the built part structural optimization for powder bed fusion additive manufacturing processes. The state of the art studies rely on existing patterns for trajectories for a fixed built shape. The shape is often optimized for its mechanical performance but rarely in a combined way with its path planning building process. In this work, a two-dimensional model (in the layer plane) of the process is proposed under a steady state assumption. Then a systematic path optimization approach, free from a priori restrictions and previously developed in [M. Boissier, G. Allaire, and C. Tournier [Struct. Multidiscip. Optim., 61 (2020), pp. 2437–2466], is coupled to a structural optimization tool, both of them based on shape optimization theory. This multiphysics optimization leads to innovative and promising results. First, they confirm that it is essential to take into account the part shape in the scanning path optimization. Second, they also give hints to some design recipes: the material and the source parameters must be related to the thickness of the bars that compose the structure. Indeed, the thickness of a bar is a key ingredient which determines the type of path pattern to scan it: straight line, Omega-pattern, and Wave-pattern.

Terramechanics models augmented by machine learning representations

The field of terramechanics focuses largely on two types of simulation approaches. First, the classical semi-empirical methods that rely on empirically determined soil parameters and equations to calculate the soil reaction forces acting on a wheel, track or tool. One major drawback to these methods is that they are only valid under steady-state conditions. The more flexible modelling approaches are discrete or finite element methods (DEM, FEM) that discretize the soil into elements. These computationally demanding approaches do away with the steady state assumption at the cost of including more model parameters that can be difficult to accurately tune. Model-free approaches in which machine learning algorithms are used to predict soil reaction forces have been explored in the past, but the use of these models comes at the cost of the valuable insight that the semi-empirical models provide. In this work, we presume that in a dynamic simulation, the soil reaction forces can be divided into a steady state component that can be captured using semi-empirical models and a dynamic component that cannot. We propose an augmented modelling approach in which a neural network is trained to predict the dynamic component of the reaction forces. We explore how this theory can be applied to the simulation of a soil-cutting blade using the Fundamental Earthmoving Equation and of a wheel driving over soft soil using the Bekker wheel-soil model.