Verification and Validation of High-Resolution Inviscid and Viscous Conical Nozzle Flows

Capturing elaborated flow structures and phenomena is required for well-solved numerical flows.The finite difference methods allow simple discretization of mesh and model equations.However,they need simpler meshes,e.g.,rectangular.The inverse Lax-Wendroff(ILW)procedure can handle complex geometries for rectangular meshes.High-resolution and high-order methods can capture elaborated flow structures and phenomena.They also have strong mathematical and physical backgrounds,such as positivity-preserving,jump conditions,and wave propagation concepts.We perceive an effort toward direct numerical simulation,for instance,regarding weighted essentially non-oscillatory(WENO)schemes.Thus,we propose to solve a challenging engineering application without turbulence models.We aim to verify and validate recent high-resolution and high-order methods.To check the solver accuracy,we solved vortex and Couette flows.Then,we solved inviscid and viscous nozzle flows for a conical profile.We employed the finite difference method,positivity-preserving Lax-Friedrichs splitting,high-resolution viscous terms discretization,fifth-order multi-resolution WENO,ILW,and third-order strong stability preserving Runge-Kutta.We showed the solver is high-order and captured elaborated flow structures and phenomena.One can see oblique shocks in both nozzle flows.In the viscous flow,we also captured a free-shock separation,recirculation,entrainment region,Mach disk,and the diamond-shaped pattern of nozzle flows.

Experimental Analysis of the Flow Characteristics of an Adjustable Critical-Flow Venturi Nozzle

The response of an adjustable critical-flow Venturi nozzle is investigated through a set indoor experiments aimed to determine the related critical flow rate,critical pressure ratio,and discharge coefficient.The effect of a variation in the cone displacement and liquid content on the critical flow characteristics is examined in detail and it is shown that the former can be used to effectively adjust the critical flow rate.The critical pressure ratio of the considered nozzle is above 0.85,and the critical flow control deviation of the gas flow is within±3%.Liquid flow can reduce the gas critical mass flow rate accordingly,especially for the cases with larger liquid volume and lower inlet pressure.The set of results and conclusions provided are intended to support the optimization of steam injection techniques in the context of heavy oil recovery processes.

Local Solution of Three-Dimensional Axisymmetric Supersonic Flow in a Nozzle

In this paper, we construct a local supersonic flow in a 3-dimensional axis-symmetry nozzle when a uniform supersonic flow inserts the throat. We apply the local existence theory of boundary value problem for quasilinear hyperbolic system to solve this problem. The boundary value condition is set in particular to guarantee the character number condition. By this trick, the theory in quasilinear hyperbolic system can be employed to a large range of the boundary value problem.

Numerical and Experimental Studies of an Arc-heated Nonequilibrium Nozzle Flow

The arc-heated high-temperature gas is rotationally and vibrationally excited, and partially dissociated and ionized. When such gas flows inside a nozzle, energy transfers from rotational and vibrational energy modes to translational energy mode, and, in addition, recombination reactions occur. These processes are in thermal and chemical nonequilibrium. The present computations treat arc-heated nonequilibrium nozzle flows using a six temperature model (translational, rotational, N2 vibrational, O2 vibrational, NO vibrational and electron temperatures), and nonequilibrium chemical reactions of air. From the calculated flow properties, emission spectra at the nozzle exit were re-constructed by using the code for computing spectra of high temperature air. On the other hand, measurements of N2+(1-) emission spectra were conducted at the nozzle exit in the 20 kW arc-heated wind tunnel. Vibrational and rotational temperatures of N2 were determined using a curve fitting method on N2+(1-) emission spectra, with the vibrational and rotational temperatures for N2 and N2+ being assumed equal. Comparison of the measured and computed results elucidated that the experimental temperatures were larger than the computed ones. At present, we are trying to reveal the main reason for the discrepancy between the computed and measured N2 vibrational and rotational temperatures.

AN IMPLICIT ALGORITHM OF THIN LAYER EQUATIONS IN VISCOUS，TRANSONIC，TWO－PHASE NOZZLE FLOW

Omitting viscosity along flow direction, we have simplified the dimensionless N-Sequations in arbitrary curved coordinate system as the thin layer equations. Using theimplicit approximate-factorization algorithm to solve the gas-phase governing equ-ations and the characteristic method to follow the tracks of particles, we then obtainedthe full coupled numerical method of two-phase.transonic, turbulent flow. Here, par- ticle size may be grouped, the subsonic boundary condition at entry of nozzle is ireatedby quasi-characteristic method in reference plane and the algebraic model is used forturbulent flow. These methods are applied in viscous two-phase flow. calculation of ro-cket nozzle and in the prediciton of thrust and specific impulse for solid propellant ro-cket motor. The calculation results are in good agreement with the measurerment va-lues. Moreover, the influences of different particle radius, different particle mass frac-tion and particle size grouped on flow field have been discussed, and the influences of particle two-dimensional radial velosity component and viscosity on specific impulse ofrocket motor have been analysed.The method of this paper possesses the advantage of saving computer time. More important, the effect is more obvious for the calculation of particle size being grouped.

Feasibility study of symmetric solution of molecular argon flow inside microscale nozzles

The computational cost of numerical methods in microscopic-scales such as molecular dynamics(MD) is a deterrent factor that limits simulations with a large number of particles. Hence, it is desirable to decrease the computational cost and run time of simulations, especially for problems with a symmetrical domain. However, in microscopic-scales, implementation of symmetric boundary conditions is not straightforward. Previously, the present authors have successfully used a symmetry boundary condition to solve molecular flows in constant-area channels. The results obtained with this approach agree well with the benchmark cases. Therefore, it has provided us with a sound ground to further explore feasibility of applying symmetric solutions of micro-fluid flows in other geometries such as variable-area ducts. Molecular flows are solved for the whole domain with and without the symmetric boundary condition. Good agreement has been reached between the results of the symmetric solution and the whole domain solution. To investigate robustness of the proposed method, simulations are conducted for different values of affecting parameters including an external force, a flow density, and a domain length. The results indicate that the symmetric solution is also applicable to variable-area ducts such as micro-nozzles.

Numerical Study on the Effects of Contraction Ratio in a Two-Phase Flow Injection Nozzle

The Euler-Euler numerical method was used to investigate the effects of contraction ratio on twophase flow mixing with mass transfer in the flow injection nozzle. The geometric shape of the nozzle was modified to improve carbonation efficiency. A gas inlet hole was created to increase the flow mixing of CO2 with water. A nozzle throat was also introduced to increase the gas dissolution by increasing flow rates. Various contraction ratios of nozzle throat, inlet gas and liquid velocities, and gas bubble sizes were employed to determine their effects on gas hold-up, gas concentration, and mass transfer coefficient. Results revealed that the flow injection nozzle with high contraction ratios improved carbonation because of high gas hold-up. Gas concentration was directly related to contraction ratio and gas flow velocities. Carbonation reduced when high liquid velocities and large gas bubbles were employed because of inefficient flow mixing. This study indicated that flow injection nozzle with large contraction ratios were suitable for carbonation because of their ability to increase gas hold-up, gas concentration, and mass transfer coefficient.

A New Distribution Method for Wet Steam Injection Optimization

A new approach and a new related distribution system are proposed to address the issue of uneven steam injection caused by the different suction capacities of the used wells during the application of steam“stimulation”methods for enhanced oil recovery.The new distribution system consists of a swirler,spiral dividing baffles,and critical flow nozzles.Numerical simulations are used to analyze the flow-field and degree of steam homogeneity obtained with such an approach.The results indicate that a higher inlet pressure leads to better results.Additionally,the internal flow field becomes more stable,and the deviation from an even distribution reduces to±4.0%even when the resistance of each branch is inconsistent.Furthermore,field tests have yielded satisfactory results.

Characteristics of compressible flow of supercritical kerosene

In this paper, compressible flow of aviation kerosene at supercritical conditions has been studied both numerically and experimentally. The thermophysical properties of supercritical kerosene are calculated using a 10- species surrogate based on the principle of extended corresponding states （ECS）. Isentropic acceleration of supercritical kerosene to subsonic and supersonic speeds has been analyzed numerically. It has been found that the isentropic relationships of supercritical kerosene are significantly dif- ferent from those of ideal gases, A two-stage fuel heating and delivery system is used to heat the kerosene up to a tem- perature of 820 K and pressure of 5.5 MPa with a maximum mass flow rate of 100 g/s. The characteristics of supercritical kerosene flows in a converging-diverging nozzle （Laval nozzle） have been studied experimentally. The results show that stable supersonic flows of kerosene could be established in the temperature range of 730 K-820 K and the measurements in the wall pressure agree with the numerical calculation.

Flow field, heat transfer and inclusion behavior in a round bloom mold under effect of a swirling flow submerged entry nozzle

Flow field,heat transfer and inclusion behavior in a 700 mm round bloom mold under the effect of a swirling flow submerged entry nozzle(SEN)were investigated with the aim to enhance the casting process.The results indicate that the impinging flow phenomenon,which is commonly observed in conventional single-port SEN casting,was completely suppressed by the swirling flow SEN coming from a novel swirling flow generator design in tundish.Steel from the SEN port moved towards the mold wall in 360 direction,leading to a uniform temperature distribution in the mold.Compared to a conventional single-port SEN casting,the steel super-heat was decreased by about 5 K at the mold center,and the temperature was increased by around 3.5 K near the meniscus.In addition,the removal ratio of inclusions to the mold top surface in the swirling flow SEN casting was found to be increased.Specifically,the removal ratio of spherical inclusions with diameters of 1,10,50 and 100μm was increased by 18.2%,18.5%,22.6% and 42.7%,respectively.Furthermore,the ratio was raised by 18.2%,20.8%,21.5% and 44.1%for non-spherical inclusions,respectively.

Cryogenic Cavitating Flow in 2D Laval Nozzle

Cavitation is one of the troublesome problems in rocket turbo pumps,and since most of high-efficiency rocket propellants are cryogenic fluids,so called 'thermodynamic effect' becomes more evident than in water.In the present study.numerical and experimental study of liquid nitrogen cavitation in 2D Laval nozzle was carried out ,so that the influence of thermodynamic effect was examined.It was revealed that temperature and cavitation have strong inter-relationship with each other in thermo-sensitive cryogenic fluids.

Theoretical Calculations and Experimental Verification for the Pumping Effect Caused by the Dynamic Micro-tapered Angle

The atomizer with micro cone apertures has advantages of ultra-fine atomized droplets, low power consumption and low temperature rise. The current research of this kind of atomizer mainly focuses on the performance and its application while there is less research of the principle of the atomization. Under the analysis of the dispenser and its micro-tapered aperture＇s deformation, the volume changes during the deformation and vibration of the micro-tapered aperture on the dispenser are calculated by coordinate transformation. Based on the characters of the flow resistance in a cone aperture, it is found that the dynamic cone angle results from periodical changes of the volume of the micro-tapered aperture of the atomizer and this change drives one-way flows. Besides, an experimental atomization platform is established to measure the atomization rates with different resonance frequencies of the cone aperture atomizer. The atomization performances of cone aperture and straight aperture atomizers are also measured. The experimental results show the existence of the pumping effect of the dynamic tapered angle. This effect is usually observed in industries that require low dispersion and micro- and nanoscale grain sizes, such as during production of high-pressure nozzles and inhalation therapy. Strategies to minimize the pumping effect of the dynamic cone angle or improve future designs are important concerns. This research proposes that dynamic micro-tapered angle is an important cause of atomization of the atomizer with micro cone apertures.

Numerical analysis of heat transfer intensity from twin slot vertical jet impingement on strip surface after hot rolling

The flow field and heat transfer of the strip surface due to the twin slot vertical jet impingement were investigated using the ANSYS FLUENT.The RNG k-ε model was carried out in the turbulent calculation.Systematic parametric research was conducted by varying the jet velocity of nozzle exit(V=5 m/s,7.5 m/s,10 m/s),the temperature of cooling water(T_w=280 K,300 K),the normalized spacing from the nozzle to the strip surface(H=10,15,20,33),and the normalized spacing from the nozzle to nozzle centerline(W=0,15,30).The velocity streamline of the flow domain and the general trend of the distribution of the local Nusselt number on the impingement surface of strip were obtained.The result indicate that,the average Nusselt number increases by about70%(90%) as the jet velocity is increased from 5 m/s to 7.5 m/s(from 7.5 m/s to 10 m/s),and T_w,Hand//have minimal effect on it.While the valley Nusselt number decreases by about 10%-43%with the increase of H and W.The functional relationship between the average Nusselt number and the systematic parameters is derived by the least square regression method.

Optimal Design of Two-Chamber Gas Distributor with CFD Approach

Computational fluid dynamics( CFD) is used to investigate a new type of two-chamber natural gas distributor,which has a natural gas inlet and nine nozzle outlets. The uniformity at the outlet of distributor is practice proven to have significant degree influence on its comprehensive performance. To improve the uniformity at the nozzles of the gas distributor,CFD modeling with the RNG k-ε turbulence model is undertaken to understand the mass flow rate of nozzles with reference to different length of chambers and the most optimal length is obtained. The internal flow pattern of the natural gas distributor is analyzed. It is found that the local maximum deviation of the nozzle outflow rate increases with the increase of chambers length when the length is more than 64 mm. The results provide useful suggestions for the optimal design of two-chamber natural gas distributor.

Producing ultra-high-speed nitrogen jets by arc heating in a low-pressure chamber

Pure nitrogen gas was heated with direct current arc, at input powers from several hundred Watt to over 5 kW, and then injected through a nozzle into a chamber at 1 or 10 Pa pressure, with the purpose of accelerating the gas to very high speed around 7 km/s. Various structures of the arc generator and gas expansion nozzle were examined. Results show that bypass exhausting of the boundary layer before it enters the nozzle divergent section can greatly increase flow speed of the jet, thus it might be possible to use nitrogen as a working gas in high speed gas dynamic test facilities.

Study of Spiral Flow Generated through an Annular Slit

The effect of pressurized air inlets in the reservoir upstream of the annular slit on characteristics of the axial and tangential velocity components is investigated numerically, and the mechanism of occurrence of spiral nozzle flow is clarified. In simulations, Unified Platform for Aerospace Computational Simulation (UPACS) is used. The governing equations under consideration are the unsteady compressible Navier - Stokes. A second-order finite volume scheme with MUSCL (Roe scheme) is used to discretize the spatial derivatives, and a second order-central difference scheme for the viscous terms, and a MFGS (Matrix Free Gauss Seidel) is employed for time integration. Spalart-Allmaras model was used as a turbulence model. The results obtained are compared with velocity distributions in the experiment measured by the two-component fiber optic laser Doppler velocimeter system. The existence of discrete pressurized air inlets that leads to the occurrence of asymmetrical characteristics is a very important factor for the formation of spiral flow.

Visualization of Unsteady Gas/Vapor Expansion Flows

High speed expansion flows of pure vapors or gas/vapor mixtures are important to many technical applications, e.g. to steam turbines, jet engines, and for safety control of pressurized power plants.The sudden cooling of the fluid flow leads to condensation and nonequilibrium two-phase now with instabilities and periodic shock formation at mean frequencies of about 1 kHz. Modelling and control of this dynamical problem is not only important with respect to erosion, it also may cause flutter excitation and serious demolition of technical facilities. In numerical simulations, the time dependent 2-D Elller equations collpled to four equations describing the process of homogeneous nucleation and droplet growth are solved by a MUSCL-type finite volume method. The results are compared with experiments carried out in an atmospheric supersonic wind tunnel. By application of this numerical method to internal flows (nozzles) we found different modes of instabilities including bifurcations. At the stability limit a sharp frequency minimum was found for symmetric oscillations in slender nozzles. It separates oscillation modes where the oncoming subsonic flow remains unchanged from the oscillatory state where a shock monotonically moves upstream into the oncoming flow. For different nozzles we detected a new unsymmetric oscillation mode with a complex system of upstream moving oblique shocks. Here the frequency curve shows the typical structure of a bifurcation problem, which is definitely not controlled by viscous effects but by instabilities of the interaction of flow and phase transition process.

A New Approach of High OrderWell-Balanced Finite Volume WENO Schemes and Discontinuous Galerkin Methods for a Class of Hyperbolic Systems with Source Terms

Hyperbolic balance laws have steady state solutions in which the flux gradients are nonzero but are exactly balanced by the source terms.In our earlier work[31–33],we designed high order well-balanced schemes to a class of hyperbolic systems with separable source terms.In this paper,we present a different approach to the same purpose:designing high order well-balanced finite volume weighted essentially non-oscillatory(WENO)schemes and RungeKutta discontinuous Galerkin(RKDG)finite element methods.We make the observation that the traditional RKDG methods are capable of maintaining certain steady states exactly,if a small modification on either the initial condition or the flux is provided.The computational cost to obtain such a well balanced RKDG method is basically the same as the traditional RKDG method.The same idea can be applied to the finite volume WENO schemes.We will first describe the algorithms and prove the well balanced property for the shallow water equations,and then show that the result can be generalized to a class of other balance laws.We perform extensive one and two dimensional simulations to verify the properties of these schemes such as the exact preservation of the balance laws for certain steady state solutions,the non-oscillatory property for general solutions with discontinuities,and the genuine high order accuracy in smooth regions.

Shock Wave-Boundary Layer Interaction in Forced Shock Oscillations

The flow in transonic diffusers as well as in supersonic air intakes becomes often unsteady due to shock wave boundary layer interaction. The oscillations may be induced by natural separation unsteadiness or may be forced by boundary conditions. Significant improvement of CFD tools, increase of computer resources as well as development of experimental methods have again.drawn the attention of researchers to this topic. To investigate the problem forced oscillations of transonic turbulent flow in asymmetric two-dimensional Laval nozzle were considered. A viscous, perfect gas flow, was numerically simulated using the Reynolds-averaged compressible Navier-Stokes solver SPARC, employing a two-equation, eddy viscosity, turbulence closure in the URANS approach.For time-dependent and stationary flow simulations, Mach numbers upstream of the shock between 1.2 and 1.4 were considered. Comparison of computed and experimental data for steady states generally gave acceptable agreement. In the case of forced oscillations, a harmonic pressure variation was prescribed at the exit plane resulting in shock wave motion. Excitation frequencies between 0 Hz and 1024 Hz were investigated at the same pressure amplitude.The main result of the work carried out is the relation between the amplitude of the shock wave motion and the excitation frequency in the investigated range. Increasing excitation frequency resulted in decreasing amplitude of the shock movement. At high frequencies a natural mode of shock oscillation (of small amplitude) was observed which is not sensitive to forced excitement.