1、 PART 23 Guidance Manual for Model Testing ANSI/ ASME PTC 19.23 -1980 INSTRUMENTS AND APPARATUS THE AMERICAN SOCIETY OF MECHANICAL ENGINEERS United Engineering Center 345 East 47th Street Nevv York, N.Y. 10017 No part of this document may be reproduced in any form, in an electronic retrieval system
2、or otherwise, without the prior written permission of the publisher. Date of Issuance: April15, 1980 Copyright 1980 THE AMERICAN SOCIETY OF MECHANICAL ENGINEERS All Rights Reserved Printed in U.S.A. FOREWORD In 1971 the PTC Supervisory Committee, then called the PTC Standing Committee, recognized th
3、at the high cost of prototype testing had resulted in increased interest in the use of models to confirm or extend performance data. The Supervisory Committee suggested that a group of specialists in several areas of Model Testing undertake to study the larger aspects and implica tions of Model Test
4、ing. The result of this suggestion was the formation in March 1972 of PTC 37 on Model Testing. The Committee was later designated PTC 19.23. This Committee was charged with the responsibility of surveying the varied fields of PTC activity in which the techniques, opportunities for, and the limitatio
5、ns of, Model Testing may be useful. The initial concept was to develop a Performance Test Code. After further delibera tions, it was agreed, with the permission of the PTC Supervisory Committee, based upon the complexities of the subject matter and the uniqueness of its application, to prepare an In
6、stru ments and Apparatus Supplement on Code Applications of Model Experiments, Guidance Manual for Model Testing). This document was submitted on various occasions to the PTC Supervisory Committee and interested parties for review and comment. Comments received as a result of this review were duly n
7、oted and many of them were incorporated in the document. This I on of (p) (dimensionless force)= a function of (dimensionless viscosity) The test results can now be plotted as a single curve on a single curve sheet. The 2 in the force coefficient has been arbitrarily added since (p V2 /2) = q is the
8、 well known velocity pressure. 4 SIMILITUDE (SIMILARITY) The previous list of dimensionl ess numbers presents historically useful engineerin g concepts. Before these con cepts are used in modeling, consi derations of sim ilitude SECTION 1 must be considered. Among these are geometric, kinematic and
9、dynamic similitu de. In the case of fluid mechanics consideration of specific sfmi litude vary from one model ing problem to another. Geometric and kinematic simili tude must be considered before dynamic similitude such as NR e NFr can be applied . 4.1 Geometric similarity requires that the model (l
10、arger, equal to, or smal ler than the prototype) must be a geo metrically accurate reproduction of the prototype. That is (X, Y, Z)prototype = K (x, y, z)model where X, Y, Z . . (1) are the coordinates and K is the size scale factor. The surface finish and clearances to be used in fabricat ing the m
11、odel are derived from an evaluation of their effects on the phenomenon being evaluated. Under certain conditions, such as in modeling of rivers, it may be desirable to create a distorted geometric model, i.e., one in which the vertical and horizontal scale factors are not equal. Scaling down the len
12、gth of a river to fit into the laboratory, will lead to very small depths in the model, un less the model is distorted. Kinematic similarity requires that the motion of the fluid, in the system being stud ied, is the same in both the model and prototype. For th is to be true, tben the velocity ratio
13、s Vx Y z V. =constant x,y, z (2) must exist. Also, the acceleration ratios Ax, Y,z A =cons tant x,y,z (3) must exist. 4.2 Dynamic similarity requires that the forces acting on the corresponding masses between the prototype and the model, (F/m)x, Y,Z = constant (F/mlx, y, z (4) must be related. The R
14、eynolds number NR e , or the Froude number NFr are examples from fluid mechanics. The idea of dynamic similitude. is derived from the con sideration that the dimensionless numbers are typically ratios of transport functions and/or other specific proper ties of the system being modeled. Typically (1
15、0) N R e Inertia forces/Viscous forces N Fr Inertia forces/Gravity forces NEu Pressure forces/Inertia forces N we In ertia fo rc es/Surface tension forces NMa Local ve loc ity /Acoustical velocity 4 ANSI/ASME PTC 19.23- 1980 N N u = Convective heat transfer/Conductive heat transfer The above dynamic
16、 dimensionless numbers should not be considered to be exclusive in themselves. There are cases where experimental data is correlated better by ratios of dimensionless numbers such as: NKn (Knudsen no.) Nst (Stanton no .) N Pe (Peclet no.) NRe fNMa NNufNp, NRe Np, The classical case in heat transfer
17、is (5) (6) (7) (7) where a, b, and C are experimentally derived empirical constants. Even in this case, the data is correlated only within a band of 15 percent and is also dependent on whether the fluid is being heated or cooled. This poor correlation is evidently due to the fact that turbulence lev
18、els and velocity distributions have not been the same in the different tests. Subsequent sections of this presentation will cite examples of the typical application and interpretation of dimensionless numbers. Section 2 will provide examples of the application of these techniques to real problems, t
19、aken from current industrial practice. 5 SOME MODELING EXAMPLES USING DIMEN SIONLESS NUMBERS Much time, effort and expense may be saved through a knowledgeable application of modeling using similitude and dimensionless numbers. Some selected examples are presented here to point out the advantages of
20、 using dimen sional analysis, especially for the testing of models. 5.1 The Pendulum The simple pendulum affords an excellent example for demonstrating the principles of model testing. A dimen sional analysis shows that the period (t) of a pendulum multiplied by the square root of the ratio of the a
21、ccelera tion of gravity (g) divided by its length is a function of the amplitude (O) of its swing and is independent of its mass (m) . (t .Ji!i-) = function of (8) (8) Any one of the pendulums shown in Fig . 1 (a) could be used as a test model for any of the others, for the analysis of this system s
22、hows: ANSI/ASME PTC 19.23-1980 PERIOD t FIG. 1 (a) g = 9000 t = 1 300 t PROTOTYPE MODEL (t Jg/0) = 1 X J 900 = 300 FIG. 1 (b) For small amplitudes (8), all pendulums, short or long, fast or slow, will give the same value (21r) for the dimen sionless period. This is only true, however, if the damping
23、 effect of the air and support is negligibly small. When air damping is to be taken into consideration, a dimensionless number must be introduced which will include a measure of the viscosity of the air. Reynolds number ;:)or VPiJ could be used . 5.2 A Vibration Dynamic Damper The modeling principle
24、 above was applied in a device for the testing of a Vibration damper for turbine blades. 5 SECTION 1 To test such a damper in a rotating rig would have been difficult and costly, as there were no instruments available to measure the vibration during rotation. The model test technique shown in Fig. 1
25、 (b), consisted of a cylindrical rod located in a cylindrical hole of slightly larger diameter. The rod, acted upon by centrifugal force, performed as a pendulum. The damper was tested in a stationary arrange ment, at one g instead of 9000 g, at ten times the size, and at a period 300 times as long,
26、 as would be the case in the rotating prototype. However, the value oft J“f was the same in model and prototype. 5.3 Incompressible Flow Turbine Blade Cascade Study Modeling can lead to substantial savings in the aerody namic testing of turbomach inery, especially when the effects of Mach number are
27、 small. When such items as viscosity and fluid density are the same, the power of this type of machinery varies as the product of the velocity cubed ( V3), times the square of the size (L 2). Then: Power (P) ex Flow X Kinetic energy ( V2 /2g) ex VA X V2 exV3L2 (10) and the Reynolds number varies as
28、the. product of the velocity ( V) and the size (L). (11) Thus the power for the same Reynolds number varies inversely with the size (L ). (See Fig. 2.) Hence, a turbine or a cascade ten times larger, with 1/10 the velocity, will require 1/10 the air power to test it pro vided, the Reynolds numbers a
29、re the same. Large low speed turbines or large low velocity cascades, require less air or steam power, can be constructed more accurately, and are affected less by the presence of instrument probes. The above reasoning can be applied to all fluid compressors, pumps and turbines. 5.4 Compressible Flo
30、w Turbine Study If the effects of Mach number are important, and the prototype Reynolds number is large enough to cause the flow to be turbulent, or the flow is turbulent for other reasons, one could reduce the Reynolds number by reduc ing the model size while maintaining the prototype Mach number a
31、nd still achieve flow similarity. With this model the power varies as the square of the model size. A half size model (turbine or compressor Fig. 3) will have one quarter of the prototype power and twice the rotational speed. This approach causes difficulties of manufacturing half size blades, surfa
32、ce finish and instrument size. An alternative to the above method is to reduce the pressure level while maintaining full size. This reduces the SECTION 1 v -/ / - / v - / (NR ) a 10 C- = C V e 10 -_,., V= 1 V= 1 w = 2 p = 1/4 FIG. 3 V = 1 w = 1 P = 1 V= 1 Reynolds number, maintains the Mach number,
33、and re duces the mass flow and power required, in proportion to the pressure. This method avoids the com pi ications and tooling needed to manufacture a scale model. The above examples indicate the latitud e that is avai l able when designing models while maintaining predeter mined dimensionless num
34、bers. No mention of surface roughness has been made in Sec tions 5.3 and 5.4. In general, the roughness of the model Pa1oo c2 x -1000 c2 v3 10 FIG. 2 6 must be exactly similar to the prototype. If however, the flow is laminar, the effects of roughness have been found to be very small, as for example
35、 in boundary layer or in pipe flows. If the flow is turbulent, one can either: or or (1) Match the roughness of the model and the proto type. (2) Induce turbulent flow on the model at the calcu lated transition point by means of artificial rough ness such as nails or airfoils (as is done when testin
36、g model boats). (3) Make use of the fact that roughness, smaller than a certain amount, have nO effec on the flow and the model is considered aerodynamically smooth. This roughness is smaller than the thickness of the laminar sublayer hkh is under the turbulent boundary layer. lhe Cyridlds humber, b
37、ased on the ro ughness size, must be less than 100. The modeling of two phase flows as occurs when moist steam flows through turbines or piping is difficult to ac complish. In a turbine ttw LlhS shedding of droplets off the upstream blades and the centrifuging of the moisture off the rotating.blatlo
38、sevidently requires a rotat ing test to obtain similr,jrity btlttWecn model and prototype. ANSI/ASM E PTC 19.23- 1980 In the case of piping where liquid collects in horizontal runs, ad ditional dimensional numbers based on liquid density, gravity, surface tension and viscosity must be in troduccd. 5
39、.5 Flow Induced Turbulence The general characterization of flow turbulence by the Reynolds number DV NRe= v (12) can be misleading. The following are several examples of how the Reynolds number criteria is used to describe or evaluate various phenomena. 5 .5.1 Flow Over a Flat Plate The development
40、of a flow field over a flat pl ate is il lustrated by Fig. 4121 *. Here, a flat plate with a sharp leading edge is located parallel to the fluid velocity vectors. The viscous effects first form a laminar boundary layer where the viscous drag is a function of stress on the plate T = pA (dv/dy. FIG. 4
41、 When the velocity gradient (dv/dy) exceeds the shear stress capability of the fluid, the flow becomes turbulent. The momentum transfer of Vt into V2, Fig. 5131, again adds to the viscous drag of the system. The results arc characterized by the relationship: NRe = x Vpfp (14 where x is the distance
42、downstream from the leading edge of the flat plate. Hence, there is a dimension x, where fully developed turbulent boundary layer flow is established. The boundary layer thickness is shown in Fig. 4 as 8. 5.5.2 Pipe Flow Historically, the Reynolds number turbulence concept ha been useful in calculat
43、ing the pressure drop of fully *Numbers in brackets identify references in Item 7 of Section I. 7 SECTION 1 developed pipe flow. Typically, the Moodyl11 diagram, Fig. 6, relates the friction factor f to NR e and the relative roughness E/D, where f is the median height of the source of roughness on t
44、he inside diameter of the pipe D. The Moody diagram is only applicable for flow conditions at least 20 diameters downstream from the pipe inlet or from a turbulence inducing device. This permits the full hydraulic development of the boundary layer as noted in Fig. 4. v, FIG. 5 5.5.3 Flow Past a Sphe
45、re The analysis and experimental data on the sphere afford further insights into the proper interpretation of dimen sionless numbers. The plot of drag coefficient of a sphere, Fig. 7, has a characteristic cusp at a Reynolds number of about 3 X 105 The location of this cusp has been found to depend o
46、n the surface roughness of the sphere and also on the free stream turbulence, both of which influence the flow separation point and therefore the drag of th e sphere. Without this empirical knowledge one might assume the drag coefficient is a function of the Reynolds and Mach numbers and ignore the
47、effects of surface roughness and turbulence. Therefore, turbulence and surface roughness must be considered also to get model to full scale correla tion. 5.5.4 Flow in Pipe Bencls The preceding discussion of turbulence was based only on the viscous properties and the resultant boundary layer of the
48、fluid stream . Other turbulence-producing agents arc encountered in real fluid flow systems. Figure 8 indicates the creation of secondary flow systems when a fluid tra verses a pipe bend 141 . Here the ccn trifugal forces due to turning create a pressure gradient of (pt - p2 /d. The lower momentum b
49、oundary layer on the wall of the pipe permits the pressure gradient to initiate a secondary flow on the wall from Pt to p2. This secondary flow adds to the pressure drop of the system by increasing the velocity gradient at the pipe wall. Additional fluid energy is con verted to heat by the viscous dissipation of the free stream turbulence of the vortices. a: 0 f-u t= z VI VI s: IT1 -o -1 n N ,., I D 00 0 ANSI/ASME PTC 19.23-1980 SECTION 1 = . f- f-r-f-1. f- f-r-f-
