Segment types: ISODUct, INSDUct, ISOCOne, INSCOne
ISODUCT comments typed here are retained in output 3.14e-4 m2 area 0.0628 m perim 0.1 m length helium gas copper solidISOCONE this one is square 1.0 m2 Initial Area 4.0 m In Perim 2.0 m Length 0.25 m2 Final area 2.0 m Final perim air gas ideal solid
INSDUct and INSCOne use same formats as ISODUct and ISOCOne, respectively.
Use for ducts and cones of any cross-sectional shape (e.g., square,
circular)
by giving suitable area and perimeter. Use when all dimensions are large
compared to 
and 
. Temperature is uniform.
In ducts, p(x) propagates according to complex wavevector k, given by
Propagation is computed using
In cones, p propagates according to the lossy Webster horn equation:
The perimeter varies linearly from its initial value to its final value. Area varies quadratically, so that circular cones have circular cross-sections everywhere. The diameter varies linearly with axial position.
In ISOthermal ducts and cones, H = W everywhere. This assumes that the duct/cone is thermally anchored, so power dissipation is carried away externally. Thermoacoustic heat transport along the perimeter, which in fact contributes a small difference between H and W, is neglected.
In INSulated ducts and cones, the power dissipation is deposited in the adjacent heat exchanger. If several INSDUcts and/or INSCOnes are strung together, the power dissipated in all of them should show up in the nearest heat exchanger. This feature of DELTAE is not yet fully bugproof. For example, a BRANCh between a heat exchanger and INSDUct ruins the thermal link; initial ENDCAps do not share the thermal link to the heat exchangers; and nonzero real targets in SOFTEnd and HARDEnd cause INSDUct to give nonsense. Use with caution. If results look unreasonable, they are.
(See also STKDUct, which allows a temperature gradient along a duct. It is described under Stacks below.)
Segment types: COMPLiance, ENDCAp, IMPEDance
ENDCAP a surface with thermal dissipation 1.134e-3 m2 Area SAMEAS 0 Gas ideal solidCOMPLIANCE this one is a sphere 0.1257 m2 Area 4.19e-3 m3 Volume 0.859hexe Gas nickel solid
IMPEDANCE just a lumped series impedance 1.0 Pa-s/m3 Re(Z) -0.2 Pa-s/m3 Im(Z) helium ! Blank lines at "solid" location are interpreted as "ideal" solid
An endcap is a surface area with thermal dissipation. It always absorbs work. A compliance is exactly that: a lumped acoustic volume element with surface thermal dissipation. An impedance is a lumped series complex impedance.
An endcap does not affect pressure amplitude; volumetric flow changes according to
Pressure p is unchanged by a compliance; volumetric flow changes according to
At an impedance, volumetric velocity is unchanged; pressure changes according to p_out = p_in - ZU.
Segment types: BRANCh, OPNBRanch, VDUCEr, IDUCEr, VSPEAker, ISPEAker
BRANCH .1 Pa-s/m3 Re(Z) 1. Pa-s/m3 Im(Z) 0.500hear idealOPNBRANCH .05 Pa-s/m Re(Z)/k^2 .2 Pa-s/m2 Im(Z)/k air
VDUCER 1.000E-09 a Re(Ze) ohms .000 b Im(Ze) ohms 1.000E+04 c Re(T1) V-s/m^3 .000 d Im(T2) V-s/m^3 -1.000E+04 e Re(T2) Pa/A .000 f Im(T2) Pa/A 1.000E-09 g Re(Zm) Pa-s/m^3 1.000E-09 h Im(Zm) Pa-s/m^3 10.0 i AplVol V SAMEAS 0 Gas type ideal Solid type
IDUCEr: same as VDUCEr, except that current appears in line i instead of voltage.
VSPEAKER
6.000E-04 a Area m^2
6.00 b R ohms
.000 c L H
8.00 d B x L T-m
5.000E-03 e M kg
.000 f K N/m
.000 g Rm N-s/m
-22.5 h AplVol V
SAMEAS 0 Gas type
ideal Solid type
ISPEAker: same as VSPEAker, except that current appears in line h instead of voltage.
BRANCh and OPNBRanch are side branches with fixed impedances. With
BRANCh, the
user specifies the real and imaginary parts of the impedance, assumed
independent of frequency. OPNBRanch incorporates the frequency dependence
of
radiation impedance to 
solid angle. Thus
radiation impedance at the end of an open tube can be modeled as an OPNBRanch followed
immediately by a HARDEnd.
Figure V.1: BRANCH (left) and 'DUCER or 'SPEAKER (right).
The 'DUCErs and 'SPEAkers are electroacoustic transducers. 'DUCErs have frequency-independent parameters; 'SPEAkers let the user specify mass, spring constant, force constant, resistance, and inductance, so that frequency-dependent (even resonant) transducers can be modeled. With IDUCEr and ISPEAker, the user specifies the (real) current, and each pass of DELTAE calculates the (complex) voltage; with VDUCEr and VSPEAker, the user specifies voltage, and DELTAE computes current. IDUCEr and ISPEAker cannot be used with zero mechanical impedance because this would lead to a division of zero by zero (see below). Hence, use VDUCEr or VSPEAker for resonant or massless-and-springless transducers.
'SPEAker-type segments incorporate dissipation losses over their area as if they included an ENDCAp, but 'DUCEr-type segments, which have no area parameter, do not.
A branch is a side branch with complex impedance Z. Pressure is unchanged,
but volumetric velocity changes according to U_out = U_in - p/Z. For an
open branch,
the numbers in the input file are multiplied by 
and 
respectively
to obtain the impedance.
A transducer is an object attached as shown in the figure like a branch
impedance, but obeying the complex equations 
.
There are three cases of interest:
.
.
.
In the case of speakers, 
. Thermal surface losses are computed for
area A using the same formula as for an ENDCAp.
Segment types: HXFRSt, HXMIDl, HXLASt
HXFRST room temp heat exchanger SAMEAS 1 Area 0.600 GasA/A 6.35e-3 m Length 1.9e-4 m y0 -20.0 W HeatIn 300. K Est-T SAMEAS 0 Gas copper solid
HXMIDl and HXLASt use same format.
Heat exchangers are used to inject or remove heat. They necessarily have surface area, so they experience both viscous and thermal dissipation of acoustic power. They are assumed to have parallel-plate geometry.
Heat exchangers have a temperature difference between metal temperature and fluid mean temperature that is proportional to the heat flow. The proportionality constant is not well verified experimentally; we believe it to within a factor of 2.
In heat exchangers, p(x) propagates according to
with complex wavevector k, given by
assuming parallel plate geometry in computing 
:
There are 3 kinds of heat exchanger, depending on position relative to stack or stacks: HXFRSt, HXLASt, and HXMIDl. For 'FRSt and 'MIDl, the heat flow Q is an input for each pass of DELTAE; for 'LASt it is a result. Positive heat flows into the apparatus.
'FRSt or 'MIDl: H_out = H_in - Q.
'LASt: Q = H_out - H_in. H_out = [0 if next segment is INSDUct or INSCOne; W_out otherwise].
Metal temperature is computed relative to gas mean temperature using
where x_eff = min{displacement amplitude, HX length}. This expression may be quite inaccurate, but we believe it is better than nothing. A little experimental evidence for it is presented in J. Acoust. Soc. Am. 92, 1151 (1992). It is the only computation in DELTAE that is not correct in the acoustic approximation. If you dislike it, use the gas temperatures (available as outputs in the stack segment) instead of the metal temperatures for plotting or targeting (using freetargets).
Segment types: STKSLab, STKREct, STKCIrc, STKDUct, STKPIns
STKSLAB parallel-plate stack SAMEAS 1 Area 0.724 GasA/A 7.85e-2 m Length 1.8e-4 m y0 4.0e-5 m Lplate SAMEAS 0 Gas kapton SolidSTKRECT rectangular stack SAMEAS 1 Area 0.694 GasA/A 7.85e-2 m Length 2.0e-4 m a 4.0e-5 m Lplate 2.0e-4 m b SAMEAS 0 Gas stainless Solid STKCIRC approximates hexagonal honeycomb stack SAMEAS 1 (m^2) total area 0.81 gas area/total area 0.279 (m) length 0.50e-3 (m) r0 0.05e-3 (m) L:half of sht thcknss helium gas type stainless stack material STKDUCT boundary-layer approx 0.01 m2 area 0.4 m perimeter 1. m length 0.001 m2 wall material's cross-sectional area helium stainless STKPINS Keolian's pinstack invention sameas 2a a area m^2 3.2e-4 b 2y0 m 2y0 = nearest-neighbor distance in the hexagonal lattice 0.1 c Length m 4.e-5 d R pin m pin radius helium stainless
If you don't know what stacks are used for, read some background material on thermoacoustics.
Use STKSLab for parallel-plate or jellyroll stacks (or regenerators). Use STKREct for square or rectangular pores whose aspect ratio is not large [see Arnott, Bass, & Raspet, J. Acoust. Soc. Am. 90, 3228 (1991).]. Use STKCIrc for circular or hexagonal pores. Use STKPIns for stacks comprised of pin arrays (see J. Acoust. Soc. Am. 94, 941 (1993)). If pore size or plate separation is much greater than thermal and viscous penetration depths, use STKDUct.
Each end of a stack must abut a heat exchanger or another stack.
Pressure propagates according to Rott's wave equation
subject to the condition that enthalpy flow H_2 is independent of x, which imposes the following condition on T_m(x):
For STKSLab,
For STKREct,
For STKCIrc,
For STKDUct,
For STKPIns,
Because of the need to compute specialized functions, STKCIrcs compute more slowly than STKSLabs or STKDUcts; STKPIns are slower still, and STKREcts are very slow, especially for large aspect ratios. In the latter case, we recommend that STKSLabs be used until initial guesses and geometry are very close to finalized for this reason.
Segment types: TITLE, BEGIN, HARDEnd, SOFTEnd
TITLE comments here are reproduced in .DAT and .OUT BEGIN 1.0e6 Pa Mean P 500. Hz Freq. 300. K T-beg 3.0e4 Pa |p|@0 0.0 deg Ph(p)0 5.0e-4 m3/s |V|@0 0.000 deg Ph(V)0 helium Gas HARDEND 0.000 R(1/Z) 0.000 I(1/Z) SAMEAS 0 Gas type SOFTEND 0. Re(Z) 0. Im(Z) water
The initial segments of all input files must be TITLE and BEGIN. TITLE is just used to give a comment field that gets reproduced in all subsequent files, so put a descriptive name in its comment field. BEGIN is counted as the zeroth segment of the file. It is used to initialize variables that are the same in all segments (i.e., frequency and mean pressure), and those five variables required each pass of DELTAE to get started i.e., real and imaginary parts of pressure amplitude and volume velocity, and mean temperature). (Gas type isn't really used here, but you have to give one anyway.)
The final segment (except free targets) must be either HARDEnd or SOFTEnd. These contain two default targets. Use HARDEnd if you want the complex volume velocity at the end of the apparatus to be zero. This is the usual case in a closed system. Use SOFTEnd if you want complex pressure amplitude at the end to be zero. We find this useful for symmetrical systems, where SOFTEnd indicates that the rest of the apparatus is a mirror image of what is in the input file, and forces a complex pressure node.
Disable these as targets if you just want DELTAE to pass through the calculation only once. This approach is useful in early stages of debugging a new model that doesn't readily converge-it may let you see what's out of whack. Set these targets nonzero to model a nonzero end impedance-or use BRANCh or OPNBRanch.
Segment types: FREETarget, DIFFTarget, PRODTarget, QUOTArget, EFFRTarget,
COPRTarget, VOLMTarget
FREETARGET 500. Watts of power targeted at driver 3G Address of computed power at driver DIFFTARGET 0.00 a targeted difference 1B b D1Addr 1L c D2Addr PRODTARGET similar to DIFFTarget. 0.00 a targeted product 1B b M1Addr 1L c M2Addr QUOTARGET 1.0 desired quotient 1A numerator address 6A denominator address EFFRTARGET 0.2 desired 2nd law efficiency 7F work (numerator address) 4G heat (denominator address) 4H T hot address 6H T cold address COPRTARGET 0.2 desired 2nd law efficiency 7G heat (numerator address) 2F work (denominator address) 6H T hot address 4G T cold address VOLMTARGET 0.50 a targeted volume (cubic meters) 1A b BegAddr 10A c EndAddr
Use this class of segments to create targets other than DELTAE default targets (which include only end impedances and heat exchanger heats and temperatures). You may also use them for simple arithmetic operations on results.
Segment types: TEE, TBRANch, UNION
TEE branch file to load 5
branch.in
TBRAN the fork 2
4.412E+07 a Re(Zb) Pa-s/m^3 G
-3.528E+06 b Im(Zb) Pa-s/m^3 G
sameas 0 Gas type
ideal Solid type
UNION below the branch
4 segment number of SOFTEND of the TBRANCH
3.e4 |p| @ end (Pa)
0. ph(p) @end
sameas 0 Gas type
ideal Solid type
Use TBRANch for branched systems too complicated for BRANCh or OPNBRanch.
When it encounters a TBRANch, DELTAE treats subsequent segments as the sequential members of a branch until it reaches a HARD- or SOFTEnd, then it ``returns to the trunk," treating the rest of the segments as trunk members. If the system is multiply connected, a UNION segment in the trunk tells DELTAE where to connect the branch's SOFTEnd back to the trunk.
If UNION is used, the branch's SOFTEnd impedance targets should not be used; instead, enable the UNION's targets to ensure that (complex) p is equal at the SOFTEnd of the branch and at the UNION in the trunk. The guessed branch impedance determines how the (complex) volume velocity splits up at the TBRANch. UNION targets are a special case in that their values are dynamically rewritten by DELTAE during iterations, depending on the most recent results at the named SOFTEnd. The real input parameters (magnitude and phase of pressure) can have any value when the input file is written. DELTAE will overwrite them during each pass with the current magnitude and phase of pressure at the referenced SOFTEnd
When DELTAE encounters a TEE, it loads the named file into the model, and replaces the BEGIN segment of the branch file with a TBRANch segment. It tries to guess starting values for the complex branch impedance, and then adjusts the addresses in any sameas declarations and free target-type segments occurring in the branch (or after the branch point) by the number of segments in the branch. Once the file has been read in, the TEE segment disappears-the .out file and (d)isplayed segments will be the composite model. The file may have any name (e.g. branch.in, stub.out, branch.tee), but it must be specified with the complete suffix.
At a TBRANch, the branch complex impedance determines how much volume velocity leaves the trunk into the branch. At a UNION, exit volume velocity equals inlet volume velocity plus volume velocity at the branch's SOFTEnd.
Segment type: THERMOphys
THERMO sameas 0
Use THERMO to provide a record of thermophysical properties and penetration depths at a given location in the apparatus. With plotting features, can be used to generate a table of thermophysical properties.