Internal Viscous Flow Research Articles

Analytical and Computational Modeling of Relaxation Times for Non-Newtonian Fluids

With the availability of efficient and sophisticated finite element analysis (FEA) and computational fluid dynamics (CFD) tools, engineering designs are becoming more software-driven and simulation-based. However, the insights relevant to engineering designs tend to be hidden within massive temporal and spatial data produced with full-fledged three-dimensional simulations. In this paper, we present a preliminary study of the controlled intermittent dispensing of a typical non-Newtonian glue employed in the manufacturing of electric vehicles (EVs). The focus of the study is on the scaling issues derived from different computational and analytical models of interest and importance to the precision control of this non-Newtonian fluid, the lowest dynamic viscosity of which at extremely high shear rates is nearly four million times that of water. More specifically, the abrupt change of the inlet pressure with a constant outlet or ambient pressure and various modeling strategies for transient viscous internal flow with both Newtonian and non-Newtonian fluids are modeled and compared. The analytical and computational results of the developing Newtonian fluid, i.e., water, are derived and computed for validation and verification purposes before the actual applications to the developing non-Newtonian fluid. The concept of a well-established relaxation time before the onset of the steady solution for Newtonian fluids has been validated with both analytical and computational approaches before its expansion and adoption to non-Newtonian fluids with complex rheological behaviors. Other issues attributed to transient operations and precision controls of non-Newtonian fluid delivery involve the pressure pulse and pressure wave propagation within the flexible pipe with compressible or almost incompressible non-Newtonian fluids with a constant pressure at the outlet and a constant mass flow rate or average axial velocity at the inlet, which will be addressed in a separate paper.

Numerical investigation of flow characteristics in the front and rear chambers of centrifugal pump and pump as turbine

To investigate the flow characteristics in front chamber and rear chamber in pump mode and pump as turbine mode, a 3D computational model of a centrifugal pump was established, including the front and rear chamber. Based on Realizable k-ε turbulence model, numerical calculations of incompressible flow were carried out for internal viscous flow in two operating modes. Further analysis was conducted on the flow stability and hydraulic losses under two modes using energy gradient theory and entropy production theory. The numerical simulation results are within reasonable error compared to the experimental results in pump operation mode, which ensures the reliability of the numerical calculation method. The results indicate that the volumetric efficiency in both two modes is on an upward trend with increasing flow, but the volumetric efficiency of the pump mode is more significantly affected by changes in flow; the distribution patterns of dimensionless circumferential velocity and dimensionless radial velocity in the front and rear chambers under two operating modes are similar, but the distribution pattern of dimensionless radial velocity in the front chamber in turbine mode is significantly different from other operating conditions; flow instability is most likely to occur at the outlet of impeller, and the energy loss in clearance of wear-rings is greater than that in the pump chamber.

Growing Structure Based on Viscous Actuation of Constrained Multistable Elements

AbstractGrowing soft materials which follow a three dimensional (3D) path in space are critical to applications such as search and rescue and minimally invasive surgery. Herein, a concept for a single‐input growing multi‐stable soft material, based on a constrained straw‐like structure is presented. This class of materials are capable of maneuvering and transforming their configuration by elongation while executing multiple turns. This is achieved by sequenced actuation of bi‐stable frusta with predefined constraints. Internal viscous flow and variations in the stability threshold of the individual cells enable sequencing and control of the robot's movement so as to follow a desired 3D path as the structure grows. A theoretical description of the shape and dynamics resulting from a particular set of constraints is derived. To validate the model and demonstrate the suggested concept, experiments of maneuvering in models of residential and biological environments are presented. In addition to performing complex 3D maneuvers, the tubular structure of these robots may also be used as a conduit to reach inaccessible regions, which is demonstrated experimentally.

The Effect of Blade Angle Deviation on Mixed Inflow Turbine Performances

The choice of blades for mixed turbines is to achieve the required deflection with minimal losses. In addition, it is necessary that the blade functions without a detachment in a wide area outside the nominal operating point of the machine. In the blade profile study, it is required to satisfy the conditions relating to fluid mechanics and those relating to the possibility of realization of construction. The work carried out presents the effect of the blade deviation angle on the geometric blade shape and the performance of the mixed inflow turbine on keeping the same rotor casing in order to improve its performances. It was remarked that the efficiency is proportional to the deviation angle’s increase, but the rotor became heavy. It has been determined that the effect of the blade deviation angle on mixed inflow performances decreases dramatically starting from the angle −20° for a 100% of machine load. It was urged to avoid relying on angles greater than −20 as values for blade deviation angles. The study noted that the maximum obtained in the output work and power is related to the highest the efficiency for a specific optimum design case (−35° of deviation blade angle) due to the increase in the contact surface between the blade and the fluid, but the problem is that the rotor gets a little heavy (4.37% weight gain). Among recommendations, attention was given to the more significant absolute exit kinetic energies, for values of deviation blade angle between -10° and −20°, where an exhaust diffuser is recommended to use to recover a part of it into a greater expansion ratio. These simulation results were obtained using a CFD calculation code-named CFX.15. This code allowed for the resolution of the averaged dynamic equations governing the stationary, compressible, and viscous internal flow.

A velocity-vorticity method for highly viscous 3D flows with application to digital rock physics

In this article, we present a numerical iterative method for the solution of internal viscous and incompressible flows in real porous three-dimensional bodies at their pore scale. We use the penalized formulation of the problem involving velocity and vorticity: an operator splitting allows to split apart the diffusion (inherited from Stokes equation) and the penalization phenomena (which takes into account the solid matrix). By means of the numerical analysis of the splitting, we exhibit the penalization coefficient which is actually effective. This method allows to deal only with fast-evaluation operators, that is to say scaling at most as O(nlog⁡n) where n is the number of underlying grid points, such as straightforward computations of finite differences schemes or FFT solver. The numerical analysis and implementation solutions are presented, and validated on various digital rock physics geometries acquired by micro-tomography, using numerical and physical diagnostics. To enforce this validation, we also present permeability estimations of several porous samples. The simulation of transport of passive and active scalars is finally investigated in order to perform the practical upscaling to 1D models of transport and diffusion at the Darcy scale.

Theory of the flow-induced deformation of shallow compliant microchannels with thick walls.

Long, shallow microchannels embedded in thick, soft materials are widely used in microfluidic devices for lab-on-a-chip applications. However, the bulging effect caused by fluid-structure interactions between the internal viscous flow and the soft walls has not been completely understood. Previous models either contain a fitting parameter or are specialized to channels with plate-like walls. This work is a theoretical study of the steady-state response of a compliant microchannel with a thick wall. Using lubrication theory for low-Reynolds-number flows and the theory for linearly elastic isotropic solids, we obtain perturbative solutions for the flow and deformation. Specifically, only the channel's top wall deformation is considered, and the ratio between its thickness t and width w is assumed to be (t/w)2≫1. We show that the deformation at each stream-wise cross section can be considered independently, and that the top wall can be regarded as a simply supported rectangle subject to uniform pressure at its bottom. The stress and displacement fields are found using Fourier series, based on which the channel shape and the hydrodynamic resistance are calculated, yielding a new flow rate-pressure drop relation without fitting parameters. Our results agree favourably with, and thus rationalize, previous experiments.

Finiteness of corner vortices

Till date, the sequence of vortices present in the solid corners of steady internal viscous incompressible flows, widely known as Moffatt vortices was thought to be infinite. However, the already existing and most recent geometric theories on incompressible viscous flows that express vortical structures in terms of critical points in bounded domains, indicate a strong opposition to this notion of infiniteness. In this study, we endeavor to bridge the gap between the two opposing stream of thoughts by addressing what might have gone wrong and pinpoint the shortcomings on the assumptions of the existing theorems on Moffatt vortices. We provide our own set of proofs for establishing the finiteness of the sequence of Moffatt vortices by making use of the continuum hypothesis and Kolmogorov scale, which guarantee a non-zero scale for the smallest vortex structure possible in incompressible viscous flows. We point out that the notion of infiniteness resulting from discrete self-similarity of the vortex structures is not physically feasible. The centers of these vortices have been quantified by us as fixed points through Brouwer fixed-point theorem and boundary of a vortex as circle cell. With the aid of these new developments and making use of some existing theorems in topology along with some elementary concept of mathematical analysis, we provide several approaches to delve into this issue. All these approaches converge to the same conclusion that the sequence of Moffatt vortices cannot be infinite; in fact, it is at most finite.

Adjoint aerodynamic optimization of a transonic fan rotor blade with a localized two-level mesh deformation method

We present an optimization platform for turbomachinery with complex mesh configuration in a parallel computation environment. A continuous adjoint solver for 3-D viscous internal flow is coded under the same parallel framework as the flow solver. To meet the various permitted extents of reshaping on blade surface and to cut down the computational cost in grid perturbation, a localized two-level mesh deformation method is developed based on Gaussian radial basis function (RBF). This method works efficiently for both the O mesh surrounding the blade and the O–H mesh inside tip gap. In the optimization of the transonic NASA Rotor 67 for high adiabatic efficiency with a mass flow rate constraint, an adjoint sensitivity analysis is conducted. The relations between the design sensitive regions and physical phenomena in internal flow are discussed. Flow fields before and after the adjoint optimization are investigated, including shock system, tip leakage flow, and flow separation.

Leveraging Internal Viscous Flow to Extend the Capabilities of Beam-Shaped Soft Robotic Actuators.

Elastic deformation of beam-shaped structures due to embedded fluidic networks (EFNs) is mainly studied in the context of soft actuators and soft robotic applications. Currently, the effects of viscosity are not examined in such configurations. In this work, we introduce an internal viscous flow and present the extended range of actuation modes enabled by viscosity. We analyze the interaction between elastic deflection of a slender beam and viscous flow in a long serpentine channel embedded within the beam. The embedded network is positioned asymmetrically with regard to the neutral plane and thus pressure within the channel creates a local moment deforming the beam. Under assumptions of creeping flow and small deflections, we obtain a fourth-order integro-differential equation governing the time-dependent deflection field. This relation enables the design of complex time-varying deformation patterns of beams with EFNs. Leveraging viscosity allows to extend the capabilities of beam-shaped actuators such as creation of inertia-like standing and moving wave solutions in configurations with negligible inertia and limiting deformation to a small section of the actuator. The results are illustrated experimentally.

Numerical study of red blood cell motion and deformation through a michrochannel using lattice Boltzmann-immersed boundary method

In this research, motion and deformation of both healthy and sick red blood cell (RBC) are simulated in a vessel with and without stenosis for incompressible and viscous internal flow using the combined lattice Boltzmann-immersed boundary method. The surface of RBC is considered to be a deformable immersed body in the fluid flow. The RBC membrane is represented in Lagrangian coordinates, while the fluid flow field is discretized by a uniform and fixed Eulerian mesh. The interaction of the fluid and RBC is modeled using an appropriate form of the Dirac delta function. Two geometrically different channels, namely, a simple channel and a channel with a stenosis, are considered. In the cases, when the RBC is placed on the symmetry axis of the channel, they continue to move and deform without any lift force and rotation induced. The healthy RBC always shows more deformation along the channel in comparison by sick one. The obtained results show that a sick RBC cannot pass the constricted area and become constricted, so that it causes serious problems for human body. The present results have been compared with the available experimental and numerical results which show good agreements.

Numerical study of the Yosida method applied to viscous incompressible internal flows with open boundary conditions

The Yosida methods for incompressible viscous flows are investigated numerically in the aspect of local and global errors of volume conservation. Unsteady Stokes and Navier–Stokes flows past an obstacle inserted into 2D channel are used as the test cases. Open boundary conditions are imposed at the channel’s inlet and outlet. The results obtained by the Yosida-based Spectral Element Method (SEM) solvers are compared to the results obtained by the SEM solver using exact factorization of the Uzawa system. Analysis of parametric variation of the velocity divergence and the flow rate errors is presented. It is concluded that switching to higher-order Uzawa methods reduces substantially volume conservation errors and removes numerical artifacts observed at the channel’s inlet when the basic Yosida method is used.

Constrained Adjoint-Based Aerodynamic Shape Optimization of a Single-Stage Transonic Compressor

This paper develops a discrete adjoint formulation for the constrained aerodynamic shape optimization in a multistage turbomachinery environment. The adjoint approach for viscous internal flow problems and the corresponding adjoint boundary conditions are discussed. To allow for a concurrent rotor/stator optimization, a nonreflective adjoint mixing-plane formulation is proposed. A sequential-quadratic programming algorithm is utilized to determine an improved airfoil shape based on the objective function gradient provided by the adjoint solution. The functionality of the proposed optimization method is demonstrated by the redesign of a midspan section of a single-stage transonic compressor. The objective is to maximize the isentropic efficiency while constraining the mass flow rate and the total pressure ratio.

Design of a Multijet Omnidirectional Propulsion System for Small Jet-Boats

Jet-boats perform remarkably well at high-speed but lack low speed maneuverability for tight maneuvers such as docking. This paper presents a joystick controlled omnidirectional propulsion system for jet-boats. The concept uses a set of fixed jet nozzles disposed around the hull. When a force is commanded by the joystick, valves on each nozzle modulate the flow so that the sum of nozzle thrusts correspond to the commanded force. The positions and angles of the nozzles are optimized with an index of omnidirectionality quality based on the projection of a set of force solutions on a shell with the shape of a desired force space. The choice of valve positions and engine speeds is done by the numerical inversion of an internal viscous flow model. A 3D simulator, backed by experimental results, serves to (1) evaluate the ability of the proposed concept in meeting its design requirements and (2) develop control algorithms. Experimental results show that the proposed omnidirectional system is effective for low speed maneuverability with open-loop force control. The present work also offers an effective omnidirectional propulsion system that is easy to enhance with advanced control laws. Velocity feedback control is given as an example and shows important improvement of maneuverability and robustness to miscalibration.

A Novel 2D Incompressible Viscous Inverse Design Method for Internal Flows Using Flexible String Algorithm

In this investigation, the flexible string algorithm (FSA), used before for inverse design of subsonic and supersonic ducts in compressible flows with and without normal shock, is developed and applied for inverse design of 2D incompressible viscous internal flow with and without separation. In the proposed method, the duct wall shape is changed under an algorithm based on deformation of a virtual flexible string in flow. At each modification step, the difference between current and target wall pressure distributions is applied to the string. The method is an iterative inverse design method and utilizes the analysis code for the flow field solution as a black-box. Some validation test cases and design examples are presented here, which show the robustness and flexibility of the method in handling complex geometries. In cases with separated flow pressure distribution, a unique solution for inverse design problem does not exist. The design algorithm is a physical and quick converging approach and can efficiently utilize commercial flow analysis software.

English

The present work describes the study on complex internal viscous flow in a scramjet. The dissociation of air in complex scramjet model using two dimensional computational fluid dynamics and also at fuel-off conditions on combustion chamber is presented. The results of free-stream flow attio Mach 4 at different altitudes viz 25km, 30km and 35km in the combustion chamber are compared. For computational aid Green Gauss cell based gradient option is used with steady time and absolute velocity formulation.

Analysis and Optimization of the Internal Flow in Centrifugal Compressor Volute

The 3D internal viscous flow in the last stage of a centrifugal compressor is analyzed numerically with commercial computational fluid dynamic software NUMECA. The geometric model includes the close-type impeller, the vaneless diffuser and the volute. Based on the analytic results, modifications to the constant width volute are proposed and the stage efficiency is increased by 4.5%. The same approach is applied on the last stage of another centrifugal compressor and the efficiency is also increased by 4.5%. Through summing up the effect of different parameters, the code for the aerodynamic design of the welding type volute is developed. The code is tested on another compressor with a constant height volute and the last stage efficiency is increased by 3%. Numerical experiments prove that the code can be used for the aerodynamic design of all welding type volutes.

Vorticity generation and acoustic resonance of simulated solid rocket motor chamber with high wave number wall injection

An asymptotic technique is integrated with computational solution development to describe the generation and evolution of intense unsteady vorticity and the accompanying temperature response in a model of solid rocket motor (SRM) chamber with low Mach number, weakly viscous internal flow. The chamber considered here has a rectangular cross-section, has to equally permeable walls, closed at the head end, and is opened at the downstream end. An initially steady internal flow from steady sidewall injection is generated. Then an additional transient sidewall mass injection with different wave numbers at non-resonance and resonance frequencies is imposed on the generated steady one. This mechanism is used to simulate the transient propellant combustion occurring on the sidewall in a real SRM chamber. The analytical approach is based on the reduced form of the Navier–Stokes using asymptotic technique. The results show that unexpectedly large transient shear stresses and temperature gradients are created at the sidewall of the chamber at resonance frequencies and low wave numbers. A comparison between the analytical, computational and experimental results is performed.

Stokes flow inside an evaporating liquid line for any contact angle

Evaporation of droplets or liquid films lying on a substrate induces internal viscous flow, which affects the transport of suspended particles and, thus, the final deposit profile in numerous applications. In this work, the problem of Stokes flow inside a two-dimensional droplet, representing the cross section of an evaporating liquid line lying on a flat surface, is considered. The stream function formulation is adopted, leading to the biharmonic equation in bipolar coordinates. A solution in closed form is obtained for any contact angle in (0,pi) and is, thus, valid for both hydrophilic and hydrophobic substrates. The solution can be used with any type of evaporation mechanism, including diffusion, convection, or kinetically controlled modes. Both pinned and depinned contact lines are considered. For the boundary conditions to be compatible at the contact lines, the Navier slip boundary condition is applied on the substrate. Numerical results are presented for kinetically and diffusion controlled evaporation. For pinned contact lines, the flow inside the evaporating liquid line is directed towards the edges, thus, promoting the coffee stain phenomenon. In the case of depinned contact lines and contact angle less than pi/2 , the flow is directed towards the center of the droplet, whereas, for strongly hydrophobic substrates it is directed outwards.

Direct Design of Ducts

This paper describes a method for calculating the shape of duct that leads to a prescribed pressure distribution on the duct walls. The proposed design method is computationally inexpensive, robust, and a simple extension of existing computational fluid dynamics methods; it permits the duct shape to be directly calculated by including the coordinates that define the shape of the duct wall as dependent variables in the formulation. This “direct design method” is presented by application to two-dimensional ideal flow in ducts. The same method applies to many problems in thermofluids, including the design of boundary shapes for three-dimensional internal and external viscous flows.

Adaptive and fixed segmented domain decomposition multigrid procedures for internal viscous flows

A segmented domain decomposition multigrid procedure is reviewed. The methodology is outlined for both an adaptive formulation applied primarily to inlet, nozzle and duct flows, and for a fixed, predetermined, subdomain formulation applied for turbomachinery geometries. The procedure has been considered for both low and high speed flows in two- and three-dimensions, and for laminar and turbulent-model applications. With these procedures, the grids remain uniform in each subdomain; although the global grid appears to be highly stretched. This formulation allows for computations with a high degree of accuracy and grid independence at reasonable computer cost. This is generally not possible to replicate with full domain multigrid procedures on stretched grids with large cell aspect ratio.