Classifications

• • G—PHYSICS
  • G06—COMPUTING OR CALCULATING; COUNTING
  • G06F—ELECTRIC DIGITAL DATA PROCESSING
  • G06F30/00—Computer-aided design [CAD]
  • G06F30/20—Design optimisation, verification or simulation
  • G06F30/23—Design optimisation, verification or simulation using finite element methods [FEM] or finite difference methods [FDM]
• • G—PHYSICS
  • G06—COMPUTING OR CALCULATING; COUNTING
  • G06F—ELECTRIC DIGITAL DATA PROCESSING
  • G06F2119/00—Details relating to the type or aim of the analysis or the optimisation
  • G06F2119/10—Noise analysis or noise optimisation

Definitions

• This description relates to a data processing apparatus for processing data representing acoustic properties of a porous medium modeled in accordance with tortuosity.
• High Reynolds number flow has been simulated by generating discretized solutions of the Navier-Stokes differential equations by performing high-precision floating point arithmetic operations at each of many discrete spatial locations on variables representing the macroscopic physical quantities (e.g., density, temperature, flow velocity).
• Another approach replaces the differential equations with what is generally known as lattice gas (or cellular) automata, in which the macroscopic-level simulation provided by solving the Navier-Stokes equations is replaced by a microscopic-level model that performs operations on particles moving between sites on a lattice.
• one innovative aspect of the subject matter described in this specification can be embodied in methods that include, in aspect 1, the actions of generating by a first data processing program of the data processing apparatus, a model of acoustic behavior of a fluid in a porous medium including an effect of tortuosity, with the model comprising a time variable indicative of a sound speed of the fluid.
• the methods include the actions of reseating the time variable of the model based on the sound speed in a fluid in the porous medium.
• the methods also include the actions of simulating the acoustic behavior including the effect of tortuosity of the porous medium based on the reseating of the time variable within the model.
• the method can include the action of determining acoustic behavior within the model including the effect of the tortuosity of the porous medium.
• the acoustic behavior may include dissipation and propagation of sound waves.
• reseating the time variable may include adjusting the amount of time represented by one simulation time step.
• simulating the acoustic behavior may include simulating fluid flow through or within the volumetric region.
• the model may include a momentum sink that accounts for acoustic losses of the porous medium.
• reseating the time variable may be based on the nominal sound speed of a fluid and a sound speed of the fluid in the porous medium.
• the fluid can be represented by elements, the elements can include one or more of mass, density, momentum, pressure, velocity, temperature, energy, mass fluxes, momentum fluxes, and energy fluxes within the fluid.
• reseating the time variable may include reseating a temperature of the model.
• reseating the time variable may include reseating a pressure of the model.
• reseating the time variable may include reseating the velocity of the fluid.
• reseating the time variable may include reseating the resistance of the porous medium.
• the systems and techniques may be implemented using a lattice gas simulation that employs a Lattice Boltzmann formulation.
• the traditional lattice gas simulation assumes a limited number of particles at each lattice site, with the particles being represented by a short vector of bits.
• Each bit represents a particle moving in a particular direction.
• one bit in the vector might represent the presence (when set to 1) or absence (when set to 0) of a particle moving along a particular direction.
• Such a vector might have six bits, with, for example, the values 110000 indicating two particles moving in opposite directions along the X axis, and no particles moving along the Y and Z axes.
• a set of collision rules governs the behavior of collisions between particles at each site (e.g., a 110000 vector might become a 001100 vector, indicating that a collision between the two particles moving along the X axis produced two particles moving away along the Y axis).
• the rules are implemented by supplying the state vector to a lookup table, which performs a permutation on the bits (e.g., transforming the 110000 to 001100). Particles are then moved to adjoining sites (e.g., the two particles moving along the Y axis would be moved to neighboring sites to the left and right along the Y axis).
• the state vector at each lattice site includes many more bits (e.g., 54 bits for subsonic flow) to provide variation in particle energy and movement direction, and collision rules involving subsets of the full state vector arc employed.
• more man a single particle is permitted to exist in each momentum state at each lattice site, or voxel (these two terms are used interchangeably throughout this document).
• 0-255 particles could be moving in a particular direction at a particular voxel.
• the state vector instead of being a set of bits, is a set of integers (e.g., a set of eight-bit bytes providing integers in the range of 0 to 255), each of which represents the number of particles in a given state.
• LBM Lattice Boltzmann Methods
• F(x,t) represents an external or self-consistently generated body-force at (x,t) .
• the collision term C represents interactions of particles of various velocities and locations. It is important to stress that, without specifying a particular form for the collision term C, the above Boltzmann equation is applicable to all fluid systems, and not just to the well known situation of rarefied gases (as originally constructed by
• C includes a complicated multi-dimensional integral of two- point correlation functions.
• BGK operator is constructed according to the physical argument that, no matter what the details of the collisions, the distribution function approaches a well-defined local equilibrium given by via collisions:
• the parameter r represents a characteristic relaxation time to equilibrium via collisions.
• the relaxation time is typically taken as a constant.
• this relaxation time is a function of hydrodynamic variables like rate of strain, turbulent kinetic energy and others.
• a turbulent flow may be represented as a gas of turbulence particles ("eddies") with the locally determined characteristic properties.
• One of the direct benefits is that there is no problem handling the movement of the interface on a solid surface, which helps to enable lattice-Boltzmann based simulation software to successfully simulate complex turbulent aerodynamics.
• certain physical properties from the boundary such as finite roughness surfaces, can also be incorporated in the force.
• the BGK collision operator is purely local, while the calculation of the self-consistent body-force can be accomplished via near-neighbor information only. Consequently, computation of the Boltzmann-BGK equation can be effectively adapted for parallel processing.
• the set of velocity values are selected in such a way that they form certain lattice structures when spanned in the configuration space.
• the dynamics of such discrete systems obeys the LBE having the
• FIGS. 1 and 2 illustrate velocity components of two LBM models.
• FIG. 3 is a flow chart of a procedure followed by a physical process simulation system.
• FIG. 4 is a perspective view of a micro-block.
• FIGS. 5 A and 5B are illustrations of lattice structures used by the system of FIG.
• FIGS. 6 and 7 illustrate variable resolution techniques.
• FIG. 8 illustrates regions affected by a facet of a surface.
• FIG. 9 illustrates movement of particles from a voxel to a surface.
• FIG. 10 illustrates movement of particles from a surface to a surface.
• FIG. 11 is a flow chart of a procedure for performing surface dynamics.
• FIG. 12 illustrates an interface between voxels of different sizes.
• FIG. 13 is a flow chart of a procedure for simulating interactions with facets under variable resolution conditions.
• FIG.14 is a schematic view of an exemplary porous media model .
• FIG. 15 is a schematic view of exemplary double-sided surfels.
• FIG. 16 is a schematic view of an exemplary system for modeling acoustic absorption.
• FIGS. 17A and 17B are schematic views of other exemplary porous media models.
• FIG. 18 is a schematic view of another exemplary porous media model.
• FIG. 19 illustrates absorption coefficients as a function of frequency.
• FIGS. 20-22 illustrate absorption coefficients as functions of frequency.
• FIG. 23 illustrates an interior of a vehicle.
• FIG. 24 illustrates an aircraft landing system
• FIG. 25 illustrates an example of tortuosity in a porous medium.
• FIG. 26 shows the effects of tortuosity on the curve of absorption coefficient versus frequency for the NASA ceramic liner porous media.
• FIG. 27 is a flow chart of an example process for processing data representing acoustic properties of a porous medium modeled in accordance with tortuosity
• a given volumetric model for sound propagation in an absorbing material can be put in the form of a locally-reacting, frequency-dependent, complex impedance at the interface between two different media.
• impedance models may be used in approaches such as the Boundary Element Methods (BEM), the Finite Elements Methods (FEM), and the Statistical Energy Analysis (SEA) methods, and may be implemented as boundary conditions in the frequency domain.
• BEM Boundary Element Methods
• FEM Finite Elements Methods
• SEA Statistical Energy Analysis
• CFD Computational Fluid Dynamics
• CAA Computational AeroAcoustics
• the approach eliminates numerical stability problems since the impedance is realized in a way that satisfies passive, causal, and real conditions.
• LBM Lattice Boltzmann Method
• a time- explicit CFD/CAA solution method based on the Lattice Boltzmann Method (LBM), such as the PowerFLOW system available from Exa Corporation of Burlington, Massachusetts.
• LBM starts from a "mesoscopic" Boltzmann kinetic equation to predict macroscopic fluid dynamics.
• the resulting compressible and unsteady solution method may be used for predicting a variety of complex flow physics, such as aeroacoustics and pure acoustics problems.
• a porous media model is used to represent the flow resistivity of various components, such as air filters, radiators, heat exchangers, evaporators, and other components, which are encountered in simulating flow, such as through HVAC systems, vehicle engine compartments, and other applications.
• a general discussion of a LBM-based simulation system is provided below and followed by a discussion of a volumetric modeling approach for acoustic absorption and other phenomena and a porous media interface model that may be used to support such a volumetric modeling approach.
• fluid flow may be represented by the distribution function values evaluated at a set of discrete
• Equation 4 The dynamics of the distribution function is governed by Equation 4
• the streaming process is when a pocket of fluid starts out at a grid location, and then moves along one of the velocity- vectors to the next grid location. At that point, the "collision factor,” i.e., the effect of nearby pockets of fluid on the starting pocket of fluid, is calculated.
• the fluid can only move to another grid location, so the proper choice of the velocity vectors is necessary so that all the components of all velocities are multiples of a common speed.
• the right-hand side of the first equation is the aforementioned "collision operator" which represents the change of the distribution function due to the collisions among the pockets of fluids.
• the particular form of the collision operator used here is due to Bhatnagar, Gross and Krook (BGK). It forces the distribution function to go to the prescribed values given by the second equation, which is the "equilibrium" form.
• Equation (3) the collective values of c i and w i define a LBM model.
• the LBM model can be implemented efficiently on scalable computer platforms and run with great robustness for time unsteady flows and complex boundary conditions.
• a standard technique of obtaining the macroscopic equation of motion for a fluid system from the Boltzmann equation is the Chapman-Enskog method in which successive approximations of the full Boltzmann equation are taken.
• a small disturbance of the density travels at the speed of sound.
• the speed of the sound is generally determined by the temperature.
• the importance of the effect of compressibility in a flow is measured by the ratio of the characteristic velocity and the sound speed, which is known as the Mach number.
• a first model (2D-1) 100 is a two-dimensional model that includes 21 velocities. Of these 21 velocities, one (105) represents particles that are not moving; three sets of four velocities represent particles that are moving at either a normalized speed (r) (110-113), twice the normalized speed (2r) (120-123), or three times the normalized speed (3r) (130-133) in either the positive or negative direction along either the x oxy axis of the lattice; and two sets of four velocities represent particles that are moving at the normalized speed (r) (140-143) or twice the normalized speed (2r) (150-153) relative to both of the * and.v lattice axes.
• a second model (3D-1) 200 is a three-dimensional model that includes 39 velocities, where each velocity is represented by one of the arrowheads of FIG. 2. Of these 39 velocities, one represents particles that are not moving; three sets of six velocities represent particles that are moving at either a normalized speed (r), twice the normalized speed (2r), or three times the normalized speed (3r) in either the positive or negative direction along the x, y or z axis of the lattice; eight represent particles that are moving at the normalized speed (r) relative to all three of the x, y, z lattice axes; and twelve represent particles that are moving at twice the normalized speed (2r) relative to two of the x, y, z lattice axes.
• More complex models such as a 3D-2 model includes 101 velocities and a 2D-2 model includes 37 velocities also may be used.
• the velocities are more clearly described by their component along each axis as documented in Tables 1 and 2 respectively.
• one represents particles that are not moving (Group 1); three sets of six velocities represent particles that are moving at either a normalized speed (r), twice the normalized speed (2r), or three times the normalized speed (3r) in either the positive or negative direction along the x, y or z axis of the lattice (Groups 2, 4, and 7); three sets of eight represent particles that are moving at the normalized speed (r), twice the normalized speed (2r), or three times the normalized speed (3r) relative to all three of the x, y, z lattice axes (Groups 3, 8, and 10); twelve represent particles that are moving at twice the normalized speed (2r) relative to two of the x, y, z lattice axes (Group 6); twenty four represent particles that are moving at the normalized speed (r) and twice the normalized speed (2r) relative to two of the x, y, z lattice axes, and not moving
• one represents particles that are not moving (Group 1); three sets of four velocities represent particles that are moving at either a normalized speed (r), twice the normalized speed (2r), or three times the normalized speed (3r) in either the positive or negative direction along either the x or y axis of the lattice (Groups 2, 4, and 7); two sets of four velocities represent particles that are moving at the normalized speed (r) or twice the normalized speed (2r) relative to both of the x and y lattice axes; eight velocities represent particles that are moving at the normalized speed (r) relative to one of the x and y lattice axes and twice the normalized speed (2r) relative to the other axis; and eight velocities represent particles that are moving at the normalized speed (r) relative to one of the x and y lattice axes and three times the normalized speed (3r) relative to the other axis
• the LBM models described above provide a specific class of efficient and robust discrete velocity kinetic models for numerical simulations of flows in both two-and three- dimensions.
• a model of this kind includes a particular set of discrete velocities and weights associated with those velocities.
• the velocities coincide with grid points of Cartesian coordinates in velocity space which facilitates accurate and efficient implementation of discrete velocity models, particularly the kind known as the lattice Boltzmann models. Using such models, flows can be simulated with high fidelity.
• a physical process simulation system operates according to a procedure 300 to simulate a physical process such as fluid flow.
• a simulation space is modeled as a collection of voxels (step 302).
• the simulation space is generated using a computer-aided-design (CAD) program.
• CAD computer-aided-design
• a CAD program could be used to draw a micro-device positioned in a wind tunnel.
• data produced by the CAD program is processed to add a lattice structure having appropriate resolution and to account for objects and surfaces within the simulation space.
• the resolution of the lattice may be selected based on the Reynolds number of the system being simulated.
• the Reynolds number is related to the viscosity (v) of the flow, the characteristic length (L) of an object in the flow, and the characteristic velocity (u) of the flow:
• the characteristic length of an object represents large scale features of the object. For example, if flow around a micro-device were being simulated, the height of the micro-device might be considered to be the characteristic length.
• the resolution of the simulation may be increased, or areas of increased resolution may be employed around the regions of interest.
• the dimensions of the voxels decrease as the resolution of the lattice increases.
• the state space is represented as fi (x, t), where fi represents the number of elements, or particles, per unit volume in state / ' (i.e., the density of particles in state i) at a lattice site denoted by the three-dimensional vector x at a time t.
• fi represents the number of elements, or particles, per unit volume in state / ' (i.e., the density of particles in state i) at a lattice site denoted by the three-dimensional vector x at a time t.
• the number of particles is referred to simply asfi
• the number of states is determined by the number of possible velocity vectors within each energy level.
• the velocity vectors consist of integer linear speeds in a space having three dimensions: x, y, and z.
• the number of states is increased for multiple- species simulations.
• Each state i represents a different velocity vector at a specific energy level (i.e., energy level zero, one or two).
• the velocity c, of each state is indicated with its "speed" in each of the three dimensions as follows:
• the energy level zero state represents stopped particles that are not moving in any dimension, i.e Energy level one states represent particles having a ⁇ 1
• Energy level two states represent particles having either a ⁇ 1 speed in all three dimensions, or a ⁇ 2 speed in one of the three dimensions and a zero speed in the other two dimensions.
• Generating all of the possible permutations of the three energy levels gives a total of 39 possible states (one energy zero state, 6 energy one states, 8 energy three states, 6 energy four states, 12 energy eight states and 6 energy nine states.).
• Each voxel (i.e., each lattice site) is represented by a state vector ⁇ ( ⁇ ).
• the state vector completely defines the status of the voxel and includes 39 entries.
• the 39 entries correspond to the one energy zero state, 6 energy one states, 8 energy three states, 6 energy four states, 12 energy eight states and 6 energy nine states.
• the voxels are grouped in 2x2x2 volumes called microblocks.
• the microblocks are organized to permit parallel processing of the voxels and to minimize the overhead associated with the data structure.
• a short-hand notation for the voxels in the microblock is defined as (n), where n represents the relative position of the lattice site within the microblock and ne ⁇ 0,1,2, . . . , 7 ⁇ .
• a microblock is illustrated in FIG. 4. Referring to FIGs. 5A and 5B, a surface S (FIG. 3A) is represented in the simulation space (FIG. 5B) as a collection of facets F a :
• each facet F a has a unit normal ( « «), a surface area a center location and a facet distribution function that describes the surface dynamic
• different levels of resolution may be used in different regions of the simulation space to improve processing efficiency.
• the region 650 around an object 655 is of the most interest and is therefore simulated with the highest resolution.
• decreasing levels of resolution i.e., expanded voxel volumes
• regions 660, 665 that are spaced at increasing distances from the object 655.
• a lower level of resolution may be used to simulate a region 770 around less significant features of an object 775 while the highest level of resolution is used to simulate regions 780 around the most significant features (e.g., the leading and trailing surfaces) of the object 775.
• Outlying regions 785 are simulated using the lowest level of resolution and the largest voxels.
• Voxels affected by one or more facets are identified (step 304).
• Voxels may be affected by facets in a number of ways.
• a voxel that is intersected by one or more facets is affected in that the voxel has a reduced volume relative to non-intersected voxels. This occurs because a facet, and material underlying the surface represented by the facet, occupies a portion of the voxel.
• a fractional factor ?i(x) indicates the portion of the voxel that is unaffected by the facet (i.e., the portion that can be occupied by a fluid or other materials for which flow is being simulated).
• Pr (x) equals one.
• Voxels that interact with one or more facets by transferring particles to the facet or receiving particles from the facet are also identified as voxels affected by the facets. All voxels that are intersected by a facet will include at least one state that receives particles from the facet and at least one state that transfers particles to the facet. In most cases, additional voxels also will include such states.
• a facet Fa receives particles from, or transfers particles to, a region defined by a parallelepiped Gia having a height defined by the magnitude of the vector dot product of the velocity vector ci and the unit normal rta of the facet (
• the facet F a receives particles from the volume Via when the velocity vector of the state is directed toward the facet (
• this expression must be modified when another facet occupies a portion of the parallelepiped Gm, a condition that could occur in the vicinity of non-convex features such as interior corners.
• the parallelepiped Gta of a facet Fa may overlap portions or all of multiple voxels.
• the number of voxels or portions thereof is dependent on the size of the facet relative to the size of the voxels, the energy of the state, and the orientation of the facet relative to the lattice structure.
• the number of affected voxels increases with the size of the facet. Accordingly, the size of the facet, as noted above, is typically selected to be on the order of or smaller than the size of the voxels located near the facet.
• Viafx The portion of a voxel N(x) overlapped by a parallelepiped Gia is defined as Viafx).
• the flux Viafx) of state i particles that move between a voxel N(x) and a facet Fa equals the density of state / ' particles in the voxel multiplied by the volume
• a timer is initialized to begin the simulation (step 306).
• movement of particles from voxel to voxel is simulated by an advection stage (steps 308-316) that accounts for interactions of the particles with surface facets.
• a collision stage (step 318) simulates the interaction of particles within each voxel.
• the timer is incremented (step 320). If the incremented timer does not indicate that the simulation is complete (step 322), the advection and collision stages (steps 308-320) are repeated. If the incremented timer indicates that the simulation is complete (step 322), results of the simulation are stored and/or displayed (step 324).
• each facet must meet four boundary conditions.
• the combined mass of particles received by a facet must equal the combined mass of particles transferred by the facet (i.e., the net mass flux to the facet must equal zero).
• the combined energy of particles received by a facet must equal the combined energy of particles transferred by the facet (i.e., the net energy flux to the facet must equal zero).
• the other two boundary conditions are related to the net momentum of particles interacting with a facet.
• the net tangential momentum flux must equal zero and the net normal momentum flux must equal the local pressure at the facet.
• the components of the combined received and transferred momentums that are perpendicular to the normal no of the facet i.e., the tangential components
• the difference between the components of the combined received and transferred momentums that are parallel to the normal n a of the facet i.e., the normal components
• particles are gathered from the voxels and provided to the facets (step 308).
• the flux of state / ' particles between a voxel N(x) and a facet F a is:
• particles are moved between facets (step 310). If the parallelepiped Gta for an incoming state (cm a ⁇ 0) of a facet F a is intersected by another facet i3 ⁇ 4 then a portion of the state i particles received by the facet F a will come from the facet Fp. In particular, facet Fa will receive a portion of the state i particles produced by facet Fp during the previous time increment.
• FIG. 10 illustrates a portion 1000 of the parallelepiped G, a that is intersected by facet Fp equals a portion 1005 of the parallelepiped ⁇ that is intersected by facet Fa.
• the intersected portion is denoted as Using this term, the flux of state i particles between a facet ⁇ and a
• facet may be desc ribed as:
• the state vector N(a) for the facet also referred to as a facet distribution function, has 54 entries corresponding to the 54 entries of the voxel state vectors.
• the input states of the facet distribution function N(a) are set equal to the flux of particles into those states divided by the volume Via :
• the facet distribution function is a simulation tool for generating the output flux from a facet, and is not necessarily representative of actual particles. To generate an accurate output flux, values are assigned to the other states of the distribution function. Outward states are populated using the technique described above for populating the inward states:
• TKJTHER (a) is determined using the technique described above for generating but applying the technique to states other than incoming
• YIOTHER (a) may be generated using values of
• states having zero velocity i.e., rest states and states (0, 0, 0, 2) and (0, 0, 0, -2) are initialized at the beginning of the simulation based on initial conditions for temperature and pressure. These values are then adjusted overtime.
• step 312 surface dynamics are performed for each facet to satisfy the four boundary conditions discussed above (step 312).
• a procedure for performing surface dynamics for a facet is illustrated in FIG. 11. Initially, the combined momentum normal to the facet Fa is determined (step 1105) by determining the combined momentum P(a) of the particles at the facet as:
• a Boltzmann distribution may be achieved by applying a set of collision rules
• An outgoing flux distribution for the facet F a is then determined (step 1120) based on the incoming flux distribution and the Boltzmann distribution.
• the difference between the incoming flux distribution ⁇ ; (a) and the Boltzmann distribution is determined as:
• the outgoing flux distribution may be further refined to:
• ha is a first tangential vector that is
• n perpendicular to both n a and and and are distribution functions corresponding to the energy (j) of the state / and the indicated tangential vector.
• the distribution functions are determined according to:
• pa is the equilibrium pressure at the facet Fa and is based on the averaged density and temperature values of the voxels that provide particles to the facet
• ua is the average velocity at the facet
• the difference between the input energy and the output energy is measured for each energy level j as: where the index j denotes the energy of the state i. This energy difference is then used to generate a difference term:
• particles arc moved between voxels along the three- dimensional rectilinear lattice (step 314).
• This voxel to voxel movement is the only movement operation performed on voxels that do not interact with the facets (i.e., voxels that are not located near a surface).
• voxels that are not located near enough to a surface to interact with the surface constitute a large majority of the voxels.
• Each of the separate states represents particles moving along the lattice with integer speeds in each of the three dimensions: x, y, and z.
• the integer speeds include: 0, ⁇ 1, and ⁇ 2.
• the sign of the speed indicates the direction in which a particle is moving along the corresponding axis.
• the particle will continue to move along the lattice at the same speed and direction.
• the move operation becomes slightly more complicated for voxels that interact with one or more surfaces. This can result in one or more fractional particles being transferred to a facet. Transfer of such fractional particles to a facet results in fractional particles remaining in the voxels. These fractional particles are transferred to a voxel occupied by the facet. For example, referring to FIG. 9, when a portion 900 of the state i particles for a voxel 905 is moved to a facet 910 (step 308), the remaining portion 915 is moved to a voxel 920 in which the facet 910 is located and from which particles of state i are directed to the facet 910.
• N(x) is the source voxel.
• step 316 the outgoing particles from each facet are scattered to the voxels.
• this step is the reverse of the gather step by which particles were moved from the voxels to the facets.
• the number of state i particles that move from a facet Fa to a voxel is:
• an amount of mass equal to the value gained (due to underflow) or lost (due to overflow) is added back to randomly (or sequentially) selected states having the same energy and that are not themselves subject to overflow or underflow.
• the additional momentum resulting from this addition of mass and energy is accumulated and added to the momentum from the truncation.
• both mass and energy are corrected when the mass counter reaches zero.
• the momentum is corrected using pushing/pulling techniques until the momentum accumulator is returned to zero.
• fluid dynamics are performed (step 318).
• This step may be referred to as microdynamics or intravoxel operations.
• the advection procedure may be referred to as intervoxel operations.
• the microdynamics operations described below may also be used to collide particles at a facet to produce a Boltzmann distribution.
• the fluid dynamics is ensured in the lattice Boltzmann equation models by a particular collision operator known as the BGK collision model.
• This collision model mimics the dynamics of the distribution in a real fluid system.
• the collision process can be well described by the right-hand side of Equation 1 and Equation 2.
• the conserved quantities of a fluid system specifically the density, momentum and the energy are obtained from the distribution function using Equation 3.
• the equilibrium distribution function noted by / * * in equation (2), is fully specified by Equation (4).
• the choice of the velocity vector set a, the weights, both are listed in Table 1, together with Equation 2 ensures that the macroscopic behavior obeys the correct hydrodynamic equation.
• variable resolution employs voxels of different sizes, hereinafter referred to as coarse voxels 12000 and fine voxels 1205.
• coarse voxels 12000 and fine voxels 1205.
• fine voxels 1205. The interface between regions of coarse and fine voxels is referred to as a variable resolution (VR) interface 1210.
• VR variable resolution
• facets may interact with voxels on both sides of the VR interface. These facets are classified as VR interface facets 1215 (Faic) or VR fine facets 1220 (FOJF).
• a VR interface facet 1215 is a facet positioned on the coarse side of the VR interface and having a coarse parallelepiped 1225 extending into a fine voxel.
• a coarse parallelepiped is one for which ci is dimensioned according to the dimensions of a coarse voxel, while a fine parallelepiped is one for which Ci is dimensioned according to the dimensions of a fine voxel.
• a VR fine facet 1220 is a facet positioned on the fine side of the VR interface and having a fine parallelepiped 1230 extending into a coarse voxel. Processing related to interface facets may also involve interactions with coarse facets 1235 (F «c) and fine facets 1240 (FOF).
• VR facets For both types of VR facets, surface dynamics are performed at the fine scale, and operate as described above. However, VR facets differ from other facets with respect to the way in which particles advect to and from the VR facets.
• Interactions with VR facets are handled using a variable resolution procedure 1300 illustrated in FIG. 13. Most steps of this procedure are carried out using the comparable steps discussed above for interactions with non-VR facets.
• the procedure 1300 is performed during a coarse time step (i.e., a time period corresponding to a coarse voxel) that includes two phases that each correspond to a fine time step.
• the facet surface dynamics are performed during each fine time step.
• a VR interface facet Faic is considered as two identically sized and oriented fine facets that are referred to, respectively, as a black facet Faicb and a red facet Faio.
• the black facet Faia is associated with the first fine time step within a coarse time step while the red facet Faicr is associated with the second fine time step within a coarse time step.
• particles are moved (advected) between facets by a first surface-to- surface advection stage (step 1302).
• Particles are moved from black facets Faia to coarse facets Fpc with a weighting factor of V-ap that corresponds to the volume of the unblocked portion of the coarse parallelepiped (FIG. 12, 1225) that extends from a facet F a and that lies behind a facet Ffi less the unblocked portion of the fine parallelepiped (FIG. 12, 1245) that extends from the facet Fa and that lies behind the facet ⁇ .
• the magnitude of a for a fine voxel is one half the magnitude of a for a coarse voxel.
• the volume of a parallelepiped for a facet F a is defined as: Accordingly, because the surface areata of a facet does not change between coarse and fine parallelepipeds, and because the unit normal n a always has a magnitude of one, the volume of a fine parallelepiped corresponding to a facet is one half the volume of the corresponding coarse parallelepiped for the facet.
• Particles are moved from coarse facets to black facets Ffiia with a weighting
• Vafi volume of the unblocked portion of the fine parallelepiped that extends from a facet Fa and that lies behind a facet
• Particles are moved from red facets Faicr to coarse facets with a weighting
• Particles are moved from red facets Faicr to black facets F with a weighting
• particles are moved from fine facets FOIF or FOF to other fine facets FpiF or with the same weighting factor, and from coarse facets F a c to other coarse facets Fc with a weighting factor of Vcafi that corresponds to the volume of the unblocked portion of the coarse parallelepiped that extends from a facet F a and that lies behind a facet F
• particles are gathered from the voxels in a first gather stage (steps 1304-1310). Particles are gathered for fine facets from fine voxels using fine parallelepipeds (step 1304), and for coarse facets Fac from coarse voxels using coarse parallelepipeds (step 1306). Particles are then gathered for black facets Faim and for VR fine facets Fair from both coarse and fine voxels using fine parallelepipeds (step 1308). Finally, particles are gathered for red facets Fainr from coarse voxels using the differences between coarse parallelepipeds and fine paralllelepipeds (step 1310).
• coarse voxels that interact with fine voxels or VR facets are exploded into a collection of fine voxels (step 1312).
• the states of a coarse voxel that will transmit particles to a fine voxel within a single coarse time step are exploded.
• the appropriate states of a coarse voxel that is not intersected by a facet are exploded into eight fine voxels oriented like the microblock of FIG. 4.
• the appropriate states of coarse voxel that is intersected by one or more facets are exploded into a collection of complete and/or partial fine voxels corresponding to the portion of the coarse voxel that is not intersected by any facets.
• the particle densities N/ (x) for a coarse voxel and the fine voxels resulting from the explosion thereof are equal, but the fine voxels may have fractional factors Pf that differ from the fractional factor of the coarse voxel and from the fractional factors of the other fine voxels.
• step 1314 surface dynamics are performed for the fine facets FaiF and FOF (step 1314), and for the black facets Faia (step 1316). Dynamics are performed using the procedure illustrated in FIG. 11 and discussed above.
• particles are moved between fine voxels (step 1318) including actual fine voxels and fine voxels resulting from the explosion of coarse voxels. Once the particles have been moved, particles are scattered from the fine facets FOIF and FOF to the fine voxels (step 1320).
• Particles are also scattered from the black facets Faia to the fine voxels (including the fine voxels that result from exploding a coarse voxel) (step 1322). Particles are scattered to a fine voxel if the voxel would have received particles at that time absent the presence of a surface.
• particles are scattered to a voxel N(x) when the voxel is an actual fine voxel (as opposed to a fine voxel resulting from the explosion of a coarse voxel), when a voxel that is one velocity unit beyond the voxel N(x) is an actual fine voxel, or when the voxel N that is one velocity unit beyond the voxel N(x) is a
• the first fine time step is completed by performing fluid dynamics on the fine voxels (step 1324).
• the voxels for which fluid dynamics are performed do not include the fine voxels that result from exploding a coarse voxel (step 1312).
• the procedure 1300 implements similar steps during the second fine time step. Initially, particles are moved between surfaces in a second surface-to-surface advection stage (step 1326). Particles are advected from black facets to red facets, from black facets to fine facets, from fine facets to red facets, and from fine facets to fine facets.
• particles are gathered from the voxels in a second gather stage (steps 1328-1330). Particles are gathered for red facets FaiRr from fine voxels using fine parallelepipeds (step 1328). Particles also are gathered for fine facets FOF and FOIF from fine voxels using fine parallelepipeds (step 1330).
• particles are moved between voxels using fine resolution (step 1338) so that particles are moved to and from fine voxels and fine voxels representative of coarse voxels.
• Particles are then moved between voxels using coarse resolution (step 1340) so that particles are moved to and from coarse voxels.
• particles are scattered from the facets to the voxels while the fine voxels that represent coarse voxels (i.e., the fine voxels resulting from exploding coarse voxels) are coalesced into coarse voxels (step 1342).
• particles are scattered from coarse facets to coarse voxels using coarse voxels.
• ⁇ x is the PM resistivity.
• porosity between 0 and 1
• the interface effect may be significant for certain types of applications, such as flow acoustics.
• FIG. 14 illustrates a fluid F flowing toward an interface surface 1401 of a porous medium PM with porosity ⁇ .
• the fraction of the surface mat is penetrable and into which the fluid may flow is only ⁇ .
• the fraction of the surface that is blocked by the PM solid structure is 1- ⁇ .
• the fluid particles may include particle distributions or fluxes of hydrodynamic and thermodynamic properties such as mass fluxes, momentum fluxes, and energy fluxes.
• the fluid particles, or elements may include properties such as mass, density, momentum, pressure, velocity, temperature, and energy.
• the elements may be associated with any fluid, flow, or thermodynamic related quantity although not exhaustively identified herein.
• Either a frictional wall (bounce-back or turbulent wall) BC or a frictionless wall BC can be applied.
• the fraction of particles allowed to move into the PM affects the mass and momentum conditions in the direction normal to the interface.
• a frictionless wall or a frictional wall BC can be applied (as is true for a "typical" wall boundary).
• a frictionless wall BC maintains the surface tangential fluid velocity on the wall by not modifying the flux of tangential momentum at the interface.
• a frictional wall BC does alter the tangential momentum flux to achieve, for example, a no-slip wall boundary condition, or a turbulent wall model.
• the PM interface X can be described by so-called double-sided surface elements (i.e., surfels), as shown in FIG. 15.
• a set of paired surfels S form a double-layered surface having an inner surface A and outer surface B.
• the inner surface A interacts with the PM and the outer surface B interacts with fluid domain Fd.
• each inner surfel has the exact same shape and size as its paired outer surfel, and each inner surfel is only in touch with the paired outer surfel.
• the standard surfel gather and scatter scheme is performed on each side of the surface A, B, and with the condition that the ⁇ fraction of incoming particles from the fluid side F pass through to the PM side while all of the incoming particles ⁇ from the PM side pass through to the fluid side F.
• Advantages of this approach include simplified handling of the complex PM interface, exact satisfaction of conservation laws, and easy realization of specified fluid boundary conditions on PM interface.
• This approach in effect, introduces a PM interface resistance which is not proportional to a PM thickness and therefore cannot be included in approximation of Darcy's law.
• the approach accounts for the flow details at the PM interface and improves simulation results of certain types of flow problems, such as the modeling of acoustic absorption.
• a fluid flow region FF may be adjacent to a region PM occupied by a PM material with sound absorbing properties, with a PM interface X providing the interface between the fluid flow region FF and the region PM, and a wall interface Y providing the interface between the region PM and a wall W.
• the fluid flow region FF and the region PM can be, in effect, treated as two separate simulation spaces having different properties (e.g., in the region PM, an increased impedance may be used to account for the presence of the PM impedance), with movements ⁇ and 1- ⁇ between the two simulation spaces FF, PM being governed by the properties of the PM interface, as discussed above.
• CFD Computational Fluid Dynamics
• CAA Computational AeroAcoustics
• a time-explicit CFD/CAA solution method based on the Lattice Boltzmann Method (LBM), which has evolved over the last two decades as an alternative numerical method to traditional CFD, may be used.
• LBM Lattice Boltzmann Method
• the resulting compressible and unsteady solution method may be used for predicting a variety of complex flow physics, such as aeroacoustics and pure acoustics problems.
• a porous media model is used to represent the flow resistivity of various components, such as air filters, radiators, heat exchangers, evaporators, and other components, which are encountered in simulating flow, such as through HVAC systems, vehicle engine compartments, and other applications.
• the propagation of sound waves inside a homogeneous and passive absorbing material with a porosity close to is macroscopically fully characterized by the material's characteristic impedance Z and complex wave number .
• the complex impedance at normal incidence at the air/material interface lam is:
• the complex surface impedance is expressed as a function of its real and imaginary parts, the resistance R(OJ) and the reactance X(a>), respectively.
• the material absorption coefficient a(a>) is defined by:
• the surface impedance can be measured in an impedance tube using a two-microphone method as described below.
• the LBM-based method can be used to compute unsteady flow and the generation and propagation of acoustics waves.
• external forces can be included in the fluid dynamics by altering the local-instantaneous particle distributions during the collision step.
• the external force applied per unit time effectively becomes a momentum source/sink.
• This technique can be used, for example, to model buoyancy effects due to gravity.
• the method implements a porous media model by applying an external force based on Darcy's law for flow resistivity as a function of flow velocity.
• the effect of a porous medium on the flow is achieved by removing an amount of momentum at each volumetric location of the porous region such that the correct pressure gradient is achieved, resulting in the correct overall pressure drop.
• a 3D circular impedance tube 1801 as shown in FIG. 18, can be simulated.
• the tube walls 1802 are presumed as rigid and frictionless, and a time-varying pressure boundary condition representing white noise is applied at the inlet 1803.
• the layer of thickness "d" represents an absorbing material and is a porous media region PM , characterized by flow resistivity ⁇ ⁇ in the x-direction and infinite resistance in the other directions.
• An air layer of thickness "e" can be included between the porous media region PM and the right-hand side rigid wall 1804.
• the time step is s and the simulations are run for a time of
• FIGS. 20-22 some exemplary preUminary results are shown with a 30 ppw simulation with LBM-PM model results, Allard-Champoux model results, and experimental data.
• the thickness "d" of the PM is 26.5mm
• the thickness "e” of the air is 0.0mm
• flow resistivity " ⁇ ” is 23150 rayls/m.
• the thickness "d" of the PM is 26.5mm
• the thickness "e” of the air is 48.5mm
• the flow resistivity' " ⁇ ” is 23150 rayls/m.
• the thickness "d" of the PM is 120.0mm
• the thickness "e” of the air is 48.5mm
• the flow resistivity " ⁇ " is 23150 rayls/m.
• the validity of the Allard-Champoux model is confirmed, and the simulation results also correlate well to the LBM-PM model and to the experimental results.
• the frequency dependence of the absorption coefficient is well-captured for each Configuration, including non-monotonic behavior.
• the LBM-PM model approach correctly captures both flow and acoustic effects, even for a material that has a significant flow resistance effect but a negligible effect on acoustics.
• HVAC heating, ventilation, and air conditioning
• the HVAC system is complex, consisting of a blower and mixing unit coupled to many ducts through which air is transported to various locations, including faces and feet of front and rear passengers, as well as windshield and sideglass defrost.
• the blower must supply sufficient pressure head to achieve desired air flow rates for each thermal comfort setting. Noise is generated due to the blower rotation, and by the turbulent air flow in the mixing unit, through the twists and turns of the ducts, and exiting the registers (ventilation outlets).
• noise heard by passengers due to the HVAC system of a vehicle 2300 may be the noise absorbed at an interior cabin 2302.
• the noise may result from a blower of the vehicle that includes a radial fan which generates noise from the interaction of the moving blades with the surrounding air, and the impact of the moving air on nearby static components, such as seats 2304 and interior roof 2306 of the vehicle.
• This fan noise is acoustically propagated through the complex network of ducts, out of the registers, and into the interior cabin 2302.
• the duct and mixing unit flow noise sources are generated mainly by flow separations and vortices resulting from the detailed geometric features, and are also acoustically propagated through the system. Noise due to the flow exiting the registers depends on the fine details of the grill and its orientation, and the resulting outlet jets which mix with the ambient air and may impact surfaces, such as the windshield 2308 (e.g., for defrost). Therefore, the requirements for numerical flow- acoustic predictions may be accomplished using the exemplary modeling, as detailed above, whereby the interior cabin 2302 may be considered a fluid of a first volume and the static components and surfaces within the interior cabin 2302 may be considered a second volume occupied by a porous medium. By implementing the exemplary modeling, complex geometries may be investigated to provide predictions of the fan and flow induced noise sources, and their acoustic propagation all the way through the system to the locations of the passengers at the interior cabin 2302 of the vehicle 2300.
• the exemplary modeling provides accurate numerical noise prediction for fully detailed automotive HVAC systems, such as accurate predictions of the complex flow structures, corresponding noise sources, and resulting propagated acoustics to the passenger head space locations, including effects of geometric details throughout the integrated system.
• the transient flow characteristics and acoustics can be determined, including the rotating fan flow and noise, as well as direct prediction of acoustic propagation throughout the system.
• the exemplary modeling can obtain early noise assessment of proposed designs and evaluate potential design options, and/or diagnose and improve noise problems on an existing design.
• the exemplary model provides visualization capabilities to allow identification and insight into sources of noise, including band-filtered pressure analyses to isolate phenomena at specific frequency bands of interest. Predicted spectra at passenger locations can be converted to audio files for comparative listening to the effects of various design options.
• the exemplary modeling also provides accurate HVAC system pressures, flow rates, and thermal mixing behavior— hence it can be used to assess multi-disciplinary design tradeoffs to design the HVAC system with optimal aero, thermal, and acoustic performance.
• the exemplary modeling may be used to provide detailed flow behavior and resulting near-field sources for either a vehicle component of interest, such as an aircraft landing gear assembly 2400, as shown in FIG. 24, or a complete vehicle.
• transient solutions accurately predict the complex time-dependent flow structures, corresponding noise sources, and can accommodate the required realistic detailed geometry, such various components 2402 of the aircraft landing gear assembly 2400.
• the results can be coupled to a far-field propagation module to easily and efficiently predict the far-field noise at any location, whereby the region surrounding the aircraft landing gear assembly 2400 may be considered a fluid of a first volume and regions between the components 2402 of the aircraft landing gear assembly 2400 may be represented as a second volume occupied by a porous medium.
• the exemplary modeling allows for early noise assessment and optimization, including noise certification evaluation (e.g. using the Evolution of Perceived Noise Level EPNL metric) before a final prototype is built.
• noise certification evaluation e.g. using the Evolution of Perceived Noise Level EPNL metric
• visualization of the exemplary modeling can provide insight into sources of noise, including band-filtered pressure analyses to isolate phenomena at specific frequency bands of interest, for example to find the cause of a peak observed in a far-field spectrum.
• the PM model may account of tortuosity of the medium. For example, it may be desirable to model the acoustic behavior of sound waves as the waves propagate through a porous medium. Modelling this behavior can be difficult to when the exact geometry of the porous medium is unknown, (e.g. when modeling the propagation of acoustic waves through, for example, foam padding).
• Tortuosity can be defined as
• / is streamline length 2504
• d is the thickness 2502 of porous media (PM) domain
• co is the sound speed of fluid in the void space
• c is the sound speed in PM.
• LBM Lattice Boltzmann Model
• u is the fluid velocity
• static pressure is characteristic density
• ⁇ is the fluid velocity
• the system (49) has the same form as the system (48), meaning that the same solver of (48) can be used to solve (49).
• FIG. 26 shows the effects of tortuosity on the curve of absorption coefficient versus frequency for the NASA ceramic liner porous media.
• the liner is composed of straight micro circular tubes with porosity of 0.57 and tortuosity of 1.0.
• the first line 2602 and second line 2604 are PowerFLOW (registry 17836) results with the tortuosity equal to 2.0 and 1.0 respectively.
• the frequency corresponding to the first line 2602 curve is scaled by the factor of 1/ V2 , which agrees with the tortuosity of 2 for this case and is in full agreement with the time scaling given by Eq. (46).
• FIG. 27 is a flow chart of an example process 2700 for processing data representing acoustic properties of a porous medium modeled in accordance with tortuosity.
• the process can be performed by a data processing apparatus, such as a computer system.
• the process 2700 includes generating 2702 a model of acoustic behavior of a fluid filled porous media including an effect of tortuosity, with the model comprising a time variable indicative of a sound speed of the fluid.
• the process 2700 includes reseating 2704 the time variable of the model based on the sound speed in a fluid in the porous medium. Reseating the time variable can include adjusting the amount of time represented by one simulation time step.
• the time may be rescaled based on a streamline length of the porous medium and a thickness of the porous medium being simulated. As the time is rescaled, the temperature and/or pressure within the model may also be rescaled.
• the process 2700 includes simulating 2706 the acoustic behavior including the effect of tortuosity of the porous medium based on the reseating of the time variable within the model.
• the simulation can be used to determine acoustic behavior within the model in accordance with the simulated tortuosity.
• the acoustic behavior may include simulating the dissipation and propagation of acoustic waves.
• Embodiments of the subject matter and the operations described in this specification can be implemented in digital electronic circuitry, or in computer software, firmware, or hardware, including the structures disclosed in this specification and their structural equivalents, or in combinations of one or more of them.
• Embodiments of the subject matter described in this specification can be implemented as one or more computer programs (also referred to as a data processing program) (i.e., one or more modules of computer program instructions, encoded on computer storage medium for execution by, or to control the operation of, data processing apparatus).
• a computer storage medium can be, or be included in, a computer-readable storage device, a computer-readable storage substrate, a random or serial access memory array or device, or a combination of one or more of them.
• the computer storage medium can also be, or be included in, one or more separate physical components or media (e.g., multiple CDs, disks, or other storage devices).
• the subject matter may be implemented on computer program instructions stored on a non-transitory computer storage medium.
• the operations described in this specification can be implemented as operations performed by a data processing apparatus on data stored on one or more computer- readable storage devices or received from other sources.
• the term "data processing apparatus” encompasses all kinds of apparatus, devices, and machines for processing data, including by way of example: a programmable processor, a computer, a system on a chip, or multiple ones, or combinations, of the foregoing.
• the apparatus can include special purpose logic circuitry (e.g., an FPGA (field programmable gate array) or an ASIC (application specific integrated circuit)).
• the apparatus can also include, in addition to hardware, code that creates an execution environment for the computer program in question (e.g., code that constitutes processor firmware, a protocol stack, a database management system, an operating system, a cross- platform runtime environment, a virtual machine, or a combination of one or more of them).
• the apparatus and execution environment can realize various different computing model infrastructures, such as web services, distributed computing and grid computing infrastructures.
• a computer program (also known as a program, software, software application, script, or code) can be written in any form of programming language, including compiled or interpreted languages, declarative or procedural languages, and it can be deployed in any form, including as a stand-alone program or as a module, component, subroutine, object, or other unit suitable for use in a computing environment.
• a computer program may, but need not, correspond to a file in a file system.
• a program can be stored in a portion of a file that holds other programs or data (e.g., one or more scripts stored in a markup language document), in a single file dedicated to the program in question, or in multiple coordinated files (e.g., files that store one or more modules, sub programs, or portions of code).
• a computer program can be deployed to be executed on one computer or on multiple computers that are located at one site or distributed across multiple sites and interconnected by a communication network.
• the processes and logic flows described in this specification can be performed by one or more programmable processors executing one or more computer programs to perform actions by operating on input data and generating output.
• the processes and logic flows can also be performed by, and apparatus can also be implemented as, special purpose logic circuitry (e.g., an FPGA (field programmable gate array) or an ASIC (application specific integrated circuit)).
• special purpose logic circuitry e.g., an FPGA (field programmable gate array) or an ASIC (application specific integrated circuit)
• processors suitable for the execution of a computer program include, by way of example, both general and special purpose microprocessors, and any one or more processors of any kind of digital computer.
• a processor will receive instructions and data from a read only memory or a random access memory or both.
• the essential elements of a computer are a processor for performing actions in accordance with instructions and one or more memory devices for storing instructions and data.
• a computer will also include, or be operatively coupled to receive data from or transfer data to, or both, one or more mass storage devices for storing data (e.g., magnetic, magneto optical disks, or optical disks), however, a computer need not have such devices.
• a computer can be embedded in another device (e.g., a mobile telephone, a personal digital assistant (PDA), a mobile audio or video player, a game console, a Global Positioning System (GPS) receiver, or a portable storage device (e.g., a universal serial bus (USB) flash drive)).
• Devices suitable for storing computer program instructions and data include all forms of non-volatile memory, media and memory devices, including by way of example, semiconductor memory devices (e.g., EPROM, EEPROM, and flash memory devices), magnetic disks (e.g., internal hard disks or removable disks), magneto optical disks, and CD ROM and DVD-ROM disks.
• the processor and the memory can be supplemented by, or incorporated in, special purpose logic circuitry.
• a computer having a display device (e.g., a CRT (cathode ray tube) or LCD (liquid crystal display) monitor) for displaying information to the user and a keyboard and a pointing device (e.g., a mouse or a trackball) by which the user can provide input to the computer.
• a display device e.g., a CRT (cathode ray tube) or LCD (liquid crystal display) monitor
• a keyboard and a pointing device e.g., a mouse or a trackball
• Other kinds of devices can be used to provide for interaction with a user as well; for example, feedback provided to the user can be any form of sensory feedback (e.g., visual feedback, auditory feedback, or tactile feedback) and input from the user can be received in any form, including acoustic, speech, or tactile input.
• a computer can interact with a user by sending documents to and receiving documents from a device that is used by the user (for example, by sending web pages to a web
• Embodiments of the subject matter described in this specification can be implemented in a computing system that includes a back end component (e.g., as a data server), or that includes a middleware component (e.g., an application server), or that includes a front end component (e.g., a user computer having a graphical user interface or a Web browser through which a user can interact with an implementation of the subject matter described in this specification), or any combination of one or more such back end, middleware, or front end components.
• the components of the system can be interconnected by any form or medium of digital data communication (e.g., a communication network).
• Examples of communication networks include a local area network (“LAN”) and a wide area network (“WAN”), an inter-network (e.g., the Internet), and peer-to-peer networks (e.g., ad hoc peer-to-peer networks).
• LAN local area network
• WAN wide area network
• inter-network e.g., the Internet
• peer-to-peer networks e.g., ad hoc peer-to-peer networks.
• the computing system can include users and servers.
• a user and server are generally remote from each other and typically interact through a communication network. The relationship of user and server arises by virtue of computer programs running on the respective computers and having a user-server relationship to each other.
• a server transmits data (e.g., an HTML page) to a user device (e.g., for purposes of displaying data to and receiving user input from a user interacting with the user device).
• Data generated at the user device e.g., a result of the user interaction

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