3d Vortex Simulation of Intake Flow in a Port Cylinder With a Valve Seat

8/8/2019 3d Vortex Simulation of Intake Flow in a Port Cylinder With a Valve Seat

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961195

3D Vortex Simulation of Intake Flowin a Port-Cylinder with a Valve

Seat and a Moving Piston

Adrin Gharakhani and Ahmed. F. GhoniemMassachusetts Institute of Technology

Reprinted from: Modeling Techniques in SI and CI Engines(SP-1178)


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961195

3D Vortex Simulation of Intake Flowin a Port-Cylinder with a Valve

Seat and a Moving Piston

Adrin Gharakhani and Ahmed. F. Ghoniem

Massachusetts Institute of TechnologyCopyright 1996 Society of Automotive Engineers, Inc.

ABSTRACT

A Lagrangian random vortex-boundary elementmethod has been developed for the simulation ofunsteady incompressible flow inside three-dimensionaldomains with time-dependent boundaries, similar to ICengines. The solution method is entirely grid-free in the

fluid domain and eliminates the difficult task of volumetricmeshing of the complex engine geometry. Furthermore,due to the Lagrangian evaluation of the convectiveprocesses, numerical viscosity is virtually removed; thuspermitting the direct simulation of flow at high Reynoldsnumbers. In this paper, a brief description of the numericalmethodology is given, followed by an example of inductionflow in an off-centered port-cylinder assembly with aharmonically driven piston and a valve seat situateddirectly below the port. The predicted flow is shown toresemble the flow visualization results of a laboratoryexperiment, despite the crude approximation used torepresent the geometry.

INTRODUCTION

Computational fluid dynamics is fast becoming aserious alternative to the empirical cut-and-try approach inthe design and analysis of IC engines. Numerous newly-developed methodologies and their applications haveappeared in the literature, ranging from the 2-D/axisymmetric flow in port-cylinder configurations [1-5],with and without a poppet valve, to the more realisticthree-dimensional flow in the intake ports and the cylinderof the engine, including moving valves [6-9]. However,despite the enormous progress achieved so far, severalcomputational and physical modeling difficulties remainunresolved.

In grid-based computational methods, the accurate,efficient and automatic volumetric meshing of typical time-varying engine configurations remains a challenging task.To obtain a well-behaved solution, the mesh generationalgorithm must resolve the widely varying geometriclength scales in the engine accurately. In addition, it mustbe capable of capturing the high velocity gradients withinthe thin concentrated jets around the intake valve, as wellas the large scale turbulent flow structures in the cylinder.Moreover, due to the highly convoluted nature of the flow,care must be exercised in order not to create degenerate

meshes.

The most adverse consequence of a poor-qualitmeshing is the introduction of false diffusion into the flowfield which, for the engine problem, leads to weaker largeeddy vortical structures and faster than expected decarates. False diffusion may be reduced by increasing thmesh resolution and/or applying adaptive griddintechnology, both of which can become computationalltoo expensive in a complex engine geometryAlternatively, false diffusion may be minimized by aligninthe streamwise side of the finite volume along the locastreamline. This can best be achieved using a Lagrangiamotion of the mesh nodes. However, given the complexitof engine flows, this approach may eventually lead tdegenerate finite volumes.

In this paper, an alternative approach is presentedbased on the random vortex-boundary element methofor the simulation of unsteady flow in 3-D geometries witmoving boundaries of the type encountered in enginesThe Navier-Stokes equations are expressed in th

vorticity transport formulation, and are discretized using collection of spherical vortex elements. The elemenvelocity is expressed as a superposition of a vorticacomponent evaluated by the Biot-Savart law, and potential component obtained from the solution of a 3-DNeumann problem over the domain. The convection anstretch of vorticity are evaluated in the Lagrangian framof reference (without the need for grids) and its diffusion idescribed stochastically by the random walk method. Thboundary element method is used to solve a 3-D Laplacequation that defines the potential flow and imposes thenormal flux boundary condition on the boundary surfaces without having to discretize the domain interior. The noslip boundary condition is satisfied by generating vorticit

tiles at the boundaries. Within a thin prespecified regionear the boundary, the tiles convect and diffuse in theLagrangian frame of reference according to the Prandequations. Beyond this region, the tiles are converted tospherical vortex elements.

The Lagrangian vortex-boundary element method igrid-free in the fluid domain. As a result, the complex tasof volumetric meshing of the interior of an engine ireduced to the far simpler task of meshing its surfacesThe method is self-adaptive and capable of dynamicallconcentrating computational elements in regions witsignificant velocity


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gradients, such as in shear layers and jets. Mostimportantly, due to the Lagrangian evaluation ofconvection, artificial diffusion is minimized (theoretically, itis zero.) This makes the scheme an excellent candidate forthe direct simulation of flow at high Reynolds numbers; italso enables one to ascertain the correctness of subgridscale viscosity or other turbulence models with moreconfidence.

The potential advantages of the vortex-boundaryelement method have been demonstrated using a

simulation of the unsteady flow over an impulsively startedcubic bluff body [10], and flow inside a simplified cylinderconnected to an off-centered port and driven by aharmonically moving piston [11]. A massively parallelversion of the method has also been completed todemonstrate its inherent parallel advantages [12].

In this paper, we present a brief description of the 3-Dvortex-boundary element method; the detailed formulationand the parametric study of its accuracy are given in [13-15]. We also show results from the simulation of inductionflow caused by a harmonically driven piston inside acylinder and an off-centered port, containing a valve seat.At present, the boundary surface may be approximatedusing plane rectangular boundary elements and tiles only,

analogous to the staircase discretization in 2-D. Theextension to the body-fitted discretization of the boundaryis under development. To reduce the computational cost,the Reynolds number based on the piston diameter and itsmaximum speed was set at 350. The choice for the lowReynolds number was also based on a parametric study,using the visualization results of flow in an axisymmetricengine with a poppet valve [16], which concluded that thelarge scale features of the vortical structures duringinduction are quite independent of the Reynolds number.In addition, in an unpublished work using an axisymmetricrandom vortex-finite element simulation of flow in the samegeometry, we have observed similar results at lowerReynolds numbers of 350 and 10,000. The objectives ofthe present simplified engine flow simulation are (1) todemonstrate the potential advantages of using aninternally grid-free simulation technique, and (2) to explore,qualitatively, the initiation and growth of large unsteadyvortical structures in the cylinder. The simulation is shownto closely reproduce the main characteristics of a similarflow visualization experiment, despite differences ingeometry and flow conditions between the two cases.

FORMULATION

THE INTERIOR - The Navier-Stokes equations forincompressible flow inside a three-dimensional domain,D, and with boundary surfaces, #D, are expressed in thefollowing vorticity transport form:

where x = (x, y, z) is the position vector normalized by areference length, L; u(x, t) = (u, v, w) is the velocity vectornormalized by a characteristic speed, U; t is the time

normalized by L/U; Re = UL/v is the Reynolds number,

and v is the kinematic viscosity. (x, t) = (x, y, z) = ^u is the vorticity vector and ^ represents the vectorproduct. On the boundary, the velocity is expressed interms of the local orthogonal coordinate system, --nwhere = (x, y, z,) and = (x, y, z) are the unittangents to the boundary, and n= (nx, ny, nz) is the unit

outward normal to it.

The vorticity field in Eq. (1) is discretized using acollection of Nv vortex elements; each centered at xj, with

element volume Vj and vorticity vector j:

where g(x) = is a smoothed delta function having

a spherical core with radius , and j(t) = j(t)Vj is thevolumetric vorticity. We used the second order core

function g(x) = [1 - tanh2( 3)], selected from an

available list [17].In Eqs. (1), the velocity and its gradients at a point are

evaluated as a superposition of a vortical field, u, in free

space and a potential flow, uP, inside the domain, such

that continuity and the normal flux boundary condition aresatisfied. Given the smooth vorticity distribution (2) andusing the Biot-Savart law, the discrete vortical velocity andits gradients at the vortex element centers are evaluatedas follows:

The accuracy and convergence properties

of the vortex element method are found in [18-23].

The potential component of the velocity and its

gradients at a point are obtained by solving the following 3-D Neumann problem for the interior:

2(x) = 0 x D (4a)q(x0) = - uP(x0).n = (u(x0) - u(x0)).n x0 D (4b)

where is the potential distribution, the gradient of whichyields the potential velocity, and q is the normal flux. Apiecewise linear variation of the boundary potential and itsnormal flux is assumed over a set of M boundary elementsdiscretizing the boundary surface. To preserve the gridfree character of the vortical flow solution, the directboundary

1

3------g

x

-----

3

4------ x

K 0( )x

4 3-------------=


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element method is used to obtain the potential flow. Thedetails of the accurate solution of this problem are givenelsewhere [13, 15]. Having obtained the potentialdistribution on the boundary, the potential velocity and itsgradients at the vortex element locations are evaluatedusing the following regularized formulations [13, 24]:

where G(x0, xi) = ,j, l, mand p indices indicate

direction with respect to the global coordinate system andfollow the Einstein rule; (.), represents differentiation withrespect to x0 in the r-th direction, jp is the Kroneckerdelta and jpl is the antisymmetric permutation tensor.Sk(x0) is the surface area of the k-th element. The first

and second degree tangential derivatives of the boundarypotential and flux distributions are assigned piecewiselinear variation across the elements. See [15] for details.

Applying viscous splitting algorithm to the Lagrangianformulation of the Navier-Stokes equations [25], and using

the vorticity element distribution (2) yields the following setof ordinary differential equations for the grid-freeprescription of the vorticity field evolution:

where i describes the trajectory of the i-th vortex elementinitially at i,o and with vorticity i,o, t0 is the time it is

introduced into the domain, t = (tk+1 - tk) is theintegration timestep, and F[.] represents the integrationscheme. The second order modified Euler method wasused for the present study. Eq. (6c) is the stochasticapproximation for the diffusion process, and i = (x, y,z)i are random variables in each of the three coordinatedirections, selected independently from a Gaussiandistribution with zero mean and variance equal to 2t/Re.

Note that the random walk method is not a model fordiffusion, but an "exact" solution. See [26] for details of themethod and the parametric tests of accuracy andconvergence.

THE BOUNDARIES - In what follows, the processes ofvorticity generation on a rectangular wall and its evolutionwithin a thin region near the wall are presented. (Theapproach is applied to all walls simultaneously.) Alvariables are defined with respect to the local coordinatesystem, z is selected normal to the wall and into the flowinterior, and z= 0 represents the wall surface.

The application of the normal flux boundary condition(4b) to the flow field yields a tangential velocity on thedomain boundary that is different from the no-slipboundary condition. This velocity jump on the wall is equato the amount of surface vorticity that must be generatedto satisfy the no-slip condition. We discretize the jumpdistribution on the wall using a set of rectangular vortex

tiles - each with sides and , and surface vorticity

(xi, yi, 0, t) at its center, (xi, yi, 0). The tile vorticity is

linked to the velocity jumps at the center of the boundaryelements, and is obtained by summing the area-weighted jump contributions from all boundary elements that areshadowed by the vortex tile:

where MB is the number of boundary elements on a wal

segment. Each element is defined by its sides andand an area-averaged velocity jump ukm at the

center, (xm, ym, 0). The area-weighted velocity jump

contributions from the boundary elements to the tiles are

given by (xi, xj, , ) = - Max

Min( , )))/ (Indices 1 and 2 used with the

surface vorticity and the velocity jump denote the x and ydirections, respectively.) To maintain a finer discretizationof the flow in the direction normal to the wall, the tiles are

split into Ns.i = ( (xi, y i, 0, t)l/max + 0.5) stacks of tiles -each with surface vorticity equal to (xi, yi, 0, t) = (xi, y i0, t)/Ns.i [27-30]. max is a user-specified maximum

surface vorticity.

The evolution of the wall-generated vortex tiles within athin region near the boundary Dhis assumed to be locally

two-dimensional and is approximated by the Prandtequations [31]:

where (x, t) = (x, y, z) . (U, V, 0) is

the velocity at the edge of the boundary layer as seen bythe wall, and is obtained from the Navier-Stokes solution

in the interior. b = BLTC is a user-specified

boundary

1

4 x0 xr--------------------------

hxit

hyit

hxm

b

hymb

hxit

hxjb hxi

thxj

b+( )

2-------------------------

hxit

hxjb

+( )

2-------------------------

xi xjhxi

thxj

b+( )2

------------------------- hxit

vz

-----uz

----- 0, ,

2 t Re


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thickness, within which the Prandtl approximation isapplied. Note that bis unrelated to the physical boundarylayer thickness, and remains constant in space and timeduring the simulation. BLTCis assigned in the range 1.0 -3.0 such that the tiles will jump into the flow interior in afew timesteps with relatively high probability [4, 27].

Within layer b, the discretized u and v velocitycomponents at the tile centers (xi, yi, zi) are derived by

directly integrating the approximate definitions for y and

x, respectively, and applying velocity boundaryconditions (8d) and (8e):

where l(xi, yi) = (xi, xl, , ))(yi, yl, , ), NT isthe total number of vortex tiles, s is the Heaviside stepfunction, and (U1., U2.) (U, V). The w component isobtained by satisfying continuity:

where the divided difference rule is applied toapproximate the derivatives, and

The grid-free evaluation of (8a), using a first order Eulertime integration, is given as follows:

where (xi, yi, zi) denote the tile trajectory in this context.Note that Eq. (12b) simulates diffusion normal to the walland into the domain interior by reflecting tiles that jumpbelow the wall back into the field [30].

During each timestep, vortex elements convect, stretchand diffuse in the interior. An element is eliminated, if itleaves the domain or jumps into the boundary region.(The trajectory of the elements is such that the normal fluxboundary condition is imposed on the flow.) The tiles inthe boundary domain are convected concurrently with theevolution of vorticity in the interior. New tiles are thencreated on the solid walls to satisfy the no-slip boundarycondition. Finally, all tiles are diffused normal to the wall -

signifying the end of the computational timestep. If a tile jumps into the flow interior, it is converted into a vortex

element with volumetric vorticity (x, t) = (x, t) and

core radius = Max( ). This sets the beginning of thenext timestep. See [15] for the details of the vortex-boundary element method.

RESULTS

Results from the simulation of intake flow in an off-centered port-cylinder assembly with a valve seat and aharmonically moving piston are presented herein. Thecircular cross-section of the engine was approximatedusing a staircase idealization, as depicted by theschematic diagram in Fig. 1.

The flow was generated by the harmonic displacementof the piston from rest at the top dead center (TDC) to restat the bottom dead center (BDC) positions. A uniformvelocity profile was assigned at the inlet of the port and itsvalue obtained by applying the no-flux boundary conditionto the remaining boundary surfaces and satisfying thecontinuity requirement. The no-slip boundary condition

was applied to all solid boundaries. All length scales werenormalized by the cylinder diameter, Dc, and their values

declared in Fig. 1. The velocity was normalized by themaximum piston speed at 90 crank angle, Vm. The

Reynolds number based on Dc and Vm was set at 350

The induction process was discretized by 200 equatimesteps, corresponding to a 0.9 crank angle. For thepresent study, the simulation was stopped at 150timesteps or equivalently at 135 crank angleAdditionally, max = 0.5 and BLTC = 1.5 were set.

Time-varying boundary elements were used todiscretize the cylinder wall along its length, Lc, which

changes in time due to the piston motion. For this

purpose, a maximum number of boundary elementsNmax, was used to discretize the maximum length of the

cylinder wall, Lmax, corresponding to the piston position at

BDC. The instantaneous number of elements, N, wasobtained using the relation N = Max (1, NmaxLc/Lmax +

0.5). The same procedure was repeated for the vortextiles. In addition to saving CPU time, this approachmaintains a nominal elemental mesh size in the order ofLmax/Nmax; which, for the present study, was set to 0.05

and 0.1 for the boundary elements and tiles, respectivelyIn contrast, selecting a fixed value for N would yieldextremely thin elements in the direction of piston motion atthe beginning of the computation, and would lead toinaccurate flow predictions. For all other surfaces, theboundary element and tile sizes were fixed at 0.05 and0.1, respectively. 1,392 boundary elements were used todiscretize the domain at TDC, which increased to 2,512 at135 crank angle. The velocity jump discretizationrequired 404 and 740 tiles, respectively. The number ofvortex elements reached 23,191 at the end of thesimulation. It is interesting to note that a simulation of flowin the same port-cylinder geometry and using an identicaset of computational parameters, but without a valve seatled to the generation of only 9,095 vortex elements at135 crank angle. This is the first indication that themajority of vortex elements are generated within the shearlayers around the intake

hxit

hxlt

hyit

hylt

hxt

hyt

hxt

hxt


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jet at the port boundary and the seat circumference. Thepresence of a seat increases the jet velocity and hencethe shear on both sides of the jet.

Fig. 2 depicts the side view of the trajectory of thevortex elements, and their velocity, within a slice ofvolume with 0.15 thickness and plane of symmetry lyingon the plane of symmetry of the engine - region B in Fig.1. Fig. 3 depicts a similar visualization within region A inFig. 1. The velocity vectors are represented by sticks, andtheir origins at the vortex element locations are depictedas solid circles. In Figs. 2 and 3, the envelope of thevortex elements in the port depicts the development of the

familiar boundary layer on the port wall. Note that as thepiston accelerates from TDC to its peak speed at mid-stroke, and decelerates thereafter to rest at BDC, theeffective Reynolds number in the port increases anddecreases correspondingly. As a result, the boundarylayer on the intake port wall experiences a decrease andincrease in its thickness, respectively. Furthermore, theabsence of vortex elements in the inner region of theintake port points to the existence of a wide potential corethere. The extension of this core into the chamber, whichbifurcates around the valve seat, marks the jet core as it isissued from the port into the chamber (Figs. 2 and 3.) The

high-velocity vortex elements on the outer surface of thejet core depict the jet shear layer. Also notice that near thewalls, the vortex elements are separated from the formerby a very thin region. This region is the so called boundarydomain, within which the Prandtl boundary layerapproximation is used to evaluate the evolution of thewall-generated vortex tiles. (The tiles are not shown in thefigures for clarity of presentation.) Note that the boundaryregion is thinner than the physical boundary layer(depicted by the outer envelope of the vortex elements

near the wall.) In addition, unlike the physical boundarylayer, which is controlled by the instantaneous Reynoldsnumber, the thickness of the boundary region is fixed intime and specified by the global Reynolds number.

As the piston proceeds toward BDC, the valve seatdirectly below the intake port deflects the incoming jetfrom the port and fans it out radially into the cylinder. Thehigh velocity gradients, caused by the interaction betweenthe inner surface of the conical jet in the cylinder and theside-walls of the valve seat, generate vorticity on the latterinstantly. During the early stages of the induction processthe cylinder contains minimal vorticity and the flow within itmay be viewed primarily as potential. Consequentlydictated by the potential flow properties and as seen in

Figs. 2 and 3 (27 and 36 crank angles,) the valve-generated elements convect sharply under the seattoward the centerline and initiate the development of aprimary (or valve) toroidal eddy. Concurrent with thedevelopment of the valve eddy, the outer surface of theconical jet separates from the port due to the suddenexpansion at the interface of the port and the cylinderhead, and begins to roll up at the top corner of the cylinderinto a secondary toroidal eddy. In what follows, for thesake of simplicity, references to left and right eddies implythe left and right cross-sections of the toroidal eddy,respectively. Similarly, left and right jets refer to thecorresponding cross-sections of the conical jet.

During the early stages of the induction process, theleft and right eddies in regions B and A (Figs. 2 and 3respectively) are basically circular and equal in diameterIn both cases, the eddies remain centered symmetricallywith respect to the valve axis, in the proximity of the valveseat edges, until about 50 crank angle. As the flowdevelops further (until 90) the left and right jetscontinuously supply fluid to, and grow the size of theirrespective eddies. The latter evolve into ellipses whosemajor axes are parallel to the jets that drive them. Theeddies in region B (Fig. 2) experience an unequal growthin size. From TDC through the mid-stroke, the left eddygrows such that its center stays essentially stationarybelow the left edge of the valve seat. At 90, the left eddy

center is below the valve seat by approximately a fourth ofthe gap between the valve bottom and the piston. On theother hand, due to the geometric asymmetry, the righteddy in region B (Fig. 2) rolls radially outward and axiallydownward, away from the valve seat, such that by 90crank angle it is centered half-way between the right edgeof the valve seat and the cylinder wall on the right.Moreover, the vertical position of the right eddy center isat approximately two thirds of the valve-piston gap belowthe valve seat. The eddies in region A (Fig. 3) remain, forall practical purposes, symmetric with respect to the planeof symmetry of the

Figure 1: Schematic diagram of the port-cylinder

geometry. Integers refer to units of length

0.05.


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Figure 2: Vortex element trajectories within volume B in Fig. 1. Normalization in each

time frame is based on the instantaneous maximum speed in the field.


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Figure 2: (Continued)


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Figure 3: Vortex element trajectories within volume A in Fig. 1. Normalization in each

time frame is based on the instantaneous maximum speed in the field.


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Figure 3: (Continued)


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engine. Indeed the flow structure closely resembles thatobserved in axisymmetric valved engines [16]. In thiscase, both left and right eddy centers slowly migrateradially out and axially down. By mid-stroke, the centersare positioned half-way between the valve seat and thepiston, and away from the valve edges by a third of thedistance between the seat edge and the cylinder wall.

Note that the vertical position of the eddy centers inFig. 3 project onto the axis of symmetry of the inlet port

(and the valve) in Fig. 2. Connecting the three centerpositions in Fig. 2, one can reconstruct the evolution of thetoroidal eddy as follows. During the initial stages ofinduction, the core (or cross-section) of the primarytoroidal eddy is azimuthally uniform - starting with acircular shape and slowly growing into an elliptical core.The initial diameter of the toroidal eddy is smaller than thevalve diameter, and its axis of rotation is normal to thepiston face. During this stage, the dynamics of the torus isquite similar to the behavior of ring vortices in free space.As time progresses, the conical jet continuously suppliesfluid to the primary eddy, so that the core of the lattercontinues to grow. In the mean time, due to the combinedeffects of the geometric asymmetry of the flow in the xz

plane and the expansion caused by the piston motion, thediameter of the torus expands radially out while its axis ofrotation begins to tilt in the positive x direction. The tiltingof the torus proceeds as if a section of it is hinged oranchored near the valve seat (left eddy in Fig. 2.) The tiltangle of the toroidal axis of rotation with respect to the z-axis is 20-30 at mid-stroke.

Beyond mid-stroke, a weak counter-rotating toroidaleddy develops at the corner between the piston and thecylinder wall. In addition, the primary toroidal eddy beginsto lose its coherence. In particular, the flow in region B(Fig. 2) appears to break up into multiple smaller scalevortical structures. The flow in region A (Fig. 3) remainsweakly symmetric and displays a mild coherence. We willreturn to this topic shortly.

In addition to creating the primary toroidal vortex, theconical jet traps a secondary toroidal vortex at the top ofthe cylinder. The structure of this weak torus remainsstable during the entire simulation, although its core sizeand shape change in time due to the unsteady dynamicsof the entrapping jet. As shown in Figs. 2 and 3, the coresize and shape of the torus around its azimuth areprimarily defined by the distance between the port and thecylinder walls.

Note that, within the limited range of parameterstested, the break up of the primary toroidal eddy after mid-stroke, into smaller less coherent vortical structures was

found to be independent of the temporal and spatialresolutions of the predictions. Therefore, we propose thatthe observed break up is due to the inherent instabilitywhose mode is probably selected by perturbations causedby the numerical discretization of the engine surfaces.Before we elaborate on this proposition, we refer to aseries of flow visualization experiments conducted byEkchian and Hoult [16], on a valved axisymmetric engineand an engine with an off-centered valve. (The geometryof the latter case is similar to that of the presentsimulation.) Fig. 4 is a reproduction of the flowvisualization results for the case with the off-centered

valve, within regions A and B in Fig. 1. Note the similaritybetween the experiment and the present simulationdespite the detailed differences in the geometries and flowconditions. The differences include the Reynolds numberthe valve lift and its exact off-center position, the staircasediscretization of the engine geometry, and the valvesimplification by a seat. The two relevant conclusionsmade by Ekchian and Hoult [16] - as a result of movingthe valve from the center of the engine cylinder toward itsedge - were: (1) "the planes of the axes of rotation of the

vortices are no longer perpendicular to the cylinder axisbut are tipped at an angle to it," and (2) "the lifetime of thevortex is shorter."

We proceed with our proposed explanation of the

observed break up of the flow coherence near the cylindertop by focusing on the dynamics of the primary toroidaeddy as a single three-dimensional structure. As wementioned earlier, the dynamics of the primary toroidaeddy in its simplest form - during the initial stages of theinduction step - closely resembles the dynamics of avortex ring moving in free space. The latter has beenanalyzed extensively [32, 33], as well as investigatedexperimentally [34, 35] and computationally [36]. In factEkchian [37] was able to predict vortex breakdown inaxisymmetric engines with poppet valves, using lineartheories of the inviscid instability of ring vortices. In a

Figure 4: Flow visualization in a motored engine

with an off-centered valve (Ekchian and

Hoult.) A and B correspond to the planar

views in Figure 1. (Bore/Stroke = 1.35,

R.P.M. = 750, Lift = 0.21)


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parametric study by Knio and Ghoniem [36], vortex ringswere excited by a sinusoidal perturbation in the radialdirection, using an integer number of waves around theazimuth of the rings. The computations predicted thedevelopment and growth of streamwise vortices aroundthe ring azimuth, whose stability mode depends on thenature of the perturbation as well as the ring. Morespecifically, the most unstable wavenumbers were foundto be proportional to the ratio of the ring radius to the core

size. Additionally, outside a narrow band around the mostunstable wavenumbers, the rings were shown to oscillatestably. In long time computations, these perturbationsgrow leading to the break up of the ring.

In the present computation, the circular cross sectionof the port and the valve seat are discretized by 20unequal staircase segments, as depicted in Fig. 1. As aresult, the contour of the discretized circles imparts smallperturbations with multiplicity of wavenumbers on theinner and outer surfaces of the conical jet, as well as theperimeter of the primary torus. The growth of theseperturbations, via the mechanism mentioned earlier, leadsto the development of streamwise vortices around theazimuth of the torus, accompanied by initially mildoscillations. The tilting and the radial expansion of thetoroidal vortex lead to further stretch and the additionalamplification of the waves, such that eventually break-upis observed. While the origin of the initial perturbation isnumerical (e.g., the discretization of the circle into astaircase-shaped polygon,) in practice one encountersother perturbations due to turbulence that lead to a similarbreak up of the vortex - as verified by the experiment inFig. 4.

Fig. 5 depicts the evolution of = 0.18 surfaces,where is the local vorticity, normalized by theinstantaneous maximum vorticity in the field. The localvalue of vorticity was evaluated on a uniform grid using its

definition as the curl of the velocity. corresponds tothe enstrophy, which can also be regarded as a measureof the energy dissipation rate per unit volume, and can beused to detect regions of high energy dissipation, shearand mixing within a flow. The constant value of 0.18 wasselected to focus on the flow in the vicinity of the valveseat. Note that since normalization in each time frame isdone with respect to its instantaneous maximum, thedisplayed iso-surfaces do not correspond to the evolutionof a particular enstrophy value. For example, the largervolume of vorticity at 135, as compared to say 108, doesnot necessarily imply a corresponding increase in vorticity.Notice the development of relatively strong vorticity

patches below the valve seat (from 27 to 45 crankangles.) The patches correspond to the streamwisevorticity in the primary toroidal vortex. The development ofstreamwise vorticity near the corners of the seatcorrespond to the growth of perturbations caused by theapproximate representation of the valve seat. Beyond 50crank angle and until approximately the mid-stroke, aniso-surface representing a coherent toroidal vortex with anon-circular core is distinctly visible. The perturbationsassociated with the observed waviness of the iso-surfacegrow and lead, in the later stages, to the break up of thetorus, and the formation of a "spotty" vorticity.

CONCLUSIONS

A three-dimensional vortex-boundary element methodhas recently been developed for the simulation of flow inthe time-dependent geometry of engines. A briefdescription of the approach was presented in this paperfollowed by an example of intake flow inside a circularchamber, containing a valve seat and fitted with an off-centered port at one end and a harmonically movingpiston at the other. The circular cross-section of theengine was represented by a staircase idealization. TheReynolds number based on the piston diameter and itsmaximum speed was set at 350. In order to save CPUtime and to eliminate the generation of high aspect ratioelements, a time-varying number of surface meshes wasused to discretize the cylinder walls. 404 vortex tiles and1,392 boundary elements were used to mesh the domainat TDC, which grew to 740 and 2,512, respectively, at135 crank angle.

Results show that the flow inside the chamber isdominated by a primary toroidal eddy, which is generateddue to the interaction of the valve seat with the jet issuedfrom the intake port. The axis of rotation of the torus isinitially normal to the piston. However, due to the

asymmetry of the engine geometry and the expansioncaused by the piston motion, the torus continues toexpand radially out while its rotational axis begins to tilt toa 20-30 angle with respect to the normal to the pistonface. The vortex structure remains coherent until 90crank angle. However, beyond the mid-stroke, thegeometry-induced perturbations experienced by thetoroidal vortex grow and eventually lead to the break up ofthe vortical structure into smaller, less coherent eddiesThis process was corroborated by experimental evidenceIn addition to the primary torus, the jet separation wasseen to give rise to a stable secondary vortex torus at thetop corner of the chamber. The size and shape of thelatter were seen to be dependent on the relative position

of the port with respect to the chamber.The oscillations which are observed around theazimuth of the primary toroidal eddy result fromperturbations introduced in the numerical discretization ofthe valve seat. In practice, the origin of theseperturbations could be the turbulence present in theincoming flow.

ACKNOWLEDGMENTS

This project was funded by FORD Motor CompanyThe numerical experiments were performed on the CrayC90 at the Pittsburgh Supercomputing Center.

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Figure 5: Iso-surfaces of . = 0.18, where is the vorticity vector normalized

by the instantaneous maximum field vorticity.

Documents

3d Vortex Simulation of Intake Flow in a Port Cylinder With a Valve Seat