# N. P. Kruyt's research while affiliated with University of Twente and other places

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## Publications (78)

The microstructure of granular materials has a significant influence on their macroscopic quasi-static strength and deformational behaviour. This microstructure is often quantified by a second-order fabric tensor that describes the primary orientational statistics of interparticle contacts. Here, it is investigated how the fabric tensor changes whe...

Axial fans with small hub-to-tip diameter ratio (HTR) are widely used in industry, especially for cooling and ventilation purposes. Optimization of their aerodynamic performance is important, for which the vortex distribution method is well-established for axial fans with medium to high HTR. However, only few studies have focused on small HTR fans....

Axial fans with low hub-to-tip diameter ratio are used in many branches of industry. Optimization of their aerodynamic performance is important, for which using sweep, dihedral and skew of the blades' stacking line form an important method. Investigations on axial fans with medium to high hub-to-tip diameter ratio have shown that forward sweep of b...

For granular materials, the kinematic degrees of freedom at the microscale of particles are the particles' displacements and rotations. In classical continuum mechanics, the kinematic degree of freedom at the macroscale is the (local) displacement field. The rotation of a material element is not independent but is determined by the antisymmetric pa...

Fabric anisotropy is a key component to understand the behaviour of granular soils. In general, experimental data on fabric anisotropy for real granular soils are very limited, especially in the critical state. In this paper, x-ray tomography measurements are used to provide experimental data on contact fabric anisotropy inside shear bands for two...

The current study investigates the non-coaxial plastic flow in granular media where the principal directions of incremental plastic strain differ from those of the current stress (and of the current fabric tensor). The stress probing technique is used with Discrete Element Method simulations to capture the plastic response of a 2D granular assembly...

Rotor-only ducted axial fans with small hub-to-tip diameter ratio are widely used in many branches of industry, especially for cooling and ventilation purposes. For such fans, extensive regions of backflow are present downstream of the fan near the hub. Only few Computational Fluid Dynamics (CFD) studies for such fans have been reported in the scie...

Micromechanical studies of granular materials have demonstrated the importance of their microstructure to their behaviour. This microstructure is often characterized by fabric tensors. Experimental and computational studies have shown that the fabric can change significantly during deformation. Therefore, the evolution of fabric is important to con...

This study focuses on properties of axisymmetric capillary bridges between spherical particles in the pendular regime under suction control. Using the toroidal approximation in combination with the governing Young-Laplace equation, analytical expressions for the rupture distance (dependent on the suction) and for the capillary force (dependent on t...

Three‐dimensional Discrete Element Method simulations have been performed to study the deformation of cross‐anisotropic granular materials under principal stress rotation (PSR), for rotation planes oriented at different angles θ with respect to the bedding plane. The simulations have been conducted with a novel technique for applying specified stre...

In this micromechanical study of the behaviour of granular materials, relationships are investigated between deformation at the continuum macro-scale and at the micro-scale of interparticle contacts. Special attention is paid to the role of the microstructure, or fabric, as it is well known to have a strong influence on the behaviour of granular ma...

An analytical theory has been developed for the capillary bridge force between non-perfectly wettable, equal-sized spherical particles for the pendular regime. In this theory, the meridional profile of the axisymmetric capillary bridge is represented by part of an ellipse. The geometrical parameters in this description are determined from the bound...

The stress-deformation behaviour of granular media is known to be directly linked to details of the underlying microstructure of contacts, or fabric. The notion of contact fabric and its role in defining stress and strain motivate the present study to explore the evolution of fabric in response to small strain probes applied to initially isotropic...

The effect of trimming of radial impellers on the hydraulic performance of low specific-speed centrifugal pumps is studied. Prediction methods from literature, together with a new prediction method that is based on the simplified description of the flow field in the impeller, are used to quantify the effect of trimming on the hydraulic performance....

Forced convective heat transfer from smooth, solid and isothermal spheres of various diameters has been studied experimentally in air flows with various free-stream velocities. The average heat transfer coefficient has been determined from the steady measured power input to a heating element inside the spheres and the steady measured temperatures o...

Hill’s first-order lemma in continuum mechanics has been derived in the literature for quasi-static cases and for dynamic cases in the absence of body forces. In this manuscript, a generalized first-order Hill identity is first derived in an Eulerian dynamic description including body forces. Then, a second-order Hill identity using a Lagrangian de...

An analytical theory has been developed for properties of a steady, axisymmetric liquid–gas capillary bridge that is present between two identical, perfectly wettable, rigid spheres. In this theory the meridional profile of the capillary bridge surface is represented by a part of an ellipse. Parameters in this geometrical description are determined...

In micromechanics of granular materials, relationships are investigated between micro-scale characteristics of particles and contacts and macro-scale, continuum characteristics. Dilatancy is an important property of granular materials, defined as volume changes (dilative or compressive) induced by shear deformation. To obtain detailed information a...

In an influential study on the micromechanical origin of stress transmission in granular materials, Radjaï et al. (1998) have proposed a division of the network of interparticle contacts into ‘weak’ and ‘strong’ contacts. This division is based on a comparison of the force at contacts with the average (over all contacts) force. They observed, from...

Granular materials are special materials, from the continuum-mechanical viewpoint, in the sense that they possess a clear microstructure of grains and intergrain contacts. In addition, the grains have translational as well as rotational degrees of freedom. Here a micromechanical expression is formulated for the average displacement gradient tensor...

The behaviour of nearly neutrally-buoyant suspensions has been studied experimentally, using a concentric-cylinder rheometer. The effect on the suspension viscosity of: (i) solid fraction, (ii) diameter of the solid, spherical particles, (iii) viscosity of the suspending liquid, and (iv) shear rate has been determined experimentally, where all susp...

In micromechanics of quasi-static deformation of granular materials, relationships are investigated between the macro-scale, continuum-mechanical characteristics, and the micro-scale characteristics at the particle and interparticle contact level. An important micromechanical quantity is the fabric tensor that reflects the distribution of contact o...

In micromechanics of granular materials, relationships are investigated between micro-scale characteristics of particles and contacts and macro-scale continuum characteristics. For three-dimensional isotropic assemblies the macro-scale elastic characteristics are described by the bulk and the shear modulus, which depend on the micro-scale character...

The inverse problem of blade design for centrifugal pumps and fans has been studied. The solution to this problem provides the geometry of rotor blades that realize specified performance characteristics, together with the corresponding flow field. Here a three-dimensional solution method is described in which the so-called meridional geometry is fi...

The geometrical characteristics of the critical state are studied, using twodimensional Discrete Element Method simulations. Various simulations have been performed in order to study the effect on the critical-state fabric tensor of interparticle friction and of the type of loading. The results for the fabric tensor, from simulations with different...

The wave-propagation characteristics of dense granular materials have been studied from the micromechanical viewpoint, in which relationships are sought between properties at the micro-scale of particles and interparticle contacts and properties at the continuum, macro-scale. The dispersion and damping characteristics have been determined from a th...

In micromechanical studies of granular materials, relations are investigated between macro-level, continuum characteristics and micro-level, (inter) particle characteristics. For quasi-static deformation of granular materials, the fabric tensor is an important micromechanical characteristic that describes the orientational distribution of contacts...

Plastic deformation of granular materials is investigated from the micromechanical viewpoint, in which the assembly of particles and interparticle contacts is considered as a mechanical structure. This is done in three ways. Firstly, by investigating the degree of redundancy of the system by comparing the number of force degrees of freedom at conta...

In micromechanics of the elastic behaviour of granular materials, the macro-scale continuum elastic moduli are expressed in terms of micro-scale parameters, such as coordination number (the average number of contacts per particle) and interparticle contact stiffnesses in normal and tangential directions. It is well-known that mean-field theory give...

The deformation characteristics of idealized granular materials have been studied from the micro-mechanical viewpoint, using Bagi’s three-dimensional micro-mechanical formulation for the strain tensor [Bagi, K., 1996. Mechanics of Materials 22, 165-177]. This formulation is based on the Delaunay tessellation of space into tetrahedra. The set of edg...

Two-dimensional particle image velocimetry measurements and three-dimensional computational fluid dynamics (CFD) analyses have been performed on the steady velocity field inside the shrouded impeller of a low specific-speed centrifugal pump operating with a vaneless diffuser. Flow rates ranging from 80% to 120% of the design flow rate are considere...

The propagation of mechanical waves, such as sound, through granular materials is important in many disciplines of engineering. Here wave propagation is studied from the micromechanical viewpoint, in which relationships are investigated between macroscopic wave propagation characteristics and microscopic particle and interparticle characteristics....

An important objective of recent research on micro-mechanics of granular materials is to develop macroscopic constitutive relations in terms of micro-mechanical quantities at inter-particle contacts. Although the micro-mechanical formulation of the stress tensor is well established, the corresponding formulation for the st rain tensor has proven to...

Plasticity of granular materials during quasi‐static deformation is investigated, using a two‐dimensional Discrete Element Method simulation of biaxial deformation. From the detailed, discrete information obtained from this simulation, macroscopic continuum plasticity is viewed from the structural‐mechanics viewpoint in three different ways. Firstl...

The interlink between particle-scale properties and macroscopic behavior of three-dimensional granular media subjected to mechanical loading is studied intensively by scientists and engineers, but not yet well understood. Here we study the role of key particle-scale properties, such as interparticle friction and particle elastic modulus, in the fun...

A micromechanical theory is formulated for quasi-static deformation of granular materials, which is based on information theory. A reasoning is presented that leads to the definition of an information entropy that is appropriate for quasi-static deformation of granular materials. This definition is based on the hypothesis that relative displacement...

Micromechanics of granular materials deals with the relation between microscopic and macroscopic characteristics. This study
focuses on elastic behaviour. An overview of micromechanics of granular materials is given. Two regimes are identified, uniform
strain and uniform stress. It follows from extremum principles that these regimes correspond to u...

We determine the elastic moduli of two-dimensional assemblies of disks by computer simulations. The disks interact through elastic contact forces, which oppose the relative displacement at the contact points by means of a normal and a tangential stiffness, both taken constant. Our simulations confirm that the uniform strain assumption results in in...

To describe the heterogeneous nature of stress transmission in granular materials, the concept of the "strong" network consisting of contacts with large normal forces has been proposed by Radjaï [Phys. Rev. Lett. 80, 61 (1998)]. The shear stress is mainly determined by this strong network. The dual viewpoint is adopted here, by not only considering...

1] Tidal sandbanks are large-scale bed features present in many shallow shelf seas. Here we investigate the effect of nonuniform sediment on their dynamics, with a particular aim to explain observed surficial grain size variations over tidal sandbanks from a process-based modeling perspective. To this end, we use a linear stability analysis that de...

The shear modulus of two-dimensional liquid foams in the dry limit of low liquid content has been studied theoretically. The focus is on the effect of geometrical disorder on the shear modulus (besides the influence of surface tension). Various theoretical predictions are formulated that are all based on the assumptions of isotropic geometrical cha...

The effect of the interparticle friction coefficient μ on macroscopic, continuum characteristics, such as shear strength and dilatancy rate, of granular materials in quasi-static deformation is investigated using two-dimensional discrete element simulations of biaxial tests with various values for μ. Qualitatively, the macroscopic behaviour observe...

Longitudinal and transverse mixing in horizontal rotary kilns has been studied, using a three-dimensional Discrete Element Method approach. The focus is on the effect of the main operating conditions, i.e., the filling degree and the rotational speed of the rotary kiln, on quantitative measures of longitudinal and transverse mixing. Discrete Elemen...

The occurrence of cavitation is one of the main limiting factors in the operation and design of centrifugal pumps. In this paper a model for the prediction of sheet cavitation is described. This model has been implemented in a three-dimensional finite-element package, employing the potential-flow approximation of the governing flow equations. At th...

The development of an inverse-design method for the impellers of centrifugal pumps is presented. The flow inside the impeller channel is assumed to be irrotational, inviscid and incompressible. With the inverse-design method infinitely-thin impeller blades can be designed for a given meridional geometry and design conditions. The main design parame...

A study is made of kinematic and static assumptions for homogenization in micromechanics of granular materials for two cases. The first case considered deals with the elastic behaviour of isotropic, two-dimensional assemblies with bonded contacts. Using a minimum potential energy principle and estimated particle displacement and rotation fields, up...

A theory of critical state and of the evolution of coordination number during quasi-static deformations of granular materials is developed, based on the interpretation of several discrete element simulations of plane granular assemblies with a range of interparticle friction from nearly frictionless to infinitely rough. The theory is based on the c...

To increase the understanding of complex flows in dredging cutter heads, an experimental and numerical investigation of these flows has been made. As a first step toward the investigation of the mixture flow in a complete cutter head that actually cuts the soil, the simplified case of the flow of water in a freely rotating cutter head is considered...

The probability density functions (PDFs) of contact forces in anisotropic, cohesionless and frictional granular materials are studied numerically and theoretically. Using discrete element simulations of biaxial deformation of a large two-dimensional assembly consisting of 200,000 disks, it is observed that the PDFs for the normal and tangential com...

A theoretical framework is presented for the statics and kinematics of discrete Cosserat-type granular materials. In analogy to the force and moment equilibrium equations for particles, compatibility equations for closed loops are formulated in the two-dimensional case for relative displacements and relative rotations at contacts. By taking moments...

A theory is developed for the probability density functions of contact forces for cohesionless, frictional granular materials in quasi-static equilibrium. This theory is based on a maximum information entropy principle, with an expression for information entropy that is appropriate for granular materials. Entropy is maximized under the constraints...

This study deals with bounds for the effective elastic moduli of granular materials in terms of micromechanical parameters. The case considered is that of two-dimensional isotropic assemblies of non-rotating particles with bonded contacts and a linear elastic contact constitutive relation. Based on variational principles, rigorous upper and lower b...

In statistical physics of dilute gases maximum entropy methods are widely used for theoretical predictions of macroscopic quantities in terms of microscopic quantities. In this study an analogous approach to the mechanics of quasi-static deformation of granular materials is proposed. The reasoning is presented that leads to the definition of an ent...

The elastic behaviour of isotropic assemblies of granular materials consisting of two-dimensional, bonded and non-rotating particles is studied from the micromechanical viewpoint. Discrete element simulations have been performed of assemblies of 50,000 particles with various coordination numbers (average number of contacts per particle) and various...

The hydraulic performance of an industrial mixed-flow pump is analyzed using a three-dimensional potential flow model to compute the unsteady flow through the entire pump configuration. Subsequently, several additional models that use the potential flow results are employed to assess the losses. Computed head agrees well with experiments in the ran...

The flow in the volute of a low specific-speed pump was studied both experimentally and numerically near its design point. Measurements included time-averaged values of velocity and static pressure at a large number of locations in the volute. The numerical computations were based on the unsteady three-dimensional potential flow model for the core...

A numerical method is presented for the computation of unsteady, three-dimensional potential flows in hydraulic pumps and turbines. The superelement method has been extended in order to eliminate slave degrees of freedom not only from the governing Laplace equation, but also from the Kutta conditions. The resulting superelement formulation is invar...

In this micro-mechanical study of the behaviour of granular materials, a minimum potential energy and a minimum complementary energy principle are derived for the elastic moduli of two-dimensional, bonded assemblies of particles. These extremum principles are used to obtain bounds on the elastic moduli. Statistical versions of these energy principl...

The partitioning of graphs is a frequently occurring problem in science and engineering. The spectral graph partitioning method is a promising heuristic method for this class of problems. Its main disadvantage is the large computing time required to solve a special eigenproblem. Here a simple and efficient method is proposed to reduce this computin...

In order to develop constitutive relations for granular materials from the micromechanical viewpoint, general expressions relating macroscopic stress and strain to contact forces and particle displacements are required. Such an expression for the stress tensor under quasi-static conditions is well established in the literature, but a corresponding...

A theoretical and experimental study was made of the conveying speed with which granular materials are transported by vibratory conveyors. The basic assumption made is that the layer of granular material can be considered as a point mass. The theory incorporates rest, slide, and flight phases of the material. Although the emphasis of this study is...

A theoretical and experimental study is performed of rapid, fully developed flows of cohesionless granular materials down inclined chutes with a rough

A well-known class of constitutive relations for cohesionless granular materials are the double-sliding models. The double-sliding model proposed by Spencer (J. Mech. Phys. Solids, 12, 337, 1964) for incompressible materials as well as those of Spencer and Kingston (Rheol. Acta, 12, 194, 1974) and Mehrabadi and Cowin (J. Mech. Phys. Solids.26, 269,...

Various theories exist for predicting the pressure on the walls of bins filled with granular material. These theories, such as Janssen's (1895) theory, usually neglect the effect of the compressibility of the granular material, which is relevant for many materials. Here this effect is studied numerically, and the results are compared with a new app...

The relation between the hypo-elastic constitutive law and Mehrabadi and Cowin's dilatant double-sliding model for cohesionless granular materials is studied. Conditions that must be satisfied by hypo-elastic analogues of the double-sliding model are derived constructively, and a simple example is given.

In this paper a total linearization method is derived for solving steady viscous free boundary flow problems (including capillary effects) by the finite element method. It is shown that the influence of the geometrical unknown in the totally linearized weak formulation can be expressed in terms of boundary integrals. This means that the implementat...

A micromechanical study is made of the relationship between interparticle friction coefficient and macroscopic continuum friction and dissipation in idealised granular materials, using Discrete Element Method simulations with varying . As expected, mac-roscopic friction and dilatancy increase with . Surprisingly, dissipation is present even when or...

## Citations

... A suction anchor is installed by the inner suction inside the caisson (Fu et al., 2021;Guo et al., 2012;Zhao et al., 2022). Some pumps work to maintain the suction inside the anchor. ...

... The two scholars adopted the CFD-based simulation strategy already verified on the baseline axial fan in 2022 and studied the impact of different eddy current distributions on the aerodynamic performance. The current CFD parameters showed that the design of free vortex distribution and polynomial vortex distribution met the expected pressure rise, and the overall static and overall efficiency significantly improved (maximum increase of 3.9% and 4.6%, respectively) [95]. Lee and Kil (2020) used the streamline curvature method to predict the flow and performance of axial-flow fans and made the empirical correlation between flow deviation and pressure loss. ...

... The potential drawback in efficiency was not discussed in detail. Nevertheless, the idea in their subsequent paper [7] was to quantify the potential of the overall blade sweep, dihedral, and skew on the aerodynamic performance of such fans. They found only minor benefits. ...

... This indicates that the larger plastic strains are triggered more rapidly when the loading direction is non-coaxial with the current stress. The larger plastic deformations associated with such non-coaxial loading is expected in the non-coaxial and tangential plasticity theories (Rudnicki and Rice 1975;Hashiguchi 1998;Yu and Yuan 2006;Pouragha et al. 2021). ...

... The concept of ACST is rooted in thermodynamics and DEM modeling, and the anisotropic, unique fabric at the critical state has been marginally touched using an experimental approach [29,[31][32][33] X-ray micro-tomography and the corresponding image processing techniques have been recently developed as rapid and drastic powerful tools to investigate the grainscale behavior of granular materials [34]. These tools have provided valuable shreds of evidence for microstructural characterization [31,[34][35][36][37][38][39][40][41]. ...

... where sym( ) is the symmetric part of a tensor . Despite all its assumptions (see for example Rothenburg and Kruyt, 2001), the uniformstrain theory is important since it allows to identify an important variable (sym( ⋅ ⋅ )) for fabric evolution. This theoretical result (that does not require model parameters) in Eq. (19) confirms the finding from DEM simulations in Pouragha (2022) that the total strain ratė, rather than the elastic or the plastic strain rate, is important for the fabric rate. ...

... For instance, Lindemann et al. [5] suggested a design method for a small hub-to-tip ratio with swept blades, based on an empirical axial and tangential velocity distribution in the spanwise direction from hub to blade. In a more recent paper, Wang and Kruyt [6] studied small hub-to-tip ratio fans. Among others, they analysed the influence of nonaerodynamically shaped parts of the blades and showed "that the presence of non-airfoil sections near the root has a minor influence on the pressure coefficient and hence on the total-to-static efficiency (of the fan), due the formation of a vortex upstream from the blades near the hub. ...

... inherent anisotropy), an evolution rule can be formulated to incorporate the influence of the changing microstructure. In the literature, there are examples of models incorporating either an evolution rule (Wan & Guo, 2001;Li & Dafalias, 2012;Papadimitriou et al., 2019;Petalas et al., 2020;Yang et al., 2020;Zhao & Kruyt, 2020;Norouzi & Lashkari, 2021) or a fixed fabric tensor throughout the shearing process (Li & Dafalias, 2002Yanget al., 2008;Yao et al., 2017). Although the models with a fixed fabric adequately simulate the soil behaviour, many recent granular level experimental and numerical observations carried out using X-ray computed tomography (CT) and the discrete-element method (DEM), respectively, show that anisotropic behaviour is not a fixed phenomenon arising solely from the initial depositional formation process, but an evolving phenomenon where a continuous evolution of the fabric composition takes place towards its critical state value (Li & Li, 2009;Fu & Dafalias, 2011;Kruyt, 2012;Guo & Zhao, 2013;Fu & Dafalias, 2015;Wang et al., 2017;Yang & Wu, 2017;Wiebicke, 2020;Wiebicke et al., 2020;Zhao & Kruyt, 2020;Zhao et al., 2021). ...

... RANS method are known as comprehensive and cost effective tools rather than conducting costly experiments to analyze the performance of different types of fans and blowers. [3][4][5][6][7][8][9] Solving RANS equations for the vacuum cleaner model which leads to calculation of the fan characteristics such as shaft power, suction power, etc. enables us to determine the optimal geometrical parameters for the fan components in framework of the optimization process. 1,10 As the size of the vacuum cleaners gets smaller, the necessity to reduce the dimensions of the main components has increased. ...

... In the clean and ideal soil particle assembly, the bonding effect can be ignored and the van der Waals forces between the particles are relatively small, so the capillary force needs to be studied emphatically to establish a particle scale unsaturated soil constitutive law (Payam & Fathipour, 2011;Wang, Su, Xu, Rong, & Xie, 2016). Three approaches can be used to study capillary bridges: theoretical approach (Zhao, Kruyt, & Millet, 2020), experimental approach (Gras, Delenne, & El Youssoufi, 2013), and numerical approach (Hua, Ocone, & Yang, 2022). The study of the capillary bridge mainly focused on two aspects: a water bridge with constant water content and a water bridge under constant suction. ...