Tube Elements

Specifies method for defining tube geometry parameters: hydraulic diameter (DHI), wetted perimeter (PWI), and flow area (AFI).

The following 5 FLAG settings are set automatically by the GUI based on the selections made for Geometric Input Type and Size. Inputs are recalculated to fit within one of the 5 FLAG settings when saved to the database.

1: DHI is constant; input one value of DHI only. No PWI or AFI necessary. Assumes circular tubes.

2: DHI = inlet diameter, exit diameter; input two values for DHI only. No PWI or AFI necessary. Assumes linearly tapered circular tube.

3: DHI and PWI will be input for every station in tube beginning with inlet, ending with exit. Must account for every station in tube.

4: DHI will be input for every station. Assumes circular so need not input PWI or AFI. Input from inlet to exit must account for every station in tube.

5: PWI and AFI will be input at inlet and exit only. Assumes linear taper in PWI and AFI. (See below for DHI, PWI, and AFI definitions.)

Number of Stations

(NSTA)

Number of stations in the tube.

Station 1 is at the inlet plane; station NSTA is at the exit plane. NSTA can range from 2 to 20. During the solution process, the tube will be discretized into NSTA minus one segments with average temperatures, pressures, and Reynolds Numbers for each segment.

A tube should be modelled with at least five stations. The number of stations can have a big impact on the convergence of attached chambers. If a chamber attached to this element is having difficulty converging, try increasing the number of stations.

Inlet Head Loss Type:

K – Incompr Loss Coef

[Inlet K]

Or

Cd – Compr Loss Coef

[Inlet Cd]

Or

Upstream Cross Flow

(HL_FLAG)

Specifies the method for calculating head loss at the inlet plane.

Allowable values for HL_FLAG are: -20, the range of -1. to 0., and the range of all positive real numbers.

HL_FLAG = 0. or any positive real number

HL_FLAG will be used as the inlet head loss coefficient, K _in, defined as:

K_in = inlet head loss / dynamic head, or

$K_{in}=\frac{P_{T,supply}-P_{T,after loss}}{0.5 \rho V^2}$

The discharge coefficient, Cd, will be calculated from K_in by the following incompressible relation:

$Cd=\frac{1.0}{\sqrt{1.0+K_{in}}}$

HL_FLAG = -1.+ to 0.

HL_FLAG will be interpreted as a discharge coefficient, Cd. The inlet loss coefficient, K _in will be calculated from Cd by the incompressible relation:

$K_{in}={\left(\frac{1.0}{Cd}\right)}^2-1.0$

HL_FLAG = -20

The tube inlet loss is assumed to be due to a cross flow velocity at the tube’s inlet and is calculated according to Ref. 2.

The data used is for a tube with L/D > 2.83, where the flow has recovered from the inlet effects and is at right angles to the cross flow.

The method is valid for both upstream momentum and upstream inertial chambers. It is not valid for upstream plenum chambers.

Length

(LENGTH)

Entrance Adder

(STLEN)

Starting length (in) used for the HTC inlet multiplier.

Used to modify X in calculating h_x/h_o (see IHF):

$X=X_{meas}+STLEN$

where X_meas = Distance from tube inlet (station 1).

At station 1, X equals STLEN. If one physical tube is modelled as two or more elements strung together, STLEN should include the cumulative length of all tube elements leading into the current element unless something physical re-establishes the boundary layer. See also the IHF flag.

Portion of Ustrm Cham. Dyn. Head Lost

(DQ_IN)

Inlet dynamic head loss. Valid range is 0.0 to 1.0 inclusive. An entry outside this range will cause a warning message and the value used will be 0 or 1 (whichever value is closest to the entry).

If DQ_IN > 0 and the upstream chamber has a positive component of relative velocity aligned with the centerline of the orifice, the driving pressure will be reduced by the equation:

$Pin=P{s}_{upstream}+\left(1.0-D{Q}_{IN}\right)*\left(Pi{n}_{no-loss}-P{s}_{upstream}\right)$

(Default value = 0.)

Radius In

(RIN)

Radius (in) to the tube inlet from the engine centerline.

(If the tube is rotating a RIN>0 is required.)

Radius Exit

(REX)

Radius (in) to the tube exit from the engine centerline.

(If the tube is rotating a REX>0 is required.)

Rotor Index

(RPMSEL)

Element rotational speed pointer.

0.0: Specifies a stationary element.

1.0: Rotor 1, RPM = general data ELERPM(1).

2.0: Rotor 2, RPM = general data ELERPM(2).

3.0: Rotor 3, RPM = general data ELERPM(3).

Element Inlet Orientation: Tangential Angle

(THETA)

Angle (deg) between the element centerline at the entrance of the element and the reference direction.

If the element is rotating or directly connected to one or more rotating elements, the reference direction is defined as parallel to the engine centerline and the angle is the projected angle in the tangential direction. Otherwise, the reference direction is arbitrary but assumed to be the same as the reference direction for all other elements attached to the upstream chamber.

Theta for an element downstream of a plenum chamber has no impact on the solution except to set the default value of THETA_EX.

(See also THETA_EX)

Element Inlet Orientation: Radial Angle

(PHI)

Angle (deg) between the element centerline at the entrance of the element and the THETA direction. (spherical coordinate system)

Phi for an element downstream of a plenum chamber has no impact on the solution except to set the default value of PHI_EX.

(See also PHI_EX)

13

14

15

Exit K Loss:

Axial (K_EXIT_Z)

Tangential (K_EXIT_U)

Radial (K_EXIT_R)

Head loss factors in the Z, U, and R directions based on the spherical coordinate system of theta and phi.

Z = the axial direction. (theta=0 and phi=0)

U = the tangential direction. (theta=90 and phi=0)

R = the radial direction. (theta=0 and phi=90)

Valid values of K_EXIT_i (i = Z, U, R) range from zero (default) to one.

The three loss factors reduce the corresponding three components of velocity exiting the element.

$V_{actual exit idir}=V_{noloss exit idir}*\sqrt{1-K\_EXIT\_idir}$

(Default value provides no loss, K_EXIT_i=0)

Friction Multiplier

(FM)

Friction factor multiplier.

The same value will be applied at each station.

(Default value = 1.; can be 0. For no friction)

Roughness

(ROUGHNESS)

Sand-grain roughness of the tube wall (in)

Used with to Swamee-Jain approximation of the Colebrook-White equation to calculate tube friction factor. (If FMULT is not equal to 1, then roughness is not recommended to be used.)

The tube wall temperature (F) used for the turbulator calculations.

(TWI is used for the non-turbulated portion of the wall).

Nusselt correlation coefficient for use in the equation:

$Nu=CHTURB*R{e}^{0.8}*P{r}^{0.4}$

(Recommended value is 0.05)

Friction factor for the turbulated portion (XTURB) of the tube.

(Recommended value is 0.05).

Laminar Nusselt Number if “Laminar HTC Relation” = constant.

Value of Nusselt Number to be used if tube Reynolds Number is less than REYTRAN (laminar flow).

Assumed constant for Re < REYTRAN. No entrance multiplier for “h” is used.

(Default is 4.36 for fully developed laminar flow in a circular tube. See heat transfer textbooks for values of noncircular tubes.)

Heat Transfer Coefficient Multiplier

(HM)

Heat transfer coefficient multiplier.

The same value will be applied at each station.

(Default value = 1.0; can be 0.0 if adiabatic)

If HM is set to zero, user inputted wall temperature (TWI) is ignored for Reynolds number calculations.

Flag to specify how the program shall calculate the HTC inlet multiplier, as a function of the distance past the element inlet. If one physical tube is modeled as two or more elements strung together, IHF flags 1 through 4 should not be used after the first element unless there is something physical at the break point to reestablish the boundary layer(or set STLEN to the cumulative length of the leading tube elements.

Allowable values are 0, 1, 2, 3, 4. The HTC inlet multiplier is evaluated as a function of hydraulic diameter (DHI) and length (X) as follows:

Equations can be found in reference 3 and many heat transfer textbooks.

NOTE: Flow Simulator GUI is set up with a default value of IHF = 1.

Only used if the Heat Transfer option is “Inner/Outer Wall Convection”

Allowable values are integers from 0 through 4, with IWC equal to the number of circumferential segments into which the tube perimeter is split.

If a nonzero value is specified for IWC, then the user must also provide input for FGH, HGH, and TGH (defined below).

When IWC > 0.0, user inputted wall temperature (TWI) is ignored.

Angle (deg) between the element exit centerline and the reference direction.

THETA_EX is an optional variable to be used if the orientation of the element exit differs from that of the element inlet.

The default value (THETA_EX = -999) will result in the assumption that THETA_EX = THETA.

Other values will be interpreted in the manner presented in the description of THETA.

Angle (deg) between the element exit centerline and the THETA_EX direction.

PHI_EX is an optional variable to be used if the orientation of the element exit differs from that of the element inlet.

The default value (PHI_EX = -999) will result in the assumption that PHI_EX = PHI.

Other values will be interpreted in the manner presented in the description of PHI.

Heat input (BTU/s) per stream.

Q applied will be NLU * QIN. The heat is added evenly at each tube station.

If QIN is not equal to zero, HM will be set to zero (no calculated heat transfer to wall) and Twall will be adjusted (for fluid properties).

Number of bends along a tube.

A maximum of 20 bends may be specified on any one tube.

See bend array inputs below for more information.

A flag that specifies how to calculate tube station wall temperatures (TWALL), and allows for several other types of heat transfer to the tube.

Flow Simulator GUI will automatically set this flag based on the selected options for ‘Heat Transfer’ and ‘Wall Temperature Base’.

1) TWALL is calculated based on wall convection.

5) Keep user input values for TWALL.

6) TWALL is based on upstream TT plus pumping Delta.

7) TWALL is based on upstream TT plus QIN.

11) QIN in Btu/s for each station

12) QIN in Btu/lbm for each station

13) Delta T for each station

14) Fluid T for each station

15) NTU for each station

16) HA for each station

When TWALL_FLG >= 5.0, the heat transfer coefficient multiplier (HM) is ignored and assumed to be zero.

Default is 1.0. Also, both the Flow Simulator Solver and GUI will correct TWALL_FLG=0.0 to the appropriate value based on IHF and QIN.

A flag that specifies which friction relation is used.

0.0: Smooth Wall Power law (Abuaf)

1.0: Swamee-Jain (approx. to Colebrook-White)

2.0: Fixed friction coefficient (set on CFTURB field)

Swamee-Jain (1.0) is recommended for non-zero roughness.

Wall/Sink Temperature

(TSINK)

Bend/Tube HTC Multiplier

(HM_BEND)

Turbulent HTC Relation

(HTC_RELATION)

The “Duct Flow” Nu correlation used for turbulent flow.

See the “HTC Correlations” in the “General Functions and Routines” section for the equations.

-2) User Input Nu

-1) User Input HTC

1) Lapides-Goldstein

2) Dittus-Boelter

3) Sieder-Tate Combo

4) Gnielinski Combo

5) Bhatti-Shah

7) Sieder-Tate Turbulent Only

8) Gnielinski-Turbulent Only

Cross-Section Shape

(DUCT_SHAPE)

The cross-section shape of the tube. The choice will affect the geometry inputs that can be used. A circular tube just needs a diameter, while the other options need 2 of these 3 (Hydraulic Diameter, Area, Perimeter). The cross-section shape can affect the hydraulic diameter used in friction and heat transfer calculations. Ref 7, Sec 6.3

1. Arbitrary Shape
2. Circle
3. Ellipse
4. Isosceles Triangle
5. Rectangle

Aspect Ratio

(ASPECT_RATIO)

Laminar Friction Effects

(FLAM_INLET_EFF)

Laminar friction effects to use at the duct inlet. See the “Friction Correlations” in the “General Functions and Routines” section for the equations.

1. Off, assume fully developed laminar flow.
2. Muzychka-Yovanovich

Laminar HTC Relation

(NU_LAM_METHOD)

The “Duct Flow” Nu correlation used for laminar flow.

See the “HTC Correlations” in the “General Functions and Routines” section for the equations.

0) User Input Nu

1,4,5) Muzychka-Yovanovich

2) Hausen

Wall Temperature

(TWI)

(array of 20 values in 4 lines of 5 each)

Tube wall inside surface temperature (F).

Input NSTA values (i.e., input a value of TWI for each station along the tube, from the inlet station to the exit station).

Wall temperature is an unnecessary input when IWC > 0 or when TWALL_FLG = 6 or 7. It is also unnecessary for TWALL_FLG = 1 if HM = 0.

Area

(AFI)

(array of 20 values in 4 lines of 5 each)

Tube mechanical flow area (in²).

AFI is used only when FLAG = 5.

When used, input two values, the first for the area at the tube inlet station and the second for the area at the tube exit station.

Hydraulic Diameter

(DHI)

(array of 20 values in 4 lines of 5 each)

Tube hydraulic diameter (in).

DHI is used for values of FLAG of 1 through 4 only

1. DHI is constant; input a single value
2. Input DHI at inlet and exit stations: two values
3. Input DHI at every station
4. Input DHI at every station

Wetted Perimeter

(PWI)

(array of 20 values in 4 lines of 5 each)

Tube wetted perimeter (in).

PWI is used for values of FLAG of 3 and 5 only

3) Input PWI at every station

5) Input PWI at inlet and exit stations; two values

External Heat Transfer Fraction [Fraction] (FGH)

(array of 4 values and only IWC values used)

See IWC above

Decimal fraction of the tube perimeter associated with HGH and TGH array entries. Constant over the length of the tube.

Any part of the tube perimeter not accounted for is assumed to be adiabatic. For example, if the entire perimeter is subjected to convection, the sum of FGH’s should be 1.0

External Heat Transfer H [Ext H] (HGH)

(array of 4 values and only IWC values used)

External Heat Transfer Temperature [Ext T] (TGH)

(array of 4 values and only IWC values used)

Bend Radius (BEND_RADIUS)

(array of 20 values in 4 lines of 5 each, NUM_BENDS values used)

Radius (in) of bend along tube centerline.

(See ‘ r ’ from graphic for COMBINATION_ANGLE below)

Each bend counted in NUM_BENDS must have a specified bend radius. Enter bends in order based on distance from beginning of tube (DIST_FR_STRT).

Bend Angle (BEND_ANGLE)

(array of 20 values in 4 lines of 5 each, NUM_BENDS values used)

Angle (deg) between the entering and exiting lengths of the bend.

Each bend must have a specified angle.

The maximum bend angle is 180°.

Distance from Start (DIST_FR_STRT)

(array of 20 values in 4 lines of 5 each, NUM_BENDS values used)

Distance (in) from the beginning of the tube to the start of the bend.

If the tube contains two bends or more, this distance should not include the arc length of any previous bend.

Loss Multiplier (LOSS_MULT)

(array of 20 values in 4 lines of 5 each, NUM_BENDS values used)

Combination Angle (COMBINATION_ANGLE)

(array of 20 values in 4 lines of 5 each, NUM_BENDS minus one values used)

Relative angle (deg) between two bends in series.

The number of COMBINATION_ANGLE entries will be NUM_BENDS – 1. The first entry will be the combination angle between bends 1 and 2.

A COMBINATION_ANGLE of 0 degrees defines an ‘S’ shaped bend and 180 degrees defines a ‘U’ shaped bend.

The allowable range is 0 to 180 degrees.

Radius to the tube inlet from the engine centerline.

(Usually, an echo of the input unless modified inside Flow Simulator.)

Radius to the exit from the engine centerline.

(Usually, an echo of the input unless modified inside Flow Simulator.)

(SPECIFIED_)

(CROSSFLOW_)

INLET_HEAD_LOSS

Head loss coefficient at the tube inlet.

This will be an echo of the user input if a 0 or positive value was specified for the tube head loss (HL_FLAG). Otherwise, it will be calculated by Flow Simulator based on the type of head loss specified.

NOTE: Does not include calculated head loss for tube bends or junctions.

Heat flow

QIN is heat added to (positive values) or removed from (negative) the fluid flowing through the tube. In cases where multiple flow streams are modeled by a single element (i.e. NED and NLU not equal to 1), the value of QIN should be set to model the heat flow from only one of the restrictions. The QIN will be spread evenly over all tube segments.

Overall discharge coefficient for the tube.

(Actual Tube Flow Function / Ideal Tube Flow Function)

Discharge coefficient that could be used with an orifice element to achieve the same mass flow as the tube.

Orifice using tube station 1 area and nonrotating tube.

Friction factor multiplier.

(Usually, an echo of FM input unless modified inside Flow Simulator.)

Heat transfer coefficient multiplier.

(Usually, an echo of HM input unless modified inside Flow Simulator.)

Fluid Reynolds number used in the friction calculation at the tube station.

$R{e}_{yf}=\frac{\dot{m} D_h}{A {\mu }_{film}}$

$\dot{m}=tube mass flow$

$D_h=tube hydralic diameter$

$A=tube area$

${\mu }_{film}=fluid viscosity based on T_{film}$

$T_{film}=\frac{T_s+T_{wall}}{2}$

Average fluid Reynolds number used in the HTC calculation for the tube segment. Adjust REYN to account for different fluid density near the wall. Density is assumed to follow ideal gas equation.

$R{e}_{yn}=R{e}_{yf}\frac{T_s}{T_{film}}$

$T_{film}=\frac{T_s+T_{wall}}{2}$

Entrance length for heat transfer.

Calculated as the sum of the starting length (STLEN) and the distance from the tube inlet to the tube segment midpoint.

NUMBER_OF_BENDS_

IN_TUBE

Radius of bend along tube centerline.

(Usually, an echo of the input unless modified inside Flow Simulator.)

Angle between the entering and exiting lengths of the bend.

(Usually, an echo of the input unless modified inside Flow Simulator.)

Distance from tube inlet to the start of the bend.

(Usually, an echo of the input unless modified inside Flow Simulator.)

K_MULTIPLIER_FOR_

BEND_INTERACTIONS

SUM_OF_K_

FOR_ALL_BENDS

SUM_OF_DELTAP_

FOR_ALL_BENDS

RESULTANT_INLET_

HEAD_LOSS_

COEFFICIENT

Overall inlet head loss coefficient.

Includes specified inlet head loss as well as losses due to bends and/or junctions.

Only reported if the tube has bends or a junction is associated with the upstream chamber (based on flow direction).

Fraction of the tube circumference that is turbulated.

(Usually, an echo of the input unless modified inside Flow Simulator.)

Tube wall temperature used for turbulator calculations

(Usually, an echo of TWTURB input unless modified inside Flow Simulator.)

Nusselt correlation coefficient

(Usually, an echo of CHTURB input unless modified inside Flow Simulator.)

Friction factor used for turbulator calculations

(Usually, an echo of CFTURB input unless modified inside Flow Simulator.)

Calculated temperature of tube wall circumferential segments.

There will be IWC values.