Shock-wave laminar boundary-layer interaction in supercritical transonic flow

The interaction between an oblique shock wave and a laminar boundary layer in a supercritical transonic flow is studied numerically for shock strengths sufficiently large that separation occurs. Of particular interest is the behavior of the solution as the shock strength parameter is increased towards an order one value. It is found that the separation and reattachment regions tend to become distinct, with an intervening plateau region of nearly constant pressure, as the shock strength increases. A possible limit structure for order one shock strengths is also suggested.     

Shock fitting in conical supersonic full potential flows

The full potential equation is solved implicitly for supersonic conical flows with the bow shock fitted as an external boundary. Existing potential flow computational procedures capture the embedded crossflow shock within the context of transonic relaxation schemes. In this study, the crossflow shock is fitted for the first time in potential flow as an internal boundary. Hence, all shocks are implicitly fit making the computation fully conservative. For thin elliptic cones, the outer segment of the crossflow shock was found to be oblique to the incoming or supersonic crossflow. This behavior was not found for circular cones. The shock fitted solutions are compared to both Euler and potential captured solutions. The full potential shock fitted results are in favorable agreement with conservative captured solutions.     

Numerical studies in high Reynolds number aerodynamics

Two numerical approaches are presented for the computation of viscous compressible flows at high Reynolds' numbers. In the first approach, named global approach, the whole flow field, which includes viscous and inviscid regions, is determined as the solution of a single set of equations, which may be the full Navier-Stokes equations, or some approximate form of these equations. The second approach, named coupling approach, consists in solving two different sets of equations in their respective domains simultaneously; one of the two sets governs an inviscid flow whose boundary conditions are provided by the viscous effects, determined by the other set.The discussion of the global approach is centred on two particular features of the finite-difference method used: a discretization technique, directly in the physical plane with arbitrary meshes: and a mesh adaptation technique, which combines a coordinate transformation to fit the mesh system to particular lines in the flow, and a technique of dichotomy for mesh refinement. Numerical results are presented for an axisymmetric compression corner and a shock-boundary layer interaction on a flat plate, both in supersonic regime, and for a transonic nozzle flow.For the coupling approach, emphasis is given firstly to the improvement resulting from an interacting analysis where the viscous and inviscid computations are matched, and not only patched. It is shown that the parabolic problems associated with simple viscous theories are always replaced by elliptic problems, even for supersonic flows, and that “supercritical interactions” or “critical points”, as defined by Crocco-Lees, are removed. Secondly, a new coupling method, fully automatized and capable of solving directly a well-posed problem for supersonic flow, is illustrated by examples involving shock wave-boundary layer interactions and reverse flow bubbles; they concern flows over symmetrical transonic airfoils and supersonic compression ramps.     

Mesomechanical simulation of shock compaction of porous aluminum

A mesomechanical simulation of shock loading of porous aluminum has been carried out for thermo-elastic-plastic medium using a modified 2D SPH method. The periodic structure of porous aluminum is set explicitly and possesses the properties of a solid aluminum. The shock compression is modeled by the impingement of a porous plate with a rigid wall. The calculated flow fields of the material show the main moments of loading dynamics: a multiwave shock structure at a low shock intensity, collapse of the pores in a strong shock wave, and the formation of material compaction in two stages at the front, the formation of pressure oscillations behind the shock front, and the influence of thermal conductivity on oscillation damping. The calculated Hugoniot adiabat is in good agreement with the experimental data.     

Noncentered schemes and schock propagation problems

In this paper, the noncentered difference scheme given by Mac Cormack for the numerical solution of the gas dynamics equations is studied from a theoretical point of view, and its computational properties are tested for shock propagation problems. By means of a nonlinear analysis for a scalar equation, it is shown why there is no oscillations in the shock profile when the directions of the differences are correctly chosen. Computations are made for the propagation of a shock wave in a channel and along a curve wall. The results are compared to those given by Whitham's theory.     

The use of a pocket computer in gas dynamics

A pocket computer (Casio model FX-702P) has been utilized to solve some problems arising in gas dynamics. The programs reported cover algebraic calculations, solution of transcendental equations and finite difference solutions of coupled, nonlinear ordinary differential equations. In gas dynamics terms, the algebraic computations pertain to properties variation in isentropic flow, Rayleigh flow and Fanno flow. The transcendental equations solved are those arising in Prandtl-Meyer flow and oblique shock analysis. Problems of pipe flow with simultaneous friction and heat transfer, unsteady discharge of a variable-volume tank through a convergent nozzle, Taylor-Maccoll flow over a cone and flow in a rocket nozzle with secondary injection of oxidant in the divergent section, are used as illustrative examples of coupled, nonlinear ordinary differential equations.     

Solution of magnetohydrodynamic flow in a rectangular duct by differential quadrature method

The polynomial based differential quadrature and the Fourier expansion based differential quadrature method are applied to solve magnetohydrodynamic (MHD) flow equations in a rectangular duct in the presence of a transverse external oblique magnetic field. Numerical solution for velocity and induced magnetic field is obtained for the steady-state, fully developed, incompressible flow of a conducting fluid inside of the duct. Equal and unequal grid point discretizations are both used in the domain and it is found that the polynomial based differential quadrature method with a reasonable number of unequally spaced grid points gives accurate numerical solution of the MHD flow problem. Some graphs are presented showing the behaviours of the velocity and the induced magnetic field for several values of Hartmann number, number of grid points and the direction of the applied magnetic field.     

The method of boundary condition transfer in application to modeling near-wall turbulent flows

Generalized wall functions in application to high-Reynolds-number turbulence models are derived. The wall functions are based on transfer of a boundary condition from a wall to some intermediate boundary near the wall (usually the first nearest to the wall mesh point but that is not obligatory). The boundary conditions on the intermediate boundary are of Robin-type and represented in a differential form. The wall functions are obtained in an analytical easy-to-implement form, can take into account source terms such as pressure gradient and buoyancy forces, and do not include free parameters. The log-profile assumption is not used in this approach. Both Dirichlet and Newman boundary-value problems are considered. A method for complementing solution near the wall is suggested. Although the generalized wall functions are obtained for the k– model, generalization to other turbulence models is straightforward. The general approach suggested is applicable to studying high-temperature regimes with variable laminar viscosity and density. A robust numerical algorithm is proposed for implementation of Robin-type wall functions. Test results made for a channel flow and axisymmetric impinging jet have showed reasonably good accuracy, reached without any case-dependent turning, and a weak dependence of the solution on the location of the intermediate boundary where the boundary conditions are set. It is demonstrated that the method of boundary condition transfer applied to low-Reynolds-number turbulence models can be used as a decomposition method.     

Direct numerical simulation of transitional flow at high Mach number coupled with a thermal wall model

In transitional and turbulent high speed boundary-layer flows the wall thermal boundary conditions play an important role and in many cases an assumption of a constant temperature or a specified heat flux may not be appropriate for numerical simulations. In this paper we extend a formulation for direct numerical simulation of compressible flows to include a thin plate that is thermally fully coupled to the flow. Even without such thermal coupling compressible flows with shock waves and turbulence represent a challenge for numerical methods. In this paper we review the scaling properties of algorithms, based on explicit high-order finite differencing combined with shock capturing, that are suitable for dealing with such flows. An application is then considered in which an isolated roughness element is of sufficient height to trigger transition in the presence of acoustic forcing. With the thermal wall model included it is observed that the plate heats up sufficiently during the simulation for the transition process to be halted and the flow consequently re-laminarises.     

Resonance in a piston-driven cavity

Direct finite difference techniques utilizing an artificial dissipation method are applied to the flow generated in a cavity. The cavity is a cylinder closed at one end and sealed with an oscillating wall at the other end. The gas dynamic equations are transformed to Lagrangian coordinates and an artificial dissipation is introduced via an artificial pressure which is negligible except near a shock. Von Neumann and Richtmeyer's method for differencing is applied and a solution is obtained by means of an explicit algorithm. Typical results are presented for a resonance and a non-resonance condition. The theoretical model shows that three to four oscillations of the moving wall are needed from time equal to zero to establish a resonance condition. The theory adequately describes the physical process which has been observed in cylindrical tubes and the results are in agreement with Sturtevant's experiments.     

The active disturbance rejection and sliding mode control approach to the stabilization of the Euler–Bernoulli beam equation with boundary input disturbance

In this paper, we are concerned with the boundary feedback stabilization of a one-dimensional Euler–Bernoulli beam equation with the external disturbance flowing to the control end. The active disturbance rejection control (ADRC) and sliding mode control (SMC) are adopted in investigation. By the ADRC approach, the disturbance is estimated through an extended state observer and canceled online by the approximated one in the closed-loop. It is shown that the external disturbance can be attenuated in the sense that the resulting closed-loop system under the extended state feedback tends to any arbitrary given vicinity of zero as the time goes to infinity. In the second part, we use the SMC to reject the disturbance by removing the condition in ADRC that the derivative of the disturbance is supposed to be bounded. The existence and uniqueness of the solution for the closed-loop via SMC are proved, and the monotonicity of the “reaching condition” is presented without the differentiation of the sliding mode function, for which it may not always exist for the weak solution of the closed-loop system. The numerical simulations validate the effectiveness of both methods.     

On strong shock waves of annihilation

In the framework of special relativity theory, we give a piecewise-constant solution to the onedimensional problem of collision of a combination of particles and antiparticles with a flat wall which results in an annihilation shock wave. We assume that there is a complete transition of antimatter into the energy of remaining matter and outgoing radiation directed from the wall and, in its turn, separated from the incoming flow by a null rupture surface. The initial pressure in the mixture is neglected. We have constructed and investigated the Taub annihilation adiabat, including the Jouguet mode. Several limiting cases are considered as well, including a small concentration of antimatter, a small difference between the concentrations of matter and antimatter, the absence of directional radiation, and nonrelativistic velocity of the incoming flow.     

Design and fabrication of microchannel test rig for ultra-micro wave rotors

Wave rotor technology has shown a significant potential for performance improvement of thermodynamic cycles. The wave rotor is an unsteady flow machine that utilizes shock waves to transfer energy from a high energy fluid to a low energy fluid, increasing both the temperature and the pressure of the low energy fluid. At microscale, shock wave compression was shown analytically to have higher efficiency than compression by mechanical devices such as impellers or pistons. A second step in proving this superiority of shock wave compression is to design and test a microscale shock tube, which is a perfect model for one of the wave rotor channels. Last step is fabrication of a full wave rotor manufactured using traditional MEMS technology. The paper summarizes the conclusions of the analytical study, describes the details of fabrication of micro shock tube test rig and the design of the ultra-micro wave rotor (UμWR). Florin Iancu is currently employed by Johnson Controls Inc., in York, PA, USA. Research was conducted while he was a Ph.D. candidate at Michigan State University.     

Flow due to a sink near a vertical wall, in infinitely deep fluid

Flow caused by a point sink in an otherwise stagnant fluid is studied using numerical methods based on integral-equation techniques and an asymptotic solution for small Froude number. There is a vertical wall present on a plane close to the sink, so that the flow is fully three dimensional. The fluid is of infinite depth, but a free-surface bounds it above. Steady solutions are presented for various Froude numbers and distances of the source from the wall. It is shown that the numerical results and asymptotic formula are in good agreement for small Froude numbers, but the results suggest that the non-linear solution ultimately forms some limiting structure at sufficiently large Froude number.     

Boundary stabilization of a cascade of ODE‐wave systems subject to boundary control matched disturbance

In this paper, we are concerned with a cascade of ODE‐wave systems with the control actuator‐matched disturbance at the boundary of the wave equation. We use the sliding mode control (SMC) technique and the active disturbance rejection control method to overcome the disturbance, respectively. By the SMC approach, the disturbance is supposed to be bounded only. The existence and uniqueness of solution for the closed‐loop via SMC are proved, and the monotonicity of the ‘reaching condition’ is presented without the differentiation of the sliding mode function, for which it may not always exist for the weak solution of the closed‐loop system. Considering that the SMC usually requires the large control gain and may exhibit chattering behavior, we then develop an active disturbance rejection control to attenuate the disturbance. The disturbance is canceled in the feedback loop. The closed‐loop systems with constant high gain and time‐varying high gain are shown respectively to be practically stable and asymptotically stable. Then we continue to consider output feedback stabilization for this coupled ODE‐wave system, and we design a variable structure unknown input‐type state observer that is shown to be exponentially convergent. The disturbance is estimated through the extended state observer and then canceled in the feedback loop by its approximated value. These enable us to design an observer‐based output feedback stabilizing control to this uncertain coupled system. Copyright © 2016 John Wiley & Sons, Ltd.     

Conservative Models and Numerical Methods for Compressible Two-Phase Flow

The paper presents the computational framework for solving hyperbolic models for compressible two-phase flow by finite volume methods. A hierarchy of two-phase flow systems of conservation-form equations is formulated, including a general model with different phase velocities, pressures and temperatures; a simplified single temperature model with equal phase temperatures; and an isentropic model. The solution of the governing equations is obtained by the MUSCL-Hancock method in conjunction with the GFORCE and GMUSTA fluxes. Numerical results are presented for the water faucet test case, the Riemann problem with a sonic point and the water-air shock tube test case. The effect of the pressure relaxation rate on the numerical results is also investigated.     

Fluid physics around conductive deformable flaps within an induced-charge electrokinetically driven microsystem

The induced-charge electrokinetic motion of a conductive deformable flap (which is installed on the walls of a microchannel) is numerically studied in this article. The relationship between the flap orientation (i.e., vertical, horizontal and oblique positions) and its motion is studied. Stagnation point concept is used to explain the behavior of the flap at different situations. The stagnation point is defined as a point on the flap surface where the induced zeta potential is zero. Thus, the flow velocity at this point becomes zero, and the pressure gradient will be maximum. The direction of the flap motion is determined by the location of the stagnation point. As an example, here, it is shown that the obtuse conductive flap moves in the opposite direction of the flow field because in this case, the stagnation point is located on the back surface of the flap. Interaction of two vertical conductive flaps (located at different distances from each other) is also investigated in this paper. The results indicate that if both of the conductive flaps are fixed on the same microchannel wall, two vortices with opposite spin directions are generated between them. These vortices create a low-pressure zone through which the two flaps attract one another. However, when each flap is fixed on upper and lower microchannel walls, the two vortices with same spin directions are generated between the flaps. These two vortices merge and form a high-pressure zone through which two flaps repel each other.     

Reassessment of the role of intra-abdominal pressure in spinal compression

Biomechanical models used to estimate loads on the lumbar spine often predict internal low back forces for heavy lifts that exceed known tissue tolerances, yet the particular lift caused no apparent damage to the lifter. To deal with this paradox, many researchers have incorporated some form of spinal compression alleviation from intra-abdominal pressure (IAP). The purpose of this work was to re-examine some of the issues involved in the feasibility of IAP to reduce spinal loads during stressful lifts. Questions remain over the trade-off between the beneficial tensile force on the spine, exerted via the diaphragm and pelvic floor when IAP is produced, and the undesirable compressive effects of abdominal muscular force required to maintain the pressure within the abdomen. Various strategies of modelling IAP and its effects on low back loading were employed, Three major differences between this and most previous models of IAP effects were the attempt to quantify the size of abdominal muscle forces and the utilization of a considerably smaller diaphragm cross-sectional area and corresponding IAP moment arm. Abdominal EMG recorded from rectus abdominis, external oblique and internal oblique generally indicated low levels of activity throughout the high loading phase of the lifts. However, model output predicted that the compressive forces generated by the abdominal wall musculature were larger than the beneficial action of those forces thought to alleviate spinal compression via IAP. These results suggest that modelling IAP as a force vector which produces a trunk extensor moment and lumbar disc compression alleviation, without accounting for the compressive effects of abdominal muscle forces required to produce the IAP, is incorrect. This does not exclude a possible role of IAP in assisting the trunk during loading, only that the role of IAP is not modelled properly at present. IAP may indeed play a role in spinal stabilization as yet not well understood.     

Semi-analytical solutions of pulsating flow in a helically rough-walled microtube

The influence of a helically rough wall surface on fully developed pulsating laminar flows in microtube is investigated through a semi-analytical method. A two-dimensional simple harmonic function is chosen to model helically wavy structure. The velocity and pressure are decomposed into space-averaged and disturbance terms and the corresponding governing equations are established. Pulsating flow is split into a steady term and an oscillatory term based on a given oscillatory pressure drop, and the governing equations for the oscillatory terms are presented together with their steady counterparts. Analytical solutions are obtained for the space-averaged equations and a spectral collocation method is used to solve the disturbance equations numerically. An iterative approach is adopted for the coupled equations with respect to space-averaged velocities and disturbance velocities. The computational results show that a Reynolds stress layer (RSL) and a secondary swirling velocity are present in the rough-walled microtube. The relative amplitude of the waviness of the wall, its wavenumber, and the Reynolds number are found to be important parameters influencing the Reynolds stress and RSL, as well as the space-averaged velocities and pressure drop. The direction of rotation of the swirling velocity is found to depend on the sign of the azimuthal wavenumber. In addition to the parameters of the rough wall and the Reynolds number, both the oscillatory pressure drop and frequency are important factors influencing the pulsating flow and the phase shift of the space-averaged velocity.     

Disturbance decoupling for time delay systems

In this paper the disturbance decoupling problem associated with a class of linear and nonlinear time delay systems is considered. The solution to this problem is given in terms of the relative degrees associated with the input and the disturbance of the corresponding time delay systems. A stability study using some results due to Pontryagin is presented for the resultant closed-loop system when the delay system is linear. Also, an approximate causal solution is proposed for the nonlinear time delay system based on its linearization around an equilibrium point. © 1997 by John Wiley & Sons, Ltd.