PRACTICAL DESIGN AGAINST PUMP PULSATIONS by Mark A. Corbo President and Chief Engineer and Charles F. Stearns Engineering Consultant No Bull Engineering, PLLC Delmar, New York where a fluid excitation is coincident with both an acoustic Mark A. Corbo is President and Chief resonance and a mechanical resonance of the piping system, large Engineer of No Bull Engineering, a high piping vibrations, noise, and failures of pipes and attachments can technology engineering/consulting firm in occur. Other problems that uncontrolled pulsations can generate Delmar, New York. He provides rotating include cavitation in the suction lines, valve failures, and degrada- equipment consulting services in the forms tion of pump hydraulic performance. The potential for problems of engineering design and analysis, trou- greatly increases in multiple pump installations due to the higher bleshooting, and third-party design audits energy levels, interaction between pumps, and more complex to the turbomachinery and aerospace piping systems involved. industries. Before beginning his consulting The aim of this tutorial is to provide users with a basic under- career at Mechanical Technology Incorpo- standing of pulsations, which are simply pressure disturbances that rated, he spent 12 years in the aerospace travel through the fluid in a piping system at the speed of sound, industry designing gas turbine engine pumps, valves, and controls. their potential for generating problems, and acoustic analysis and, His expertise includes rotordynamics, fluid-film journal and thrust also, to provide tips for prevention of field problems. The target bearings, acoustic simulations, Simulink dynamic simulations, audience is users who have had little previous exposure to this hydraulic and pneumatic flow analysis, and mechanical design. subject. Accordingly, the tutorial neglects the high level mathemat- Mr. Corbo has B.S. and M.S. degrees (Mechanical Engineering) ics in the interest of presenting fundamental concepts in physically from Rensselaer Polytechnic Institute. He is a registered Pro- meaningful ways in the hope that benefit will be provided to the fessional Engineer in the State of New York and a member of layman. ASME, STLE, and The Vibration Institute. He has authored several technical publications, including one that won the “Best Case INTRODUCTION Study” award at Bently Nevada’s 2001 ISCORMA rotordynamics Overview conference. One of the foremost concerns facing pump users today is that of pulsation problems in their piping systems and manifolds. In cases Charles F. (Chuck) Stearns is an Engineer- where a fluid excitation is coincident with both an acoustic ing Consultant for No Bull Engineering, in resonance and a mechanical resonance of the piping system, large Delmar, New York, a position he has held piping vibrations, noise, and failures of pipes and attachments can occur. Other problems that uncontrolled pulsations can generate for five years. In this position, he is respon- include cavitation in the suction lines, valve failures, and degrada- sible for performing acoustic simulations, tion of pump hydraulic performance. The potential for problems Simulink dynamic simulations, and design greatly increases in multiple pump installations due to the higher and analysis of hydraulic control systems energy levels, interaction between pumps, and more complex for various clients in the aerospace and tur- piping systems involved. bomachinery industries. Mr. Stearns was The aim of this tutorial is to provide users with a basic under- the Chief Engineer in the Hydromechanical standing of pulsations, which are simply pressure disturbances that Fuel Controls Department at Hamilton travel through the fluid in a piping system at the speed of sound, Standard for almost 30 years, during which time he accumulated their potential for generating problems, and acoustic analysis and, more than 50 patents for innovative concepts in the field of also, to provide tips for prevention of field problems. The target hydraulic and pneumatic control systems. Since his retirement from audience is users who have had little previous exposure to this Hamilton Standard in 1987, he has remained active in the subject. Accordingly, the tutorial neglects the high level mathemat- aerospace industry as a consultant. His fields of expertise include ics in the interest of presenting fundamental concepts in physically hydraulic and pneumatic analysis, acoustic analysis, Simulink meaningful ways in the hope that benefit will be provided to the dynamic simulations, aircraft engine controls, and mechanical layman. design. Accordingly, the tutorial begins with a discussion of pulsations Mr. Stearns has a B.S. degree (Mechanical Engineering) from and why they are important in pumping systems. Since pulsation the University of Rhode Island. problems are almost always associated with the resonant excitation of acoustic natural frequencies, the fundamental concepts of ABSTRACT acoustic natural frequencies, mode shapes, acoustic impedance, and resonance are described. For the many users who are familiar One of the foremost concerns facing pump users today is that of with mechanical systems, an analogy with mechanical natural fre- pulsation problems in their piping systems and manifolds. In cases quencies is drawn and the basic acoustic elements of compliance, 137 138 PROCEEDINGS OF THE TWENTY-SECOND INTERNATIONAL PUMP USERS SYMPOSIUM • 2005 inertia, and resistance are compared to their mechanical equiva- occurs, fluctuating pressures and flows are superimposed on the lents (springs, masses, and dampers, respectively). Natural steady-state values. For example, since the fluctuations are sinu- frequency equations and mode shapes are then given for the soidal in nature, the pressure at a given point can be expressed as simplest piping systems, the quarter-wave stub and half-wave follows: element. The dependence of acoustic natural frequencies on piping = +•ω diameters, lengths, end conditions, and the local acoustic velocity P(tP) SS P CYCLIC sin( t) (1) (which, itself, is dependent on many parameters) is also discussed. The three most common pulsation excitation sources in pumping Where: systems are then described in detail. The first and probably best- P (t) = Pressure at a given point as a function of time known is the pumping elements, particularly those of reciprocating PSS = Steady-state pressure pumps. Although reciprocating pumps, and their characteristic PCYCLIC = Fluctuating pressure (pulsation) pulsatile flows, are deservedly infamous in this area, pulsations at The flow and velocity behave in exactly the same manner. Thus, vane-passing frequency can also occur in centrifugal pumps, espe- when one speaks of the pressure or flow at a point, it could refer to cially when running at off-design conditions and possessing one of two quantities—the steady-state value or the fluctuating positively-sloped head-flow characteristics. Second, excitations value. However, since the main focus of this tutorial is on pulsa- can arise due to vortex shedding arising at piping discontinuities tions, the discussion almost always focuses on the fluctuating such as tees and valves. Finally, transient excitations due to a value, not the steady-state value. This should be kept in mind when sudden change in the piping system, such as the opening or closing a statement such as, “at a velocity node, the velocity is zero,” is of a valve, can lead to the so-called “water hammer” problems. made. That type of statement is sometimes a source of confusion The tutorial then addresses the various pulsation control since the steady-state velocity at a velocity node is quite often not elements that are available and methods for sizing them and zero (although it could be). In any case, the point to remember is locating them within the system. Elements discussed in detail that, unless otherwise specified, the discussion applies to the fluc- include surge volumes, accumulators (which include a gas-filled tuating parameters, not the steady-state ones. bladder to allow significant size reduction), acoustic filters (networks of acoustic volumes and inertia elements), and dissipa- FUNDAMENTALS tive elements such as orifices. The advantages and disadvantages of each type, including the frequency ranges over which each is most Mechanical Waves effective, are discussed in detail. Emphasis is placed on proper In order to understand how pressure pulsations travel through location of these elements since a perfectly-sized element placed at the piping systems of pumps, one must first have a basic familiar- the wrong point in the system can actually do more harm than ity with mechanical waves and their behavior. These fundamentals good. can be found in most elementary physics texts. One of the best treatments of this subject that the authors have seen is that of General Rules Resnick and Halliday (1977), which, not surprisingly, is a physics A pulsation is simply a fluctuation in pressure that occurs in the text. Accordingly, the following discussion follows their general piping system of a pump. Pulsations are generated by all kinds of treatment. physical phenomena, including the action of a reciprocating pump, A mechanical wave is simply a disturbance that travels through vortex shedding at a discontinuity in a pipe, and vane-passing a medium. Unlike electromagnetic waves, mechanical waves will effects in centrifugal impellers. These simple pulsations are usually not travel through a vacuum—they need a solid, liquid, or gas not large enough