Homepage of Niels P. Kruyt

Address

Department of Mechanical Engineering

University of Twente

P.O. Box 217

7500 AE Enschede

The Netherlands

Tel: +31-53-489 2528

Fax: +31-53-489 3695

E-mail: n.p.kruyt AT utwente.nl

Research interests

Fluid mechanics of turbomachines

  • centrifugal pumps
  • inverse-design methods
  • optimization methods

Granular materials

  • constitutive modelling
  • micromechanics
  • discrete element method
  • vibratory conveyors
  • mixing in rotary kilns

Fluid mechanics of turbomachines

Introduction

Turbomachines, and centrifugal pumps in particular, are of major importance to contemporary society. Everyone deals with them directly or indirectly in one's daily life. Examples are pumps for boiler units, drinking water supply, energy generating plants and process industry. Centrifugal pumps have been in use for many years. Therefore, the innocent reader could assume that further research is no longer required in this field, under the slogan “everything has been investigated and solved before”. However, this is not correct. Developments are still continuing rapidly, for example to smaller dimensions, higher speeds and efficiencies and new areas of application.

These developments are stimulated by improved manufacturing and computer simulation techniques. A technique like CAD-CAM makes it possible to manufacture a new design quickly and economically. By simulating the flow in centrifugal pumps, the designer can optimize these using computers instead of through actual tests. This approach is widely accepted in aircraft design (“computer wind tunnel”). In contrast, new centrifugal pumps are usually developed as modifications to existing designs by a trial-and-error method, which is time-consuming and expensive. The new approach based on flow simulations is especially suitable for designing engineered centrifugal pumps that must meet specific customer specifications. Then it is frequently necessary to deviate from existing types of centrifugal pumps: new concepts need to be developed.

Objective

The objective of the research at the Turbomachinery Laboratory of the Department of Mechanical Engineering at the University of Twente in the Netherlands is to contribute to the scientific knowledge of the relevant flow phenomena in centrifugal pumps. In addition, an objective is to make this knowledge available to the pump designer, amongst others by developing tools for simulating time-dependent, three-dimensional flows in centrifugal pumps. Such a tool will only be accepted in a design environment when the results are accurate and are obtained quickly.

Approach

The approach of the research consist of a combination of

  • experiments for increasing the understanding of the important flow phenomena
  • flow modelling for obtaining the governing equations
  • numerical simulations for computing the flow

Difficulties that arise in this approach are (1) complex equations, (2) geometries and (3) unsteady flows.

Complex equations

The approach is based on the fundamental conservation laws of physics. Based on an asymptotic analysis the equations for the main flow can be simplified. This main flow is inviscid, irrotational and incompressible. This means that the main flow is an unsteady potential flow. Viscous effects are only important in boundary layers along walls and in wakes behind the impeller blades. These assumptions are valid around the best efficiency point.

Complex geometries

The geometries are very complex, due to their three-dimensional doubly-curved shape of the impeller blades (and sometimes diffuser blades). The volute also has a complicated shape.

Unsteady flows

The rotation of the impeller with respect to the volute causes the flow to be unsteady, especially at off-design conditions of the pump. Usually the flow in both parts is considered separately. This simplifies the problem, but it is becoming clear that a correct description of the interaction between impeller and volute is very important.

Current research projects that are described here deal with:

  • experimental investigations
  • cavitation analyses
  • impeller-volute interaction

Experiments

For measuring velocities and pressures in impeller channels and volutes a test-rig is available in the Turbomachinery Laboratory. With this test-rig it is possible to directly measure the relative velocity in the impeller channels, since the equipment rotates with the impeller. Velocities are measured using “Laser Doppler Velocimetry” (LDV). Using two laser beams the two components of the velocity are measured that are in the plane perpendicular to the laser beams. The relative flow field in a number of two-dimensional impellers has been determined. These showed that the flow field is accurately described by the potential flow model. Currently, the test-rig is being adapted to three-dimensional measurements. This is especially important for mixed-flow impellers. To this end, an impeller has been manufactured from plexi-glass. The principle of the modified test-rig is that by measuring two components of the velocity in two different planes, the three-dimensional velocity field is obtained.

Numerical simulations

For reasons of efficiency and computing times a completely new system has been developed for simulating numerically the flow in impeller-volute configurations. The system is called COMPASS, an acronym for Centrifugal Or Mixed-flow Pump Analysis System. It is based on the finite-element method with substructuring and implicit Kutta conditions as special features. With this system unsteady potential flows in impeller and volute are computed. Thus the interaction between impeller and volute is properly accounted for. To this end the computational domain is divided into blocks with a cubical topology. Blocks in impeller and volute are separated by a conical surface along which the impeller blocks slide. In this way the rotation of the impeller is simulated.

The system is easy to use, since the geometry of impeller and volute are described parametrically. The mesh generation is also automated. Finally, the post-processing of velocity and pressure field is integrated into the system. An example of such a visualization of the pressure on the impeller blades is shown below.

An important quantity to the designer of a pump is its efficiency under various operating conditions. In order to predict the efficiency the viscous losses need to be quantified. An inviscid model can not directly give these. Yet it is possible to estimate the various sources of loss, based on the inviscid core velocities in the pump. To this end, viscous loss models were adapted from the literature.

Impeller-volute interaction

Here some results are shown of the simulations in an industrial mixed-flow pump of Flowserve in Hengelo. These simulations were performed with COMPASS. The employed mesh is shown above; the comparison of the computed head and efficiency with measured values is shown below.

Note that to obtain these performance curves, unsteady computations were performed, and the results were subsequently averaged over time.

Cavitation analyses

An important flow phenomenon in pumps is cavitation. Herewith the inception of bubbles is meant, that arise when the local pressure drops below the vapour pressure of the liquid being pumped. This drop in static pressure is caused by the acceleration of the fluid around the impeller nose. Downstream in the impeller these bubbles cavitation implode as a result of the higher pressure. This can cause damage to the blades, the so-called cavitation erosion, which reduces their life expectancy. Furthermore, these implosions increase the noise level. Cavitation performance is usually expressed in an NPSH-Q graph. NPSH is Net Positive Suction Head, the stagnation pressure at the inlet necessary such that no cavitation occurs and Q is the flow rate. When the actual inlet pressure and the NPSH-characteristics are known, the operating range and the life expectation can be predicted. A centrifugal pump should be designed so that over the complete operating range the NPSH value does not exceed the available inlet stagnation pressure.

Current research deals with the prediction of cavitation inception on the basis of completely three-dimensional potential flow computations with COMPASS. This is the correct approach, contrary to commonly used quasi three-dimensional models that require empirical coefficients. This research is funded by Flowserve Hengelo and NOVEM. The figure below shows the result of such a computation for a mixed-flow impeller. In addition measured NPSH-inception values are shown. Both visual and acoustic measurements were made. It is clear that over a wide range the cavitation inception characteristics are correctly predicted.

This opened the way for parametric optimization studies in which the shape of the nose profile is modified. An example is shown below, demonstrating the advantageous effect of an asymmetrical profile.

Currently, the cavitation model is being extended in order to compute, for inlet pressures below inception values, the shape of the cavitation sheet.

Outlook

During the past few years major advances have been made in predicting the hydraulic performance of pumps. Especially complete impeller-volute configurations can now be analysed, contrary to other research groups that only study components of pumps with their viscous computations. Therefore industry shows increasing interest in the hydraulic analysis system COMPASS. This system will be further improved by refining the hydraulic models. In first instance the models for leakage flow, disc friction, mixing losses and three-dimensional boundary layers will be considered. Additional experimental work will be done on the velocity and pressure fields in mixed-flow pumps. COMPASS will also be used in optimization studies of efficiency, cavitation etc.

A permanent factor in this research is the close cooperation with industry. The importance of this cooperation lies in the coordination of the direction of the research and in the transfer of the developed technological knowledge to companies.

Inverse-design and optimisation methods

Currently, advanced design methods are being developed that are based on inverse-design and optimization methods.

In inverse-design methods, the duty of the impeller is specified in terms of flowrate, angular velocity, head, some “blade loading” and meridional geometry. From these, the blade geometry is computed; the blade curvature is thus the result.

The inverse-design methods and the optimisation methods are described in detail in the Ph.D. thesis of Remko Westra.

CFD for pump design: a tutorial

Tutorial presented at the 5th International Symposium on Pumping Machinery, 2005 ASME Fluids Engineering Division Summer Meeting and Exhibition, 19-23 June, Houston, USA. [pps] (9.5 MB)

Prediction of aerodynamic performance and noise production of axial fans

M.Sc Thesis of Robin van de Vondervoort, April 2015

Industrial cooperation

  • Flowserve (Hengelo, the Netherlands)
  • IHC (Kinderdijk, the Netherlands)
  • SPX (Assen, the Netherlands)
  • Aeronamics (Almelo, the Netherlands)
  • Philips Domestic & Appliance Products (Drachten, the Netherlands)
  • Vostermans (Venlo, the Netherlands)
  • Ballast Nedam Dredging (Zeist, the Netherlands)
  • Boskalis (Papendrecht, the Netherlands)
  • De Groot Nijkerk (Nijkerk, the Netherlands)
  • Howden (Hengelo, the Netherlands)

Industrial cooperation is done via TurboValley.

Teaching

  • Fluid mechanics of turbomachines 1 (115472)
  • Fluid mechanics of turbomachines 2 (115476)

Granular materials

  • Tessellations and granular materials
    (Contribution to Subdivide and Tile: Triangulating spaces for understanding the world, Leiden, the Netherlands, November 2009).
  • Strength, dilatancy, energy and dissipation in quasi-static deformation of granular materials
  • (Contribution to Powders & Grains 2005, Stuttgart, Germany, July 2005).
  • Statistics of forces and relative displacements at contacts in biaxial deformation of granular materials
    (Contribution to Workshop on Quasi-static Deformations of Particulate Materials, Budapest, Hungary, August 2003).
  • Slow flows of granular materials
    (Contribution to J.M. Burgers Centre Course on Granular Materials, Enschede, the Netherlands, February 2003).
  • Kinematic and static assumptions for homogenization in micromechanics of granular materials
    (Presentation at ASME/ASCE Mechanics and Materials Conference: Current Developments in Micromechanics of Random Heterogeneous Materials and Bodies, San Diego, USA, June 2001).
  • Micromechanics of flowing granular materials
  • (Presentation at FOM 2000 Meeting, Veldhoven, the Netherlands, October 2000).
  • Micromechanics of the elastic behaviour of granular materials
    (Presentation at Continuous and Discontinuous Modelling of Cohesive Frictional Materials, Stuttgart, Germany, April 2000).
  • Micromechanical definition of the strain tensor for granular materials: a Matlab implementation

Scientific papers

  •  Kruyt, N.P (2016)
    On weak and strong contact force networks in granular materials
    International Journal of Solids and Structures (accepted)
  •  Kruyt, N.P. & Rothenburg, L. (2016)
    A micromechanical study of dilatancy of granular materials
    Journal of the Mechanics and Physics of Solids (accepted)
  •  Kruyt, N.P. (2015)
    A reappraisal of the concept of the strong/weak force networks for granular materials
    Particles 2015, Paper 39, Barcelona, Spain
  • Krakers, L.A. & Kruyt, N.P. & Rutjes, C. (2015)
    Full-scale validation of a comprehensive criterion to predict fish-friendliness of pumps
    ASME-JSME-KSME Joint Fluids Engineering Conference 2015, Paper AJK2015-FED, Seoul, Korea.
  • Rothenburg, L. & Kruyt, N.P. (2015)
    On energy dissipation in granular materials
    9th European Solid Mechanics Conference, Paper 163, Madrid, Spain.
  • Kruyt, N.P. & Rothenburg, L. (2015)
    Micromechanical study of dilatancy of granular materials,
    9th European Solid Mechanics Conference, Paper 118, Madrid, Spain.
  • Kruyt, N.P. & Millet, O. & Nicot, F. (2015)
    Deformation analysis of granular materials at micro and macro scales
    Geomechanics from Micro to Macro, pp. 753–757, eds. K. Soga & K. Kumar & G. Biscontin & M. Kuo, Taylor & Francis, London, UK.
  • Kruyt, N.P. & Millet, O. & Nicot, F. (2014)
    Macroscopic strains in granular materials accounting for grain rotations
    Granular Matter 16 933–944.
  • Kruyt, N.P. & Pennings, P.C. & Faasen, R. (2014)
    Optimisation of efficiency of axial fans
    Proceedings 12th European Fluid Machinery Congress, pp.13–20, Woodhead Publishing, Cambridge, UK.
  • Kruyt, N.P. (2014)
    An analytical micromechanical theory for the elastic moduli of isotropic granular materials
    2014 EMI Conference, Paper 42, Hamilton, Ontario, Canada.
  • Kruyt, N.P. & Millet, O. & Nicot, F. (2014)
    Elucidating the role of particle rotations on deformation in granular materials
    Modeling Granular Media across Scales, Montpellier, France.
  • Kruyt, N.P. & Rothenburg, L. (2014)
    On micromechanical characteristics of the critical state of two-dimensional granular materials
    Acta Mechanica 225 2301–2318.
  • Konijn, B.J. & Sanderink, O.B.J. & Kruyt, N.P. (2014)
    Experimental study of the viscosity of suspensions: effect of solid fraction, particle size and suspending liquid
    Powder Technology 266 61–69.
  • Kruyt, N.P. & R.W. Westra (2014)
    On the inverse problem of blade design for centrifugal pumps and fans
    Inverse Problems 30 065003.
  • Kruyt, N.P. (2014)
    Micromechanical study of elastic moduli of three-dimensional granular assemblies
    International Journal of Solids and Structures 51 2336–2344.
  • Millet, O. & Kruyt, N.P. & Nicot, F. (2013)
    On the importance of particle rotations for macroscopic strains in granular assemblies
    Particles 2013, Paper A37, Stuttgart, Germany.
  • Kruyt, N.P. (2013)
    The critical state of granular materials and its stability: a micromechanical view
    Particles 2013, Paper A3, Stuttgart, Germany.
  • Kruyt, N.P. & Millet, O. & Nicot, F. (2013)
    From microstructure to the macroscopic strains in granular soils
    XVI French-Polish Colloquium of Soil and Rock Mechanics, Montpellier, France.
  • Konijn, B.J. & Sanderink, O.B.J. & Kruyt, N.P. (2013)
    Experimental study on the behaviour of suspensions
    8th International Conference on Multiphase Flow, Paper 433, Jeju, Korea.
  • Kruyt, N.P. (2013)
    Micromechanics of the critical state of idealised granular materials
    Constitutive Modelling of Geomaterials: Advances and New Applications, pp. 193–198, eds. Q. Yang & J.-M. Zhang & H. Zheng & Y. Yao, Springer-Verlag, Berlin, Germany.
  • Kruyt, N.P. & Rothenburg, L. (2012)
    On shear strength and fabric of granular materials
    8th European Solid Mechanics Conference, Paper 36086, eds. G.A. Holzapfel & R.W. Ogden, Graz, Austria.
  • Kruyt, N.P. (2012)
    Micromechanical study of dispersion and damping characteristics of granular materials
    Journal of Mechanics and Materials of Structures 7 347–361.
  • Kruyt, N.P. (2012)
    Micromechanical study of fabric evolution in quasi-static deformation of granular materials
    Mechanics of Materials 44 120–129.
  • Kruyt, N.P. (2010)
    Micromechanical study of plasticity of granular materials
    Comptes Rendus Mécanique 338 596–603.
  • Westra, R.W. & Broersma, L. & van Andel, K. & Kruyt, N.P. (2010)
    PIV measurements and CFD computations of secondary flow in a centrifugal pump impeller
    Journal of Fluids Engineering (Transactions of the ASME) 132 061104.
  • Durán, O. & Kruyt, N.P. & Luding, S. (2010)
    Micro-mechanical analysis of deformation characteristics of three-dimensional granular materials
    International Journal of Solids and Structures 47 2234–2245.
  • Kruyt, N.P. (2010)
    Three-dimensional lattice-based dispersion relations for granular materials
    IUTAM-ISIMM Symposium on Mathematical Modeling and Physical Instances of Granular Flows, AIP Conference Proceedings Vol.1227, pp.405–415, eds. J.D. Goddard & J.T. Jenkins & P. Giovine.
  • Durán, O. & Kruyt, N.P. & Luding, S. (2010)
    Analysis of three-dimensional micro-mechanical strain formulations for granular materials: evaluation of accuracy
    International Journal of Solids and Structures 47 251–260.
  • Kruyt, N.P. & Agnolin, I. & Luding, S. & Rothenburg, L. (2010)
    Micromechanical study of elastic moduli of loose granular materials
    Journal of the Mechanics and Physics of Solids 58 1286–1301.
  • Kruyt, N.P. (2009)
    Micromechanical study of elastic behaviour of granular materials
    Particles 2009, pp. 183–186, eds. E. Onate & D.R.J. Owen, Barcelona, Spain.
  • Kruyt, N.P. (2009)
    Force fluctuations in quasi-static deformation of granular materials: deviations from mean-field behaviour
    7th European Solid Mechanics Conference, pp.201–202, eds. J. Ambrosio & M.T. Silva, Lisbon, Portugal.
  • Westra, R.W. & Broersma, L. & van Andel, K. & Kruyt, N.P. (2009)
    Secondary flows in centrifugal pump impellers: PIV measurements and CFD computations
    2009 ASME 6th International Symposium on Pumping Machinery, Paper FEDSM2009-78275, Vail, CO, USA.
  • Kruyt, N.P. & Rothenburg, L. (2009)
    Plasticity of granular materials: a structural-mechanics view
    Powders & Grains 2009, AIP Conference Proceedings Vol.1145, pp.1073–1076, eds. M. Nakagawa & S. Luding.
  • Antony, S.J. & Kruyt, N.P. (2009)
    Role of interparticle friction and particle-scale elasticity on shear-strength mechanism in three-dimensional granular media
    Physical Review E 79 031308.
  • Rothenburg, L. & Kruyt, N.P. (2009)
    Micromechanical definition of an entropy for quasi-static deformation of granular materials
    Journal of the Mechanics and Physics of Solids 57 634–655.
  • Westra, R.W. & Kruyt, N.P. & Andel, K. van & Hoeijmakers, H.W.M. (2008)
    An optimization method for centrifugal pump impellers
    The 12th International Symposium on Transport Phenomena and Dynamics of Rotating Machinery, Honolulu, Hawaii, Paper ISROMAC12-2008-20147.
  • Agnolin, I. & Kruyt, N.P. (2008)
    On the elastic moduli of two-dimensional assemblies of disks: relevance and modeling of fluctuations in particle displacements and rotations
    Computers and Mathematics with Applications 55 245–256.
  • Kruyt, N.P. (2007)
    On the shear modulus of two-dimensional liquid foams: a theoretical study of the effect of geometrical disorder
    Journal of Applied Mechanics (Transactions of the ASME) 74 560–567.
  • Kruyt, N.P. & Antony, S.J. (2007)
    On force, relative-displacement and work networks in granular materials subjected to quasi-static deformation
    Physical Review E 75 051308.
  • Roos, P.C. & Wemmenhove, R. & Hulscher, S.J.M.H. & Hoeijmakers, H.W.M. & Kruyt, N.P. (2007)
    Modelling the effect of nonuniform sediment on the dynamics of offshore tidal sandbanks
    Journal of Geophysical Research 112 F02011.
  • Kruyt, N.P. & Rothenburg, L. (2006)
    Shear strength, dilatancy, energy and dissipation in quasi-static deformation of granular materials
    Journal of Statistical Mechanics: Theory and Experiment P07021.
  • Westra, R.W. & Kruyt, N.P. & Hoeijmakers, H.W.M. (2005)
    An inverse-design method for centrifugal pump impellers
    2005 ASME 5th International Symposium on Pumping Machinery, Paper FEDSM2005-77283, Houston, TX, USA.
  • Kruyt, N.P. & Rothenburg, L. (2005)
    Strength, dilatancy, energy and dissipation in quasi-static deformation of granular materials
    Powders & Grains 2005, pp.251–255, eds. R. Garcia-Rojo & H.J. Herrmann & S. McNamara, Balkema, Leiden, the Netherlands.
  • Finnie, G.F. & Kruyt, N.P. & Ye, M. & Zeilstra, C. & Kuipers, J.A.M (2005)
    Longitudinal and transverse mixing in rotary kilns: a Discrete Element Method approach
    Chemical Engineering Science 60 4083–4091.
  • Kruyt, N.P. & Rothenburg, L. (2004)
    Micromechanical study of macroscopic friction and dissipation in idealised granular materials: the effect of interparticle friction
    21st International Conference on Theoretical and Applied Mechanics 2004, Warsaw, Poland.
  • Kruyt, N.P. & Rothenburg, L. (2004)
    Kinematic and static assumptions for homogenization in micromechanics of granular materials
    Mechanics of Materials 36 1157–1173.
  • Kruyt, N.P. & Rothenburg, L. (2004)
    On the microscopic origin of the macroscopic frictional behaviour of granular materials
    17th ASCE Engineering Mechanics Division Conference, Paper 55, eds. V. Kaliakin & J.T. Kirby & B. Bhattacharya & J.A. Yamamuro & H.W. Shenton, Newark, DE, USA.
  • Rothenburg, L. & Kruyt, N.P. (2004)
    Critical state and evolution of coordination number in simulated granular materials
    International Journal of Solids and Structures 41 5763–5774
  • Rothenburg, L. & Kruyt, N.P. (2003)
    Micromechanical study of critical state in granular materials
    Quasi-static Deformations of Particulate Materials, pp.203–212, ed. K. Bagi, Publishing Company of Budapest University of Technology and Economics, Budapest, Hungary.
  • Kruyt, N.P. & Rothenburg, L. (2003)
    Statistics of forces and relative displacements at contacts in biaxial deformation of granular materials
    Quasi-static Deformations of Particulate Materials, pp.141–150, ed. K. Bagi, Publishing Company of Budapest University of Technology and Economics, Budapest, Hungary.
  • Dekker, M.A. & Kruyt, N.P. & Burger, M. den & Vlasblom, W.J. (2003)
    Experimental and numerical investigation of cutter-head dredging-flows
    Journal of Waterway, Port, Coastal, and Ocean Engineering (Transactions of the ASCE) 129 203–209.
  • Kruyt, N.P. (2003)
    Contact forces in anisotropic frictional granular materials
    International Journal of Solids and Structures 40 3537–3556.
  • Kruyt, N.P. (2003)
    Statics and kinematics of discrete Cosserat-type granular materials
    International Journal of Solids and Structures 40 511–534.
  • Kruyt, N.P. & Rothenburg, L. (2002)
    Maximum entropy methods in the mechanics of quasi-static deformation of granular materials
    Proceedings International Mechanical Engineering Congress & Exhibition 2002, IMECE02-32494, ASME, New Orleans, LA, USA.
  • Kruyt, N.P. & Rothenburg, L. (2002)
    Probability density functions of contact forces for cohesionless frictional granular materials
    International Journal of Solids and Structures 39 571–583.
  • Kruyt, N.P. & Rothenburg, L. (2002)
    Micromechanical bounds for the elastic moduli of granular materials
    International Journal of Solids and Structures 39 311–324.
  • Rothenburg, L. & Kruyt, N.P. (2001)
    Rock strength and mining applications: a micromechanics view
    Proceedings International Conference on Civil Engineering 2001, pp.67–80, Interline Publishing, Bangalore, India.
  • Esch, B.P.M. van & Kruyt, N.P. (2001)
    Hydraulic performance of a mixed-flow pump: unsteady inviscid computations and loss models
    Journal of Fluids Engineering (Transactions of the ASME) 123 256–264.
  • Kruyt, N.P. & Rothenburg, L. (2001)
    Statistics of the elastic behaviour of granular materials
    International Journal of Solids and Structures 38 4879–4899.
  • Rothenburg, L. & Kruyt, N.P. (2001)
    On limitations of the uniform strain assumption in micromechanics of granular materials
    Powders and Grains 2001: 4th International Conference on Micromechanics of Granular Media, pp.191–194, ed. Y. Kishino, Balkema Publishers, Rotterdam, the Netherlands.
  • Kelder, J.D.H. & Dijkers, R.J.H. & Esch, B.P.M. van & Kruyt, N.P. (2001)
    Experimental and theoretical study of the flow in the volute of a low specific-speed pump
    Fluid Dynamics Research 28 267–280.
  • Kruyt, N.P. & Rothenburg, L. (2001)
    Micromechanics of the elastic behaviour of granular materials
    Continuous and Discontinuous Modelling of Cohesive Frictional Materials, pp.129–142, eds. P.A. Vermeer & S. Diebels & W. Ehlers & H.J. Herrmann & S. Luding & E. Ramm, Springer-Verlag, Berlin, Germany.
  • Steinbusch, P.J. & Vlasblom, W.J. & Burger, M. den & Kruyt, N.P. (1999)
    Numerical simulation of the flow generated by cutter heads
    Hydrotransport 14: 14th International Conference on Slurry Handling and Pipeline Transport, pp. 435–443, BHR Group.
  • Kruyt, N.P. & Esch, B.P.M. van & Jonker, J.B. (1999)
    A superelement-based method for computing unsteady three-dimensional potential flows in hydraulic turbomachines
    Communications in Numerical Methods in Engineering 15 381–397.
  • Kruyt, N.P. & Rothenburg, L. (1998)
    Statistical theories for the elastic moduli of two-dimensional assemblies of granular materials
    International Journal of Engineering Science 36 1127–1142.
  • Kruyt, N.P. (1997)
    A conjugate gradient method for the spectral partitioning of graphs
    Parallel Computing 22 1493–1502.
  • Esch, B.P.M. van & Kruyt, N.P. & Jonker, J.B. (1997)
    An inviscid-viscous coupling method for computing flows in entire pump configurations
    Third ASME Pumping Machinery Symposium, FED-SM97-3373, ASME, Vancouver, BC, Canada.
  • Sloot, E.M. & Kruyt, N.P. (1996)
    Theoretical and experimental study of the transport of granular materials by inclined vibratory conveyors
    Powder Technology 87 203–210.
  • Kruyt, N.P. & Rothenburg, L. (1996)
    Micromechanical definition of the strain tensor for granular materials
    Journal of Applied Mechanics (Transactions of the ASME) 63 706–711.
  • Kruyt, N.P. & Esch, B.P.M. van & Jonker, J.B. (1996)
    A tool for the analysis of unsteady potential flows in centrifugal and mixed-flow pumps
    Pump Congress 1996, Paper C8-2, September 1996, Karlsruhe, Germany.
  • Kruyt, N.P. & Esch, B.P.M. van & Jonker, J.B. (1995)
    Analysis of three-dimensional potential flows in centrifugal and mixed-flow pumps by a finite element method
    Tenth Conference on Fluid Machinery, pp.242–251, Budapest, Hungary, ed. A. Szabo.
  • Esch, B.P.M. van & Kruyt, N.P. & Jonker, J.B. (1995)
    An efficient method for computing three-dimensional potential flows in hydraulic turbomachines
    Ninth International Conference on Finite Elements in Fluids – New Trends and Applications, pp.633–644, Venice, Italy, eds. M. Morandi Cecchi & K. Morgan & J. Periaux & B.A. Schrefler & O.C. Zienkiewicz.
  • Esch, B.P.M. van & Kruyt, N.P. (1995)
    Analysis of the flow in a centrifugal pump using a multi-block finite element method for computing three-dimensional potential flows
    ERCOFTAC Seminar and Workshop on 3D Turbomachinery Flow Prediction III, part III, pp.19–25, Val d'Isère, France.
  • Kruyt, N.P. (1994)
    Aspects of constitutive relations for cohesionless granular materials
    Ph.D. Thesis, Department of Mechanical Engineering, University of Twente, Enschede, the Netherlands.
  • Kruyt, N.P. (1993)
    Results of Jenike's (1987) radial stress field theory for the flow of granular materials in conical hoppers: flow regimes and flow factors
    Powder Technology 76 109–112.
  • Kruyt, N.P. (1993)
    Towards micro-mechanical constitutive relations for granular materials
    Modern Approaches to Plasticity, pp.147–178, Horton, Greece, ed. D. Kolymbas, Elsevier, Amsterdam, the Netherlands.
  • Kruyt, N.P. & Verël, W.J.Th. (1992)
    Experimental and theoretical study of rapid flows of cohesionless granular materials down inclined chutes
    Powder Technology 73 109–115.
  • Kruyt, N.P. (1990)
    An analysis of the generalized double-sliding models for cohesionless granular materials
    Journal of the Mechanics and Physics of Solids 38 27–35.
  • Kruyt, N.P. (1990)
    Density effects in two-dimensional bins
    Journal of Applied Mechanics (Transactions of the ASME) 57 1032–1035.
  • Kruyt, N.P. (1989)
    On hypo-elastic analogues of the dilatant double-sliding model
    International Journal for Numerical and Analytical Methods in Geomechanics 13 303–309.
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Last updated 9 March 2016