Probe Calculation

Sa THERMOWELL VELOCITY CALCULATIONS When fluid flows past a thermowell, low pressure vortices are formed in the wake downstream of the well. These vortices shed from alternate sides of the well and the resulting differential pressure produces two periodic forces on the thermowell: (i) an oscillating-lift force, transverse to the fluid flow at frequency fs (ii) an oscillating-drag force, in-line with the fluid flow at frequency 2fs Vortex shedding can occur at frequencies from 50Hz to 1500Hz. The vortex shedding frequency (Strouhal Frequency) increases linearly with fluid velocity, but the forces increase with the square of the velocity. When the Strouhal Frequency approaches the natural frequency of the thermowell, it can lock-in to the natural frequency causing resonance, with greatly magnified forces. To prevent lock-in, the natural frequency of the thermowell must be higher than either the in-line or the transverse resonance condition. Operation through the in-line resonance is acceptable only if the cyclic stresses at the resonance condition are acceptably small. The fluid velocity at which resonance occurs is referred to as a velocity critical. There are two velocity criticals for each natural frequency of the thermowell: one describing the transverse and the other describing the in-line response. Since in-line force fluctuates at twice the frequency of the transverse force, the corresponding velocity critical is approximately one half that requires for transverse resonance. If the natural frequency of the thermowell overlaps either fs or 2fs, a large resonant buildup in vibration amplitude can occur. The major cause of thermowell failure is fatigue due to resonance. A high enough level of damping may allow the thermowell to operate at the in-line or even the transverse resonance frequencies. In addition to frequency limits, the stresses within the thermowell and forces applied are also critical to evaluating the suitability of a thermowell for a specific process application. The 4 quantitative criteria to be evaluated are: 1: Frequency Limit: Resonant frequency of the thermowell must be sufficiently high so that destructive oscillations are not excited by the fluid flow. The steady-state (s-s) fluid velocity should meet one of the following conditions: fs(s-s) < 0.4•fn OR 0.6•fn < fs(s-s) < 0.8•fn 2: Static Stress Limit: Steady-state stresses are the result of hydrostatic fluid pressure and non-oscillating drag forces on the thermowell, and are calculated at the location of maximum stress. If the thermowell is partially shielded or has a reduced tip, the calculation must be performed with those considerations. The maximum steady- state stress on the thermowell at design velocity must not exceed the allowable stress as determined by the Von Mises Criteria. 3: Dynamic Stress Limit: Dynamic stresses are a result of the periodic drag forces that cause in-line oscillations and the periodic lift forces that cause transverse oscillations. If the thermowell is intended to operate above the in-line velocity critical, there are cyclic stresses at the in-line resonance to consider as it passes through that point on the way to the design velocity. The maximum dynamic stress must not exceed the allowable fatigue stress limit. The magnification factors are calculated and applied to the cyclical stress equations, then the cyclic drag and lift forces are calculated at the design velocity. The maximum combined lift and drag stress must not exceed the fatigue stress limit. 4: Hydrostatic Pressure Limit: The external pressure must not exceed the minimum pressure rating of the thermowell tip, shank, or flange (or threads) at the operating temperature. S0 THERMOWELL VELOCITY CALCULATIONS Dimensional Limits Dimension Tapered/Straight Reduced-Tip Min Max Min Max Unsupported Length L 2.5 24 5 24 Bore Diameter d 0.26 0.26 Tip Diameter B 0.36 1.83 0.50 0.88 Shank Diameter A 0.63 1.50 Min Wall Thickness (B-d)/2 0.12 0.12 Taper Ratio B/A 0.58 1.00 Bore Ratio d/B 0.16 0.71 0.16 0.71 Aspect Ratio L/B 2.00 Length Ratio Ls/L 0 0.60 Unsupported Length (L) Flanged (& Van-Stone) = Immersion length Threaded = Immersion length (factor added by the calculation) Socket-Weld & Weld-In = Distance from weld point (if in doubt, use OAL) Frequency Limit In cases where the thermowell passes the cyclic stress condition for operation at the in-line resonance condition, care shall still be taken that in steady state the flow condition will not coincide with the thermowell resonance. The steady-state fluid velcoity should meet one of the following conditions: fs(s-s) < 0.4fn OR 0.6fn < fs(s-s) < 0.8fn Low Fluid Velocities At very low fluid velocities, the risk or thermowell failure is greatly reduced. The calculations of natural frequency and frequency limits, steady-state stress and oscillating stress do not need to be performed if the following criteria are met: V < 2.1 fps B ≥ 0.5" A-d ≥ .376" S ≥ 10 ksi L ≤ 24" Sf ≥ 3 ksi A ≥ 0.5" Not subject to stress corrosion The calculation of the external pressure rating shall still be performed. Not Addressed Interaction of multiple thermowells in close proximity In-coherent excitation of structural vibrations by broad-band high frequency turbulence. Vibration due to pulsed fluid flow NOTES Clear fields if info not available or not applicable If Fluid Velocity unknown, leave blank and fill in Flow Rate & Pipe ID Flanged wells are assumed to have full penetration welds Sensor mass correction factor used = .96 (≡ 169lb/ft3) Allowable external pressure calculated per 6-13 of PTC 19.31 Bore size limited to 0.26"; reduced tip diam to 0.5" When Steam, Water or Air selected as fluid, density & viscosity are calculated if fields left blank. DISCLAIMER These calculations are performed in accordance with PTC 19.3 TW-2010. The results should only be used as a guide for thermowell selection. Thermo-Kinetics assumes no responsibility for failure of a thermowell based on the results of these calculations, and accepts no liability directly or consequential arising from error or misinformation supplied herein, or due to program missuse. S1 Probe Wake Ferquency Company: Tag No: Project No: Date: Reference: Rev: PROCESS DATA FREQUENCY LIMIT Fluid W Water Fluid G Gas Natural Frequency (fn) 223 Hz Operating Temperature T 105.0 C Operating Temperature T 221 °F Wake Frequency (fs) 85 Hz Operarating Pressure P 51.9 Bar Operarating Pressure P 752.758 psi Frequency Ratio (fs/fn) 0.38 Fluid Velocity * V 9.5 m/s Fluid Velocity * V 31.2 ft/s Frequency Criteria fs < 0.4 • fn Density r 28.37 kg/m3 Density r 1.771 lb/ft³ Wake Frequency Limit 89 Hz PASS Viscosity (Dynamic) µ 0.0146000000 CP Viscosity (Dynamic) µ 35318.68 lb/ft-s x 10-6 (Dynamic = Kinematic x Density) (Dynamic = Kinematic x Density) * Velocity can be calc from Flow Rate & Pipe ID * Velocity can be calc from Flow Rate & Pipe ID PRESSURE STRESS (See equation on S3) (See equation on S3) Pressure Limit 6,620 psi Max Operating Pressure 753 psi WELL DATA Safety Factor 8.8 PASS Mounting T Threaded Shank S Straight Unsupported Length L 9.0 in STEADY-STATE STRESS Root Diameter A 0.750 in Stress Limit 23,550 psi Tip Diameter B 0.750 in Stress @ Design Velocity 253 psi Bore Diameter d 0.250 in Safety Factor 93.2 PASS Fillet Radius at Root b 0.000 in Min Tip Thickness t 0.250 in DYNAMIC STRESS Shielded Length Lo 0.0 in Stress Limit 7,655 psi N.R. Stress @ Design Velocity 379 psi N.R. Safety Factor 20.2 PASS 67 N.R. Mtg Code (ref S2) TS TS Cyclic Stress @ In-Line Resonance Material 13 13 316 Fluid Velocity (for In-L Resonance) 255 fps Modulus of Elasticity E 23.8 psi x 10-6 In-Line Stress Calculation NOT Required Allowable Stress S 15.7 psi X 10-3 Stress @ In-L Resonance 2,115,605 psi Fatigue Stress Limit Sf 9.10 psi X 10-3 Safety Factor 0.0 N.R. Well Density Pm 0.285 lb/in³ Dens: Default p: 0.075 r = 1.771 A: Re 2.5 In-Line Resonance suppressed Visc: Default �: 1.50E-05 � = 3.53E-02 B: Re < 10E5 & Ns > 64 In-Line & Transv Res suppressed C C: Re ≥ 10E5 OR Ns ≤ 2.5 Calculate Freq Limits NATURAL FREQUENCY CALCULATION Dynamic Viscosity � = 3.53E-02 lb/ft-s Reynolds No = V*B*r/� Re = 9.77E+01 Strouhal Number Ns = 0.1704524194 NsCalc: 0.17 Approx Nat'l Freq fa = 247 Hz Da = 0.75 I = 0.0155 m = 0.112 Correction Factors Hf = 0.985 T or S Hf1 = 0.985 for R Hf2 = 0.934 Fluid Mass Haf = 0.9982 y1 = 1.000 y2 = 1.675 Sensor Mass Has = 0.9922 � = 2.923 Mounting Hc = 0.9250 F&V = 0.949 S&W = 0.950 T = 0.925 In Situ Natural Frequency fn = 223 Hz FREQUENCY LIMIT CALCULATION Scruton Number Nsc = 1.22 Re = 9.77E+01 Wake Frequency fs = 85.0 Hz Freq Ratio r = 0.38 Geometry Factor (G) GSP0 = 247.518 GSP1 = 742.55 No Shld T,S GSP2 = 660.05 Shielded T,S GSP3 = 742.55 No Shld R (fs=fn/2=Ns•V/B) GSP4 = 742.55 Shld (LoL-Ls) R L-Ls: 9.0 254.58 22